Finite Group Databasebeta

← #17199713

Subgroups — #17199713

Order 4352.

2660 conjugacy classes of subgroups.

The subgroup lattice has 1684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763477C211yesmaximal, characteristic
2#14531942C211yesmaximal, characteristic, complemented
3#14531941C211yesmaximal, characteristic, complemented
4#14531940C211yesmaximal, characteristic, complemented
5#14531939C211yesmaximal, characteristic, complemented
6#14531847C211yesmaximal, characteristic, complemented
7#14531847C211yesmaximal, characteristic, complemented
8#14531846C211yesmaximal, characteristic, complemented
9#14531803C211yesmaximal, characteristic, complemented
10#14531801C211yesmaximal, characteristic, complemented
11#14531738C211yesmaximal, characteristic, complemented
12#14531691C211yesmaximal, characteristic, complemented
13#14531690C211yesmaximal, characteristic, complemented
14#14531682C211yesmaximal, characteristic, complemented
15#14531611C211yesmaximal, characteristic, complemented
16#14531610C211yesmaximal, characteristic, complemented
17#14531505C211yesmaximal, characteristic, complemented
18#14531505C211yesmaximal, characteristic, complemented
19#14531488C211yesmaximal, characteristic, complemented
20#14531483C211yesmaximal, characteristic, complemented
21#14531482C211yesmaximal, characteristic, complemented
22#14531474C211yesmaximal, characteristic, complemented
23#14531472C211yesmaximal, characteristic, complemented
24#14531426C211yesmaximal, characteristic, complemented
25#14531425C211yesmaximal, characteristic, complemented
26#14531373C211yesmaximal, characteristic, complemented
27#14531371C211yesmaximal, characteristic, complemented
28C4×#10587626C211yesmaximal, characteristic, complemented
29#14531257C211yesmaximal, characteristic, complemented
30#14531244C211yesmaximal, characteristic, complemented
31C17×#2325C211yesmaximal, characteristic, complemented
32C22×#63252C2211yescharacteristic
33C22×#63254C2211yescharacteristic
34#11763477C4116yescomplemented
35C2×#10587626C2211yescharacteristic
36C2×#10587626C2211yescharacteristic
37C2×#10587626C2211yescharacteristic
38C2×#10587581C2211yescharacteristic
39C2×#10587570C2211yescharacteristic
40C2×#10587570C2211yescharacteristic
41C2×#10587625C2211yescharacteristic
42C2×#10587625C2211yescharacteristic
43C2×#10587573C2211yescharacteristic
44C2×C4×D68C2211yescharacteristic
45C2×#10587579C2211yescharacteristic
46C2×C4×C22⋊D17C2211yescharacteristic
47C2×C4×C22⋊D17C2211yescharacteristic
48C2×C4×C22⋊D17C2211yescharacteristic
49C2×C4×C22⋊D17C2211yescharacteristic
50C2×C4×C22⋊D17C2211yescharacteristic
51C2×C4×C22⋊D17C2211yescharacteristic
52C2×C4×C22⋊D17C2211yescharacteristic
53C2×C4×C22⋊D17C2211yescharacteristic
54C2×C4×C22⋊D17C2211yescharacteristic
55C2×#10587567C2211yescharacteristic
56C2×#10587567C2211yescharacteristic
57C2×#10587567C2211yescharacteristic
58C2×#10587567C2211yescharacteristic
59C2×#10587567C2211yescharacteristic
60C2×#10587567C2211yescharacteristic
61C2×#10587578C2211yescharacteristic
62C2×#10587563C2211yescharacteristic
63C22×#63225C2211yescharacteristic
64C2×C4⋊C4×D17C2211yescharacteristic
65#11762713C2211yescharacteristic
66#11762713C2211yescharacteristic
67#11762713C2211yescharacteristic
68#11762713C2211yescharacteristic
69#11762712C2211yescharacteristic
70#11762712C2211yescharacteristic
71#11762711C2211yescharacteristic
72#11762710C2211yescharacteristic
73#11762709C2211yescharacteristic
74#11762709C2211yescharacteristic
75#11762709C2211yescharacteristic
76#11762709C2211yescharacteristic
77#11762709C2211yescharacteristic
78#11762709C2211yescharacteristic
79#11762709C2211yescharacteristic
80#11762709C2211yescharacteristic
81#11762709C2211yescharacteristic
82#11762709C2211yescharacteristic
83#11762709C2211yescharacteristic
84#11762709C2211yescharacteristic
85#11762706C2211yescharacteristic
86#11762706C2211yescharacteristic
87#11762706C2211yescharacteristic
88#11762704C2211yescharacteristic
89#11762704C2211yescharacteristic
90#11762704C2211yescharacteristic
91#11762702C2211yescharacteristic
92#11762702C2211yescharacteristic
93#11762700C2211yescharacteristic
94#11762700C2211yescharacteristic
95#11762699C2211yescharacteristic
96#11762699C2211yescharacteristic
97#11762698C2211yescharacteristic
98#11762698C2211yescharacteristic
99#11762697C2211yescharacteristic
100#11762697C2211yescharacteristic
101#11762696C2211yescharacteristic
102#11762695C2211yescharacteristic
103#11762695C2211yescharacteristic
104#11762693C2211yescharacteristic
105#11762691C2211yescharacteristic
106#11762690C2211yescharacteristic
107#11762689C2211yescharacteristic
108#11762689C2211yescharacteristic
109#11762689C2211yescharacteristic
110#11762689C2211yescharacteristic
