Finite Group Databasebeta

← #17001938

Subgroups — #17001938

Order 4352.

1004 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14542519C211yesmaximal, characteristic
2#14531644C211yesmaximal, characteristic, complemented
3#14527362C211yesmaximal, characteristic, complemented
4#14527345C211yesmaximal, characteristic, complemented
5#14527341C211yesmaximal, characteristic, complemented
6#14527332C211yesmaximal, characteristic, complemented
7#14527323C211yesmaximal, characteristic, complemented
8#14527314C211yesmaximal, characteristic, complemented
9#14527310C211yesmaximal, characteristic, complemented
10#14527293C211yesmaximal, characteristic, complemented
11#14527289C211yesmaximal, characteristic, complemented
12#14527280C211yesmaximal, characteristic, complemented
13#14527271C211yesmaximal, characteristic, complemented
14C2×#11762544C211yesmaximal, characteristic, complemented
15C17×#2924C211yesmaximal, characteristic, complemented
16#11763522—21no—
17#11763507—21no—
18#11763503—21no—
19#11763483—21no—
20#11763483—21no—
21#11763460—21no—
22#11763449—21no—
23#11763449—21no—
24#11763437C411yescharacteristic, complemented
25#11763430C411yescharacteristic, complemented
26#11763430C411yescharacteristic, complemented
27#11763414C411yescharacteristic, complemented
28#11763414C411yescharacteristic, complemented
29#11763378C411yescharacteristic, complemented
30#11763359C2211yescharacteristic
31#11763359C2211yescharacteristic
32#11763343C2211yescharacteristic
33#11763343C2211yescharacteristic
34#11763320C2211yescharacteristic
35C2×#10587616C2211yescharacteristic
36#11763289C411yescharacteristic, complemented
37#11763283C411yescharacteristic, complemented
38#11762695—21no—
39#11762695—21no—
40#11762684—21no—
41#11762677C2211yescharacteristic, complemented
42#11762675C2211yescharacteristic, complemented
43#11762672C2211yescharacteristic
44C4×C4⋊Dic17C2211yescharacteristic, complemented
45C22⋊C4×Dic17—21no—
46#11762655C2211yescharacteristic, complemented
47C2×#10587502C2211yescharacteristic
48#11762547C2211yescharacteristic, complemented
49#11762547C2211yescharacteristic, complemented
50#11762547C2211yescharacteristic, complemented
51#11762547C2211yescharacteristic, complemented
52#11762544C2211yescharacteristic
53#11762544C2211yescharacteristic
54#11762544C2211yescharacteristic
55#11762544C2211yescharacteristic
56#11762544C2211yescharacteristic
57#11762544C2211yescharacteristic
58#11762544C2211yescharacteristic
59#11762544C2211yescharacteristic
60#11762544C2211yescharacteristic, complemented
61#11762544C2211yescharacteristic, complemented
62#11762544C2211yescharacteristic, complemented
63#11762544C2211yescharacteristic, complemented
64C2×C17×#117C2211yescharacteristic
65C17×#433—21no—
66C17×#433—21no—
67C17×#432C2211yescharacteristic, complemented
68C17×#432C2211yescharacteristic, complemented
69C17×#431C2211yescharacteristic, complemented
70C17×#431C2211yescharacteristic, complemented
