Finite Group Databasebeta

← #17204505

Subgroups — #17204505

Order 4352.

2804 conjugacy classes of subgroups.

The subgroup lattice has 1708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763345C211yesmaximal, characteristic, complemented
2C2×#11763315C211yesmaximal, characteristic, complemented
3#14533929C211yesmaximal, characteristic, complemented
4#14533914C211yesmaximal, characteristic, complemented
5#14533899C211yesmaximal, characteristic, complemented
6#14533884C211yesmaximal, characteristic, complemented
7#14533875C211yesmaximal, characteristic, complemented
8#14533855C211yesmaximal, characteristic, complemented
9#14533849C211yesmaximal, characteristic, complemented
10#14533834C211yesmaximal, characteristic, complemented
11#14533792C211yesmaximal, characteristic, complemented
12#14533748C211yesmaximal, characteristic, complemented
13#14533712C211yesmaximal, characteristic, complemented
14#14533677C211yesmaximal, characteristic, complemented
15#14533104C211yesmaximal, characteristic, complemented
16#14532337C211yesmaximal, characteristic, complemented
17#14532320C211yesmaximal, characteristic, complemented
18#14532051C211yesmaximal, characteristic, complemented
19#14532046C211yesmaximal, characteristic, complemented
20#14532023C211yesmaximal, characteristic, complemented
21#14531998C211yesmaximal, characteristic, complemented
22#124×Dic17C211yesmaximal, characteristic, complemented
23#14531309C211yesmaximal, characteristic, complemented
24#14531296C211yesmaximal, characteristic, complemented
25#14531294C211yesmaximal, characteristic, complemented
26#14531283C211yesmaximal, characteristic, complemented
27#14531271C211yesmaximal, characteristic, complemented
28#14531244C211yesmaximal, characteristic, complemented
29C4×#10587567C211yesmaximal, characteristic, complemented
30C2×C22⋊C4×Dic17C211yesmaximal, characteristic, complemented
31C17×#2472C211yesmaximal, characteristic, complemented
32C22×#63254C2211yescharacteristic
33C24×Dic17C2211yescharacteristic
34#11763345—28no—
35C2×#10587584C2211yescharacteristic, complemented
36C2×#10587584C2211yescharacteristic, complemented
37C2×#10587576C2211yescharacteristic, complemented
38C2×#10587633C2211yescharacteristic, complemented
39#11763315—28no—
40C2×#10587572C2211yescharacteristic
41C2×#10587572C2211yescharacteristic
42C2×#10587572C2211yescharacteristic
43C2×#10587621C2211yescharacteristic
44C2×#10587621C2211yescharacteristic
45C2×#10587564C2211yescharacteristic
46C2×#10587564C2211yescharacteristic
47C2×#10587616C2211yescharacteristic
48C2×#10587570C2211yescharacteristic
49C2×#10587625C2211yescharacteristic
50C2×#10587625C2211yescharacteristic
51C2×#10587625C2211yescharacteristic
52C2×#10587639C2211yescharacteristic
53C2×#10587639C2211yescharacteristic
54C2×Q8×Dic17C2211yescharacteristic, complemented
55C2×D4×Dic17C2211yescharacteristic
56C2×D4×Dic17C2211yescharacteristic
57C2×#10587579C2211yescharacteristic, complemented
58C2×C4×C22⋊D17C2211yescharacteristic
59C2×#10587567C2211yescharacteristic
60C2×#10587567C2211yescharacteristic
61C2×#10587567C2211yescharacteristic
62C2×#10587567C2211yescharacteristic
63C2×#10587567C2211yescharacteristic
64C2×#10587567C2211yescharacteristic
65C2×#10587567C2211yescharacteristic, complemented
66C2×#10587578C2211yescharacteristic, complemented
67C2×#10587578C2211yescharacteristic, complemented
68C2×#10587563C2211yescharacteristic
69C22×C22⋊Dic17C2211yescharacteristic
70C22×C4×Dic17C2211yescharacteristic
71C22×C4×Dic17C2211yescharacteristic
72C2×C42×D17C2211yescharacteristic, complemented
73#11762749C2211yescharacteristic, complemented
74#11762749C2211yescharacteristic, complemented
75#11762745C2211yescharacteristic
76#11762745C2211yescharacteristic
77#11762743C2211yescharacteristic, complemented
78#11762743C2211yescharacteristic, complemented
79#11762740C2211yescharacteristic, complemented
80#11762739C2211yescharacteristic, complemented
81#11762738C2211yescharacteristic, complemented
82#11762738C2211yescharacteristic, complemented
83#11762736C2211yescharacteristic, complemented
84#11762732C2211yescharacteristic
85#11762732C2211yescharacteristic
86#11762732C2211yescharacteristic
87#11762732C2211yescharacteristic, complemented
88#11762729C2211yescharacteristic, complemented
89#11762728C2211yescharacteristic, complemented
90#11762724C2211yescharacteristic
91#11762724C2211yescharacteristic
92#11762724C2211yescharacteristic
93#11762724C2211yescharacteristic
94#11762724C2211yescharacteristic, complemented
95#11762724C2211yescharacteristic, complemented
96#11762722C2211yescharacteristic, complemented
97#11762718C2211yescharacteristic
98#11762718C2211yescharacteristic, complemented
99#11762717C2211yescharacteristic
100#11762717C2211yescharacteristic
101#11762716C2211yescharacteristic, complemented
102#11762715C2211yescharacteristic, complemented
103#11762714C2211yescharacteristic, complemented
104#11762712C2211yescharacteristic
105#11762712C2211yescharacteristic
106#11762709C2211yescharacteristic
107#11762709C2211yescharacteristic
108#11762709C2211yescharacteristic
109#11762709C2211yescharacteristic, complemented
110#11762706C2211yescharacteristic, complemented
111#11762706C2211yescharacteristic, complemented
112#11762704C2211yescharacteristic, complemented
113#11762704C2211yescharacteristic, complemented
114#11762703C2211yescharacteristic, complemented
115#11762703C2211yescharacteristic, complemented
116#11762702C2211yescharacteristic
117#11762702C2211yescharacteristic
