Finite Group Databasebeta

← #17242678

Subgroups — #17242678

Order 4352.

2078 conjugacy classes of subgroups.

The subgroup lattice has 1622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14537075C211yesmaximal, characteristic, complemented
2#14537065C211yesmaximal, characteristic, complemented
3#14536432C211yesmaximal, characteristic, complemented
4#14536427C211yesmaximal, characteristic, complemented
5#14536258C211yesmaximal, characteristic, complemented
6#14536168C211yesmaximal, characteristic, complemented
7#14536058C211yesmaximal, characteristic, complemented
8#14536011C211yesmaximal, characteristic, complemented
9#14535992C211yesmaximal, characteristic, complemented
10#14535926C211yesmaximal, characteristic, complemented
11#14535851C211yesmaximal, characteristic, complemented
12#14535538C211yesmaximal, characteristic, complemented
13#14535484C211yesmaximal, characteristic, complemented
14#14535476C211yesmaximal, characteristic, complemented
15#14535401C211yesmaximal, characteristic, complemented
16#14535398C211yesmaximal, characteristic, complemented
17#14535215C211yesmaximal, characteristic, complemented
18#14535021C211yesmaximal, characteristic, complemented
19#14534568C211yesmaximal, characteristic, complemented
20#14534532C211yesmaximal, characteristic, complemented
21#14533716C211yesmaximal, characteristic, complemented
22#14533676C211yesmaximal, characteristic, complemented
23#14532509C211yesmaximal, characteristic, complemented
24#14532329C211yesmaximal, characteristic, complemented
25#14532314C211yesmaximal, characteristic, complemented
26#14532255C211yesmaximal, characteristic, complemented
27#14532240C211yesmaximal, characteristic, complemented
28#14532225C211yesmaximal, characteristic, complemented
29#14531418C211yesmaximal, characteristic, complemented
30C2×#11762683C211yesmaximal, characteristic, complemented
31C17×#2325C211yesmaximal, characteristic, complemented
32C23×C4×D17C2211yescharacteristic
33C2×#10587576C2211yescharacteristic, complemented
34C2×#10587572C2211yescharacteristic
35C2×#10587615C2211yescharacteristic
36C2×#10587569C2211yescharacteristic
37C2×#10587569C2211yescharacteristic
38C2×#10587621C2211yescharacteristic
39C2×#10587621C2211yescharacteristic
40C2×#10587616C2211yescharacteristic
41C2×#10587570C2211yescharacteristic
42C2×#10587570C2211yescharacteristic
43C2×#10587625C2211yescharacteristic
44C2×#10587625C2211yescharacteristic
45C2×#10587624C2211yescharacteristic, complemented
46C2×#10587568C2211yescharacteristic
47C2×#10587623C2211yescharacteristic
48C2×#10587623C2211yescharacteristic
49C2×C4×C22⋊D17C2211yescharacteristic
50C22×C4⋊Dic17C2211yescharacteristic
51C22×#63225C2211yescharacteristic
52C22×#63227C2211yescharacteristic
53C22×#63227C2211yescharacteristic
54#11762751C2211yescharacteristic, complemented
55#11762751C2211yescharacteristic, complemented
56#11762750C2211yescharacteristic, complemented
57#11762750C2211yescharacteristic, complemented
58#11762747C2211yescharacteristic, complemented
59#11762745C2211yescharacteristic, complemented
60#11762745C2211yescharacteristic, complemented
61#11762744C2211yescharacteristic
62#11762744C2211yescharacteristic
63#11762744C2211yescharacteristic
64#11762743C2211yescharacteristic, complemented
65#11762743C2211yescharacteristic, complemented
66#11762743C2211yescharacteristic, complemented
67#11762743C2211yescharacteristic, complemented
68#11762741C2211yescharacteristic, complemented
69#11762741C2211yescharacteristic, complemented
70#11762740C2211yescharacteristic, complemented
71#11762739C2211yescharacteristic, complemented
72#11762737C2211yescharacteristic, complemented
73#11762737C2211yescharacteristic, complemented
74#11762737C2211yescharacteristic, complemented
75#11762737C2211yescharacteristic, complemented
76#11762735C2211yescharacteristic
77#11762734C2211yescharacteristic, complemented
78#11762733C2211yescharacteristic, complemented
79#11762733C2211yescharacteristic, complemented
80#11762732C2211yescharacteristic, complemented
81#11762732C2211yescharacteristic, complemented
82#11762732C2211yescharacteristic, complemented
83#11762732C2211yescharacteristic, complemented
84#11762731C2211yescharacteristic
85#11762731C2211yescharacteristic
86#11762731C2211yescharacteristic
87#11762731C2211yescharacteristic, complemented
88#11762726C2211yescharacteristic
89#11762726C2211yescharacteristic
90#11762726C2211yescharacteristic
91#11762725C2211yescharacteristic
92#11762725C2211yescharacteristic, complemented
93#11762725C2211yescharacteristic, complemented
94#11762725C2211yescharacteristic, complemented
95#11762724C2211yescharacteristic
96#11762724C2211yescharacteristic
97#11762724C2211yescharacteristic, complemented
98#11762724C2211yescharacteristic, complemented
99#11762718C2211yescharacteristic
100#11762717C2211yescharacteristic
101#11762717C2211yescharacteristic
102#11762712C2211yescharacteristic, complemented
