Finite Group Databasebeta

← #29682029

Subgroups — #29682029

Order 15616.

1748 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459152C211yesmaximal, characteristic
2#21459020C211yesmaximal, characteristic, complemented
3C2×#16839735C211yesmaximal, characteristic, complemented
4C2×#16839735C211yesmaximal, characteristic, complemented
5C2×#16839735C211yesmaximal, characteristic, complemented
6#21446360C218yesmaximal, complemented
7#21445551C211yesmaximal, characteristic, complemented
8C61×#1740C211yesmaximal, characteristic, complemented
9C22×#11758222C2211yescharacteristic
10C22×#11758222C2211yescharacteristic
11#16840343—22no—
12#16840338—21no—
13#16840338C412yescomplemented
14#16840331—21no—
15#16840331C412yescomplemented
16#16840324C2214yes—
17#16840312—22no—
18#16840274—22no—
19#16840274C414yescomplemented
20#16840243—22no—
21#16840242—22no—
22#16840239—21no—
23#16840236—21no—
24#16840235C2214yes—
25C4×#11758222—22no—
26#16840230—22no—
27C2×#14519736C2211yescharacteristic
28C2×#14519736C2211yescharacteristic
29#117×D61—22no—
30#16839735—22no—
31#16839735—22no—
32#16839735—22no—
33#16839735—22no—
34#16839735—22no—
35#16839735—22no—
36C2×#14519691C2214yes—
37C2×#14519691C2214yes—
38C2×#14519691C2214yes—
39#16839528C2214yes—
40C2×#117×C61C2211yescharacteristic
41C2×#117×C61C2211yescharacteristic
42C2×#117×C61C2211yescharacteristic
43C61×#342C2214yes—
44C2×#11758222—21no—
45C2×#11758222—21no—
46C2×#11758222—21no—
47C2×#11758222—21no—
48C2×#11758222—21no—
49C2×#11758222—21no—
50C2×#11758222—21no—
51C2×#11758222—21no—
52C2×#11758222—21no—
53C2×#11758222—21no—
54C2×#11758222—21no—
55C2×#11758222—21no—
56C2×#11758222—21no—
57C2×#11758222—21no—
58C2×#11758222—21no—
59C2×#11758222—21no—
60C2×#11758222—21no—
61C2×#11758222—21no—
62C2×#11758222—21no—
63C2×#11758222—21no—
64C2×#11758222C2×C412yes—
65C2×#11758222C2×C412yes—
66C2×#11758222D412yes—
67C2×#11758222D412yes—
68C22×Dic122C2×C411yescharacteristic, complemented
69C22×Dic122D411yescharacteristic
70C22×D244C2×C411yescharacteristic, complemented
71C22×D244D411yescharacteristic
72C22×C22⋊D61C2312yes—
73C22×C22⋊D61C2312yes—
74C22×C4×D61C2×C412yescomplemented
75C22×C4×D61D412yes—
76#14519777—22no—
77#14519774—22no—
78#14519765—22no—
79#14519765—22no—
80#14519761—24no—
81#14519761C2×C418yescomplemented
82#14519757—24no—
83#14519757—24no—
84#14519752—24no—
85#14519752—24no—
86#14519751—28no—
87#14519747—24no—
88#14519747C2×C418yescomplemented
89C4×Dic122—24no—
90#14519742—24no—
91C4×D244—24no—
92C4×D244—28no—
93#14519739—24no—
94C4×C22⋊D61—28no—
95#14519737—28no—
96#14519736—21no—
97#14519736—21no—
98#14519736—21no—
99#14519736—21no—
100#14519736—21no—
101#14519736—21no—
102#14519736D412yescomplemented
103#14519736D412yescomplemented
104#14519735—24no—