71C17×#424—21no—
72C17×#407C2211yescharacteristic
73C2×C17×C22⋊C8C2211yescharacteristic
74C17×#405—21no—
75C23×C4×C17C2311yescharacteristic
76C22×C22⋊D17—21no—
77C23×Dic17—21no—
78C2×#63252—21no—
79C2×#63252—21no—
80C2×#63252C2×C411yescharacteristic
81C22×D68C2×C411yescharacteristic
82C2×M16×C17—21no—
83C22×C8×C17—21no—
84C17×#117C2×C411yescharacteristic
85C17×#117C2×C411yescharacteristic
86C17×#117C2×C411yescharacteristic
87C17×#117C2×C411yescharacteristic
88C17×#117D411yescharacteristic
89C17×#117D411yescharacteristic
90C17×#117D411yescharacteristic
91C17×#117D411yescharacteristic
92C2×C4⋊C4×C17D411yescharacteristic
93C2×C4⋊C4×C17D411yescharacteristic
94C2×C22⋊C4×C17D411yescharacteristic
95C2×C22⋊C4×C17D411yescharacteristic
96C2×C42×C17C2311yescharacteristic
97C2×C42×C17C2311yescharacteristic
98#10587639—21no—
99C2×C22⋊Dic17—21no—
100#10587616—21no—
101#10587616—21no—
102#10587616—21no—
103#10587616—21no—
104#10587616C2×C411yescharacteristic
105#10587616C2×C411yescharacteristic
106#10587616C2×C411yescharacteristic
107#10587616C2311yescharacteristic
108#10587616C2311yescharacteristic
109#10587616C2311yescharacteristic
110#10587615—21no—
111#10587615—21no—
112#10587615—21no—
113C4×C22⋊D17—21no—
114C4×C22⋊D17—21no—
115C4×C22⋊D17—21no—
116C4×C22⋊D17—21no—
117C2×#63227—21no—
118#10587612C2×C411yescharacteristic
119C2×C4⋊Dic17—21no—
120C2×C4⋊Dic17—21no—
121C2×C4⋊Dic17C2×C411yescharacteristic
122#10587610C2×C411yescharacteristic
123#10587610C2311yescharacteristic
124C2×C4×Dic17—21no—
125C2×C4×Dic17—21no—
126#10587584—21no—
127#10587584—21no—
128#10587582—21no—
129#10587582—21no—
130#10587581—21no—
131#10587581—21no—
132#10587580—21no—
133#10587580—21no—
134#10587580—21no—
135#10587580—21no—
136#10587579—21no—
137#10587579—21no—
138#10587578—21no—
139C4⋊C4×D17—21no—
140#10587576—21no—
141#10587574—21no—
142#10587571—21no—
143#10587571—21no—
144#10587570—21no—
145#10587570—21no—
146#10587570—21no—
147#10587570—21no—
148#10587569—21no—
149#10587569—21no—
150#10587568—21no—
151#10587568—21no—
152#10587567—21no—
153#10587567—21no—
154C22⋊C4×D17—21no—
155C22⋊C4×D17—21no—
156#10587564—21no—
157#10587564—21no—
158#10587562—21no—
159#10587562—21no—
160#10587561—21no—
161#10587561—21no—
162#10587561C2×C411yescharacteristic, complemented
163#10587561C2×C411yescharacteristic, complemented
164#10587560C2×C411yescharacteristic, complemented
165#10587560C2×C411yescharacteristic, complemented
166C4×D68—21no—
167C4×D68—21no—
168C4×D68C2×C411yescharacteristic, complemented
169C4×D68C2×C411yescharacteristic, complemented
170C4×D68C2×C411yescharacteristic, complemented
171C4×D68C2×C411yescharacteristic, complemented
172C4×D68C2×C411yescharacteristic, complemented
173C4×D68C2×C411yescharacteristic, complemented
174#10587558—21no—
175#10587558—21no—
176#10587556C2×C411yescharacteristic, complemented
177#10587556C2×C411yescharacteristic, complemented
178#10587555C2×C411yescharacteristic, complemented
