Finite Group Databasebeta

← #29727360

Subgroups — #29727360

Order 15616.

1012 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840027C211yesmaximal, characteristic, complemented
2#21455440C211yesmaximal, characteristic
3C2×#16839901C211yesmaximal, characteristic, complemented
4#21454546C211yesmaximal, characteristic, complemented
5C22×#14519696C211yesmaximal, characteristic, complemented
6#21447186C211yesmaximal, characteristic, complemented
7#21447115C211yesmaximal, characteristic, complemented
8#21447079C211yesmaximal, characteristic, complemented
9#21446930C211yesmaximal, characteristic, complemented
10#21446721C211yesmaximal, characteristic, complemented
11#21446477C211yesmaximal, characteristic, complemented
12#21446336C211yesmaximal, characteristic, complemented
13#21446280C211yesmaximal, characteristic, complemented
14#21446023C211yesmaximal, characteristic, complemented
15C61×#3004C211yesmaximal, characteristic, complemented
16C2×#14519802C2211yescharacteristic
17C22×#11758201C2211yescharacteristic
18C22×#11758201C2211yescharacteristic
19C2×#14519784C2211yescharacteristic
20C22×#11758194C2211yescharacteristic
21C22×#11758194C2211yescharacteristic
22C2×#14519751C2211yescharacteristic
23#16840027—24no—
24#16840013—21no—
25#16840010—21no—
26#16839996—21no—
27#16839993—21no—
28#16839901—21no—
29#16839901—21no—
30#16839901—21no—
31#16839901—21no—
32#16839840—21no—
33#16839834—21no—
34#16839834—21no—
35D4×#92418—21no—
36C2×#14519712C2211yescharacteristic
37C2×#14519712C2211yescharacteristic
38#16839805C2211yescharacteristic
39#16839789C2211yescharacteristic
40#16839766C2211yescharacteristic
41#16839763C2211yescharacteristic
42C2×#14519701C2211yescharacteristic
43C2×#14519701C2211yescharacteristic
44C2×#14519696—24no—
45C2×#14519696C2211yescharacteristic
46C2×#14519696C2211yescharacteristic
47C2×#14519696C2211yescharacteristic
48C2×#14519696C2211yescharacteristic
49C2×#14519693C2211yescharacteristic
50C2×#14519693C2211yescharacteristic
51#16839729C2211yescharacteristic
52C2×C22⋊#92418C2211yescharacteristic
53#16839718C2211yescharacteristic
54#16839530C2211yescharacteristic
55#16839530C2211yescharacteristic
56#16839526C2211yescharacteristic
57#16839526C2211yescharacteristic
58C23×Q8×C61C2211yescharacteristic
59C2×#137×C61C2211yescharacteristic
60C2×#137×C61C2211yescharacteristic
61C61×#525C2211yescharacteristic
62C61×#451—21no—
63C61×#451—21no—
64C61×#448—21no—
65C61×#448—21no—
66C61×#419C2211yescharacteristic
67C61×#419C2211yescharacteristic
68C61×#407C2211yescharacteristic
69C22×D244C2311yescharacteristic
70C22×C22⋊D61—21no—
71#14519802—22no—
72#14519802—41no—
73C2×#11758201—21no—
74C2×#11758201—22no—
75C2×#11758201—22no—
76C2×#11758201—21no—
77C2×#11758201—21no—
78C2×#11758201—21no—
79C2×#11758201—21no—
80C2×#11758201—41no—
81C2×#11758201—41no—
82C2×#11758199—21no—
83#14519784—22no—
84#14519784—41no—
85C2×#11758194—21no—
86C2×#11758194—21no—
87C2×#11758194—21no—
88C2×#11758194—22no—
89C2×#11758194—22no—
