Finite Group Databasebeta

← #30616070

Subgroups — #30616070

Order 15616.

890 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462303C211yesmaximal, characteristic, complemented
2#21462258C211yesmaximal, characteristic
3#21461899C211yesmaximal, characteristic, complemented
4#21461898C211yesmaximal, characteristic, complemented
5#21461883C211yesmaximal, characteristic, complemented
6#21461880C211yesmaximal, characteristic, complemented
7#21461812C211yesmaximal, characteristic
8#21461812C211yesmaximal, characteristic
9#21461784C211yesmaximal, characteristic
10#21461782C211yesmaximal, characteristic
11#21461633C211yesmaximal, characteristic, complemented
12C4×#14519840C211yesmaximal, characteristic, complemented
13C4×#14519839C211yesmaximal, characteristic
14#21461539C211yesmaximal, characteristic, complemented
15#440×D61C211yesmaximal, characteristic
16C2×D4×#6923C2211yescharacteristic
17C2×D4×#6923C2211yescharacteristic
18C2×#14519846C2211yescharacteristic
19C2×#14519845C2211yescharacteristic
20C2×#14519840C2211yescharacteristic
21C2×#14519840C2211yescharacteristic
22C2×#14519839C2211yescharacteristic
23C2×#14519839C2211yescharacteristic
24C4×D61⋊C8C2211yescharacteristic
25(C2×#6923)⋊Q8C2211yescharacteristic
26(C2×#6923)⋊Q8C2211yescharacteristic
27#16840713C2211yescharacteristic
28#16840713C2211yescharacteristic
29#16840711—21no—
30#16840711—21no—
31#16840707—21no—
32#16840706—21no—
33C4⋊C4×#6923C2211yescharacteristic
34C4⋊C4×#6923C2211yescharacteristic
35C4×C4⋊#6923C2211yescharacteristic
36C4×C4⋊#6923C2211yescharacteristic
37C22⋊C4×#6923—21no—
38C22⋊C4×#6923—21no—
39C4×C22⋊#6923—21no—
40#16840698C2211yescharacteristic
41C2×(C2×#6923)⋊C4—21no—
42#16840636C2211yescharacteristic
43#16840636C2211yescharacteristic
44#16840635C2211yescharacteristic
45#16840635C2211yescharacteristic
46#16840635C2211yescharacteristic
47#16840635C2211yescharacteristic
48(C2×#6923)⋊C8C2211yescharacteristic
49(C2×#6923)⋊C8C2211yescharacteristic
50(C2×#6923)⋊C8C2211yescharacteristic
51(C2×#6923)⋊C8C2211yescharacteristic
52C2×SD16×D61C2211yescharacteristic
53C4×Q8×D61C2211yescharacteristic
54C4×D4×D61C2211yescharacteristic
55#16839865C411yescharacteristic, complemented
56#16839864C411yescharacteristic, complemented
57#16839863C411yescharacteristic, complemented
58#16839862C411yescharacteristic, complemented
59#16839861C411yescharacteristic, complemented
60#16839860C411yescharacteristic, complemented
61#16839859C411yescharacteristic, complemented
62#107×D61C2211yescharacteristic
63#103×D61C2211yescharacteristic
64#102×D61C2211yescharacteristic
65#97×D61C2211yescharacteristic
66C61×#440C411yescharacteristic, complemented
67C23×#6923—21no—
68C23×#6923—21no—