111#11762688C2211yescharacteristic
112#11762688C2211yescharacteristic
113#11762688C2211yescharacteristic
114#11762688C2211yescharacteristic
115#11762687C2211yescharacteristic
116#11762687C2211yescharacteristic
117#11762687C2211yescharacteristic
118#11762687C2211yescharacteristic
119#11762687C2211yescharacteristic
120#11762687C2211yescharacteristic
121#11762687C2211yescharacteristic
122#11762687C2211yescharacteristic
123#11762686C2211yescharacteristic
124#11762686C2211yescharacteristic
125#11762685C2211yescharacteristic
126#11762685C2211yescharacteristic
127#11762685C2211yescharacteristic
128#11762685C2211yescharacteristic
129#11762685C2211yescharacteristic
130#11762685C2211yescharacteristic
131#11762684C2211yescharacteristic
132#11762684C2211yescharacteristic
133#11762683C2211yescharacteristic
134#11762683C2211yescharacteristic
135#11762683C2211yescharacteristic
136#11762683C2211yescharacteristic
137#11762682C2211yescharacteristic
138#11762682C2211yescharacteristic
139#11762680C2211yescharacteristic
140#11762680C2211yescharacteristic
141#11762678C2211yescharacteristic
142#11762673C2211yescharacteristic
143#11762673C2211yescharacteristic
144#11762672C2211yescharacteristic
145#11762671C2211yescharacteristic
146#11762671C2211yescharacteristic
147#11762670C2211yescharacteristic
148#11762669C2211yescharacteristic
149#11762668C2211yescharacteristic
150#11762668C2211yescharacteristic
151#11762668C2211yescharacteristic
152#11762667C2211yescharacteristic
153#11762667C2211yescharacteristic
154#11762667C2211yescharacteristic
155#11762666C2211yescharacteristic
156#11762666C2211yescharacteristic
157C4⋊C4×Dic17C2211yescharacteristic
158C4×#63225C2211yescharacteristic
159C4×#63225C2211yescharacteristic
160#11762660C2211yescharacteristic
161#11762660C2211yescharacteristic
162#11762660C2211yescharacteristic
163#11762660C2211yescharacteristic
164#11762660C2211yescharacteristic
165C22⋊C4×Dic17C2211yescharacteristic
166#11762656C2211yescharacteristic
167#11762654C2211yescharacteristic
168#11762654C2211yescharacteristic
169C2×#10587502C2211yescharacteristic
170#95×D17C2211yescharacteristic
171#95×D17C2211yescharacteristic
172C42×Dic17C2211yescharacteristic
173C2×C17×#121C2211yescharacteristic
174C2×C4×D4×C17C2211yescharacteristic
175C2×C4×D4×C17C2211yescharacteristic
176C17×#388C2211yescharacteristic
177C17×#388C2211yescharacteristic
178C17×#387C2211yescharacteristic
179C17×#387C2211yescharacteristic
180C17×#386C2211yescharacteristic
181C17×#386C2211yescharacteristic
182C17×#386C2211yescharacteristic
183C17×#386C2211yescharacteristic
184C17×#385C2211yescharacteristic
185C17×#385C2211yescharacteristic
186C17×#380C2211yescharacteristic
187C2×C17×#95C2211yescharacteristic
188C22×D4×C17C2311yescharacteristic
189C22×D4×C17C2311yescharacteristic
190C22×D4×C17C2311yescharacteristic
191C23×C4×C17C2311yescharacteristic
192C23×C4×C17C2311yescharacteristic
193C23×C4×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
204C22×C22⋊D17C2311yescharacteristic
205C23×Dic17C2311yescharacteristic
206C23×Dic17C2311yescharacteristic
207C23×Dic17C2311yescharacteristic
208C23×Dic17C2311yescharacteristic
209C2×#63254—42no—
210C2×#63254—42no—
211C2×#63254C2×C418yescomplemented
212C2×#63252—42no—
213C2×#63252—42no—
214C2×#63252C2×C418yescomplemented
215C22×D68C2311yescharacteristic
216C22×D68C2311yescharacteristic
217C22×D68C2311yescharacteristic
218C22×C4×D17C2311yescharacteristic
219C22×C4×D17C2311yescharacteristic
220C22×C4×D17C2311yescharacteristic
221C22×C4×D17C2311yescharacteristic
222C22×C4×D17C2311yescharacteristic
223C22×C4×D17C2311yescharacteristic
224C22×C4×D17C2311yescharacteristic
225C22×C4×D17C2311yescharacteristic
226C22×C4×D17C2311yescharacteristic
227C22×Dic34C2311yescharacteristic
228C17×#121C2×C418yescomplemented
229C4×D4×C17—42no—
230C4×D4×C17—42no—
231C2×C4⋊C4×C17C2311yescharacteristic
232C2×C4⋊C4×C17C2311yescharacteristic
233C2×C4⋊C4×C17C2311yescharacteristic
234C2×C4⋊C4×C17C2311yescharacteristic
235C2×C4⋊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×C42×C17C2311yescharacteristic
247C2×C42×C17C2311yescharacteristic
248C2×C22⋊Dic17C2311yescharacteristic
249C2×C22⋊Dic17C2311yescharacteristic
250C2×C22⋊Dic17C2311yescharacteristic
251C2×C22⋊Dic17C2311yescharacteristic
252C2×C22⋊Dic17C2311yescharacteristic
253C2×C22⋊Dic17C2311yescharacteristic
254C2×C22⋊Dic17C2311yescharacteristic
255C2×C22⋊Dic17C2311yescharacteristic
256C2×C22⋊Dic17C2311yescharacteristic
257C2×C22⋊Dic17C2311yescharacteristic
258C2×C22⋊Dic17C2311yescharacteristic
259#10587626C2×C418yescomplemented
260#10587626C2×C418yescomplemented
261#10587626C2×C418yescomplemented
262#10587625C2×C418yescomplemented
263#10587625C2×C418yescomplemented
264C4×C22⋊D17—42no—
265C4×C22⋊D17—42no—