103#11762711C2211yescharacteristic
104#11762709C2211yescharacteristic
105#11762709C2211yescharacteristic
106#11762709C2211yescharacteristic
107#11762709C2211yescharacteristic
108#11762708C2211yescharacteristic, complemented
109#11762707C2211yescharacteristic, complemented
110#11762705C2211yescharacteristic, complemented
111#11762705C2211yescharacteristic, complemented
112#11762701C2211yescharacteristic
113#11762701C2211yescharacteristic
114#11762700C2211yescharacteristic
115#11762700C2211yescharacteristic
116#11762700C2211yescharacteristic
117#11762700C2211yescharacteristic, complemented
118#11762698C2211yescharacteristic, complemented
119#11762698C2211yescharacteristic, complemented
120#11762693C2211yescharacteristic, complemented
121#11762693C2211yescharacteristic, complemented
122#11762691C2211yescharacteristic, complemented
123#11762691C2211yescharacteristic, complemented
124#11762689C2211yescharacteristic
125#11762689C2211yescharacteristic
126#11762688C2211yescharacteristic
127#11762688C2211yescharacteristic
128#11762688C2211yescharacteristic
129#11762688C2211yescharacteristic
130#11762688C2211yescharacteristic, complemented
131#11762687C2211yescharacteristic
132#11762687C2211yescharacteristic
133#11762687C2211yescharacteristic
134#11762687C2211yescharacteristic
135#11762685C2211yescharacteristic
136#11762685C2211yescharacteristic
137#11762685C2211yescharacteristic
138#11762685C2211yescharacteristic
139#11762684C2211yescharacteristic
140#11762684C2211yescharacteristic
141#11762683C2211yescharacteristic
142#11762683C2211yescharacteristic
143#11762683C2211yescharacteristic
144#11762683C2211yescharacteristic
145#11762683C2211yescharacteristic
146#11762683C2211yescharacteristic
147#11762683C2211yescharacteristic
148#11762683C2211yescharacteristic
149#11762683C2211yescharacteristic
150#11762683C2211yescharacteristic
151#11762682C2211yescharacteristic
152#11762682C2211yescharacteristic
153#11762682C2211yescharacteristic, complemented
154#11762676C2211yescharacteristic, complemented
155#11762674C2211yescharacteristic, complemented
156#11762673C2211yescharacteristic, complemented
157#11762672C2211yescharacteristic, complemented
158#11762671C2211yescharacteristic
159#11762671C2211yescharacteristic
160#11762671C2211yescharacteristic, complemented
161#11762670C2211yescharacteristic
162#11762669C2211yescharacteristic, complemented
163#11762668C2211yescharacteristic
164#11762668C2211yescharacteristic
165#11762668C2211yescharacteristic, complemented
166#11762667C2211yescharacteristic
167#11762667C2211yescharacteristic
168#11762666C2211yescharacteristic, complemented
169#11762664C2211yescharacteristic
170C4×C22⋊Dic17C2211yescharacteristic
171C2×#10587502C2211yescharacteristic
172C2×C17×#121C2211yescharacteristic
173C2×C4×D4×C17C2211yescharacteristic
174C2×C4×D4×C17C2211yescharacteristic
175C17×#388C2211yescharacteristic, complemented
176C17×#388C2211yescharacteristic, complemented
177C17×#387C2211yescharacteristic, complemented
178C17×#387C2211yescharacteristic, complemented
179C17×#386C2211yescharacteristic
180C17×#386C2211yescharacteristic
181C17×#386C2211yescharacteristic, complemented
182C17×#386C2211yescharacteristic, complemented
183C17×#385C2211yescharacteristic, complemented
184C17×#385C2211yescharacteristic, complemented
185C17×#380C2211yescharacteristic
186C2×C17×#95C2211yescharacteristic
187C24×D17C2311yescharacteristic
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
203C23×Dic17C2311yescharacteristic
204C23×Dic17C2311yescharacteristic
205C23×Dic17C2311yescharacteristic
206C22×D68C2311yescharacteristic
207C22×D68C2311yescharacteristic
208C22×C4×D17—42no—
209C22×C4×D17—42no—
210C22×C4×D17—42no—
211C22×C4×D17C2311yescharacteristic
212C22×C4×D17C2311yescharacteristic
213C22×C4×D17C2311yescharacteristic
214C22×C4×D17C2311yescharacteristic
215C22×C4×D17C2311yescharacteristic
216C17×#121—24no—
217C4×D4×C17—42no—
218C4×D4×C17—42no—
219C2×C4⋊C4×C17C2311yescharacteristic
220C2×C4⋊C4×C17C2311yescharacteristic
221C2×C4⋊C4×C17C2311yescharacteristic
222C2×C4⋊C4×C17C2311yescharacteristic
223C2×C4⋊C4×C17C2311yescharacteristic
224C2×C22⋊C4×C17C2311yescharacteristic
225C2×C22⋊C4×C17C2311yescharacteristic
226C2×C22⋊C4×C17C2311yescharacteristic
227C2×C22⋊C4×C17C2311yescharacteristic
228C2×C22⋊C4×C17C2311yescharacteristic
229C2×C22⋊C4×C17C2311yescharacteristic
230C2×C22⋊C4×C17C2311yescharacteristic
231C2×C22⋊C4×C17C2311yescharacteristic
232C2×C22⋊C4×C17C2311yescharacteristic
233C2×C22⋊C4×C17C2311yescharacteristic
234C2×C42×C17C2311yescharacteristic
235C2×C42×C17C2311yescharacteristic
236C2×C22⋊Dic17C2311yescharacteristic
237C2×C22⋊Dic17C2311yescharacteristic
238C2×C22⋊Dic17C2311yescharacteristic
239C2×C22⋊Dic17C2311yescharacteristic
240C2×C22⋊Dic17C2311yescharacteristic
241C2×C22⋊Dic17C2311yescharacteristic
242C2×C22⋊Dic17C2311yescharacteristic
243C2×C22⋊Dic17C2311yescharacteristic
244C2×C22⋊Dic17C2311yescharacteristic