105#14519734—24no—
106#14519733—24no—
107C2×C4⋊Dic61—21no—
108C2×C4⋊Dic61—21no—
109C4⋊C4×D61—24no—
110C2×C22⋊Dic61C2312yes—
111C2×C22⋊Dic61C2312yes—
112C22⋊C4×D61—24no—
113C2×C4×Dic61—21no—
114C2×C4×Dic61—21no—
115C42×D61—24no—
116#14519691—28no—
117#14519691—28no—
118#14519691—28no—
119C23×C4×C61C2311yescharacteristic
120#117×C61—21no—
121#117×C61—21no—
122#117×C61—21no—
123#117×C61—21no—
124#117×C61—21no—
125#117×C61—21no—
126#117×C61—21no—
127#117×C61—21no—
128#117×C61C2×C412yescomplemented
129#117×C61C2×C412yescomplemented
130#117×C61D412yescomplemented
131#117×C61D412yescomplemented
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61—21no—
135C2×C22⋊C4×C61C2312yes—
136C2×C22⋊C4×C61C2312yes—
137C2×C22⋊C4×C61C2312yes—
138C2×C42×C61—21no—
139C2×C42×C61—21no—
140C2×C42×C61—21no—
141C24×C61C2411yescharacteristic
142C23×D61C22×C412yes—
143C23×D61C2×D412yes—
144C22×C4×C61—22no—
145C22×C4×C61—22no—
146C22×C4×C61—22no—
147C22×C4×C61C22×C411yescharacteristic
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61#4111yescharacteristic
158C22×C4×C61#4111yescharacteristic
159C22×C4×C61#4111yescharacteristic
160C22×C4×C61#4111yescharacteristic
161C2×C22⋊D61—22no—
162C2×C22⋊D61—22no—
163C2×C22⋊D61—22no—
164C2×C22⋊D61—22no—
165C2×C22⋊D61—22no—
166C2×C22⋊D61—22no—
167C2×C22⋊D61—22no—
168C2×C22⋊D61—22no—
169C2×C22⋊D61—22no—
170C2×C22⋊D61—22no—
171C2×C22⋊D61C22×C414yes—
172C2×C22⋊D61C2×D414yes—
173C22×Dic61—22no—
174C22×Dic61—22no—
175C22×Dic61C22×C412yes—
176C22×Dic61C2×D412yes—
177#11758222—22no—
178#11758222—22no—
179#11758222—22no—
180#11758222—22no—
181#11758222—22no—
182#11758222—22no—
183#11758222—22no—
184#11758222—22no—
185#11758222—22no—
186#11758222—22no—
187#11758222—22no—
188#11758222—22no—
189#11758222—22no—
190#11758222—22no—
191#11758222—22no—
192#11758222—22no—
193#11758222—41no—
194#11758222—41no—
195#11758222—41no—
196#11758222—41no—
197#11758222—41no—
198#11758222—41no—
199#11758222—41no—
200#11758222—41no—
201#11758222—41no—
202#11758222—41no—
203#11758222—41no—
204#11758222—41no—
205#11758222—41no—
206#11758222—41no—
207#11758222—41no—
208#11758222—41no—
209C2×D244—21no—
210C2×D244—21no—
211C2×D244—21no—
212C2×D244—21no—
213C2×D244—21no—
214C2×D244—21no—
215C2×D244—21no—
216C2×D244—21no—
217C2×D244—21no—
218C2×D244—21no—
219C2×D244—28no—
220C2×D244C22⋊C412yes—
221C2×D244C22⋊C412yes—
222C2×C4×D61—22no—
223C2×C4×D61—22no—
224C2×C4×D61—22no—
225C2×C4×D61—22no—
226C2×C4×D61—22no—
227C2×C4×D61—22no—
228C2×C4×D61—22no—
229C2×C4×D61—22no—
230C2×C4×D61—22no—
231C2×C4×D61—22no—
232C2×C4×D61—28no—
233C2×C4×D61C22⋊C414yes—
234C2×C4×D61C22⋊C414yes—
235C2×Dic122—21no—
236C2×Dic122—21no—
237C2×Dic122—21no—
238C2×Dic122—21no—
239C2×Dic122—21no—
240C2×Dic122—21no—
241C2×Dic122—21no—