266C4×C22⋊D17—42no—
267C4×C22⋊D17—42no—
268C4×C22⋊D17—42no—
269C4×C22⋊D17—42no—
270C4×C22⋊D17—42no—
271C4×C22⋊D17—42no—
272C4×C22⋊D17C2×C418yescomplemented
273C2×#63227C2311yescharacteristic
274C2×#63227C2311yescharacteristic
275C2×#63227C2311yescharacteristic
276C2×#63227C2311yescharacteristic
277C2×#63227C2311yescharacteristic
278C2×#63227C2311yescharacteristic
279C2×#63227C2311yescharacteristic
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×C4⋊Dic17C2311yescharacteristic
295C2×C4⋊Dic17C2311yescharacteristic
296C2×C4⋊Dic17C2311yescharacteristic
297C2×C4⋊Dic17C2311yescharacteristic
298C2×#63225—42no—
299C2×#63225C2311yescharacteristic
300C2×#63225C2311yescharacteristic
301C2×#63225C2311yescharacteristic
302C2×#63225C2311yescharacteristic
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×C4×Dic17C2311yescharacteristic
317C2×C4×Dic17C2311yescharacteristic
318C2×C4×Dic17C2311yescharacteristic
319C2×C4×Dic17C2311yescharacteristic
320C2×C4×Dic17C2311yescharacteristic
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
331#10587581C2×C418yescomplemented
332#10587579—42no—
333#10587578—42no—
334C4⋊C4×D17—42no—
335#10587573C2×C418yescomplemented
336#10587570C2×C418yescomplemented
337#10587570C2×C418yescomplemented
338#10587567—42no—
339#10587567—42no—
340#10587567—42no—
341#10587567—42no—
342#10587567C2×C418yescomplemented
343#10587567C2×C418yescomplemented
344#10587563—42no—
345C4×D68—42no—
346C17×#95C2311yescharacteristic
347C17×#95C2311yescharacteristic
348C17×#95C2311yescharacteristic
349C17×#95C2311yescharacteristic
350C17×#95C2311yescharacteristic
351C17×#95C2311yescharacteristic
352C17×#95C2311yescharacteristic
353C17×#95C2311yescharacteristic
354C17×#95C2311yescharacteristic
355C17×#95C2311yescharacteristic
356#10587502C2311yescharacteristic
357#10587502C2311yescharacteristic
358#10587502C2311yescharacteristic
359#10587502C2311yescharacteristic
360#10587502C2311yescharacteristic
361#10587502C2311yescharacteristic
362#10587502C2311yescharacteristic
363#10587502C2311yescharacteristic
364#10587502C2311yescharacteristic
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
382C24×C17C2411yescharacteristic
383C24×C17C2411yescharacteristic
384C24×C17C2411yescharacteristic
385C23×D17C2411yescharacteristic
386C23×D17C2411yescharacteristic
387C23×D17C2411yescharacteristic
388C2×D4×C17—41no—
389C2×D4×C17—41no—
390C2×D4×C17—41no—
391C2×D4×C17—41no—
392C2×D4×C17—41no—
393C2×D4×C17—41no—
394C2×D4×C17C22×C414yes—
395C2×D4×C17C22×C414yes—
396C2×D4×C17C22×C414yes—
397C22×C4×C17—22no—
398C22×C4×C17—22no—
399C22×C4×C17—41no—
400C22×C4×C17—41no—
401C22×C4×C17—41no—
402C22×C4×C17—41no—
403C22×C4×C17—41no—
404C22×C4×C17—41no—
405C22×C4×C17—41no—
406C22×C4×C17—41no—
407C22×C4×C17—41no—
408C22×C4×C17—41no—
409C22×C4×C17—41no—
410C22×C4×C17—41no—
411C22×C4×C17C22×C414yes—
412C22×C4×C17C2411yescharacteristic
413C22×C4×C17C2411yescharacteristic
414C22×C4×C17C2411yescharacteristic
415C22×C4×C17C2411yescharacteristic
416C22×C4×C17C2411yescharacteristic
417C22×C4×C17C2411yescharacteristic
418C22×C4×C17C2411yescharacteristic
419C22×C4×C17C2411yescharacteristic
420C22×C4×C17C2411yescharacteristic
421C22×C4×C17C2411yescharacteristic
422C22×C4×C17C2411yescharacteristic
423C22×C4×C17C2411yescharacteristic
424C2×C22⋊D17—22no—
425C2×C22⋊D17—22no—
426C2×C22⋊D17—22no—
427C2×C22⋊D17—22no—
428C2×C22⋊D17—22no—
429C2×C22⋊D17—22no—
430C2×C22⋊D17—22no—
431C2×C22⋊D17—22no—
432C2×C22⋊D17—22no—
433C2×C22⋊D17—22no—
434C2×C22⋊D17—41no—
435C2×C22⋊D17—41no—
436C2×C22⋊D17—41no—
437C2×C22⋊D17—41no—
438C2×C22⋊D17—41no—
439C2×C22⋊D17—41no—
440C2×C22⋊D17—41no—
441C2×C22⋊D17—41no—
442C2×C22⋊D17C22×C414yes—
443C2×C22⋊D17C22×C414yes—
444C2×C22⋊D17C22×C414yes—
445C2×C22⋊D17C22×C414yes—
446C2×C22⋊D17C22×C414yes—
447C2×C22⋊D17C22×C414yes—
448C2×C22⋊D17C22×C414yes—
449C2×C22⋊D17C22×C414yes—
450C2×C22⋊D17C22×C414yes—
451C22×Dic17—22no—
452C22×Dic17—22no—
453C22×Dic17—41no—
454C22×Dic17—41no—
455C22×Dic17—41no—
456C22×Dic17—41no—
457C22×Dic17—41no—
458C22×Dic17—41no—
459C22×Dic17—41no—
460C22×Dic17—41no—
461C22×Dic17C22×C414yes—
462C22×Dic17C22×C414yes—
463C22×Dic17C2411yescharacteristic
464C22×Dic17C2411yescharacteristic
465C22×Dic17C2411yescharacteristic
466C22×Dic17C2411yescharacteristic
467C22×Dic17C2411yescharacteristic
468C22×Dic17C2411yescharacteristic
469C22×Dic17C2411yescharacteristic
470C22×Dic17C2411yescharacteristic
471C22×Dic17C2411yescharacteristic
472C22×Dic17C2411yescharacteristic
473C22×Dic17C2411yescharacteristic
474C22×Dic17C2411yescharacteristic
475C22×Dic17C2411yescharacteristic
476#63254—416no—
477#63252—416no—
478C2×D68—41no—
479C2×D68—41no—
480C2×D68—41no—
481C2×D68—41no—
482C2×D68—41no—
483C2×D68—41no—
484C2×D68C22×C414yes—
485C2×D68C22×C414yes—
