Finite Group Databasebeta

← #29645993

Subgroups — #29645993

Order 15616.

1020 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
1C2×#16840290C211yesmaximal, characteristic
2#21454447C211yesmaximal, characteristic, complemented
3#431×D61C211yesmaximal, characteristic, complemented
4#21444187C212yesmaximal, complemented
5#21444185C212yesmaximal, complemented
6#21444181C212yesmaximal, complemented
7#21444177C212yesmaximal
8#21444133C211yesmaximal, characteristic, complemented
9#21444131C211yesmaximal, characteristic, complemented
10#21444131C211yesmaximal, characteristic, complemented
11C61×#1458C211yesmaximal, characteristic, complemented
12#16840290—21no—
13#16840290—21no—
14#16840290—21no—
15#16840290—21no—
16#16840290—21no—
17#16840290—21no—
18#16840290—21no—
19#16840290—21no—
20C2×#14519772C2211yescharacteristic
21C2×#14519770C2211yescharacteristic
22C2×#14519767C411yescharacteristic
23C2×#14519763C411yescharacteristic
24C2×#14519762C411yescharacteristic
25C2×#14519759C411yescharacteristic
26C2×#14519755C2211yescharacteristic
27C2×#14519750C2211yescharacteristic
28C2×C4×Dic122C411yescharacteristic
29C2×C4×D244C411yescharacteristic
30C2×C4×C22⋊D61C411yescharacteristic
31C2×C4×C22⋊D61C411yescharacteristic
32C2×#14519734C2211yescharacteristic
33C2×C42×D61C2211yescharacteristic
34#16839818—21no—
35#16839816C2212yes—
36#16839815C2211yescharacteristic
37#16839815C2211yescharacteristic
38#16839814—21no—
39#16839813—21no—
40#16839813—21no—
41#16839812C2212yes—
42#16839784—21no—
43C4⋊C8×D61—21no—
44#16839724C2212yes—
45C22⋊C8×D61C2212yes—
46C4×#11758189—21no—
47C4×C8×D61—21no—
48#16839488C2212yes—
49#16839487C2212yes—
50#16839487C2212yes—
51#16839486C2212yes—
52#16839485C2212yes—
53#16839485C2212yes—
54C2×#117×C61C2211yescharacteristic
55C61×#431C2211yescharacteristic
56C61×#431C2211yescharacteristic
57C61×#324C2212yes—
58C61×#323C2212yes—
59C22×Dic122C2×C411yescharacteristic
60C22×D244C2×C411yescharacteristic
61C22×C22⋊D61C2×C411yescharacteristic
62C22×C22⋊D61C2×C411yescharacteristic
63C22×C4×D61C2×C411yescharacteristic
64C22×C4×D61C2×C411yescharacteristic
65C22×C4×D61C2×C411yescharacteristic
66C22×C4×D61C2311yescharacteristic
67C2×#11758189—22no—
68C2×C8×D61—22no—
69#14519772—21no—
70#14519772—21no—
71#14519772—21no—
72#14519772—21no—
73#14519770—21no—
74#14519770—21no—
75#14519770—21no—
76#14519770—21no—
77#14519767—21no—
78#14519767—21no—
79#14519767—21no—
80#14519767—21no—
81#14519763—21no—
82#14519763—21no—
83#14519763—21no—
84#14519763—21no—
85#14519762—21no—
86#14519762—21no—
87#14519762—21no—
88#14519762—21no—
89#14519759—21no—
90#14519759—21no—
91#14519759—21no—
92#14519759—21no—
93#14519755—21no—
94#14519755—21no—
95#14519755—21no—
