Finite Group Databasebeta

← #17241474

Subgroups — #17241474

Order 4352.

2214 conjugacy classes of subgroups.

The subgroup lattice has 1706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14537065C211yesmaximal, characteristic, complemented
2#14537065C211yesmaximal, characteristic, complemented
3#14535998C211yesmaximal, characteristic, complemented
4#14535996C211yesmaximal, characteristic, complemented
5#14535993C211yesmaximal, characteristic, complemented
6#14535992C211yesmaximal, characteristic, complemented
7#14535905C211yesmaximal, characteristic, complemented
8#14535901C211yesmaximal, characteristic, complemented
9#14535897C211yesmaximal, characteristic, complemented
10#14535893C211yesmaximal, characteristic, complemented
11#14535433C211yesmaximal, characteristic, complemented
12#14535429C211yesmaximal, characteristic, complemented
13#14535425C211yesmaximal, characteristic, complemented
14#14535421C211yesmaximal, characteristic, complemented
15#14535026C211yesmaximal, characteristic, complemented
16#14535025C211yesmaximal, characteristic, complemented
17#14535023C211yesmaximal, characteristic, complemented
18#14535020C211yesmaximal, characteristic, complemented
19#14534888C211yesmaximal, characteristic, complemented
20#14534756C211yesmaximal, characteristic, complemented
21#14532525C211yesmaximal, characteristic, complemented
22#14532519C211yesmaximal, characteristic, complemented
23#14532517C211yesmaximal, characteristic, complemented
24#14532326C211yesmaximal, characteristic, complemented
25#14532322C211yesmaximal, characteristic, complemented
26#14532318C211yesmaximal, characteristic, complemented
27#14532314C211yesmaximal, characteristic, complemented
28#14531485C211yesmaximal, characteristic, complemented
29#14531482C211yesmaximal, characteristic, complemented
30C2×#11762666C211yesmaximal, characteristic, complemented
31C17×#2443C211yesmaximal, characteristic, complemented
32C23×C4×D17C2211yescharacteristic
33C2×#10587580C2211yescharacteristic, complemented
34C2×#10587572C2211yescharacteristic, complemented
35C2×#10587569C2211yescharacteristic, complemented
36C2×#10587581C2211yescharacteristic
37C2×#10587616C2211yescharacteristic
38C2×#10587616C2211yescharacteristic
39C2×#10587570C2211yescharacteristic
40C2×#10587570C2211yescharacteristic
41C2×#10587570C2211yescharacteristic
42C2×#10587570C2211yescharacteristic
43C2×#10587570C2211yescharacteristic
44C2×#10587625C2211yescharacteristic
45C2×#10587625C2211yescharacteristic
46C2×#10587625C2211yescharacteristic
47C2×#10587625C2211yescharacteristic
48C2×#10587625C2211yescharacteristic
49C2×#10587568C2211yescharacteristic
50C2×#10587568C2211yescharacteristic
51C2×#10587623C2211yescharacteristic
52C2×#10587623C2211yescharacteristic
53C2×D4×Dic17C2211yescharacteristic
54C2×C4×C22⋊D17C2211yescharacteristic
55C2×#10587567C2211yescharacteristic
56C22×C4⋊Dic17C2211yescharacteristic
57C22×#63227C2211yescharacteristic
58C22×#63227C2211yescharacteristic
59#11762750C2211yescharacteristic, complemented
60#11762750C2211yescharacteristic, complemented
61#11762749C2211yescharacteristic, complemented
62#11762747C2211yescharacteristic, complemented
63#11762746C2211yescharacteristic, complemented
64#11762745C2211yescharacteristic, complemented
65#11762745C2211yescharacteristic, complemented
66#11762745C2211yescharacteristic, complemented
67#11762744C2211yescharacteristic, complemented
68#11762744C2211yescharacteristic, complemented
69#11762744C2211yescharacteristic, complemented
70#11762743C2211yescharacteristic, complemented
71#11762743C2211yescharacteristic, complemented
72#11762742C2211yescharacteristic, complemented
73#11762742C2211yescharacteristic, complemented
74#11762741C2211yescharacteristic, complemented
75#11762740C2211yescharacteristic, complemented
76#11762739C2211yescharacteristic, complemented
77#11762736C2211yescharacteristic, complemented
78#11762735C2211yescharacteristic, complemented
79#11762734C2211yescharacteristic, complemented
80#11762733C2211yescharacteristic
81#11762731C2211yescharacteristic
82#11762731C2211yescharacteristic
83#11762731C2211yescharacteristic
84#11762727C2211yescharacteristic
85#11762727C2211yescharacteristic
86#11762726C2211yescharacteristic
87#11762726C2211yescharacteristic
88#11762726C2211yescharacteristic, complemented
