Finite Group Databasebeta

← #17899168

Subgroups — #17899168

Order 4352.

2094 conjugacy classes of subgroups.

The subgroup lattice has 1236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14542114C211yesmaximal, characteristic
2#14537861C212yesmaximal, complemented
3#14537856C212yesmaximal, complemented
4#14537852C212yesmaximal, complemented
5#14537849C212yesmaximal, complemented
6#14537842C211yesmaximal, characteristic, complemented
7#14537840C211yesmaximal, characteristic, complemented
8#14537836C211yesmaximal, characteristic, complemented
9#14537834C212yesmaximal, complemented
10#14537830C212yesmaximal, complemented
11#14537513C212yesmaximal, complemented
12#14537510C212yesmaximal, complemented
13#14537484C212yesmaximal, complemented
14#14537475C212yesmaximal, complemented
15#14537440C212yesmaximal, complemented
16#14537234C212yesmaximal, complemented
17#14537226C211yesmaximal, characteristic, complemented
18D17×#408C211yesmaximal, characteristic, complemented
19C17×#2978C211yesmaximal, characteristic, complemented
20C22×#63252C2211yescharacteristic
21C2×#41×D17C2211yescharacteristic
22C2×#10587593C2212yes—
23C2×#10587593C2212yes—
24C22×#63218C2211yescharacteristic, complemented
25C2×M16×D17C2211yescharacteristic, complemented
26C2×M16×D17C2211yescharacteristic, complemented
27C22×C8×D17C2211yescharacteristic, complemented
28#11763389C412yes—
29#11763388C412yes—
30#11763382C412yes—
31#11763381C411yescharacteristic
32#11763381C411yescharacteristic
33#11763375C412yes—
34#11763374C411yescharacteristic
35#11763374C411yescharacteristic
36#11763370C411yescharacteristic
37#11763370C411yescharacteristic
38#11763369C411yescharacteristic
39#11763369C411yescharacteristic
40#11763356C2212yes—
41#11763356C2212yes—
42#11763321C2211yescharacteristic
43#11763320C2211yescharacteristic
44#11763318C2212yes—
45#11763318C2212yes—
46#11763316C2211yescharacteristic
47#117×D17C2211yescharacteristic
48#11762888C2212yescomplemented
49#11762886C2212yescomplemented
50#11762885C2212yescomplemented
51#11762885C2212yescomplemented
52#11762885C2212yescomplemented
53#11762884C2212yescomplemented
54#11762883C2212yescomplemented
55#11762882C2212yescomplemented
56#11762882C2212yescomplemented
57#11762881C2212yescomplemented
58#11762881C2212yescomplemented
59#11762880C2212yescomplemented
60#11762879C2212yescomplemented
61#11762879C2212yescomplemented
62#11762878C2212yescomplemented
63#11762878C2212yescomplemented
64#11762878C2212yescomplemented
65#11762877C2212yescomplemented
66#11762877C2212yescomplemented
67#11762877C2212yescomplemented
68C8×D68C2212yescomplemented
69D4×#3622C2212yescomplemented
70D4×#3622C2212yescomplemented
71#11762874C2212yescomplemented
72C8×C22⋊D17C2212yescomplemented
73#11762872C2212yescomplemented
74#11762872C2212yescomplemented
75#11762872C2212yescomplemented
76#11762870C2212yescomplemented
77#11762867C2212yescomplemented
78#11762867C2212yescomplemented
79#11762865C2212yescomplemented
80#11762864C2212yescomplemented
81#11762861C2212yescomplemented
82#11762860C2212yescomplemented
83#11762834C2212yescomplemented
84#11762834C2212yescomplemented
85#11762777C2211yescharacteristic, complemented
86#11762777C2211yescharacteristic, complemented
87#11762777C2212yescomplemented
88#11762777C2212yescomplemented
89#11762776C2211yescharacteristic
90#11762776C2211yescharacteristic
91#11762775C2211yescharacteristic, complemented
92#11762775C2211yescharacteristic, complemented
93#11762774C2212yes—
94#11762774C2212yes—
95#11762774C2212yes—
96#11762774C2212yes—
97#11762774C2212yescomplemented
98#11762774C2212yescomplemented
99#11762774C2212yescomplemented
100#11762774C2212yescomplemented
101#11762771C2212yes—
102#11762771C2212yescomplemented
103#11762771C2212yescomplemented
