Finite Group Databasebeta

← #29647586

Subgroups — #29647586

Order 15616.

882 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459907C211yesmaximal, characteristic
2#21454906C211yesmaximal, characteristic, complemented
3#21448467C211yesmaximal, characteristic, complemented
4#21444397C211yesmaximal, characteristic
5#21444395C211yesmaximal, characteristic
6#21444381C211yesmaximal, characteristic, complemented
7#21444370C211yesmaximal, characteristic, complemented
8#21444368C211yesmaximal, characteristic, complemented
9#21444356C211yesmaximal, characteristic
10#21444355C211yesmaximal, characteristic
11#21444343C211yesmaximal, characteristic
12#21444329C211yesmaximal, characteristic, complemented
13#21444316C211yesmaximal, characteristic, complemented
14#21444304C211yesmaximal, characteristic
15C61×#1518C211yesmaximal, characteristic, complemented
16#16840488C411yescharacteristic, complemented
17#16840488C411yescharacteristic, complemented
18#16840487C411yescharacteristic, complemented
19#16840487C411yescharacteristic, complemented
20#16840486C411yescharacteristic, complemented
21#16840484C411yescharacteristic, complemented
22#16840484C411yescharacteristic, complemented
23#16840454—21no—
24#16840445—21no—
25#16840445—21no—
26#16840427C411yescharacteristic, complemented
27#16840425—21no—
28#16840371—21no—
29#16840371—21no—
30#16840370—21no—
31#16840314C2211yescharacteristic
32#16840314C2211yescharacteristic
33#16840298C2211yescharacteristic
34#16840298C2211yescharacteristic
35#16840296C2211yescharacteristic
36#16840238—21no—
37C2×C4×Dic122C2211yescharacteristic
38#16839892—21no—
39#16839891—21no—
40#16839891—21no—
41C8×Dic122—21no—
42#16839819C2211yescharacteristic
43#16839816C2211yescharacteristic
44#16839816C2211yescharacteristic
45#16839812C2211yescharacteristic
46#16839812C2211yescharacteristic
47#16839666—21no—
48#16839657—21no—
49#16839645—21no—
50#16839643—21no—
51#16839630C2211yescharacteristic
52#16839629C2211yescharacteristic
53#16839626C2211yescharacteristic
54#16839613C2211yescharacteristic
55#16839607C2211yescharacteristic
56#16839500C2211yescharacteristic
57#16839500C2211yescharacteristic
58#16839499C2211yescharacteristic
59#16839499C2211yescharacteristic
60#16839499C2211yescharacteristic
61#16839499C2211yescharacteristic
62#16839498C2211yescharacteristic
63#16839498C2211yescharacteristic
64#16839497C2211yescharacteristic
65#16839497C2211yescharacteristic
66#16839495C2211yescharacteristic
67#16839495C2211yescharacteristic
68C61×#533C2211yescharacteristic
69C61×#431C2211yescharacteristic
70C61×#382C2211yescharacteristic
71C61×#328C2211yescharacteristic
72C61×#328C2211yescharacteristic
73C61×#328C2211yescharacteristic
74C61×#328C2211yescharacteristic
75C22×Dic122D411yescharacteristic
76C2×Q8×D61—21no—
77#14519776—21no—
78#14519776—21no—
