Finite Group Databasebeta

← #30622204

Subgroups — #30622204

Order 15616.

906 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840802C211yesmaximal, characteristic
2C2×Q16×#6923C211yesmaximal, characteristic
3#21462348C211yesmaximal, characteristic
4#21462334C211yesmaximal, characteristic
5#21461950C211yesmaximal, characteristic
6#21461932C211yesmaximal, characteristic
7#21461910C211yesmaximal, characteristic
8#21461908C211yesmaximal, characteristic
9#21461813C211yesmaximal, characteristic
10#21461813C211yesmaximal, characteristic
11#21461785C211yesmaximal, characteristic
12#21461783C211yesmaximal, characteristic
13#21461620C211yesmaximal, characteristic
14#21461591C211yesmaximal, characteristic
15#462×D61C211yesmaximal, characteristic
16C2×Q8×#6923C2211yescharacteristic
17C2×Q8×#6923C2211yescharacteristic
18C2×Q8×#6923C2211yescharacteristic
19C2×Q8×#6923C2211yescharacteristic
20#16840802—24no—
21Q16×#6923—24no—
22C2×#14519846C2211yescharacteristic
23C2×#14519845C2211yescharacteristic
24C2×#14519840C2211yescharacteristic
25C2×#14519840C2211yescharacteristic
26C2×#14519840C2211yescharacteristic
27C2×#14519840C2211yescharacteristic
28C2×#14519840C2211yescharacteristic
29C2×#14519840C2211yescharacteristic
30#16840721C2211yescharacteristic
31C2×#14519831C2211yescharacteristic
32C2×C8×#6923C2211yescharacteristic
33(C2×#6923)⋊Q8C2211yescharacteristic
34(C2×#6923)⋊Q8C2211yescharacteristic
35#16840713—21no—
36#16840713—21no—
37#16840713—21no—
38#16840713C2211yescharacteristic
39#16840713C2211yescharacteristic
40#16840711—21no—
41#16840711—21no—
42#16840706—21no—
43#16840706C2211yescharacteristic
44C4⋊C4×#6923—21no—
45C4×C4⋊#6923—21no—
46C4×C4⋊#6923C2211yescharacteristic
47C4×C4⋊#6923C2211yescharacteristic
48#16840636C2211yescharacteristic
49#16840636C2211yescharacteristic
50#16840635C2211yescharacteristic
51#16840635C2211yescharacteristic
52(C2×#6923)⋊C8C2211yescharacteristic
53(C2×#6923)⋊C8C2211yescharacteristic
54C2×Q16×D61C2211yescharacteristic
55C2×Q16×D61C2211yescharacteristic
56C4⋊Q8×D61C2211yescharacteristic
57C4×Q8×D61C2211yescharacteristic
58#16839973C411yescharacteristic, complemented
59#16839972C411yescharacteristic, complemented
60#16839971C411yescharacteristic, complemented
61#16839971C411yescharacteristic, complemented
62#16839970C411yescharacteristic, complemented
63#16839970C411yescharacteristic, complemented
64#16839969C411yescharacteristic, complemented
65C4⋊C8×D61C2211yescharacteristic
66#103×D61C2211yescharacteristic
67#103×D61C2211yescharacteristic
68C61×#462C411yescharacteristic, complemented
69C2×D61⋊C8C2311yescharacteristic
70C2×D61⋊C8C2311yescharacteristic
71Q8×#6923—22no—
72Q8×#6923—22no—
73Q8×#6923—22no—
74Q8×#6923—22no—
75Q8×#6923—41no—
76Q8×#6923—41no—
77Q8×#6923—41no—
78Q8×#6923—41no—
79C2×C4⋊#6923—21no—
80C2×C4⋊#6923—21no—
81C2×C4⋊#6923—21no—
82C2×C4⋊#6923—21no—
83C2×C4⋊#6923—21no—
84C2×C4⋊#6923—21no—
85C2×C4⋊#6923D411yescharacteristic
86C2×C4⋊#6923D411yescharacteristic
