Finite Group Databasebeta

← #17899546

Subgroups — #17899546

Order 4352.

1882 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14542338C211yesmaximal, characteristic
2#14537942C212yesmaximal, complemented
3#14537942C212yesmaximal, complemented
4#14537940C212yesmaximal, complemented
5#14537931C212yesmaximal, complemented
6#14537921C212yesmaximal, complemented
7#14537920C212yesmaximal, complemented
8#14537906C212yesmaximal, complemented
9#14537893C212yesmaximal, complemented
10#14537730C211yesmaximal, characteristic, complemented
11#14537717C211yesmaximal, characteristic, complemented
12M16×C22⋊D17C211yesmaximal, characteristic, complemented
13#14537509C211yesmaximal, characteristic, complemented
14#14537508C211yesmaximal, characteristic, complemented
15#14537478C211yesmaximal, characteristic, complemented
16#14537477C211yesmaximal, characteristic, complemented
17C2×C8×C22⋊D17C211yesmaximal, characteristic, complemented
18#14537442C211yesmaximal, characteristic, complemented
19#14537441C211yesmaximal, characteristic, complemented
20#14537427C211yesmaximal, characteristic, complemented
21#14537351C211yesmaximal, characteristic, complemented
22D17×#424C211yesmaximal, characteristic, complemented
23C2×C17×#424C211yesmaximal, characteristic, complemented
24C2×#10587593C2211yescharacteristic
25C2×#10587587C2211yescharacteristic
26C2×M16×D17C2211yescharacteristic
27C22×C8×D17C2211yescharacteristic
28#11763527C411yescharacteristic
29#11763522C411yescharacteristic
30#11763514C411yescharacteristic
31#11763507C411yescharacteristic
32#11763503C411yescharacteristic
33#11763498C411yescharacteristic
34#11763494C411yescharacteristic
35#11763492C412yes—
36#11763485C412yes—
37#11763483C412yes—
38#11763460C411yescharacteristic
39#11763449C412yes—
40#11763362C2211yescharacteristic
41#11763343C2212yes—
42#11763337C2212yes—
43#11763337C2212yes—
44#11763321C2211yescharacteristic
45#11763320C2211yescharacteristic
46C4×#63252C2212yes—
47#11763277C2211yescharacteristic
48C2×C4×C22⋊D17C2211yescharacteristic
49#117×D17C2211yescharacteristic
50#11762938C2212yescomplemented
51#11762938C2212yescomplemented
52#11762938C2212yescomplemented
53#11762938C2212yescomplemented
54#11762936C2212yescomplemented
55#11762933C2212yescomplemented
56#11762933C2212yescomplemented
57#11762933C2212yescomplemented
58#11762886C2212yescomplemented
59#11762885C2212yes—
60#11762885C2212yescomplemented
61#11762880C2212yes—
62#11762880C2212yescomplemented
63#11762880C2212yescomplemented
64#11762880C2212yescomplemented
65#11762879C2212yescomplemented
66#11762879C2212yescomplemented
67#11762879C2212yescomplemented
68#11762879C2212yescomplemented
69#11762878C2212yes—
70#11762878C2212yescomplemented
71#11762874C2212yescomplemented
72#11762874C2212yescomplemented
73#11762874C2212yescomplemented
74C8×C22⋊D17C2212yes—
75C8×C22⋊D17C2211yescharacteristic
76C8×C22⋊D17C2211yescharacteristic
77C8×C22⋊D17C2211yescharacteristic
78C8×C22⋊D17C2211yescharacteristic
79C8×C22⋊D17C2211yescharacteristic
80C8×C22⋊D17C2211yescharacteristic
81C8×C22⋊D17C2211yescharacteristic
82C8×C22⋊D17C2211yescharacteristic
83C8×C22⋊D17C2212yescomplemented
84C8×C22⋊D17C2212yescomplemented
85C8×C22⋊D17C2212yescomplemented
86#11762870C2212yescomplemented
87#11762870C2212yescomplemented
88#11762869C2212yescomplemented
89#11762869C2212yescomplemented
90#11762869C2212yescomplemented
91#11762869C2212yescomplemented
92#11762866C2212yescomplemented
93#11762865C2212yescomplemented
94#11762862C2212yescomplemented
95#11762861C2212yescomplemented
96#11762861C2212yescomplemented
97#11762861C2212yescomplemented
98#11762837C2211yescharacteristic
99#11762836C2211yescharacteristic
100#11762836C2211yescharacteristic
101#11762835C2211yescharacteristic
