Finite Group Databasebeta

← #29727292

Subgroups — #29727292

Order 15616.

986 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840034C211yesmaximal, characteristic, complemented
2#21455445C211yesmaximal, characteristic
3#21455053C211yesmaximal, characteristic
4#21454540C211yesmaximal, characteristic
5C22×#14519696C211yesmaximal, characteristic, complemented
6#21447184C211yesmaximal, characteristic, complemented
7#21447119C211yesmaximal, characteristic, complemented
8#21447084C211yesmaximal, characteristic, complemented
9#21446938C211yesmaximal, characteristic, complemented
10#21446735C211yesmaximal, characteristic, complemented
11#21446471C211yesmaximal, characteristic, complemented
12#21446337C211yesmaximal, characteristic, complemented
13#21446288C211yesmaximal, characteristic, complemented
14#21446026C211yesmaximal, characteristic, complemented
15C2×C61×#451C211yesmaximal, characteristic, complemented
16C2×#14519808C2211yescharacteristic
17C2×#14519808C2211yescharacteristic
18C2×#14519808C2211yescharacteristic
19C2×#14519783C2211yescharacteristic
20C22×#11758194C2211yescharacteristic
21C22×#11758194C2211yescharacteristic
22#16840273C2211yescharacteristic
23#16840034—24no—
24#16840018—21no—
25#16840010—21no—
26#16840001—21no—
27#16839993—21no—
28#16839918—21no—
29#16839918—21no—
30#16839901—21no—
31#16839901—21no—
32#16839837—21no—
33#16839836—21no—
34#16839830—21no—
35#16839825—21no—
36C2×#14519713C2211yescharacteristic
37C2×#14519713C2211yescharacteristic
38#16839802C2211yescharacteristic
39#16839788C2211yescharacteristic
40#16839771C2211yescharacteristic
41#16839771C2211yescharacteristic
42#16839771C2211yescharacteristic
43#16839761C2211yescharacteristic
44C2×#14519696—24no—
45C2×#14519696C2211yescharacteristic
46C2×#14519696C2211yescharacteristic
47C2×#14519696C2211yescharacteristic
48C2×#14519696C2211yescharacteristic
49C2×#14519696C2211yescharacteristic
50C2×#14519696C2211yescharacteristic
51#16839728C2211yescharacteristic
52#16839726C2211yescharacteristic
53#16839717C2211yescharacteristic
54#16839531C2211yescharacteristic
55#16839531C2211yescharacteristic
56#16839527C2211yescharacteristic
57#16839527C2211yescharacteristic
58C23×Q8×C61C2211yescharacteristic
59C22×Q16×C61C2211yescharacteristic
60C22×Q16×C61C2211yescharacteristic
61C2×C22⋊Q8×C61C2211yescharacteristic
62C61×#451—21no—
63C61×#451—21no—
64C61×#451—21no—
65C61×#451—21no—
66C2×#103×C61C2211yescharacteristic
67C2×#103×C61C2211yescharacteristic
68C2×C22⋊C8×C61C2211yescharacteristic
69C2×#11758222C2311yescharacteristic
70#14519808—22no—
71#14519808—22no—
72#14519808—22no—
73#14519808—41no—
74#14519808—41no—
75#14519808—41no—
76C2×#11758202—21no—
77C2×#11758202—21no—
78C2×#11758202—21no—
79C2×#11758201—21no—
80C2×#11758201—21no—
81C2×#11758201—21no—
82#14519783—22no—
83#14519783—41no—
84C2×#11758194—21no—
85C2×#11758194—21no—
86C2×#11758194—22no—
87C2×#11758194—22no—
88C2×#11758194—41no—
89C2×#11758194—41no—