87C2×C4⋊#6923C2311yescharacteristic
88C2×C4⋊#6923C2311yescharacteristic
89C2×C4⋊#6923C2311yescharacteristic
90C2×C4⋊#6923C2311yescharacteristic
91C2×C4×#6923—21no—
92C2×C4×#6923—21no—
93C2×C4×#6923—21no—
94C2×C4×#6923—21no—
95C2×C4×#6923—21no—
96C2×C4×#6923C2311yescharacteristic
97C2×C4×#6923C2311yescharacteristic
98#14519846—22no—
99#14519845—22no—
100#14519840—22no—
101#14519840—22no—
102#14519840—22no—
103#14519840—41no—
104#14519840—41no—
105#14519840D414yes—
106#14519832—21no—
107#14519832—21no—
108#14519831—22no—
109C8×#6923—22no—
110(C2×#6923)⋊C4—21no—
111(C2×#6923)⋊C4—21no—
112(C2×#6923)⋊C4—21no—
113(C2×#6923)⋊C4—21no—
114(C2×#6923)⋊C4—21no—
115(C2×#6923)⋊C4—21no—
116(C2×#6923)⋊C4—21no—
117(C2×#6923)⋊C4—21no—
118(C2×#6923)⋊C4—21no—
119(C2×#6923)⋊C4D411yescharacteristic
120(C2×#6923)⋊C4D411yescharacteristic
121C2×Q8×D61C2311yescharacteristic
122C2×Q8×D61C2311yescharacteristic
123C2×Q8×D61C2311yescharacteristic
124C2×Dic244C2×C411yescharacteristic
125C2×Dic244C2×C411yescharacteristic
126C2×#11758202C2×C411yescharacteristic
127C2×#11758202C2×C411yescharacteristic
128C2×#11758202C2×C411yescharacteristic
129C2×#11758202C2×C411yescharacteristic
130Q16×D61—22no—
131Q16×D61—22no—
132Q16×D61—22no—
133Q16×D61—22no—
134C2×C8×D61C2311yescharacteristic
135C2×C8×D61C2311yescharacteristic
136#14519777C2×C411yescharacteristic
137#14519776—21no—
138#14519776—21no—
139#14519775C2×C411yescharacteristic
140#14519775C2×C411yescharacteristic
141Q8×Dic61C2×C411yescharacteristic
142C4×Dic122—21no—
143C4×Dic122C2×C411yescharacteristic
144#14519742—21no—
145#14519742C2×C411yescharacteristic
146C4⋊C4×D61—21no—
147C4⋊C4×D61—21no—
148C4⋊C4×D61—21no—
149C4⋊C4×D61C2311yescharacteristic
150C42×D61—21no—
151C42×D61C2311yescharacteristic
152C4⋊#92418C2×C411yescharacteristic
153#14519706C2×C411yescharacteristic
154#14519706C2×C411yescharacteristic
155#14519702C2×C411yescharacteristic
156#14519702C2×C411yescharacteristic
157#14519701C2×C411yescharacteristic
158#14519701C2×C411yescharacteristic
159#14519700C2×C411yescharacteristic
160#14519700C2×C411yescharacteristic
161C2×Q16×C61C2×C411yescharacteristic
162C2×Q16×C61C2×C411yescharacteristic
163C4⋊Q8×C61C2×C411yescharacteristic
164C4×Q8×C61C2×C411yescharacteristic
165C4⋊C8×C61C2×C411yescharacteristic
166#103×C61C2×C411yescharacteristic
167#103×C61C2×C411yescharacteristic
168C22×#6923—21no—
169C22×#6923—21no—
170C22×#6923—21no—
171C22×#6923—21no—
172C22×#6923C2×D411yescharacteristic
173C22×#6923C2×D411yescharacteristic
174C22×#6923C2×D411yescharacteristic
175C22×#6923C2×D411yescharacteristic
176C2×Q8×C61C22×C411yescharacteristic
177C2×Q8×C61C22×C411yescharacteristic
178C2×Q8×C61C22×C411yescharacteristic
179Q8×D61—21no—
180Q8×D61—21no—
181Q8×D61—21no—
182Q8×D61—21no—
183Q8×D61—21no—
184Q8×D61—21no—
185Q8×D61—21no—
186Q8×D61—21no—
187Q8×D61—21no—
188Q8×D61—21no—
189Q8×D61C2×D412yes—
190Q8×D61#4112yes—
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195C2×C4×D61C2×D411yescharacteristic