242C2×Dic122—21no—
243C2×Dic122—21no—
244C2×Dic122—21no—
245C2×Dic122C22⋊C412yes—
246C2×Dic122C22⋊C412yes—
247C4⋊C4×C61—22no—
248C4⋊C4×C61—22no—
249C4⋊C4×C61—22no—
250C4⋊C4×C61—22no—
251C4⋊C4×C61—41no—
252C4⋊C4×C61—41no—
253C22⋊C4×C61—22no—
254C22⋊C4×C61—22no—
255C22⋊C4×C61—22no—
256C22⋊C4×C61—22no—
257C22⋊C4×C61C22×C414yes—
258C22⋊C4×C61C2×D414yes—
259C42×C61—22no—
260C42×C61—22no—
261C42×C61—22no—
262C42×C61—22no—
263C42×C61—41no—
264C42×C61—41no—
265C22⋊Dic61—22no—
266C22⋊Dic61—22no—
267C22⋊Dic61—22no—
268C22⋊Dic61C2×D414yes—
269#11758198—28no—
270#11758198—28no—
271#11758198—28no—
272C4⋊Dic61—22no—
273C4⋊Dic61—22no—
274C4⋊Dic61—28no—
275C4⋊Dic61—41no—
276C4⋊Dic61—41no—
277#11758196—28no—
278C4×Dic61—28no—
279C4×Dic61—22no—
280C4×Dic61—22no—
281C4×Dic61—41no—
282C4×Dic61—41no—
283C23×C61—81no—
284C23×C61C23×C411yescharacteristic
285C23×C61C22×D411yescharacteristic
286C23×C61C22×D411yescharacteristic
287C23×C61C22×D411yescharacteristic
288C23×C61C22×D411yescharacteristic
289C23×C61C2×#4111yescharacteristic
290C23×C61C2×#4111yescharacteristic
291C22×D61—22no—
292C22×D61—22no—
293C22×D61—22no—
294C22×D61—22no—
295C22×D61—22no—
296C22×D61—82no—
297C22×D61—82no—
298C22×D61C2×C22⋊C414yes—
299C2×C4×C61—24no—
300C2×C4×C61—24no—
301C2×C4×C61—42no—
302C2×C4×C61—82no—
303C2×C4×C61—82no—
304C2×C4×C61—82no—
305C2×C4×C61C2×C22⋊C411yescharacteristic
306C2×C4×C61C2×C22⋊C411yescharacteristic
307C2×C4×C61C2×C22⋊C411yescharacteristic
308C2×C4×C61C2×C22⋊C411yescharacteristic
309C2×C4×C61C4×D411yescharacteristic
310C2×C4×C61C4×D411yescharacteristic
311C2×C4×C61C4×D411yescharacteristic
312C2×C4×C61C4×D411yescharacteristic
313C2×C4×C61C4×D411yescharacteristic
314C2×C4×C61C4×D411yescharacteristic
315C2×C4×C61C4×D411yescharacteristic
316C2×C4×C61C4×D411yescharacteristic
317C2×C4×C61#12011yescharacteristic
318C2×C4×C61#12011yescharacteristic
319C2×C4×C61#12011yescharacteristic
320C2×C4×C61#12011yescharacteristic
321C2×C4×C61#12111yescharacteristic
322C2×C4×C61#12111yescharacteristic
323C2×C4×C61#12111yescharacteristic
324C2×C4×C61#12111yescharacteristic
325C2×C4×C61#12111yescharacteristic
326C2×C4×C61#12111yescharacteristic
327C2×C4×C61#12111yescharacteristic
328C2×C4×C61#12111yescharacteristic
329C2×C4×C61#12311yescharacteristic
330C2×C4×C61#12311yescharacteristic
331C2×C4×C61#12311yescharacteristic
332C2×C4×C61#12311yescharacteristic
333C22⋊D61—24no—
334C22⋊D61—24no—
335C22⋊D61—24no—
336C22⋊D61—24no—
337C22⋊D61—42no—
338C22⋊D61—42no—
339C22⋊D61—42no—
340C22⋊D61—42no—
341C2×Dic61—22no—
342C2×Dic61—22no—
343C2×Dic61—22no—
344C2×Dic61—22no—
345C2×Dic61—22no—
346C2×Dic61—24no—
347C2×Dic61—42no—
348C2×Dic61—82no—
349C2×Dic61—82no—
350C2×Dic61C2×C22⋊C414yes—
351D244—22no—
352D244—22no—
353D244—22no—
354D244—22no—
355D244—41no—