89#11762725C2211yescharacteristic
90#11762725C2211yescharacteristic
91#11762725C2211yescharacteristic, complemented
92#11762725C2211yescharacteristic, complemented
93#11762724C2211yescharacteristic
94#11762724C2211yescharacteristic
95#11762719C2211yescharacteristic
96#11762718C2211yescharacteristic
97#11762718C2211yescharacteristic
98#11762718C2211yescharacteristic, complemented
99#11762718C2211yescharacteristic, complemented
100#11762717C2211yescharacteristic
101#11762717C2211yescharacteristic, complemented
102#11762717C2211yescharacteristic, complemented
103#11762711C2211yescharacteristic
104#11762710C2211yescharacteristic
105#11762709C2211yescharacteristic
106#11762709C2211yescharacteristic
107#11762703C2211yescharacteristic, complemented
108#11762702C2211yescharacteristic, complemented
109#11762701C2211yescharacteristic
110#11762701C2211yescharacteristic, complemented
111#11762700C2211yescharacteristic
112#11762700C2211yescharacteristic, complemented
113#11762699C2211yescharacteristic
114#11762699C2211yescharacteristic, complemented
115#11762698C2211yescharacteristic
116#11762698C2211yescharacteristic, complemented
117#11762697C2211yescharacteristic, complemented
118#11762696C2211yescharacteristic, complemented
119#11762695C2211yescharacteristic, complemented
120#11762694C2211yescharacteristic, complemented
121#11762693C2211yescharacteristic, complemented
122#11762692C2211yescharacteristic, complemented
123#11762691C2211yescharacteristic, complemented
124#11762690C2211yescharacteristic, complemented
125#11762689C2211yescharacteristic
126#11762688C2211yescharacteristic
127#11762688C2211yescharacteristic
128#11762688C2211yescharacteristic
129#11762688C2211yescharacteristic
130#11762688C2211yescharacteristic, complemented
131#11762687C2211yescharacteristic
132#11762687C2211yescharacteristic
133#11762687C2211yescharacteristic
134#11762687C2211yescharacteristic
135#11762687C2211yescharacteristic
136#11762687C2211yescharacteristic
137#11762686C2211yescharacteristic
138#11762686C2211yescharacteristic
139#11762686C2211yescharacteristic, complemented
140#11762685C2211yescharacteristic
141#11762685C2211yescharacteristic
142#11762685C2211yescharacteristic
143#11762685C2211yescharacteristic
144#11762685C2211yescharacteristic, complemented
145#11762685C2211yescharacteristic, complemented
146#11762684C2211yescharacteristic
147#11762684C2211yescharacteristic, complemented
148#11762683C2211yescharacteristic, complemented
149#11762683C2211yescharacteristic, complemented
150#11762682C2211yescharacteristic
151#11762682C2211yescharacteristic, complemented
152#11762681C2211yescharacteristic
153#11762681C2211yescharacteristic, complemented
154#11762680C2211yescharacteristic, complemented
155#11762680C2211yescharacteristic, complemented
156#11762668C2211yescharacteristic
157#11762668C2211yescharacteristic
158#11762668C2211yescharacteristic
159#11762668C2211yescharacteristic
160#11762667C2211yescharacteristic
161#11762667C2211yescharacteristic
162#11762666C2211yescharacteristic
163#11762666C2211yescharacteristic
164#11762666C2211yescharacteristic
165#11762666C2211yescharacteristic
166#11762666C2211yescharacteristic
167#11762666C2211yescharacteristic
168#11762666C2211yescharacteristic
169#11762666C2211yescharacteristic
170C2×#10587502C2211yescharacteristic
171C2×#10587502C2211yescharacteristic
172C2×C17×#123C2211yescharacteristic, complemented
173C2×C17×#121C2211yescharacteristic
174C2×C4×D4×C17C2211yescharacteristic
175C22×C4⋊C4×C17C2211yescharacteristic
176C17×#399C2211yescharacteristic, complemented
177C17×#398C2211yescharacteristic, complemented
178C17×#397C2211yescharacteristic, complemented
179C17×#394C2211yescharacteristic, complemented
180C17×#388C2211yescharacteristic, complemented
181C17×#387C2211yescharacteristic, complemented
182C17×#386C2211yescharacteristic
183C17×#386C2211yescharacteristic
184C17×#386C2211yescharacteristic
185C17×#385C2211yescharacteristic
186C17×#385C2211yescharacteristic, complemented
187C24×D17C2311yescharacteristic
188C22×D4×C17C2311yescharacteristic
189C22×D4×C17C2311yescharacteristic
190C22×D4×C17C2311yescharacteristic
191C23×C4×C17C2311yescharacteristic
192C23×C4×C17C2311yescharacteristic
193C23×C4×C17C2311yescharacteristic
194C23×C4×C17C2311yescharacteristic