245C2×C22⋊Dic17C2311yescharacteristic
246C2×C22⋊Dic17C2311yescharacteristic
247C2×C22⋊Dic17C2311yescharacteristic
248C2×C22⋊Dic17C2311yescharacteristic
249#10587625—42no—
250#10587625—42no—
251#10587624—42no—
252#10587623—42no—
253#10587623—42no—
254#10587621—42no—
255#10587621—42no—
256#10587616—42no—
257#10587615—42no—
258C4×C22⋊D17—24no—
259C2×#63227—24no—
260C2×#63227—42no—
261C2×#63227C2311yescharacteristic
262C2×#63227C2311yescharacteristic
263C2×#63227C2311yescharacteristic
264C2×#63227C2311yescharacteristic
265C2×#63227C2311yescharacteristic
266C2×#63227C2311yescharacteristic
267C2×#63227C2311yescharacteristic
268C2×#63227C2311yescharacteristic
269C2×#63227C2311yescharacteristic
270C2×#63227C2311yescharacteristic
271C2×#63227C2311yescharacteristic
272C2×#63227C2311yescharacteristic
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×C4⋊Dic17—42no—
289C2×C4⋊Dic17C2311yescharacteristic
290C2×C4⋊Dic17C2311yescharacteristic
291C2×C4⋊Dic17C2311yescharacteristic
292C2×C4⋊Dic17C2311yescharacteristic
293C2×C4⋊Dic17C2311yescharacteristic
294C2×C4⋊Dic17C2311yescharacteristic
295C2×C4⋊Dic17C2311yescharacteristic
296C2×C4⋊Dic17C2311yescharacteristic
297C2×C4⋊Dic17C2311yescharacteristic
298C2×C4⋊Dic17C2311yescharacteristic
299C2×#63225—42no—
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×#63225C2311yescharacteristic
317C2×#63225C2311yescharacteristic
318C2×#63225C2311yescharacteristic
319C2×C4×Dic17C2311yescharacteristic
320C2×C4×Dic17C2311yescharacteristic
321C2×C4×Dic17C2311yescharacteristic
322#10587576—42no—
323#10587572—42no—
324#10587570—42no—
325#10587570—42no—
326#10587569—42no—
327#10587569—42no—
328#10587568—42no—
329C17×#95C2311yescharacteristic
330C17×#95C2311yescharacteristic
331C17×#95C2311yescharacteristic
332C17×#95C2311yescharacteristic
333C17×#95C2311yescharacteristic
334C17×#95C2311yescharacteristic
335C17×#95C2311yescharacteristic
336C17×#95C2311yescharacteristic
337C17×#95C2311yescharacteristic
338C17×#95C2311yescharacteristic
339#10587502C2311yescharacteristic
340#10587502C2311yescharacteristic
341#10587502C2311yescharacteristic
342#10587502C2311yescharacteristic
343#10587502C2311yescharacteristic
344#10587502C2311yescharacteristic
345#10587502C2311yescharacteristic
346#10587502C2311yescharacteristic
347#10587502C2311yescharacteristic
348#10587502C2311yescharacteristic
349#10587502C2311yescharacteristic
350#10587502C2311yescharacteristic
351#10587502C2311yescharacteristic
352#10587502C2311yescharacteristic
353#10587502C2311yescharacteristic
354#10587502C2311yescharacteristic
355#10587502C2311yescharacteristic
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
369C24×C17C2411yescharacteristic
370C24×C17C2411yescharacteristic
371C24×C17C2411yescharacteristic
372C23×D17—22no—
373C23×D17—22no—
374C23×D17—22no—
375C23×D17—22no—
376C23×D17—22no—
377C23×D17—41no—
378C23×D17—41no—
379C23×D17C2411yescharacteristic
380C23×D17C2411yescharacteristic
381C23×D17C2411yescharacteristic
382C2×D4×C17—22no—
383C2×D4×C17—22no—
384C2×D4×C17—22no—
385C2×D4×C17—22no—
386C2×D4×C17—22no—
387C2×D4×C17—22no—
388C2×D4×C17—22no—
389C2×D4×C17—41no—
390C2×D4×C17—41no—
391C22×C4×C17—22no—
392C22×C4×C17—22no—
393C22×C4×C17—41no—
394C22×C4×C17—41no—
395C22×C4×C17—41no—
396C22×C4×C17—41no—
397C22×C4×C17—41no—
398C22×C4×C17—41no—
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#4114yes—
406C22×C4×C17C2411yescharacteristic
407C22×C4×C17C2411yescharacteristic
408C22×C4×C17C2411yescharacteristic
409C22×C4×C17C2411yescharacteristic
410C22×C4×C17C2411yescharacteristic
411C22×C4×C17C2411yescharacteristic
412C22×C4×C17C2411yescharacteristic
413C22×C4×C17C2411yescharacteristic
414C22×C4×C17C2411yescharacteristic
415C22×C4×C17C2411yescharacteristic
416C22×C4×C17C2411yescharacteristic
417C22×C4×C17C2411yescharacteristic
418C2×C22⋊D17—22no—
419C2×C22⋊D17—22no—
420C2×C22⋊D17—22no—
421C2×C22⋊D17—22no—
422C2×C22⋊D17—22no—
423C2×C22⋊D17—22no—
424C2×C22⋊D17—22no—
425C2×C22⋊D17—22no—
426C2×C22⋊D17—41no—
427C2×C22⋊D17—41no—
428C2×C22⋊D17—41no—
429C2×C22⋊D17—41no—
430C2×C22⋊D17—41no—
431C2×C22⋊D17—41no—
432C2×C22⋊D17—41no—
433C2×C22⋊D17—41no—
434C2×C22⋊D17—41no—
435C2×C22⋊D17—41no—
436C2×C22⋊D17—41no—
437C2×C22⋊D17—41no—
438C2×C22⋊D17—41no—
439C22×Dic17—22no—
440C22×Dic17—22no—
441C22×Dic17—22no—
442C22×Dic17—22no—
443C22×Dic17—22no—
444C22×Dic17—22no—
445C22×Dic17—41no—
446C22×Dic17—41no—
447C22×Dic17—41no—
448C22×Dic17C2411yescharacteristic
449C22×Dic17C2411yescharacteristic
450C22×Dic17C2411yescharacteristic
451C22×Dic17C2411yescharacteristic
452C22×Dic17C2411yescharacteristic
453C22×Dic17C2411yescharacteristic
454C22×Dic17C2411yescharacteristic
455C22×Dic17C2411yescharacteristic
456C22×Dic17C2411yescharacteristic
457C22×Dic17C2411yescharacteristic
458C22×Dic17C2411yescharacteristic
459C22×Dic17C2411yescharacteristic
460C22×Dic17C2411yescharacteristic
461C2×D68—22no—
462C2×D68—22no—
463C2×D68—41no—
464C2×D68—41no—
465C2×D68—41no—