79#14519776C2×C411yescharacteristic
80#14519776C2×C411yescharacteristic
81#14519775—21no—
82#14519775C2×C411yescharacteristic
83#14519775C2×C411yescharacteristic
84#14519772—21no—
85#14519772—21no—
86#14519772—21no—
87#14519772—21no—
88#14519772—21no—
89#14519772—21no—
90#14519771—21no—
91#14519771—21no—
92#14519771—21no—
93#14519769—21no—
94#14519769—21no—
95#14519769C2×C411yescharacteristic
96#14519768—21no—
97#14519768—21no—
98#14519768—21no—
99#14519768C2×C411yescharacteristic
100#14519768C2×C411yescharacteristic
101#14519767—21no—
102#14519767—21no—
103#14519767—21no—
104#14519767—21no—
105#14519767—21no—
106#14519767—21no—
107#14519766C2×C411yescharacteristic
108#14519766C2×C411yescharacteristic
109#14519765C2×C411yescharacteristic
110#14519761—21no—
111#14519761—21no—
112#14519760—21no—
113#14519757—21no—
114#14519756C2311yescharacteristic
115#14519755—21no—
116#14519755—21no—
117#14519755—21no—
118#14519755—21no—
119#14519754—21no—
120#14519754—21no—
121#14519753—21no—
122#14519751C2311yescharacteristic
123Q8×Dic61—21no—
124Q8×Dic61C2×C411yescharacteristic
125Q8×Dic61C2×C411yescharacteristic
126Q8×Dic61C2×C411yescharacteristic
127Q8×Dic61C2×C411yescharacteristic
128C4×Dic122—21no—
129C4×Dic122—21no—
130C4×Dic122C2×C411yescharacteristic
131C4×Dic122C2×C411yescharacteristic
132C4×Dic122C2×C411yescharacteristic
133C4×Dic122C2×C411yescharacteristic
134C4×Dic122C2×C411yescharacteristic
135C4×Dic122D411yescharacteristic
136C4×Dic122D411yescharacteristic
137C4×Dic122D411yescharacteristic
138C4×Dic122D411yescharacteristic
139#14519742—21no—
140#14519742—21no—
141#14519742—21no—
142#14519742C2×C411yescharacteristic
143#14519742C2×C411yescharacteristic
144C4×D244C2×C411yescharacteristic
145#14519739C2×C411yescharacteristic
146#14519739C2×C411yescharacteristic
147C4×C22⋊D61—21no—
148#14519737—21no—
149#14519737—21no—
150#14519735—21no—
151#14519735—21no—
152#14519735—21no—
153#14519734—21no—
154#14519734—21no—
155#14519734—21no—
156#14519733—21no—
157#14519733—21no—
158C2×C4⋊Dic61D411yescharacteristic
159C2×#11758196—21no—
160C2×#11758196—21no—
161C2×#11758196D411yescharacteristic
162C2×#11758196D411yescharacteristic
163C2×C4×Dic61—21no—
164C2×C4×Dic61—21no—
165C2×C4×Dic61C2311yescharacteristic
166C2×C4×Dic61C2311yescharacteristic
167C4⋊#92418—21no—
168#14519706—21no—
169#14519706—21no—
170#14519706—21no—
171#14519706—21no—
172C22⋊#92418C2311yescharacteristic
173C22⋊#92418C2311yescharacteristic
174#14519688—21no—
175#14519687—21no—
176#14519687—21no—
177C8×Dic61—21no—
178C8×Dic61—21no—
179#14519684—21no—
180#14519684—21no—
181#14519684—21no—
182#14519684—21no—
183#14519684—21no—
184#14519684—21no—
185#14519684C2311yescharacteristic
186#14519684C2311yescharacteristic
187C4⋊Q8×C61C2×C411yescharacteristic
188C4⋊Q8×C61C2×C411yescharacteristic
189#125×C61—21no—