195C22×C22⋊D17C2311yescharacteristic
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
209C22×D68C2311yescharacteristic
210C22×D68C2311yescharacteristic
211C22×D68C2311yescharacteristic
212C22×D68C2311yescharacteristic
213C22×D68C2311yescharacteristic
214C22×C4×D17—24no—
215C22×C4×D17—42no—
216C22×C4×D17—42no—
217C22×C4×D17C2311yescharacteristic
218C22×C4×D17C2311yescharacteristic
219C22×C4×D17C2311yescharacteristic
220C22×C4×D17C2311yescharacteristic
221C22×C4×D17C2311yescharacteristic
222C22×C4×D17C2311yescharacteristic
223C17×#123—42no—
224C17×#121—42no—
225C4×D4×C17—42no—
226C2×C4⋊C4×C17—42no—
227C2×C4⋊C4×C17C2311yescharacteristic
228C2×C4⋊C4×C17C2311yescharacteristic
229C2×C4⋊C4×C17C2311yescharacteristic
230C2×C4⋊C4×C17C2311yescharacteristic
231C2×C4⋊C4×C17C2311yescharacteristic
232C2×C4⋊C4×C17C2311yescharacteristic
233C2×C4⋊C4×C17C2311yescharacteristic
234C2×C4⋊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×C42×C17C2311yescharacteristic
247C2×C22⋊Dic17C2311yescharacteristic
248C2×C22⋊Dic17C2311yescharacteristic
249C2×C22⋊Dic17C2311yescharacteristic
250C2×C22⋊Dic17C2311yescharacteristic
251C2×C22⋊Dic17C2311yescharacteristic
252C2×C22⋊Dic17C2311yescharacteristic
253C2×C22⋊Dic17C2311yescharacteristic
254C2×C22⋊Dic17C2311yescharacteristic
255C2×C22⋊Dic17C2311yescharacteristic
256#10587625—24no—
257#10587625—24no—
258#10587625—42no—
259#10587625—42no—
260#10587625—42no—
261#10587623—42no—
262#10587623—42no—
263D4×Dic17—42no—
264#10587616—42no—
265#10587616—42no—
266C4×C22⋊D17—42no—
267C2×#63227—42no—
268C2×#63227—42no—
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×#63227C2311yescharacteristic
289C2×#63227C2311yescharacteristic
290C2×#63227C2311yescharacteristic
291C2×#63227C2311yescharacteristic
292C2×#63227C2311yescharacteristic
293C2×#63227C2311yescharacteristic
294C2×#63227C2311yescharacteristic
295C2×#63227C2311yescharacteristic
296C2×#63227C2311yescharacteristic
297C2×#63227C2311yescharacteristic
298C2×#63227C2311yescharacteristic
299C2×#63227C2311yescharacteristic
300C2×#63227C2311yescharacteristic
301C2×C4⋊Dic17—42no—
302C2×C4⋊Dic17C2311yescharacteristic
303C2×C4⋊Dic17C2311yescharacteristic
304C2×C4⋊Dic17C2311yescharacteristic
305C2×C4⋊Dic17C2311yescharacteristic
306C2×C4⋊Dic17C2311yescharacteristic
307C2×C4⋊Dic17C2311yescharacteristic
308C2×C4⋊Dic17C2311yescharacteristic
309C2×C4⋊Dic17C2311yescharacteristic
310C2×#63225C2311yescharacteristic
311C2×#63225C2311yescharacteristic
312C2×#63225C2311yescharacteristic
313C2×#63225C2311yescharacteristic
314C2×#63225C2311yescharacteristic
315C2×#63225C2311yescharacteristic
316C2×#63225C2311yescharacteristic
317C2×#63225C2311yescharacteristic
318C2×#63225C2311yescharacteristic
319C2×#63225C2311yescharacteristic
320C2×#63225C2311yescharacteristic
321C2×#63225C2311yescharacteristic
322C2×#63225C2311yescharacteristic
323C2×#63225C2311yescharacteristic
324C2×C4×Dic17C2311yescharacteristic
325C2×C4×Dic17C2311yescharacteristic
326C2×C4×Dic17C2311yescharacteristic
327#10587581—42no—
328#10587580—42no—
329#10587572—42no—
330#10587570—42no—
331#10587570—42no—
332#10587570—42no—
333#10587570—42no—
334#10587570—42no—
335#10587569—42no—
336#10587568—42no—
337#10587568—42no—
338#10587567—42no—
339C17×#95C2311yescharacteristic
340C17×#95C2311yescharacteristic
341C17×#95C2311yescharacteristic
342C17×#95C2311yescharacteristic
343C17×#95C2311yescharacteristic
344C17×#95C2311yescharacteristic
345C17×#95C2311yescharacteristic
346C17×#95C2311yescharacteristic
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
369#10587502C2311yescharacteristic
370#10587502C2311yescharacteristic
371#10587502C2311yescharacteristic
372#10587502C2311yescharacteristic
373#10587502C2311yescharacteristic
374#10587502C2311yescharacteristic
375C24×C17C2411yescharacteristic
376C24×C17C2411yescharacteristic
377C24×C17C2411yescharacteristic
378C23×D17—22no—
379C23×D17—22no—
380C23×D17—22no—
381C23×D17—22no—
382C23×D17—22no—
383C23×D17—41no—
384C23×D17—41no—
385C23×D17C2411yescharacteristic
386C23×D17C2411yescharacteristic
387C23×D17C2411yescharacteristic
388C23×D17C2411yescharacteristic
389C2×D4×C17—22no—
390C2×D4×C17—22no—
391C2×D4×C17—22no—
392C2×D4×C17—22no—
393C2×D4×C17—22no—
394C2×D4×C17—22no—
395C2×D4×C17—41no—
396C2×D4×C17—41no—
397C2×D4×C17—41no—
398C22×C4×C17—22no—