102#11762834C2212yescomplemented
103#11762834C2212yescomplemented
104#11762834C2212yescomplemented
105#11762834C2212yescomplemented
106#11762832C2211yescharacteristic
107#11762831C2212yescomplemented
108C2×#10587485C2211yescharacteristic
109C4⋊C8×D17C2212yescomplemented
110C4⋊C8×D17C2212yescomplemented
111C4⋊C8×D17C2212yescomplemented
112#11762777C2211yescharacteristic
113#11762775C2211yescharacteristic
114#11762773C2211yescharacteristic
115#11762772C2211yescharacteristic
116C2×C22⋊#3622C2211yescharacteristic
117C2×#10587491C2211yescharacteristic
118#11762767C2211yescharacteristic
119#11762765C2211yescharacteristic
120#11762765C2211yescharacteristic
121#11762764C2211yescharacteristic
122M16×Dic17C2211yescharacteristic
123C2×C8×Dic17C2211yescharacteristic
124C22×M16×C17C2211yescharacteristic
125C23×C8×C17C2211yescharacteristic
126C2×C17×#117C2211yescharacteristic
127C17×#424C2211yescharacteristic
128C17×#424C2211yescharacteristic
129C17×#424C2211yescharacteristic
130C17×#424C2211yescharacteristic
131C17×#424C2212yescomplemented
132C17×#424C2212yescomplemented
133C2×C17×C4⋊C8C2212yescomplemented
134C2×C17×C4⋊C8C2212yescomplemented
135C23×C4×C17C2311yescharacteristic
136C22×C22⋊D17C2×C411yescharacteristic
137C2×#63252C2×C412yes—
138C2×#63252C2311yescharacteristic
139C22×C4×D17C2311yescharacteristic
140C2×M16×C17—42no—
141C2×M16×C17C2311yescharacteristic
142C2×M16×C17C2311yescharacteristic
143C2×M16×C17C2312yes—
144C22×C8×C17—42no—
145C22×C8×C17C2311yescharacteristic
146C22×C8×C17C2311yescharacteristic
147C22×C8×C17C2311yescharacteristic
148C22×C8×C17C2311yescharacteristic
149C22×C8×C17C2311yescharacteristic
150C22×C8×C17C2311yescharacteristic
151C22×C8×C17C2312yes—
152C17×#117C2×C412yes—
153C17×#117C2×C411yescharacteristic
154C17×#117C2×C411yescharacteristic
155C17×#117C2311yescharacteristic
156C17×#117C2311yescharacteristic
157C17×#117C2312yes—
158C2×C4⋊C4×C17C2×C411yescharacteristic
159C2×C4⋊C4×C17C2×C411yescharacteristic
160C2×C22⋊C4×C17C2×C412yes—
161C2×C42×C17C2312yes—
162#10587639C2×C412yes—
163C2×C22⋊Dic17C2×C411yescharacteristic
164#10587616C2×C411yescharacteristic
165#10587616C2×C411yescharacteristic
166#10587616C2×C412yes—
167#10587615C2×C412yes—
168#10587615C2×C412yes—
169#10587615C2×C412yes—
170C4×C22⋊D17C2×C411yescharacteristic
171C4×C22⋊D17C2×C412yes—
172C4×C22⋊D17C2×C411yescharacteristic
173C4×C22⋊D17C2×C411yescharacteristic
174C4×C22⋊D17C2×C412yes—
175C4×C22⋊D17C2×C411yescharacteristic
176C4×C22⋊D17C2311yescharacteristic
177C4×C22⋊D17C2311yescharacteristic
178C4×C22⋊D17C2311yescharacteristic
179C4×C22⋊D17C2311yescharacteristic
180C4×C22⋊D17C2312yes—
181C4×C22⋊D17C2312yes—
182C2×#63227C2×C411yescharacteristic
183#10587612C2×C412yes—
184#10587612C2311yescharacteristic
185#10587610C2×C412yes—
186#10587610C2×C411yescharacteristic
187#10587610C2×C411yescharacteristic
188C2×#63225C2×C411yescharacteristic
189C2×C4×Dic17C2311yescharacteristic
190C2×#63223C2311yescharacteristic
191C2×#63223C2311yescharacteristic
192C22×#3622C2311yescharacteristic
193C22×#3622C2311yescharacteristic
194#10587593—42no—
195M16×D17—42no—
196#10587587—42no—
197C2×#63218C2312yes—
198C2×#63218C2312yes—
199C2×#63218C2312yes—
200C2×C8×D17—42no—
201C2×C8×D17C2311yescharacteristic
202C2×C8×D17C2311yescharacteristic
203C2×C8×D17C2311yescharacteristic
204C2×C8×D17C2311yescharacteristic
205C2×C8×D17C2312yes—
206C2×C8×D17C2312yes—
207C2×C8×D17C2312yes—
208#10587584C2×C412yes—
209#10587584C2×C412yes—
210#10587583C2×C411yescharacteristic
211#10587583C2×C411yescharacteristic
212#10587582C2×C412yes—
213#10587582C2×C412yes—
214#10587581C2×C411yescharacteristic
215#10587581C2×C411yescharacteristic
216#10587580C2×C412yes—
217#10587580C2×C412yes—
218#10587579C2×C411yescharacteristic
219#10587579C2×C411yescharacteristic