190C22⋊Q8×C61—21no—
191C22⋊Q8×C61C2311yescharacteristic
192C22⋊Q8×C61C2311yescharacteristic
193C4×Q8×C61—21no—
194C4×Q8×C61C2×C411yescharacteristic
195C4×Q8×C61C2×C411yescharacteristic
196#117×C61—21no—
197C2×C4⋊C4×C61—21no—
198C2×C42×C61C2311yescharacteristic
199C4⋊C8×C61—21no—
200C22⋊C8×C61C2311yescharacteristic
201C22⋊C8×C61C2311yescharacteristic
202C4×C8×C61—21no—
203#95×C61—21no—
204#95×C61C2311yescharacteristic
205#95×C61C2311yescharacteristic
206C2×Q8×C61—21no—
207C2×Q8×C61C22×C411yescharacteristic
208C2×Q8×C61C22×C411yescharacteristic
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61C2×D411yescharacteristic
212C22×C4×C61C2×D411yescharacteristic
213C22×C4×C61C2411yescharacteristic
214C2×C22⋊D61—21no—
215C22×Dic61—21no—
216C22×Dic61—21no—
217C22×Dic61C2×D411yescharacteristic
218C22×Dic61C2×D411yescharacteristic
219C22×Dic61C2×D411yescharacteristic
220C22×Dic61C2×D411yescharacteristic
221Q8×D61—44no—
222C2×D244C22×C411yescharacteristic
223C2×C4×D61—21no—
224C2×C4×D61—21no—
225C2×C4×D61—21no—
226C2×Dic122—21no—
227C2×Dic122—21no—
228C2×Dic122—42no—
229C2×Dic122C22⋊C411yescharacteristic
230C2×Dic122C22⋊C411yescharacteristic
231C2×Dic122C22⋊C411yescharacteristic
232C2×Dic122C22⋊C411yescharacteristic
233C2×Dic122C22×C411yescharacteristic
234C2×C8×C61—21no—
235C2×C8×C61—21no—
236C4⋊C4×C61—21no—
237C4⋊C4×C61—21no—
238C4⋊C4×C61—21no—
239C4⋊C4×C61—21no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61—81no—
244C4⋊C4×C61C22×C411yescharacteristic
245C4⋊C4×C61C22×C411yescharacteristic
246C22⋊C4×C61—21no—
247C22⋊C4×C61—21no—
248C42×C61—21no—
249C42×C61—21no—
250C42×C61C22×C411yescharacteristic
251C42×C61C22×C411yescharacteristic
252C42×C61C2×D411yescharacteristic
253C42×C61C2×D411yescharacteristic
254C22⋊Dic61—21no—
255#11758198—21no—
256#11758198—21no—
257#11758198—21no—
258#11758198—21no—
259#11758198—21no—
260#11758198—21no—
261#11758198—21no—
262#11758198—21no—
263#11758198—21no—
264#11758198—21no—
265C4⋊Dic61—21no—
266C4⋊Dic61—21no—
267C4⋊Dic61—21no—
268C4⋊Dic61—21no—
269C4⋊Dic61—21no—
270C4⋊Dic61—21no—
271C4⋊Dic61C22⋊C411yescharacteristic
272C4⋊Dic61C22⋊C411yescharacteristic
273C4⋊Dic61C22⋊C411yescharacteristic
274C4⋊Dic61C22⋊C411yescharacteristic
275C4⋊Dic61C22×C411yescharacteristic
276C4⋊Dic61C22×C411yescharacteristic
277#11758196—21no—
278#11758196—21no—
279#11758196—21no—
280#11758196—21no—
281#11758196—21no—
282#11758196—21no—
283#11758196—21no—
284#11758196—21no—
285#11758196—21no—
286#11758196—21no—
287#11758196—21no—
288#11758196—21no—
289#11758196—21no—
290#11758196—21no—
291#11758196—42no—
292#11758196—81no—
293#11758196C22⋊C411yescharacteristic
294#11758196C22⋊C411yescharacteristic
295#11758196C22⋊C411yescharacteristic
296#11758196C22⋊C411yescharacteristic
297#11758196C22⋊C411yescharacteristic
298#11758196C22⋊C411yescharacteristic