69C2×D61⋊C8C2311yescharacteristic
70C2×D61⋊C8C2311yescharacteristic
71D4×#6923—22no—
72D4×#6923—22no—
73D4×#6923—22no—
74D4×#6923—22no—
75C2×C4⋊#6923—21no—
76C2×C4⋊#6923—21no—
77C2×C4⋊#6923C2311yescharacteristic
78C2×C4⋊#6923C2311yescharacteristic
79C2×C4⋊#6923C2311yescharacteristic
80C2×C4⋊#6923C2311yescharacteristic
81C2×C22⋊#6923—21no—
82C2×C22⋊#6923—21no—
83C2×C4×#6923—21no—
84C2×C4×#6923—21no—
85C2×C4×#6923—21no—
86C2×C4×#6923—21no—
87C2×C4×#6923C2311yescharacteristic
88C2×C4×#6923C2311yescharacteristic
89#14519846—22no—
90#14519845—22no—
91#14519840—22no—
92#14519840—22no—
93#14519839—22no—
94#14519839—22no—
95C4×#92420—21no—
96C4×#92420—21no—
97(C2×#6923)⋊C4—21no—
98(C2×#6923)⋊C4—21no—
99(C2×#6923)⋊C4—21no—
100(C2×#6923)⋊C4—21no—
101(C2×#6923)⋊C4—21no—
102(C2×#6923)⋊C4—21no—
103(C2×#6923)⋊C4—21no—
104(C2×#6923)⋊C4—21no—
105(C2×#6923)⋊C4—21no—
106(C2×#6923)⋊C4—21no—
107(C2×#6923)⋊C4D411yescharacteristic
108(C2×#6923)⋊C4D411yescharacteristic
109(C2×#6923)⋊C4D411yescharacteristic
110(C2×#6923)⋊C4D411yescharacteristic
111C2×Q8×D61C2311yescharacteristic
112C2×D4×D61C2311yescharacteristic
113C22×C4×D61—21no—
114C2×#11758190C2×C411yescharacteristic
115C2×#11758200C2×C411yescharacteristic
116C2×#11758201C2×C411yescharacteristic
117SD16×D61—22no—
118SD16×D61—22no—
119C2×C8×D61C2311yescharacteristic
120C2×C8×D61C2311yescharacteristic
121Q8×Dic61C2×C411yescharacteristic, complemented
122C4×Dic122—21no—
123C4×Dic122C2×C411yescharacteristic, complemented
124#14519742—21no—
125#14519742C2×C411yescharacteristic, complemented
126C4×D244C2×C411yescharacteristic
127D4×Dic61C2×C411yescharacteristic
128#14519739C2×C411yescharacteristic
129C4×C22⋊D61—21no—
130#14519737—21no—
131C4⋊C4×D61—21no—
132C4⋊C4×D61C2311yescharacteristic
133C4⋊C4×D61C2311yescharacteristic
134C22⋊C4×D61—21no—
135C42×D61—21no—
136C42×D61C2311yescharacteristic
137#14519711C2×C411yescharacteristic, complemented
138#14519710C2×C411yescharacteristic, complemented
139#14519710C2×C411yescharacteristic, complemented
140#14519702C2×C411yescharacteristic, complemented
141#14519701C2×C411yescharacteristic, complemented
142#14519700C2×C411yescharacteristic, complemented
143#14519699C2×C411yescharacteristic
144#14519698C2×C411yescharacteristic
145#14519697C2×C411yescharacteristic
146#14519688C2×C411yescharacteristic, complemented
147#14519687C2×C411yescharacteristic, complemented
148#14519687C2×C411yescharacteristic, complemented
149C2×SD16×C61C2×C411yescharacteristic
150C4×Q8×C61C2×C411yescharacteristic, complemented
151C4×D4×C61C2×C411yescharacteristic
152#107×C61C2×C411yescharacteristic, complemented
153#103×C61C2×C411yescharacteristic, complemented