96#14519755—21no—
97#14519750—21no—
98#14519750—21no—
99#14519750—21no—
100#14519750—21no—
101C4×Dic122—21no—
102C4×Dic122—21no—
103C4×Dic122—21no—
104C4×Dic122—21no—
105C4×D244—21no—
106C4×D244—21no—
107C4×D244—21no—
108C4×D244—21no—
109C4×C22⋊D61—21no—
110C4×C22⋊D61—21no—
111C4×C22⋊D61—21no—
112C4×C22⋊D61—21no—
113C4×C22⋊D61—21no—
114C4×C22⋊D61—21no—
115C4×C22⋊D61—21no—
116C4×C22⋊D61—21no—
117#14519734—21no—
118#14519734—21no—
119#14519734—21no—
120#14519734—21no—
121C2×C4⋊Dic61C2×C411yescharacteristic
122C2×C4⋊Dic61C2×C411yescharacteristic
123C2×#11758196C2×C411yescharacteristic
124C2×#11758196C2×C411yescharacteristic
125C2×#11758196C2×C411yescharacteristic
126C2×#11758196C2×C411yescharacteristic
127C2×#11758196C2×C411yescharacteristic
128C2×#11758196C2311yescharacteristic
129C2×C22⋊Dic61C2×C411yescharacteristic
130C2×C22⋊Dic61C2×C411yescharacteristic
131C2×#11758198C2×C411yescharacteristic
132C2×#11758198C2×C411yescharacteristic
133C2×#11758198C2×C411yescharacteristic
134C2×#11758198C2×C411yescharacteristic
135C2×#11758198C2×C411yescharacteristic
136C2×#11758198C2311yescharacteristic
137C2×C4×Dic61C2×C411yescharacteristic
138C2×C4×Dic61C2×C411yescharacteristic
139C2×C4×Dic61C2×C411yescharacteristic
140C2×C4×Dic61C2311yescharacteristic
141C42×D61D411yescharacteristic
142C42×D61D411yescharacteristic
143C42×D61D411yescharacteristic
144C42×D61D411yescharacteristic
145C42×D61D411yescharacteristic
146C42×D61D411yescharacteristic
147C42×D61D411yescharacteristic
148C42×D61D411yescharacteristic
149C4⋊#92418—21no—
150C4⋊#92418—21no—
151#14519706—22no—
152#14519706—22no—
153C22⋊#92418C2312yes—
154C22⋊#92418C2312yes—
155#14519689—22no—
156#14519689—22no—
157#14519687—22no—
158C4×#92418—21no—
159C4×#92418—21no—
160C8×Dic61—22no—
161C23×C4×C61C2×C411yescharacteristic
162#117×C61—21no—
163#117×C61—21no—
164#117×C61—21no—
165#117×C61—21no—
166C2×C4⋊C4×C61C2×C411yescharacteristic
167C2×C4⋊C4×C61C2311yescharacteristic
168C2×C22⋊C4×C61C2×C411yescharacteristic
169C2×C22⋊C4×C61C2311yescharacteristic
170C2×C42×C61C2×C411yescharacteristic
171C2×C42×C61C2311yescharacteristic
172C4⋊C8×C61—21no—
173C4⋊C8×C61—21no—
174C22⋊C8×C61C2312yes—
175C22⋊C8×C61C2312yes—
176C4×C8×C61—21no—
177C4×C8×C61—21no—
178C24×C61C22×C411yescharacteristic
179C23×D61C22×C411yescharacteristic
180C23×D61C22×C411yescharacteristic
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—22no—
184C22×C4×C61—22no—
185C22×C4×C61C22×C411yescharacteristic
186C22×C4×C61C22×C411yescharacteristic
187C22×C4×C61C22×C411yescharacteristic
188C22×C4×C61C22×C411yescharacteristic
189C22×C4×C61C22×C411yescharacteristic
190C22×C4×C61C2411yescharacteristic
191C2×C22⋊D61—21no—
192C2×C22⋊D61—21no—
193C2×C22⋊D61—21no—
