Finite Group Databasebeta

← #30622728

Subgroups — #30622728

Order 15616.

914 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840809C211yesmaximal, characteristic, complemented
2C2×#16840805C211yesmaximal, characteristic, complemented
3#21462564C211yesmaximal, characteristic, complemented
4#21462562C211yesmaximal, characteristic, complemented
5#21461984C211yesmaximal, characteristic, complemented
6#21461983C211yesmaximal, characteristic, complemented
7#21461975C211yesmaximal, characteristic, complemented
8#21461972C211yesmaximal, characteristic, complemented
9#21461811C211yesmaximal, characteristic, complemented
10#21461810C211yesmaximal, characteristic, complemented
11#21461810C211yesmaximal, characteristic, complemented
12#21461808C211yesmaximal, characteristic, complemented
13#21461639C211yesmaximal, characteristic, complemented
14#21461617C211yesmaximal, characteristic, complemented
15#21456261C211yesmaximal, characteristic
16C2×#14519865C2211yescharacteristic
17C2×#14519864C2211yescharacteristic
18C2×#14519864C2211yescharacteristic
19C2×#14519864C2211yescharacteristic
20#16840809—24no—
21#16840805—24no—
22#16840797—21no—
23#16840795—21no—
24#16840794—21no—
25#16840793—21no—
26#16840793—21no—
27#16840791—21no—
28#16840789—21no—
29D4×#92420—21no—
30C2×#14519848C2211yescharacteristic
31C2×#14519847C2211yescharacteristic
32D61⋊(C4⋊C8)C2211yescharacteristic
33C2×#14519842C2211yescharacteristic
34C2×#14519842C2211yescharacteristic
35C2×#14519841C2211yescharacteristic
36C2×#14519841C2211yescharacteristic
37C2×#14519841C2211yescharacteristic
38C2×#14519841C2211yescharacteristic
39C2×#14519841C2211yescharacteristic
40C2×#14519841C2211yescharacteristic
41#16840737C2211yescharacteristic
42#16840736C2211yescharacteristic
43#16840736C2211yescharacteristic
44#16840736C2211yescharacteristic
45C4×#11758213C2211yescharacteristic
46C4×#11758213C2211yescharacteristic
47C2×#14519831C2211yescharacteristic
48C2×C8×#6923C2211yescharacteristic
49C4×C4⋊#6923C2211yescharacteristic
50#16840638C2211yescharacteristic
51#16840638C2211yescharacteristic
52(C2×#6923)⋊C8C2211yescharacteristic
53(C2×#6923)⋊C8C2211yescharacteristic
54C2×#14519798C2211yescharacteristic
55C2×#14519798C2211yescharacteristic
56C2×#14519796C2211yescharacteristic
57C2×#14519796C2211yescharacteristic
58#16840311C2211yescharacteristic
59#16840310C2211yescharacteristic
60#16840157C411yescharacteristic, complemented
61#16840156C411yescharacteristic, complemented
62#16840153C411yescharacteristic, complemented
63#16840153C411yescharacteristic, complemented
64#16840150C411yescharacteristic, complemented
65#16840150C411yescharacteristic, complemented
66#16840149C411yescharacteristic, complemented
67#97×D61C2211yescharacteristic
68C61×#496C411yescharacteristic, complemented
69#14519865—22no—
70#14519865—41no—
71#14519864—22no—
72#14519864—22no—
73#14519864—22no—
74#14519864—41no—
75#14519864—41no—
76#14519864—41no—
77C2×#11758213—21no—
78C2×#11758213C2311yescharacteristic
79C2×#11758213C2311yescharacteristic
80C2×#11758213C2311yescharacteristic