154#102×C61C2×C411yescharacteristic
155#97×C61C2×C411yescharacteristic, complemented
156C23×D61—21no—
157C22×#6923—21no—
158C22×#6923—21no—
159C22×#6923—24no—
160C22×#6923—24no—
161C22×#6923—21no—
162C22×#6923—21no—
163C22×#6923—81no—
164C22×#6923—81no—
165C22×#6923—81no—
166C22×#6923—81no—
167C22×#6923C2×D411yescharacteristic
168C22×#6923C2×D411yescharacteristic
169C22×#6923C2×D411yescharacteristic
170C22×#6923C2×D411yescharacteristic
171C2×Q8×C61C22×C411yescharacteristic
172C2×D4×C61C22×C411yescharacteristic
173C22×C4×C61—21no—
174C2×C22⋊D61—21no—
175C22×Dic61—21no—
176Q8×D61—21no—
177Q8×D61—21no—
178Q8×D61—21no—
179Q8×D61—21no—
180D4×D61—21no—
181D4×D61—21no—
182D4×D61#4112yes—
183D4×D61#4112yes—
184C2×D244C22×C411yescharacteristic
185C2×C4×D61—21no—
186C2×C4×D61—21no—
187C2×C4×D61—21no—
188C2×C4×D61—21no—
189C2×C4×D61—21no—
190C2×C4×D61—81no—
191C2×C4×D61—81no—
192C2×C4×D61C2×D411yescharacteristic
193C2×C4×D61C2×D411yescharacteristic
194C2×C4×D61C2411yescharacteristic
195C2×Dic122—21no—
196C2×Dic122C22×C411yescharacteristic
197C22⋊#6923—24no—
198C22⋊#6923—24no—
199C2×#92420—21no—
200C2×#92420—21no—
201C4⋊#6923—21no—
202C4⋊#6923—21no—
203C4⋊#6923—21no—
204C4⋊#6923—21no—
205C4⋊#6923—21no—
206C4⋊#6923—21no—
207C4⋊#6923—81no—
208C4⋊#6923—81no—
209C4⋊#6923#4112yes—
210C4⋊#6923#4112yes—
211C4×#6923—21no—
212C4×#6923—21no—
213C4×#6923—21no—
214C4×#6923—21no—
215C4×#6923—81no—
216C4×#6923—81no—
217C4×#6923—81no—
218C4×#6923—81no—
219D61⋊C8—21no—
220D61⋊C8—21no—
221D61⋊C8—21no—
222D61⋊C8—21no—
223SD16×C61—22no—
224C2×C8×C61C22×C411yescharacteristic
225C2×C8×C61C22×C411yescharacteristic
226C4⋊C4×C61—21no—
227C4⋊C4×C61C22×C411yescharacteristic
228C4⋊C4×C61C22×C411yescharacteristic
229C22⋊C4×C61—21no—
230C42×C61—21no—
231C42×C61C22×C411yescharacteristic
232C22⋊Dic61—21no—
233#11758201—22no—
234#11758200—22no—
235#11758198—21no—
236#11758198—21no—
237C4⋊Dic61—21no—
238C4⋊Dic61C22×C411yescharacteristic
239C4⋊Dic61C22×C411yescharacteristic
240#11758196—21no—
241#11758196—21no—
242#11758196—21no—
243#11758196—21no—
244C4×Dic61—21no—
245C4×Dic61—21no—
246C4×Dic61—21no—
247C4×Dic61C22×C411yescharacteristic
248C4×Dic61#4111yescharacteristic
249C4×Dic61#4111yescharacteristic
250C2×#92418C22×C411yescharacteristic
251C2×#92418C22×C411yescharacteristic
252#11758190—22no—
253C8×D61—21no—
254C8×D61—21no—
255C8×D61—21no—
256C8×D61—21no—
257C23×C61—21no—
258C22×D61—21no—
259C22×D61—22no—
260C22×D61—22no—
261C22×D61—41no—
262C22×D61—41no—
263C22×D61—41no—
264C22×D61—41no—
265C22×D61C22×D411yescharacteristic
266C2×#6923—21no—
267C2×#6923—21no—
268C2×#6923—21no—
269C2×#6923—21no—
270C2×#6923—22no—
271C2×#6923—22no—
272C2×#6923—21no—
273C2×#6923—21no—
274C2×#6923—21no—