118#11762702C2211yescharacteristic
119#11762702C2211yescharacteristic, complemented
120#11762702C2211yescharacteristic, complemented
121#11762701C2211yescharacteristic, complemented
122#11762700C2211yescharacteristic, complemented
123#11762700C2211yescharacteristic, complemented
124#11762698C2211yescharacteristic, complemented
125#11762697C2211yescharacteristic, complemented
126#11762696C2211yescharacteristic, complemented
127#11762696C2211yescharacteristic, complemented
128#11762688C2211yescharacteristic
129#11762687C2211yescharacteristic, complemented
130#11762686C2211yescharacteristic
131#11762686C2211yescharacteristic
132#11762686C2211yescharacteristic
133#11762685C2211yescharacteristic
134#11762685C2211yescharacteristic
135#11762685C2211yescharacteristic
136#11762685C2211yescharacteristic, complemented
137#11762685C2211yescharacteristic, complemented
138#11762682C2211yescharacteristic
139#11762681C2211yescharacteristic
140#11762681C2211yescharacteristic
141#11762681C2211yescharacteristic
142#11762675C2211yescharacteristic, complemented
143#11762670C2211yescharacteristic
144#11762668C2211yescharacteristic, complemented
145#11762667C2211yescharacteristic
146C4×#63225C2211yescharacteristic, complemented
147#11762660C2211yescharacteristic, complemented
148#11762660C2211yescharacteristic, complemented
149#11762660C2211yescharacteristic, complemented
150#11762660C2211yescharacteristic, complemented
151#11762660C2211yescharacteristic, complemented
152C22⋊C4×Dic17C2211yescharacteristic
153C22⋊C4×Dic17C2211yescharacteristic
154C22⋊C4×Dic17C2211yescharacteristic
155C22⋊C4×Dic17C2211yescharacteristic
156C22⋊C4×Dic17C2211yescharacteristic
157C22⋊C4×Dic17C2211yescharacteristic
158C22⋊C4×Dic17C2211yescharacteristic
159C22⋊C4×Dic17C2211yescharacteristic
160C22⋊C4×Dic17C2211yescharacteristic
161C22⋊C4×Dic17C2211yescharacteristic
162C22⋊C4×Dic17C2211yescharacteristic
163C22⋊C4×Dic17C2211yescharacteristic
164C22⋊C4×Dic17C2211yescharacteristic, complemented
165C22⋊C4×Dic17C2211yescharacteristic, complemented
166C22⋊C4×Dic17C2211yescharacteristic, complemented
167C4×#63227C2211yescharacteristic, complemented
168#11762656C2211yescharacteristic, complemented
169#11762656C2211yescharacteristic, complemented
170#11762656C2211yescharacteristic, complemented
171C2×#10587502C2211yescharacteristic
172C2×#10587502C2211yescharacteristic
173C42×Dic17C2211yescharacteristic, complemented
174C2×C17×#124C2211yescharacteristic
175C2×C17×C22⋊Q8C2211yescharacteristic
176C2×C17×#120C2211yescharacteristic
177C22×C22⋊C4×C17C2211yescharacteristic
178C17×#397C2211yescharacteristic
179C17×#394C2211yescharacteristic
180C17×#394C2211yescharacteristic
181C17×#393C2211yescharacteristic
182C17×#390C2211yescharacteristic
183C17×#388C2211yescharacteristic
184C17×#388C2211yescharacteristic
185C17×#386C2211yescharacteristic
186C17×#386C2211yescharacteristic
187C17×#379C2211yescharacteristic
188C4×C22⋊C4×C17C2211yescharacteristic
189C25×C17C2311yescharacteristic
190C22×Q8×C17C2311yescharacteristic
191C22×D4×C17C2311yescharacteristic
192C22×D4×C17C2311yescharacteristic
193C22×D4×C17C2311yescharacteristic
194C23×C4×C17C2311yescharacteristic
195C23×C4×C17C2311yescharacteristic
196C22×C22⋊D17C2311yescharacteristic
197C22×C22⋊D17C2311yescharacteristic
198C22×C22⋊D17C2311yescharacteristic
199C22×C22⋊D17C2311yescharacteristic
200C22×C22⋊D17C2311yescharacteristic
201C22×C22⋊D17C2311yescharacteristic
202C22×C22⋊D17C2311yescharacteristic
203C22×C22⋊D17C2311yescharacteristic
204C23×Dic17—24no—
205C23×Dic17—24no—
206C23×Dic17—42no—
207C23×Dic17C2311yescharacteristic
208C23×Dic17C2311yescharacteristic
209C23×Dic17C2311yescharacteristic
210C23×Dic17C2311yescharacteristic
211C23×Dic17C2311yescharacteristic
212C23×Dic17C2311yescharacteristic
213C23×Dic17C2311yescharacteristic
214C23×Dic17C2311yescharacteristic
215C23×Dic17C2311yescharacteristic
216C2×#63254—24no—
217C2×#63254—24no—
218C2×#63254—42no—
219C22×D68C2311yescharacteristic
220C22×C4×D17C2311yescharacteristic
221C22×C4×D17C2311yescharacteristic
222C22×C4×D17C2311yescharacteristic
223C22×C4×D17C2311yescharacteristic
224C22×Dic34C2311yescharacteristic
225C17×#124—24no—
226C17×C22⋊Q8—24no—
227C17×#120—24no—
228C2×C4⋊C4×C17C2311yescharacteristic
229C2×C4⋊C4×C17C2311yescharacteristic
230C2×C4⋊C4×C17C2311yescharacteristic
231C2×C22⋊C4×C17—24no—
232C2×C22⋊C4×C17C2311yescharacteristic
233C2×C22⋊C4×C17C2311yescharacteristic
234C2×C22⋊C4×C17C2311yescharacteristic
235C2×C22⋊C4×C17C2311yescharacteristic
236C2×C22⋊C4×C17C2311yescharacteristic
237C2×C22⋊C4×C17C2311yescharacteristic
238C2×C22⋊C4×C17C2311yescharacteristic
239C2×C22⋊C4×C17C2311yescharacteristic
240C2×C22⋊C4×C17C2311yescharacteristic
241C2×C22⋊C4×C17C2311yescharacteristic
242C2×C22⋊C4×C17C2311yescharacteristic
243C2×C22⋊C4×C17C2311yescharacteristic
244C2×C22⋊C4×C17C2311yescharacteristic
245C2×C22⋊C4×C17C2311yescharacteristic
246C2×C22⋊C4×C17C2311yescharacteristic
247C2×C22⋊C4×C17C2311yescharacteristic
248C2×C22⋊C4×C17C2311yescharacteristic
249C2×C42×C17C2311yescharacteristic
250C2×C42×C17C2311yescharacteristic
251#10587639—24no—
252#10587639—24no—
253C2×C22⋊Dic17—24no—
254C2×C22⋊Dic17C2311yescharacteristic
255C2×C22⋊Dic17C2311yescharacteristic
256C2×C22⋊Dic17C2311yescharacteristic
257C2×C22⋊Dic17C2311yescharacteristic
258C2×C22⋊Dic17C2311yescharacteristic
259C2×C22⋊Dic17C2311yescharacteristic
260C2×C22⋊Dic17C2311yescharacteristic
261C2×C22⋊Dic17C2311yescharacteristic
262C2×C22⋊Dic17C2311yescharacteristic