486C2×D68C22×C414yes—
487C2×C4×D17—22no—
488C2×C4×D17—22no—
489C2×C4×D17—22no—
490C2×C4×D17—22no—
491C2×C4×D17—41no—
492C2×C4×D17—41no—
493C2×C4×D17—41no—
494C2×C4×D17—41no—
495C2×C4×D17—41no—
496C2×C4×D17—41no—
497C2×C4×D17—41no—
498C2×C4×D17—41no—
499C2×C4×D17—41no—
500C2×C4×D17—41no—
501C2×C4×D17—41no—
502C2×C4×D17—41no—
503C2×C4×D17—41no—
504C2×C4×D17—41no—
505C2×C4×D17—41no—
506C2×C4×D17—41no—
507C2×C4×D17—41no—
508C2×C4×D17—41no—
509C2×C4×D17—41no—
510C2×C4×D17—41no—
511C2×C4×D17C22×C414yes—
512C2×C4×D17C22×C414yes—
513C2×C4×D17C22×C414yes—
514C2×Dic34—22no—
515C2×Dic34—22no—
516C2×Dic34C22×C414yes—
517C4⋊C4×C17—22no—
518C4⋊C4×C17—41no—
519C4⋊C4×C17—41no—
520C4⋊C4×C17—41no—
521C4⋊C4×C17C22×C414yes—
522C22⋊C4×C17—22no—
523C22⋊C4×C17—41no—
524C22⋊C4×C17—41no—
525C22⋊C4×C17—41no—
526C22⋊C4×C17—41no—
527C22⋊C4×C17—41no—
528C22⋊C4×C17—41no—
529C22⋊C4×C17—41no—
530C22⋊C4×C17C22×C414yes—
531C22⋊C4×C17C22×C414yes—
532C42×C17—22no—
533C42×C17—41no—
534C22⋊Dic17—41no—
535C22⋊Dic17—41no—
536C22⋊Dic17—41no—
537C22⋊Dic17—41no—
538C22⋊Dic17—41no—
539C22⋊Dic17—41no—
540C22⋊Dic17—41no—
541C22⋊Dic17—41no—
542C22⋊Dic17—41no—
543C22⋊Dic17—41no—
544C22⋊Dic17C22×C414yes—
545#63227—22no—
546#63227—41no—
547#63227—41no—
548#63227—41no—
549#63227—41no—
550#63227—41no—
551#63227—41no—
552#63227—41no—
553#63227—41no—
554#63227—41no—
555#63227—41no—
556#63227—41no—
557#63227—41no—
558#63227—41no—
559#63227—41no—
560#63227—41no—
561#63227—41no—
562#63227—41no—
563#63227C22×C414yes—
564#63227C22×C414yes—
565#63227C22×C414yes—
566C4⋊Dic17—41no—
567C4⋊Dic17—41no—
568C4⋊Dic17—41no—
569C4⋊Dic17—41no—
570#63225—22no—
571#63225—22no—
572#63225—22no—
573#63225—22no—
574#63225—22no—
575#63225—22no—
576#63225—22no—
577#63225—22no—
578#63225—22no—
579#63225—41no—
580#63225—41no—
581#63225—41no—
582#63225—41no—
583#63225—41no—
584#63225C22×C414yes—
585#63225C22×C414yes—
586#63225C22×C414yes—
587C4×Dic17—22no—
588C4×Dic17—22no—
589C4×Dic17—22no—
590C4×Dic17—22no—
591C4×Dic17—22no—
592C4×Dic17—22no—
593C4×Dic17—22no—
594C4×Dic17—22no—
595C4×Dic17—41no—
596C4×Dic17—41no—
597C4×Dic17—41no—
598C4×Dic17—41no—
599C4×Dic17C22×C414yes—
600C4×Dic17C22×C414yes—
601C4×Dic17C22×C414yes—
602#34494—171nomaximal, Sylow
603C23×C17—21no—
604C23×C17—21no—
605C23×C17—21no—
606C23×C17—21no—
607C23×C17—21no—
608C23×C17—21no—
609C23×C17—21no—
610C23×C17—21no—
611C23×C17—21no—
612C23×C17—21no—
613C23×C17—21no—
614C23×C17—21no—
615C23×C17—21no—
616C23×C17—21no—
617C23×C17—21no—
618C23×C17—21no—
619C23×C17—21no—
620C23×C17—21no—
621C23×C17C23×C412yes—
622C23×C17C23×C412yes—
623C23×C17C23×C412yes—
624C23×C17C2511yescharacteristic
625C22×D17—21no—
626C22×D17—21no—
627C22×D17—21no—
628C22×D17—21no—
629C22×D17—21no—
630C22×D17—21no—
631C22×D17—21no—
632C22×D17—21no—
633C22×D17—21no—
634C22×D17—21no—
635C22×D17—21no—
636C22×D17—21no—
637C22×D17—21no—
638C22×D17—21no—
639C22×D17—21no—
640C22×D17—21no—
641C22×D17—21no—
642C22×D17—21no—
643C22×D17C23×C412yes—
644C22×D17C23×C412yes—
645C22×D17C23×C412yes—
646D4×C17—44no—
647D4×C17—44no—
648D4×C17—44no—
649C2×C4×C17—21no—
650C2×C4×C17—21no—
651C2×C4×C17—21no—
652C2×C4×C17—21no—
653C2×C4×C17—21no—
654C2×C4×C17—21no—
655C2×C4×C17—21no—
656C2×C4×C17—21no—
657C2×C4×C17—21no—
658C2×C4×C17—21no—
659C2×C4×C17—21no—
660C2×C4×C17—21no—
661C2×C4×C17—21no—
662C2×C4×C17—21no—
663C2×C4×C17—21no—
664C2×C4×C17—21no—
665C2×C4×C17—21no—
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—44no—
681C2×C4×C17—82no—
682C2×C4×C17—82no—
683C2×C4×C17—82no—
684C2×C4×C17—82no—
685C2×C4×C17C23×C412yes—
686C2×C4×C17C23×C412yes—
687C2×C4×C17C23×C412yes—
688C2×C4×C17C23×C412yes—
689C2×C4×C17H(5,𝔽2)12yes—
690C22⋊D17—28no—
691C22⋊D17—28no—
692C22⋊D17—28no—
693C22⋊D17—28no—
694C22⋊D17—28no—
695C22⋊D17—44no—
696C22⋊D17—44no—
697C22⋊D17—44no—
698C22⋊D17—44no—
699C2×Dic17—21no—
700C2×Dic17—21no—
701C2×Dic17—21no—
702C2×Dic17—21no—
703C2×Dic17—21no—
704C2×Dic17—21no—
705C2×Dic17—28no—
706C2×Dic17—21no—
707C2×Dic17—21no—
708C2×Dic17—21no—
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—21no—
724C2×Dic17—21no—
725C2×Dic17—21no—
726C2×Dic17—21no—
727C2×Dic17—21no—
728C2×Dic17—21no—
729C2×Dic17—21no—
730C2×Dic17—44no—
731C2×Dic17—82no—
732C2×Dic17—82no—
733C2×Dic17C23×C412yes—
734C2×Dic17C23×C412yes—
735C2×Dic17C23×C412yes—
736C2×Dic17C23×C412yes—
737C2×Dic17C23×C412yes—
738C2×Dic17H(5,𝔽2)12yes—
739C2×Dic17H(5,𝔽2)12yes—
740C2×Dic17H(5,𝔽2)12yes—
741C2×Dic172−1+412yes—
742D68—44no—
743D68—44no—
744D68—44no—
745C4×D17—28no—
746C4×D17—44no—
747C4×D17—44no—
748C4×D17—82no—
749C4×D17—82no—
750C4×D17—82no—
751C4×D17—82no—
752C4×D17—82no—
753C4×D17—82no—
754Dic34—28no—
755C2×#550—171no—
756#2377—171no—
757#2377—171no—
758#2377—171no—
759#2377—171no—
760#2366—171no—
761#2366—171no—