220#10587578C2×C411yescharacteristic
221#10587578C2×C411yescharacteristic
222C4⋊C4×D17C2×C411yescharacteristic
223C4⋊C4×D17C2×C411yescharacteristic
224#10587576C2×C411yescharacteristic
225#10587576C2×C411yescharacteristic
226#10587575C2×C412yes—
227#10587575C2×C412yes—
228#10587574C2×C411yescharacteristic
229#10587574C2×C411yescharacteristic
230#10587573C2×C411yescharacteristic
231#10587573C2×C411yescharacteristic
232#10587572C2×C412yes—
233#10587571C2×C412yes—
234#10587571C2×C412yes—
235#10587570C2×C412yes—
236#10587570C2×C412yes—
237#10587569C2×C412yes—
238#10587569C2×C412yes—
239#10587568C2×C412yes—
240#10587567C2×C412yes—
241#10587567C2×C412yes—
242C22⋊C4×D17C2×C412yes—
243#10587565C2×C412yes—
244#10587565C2×C412yes—
245#10587564C2×C412yes—
246#10587564C2×C412yes—
247#10587563C2×C412yes—
248#10587562C2×C412yes—
249#10587562C2×C412yes—
250#10587561C2×C412yes—
251C4×D68C2×C412yes—
252C4×D68C2312yes—
253C4×D68C2312yes—
254#10587558C2×C412yes—
255#10587558C2×C412yes—
256#10587558C2312yes—
257#10587558C2312yes—
258C42×D17C2312yes—
259C42×D17C2312yes—
260#10587556C2×C412yes—
261C4×Dic34C2×C412yes—
262C4×Dic34C2312yes—
263C4×Dic34C2312yes—
264C17×C4⋊C8C2312yes—
265C17×C4⋊C8C2312yes—
266C17×C4⋊C8C2312yes—
267C17×C4⋊C8C2312yes—
268C17×C4⋊C8C2312yes—
269C17×C4⋊C8C2312yes—
270C17×C4⋊C8C2312yes—
271C17×C4⋊C8C2312yes—
272C22⋊#3622C2311yescharacteristic
273C22⋊#3622C2311yescharacteristic
274C22⋊#3622C2311yescharacteristic
275C22⋊#3622C2311yescharacteristic
276C22⋊#3622C2312yes—
277C22⋊#3622C2312yes—
278#10587491C2311yescharacteristic
279#10587491C2311yescharacteristic
280#10587491C2311yescharacteristic
281#10587491C2311yescharacteristic
282#10587491C2312yes—
283#10587491C2312yes—
284#10587491C2312yes—
285#10587491C2312yes—
286#10587491C2312yes—
287#10587491C2312yes—
288#10587486C2312yes—
289#10587486C2312yes—
290#10587486C2312yes—
291#10587485C2311yescharacteristic
292#10587485C2312yes—
293#10587485C2312yes—
294#10587485C2312yes—
295#10587485C2312yes—
296#10587485C2312yes—
297#10587485C2311yescharacteristic
298#10587485C2311yescharacteristic
299#10587485C2311yescharacteristic
300#10587485C2312yes—
301C8×Dic17C2311yescharacteristic
302C8×Dic17C2311yescharacteristic
303C8×Dic17C2311yescharacteristic
304C8×Dic17C2311yescharacteristic
305C8×Dic17C2312yes—
306C8×Dic17C2312yes—
307C8×Dic17C2312yes—
308C4⋊#3622C2312yes—
309C4⋊#3622C2312yes—
310C4⋊#3622C2312yes—
311C4⋊#3622C2312yes—
312#10587474C2312yes—
313#10587474C2312yes—
314C4×#3622C2312yes—
315C4×#3622C2312yes—
316C24×C17C22×C411yescharacteristic
317C23×D17C22×C411yescharacteristic
318C22×C4×C17—22no—
319C22×C4×C17—22no—
320C22×C4×C17C22×C412yes—
321C22×C4×C17C22×C411yescharacteristic
322C22×C4×C17C22×C411yescharacteristic
323C22×C4×C17C22×C411yescharacteristic
324C22×C4×C17C22×C412yes—
325C22×C4×C17C2411yescharacteristic
326C22×C4×C17C2411yescharacteristic
327C22×C4×C17C2411yescharacteristic
328C2×C22⋊D17—24no—
329C2×C22⋊D17C22×C412yes—
330C2×C22⋊D17C22×C412yes—
331C2×C22⋊D17C22×C411yescharacteristic
332C2×C22⋊D17C22×C411yescharacteristic
333C2×C22⋊D17C22×C411yescharacteristic
334C2×C22⋊D17C22×C412yes—
335C2×C22⋊D17C22×C411yescharacteristic
336C22×Dic17C22×C411yescharacteristic
337C22×Dic17C22×C411yescharacteristic
338C22×Dic17C22×C411yescharacteristic
339#63252—22no—
340#63252—22no—
341#63252—28no—
342C2×D68C22×C412yes—
343C2×D68C22×C411yescharacteristic
344C2×D68C22×C412yes—
345C2×C4×D17—22no—
346C2×C4×D17—22no—
347C2×C4×D17C22×C411yescharacteristic
348C2×C4×D17C22×C411yescharacteristic
349C2×C4×D17C22×C412yes—
350C2×C4×D17C22×C412yes—
351C2×C4×D17C22×C412yes—
352C2×C4×D17C22×C412yes—
353C2×C4×D17C2411yescharacteristic
354C2×C4×D17C2411yescharacteristic
355C2×C4×D17C2412yes—
356C2×Dic34C22×C412yes—