263C2×C22⋊Dic17C2311yescharacteristic
264C2×C22⋊Dic17C2311yescharacteristic
265C2×C22⋊Dic17C2311yescharacteristic
266C2×C22⋊Dic17C2311yescharacteristic
267C2×C22⋊Dic17C2311yescharacteristic
268C2×C22⋊Dic17C2311yescharacteristic
269#10587633—24no—
270Q8×Dic17—24no—
271#10587625—24no—
272#10587625—24no—
273#10587625—24no—
274#10587621—24no—
275#10587621—24no—
276D4×Dic17—24no—
277D4×Dic17—24no—
278#10587616—24no—
279C4×C22⋊D17—24no—
280C2×#63227C2311yescharacteristic
281C2×#63227C2311yescharacteristic
282C2×#63227C2311yescharacteristic
283C2×#63227C2311yescharacteristic
284C2×#63227C2311yescharacteristic
285C2×#63227C2311yescharacteristic
286C2×#63227C2311yescharacteristic
287C2×#63227C2311yescharacteristic
288C2×#63227C2311yescharacteristic
289C2×#63227C2311yescharacteristic
290C2×#63227C2311yescharacteristic
291C2×#63227C2311yescharacteristic
292C2×#63227C2311yescharacteristic
293C2×#63227C2311yescharacteristic
294C2×#63227C2311yescharacteristic
295C2×#63227C2311yescharacteristic
296C2×C4⋊Dic17C2311yescharacteristic
297C2×C4⋊Dic17C2311yescharacteristic
298C2×C4⋊Dic17C2311yescharacteristic
299C2×C4⋊Dic17C2311yescharacteristic
300C2×C4⋊Dic17C2311yescharacteristic
301C2×C4⋊Dic17C2311yescharacteristic
302C2×C4⋊Dic17C2311yescharacteristic
303C2×#63225C2311yescharacteristic
304C2×#63225C2311yescharacteristic
305C2×#63225C2311yescharacteristic
306C2×#63225C2311yescharacteristic
307C2×#63225C2311yescharacteristic
308C2×#63225C2311yescharacteristic
309C2×#63225C2311yescharacteristic
310C2×#63225C2311yescharacteristic
311C2×#63225C2311yescharacteristic
312C2×#63225C2311yescharacteristic
313C2×#63225C2311yescharacteristic
314C2×#63225C2311yescharacteristic
315C2×#63225C2311yescharacteristic
316C2×#63225C2311yescharacteristic
317C2×#63225C2311yescharacteristic
318C2×#63225C2311yescharacteristic
319C2×C4×Dic17—24no—
320C2×C4×Dic17—42no—
321C2×C4×Dic17C2311yescharacteristic
322C2×C4×Dic17C2311yescharacteristic
323C2×C4×Dic17C2311yescharacteristic
324C2×C4×Dic17C2311yescharacteristic
325C2×C4×Dic17C2311yescharacteristic
326C2×C4×Dic17C2311yescharacteristic
327C2×C4×Dic17C2311yescharacteristic
328C2×C4×Dic17C2311yescharacteristic
329C2×C4×Dic17C2311yescharacteristic
330C2×C4×Dic17C2311yescharacteristic
331C2×C4×Dic17C2311yescharacteristic
332C2×C4×Dic17C2311yescharacteristic
333C2×C4×Dic17C2311yescharacteristic
334C2×C4×Dic17C2311yescharacteristic
335C2×C4×Dic17C2311yescharacteristic
336C2×C4×Dic17C2311yescharacteristic
337C2×C4×Dic17C2311yescharacteristic
338#10587584—24no—
339#10587584—24no—
340#10587579—24no—
341#10587578—24no—
342#10587578—24no—
343#10587576—24no—
344#10587572—24no—
345#10587572—24no—
346#10587572—24no—
347#10587570—24no—
348#10587567—24no—
349#10587567—24no—
350#10587567—24no—
351#10587567—24no—
352#10587567—42no—
353#10587567—42no—
354#10587567D418yescomplemented
355#10587564—24no—
356#10587564—24no—
357#10587563—24no—
358C42×D17—42no—
359C17×#95C2311yescharacteristic
360C17×#95C2311yescharacteristic
361C17×#95C2311yescharacteristic
362C17×#95C2311yescharacteristic
363C17×#95C2311yescharacteristic
364C17×#95C2311yescharacteristic
365#10587502C2311yescharacteristic
366#10587502C2311yescharacteristic
367#10587502C2311yescharacteristic
368#10587502C2311yescharacteristic
369#10587502C2311yescharacteristic
370#10587502C2311yescharacteristic
371#10587502C2311yescharacteristic
372#10587502C2311yescharacteristic
373#10587502C2311yescharacteristic
374#10587502C2311yescharacteristic
375#10587502C2311yescharacteristic
376#10587502C2311yescharacteristic
377#10587502C2311yescharacteristic
378#10587502C2311yescharacteristic
379#10587502C2311yescharacteristic
380#10587502C2311yescharacteristic
381#10587502C2311yescharacteristic
382#10587502C2311yescharacteristic
383#10587502C2311yescharacteristic
384#10587502C2311yescharacteristic
385#10587502C2311yescharacteristic
386#10587502C2311yescharacteristic
387#10587502C2311yescharacteristic
388#10587502C2311yescharacteristic
389#10587502C2311yescharacteristic
390#10587502C2311yescharacteristic
391C24×C17—22no—
392C24×C17—22no—
393C24×C17—22no—
394C24×C17—22no—
395C24×C17—22no—
396C24×C17—41no—
397C24×C17—41no—
398C24×C17C2411yescharacteristic
399C24×C17C2411yescharacteristic
400C24×C17C2411yescharacteristic
401C24×C17C2411yescharacteristic
402C23×D17C2411yescharacteristic
403C23×D17C2411yescharacteristic
404C2×Q8×C17—22no—
405C2×Q8×C17—22no—
406C2×Q8×C17—41no—
407C2×D4×C17—22no—
408C2×D4×C17—22no—
409C2×D4×C17—22no—
410C2×D4×C17—22no—
411C2×D4×C17—22no—
412C2×D4×C17—22no—
413C2×D4×C17—22no—
414C2×D4×C17—41no—
415C2×D4×C17—41no—
416C22×C4×C17—22no—
417C22×C4×C17—22no—
418C22×C4×C17—22no—
419C22×C4×C17—22no—
420C22×C4×C17—41no—
421C22×C4×C17—41no—
422C22×C4×C17C2411yescharacteristic
423C22×C4×C17C2411yescharacteristic
424C22×C4×C17C2411yescharacteristic
425C22×C4×C17C2411yescharacteristic
426C22×C4×C17C2411yescharacteristic
427C22×C4×C17C2411yescharacteristic
428C22×C4×C17C2411yescharacteristic
429C22×C4×C17C2411yescharacteristic
430C22×C4×C17C2411yescharacteristic
431C22×C4×C17C2411yescharacteristic
432C22×C4×C17C2411yescharacteristic
433C2×C22⋊D17—22no—
434C2×C22⋊D17—22no—
435C2×C22⋊D17—22no—
436C2×C22⋊D17—22no—
437C2×C22⋊D17—22no—
438C2×C22⋊D17—22no—
439C2×C22⋊D17—22no—
440C2×C22⋊D17—22no—
441C2×C22⋊D17—22no—
442C2×C22⋊D17—22no—
443C2×C22⋊D17—22no—
444C2×C22⋊D17—22no—
445C2×C22⋊D17—22no—
446C2×C22⋊D17—22no—
447C2×C22⋊D17—22no—
448C2×C22⋊D17—22no—
449C2×C22⋊D17—41no—
450C2×C22⋊D17—41no—