104C2×C22⋊#3622C2212yescomplemented
105C22⋊C8×D17C2212yes—
106C22⋊C8×D17C2212yescomplemented
107C22⋊C8×D17C2212yescomplemented
108#11762766C2212yescomplemented
109#11762763C2212yescomplemented
110C17×#525C2211yescharacteristic
111C17×#436C2212yescomplemented
112C17×#436C2212yescomplemented
113C17×#435C2212yescomplemented
114C17×#435C2212yescomplemented
115C17×#433C2212yescomplemented
116C17×#408C2211yescharacteristic
117C17×#408C2211yescharacteristic
118C17×#407C2212yescomplemented
119C2×#41×C17C2311yescharacteristic
120C23×C4×C17C2311yescharacteristic
121C22×C22⋊D17C2×C411yescharacteristic
122C22×C22⋊D17C2×C411yescharacteristic
123#41×D17—42no—
124#41×D17—42no—
125C2×#63256C2×C411yescharacteristic
126C2×Q8×D17C2×C411yescharacteristic
127C2×#63254C2×C411yescharacteristic
128C2×#63254C2×C411yescharacteristic
129C2×#63254C2×C411yescharacteristic
130C2×D4×D17C2×C411yescharacteristic
131C2×D4×D17C2×C411yescharacteristic
132C2×D4×D17C2×C411yescharacteristic
133C2×#63252—42no—
134C2×#63252—42no—
135C2×#63252C2×C412yes—
136C2×#63252C2×C412yes—
137C2×#63252C2312yes—
138C2×#63252C2311yescharacteristic
139C2×#63252C2311yescharacteristic
140C2×#63252C2311yescharacteristic
141C2×#63252C2312yes—
142C22×D68C2×C411yescharacteristic
143C22×C4×D17C2311yescharacteristic
144C22×C4×D17C2311yescharacteristic
145C22×C4×D17C2311yescharacteristic
146C22×C4×D17C2311yescharacteristic
147C22×Dic34C2×C411yescharacteristic
148C2×M16×C17C2311yescharacteristic
149C2×M16×C17C2311yescharacteristic
150C2×M16×C17C2312yes—
151C2×M16×C17C2312yes—
152C22×C8×C17C2311yescharacteristic
153C22×C8×C17C2311yescharacteristic
154C17×#123C2×C411yescharacteristic
155C17×#123C2×C411yescharacteristic
156C17×C22⋊Q8C2×C412yes—
157C17×#121C2×C412yes—
158C17×#120C2×C411yescharacteristic
159C17×#120C2×C411yescharacteristic
160C4×D4×C17C2312yes—
161C4×D4×C17C2312yes—
162C17×#117C2311yescharacteristic
163#10587639C2×C411yescharacteristic
164#10587639C2×C411yescharacteristic
165#10587632C2×C412yes—
166#10587626C2×C412yes—
167#10587626C2×C412yes—
168#10587625C2×C412yes—
169#10587625C2×C412yes—
170#10587624C2×C412yes—
171#10587624C2×C412yes—
172#10587624C2×C412yes—
173#10587623C2×C411yescharacteristic
174#10587623C2×C411yescharacteristic
175#10587623C2×C412yes—
176#10587623C2×C412yes—
177#10587621C2×C411yescharacteristic
178#10587621C2×C411yescharacteristic
179#10587616C2×C412yes—
180#10587615C2×C411yescharacteristic
181#10587615C2×C411yescharacteristic
182C4×C22⋊D17C2312yes—
183C4×C22⋊D17C2312yes—
184C4×C22⋊D17C2312yes—
185C4×C22⋊D17C2312yes—
186#10587612C2311yescharacteristic
187#10587610C2×C412yes—
188C2×#63223C2311yescharacteristic
189C2×#63223C2311yescharacteristic
190C22×#3622C2312yes—
191C22×#3622C2312yes—
192C22×#3622C2311yescharacteristic
193C22×#3622C2311yescharacteristic
194#10587593—44no—
195#10587593—44no—
196M16×D17—42no—
197M16×D17—42no—
198C2×#63218—42no—
199C2×#63218C2312yes—
200C2×#63218C2312yes—
201C2×#63218C2312yes—
202C2×#63218C2312yes—
203C2×#63218C2312yes—
204C2×#63218C2312yes—
205C2×C8×D17—42no—
206C2×C8×D17C2312yes—
207C2×C8×D17C2312yes—
208C2×C8×D17C2312yes—
209C2×C8×D17C2312yes—
210C2×C8×D17C2312yes—
211C2×C8×D17C2312yes—
212#10587583C2×C412yes—
213#10587582C2×C412yes—
214#10587582C2×C412yes—
215#10587581C2×C412yes—
216#10587581C2×C412yes—
217#10587581C2×C412yes—
218#10587580C2×C412yes—
219#10587580C2×C412yes—
220#10587578C2×C412yes—
221C4⋊C4×D17C2×C412yes—
222#10587574C2×C412yes—
223#10587574C2×C412yes—
224#10587572C2×C411yescharacteristic
225#10587572C2×C411yescharacteristic
226#10587571C2×C412yes—
227#10587571C2×C412yes—
228#10587571C2×C412yes—
229#10587571C2×C412yes—
230#10587570C2×C412yes—
231#10587570C2×C412yes—
232#10587570C2×C412yes—
233#10587570C2×C412yes—
234#10587570C2×C412yes—