196C2×C4×D61C2×D411yescharacteristic
197C2×C4×D61C2411yescharacteristic
198C2×Dic122—21no—
199C2×Dic122—21no—
200C2×Dic122—21no—
201C2×Dic122C22×C411yescharacteristic
202C2×Dic122C22×C411yescharacteristic
203C2×Dic122C22×C411yescharacteristic
204C2×#92420—21no—
205C2×#92420—21no—
206C4⋊#6923—22no—
207C4⋊#6923—21no—
208C4⋊#6923—21no—
209C4⋊#6923—21no—
210C4⋊#6923—21no—
211C4⋊#6923—21no—
212C4⋊#6923—21no—
213C4⋊#6923—21no—
214C4⋊#6923—41no—
215C4⋊#6923—42no—
216C4⋊#6923—42no—
217C4⋊#6923—42no—
218C4⋊#6923—42no—
219C4⋊#6923—42no—
220C4⋊#6923—42no—
221C4⋊#6923C2×D412yes—
222C4×#6923—21no—
223C4×#6923—21no—
224C4×#6923—21no—
225C4×#6923—21no—
226C4×#6923—42no—
227C4×#6923—42no—
228C4×#6923—42no—
229C4×#6923—42no—
230C4×#6923—42no—
231D61⋊C8—21no—
232D61⋊C8—21no—
233D61⋊C8—21no—
234D61⋊C8C2×D412yes—
235Q16×C61—22no—
236Q16×C61—22no—
237C2×C8×C61C22×C411yescharacteristic
238C2×C8×C61C22×C411yescharacteristic
239C4⋊C4×C61—21no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61C22×C411yescharacteristic
243C42×C61—21no—
244C42×C61C22×C411yescharacteristic
245#11758202—22no—
246#11758202—22no—
247#11758202—22no—
248#11758202—22no—
249C4⋊Dic61—21no—
250C4⋊Dic61—21no—
251C4⋊Dic61—21no—
252C4⋊Dic61C22×C411yescharacteristic
253#11758196—21no—
254#11758196—21no—
255#11758196—21no—
256#11758196—21no—
257#11758196—21no—
258#11758196—21no—
259#11758196—21no—
260C4×Dic61—21no—
261C4×Dic61—21no—
262C4×Dic61—21no—
263C4×Dic61C22×C411yescharacteristic
264C4×Dic61#4111yescharacteristic
265C4×Dic61#4111yescharacteristic
266C2×#92418C22×C411yescharacteristic
267C2×#92418C22×C411yescharacteristic
268Dic244—22no—
269Dic244—22no—
270C8×D61—21no—
271C8×D61—21no—
272C8×D61—21no—
273C8×D61—21no—
274C22×D61C22×D411yescharacteristic
275C2×#6923—21no—
276C2×#6923—21no—
277C2×#6923—21no—
278C2×#6923—21no—
279C2×#6923—21no—
280C2×#6923—22no—
281C2×#6923—21no—
282C2×#6923—21no—
283C2×#6923—21no—
284C2×#6923—21no—
285C2×#6923—21no—
286C2×#6923—21no—
287C2×#6923—41no—
288C2×#6923—41no—
289C2×#6923—41no—
290C2×#6923—41no—
291C2×#6923—41no—
292C2×#6923—41no—
293C2×#6923—41no—
294C2×#6923—41no—
295C2×#6923—41no—
296C2×#6923—41no—
297C2×#6923—41no—
298C2×#6923#13712yes—
299Q8×C61—21no—
300Q8×C61—21no—
301Q8×C61—21no—
302Q8×C61—21no—
303Q8×C61—21no—
304Q8×C61C4×D412yes—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—21no—
309C2×C4×C61C4×D411yescharacteristic
310C2×C4×C61C4×D411yescharacteristic
311C2×C4×C61C23×C411yescharacteristic
312C2×Dic61—21no—
313C2×Dic61—21no—
314C2×Dic61—21no—
315C2×Dic61—21no—
316C2×Dic61C4×D411yescharacteristic
317C2×Dic61C4×D411yescharacteristic
318C2×Dic61C2×#4111yescharacteristic
319C4×D61—22no—
320C4×D61—22no—
321C4×D61—21no—
322C4×D61—21no—
323C4×D61—21no—
324C4×D61—21no—
325C4×D61—41no—
326C4×D61—41no—
327C4×D61—41no—
328C4×D61—41no—
329C4×D61—41no—
330C4×D61—41no—
331C4×D61C22×D411yescharacteristic
332C4×D61C2×#4111yescharacteristic
333C4×D61H(5,𝔽2)11yescharacteristic