451C2×C22⋊D17—41no—
452C2×C22⋊D17—41no—
453C2×C22⋊D17—41no—
454C2×C22⋊D17—41no—
455C2×C22⋊D17—41no—
456C2×C22⋊D17C2×D414yes—
457C22×Dic17—22no—
458C22×Dic17—22no—
459C22×Dic17—22no—
460C22×Dic17—22no—
461C22×Dic17—22no—
462C22×Dic17—22no—
463C22×Dic17—22no—
464C22×Dic17—22no—
465C22×Dic17—22no—
466C22×Dic17—22no—
467C22×Dic17—22no—
468C22×Dic17—22no—
469C22×Dic17—22no—
470C22×Dic17—22no—
471C22×Dic17—22no—
472C22×Dic17—22no—
473C22×Dic17—22no—
474C22×Dic17—22no—
475C22×Dic17—22no—
476C22×Dic17—41no—
477C22×Dic17—41no—
478C22×Dic17—41no—
479C22×Dic17—41no—
480C22×Dic17—41no—
481C22×Dic17—416no—
482C22×Dic17C2×D414yes—
483C22×Dic17#4114yes—
484C22×Dic17#4114yescomplemented
485C22×Dic17C2411yescharacteristic
486C22×Dic17C2411yescharacteristic
487C22×Dic17C2411yescharacteristic
488C22×Dic17C2411yescharacteristic
489C22×Dic17C2411yescharacteristic
490C22×Dic17C2411yescharacteristic
491C22×Dic17C2411yescharacteristic
492C22×Dic17C2411yescharacteristic
493C22×Dic17C2411yescharacteristic
494C22×Dic17C2411yescharacteristic
495C22×Dic17C2411yescharacteristic
496C22×Dic17C2411yescharacteristic
497C22×Dic17C2411yescharacteristic
498C22×Dic17C2411yescharacteristic
499#63254—416no—
500C2×D68—22no—
501C2×D68—22no—
502C2×D68—41no—
503C2×C4×D17—22no—
504C2×C4×D17—22no—
505C2×C4×D17—22no—
506C2×C4×D17—22no—
507C2×C4×D17—22no—
508C2×C4×D17—22no—
509C2×C4×D17—22no—
510C2×C4×D17—22no—
511C2×C4×D17—41no—
512C2×C4×D17—41no—
513C2×C4×D17—41no—
514C2×C4×D17C2×D414yes—
515C2×Dic34—22no—
516C2×Dic34—22no—
517C2×Dic34—41no—
518C4⋊C4×C17—22no—
519C4⋊C4×C17—22no—
520C4⋊C4×C17—22no—
521C22⋊C4×C17—22no—
522C22⋊C4×C17—22no—
523C22⋊C4×C17—22no—
524C22⋊C4×C17—22no—
525C22⋊C4×C17—22no—
526C22⋊C4×C17—22no—
527C22⋊C4×C17—22no—
528C22⋊C4×C17—22no—
529C22⋊C4×C17—22no—
530C22⋊C4×C17—22no—
531C22⋊C4×C17—22no—
532C22⋊C4×C17—41no—
533C22⋊C4×C17—41no—
534C22⋊C4×C17—41no—
535C22⋊C4×C17—41no—
536C22⋊C4×C17C2×D414yes—
537C22⋊C4×C17#4114yescomplemented
538C42×C17—22no—
539C42×C17—41no—
540C22⋊Dic17—22no—
541C22⋊Dic17—22no—
542C22⋊Dic17—22no—
543C22⋊Dic17—22no—
544C22⋊Dic17—22no—
545C22⋊Dic17—22no—
546C22⋊Dic17—22no—
547C22⋊Dic17—22no—
548C22⋊Dic17—22no—
549C22⋊Dic17—22no—
550C22⋊Dic17—22no—
551C22⋊Dic17—22no—
552C22⋊Dic17—22no—
553C22⋊Dic17—22no—
554C22⋊Dic17#4114yescomplemented
555#63227—22no—
556#63227—22no—
557#63227—22no—
558#63227—22no—
559#63227—22no—
560#63227—22no—
561#63227—22no—
562#63227—22no—
563#63227—22no—
564#63227—22no—
565#63227—22no—
566#63227—22no—
567#63227—22no—
568#63227—41no—
569#63227—41no—
570#63227C2×D414yes—
571C4⋊Dic17—22no—
572C4⋊Dic17—22no—
573C4⋊Dic17—22no—
574C4⋊Dic17—22no—
575C4⋊Dic17—22no—
576C4⋊Dic17—22no—
577C4⋊Dic17—22no—
578#63225—22no—
579#63225—22no—
580#63225—22no—
581#63225—22no—
582#63225—22no—
583#63225—22no—
584#63225—22no—
585#63225—22no—
586#63225—22no—
587#63225—22no—
588#63225—22no—
589#63225—41no—
590#63225—41no—
591#63225—41no—
592#63225—41no—
593#63225C2×D414yes—
594C4×Dic17—22no—
595C4×Dic17—22no—
596C4×Dic17—22no—
597C4×Dic17—22no—
598C4×Dic17—22no—
599C4×Dic17—22no—
600C4×Dic17—22no—
601C4×Dic17—22no—
602C4×Dic17—22no—
603C4×Dic17—22no—
604C4×Dic17—22no—
605C4×Dic17—22no—
606C4×Dic17—41no—
607C4×Dic17—41no—
608C4×Dic17—41no—
609C4×Dic17—41no—
610C4×Dic17C2×D414yes—
611#34829—171nomaximal, Sylow
612C23×C17—21no—
613C23×C17—21no—
614C23×C17—21no—
615C23×C17—21no—
616C23×C17—28no—
617C23×C17—21no—
618C23×C17—21no—
619C23×C17—21no—
620C23×C17—21no—
621C23×C17—21no—
622C23×C17—21no—
623C23×C17—21no—
624C23×C17—21no—
625C23×C17—21no—
626C23×C17—21no—
627C23×C17—21no—
628C23×C17—21no—
629C23×C17—21no—
630C23×C17—21no—
631C23×C17—21no—
632C23×C17—21no—
633C23×C17—21no—
634C23×C17—21no—
635C23×C17—21no—
636C23×C17—44no—
637C23×C17—44no—
638C23×C17—44no—
639C23×C17—44no—
640C23×C17—44no—
641C23×C17—44no—
642C23×C17C22×D412yes—
643C23×C17C2×#4112yes—
644C23×C17C2×#4112yes—
645C23×C17C2×#4112yes—
646C23×C17C2×#4112yes—
647C23×C17C2511yescharacteristic
648C22×D17—21no—
649C22×D17—21no—
650C22×D17—21no—
651C22×D17—21no—
652C22×D17—21no—
653C22×D17—21no—
654C22×D17—21no—
655C22×D17—21no—
656C22×D17—21no—
657C22×D17—21no—
658C22×D17—21no—
659C22×D17—21no—
660C22×D17—21no—
661C22×D17C22×D412yes—
662Q8×C17—44no—
663D4×C17—44no—
664D4×C17—44no—
665D4×C17—44no—
666C2×C4×C17—21no—
667C2×C4×C17—21no—
668C2×C4×C17—21no—
669C2×C4×C17—21no—
670C2×C4×C17—21no—
671C2×C4×C17—21no—
672C2×C4×C17—21no—
673C2×C4×C17—21no—
674C2×C4×C17—21no—
675C2×C4×C17—21no—
676C2×C4×C17—21no—
677C2×C4×C17—21no—
678C2×C4×C17—21no—
679C2×C4×C17—21no—
680C2×C4×C17—21no—
681C2×C4×C17—21no—
682C2×C4×C17—21no—
683C2×C4×C17—21no—
684C2×C4×C17—21no—
685C2×C4×C17—21no—
686C2×C4×C17—21no—
687C2×C4×C17—21no—
688C2×C4×C17—21no—
689C2×C4×C17—21no—
690C2×C4×C17—21no—
691C2×C4×C17—21no—
692C2×C4×C17—21no—
693C2×C4×C17—21no—
694C2×C4×C17—21no—
695C2×C4×C17—44no—
696C2×C4×C17—44no—
697C2×C4×C17C22×D412yes—
698C2×C4×C17C22×D412yes—
699C2×C4×C17C2×#4112yes—
700C2×C4×C17C2×#4112yes—
701C22⋊D17—28no—
702C22⋊D17—44no—
703C22⋊D17—44no—
704C22⋊D17—44no—
705C22⋊D17—44no—
706C22⋊D17—44no—
707C22⋊D17—44no—
708C22⋊D17—44no—
709C2×Dic17—21no—
710C2×Dic17—21no—
711C2×Dic17—21no—
712C2×Dic17—21no—
713C2×Dic17—21no—
714C2×Dic17—21no—
715C2×Dic17—21no—
716C2×Dic17—21no—
717C2×Dic17—21no—
718C2×Dic17—21no—
719C2×Dic17—21no—
720C2×Dic17—21no—
721C2×Dic17—21no—
722C2×Dic17—21no—
723C2×Dic17—28no—
724C2×Dic17—28no—
725C2×Dic17—21no—
726C2×Dic17—21no—
727C2×Dic17—21no—
728C2×Dic17—21no—
729C2×Dic17—21no—
730C2×Dic17—21no—