90C2×#11758194—41no—
91C2×#11758194—41no—
92C2×#11758194C2311yescharacteristic
93C2×#11758194C2311yescharacteristic
94C2×#11758194C2311yescharacteristic
95C2×#11758194C2311yescharacteristic
96C22×#92418—21no—
97C22×#92418—21no—
98C22×#92418—21no—
99C22×#92418C2311yescharacteristic
100C22×#92418C2311yescharacteristic
101#14519751—21no—
102#14519751—21no—
103#14519751—21no—
104#14519751—21no—
105C2×C4⋊Dic61C2311yescharacteristic
106C2×#11758198—21no—
107#14519712—22no—
108#14519712—41no—
109#14519710—21no—
110#14519708—21no—
111C4⋊#92418—21no—
112C4⋊#92418—21no—
113#14519701—21no—
114#14519701—21no—
115#14519701—21no—
116#14519701—21no—
117#14519701—21no—
118#14519698—21no—
119#14519697—21no—
120#14519697—21no—
121#14519696—22no—
122#14519696—22no—
123#14519696—22no—
124#14519696D414yescomplemented
125#14519693—22no—
126#14519693—41no—
127C22⋊#92418—21no—
128C22⋊#92418—21no—
129C22⋊#92418D411yescharacteristic
130C22⋊#92418D411yescharacteristic
131C22⋊#92418D411yescharacteristic
132C22⋊#92418D411yescharacteristic
133#14519688—21no—
134C4×#92418—21no—
135C2×#41×C61C2311yescharacteristic
136C22×Q8×C61—22no—
137C22×Q8×C61—22no—
138C22×Q8×C61—21no—
139C22×Q8×C61—21no—
140C22×Q8×C61—21no—
141C22×Q8×C61—21no—
142C22×Q8×C61—21no—
143C22×Q8×C61—41no—
144C22×Q8×C61—41no—
145C22×Q8×C61C2311yescharacteristic
146C22×Q8×C61C2311yescharacteristic
147C23×C4×C61—21no—
148C23×C4×C61C2311yescharacteristic
149#137×C61—22no—
150#137×C61—22no—
151#137×C61—41no—
152#137×C61—41no—
153C2×Q16×C61—21no—
154C2×Q16×C61—21no—
155C2×SD16×C61—21no—
156C2×SD16×C61—21no—
157C2×M16×C61C2311yescharacteristic
158C2×M16×C61C2311yescharacteristic
159#123×C61—21no—
160C22⋊Q8×C61D411yescharacteristic
161C22⋊Q8×C61D411yescharacteristic
162#121×C61D411yescharacteristic
163#121×C61D411yescharacteristic
164#120×C61—21no—
165C4×D4×C61—21no—
166C4×D4×C61—21no—
167#117×C61C2311yescharacteristic
168#103×C61—21no—
169#103×C61—21no—
170#103×C61—21no—
171#103×C61—21no—
172C22⋊C8×C61—21no—
173C22⋊C8×C61—21no—
174C24×C61#4111yescharacteristic
175C23×D61—21no—
176#41×C61—21no—
177#41×C61—21no—
178#41×C61—21no—
179#41×C61—21no—
180C2×Q8×C61—24no—
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—42no—
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—41no—
201C2×Q8×C61—41no—
202C2×Q8×C61C2×D412yes—
203C2×Q8×C61C2×D411yescharacteristic
204C2×Q8×C61#4112yes—
205C2×D4×C61—21no—
206C2×D4×C61—21no—
207C2×D4×C61—21no—
208C2×D4×C61C2×D411yescharacteristic
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—24no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—42no—
218C22×C4×C61—41no—
219C22×C4×C61—41no—
220C22×C4×C61C2×D411yescharacteristic
221C22×C4×C61C2×D411yescharacteristic
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61#4111yescharacteristic
225C22×C4×C61C2411yescharacteristic
226C2×C22⋊D61—41no—
227C2×C22⋊D61—41no—
228C2×C22⋊D61—82no—
229C22×Dic61—21no—
230C2×D244—21no—
231C2×D244—21no—
232C2×D244—21no—
233C2×D244—21no—
234C2×D244—21no—