179#10587555C2×C411yescharacteristic, complemented
180C4×Dic34C2×C411yescharacteristic, complemented
181C4×Dic34C2×C411yescharacteristic, complemented
182C17×C4⋊C8—21no—
183C17×C4⋊C8—21no—
184C17×C4⋊C8—21no—
185C17×C4⋊C8—21no—
186C17×C22⋊C8—21no—
187C17×C22⋊C8—21no—
188C17×C22⋊C8C2311yescharacteristic
189C17×C22⋊C8C2311yescharacteristic
190C17×C22⋊C8C2311yescharacteristic
191C17×C22⋊C8C2311yescharacteristic
192C17×#97—21no—
193C17×#97—21no—
194C4×C8×C17—21no—
195C4×C8×C17—21no—
196#10587502—21no—
197#10587502—21no—
198#10587502—21no—
199#10587502—21no—
200#10587502—21no—
201#10587502—21no—
202#10587502C2311yescharacteristic
203#10587502C2311yescharacteristic
204#10587502C2311yescharacteristic
205#10587502C2311yescharacteristic
206C24×C17C2×D411yescharacteristic
207C23×D17—21no—
208C22×C4×C17—42no—
209C22×C4×C17C22×C411yescharacteristic
210C22×C4×C17C22×C411yescharacteristic
211C22×C4×C17C2×D411yescharacteristic
212C22×C4×C17C2×D411yescharacteristic
213C22×C4×C17C2×D411yescharacteristic
214C22×C4×C17C2×D411yescharacteristic
215C22×C4×C17C2×D411yescharacteristic
216C22×C4×C17C2×D411yescharacteristic
217C22×C4×C17C2×D411yescharacteristic
218C22×C4×C17C2411yescharacteristic
219C2×C22⋊D17—21no—
220C2×C22⋊D17—21no—
221C2×C22⋊D17—21no—
222C2×C22⋊D17—21no—
223C2×C22⋊D17—21no—
224C2×C22⋊D17—21no—
225C2×C22⋊D17—21no—
226C2×C22⋊D17—81no—
227C2×C22⋊D17—81no—
228C22×Dic17—21no—
229C22×Dic17—21no—
230C22×Dic17—21no—
231C22×Dic17—21no—
232C22×Dic17—21no—
233C22×Dic17—42no—
234C22×Dic17—42no—
235C22×Dic17—81no—
236#63252—42no—
237#63252—81no—
238#63252—81no—
239#63252—81no—
240#63252—81no—
241C2×D68—21no—
242C2×D68—21no—
243C2×D68—21no—
244C2×D68—21no—
245C2×D68—21no—
246C2×D68—42no—
247C2×D68C22×C411yescharacteristic
248C2×D68C22×C411yescharacteristic
249C2×D68C22×C411yescharacteristic
250C2×C4×D17—21no—
251C2×C4×D17—21no—
252C2×C4×D17—21no—
253C2×C4×D17—21no—
254C2×C4×D17—21no—
255C2×C4×D17—21no—
256C2×C4×D17—21no—
257C2×Dic34—21no—
258C2×Dic34—21no—
259C2×Dic34C22×C411yescharacteristic
260M16×C17—42no—
261C2×C8×C17—21no—
262C2×C8×C17—21no—
263C2×C8×C17—21no—
264C2×C8×C17—21no—
265C2×C8×C17—42no—
266C4⋊C4×C17C22⋊C411yescharacteristic
267C4⋊C4×C17C22⋊C411yescharacteristic
268C4⋊C4×C17C22⋊C411yescharacteristic
269C4⋊C4×C17C22⋊C411yescharacteristic
270C4⋊C4×C17C22⋊C411yescharacteristic
271C4⋊C4×C17C22⋊C411yescharacteristic
272C4⋊C4×C17C22⋊C411yescharacteristic
273C4⋊C4×C17C22⋊C411yescharacteristic
274C22⋊C4×C17C22⋊C411yescharacteristic
275C22⋊C4×C17C22⋊C411yescharacteristic
276C22⋊C4×C17C22⋊C411yescharacteristic
277C22⋊C4×C17C22⋊C411yescharacteristic
278C22⋊C4×C17C22⋊C411yescharacteristic
279C22⋊C4×C17C22⋊C411yescharacteristic
280C22⋊C4×C17C22⋊C411yescharacteristic
281C22⋊C4×C17C22⋊C411yescharacteristic
282C42×C17C22×C411yescharacteristic
283C42×C17C22×C411yescharacteristic
284C42×C17C22×C411yescharacteristic
285C42×C17C22×C411yescharacteristic
286C42×C17C2×D411yescharacteristic
287C42×C17C2×D411yescharacteristic