399C22×C4×C17—22no—
400C22×C4×C17—22no—
401C22×C4×C17—22no—
402C22×C4×C17—22no—
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×C17C2411yescharacteristic
411C22×C4×C17C2411yescharacteristic
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
422C2×C22⋊D17—22no—
423C2×C22⋊D17—22no—
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⋊D17—41no—
443C2×C22⋊D17—41no—
444C2×C22⋊D17—41no—
445C2×C22⋊D17—41no—
446C2×C22⋊D17—41no—
447C2×C22⋊D17—41no—
448C2×C22⋊D17—41no—
449C2×C22⋊D17—41no—
450C2×C22⋊D17—41no—
451C2×C22⋊D17—41no—
452C22×Dic17—22no—
453C22×Dic17—22no—
454C22×Dic17—41no—
455C22×Dic17—41no—
456C22×Dic17—41no—
457C22×Dic17—41no—
458C22×Dic17—41no—
459C22×Dic17—41no—
460C22×Dic17—41no—
461C22×Dic17—41no—
462C22×Dic17—41no—
463C22×Dic17#4114yes—
464C22×Dic17C2411yescharacteristic
465C22×Dic17C2411yescharacteristic
466C22×Dic17C2411yescharacteristic
467C22×Dic17C2411yescharacteristic
468C22×Dic17C2411yescharacteristic
469C22×Dic17C2411yescharacteristic
470C22×Dic17C2411yescharacteristic
471C22×Dic17C2411yescharacteristic
472C22×Dic17C2411yescharacteristic
473C22×Dic17C2411yescharacteristic
474C22×Dic17C2411yescharacteristic
475C22×Dic17C2411yescharacteristic
476C2×D68—22no—
477C2×D68—22no—
478C2×D68—22no—
479C2×D68—22no—
480C2×D68—41no—
481C2×D68—41no—
482C2×D68—41no—
483C2×D68—41no—
484C2×D68—41no—
485C2×D68—41no—
486C2×D68—41no—
487C2×D68—41no—
488C2×D68—41no—
489C2×D68—41no—
490C2×D68—41no—
491C2×C4×D17—22no—
492C2×C4×D17—22no—
493C2×C4×D17—22no—
494C2×C4×D17—22no—
495C2×C4×D17—22no—
496C2×C4×D17—22no—
497C2×C4×D17—22no—
498C2×C4×D17—22no—
499C2×C4×D17—41no—
500C2×C4×D17—41no—
501C2×C4×D17—41no—
502C2×C4×D17—41no—
503C2×C4×D17—416no—
504C2×C4×D17—41no—
505C2×C4×D17—41no—
506C2×C4×D17—41no—
507C2×C4×D17—41no—
508C2×C4×D17—41no—
509C2×C4×D17—41no—
510C4⋊C4×C17—22no—
511C4⋊C4×C17—22no—
512C4⋊C4×C17—41no—
513C4⋊C4×C17—41no—
514C4⋊C4×C17—41no—
515C4⋊C4×C17—41no—
516C4⋊C4×C17—41no—
517C4⋊C4×C17—41no—
518C22⋊C4×C17—22no—
519C22⋊C4×C17—22no—
520C22⋊C4×C17—22no—
521C22⋊C4×C17—22no—
522C22⋊C4×C17—22no—
523C22⋊C4×C17—22no—
524C22⋊C4×C17—41no—
525C22⋊C4×C17—41no—
526C22⋊C4×C17—41no—
527C22⋊C4×C17—41no—
528C22⋊C4×C17—41no—
529C42×C17—41no—
530C22⋊Dic17—22no—
531C22⋊Dic17—22no—
532C22⋊Dic17—22no—
533C22⋊Dic17—22no—
534C22⋊Dic17—41no—
535C22⋊Dic17—41no—
536C22⋊Dic17—41no—
537C22⋊Dic17—41no—
538C22⋊Dic17—41no—
539#63227—22no—
540#63227—22no—
541#63227—22no—
542#63227—22no—
543#63227—22no—
544#63227—22no—
545#63227—22no—
546#63227—22no—
547#63227—22no—
548#63227—22no—
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#63227—41no—
564#63227—41no—
565#63227—41no—
566#63227—41no—
567#63227—41no—
568#63227—41no—
569#63227—41no—
570#63227—41no—
571C4⋊Dic17—22no—
572C4⋊Dic17—22no—
573C4⋊Dic17—41no—
574C4⋊Dic17—41no—
575C4⋊Dic17—41no—
576C4⋊Dic17—41no—
577C4⋊Dic17—41no—
578C4⋊Dic17—41no—
579#63225—22no—
580#63225—22no—
581#63225—41no—
582#63225—41no—
583#63225—41no—
584#63225—41no—
585#63225—41no—
586#63225—41no—
587#63225—41no—
588#63225—41no—
589#63225—41no—
590#63225—41no—
591#63225—41no—
592#63225—41no—
593C4×Dic17—41no—
594C4×Dic17—41no—
595C4×Dic17—41no—
596#36727—171nomaximal, Sylow
597C23×C17—21no—
598C23×C17—21no—
599C23×C17—21no—
600C23×C17—21no—
601C23×C17—21no—
602C23×C17—21no—
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×C17C2×#4112yes—
616C23×C17H(5,𝔽2)12yes—
617C23×C17H(5,𝔽2)12yes—
618C23×C17C2511yescharacteristic
619C22×D17—28no—
620C22×D17—21no—
621C22×D17—21no—
622C22×D17—21no—
623C22×D17—21no—
624C22×D17—21no—
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×D17—21no—
644C22×D17—21no—
645C22×D17—21no—
646C22×D17—44no—
647C22×D17—44no—
648C22×D17—44no—
649C22×D17—44no—
650C22×D17—44no—
651C22×D17—44no—
652C22×D17H(5,𝔽2)12yes—
653C22×D172−1+412yes—
654D4×C17—44no—
655D4×C17—44no—
656D4×C17—82no—
657C2×C4×C17—28no—
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—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—82no—
693C2×C4×C17—82no—
694C2×C4×C17—82no—
695C2×C4×C17H(5,𝔽2)12yes—
696C2×C4×C17H(5,𝔽2)12yes—
697C22⋊D17—44no—
698C22⋊D17—44no—
699C22⋊D17—82no—
700C22⋊D17—82no—
701C22⋊D17—82no—
702C22⋊D17—82no—
703C22⋊D17—82no—
704C22⋊D17—82no—
705C22⋊D17—82no—
706C22⋊D17—82no—
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—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—44no—