762#2366—171no—
763#2361—171no—
764#2361—171no—
765#2355—171no—
766#2349—171no—
767#2349—171no—
768D4×C4⋊C4—171no—
769#2339—171no—
770#2339—171no—
771#2328—171no—
772#2328—171no—
773#2325—171no—
774#2325—171no—
775#2325—171no—
776#2325D1711yescharacteristic, complemented
777#2324—171no—
778#2324—171no—
779#2319—171no—
780#2319—171no—
781#2311—171no—
782#2311—171no—
783C4×#127—171no—
784#2295—171no—
785#2293—171no—
786C22×C17—22no—
787C22×C17—22no—
788C22×C17—22no—
789C22×C17—22no—
790C22×C17—22no—
791C22×C17—22no—
792C22×C17—22no—
793C22×C17—22no—
794C22×C17—22no—
795C22×C17—41no—
796C22×C17—41no—
797C22×C17—41no—
798C22×C17—41no—
799C22×C17—41no—
800C22×C17—41no—
801C22×C17—41no—
802C22×C17—41no—
803C22×C17—41no—
804C22×C17—41no—
805C22×C17—41no—
806C22×C17—41no—
807C22×C17C24×C411yescharacteristic
808C22×C17C2×H(5,𝔽2)11yescharacteristic
809C22×C17C2×H(5,𝔽2)11yescharacteristic
810C22×C17C2×H(5,𝔽2)11yescharacteristic
811C22×C17C2×H(5,𝔽2)11yescharacteristic
812C22×C17C2×2−1+411yescharacteristic
813C22×C17#58511yescharacteristic
814C2×D17—22no—
815C2×D17—22no—
816C2×D17—22no—
817C2×D17—22no—
818C2×D17—22no—
819C2×D17—22no—
820C2×D17—22no—
821C2×D17—22no—
822C2×D17—22no—
823C2×D17—41no—
824C2×D17—41no—
825C2×D17—41no—
826C2×D17—41no—
827C2×D17—41no—
828C2×D17—41no—
829C2×D17—41no—
830C2×D17—41no—
831C2×D17—41no—
832C2×D17—41no—
833C2×D17—41no—
834C2×D17—41no—
835C4×C17—22no—
836C4×C17—22no—
837C4×C17—22no—
838C4×C17—22no—
839C4×C17—22no—
840C4×C17—41no—
841C4×C17—41no—
842C4×C17—41no—
843C4×C17—41no—
844C4×C17—41no—
845C4×C17—41no—
846C4×C17—41no—
847Dic17—22no—
848Dic17—22no—
849Dic17—22no—
850Dic17—41no—
851Dic17—41no—
852Dic17—41no—
853Dic17—41no—
854Dic17—41no—
855Dic17—41no—
856Dic17—41no—
857Dic17—41no—
858Dic17#51814yes—
859Dic17#52014yes—
860C22×#41—171no—
861C22×#41—171no—
862#550—1716no—
863C2×#127—171no—
864C2×#127—171no—
865C2×#127—171no—
866C2×#121—171no—
867C2×#121—171no—
868C2×#121—171no—
869C2×#121—171no—
870C2×#121—171no—
871C2×#121C2×D1711yescharacteristic
872C2×C4×Q8—171no—
873C2×C4×D4—171no—
874C2×C4×D4—171no—
875C2×C4×D4—171no—
876C2×C4×D4—171no—
877C2×C4×D4—171no—
878C2×C4×D4—171no—
879C2×C4×D4—171no—
880C2×C4×D4—171no—
881C2×C4×D4—171no—
882C2×C4×D4—171no—
883C2×C4×D4—171no—
884C2×C4×D4—171no—
885C2×C4×D4—171no—
886C2×C4×D4—171no—
887C2×C4×D4—171no—
888C2×C4×D4—171no—
889C2×C4×D4—171no—
890C2×C4×D4C2×D1711yescharacteristic
891C2×C4×D4C2×D1711yescharacteristic
892C2×#117—171no—
893C2×#117—171no—
894C22×C4⋊C4—171no—
895C22×C4⋊C4—171no—
896#391—171no—
897#391—171no—
898#391—171no—
899#391—171no—
900#390—171no—
901#390—171no—
902#390—171no—
903#390—171no—
904#390—171no—
905#390—171no—
906#390—171no—
907#390—171no—
908#390—171no—
909#390—171no—
910#390—171no—
911#390—171no—
912#390—171no—
913#390—171no—
914#390—171no—
915#390—171no—
916#389—171no—
917#389—171no—
918#389—171no—
919#389—171no—
920#389—171no—
921#389—171no—
922#388—171no—
923#388—171no—
924#388—171no—
925#388—171no—
926#388—171no—
927#388—171no—
928#388—171no—
929#388—171no—
930#388—171no—
931#388—171no—
932#388C2×D1711yescharacteristic
933#388C2×D1711yescharacteristic
934#387—171no—
935#387—171no—
936#387—171no—
937#387—171no—
938#387—171no—
939#387—171no—
940#387C2×D1711yescharacteristic
941#387C2×D1711yescharacteristic
942#386—171no—
943#386—171no—
944#386—171no—
945#386—171no—
946#386—171no—
947#386—171no—
948#386—171no—
949#386—171no—
950#386—171no—
951#386—171no—
952#386—171no—
953#386—171no—
954#386—171no—
955#386—171no—
956#386—171no—
957#386—171no—
958#386—171no—
959#386—171no—
960#386—171no—
961#386—171no—
962#386—171no—
963#386—171no—
964#386—171no—
965#386—171no—
966#386C2×D1711yescharacteristic
967#386C2×D1711yescharacteristic
968#386C2×D1711yescharacteristic
969#386C2×D1711yescharacteristic
970#385—171no—
971#385—171no—
972#385—171no—
973#385—171no—
974#385—171no—
975#385—171no—
976#385—171no—
977#385—171no—
978#385—171no—
979#385—171no—
980#385C2×D1711yescharacteristic
981#385C2×D1711yescharacteristic
982#384—171no—
983#382—171no—
984#382—171no—
985#381—171no—
986#381—171no—
987#381—171no—
988#381—171no—
989#380—171no—
990#380—171no—
991#380—171no—
992#380—171no—
993#380—171no—
994#380—171no—
995#380—171no—
996#380—171no—
997#380—171no—
998#380C2×D1711yescharacteristic
999C4×C4⋊C4—171no—
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×C4⋊C4—171no—
1007C4×C22⋊C4—171no—
1008C4×C22⋊C4—171no—
1009#376—171no—
1010#376—171no—
1011C2×#95—171no—
1012C2×#95—171no—
1013C2×#95—171no—
1014C2×#95C2×D1711yescharacteristic
1015C43—171no—
1016C2×C17—42no—
1017C2×C17—42no—
1018C2×C17—42no—
1019C2×C17C2×#51811yescharacteristic
1020C2×C17C2×#52011yescharacteristic
1021C2×C17C4×H(5,𝔽2)11yescharacteristic
1022C2×C17#354311yescharacteristic