288C42×C17C2×D411yescharacteristic
289C42×C17C2×D411yescharacteristic
290C22⋊Dic17—21no—
291C22⋊Dic17—21no—
292C22⋊Dic17—21no—
293C22⋊Dic17—42no—
294#63227—21no—
295#63227—21no—
296#63227—21no—
297#63227—21no—
298#63227—21no—
299#63227—21no—
300#63227—21no—
301#63227—21no—
302#63227—21no—
303#63227—21no—
304#63227—21no—
305#63227—21no—
306#63227—21no—
307#63227—21no—
308#63227—21no—
309#63227—21no—
310C4⋊Dic17—21no—
311C4⋊Dic17—21no—
312C4⋊Dic17—21no—
313C4⋊Dic17—42no—
314C4⋊Dic17—81no—
315C4⋊Dic17C22×C411yescharacteristic
316C4⋊Dic17C22×C411yescharacteristic
317C4⋊Dic17C22×C411yescharacteristic
318C4⋊Dic17C22×C411yescharacteristic
319#63225—21no—
320#63225—21no—
321#63225—21no—
322#63225—21no—
323#63225—21no—
324#63225—21no—
325#63225—21no—
326#63225—21no—
327C4×Dic17—21no—
328C4×Dic17—21no—
329C4×Dic17—21no—
330C4×Dic17—42no—
331C4×Dic17—81no—
332#17604—171nomaximal, Sylow
333C23×C17—21no—
334C23×C17—21no—
335C23×C17—22no—
336C23×C17—41no—
337C23×C17C2×C22⋊C411yescharacteristic
338C23×C17C2×C22⋊C411yescharacteristic
339C23×C17C22×D411yescharacteristic
340C22×D17—21no—
341C22×D17—21no—
342C22×D17—21no—
343C22×D17—42no—
344C22×D17—81no—
345C22×D17—81no—
346C2×C4×C17—21no—
347C2×C4×C17—21no—
348C2×C4×C17—21no—
349C2×C4×C17—21no—
350C2×C4×C17—22no—
351C2×C4×C17—22no—
352C2×C4×C17—41no—
353C2×C4×C17—41no—
354C2×C4×C17—41no—
355C2×C4×C17—41no—
356C2×C4×C17—41no—
357C2×C4×C17—41no—
358C2×C4×C17C2×C22⋊C411yescharacteristic
359C2×C4×C17C2×C22⋊C411yescharacteristic
360C2×C4×C17C2×C22⋊C411yescharacteristic
361C2×C4×C17C2×C22⋊C411yescharacteristic
362C2×C4×C17C2×C22⋊C411yescharacteristic
363C2×C4×C17C2×C22⋊C411yescharacteristic
364C2×C4×C17C2×C22⋊C411yescharacteristic
365C2×C4×C17C2×C22⋊C411yescharacteristic
366C2×C4×C17C2×C22⋊C411yescharacteristic
367C2×C4×C17C2×C22⋊C411yescharacteristic
368C2×C4×C17C23×C411yescharacteristic
369C2×C4×C17C22×D411yescharacteristic
370C22⋊D17—41no—
371C22⋊D17—41no—
372C22⋊D17—41no—
373C22⋊D17—41no—
374C22⋊D17—41no—
375C22⋊D17—41no—
376C22⋊D17—42no—
377C22⋊D17—81no—
378C22⋊D17—81no—
379C22⋊D17—81no—
380C2×Dic17—22no—
381C2×Dic17—21no—
382C2×Dic17—21no—
383C2×Dic17—21no—
384C2×Dic17—21no—
385C2×Dic17—21no—
386C2×Dic17—41no—
387C2×Dic17—41no—
388C2×Dic17—41no—
389C2×Dic17—41no—
390C2×Dic17—41no—
391C2×Dic17—41no—
392C2×Dic17—41no—
393C2×Dic17—41no—
394C2×Dic17—41no—
395C2×Dic17—41no—
396C2×Dic17—41no—
397C2×Dic17—81no—
398C2×Dic17—84no—
399D68—41no—
400D68—41no—
401D68—41no—
402D68—42no—
403D68—81no—
404D68—81no—
405D68—81no—
406D68—81no—
407C4×D17—42no—
408C4×D17—81no—
409C4×D17—81no—
410C4×D17—81no—
411C4×D17—81no—
412C4×D17—81no—
413C4×D17—81no—
414Dic34—41no—
415Dic34—81no—
416Dic34—81no—
417C8×C17—41no—
418C8×C17—41no—
419C8×C17—41no—
420C8×C17—41no—
421#3494—171no—
422#2924D1711yescharacteristic, complemented
423#2343—171no—
424#1521—171no—
425#1517—171no—
426#1516—171no—
427#1514—171no—
428#1512—171no—
429#1510—171no—
430#1509—171no—
431#1505—171no—
432#1504—171no—