466C2×D68—41no—
467C2×C4×D17—22no—
468C2×C4×D17—22no—
469C2×C4×D17—22no—
470C2×C4×D17—22no—
471C2×C4×D17—22no—
472C2×C4×D17—41no—
473C2×C4×D17—41no—
474C2×C4×D17—41no—
475C2×C4×D17—41no—
476C2×C4×D17—41no—
477C2×C4×D17—41no—
478C2×C4×D17—41no—
479C2×C4×D17—41no—
480C2×C4×D17—416no—
481C2×C4×D17—41no—
482C2×C4×D17—41no—
483C4⋊C4×C17—22no—
484C4⋊C4×C17—41no—
485C4⋊C4×C17—41no—
486C4⋊C4×C17—41no—
487C4⋊C4×C17—41no—
488C22⋊C4×C17—22no—
489C22⋊C4×C17—22no—
490C22⋊C4×C17—22no—
491C22⋊C4×C17—22no—
492C22⋊C4×C17—41no—
493C22⋊C4×C17—41no—
494C22⋊C4×C17—41no—
495C22⋊C4×C17—41no—
496C22⋊C4×C17—41no—
497C22⋊C4×C17—41no—
498C42×C17—41no—
499C42×C17—41no—
500C22⋊Dic17—22no—
501C22⋊Dic17—22no—
502C22⋊Dic17—22no—
503C22⋊Dic17—22no—
504C22⋊Dic17—41no—
505C22⋊Dic17—41no—
506C22⋊Dic17—41no—
507C22⋊Dic17—41no—
508C22⋊Dic17—41no—
509C22⋊Dic17—41no—
510C22⋊Dic17—41no—
511C22⋊Dic17—41no—
512C22⋊Dic17—41no—
513#63227—22no—
514#63227—22no—
515#63227—22no—
516#63227—22no—
517#63227—22no—
518#63227—22no—
519#63227—22no—
520#63227—22no—
521#63227—22no—
522#63227—41no—
523#63227—41no—
524#63227—41no—
525#63227—41no—
526#63227—41no—
527#63227—41no—
528#63227—41no—
529#63227—41no—
530#63227—41no—
531#63227—41no—
532#63227—41no—
533#63227—41no—
534#63227—41no—
535#63227—41no—
536#63227—41no—
537#63227—41no—
538#63227—41no—
539#63227—41no—
540C4⋊Dic17—22no—
541C4⋊Dic17—22no—
542C4⋊Dic17—22no—
543C4⋊Dic17—41no—
544C4⋊Dic17—41no—
545C4⋊Dic17—41no—
546C4⋊Dic17—41no—
547C4⋊Dic17—41no—
548C4⋊Dic17—41no—
549C4⋊Dic17—41no—
550#63225—22no—
551#63225—22no—
552#63225—41no—
553#63225—41no—
554#63225—41no—
555#63225—41no—
556#63225—41no—
557#63225—41no—
558#63225—41no—
559#63225—41no—
560#63225—41no—
561#63225—41no—
562#63225—41no—
563#63225—41no—
564#63225—41no—
565#63225—41no—
566#63225—41no—
567#63225—41no—
568#63225—41no—
569C4×Dic17—22no—
570C4×Dic17—41no—
571C4×Dic17—41no—
572#36777—171nomaximal, Sylow
573C23×C17—21no—
574C23×C17—21no—
575C23×C17—21no—
576C23×C17—21no—
577C23×C17—21no—
578C23×C17—21no—
579C23×C17—21no—
580C23×C17—21no—
581C23×C17—21no—
582C23×C17—21no—
583C23×C17—21no—
584C23×C17—21no—
585C23×C17—21no—
586C23×C17—21no—
587C23×C17—21no—
588C23×C17—21no—
589C23×C17—21no—
590C23×C17—21no—
591C23×C17C2×#4112yes—
592C23×C17H(5,𝔽2)12yes—
593C23×C17H(5,𝔽2)12yes—
594C23×C17C2511yescharacteristic
595C22×D17—28no—
596C22×D17—21no—
597C22×D17—21no—
598C22×D17—21no—
599C22×D17—21no—
600C22×D17—21no—
601C22×D17—21no—
602C22×D17—21no—
603C22×D17—21no—
604C22×D17—21no—
605C22×D17—21no—
606C22×D17—21no—
607C22×D17—21no—
608C22×D17—21no—
609C22×D17—21no—
610C22×D17—21no—
611C22×D17—21no—
612C22×D17—21no—
613C22×D17—21no—
614C22×D17—21no—
615C22×D17—44no—
616C22×D17—44no—
617C22×D17—44no—
618C22×D17—44no—
619C22×D17—44no—
620C22×D17—44no—
621C22×D17H(5,𝔽2)12yes—
622C22×D172−1+412yes—
623D4×C17—44no—
624D4×C17—44no—
625D4×C17—82no—
626C2×C4×C17—21no—
627C2×C4×C17—21no—
628C2×C4×C17—21no—
629C2×C4×C17—21no—
630C2×C4×C17—21no—
631C2×C4×C17—21no—
632C2×C4×C17—21no—
633C2×C4×C17—21no—
634C2×C4×C17—21no—
635C2×C4×C17—21no—
636C2×C4×C17—21no—
637C2×C4×C17—21no—
638C2×C4×C17—21no—
639C2×C4×C17—21no—
640C2×C4×C17—21no—
641C2×C4×C17—21no—
642C2×C4×C17—21no—
643C2×C4×C17—21no—
644C2×C4×C17—21no—
645C2×C4×C17—21no—
646C2×C4×C17—21no—
647C2×C4×C17—21no—
648C2×C4×C17—21no—
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—44no—
661C2×C4×C17—44no—
662C2×C4×C17—82no—
663C2×C4×C17—82no—
664C2×C4×C17—82no—
665C2×C4×C17C2×#4112yes—
666C2×C4×C17C2×#4112yes—
667C22⋊D17—44no—
668C22⋊D17—82no—
669C22⋊D17—82no—
670C22⋊D17—82no—
671C22⋊D17—82no—
672C22⋊D17—82no—
673C22⋊D17—82no—
674C2×Dic17—21no—
675C2×Dic17—21no—
676C2×Dic17—21no—
677C2×Dic17—21no—
678C2×Dic17—21no—
679C2×Dic17—21no—
680C2×Dic17—21no—
681C2×Dic17—21no—
682C2×Dic17—21no—
683C2×Dic17—21no—
684C2×Dic17—21no—
685C2×Dic17—21no—
686C2×Dic17—21no—
687C2×Dic17—21no—
688C2×Dic17—21no—
689C2×Dic17—21no—
690C2×Dic17—21no—
691C2×Dic17—21no—
692C2×Dic17—21no—
693C2×Dic17—21no—
694C2×Dic17—21no—
695C2×Dic17—21no—
696C2×Dic17—21no—
697C2×Dic17—21no—
698C2×Dic17—21no—
699C2×Dic17—21no—
700C2×Dic17—21no—
701C2×Dic17—21no—
702C2×Dic17—21no—
703C2×Dic17—21no—
704C2×Dic17—21no—
705C2×Dic17—21no—
706C2×Dic17—21no—
707C2×Dic17—21no—
708C2×Dic17—21no—
709C2×Dic17—21no—
710C2×Dic17—21no—
711C2×Dic17—21no—
712C2×Dic17—44no—
713C2×Dic17—44no—
714C2×Dic17—82no—
715C2×Dic17H(5,𝔽2)12yes—
716D68—82no—
717D68—82no—
718C4×D17—44no—
719C4×D17—44no—
720C4×D17—44no—
721C4×D17—44no—
722C4×D17—82no—
723#2849—171no—
724#2847—171no—
725#2780—171no—
726#2780—171no—
727#2768—171no—
728#2761—171no—
729#2753—171no—
730#2749—171no—
731#2748—171no—
732#2743—171no—
733#2738—171no—
734#2711—171no—
735#2707—171no—
736#2706—171no—
737#2701—171no—
738#2701—171no—
739#2688—171no—
740#2671—171no—
741#2623—171no—
742#2618—171no—
743#2539—171no—
744#2534—171no—
745#2442—171no—
746#2425—171no—
747#2424—171no—
748#2419—171no—
749#2418—171no—
750#2416—171no—