299#11758196C22⋊C411yescharacteristic
300#11758196C22⋊C411yescharacteristic
301C4×Dic61—21no—
302C4×Dic61—21no—
303C4×Dic61—21no—
304C4×Dic61—21no—
305C4×Dic61—21no—
306C4×Dic61—21no—
307C4×Dic61—21no—
308C4×Dic61—42no—
309C4×Dic61—81no—
310C4×Dic61C22×C411yescharacteristic
311C4×Dic61C22×C411yescharacteristic
312C4×Dic61C22×C411yescharacteristic
313C4×Dic61C22×C411yescharacteristic
314C4×Dic61C2×D411yescharacteristic
315C4×Dic61C2×D411yescharacteristic
316C4×Dic61C2×D411yescharacteristic
317C4×Dic61C2×D411yescharacteristic
318C2×#92418—21no—
319C2×#92418—21no—
320C23×C61C22×D411yescharacteristic
321C22×D61—21no—
322Q8×C61—42no—
323Q8×C61—41no—
324Q8×C61—41no—
325C2×C4×C61—21no—
326C2×C4×C61—21no—
327C2×C4×C61—21no—
328C2×C4×C61—21no—
329C2×C4×C61—21no—
330C2×C4×C61—21no—
331C2×C4×C61—41no—
332C2×C4×C61—41no—
333C2×C4×C61—41no—
334C2×C4×C61—41no—
335C2×C4×C61—41no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61—41no—
339C2×C4×C61C2×C22⋊C411yescharacteristic
340C2×C4×C61C2×C22⋊C411yescharacteristic
341C2×C4×C61C2×C22⋊C411yescharacteristic
342C2×C4×C61C2×C22⋊C411yescharacteristic
343C2×C4×C61C23×C411yescharacteristic
344C2×C4×C61C22×D411yescharacteristic
345C22⋊D61—41no—
346C22⋊D61—41no—
347C2×Dic61—21no—
348C2×Dic61—21no—
349C2×Dic61—21no—
350C2×Dic61—21no—
351C2×Dic61—22no—
352C2×Dic61—21no—
353C2×Dic61—21no—
354C2×Dic61—21no—
355C2×Dic61—41no—
356C2×Dic61—41no—
357C2×Dic61—41no—
358C2×Dic61—41no—
359C2×Dic61—41no—
360C2×Dic61—41no—
361C2×Dic61—41no—
362C2×Dic61C2×C22⋊C411yescharacteristic
363C2×Dic61C2×C22⋊C411yescharacteristic
364C2×Dic61C2×C22⋊C411yescharacteristic
365C2×Dic61C2×C22⋊C411yescharacteristic
366C2×Dic61C2×C22⋊C411yescharacteristic
367C2×Dic61C2×C22⋊C411yescharacteristic
368C2×Dic61C2×C22⋊C411yescharacteristic
369C2×Dic61C2×C22⋊C411yescharacteristic
370D244—41no—
371C4×D61—42no—
372C4×D61—42no—
373C4×D61—42no—
374Dic122—22no—
375Dic122—22no—
376Dic122—41no—
377Dic122—41no—
378Dic122—42no—
379Dic122—42no—
380Dic122—41no—
381C8×C61—41no—
382C8×C61—41no—
383#92418—41no—
384#92418—41no—
385#17601—611nomaximal, Sylow
386C22×C61—21no—
387C22×C61—21no—
388C22×C61C22×C22⋊C411yescharacteristic
389C22×C61#57711yescharacteristic
390C22×C61#57811yescharacteristic
391C2×D61—41no—
392C2×D61—41no—
393C2×D61—41no—
394C4×C61—21no—
395C4×C61—21no—
396C4×C61—21no—
397C4×C61—21no—
398C4×C61—21no—
399C4×C61—21no—
400C4×C61—41no—
401C4×C61—41no—
402C4×C61—41no—
403C4×C61—41no—
404C4×C61—81no—
405C4×C61—81no—
406Dic61—21no—
407Dic61—21no—
408Dic61—21no—
409Dic61—21no—
410Dic61—21no—
411Dic61—21no—
412Dic61—21no—
413Dic61—41no—
414Dic61—41no—
415Dic61—41no—
416Dic61—81no—
417Dic61—81no—
418Dic61#42112yes—
419#3523—611no—
420#2984—611no—
421#2320—611no—
422#1521—611no—
423#1521—611no—
424#1518—611no—
425#1518D6111yescharacteristic, complemented