1023C2×C17#354611yescharacteristic
1024C2×C17#354811yescharacteristic
1025C2×C17#355411yescharacteristic
1026D17—42no—
1027D17—42no—
1028D17—42no—
1029C2×#41—178no—
1030C2×#41—178no—
1031C2×#41—682no—
1032C2×#41—682no—
1033C2×#41—682no—
1034C2×#41—682no—
1035C22×Q8—171no—
1036C22×D4—171no—
1037C22×D4—171no—
1038C22×D4—171no—
1039C22×D4—171no—
1040C22×D4—171no—
1041C22×D4—171no—
1042C22×D4—171no—
1043C22×D4—171no—
1044C22×D4—171no—
1045C22×D4—171no—
1046C22×D4—171no—
1047C22×D4—171no—
1048C22×D4C22×D1711yescharacteristic
1049C22×D4C22×D1711yescharacteristic
1050C22×D4C22×D1711yescharacteristic
1051C23×C4—171no—
1052C23×C4—171no—
1053C23×C4—171no—
1054C23×C4—171no—
1055C23×C4—171no—
1056C23×C4—171no—
1057C23×C4—171no—
1058C23×C4—171no—
1059C23×C4—171no—
1060C23×C4—171no—
1061C23×C4—171no—
1062C23×C4—171no—
1063C23×C4—171no—
1064C23×C4C22×D1711yescharacteristic
1065C23×C4C22×D1711yescharacteristic
1066C23×C4C22×D1711yescharacteristic
1067C23×C4C22×D1711yescharacteristic
1068C23×C4C22×D1711yescharacteristic
1069#127—178no—
1070#127—178no—
1071#127—178no—
1072#121—178no—
1073#121—178no—
1074#121—178no—
1075#121—178no—
1076#121—178no—
1077#121C4×D1718yescomplemented
1078C4×Q8—178no—
1079C4×D4—42no—
1080C4×D4—42no—
1081C4×D4—178no—
1082C4×D4—178no—
1083C4×D4—178no—
1084C4×D4—682no—
1085C4×D4—682no—
1086C4×D4—682no—
1087C4×D4—682no—
1088C4×D4—682no—
1089C4×D4—682no—
1090C4×D4—682no—
1091C4×D4—682no—
1092C4×D4—682no—
1093C4×D4—682no—
1094C4×D4—682no—
1095C4×D4—682no—
1096C4×D4—682no—
1097C4×D4—682no—
1098#117—682no—
1099#117—682no—
1100C2×C4⋊C4—171no—
1101C2×C4⋊C4—171no—
1102C2×C4⋊C4—171no—
1103C2×C4⋊C4—171no—
1104C2×C4⋊C4—171no—
1105C2×C4⋊C4—171no—
1106C2×C4⋊C4—171no—
1107C2×C4⋊C4—171no—
1108C2×C4⋊C4—171no—
1109C2×C4⋊C4—171no—
1110C2×C4⋊C4—171no—
1111C2×C4⋊C4—171no—
1112C2×C4⋊C4—171no—
1113C2×C4⋊C4—171no—
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—682no—
1122C2×C4⋊C4—682no—
1123C2×C4⋊C4C22×D1711yescharacteristic
1124C2×C4⋊C4C22×D1711yescharacteristic
1125C2×C4⋊C4C22×D1711yescharacteristic
1126C2×C4⋊C4C22×D1711yescharacteristic
1127C2×C4⋊C4C22×D1711yescharacteristic
1128C2×C22⋊C4—171no—
1129C2×C22⋊C4—171no—
1130C2×C22⋊C4—171no—
1131C2×C22⋊C4—171no—
1132C2×C22⋊C4—171no—
1133C2×C22⋊C4—171no—
1134C2×C22⋊C4—171no—
1135C2×C22⋊C4—171no—
1136C2×C22⋊C4—171no—
1137C2×C22⋊C4—171no—
1138C2×C22⋊C4—171no—
1139C2×C22⋊C4—171no—
1140C2×C22⋊C4—171no—
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⋊C4C22×D1711yescharacteristic
1161C2×C22⋊C4C22×D1711yescharacteristic
1162C2×C22⋊C4C22×D1711yescharacteristic
1163C2×C22⋊C4C22×D1711yescharacteristic
1164C2×C22⋊C4C22×D1711yescharacteristic
1165C2×C22⋊C4C22×D1711yescharacteristic
1166C2×C22⋊C4C22×D1711yescharacteristic
1167C2×C22⋊C4C22×D1711yescharacteristic
1168C2×C22⋊C4C22×D1711yescharacteristic
1169C2×C22⋊C4C22×D1711yescharacteristic
1170C2×C42—171no—
1171C2×C42—171no—
1172C2×C42—171no—
1173C2×C42—171no—
1174C2×C42—171no—
1175C2×C42—171no—
1176C2×C42—171no—
1177C2×C42—171no—
1178C2×C42—171no—
1179C2×C42—171no—
1180C2×C42—171no—
1181C2×C42—171no—
1182C2×C42—171no—
1183C2×C42—171no—
1184C2×C42—171no—
1185C2×C42C22×D1711yescharacteristic
1186C2×C42C22×D1711yescharacteristic
1187#95—171no—
1188#95—171no—
1189#95—171no—
1190#95—171no—
1191#95—171no—
1192#95—171no—
1193#95—171no—
1194#95—171no—
1195#95—171no—
1196#95—171no—
1197#95—171no—
1198#95—171no—
1199#95—171no—
1200#95—171no—
1201#95—171no—
1202#95—171no—
1203#95—171no—
1204#95—171no—
1205#95—171no—
1206#95—171no—
1207#95—171no—
1208#95—171no—
1209#95—171no—
1210#95—171no—
1211#95—171no—
1212#95—171no—
1213#95C22×D1711yescharacteristic
1214#95C22×D1711yescharacteristic
1215#95C22×D1711yescharacteristic
1216#95C22×D1711yescharacteristic
1217#95C22×D1711yescharacteristic
1218#95C22×D1711yescharacteristic
1219#95C22×D1711yescharacteristic
1220#95C22×D1711yescharacteristic
1221#95C22×D1711yescharacteristic
1222#95C22×D1711yescharacteristic
1223C17#3449411yescharacteristic, complemented, Sylow
1224C24—171no—
1225C24—171no—
1226C24—171no—
1227C24C23×D1711yescharacteristic
1228C24C23×D1711yescharacteristic
1229C24C23×D1711yescharacteristic
1230#41—6816no—
1231#41—6816no—
1232C2×Q8—174no—
1233C2×Q8—342no—
1234C2×Q8—342no—
1235C2×D4—41no—
1236C2×D4—41no—
1237C2×D4—41no—
1238C2×D4—41no—
1239C2×D4—41no—
1240C2×D4—41no—
1241C2×D4—174no—
1242C2×D4—174no—
1243C2×D4—174no—
1244C2×D4—174no—
1245C2×D4—174no—
1246C2×D4—174no—
1247C2×D4—174no—
1248C2×D4—174no—
1249C2×D4—174no—
1250C2×D4—174no—
1251C2×D4—174no—
1252C2×D4—174no—
1253C2×D4—342no—
1254C2×D4—342no—
1255C2×D4—342no—
1256C2×D4—342no—
1257C2×D4—342no—
1258C2×D4—342no—
1259C2×D4—342no—
1260C2×D4—342no—
1261C2×D4—342no—
1262C2×D4—342no—
1263C2×D4—681no—
1264C2×D4—681no—
1265C2×D4—681no—
1266C2×D4—681no—