334C4×D612−1+411yescharacteristic
335Dic122—21no—
336Dic122—22no—
337Dic122—22no—
338Dic122—21no—
339Dic122—21no—
340Dic122—21no—
341Dic122—21no—
342Dic122—41no—
343Dic122—41no—
344Dic122—41no—
345Dic122—41no—
346Dic122C4×D412yes—
347#92420—22no—
348#92420—41no—
349C8×C61—21no—
350C8×C61—21no—
351#92418—21no—
352#92418—21no—
353#23014—611nomaximal, Sylow
354C22×C61C2×C4×D411yescharacteristic
355C2×D61D4211yescharacteristic
356C2×D61#54811yescharacteristic
357C2×D61C2×#13711yescharacteristic
358C2×D61#57511yescharacteristic
359C2×D61#57811yescharacteristic
360C2×D61#57811yescharacteristic
361#6923—22no—
362#6923—41no—
363#6923—41no—
364#6923—42no—
365#6923—41no—
366#6923—81no—
367#6923—81no—
368#6923—81no—
369C4×C61—22no—
370C4×C61—21no—
371C4×C61—21no—
372C4×C61—41no—
373C4×C61—41no—
374C4×C61—41no—
375C4×C61C2×C4×D411yescharacteristic
376C4×C61#52011yescharacteristic
377Dic61—22no—
378Dic61—21no—
379Dic61—21no—
380Dic61—41no—
381Dic61—41no—
382Dic61—41no—
383Dic61#54711yescharacteristic
384Dic61#55311yescharacteristic
385C2×#462—611no—
386C2×#441—611no—
387C2×C4×Q16—611no—
388#2365—611no—
389#2351—611no—
390#1960—611no—
391#1949—611no—
392#1935—611no—
393#1933—611no—
394#1878—611no—
395#1878—611no—
396#1865—611no—
397#1863—611no—
398#1771—611no—
399#1763—611no—
400C2×C61#236111yescharacteristic
401C2×C61C4×#13711yescharacteristic
402C2×C61#295011yescharacteristic
403D61#326911yescharacteristic
404D61#327011yescharacteristic
405D61#337411yescharacteristic
406D61#337711yescharacteristic
407C22×Q16—611no—
408C22×Q16—611no—
409C2×C4⋊Q8—611no—
410C2×C4×Q8—611no—
411C2×C4×Q8—611no—
412C2×C4×Q8—611no—
413C2×C4×Q8—611no—
414C2×C4×Q8—611no—
415#462—611no—
416#462—611no—
417#462—611no—
418#462—611no—
419#462—611no—
420#462—611no—
421#462—611no—
422#462#692311yescharacteristic, complemented
423#441—1224no—
424C4×Q16—1224no—
425C2×#107—611no—
426C2×#106—611no—
427C2×C4⋊C8—611no—
428C2×#103—611no—
429C2×#103—611no—
430C2×#103—611no—
431C2×#103—611no—
432C2×#103—611no—
433C2×#103—611no—
434C2×#103—611no—
435C2×#103—611no—
436C2×#97—611no—
437C2×#97—611no—
438C2×C4×C8—611no—
439#391—611no—
440#391—611no—
441#389—611no—
442#389—611no—
443#389—1221no—
444#389—1221no—
445#389—1221no—
446#387—1221no—
447#387—1221no—
448#382—611no—
449#382—1221no—
450C4×C4⋊C4—611no—
451C4×C4⋊C4—611no—
452C4×C4⋊C4—1221no—
453C4×C4⋊C4—1221no—
454#340—611no—
455#340—611no—
456#340—611no—
457#340—611no—
458#336—611no—
459#336—611no—
460C61#2301411yescharacteristic, complemented, Sylow
461C22×Q8—611no—
462C22×Q8—611no—
463C22×Q8—611no—
464C2×Q16—611no—
465C2×Q16—611no—
466C2×Q16—611no—
467C2×Q16—611no—
468C2×Q16—611no—
469C2×Q16—611no—
470C2×Q16—1222no—
471C2×Q16—1222no—
472C2×Q16—1222no—
473C2×Q16—1222no—
474C2×Q16C2×#692311yescharacteristic
475C2×Q16C2×#692311yescharacteristic
476C22×C8—611no—
477C22×C8—611no—
478C22×C8—611no—
479C22×C8—611no—
480C4⋊Q8—611no—
481C4⋊Q8—611no—
482C4⋊Q8—611no—
483C4⋊Q8—1221no—
484C4⋊Q8—1221no—