742C2×Dic17—82no—
743C2×Dic17—82no—
744C2×Dic17—82no—
745C2×Dic17C2×#4112yes—
746C2×Dic17C2×#4112yes—
747D68—82no—
748D68—82no—
749D68—82no—
750D68—82no—
751D68—82no—
752C4×D17—44no—
753C4×D17—44no—
754C4×D17—44no—
755C4×D17—44no—
756C4×D17—82no—
757C4×D17—82no—
758#2847—171no—
759#2847—171no—
760#2748—171no—
761#2748—171no—
762#2748—171no—
763#2748—171no—
764#2741—171no—
765#2741—171no—
766#2741—171no—
767#2741—171no—
768#2703—171no—
769#2703—171no—
770#2703—171no—
771#2703—171no—
772#2671—171no—
773#2671—171no—
774#2671—171no—
775#2671—171no—
776#2656—171no—
777#2646—171no—
778#2443—171no—
779#2443—171no—
780#2443—171no—
781#2443D1711yescharacteristic, complemented
782#2424—171no—
783#2424—171no—
784#2424—171no—
785#2424—171no—
786#2325—171no—
787#2325—171no—
788C2×#380—171no—
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×C17—41no—
808C22×C17—41no—
809C22×C17#54014yes—
810C22×C17C22×#4111yescharacteristic
811C22×C17C2×H(5,𝔽2)11yescharacteristic
812C22×C17C2×H(5,𝔽2)11yescharacteristic
813C22×C17C2×H(5,𝔽2)11yescharacteristic
814C22×C17C2×H(5,𝔽2)11yescharacteristic
815C22×C17C2×H(5,𝔽2)11yescharacteristic
816C22×C17C2×2−1+411yescharacteristic
817C2×D17—22no—
818C2×D17—22no—
819C2×D17—22no—
820C2×D17—22no—
821C2×D17—22no—
822C2×D17—22no—
823C2×D17—416no—
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—
835C2×D17—41no—
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—
846C4×C17—22no—
847C4×C17—22no—
848C4×C17—41no—
849C4×C17—41no—
850C4×C17—41no—
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—41no—
861Dic17—41no—
862Dic17—41no—
863Dic17—41no—
864Dic17—41no—
865Dic17—41no—
866Dic17—41no—
867Dic17—41no—
868Dic17—41no—
869Dic17—41no—
870C24×C4—171no—
871C2×#123—171no—
872C2×#123—171no—
873C2×#123—171no—
874C2×#123C2×D1711yescharacteristic, complemented
875C2×#121—171no—
876C2×#121—171no—
877C2×#121—171no—
878C2×#121—171no—
879C2×#121—171no—
880C2×#121—171no—
881C2×#121—171no—
882C2×#121—171no—
883C2×#121—171no—
884C2×#121—171no—
885C2×#121—171no—
886C2×#121—171no—
887C2×#121—171no—
888C2×#121C2×D1711yescharacteristic
889C2×#120—171no—
890C2×#120—171no—
891C2×#120—171no—
892C2×#120—171no—
893C2×C4×D4—171no—
894C2×C4×D4—171no—
895C2×C4×D4—171no—
896C2×C4×D4C2×D1711yescharacteristic
897C22×C4⋊C4—171no—
898C22×C4⋊C4C2×D1711yescharacteristic
899C22×C22⋊C4—171no—
900C22×C22⋊C4—171no—
901#400—171no—
902#400—171no—
903#400—171no—
904#400—171no—
905#399—171no—
906#399—171no—
907#399—171no—
908#399—171no—
909#399—171no—
910#399—171no—
911#399—171no—
912#399C2×D1711yescharacteristic, complemented
913#398—171no—
914#398—171no—
915#398—171no—
916#398—171no—
917#398—171no—
918#398—171no—
919#398—171no—
920#398C2×D1711yescharacteristic, complemented
921#397—171no—
922#397—171no—
923#397—171no—
924#397C2×D1711yescharacteristic, complemented
925#396—171no—
926#396—171no—
927#396—171no—
928#396—171no—
929#394—171no—
930#394—171no—
931#394—171no—
932#394—171no—
933#394—171no—
934#394—171no—
935#394—171no—
936#394—171no—
937#394—171no—
938#394—171no—
939#394—171no—
940#394C2×D1711yescharacteristic, complemented
941#392—171no—
942#392—171no—
943#392—171no—
944#392—171no—
945#392—171no—
946#392—171no—
947#392—171no—
948#392—171no—
949#390—171no—
950#390—171no—
951#390—171no—
952#390—171no—
953#388—171no—
954#388—171no—
955#388—171no—
956#388—171no—
957#388—171no—
958#388—171no—
959#388—171no—
960#388—171no—
961#388—171no—
962#388—171no—
963#388—171no—
964#388C2×D1711yescharacteristic, complemented
965#387—171no—
966#387—171no—
967#387—171no—
968#387—171no—
969#387—171no—
970#387—171no—
971#387—171no—
972#387C2×D1711yescharacteristic, complemented
973#386—171no—
974#386—171no—
975#386—171no—
976#386—171no—
977#386—171no—
978#386—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#386—171no—
990#386—171no—
991#386—171no—
992#386—171no—
993#386—171no—
994#386C2×D1711yescharacteristic
995#386C2×D1711yescharacteristic
996#386C2×D1711yescharacteristic
997#385—171no—
998#385—171no—
999#385—171no—
1000#385—171no—
1001#385—171no—
1002#385—171no—
1003#385—171no—
1004#385—171no—
1005#385—171no—
1006#385—171no—
1007#385C2×D1711yescharacteristic
1008#385C2×D1711yescharacteristic, complemented
1009#380—171no—
1010#380—171no—
1011#380—171no—
1012#380—171no—
1013#380—171no—
1014#380—171no—