426#1515—611no—
427#1515—611no—
428#1512—611no—
429#1512—611no—
430#1509—611no—
431#1506—611no—
432#1503—611no—
433#1500—611no—
434C2×C61—21no—
435C2×C61—21no—
436C2×C61#288411yescharacteristic
437C2×C61#289811yescharacteristic
438C2×C61C2×#42111yescharacteristic
439D61—81no—
440#557—611no—
441#557—611no—
442#557—611no—
443#557—611no—
444#556—611no—
445#556—611no—
446#556—611no—
447#552—1221no—
448#552—1221no—
449#552—1221no—
450D4×Q8—611no—
451D4×Q8—1221no—
452#541—1221no—
453#541—1221no—
454#541—1221no—
455#533—611no—
456#533—611no—
457#533C2×D6111yescharacteristic
458#529—611no—
459#529—611no—
460#529—611no—
461#519—1221no—
462C2×C4×Q8—611no—
463#446—1221no—
464#446—1221no—
465#446—1221no—
466C8×Q8—1221no—
467#432—611no—
468#432—611no—
469#432—611no—
470#431—611no—
471#431—611no—
472#431C2×D6111yescharacteristic
473#391—1221no—
474#389—1221no—
475#387—1221no—
476#387—1221no—
477#383—611no—
478#383—611no—
479#382—611no—
480#382C2×D6111yescharacteristic
481C4×C4⋊C4—611no—
482#376—611no—
483#328—611no—
484#328—611no—
485#328—611no—
486#328—611no—
487#328—611no—
488#328—611no—
489#328—611no—
490#328—611no—
491#328C2×D6111yescharacteristic
492#328C2×D6111yescharacteristic
493#328C2×D6111yescharacteristic
494#328C2×D6111yescharacteristic
495#327—611no—
496#327—611no—
497#327—611no—
498#327—611no—
499C61#1760111yescharacteristic, complemented, Sylow
500C22×Q8—611no—
501C22×Q8—1221no—
502C4⋊Q8—611no—
503C4⋊Q8—611no—
504C4⋊Q8—611no—
505C4⋊Q8—611no—
506C4⋊Q8—1221no—
507C4⋊Q8—1221no—
508C4⋊Q8—1221no—
509C4⋊Q8C4×D6111yescharacteristic
510C4⋊Q8C4×D6111yescharacteristic
511#126—1221no—
512#126—1221no—
513#126—1221no—
514#126—1221no—
515#126—1221no—
516#126—1221no—
517#126—1221no—
518#126—1221no—
519#126—1221no—
520#125—21no—
521#125—611no—
522#125—611no—
523#125—611no—
524#125—1221no—
525#125—1221no—
526#125—1221no—
527#125—1221no—
528#125—1221no—
529#125—1221no—
530#125—1221no—
531#125—1221no—
532#125—1221no—
533#125—1221no—
534#125—1221no—
535#124—611no—
536#124—611no—
537#124—611no—
538#123—1221no—
539#123—1221no—
540#123—1221no—
541C22⋊Q8—21no—
542C22⋊Q8—611no—
543C22⋊Q8—1221no—
544C22⋊Q8—1221no—
545C22⋊Q8—1221no—
546C22⋊Q8—1221no—
547C22⋊Q8—1221no—
548C22⋊Q8—1221no—
549C22⋊Q8—1221no—
550C22⋊Q8—1221no—
551C22⋊Q8C22×D6111yescharacteristic
552C22⋊Q8C22×D6111yescharacteristic
553#121—611no—
554C4×Q8—21no—
555C4×Q8—611no—
556C4×Q8—611no—
557C4×Q8—611no—
558C4×Q8—611no—
559C4×Q8—611no—
560C4×Q8—611no—
561C4×Q8—611no—
562C4×Q8—611no—
563C4×Q8—611no—
564C4×Q8—611no—
565C4×Q8—611no—
566C4×Q8—611no—
567C4×Q8—611no—
568C4×Q8—611no—
569C4×Q8—611no—
570C4×Q8—1221no—
571C4×Q8—1221no—
572C4×Q8—1221no—
573C4×Q8—1221no—
574C4×Q8—1221no—
575C4×Q8—1221no—
576C4×Q8C4×D6111yescharacteristic
577C4×Q8C4×D6111yescharacteristic
578C4×D4—611no—
579C4×D4—611no—
580C4×D4—611no—