485C4⋊Q8C2×#692311yescharacteristic
486C4×Q8—611no—
487C4×Q8—611no—
488C4×Q8—611no—
489C4×Q8—1221no—
490C4×Q8—1221no—
491C4×Q8—1222no—
492C4×Q8—1222no—
493C4×Q8—1222no—
494C4×Q8—1222no—
495C4×Q8—2441no—
496C4×Q8—2441no—
497C4×Q8—2441no—
498C4×Q8—2441no—
499C4×Q8C2×#692311yescharacteristic
500C2×C4⋊C4—611no—
501C2×C4⋊C4—611no—
502C2×C4⋊C4—611no—
503C2×C4⋊C4—611no—
504C2×C4⋊C4—611no—
505C2×C4⋊C4—611no—
506C2×C4⋊C4—611no—
507C2×C4⋊C4—1221no—
508C2×C4⋊C4—1221no—
509C2×C4⋊C4—1221no—
510C2×C4⋊C4—1221no—
511C2×C4⋊C4—1221no—
512C2×C4⋊C4—1221no—
513C2×C4⋊C4—1221no—
514C2×C4⋊C4—1221no—
515C2×C4⋊C4—1221no—
516C2×C42—611no—
517C2×C42—611no—
518C2×C42—611no—
519C2×C42—1221no—
520C2×C42—1221no—
521C2×C42—1221no—
522C2×C42—1221no—
523C2×C42—1221no—
524C2×C42—1221no—
525#107—1222no—
526#106—1222no—
527C4⋊C8—611no—
528C4⋊C8—611no—
529C4⋊C8—611no—
530C4⋊C8C2×#692311yescharacteristic
531#103—614no—
532#103—611no—
533#103—611no—
534#103—611no—
535#103—611no—
536#103—611no—
537#103—611no—
538#103—1222no—
539#103—1222no—
540#103—1222no—
541#103—2441no—
542#103—2441no—
543#103C2×#692311yescharacteristic
544#103C2×#692311yescharacteristic
545#97—1221no—
546#97—1221no—
547#97—1222no—
548C4×C8—1222no—
549#95—611no—
550#95—611no—
551#95—1221no—
552#95—1221no—
553#95—1221no—
554#95—1221no—
555#95—1221no—
556#95—1221no—
557#95—1221no—
558#95—1221no—
559#95—1221no—
560C2×Q8—612no—
561C2×Q8—612no—
562C2×Q8—611no—
563C2×Q8—611no—
564C2×Q8—611no—
565C2×Q8—1221no—
566C2×Q8—1221no—
567C2×Q8—1221no—
568C2×Q8—1221no—
569C2×Q8—1221no—
570C2×Q8—1221no—
571C2×Q8—1221no—
572C2×Q8—1221no—
573C2×Q8—1221no—
574C2×Q8—1221no—
575C2×Q8—1221no—
576C2×Q8—1221no—
577C2×Q8—1221no—
578C2×Q8C22×#692311yescharacteristic
579C2×Q8C22×#692311yescharacteristic
580C2×Q8C22×#692311yescharacteristic
581C22×C4—611no—
582C22×C4—611no—
583C22×C4—611no—
584C22×C4—611no—
585C22×C4—611no—
586C22×C4—611no—
587C22×C4—611no—
588C22×C4—1221no—
589C22×C4—1221no—
590C22×C4—1221no—
591C22×C4—1221no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—1221no—
595C22×C4—1221no—
596Q16—22no—
597Q16—22no—
598Q16—1222no—
599Q16—1222no—
600Q16—1222no—
601Q16—1222no—
602Q16—1222no—
603Q16—1222no—
604C2×C8—612no—
605C2×C8—611no—
606C2×C8—611no—
607C2×C8—1221no—
608C2×C8—1221no—
609C2×C8—1221no—
610C2×C8—1221no—
611C2×C8—1221no—
612C2×C8—1221no—
613C2×C8—1221no—
614C2×C8—1221no—
615C2×C8—1221no—
616C2×C8C22×#692311yescharacteristic
617C2×C8C22×#692311yescharacteristic
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—612no—
622C4⋊C4—611no—
623C4⋊C4—1221no—
624C4⋊C4—1221no—
625C4⋊C4—1221no—
626C4⋊C4—1221no—
627C4⋊C4—1221no—
628C4⋊C4—1221no—
629C4⋊C4—1221no—
630C4⋊C4—1221no—
631C4⋊C4—1222no—
632C4⋊C4—1221no—
633C4⋊C4—1221no—
634C4⋊C4—1221no—
635C4⋊C4—1221no—
636C4⋊C4—1221no—
637C4⋊C4—1221no—
638C4⋊C4—1221no—
639C4⋊C4—1221no—
640C4⋊C4—1221no—
641C4⋊C4—2442no—
642C4⋊C4—2441no—
643C4⋊C4—2442no—
644C4⋊C4—2442no—
645C4⋊C4—2442no—
646C4⋊C4—2442no—
647C4⋊C4—2442no—