751#2325D1711yescharacteristic, complemented
752#2318—171no—
753C2×#385—171no—
754C22×C17—22no—
755C22×C17—22no—
756C22×C17—22no—
757C22×C17—22no—
758C22×C17—22no—
759C22×C17—22no—
760C22×C17—41no—
761C22×C17—41no—
762C22×C17—41no—
763C22×C17—41no—
764C22×C17—41no—
765C22×C17—41no—
766C22×C17—41no—
767C22×C17—41no—
768C22×C17—41no—
769C22×C17—41no—
770C22×C17—41no—
771C22×C17—41no—
772C22×C17—41no—
773C22×C17—41no—
774C22×C17#54014yes—
775C22×C17C22×#4111yescharacteristic
776C22×C17C2×H(5,𝔽2)11yescharacteristic
777C22×C17C2×H(5,𝔽2)11yescharacteristic
778C22×C17C2×H(5,𝔽2)11yescharacteristic
779C22×C17C2×H(5,𝔽2)11yescharacteristic
780C22×C17C2×2−1+411yescharacteristic
781C22×C17#58511yescharacteristic
782C2×D17—22no—
783C2×D17—22no—
784C2×D17—22no—
785C2×D17—22no—
786C2×D17—22no—
787C2×D17—22no—
788C2×D17—416no—
789C2×D17—41no—
790C2×D17—41no—
791C2×D17—41no—
792C2×D17—41no—
793C2×D17—41no—
794C2×D17—41no—
795C2×D17—41no—
796C2×D17—41no—
797C2×D17—41no—
798C2×D17—41no—
799C2×D17—41no—
800C2×D17—41no—
801C2×D17—41no—
802C2×D17—41no—
803C2×D17—41no—
804C4×C17—22no—
805C4×C17—22no—
806C4×C17—41no—
807C4×C17—41no—
808C4×C17—41no—
809C4×C17—41no—
810C4×C17—41no—
811C4×C17—41no—
812C4×C17—41no—
813C4×C17—41no—
814C4×C17—41no—
815C4×C17—41no—
816Dic17—22no—
817Dic17—41no—
818Dic17—41no—
819Dic17—41no—
820Dic17—41no—
821Dic17—41no—
822Dic17—41no—
823Dic17—41no—
824Dic17—41no—
825Dic17—41no—
826Dic17—41no—
827Dic17—41no—
828Dic17—41no—
829C24×C4—171no—
830C2×#125—171no—
831C2×#123—171no—
832C2×#123—171no—
833C2×#123—171no—
834C2×#123—171no—
835C2×#123—171no—
836C2×#123—171no—
837C2×#121—171no—
838C2×#121—171no—
839C2×#121—171no—
840C2×#121—171no—
841C2×#121—171no—
842C2×#121—171no—
843C2×#121C2×D1711yescharacteristic
844C2×#120—171no—
845C2×#120—171no—
846C2×#120—171no—
847C2×C4×D4—171no—
848C2×C4×D4C2×D1711yescharacteristic
849C2×C4×D4C2×D1711yescharacteristic
850C22×C4⋊C4—171no—
851C22×C4⋊C4—171no—
852C22×C22⋊C4—171no—
853C22×C22⋊C4—171no—
854#400—171no—
855#400—171no—
856#400—171no—
857#400—171no—
858#400—171no—
859#399—171no—
860#399—171no—
861#399—171no—
862#399—171no—
863#399—171no—
864#398—171no—
865#398—171no—
866#398—171no—
867#398—171no—
868#398—171no—
869#398—171no—
870#398—171no—
871#398—171no—
872#397—171no—
873#397—171no—
874#397—171no—
875#397—171no—
876#397—171no—
877#397—171no—
878#396—171no—
879#396—171no—
880#396—171no—
881#396—171no—
882#396—171no—
883#396—171no—
884#396—171no—
885#396—171no—
886#396—171no—
887#396—171no—
888#394—171no—
889#394—171no—
890#394—171no—
891#394—171no—
892#394—171no—
893#394—171no—
894#394—171no—
895#394—171no—
896#394—171no—
897#394—171no—
898#394—171no—
899#392—171no—
900#392—171no—
901#392—171no—
902#390—171no—
903#390—171no—
904#390—171no—
905#390—171no—
906#390—171no—
907#390—171no—
908#389—171no—
909#389—171no—
910#389—171no—
911#389—171no—
912#388—171no—
913#388—171no—
914#388—171no—
915#388—171no—
916#388—171no—
917#388—171no—
918#388—171no—
919#388—171no—
920#388C2×D1711yescharacteristic, complemented
921#388C2×D1711yescharacteristic, complemented
922#387—171no—
923#387—171no—
924#387—171no—
925#387—171no—
926#387C2×D1711yescharacteristic, complemented
927#387C2×D1711yescharacteristic, complemented
928#386—171no—
929#386—171no—
930#386—171no—
931#386—171no—
932#386—171no—
933#386—171no—
934#386—171no—
935#386—171no—
936#386—171no—
937#386—171no—
938#386—171no—
939#386—171no—
940#386—171no—
941#386—171no—
942#386—171no—
943#386C2×D1711yescharacteristic
944#386C2×D1711yescharacteristic
945#386C2×D1711yescharacteristic, complemented
946#386C2×D1711yescharacteristic, complemented
947#385—171no—
948#385—171no—
949#385—171no—
950#385—171no—
951#385—171no—
952#385—171no—
953#385—171no—
954#385—171no—
955#385—171no—
956#385—171no—
957#385—171no—
958#385—171no—
959#385—171no—
960#385—171no—
961#385—171no—
962#385C2×D1711yescharacteristic, complemented
963#385C2×D1711yescharacteristic, complemented
964#383—171no—
965#382—171no—
966#382—171no—
967#381—171no—
968#381—171no—
969#381—171no—
970#381—171no—
971#381—171no—
972#380—171no—
973#380—171no—
974#380—171no—
975#380—171no—
976#380—171no—
977#380—171no—
978#380—171no—
979#380C2×D1711yescharacteristic
980#379—171no—
981C4×C22⋊C4—171no—
982C2×#95—171no—
983C2×#95C2×D1711yescharacteristic
984C2×C17—24no—
985C2×C17—81no—
986C2×C17—81no—
987C2×C17C2×#54011yescharacteristic
988C2×C17#349211yescharacteristic
989C2×C17#350511yescharacteristic
990C2×C17#353211yescharacteristic
991C2×C17#353411yescharacteristic
992C2×C17#353511yescharacteristic
993C2×C17#353611yescharacteristic
994D17—42no—
995D17—42no—
996D17—81no—
997C25—171no—
998C22×D4—171no—
999C22×D4—171no—
1000C22×D4—171no—
1001C22×D4—171no—
1002C22×D4—171no—
1003C22×D4—171no—
1004C22×D4—171no—
1005C22×D4—171no—
1006C22×D4—171no—
1007C22×D4C22×D1711yescharacteristic
1008C22×D4C22×D1711yescharacteristic
1009C22×D4C22×D1711yescharacteristic
1010C23×C4—171no—
1011C23×C4—171no—