731C2×Dic17—21no—
732C2×Dic17—21no—
733C2×Dic17—21no—
734C2×Dic17—21no—
735C2×Dic17—21no—
736C2×Dic17—21no—
737C2×Dic17—21no—
738C2×Dic17—21no—
739C2×Dic17—21no—
740C2×Dic17—21no—
741C2×Dic17—21no—
742C2×Dic17—21no—
743C2×Dic17—44no—
744C2×Dic17—44no—
745C2×Dic17—44no—
746C2×Dic17—44no—
747C2×Dic17—44no—
748C2×Dic17—44no—
749C2×Dic17—44no—
750C2×Dic17C22×D412yes—
751C2×Dic17C22×D412yes—
752C2×Dic17C22×D412yes—
753C2×Dic17C2×#4112yes—
754C2×Dic17C2×#4112yes—
755C2×Dic17C2×#4112yes—
756C2×Dic17C2×#4112yes—
757C2×Dic17C2×#4112yes—
758C2×Dic17C2×#4112yes—
759C2×Dic17H(5,𝔽2)12yes—
760D68—44no—
761C4×D17—28no—
762C4×D17—44no—
763C4×D17—44no—
764C4×D17—44no—
765Dic34—44no—
766C2×#529—171no—
767C2×#525—171no—
768#2560—171no—
769#2559—171no—
770#2558—171no—
771#2557—171no—
772#2556—171no—
773#2555—171no—
774#2554—171no—
775#2553—171no—
776#2549—171no—
777#2543—171no—
778#2539—171no—
779#2534—171no—
780#2488—171no—
781#2472D1711yescharacteristic, complemented
782#2425—171no—
783#2424—171no—
784#2396—171no—
785#2395—171no—
786#2392—171no—
787#2388—171no—
788C4×#124—171no—
789C4×#123—171no—
790C4×#121—171no—
791C4×#121—171no—
792C4×#120—171no—
793#2297—171no—
794#2293—171no—
795C42×D4—171no—
796C2×C4×C22⋊C4—171no—
797C22×C17—22no—
798C22×C17—22no—
799C22×C17—22no—
800C22×C17—22no—
801C22×C17—22no—
802C22×C17—22no—
803C22×C17—22no—
804C22×C17—22no—
805C22×C17—22no—
806C22×C17—22no—
807C22×C17—22no—
808C22×C17—22no—
809C22×C17—416no—
810C22×C17—41no—
811C22×C17—41no—
812C22×C17—41no—
813C22×C17—41no—
814C22×C17—41no—
815C22×C17—41no—
816C22×C17—41no—
817C22×C17—41no—
818C22×C17—41no—
819C22×C17—41no—
820C22×C17—41no—
821C22×C17—41no—
822C22×C17—41no—
823C22×C17—41no—
824C22×C17—41no—
825C22×C17#53214yes—
826C22×C17C23×D411yescharacteristic
827C22×C17C22×#4111yescharacteristic
828C22×C17C22×#4111yescharacteristic
829C22×C17C22×#4111yescharacteristic
830C22×C17C22×#4111yescharacteristic
831C22×C17C2×H(5,𝔽2)11yescharacteristic
832C22×C17#58511yescharacteristic
833C2×D17—22no—
834C2×D17—22no—
835C2×D17—22no—
836C2×D17—41no—
837C2×D17—41no—
838C2×D17—41no—
839C2×D17—41no—
840C2×D17—41no—
841C2×D17—41no—
842C2×D17—41no—
843C2×D17—41no—
844C2×D17—41no—
845C2×D17—41no—
846C2×D17—41no—
847C4×C17—22no—
848C4×C17—22no—
849C4×C17—22no—
850C4×C17—22no—
851C4×C17—41no—
852C4×C17—41no—
853C4×C17—41no—
854C4×C17—41no—
855C4×C17—41no—
856C4×C17—41no—
857C4×C17—41no—
858Dic17—22no—
859Dic17—22no—
860Dic17—22no—
861Dic17—22no—
862Dic17—22no—
863Dic17—22no—
864Dic17—22no—
865Dic17—41no—
866Dic17—41no—
867Dic17—41no—
868Dic17—41no—
869Dic17—41no—
870Dic17—41no—
871Dic17#54614yes—
872C22×#41—171no—
873C24×C4—171no—
874#529—348no—
875C2×#126—171no—
876C2×#126—171no—
877C2×#125—171no—
878C2×#124—171no—
879C2×#124C2×D1711yescharacteristic
880#525—348no—
881C2×#123—171no—
882C2×#123—171no—
883C2×#123—171no—
884C2×#123—171no—
885C2×#123—171no—
886C2×C22⋊Q8—171no—
887C2×C22⋊Q8—171no—
888C2×C22⋊Q8C2×D1711yescharacteristic
889C2×#121—171no—
890C2×#121—171no—
891C2×#121—171no—
892C2×#121—171no—
893C2×#121—171no—
894C2×#120—171no—
895C2×#120—171no—
896C2×#120C2×D1711yescharacteristic
897C2×C4×Q8—171no—
898C2×C4×D4—171no—
899C2×C4×D4—171no—
900C2×C4×D4—171no—
901C2×C4×D4—171no—
902C2×C4×D4—171no—
903C2×C4×D4—171no—
904C2×C4×D4—171no—
905C2×C4×D4—171no—
906C2×C4×D4—171no—
907C2×C4×D4—171no—
908C2×C4×D4—171no—
909C2×#117—171no—
910C2×#117—171no—
911C2×#117—171no—
912C22×C22⋊C4—171no—
913C22×C22⋊C4C2×D1711yescharacteristic
914C22×C42—171no—
915C22×C42—171no—
916C22×C42—171no—
917#400—171no—
918#400—171no—
919#399—171no—
920#399—171no—
921#398—171no—
922#398—171no—
923#398—171no—
924#398—171no—
925#397—171no—
926#397—171no—
927#397—171no—
928#397C2×D1711yescharacteristic
929#396—171no—
930#396—171no—
931#396—171no—
932#396—171no—
933#395—171no—
934#395—171no—
935#394—171no—
936#394—171no—
937#394—171no—
938#394—171no—
939#394—171no—
940#394—171no—
941#394C2×D1711yescharacteristic
942#394C2×D1711yescharacteristic
943#393—171no—
944#393C2×D1711yescharacteristic
945#392—171no—
946#392—171no—
947#392—171no—
948#392—171no—
949#391—171no—
950#391—171no—
951#391—171no—
952#390—171no—
953#390—171no—
954#390—171no—
955#390—171no—
956#390—171no—
957#390—171no—
958#390C2×D1711yescharacteristic
959#389—171no—
960#389—171no—
961#389—171no—
962#389—171no—
963#388—171no—
964#388—171no—
965#388—171no—
966#388—171no—
967#388—171no—
968#388—171no—
969#388—171no—
970#388—171no—
971#388—171no—
972#388—171no—
973#388—171no—
974#388—171no—
975#388C2×D1711yescharacteristic
976#388C2×D1711yescharacteristic
977#387—171no—
978#387—171no—
979#386—171no—
980#386—171no—
981#386—171no—
982#386—171no—
983#386—171no—
984#386—171no—
985#386—171no—
986#386—171no—
987#386—171no—
988#386—171no—
989#386C2×D1711yescharacteristic
990#386C2×D1711yescharacteristic
991#385—171no—
992#385—171no—
993#385—171no—
994#385—171no—
995#382—171no—
996#381—171no—
997#380—171no—
998#380—171no—
999#379C2×D1711yescharacteristic
1000C4×C4⋊C4—171no—
1001C4×C4⋊C4—171no—
1002C4×C4⋊C4—171no—
1003C4×C4⋊C4—171no—
1004C4×C4⋊C4—171no—
1005C4×C4⋊C4—171no—
1006C4×C22⋊C4—171no—
1007C4×C22⋊C4—171no—
1008C4×C22⋊C4—171no—
1009C4×C22⋊C4—171no—
1010C4×C22⋊C4—171no—
1011C4×C22⋊C4—171no—
1012C4×C22⋊C4—171no—
1013C4×C22⋊C4—171no—
1014C4×C22⋊C4—171no—
1015C4×C22⋊C4—171no—
1016C4×C22⋊C4—171no—
1017C4×C22⋊C4—171no—
1018C4×C22⋊C4—171no—
1019C4×C22⋊C4—171no—
1020C4×C22⋊C4—171no—
1021C4×C22⋊C4—171no—
1022C4×C22⋊C4—171no—
1023C4×C22⋊C4—171no—
1024C4×C22⋊C4—171no—