356D244—41no—
357D244—41no—
358D244—41no—
359D244—88no—
360C4×D61—24no—
361C4×D61—24no—
362C4×D61—24no—
363C4×D61—24no—
364C4×D61—42no—
365C4×D61—42no—
366C4×D61—42no—
367C4×D61—42no—
368C4×D61—88no—
369Dic122—22no—
370Dic122—22no—
371Dic122—22no—
372Dic122—22no—
373Dic122—41no—
374Dic122—41no—
375Dic122—41no—
376Dic122—41no—
377#21014—611nomaximal, Sylow
378C22×C61—41no—
379C22×C61—41no—
380C22×C61—41no—
381C22×C61—41no—
382C22×C61—41no—
383C22×C61—41no—
384C22×C61—41no—
385C22×C61C22×C22⋊C411yescharacteristic
386C22×C61C2×C4×D411yescharacteristic
387C22×C61C2×C4×D411yescharacteristic
388C22×C61C2×#12011yescharacteristic
389C22×C61C2×#12111yescharacteristic
390C22×C61C2×#12111yescharacteristic
391C22×C61C2×#12311yescharacteristic
392C2×D61—24no—
393C2×D61—44no—
394C2×D61—44no—
395C2×D61—44no—
396C2×D61—42no—
397C2×D61—82no—
398C2×D61—82no—
399C2×D61—82no—
400C4×C61—44no—
401C4×C61—44no—
402C4×C61—82no—
403C4×C61#38611yescharacteristic
404C4×C61#38611yescharacteristic
405C4×C61#38611yescharacteristic
406C4×C61#38611yescharacteristic
407C4×C61#38611yescharacteristic
408C4×C61#38611yescharacteristic
409C4×C61#38611yescharacteristic
410C4×C61#38611yescharacteristic
411Dic61—24no—
412Dic61—44no—
413Dic61—42no—
414Dic61—82no—
415#3449—611no—
416#3428—611no—
417C2×#410—611no—
418C2×#410—611no—
419C2×#410—611no—
420#1913—618no—
421#1740—611no—
422#1740D6111yescharacteristic, complemented
423C2×C61—21no—
424C2×C61—21no—
425C2×C61—21no—
426C2×C61—21no—
427C2×C61—21no—
428C2×C61—21no—
429C2×C61—21no—
430C2×C61C2×#38611yescharacteristic
431D61—44no—
432D61—82no—
433C22×#41—611no—
434C22×#41—611no—
435#537—1222no—
436#536—612no—
437#536—1221no—
438#535—612no—
439#535—1221no—
440#534—614no—
441#532—1222no—
442#525—614no—
443#525—1222no—
444#520—1222no—
445#520—1222no—
446#519—1221no—
447#518—614no—
448#518—1221no—
449C4×#41—1222no—
450C4×#41—1222no—
451C2×#117—611no—
452C2×#117—611no—
453C2×#117—1222no—
454C2×#117C2×D6111yescharacteristic
455C2×#117C2×D6111yescharacteristic
456C2×#117C2×D6111yescharacteristic
457#410—1222no—
458#410—1222no—
459#410—1222no—
460#410—1222no—
461#410—1222no—
462#410—1222no—
463C2×#99—614no—
464C2×#99—614no—
465C2×#99—614no—
466#342—614no—
467#342C2×D6114yes—
468C61#2101411yescharacteristic, complemented, Sylow
469C2×#41—612no—
470C2×#41—612no—
471C2×#41—612no—
472C2×#41—612no—
473C2×#41—1221no—
474C2×#41—1221no—
475C2×#41—1221no—
476C2×#41—1221no—
477C2×#41—1221no—
478C2×#41—1221no—
479C2×#41—1221no—
480C2×#41—1221no—
481C2×#41—1221no—
482C2×#41—1221no—
483C2×#41—1221no—
484C2×#41—1221no—
485C2×#41—1221no—
486C2×#41—1221no—
487C2×#41—1221no—
488C2×#41—1221no—
489C2×#41—1221no—
490C2×#41—1221no—
491C2×#41—1221no—
492C2×#41—1221no—
493C22×Q8—611no—
494C22×Q8—611no—