1012C23×C4—171no—
1013C23×C4—171no—
1014C23×C4—171no—
1015C23×C4—171no—
1016C23×C4—171no—
1017C23×C4—171no—
1018C23×C4—682no—
1019C23×C4—682no—
1020C23×C4—682no—
1021C23×C4C22×D1711yescharacteristic
1022C23×C4C22×D1711yescharacteristic
1023C23×C4C22×D1711yescharacteristic
1024C23×C4C22×D1711yescharacteristic
1025C23×C4C22×D1711yescharacteristic
1026#125—682no—
1027#123—682no—
1028#123—682no—
1029#123—682no—
1030#123—682no—
1031#123—682no—
1032#123—682no—
1033#121—24no—
1034#121—682no—
1035#121—682no—
1036#121—682no—
1037#121—682no—
1038#121—682no—
1039#121—682no—
1040#120—682no—
1041#120—682no—
1042#120—682no—
1043C4×D4—42no—
1044C4×D4—42no—
1045C4×D4—344no—
1046C2×C4⋊C4—171no—
1047C2×C4⋊C4—171no—
1048C2×C4⋊C4—171no—
1049C2×C4⋊C4—171no—
1050C2×C4⋊C4—171no—
1051C2×C4⋊C4—171no—
1052C2×C4⋊C4—171no—
1053C2×C4⋊C4—171no—
1054C2×C4⋊C4—171no—
1055C2×C4⋊C4—171no—
1056C2×C4⋊C4—171no—
1057C2×C4⋊C4—171no—
1058C2×C4⋊C4—171no—
1059C2×C4⋊C4—171no—
1060C2×C4⋊C4—171no—
1061C2×C4⋊C4—171no—
1062C2×C4⋊C4—171no—
1063C2×C4⋊C4—171no—
1064C2×C4⋊C4—171no—
1065C2×C4⋊C4—171no—
1066C2×C4⋊C4—171no—
1067C2×C4⋊C4—171no—
1068C2×C4⋊C4—171no—
1069C2×C4⋊C4—171no—
1070C2×C4⋊C4—171no—
1071C2×C4⋊C4—171no—
1072C2×C4⋊C4—171no—
1073C2×C4⋊C4—171no—
1074C2×C4⋊C4—171no—
1075C2×C4⋊C4—682no—
1076C2×C4⋊C4—682no—
1077C2×C4⋊C4C22×D1711yescharacteristic
1078C2×C4⋊C4C22×D1711yescharacteristic
1079C2×C4⋊C4C22×D1711yescharacteristic
1080C2×C4⋊C4C22×D1711yescharacteristic
1081C2×C4⋊C4C22×D1711yescharacteristic
1082C2×C22⋊C4—171no—
1083C2×C22⋊C4—171no—
1084C2×C22⋊C4—171no—
1085C2×C22⋊C4—171no—
1086C2×C22⋊C4—171no—
1087C2×C22⋊C4—171no—
1088C2×C22⋊C4—171no—
1089C2×C22⋊C4—171no—
1090C2×C22⋊C4—171no—
1091C2×C22⋊C4—171no—
1092C2×C22⋊C4—171no—
1093C2×C22⋊C4—171no—
1094C2×C22⋊C4—171no—
1095C2×C22⋊C4—171no—
1096C2×C22⋊C4—171no—
1097C2×C22⋊C4—171no—
1098C2×C22⋊C4—171no—
1099C2×C22⋊C4—171no—
1100C2×C22⋊C4—171no—
1101C2×C22⋊C4—171no—
1102C2×C22⋊C4—171no—
1103C2×C22⋊C4—171no—
1104C2×C22⋊C4—171no—
1105C2×C22⋊C4—171no—
1106C2×C22⋊C4—171no—
1107C2×C22⋊C4—171no—
1108C2×C22⋊C4—171no—
1109C2×C22⋊C4—171no—
1110C2×C22⋊C4—171no—
1111C2×C22⋊C4—171no—
1112C2×C22⋊C4—171no—
1113C2×C22⋊C4—171no—
1114C2×C22⋊C4—171no—
1115C2×C22⋊C4—171no—
1116C2×C22⋊C4—171no—
1117C2×C22⋊C4—171no—
1118C2×C22⋊C4—171no—
1119C2×C22⋊C4—171no—
1120C2×C22⋊C4—171no—
1121C2×C22⋊C4—171no—
1122C2×C22⋊C4—344no—
1123C2×C22⋊C4—682no—
1124C2×C22⋊C4C22×D1711yescharacteristic
1125C2×C22⋊C4C22×D1711yescharacteristic
1126C2×C22⋊C4C22×D1711yescharacteristic
1127C2×C22⋊C4C22×D1711yescharacteristic
1128C2×C22⋊C4C22×D1711yescharacteristic
1129C2×C22⋊C4C22×D1711yescharacteristic
1130C2×C22⋊C4C22×D1711yescharacteristic
1131C2×C22⋊C4C22×D1711yescharacteristic
1132C2×C22⋊C4C22×D1711yescharacteristic
1133C2×C22⋊C4C22×D1711yescharacteristic
1134C2×C42—171no—
1135C2×C42—171no—
1136C2×C42—171no—
1137C2×C42C22×D1711yescharacteristic
1138C2×C42C22×D1711yescharacteristic
1139#95—171no—
1140#95—171no—
1141#95—171no—
1142#95—171no—
1143#95—171no—
1144#95—171no—
1145#95—171no—
1146#95—171no—
1147#95—171no—
1148#95—171no—
1149#95—171no—
1150#95—171no—
1151#95—171no—
1152#95—171no—
1153#95—171no—
1154#95—171no—
1155#95—171no—
1156#95—171no—
1157#95—171no—
1158#95—171no—
1159#95—171no—
1160#95—171no—
1161#95—171no—
1162#95—171no—
1163#95—171no—
1164#95—171no—
1165#95—171no—
1166#95—171no—
1167#95—171no—
1168#95—171no—
1169#95C22×D1711yescharacteristic
1170#95C22×D1711yescharacteristic
1171#95C22×D1711yescharacteristic
1172#95C22×D1711yescharacteristic
1173#95C22×D1711yescharacteristic
1174#95C22×D1711yescharacteristic
1175#95C22×D1711yescharacteristic
1176#95C22×D1711yescharacteristic
1177#95C22×D1711yescharacteristic
1178#95C22×D1711yescharacteristic
1179C17#3677711yescharacteristic, complemented, Sylow
1180C24—171no—
1181C24—171no—
1182C24—171no—
1183C24—342no—
1184C24—342no—
1185C24—342no—
1186C24—342no—
1187C24—342no—
1188C24—681no—
1189C24—681no—
1190C24C23×D1711yescharacteristic
1191C24C23×D1711yescharacteristic
1192C24C23×D1711yescharacteristic
1193C2×D4—22no—
1194C2×D4—22no—
1195C2×D4—22no—
1196C2×D4—22no—
1197C2×D4—22no—
1198C2×D4—22no—
1199C2×D4—22no—
1200C2×D4—41no—
1201C2×D4—41no—
1202C2×D4—342no—
1203C2×D4—342no—
1204C2×D4—342no—
1205C2×D4—342no—
1206C2×D4—342no—
1207C2×D4—342no—
1208C2×D4—342no—
1209C2×D4—342no—
1210C2×D4—342no—
1211C2×D4—342no—
1212C2×D4—681no—
1213C2×D4—681no—
1214C2×D4—681no—
1215C2×D4—681no—
1216C2×D4—681no—
1217C2×D4—681no—
1218C2×D4—681no—
1219C2×D4—681no—
1220C2×D4—681no—
1221C2×D4—681no—
1222C2×D4—681no—
1223C2×D4—681no—
1224C2×D4—681no—
1225C2×D4—681no—
1226C2×D4—681no—
1227C2×D4—681no—
1228C2×D4—681no—
1229C22×C4—22no—
1230C22×C4—22no—
1231C22×C4—41no—
1232C22×C4—41no—
1233C22×C4—41no—
1234C22×C4—41no—
1235C22×C4—41no—
1236C22×C4—41no—
1237C22×C4—41no—
1238C22×C4—41no—
1239C22×C4—41no—
1240C22×C4—41no—
1241C22×C4—41no—
1242C22×C4—41no—
1243C22×C4—171no—
1244C22×C4—171no—
1245C22×C4—171no—
1246C22×C4—171no—