235C2×D244—21no—
236Q16×C61—42no—
237Q16×C61—42no—
238SD16×C61—42no—
239SD16×C61—42no—
240M16×C61—21no—
241M16×C61—21no—
242M16×C61—21no—
243M16×C61—21no—
244C2×C8×C61—21no—
245C2×C8×C61—21no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61C2×D411yescharacteristic
249C4⋊C4×C61C2×D411yescharacteristic
250C22⋊C4×C61—21no—
251C22⋊C4×C61—21no—
252C22⋊C4×C61—21no—
253C22⋊C4×C61—21no—
254C22⋊C4×C61—21no—
255C42×C61—21no—
256#11758201—42no—
257#11758201—42no—
258#11758201—42no—
259#11758201—42no—
260#11758201—42no—
261#11758199—42no—
262#11758198—41no—
263#11758198—41no—
264C4⋊Dic61—21no—
265C4⋊Dic61—21no—
266#11758194—21no—
267#11758194—21no—
268#11758194—21no—
269#11758194—21no—
270#11758194—21no—
271#11758194—21no—
272#11758194—42no—
273#11758194—42no—
274#11758194—42no—
275#11758194C2×D412yes—
276#11758194C2×D412yes—
277C2×#92418—21no—
278C2×#92418—21no—
279C2×#92418—21no—
280C2×#92418—21no—
281C2×#92418—21no—
282C2×#92418—21no—
283C2×#92418—21no—
284C2×#92418—21no—
285C2×#92418—42no—
286C2×#92418—42no—
287C2×#92418—42no—
288C2×#92418C2×D411yescharacteristic
289C2×#92418C2×D411yescharacteristic
290C2×#92418C2×D411yescharacteristic
291C2×#92418C2×D411yescharacteristic
292C23×C61—21no—
293C23×C61—21no—
294C23×C61—22no—
295C23×C61—21no—
296C23×C61—41no—
297C23×C61#12111yescharacteristic
298C23×C61#12111yescharacteristic
299C23×C61C2×#4111yescharacteristic
300C22×D61—41no—
301C22×D61—41no—
302C22×D61—41no—
303C22×D61—81no—
304C22×D61—81no—
305Q8×C61—21no—
306Q8×C61—22no—
307Q8×C61—22no—
308Q8×C61—22no—
309Q8×C61—22no—
310Q8×C61—21no—
311Q8×C61—44no—
312Q8×C61—44no—
313Q8×C61—41no—
314Q8×C61—41no—
315Q8×C61—41no—
316Q8×C61—41no—
317D4×C61—21no—
318D4×C61—21no—
319D4×C61—41no—
320D4×C61—41no—
321D4×C61—42no—
322D4×C61—81no—
323C2×C4×C61—21no—
324C2×C4×C61—21no—
325C2×C4×C61—21no—
326C2×C4×C61—21no—
327C2×C4×C61—21no—
328C2×C4×C61—21no—
329C2×C4×C61—21no—
330C2×C4×C61—21no—
331C2×C4×C61—21no—
332C2×C4×C61—21no—
333C2×C4×C61—21no—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—44no—
339C2×C4×C61—44no—
340C2×C4×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61—41no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61#12111yescharacteristic
347C2×C4×C61#12111yescharacteristic
348C2×C4×C61C22×D411yescharacteristic
349C2×C4×C61C22×D411yescharacteristic
350C2×C4×C61C22×D411yescharacteristic
351C2×C4×C61C2×#4111yescharacteristic
352C2×C4×C61H(5,𝔽2)11yescharacteristic
353C2×C4×C61H(5,𝔽2)11yescharacteristic
354C22⋊D61—82no—
355C22⋊D61—82no—
356C2×Dic61—41no—
357C2×Dic61—81no—
358D244—41no—
359D244—41no—
360D244—41no—
361D244—41no—
362C8×C61—41no—
363C8×C61—41no—
364#92418—21no—
365#92418—21no—
366#92418—22no—
367#92418—22no—
368#92418—21no—
369#92418—21no—
370#92418—41no—
371#92418—41no—
372#25146—611nomaximal, Sylow
373C22×C61—21no—
374C22×C61—21no—
375C22×C61—21no—
376C22×C61—21no—
377C22×C61—21no—
378C22×C61—21no—
379C22×C61—21no—
380C22×C61—42no—
381C22×C61—42no—
382C22×C61—41no—
383C22×C61—41no—
384C22×C61—41no—