495C22×D4—612no—
496C22×D4—612no—
497C22×D4—611no—
498C22×D4—611no—
499C23×C4—612no—
500C23×C4—612no—
501C23×C4C22×D6111yescharacteristic
502C4⋊Q8—1222no—
503#127—1222no—
504#124—1222no—
505#124—1222no—
506#123—618no—
507#123—1224no—
508C22⋊Q8—1224no—
509C22⋊Q8—1224no—
510#121—1224no—
511#121—1224no—
512#121—1228no—
513#120—618no—
514#120—1224no—
515C4×Q8—1224no—
516C4×Q8—1224no—
517C4×D4—1228no—
518C4×D4—1224no—
519C4×D4—1228no—
520C4×D4—1224no—
521C4×D4—1228no—
522#117—21no—
523#117—21no—
524#117—21no—
525#117—21no—
526#117—21no—
527#117—21no—
528#117—21no—
529#117—21no—
530#117—612no—
531#117—612no—
532#117—1224no—
533#117—1224no—
534#117—1224no—
535#117—1221no—
536#117—1221no—
537#117—1221no—
538#117—1221no—
539#117—1221no—
540#117—1221no—
541#117C4×D6112yescomplemented
542#117C4×D6112yescomplemented
543#117D24412yescomplemented
544#117D24412yescomplemented
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—1224no—
549C2×C4⋊C4—1221no—
550C2×C4⋊C4—1221no—
551C2×C22⋊C4—612no—
552C2×C22⋊C4—612no—
553C2×C22⋊C4—1224no—
554C2×C22⋊C4C22×D6112yes—
555C2×C22⋊C4C22×D6112yes—
556C2×C22⋊C4C22×D6112yes—
557C2×C42—21no—
558C2×C42—21no—
559C2×C42—21no—
560C2×C42—1224no—
561C2×C42—1221no—
562C2×C42—1221no—
563#99—1228no—
564#99—1228no—
565#99—1228no—
566C24—612no—
567C24—612no—
568C24C23×D6111yescharacteristic
569#41—1222no—
570#41—1222no—
571#41—1222no—
572#41—1222no—
573#41—1222no—
574#41—1222no—
575#41—1222no—
576#41—1222no—
577#41—1222no—
578#41—1222no—
579#41—1222no—
580#41—1222no—
581#41—1222no—
582#41—1222no—
583#41—1222no—
584#41—1222no—
585#41—2441no—
586#41—2441no—
587#41—2441no—
588#41—2441no—
589#41—2441no—
590#41—2441no—
591#41—2441no—
592#41—2441no—
593#41—2441no—
594#41—2441no—
595#41—2441no—
596#41—2441no—
597#41—2441no—
598#41—2441no—
599#41—2441no—
600#41—2441no—
601C2×Q8—612no—
602C2×Q8—612no—
603C2×Q8—1221no—
604C2×Q8—1221no—
605C2×Q8—1221no—
606C2×Q8—1221no—
607C2×Q8—1221no—
608C2×Q8—1221no—
609C2×Q8—1221no—
610C2×Q8—1221no—
611C2×Q8—1221no—
612C2×Q8—1221no—
613C2×D4—614no—
614C2×D4—614no—
615C2×D4—612no—
616C2×D4—612no—
617C2×D4—1228no—
618C2×D4—1222no—
619C2×D4—1222no—
620C2×D4—1222no—
621C2×D4—1222no—
622C2×D4—1222no—
623C2×D4—1222no—
624C2×D4—1222no—
625C2×D4—1222no—
626C2×D4—1222no—
627C2×D4—1222no—
628C2×D4—1221no—
629C2×D4—1221no—
630C2×D4—1221no—
631C2×D4—1221no—
632C2×D4—1221no—
633C2×D4—1221no—
634C2×D4—1221no—
635C2×D4—1221no—
636C2×D4—1221no—
637C2×D4—1221no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—612no—
642C22×C4—614no—
643C22×C4—614no—
644C22×C4—612no—
645C22×C4—1228no—
646C22×C4—1222no—
647C22×C4—1222no—
648C22×C4—1222no—
649C22×C4—1222no—
650C22×C4—1222no—
651C22×C4—1222no—
652C22×C4—1222no—
653C22×C4—1222no—
654C22×C4—1222no—
655C22×C4—1222no—
656C22×C4—1222no—
