Finite Group Databasebeta

← #30617026

Subgroups — #30617026

Order 15616.

932 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840802C211yesmaximal, characteristic
2C2×Q16×#6923C211yesmaximal, characteristic
3#21462310C211yesmaximal, characteristic
4#21462259C211yesmaximal, characteristic
5#21461985C211yesmaximal, characteristic
6#21461932C211yesmaximal, characteristic
7#21461899C211yesmaximal, characteristic
8#21461898C211yesmaximal, characteristic
9#21461813C211yesmaximal, characteristic
10#21461813C211yesmaximal, characteristic
11#21461690C211yesmaximal, characteristic
12#21461608C211yesmaximal, characteristic
13#21461592C211yesmaximal, characteristic
14#103×#6923C211yesmaximal, 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
24D61⋊(C4⋊C8)C2211yescharacteristic
25C2×#14519840C2211yescharacteristic
26C2×#14519840C2211yescharacteristic
27C2×#14519840C2211yescharacteristic
28C2×#14519840C2211yescharacteristic
29C2×#14519840C2211yescharacteristic
30C2×#14519840C2211yescharacteristic
31C2×#14519831C2211yescharacteristic
32C2×C8×#6923C2211yescharacteristic
33(C2×#6923)⋊Q8C2211yescharacteristic
34(C2×#6923)⋊Q8C2211yescharacteristic
35#16840711—21no—
36#16840711—21no—
37#16840711—21no—
38#16840711—21no—
39#16840706C2211yescharacteristic
40C4⋊C4×#6923—21no—
41C4⋊C4×#6923—21no—
42C4⋊C4×#6923C2211yescharacteristic
43C4⋊C4×#6923C2211yescharacteristic
44C4×C4⋊#6923—21no—
45C4×C4⋊#6923C2211yescharacteristic
46#16840698—21no—
47#16840698C2211yescharacteristic
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—22no—
76Q8×#6923—22no—
77Q8×#6923—22no—
78Q8×#6923D414yes—
79C2×C4⋊#6923—21no—
80C2×C4⋊#6923—21no—
81C2×C4⋊#6923—21no—
82C2×C4⋊#6923—21no—
83C2×C4⋊#6923C2311yescharacteristic
84C2×C4⋊#6923C2311yescharacteristic
85C2×C4⋊#6923C2311yescharacteristic
86C2×C4⋊#6923C2311yescharacteristic
87C2×C4×#6923—21no—
88C2×C4×#6923—21no—
89C2×C4×#6923—21no—
90C2×C4×#6923—21no—
91C2×C4×#6923—21no—
92C2×C4×#6923—21no—
93C2×C4×#6923—21no—
94C2×C4×#6923C2311yescharacteristic
95C2×C4×#6923C2311yescharacteristic
96#14519846—22no—
97#14519845—22no—
98#14519844—21no—
99C4⋊#92420—21no—
100#14519840—22no—
101#14519840—22no—
102#14519840—22no—
103#14519840—22no—
104#14519840—22no—
105#14519840—22no—
106#14519831—22no—
107C8×#6923—22no—
108(C2×#6923)⋊C4—21no—
109(C2×#6923)⋊C4—21no—
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)⋊C4D411yescharacteristic
118(C2×#6923)⋊C4D411yescharacteristic
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—24no—
207C4⋊#6923—24no—
208C4⋊#6923—21no—
209C4⋊#6923—21no—
210C4⋊#6923—21no—
211C4⋊#6923—21no—
212C4⋊#6923—21no—