385C22×C61#47112yescomplemented
386C22×C61C2×#12111yescharacteristic
387C22×C61#52511yescharacteristic
388C22×C61#53811yescharacteristic
389C2×D61—81no—
390C2×D61—81no—
391C2×D61—81no—
392C2×D61—161no—
393C2×D61—161no—
394C4×C61—21no—
395C4×C61—21no—
396C4×C61—42no—
397C4×C61—42no—
398C4×C61—41no—
399C4×C61—41no—
400C4×C61—41no—
401C4×C61D4211yescharacteristic
402C4×C61D4211yescharacteristic
403C4×C61#54611yescharacteristic
404C4×C61#54611yescharacteristic
405Dic61—81no—
406C2×#471—611no—
407#3055—611no—
408#3004D6111yescharacteristic, complemented
409C2×#448—611no—
410#2933—611no—
411C22×#101—611no—
412#2064—611no—
413#2052—611no—
414#2046—611no—
415#2019—611no—
416#1977—611no—
417#1930—611no—
418#1908—611no—
419#1900—611no—
420#1855—611no—
421C2×C61—21no—
422C2×C61—21no—
423C2×C61—22no—
424C2×C61—41no—
425C2×C61—81no—
426C2×C61#242411yescharacteristic
427C2×C61C2×#47111yescharacteristic
428C2×C61#306911yescharacteristic
429D61—161no—
430C23×Q8C2×D6111yescharacteristic
431C2×#137C2×D6111yescharacteristic
432C2×#137C2×D6111yescharacteristic
433C2×AGL(1,ℤ/8)—611no—
434C22×SD16—611no—
435C22×SD16—611no—
436C2×#131—611no—
437C22×M16—611no—
438C22×M16—611no—
439#525C2×D6111yescharacteristic
440C2×#121—611no—
441#471—1224no—
442#469—1221no—
443#468—1221no—
444#466—1221no—
445#465—1221no—
446#451—21no—
447#451—21no—
448#448—21no—
449#448—21no—
450#448—1221no—
451#448—1221no—
452#448—1221no—
453#448—1221no—
454#436—1221no—
455#435—1221no—
456#435—1221no—
457C8×D4—1221no—
458C2×#108—611no—
459C2×#108—611no—
460#428—611no—
461#424—611no—
462#419C2×D6111yescharacteristic
463#419C2×D6111yescharacteristic
464#418—611no—
465#417—611no—
466C2×#103—611no—
467C2×#103—611no—
468C2×#101—611no—
469C2×#101—611no—
470C2×#101—611no—
471C2×#101—611no—
472C2×#101—1224no—
473C2×#100—611no—
474C2×#100—611no—
475#408—611no—
476#407C2×D6111yescharacteristic
477C2×C22⋊C8—611no—
478#405—611no—
479#343—611no—
480#343—611no—
481#341—611no—
482#341—611no—
483C61#2514611yescharacteristic, complemented, Sylow
484C2×#41C22×D6111yescharacteristic
485C22×Q8—22no—
486C22×Q8—22no—
487C22×Q8—21no—
488C22×Q8—21no—
489C22×Q8—21no—
490C22×Q8—21no—
491C22×Q8—21no—
492C22×Q8—41no—
493C22×Q8—41no—
494C22×Q8C22×D6111yescharacteristic
495C22×Q8C22×D6111yescharacteristic
496C22×D4—611no—
497C22×D4—1221no—
498C23×C4—21no—
499C23×C4C22×D6111yescharacteristic
500#137—22no—
501#137—22no—
502#137—41no—
503#137—41no—
504AGL(1,ℤ/8)—1222no—
505AGL(1,ℤ/8)—2441no—
506C2×Q16—21no—
507C2×Q16—21no—
508C2×SD16—21no—
509C2×SD16—21no—
510C2×SD16—1221no—
511C2×SD16—1221no—
512C2×SD16—1221no—
513C2×SD16—1221no—
514C2×SD16—1222no—
515C2×SD16—1222no—
516C2×SD16—1221no—
517C2×SD16—2441no—
518C2×SD16—2441no—
519C2×D8—1221no—
520#131—1222no—
521#131—2441no—
522C2×M16—611no—
523C2×M16—611no—
524C2×M16—611no—
525C2×M16—611no—
526C2×M16—1221no—
527C2×M16—1221no—
528C2×M16—1221no—
529C2×M16—1222no—
530C2×M16—1222no—
531C2×M16—2441no—
532C2×M16—2441no—
533C2×M16C22×D6111yescharacteristic