357C2×Dic34C22×C411yescharacteristic
358C2×Dic34C22×C412yes—
359M16×C17—22no—
360M16×C17—22no—
361M16×C17—42no—
362C2×C8×C17—22no—
363C2×C8×C17—22no—
364C2×C8×C17—41no—
365C2×C8×C17—41no—
366C2×C8×C17—41no—
367C2×C8×C17—41no—
368C2×C8×C17—42no—
369C2×C8×C17C2411yescharacteristic
370C2×C8×C17C2411yescharacteristic
371C2×C8×C17C2411yescharacteristic
372C2×C8×C17C2411yescharacteristic
373C2×C8×C17C2412yes—
374C2×C8×C17C2412yes—
375C4⋊C4×C17C22×C411yescharacteristic
376C4⋊C4×C17C22×C411yescharacteristic
377C4⋊C4×C17C22×C411yescharacteristic
378C4⋊C4×C17C22×C411yescharacteristic
379C4⋊C4×C17C22×C412yes—
380C4⋊C4×C17C22×C412yes—
381C22⋊C4×C17C22×C412yes—
382C22⋊C4×C17C22×C412yes—
383C22⋊C4×C17C22×C412yes—
384C22⋊C4×C17C22×C412yes—
385C42×C17C22×C412yes—
386C42×C17C22×C412yes—
387C42×C17C2412yes—
388C42×C17C2412yes—
389C22⋊Dic17C22×C412yes—
390C22⋊Dic17C22×C411yescharacteristic
391C22⋊Dic17C22×C412yes—
392C22⋊Dic17C22×C411yescharacteristic
393C22⋊Dic17C22×C412yes—
394C22⋊Dic17C22×C411yescharacteristic
395C22⋊Dic17C22×C411yescharacteristic
396#63227C22×C411yescharacteristic
397#63227C22×C412yes—
398#63227C22×C412yes—
399#63227C22×C412yes—
400#63227C22×C412yes—
401#63227C22×C412yes—
402#63227C22×C412yes—
403#63227C22×C412yes—
404#63227C22×C412yes—
405#63227C22×C412yes—
406#63227C22×C411yescharacteristic
407#63227C22×C411yescharacteristic
408#63227C22×C412yes—
409#63227C22×C411yescharacteristic
410C4⋊Dic17C22×C412yes—
411C4⋊Dic17C22×C412yes—
412C4⋊Dic17C22×C412yes—
413C4⋊Dic17C22×C412yes—
414C4⋊Dic17C22×C411yescharacteristic
415C4⋊Dic17C22×C411yescharacteristic
416#63225C22×C411yescharacteristic
417#63225C22×C412yes—
418#63225C22×C412yes—
419#63225C22×C412yes—
420#63225C22×C412yes—
421#63225C22×C412yes—
422#63225C22×C411yescharacteristic
423#63225C22×C412yes—
424#63225C22×C412yes—
425#63225C22×C412yes—
426#63225C22×C412yes—
427#63225C22×C411yescharacteristic
428#63225C22×C412yes—
429#63225C22×C411yescharacteristic
430C4×Dic17C22×C412yes—
431C4×Dic17C22×C412yes—
432C4×Dic17C22×C412yes—
433C4×Dic17C22×C412yes—
434C4×Dic17C22×C411yescharacteristic
435C4×Dic17C22×C411yescharacteristic
436C4×Dic17C2411yescharacteristic
437C4×Dic17C2412yes—
438C4×Dic17C2411yescharacteristic
439#63223—22no—
440#63223—22no—
441C2×#3622—22no—
442C2×#3622—22no—
443C2×#3622C2411yescharacteristic
444C2×#3622C2411yescharacteristic
445C2×#3622C2412yes—
446C2×#3622C2412yes—
447C2×#3622C2411yescharacteristic
448C2×#3622C2411yescharacteristic
449#63218—42no—
450#63218—42no—
451#63218—42no—
452C8×D17—41no—
453C8×D17—41no—
454C8×D17—41no—
455C8×D17—41no—
456C8×D17—42no—
457C8×D17—42no—
458C8×D17—42no—
459#60271—171nomaximal, Sylow
460C23×C17—22no—
461C23×C17—22no—
462C23×C17—41no—
463C23×C17C23×C411yescharacteristic
464C23×C17C23×C411yescharacteristic
465C23×C17C23×C411yescharacteristic
466C22×D17—22no—
467C22×D17—22no—
468C22×D17—41no—
469C22×D17C23×C412yes—
470C22×D17C23×C411yescharacteristic
471C22×D17C23×C411yescharacteristic
472C2×C4×C17—22no—
473C2×C4×C17—24no—
474C2×C4×C17—22no—
475C2×C4×C17—22no—
476C2×C4×C17—21no—
477C2×C4×C17—21no—
478C2×C4×C17—21no—
479C2×C4×C17—21no—
480C2×C4×C17—42no—
481C2×C4×C17C23×C411yescharacteristic
482C2×C4×C17C23×C412yes—
483C2×C4×C17C23×C412yes—
484C2×C4×C17C23×C412yes—
485C2×C4×C17C23×C412yes—
486C2×C4×C17C23×C411yescharacteristic
487C2×C4×C17C23×C411yescharacteristic
488C2×C4×C17H(5,𝔽2)12yes—
489C2×C4×C172−1+412yes—
490C2×C4×C17C2511yescharacteristic
491C22⋊D17—24no—
492C22⋊D17—24no—
493C22⋊D17—22no—
494C22⋊D17—22no—
495C22⋊D17—22no—
496C22⋊D17—42no—
497C22⋊D17#13114yescomplemented
498C2×Dic17—22no—
499C2×Dic17—22no—
500C2×Dic17—41no—
501C2×Dic17C23×C411yescharacteristic
502C2×Dic17C23×C412yes—
503C2×Dic17C23×C412yes—
504C2×Dic17C23×C412yes—
505C2×Dic17C23×C411yescharacteristic