648C4⋊C4C22×#692311yescharacteristic
649C42—21no—
650C42—611no—
651C42—611no—
652C42—611no—
653C42—1221no—
654C42—1221no—
655C42—1221no—
656C42—1221no—
657C42—1221no—
658C42—1221no—
659C42—1221no—
660C42—2442no—
661C42—2442no—
662C42—2442no—
663C42—2442no—
664C42—2442no—
665C42C22×#692311yescharacteristic
666C23—611no—
667Q8—21no—
668Q8—21no—
669Q8—21no—
670Q8—21no—
671Q8—21no—
672Q8—612no—
673Q8—1222no—
674Q8—1222no—
675Q8—1221no—
676Q8—1221no—
677Q8—1221no—
678Q8—1221no—
679Q8—1221no—
680Q8—2441no—
681Q8—2441no—
682Q8—2441no—
683Q8—2441no—
684Q8D4×#692312yes—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—611no—
690C2×C4—611no—
691C2×C4—611no—
692C2×C4—611no—
693C2×C4—611no—
694C2×C4—612no—
695C2×C4—611no—
696C2×C4—611no—
697C2×C4—1222no—
698C2×C4—1221no—
699C2×C4—1221no—
700C2×C4—1221no—
701C2×C4—1221no—
702C2×C4—1222no—
703C2×C4—1221no—
704C2×C4—1221no—
705C2×C4—1221no—
706C2×C4—1221no—
707C2×C4—1221no—
708C2×C4—1221no—
709C2×C4—1222no—
710C2×C4—1221no—
711C2×C4—1221no—
712C2×C4—1221no—
713C2×C4—1221no—
714C2×C4—1221no—
715C2×C4—1221no—
716C2×C4—1221no—
717C2×C4—1221no—
718C2×C4—1221no—
719C2×C4—2441no—
720C2×C4—2441no—
721C2×C4—2441no—
722C2×C4—2441no—
723C2×C4—2441no—
724C2×C4—2441no—
725C2×C4—2441no—
726C2×C4—2441no—
727C2×C4—2441no—
728C2×C4—2441no—
729C2×C4—2441no—
730C2×C4—2441no—
731C2×C4—2441no—
732C2×C4—2441no—
733C2×C4—2441no—
734C2×C4—2441no—
735C2×C4—2441no—
736C2×C4D4×#692311yescharacteristic
737C2×C4D4×#692311yescharacteristic
738C2×C4C23×#692311yescharacteristic
739C8—21no—
740C8—21no—
741C8—1222no—
742C8—1221no—
743C8—1221no—
744C8—2441no—
745C22—611no—
746C22—611no—
747C22—611no—
748C22—611no—
749C22—611no—
750C22—611no—
751C22C2×D4×#692311yescharacteristic
752C4—21no—
753C4—21no—
754C4—22no—
755C4—41no—
756C4—41no—
757C4—41no—
758C4—611no—
759C4—611no—
760C4—1222no—
761C4—1221no—
762C4—1221no—
763C4—1222no—
764C4—4881no—
765C4—4881no—
766C4—4881no—
767C4—2441no—
768C4—2441no—
769C4—2441no—
770C4—2442no—
771C4—2441no—
772C4—2441no—
773C4—2441no—
774C4C2×D4×#692311yescharacteristic
775C4#1684083111yescharacteristic
776C2—611no—
777C2—611no—
778C2—611no—
779C2—611no—
780C2#2146234411yescharacteristic
781C2#137×#692311yescharacteristic
782C2#2146258011yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#462C4
socleC22×C61C2×C4×D4
prime radicalC22×D61C22×D4
cosocleC2×C4×D61C24
hypercenter#462#6923
hypocenterC61#23014
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
58. #16839973C4semidirect
59. #16839972C4semidirect
60. #16839971C4semidirect
61. #16839971C4semidirect
62. #16839970C4semidirect
63. #16839970C4semidirect
64. #16839969C4semidirect
68. C61×#462C4semidirect
422. #462#6923semidirect
460. C61#23014semidirect

Maximal subgroups

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

subgroupindex
C2×#168408022
C2×Q16×#69232
#214623482
#214623342
#214619502
#214619322
#214619102
#214619082
#214618132
#214617852
#214617832
#214616202
#214615912
#462×D612
#2301461