433#1502—171no—
434#1500—171no—
435C2×#327—171no—
436C22×C17—21no—
437C22×C17—21no—
438C22×C17—21no—
439C22×C17—21no—
440C22×C17—21no—
441C22×C17—21no—
442C22×C17—21no—
443C22×C17—42no—
444C22×C17—42no—
445C22×C17#41012yes—
446C22×C17C22×C22⋊C411yescharacteristic
447C22×C17#57611yescharacteristic
448C22×C17#57711yescharacteristic
449C2×D17—41no—
450C2×D17—41no—
451C2×D17—41no—
452C2×D17—41no—
453C2×D17—41no—
454C2×D17—41no—
455C2×D17—41no—
456C2×D17—41no—
457C2×D17—41no—
458C2×D17—162no—
459C4×C17—21no—
460C4×C17—21no—
461C4×C17—21no—
462C4×C17—21no—
463C4×C17—21no—
464C4×C17—21no—
465C4×C17—21no—
466C4×C17—21no—
467C4×C17—21no—
468C4×C17—21no—
469C4×C17—21no—
470C4×C17—21no—
471Dic17—42no—
472Dic17—41no—
473Dic17—41no—
474Dic17—41no—
475Dic17—41no—
476Dic17—41no—
477Dic17—81no—
478Dic17—81no—
479Dic17—81no—
480#555—341no—
481#553—341no—
482#553—341no—
483#551—341no—
484#551—341no—
485#547—341no—
486#546—341no—
487#546—341no—
488#544—171no—
489#542—171no—
490#542—171no—
491#540—171no—
492#540—171no—
493#535—171no—
494#532—171no—
495#532—171no—
496#529—171no—
497#529—171no—
498#525—171no—
499C2×#121—171no—
500#520—171no—
501#518—171no—
502C2×#117C2×D1711yescharacteristic
503#433—21no—
504#433—21no—
505#432C2×D1711yescharacteristic, complemented
506#432C2×D1711yescharacteristic, complemented
507#431C2×D1711yescharacteristic, complemented
508#431C2×D1711yescharacteristic, complemented
509#424—21no—
510#407C2×D1711yescharacteristic
511C2×C22⋊C8C2×D1711yescharacteristic
512#405—21no—
513#387—341no—
514#387—341no—
515#385—341no—
516#383—171no—
517#382—171no—
518#381—171no—
519C4×C4⋊C4—171no—
520C4×C22⋊C4—341no—
521#376—171no—
522C2×#95—171no—
523#328—171no—
524#328—171no—
525#328—171no—
526#328—171no—
527#327—171no—
528#327—171no—
529#327—171no—
530#327—171no—
531#327—171no—
532#327—171no—
533#327—171no—
534#327—171no—
535#327—171no—
536#327—171no—
537#327—171no—
538#327—171no—
539C2×C17—21no—
540C2×C17—21no—
541C2×C17—22no—
542C2×C17—41no—
543C2×C17C2×#41011yescharacteristic
544C2×C17#289711yescharacteristic
545C2×C17#290111yescharacteristic
546D17—81no—
547D17—81no—
548D17—81no—
549C2×#41—171no—
550C2×#41—341no—
551C2×#41—341no—
552C22×D4—171no—
553C22×D4—341no—
554C23×C4—341no—
555C23×C4C22×D1711yescharacteristic
556C2×M16—21no—
557C22×C8—21no—
558C4⋊Q8—171no—
559C4⋊Q8—171no—
560C4⋊Q8—341no—
561#127—171no—
562#127—171no—
563#126—341no—
564#126—341no—
565#126—341no—
566#126—341no—
567#125—171no—
568#125—171no—
569#125—341no—
570#124—171no—
571#124—171no—
572#124—341no—
573#124—341no—
574#124—341no—
575#124—341no—
576#123—341no—
577#123—341no—
578#123—341no—
579#123—341no—
580#123—341no—
581#123—341no—
582#123—341no—
583#123—341no—
584#123—341no—
585C22⋊Q8—171no—
586C22⋊Q8—171no—
587C22⋊Q8—341no—
588C22⋊Q8—341no—
589C22⋊Q8—341no—
590C22⋊Q8—341no—
591#121—171no—
592#121—171no—
593#121—171no—
594#121—171no—
595#121—171no—
596#121—171no—
597#121—341no—
598#121—341no—
599#121—341no—
600#121—341no—