213C4⋊#6923—21no—
214C4⋊#6923—42no—
215C4⋊#6923—42no—
216C4⋊#6923C2×D412yes—
217C4⋊#6923#4112yes—
218C4×#6923—24no—
219C4×#6923—24no—
220C4×#6923—21no—
221C4×#6923—21no—
222C4×#6923—42no—
223C4×#6923—42no—
224C4×#6923—81no—
225C4×#6923—81no—
226C4×#6923—81no—
227C4×#6923C2×D412yes—
228C4×#6923#4112yes—
229D61⋊C8—21no—
230D61⋊C8—21no—
231D61⋊C8—21no—
232D61⋊C8—21no—
233Q16×C61—22no—
234Q16×C61—22no—
235C2×C8×C61C22×C411yescharacteristic
236C2×C8×C61C22×C411yescharacteristic
237C4⋊C4×C61—21no—
238C4⋊C4×C61—21no—
239C4⋊C4×C61—21no—
240C4⋊C4×C61C22×C411yescharacteristic
241C42×C61—21no—
242C42×C61C22×C411yescharacteristic
243#11758202—22no—
244#11758202—22no—
245#11758202—22no—
246#11758202—22no—
247C4⋊Dic61—21no—
248C4⋊Dic61—21no—
249C4⋊Dic61—21no—
250C4⋊Dic61C22×C411yescharacteristic
251#11758196—21no—
252#11758196—21no—
253#11758196—21no—
254#11758196—21no—
255#11758196—21no—
256#11758196—21no—
257#11758196—21no—
258C4×Dic61—21no—
259C4×Dic61—21no—
260C4×Dic61—21no—
261C4×Dic61C22×C411yescharacteristic
262C4×Dic61#4111yescharacteristic
263C4×Dic61#4111yescharacteristic
264C2×#92418C22×C411yescharacteristic
265C2×#92418C22×C411yescharacteristic
266Dic244—22no—
267Dic244—22no—
268C8×D61—21no—
269C8×D61—21no—
270C8×D61—21no—
271C8×D61—21no—
272C22×D61C22×D411yescharacteristic
273C2×#6923—21no—
274C2×#6923—21no—
275C2×#6923—21no—
276C2×#6923—21no—
277C2×#6923—22no—
278C2×#6923—21no—
279C2×#6923—21no—
280C2×#6923—22no—
281C2×#6923—21no—
282C2×#6923—21no—
283C2×#6923—21no—
284C2×#6923—21no—
285C2×#6923—41no—
286C2×#6923—41no—
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#12112yes—
296C2×#6923#12112yes—
297Q8×C61—21no—
298Q8×C61—21no—
299Q8×C61—21no—
300Q8×C61—21no—
301Q8×C61—21no—
302Q8×C61C4×D412yes—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61C4×D411yescharacteristic
308C2×C4×C61C4×D411yescharacteristic
309C2×C4×C61C23×C411yescharacteristic
310C2×Dic61—21no—
311C2×Dic61—21no—
312C2×Dic61—21no—
313C2×Dic61—21no—
314C2×Dic61C4×D411yescharacteristic
315C2×Dic61C4×D411yescharacteristic
316C2×Dic61C2×#4111yescharacteristic
317C4×D61—22no—
318C4×D61—22no—
319C4×D61—21no—
320C4×D61—21no—
321C4×D61—21no—
322C4×D61—21no—
323C4×D61—41no—
324C4×D61—41no—
325C4×D61—41no—
326C4×D61—41no—
327C4×D61—41no—
328C4×D61—41no—
329C4×D61C22×D411yescharacteristic
330C4×D61C2×#4111yescharacteristic
331C4×D61C2×#4111yescharacteristic
332C4×D61C2×#4111yescharacteristic
333Dic122—21no—
334Dic122—22no—
335Dic122—22no—
336Dic122—21no—
337Dic122—21no—
338Dic122—21no—
339Dic122—21no—
340Dic122—41no—
341Dic122—41no—
342Dic122—41no—
343Dic122—41no—
344Dic122C4×D412yes—