81C2×#11758213C2311yescharacteristic
82C2×#11758217—21no—
83C2×#11758217—21no—
84C2×#11758217—21no—
85C2×D61⋊C8—21no—
86C2×D61⋊C8C2311yescharacteristic
87C2×D61⋊C8C2311yescharacteristic
88C22×#92420—21no—
89C22×#92420—21no—
90C22×#92420—21no—
91C2×C4⋊#6923—21no—
92C2×C4×#6923C2311yescharacteristic
93C2×C4×#6923C2311yescharacteristic
94#14519848—22no—
95#14519847D414yescomplemented
96#14519844D411yescharacteristic
97#14519844D411yescharacteristic
98C4⋊#92420D411yescharacteristic
99C4⋊#92420D411yescharacteristic
100#14519842—22no—
101#14519842—41no—
102#14519841—22no—
103#14519841—22no—
104#14519841—22no—
105#14519841—41no—
106#14519841—41no—
107#14519841—41no—
108#14519834—21no—
109#14519834—21no—
110C22⋊#92420—21no—
111C22⋊#92420—21no—
112C22⋊#92420—21no—
113C22⋊#92420—21no—
114C22⋊#92420—21no—
115C22⋊#92420—21no—
116#14519832—21no—
117#14519832—21no—
118#14519831—22no—
119C4×#92420—21no—
120C4×#92420—21no—
121C8×#6923—22no—
122(C2×#6923)⋊C4—21no—
123C2×#11758226C2311yescharacteristic
124C2×#11758224C2311yescharacteristic
125C2×#11758224C2311yescharacteristic
126C2×#11758224C2311yescharacteristic
127#14519798—22no—
128#14519798—22no—
129#14519798—41no—
130#14519798—41no—
131#14519796—22no—
132#14519796—22no—
133#14519796—41no—
134#14519796—41no—
135C2×Dic244C2×C411yescharacteristic
136C2×Dic244C2×C411yescharacteristic
137C2×#11758202C2×C411yescharacteristic
138C2×#11758202C2×C411yescharacteristic
139C2×#11758190C2×C411yescharacteristic
140C2×#11758190C2×C411yescharacteristic
141C2×#11758200C2×C411yescharacteristic
142C2×#11758200C2×C411yescharacteristic
143C2×#11758200C2×C411yescharacteristic
144C2×#11758200C2×C411yescharacteristic
145C2×#11758199C2×C411yescharacteristic
146C2×#11758199C2×C411yescharacteristic
147C2×C8×D61C2311yescharacteristic
148C2×C8×D61C2311yescharacteristic
149#14519777C2×C411yescharacteristic
150#14519775C2×C411yescharacteristic
151#14519773C2×C411yescharacteristic
152#14519765C2×C411yescharacteristic
153#14519764C2×C411yescharacteristic
154#14519764C2×C411yescharacteristic
155#14519750—21no—
156#14519750—21no—
157#14519748—21no—
158#14519748—21no—
159D4×Dic61—21no—
160D4×Dic61—21no—
161#14519737—21no—
162#14519737—21no—
163C42×D61C2311yescharacteristic
164#14519688C2×C411yescharacteristic
165#14519687C2×C411yescharacteristic
166#14519687C2×C411yescharacteristic
167C2×SD16×C61C2×C411yescharacteristic
168C2×SD16×C61C2×C411yescharacteristic
169C2×D8×C61C2×C411yescharacteristic
170C2×D8×C61C2×C411yescharacteristic
171#127×C61C2×C411yescharacteristic
172#124×C61C2×C411yescharacteristic
173#97×C61C2×C411yescharacteristic
174C22×#6923—21no—
175C22×#6923—21no—
176C2×Q8×C61C22×C411yescharacteristic
177C2×D4×C61—21no—
178C2×D4×C61—21no—
179C2×D4×C61C22×C411yescharacteristic
180C2×D4×C61C22×C411yescharacteristic
181C2×D4×C61C22×C411yescharacteristic
182C2×C22⋊D61—21no—
183C2×C22⋊D61—21no—
184C2×C22⋊D61—21no—
185C2×C22⋊D61—21no—
186C2×C22⋊D61—21no—
187C22×Dic61—21no—
188C22×Dic61—21no—
189C22×Dic61—21no—
190#11758226—21no—
191#11758226—21no—
192#11758226—21no—
193#11758226—21no—
194#11758224—21no—
195#11758224—21no—