657C22×C4—1222no—
658C22×C4C2×C4×D6111yescharacteristic
659C22×C4C2×C4×D6111yescharacteristic
660C22×C4C2×D24411yescharacteristic
661C22×C4C2×D24411yescharacteristic
662C22×C4#1175822211yescharacteristic
663C22×C4#1175822211yescharacteristic
664C22×C4D4×D6111yescharacteristic
665C22×C4D4×D6111yescharacteristic
666C22×C4D4×D6111yescharacteristic
667C22×C4D4×D6111yescharacteristic
668C22×C4D4×D6111yescharacteristic
669C22×C4D4×D6111yescharacteristic
670C22×C4#1175822611yescharacteristic
671C22×C4#1175822611yescharacteristic
672C4⋊C4—22no—
673C4⋊C4—22no—
674C4⋊C4—22no—
675C4⋊C4—22no—
676C4⋊C4—41no—
677C4⋊C4—41no—
678C4⋊C4—1228no—
679C4⋊C4—1228no—
680C4⋊C4—1222no—
681C4⋊C4—1222no—
682C4⋊C4—2441no—
683C4⋊C4—2441no—
684C22⋊C4—22no—
685C22⋊C4—22no—
686C22⋊C4—22no—
687C22⋊C4—22no—
688C22⋊C4—614no—
689C22⋊C4—1228no—
690C22⋊C4—1228no—
691C22⋊C4—1228no—
692C22⋊C4—1222no—
693C22⋊C4—1222no—
694C22⋊C4—1222no—
695C22⋊C4C2×C4×D6114yes—
696C22⋊C4C2×D24414yes—
697C42—22no—
698C42—22no—
699C42—22no—
700C42—22no—
701C42—41no—
702C42—41no—
703C42—1228no—
704C42—1222no—
705C42—1222no—
706C42—2441no—
707C42—2441no—
708C23—81no—
709C23—614no—
710C23—1222no—
711C23—1222no—
712C23—1222no—
713C23—1222no—
714C23—1222no—
715C23—4882no—
716C23—4882no—
717C23C22×C4×D6111yescharacteristic
718C23C2×D4×D6111yescharacteristic
719C23C2×D4×D6111yescharacteristic
720C23C2×D4×D6111yescharacteristic
721C23C22×D24411yescharacteristic
722C23C2×#1175822211yescharacteristic
723C23C2×#1175822611yescharacteristic
724Q8—1222no—
725Q8—1222no—
726Q8—1222no—
727Q8—1222no—
728Q8—2441no—
729Q8—2441no—
730Q8—2441no—
731Q8—2441no—
732D4—1224no—
733D4—1224no—
734D4—1224no—
735D4—1224no—
736D4—1222no—
737D4—1222no—
738D4—1222no—
739D4—1222no—
740D4—4888no—
741D4—2442no—
742D4—2442no—
743D4—2442no—
744D4—2442no—
745D4—2441no—
746D4—2441no—
747D4—2441no—
748D4—2441no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—42no—
752C2×C4—82no—
753C2×C4—82no—
754C2×C4—82no—
755C2×C4—614no—
756C2×C4—1222no—
757C2×C4—1222no—
758C2×C4—1224no—
759C2×C4—1224no—
760C2×C4—1224no—
761C2×C4—1224no—
762C2×C4—1222no—
763C2×C4—1222no—
764C2×C4—1222no—
765C2×C4—1224no—
766C2×C4—4888no—
767C2×C4—4882no—
768C2×C4—4882no—
769C2×C4—2442no—
770C2×C4—2442no—
771C2×C4—2442no—
772C2×C4—2442no—
773C2×C4—2442no—
774C2×C4C22⋊C4×D6111yescharacteristic
775C2×C4C22⋊C4×D6111yescharacteristic
776C2×C4C22⋊C4×D6111yescharacteristic
777C2×C4C22⋊C4×D6111yescharacteristic
778C2×C4#1451973911yescharacteristic
779C2×C4#1451973911yescharacteristic
780C2×C4#1451973911yescharacteristic
781C2×C4#1451973911yescharacteristic
782C2×C4C4×D24411yescharacteristic
783C2×C4C4×D24411yescharacteristic
784C2×C4C4×D24411yescharacteristic
785C2×C4C4×D24411yescharacteristic
786C2×C4#1451974711yescharacteristic