534C2×M16C22×D6111yescharacteristic
535C22×C8—611no—
536C22×C8—611no—
537C22×C8—1221no—
538C22×C8—1221no—
539C22×C8—1221no—
540#123—21no—
541C22⋊Q8C22⋊D6111yescharacteristic
542C22⋊Q8C22⋊D6111yescharacteristic
543#121—1221no—
544#121—1221no—
545#121—1221no—
546#121—1221no—
547#121C22⋊D6111yescharacteristic
548#121C22⋊D6111yescharacteristic
549#120—21no—
550C4×D4—21no—
551C4×D4—21no—
552#117C22×D6111yescharacteristic
553C2×C4⋊C4—611no—
554C2×C22⋊C4—1221no—
555#108—1222no—
556#108—2441no—
557#107—1221no—
558#106—1221no—
559C4⋊C8—1221no—
560C4⋊C8—1221no—
561#103—21no—
562#103—21no—
563#103—21no—
564#103—21no—
565#103—1221no—
566#103—1221no—
567#103—1221no—
568#103—1221no—
569#103—1221no—
570#102—1221no—
571#102—1221no—
572#102—1221no—
573#101—614no—
574#101—1222no—
575#101—1222no—
576#101—1222no—
577#100—1222no—
578#100—2441no—
579C22⋊C8—21no—
580C22⋊C8—21no—
581C22⋊C8—611no—
582C22⋊C8—611no—
583C22⋊C8—611no—
584C22⋊C8—611no—
585C22⋊C8—1221no—
586C22⋊C8—1221no—
587#97—1221no—
588C4×C8—1221no—
589C24—1221no—
590C24#1175822411yescharacteristic
591#41—21no—
592#41—21no—
593#41—21no—
594#41—21no—
595C2×Q8—24no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—42no—
607C2×Q8—42no—
608C2×Q8—42no—
609C2×Q8—42no—
610C2×Q8—42no—
611C2×Q8—42no—
612C2×Q8—42no—
613C2×Q8—42no—
614C2×Q8—42no—
615C2×Q8—41no—
616C2×Q8—41no—
617C2×Q8D4×D6112yes—
618C2×Q8#1175822412yes—
619C2×Q8C2×C22⋊D6111yescharacteristic
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—1221no—
624C2×D4—1221no—
625C2×D4—1221no—
626C2×D4—1221no—
627C2×D4—1221no—
628C2×D4—1221no—
629C2×D4—4882no—
630C2×D4—2441no—
631C2×D4—2441no—
632C2×D4C2×C22⋊D6111yescharacteristic
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—24no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—42no—
642C22×C4—41no—
643C22×C4—41no—
644C22×C4—1221no—
645C22×C4D4×D6111yescharacteristic
646C22×C4D4×D6111yescharacteristic
647C22×C4#1175822411yescharacteristic
648C22×C4C2×C22⋊D6111yescharacteristic
649C22×C4C2×C22⋊D6111yescharacteristic
650C22×C4C23×D6111yescharacteristic
651Q16—42no—
652Q16—42no—
653SD16—42no—
654SD16—42no—
655SD16—2442no—
656SD16—2442no—
657SD16—2442no—
658SD16—2442no—
659SD16—2442no—
660D8—2442no—
661M16—21no—
662M16—21no—
663M16—21no—
664M16—21no—
665M16—612no—
666M16—612no—
667M16—1221no—
668M16—1221no—
669M16—1221no—
670M16—1221no—
671M16—1221no—
672M16—1221no—
673M16—2442no—
674M16—2442no—
675M16—2442no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—611no—
679C2×C8—611no—
680C2×C8—611no—
681C2×C8—611no—
682C2×C8—1221no—
683C2×C8—1221no—
684C2×C8—1221no—
685C2×C8—1221no—
686C2×C8—1221no—
687C2×C8—1221no—
688C2×C8—1221no—
689C2×C8—1221no—
690C2×C8—2442no—
691C2×C8—2442no—
692C2×C8—2442no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—1221no—
696C4⋊C4—1221no—
697C4⋊C4C2×C22⋊D6111yescharacteristic
698C4⋊C4C2×C22⋊D6111yescharacteristic
699C22⋊C4—21no—
700C22⋊C4—21no—
701C22⋊C4—21no—
702C22⋊C4—21no—
703C22⋊C4—21no—
704C22⋊C4—2441no—
705C22⋊C4—2441no—