581C4×D4—1221no—
582C4×D4—1221no—
583C4×D4—1221no—
584#117—21no—
585#117—1221no—
586#117—1221no—
587#117—1221no—
588#117—1221no—
589#117—1221no—
590#117—1221no—
591#117—1221no—
592#117—1221no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—611no—
595C2×C4⋊C4—611no—
596C2×C4⋊C4—611no—
597C2×C4⋊C4—1221no—
598C2×C4⋊C4—1221no—
599C2×C42—611no—
600C2×C42—611no—
601C2×C42—1221no—
602C2×C42—1221no—
603C2×C42C22×D6111yescharacteristic
604C4⋊C8—21no—
605C4⋊C8—1221no—
606C4⋊C8—1221no—
607C4⋊C8—1221no—
608C4⋊C8—1221no—
609C4⋊C8—1221no—
610C22⋊C8—611no—
611C22⋊C8—611no—
612C22⋊C8C22×D6111yescharacteristic
613C22⋊C8C22×D6111yescharacteristic
614#97—1221no—
615#97—1221no—
616#97—1221no—
617C4×C8—21no—
618C4×C8—1221no—
619C4×C8—1221no—
620#95—21no—
621#95—611no—
622#95—611no—
623#95—1221no—
624#95—1221no—
625#95—1221no—
626#95—1221no—
627#95—1221no—
628#95—1221no—
629#95C22×D6111yescharacteristic
630#95C22×D6111yescharacteristic
631C2×Q8—21no—
632C2×Q8—611no—
633C2×Q8—611no—
634C2×Q8—611no—
635C2×Q8—611no—
636C2×Q8—611no—
637C2×Q8—1221no—
638C2×Q8—1221no—
639C2×Q8—2442no—
640C2×Q8—2444no—
641C2×Q8C2×C4×D6111yescharacteristic
642C2×Q8C2×C4×D6111yescharacteristic
643C2×D4—611no—
644C2×D4—1221no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—611no—
648C22×C4—611no—
649C22×C4—611no—
650C22×C4—611no—
651C22×C4—1221no—
652C22×C4—1221no—
653C22×C4—1221no—
654C22×C4—1221no—
655C22×C4—1221no—
656C22×C4D4×D6111yescharacteristic
657C22×C4D4×D6111yescharacteristic
658C22×C4C23×D6111yescharacteristic
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—1221no—
662C2×C8—1221no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—81no—
671C4⋊C4—611no—
672C4⋊C4—611no—
673C4⋊C4—611no—
674C4⋊C4—611no—
675C4⋊C4—611no—
676C4⋊C4—611no—
677C4⋊C4—611no—
678C4⋊C4—611no—
679C4⋊C4—611no—
680C4⋊C4—611no—
681C4⋊C4—611no—
682C4⋊C4—611no—
683C4⋊C4—611no—
684C4⋊C4—611no—
685C4⋊C4—1221no—
686C4⋊C4—1221no—
687C4⋊C4—1221no—
688C4⋊C4—1221no—
689C4⋊C4—1221no—
690C4⋊C4—1221no—
691C4⋊C4—1221no—
692C4⋊C4—1221no—
693C4⋊C4—1221no—
694C4⋊C4—1221no—
695C4⋊C4—1221no—
696C4⋊C4—1221no—
697C4⋊C4—1221no—
698C4⋊C4—1221no—
699C4⋊C4—1221no—
700C4⋊C4—1221no—
701C4⋊C4—1221no—
702C4⋊C4—1221no—
703C4⋊C4—1221no—
704C4⋊C4—1221no—
705C4⋊C4—4881no—
706C4⋊C4—2442no—
707C4⋊C4C2×C4×D6111yescharacteristic
708C4⋊C4C2×C4×D6111yescharacteristic
709C22⋊C4—21no—
710C22⋊C4—21no—
711C22⋊C4—1221no—
712C22⋊C4—1221no—
713C22⋊C4—1221no—
714C22⋊C4—1221no—
715C22⋊C4—1221no—
716C22⋊C4—1221no—
717C22⋊C4—1221no—
718C22⋊C4—1221no—
719C22⋊C4—1221no—
720C22⋊C4—1221no—
721C22⋊C4—1221no—
722C42—21no—
723C42—21no—
724C42—611no—
725C42—611no—
726C42—611no—
727C42—611no—
728C42—611no—
729C42—611no—
730C42—611no—
731C42—611no—
732C42—1221no—
733C42—1221no—
734C42—1221no—
735C42—1221no—
736C42—1221no—
737C42—1221no—
738C42—1221no—
739C42—4881no—