194C2×C22⋊D61—21no—
195C2×C22⋊D61—42no—
196C2×C22⋊D61—42no—
197C22×Dic61C22×C411yescharacteristic
198C22×Dic61C22×C411yescharacteristic
199C22×Dic61C22×C411yescharacteristic
200C22×Dic61C22×C411yescharacteristic
201C22×Dic61C22×C411yescharacteristic
202C22×Dic61C22×C411yescharacteristic
203C2×D244—21no—
204C2×D244—21no—
205C2×D244—42no—
206C2×C4×D61—22no—
207C2×C4×D61—22no—
208C2×C4×D61—21no—
209C2×C4×D61—21no—
210C2×C4×D61—22no—
211C2×C4×D61—22no—
212C2×C4×D61—42no—
213C2×C4×D61—42no—
214C2×C4×D61C22⋊C411yescharacteristic
215C2×C4×D61C22⋊C411yescharacteristic
216C2×C4×D61C22⋊C411yescharacteristic
217C2×C4×D61C22⋊C411yescharacteristic
218C2×C4×D61C22⋊C411yescharacteristic
219C2×C4×D61C22⋊C411yescharacteristic
220C2×C4×D61C22⋊C411yescharacteristic
221C2×C4×D61C22⋊C411yescharacteristic
222C2×C4×D61C2×D411yescharacteristic
223C2×C4×D61C2×D411yescharacteristic
224C2×C4×D61C2×D411yescharacteristic
225C2×C4×D61C2×D411yescharacteristic
226C2×Dic122—21no—
227C2×Dic122—21no—
228C2×Dic122—42no—
229C2×C8×C61—22no—
230C2×C8×C61—22no—
231C4⋊C4×C61—21no—
232C4⋊C4×C61—21no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61—21no—
235C22⋊C4×C61—21no—
236C22⋊C4×C61—21no—
237C22⋊C4×C61—21no—
238C22⋊C4×C61—21no—
239C42×C61—21no—
240C42×C61—21no—
241C42×C61C2×D411yescharacteristic
242C42×C61C2×D411yescharacteristic
243C42×C61C2×D411yescharacteristic
244C42×C61C2×D411yescharacteristic
245C22⋊Dic61—21no—
246C22⋊Dic61—21no—
247C22⋊Dic61—21no—
248C22⋊Dic61—21no—
249#11758198—21no—
250#11758198—21no—
251#11758198—21no—
252#11758198—21no—
253#11758198—21no—
254#11758198—21no—
255#11758198—21no—
256#11758198—21no—
257#11758198—21no—
258#11758198—21no—
259#11758198—21no—
260#11758198—21no—
261C4⋊Dic61—21no—
262C4⋊Dic61—21no—
263C4⋊Dic61—21no—
264C4⋊Dic61—21no—
265#11758196—21no—
266#11758196—21no—
267#11758196—21no—
268#11758196—21no—
269#11758196—21no—
270#11758196—21no—
271#11758196—21no—
272#11758196—21no—
273#11758196—21no—
274#11758196—21no—
275#11758196—21no—
276#11758196—21no—
277C4×Dic61—21no—
278C4×Dic61—21no—
279C4×Dic61C22⋊C411yescharacteristic
280C4×Dic61C22⋊C411yescharacteristic
281C4×Dic61C22⋊C411yescharacteristic
282C4×Dic61C22⋊C411yescharacteristic
283C4×Dic61C22⋊C411yescharacteristic
284C4×Dic61C22⋊C411yescharacteristic
285C4×Dic61C22⋊C411yescharacteristic
286C4×Dic61C22⋊C411yescharacteristic
287C4×Dic61C2×D411yescharacteristic
288C4×Dic61C2×D411yescharacteristic
289C4×Dic61C2×D411yescharacteristic
290C4×Dic61C2×D411yescharacteristic
291C2×#92418—22no—
292C2×#92418—22no—
293#11758189—44no—
294C8×D61—44no—
295C23×C61—21no—
296C23×C61—21no—
297C23×C61—21no—
298C23×C61—41no—
299C23×C61—41no—
300C23×C61C23×C411yescharacteristic
301C22×D61—21no—
302C22×D61—21no—