506C2×Dic17C23×C411yescharacteristic
507C2×Dic17C23×C411yescharacteristic
508C2×Dic17C23×C411yescharacteristic
509C2×Dic17C23×C411yescharacteristic
510D68—24no—
511D68—22no—
512D68—42no—
513C4×D17—24no—
514C4×D17—22no—
515C4×D17—22no—
516C4×D17—21no—
517C4×D17—21no—
518C4×D17—22no—
519C4×D17—21no—
520C4×D17—21no—
521C4×D17—22no—
522C4×D17—24no—
523C4×D17—42no—
524C4×D17—42no—
525Dic34—22no—
526Dic34—24no—
527Dic34—42no—
528C8×C17—21no—
529C8×C17—21no—
530C8×C17—21no—
531C8×C17—21no—
532C8×C17—22no—
533C8×C17—22no—
534#3622—21no—
535#3622—21no—
536#3622—22no—
537#3622—21no—
538#3622—21no—
539#3622—22no—
540#3475—171no—
541#2994—172no—
542#2994—172no—
543#2994—172no—
544#2993—172no—
545#2992—172no—
546#2992—172no—
547#2990—172no—
548#2988—172no—
549#2962—171no—
550#2960—171no—
551D4×M16—171no—
552#2933—171no—
553#2933—171no—
554#2929—171no—
555#2929—171no—
556C2×C8×D4—171no—
557#2924—171no—
558#2924—171no—
559#2922—171no—
560#2906—171no—
561C2×#424—171no—
562C2×#424D1711yescharacteristic, complemented
563C22×C17—21no—
564C22×C17—21no—
565C22×C17—21no—
566C22×C17—21no—
567C22×C17—21no—
568C22×C17—21no—
569C22×C17—21no—
570C22×C17—44no—
571C22×C17#52012yes—
572C22×C17C2×#13112yes—
573C22×C17C24×C411yescharacteristic
574C2×D17—21no—
575C2×D17—21no—
576C2×D17—21no—
577C2×D17—22no—
578C2×D17—22no—
579C2×D17—21no—
580C2×D17—22no—
581C2×D17—21no—
582C2×D17—44no—
583C2×D17C2×#13112yes—
584C4×C17—21no—
585C4×C17—21no—
586C4×C17—22no—
587C4×C17—22no—
588C4×C17—22no—
589C4×C17—22no—
590C4×C17#52012yes—
591C4×C17C2×H(5,𝔽2)11yescharacteristic
592C4×C17C2×2−1+411yescharacteristic
593Dic17—22no—
594Dic17—21no—
595Dic17—21no—
596Dic17—22no—
597Dic17—21no—
598Dic17—21no—
599Dic17—22no—
600Dic17—21no—
601Dic17C2×#13112yes—
602C2×#131—171no—
603C2×#131—171no—
604C22×M16—171no—
605C22×M16C2×D1711yescharacteristic
606C23×C8—171no—
607C23×C8C2×D1711yescharacteristic
608#556—171no—
609#555—171no—
610#554—171no—
611#553—171no—
612#553—171no—
613#552—172no—
614#552—171no—
615#552—171no—
616#551—172no—
617#551—172no—
618#547—171no—
619#546—172no—
620#533—171no—
621#529—172no—
622#529—172no—
623#529—172no—
624#525—171no—
625#525—171no—
626C4×#41—171no—
627C4×#41—172no—
628C2×C4×D4—171no—
629C2×#117—171no—
630C2×#117C2×D1711yescharacteristic
631#446—172no—
632#446—172no—
633#446—172no—
634#446—172no—
635#446—172no—
636C8×Q8—172no—
637C8×Q8—172no—
638C8×Q8—172no—
639#436—172no—
640#436—172no—
641#436—172no—
642#435—172no—
643#435—172no—
644#435—172no—
645#435—172no—
646#435—172no—
647#435—172no—
648#435—172no—
649#435—172no—
650#435—172no—
651#435—172no—
652C8×D4—171no—
653C8×D4—171no—
654C8×D4—171no—
655C8×D4—171no—
656C8×D4—171no—
657C8×D4—171no—
658C8×D4—171no—
659C8×D4—171no—
660C8×D4—172no—
661C8×D4—172no—
662C8×D4—172no—
663C8×D4—172no—
664C8×D4—172no—
665C8×D4—172no—
666C8×D4—172no—
667#433—172no—
668#433—172no—
669#433—172no—
670#433—172no—
671#433—172no—
672#433—172no—
673#432—172no—
674#432—172no—
675#431—172no—
676#431—172no—
677#431—172no—
678#431—172no—
679#424—171no—
680#424—171no—
681#424—171no—
682#424—171no—
683#424—172no—
684#424—172no—
685#424—172no—
686#424—172no—
687#424C2×D1711yescharacteristic
688#424C2×D1711yescharacteristic
689#424C2×D1711yescharacteristic
690#424C2×D1711yescharacteristic
691#424C2×D1712yescomplemented
692#424C2×D1712yescomplemented
693#423—171no—
694#423—172no—
695C2×C4⋊C8—171no—
696C2×C4⋊C8—172no—
697C2×C4⋊C8—172no—
698C2×C4⋊C8—172no—
699C2×C4⋊C8C2×D1712yescomplemented
700C2×C4⋊C8C2×D1712yescomplemented
701#408—171no—
702#408—171no—
703#407—171no—
704#407—171no—
705C2×C22⋊C8—171no—
706C2×C22⋊C8—171no—
707#405—171no—
708#405—171no—
709#405—171no—
710#405—171no—
711C4×M16—171no—
712C2×C4×C8—171no—
713C2×C17—22no—
714C2×C17—22no—
715C2×C17—41no—