235#10587570C2×C412yes—
236#10587569C2×C412yes—
237#10587569C2×C412yes—
238#10587568C2×C412yes—
239#10587568C2×C412yes—
240#10587568C2×C411yescharacteristic
241#10587568C2×C411yescharacteristic
242C22⋊C4×D17C2×C411yescharacteristic
243C22⋊C4×D17C2×C411yescharacteristic
244#10587564C2×C412yes—
245#10587564C2×C412yes—
246#10587563C2×C411yescharacteristic
247#10587563C2×C411yescharacteristic
248C4×D68C2312yes—
249C4×D68C2312yes—
250#10587558C2312yes—
251C42×D17C2312yes—
252C17×C4⋊C8C2312yes—
253C17×C4⋊C8C2312yes—
254C17×C22⋊C8C2312yes—
255C17×C22⋊C8C2312yes—
256C17×C22⋊C8C2312yes—
257C17×C22⋊C8C2312yes—
258C17×C22⋊C8C2312yes—
259C17×C22⋊C8C2312yes—
260C17×#97C2312yes—
261C4×C8×C17C2312yes—
262C22⋊#3622C2312yes—
263C22⋊#3622C2312yes—
264C22⋊#3622C2312yes—
265C22⋊#3622C2312yes—
266C22⋊#3622C2312yes—
267C22⋊#3622C2312yes—
268#10587491C2312yes—
269#10587491C2312yes—
270#10587491C2312yes—
271#10587491C2312yes—
272#10587491C2312yes—
273#10587491C2312yes—
274#10587491C2312yes—
275#10587491C2312yes—
276#10587491C2312yes—
277#10587491C2312yes—
278#10587491C2312yes—
279#10587491C2312yes—
280#10587486C2312yes—
281#10587486C2312yes—
282#10587485C2312yes—
283#10587485C2312yes—
284#10587485C2312yes—
285#10587485C2312yes—
286C8×Dic17C2312yes—
287C8×Dic17C2312yes—
288C4⋊#3622C2312yes—
289C4⋊#3622C2312yes—
290#10587474C2312yes—
291C4×#3622C2312yes—
292C24×C17C22×C411yescharacteristic
293C23×D17C22×C411yescharacteristic
294C23×D17C22×C411yescharacteristic
295C23×D17C22×C411yescharacteristic
296C23×D17C22×C411yescharacteristic
297#41×C17—41no—
298#41×C17—41no—
299C2×Q8×C17C22×C411yescharacteristic
300C2×D4×C17C22×C411yescharacteristic
301C2×D4×C17C22×C411yescharacteristic
302C2×D4×C17C22×C411yescharacteristic
303C2×D4×C17C22×C412yes—
304C2×D4×C17C22×C412yes—
305C22×C4×C17—41no—
306C22×C4×C17—41no—
307C22×C4×C17C22×C412yes—
308C22×C4×C17C22×C411yescharacteristic
309C22×C4×C17C2411yescharacteristic
310C22×C4×C17C2411yescharacteristic
311C22×C4×C17C2412yes—
312C22×C4×C17C2411yescharacteristic
313C2×C22⋊D17—42no—
314C2×C22⋊D17—42no—
315C2×C22⋊D17C22×C412yes—
316C2×C22⋊D17C22×C412yes—
317C2×C22⋊D17C22×C412yes—
318C2×C22⋊D17C22×C412yes—
319C2×C22⋊D17C22×C411yescharacteristic
320C2×C22⋊D17C22×C411yescharacteristic
321C2×C22⋊D17C22×C411yescharacteristic
322C2×C22⋊D17C22×C411yescharacteristic
323C2×C22⋊D17C22×C411yescharacteristic
324C2×C22⋊D17C22×C411yescharacteristic
325C2×C22⋊D17C22×C412yes—
326C2×C22⋊D17C22×C412yes—
327C2×C22⋊D17C22×C412yes—
328C2×C22⋊D17C22×C412yes—
329C22×Dic17C22×C411yescharacteristic
330C22×Dic17C22×C411yescharacteristic
331C22×Dic17C22×C411yescharacteristic
332C22×Dic17C22×C411yescharacteristic
333#63256—42no—
334Q8×D17—42no—
335#63254—42no—
336#63254—42no—
337#63254—42no—
338D4×D17—42no—
339D4×D17—42no—
340D4×D17—42no—
341#63252—24no—
342#63252—24no—
343#63252—44no—
344#63252—42no—
345#63252—42no—
346#63252—41no—
347#63252—41no—
348#63252—41no—
349#63252—41no—
350#63252—41no—
351#63252—41no—
352#63252—44no—
353C2×D68—42no—
354C2×D68C22×C412yes—
355C2×D68C22×C412yes—
356C2×D68C22×C411yescharacteristic
357C2×D68C22×C411yescharacteristic
358C2×D68C22×C411yescharacteristic
359C2×D68C22×C412yes—
360C2×D68C22×C412yes—
361C2×C4×D17—22no—
362C2×C4×D17—22no—
363C2×C4×D17—22no—
364C2×C4×D17—22no—
365C2×C4×D17—22no—
366C2×C4×D17—22no—
367C2×C4×D17—41no—
368C2×C4×D17—41no—
369C2×C4×D17C22×C411yescharacteristic
370C2×C4×D17C22×C411yescharacteristic
371C2×C4×D17C22×C411yescharacteristic
372C2×C4×D17C22×C411yescharacteristic
373C2×C4×D17C22×C411yescharacteristic
374C2×C4×D17C22×C411yescharacteristic
375C2×C4×D17C22×C412yes—
376C2×C4×D17C22×C412yes—
377C2×C4×D17C22×C412yes—
378C2×C4×D17C2411yescharacteristic
379C2×C4×D17C2411yescharacteristic
380C2×C4×D17C2411yescharacteristic