303C22×D61—22no—
304C22×D61—21no—
305C22×D61—21no—
306C22×D61—21no—
307C22×D61—41no—
308C22×D61—41no—
309C22×D61—41no—
310C22×D61C2×C22⋊C411yescharacteristic
311C22×D61C2×C22⋊C411yescharacteristic
312C2×C4×C61—21no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—21no—
317C2×C4×C61—41no—
318C2×C4×C61—41no—
319C2×C4×C61—42no—
320C2×C4×C61—42no—
321C2×C4×C61—41no—
322C2×C4×C61—41no—
323C2×C4×C61C2×C22⋊C411yescharacteristic
324C2×C4×C61C2×C22⋊C411yescharacteristic
325C2×C4×C61C2×C22⋊C411yescharacteristic
326C2×C4×C61C2×C22⋊C411yescharacteristic
327C2×C4×C61#13112yes—
328C2×C4×C61#13112yes—
329C2×C4×C61C22×D411yescharacteristic
330C2×C4×C61C22×D411yescharacteristic
331C22⋊D61—42no—
332C22⋊D61—42no—
333C22⋊D61—42no—
334C22⋊D61—42no—
335C2×Dic61—21no—
336C2×Dic61—21no—
337C2×Dic61—22no—
338C2×Dic61—21no—
339C2×Dic61—21no—
340C2×Dic61—21no—
341C2×Dic61—21no—
342C2×Dic61—21no—
343C2×Dic61—41no—
344C2×Dic61—41no—
345C2×Dic61—41no—
346C2×Dic61C2×C22⋊C411yescharacteristic
347C2×Dic61C2×C22⋊C411yescharacteristic
348C2×Dic61C2×C22⋊C411yescharacteristic
349C2×Dic61C2×C22⋊C411yescharacteristic
350C2×Dic61C2×C22⋊C411yescharacteristic
351C2×Dic61C2×C22⋊C411yescharacteristic
352D244—42no—
353D244—42no—
354C4×D61—22no—
355C4×D61—22no—
356C4×D61—22no—
357C4×D61—22no—
358C4×D61—22no—
359C4×D61—22no—
360C4×D61—22no—
361C4×D61—22no—
362C4×D61—41no—
363C4×D61—41no—
364C4×D61—41no—
365C4×D61—41no—
366C4×D61—42no—
367C4×D61—42no—
368Dic122—42no—
369Dic122—42no—
370C8×C61—42no—
371C8×C61—42no—
372#92418—42no—
373#92418—42no—
374#17380—611nomaximal, Sylow
375C22×C61—21no—
376C22×C61—21no—
377C22×C61—41no—
378C22×C61—41no—
379C22×C61—41no—
380C22×C61—81no—
381C22×C61—81no—
382C22×C61C22×C22⋊C411yescharacteristic
383C22×C61C2×#13111yescharacteristic
384C22×C61C2×#13111yescharacteristic
385C2×D61—21no—
386C2×D61—21no—
387C2×D61—21no—
388C2×D61—21no—
389C2×D61—21no—
390C2×D61—42no—
391C2×D61—42no—
392C2×D61—41no—
393C2×D61—41no—
394C2×D61—41no—
395C2×D61—81no—
396C2×D61—81no—
397C2×D61#41312yes—
398C4×C61—21no—
399C4×C61—21no—
400C4×C61—21no—
401C4×C61—21no—
402C4×C61—41no—
403C4×C61—41no—
404C4×C61—41no—
405C4×C61#40812yes—
406C4×C61#40812yes—
407Dic61—21no—
408Dic61—21no—
409Dic61—21no—
410Dic61—21no—
411Dic61—21no—
412Dic61—41no—
413Dic61—41no—
414Dic61—41no—
415Dic61#41012yes—
416C2×#529—611no—
417#2920—611no—
418C2×#431—611no—
419#1473—612no—
420#1473—612no—
421#1472—612no—
422#1471—612no—
423#1458—611no—
424#1458—611no—
425#1458—611no—
426#1458D6111yescharacteristic, complemented
427C2×C61—21no—
428C2×C61—21no—
429C2×C61—81no—
430C2×C61C2×#40811yescharacteristic
431C2×C61C2×#41011yescharacteristic
432C2×C61C2×#41311yescharacteristic
433D61—22no—
434D61—41no—