716C2×C17C2×#52011yescharacteristic
717C2×C17C22×#13111yescharacteristic
718C2×C17#357311yescharacteristic
719D17—22no—
720D17—42no—
721D17—41no—
722C2×#41—172no—
723C2×#41—171no—
724C22×D4—171no—
725C23×C4—171no—
726C23×C4C22×D1711yescharacteristic
727#131—682no—
728#131—682no—
729C2×M16—42no—
730C2×M16—171no—
731C2×M16—171no—
732C2×M16—172no—
733C2×M16—172no—
734C2×M16—172no—
735C2×M16—682no—
736C2×M16C22×D1711yescharacteristic
737C2×M16C22×D1711yescharacteristic
738C2×M16C22×D1712yes—
739C22×C8—42no—
740C22×C8—171no—
741C22×C8—171no—
742C22×C8—171no—
743C22×C8—171no—
744C22×C8—171no—
745C22×C8—171no—
746C22×C8—172no—
747C22×C8—172no—
748C22×C8—172no—
749C22×C8—682no—
750C22×C8C22×D1711yescharacteristic
751C22×C8C22×D1711yescharacteristic
752C22×C8C22×D1711yescharacteristic
753C22×C8C22×D1711yescharacteristic
754C22×C8C22×D1711yescharacteristic
755C22×C8C22×D1711yescharacteristic
756C22×C8C22×D1712yes—
757C4⋊Q8—171no—
758C4⋊Q8—171no—
759#126—172no—
760#126—172no—
761#126—172no—
762#126—172no—
763#126—172no—
764#126—172no—
765#125—172no—
766#125—172no—
767#125—171no—
768#125—171no—
769#125—172no—
770#124—172no—
771#124—172no—
772#124—172no—
773#123—172no—
774#123—172no—
775#123—172no—
776#123—172no—
777#123—172no—
778#123—172no—
779#123—172no—
780#123—172no—
781C22⋊Q8—171no—
782C22⋊Q8—171no—
783C22⋊Q8—172no—
784C22⋊Q8—171no—
785C22⋊Q8—171no—
786C22⋊Q8—172no—
787C22⋊Q8—172no—
788C22⋊Q8—172no—
789C22⋊Q8—172no—
790#121—171no—
791#121—171no—
792#121—172no—
793#121—171no—
794#121—171no—
795#121—172no—
796#121—172no—
797#120—172no—
798#120—172no—
799C4×Q8—171no—
800C4×Q8—171no—
801C4×Q8—172no—
802C4×Q8—172no—
803C4×Q8—172no—
804C4×D4—171no—
805C4×D4—171no—
806C4×D4—171no—
807C4×D4—171no—
808C4×D4—172no—
809C4×D4—172no—
810C4×D4—171no—
811C4×D4—171no—
812C4×D4—171no—
813C4×D4—171no—
814C4×D4—172no—
815C4×D4—172no—
816C4×D4—171no—
817C4×D4—171no—
818C4×D4—172no—
819C4×D4—172no—
820C4×D4—172no—
821C4×D4—172no—
822C4×D4—172no—
823#117—172no—
824#117—171no—
825#117—171no—
826#117—171no—
827#117—172no—
828#117—172no—
829#117—172no—
830#117—172no—
831#117—172no—
832#117C4×D1712yes—
833#117C4×D1711yescharacteristic
834#117C4×D1711yescharacteristic
835#117C22×D1711yescharacteristic
836#117C22×D1711yescharacteristic
837#117C22×D1712yes—
838C2×C4⋊C4—171no—
839C2×C4⋊C4—171no—
840C2×C4⋊C4—171no—
841C2×C4⋊C4C4×D1711yescharacteristic
842C2×C4⋊C4C4×D1711yescharacteristic
843C2×C22⋊C4—171no—
844C2×C22⋊C4—171no—
845C2×C22⋊C4—172no—
846C2×C22⋊C4C4×D1712yes—
847C2×C42—171no—
848C2×C42—172no—
849C2×C42—172no—
850C2×C42C22×D1712yes—
851C4⋊C8—171no—
852C4⋊C8—171no—
853C4⋊C8—172no—
854C4⋊C8—171no—
855C4⋊C8—171no—
856C4⋊C8—172no—
857C4⋊C8—172no—
858C4⋊C8—172no—
859C4⋊C8—172no—
860C4⋊C8—172no—
861C4⋊C8—172no—
862C4⋊C8—172no—
863C4⋊C8—172no—
864C4⋊C8—172no—
865C4⋊C8C22×D1712yes—
866C4⋊C8C22×D1712yes—
867C4⋊C8C22×D1712yes—
868C4⋊C8C22×D1712yes—
869C4⋊C8C22×D1712yes—
870C4⋊C8C22×D1712yes—
871C4⋊C8C22×D1712yes—
872C4⋊C8C22×D1712yes—
873C22⋊C8—171no—
874C22⋊C8—171no—
875C22⋊C8—171no—
876C22⋊C8—171no—
877C22⋊C8—172no—
878C22⋊C8—172no—
879C22⋊C8—171no—
880C22⋊C8—171no—
881C22⋊C8—171no—
882C22⋊C8—171no—
883C22⋊C8—172no—
884C22⋊C8—172no—
885C22⋊C8—172no—
886C22⋊C8—172no—
887C22⋊C8—172no—
888C22⋊C8—172no—
889#97—172no—
890#97—172no—
891#97—172no—
892#97—172no—
893#97—172no—
894C4×C8—171no—
895C4×C8—171no—
896C4×C8—171no—
897C4×C8—171no—
898C4×C8—172no—
899C4×C8—172no—
900C4×C8—172no—
901C4×C8—172no—
902C4×C8—172no—
903C17#6027111yescharacteristic, complemented, Sylow
904C24—171no—
905C24C2×C4×D1711yescharacteristic
906#41—348no—
907#41—342no—
908#41—342no—
909C2×Q8—171no—
910C2×Q8—172no—
911C2×Q8—172no—
912C2×D4—171no—
913C2×D4—172no—
914C2×D4—172no—
915C2×D4—171no—
916C2×D4—171no—
917C2×D4—171no—