1015#380—171no—
1016#380—171no—
1017#380—171no—
1018#380—171no—
1019#380—171no—
1020#380—171no—
1021#380—171no—
1022#380—171no—
1023C2×#95—171no—
1024C2×#95—171no—
1025C2×C17—24no—
1026C2×C17—81no—
1027C2×C17—81no—
1028C2×C17C2×#54011yescharacteristic
1029C2×C17#349011yescharacteristic
1030C2×C17#349211yescharacteristic
1031C2×C17#353611yescharacteristic
1032C2×C17#353611yescharacteristic
1033C2×C17#353711yescharacteristic
1034C2×C17#353711yescharacteristic
1035D17—42no—
1036D17—42no—
1037D17—81no—
1038D17—81no—
1039C25—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×D4—171no—
1049C22×D4—171no—
1050C22×D4—171no—
1051C22×D4—171no—
1052C22×D4—171no—
1053C22×D4—171no—
1054C22×D4—171no—
1055C22×D4C22×D1711yescharacteristic
1056C22×D4C22×D1711yescharacteristic
1057C22×D4C22×D1711yescharacteristic
1058C23×C4—171no—
1059C23×C4—171no—
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—344no—
1069C23×C4—682no—
1070C23×C4—682no—
1071C23×C4C22×D1711yescharacteristic
1072C23×C4C22×D1711yescharacteristic
1073C23×C4C22×D1711yescharacteristic
1074C23×C4C22×D1711yescharacteristic
1075#123—42no—
1076#123—682no—
1077#123—682no—
1078#123—682no—
1079#121—42no—
1080#121—344no—
1081#121—344no—
1082#121—682no—
1083#121—682no—
1084#121—682no—
1085#121—682no—
1086#121—682no—
1087#121—682no—
1088#121—682no—
1089#121—682no—
1090#121—682no—
1091#121—682no—
1092#121—682no—
1093#120—682no—
1094#120—682no—
1095#120—682no—
1096#120—682no—
1097C4×D4—42no—
1098C4×D4—682no—
1099C4×D4—682no—
1100C4×D4—682no—
1101C2×C4⋊C4—42no—
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—171no—
1122C2×C4⋊C4—171no—
1123C2×C4⋊C4—171no—
1124C2×C4⋊C4—682no—
1125C2×C4⋊C4C22×D1711yescharacteristic
1126C2×C4⋊C4C22×D1711yescharacteristic
1127C2×C4⋊C4C22×D1711yescharacteristic
1128C2×C4⋊C4C22×D1711yescharacteristic
1129C2×C4⋊C4C22×D1711yescharacteristic
1130C2×C4⋊C4C22×D1711yescharacteristic
1131C2×C4⋊C4C22×D1711yescharacteristic
1132C2×C4⋊C4C22×D1711yescharacteristic
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⋊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—171no—
1173C2×C22⋊C4—171no—
1174C2×C22⋊C4—682no—
1175C2×C22⋊C4—682no—
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×C42—171no—
1188C2×C42—171no—
1189C2×C42—171no—
1190C2×C42C22×D1711yescharacteristic
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#95—171no—
1214#95—171no—
1215#95—171no—
1216#95—171no—
1217#95—171no—
1218#95—171no—
1219#95C22×D1711yescharacteristic
1220#95C22×D1711yescharacteristic
1221#95C22×D1711yescharacteristic
1222#95C22×D1711yescharacteristic
1223#95C22×D1711yescharacteristic
1224#95C22×D1711yescharacteristic
1225#95C22×D1711yescharacteristic
1226#95C22×D1711yescharacteristic
1227C17#3672711yescharacteristic, complemented, Sylow
1228C24—171no—
1229C24—171no—
1230C24—171no—
1231C24—171no—
1232C24—342no—
1233C24—342no—
1234C24—342no—
1235C24—342no—
1236C24—342no—
1237C24—681no—
1238C24—681no—
1239C24C23×D1711yescharacteristic
1240C24C23×D1711yescharacteristic
1241C24C23×D1711yescharacteristic
1242C2×D4—22no—
1243C2×D4—22no—
1244C2×D4—22no—
1245C2×D4—22no—
1246C2×D4—22no—
1247C2×D4—22no—
1248C2×D4—41no—
1249C2×D4—41no—
1250C2×D4—41no—
1251C2×D4—342no—
1252C2×D4—342no—
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—342no—
1264C2×D4—342no—
1265C2×D4—342no—
1266C2×D4—342no—
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×D4—681no—
1278C2×D4—681no—
1279C2×D4—681no—
1280C2×D4—681no—
1281C2×D4—681no—
1282C2×D4—681no—
1283C2×D4—681no—
1284C2×D4—681no—
1285C2×D4—681no—
1286C2×D4—681no—
1287C2×D4—681no—
1288C2×D4—681no—
1289C2×D4—681no—
1290C2×D4—681no—
1291C2×D4—681no—
1292C2×D4—681no—
1293C2×D4—681no—
1294C2×D4—681no—
1295C2×D4—681no—
1296C22×C4—22no—
1297C22×C4—22no—
1298C22×C4—22no—
1299C22×C4—22no—
1300C22×C4—22no—
1301C22×C4—41no—
1302C22×C4—41no—
1303C22×C4—41no—
1304C22×C4—41no—
1305C22×C4—41no—
1306C22×C4—41no—
1307C22×C4—41no—
1308C22×C4—171no—
1309C22×C4—171no—
1310C22×C4—174no—
1311C22×C4—171no—
1312C22×C4—171no—
1313C22×C4—171no—
1314C22×C4—171no—
1315C22×C4—171no—
1316C22×C4—171no—
1317C22×C4—171no—
1318C22×C4—171no—
1319C22×C4—171no—
1320C22×C4—171no—
1321C22×C4—342no—
1322C22×C4—342no—
1323C22×C4—342no—
1324C22×C4—342no—
1325C22×C4—342no—
1326C22×C4—342no—
1327C22×C4—342no—
1328C22×C4—342no—
1329C22×C4—342no—