706C42—21no—
707C23—21no—
708C23—22no—
709C23—21no—
710C23—21no—
711C23—41no—
712C23—4881no—
713C23—4881no—
714C23—2441no—
715C23—2441no—
716C23—2441no—
717C23#1451974911yescharacteristic
718C23#1451974911yescharacteristic
719C23C2×#1175822411yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—21no—
723Q8—22no—
724Q8—22no—
725Q8—21no—
726Q8—44no—
727Q8—44no—
728Q8—41no—
729Q8—41no—
730Q8—41no—
731Q8—41no—
732D4—21no—
733D4—21no—
734D4—41no—
735D4—42no—
736D4—41no—
737D4—81no—
738D4—4882no—
739D4—4882no—
740D4—2441no—
741D4—2441no—
742D4—2441no—
743D4—2441no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—4881no—
768C2×C4—2441no—
769C2×C4#1451974911yescharacteristic
770C2×C4#1451974911yescharacteristic
771C2×C4C2×D4×D6111yescharacteristic
772C2×C4C2×D4×D6111yescharacteristic
773C2×C4C22×C22⋊D6111yescharacteristic
774C2×C4C2×#1175822411yescharacteristic
775C2×C4#1451982211yescharacteristic
776C2×C4#1451982211yescharacteristic
777C8—41no—
778C8—41no—
779C8—1221no—
780C8—1221no—
781C8—1222no—
782C8—1222no—
783C8—1221no—
784C8—1221no—
785C8—2441no—
786C8—2441no—
787C22—21no—
788C22—21no—
789C22—21no—
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—42no—
795C22—42no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—9761no—
800C22—9761no—
801C22—4881no—
802C22—4881no—
803C22—4881no—
804C22#1684002712yescomplemented
805C22C2×#1451974911yescharacteristic
806C22#1684026811yescharacteristic
807C22#1684034711yescharacteristic
808C4—21no—
809C4—21no—
810C4—42no—
811C4—42no—
812C4—41no—
813C4—41no—
814C4—41no—
815C4—4881no—
816C4#1684039411yescharacteristic
817C4D4×C22⋊D6111yescharacteristic
818C4#1684039911yescharacteristic
819C4#1684040611yescharacteristic
820C2—21no—
821C2—21no—
822C2—22no—
823C2—41no—
824C2—81no—
825C2—9761no—
826C2#2144935911yescharacteristic
827C2C2×#1684002711yescharacteristic
828C2#2145555311yescharacteristic
subgroupG/H
centerC22C2×#14519749
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#3004C2
socleC22×C61C2×#121
prime radical#21455440C2
hypercenter#3004D61
hypocenterC61#25146
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3004

Complements

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

NH ≅ G/Ntype
1. C2×#16840027C2semidirect
3. C2×#16839901C2semidirect
4. #21454546C2semidirect
5. C22×#14519696C2semidirect
6. #21447186C2semidirect
7. #21447115C2semidirect
8. #21447079C2semidirect
9. #21446930C2semidirect
10. #21446721C2semidirect
11. #21446477C2semidirect
12. #21446336C2semidirect
13. #21446280C2semidirect
14. #21446023C2semidirect
15. C61×#3004C2semidirect
124. #14519696D4semidirect
385. C22×C61#471semidirect
408. #3004D61semidirect
483. C61#25146semidirect
804. C22#16840027semidirect

Maximal subgroups

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

subgroupindex
C2×#168400272
#214554402
C2×#168399012
#214545462
C22×#145196962
#214471862
#214471152
#214470792
#214469302
#214467212
#214464772
#214463362
#214462802
#214460232
C61×#30042
#2514661