918C2×D4—172no—
919C2×D4—172no—
920C2×D4—171no—
921C2×D4—172no—
922C2×D4—344no—
923C22×C4—22no—
924C22×C4—22no—
925C22×C4—171no—
926C22×C4—171no—
927C22×C4—171no—
928C22×C4—172no—
929C22×C4—172no—
930C22×C4—171no—
931C22×C4—171no—
932C22×C4—171no—
933C22×C4—172no—
934C22×C4—171no—
935C22×C4—172no—
936C22×C4—172no—
937C22×C4—342no—
938C22×C4—342no—
939C22×C4C2×C4×D1712yes—
940C22×C4C2×C4×D1711yescharacteristic
941C22×C4C2×C4×D1711yescharacteristic
942C22×C4C2×C4×D1711yescharacteristic
943C22×C4C2×C4×D1712yes—
944C22×C4C23×D1711yescharacteristic
945C22×C4C23×D1711yescharacteristic
946C22×C4C23×D1711yescharacteristic
947M16—22no—
948M16—22no—
949M16—42no—
950M16—342no—
951M16—342no—
952M16—682no—
953M16—682no—
954M16—682no—
955C2×C8—22no—
956C2×C8—22no—
957C2×C8—41no—
958C2×C8—41no—
959C2×C8—41no—
960C2×C8—41no—
961C2×C8—42no—
962C2×C8—171no—
963C2×C8—172no—
964C2×C8—171no—
965C2×C8—171no—
966C2×C8—172no—
967C2×C8—171no—
968C2×C8—342no—
969C2×C8—342no—
970C2×C8—681no—
971C2×C8—681no—
972C2×C8—681no—
973C2×C8—681no—
974C2×C8—682no—
975C2×C8—682no—
976C2×C8—682no—
977C2×C8C23×D1711yescharacteristic
978C2×C8C23×D1711yescharacteristic
979C2×C8C23×D1711yescharacteristic
980C2×C8C23×D1712yes—
981C2×C8C23×D1712yes—
982C2×C8C23×D1711yescharacteristic
983C4⋊C4—171no—
984C4⋊C4—171no—
985C4⋊C4—171no—
986C4⋊C4—172no—
987C4⋊C4—172no—
988C4⋊C4—171no—
989C4⋊C4—171no—
990C4⋊C4—171no—
991C4⋊C4—172no—
992C4⋊C4—172no—
993C4⋊C4—172no—
994C4⋊C4—172no—
995C4⋊C4—172no—
996C4⋊C4—172no—
997C4⋊C4—172no—
998C4⋊C4—172no—
999C4⋊C4—172no—
1000C4⋊C4—172no—
1001C4⋊C4—172no—
1002C4⋊C4—172no—
1003C4⋊C4C2×C4×D1711yescharacteristic
1004C4⋊C4C2×C4×D1711yescharacteristic
1005C4⋊C4C2×C4×D1711yescharacteristic
1006C4⋊C4C2×C4×D1711yescharacteristic
1007C4⋊C4C2×C4×D1712yes—
1008C4⋊C4C2×C4×D1712yes—
1009C22⋊C4—171no—
1010C22⋊C4—172no—
1011C22⋊C4—171no—
1012C22⋊C4—171no—
1013C22⋊C4—171no—
1014C22⋊C4—172no—
1015C22⋊C4—172no—
1016C22⋊C4—171no—
1017C22⋊C4—172no—
1018C22⋊C4—172no—
1019C22⋊C4—171no—
1020C22⋊C4—171no—
1021C22⋊C4—171no—
1022C22⋊C4—172no—
1023C22⋊C4—172no—
1024C22⋊C4—172no—
1025C22⋊C4—172no—
1026C22⋊C4—172no—
1027C22⋊C4—172no—
1028C22⋊C4—172no—
1029C22⋊C4—172no—
1030C22⋊C4C2×C4×D1712yes—
1031C22⋊C4C2×C4×D1712yes—
1032C22⋊C4C2×C4×D1712yes—
1033C22⋊C4C2×C4×D1712yes—
1034C42—172no—
1035C42—172no—
1036C42—172no—
1037C42—171no—
1038C42—171no—
1039C42—172no—
1040C42—171no—
1041C42—171no—
1042C42—172no—
1043C42C2×C4×D1712yes—
1044C42C2×C4×D1712yes—
1045C42C23×D1712yes—
1046C42C23×D1712yes—
1047C23—22no—
1048C23—22no—
1049C23—41no—
1050C23—171no—
1051C23—171no—
1052C23—172no—
1053C23—342no—
1054C23—342no—
1055C23—681no—
1056C23C22×C4×D1711yescharacteristic
1057C23C22×C4×D1711yescharacteristic
1058C23C22×C4×D1711yescharacteristic
1059Q8—344no—
1060Q8—342no—
1061Q8—682no—
1062D4—174no—
1063D4—344no—
1064D4—342no—
1065D4—342no—
1066D4—344no—
1067D4—342no—
1068D4—344no—
1069D4—342no—
1070D4—682no—
1071D4—682no—
1072C2×C4—22no—
1073C2×C4—24no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—42no—
1081C2×C4—171no—
1082C2×C4—171no—
1083C2×C4—171no—
1084C2×C4—171no—
1085C2×C4—172no—
1086C2×C4—172no—
1087C2×C4—172no—
1088C2×C4—171no—
1089C2×C4—171no—
1090C2×C4—344no—
1091C2×C4—344no—
1092C2×C4—342no—
1093C2×C4—342no—
1094C2×C4—342no—
1095C2×C4—342no—
1096C2×C4—341no—
1097C2×C4—341no—
1098C2×C4—342no—
1099C2×C4—341no—
1100C2×C4—341no—
1101C2×C4—342no—
1102C2×C4—682no—
1103C2×C4—682no—
1104C2×C4—681no—
1105C2×C4C22×C4×D1712yes—
1106C2×C4C22×C4×D1712yes—
1107C2×C4C22×C4×D1711yescharacteristic
1108C2×C4C22×C4×D1712yes—
1109C2×C4C22×C4×D1712yes—
1110C2×C4C22×C4×D1711yescharacteristic
1111C2×C4C22×C4×D1711yescharacteristic
1112C2×C4#1058769112yes—
1113C2×C4#1058769412yes—
1114C2×C4C24×D1711yescharacteristic
1115C8—21no—