381C2×C4×D17C2412yes—
382C2×C4×D17C2411yescharacteristic
383C2×Dic34—42no—
384C2×Dic34C22×C412yes—
385C2×Dic34C22×C412yes—
386C2×Dic34C22×C411yescharacteristic
387C2×Dic34C22×C411yescharacteristic
388C2×Dic34C22×C411yescharacteristic
389M16×C17—41no—
390M16×C17—41no—
391M16×C17—42no—
392M16×C17—42no—
393C2×C8×C17—41no—
394C2×C8×C17—41no—
395C2×C8×C17C2412yes—
396C2×C8×C17C2412yes—
397C2×C8×C17C2412yes—
398C2×C8×C17C2412yes—
399C4⋊C4×C17C22×C412yes—
400C4⋊C4×C17C22×C412yes—
401C4⋊C4×C17C22×C412yes—
402C22⋊C4×C17C22×C412yes—
403C22⋊C4×C17C22×C412yes—
404C22⋊C4×C17C22×C411yescharacteristic
405C22⋊C4×C17C22×C411yescharacteristic
406C22⋊C4×C17C22×C412yes—
407C22⋊C4×C17C22×C412yes—
408C42×C17C2412yes—
409C22⋊Dic17C22×C411yescharacteristic
410C22⋊Dic17C22×C411yescharacteristic
411C22⋊Dic17C22×C412yes—
412C22⋊Dic17C22×C412yes—
413C22⋊Dic17C22×C412yes—
414C22⋊Dic17C22×C412yes—
415#63227C22×C412yes—
416#63227C22×C412yes—
417#63227C22×C412yes—
418#63227C22×C412yes—
419#63227C22×C412yes—
420#63227C22×C412yes—
421#63227C22×C412yes—
422#63227C22×C412yes—
423#63227C22×C412yes—
424#63227C22×C412yes—
425C4⋊Dic17C22×C412yes—
426C4⋊Dic17C22×C412yes—
427C4⋊Dic17C22×C412yes—
428#63225C22×C412yes—
429#63225C22×C412yes—
430#63225C22×C412yes—
431#63225C22×C412yes—
432#63225C22×C412yes—
433#63225C22×C412yes—
434C4×Dic17C22×C412yes—
435C4×Dic17C22×C412yes—
436C4×Dic17C2412yes—
437#63223—41no—
438#63223—41no—
439C2×#3622—41no—
440C2×#3622—41no—
441C2×#3622—42no—
442C2×#3622—42no—
443C2×#3622C2412yes—
444C2×#3622C2412yes—
445C2×#3622C2412yes—
446C2×#3622C2412yes—
447#63218—24no—
448#63218—24no—
449#63218—42no—
450#63218—42no—
451#63218—42no—
452#63218—42no—
453C8×D17—24no—
454C8×D17—24no—
455C8×D17—42no—
456C8×D17—42no—
457C8×D17—42no—
458C8×D17—42no—
459#60235—171nomaximal, Sylow
460C23×C17—41no—
461C23×C17—42no—
462C23×C17C23×C411yescharacteristic
463C23×C17C23×C411yescharacteristic
464C23×C17C23×C411yescharacteristic
465C23×C17C23×C412yes—
466C22×D17—22no—
467C22×D17—22no—
468C22×D17—22no—
469C22×D17—42no—
470C22×D17—41no—
471C22×D17—42no—
472C22×D17—42no—
473C22×D17—42no—
474C22×D17C23×C411yescharacteristic
475C22×D17C23×C411yescharacteristic
476C22×D17C23×C411yescharacteristic
477C22×D17C23×C412yes—
478C22×D17C23×C411yescharacteristic
479Q8×C17—41no—
480D4×C17—41no—
481D4×C17—41no—
482D4×C17—41no—
483D4×C17—42no—
484D4×C17—42no—
485C2×C4×C17—21no—
486C2×C4×C17—21no—
487C2×C4×C17—21no—
488C2×C4×C17—21no—
489C2×C4×C17—22no—
490C2×C4×C17—22no—
491C2×C4×C17—21no—
492C2×C4×C17—21no—
493C2×C4×C17—41no—
494C2×C4×C17—42no—
495C2×C4×C17C23×C412yes—
496C2×C4×C17C23×C412yes—
497C2×C4×C17C23×C412yes—
498C2×C4×C17C23×C411yescharacteristic
499C2×C4×C17C23×C411yescharacteristic
500C2×C4×C17C23×C411yescharacteristic
501C2×C4×C17C2511yescharacteristic
502C22⋊D17—24no—
503C22⋊D17—24no—
504C22⋊D17—42no—
505C22⋊D17—42no—
506C22⋊D17—41no—
507C22⋊D17—41no—
508C22⋊D17—41no—
509C22⋊D17—41no—
510C22⋊D17—41no—
511C22⋊D17—41no—
512C22⋊D17—42no—
513C22⋊D17—42no—
514C22⋊D17—42no—
515C22⋊D17—42no—
516C2×Dic17—22no—
517C2×Dic17—22no—
518C2×Dic17—22no—
519C2×Dic17—41no—
520C2×Dic17C23×C412yes—
521C2×Dic17C23×C412yes—
522C2×Dic17C23×C412yes—
523C2×Dic17C23×C411yescharacteristic
524C2×Dic17C23×C411yescharacteristic
525C2×Dic17C23×C411yescharacteristic
526C2×Dic17C23×C411yescharacteristic
527D68—24no—
528D68—42no—
529D68—42no—
530D68—42no—
531D68—41no—
532D68—41no—
533D68—41no—
534C4×D17—22no—
535C4×D17—22no—
536C4×D17—22no—
537C4×D17—21no—
538C4×D17—21no—
539C4×D17—21no—
540C4×D17—21no—
541C4×D17—21no—
542C4×D17—21no—
543C4×D17—22no—
544C4×D17—22no—
545C4×D17—22no—
546C4×D17—22no—
547C4×D17—22no—
548C4×D17—42no—
549C4×D17—42no—
550C4×D17—42no—
551C4×D17H(5,𝔽2)12yes—
552C4×D17H(5,𝔽2)12yes—
553Dic34—24no—
554Dic34—42no—