601#121—341no—
602#121—341no—
603#121—341no—
604#121—341no—
605#121—341no—
606#121—341no—
607#120—341no—
608#120—341no—
609#120—341no—
610C4×Q8—171no—
611C4×Q8—171no—
612C4×D4—171no—
613C4×D4—171no—
614C4×D4—171no—
615C4×D4—171no—
616C4×D4—171no—
617C4×D4—171no—
618C4×D4—341no—
619C4×D4—341no—
620C4×D4—341no—
621C4×D4—341no—
622C4×D4—341no—
623C4×D4—341no—
624C4×D4—341no—
625C4×D4—341no—
626C4×D4—341no—
627C4×D4—341no—
628#117—171no—
629#117—341no—
630#117—341no—
631#117—341no—
632#117C4×D1711yescharacteristic
633#117C4×D1711yescharacteristic
634#117C4×D1711yescharacteristic
635#117C4×D1711yescharacteristic
636#117C22⋊D1711yescharacteristic
637#117C22⋊D1711yescharacteristic
638#117C22⋊D1711yescharacteristic
639#117C22⋊D1711yescharacteristic
640C2×C4⋊C4—171no—
641C2×C4⋊C4—341no—
642C2×C4⋊C4—341no—
643C2×C4⋊C4—341no—
644C2×C4⋊C4D6811yescharacteristic
645C2×C4⋊C4D6811yescharacteristic
646C2×C22⋊C4—341no—
647C2×C22⋊C4—341no—
648C2×C22⋊C4—341no—
649C2×C22⋊C4—341no—
650C2×C22⋊C4D6811yescharacteristic
651C2×C22⋊C4D6811yescharacteristic
652C2×C42—341no—
653C2×C42—341no—
654C2×C42C22×D1711yescharacteristic
655C2×C42C22×D1711yescharacteristic
656C4⋊C8—21no—
657C4⋊C8—21no—
658C4⋊C8—21no—
659C4⋊C8—21no—
660C22⋊C8—21no—
661C22⋊C8—21no—
662C22⋊C8C22×D1711yescharacteristic
663C22⋊C8C22×D1711yescharacteristic
664C22⋊C8C22×D1711yescharacteristic
665C22⋊C8C22×D1711yescharacteristic
666#97—21no—
667#97—21no—
668C4×C8—21no—
669C4×C8—21no—
670#95—171no—
671#95—171no—
672#95—171no—
673#95—171no—
674#95—341no—
675#95—341no—
676#95—341no—
677#95—341no—
678#95—341no—
679#95—341no—
680C17#1760411yescharacteristic, complemented, Sylow
681C24—341no—
682C24C2×D6811yescharacteristic
683#41—682no—
684#41—1361no—
685#41—1361no—
686#41—1361no—
687#41—1361no—
688C2×Q8—171no—
689C2×Q8—341no—
690C2×Q8—341no—
691C2×D4—171no—
692C2×D4—171no—
693C2×D4—171no—
694C2×D4—341no—
695C2×D4—341no—
696C2×D4—341no—
697C2×D4—341no—
698C2×D4—341no—
699C2×D4—341no—
700C2×D4—341no—
701C2×D4—341no—
702C2×D4—341no—
703C2×D4—341no—
704C2×D4—341no—
705C2×D4—341no—
706C2×D4—682no—
707C2×D4—1361no—
708C2×D4—1361no—
709C22×C4—42no—
710C22×C4—341no—
711C22×C4—341no—
712C22×C4—341no—
713C22×C4—341no—
714C22×C4—341no—
715C22×C4—341no—
716C22×C4—341no—
717C22×C4—341no—
718C22×C4—341no—
719C22×C4—341no—
720C22×C4—341no—
721C22×C4—341no—
722C22×C4—682no—
723C22×C4—682no—
724C22×C4—1361no—
725C22×C4C2×C4×D1711yescharacteristic
726C22×C4C2×C4×D1711yescharacteristic
727C22×C4C2×D6811yescharacteristic
728C22×C4C2×D6811yescharacteristic
729C22×C4C2×D6811yescharacteristic
730C22×C4C2×D6811yescharacteristic
731C22×C4C2×D6811yescharacteristic
732C22×C4C2×C22⋊D1711yescharacteristic
733C22×C4C2×C22⋊D1711yescharacteristic
734C22×C4C23×D1711yescharacteristic
735M16—42no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—42no—
741C4⋊C4—171no—
742C4⋊C4—171no—
743C4⋊C4—171no—
744C4⋊C4—171no—
745C4⋊C4—341no—
746C4⋊C4—341no—
747C4⋊C4—341no—
748C4⋊C4—341no—
749C4⋊C4—341no—