90C2×#11758194C2311yescharacteristic
91C2×#11758194C2311yescharacteristic
92C2×#11758194C2311yescharacteristic
93C2×#11758194C2311yescharacteristic
94C2×#11758194C2311yescharacteristic
95C2×#11758194C2311yescharacteristic
96C2×#11758189—21no—
97C22×#92418—21no—
98C22×#92418—21no—
99C2×C8×D61—21no—
100#14519760—21no—
101#14519756D411yescharacteristic
102#14519756D411yescharacteristic
103#14519751D411yescharacteristic
104#14519751D411yescharacteristic
105#14519746—21no—
106C4×C22⋊D61—21no—
107C4×C22⋊D61—21no—
108#14519736C2311yescharacteristic
109#14519713—22no—
110#14519713—41no—
111#14519710—21no—
112#14519708—21no—
113#14519706—21no—
114#14519706—21no—
115#14519701—21no—
116#14519701—21no—
117#14519701—21no—
118#14519701—21no—
119#14519701—21no—
120#14519701—21no—
121#14519700—21no—
122#14519697—21no—
123#14519696—22no—
124#14519696—22no—
125#14519696—22no—
126#14519696—22no—
127#14519696—41no—
128#14519696D414yescomplemented
129C22⋊#92418—21no—
130C22⋊#92418—21no—
131#14519689—21no—
132#14519689—21no—
133#14519687—21no—
134C8×Dic61—21no—
135C22×Q8×C61—22no—
136C22×Q8×C61—22no—
137C22×Q8×C61—21no—
138C22×Q8×C61—21no—
139C22×Q8×C61—21no—
140C22×Q8×C61—21no—
141C22×Q8×C61—21no—
142C22×Q8×C61—41no—
143C22×Q8×C61—41no—
144C22×Q8×C61C2311yescharacteristic
145C22×Q8×C61C2311yescharacteristic
146C22×Q8×C61C2311yescharacteristic
147C23×C4×C61—21no—
148C23×C4×C61C2311yescharacteristic
149C2×Q16×C61—22no—
150C2×Q16×C61—22no—
151C2×Q16×C61—21no—
152C2×Q16×C61—21no—
153C2×Q16×C61—21no—
154C2×Q16×C61—21no—
155C2×Q16×C61—41no—
156C2×Q16×C61—41no—
157C22×C8×C61C2311yescharacteristic
158C22×C8×C61C2311yescharacteristic
159C22⋊Q8×C61—21no—
160C22⋊Q8×C61—21no—
161C22⋊Q8×C61—21no—
162C22⋊Q8×C61—21no—
163C2×C4⋊C4×C61—21no—
164C2×C4⋊C4×C61C2311yescharacteristic
165C2×C22⋊C4×C61—21no—
166#103×C61—21no—
167#103×C61—21no—
168#103×C61—21no—
169#103×C61—21no—
170C22⋊C8×C61D411yescharacteristic
171C22⋊C8×C61D411yescharacteristic
172C22⋊C8×C61D411yescharacteristic
173C22⋊C8×C61D411yescharacteristic
174C24×C61#4111yescharacteristic
175C2×Q8×C61—24no—
176C2×Q8×C61—21no—
177C2×Q8×C61—21no—
178C2×Q8×C61—21no—
179C2×Q8×C61—21no—
180C2×Q8×C61—21no—
181C2×Q8×C61—21no—
182C2×Q8×C61—21no—
183C2×Q8×C61—21no—
184C2×Q8×C61—21no—
185C2×Q8×C61—21no—
186C2×Q8×C61—21no—
187C2×Q8×C61—21no—
188C2×Q8×C61—21no—
189C2×Q8×C61—21no—
190C2×Q8×C61—21no—
191C2×Q8×C61—21no—
192C2×Q8×C61—42no—
193C2×Q8×C61—42no—
194C2×Q8×C61—42no—
195C2×Q8×C61—42no—
196C2×Q8×C61—42no—
197C2×Q8×C61—42no—
198C2×Q8×C61—42no—
199C2×Q8×C61—42no—
200C2×Q8×C61—42no—
201C2×Q8×C61—41no—
202C2×Q8×C61—41no—
203C2×Q8×C61C2×D412yes—
204C2×Q8×C61#4112yes—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61—24no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—42no—
215C22×C4×C61—41no—
216C22×C4×C61—41no—
217C22×C4×C61C2×D411yescharacteristic
218C22×C4×C61C2×D411yescharacteristic
219C22×C4×C61C2×D411yescharacteristic
220C22×C4×C61C2×D411yescharacteristic