1116C8—21no—
1117C8—21no—
1118C8—21no—
1119C8—22no—
1120C8—22no—
1121C8—341no—
1122C8—341no—
1123C8—342no—
1124C8—341no—
1125C8—341no—
1126C8—342no—
1127C22—21no—
1128C22—21no—
1129C22—21no—
1130C22—21no—
1131C22—21no—
1132C22—21no—
1133C22—21no—
1134C22—44no—
1135C22—172no—
1136C22—341no—
1137C22—341no—
1138C22—342no—
1139C22—341no—
1140C22—342no—
1141C22—341no—
1142C22—341no—
1143C22—342no—
1144C22—684no—
1145C22#1176329012yes—
1146C22#131×D1712yes—
1147C22C23×C4×D1711yescharacteristic
1148C4—22no—
1149C4—22no—
1150C4—22no—
1151C4—22no—
1152C4—21no—
1153C4—21no—
1154C4—172no—
1155C4—341no—
1156C4—342no—
1157C4—341no—
1158C4—342no—
1159C4—341no—
1160C4—341no—
1161C4—341no—
1162C4—342no—
1163C4#1176329012yes—
1164C4C2×#1058769111yescharacteristic
1165C4C2×#1058769411yescharacteristic
1166C2—22no—
1167C2—22no—
1168C2—41no—
1169C2—342no—
1170C2—681no—
1171C2—682no—
1172C2C2×#1176329011yescharacteristic
1173C2C2×#131×D1711yescharacteristic
1174C2#1454349511yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D17
commutator, socleC22×C17C24×C4
FittingC2×C17×#424C2
prime radical#14542338C2
cosocleC2×C4×C17C25
hypercenterC2×#424D17
hypocenterC17#60271
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×#424

Complements

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

NH ≅ G/Ntype
2. #14537942C2semidirect
3. #14537942C2semidirect
4. #14537940C2semidirect
5. #14537931C2semidirect
6. #14537921C2semidirect
7. #14537920C2semidirect
8. #14537906C2semidirect
9. #14537893C2semidirect
10. #14537730C2semidirect
11. #14537717C2semidirect
12. M16×C22⋊D17C2semidirect
13. #14537509C2semidirect
14. #14537508C2semidirect
15. #14537478C2semidirect
16. #14537477C2semidirect
17. C2×C8×C22⋊D17C2semidirect
18. #14537442C2semidirect
19. #14537441C2semidirect
20. #14537427C2semidirect
21. #14537351C2semidirect
22. D17×#424C2semidirect
23. C2×C17×#424C2semidirect
50. #11762938C22semidirect
51. #11762938C22semidirect
52. #11762938C22semidirect
53. #11762938C22semidirect
54. #11762936C22semidirect
55. #11762933C22semidirect
56. #11762933C22semidirect
57. #11762933C22semidirect
58. #11762886C22semidirect
60. #11762885C22semidirect
62. #11762880C22semidirect
63. #11762880C22semidirect
64. #11762880C22semidirect
65. #11762879C22semidirect
66. #11762879C22semidirect
67. #11762879C22semidirect
68. #11762879C22semidirect
70. #11762878C22semidirect
71. #11762874C22semidirect
72. #11762874C22semidirect
73. #11762874C22semidirect
83. C8×C22⋊D17C22semidirect
84. C8×C22⋊D17C22semidirect
85. C8×C22⋊D17C22semidirect
86. #11762870C22semidirect
87. #11762870C22semidirect
88. #11762869C22semidirect
89. #11762869C22semidirect
90. #11762869C22semidirect
91. #11762869C22semidirect
92. #11762866C22semidirect
93. #11762865C22semidirect
94. #11762862C22semidirect
95. #11762861C22semidirect
96. #11762861C22semidirect
97. #11762861C22semidirect
102. #11762834C22semidirect
103. #11762834C22semidirect
104. #11762834C22semidirect
105. #11762834C22semidirect
107. #11762831C22semidirect
109. C4⋊C8×D17C22semidirect
110. C4⋊C8×D17C22semidirect
111. C4⋊C8×D17C22semidirect
131. C17×#424C22semidirect
132. C17×#424C22semidirect
133. C2×C17×C4⋊C8C22semidirect
134. C2×C17×C4⋊C8C22semidirect
497. C22⋊D17#131semidirect
562. C2×#424D17semidirect
691. #424C2×D17semidirect
692. #424C2×D17semidirect
699. C2×C4⋊C8C2×D17semidirect
700. C2×C4⋊C8C2×D17semidirect
903. C17#60271semidirect

Maximal subgroups

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

subgroupindex
#145423382
#145379422
#145379402
#145379312
#145379212
#145379202
#145379062
#145378932
#145377302
#145377172
M16×C22⋊D172
#145375092
#145375082
#145374782
#145374772
C2×C8×C22⋊D172
#145374422
#145374412
#145374272
#145373512
D17×#4242
C2×C17×#4242
#6027117