1267C2×D4—681no—
1268C2×D4—681no—
1269C2×D4—681no—
1270C2×D4—681no—
1271C2×D4—681no—
1272C2×D4—681no—
1273C2×D4—681no—
1274C2×D4—681no—
1275C2×D4—681no—
1276C2×D4—681no—
1277C2×D4C2×C4×D1714yes—
1278C2×D4C2×C4×D1714yes—
1279C2×D4C2×C4×D1714yes—
1280C22×C4—22no—
1281C22×C4—22no—
1282C22×C4—41no—
1283C22×C4—41no—
1284C22×C4—41no—
1285C22×C4—41no—
1286C22×C4—41no—
1287C22×C4—41no—
1288C22×C4—41no—
1289C22×C4—41no—
1290C22×C4—41no—
1291C22×C4—41no—
1292C22×C4—41no—
1293C22×C4—41no—
1294C22×C4—171no—
1295C22×C4—171no—
1296C22×C4—174no—
1297C22×C4—171no—
1298C22×C4—171no—
1299C22×C4—171no—
1300C22×C4—174no—
1301C22×C4—174no—
1302C22×C4—174no—
1303C22×C4—174no—
1304C22×C4—171no—
1305C22×C4—171no—
1306C22×C4—171no—
1307C22×C4—171no—
1308C22×C4—171no—
1309C22×C4—171no—
1310C22×C4—171no—
1311C22×C4—171no—
1312C22×C4—342no—
1313C22×C4—342no—
1314C22×C4—342no—
1315C22×C4—342no—
1316C22×C4—342no—
1317C22×C4—342no—
1318C22×C4—681no—
1319C22×C4—681no—
1320C22×C4—681no—
1321C22×C4—681no—
1322C22×C4—681no—
1323C22×C4—681no—
1324C22×C4—681no—
1325C22×C4—681no—
1326C22×C4—681no—
1327C22×C4—681no—
1328C22×C4—681no—
1329C22×C4—681no—
1330C22×C4—681no—
1331C22×C4—681no—
1332C22×C4—681no—
1333C22×C4—681no—
1334C22×C4—681no—
1335C22×C4—681no—
1336C22×C4—681no—
1337C22×C4—681no—
1338C22×C4—681no—
1339C22×C4—681no—
1340C22×C4—681no—
1341C22×C4—681no—
1342C22×C4—681no—
1343C22×C4—681no—
1344C22×C4—681no—
1345C22×C4—681no—
1346C22×C4C2×C4×D1714yes—
1347C22×C4C23×D1711yescharacteristic
1348C22×C4C23×D1711yescharacteristic
1349C22×C4C23×D1711yescharacteristic
1350C22×C4C23×D1711yescharacteristic
1351C22×C4C23×D1711yescharacteristic
1352C22×C4C23×D1711yescharacteristic
1353C22×C4C23×D1711yescharacteristic
1354C22×C4C23×D1711yescharacteristic
1355C22×C4C23×D1711yescharacteristic
1356C22×C4C23×D1711yescharacteristic
1357C22×C4C23×D1711yescharacteristic
1358C22×C4C23×D1711yescharacteristic
1359C4⋊C4—22no—
1360C4⋊C4—41no—
1361C4⋊C4—41no—
1362C4⋊C4—41no—
1363C4⋊C4—174no—
1364C4⋊C4—174no—
1365C4⋊C4—174no—
1366C4⋊C4—342no—
1367C4⋊C4—342no—
1368C4⋊C4—342no—
1369C4⋊C4—342no—
1370C4⋊C4—342no—
1371C4⋊C4—342no—
1372C4⋊C4—342no—
1373C4⋊C4—342no—
1374C4⋊C4—342no—
1375C4⋊C4—681no—
1376C4⋊C4—681no—
1377C4⋊C4—681no—
1378C4⋊C4—681no—
1379C4⋊C4—681no—
1380C4⋊C4—681no—
1381C4⋊C4—681no—
1382C4⋊C4—681no—
1383C4⋊C4—681no—
1384C4⋊C4C2×C4×D1714yes—
1385C22⋊C4—22no—
1386C22⋊C4—41no—
1387C22⋊C4—41no—
1388C22⋊C4—41no—
1389C22⋊C4—41no—
1390C22⋊C4—41no—
1391C22⋊C4—41no—
1392C22⋊C4—41no—
1393C22⋊C4—174no—
1394C22⋊C4—174no—
1395C22⋊C4—174no—
1396C22⋊C4—174no—
1397C22⋊C4—342no—
1398C22⋊C4—681no—
1399C22⋊C4—681no—
1400C22⋊C4—681no—
1401C22⋊C4—681no—
1402C22⋊C4—681no—
1403C22⋊C4—681no—
1404C22⋊C4—681no—
1405C22⋊C4—681no—
1406C22⋊C4—681no—
1407C22⋊C4—681no—
1408C22⋊C4—681no—
1409C22⋊C4—681no—
1410C22⋊C4—681no—
1411C22⋊C4—681no—
1412C22⋊C4—681no—
1413C22⋊C4—681no—
1414C22⋊C4—681no—
1415C22⋊C4—681no—
1416C22⋊C4—681no—
1417C22⋊C4—681no—
1418C22⋊C4—681no—
1419C22⋊C4—681no—
1420C22⋊C4—681no—
1421C22⋊C4—681no—
1422C22⋊C4—681no—
1423C22⋊C4—681no—
1424C22⋊C4—681no—
1425C22⋊C4C2×C4×D1714yes—
1426C22⋊C4C2×C4×D1714yes—
1427C42—22no—
1428C42—41no—
1429C42—174no—
1430C42—174no—
1431C42—174no—
1432C42—342no—
1433C42—342no—
1434C42—342no—
1435C42—342no—
1436C42—342no—
1437C42—342no—
1438C42—342no—
1439C42—342no—
1440C42—681no—
1441C42—681no—
1442C42—681no—
1443C42—681no—
1444C23—21no—
1445C23—21no—
1446C23—21no—
1447C23—21no—
1448C23—21no—
1449C23—21no—
1450C23—21no—
1451C23—21no—
1452C23—21no—
1453C23—21no—
1454C23—21no—
1455C23—21no—
1456C23—21no—
1457C23—21no—
1458C23—21no—
1459C23—21no—
1460C23—21no—
1461C23—21no—
1462C23—172no—
1463C23—172no—
1464C23—172no—
1465C23—341no—
1466C23—341no—
1467C23—341no—
1468C23—341no—
1469C23—341no—
1470C23—341no—
1471C23—341no—
1472C23—341no—
1473C23—341no—
1474C23—341no—
1475C23—341no—
1476C23—341no—
1477C23—341no—
1478C23—341no—
1479C23—341no—
1480C23—341no—
1481C23—341no—
1482C23—341no—
1483C23C22×C4×D1712yes—
1484C23C22×C4×D1712yes—
1485C23C22×C4×D1712yes—
1486C23C24×D1711yescharacteristic
1487Q8—348no—
1488D4—44no—
1489D4—44no—
1490D4—44no—
1491D4—348no—
1492D4—348no—
1493D4—348no—
1494D4—348no—
1495D4—348no—
1496D4—684no—
1497D4—684no—
1498D4—684no—
1499D4—684no—
1500D4—684no—
1501D4—684no—
1502D4—684no—
1503C2×C4—21no—
1504C2×C4—21no—
1505C2×C4—21no—
1506C2×C4—21no—
1507C2×C4—21no—
1508C2×C4—21no—
1509C2×C4—21no—
1510C2×C4—21no—
1511C2×C4—21no—
1512C2×C4—21no—
1513C2×C4—21no—
1514C2×C4—21no—
1515C2×C4—21no—
1516C2×C4—21no—
1517C2×C4—21no—
1518C2×C4—21no—
1519C2×C4—21no—
1520C2×C4—21no—
1521C2×C4—21no—
1522C2×C4—21no—
1523C2×C4—21no—
1524C2×C4—21no—
1525C2×C4—21no—
1526C2×C4—21no—
1527C2×C4—21no—
1528C2×C4—21no—
1529C2×C4—21no—
1530C2×C4—21no—