740C42—2442no—
741C42C2×C4×D6111yescharacteristic
742C42C2×C4×D6111yescharacteristic
743C42D4×D6111yescharacteristic
744C42D4×D6111yescharacteristic
745C23—1221no—
746C23C2×D4×D6111yescharacteristic
747Q8—41no—
748Q8—41no—
749Q8—42no—
750Q8—1222no—
751Q8—1222no—
752Q8—2441no—
753Q8—2441no—
754Q8—2441no—
755Q8—2442no—
756Q8—2442no—
757D4—2441no—
758D4—2441no—
759D4—2441no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—611no—
775C2×C4—611no—
776C2×C4—611no—
777C2×C4—611no—
778C2×C4—611no—
779C2×C4—611no—
780C2×C4—611no—
781C2×C4—611no—
782C2×C4—1222no—
783C2×C4—1221no—
784C2×C4—1221no—
785C2×C4—1221no—
786C2×C4—1221no—
787C2×C4—1221no—
788C2×C4—1221no—
789C2×C4—1221no—
790C2×C4—2442no—
791C2×C4—2442no—
792C2×C4—2442no—
793C2×C4—2441no—
794C2×C4—2441no—
795C2×C4—2441no—
796C2×C4—2441no—
797C2×C4—2441no—
798C2×C4—2441no—
799C2×C4—2441no—
800C2×C4C22⋊C4×D6111yescharacteristic
801C2×C4C22⋊C4×D6111yescharacteristic
802C2×C4C22⋊C4×D6111yescharacteristic
803C2×C4C22⋊C4×D6111yescharacteristic
804C2×C4C22×C4×D6111yescharacteristic
805C2×C4C2×D4×D6111yescharacteristic
806C8—41no—
807C8—41no—
808C8—2441no—
809C8—2441no—
810C22—21no—
811C22—21no—
812C22—2441no—
813C22—2441no—
814C22—2441no—
815C22C2×C22⋊C4×D6111yescharacteristic
816C22#1684056811yescharacteristic
817C22#1684057511yescharacteristic
818C4—21no—
819C4—21no—
820C4—21no—
821C4—21no—
822C4—21no—
823C4—21no—
824C4—41no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4—81no—
829C4—81no—
830C4—612no—
831C4—1221no—
832C4—1221no—
833C4—1221no—
834C4—1221no—
835C4—1221no—
836C4—1221no—
837C4—1221no—
838C4—4881no—
839C4—4881no—
840C4—2441no—
841C4—2441no—
842C4—2441no—
843C2—21no—
844C2—21no—
845C2—4881no—
846C2#2145428111yescharacteristic
847C2#2145434711yescharacteristic
848C2#421×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1518C2
socleC22×C61C22×C22⋊C4
prime radical#14519751C23
cosocleC22×C4×C61C24
hypercenter#1518D61
hypocenterC61#17601
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1518

Complements

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

NH ≅ G/Ntype
2. #21454906C2semidirect
3. #21448467C2semidirect
6. #21444381C2semidirect
7. #21444370C2semidirect
8. #21444368C2semidirect
12. #21444329C2semidirect
13. #21444316C2semidirect
15. C61×#1518C2semidirect
16. #16840488C4semidirect
17. #16840488C4semidirect
18. #16840487C4semidirect
19. #16840487C4semidirect
20. #16840486C4semidirect
21. #16840484C4semidirect
22. #16840484C4semidirect
26. #16840427C4semidirect
425. #1518D61semidirect
499. C61#17601semidirect

Maximal subgroups

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

subgroupindex
#214599072
#214549062
#214484672
#214443972
#214443952
#214443812
#214443702
#214443682
#214443562
#214443552
#214443432
#214443292
#214443162
#214443042
C61×#15182
#1760161