196#11758224—21no—
197#11758224—21no—
198#11758224—21no—
199#11758224—21no—
200#11758224—21no—
201#11758224—21no—
202#11758224—21no—
203#11758224—21no—
204#11758224—21no—
205#11758224—21no—
206C2×D244—21no—
207C2×D244C22×C411yescharacteristic
208C2×C4×D61—21no—
209C2×C4×D61#4111yescharacteristic
210C2×C4×D61#4111yescharacteristic
211C2×C4×D61C2411yescharacteristic
212C2×Dic122C22×C411yescharacteristic
213C2×Dic122C22×C411yescharacteristic
214C2×Dic122C22×C411yescharacteristic
215#11758217—42no—
216#11758217—42no—
217#11758217—42no—
218C2×#92420—21no—
219C2×#92420—21no—
220C2×#92420—21no—
221C2×#92420—21no—
222C2×#92420—42no—
223C2×#92420—42no—
224C2×#92420—42no—
225C2×#92420C2×D411yescharacteristic
226C2×#92420C2×D411yescharacteristic
227C2×#92420C2×D411yescharacteristic
228C2×#92420C2×D411yescharacteristic
229C4⋊#6923—42no—
230C4×#6923—21no—
231C4×#6923—21no—
232C4×#6923—21no—
233C4×#6923—21no—
234#11758213—21no—
235#11758213—21no—
236#11758213—21no—
237#11758213—21no—
238#11758213—21no—
239#11758213—21no—
240#11758213—42no—
241#11758213C2×D412yes—
242#11758213C2×D412yes—
243D61⋊C8—21no—
244D61⋊C8—21no—
245D61⋊C8—21no—
246D61⋊C8—21no—
247D61⋊C8—42no—
248SD16×C61—22no—
249SD16×C61—41no—
250D8×C61—22no—
251D8×C61—41no—
252C2×C8×C61C22×C411yescharacteristic
253C2×C8×C61C22×C411yescharacteristic
254C22⋊C4×C61—21no—
255C22⋊C4×C61—21no—
256C42×C61C22×C411yescharacteristic
257C22⋊Dic61—21no—
258C22⋊Dic61—21no—
259C22⋊Dic61—21no—
260C22⋊Dic61—21no—
261#11758202—22no—
262#11758202—41no—
263#11758200—22no—
264#11758200—22no—
265#11758200—41no—
266#11758200—41no—
267#11758199—22no—
268#11758199—41no—
269#11758198—21no—
270#11758198—21no—
271C4⋊Dic61—21no—
272C4⋊Dic61—21no—
273#11758196—21no—
274#11758196—21no—
275C4×Dic61C22×C411yescharacteristic
276C4×Dic61C2×D411yescharacteristic
277C4×Dic61C2×D411yescharacteristic
278C2×#92418C22×C411yescharacteristic
279C2×#92418C22×C411yescharacteristic
280Dic244—22no—
281Dic244—41no—
282#11758190—22no—
283#11758190—41no—
284C8×D61—21no—
285C8×D61—21no—
286C8×D61C2×D412yes—
287C8×D61#4112yes—
288C23×C61—21no—
289C23×C61—21no—
290C23×C61—21no—
291C22×D61—21no—
292C22×D61C2×#4111yescharacteristic
293C2×#6923—22no—
294C2×#6923—41no—
295C2×#6923—41no—
296C2×#6923—41no—
297C2×#6923—41no—
298C2×#6923—41no—
299Q8×C61—21no—
300Q8×C61—21no—
301D4×C61—21no—
302D4×C61—21no—
303D4×C61—21no—
304D4×C61—21no—
305D4×C61—21no—
306D4×C61—21no—
307D4×C61—42no—
308D4×C61—81no—
309C2×C4×C61—21no—
310C2×C4×C61C4×D411yescharacteristic
311C2×C4×C61C4×D411yescharacteristic
312C2×C4×C61C23×C411yescharacteristic
313C22⋊D61—42no—
314C22⋊D61—41no—
315C22⋊D61—41no—
316C22⋊D61—41no—
317C22⋊D61—41no—
318C22⋊D61—41no—
319C22⋊D61—41no—
320C22⋊D61—81no—
321C2×Dic61—21no—
322C2×Dic61—21no—
323C2×Dic61—21no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330C2×Dic61C4×D411yescharacteristic
331C2×Dic61C4×D411yescharacteristic
332C2×Dic61C22×D411yescharacteristic
333D244—21no—
334D244—21no—
335D244—41no—
336D244—41no—
337C4×D61—41no—
338C4×D61—41no—
339C4×D61—41no—
340C4×D61—41no—
341C4×D61C22×D411yescharacteristic