275C2×#6923—21no—
276C2×#6923—21no—
277C2×#6923—21no—
278C2×#6923—21no—
279C2×#6923—21no—
280C2×#6923—41no—
281C2×#6923—41no—
282C2×#6923—41no—
283C2×#6923—41no—
284C2×#6923—41no—
285C2×#6923—41no—
286C2×#6923—41no—
287C2×#6923—41no—
288C2×#6923—41no—
289C2×#6923—41no—
290C2×#6923—84no—
291C2×#6923—84no—
292Q8×C61—21no—
293Q8×C61—21no—
294D4×C61—21no—
295D4×C61#11712yes—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—81no—
300C2×C4×C61C4×D411yescharacteristic
301C2×C4×C61C4×D411yescharacteristic
302C2×C4×C61C23×C411yescharacteristic
303C22⋊D61—22no—
304C22⋊D61—22no—
305C2×Dic61—21no—
306C2×Dic61—21no—
307C2×Dic61—21no—
308C2×Dic61—81no—
309C2×Dic61C4×D411yescharacteristic
310C2×Dic61C4×D411yescharacteristic
311C2×Dic61C2×#4111yescharacteristic
312D244—21no—
313D244#11712yes—
314C4×D61—21no—
315C4×D61—21no—
316C4×D61—21no—
317C4×D61—21no—
318C4×D61—41no—
319C4×D61—41no—
320C4×D61—41no—
321C4×D61—41no—
322C4×D61—41no—
323C4×D61—41no—
324C4×D61—81no—
325C4×D61—81no—
326C4×D61C2×#4111yescharacteristic
327C4×D61C2×#4111yescharacteristic
328C4×D61C2×#4111yescharacteristic
329C4×D61C2×#4111yescharacteristic
330Dic122—21no—
331Dic122—21no—
332Dic122—41no—
333Dic122—41no—
334#92420—41no—
335#92420—41no—
336C8×C61—21no—
337C8×C61—21no—
338#92418—21no—
339#92418—21no—
340#21125—611nomaximal, Sylow
341C22×C61—22no—
342C22×C61—41no—
343C22×C61—41no—
344C22×C61C2×C4×D411yescharacteristic
345C2×D61—22no—
346C2×D61—41no—
347C2×D61—41no—
348C2×D61—42no—
349C2×D61—42no—
350C2×D61—42no—
351C2×D61—42no—
352C2×D61#52511yescharacteristic
353C2×D61#52511yescharacteristic
354C2×D61#57611yescharacteristic
355C2×D61#57711yescharacteristic
356C2×D61#57711yescharacteristic
357C2×D61#57811yescharacteristic
358#6923—41no—
359#6923—42no—
360#6923—41no—
361#6923—41no—
362#6923—42no—
363#6923—41no—
364#6923—81no—
365#6923—81no—
366C4×C61—21no—
367C4×C61—21no—
368C4×C61—41no—
369C4×C61—41no—
370C4×C61—41no—
371C4×C61C2×#11711yescharacteristic
372C4×C61C4×#4111yescharacteristic
373Dic61—21no—
374Dic61—21no—
375Dic61—41no—
376Dic61—41no—
377Dic61—41no—
378Dic61#52911yescharacteristic
379Dic61#52911yescharacteristic
380C2×#440—611no—
381#2320—611no—
382#2275—611no—
383#1928—611no—
384#1927—611no—
385#1921—611no—
386#1918—611no—
387#1877—611no—
388#1877—611no—
389#1864—611no—
390#1862—611no—
391#1776—611no—
392C4×#103—611no—
393C4×#102—611no—
394#1746—611no—
395C2×C61—42no—
396C2×C61#229011yescharacteristic
397C2×C61#294611yescharacteristic
398C2×C61#294711yescharacteristic
399D61—42no—
400D61#311811yescharacteristic
401D61#312011yescharacteristic
402D61#312311yescharacteristic
403D61#312411yescharacteristic
404C22×SD16—611no—
405C2×C4×Q8—611no—