1247C22×C4—171no—
1248C22×C4—171no—
1249C22×C4—171no—
1250C22×C4—171no—
1251C22×C4—171no—
1252C22×C4—171no—
1253C22×C4—171no—
1254C22×C4—171no—
1255C22×C4—171no—
1256C22×C4—342no—
1257C22×C4—342no—
1258C22×C4—342no—
1259C22×C4—342no—
1260C22×C4—342no—
1261C22×C4—342no—
1262C22×C4—342no—
1263C22×C4—342no—
1264C22×C4—342no—
1265C22×C4—342no—
1266C22×C4—342no—
1267C22×C4—681no—
1268C22×C4—681no—
1269C22×C4—681no—
1270C22×C4—681no—
1271C22×C4—681no—
1272C22×C4—681no—
1273C22×C4—681no—
1274C22×C4—681no—
1275C22×C4—681no—
1276C22×C4—681no—
1277C22×C4—6816no—
1278C22×C4—681no—
1279C22×C4—681no—
1280C22×C4—681no—
1281C22×C4#6325214yes—
1282C22×C4C23×D1711yescharacteristic
1283C22×C4C23×D1711yescharacteristic
1284C22×C4C23×D1711yescharacteristic
1285C22×C4C23×D1711yescharacteristic
1286C22×C4C23×D1711yescharacteristic
1287C22×C4C23×D1711yescharacteristic
1288C22×C4C23×D1711yescharacteristic
1289C22×C4C23×D1711yescharacteristic
1290C22×C4C23×D1711yescharacteristic
1291C22×C4C23×D1711yescharacteristic
1292C22×C4C23×D1711yescharacteristic
1293C22×C4C23×D1711yescharacteristic
1294C4⋊C4—22no—
1295C4⋊C4—41no—
1296C4⋊C4—41no—
1297C4⋊C4—41no—
1298C4⋊C4—41no—
1299C4⋊C4—342no—
1300C4⋊C4—342no—
1301C4⋊C4—342no—
1302C4⋊C4—342no—
1303C4⋊C4—342no—
1304C4⋊C4—681no—
1305C4⋊C4—681no—
1306C4⋊C4—681no—
1307C4⋊C4—681no—
1308C4⋊C4—681no—
1309C4⋊C4—681no—
1310C4⋊C4—681no—
1311C4⋊C4—681no—
1312C4⋊C4—681no—
1313C4⋊C4—681no—
1314C4⋊C4—681no—
1315C4⋊C4—681no—
1316C4⋊C4—681no—
1317C4⋊C4—681no—
1318C4⋊C4—681no—
1319C4⋊C4—681no—
1320C4⋊C4—681no—
1321C4⋊C4—681no—
1322C4⋊C4—681no—
1323C4⋊C4—681no—
1324C4⋊C4—681no—
1325C4⋊C4—681no—
1326C4⋊C4—681no—
1327C4⋊C4—681no—
1328C22⋊C4—22no—
1329C22⋊C4—22no—
1330C22⋊C4—22no—
1331C22⋊C4—22no—
1332C22⋊C4—41no—
1333C22⋊C4—41no—
1334C22⋊C4—41no—
1335C22⋊C4—41no—
1336C22⋊C4—41no—
1337C22⋊C4—41no—
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—681no—
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—681no—
1361C22⋊C4—681no—
1362C22⋊C4—681no—
1363C22⋊C4—681no—
1364C22⋊C4—681no—
1365C22⋊C4—681no—
1366C22⋊C4—681no—
1367C22⋊C4—681no—
1368C22⋊C4—681no—
1369C22⋊C4—681no—
1370C22⋊C4—681no—
1371C22⋊C4—681no—
1372C22⋊C4—681no—
1373C22⋊C4—681no—
1374C22⋊C4—681no—
1375C22⋊C4—681no—
1376C22⋊C4—681no—
1377C22⋊C4—681no—
1378C42—41no—
1379C42—41no—
1380C42—342no—
1381C42—681no—
1382C42—681no—
1383C23—21no—
1384C23—21no—
1385C23—21no—
1386C23—21no—
1387C23—21no—
1388C23—21no—
1389C23—21no—
1390C23—21no—
1391C23—21no—
1392C23—21no—
1393C23—21no—
1394C23—21no—
1395C23—21no—
1396C23—21no—
1397C23—21no—
1398C23—21no—
1399C23—21no—
1400C23—21no—
1401C23—172no—
1402C23—172no—
1403C23—348no—
1404C23—341no—
1405C23—341no—
1406C23—341no—
1407C23—341no—
1408C23—341no—
1409C23—341no—
1410C23—341no—
1411C23—341no—
1412C23—341no—
1413C23—341no—
1414C23—341no—
1415C23—341no—
1416C23—341no—
1417C23—341no—
1418C23—341no—
1419C23—341no—
1420C23—341no—
1421C23—341no—
1422C23—341no—
1423C23—684no—
1424C23—684no—
1425C23—684no—
1426C23—684no—
1427C23—684no—
1428C23—684no—
1429C23C2×#6325212yes—
1430C23#1058769112yes—
1431C23#1058769612yes—
1432C23C24×D1711yescharacteristic
1433D4—44no—
1434D4—44no—
1435D4—82no—
1436D4—684no—
1437D4—1362no—
1438D4—1362no—
1439D4—1362no—
1440D4—1362no—
1441D4—1362no—
1442D4—1362no—
1443D4—1362no—
1444D4—1362no—
1445C2×C4—21no—
1446C2×C4—21no—
1447C2×C4—21no—
1448C2×C4—21no—
1449C2×C4—21no—
1450C2×C4—21no—
1451C2×C4—21no—
1452C2×C4—21no—
1453C2×C4—21no—
1454C2×C4—21no—
1455C2×C4—21no—
1456C2×C4—21no—
1457C2×C4—21no—
1458C2×C4—21no—
1459C2×C4—21no—
1460C2×C4—21no—
1461C2×C4—21no—
1462C2×C4—21no—
1463C2×C4—21no—
1464C2×C4—21no—
1465C2×C4—21no—
1466C2×C4—21no—
1467C2×C4—21no—
1468C2×C4—21no—
1469C2×C4—21no—
1470C2×C4—21no—
1471C2×C4—21no—
1472C2×C4—21no—
1473C2×C4—21no—
1474C2×C4—21no—
1475C2×C4—21no—
1476C2×C4—21no—
1477C2×C4—21no—
1478C2×C4—21no—
1479C2×C4—44no—
1480C2×C4—44no—
1481C2×C4—82no—
1482C2×C4—82no—
1483C2×C4—82no—
1484C2×C4—172no—
1485C2×C4—341no—
1486C2×C4—341no—
1487C2×C4—341no—
1488C2×C4—341no—
1489C2×C4—341no—
1490C2×C4—341no—
1491C2×C4—341no—
1492C2×C4—341no—
1493C2×C4—341no—
1494C2×C4—341no—
1495C2×C4—341no—
1496C2×C4—341no—
1497C2×C4—341no—
1498C2×C4—341no—
1499C2×C4—341no—
1500C2×C4—341no—
1501C2×C4—341no—
1502C2×C4—341no—
1503C2×C4—341no—
1504C2×C4—341no—
1505C2×C4—341no—
1506C2×C4—341no—
1507C2×C4—341no—
1508C2×C4—341no—
1509C2×C4—341no—
1510C2×C4—341no—
1511C2×C4—341no—
1512C2×C4—341no—
1513C2×C4—341no—
1514C2×C4—341no—
1515C2×C4—341no—
1516C2×C4—341no—
1517C2×C4—341no—
1518C2×C4—341no—
1519C2×C4—341no—
1520C2×C4—341no—
1521C2×C4—341no—
1522C2×C4—341no—
1523C2×C4—684no—
1524C2×C4—684no—
1525C2×C4—684no—
1526C2×C4—684no—
1527C2×C4—684no—
1528C2×C4—684no—
1529C2×C4—1362no—
1530C2×C4—1362no—
1531C2×C4C2×#6325212yes—
1532C2×C4C2×#6325212yes—
1533C22—22no—
1534C22—22no—
1535C22—22no—
1536C22—22no—
1537C22—22no—
1538C22—22no—
1539C22—41no—
1540C22—41no—
1541C22—41no—
1542C22—41no—