435D61—81no—
436#529—1221no—
437#529—1221no—
438#529—1221no—
439#529—1221no—
440#529—1221no—
441#529—1221no—
442#529—1221no—
443#529—1221no—
444C2×#126—611no—
445C2×#126—611no—
446C2×#125—611no—
447C2×#124—611no—
448C2×#123—611no—
449C2×#123—611no—
450C2×C22⋊Q8—611no—
451C2×#121—611no—
452C2×C4×Q8—611no—
453C2×C4×D4—611no—
454C2×C4×D4—611no—
455C2×C4×D4—611no—
456C2×#117—611no—
457C2×#117C2×D6111yescharacteristic
458C22×C42—611no—
459#432—612no—
460#432—1221no—
461#431—611no—
462#431—611no—
463#431—612no—
464#431—1221no—
465#431—1221no—
466#431—1221no—
467#431C2×D6111yescharacteristic
468#431C2×D6111yescharacteristic
469#423—1221no—
470C2×C4⋊C8—1221no—
471#407—612no—
472C2×C22⋊C8—612no—
473C4×M16—1221no—
474C2×C4×C8—1221no—
475#324—612no—
476#324—612no—
477#324—612no—
478#324C2×D6112yes—
479#323—612no—
480#323—612no—
481#323—612no—
482#323C2×D6112yes—
483C61#1738011yescharacteristic, complemented, Sylow
484C22×Q8—611no—
485C22×D4—611no—
486C22×D4—611no—
487C22×D4—611no—
488C23×C4—611no—
489C23×C4—611no—
490C23×C4—611no—
491C23×C4—611no—
492C23×C4C4×D6111yescharacteristic
493C2×M16—1222no—
494C22×C8—1222no—
495#126—1221no—
496#126—1221no—
497#126—1221no—
498#126—1221no—
499#126—1221no—
500#126—1221no—
501#126—1221no—
502#126—1221no—
503#125—1221no—
504#125—1221no—
505#125—1221no—
506#125—1221no—
507#124—1221no—
508#124—1221no—
509#124—1221no—
510#124—1221no—
511#123—1221no—
512#123—1221no—
513#123—1221no—
514#123—1221no—
515#123—1221no—
516#123—1221no—
517#123—1221no—
518#123—1221no—
519C22⋊Q8—1221no—
520C22⋊Q8—1221no—
521C22⋊Q8—1221no—
522C22⋊Q8—1221no—
523#121—1221no—
524#121—1221no—
525#121—1221no—
526#121—1221no—
527C4×Q8—1221no—
528C4×Q8—1221no—
529C4×Q8—1221no—
530C4×Q8—1221no—
531C4×D4—1221no—
532C4×D4—1221no—
533C4×D4—1221no—
534C4×D4—1221no—
535C4×D4—1221no—
536C4×D4—1221no—
537C4×D4—1221no—
538C4×D4—1221no—
539C4×D4—1221no—
540C4×D4—1221no—
541C4×D4—1221no—
542C4×D4—1221no—
543#117—21no—
544#117—21no—
545#117—21no—
546#117—21no—
547#117—1221no—
548#117—1221no—
549#117—1221no—
550#117—1221no—
551C2×C4⋊C4—611no—
552C2×C4⋊C4—611no—
553C2×C4⋊C4—611no—
554C2×C4⋊C4—611no—
555C2×C4⋊C4—611no—
556C2×C4⋊C4—611no—
557C2×C4⋊C4—611no—
558C2×C4⋊C4—611no—
559C2×C4⋊C4C4×D6111yescharacteristic
560C2×C4⋊C4C22×D6111yescharacteristic
561C2×C22⋊C4—611no—
562C2×C22⋊C4—611no—
563C2×C22⋊C4—611no—
564C2×C22⋊C4—611no—
565C2×C22⋊C4—611no—
566C2×C22⋊C4—611no—
567C2×C22⋊C4—611no—
568C2×C22⋊C4—611no—
569C2×C22⋊C4C4×D6111yescharacteristic
570C2×C22⋊C4C22×D6111yescharacteristic
571C2×C42—611no—
572C2×C42—611no—
573C2×C42—611no—
574C2×C42—611no—
575C2×C42—611no—
576C2×C42—611no—
577C2×C42—611no—
578C2×C42—611no—
579C2×C42—611no—
580C2×C42—611no—
581C2×C42—611no—