406C2×C4×D4—611no—
407C2×C4×D4—611no—
408C2×C4×D4—611no—
409#440—611no—
410#440—611no—
411#440—611no—
412#440—611no—
413#440—611no—
414#440—611no—
415#440—611no—
416#440#692311yescharacteristic, complemented
417C2×#107—611no—
418C2×#107—611no—
419C2×#106—611no—
420C2×#103—611no—
421C2×#103—611no—
422C2×#103—611no—
423C2×#102—611no—
424C2×#102—611no—
425C2×#102—611no—
426C2×#97—611no—
427C2×C4×C8—611no—
428#391—611no—
429#391—611no—
430#389—611no—
431#389—611no—
432#387—1221no—
433#387—1221no—
434#383—1221no—
435#382—1221no—
436C4×C4⋊C4—611no—
437C4×C4⋊C4—611no—
438C4×C4⋊C4—611no—
439C4×C4⋊C4—611no—
440C4×C22⋊C4—1221no—
441C4×C22⋊C4—1221no—
442C4×C22⋊C4—1221no—
443#376—611no—
444C2×#95—1221no—
445#340—611no—
446#340—611no—
447#340—611no—
448#340—611no—
449#340—611no—
450#340—611no—
451#336—611no—
452#336—611no—
453#336—611no—
454#336—611no—
455C61#2112511yescharacteristic, complemented, Sylow
456C22×Q8—611no—
457C22×D4—611no—
458C23×C4—1221no—
459C23×C4—1221no—
460C23×C4—1221no—
461C2×SD16—611no—
462C2×SD16—611no—
463C2×SD16—611no—
464C2×SD16—1222no—
465C2×SD16—1222no—
466C2×SD16C2×#692311yescharacteristic
467C22×C8—611no—
468C22×C8—611no—
469C22×C8—611no—
470C22×C8—611no—
471C4×Q8—611no—
472C4×Q8—611no—
473C4×Q8—611no—
474C4×Q8—1221no—
475C4×Q8—1221no—
476C4×Q8C2×#692311yescharacteristic, complemented
477C4×D4—611no—
478C4×D4—611no—
479C4×D4—611no—
480C4×D4—1221no—
481C4×D4—1221no—
482C4×D4—1222no—
483C4×D4—1222no—
484C4×D4—1222no—
485C4×D4—1222no—
486C4×D4C2×#692311yescharacteristic
487C2×C4⋊C4—611no—
488C2×C4⋊C4—611no—
489C2×C4⋊C4—611no—
490C2×C4⋊C4—611no—
491C2×C4⋊C4—611no—
492C2×C4⋊C4—611no—
493C2×C4⋊C4—1221no—
494C2×C4⋊C4—1221no—
495C2×C4⋊C4—1221no—
496C2×C22⋊C4—1221no—
497C2×C22⋊C4—1221no—
498C2×C22⋊C4—1221no—
499C2×C42—611no—
500C2×C42—611no—
501C2×C42—611no—
502C2×C42—1221no—
503C2×C42—1221no—
504C2×C42—1221no—
505C2×C42—1221no—
506C2×C42—1221no—
507#107—611no—
508#107—611no—
509#107—611no—
510#107—1222no—
511#107C2×#692311yescharacteristic, complemented
512#106—1222no—
513#103—611no—
514#103—611no—
515#103—611no—
516#103—1222no—
517#103—1222no—
518#103C2×#692311yescharacteristic, complemented
519#102—611no—
520#102—611no—
521#102—611no—
522#102—1222no—
523#102—1222no—
524#102C2×#692311yescharacteristic
525#97—611no—
526#97—611no—
527#97—611no—
528#97C2×#692311yescharacteristic, complemented
529C4×C8—1221no—
530C4×C8—1221no—
531#95—611no—
532#95—611no—
533#95—611no—
534#95—611no—
535#95—1221no—
536#95—1221no—
537#95—1221no—
538#95—1221no—
539#95—1221no—
540#95—1221no—
541#95—1221no—
542#95—1221no—
543#95—1221no—
544#95—1221no—
545C24—1221no—
546C2×Q8—611no—
547C2×Q8—1221no—
548C2×Q8—1221no—
549C2×Q8—1221no—
550C2×Q8—1221no—