787C2×C4#1451974711yescharacteristic
788C2×C4#1451974711yescharacteristic
789C2×C4#1451974711yescharacteristic
790C2×C4#1451975011yescharacteristic
791C2×C4#1451975011yescharacteristic
792C2×C4#1451975011yescharacteristic
793C2×C4#1451975011yescharacteristic
794C2×C4#1451975211yescharacteristic
795C2×C4#1451975211yescharacteristic
796C2×C4#1451975211yescharacteristic
797C2×C4#1451975211yescharacteristic
798C2×C4#1451976211yescharacteristic
799C2×C4#1451976211yescharacteristic
800C2×C4#1451976211yescharacteristic
801C2×C4#1451976211yescharacteristic
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—1224no—
810C22—4882no—
811C22—4882no—
812C22—4882no—
813C22—2444no—
814C22—2444no—
815C22—2444no—
816C22—2442no—
817C22C2×C22⋊C4×D6111yescharacteristic
818C22C2×#1451973911yescharacteristic
819C22C2×C4×D24411yescharacteristic
820C22C2×#1451974711yescharacteristic
821C22C2×#1451975011yescharacteristic
822C22C2×#1451975211yescharacteristic
823C22C2×#1451976211yescharacteristic
824C4—44no—
825C4—44no—
826C4—82no—
827C4—1224no—
828C4—4882no—
829C4—2444no—
830C4—2442no—
831C4#1683964011yescharacteristic
832C4#1683964011yescharacteristic
833C4#1683964011yescharacteristic
834C4#1683964011yescharacteristic
835C4#1683964011yescharacteristic
836C4#1683964011yescharacteristic
837C4#1683964011yescharacteristic
838C4#1683964011yescharacteristic
839C2—21no—
840C2—21no—
841C2—21no—
842C2—21no—
843C2—21no—
844C2—21no—
845C2—21no—
846C2—4882no—
847C2—2444no—
848C2C2×#1683964011yescharacteristic
subgroupG/H
centerC4#16839640
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#1740C2
socleC2×C61C2×#386
prime radical#21459152C2
cosocleC24×C61C24
hypercenter#1740D61
hypocenterC61#21014
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C23×C4 ◁ #1740

Complements

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

NH ≅ G/Ntype
2. #21459020C2semidirect
3. C2×#16839735C2semidirect
4. C2×#16839735C2semidirect
5. C2×#16839735C2semidirect
6. #21446360C2semidirect
7. #21445551C2semidirect
8. C61×#1740C2semidirect
13. #16840338C4semidirect
15. #16840331C4semidirect
19. #16840274C4semidirect
68. C22×Dic122C2×C4semidirect
70. C22×D244C2×C4semidirect
74. C22×C4×D61C2×C4semidirect
81. #14519761C2×C4semidirect
88. #14519747C2×C4semidirect
102. #14519736D4semidirect
103. #14519736D4semidirect
128. #117×C61C2×C4semidirect
129. #117×C61C2×C4semidirect
130. #117×C61D4semidirect
131. #117×C61D4semidirect
422. #1740D61semidirect
468. C61#21014semidirect
541. #117C4×D61semidirect
542. #117C4×D61semidirect
543. #117D244semidirect
544. #117D244semidirect

Maximal subgroups

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

subgroupindex
#214591522
#214590202
C2×#168397352
#214463602
#214455512
C61×#17402
#2101461