221C22×C4×C61#4111yescharacteristic
222C22×C4×C61C2411yescharacteristic
223C2×C22⋊D61—21no—
224C2×C22⋊D61—21no—
225C2×C22⋊D61—21no—
226#11758222—21no—
227#11758222—21no—
228#11758222—21no—
229#11758222—21no—
230C2×D244C2×D411yescharacteristic
231C2×C4×D61—21no—
232C2×Dic122C2×D411yescharacteristic
233Q16×C61—42no—
234Q16×C61—42no—
235Q16×C61—42no—
236Q16×C61—42no—
237C2×C8×C61—21no—
238C2×C8×C61—21no—
239C2×C8×C61—21no—
240C2×C8×C61—21no—
241C2×C8×C61C2×D411yescharacteristic
242C2×C8×C61C2×D411yescharacteristic
243C2×C8×C61C2×D411yescharacteristic
244C2×C8×C61C2×D411yescharacteristic
245C4⋊C4×C61—21no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—41no—
248C4⋊C4×C61—41no—
249C22⋊C4×C61—41no—
250C22⋊C4×C61—41no—
251C22⋊Dic61—21no—
252C22⋊Dic61—21no—
253C22⋊Dic61—21no—
254#11758202—42no—
255#11758202—42no—
256#11758202—42no—
257#11758201—42no—
258#11758201—42no—
259#11758201—42no—
260#11758198—21no—
261#11758198—21no—
262C4⋊Dic61C2×D411yescharacteristic
263C4⋊Dic61C2×D411yescharacteristic
264#11758196—21no—
265#11758196—21no—
266C4×Dic61—21no—
267#11758194—21no—
268#11758194—21no—
269#11758194—21no—
270#11758194—21no—
271#11758194—21no—
272#11758194—21no—
273#11758194—21no—
274#11758194—21no—
275#11758194—21no—
276#11758194—21no—
277#11758194—42no—
278#11758194—42no—
279#11758194C2×D412yes—
280#11758194C2×D412yes—
281C2×#92418—21no—
282C2×#92418—21no—
283C2×#92418—21no—
284C2×#92418—21no—
285C2×#92418—21no—
286C2×#92418—21no—
287C2×#92418—42no—
288C2×#92418—42no—
289#11758189—42no—
290C8×D61—42no—
291C23×C61—21no—
292C23×C61—21no—
293C23×C61—22no—
294C23×C61—41no—
295C23×C61#12111yescharacteristic
296C23×C61#12111yescharacteristic
297C23×C61C2×#4111yescharacteristic
298C22×D61—21no—
299Q8×C61—22no—
300Q8×C61—22no—
301Q8×C61—22no—
302Q8×C61—22no—
303Q8×C61—44no—
304Q8×C61—44no—
305Q8×C61—41no—
306Q8×C61—41no—
307Q8×C61—41no—
308Q8×C61—41no—
309Q8×C61—41no—
310Q8×C61—41no—
311Q8×C61—41no—
312Q8×C61—41no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—21no—
317C2×C4×C61—21no—
318C2×C4×C61—21no—
319C2×C4×C61—21no—
320C2×C4×C61—21no—
321C2×C4×C61—21no—
322C2×C4×C61—21no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—44no—
326C2×C4×C61—44no—
327C2×C4×C61—41no—
328C2×C4×C61—41no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61—41no—
332C2×C4×C61—41no—
333C2×C4×C61—41no—
334C2×C4×C61—41no—
335C2×C4×C61—81no—
336C2×C4×C61#12111yescharacteristic
337C2×C4×C61#12111yescharacteristic
338C2×C4×C61C22×D411yescharacteristic
339C2×C4×C61C22×D411yescharacteristic
340C2×C4×C61C22×D411yescharacteristic
341C2×C4×C61C2×#4111yescharacteristic
342C2×C4×C61H(5,𝔽2)11yescharacteristic
343C2×C4×C61H(5,𝔽2)11yescharacteristic
344C22⋊D61—41no—
345C22⋊D61—41no—
346C22⋊D61—42no—
347C22⋊D61—81no—
348C2×Dic61—21no—
349C2×Dic61—21no—
350C2×Dic61—21no—
351D244—21no—
352D244—21no—
353C4×D61—41no—
354C4×D61—41no—
355Dic122—21no—
356Dic122—21no—
357C8×C61—21no—
358C8×C61—21no—
359C8×C61—21no—