1543C22—41no—
1544C22—41no—
1545C22—41no—
1546C22—41no—
1547C22—41no—
1548C22—41no—
1549C22—41no—
1550C22—41no—
1551C22—41no—
1552C22—41no—
1553C22—342no—
1554C22—342no—
1555C22—342no—
1556C22—342no—
1557C22—342no—
1558C22—342no—
1559C22—6816no—
1560C22—681no—
1561C22—681no—
1562C22—681no—
1563C22—681no—
1564C22—681no—
1565C22—681no—
1566C22—681no—
1567C22—681no—
1568C22—681no—
1569C22—681no—
1570C22—681no—
1571C22—681no—
1572C22—681no—
1573C22—681no—
1574C22—681no—
1575C22#1176341014yes—
1576C22C22×#6325211yescharacteristic
1577C22H(5,𝔽2)×D1711yescharacteristic
1578C22H(5,𝔽2)×D1711yescharacteristic
1579C22C2×#1058769111yescharacteristic
1580C22C2×#1058769611yescharacteristic
1581C222−1+4×D1711yescharacteristic
1582C22#1176364411yescharacteristic
1583C4—22no—
1584C4—22no—
1585C4—41no—
1586C4—41no—
1587C4—41no—
1588C4—41no—
1589C4—41no—
1590C4—41no—
1591C4—41no—
1592C4—41no—
1593C4—41no—
1594C4—41no—
1595C4—342no—
1596C4—681no—
1597C4—681no—
1598C4—681no—
1599C4—681no—
1600C4—681no—
1601C4—681no—
1602C4—681no—
1603C4—681no—
1604C4—681no—
1605C4—681no—
1606C4—681no—
1607C4—681no—
1608C2—24no—
1609C2—81no—
1610C2—81no—
1611C2—682no—
1612C2—682no—
1613C2—1361no—
1614C2C2×#1176341011yescharacteristic
1615C2#1454248711yescharacteristic
1616C2#1454261411yescharacteristic
1617C2#1454293511yescharacteristic
1618C2#1454297111yescharacteristic
1619C2#1454299111yescharacteristic
1620C2#1454300111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2325C2
hypercenter#2325D17
hypocenterC17#36777
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2325

Complements

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

NH ≅ G/Ntype
1. #14537075C2semidirect
2. #14537065C2semidirect
3. #14536432C2semidirect
4. #14536427C2semidirect
5. #14536258C2semidirect
6. #14536168C2semidirect
7. #14536058C2semidirect
8. #14536011C2semidirect
9. #14535992C2semidirect
10. #14535926C2semidirect
11. #14535851C2semidirect
12. #14535538C2semidirect
13. #14535484C2semidirect
14. #14535476C2semidirect
15. #14535401C2semidirect
16. #14535398C2semidirect
17. #14535215C2semidirect
18. #14535021C2semidirect
19. #14534568C2semidirect
20. #14534532C2semidirect
21. #14533716C2semidirect
22. #14533676C2semidirect
23. #14532509C2semidirect
24. #14532329C2semidirect
25. #14532314C2semidirect
26. #14532255C2semidirect
27. #14532240C2semidirect
28. #14532225C2semidirect
29. #14531418C2semidirect
30. C2×#11762683C2semidirect
31. C17×#2325C2semidirect
33. C2×#10587576C22semidirect
45. C2×#10587624C22semidirect
54. #11762751C22semidirect
55. #11762751C22semidirect
56. #11762750C22semidirect
57. #11762750C22semidirect
58. #11762747C22semidirect
59. #11762745C22semidirect
60. #11762745C22semidirect
64. #11762743C22semidirect
65. #11762743C22semidirect
66. #11762743C22semidirect
67. #11762743C22semidirect
68. #11762741C22semidirect
69. #11762741C22semidirect
70. #11762740C22semidirect
71. #11762739C22semidirect
72. #11762737C22semidirect
73. #11762737C22semidirect
74. #11762737C22semidirect
75. #11762737C22semidirect
77. #11762734C22semidirect
78. #11762733C22semidirect
79. #11762733C22semidirect
80. #11762732C22semidirect
81. #11762732C22semidirect
82. #11762732C22semidirect
83. #11762732C22semidirect
87. #11762731C22semidirect
92. #11762725C22semidirect
93. #11762725C22semidirect
94. #11762725C22semidirect
97. #11762724C22semidirect
98. #11762724C22semidirect
102. #11762712C22semidirect
108. #11762708C22semidirect
109. #11762707C22semidirect
110. #11762705C22semidirect
111. #11762705C22semidirect
117. #11762700C22semidirect
118. #11762698C22semidirect
119. #11762698C22semidirect
120. #11762693C22semidirect
121. #11762693C22semidirect
122. #11762691C22semidirect
123. #11762691C22semidirect
130. #11762688C22semidirect
153. #11762682C22semidirect
154. #11762676C22semidirect
155. #11762674C22semidirect
156. #11762673C22semidirect
157. #11762672C22semidirect
160. #11762671C22semidirect
162. #11762669C22semidirect
165. #11762668C22semidirect
168. #11762666C22semidirect
175. C17×#388C22semidirect
176. C17×#388C22semidirect
177. C17×#387C22semidirect
178. C17×#387C22semidirect
181. C17×#386C22semidirect
182. C17×#386C22semidirect
183. C17×#385C22semidirect
184. C17×#385C22semidirect
751. #2325D17semidirect
920. #388C2×D17semidirect
921. #388C2×D17semidirect
926. #387C2×D17semidirect
927. #387C2×D17semidirect
945. #386C2×D17semidirect
946. #386C2×D17semidirect
962. #385C2×D17semidirect
963. #385C2×D17semidirect
1179. C17#36777semidirect

Maximal subgroups

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

subgroupindex
#145370752
#145370652
#145364322
#145364272
#145362582
#145361682
#145360582
#145360112
#145359922
#145359262
#145358512
#145355382
#145354842
#145354762
#145354012
#145353982
#145352152
#145350212
#145345682
#145345322
#145337162
#145336762
#145325092
#145323292
#145323142
#145322552
#145322402
#145322252
#145314182
C2×#117626832
C17×#23252
#3677717