1025C4×C22⋊C4C2×D1711yescharacteristic
1026C2×#95—171no—
1027C2×#95—171no—
1028C43—171no—
1029C2×C17—24no—
1030C2×C17—42no—
1031C2×C17—42no—
1032C2×C17—81no—
1033C2×C17C2×#53211yescharacteristic
1034C2×C17#344411yescharacteristic
1035C2×C17#345911yescharacteristic
1036C2×C17C2×#54611yescharacteristic
1037C2×C17D4×#4111yescharacteristic
1038C2×C17#347511yescharacteristic
1039C2×C17#348111yescharacteristic
1040D17—42no—
1041D17—81no—
1042C25C22×D1711yescharacteristic
1043C2×#41—344no—
1044C2×#41—344no—
1045C2×#41—682no—
1046C22×Q8—171no—
1047C22×Q8C22×D1711yescharacteristic
1048C22×D4—171no—
1049C22×D4—171no—
1050C22×D4—171no—
1051C22×D4—171no—
1052C22×D4—171no—
1053C22×D4—171no—
1054C22×D4—171no—
1055C22×D4—171no—
1056C22×D4—171no—
1057C22×D4C22×D1711yescharacteristic
1058C22×D4C22×D1711yescharacteristic
1059C22×D4C22×D1711yescharacteristic
1060C23×C4—171no—
1061C23×C4—171no—
1062C23×C4—171no—
1063C23×C4—171no—
1064C23×C4—171no—
1065C23×C4—171no—
1066C23×C4—171no—
1067C23×C4—171no—
1068C23×C4—171no—
1069C23×C4—171no—
1070C23×C4—171no—
1071C23×C4—171no—
1072C23×C4—171no—
1073C23×C4—344no—
1074C23×C4—344no—
1075C23×C4—682no—
1076C23×C4C22×D1711yescharacteristic
1077C23×C4C22×D1711yescharacteristic
1078#126—344no—
1079#126—344no—
1080#125—344no—
1081#124—24no—
1082#124—344no—
1083#123—344no—
1084#123—344no—
1085#123—344no—
1086#123—344no—
1087#123—344no—
1088C22⋊Q8—24no—
1089C22⋊Q8—344no—
1090C22⋊Q8—344no—
1091#121—344no—
1092#121—344no—
1093#121—344no—
1094#121—344no—
1095#121—344no—
1096#120—24no—
1097#120—344no—
1098#120—344no—
1099C4×Q8—344no—
1100C4×D4—178no—
1101C4×D4—344no—
1102C4×D4—344no—
1103C4×D4—344no—
1104C4×D4—344no—
1105C4×D4—344no—
1106C4×D4—344no—
1107C4×D4—344no—
1108C4×D4—344no—
1109C4×D4—682no—
1110C4×D4—682no—
1111#117—344no—
1112#117—344no—
1113#117—344no—
1114C2×C4⋊C4—171no—
1115C2×C4⋊C4—171no—
1116C2×C4⋊C4—171no—
1117C2×C4⋊C4—171no—
1118C2×C4⋊C4—171no—
1119C2×C4⋊C4—171no—
1120C2×C4⋊C4—171no—
1121C2×C4⋊C4—171no—
1122C2×C4⋊C4—171no—
1123C2×C4⋊C4—171no—
1124C2×C4⋊C4—171no—
1125C2×C4⋊C4—171no—
1126C2×C4⋊C4—171no—
1127C2×C4⋊C4—171no—
1128C2×C4⋊C4—171no—
1129C2×C4⋊C4—171no—
1130C2×C4⋊C4—171no—
1131C2×C4⋊C4—171no—
1132C2×C4⋊C4—171no—
1133C2×C4⋊C4—171no—
1134C2×C4⋊C4—171no—
1135C2×C4⋊C4—171no—
1136C2×C4⋊C4—171no—
1137C2×C4⋊C4C22×D1711yescharacteristic
1138C2×C4⋊C4C22×D1711yescharacteristic
1139C2×C4⋊C4C22×D1711yescharacteristic
1140C2×C22⋊C4—24no—
1141C2×C22⋊C4—171no—
1142C2×C22⋊C4—171no—
1143C2×C22⋊C4—171no—
1144C2×C22⋊C4—171no—
1145C2×C22⋊C4—171no—
1146C2×C22⋊C4—171no—
1147C2×C22⋊C4—171no—
1148C2×C22⋊C4—171no—
1149C2×C22⋊C4—171no—
1150C2×C22⋊C4—171no—
1151C2×C22⋊C4—171no—
1152C2×C22⋊C4—171no—
1153C2×C22⋊C4—171no—
1154C2×C22⋊C4—171no—
1155C2×C22⋊C4—171no—
1156C2×C22⋊C4—171no—
1157C2×C22⋊C4—171no—
1158C2×C22⋊C4—171no—
1159C2×C22⋊C4—171no—
1160C2×C22⋊C4—171no—
1161C2×C22⋊C4—171no—
1162C2×C22⋊C4—171no—
1163C2×C22⋊C4—171no—
1164C2×C22⋊C4—171no—
1165C2×C22⋊C4—171no—
1166C2×C22⋊C4—171no—
1167C2×C22⋊C4—171no—
1168C2×C22⋊C4—171no—
1169C2×C22⋊C4—171no—
1170C2×C22⋊C4—171no—
1171C2×C22⋊C4—171no—
1172C2×C22⋊C4—344no—
1173C2×C22⋊C4C22×D1711yescharacteristic
1174C2×C22⋊C4C22×D1711yescharacteristic
1175C2×C22⋊C4C22×D1711yescharacteristic
1176C2×C22⋊C4C22×D1711yescharacteristic
1177C2×C22⋊C4C22×D1711yescharacteristic
1178C2×C22⋊C4C22×D1711yescharacteristic
1179C2×C22⋊C4C22×D1711yescharacteristic
1180C2×C22⋊C4C22×D1711yescharacteristic
1181C2×C22⋊C4C22×D1711yescharacteristic
1182C2×C22⋊C4C22×D1711yescharacteristic
1183C2×C22⋊C4C22×D1711yescharacteristic
1184C2×C22⋊C4C22×D1711yescharacteristic
1185C2×C22⋊C4C22×D1711yescharacteristic
1186C2×C22⋊C4C22×D1711yescharacteristic
1187C2×C22⋊C4C22×D1711yescharacteristic
1188C2×C22⋊C4C22×D1711yescharacteristic
1189C2×C22⋊C4C22×D1711yescharacteristic
1190C2×C42—171no—
1191C2×C42—171no—
1192C2×C42—171no—
1193C2×C42—171no—
1194C2×C42—171no—
1195C2×C42—171no—
1196C2×C42—171no—
1197C2×C42—171no—
1198C2×C42—171no—
1199C2×C42—171no—
1200C2×C42—171no—
1201C2×C42—171no—
1202C2×C42—171no—
1203C2×C42—171no—
1204C2×C42—171no—
1205C2×C42—171no—
1206C2×C42—171no—
1207C2×C42—344no—
1208C2×C42—682no—
1209C2×C42—682no—
1210C2×C42C22×D1711yescharacteristic
1211C2×C42C22×D1711yescharacteristic
1212#95—171no—
1213#95—171no—
1214#95—171no—
1215#95—171no—
1216#95—171no—
1217#95—171no—
1218#95—171no—
1219#95—171no—
1220#95—171no—
1221#95—171no—
1222#95—171no—
1223#95—171no—
1224#95—171no—
1225#95—171no—
1226#95—171no—
1227#95—171no—
1228#95—171no—
1229#95—171no—
1230#95—171no—
1231#95—171no—
1232#95—171no—
1233#95—171no—
1234#95—171no—
1235#95—171no—
1236#95—171no—
1237#95—171no—
1238#95C22×D1711yescharacteristic
1239#95C22×D1711yescharacteristic
1240#95C22×D1711yescharacteristic
1241#95C22×D1711yescharacteristic
1242#95C22×D1711yescharacteristic
1243#95C22×D1711yescharacteristic
1244C17#3482911yescharacteristic, complemented, Sylow
1245C24—22no—
1246C24—22no—
1247C24—22no—
1248C24—22no—
1249C24—22no—
1250C24—41no—
1251C24—41no—
1252C24—171no—
1253C24—171no—
1254C24C23×D1711yescharacteristic
1255C24C23×D1711yescharacteristic
1256C24C23×D1711yescharacteristic
1257C24C23×D1711yescharacteristic
1258#41—6816no—
1259C2×Q8—22no—
1260C2×Q8—22no—
1261C2×Q8—41no—
1262C2×Q8—342no—
1263C2×Q8—342no—
1264C2×Q8—681no—
1265C2×D4—22no—
1266C2×D4—22no—
1267C2×D4—22no—
1268C2×D4—22no—
1269C2×D4—22no—
1270C2×D4—22no—
1271C2×D4—22no—
1272C2×D4—41no—
1273C2×D4—41no—
1274C2×D4—174no—
1275C2×D4—342no—
1276C2×D4—342no—
1277C2×D4—342no—
1278C2×D4—342no—
1279C2×D4—342no—