360C8×C61—21no—
361#92418—22no—
362#92418—22no—
363#92418—41no—
364#92418—41no—
365#92418—41no—
366#92418—41no—
367#25142—611nomaximal, Sylow
368C22×C61—21no—
369C22×C61—21no—
370C22×C61—21no—
371C22×C61—21no—
372C22×C61—21no—
373C22×C61—21no—
374C22×C61—21no—
375C22×C61—42no—
376C22×C61—42no—
377C22×C61#47312yescomplemented
378C22×C61C2×#12111yescharacteristic
379C22×C61#52511yescharacteristic
380C22×C61#53811yescharacteristic
381C2×D61—41no—
382C2×D61—41no—
383C2×D61—41no—
384C4×C61—21no—
385C4×C61—21no—
386C4×C61—42no—
387C4×C61—42no—
388C4×C61—81no—
389C4×C61—81no—
390C4×C61D4211yescharacteristic
391C4×C61D4211yescharacteristic
392C4×C61#54611yescharacteristic
393C4×C61#54611yescharacteristic
394Dic61—41no—
395Dic61—41no—
396Dic61—41no—
397C2×#473—611no—
398#3056—611no—
399#3004—611no—
400C2×#451D6111yescharacteristic, complemented
401#2933—611no—
402C22×#101—611no—
403#2064—611no—
404#2052—611no—
405#2047—611no—
406#2020—611no—
407#1979—611no—
408#1930—611no—
409#1908—611no—
410#1901—611no—
411#1855—611no—
412C2×C61—21no—
413C2×C61—21no—
414C2×C61—22no—
415C2×C61—41no—
416C2×C61#242411yescharacteristic
417C2×C61C2×#47311yescharacteristic
418C2×C61#306911yescharacteristic
419D61—81no—
420C23×Q8C2×D6111yescharacteristic
421C2×#137—611no—
422C2×#137—611no—
423C2×#137—611no—
424C22×Q16C2×D6111yescharacteristic
425C22×Q16C2×D6111yescharacteristic
426C2×#131—611no—
427C22×M16—611no—
428C22×M16—611no—
429#525—611no—
430C2×C22⋊Q8C2×D6111yescharacteristic
431#473—1224no—
432#470—1221no—
433#468—1221no—
434#467—1221no—
435#465—1221no—
436#451—21no—
437#451—21no—
438#451—21no—
439#451—21no—
440#451—1221no—
441#451—1221no—
442#448—1221no—
443#448—1221no—
444#436—1221no—
445#435—1221no—
446#435—1221no—
447C8×D4—1221no—
448C2×#108—611no—
449C2×#108—611no—
450#428—611no—
451#424—611no—
452#419—611no—
453#419—611no—
454#419—611no—
455#417—611no—
456C2×#103C2×D6111yescharacteristic
457C2×#103C2×D6111yescharacteristic
458C2×#101—611no—
459C2×#101—611no—
460C2×#101—611no—
461C2×#101—611no—
462C2×#101—611no—
463C2×#101—611no—
464C2×#101—1224no—
465#408—611no—
466#407—611no—
467C2×C22⋊C8C2×D6111yescharacteristic
468#405—611no—
469#343—611no—
470#343—611no—
471#341—611no—
472#341—611no—
473C61#2514211yescharacteristic, complemented, Sylow
474C2×#41—611no—
475C22×Q8—22no—
476C22×Q8—22no—
477C22×Q8—21no—
478C22×Q8—21no—
479C22×Q8—21no—
480C22×Q8—21no—
481C22×Q8—21no—
482C22×Q8—41no—
483C22×Q8—41no—
484C22×Q8C22×D6111yescharacteristic
485C22×Q8C22×D6111yescharacteristic
486C22×Q8C22×D6111yescharacteristic
487C23×C4—21no—
488C23×C4C22×D6111yescharacteristic
489#137—1222no—
490#137—1222no—
491#137—1222no—
492#137—2441no—
493#137—2441no—
494#137—2441no—
495C2×Q16—22no—
496C2×Q16—22no—
497C2×Q16—21no—
498C2×Q16—21no—
499C2×Q16—21no—
500C2×Q16—21no—
501C2×Q16—41no—
502C2×Q16—41no—
503C2×Q16—1221no—
504C2×Q16—1221no—
505C2×Q16—1221no—
506C2×SD16—1221no—
507C2×SD16—1221no—
508C2×SD16—1221no—
509#131—1222no—