345#92420—41no—
346#92420—41no—
347C8×C61—21no—
348C8×C61—21no—
349#92418—21no—
350#92418—21no—
351#21516—611nomaximal, Sylow
352C22×C61C2×C4×D411yescharacteristic
353C2×D61C2×#12111yescharacteristic
354C2×D61#52511yescharacteristic
355C2×D61#57711yescharacteristic
356C2×D61#57811yescharacteristic
357C2×D61#57811yescharacteristic
358C2×D61#57811yescharacteristic
359#6923—22no—
360#6923—22no—
361#6923—41no—
362#6923—42no—
363#6923—41no—
364#6923—42no—
365#6923—81no—
366#6923—81no—
367C4×C61—21no—
368C4×C61—21no—
369C4×C61—22no—
370C4×C61—41no—
371C4×C61—41no—
372C4×C61—41no—
373C4×C61C2×C4×D411yescharacteristic
374C4×C61C4×#4111yescharacteristic
375Dic61—21no—
376Dic61—21no—
377Dic61—22no—
378Dic61—41no—
379Dic61—41no—
380Dic61—41no—
381Dic61#52911yescharacteristic
382Dic61#53211yescharacteristic
383C2×#462—611no—
384C2×#441—611no—
385C2×C4×Q16—611no—
386#2327—611no—
387#2276—611no—
388#1981—611no—
389#1949—611no—
390#1928—611no—
391#1927—611no—
392#1878—611no—
393#1878—611no—
394#1805—611no—
395#1768—611no—
396#1763—611no—
397C4×#103—611no—
398C2×C61C4×#12111yescharacteristic
399C2×C61#294711yescharacteristic
400C2×C61#295011yescharacteristic
401D61#304411yescharacteristic
402D61#304611yescharacteristic
403D61#312011yescharacteristic
404D61#312711yescharacteristic
405C22×Q16—611no—
406C22×Q16—611no—
407C2×C4⋊Q8—611no—
408C2×C4×Q8—611no—
409C2×C4×Q8—611no—
410C2×C4×Q8—611no—
411C2×C4×Q8—611no—
412C2×C4×Q8—611no—
413#462—611no—
414#462—611no—
415#462—611no—
416#462—611no—
417#462—611no—
418#462—611no—
419#462—611no—
420#462#692311yescharacteristic, complemented
421#441—1224no—
422C4×Q16—1224no—
423C2×#107—611no—
424C2×#106—611no—
425C2×C4⋊C8—611no—
426C2×C4⋊C8—611no—
427C2×#103—611no—
428C2×#103—611no—
429C2×#103—611no—
430C2×#103—611no—
431C2×#103—611no—
432C2×#103—611no—
433C2×#103—611no—
434C2×#103—611no—
435C2×#97—611no—
436C2×C4×C8—611no—
437#391—611no—
438#391—611no—
439#387—1221no—
440#387—1221no—
441#387—1221no—
442#387—1221no—
443#382—611no—
444C4×C4⋊C4—611no—
445C4×C4⋊C4—611no—
446C4×C4⋊C4—611no—
447C4×C4⋊C4—1221no—
448C4×C4⋊C4—1221no—
449C4×C4⋊C4—1221no—
450#376—611no—
451#376—1221no—
452#340—611no—
453#340—611no—
454#340—611no—
455#340—611no—
456#336—611no—
457#336—611no—
458C61#2151611yescharacteristic, complemented, Sylow
459C22×Q8—611no—
460C22×Q8—611no—
461C22×Q8—611no—
462C2×Q16—611no—
463C2×Q16—611no—
464C2×Q16—611no—
465C2×Q16—611no—
466C2×Q16—611no—
467C2×Q16—611no—
468C2×Q16—1222no—
469C2×Q16—1222no—
470C2×Q16—1222no—
471C2×Q16—1222no—
472C2×Q16C2×#692311yescharacteristic
473C2×Q16C2×#692311yescharacteristic