555Dic34—41no—
556Dic34—41no—
557Dic34—41no—
558C8×C17—22no—
559C8×C17—22no—
560C8×C17—22no—
561C8×C17—22no—
562#3622—22no—
563#3622—22no—
564#3622—22no—
565#3622—22no—
566#3449—171no—
567#2981—172no—
568#2981—172no—
569#2980—172no—
570#2979—172no—
571#2978—171no—
572#2978D1711yescharacteristic, complemented
573#2977—171no—
574#2977—171no—
575#2976—172no—
576#2976—172no—
577#2933—172no—
578#2933—172no—
579#2930—172no—
580#2929—172no—
581#2924—172no—
582#2880—172no—
583#2879—171no—
584C2×#408—171no—
585C22×C17—21no—
586C22×C17—21no—
587C22×C17—21no—
588C22×C17—22no—
589C22×C17—22no—
590C22×C17—22no—
591C22×C17—22no—
592C22×C17—22no—
593C22×C17—22no—
594C22×C17—82no—
595C22×C17C24×C411yescharacteristic
596C2×D17—22no—
597C2×D17—21no—
598C2×D17—21no—
599C2×D17—21no—
600C2×D17—22no—
601C2×D17—22no—
602C2×D17—22no—
603C2×D17—22no—
604C2×D17—22no—
605C2×D17—22no—
606C2×D17—44no—
607C2×D17—82no—
608C2×D17—82no—
609C2×D17—82no—
610C2×D17#51812yes—
611C4×C17—22no—
612C4×C17—21no—
613C4×C17—21no—
614C4×C17—21no—
615C4×C17—22no—
616C4×C17—22no—
617C4×C17C2×H(5,𝔽2)11yescharacteristic
618C4×C17C2×H(5,𝔽2)11yescharacteristic
619Dic17—22no—
620Dic17—21no—
621Dic17—21no—
622Dic17—21no—
623Dic17—22no—
624Dic17—22no—
625Dic17#51812yes—
626C22×#41—171no—
627C22×#41—171no—
628C2×#131—172no—
629C2×#131—172no—
630C22×M16—171no—
631C22×M16—171no—
632C22×M16—171no—
633C23×C8—171no—
634#537—172no—
635#537—172no—
636#536—171no—
637#536—171no—
638#536—172no—
639#535—172no—
640#535—171no—
641#535—171no—
642#534—171no—
643#534—171no—
644#534—171no—
645#534—171no—
646#532—172no—
647#532—172no—
648#525—171no—
649#525—171no—
650#525—172no—
651#525—172no—
652#525—171no—
653#525C2×D1711yescharacteristic
654C2×#117—171no—
655#436—172no—
656#436—172no—
657#436—172no—
658#436—172no—
659#436—172no—
660#436—172no—
661#436C2×D1712yescomplemented
662#436C2×D1712yescomplemented
663#435—172no—
664#435—172no—
665#435—172no—
666#435—172no—
667#435—172no—
668#435—172no—
669#435—172no—
670#435—172no—
671#435—172no—
672#435—172no—
673#435—172no—
674#435—172no—
675#435—172no—
676#435—172no—
677#435C2×D1712yescomplemented
678#435C2×D1712yescomplemented
679C8×D4—172no—
680C8×D4—172no—
681C8×D4—172no—
682C8×D4—172no—
683C8×D4—172no—
684C8×D4—172no—
685C8×D4—172no—
686C8×D4—172no—
687#433—172no—
688#433—172no—
689#433—172no—
690#433C2×D1712yescomplemented
691#432—172no—
692#432—172no—
693#431—172no—
694#431—172no—
695#424—172no—
696#424—172no—
697#408—171no—
698#408—171no—
699#408—171no—
700#408—171no—
701#408—172no—
702#408—172no—
703#408—171no—
704#408—171no—
705#408—172no—
706#408—172no—
707#408—172no—
708#408—172no—
709#408—172no—
710#408—172no—
711#408—172no—
712#408—172no—
713#408C2×D1711yescharacteristic
714#408C2×D1711yescharacteristic
715#407—172no—
716#407—172no—
717#407—172no—
718#407C2×D1712yescomplemented
719C2×C22⋊C8—172no—
720C2×C22⋊C8—172no—
721C2×C22⋊C8—172no—
722C2×C22⋊C8—172no—
723#405—172no—
724#405—172no—
725C2×C17—41no—
726C2×C17—41no—
727C2×C17—41no—
728C2×C17—42no—
729C2×C17C2×#51811yescharacteristic
730C2×C17#357312yes—
731D17—22no—
732D17—41no—
733D17—41no—
734D17—41no—
735D17—42no—
736C2×#41—171no—
737C2×#41—171no—
738C2×#41—171no—
739C2×#41—171no—
740C2×#41—172no—
741C2×#41—172no—
742C2×#41—172no—
743C2×#41—171no—
744C2×#41—172no—
745C2×#41—171no—
746C2×#41—171no—
747C2×#41—682no—
748C2×#41—682no—
749C2×#41—682no—
750C2×#41—682no—
751C2×#41C22×D1711yescharacteristic
752C22×Q8—171no—
753C22×Q8—171no—
754C22×D4—171no—
755C22×D4—171no—
756C22×D4—171no—
757C22×D4—171no—
758C22×D4—171no—
759C22×D4—171no—
760C23×C4—171no—
761C23×C4—171no—
762C23×C4—171no—
763C23×C4—171no—
764C23×C4C22×D1711yescharacteristic
765#131—684no—
766#131—684no—
767C2×M16—171no—
768C2×M16—171no—
769C2×M16—172no—