510#131—2441no—
511C2×M16—611no—
512C2×M16—611no—
513C2×M16—611no—
514C2×M16—611no—
515C2×M16—611no—
516C2×M16—611no—
517C2×M16—1221no—
518C2×M16—1221no—
519C2×M16—1221no—
520C2×M16—1222no—
521C2×M16—1222no—
522C2×M16—2441no—
523C2×M16—2441no—
524C22×C8—1221no—
525C22×C8—1221no—
526C22×C8—1221no—
527C22×C8C22×D6111yescharacteristic
528C22×C8C22×D6111yescharacteristic
529#123—1221no—
530C22⋊Q8—21no—
531C22⋊Q8—21no—
532C22⋊Q8—21no—
533C22⋊Q8—21no—
534C22⋊Q8—611no—
535C22⋊Q8—611no—
536#121—611no—
537#121—611no—
538#120—1221no—
539C4×D4—1221no—
540C4×D4—1221no—
541#117—611no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4C22×D6111yescharacteristic
544C2×C22⋊C4—21no—
545#108—1222no—
546#108—2441no—
547#107—1221no—
548#106—1221no—
549C4⋊C8—1221no—
550C4⋊C8—1221no—
551#103—21no—
552#103—21no—
553#103—21no—
554#103—21no—
555#103—1221no—
556#103—1221no—
557#103—1221no—
558#103—1221no—
559#103—1221no—
560#103—1221no—
561#103—1221no—
562#102—1221no—
563#101—614no—
564#101—1222no—
565#101—1222no—
566#101—1222no—
567#101—1222no—
568#101—2441no—
569C22⋊C8—1221no—
570C22⋊C8—1221no—
571C22⋊C8—1221no—
572C22⋊C8—1221no—
573C22⋊C8C22⋊D6111yescharacteristic
574C22⋊C8C22⋊D6111yescharacteristic
575C22⋊C8C22⋊D6111yescharacteristic
576C22⋊C8C22⋊D6111yescharacteristic
577#97—1221no—
578C4×C8—1221no—
579C24#1175822411yescharacteristic
580#41—1221no—
581#41—1221no—
582#41—1221no—
583#41—1221no—
584C2×Q8—24no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8—42no—
602C2×Q8—42no—
603C2×Q8—42no—
604C2×Q8—42no—
605C2×Q8—42no—
606C2×Q8—42no—
607C2×Q8—42no—
608C2×Q8—42no—
609C2×Q8—42no—
610C2×Q8—41no—
611C2×Q8—41no—
612C2×Q8—611no—
613C2×Q8D4×D6112yes—
614C2×Q8#1175822412yes—
615C2×D4—611no—
616C2×D4—1221no—
617C2×D4—1221no—
618C2×D4—1221no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—24no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—42no—
629C22×C4—41no—
630C22×C4—41no—
631C22×C4—1221no—
632C22×C4D4×D6111yescharacteristic
633C22×C4D4×D6111yescharacteristic
634C22×C4#1175822411yescharacteristic
635C22×C4C2×C22⋊D6111yescharacteristic
636C22×C4C2×C22⋊D6111yescharacteristic
637C22×C4C23×D6111yescharacteristic
638Q16—42no—
639Q16—42no—
640Q16—42no—
641Q16—42no—
642Q16—2442no—
643Q16—2442no—
644Q16—2442no—
645SD16—2442no—
646SD16—2442no—
647SD16—2442no—
648M16—612no—
649M16—612no—
650M16—1221no—
651M16—1221no—
652M16—1221no—
653M16—1221no—
654M16—1221no—
655M16—1221no—
656M16—1221no—
657M16—1221no—
658M16—1221no—
659M16—1221no—
660M16—2442no—
661M16—2442no—
662M16—2442no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—1221no—
668C2×C8—1221no—
669C2×C8—1221no—
670C2×C8—1221no—
671C2×C8—1221no—
672C2×C8—1221no—
673C2×C8—2442no—
674C2×C8—2442no—
675C2×C8—2442no—
676C2×C8C2×C22⋊D6111yescharacteristic
677C2×C8C2×C22⋊D6111yescharacteristic
678C2×C8C2×C22⋊D6111yescharacteristic
679C2×C8C2×C22⋊D6111yescharacteristic
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—41no—
683C4⋊C4—41no—