1280C2×D4—342no—
1281C2×D4—342no—
1282C2×D4—342no—
1283C2×D4—342no—
1284C2×D4—342no—
1285C2×D4—342no—
1286C2×D4—342no—
1287C2×D4—342no—
1288C2×D4—342no—
1289C2×D4—342no—
1290C2×D4—342no—
1291C2×D4—342no—
1292C2×D4—342no—
1293C2×D4—681no—
1294C2×D4—681no—
1295C2×D4—681no—
1296C2×D4—681no—
1297C2×D4—681no—
1298C2×D4—681no—
1299C2×D4—681no—
1300C2×D4—681no—
1301C22×C4—22no—
1302C22×C4—22no—
1303C22×C4—22no—
1304C22×C4—22no—
1305C22×C4—41no—
1306C22×C4—41no—
1307C22×C4—171no—
1308C22×C4—174no—
1309C22×C4—174no—
1310C22×C4—171no—
1311C22×C4—171no—
1312C22×C4—171no—
1313C22×C4—171no—
1314C22×C4—171no—
1315C22×C4—171no—
1316C22×C4—171no—
1317C22×C4—174no—
1318C22×C4—174no—
1319C22×C4—171no—
1320C22×C4—171no—
1321C22×C4—171no—
1322C22×C4—171no—
1323C22×C4—171no—
1324C22×C4—171no—
1325C22×C4—342no—
1326C22×C4—342no—
1327C22×C4—342no—
1328C22×C4—342no—
1329C22×C4—342no—
1330C22×C4—342no—
1331C22×C4—342no—
1332C22×C4—342no—
1333C22×C4—342no—
1334C22×C4—342no—
1335C22×C4—342no—
1336C22×C4—342no—
1337C22×C4—342no—
1338C22×C4—342no—
1339C22×C4—342no—
1340C22×C4—342no—
1341C22×C4—342no—
1342C22×C4—342no—
1343C22×C4—342no—
1344C22×C4—342no—
1345C22×C4—342no—
1346C22×C4—342no—
1347C22×C4—342no—
1348C22×C4—342no—
1349C22×C4—342no—
1350C22×C4—342no—
1351C22×C4—342no—
1352C22×C4—681no—
1353C22×C4—681no—
1354C22×C4—681no—
1355C22×C4—681no—
1356C22×C4—681no—
1357C22×C4—681no—
1358C22×C4—681no—
1359C22×C4—681no—
1360C22×C4—6816no—
1361C22×C4C23×D1711yescharacteristic
1362C22×C4C23×D1711yescharacteristic
1363C22×C4C23×D1711yescharacteristic
1364C22×C4C23×D1711yescharacteristic
1365C22×C4C23×D1711yescharacteristic
1366C22×C4C23×D1711yescharacteristic
1367C22×C4C23×D1711yescharacteristic
1368C22×C4C23×D1711yescharacteristic
1369C22×C4C23×D1711yescharacteristic
1370C22×C4C23×D1711yescharacteristic
1371C22×C4C23×D1711yescharacteristic
1372C4⋊C4—22no—
1373C4⋊C4—22no—
1374C4⋊C4—22no—
1375C4⋊C4—174no—
1376C4⋊C4—342no—
1377C4⋊C4—342no—
1378C4⋊C4—342no—
1379C4⋊C4—342no—
1380C4⋊C4—342no—
1381C4⋊C4—342no—
1382C4⋊C4—342no—
1383C4⋊C4—342no—
1384C4⋊C4—342no—
1385C4⋊C4—342no—
1386C4⋊C4—342no—
1387C4⋊C4—342no—
1388C4⋊C4—342no—
1389C4⋊C4—342no—
1390C4⋊C4—342no—
1391C4⋊C4—342no—
1392C4⋊C4—342no—
1393C4⋊C4—342no—
1394C4⋊C4—681no—
1395C4⋊C4—681no—
1396C4⋊C4—681no—
1397C4⋊C4—681no—
1398C22⋊C4—22no—
1399C22⋊C4—22no—
1400C22⋊C4—22no—
1401C22⋊C4—22no—
1402C22⋊C4—22no—
1403C22⋊C4—22no—
1404C22⋊C4—22no—
1405C22⋊C4—22no—
1406C22⋊C4—22no—
1407C22⋊C4—22no—
1408C22⋊C4—22no—
1409C22⋊C4—41no—
1410C22⋊C4—41no—
1411C22⋊C4—41no—
1412C22⋊C4—41no—
1413C22⋊C4—174no—
1414C22⋊C4—174no—
1415C22⋊C4—342no—
1416C22⋊C4—342no—
1417C22⋊C4—342no—
1418C22⋊C4—342no—
1419C22⋊C4—342no—
1420C22⋊C4—342no—
1421C22⋊C4—342no—
1422C22⋊C4—342no—
1423C22⋊C4—342no—
1424C22⋊C4—342no—
1425C22⋊C4—342no—
1426C22⋊C4—342no—
1427C22⋊C4—342no—
1428C22⋊C4—342no—
1429C22⋊C4—342no—
1430C22⋊C4—342no—
1431C22⋊C4—342no—
1432C22⋊C4—342no—
1433C22⋊C4—342no—
1434C22⋊C4—342no—
1435C22⋊C4—342no—
1436C22⋊C4—342no—
1437C22⋊C4—342no—
1438C22⋊C4—342no—
1439C22⋊C4—342no—
1440C22⋊C4—342no—
1441C22⋊C4—342no—
1442C22⋊C4—681no—
1443C22⋊C4—681no—
1444C22⋊C4D4×D1714yes—
1445C22⋊C4#6325414yescomplemented
1446C42—22no—
1447C42—41no—
1448C42—174no—
1449C42—342no—
1450C42—342no—
1451C42—342no—
1452C42—342no—
1453C42—342no—
1454C42—342no—
1455C42—342no—
1456C42—342no—
1457C42—342no—
1458C42—342no—
1459C42—342no—
1460C42—342no—
1461C42—681no—
1462C42—681no—
1463C42—681no—
1464C42—681no—
1465C23—21no—
1466C23—21no—
1467C23—21no—
1468C23—21no—
1469C23—28no—
1470C23—21no—
1471C23—21no—
1472C23—21no—
1473C23—21no—
1474C23—21no—
1475C23—21no—
1476C23—21no—
1477C23—21no—
1478C23—21no—
1479C23—21no—
1480C23—21no—
1481C23—21no—
1482C23—21no—
1483C23—21no—
1484C23—21no—
1485C23—21no—
1486C23—21no—
1487C23—21no—
1488C23—21no—
1489C23—44no—
1490C23—44no—
1491C23—44no—
1492C23—44no—
1493C23—44no—
1494C23—44no—
1495C23—172no—
1496C23—341no—
1497C23—341no—
1498C23—341no—
1499C23—341no—
1500C23—341no—
1501C23—341no—
1502C23—341no—
1503C23—341no—
1504C23—341no—
1505C23—341no—
1506C23—341no—
1507C23—341no—
1508C23—341no—
1509C23C2×D4×D1712yes—
1510C23C2×#6325412yes—
1511C23#41×D1712yes—
1512C23#41×D1712yes—
1513C23#41×D1712yes—
1514C23C24×D1711yescharacteristic
1515Q8—44no—
1516Q8—684no—
1517D4—44no—
1518D4—44no—
1519D4—44no—
1520D4—348no—
1521D4—684no—
1522D4—684no—
1523D4—684no—
1524D4—684no—
1525D4—684no—
1526D4—684no—
1527D4—684no—
1528D4—684no—
1529C2×C4—21no—
1530C2×C4—21no—
1531C2×C4—21no—
1532C2×C4—21no—
1533C2×C4—21no—
1534C2×C4—21no—
1535C2×C4—21no—
1536C2×C4—21no—
1537C2×C4—21no—
1538C2×C4—21no—
1539C2×C4—21no—
1540C2×C4—21no—
1541C2×C4—21no—
1542C2×C4—21no—
1543C2×C4—21no—
1544C2×C4—21no—
1545C2×C4—21no—
1546C2×C4—21no—
1547C2×C4—21no—
1548C2×C4—21no—
1549C2×C4—21no—
1550C2×C4—21no—
1551C2×C4—21no—
1552C2×C4—21no—
1553C2×C4—21no—
1554C2×C4—21no—
1555C2×C4—21no—
1556C2×C4—21no—
1557C2×C4—21no—
1558C2×C4—44no—
1559C2×C4—44no—
1560C2×C4—172no—
1561C2×C4—172no—
1562C2×C4—172no—
1563C2×C4—172no—
1564C2×C4—172no—
1565C2×C4—172no—
1566C2×C4—172no—
1567C2×C4—172no—
1568C2×C4—172no—
1569C2×C4—172no—
1570C2×C4—348no—
1571C2×C4—348no—
1572C2×C4—348no—
1573C2×C4—341no—
1574C2×C4—341no—
1575C2×C4—341no—
1576C2×C4—341no—
1577C2×C4—341no—
1578C2×C4—341no—
1579C2×C4—341no—
1580C2×C4—341no—
1581C2×C4—341no—
1582C2×C4—341no—
1583C2×C4—341no—
1584C2×C4—341no—
1585C2×C4—341no—
1586C2×C4—341no—
1587C2×C4—341no—
1588C2×C4—341no—
1589C2×C4—341no—
1590C2×C4—341no—
1591C2×C4—341no—