770C2×M16—172no—
771C2×M16—172no—
772C2×M16—172no—
773C2×M16—172no—
774C2×M16—172no—
775C2×M16—682no—
776C2×M16—682no—
777C2×M16—682no—
778C2×M16C22×D1711yescharacteristic
779C2×M16C22×D1711yescharacteristic
780C2×M16C22×D1712yes—
781C2×M16C22×D1712yes—
782C22×C8—171no—
783C22×C8—171no—
784C22×C8—172no—
785C22×C8—172no—
786C22×C8—172no—
787C22×C8—172no—
788C22×C8—172no—
789C22×C8—172no—
790C22×C8—172no—
791C22×C8—172no—
792C22×C8—682no—
793C22×C8C22×D1711yescharacteristic
794C22×C8C22×D1711yescharacteristic
795C4⋊Q8—172no—
796C4⋊Q8—172no—
797#127—172no—
798#127—172no—
799#124—172no—
800#124—172no—
801#124—172no—
802#124—172no—
803#123—171no—
804#123—171no—
805#123—171no—
806#123—171no—
807#123—172no—
808#123—172no—
809#123—172no—
810#123—172no—
811#123—171no—
812#123—171no—
813#123C4×D1711yescharacteristic
814#123C4×D1711yescharacteristic
815C22⋊Q8—172no—
816C22⋊Q8—172no—
817C22⋊Q8—172no—
818C22⋊Q8—172no—
819C22⋊Q8—172no—
820C22⋊Q8—172no—
821C22⋊Q8—172no—
822C22⋊Q8C4×D1712yes—
823#121—172no—
824#121—172no—
825#121—172no—
826#121—172no—
827#121—172no—
828#121—172no—
829#121—172no—
830#121—172no—
831#121—172no—
832#121—172no—
833#121—172no—
834#121—172no—
835#121—172no—
836#121—172no—
837#121—172no—
838#121C4×D1712yes—
839#120—171no—
840#120—171no—
841#120—171no—
842#120—171no—
843#120—172no—
844#120—172no—
845#120—172no—
846#120—172no—
847#120—171no—
848#120—171no—
849#120C4×D1711yescharacteristic
850#120C4×D1711yescharacteristic
851C4×D4—172no—
852C4×D4—172no—
853C4×D4—172no—
854C4×D4—172no—
855C4×D4—172no—
856C4×D4—172no—
857C4×D4C22×D1712yes—
858C4×D4C22×D1712yes—
859#117—171no—
860#117—172no—
861#117—171no—
862#117—171no—
863#117—172no—
864#117C22×D1711yescharacteristic
865C2×C4⋊C4—172no—
866C2×C22⋊C4—171no—
867C2×C22⋊C4—171no—
868C2×C42—172no—
869C4⋊C8—172no—
870C4⋊C8—172no—
871C4⋊C8—172no—
872C4⋊C8—172no—
873C4⋊C8—172no—
874C4⋊C8—172no—
875C4⋊C8C22×D1712yes—
876C4⋊C8C22×D1712yes—
877C22⋊C8—172no—
878C22⋊C8—172no—
879C22⋊C8—172no—
880C22⋊C8—172no—
881C22⋊C8—172no—
882C22⋊C8—172no—
883C22⋊C8—172no—
884C22⋊C8—172no—
885C22⋊C8—172no—
886C22⋊C8—172no—
887C22⋊C8—172no—
888C22⋊C8—172no—
889C22⋊C8—172no—
890C22⋊C8—172no—
891C22⋊C8—172no—
892C22⋊C8—172no—
893C22⋊C8—172no—
894C22⋊C8—172no—
895C22⋊C8C22×D1712yes—
896C22⋊C8C22×D1712yes—
897C22⋊C8C22×D1712yes—
898C22⋊C8C22×D1712yes—
899C22⋊C8C22×D1712yes—
900C22⋊C8C22×D1712yes—
901#97—172no—
902#97—172no—
903#97—172no—
904#97C22×D1712yes—
905C4×C8—172no—
906C4×C8—172no—
907C4×C8—172no—
908C4×C8C22×D1712yes—
909C17#6023511yescharacteristic, complemented, Sylow
910C24—171no—
911C24—171no—
912C24—171no—
913C24—171no—
914C24C2×C4×D1711yescharacteristic
915#41—41no—
916#41—41no—
917#41—344no—
918#41—344no—
919#41—681no—
920#41—681no—
921#41—682no—
922#41—682no—
923#41—681no—
924#41—681no—
925#41—681no—
926#41—681no—
927#41—684no—
928#41—684no—
929#41—682no—
930#41—682no—
931#41—682no—
932#41—682no—
933C2×Q8—172no—
934C2×Q8—171no—
935C2×Q8—171no—
936C2×Q8—171no—
937C2×Q8—172no—
938C2×Q8—682no—
939C2×Q8—682no—
940C2×Q8C2×C4×D1711yescharacteristic
941C2×D4—172no—
942C2×D4—172no—
943C2×D4—172no—
944C2×D4—172no—
945C2×D4—172no—
946C2×D4—172no—
947C2×D4—171no—
948C2×D4—171no—
949C2×D4—171no—
950C2×D4—171no—
951C2×D4—172no—
952C2×D4—171no—
953C2×D4—171no—
954C2×D4—172no—
955C2×D4—172no—
956C2×D4—172no—
957C2×D4—172no—
958C2×D4—171no—
959C2×D4—171no—
960C2×D4—172no—
961C2×D4—171no—
962C2×D4—682no—
963C2×D4—682no—
964C2×D4—682no—
965C2×D4—682no—
966C2×D4—682no—
967C2×D4—682no—
968C2×D4C2×C4×D1712yes—
969C2×D4C2×C4×D1712yes—
970C2×D4C2×C4×D1711yescharacteristic
971C2×D4C2×C4×D1711yescharacteristic
972C2×D4C2×C4×D1711yescharacteristic
973C22×C4—41no—
974C22×C4—41no—
975C22×C4—171no—
976C22×C4—171no—
977C22×C4—171no—
978C22×C4—171no—