1330C22×C4—342no—
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—6816no—
1342C22×C4—681no—
1343C22×C4—681no—
1344C22×C4—681no—
1345C22×C4—681no—
1346C22×C4—681no—
1347C22×C4—681no—
1348C22×C4—681no—
1349C22×C4—681no—
1350C22×C4—681no—
1351C22×C4C23×D1711yescharacteristic
1352C22×C4C23×D1711yescharacteristic
1353C22×C4C23×D1711yescharacteristic
1354C22×C4C23×D1711yescharacteristic
1355C22×C4C23×D1711yescharacteristic
1356C22×C4C23×D1711yescharacteristic
1357C22×C4C23×D1711yescharacteristic
1358C22×C4C23×D1711yescharacteristic
1359C22×C4C23×D1711yescharacteristic
1360C22×C4C23×D1711yescharacteristic
1361C22×C4C23×D1711yescharacteristic
1362C22×C4C23×D1711yescharacteristic
1363C4⋊C4—22no—
1364C4⋊C4—22no—
1365C4⋊C4—41no—
1366C4⋊C4—41no—
1367C4⋊C4—41no—
1368C4⋊C4—41no—
1369C4⋊C4—41no—
1370C4⋊C4—41no—
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⋊C4—681no—
1385C4⋊C4—681no—
1386C4⋊C4—681no—
1387C4⋊C4—681no—
1388C4⋊C4—681no—
1389C4⋊C4—681no—
1390C4⋊C4—681no—
1391C4⋊C4—681no—
1392C4⋊C4—681no—
1393C22⋊C4—22no—
1394C22⋊C4—22no—
1395C22⋊C4—22no—
1396C22⋊C4—22no—
1397C22⋊C4—22no—
1398C22⋊C4—22no—
1399C22⋊C4—41no—
1400C22⋊C4—41no—
1401C22⋊C4—41no—
1402C22⋊C4—41no—
1403C22⋊C4—41no—
1404C22⋊C4—342no—
1405C22⋊C4—342no—
1406C22⋊C4—342no—
1407C22⋊C4—342no—
1408C22⋊C4—342no—
1409C22⋊C4—342no—
1410C22⋊C4—342no—
1411C22⋊C4—342no—
1412C22⋊C4—342no—
1413C22⋊C4—342no—
1414C22⋊C4—342no—
1415C22⋊C4—342no—
1416C22⋊C4—342no—
1417C22⋊C4—342no—
1418C22⋊C4—681no—
1419C22⋊C4—681no—
1420C22⋊C4—681no—
1421C22⋊C4—681no—
1422C22⋊C4—681no—
1423C22⋊C4—681no—
1424C22⋊C4—681no—
1425C22⋊C4—681no—
1426C22⋊C4—681no—
1427C22⋊C4—681no—
1428C22⋊C4—681no—
1429C22⋊C4—681no—
1430C22⋊C4—681no—
1431C22⋊C4—681no—
1432C22⋊C4—681no—
1433C22⋊C4—681no—
1434C22⋊C4—681no—
1435C22⋊C4—681no—
1436C22⋊C4—681no—
1437C22⋊C4—681no—
1438C22⋊C4—681no—
1439C22⋊C4—681no—
1440C22⋊C4—681no—
1441C22⋊C4—681no—
1442C22⋊C4—681no—
1443C22⋊C4—681no—
1444C22⋊C4—681no—
1445C42—41no—
1446C42—681no—
1447C42—681no—
1448C42—681no—
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—21no—
1463C23—21no—
1464C23—21no—
1465C23—21no—
1466C23—21no—
1467C23—172no—
1468C23—172no—
1469C23—348no—
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—
1483C23—341no—
1484C23—341no—
1485C23—341no—
1486C23—341no—
1487C23—341no—
1488C23—341no—
1489C23—341no—
1490C23—341no—
1491C23—341no—
1492C23—341no—
1493C23—341no—
1494C23—341no—
1495C23—341no—
1496C23—684no—
1497C23—684no—
1498C23—684no—
1499C23—684no—
1500C23—684no—
1501C23—684no—
1502C23#1058769112yes—
1503C23#41×D1712yes—
1504C23#1058769612yes—
1505C23C24×D1711yescharacteristic
1506D4—44no—
1507D4—44no—
1508D4—82no—
1509D4—684no—
1510D4—684no—
1511D4—1362no—
1512D4—1362no—
1513D4—1362no—
1514D4—1362no—
1515D4—1362no—
1516D4—1362no—
1517D4—1362no—
1518D4—1362no—
1519D4—1362no—
1520D4—1362no—
1521D4—1362no—
1522D4—1362no—
1523D4—1362no—
1524C2×C4—28no—
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—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—21no—
1559C2×C4—82no—
1560C2×C4—82no—
1561C2×C4—82no—
1562C2×C4—172no—
1563C2×C4—172no—
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—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—684no—
1599C2×C4—684no—
1600C2×C4—684no—
1601C2×C4—684no—
1602C2×C4—684no—
1603C2×C4—1362no—
1604C2×C4—1362no—
1605C2×C4—1362no—
1606C2×C4—1362no—
1607C2×C4—1362no—
1608C2×C4#1058769112yes—
1609C2×C4#1058769612yes—
1610C22—22no—
1611C22—22no—
1612C22—22no—
1613C22—22no—
1614C22—22no—
1615C22—22no—
1616C22—41no—
1617C22—41no—
1618C22—41no—
1619C22—41no—
1620C22—41no—
1621C22—41no—
1622C22—41no—
1623C22—41no—
1624C22—41no—
1625C22—41no—
1626C22—41no—
1627C22—41no—
1628C22—41no—
1629C22—41no—
1630C22—342no—
1631C22—342no—
1632C22—342no—
1633C22—342no—
1634C22—342no—
1635C22—342no—
1636C22—6816no—
1637C22—681no—
1638C22—681no—
1639C22—681no—
1640C22—681no—
1641C22—681no—
1642C22—681no—
1643C22—681no—
1644C22—681no—
1645C22—681no—
1646C22—681no—
1647C22—681no—
1648C22—681no—
1649C22—681no—
1650C22—681no—
1651C22—681no—
1652C22—681no—
1653C22—681no—
1654C22—681no—
1655C22—681no—
1656C22—681no—
1657C22—681no—
1658C22—681no—
1659C22#1176341114yes—
1660C22C2×#41×D1711yescharacteristic
1661C22H(5,𝔽2)×D1711yescharacteristic
1662C22C2×#1058769111yescharacteristic
1663C22C2×#1058769111yescharacteristic