684C4⋊C4—611no—
685C4⋊C4—611no—
686C4⋊C4—1221no—
687C4⋊C4—1221no—
688C22⋊C4—41no—
689C22⋊C4—41no—
690C22⋊C4—1221no—
691C22⋊C4—1221no—
692C22⋊C4—1221no—
693C22⋊C4—1221no—
694C22⋊C4—1221no—
695C42—1221no—
696C23—21no—
697C23—22no—
698C23—21no—
699C23—41no—
700C23—1221no—
701C23#1451974811yescharacteristic
702C23#1451974811yescharacteristic
703C23C2×#1175822411yescharacteristic
704Q8—22no—
705Q8—22no—
706Q8—22no—
707Q8—22no—
708Q8—44no—
709Q8—44no—
710Q8—41no—
711Q8—41no—
712Q8—41no—
713Q8—41no—
714Q8—41no—
715Q8—41no—
716Q8—41no—
717Q8—41no—
718Q8—1221no—
719Q8—1221no—
720D4—1221no—
721D4—1221no—
722D4—4881no—
723D4—2441no—
724D4—2442no—
725D4—2441no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—81no—
749C2×C4—1221no—
750C2×C4—1221no—
751C2×C4—1221no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4#1451974811yescharacteristic
755C2×C4#1451974811yescharacteristic
756C2×C4C2×D4×D6111yescharacteristic
757C2×C4C2×D4×D6111yescharacteristic
758C2×C4C22×C22⋊D6111yescharacteristic
759C2×C4C2×#1175822411yescharacteristic
760C2×C4#1451982211yescharacteristic
761C2×C4#1451982211yescharacteristic
762C8—21no—
763C8—21no—
764C8—21no—
765C8—21no—
766C8—1222no—
767C8—1222no—
768C8—2441no—
769C8—2441no—
770C8—2441no—
771C8—2441no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—21no—
776C22—21no—
777C22—21no—
778C22—21no—
779C22—42no—
780C22—42no—
781C22—2441no—
782C22—2441no—
783C22—2441no—
784C22#1684003412yescomplemented
785C22C2×#1451974811yescharacteristic
786C22#1684026811yescharacteristic
787C22#1684034711yescharacteristic
788C4—21no—
789C4—21no—
790C4—42no—
791C4—42no—
792C4—81no—
793C4—81no—
794C4—2441no—
795C4—2441no—
796C4—2441no—
797C4#1684039411yescharacteristic
798C4D4×C22⋊D6111yescharacteristic
799C4#1684039911yescharacteristic
800C4#1684040611yescharacteristic
801C2—21no—
802C2—22no—
803C2—21no—
804C2—41no—
805C2—4881no—
806C2#2144935111yescharacteristic
807C2C2×#1684003411yescharacteristic
808C2#2145555211yescharacteristic
subgroupG/H
centerC22C2×#14519748
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#451C2
socleC22×C61C2×#121
prime radical#16840273C22
hypercenterC2×#451D61
hypocenterC61#25142
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
1. C2×#16840034C2semidirect
5. C22×#14519696C2semidirect
6. #21447184C2semidirect
7. #21447119C2semidirect
8. #21447084C2semidirect
9. #21446938C2semidirect
10. #21446735C2semidirect
11. #21446471C2semidirect
12. #21446337C2semidirect
13. #21446288C2semidirect
14. #21446026C2semidirect
15. C2×C61×#451C2semidirect
128. #14519696D4semidirect
377. C22×C61#473semidirect
400. C2×#451D61semidirect
473. C61#25142semidirect
784. C22#16840034semidirect

Maximal subgroups

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

subgroupindex
C2×#168400342
#214554452
#214550532
#214545402
C22×#145196962
#214471842
#214471192
#214470842
#214469382
#214467352
#214464712
#214463372
#214462882
#214460262
C2×C61×#4512
#2514261