551C2×Q8—1221no—
552C2×Q8C22×#692311yescharacteristic
553C2×D4—612no—
554C2×D4—612no—
555C2×D4—611no—
556C2×D4—1221no—
557C2×D4—1221no—
558C2×D4—1221no—
559C2×D4C22×#692311yescharacteristic
560C22×C4—21no—
561C22×C4—611no—
562C22×C4—611no—
563C22×C4—611no—
564C22×C4—611no—
565C22×C4—611no—
566C22×C4—611no—
567C22×C4—611no—
568C22×C4—1221no—
569C22×C4—1221no—
570C22×C4—1221no—
571C22×C4—1221no—
572C22×C4—1221no—
573C22×C4—1224no—
574C22×C4—1224no—
575C22×C4—1221no—
576C22×C4—1221no—
577C22×C4—1221no—
578C22×C4—1221no—
579C22×C4—1221no—
580C22×C4—4881no—
581C22×C4—4881no—
582C22×C4—4881no—
583C22×C4—4881no—
584C22×C4—4881no—
585C22×C4—4881no—
586SD16—22no—
587SD16—1222no—
588SD16—1222no—
589SD16—1222no—
590C2×C8—611no—
591C2×C8—611no—
592C2×C8—1221no—
593C2×C8—1221no—
594C2×C8—1221no—
595C2×C8—1221no—
596C2×C8—1221no—
597C2×C8—1221no—
598C2×C8—1221no—
599C2×C8—1221no—
600C2×C8—1221no—
601C2×C8—1221no—
602C2×C8C22×#692311yescharacteristic
603C2×C8C22×#692311yescharacteristic
604C4⋊C4—21no—
605C4⋊C4—612no—
606C4⋊C4—612no—
607C4⋊C4—611no—
608C4⋊C4—611no—
609C4⋊C4—1221no—
610C4⋊C4—1221no—
611C4⋊C4—1221no—
612C4⋊C4—1221no—
613C4⋊C4—1221no—
614C4⋊C4—1221no—
615C4⋊C4—1221no—
616C4⋊C4—1221no—
617C4⋊C4—1221no—
618C4⋊C4—1221no—
619C4⋊C4—1221no—
620C4⋊C4—4881no—
621C4⋊C4—4881no—
622C4⋊C4C22×#692311yescharacteristic
623C4⋊C4C22×#692311yescharacteristic
624C22⋊C4—21no—
625C22⋊C4—1221no—
626C22⋊C4—1221no—
627C22⋊C4—1224no—
628C22⋊C4—1224no—
629C22⋊C4—1221no—
630C42—21no—
631C42—611no—
632C42—611no—
633C42—611no—
634C42—1221no—
635C42—1221no—
636C42—1221no—
637C42—1221no—
638C42—1221no—
639C42—1221no—
640C42—1221no—
641C42—4881no—
642C42—4881no—
643C42—4881no—
644C42—4881no—
645C42C22×#692311yescharacteristic
646C23—21no—
647C23—611no—
648C23—1222no—
649C23—1222no—
650C23—1221no—
651C23—2441no—
652C23—2441no—
653C23—2441no—
654C23—2441no—
655Q8—21no—
656Q8—21no—
657Q8—1221no—
658Q8—1221no—
659Q8—2441no—
660Q8—2441no—
661D4—21no—
662D4—612no—
663D4—1222no—
664D4—1222no—
665D4—1221no—
666D4#1451985612yes—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—81no—
671C2×C4—611no—
672C2×C4—611no—
673C2×C4—611no—
674C2×C4—611no—
675C2×C4—611no—
676C2×C4—611no—
677C2×C4—611no—
678C2×C4—1221no—
679C2×C4—1221no—
680C2×C4—1221no—
681C2×C4—1221no—
682C2×C4—1221no—
683C2×C4—1221no—
684C2×C4—1221no—
685C2×C4—1221no—
686C2×C4—1221no—
687C2×C4—1221no—
688C2×C4—1222no—
689C2×C4—1222no—
690C2×C4—1221no—
691C2×C4—1221no—
692C2×C4—1221no—
693C2×C4—1221no—
694C2×C4—1221no—
695C2×C4—1221no—
696C2×C4—1221no—
697C2×C4—1221no—
698C2×C4—1221no—
699C2×C4—4881no—
700C2×C4—4881no—
701C2×C4—4881no—
702C2×C4—4884no—
703C2×C4—4884no—
704C2×C4—2441no—