582C2×C42—611no—
583C2×C42C4×D6111yescharacteristic
584C2×C42C22×D6111yescharacteristic
585C4⋊C8—21no—
586C4⋊C8—21no—
587C4⋊C8—1222no—
588C4⋊C8—1222no—
589C4⋊C8—1221no—
590C4⋊C8—1221no—
591C22⋊C8—612no—
592C22⋊C8—612no—
593C22⋊C8—1222no—
594C22⋊C8—1222no—
595C22⋊C8C22×D6112yes—
596C22⋊C8C22×D6112yes—
597#97—1222no—
598C4×C8—21no—
599C4×C8—21no—
600C4×C8—1222no—
601C4×C8—1221no—
602C4×C8—1221no—
603C24—611no—
604C24—611no—
605C24C2×C4×D6111yescharacteristic
606C2×Q8—1221no—
607C2×Q8—1221no—
608C2×Q8—2442no—
609C2×D4—1221no—
610C2×D4—1221no—
611C2×D4—1221no—
612C2×D4—1221no—
613C2×D4—1221no—
614C2×D4—1221no—
615C2×D4—2442no—
616C2×D4—2442no—
617C2×D4—2442no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—611no—
623C22×C4—611no—
624C22×C4—611no—
625C22×C4—611no—
626C22×C4—611no—
627C22×C4—611no—
628C22×C4—611no—
629C22×C4—611no—
630C22×C4—611no—
631C22×C4—611no—
632C22×C4—611no—
633C22×C4—611no—
634C22×C4—611no—
635C22×C4—611no—
636C22×C4—611no—
637C22×C4—611no—
638C22×C4—611no—
639C22×C4—611no—
640C22×C4—1222no—
641C22×C4—1222no—
642C22×C4—1221no—
643C22×C4—1221no—
644C22×C4—1222no—
645C22×C4—1222no—
646C22×C4—2442no—
647C22×C4—2442no—
648C22×C4C2×C4×D6111yescharacteristic
649C22×C4C2×C4×D6111yescharacteristic
650C22×C4C2×C4×D6111yescharacteristic
651C22×C4C2×C4×D6111yescharacteristic
652C22×C4C2×C4×D6111yescharacteristic
653C22×C4C23×D6111yescharacteristic
654M16—2444no—
655C2×C8—22no—
656C2×C8—22no—
657C2×C8—1222no—
658C2×C8—1222no—
659C2×C8—2444no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—1221no—
665C4⋊C4—1221no—
666C4⋊C4—1221no—
667C4⋊C4—1221no—
668C4⋊C4—1221no—
669C4⋊C4—1221no—
670C4⋊C4—1221no—
671C4⋊C4—1221no—
672C4⋊C4—1221no—
673C4⋊C4—1221no—
674C4⋊C4—1221no—
675C4⋊C4—1221no—
676C4⋊C4—1221no—
677C4⋊C4—1221no—
678C4⋊C4—1221no—
679C4⋊C4—1221no—
680C22⋊C4—21no—
681C22⋊C4—21no—
682C22⋊C4—21no—
683C22⋊C4—21no—
684C22⋊C4—1221no—
685C22⋊C4—1221no—
686C22⋊C4—1221no—
687C22⋊C4—1221no—
688C22⋊C4—1221no—
689C22⋊C4—1221no—
690C22⋊C4—1221no—
691C22⋊C4—1221no—
692C22⋊C4—1221no—
693C22⋊C4—1221no—
694C22⋊C4—1221no—
695C22⋊C4—1221no—
696C22⋊C4—1221no—
697C22⋊C4—1221no—
698C22⋊C4—1221no—
699C22⋊C4—1221no—
700C42—21no—
701C42—21no—
702C42—611no—
703C42—611no—
704C42—611no—
705C42—611no—
706C42—611no—
707C42—611no—
708C42—611no—
709C42—611no—
710C42—611no—
711C42—611no—
712C42—611no—
713C42—611no—
714C42—1221no—
715C42—1221no—
716C42D4×D6111yescharacteristic
717C42D4×D6111yescharacteristic
718C42D4×D6111yescharacteristic
719C42D4×D6111yescharacteristic
720C23—21no—
721C23—21no—
722C23—21no—
723C23—41no—
724C23—41no—
725C23—611no—
726C23—611no—
727C23—1222no—
728C23—1221no—
729C23—1221no—
730C23—1221no—
731C23—1221no—
732C23—1221no—
733C23—2441no—