1531C2×C4—21no—
1532C2×C4—21no—
1533C2×C4—21no—
1534C2×C4—44no—
1535C2×C4—82no—
1536C2×C4—82no—
1537C2×C4—82no—
1538C2×C4—82no—
1539C2×C4—172no—
1540C2×C4—172no—
1541C2×C4—172no—
1542C2×C4—172no—
1543C2×C4—172no—
1544C2×C4—172no—
1545C2×C4—172no—
1546C2×C4—172no—
1547C2×C4—172no—
1548C2×C4—348no—
1549C2×C4—348no—
1550C2×C4—341no—
1551C2×C4—341no—
1552C2×C4—341no—
1553C2×C4—341no—
1554C2×C4—341no—
1555C2×C4—341no—
1556C2×C4—341no—
1557C2×C4—341no—
1558C2×C4—341no—
1559C2×C4—341no—
1560C2×C4—341no—
1561C2×C4—341no—
1562C2×C4—341no—
1563C2×C4—341no—
1564C2×C4—341no—
1565C2×C4—341no—
1566C2×C4—341no—
1567C2×C4—341no—
1568C2×C4—341no—
1569C2×C4—341no—
1570C2×C4—341no—
1571C2×C4—341no—
1572C2×C4—341no—
1573C2×C4—341no—
1574C2×C4—341no—
1575C2×C4—341no—
1576C2×C4—341no—
1577C2×C4—341no—
1578C2×C4—341no—
1579C2×C4—341no—
1580C2×C4—684no—
1581C2×C4—684no—
1582C2×C4—684no—
1583C2×C4—1362no—
1584C2×C4—1362no—
1585C2×C4—1362no—
1586C2×C4—1362no—
1587C2×C4—1362no—
1588C2×C4—1362no—
1589C2×C4—1362no—
1590C2×C4—1362no—
1591C2×C4C22×C4×D1712yes—
1592C2×C4C22×C4×D1712yes—
1593C2×C4C22×C4×D1712yes—
1594C2×C4C22×C4×D1712yes—
1595C2×C4#1058769112yes—
1596C22—22no—
1597C22—22no—
1598C22—22no—
1599C22—22no—
1600C22—22no—
1601C22—22no—
1602C22—22no—
1603C22—22no—
1604C22—22no—
1605C22—41no—
1606C22—41no—
1607C22—41no—
1608C22—41no—
1609C22—41no—
1610C22—41no—
1611C22—41no—
1612C22—41no—
1613C22—41no—
1614C22—41no—
1615C22—41no—
1616C22—41no—
1617C22—342no—
1618C22—342no—
1619C22—342no—
1620C22—342no—
1621C22—342no—
1622C22—342no—
1623C22—342no—
1624C22—342no—
1625C22—342no—
1626C22—681no—
1627C22—681no—
1628C22—681no—
1629C22—681no—
1630C22—681no—
1631C22—681no—
1632C22—681no—
1633C22—681no—
1634C22—681no—
1635C22—681no—
1636C22—681no—
1637C22—681no—
1638C22C23×C4×D1711yescharacteristic
1639C22H(5,𝔽2)×D1711yescharacteristic
1640C22H(5,𝔽2)×D1711yescharacteristic
1641C22H(5,𝔽2)×D1711yescharacteristic
1642C22C2×#1058769111yescharacteristic
1643C222−1+4×D1711yescharacteristic
1644C22#1176364511yescharacteristic
1645C4—22no—
1646C4—22no—
1647C4—22no—
1648C4—22no—
1649C4—22no—
1650C4—41no—
1651C4—41no—
1652C4—41no—
1653C4—41no—
1654C4—41no—
1655C4—41no—
1656C4—41no—
1657C4—174no—
1658C4—174no—
1659C4—342no—
1660C4—342no—
1661C4—342no—
1662C4—681no—
1663C4—681no—
1664C4—681no—
1665C4—681no—
1666C4—681no—
1667C4—681no—
1668C4—681no—
1669C4—681no—
1670C2—42no—
1671C2—42no—
1672C2—42no—
1673C2—682no—
1674C2—682no—
1675C2—682no—
1676C2D17×#51811yescharacteristic
1677C2D17×#52011yescharacteristic
1678C2C4×#1058769111yescharacteristic
1679C2#1454311111yescharacteristic
1680C2#1454314911yescharacteristic
1681C2#1454317911yescharacteristic
1682C2#1454324811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC17×#2325C2
socle, cosocleC23×C17C25
prime radicalC2×#11763477C2
hypercenter#2325D17
hypocenterC17#34494
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2325

Complements

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

NH ≅ G/Ntype
2. #14531942C2semidirect
3. #14531941C2semidirect
4. #14531940C2semidirect
5. #14531939C2semidirect
6. #14531847C2semidirect
7. #14531847C2semidirect
8. #14531846C2semidirect
9. #14531803C2semidirect
10. #14531801C2semidirect
11. #14531738C2semidirect
12. #14531691C2semidirect
13. #14531690C2semidirect
14. #14531682C2semidirect
15. #14531611C2semidirect
16. #14531610C2semidirect
17. #14531505C2semidirect
18. #14531505C2semidirect
19. #14531488C2semidirect
20. #14531483C2semidirect
21. #14531482C2semidirect
22. #14531474C2semidirect
23. #14531472C2semidirect
24. #14531426C2semidirect
25. #14531425C2semidirect
26. #14531373C2semidirect
27. #14531371C2semidirect
28. C4×#10587626C2semidirect
29. #14531257C2semidirect
30. #14531244C2semidirect
31. C17×#2325C2semidirect
34. #11763477C4semidirect
211. C2×#63254C2×C4semidirect
214. C2×#63252C2×C4semidirect
228. C17×#121C2×C4semidirect
259. #10587626C2×C4semidirect
260. #10587626C2×C4semidirect
261. #10587626C2×C4semidirect
262. #10587625C2×C4semidirect
263. #10587625C2×C4semidirect
272. C4×C22⋊D17C2×C4semidirect
331. #10587581C2×C4semidirect
335. #10587573C2×C4semidirect
336. #10587570C2×C4semidirect
337. #10587570C2×C4semidirect
342. #10587567C2×C4semidirect
343. #10587567C2×C4semidirect
776. #2325D17semidirect
1077. #121C4×D17semidirect
1223. C17#34494semidirect

Maximal subgroups

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

subgroupindex
C2×#117634772
#145319422
#145319412
#145319402
#145319392
#145318472
#145318462
#145318032
#145318012
#145317382
#145316912
#145316902
#145316822
#145316112
#145316102
#145315052
#145314882
#145314832
#145314822
#145314742
#145314722
#145314262
#145314252
#145313732
#145313712
C4×#105876262
#145312572
#145312442
C17×#23252
#3449417