1592C2×C4—341no—
1593C2×C4—341no—
1594C2×C4—341no—
1595C2×C4—341no—
1596C2×C4—341no—
1597C2×C4—341no—
1598C2×C4—341no—
1599C2×C4—341no—
1600C2×C4—341no—
1601C2×C4—341no—
1602C2×C4—341no—
1603C2×C4—341no—
1604C2×C4—341no—
1605C2×C4—684no—
1606C2×C4—684no—
1607C2×C4—684no—
1608C2×C4—684no—
1609C2×C4—684no—
1610C2×C4—684no—
1611C2×C4—684no—
1612C2×C4—684no—
1613C2×C4—684no—
1614C2×C4—684no—
1615C2×C4C2×D4×D1712yes—
1616C2×C4C2×D4×D1712yes—
1617C2×C4C2×#6325412yes—
1618C2×C4C2×#6325412yes—
1619C22—22no—
1620C22—22no—
1621C22—22no—
1622C22—22no—
1623C22—22no—
1624C22—22no—
1625C22—22no—
1626C22—22no—
1627C22—22no—
1628C22—22no—
1629C22—22no—
1630C22—22no—
1631C22—416no—
1632C22—41no—
1633C22—41no—
1634C22—41no—
1635C22—41no—
1636C22—41no—
1637C22—41no—
1638C22—41no—
1639C22—41no—
1640C22—41no—
1641C22—41no—
1642C22—41no—
1643C22—41no—
1644C22—41no—
1645C22—41no—
1646C22—41no—
1647C22—342no—
1648C22—342no—
1649C22—342no—
1650C22—681no—
1651C22—681no—
1652C22—681no—
1653C22—681no—
1654C22—681no—
1655C22—681no—
1656C22—681no—
1657C22—681no—
1658C22—681no—
1659C22—681no—
1660C22—681no—
1661C22#1176335814yes—
1662C22C22×D4×D1711yescharacteristic
1663C22C2×#41×D1711yescharacteristic
1664C22C2×#41×D1711yescharacteristic
1665C22C2×#41×D1711yescharacteristic
1666C22C22×#6325411yescharacteristic
1667C22H(5,𝔽2)×D1711yescharacteristic
1668C22#1176364411yescharacteristic
1669C4—22no—
1670C4—22no—
1671C4—22no—
1672C4—22no—
1673C4—41no—
1674C4—41no—
1675C4—41no—
1676C4—41no—
1677C4—41no—
1678C4—41no—
1679C4—41no—
1680C4—174no—
1681C4—342no—
1682C4—342no—
1683C4—342no—
1684C4—342no—
1685C4—342no—
1686C4—342no—
1687C4—342no—
1688C4—681no—
1689C4—681no—
1690C4—681no—
1691C4—681no—
1692C4—681no—
1693C4—681no—
1694C2—24no—
1695C2—42no—
1696C2—42no—
1697C2—81no—
1698C2—682no—
1699C2—1361no—
1700C2C2×#1176335811yescharacteristic
1701C2#1454207611yescharacteristic
1702C2#1454219511yescharacteristic
1703C2D17×#54611yescharacteristic
1704C2D4×#6325411yescharacteristic
1705C2#1454233911yescharacteristic
1706C2#1454238911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2472C2
hypercenter#2472D17
hypocenterC17#34829
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2472

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#11763345C2semidirect
2. C2×#11763315C2semidirect
3. #14533929C2semidirect
4. #14533914C2semidirect
5. #14533899C2semidirect
6. #14533884C2semidirect
7. #14533875C2semidirect
8. #14533855C2semidirect
9. #14533849C2semidirect
10. #14533834C2semidirect
11. #14533792C2semidirect
12. #14533748C2semidirect
13. #14533712C2semidirect
14. #14533677C2semidirect
15. #14533104C2semidirect
16. #14532337C2semidirect
17. #14532320C2semidirect
18. #14532051C2semidirect
19. #14532046C2semidirect
20. #14532023C2semidirect
21. #14531998C2semidirect
22. #124×Dic17C2semidirect
23. #14531309C2semidirect
24. #14531296C2semidirect
25. #14531294C2semidirect
26. #14531283C2semidirect
27. #14531271C2semidirect
28. #14531244C2semidirect
29. C4×#10587567C2semidirect
30. C2×C22⋊C4×Dic17C2semidirect
31. C17×#2472C2semidirect
35. C2×#10587584C22semidirect
36. C2×#10587584C22semidirect
37. C2×#10587576C22semidirect
38. C2×#10587633C22semidirect
54. C2×Q8×Dic17C22semidirect
57. C2×#10587579C22semidirect
65. C2×#10587567C22semidirect
66. C2×#10587578C22semidirect
67. C2×#10587578C22semidirect
72. C2×C42×D17C22semidirect
73. #11762749C22semidirect
74. #11762749C22semidirect
77. #11762743C22semidirect
78. #11762743C22semidirect
79. #11762740C22semidirect
80. #11762739C22semidirect
81. #11762738C22semidirect
82. #11762738C22semidirect
83. #11762736C22semidirect
87. #11762732C22semidirect
88. #11762729C22semidirect
89. #11762728C22semidirect
94. #11762724C22semidirect
95. #11762724C22semidirect
96. #11762722C22semidirect
98. #11762718C22semidirect
101. #11762716C22semidirect
102. #11762715C22semidirect
103. #11762714C22semidirect
109. #11762709C22semidirect
110. #11762706C22semidirect
111. #11762706C22semidirect
112. #11762704C22semidirect
113. #11762704C22semidirect
114. #11762703C22semidirect
115. #11762703C22semidirect
119. #11762702C22semidirect
120. #11762702C22semidirect
121. #11762701C22semidirect
122. #11762700C22semidirect
123. #11762700C22semidirect
124. #11762698C22semidirect
125. #11762697C22semidirect
126. #11762696C22semidirect
127. #11762696C22semidirect
129. #11762687C22semidirect
136. #11762685C22semidirect
137. #11762685C22semidirect
142. #11762675C22semidirect
144. #11762668C22semidirect
146. C4×#63225C22semidirect
147. #11762660C22semidirect
148. #11762660C22semidirect
149. #11762660C22semidirect
150. #11762660C22semidirect
151. #11762660C22semidirect
164. C22⋊C4×Dic17C22semidirect
165. C22⋊C4×Dic17C22semidirect
166. C22⋊C4×Dic17C22semidirect
167. C4×#63227C22semidirect
168. #11762656C22semidirect
169. #11762656C22semidirect
170. #11762656C22semidirect
173. C42×Dic17C22semidirect
354. #10587567D4semidirect
484. C22×Dic17#41semidirect
537. C22⋊C4×C17#41semidirect
554. C22⋊Dic17#41semidirect
781. #2472D17semidirect
1244. C17#34829semidirect
1445. C22⋊C4#63254semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#117633452
C2×#117633152
#145339292
#145339142
#145338992
#145338842
#145338752
#145338552
#145338492
#145338342
#145337922
#145337482
#145337122
#145336772
#145331042
#145323372
#145323202
#145320512
#145320462
#145320232
#145319982
#124×Dic172
#145313092
#145312962
#145312942
#145312832
#145312712
#145312442
C4×#105875672
C2×C22⋊C4×Dic172
C17×#24722
#3482917