1664C22C2×#1058769611yescharacteristic
1665C22C2×#1058769611yescharacteristic
1666C222−1+4×D1711yescharacteristic
1667C4—22no—
1668C4—22no—
1669C4—41no—
1670C4—41no—
1671C4—41no—
1672C4—41no—
1673C4—41no—
1674C4—41no—
1675C4—41no—
1676C4—41no—
1677C4—41no—
1678C4—41no—
1679C4—342no—
1680C4—342no—
1681C4—681no—
1682C4—681no—
1683C4—681no—
1684C4—681no—
1685C4—681no—
1686C4—681no—
1687C4—681no—
1688C4—681no—
1689C4—681no—
1690C4—681no—
1691C2—24no—
1692C2—81no—
1693C2—81no—
1694C2—682no—
1695C2—682no—
1696C2—1361no—
1697C2—1361no—
1698C2C2×#1176341111yescharacteristic
1699C2#1454246711yescharacteristic
1700C2#1454248911yescharacteristic
1701C2#1454300011yescharacteristic
1702C2#1454300711yescharacteristic
1703C2#1454301511yescharacteristic
1704C2#1454302011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2443C2
hypercenter#2443D17
hypocenterC17#36727
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2443

Complements

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

NH ≅ G/Ntype
1. #14537065C2semidirect
2. #14537065C2semidirect
3. #14535998C2semidirect
4. #14535996C2semidirect
5. #14535993C2semidirect
6. #14535992C2semidirect
7. #14535905C2semidirect
8. #14535901C2semidirect
9. #14535897C2semidirect
10. #14535893C2semidirect
11. #14535433C2semidirect
12. #14535429C2semidirect
13. #14535425C2semidirect
14. #14535421C2semidirect
15. #14535026C2semidirect
16. #14535025C2semidirect
17. #14535023C2semidirect
18. #14535020C2semidirect
19. #14534888C2semidirect
20. #14534756C2semidirect
21. #14532525C2semidirect
22. #14532519C2semidirect
23. #14532517C2semidirect
24. #14532326C2semidirect
25. #14532322C2semidirect
26. #14532318C2semidirect
27. #14532314C2semidirect
28. #14531485C2semidirect
29. #14531482C2semidirect
30. C2×#11762666C2semidirect
31. C17×#2443C2semidirect
33. C2×#10587580C22semidirect
34. C2×#10587572C22semidirect
35. C2×#10587569C22semidirect
59. #11762750C22semidirect
60. #11762750C22semidirect
61. #11762749C22semidirect
62. #11762747C22semidirect
63. #11762746C22semidirect
64. #11762745C22semidirect
65. #11762745C22semidirect
66. #11762745C22semidirect
67. #11762744C22semidirect
68. #11762744C22semidirect
69. #11762744C22semidirect
70. #11762743C22semidirect
71. #11762743C22semidirect
72. #11762742C22semidirect
73. #11762742C22semidirect
74. #11762741C22semidirect
75. #11762740C22semidirect
76. #11762739C22semidirect
77. #11762736C22semidirect
78. #11762735C22semidirect
79. #11762734C22semidirect
88. #11762726C22semidirect
91. #11762725C22semidirect
92. #11762725C22semidirect
98. #11762718C22semidirect
99. #11762718C22semidirect
101. #11762717C22semidirect
102. #11762717C22semidirect
107. #11762703C22semidirect
108. #11762702C22semidirect
110. #11762701C22semidirect
112. #11762700C22semidirect
114. #11762699C22semidirect
116. #11762698C22semidirect
117. #11762697C22semidirect
118. #11762696C22semidirect
119. #11762695C22semidirect
120. #11762694C22semidirect
121. #11762693C22semidirect
122. #11762692C22semidirect
123. #11762691C22semidirect
124. #11762690C22semidirect
130. #11762688C22semidirect
139. #11762686C22semidirect
144. #11762685C22semidirect
145. #11762685C22semidirect
147. #11762684C22semidirect
148. #11762683C22semidirect
149. #11762683C22semidirect
151. #11762682C22semidirect
153. #11762681C22semidirect
154. #11762680C22semidirect
155. #11762680C22semidirect
172. C2×C17×#123C22semidirect
176. C17×#399C22semidirect
177. C17×#398C22semidirect
178. C17×#397C22semidirect
179. C17×#394C22semidirect
180. C17×#388C22semidirect
181. C17×#387C22semidirect
186. C17×#385C22semidirect
781. #2443D17semidirect
874. C2×#123C2×D17semidirect
912. #399C2×D17semidirect
920. #398C2×D17semidirect
924. #397C2×D17semidirect
940. #394C2×D17semidirect
964. #388C2×D17semidirect
972. #387C2×D17semidirect
1008. #385C2×D17semidirect
1227. C17#36727semidirect

Maximal subgroups

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

subgroupindex
#145370652
#145359982
#145359962
#145359932
#145359922
#145359052
#145359012
#145358972
#145358932
#145354332
#145354292
#145354252
#145354212
#145350262
#145350252
#145350232
#145350202
#145348882
#145347562
#145325252
#145325192
#145325172
#145323262
#145323222
#145323182
#145323142
#145314852
#145314822
C2×#117626662
C17×#24432
#3672717