734C23—2441no—
735C23—2441no—
736C23C22×C4×D6111yescharacteristic
737Q8—2442no—
738Q8—2442no—
739D4—2442no—
740D4—2442no—
741D4—2442no—
742D4—2442no—
743D4—2442no—
744D4—2442no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—611no—
757C2×C4—611no—
758C2×C4—611no—
759C2×C4—611no—
760C2×C4—611no—
761C2×C4—611no—
762C2×C4—1222no—
763C2×C4—1222no—
764C2×C4—1222no—
765C2×C4—1222no—
766C2×C4—1222no—
767C2×C4—1221no—
768C2×C4—1221no—
769C2×C4—1222no—
770C2×C4—1222no—
771C2×C4—1222no—
772C2×C4—1222no—
773C2×C4—1221no—
774C2×C4—1221no—
775C2×C4—1221no—
776C2×C4—1221no—
777C2×C4—1221no—
778C2×C4—2441no—
779C2×C4—2441no—
780C2×C4—2441no—
781C2×C4—2441no—
782C2×C4—2441no—
783C2×C4—2442no—
784C2×C4—2442no—
785C2×C4—2441no—
786C2×C4—2441no—
787C2×C4C22⋊C4×D6111yescharacteristic
788C2×C4C22⋊C4×D6111yescharacteristic
789C2×C4C22⋊C4×D6111yescharacteristic
790C2×C4C22⋊C4×D6111yescharacteristic
791C2×C4#1451978312yes—
792C2×C4#1451978512yes—
793C2×C4C2×D4×D6111yescharacteristic
794C2×C4C2×D4×D6111yescharacteristic
795C8—42no—
796C8—42no—
797C8—2442no—
798C8—2442no—
799C22—21no—
800C22—21no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—81no—
805C22—81no—
806C22—612no—
807C22—1221no—
808C22—1221no—
809C22—1221no—
810C22—1221no—
811C22—1221no—
812C22—4881no—
813C22—4881no—
814C22—2442no—
815C22—2442no—
816C22—2441no—
817C22—2441no—
818C22—2441no—
819C22C2×C22⋊C4×D6111yescharacteristic
820C22C2×#1451978311yescharacteristic
821C22C2×#1451978511yescharacteristic
822C4—21no—
823C4—21no—
824C4—21no—
825C4—21no—
826C4—41no—
827C4—41no—
828C4—41no—
829C4—612no—
830C4—1221no—
831C4—1221no—
832C4—1221no—
833C4—1221no—
834C4—1221no—
835C4—2441no—
836C4—2441no—
837C4—2441no—
838C4#1683972712yes—
839C4#1683972712yes—
840C2—21no—
841C2—21no—
842C2—81no—
843C2—1222no—
844C2—4881no—
845C2—2441no—
846C2C2×#1683972711yescharacteristic
847C2#410×D6111yescharacteristic
848C2#413×D6111yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1458C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519750C22
cosocleC22×C4×C61C24
hypercenter#1458D61
hypocenterC61#17380
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1458

Complements

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

NH ≅ G/Ntype
2. #21454447C2semidirect
3. #431×D61C2semidirect
4. #21444187C2semidirect
5. #21444185C2semidirect
6. #21444181C2semidirect
8. #21444133C2semidirect
9. #21444131C2semidirect
10. #21444131C2semidirect
11. C61×#1458C2semidirect
426. #1458D61semidirect
483. C61#17380semidirect

Maximal subgroups

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

subgroupindex
C2×#168402902
#214544472
#431×D612
#214441872
#214441852
#214441812
#214441772
#214441332
#214441312
C61×#14582
#1738061