342C4×D61C2×#4111yescharacteristic
343C4×D61H(5,𝔽2)11yescharacteristic
344C4×D61H(5,𝔽2)11yescharacteristic
345Dic122—21no—
346Dic122—21no—
347Dic122—21no—
348Dic122—21no—
349Dic122—21no—
350Dic122—21no—
351#92420—21no—
352#92420—21no—
353#92420—21no—
354#92420—21no—
355#92420—22no—
356#92420—22no—
357#92420—41no—
358#92420—41no—
359C8×C61—21no—
360C8×C61C4×D412yes—
361#92418—21no—
362#92418C4×D412yes—
363#23181—611nomaximal, Sylow
364C22×C61—41no—
365C22×C61—41no—
366C22×C61—41no—
367C22×C61—41no—
368C22×C61—41no—
369C22×C61—41no—
370C22×C61—41no—
371C22×C61—41no—
372C22×C61—41no—
373C22×C61C2×C4×D411yescharacteristic
374C2×D61—21no—
375C2×D61—21no—
376C2×D61—41no—
377C2×D61—41no—
378C2×D61—41no—
379C2×D61#55011yescharacteristic
380C2×D61#55911yescharacteristic
381#6923—42no—
382#6923—81no—
383C4×C61—21no—
384C4×C61—21no—
385C4×C61—41no—
386C4×C61C2×C4×D411yescharacteristic
387C4×C61#51811yescharacteristic
388Dic61—21no—
389Dic61—21no—
390Dic61—41no—
391Dic61—41no—
392Dic61—41no—
393Dic61D4211yescharacteristic
394Dic61#55011yescharacteristic
395#3150—611no—
396C2×#444—611no—
397C2×#443—611no—
398#2935—611no—
399#2935—611no—
400#1980—611no—
401#1980—611no—
402#1975—611no—
403#1974—611no—
404#1876—611no—
405#1876—611no—
406#1876—611no—
407#1876—611no—
408#1778—611no—
409#1771—611no—
410C2×C61—81no—
411C2×C61—81no—
412C2×C61—81no—
413C2×C61#236611yescharacteristic
414C2×C61#295511yescharacteristic
415C2×C61#295611yescharacteristic
416D61—21no—
417D61—21no—
418D61—81no—
419C2×#135—611no—
420C2×#135—611no—
421C2×#135—611no—
422C2×#135—611no—
423C2×#131—611no—
424C2×#131—611no—
425C2×#131—611no—
426C2×#131—611no—
427#532—611no—
428#532—611no—
429#497—611no—
430#497—611no—
431#497—611no—
432#497—611no—
433#496—611no—
434#496—611no—
435#496—611no—
436#496#692311yescharacteristic, complemented
437#444—1224no—
438#443—1224no—
439#436—1221no—
440#436—1221no—
441#435—1221no—
442#435—1221no—
443#435—1221no—
444#435—1221no—
445C8×D4—1221no—
446C8×D4—1221no—
447C2×#108—611no—
448C2×#108—611no—
449C2×C4⋊C8—611no—
450C2×#104—611no—
451C2×#104—611no—
452C2×#104—611no—
453C2×#104—611no—
454C2×#104—611no—
455C2×#104—611no—
456C2×#104—611no—
457C2×#104—611no—
458#408—611no—
459#408—611no—
460#408—611no—
461#408—611no—
462C4×M16—611no—
463C4×M16—611no—
464C2×#97—611no—
465C2×#97—611no—
466C2×C4×C8—611no—
467C4×C4⋊C4—611no—
468#341—611no—
469#341—611no—
470#336—611no—
471#336—611no—
472C61#2318111yescharacteristic, complemented, Sylow
473C2×#41—611no—
474C2×#41—611no—
475C2×#41—611no—
476C2×#41—611no—
477#135—1222no—
478#135—1222no—
479#135—1222no—
480#135—1222no—
481#135—2441no—
482#135—2441no—
483#135—2441no—
484#135—2441no—
485C2×Q16—611no—
486C2×Q16—611no—
487C2×Q16—611no—
488C2×Q16—611no—
489C2×SD16—611no—
490C2×SD16—611no—
491C2×SD16—611no—
492C2×SD16—611no—
493C2×SD16—611no—
494C2×SD16—611no—
495C2×SD16C2×#692311yescharacteristic
496C2×SD16C2×#692311yescharacteristic
497C2×D8—611no—
498C2×D8—611no—
499C2×D8C2×#692311yescharacteristic
500C2×D8C2×#692311yescharacteristic
501#131—1222no—
502#131—1222no—
503#131—1222no—