474C22×C8—611no—
475C22×C8—611no—
476C22×C8—611no—
477C22×C8—611no—
478C4⋊Q8—611no—
479C4⋊Q8—611no—
480C4⋊Q8—611no—
481C4⋊Q8—1221no—
482C4⋊Q8—1221no—
483C4⋊Q8C2×#692311yescharacteristic
484C4×Q8—614no—
485C4×Q8—611no—
486C4×Q8—611no—
487C4×Q8—611no—
488C4×Q8—1221no—
489C4×Q8—1221no—
490C4×Q8—1222no—
491C4×Q8—1222no—
492C4×Q8—1222no—
493C4×Q8—1222no—
494C4×Q8—1222no—
495C4×Q8—1222no—
496C4×Q8—1222no—
497C4×Q8C2×#692311yescharacteristic
498C2×C4⋊C4—611no—
499C2×C4⋊C4—611no—
500C2×C4⋊C4—611no—
501C2×C4⋊C4—611no—
502C2×C4⋊C4—611no—
503C2×C4⋊C4—1221no—
504C2×C4⋊C4—1221no—
505C2×C4⋊C4—1221no—
506C2×C4⋊C4—1221no—
507C2×C4⋊C4—1221no—
508C2×C4⋊C4—1221no—
509C2×C4⋊C4—1221no—
510C2×C42—611no—
511C2×C42—611no—
512C2×C42—611no—
513C2×C42—1221no—
514C2×C42—1221no—
515C2×C42—1221no—
516C2×C42—1221no—
517C2×C42—1221no—
518C2×C42—1221no—
519C2×C42—1221no—
520C2×C42—1221no—
521#107—1222no—
522#106—1222no—
523C4⋊C8—611no—
524C4⋊C8—611no—
525C4⋊C8—611no—
526C4⋊C8—1221no—
527C4⋊C8—1221no—
528C4⋊C8C2×#692311yescharacteristic
529#103—611no—
530#103—611no—
531#103—611no—
532#103—611no—
533#103—611no—
534#103—611no—
535#103—1222no—
536#103—1222no—
537#103—1222no—
538#103—1222no—
539#103—1222no—
540#103—1222no—
541#103C2×#692311yescharacteristic
542#103C2×#692311yescharacteristic
543#97—1222no—
544C4×C8—1222no—
545#95—611no—
546#95—611no—
547#95—611no—
548#95—611no—
549#95—1221no—
550#95—1221no—
551#95—1221no—
552#95—1221no—
553#95—1221no—
554#95—1221no—
555#95—1221no—
556#95—1221no—
557#95—1221no—
558C2×Q8—612no—
559C2×Q8—612no—
560C2×Q8—611no—
561C2×Q8—611no—
562C2×Q8—611no—
563C2×Q8—1221no—
564C2×Q8—1221no—
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×Q8C22×#692311yescharacteristic
577C2×Q8C22×#692311yescharacteristic
578C2×Q8C22×#692311yescharacteristic
579C22×C4—611no—
580C22×C4—611no—
581C22×C4—611no—
582C22×C4—611no—
583C22×C4—611no—
584C22×C4—611no—
585C22×C4—611no—
586C22×C4—1221no—
587C22×C4—1221no—
588C22×C4—1221no—
589C22×C4—1221no—
590C22×C4—1221no—
591C22×C4—1221no—
592C22×C4—1221no—
593C22×C4—1221no—
594Q16—22no—
595Q16—22no—
596Q16—1222no—
597Q16—1222no—
598Q16—1222no—
599Q16—1222no—
600Q16—1222no—
601Q16—1222no—
602C2×C8—611no—
603C2×C8—611no—
604C2×C8—1221no—
605C2×C8—1221no—
606C2×C8—1221no—
607C2×C8—1221no—
608C2×C8—1221no—
609C2×C8—1221no—
610C2×C8—1221no—
611C2×C8—1221no—
612C2×C8—1221no—
613C2×C8—1221no—
614C2×C8C22×#692311yescharacteristic
615C2×C8C22×#692311yescharacteristic
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—612no—
620C4⋊C4—612no—
621C4⋊C4—611no—
622C4⋊C4—1221no—
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—1224no—