705C2×C4—2441no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4—2441no—
709C2×C4—2441no—
710C2×C4—2441no—
711C2×C4—2441no—
712C2×C4—2441no—
713C2×C4—2441no—
714C2×C4—2441no—
715C2×C4—2441no—
716C2×C4—2441no—
717C2×C4—2441no—
718C2×C4—2441no—
719C2×C4—2441no—
720C2×C4D4×#692311yescharacteristic
721C2×C4D4×#692311yescharacteristic
722C2×C4C23×#692311yescharacteristic
723C8—21no—
724C8—21no—
725C8—1221no—
726C8—1221no—
727C8—2441no—
728C8—2441no—
729C22—22no—
730C22—41no—
731C22—41no—
732C22—611no—
733C22—611no—
734C22—611no—
735C22—611no—
736C22—611no—
737C22—611no—
738C22—1222no—
739C22—2442no—
740C22—2442no—
741C22—2442no—
742C22—2442no—
743C22—2441no—
744C22—2441no—
745C22C2×D4×#692311yescharacteristic
746C4—21no—
747C4—21no—
748C4—41no—
749C4—41no—
750C4—41no—
751C4—611no—
752C4—611no—
753C4—1221no—
754C4—1221no—
755C4—4881no—
756C4—4881no—
757C4—2441no—
758C4—2441no—
759C4—2441no—
760C4—2441no—
761C4—2442no—
762C4—2442no—
763C4—2441no—
764C4—2441no—
765C4—2441no—
766C4C2×#1451985611yescharacteristic
767C4#41×#692311yescharacteristic
768C2—42no—
769C2—611no—
770C2—611no—
771C2—611no—
772C2—611no—
773C2—2442no—
774C2#2146227311yescharacteristic
775C2#2146257611yescharacteristic
776C2#2146257711yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#440C4
socleC22×C61C2×C4×D4
prime radicalC2×D4×D61C23
cosocleC2×C4×D61C24
hypercenter#440#6923
hypocenterC61#21125
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #21462303C2semidirect
3. #21461899C2semidirect
4. #21461898C2semidirect
5. #21461883C2semidirect
6. #21461880C2semidirect
11. #21461633C2semidirect
12. C4×#14519840C2semidirect
14. #21461539C2semidirect
55. #16839865C4semidirect
56. #16839864C4semidirect
57. #16839863C4semidirect
58. #16839862C4semidirect
59. #16839861C4semidirect
60. #16839860C4semidirect
61. #16839859C4semidirect
66. C61×#440C4semidirect
121. Q8×Dic61C2×C4semidirect
123. C4×Dic122C2×C4semidirect
125. #14519742C2×C4semidirect
137. #14519711C2×C4semidirect
138. #14519710C2×C4semidirect
139. #14519710C2×C4semidirect
140. #14519702C2×C4semidirect
141. #14519701C2×C4semidirect
142. #14519700C2×C4semidirect
146. #14519688C2×C4semidirect
147. #14519687C2×C4semidirect
148. #14519687C2×C4semidirect
150. C4×Q8×C61C2×C4semidirect
152. #107×C61C2×C4semidirect
153. #103×C61C2×C4semidirect
155. #97×C61C2×C4semidirect
416. #440#6923semidirect
455. C61#21125semidirect
476. C4×Q8C2×#6923semidirect
511. #107C2×#6923semidirect
518. #103C2×#6923semidirect
528. #97C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214623032
#214622582
#214618992
#214618982
#214618832
#214618802
#214618122
#214617842
#214617822
#214616332
C4×#145198402
C4×#145198392
#214615392
#440×D612
#2112561