504#131—1222no—
505#131—2441no—
506#131—2441no—
507#131—2441no—
508#131—2441no—
509C2×M16—611no—
510C2×M16—611no—
511C2×M16—611no—
512C2×M16—611no—
513C2×M16—1221no—
514C2×M16—1221no—
515C2×M16—1221no—
516C2×M16—1221no—
517C22×C8—611no—
518C22×C8—611no—
519C22×C8—611no—
520C22×C8—611no—
521C22×C8—1221no—
522C22×C8—1221no—
523C22×C8—1221no—
524C22×C8—1221no—
525C4⋊Q8—611no—
526C4⋊Q8—611no—
527#127—611no—
528#127C2×#692311yescharacteristic
529#124—611no—
530#124—611no—
531#124—611no—
532#124C2×#692311yescharacteristic
533#121—1221no—
534#121—1221no—
535#121—1221no—
536#121—1221no—
537C4×D4—1221no—
538C4×D4—1221no—
539C4×D4—1221no—
540C4×D4—1221no—
541C2×C4⋊C4—1221no—
542C2×C42—611no—
543C2×C42—611no—
544C2×C42—611no—
545#108—614no—
546#108—1222no—
547C4⋊C8—611no—
548C4⋊C8—611no—
549C4⋊C8—611no—
550C4⋊C8—611no—
551#104—1222no—
552#104—1222no—
553#104—1222no—
554#104—1222no—
555#104—2441no—
556#104—2441no—
557#104—2441no—
558#104—2441no—
559C22⋊C8—1221no—
560C22⋊C8—1221no—
561C22⋊C8—1221no—
562C22⋊C8—1221no—
563C22⋊C8—1221no—
564C22⋊C8—1221no—
565C22⋊C8—1221no—
566C22⋊C8—1221no—
567#97—611no—
568#97—611no—
569#97—611no—
570#97—1221no—
571#97—1221no—
572#97—1222no—
573#97C2×#692311yescharacteristic
574C4×C8—1221no—
575C4×C8—1221no—
576C4×C8—1222no—
577#95—1221no—
578#41—1221no—
579#41—1221no—
580#41—1221no—
581#41—1221no—
582#41—1221no—
583#41—1221no—
584#41—1221no—
585#41—1221no—
586#41—1221no—
587#41—1221no—
588#41—1221no—
589#41—1221no—
590#41—1221no—
591#41—1221no—
592#41—1221no—
593#41—1221no—
594C2×Q8—611no—
595C2×Q8—611no—
596C2×Q8—611no—
597C2×Q8C22×#692311yescharacteristic
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—611no—
601C2×D4—1221no—
602C2×D4—1221no—
603C2×D4—1221no—
604C2×D4—1221no—
605C2×D4—1221no—
606C2×D4—1221no—
607C2×D4C22×#692311yescharacteristic
608C2×D4C22×#692311yescharacteristic
609C2×D4C22×#692311yescharacteristic
610C22×C4—611no—
611C22×C4—611no—
612C22×C4—611no—
613C22×C4—1221no—
614C22×C4—1221no—
615C22×C4—1221no—
616C22×C4—1221no—
617C22×C4—1221no—
618C22×C4—1221no—
619Q16—1222no—
620Q16—1222no—
621Q16—2441no—
622Q16—2441no—
623SD16—22no—
624SD16—41no—
625SD16—1222no—
626SD16—1222no—
627SD16—1222no—
628SD16—2441no—
629SD16—2441no—
630SD16—2441no—
631D8—22no—
632D8—41no—
633D8—1222no—
634D8—2441no—
635M16—612no—
636M16—612no—
637M16—1221no—
638M16—1221no—
639M16—1221no—
640M16—1221no—
641M16—1221no—
642M16—1221no—
643M16—2442no—
644M16—2442no—
645M16—2442no—
646M16—2442no—
647C2×C8—611no—
648C2×C8—612no—
649C2×C8—612no—
650C2×C8—611no—
651C2×C8—611no—
652C2×C8—611no—
653C2×C8—611no—
654C2×C8—611no—
655C2×C8—1221no—
656C2×C8—1221no—
657C2×C8—1221no—
658C2×C8—1221no—
659C2×C8—1221no—
660C2×C8—1221no—
661C2×C8—1221no—
662C2×C8—1221no—
663C2×C8—1221no—
664C2×C8—1221no—
665C2×C8—2442no—
666C2×C8—2442no—
667C2×C8—2442no—
668C2×C8—2442no—
669C2×C8C22×#692311yescharacteristic
670C2×C8C22×#692311yescharacteristic
671C4⋊C4—1221no—
672C4⋊C4—1221no—
673C4⋊C4—1221no—
674C4⋊C4—1221no—
675C4⋊C4—2442no—
676C22⋊C4—21no—
677C22⋊C4—21no—
678C22⋊C4—1221no—
679C22⋊C4—1221no—
680C22⋊C4—1221no—