632C4⋊C4—1221no—
633C4⋊C4—1221no—
634C4⋊C4—1221no—
635C4⋊C4—1221no—
636C4⋊C4—1224no—
637C4⋊C4—1221no—
638C4⋊C4—1221no—
639C4⋊C4—1221no—
640C4⋊C4—2442no—
641C4⋊C4—2442no—
642C4⋊C4C22×#692311yescharacteristic
643C42—21no—
644C42—612no—
645C42—612no—
646C42—611no—
647C42—611no—
648C42—611no—
649C42—1221no—
650C42—1221no—
651C42—1221no—
652C42—1221no—
653C42—1224no—
654C42—1224no—
655C42—1221no—
656C42—4881no—
657C42—4881no—
658C42—4881no—
659C42—2442no—
660C42—2442no—
661C42C22×#692311yescharacteristic
662C23—611no—
663Q8—21no—
664Q8—21no—
665Q8—21no—
666Q8—21no—
667Q8—21no—
668Q8—612no—
669Q8—1222no—
670Q8—1222no—
671Q8—1221no—
672Q8—1221no—
673Q8—1221no—
674Q8—1221no—
675Q8—1221no—
676Q8—2441no—
677Q8—2441no—
678Q8—2441no—
679Q8—2441no—
680Q8D4×#692312yes—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—611no—
686C2×C4—611no—
687C2×C4—611no—
688C2×C4—611no—
689C2×C4—611no—
690C2×C4—612no—
691C2×C4—612no—
692C2×C4—611no—
693C2×C4—611no—
694C2×C4—1222no—
695C2×C4—1222no—
696C2×C4—1221no—
697C2×C4—1221no—
698C2×C4—1221no—
699C2×C4—1221no—
700C2×C4—1221no—
701C2×C4—1221no—
702C2×C4—1221no—
703C2×C4—1221no—
704C2×C4—1221no—
705C2×C4—1221no—
706C2×C4—1222no—
707C2×C4—1222no—
708C2×C4—1221no—
709C2×C4—1221no—
710C2×C4—1221no—
711C2×C4—1221no—
712C2×C4—1221no—
713C2×C4—1221no—
714C2×C4—1221no—
715C2×C4—1221no—
716C2×C4—2441no—
717C2×C4—2441no—
718C2×C4—2441no—
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×C4D4×#692311yescharacteristic
733C2×C4D4×#692311yescharacteristic
734C2×C4C23×#692311yescharacteristic
735C8—21no—
736C8—21no—
737C8—1221no—
738C8—1221no—
739C8—2441no—
740C8—2441no—
741C22—611no—
742C22—611no—
743C22—611no—
744C22—611no—
745C22—611no—
746C22—611no—
747C22C2×D4×#692311yescharacteristic
748C4—22no—
749C4—21no—
750C4—21no—
751C4—41no—
752C4—41no—
753C4—41no—
754C4—611no—
755C4—611no—
756C4—1222no—
757C4—1222no—
758C4—1222no—
759C4—1221no—
760C4—1221no—
761C4—4881no—
762C4—4881no—
763C4—2441no—
764C4—2441no—
765C4—2442no—
766C4—2442no—
767C4—2441no—
768C4—2441no—
769C4—2441no—
770C4C2×D4×#692311yescharacteristic
771C4#41×#692311yescharacteristic
772C2—611no—
773C2—611no—
774C2—611no—
775C2—611no—
776C2#121×#692311yescharacteristic
777C2#2146257711yescharacteristic
778C2#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#21516
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
420. #462#6923semidirect
458. C61#21516semidirect

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
#214623102
#214622592
#214619852
#214619322
#214618992
#214618982
#214618132
#214616902
#214616082
#214615922
#103×#69232
#462×D612
#2151661