979C22×C4—171no—
980C22×C4—171no—
981C22×C4—171no—
982C22×C4—171no—
983C22×C4—171no—
984C22×C4—171no—
985C22×C4—171no—
986C22×C4—171no—
987C22×C4—171no—
988C22×C4—171no—
989C22×C4—172no—
990C22×C4—172no—
991C22×C4—172no—
992C22×C4—172no—
993C22×C4—342no—
994C22×C4—342no—
995C22×C4—342no—
996C22×C4—342no—
997C22×C4—342no—
998C22×C4—342no—
999C22×C4—681no—
1000C22×C4—681no—
1001C22×C4C2×C4×D1712yes—
1002C22×C4C2×C4×D1711yescharacteristic
1003C22×C4C23×D1711yescharacteristic
1004C22×C4C23×D1712yes—
1005C22×C4C23×D1711yescharacteristic
1006C22×C4C23×D1711yescharacteristic
1007M16—41no—
1008M16—41no—
1009M16—42no—
1010M16—42no—
1011M16—344no—
1012M16—344no—
1013M16—682no—
1014M16—682no—
1015M16—682no—
1016M16—682no—
1017M16—681no—
1018M16—681no—
1019C2×C8—41no—
1020C2×C8—41no—
1021C2×C8—172no—
1022C2×C8—172no—
1023C2×C8—172no—
1024C2×C8—172no—
1025C2×C8—344no—
1026C2×C8—344no—
1027C2×C8—682no—
1028C2×C8—682no—
1029C2×C8—682no—
1030C2×C8—682no—
1031C2×C8—681no—
1032C2×C8—681no—
1033C2×C8—682no—
1034C2×C8—682no—
1035C2×C8C23×D1712yes—
1036C2×C8C23×D1712yes—
1037C2×C8C23×D1712yes—
1038C2×C8C23×D1712yes—
1039C4⋊C4—172no—
1040C4⋊C4—172no—
1041C4⋊C4—172no—
1042C4⋊C4—172no—
1043C4⋊C4—172no—
1044C4⋊C4—172no—
1045C4⋊C4—172no—
1046C4⋊C4—172no—
1047C4⋊C4—172no—
1048C4⋊C4C2×C4×D1712yes—
1049C4⋊C4C2×C4×D1712yes—
1050C4⋊C4C2×C4×D1712yes—
1051C22⋊C4—171no—
1052C22⋊C4—171no—
1053C22⋊C4—172no—
1054C22⋊C4—172no—
1055C22⋊C4—172no—
1056C22⋊C4—172no—
1057C22⋊C4—172no—
1058C22⋊C4—172no—
1059C22⋊C4—172no—
1060C22⋊C4—172no—
1061C22⋊C4—172no—
1062C22⋊C4—172no—
1063C22⋊C4—172no—
1064C22⋊C4—172no—
1065C22⋊C4—172no—
1066C22⋊C4—172no—
1067C22⋊C4C2×C4×D1711yescharacteristic
1068C22⋊C4C2×C4×D1711yescharacteristic
1069C22⋊C4C2×C4×D1712yes—
1070C22⋊C4C2×C4×D1712yes—
1071C22⋊C4C2×C4×D1712yes—
1072C22⋊C4C2×C4×D1712yes—
1073C42—172no—
1074C42—172no—
1075C42—172no—
1076C42C23×D1712yes—
1077C23—41no—
1078C23—42no—
1079C23—171no—
1080C23—171no—
1081C23—171no—
1082C23—172no—
1083C23—171no—
1084C23—342no—
1085C23—342no—
1086C23—342no—
1087C23—682no—
1088C23—681no—
1089C23—682no—
1090C23—682no—
1091C23—682no—
1092C23C22×C4×D1711yescharacteristic
1093C23C22×C4×D1711yescharacteristic
1094C23C22×C4×D1711yescharacteristic
1095C23C22×C4×D1712yes—
1096Q8—41no—
1097Q8—344no—
1098Q8—681no—
1099Q8—682no—
1100Q8—681no—
1101Q8—681no—
1102D4—41no—
1103D4—41no—
1104D4—41no—
1105D4—42no—
1106D4—42no—
1107D4—344no—
1108D4—344no—
1109D4—344no—
1110D4—681no—
1111D4—682no—
1112D4—681no—
1113D4—681no—
1114D4—682no—
1115D4—682no—
1116D4—682no—
1117D4—681no—
1118D4—681no—
1119D4—681no—
1120D4—681no—
1121D4—681no—
1122D4—681no—
1123D4—682no—
1124D4—682no—
1125D4—682no—
1126D4—682no—
1127D4—682no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—41no—
1137C2×C4—42no—
1138C2×C4—171no—
1139C2×C4—172no—
1140C2×C4—172no—
1141C2×C4—171no—
1142C2×C4—172no—
1143C2×C4—172no—
1144C2×C4—171no—
1145C2×C4—171no—
1146C2×C4—172no—
1147C2×C4—342no—
1148C2×C4—342no—
1149C2×C4—342no—
1150C2×C4—342no—
1151C2×C4—342no—
1152C2×C4—342no—
1153C2×C4—342no—
1154C2×C4—342no—
1155C2×C4—342no—
1156C2×C4—341no—
1157C2×C4—341no—
1158C2×C4—342no—
1159C2×C4—342no—
1160C2×C4—341no—
1161C2×C4—341no—
1162C2×C4—341no—
1163C2×C4—341no—
1164C2×C4—682no—
1165C2×C4—682no—
1166C2×C4—682no—
1167C2×C4—681no—
1168C2×C4C22×C4×D1712yes—
1169C2×C4C22×C4×D1712yes—
1170C2×C4C22×C4×D1711yescharacteristic
1171C2×C4C22×C4×D1711yescharacteristic
1172C2×C4C22×C4×D1712yes—
1173C2×C4C22×C4×D1711yescharacteristic
1174C2×C4C24×D1711yescharacteristic
1175C8—22no—
1176C8—22no—
1177C8—22no—
1178C8—22no—
1179C8—342no—
1180C8—342no—
1181C8—342no—
1182C8—342no—
1183C22—22no—
1184C22—22no—
1185C22—22no—
1186C22—22no—
1187C22—22no—
1188C22—21no—
1189C22—22no—
1190C22—21no—
1191C22—21no—
1192C22—82no—