750C4⋊C4—341no—
751C4⋊C4—341no—
752C4⋊C4—341no—
753C4⋊C4—341no—
754C4⋊C4—341no—
755C4⋊C4—341no—
756C4⋊C4—682no—
757C4⋊C4—1361no—
758C4⋊C4#6322711yescharacteristic
759C4⋊C4#6322711yescharacteristic
760C4⋊C4#6322711yescharacteristic
761C4⋊C4#6322711yescharacteristic
762C4⋊C4#6322711yescharacteristic
763C4⋊C4#6322711yescharacteristic
764C4⋊C4#6322711yescharacteristic
765C4⋊C4#6322711yescharacteristic
766C22⋊C4—341no—
767C22⋊C4—341no—
768C22⋊C4—341no—
769C22⋊C4—341no—
770C22⋊C4—341no—
771C22⋊C4—341no—
772C22⋊C4—341no—
773C22⋊C4—341no—
774C22⋊C4—341no—
775C22⋊C4—341no—
776C22⋊C4—341no—
777C22⋊C4—341no—
778C22⋊C4—341no—
779C22⋊C4—341no—
780C22⋊C4—341no—
781C22⋊C4—341no—
782C22⋊C4—341no—
783C22⋊C4—341no—
784C22⋊C4—341no—
785C22⋊C4—682no—
786C22⋊C4#6322711yescharacteristic
787C22⋊C4#6322711yescharacteristic
788C22⋊C4#6322711yescharacteristic
789C22⋊C4#6322711yescharacteristic
790C22⋊C4#6322711yescharacteristic
791C22⋊C4#6322711yescharacteristic
792C22⋊C4#6322711yescharacteristic
793C22⋊C4#6322711yescharacteristic
794C42—341no—
795C42—341no—
796C42—341no—
797C42—682no—
798C42—1361no—
799C42C2×C4×D1711yescharacteristic
800C42C2×C4×D1711yescharacteristic
801C42C2×C4×D1711yescharacteristic
802C42C2×C4×D1711yescharacteristic
803C42C2×C22⋊D1711yescharacteristic
804C42C2×C22⋊D1711yescharacteristic
805C42C2×C22⋊D1711yescharacteristic
806C42C2×C22⋊D1711yescharacteristic
807C23—22no—
808C23—21no—
809C23—21no—
810C23—41no—
811C23—341no—
812C23—341no—
813C23—341no—
814C23—682no—
815C23—1361no—
816C23—1361no—
817C23C2×#6322711yescharacteristic
818C23C2×#6322711yescharacteristic
819C23C22×D6811yescharacteristic
820Q8—681no—
821Q8—1361no—
822Q8—1361no—
823D4—681no—
824D4—681no—
825D4—681no—
826D4—682no—
827D4—682no—
828D4—681no—
829D4—681no—
830D4—681no—
831D4—681no—
832D4—681no—
833D4—681no—
834D4—1361no—
835D4—1361no—
836D4—1361no—
837D4—1361no—
838D4—1361no—
839D4—1361no—
840D4—1361no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—342no—
854C2×C4—341no—
855C2×C4—341no—
856C2×C4—341no—
857C2×C4—341no—
858C2×C4—341no—
859C2×C4—682no—
860C2×C4—681no—
861C2×C4—681no—
862C2×C4—681no—
863C2×C4—681no—
864C2×C4—681no—
865C2×C4—681no—
866C2×C4—681no—
867C2×C4—681no—
868C2×C4—681no—
869C2×C4—681no—
870C2×C4—681no—
871C2×C4—1361no—
872C2×C4—1361no—
873C2×C4—1361no—
874C2×C4—1361no—
875C2×C4—1361no—
876C2×C4—1361no—
877C2×C4—1361no—
878C2×C4—1364no—
879C2×C4C2×#6322711yescharacteristic
880C2×C4C2×#6322711yescharacteristic
881C2×C4C2×#6322711yescharacteristic
882C2×C4C2×#6322711yescharacteristic
883C2×C4C2×#6322711yescharacteristic
884C2×C4C2×#6322711yescharacteristic
885C2×C4C2×#6322711yescharacteristic
886C2×C4C2×#6322711yescharacteristic
887C2×C4C2×#6322711yescharacteristic
888C2×C4C2×#6322711yescharacteristic
889C2×C4C22×C4×D1711yescharacteristic
890C2×C4C22×C22⋊D1711yescharacteristic
891C8—41no—
892C8—41no—
893C8—41no—
894C8—41no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—42no—
903C22—42no—