681C22⋊C4—1221no—
682C22⋊C4—1221no—
683C22⋊C4—1221no—
684C42—611no—
685C42—611no—
686C42—611no—
687C42—1221no—
688C42—1221no—
689C42—1221no—
690C42—1221no—
691C42C22×#692311yescharacteristic
692C23—21no—
693C23—21no—
694C23—21no—
695C23—611no—
696C23—1221no—
697Q8—21no—
698Q8—21no—
699Q8—1221no—
700Q8—1221no—
701Q8—1221no—
702Q8—1221no—
703Q8—1221no—
704Q8—1221no—
705D4—21no—
706D4—21no—
707D4—21no—
708D4—21no—
709D4—21no—
710D4—21no—
711D4—42no—
712D4—81no—
713D4—1221no—
714D4—1221no—
715D4—4881no—
716D4—2441no—
717D4—2441no—
718D4—2442no—
719D4—2441no—
720D4—2441no—
721D4—2441no—
722D4—2441no—
723D4—2441no—
724D4—2441no—
725C2×C4—21no—
726C2×C4—611no—
727C2×C4—611no—
728C2×C4—611no—
729C2×C4—611no—
730C2×C4—611no—
731C2×C4—611no—
732C2×C4—611no—
733C2×C4—1222no—
734C2×C4—1221no—
735C2×C4—1221no—
736C2×C4—1221no—
737C2×C4—2441no—
738C2×C4—2441no—
739C2×C4—2441no—
740C2×C4—2441no—
741C2×C4—2441no—
742C2×C4—2441no—
743C2×C4—2441no—
744C2×C4—2441no—
745C2×C4—2441no—
746C2×C4—2441no—
747C2×C4—2441no—
748C2×C4—2441no—
749C2×C4—2441no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4D4×#692311yescharacteristic
753C2×C4D4×#692311yescharacteristic
754C2×C4C23×#692311yescharacteristic
755C8—21no—
756C8—612no—
757C8—1221no—
758C8—1221no—
759C8—1221no—
760C8—1221no—
761C8—1222no—
762C8—1222no—
763C8—1221no—
764C8—2441no—
765C8—2441no—
766C8D4×#692312yes—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—611no—
777C22—611no—
778C22—1221no—
779C22—1221no—
780C22—2441no—
781C22—2441no—
782C22—2441no—
783C22C2×D4×#692311yescharacteristic
784C4—21no—
785C4—21no—
786C4—41no—
787C4—611no—
788C4—611no—
789C4—1221no—
790C4—1221no—
791C4—4881no—
792C4—2442no—
793C4—2441no—
794C4—2441no—
795C4—2441no—
796C4C2×D4×#692311yescharacteristic
797C4#1684082911yescharacteristic
798C2—81no—
799C2—81no—
800C2—81no—
801C2—1221no—
802C2—1221no—
803C2—4881no—
804C2#2146234911yescharacteristic
805C2#2146259111yescharacteristic
806C2#2146259311yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#496C4
socleC22×C61C2×C4×D4
prime radical#21456261C2
cosocleC2×C4×D61C24
hypercenter#496#6923
hypocenterC61#23181
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. C2×#16840809C2semidirect
2. C2×#16840805C2semidirect
3. #21462564C2semidirect
4. #21462562C2semidirect
5. #21461984C2semidirect
6. #21461983C2semidirect
7. #21461975C2semidirect
8. #21461972C2semidirect
9. #21461811C2semidirect
10. #21461810C2semidirect
11. #21461810C2semidirect
12. #21461808C2semidirect
13. #21461639C2semidirect
14. #21461617C2semidirect
60. #16840157C4semidirect
61. #16840156C4semidirect
62. #16840153C4semidirect
63. #16840153C4semidirect
64. #16840150C4semidirect
65. #16840150C4semidirect
66. #16840149C4semidirect
68. C61×#496C4semidirect
95. #14519847D4semidirect
436. #496#6923semidirect
472. C61#23181semidirect

Maximal subgroups

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

subgroupindex
C2×#168408092
C2×#168408052
#214625642
#214625622
#214619842
#214619832
#214619752
#214619722
#214618112
#214618102
#214618082
#214616392
#214616172
#214562612
#2318161