1193C22—172no—
1194C22—342no—
1195C22—342no—
1196C22—342no—
1197C22—342no—
1198C22—342no—
1199C22—342no—
1200C22—341no—
1201C22—341no—
1202C22—341no—
1203C22—342no—
1204C22—684no—
1205C22—1362no—
1206C22—1362no—
1207C22—1362no—
1208C22C23×C4×D1711yescharacteristic
1209C4—22no—
1210C4—22no—
1211C4—21no—
1212C4—22no—
1213C4—21no—
1214C4—21no—
1215C4—172no—
1216C4—342no—
1217C4—342no—
1218C4—341no—
1219C4—341no—
1220C4—341no—
1221C4—342no—
1222C4H(5,𝔽2)×D1711yescharacteristic
1223C4H(5,𝔽2)×D1711yescharacteristic
1224C2—41no—
1225C2—42no—
1226C2—41no—
1227C2—41no—
1228C2—342no—
1229C2—681no—
1230C2—681no—
1231C2—681no—
1232C2—682no—
1233C2D17×#51811yescharacteristic
1234C2#1454349712yes—
subgroupG/H
center, FrattiniC2×C4C24×D17
commutator, socleC22×C17C24×C4
FittingC17×#2978C2
prime radical#14542114C2
cosocleC2×C4×C17C25
hypercenter#2978D17
hypocenterC17#60235
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ #2978

Complements

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

NH ≅ G/Ntype
2. #14537861C2semidirect
3. #14537856C2semidirect
4. #14537852C2semidirect
5. #14537849C2semidirect
6. #14537842C2semidirect
7. #14537840C2semidirect
8. #14537836C2semidirect
9. #14537834C2semidirect
10. #14537830C2semidirect
11. #14537513C2semidirect
12. #14537510C2semidirect
13. #14537484C2semidirect
14. #14537475C2semidirect
15. #14537440C2semidirect
16. #14537234C2semidirect
17. #14537226C2semidirect
18. D17×#408C2semidirect
19. C17×#2978C2semidirect
24. C22×#63218C22semidirect
25. C2×M16×D17C22semidirect
26. C2×M16×D17C22semidirect
27. C22×C8×D17C22semidirect
48. #11762888C22semidirect
49. #11762886C22semidirect
50. #11762885C22semidirect
51. #11762885C22semidirect
52. #11762885C22semidirect
53. #11762884C22semidirect
54. #11762883C22semidirect
55. #11762882C22semidirect
56. #11762882C22semidirect
57. #11762881C22semidirect
58. #11762881C22semidirect
59. #11762880C22semidirect
60. #11762879C22semidirect
61. #11762879C22semidirect
62. #11762878C22semidirect
63. #11762878C22semidirect
64. #11762878C22semidirect
65. #11762877C22semidirect
66. #11762877C22semidirect
67. #11762877C22semidirect
68. C8×D68C22semidirect
69. D4×#3622C22semidirect
70. D4×#3622C22semidirect
71. #11762874C22semidirect
72. C8×C22⋊D17C22semidirect
73. #11762872C22semidirect
74. #11762872C22semidirect
75. #11762872C22semidirect
76. #11762870C22semidirect
77. #11762867C22semidirect
78. #11762867C22semidirect
79. #11762865C22semidirect
80. #11762864C22semidirect
81. #11762861C22semidirect
82. #11762860C22semidirect
83. #11762834C22semidirect
84. #11762834C22semidirect
85. #11762777C22semidirect
86. #11762777C22semidirect
87. #11762777C22semidirect
88. #11762777C22semidirect
91. #11762775C22semidirect
92. #11762775C22semidirect
97. #11762774C22semidirect
98. #11762774C22semidirect
99. #11762774C22semidirect
100. #11762774C22semidirect
102. #11762771C22semidirect
103. #11762771C22semidirect
104. C2×C22⋊#3622C22semidirect
106. C22⋊C8×D17C22semidirect
107. C22⋊C8×D17C22semidirect
108. #11762766C22semidirect
109. #11762763C22semidirect
111. C17×#436C22semidirect
112. C17×#436C22semidirect
113. C17×#435C22semidirect
114. C17×#435C22semidirect
115. C17×#433C22semidirect
118. C17×#407C22semidirect
572. #2978D17semidirect
661. #436C2×D17semidirect
662. #436C2×D17semidirect
677. #435C2×D17semidirect
678. #435C2×D17semidirect
690. #433C2×D17semidirect
718. #407C2×D17semidirect
909. C17#60235semidirect

Maximal subgroups

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

subgroupindex
#145421142
#145378612
#145378562
#145378522
#145378492
#145378422
#145378402
#145378362
#145378342
#145378302
#145375132
#145375102
#145374842
#145374752
#145374402
#145372342
#145372262
D17×#4082
C17×#29782
#6023517