904C22—2722no—
905C22—681no—
906C22—681no—
907C22—681no—
908C22—681no—
909C22—681no—
910C22—681no—
911C22—681no—
912C22—681no—
913C22—681no—
914C22#1176278212yes—
915C22C22×#6322711yescharacteristic
916C22#1176361411yescharacteristic
917C22#1176362111yescharacteristic
918C4—21no—
919C4—21no—
920C4—21no—
921C4—21no—
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—21no—
927C4—21no—
928C4—21no—
929C4—21no—
930C4—682no—
931C4—681no—
932C4—681no—
933C4—681no—
934C4—681no—
935C4—681no—
936C4—1361no—
937C4—1361no—
938C4—1361no—
939C2—21no—
940C2—21no—
941C2—22no—
942C2—41no—
943C2—1361no—
944C2—1361no—
945C2—1361no—
946C2C2×#1176278211yescharacteristic
947C2#1453731111yescharacteristic
948C2#1453732911yescharacteristic
subgroupG/H
centerC22C22×#63227
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#2924C2
socleC22×C17C22×C22⋊C4
prime radical#14542519C2
cosocleC22×C4×C17C24
hypercenter#2924D17
hypocenterC17#17604
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2924

Complements

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

NH ≅ G/Ntype
2. #14531644C2semidirect
3. #14527362C2semidirect
4. #14527345C2semidirect
5. #14527341C2semidirect
6. #14527332C2semidirect
7. #14527323C2semidirect
8. #14527314C2semidirect
9. #14527310C2semidirect
10. #14527293C2semidirect
11. #14527289C2semidirect
12. #14527280C2semidirect
13. #14527271C2semidirect
14. C2×#11762544C2semidirect
15. C17×#2924C2semidirect
24. #11763437C4semidirect
25. #11763430C4semidirect
26. #11763430C4semidirect
27. #11763414C4semidirect
28. #11763414C4semidirect
29. #11763378C4semidirect
36. #11763289C4semidirect
37. #11763283C4semidirect
41. #11762677C22semidirect
42. #11762675C22semidirect
44. C4×C4⋊Dic17C22semidirect
46. #11762655C22semidirect
48. #11762547C22semidirect
49. #11762547C22semidirect
50. #11762547C22semidirect
51. #11762547C22semidirect
60. #11762544C22semidirect
61. #11762544C22semidirect
62. #11762544C22semidirect
63. #11762544C22semidirect
67. C17×#432C22semidirect
68. C17×#432C22semidirect
69. C17×#431C22semidirect
70. C17×#431C22semidirect
162. #10587561C2×C4semidirect
163. #10587561C2×C4semidirect
164. #10587560C2×C4semidirect
165. #10587560C2×C4semidirect
168. C4×D68C2×C4semidirect
169. C4×D68C2×C4semidirect
170. C4×D68C2×C4semidirect
171. C4×D68C2×C4semidirect
172. C4×D68C2×C4semidirect
173. C4×D68C2×C4semidirect
176. #10587556C2×C4semidirect
177. #10587556C2×C4semidirect
178. #10587555C2×C4semidirect
179. #10587555C2×C4semidirect
180. C4×Dic34C2×C4semidirect
181. C4×Dic34C2×C4semidirect
422. #2924D17semidirect
505. #432C2×D17semidirect
506. #432C2×D17semidirect
507. #431C2×D17semidirect
508. #431C2×D17semidirect
680. C17#17604semidirect

Maximal subgroups

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

subgroupindex
#145425192
#145316442
#145273622
#145273452
#145273412
#145273322
#145273232
#145273142
#145273102
#145272932
#145272892
#145272802
#145272712
C2×#117625442
C17×#29242
#1760417