Finite Group Databasebeta

← #29682027

Subgroups — #29682027

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#21459148C211yesmaximal, characteristic
2#21459020C211yesmaximal, characteristic, complemented
3C2×#16839736C211yesmaximal, characteristic, complemented
4C2×#16839735C211yesmaximal, characteristic, complemented
5#21446358C218yesmaximal, complemented
6#21445552C211yesmaximal, characteristic, complemented
7#21445551C211yesmaximal, characteristic, complemented
8C2×C61×#410C211yesmaximal, characteristic, complemented
9C22×#11758222C2211yescharacteristic
10#16840340—22no—
11#16840336C412yescomplemented
12#16840333—21no—
13#16840329C412yescomplemented
14#16840326—21no—
15#16840321C2214yes—
16#16840308—22no—
17#16840273C414yescomplemented
18#16840269—22no—
19#16840243—22no—
20#16840242—22no—
21#16840239—21no—
22#16840236—21no—
23#16840235C2214yes—
24C4×#11758222—22no—
25#16840230—22no—
26C2×#14519736C2211yescharacteristic
27C2×#14519736C2211yescharacteristic
28C2×#14519736C2211yescharacteristic
29#117×D61—22no—
30#16839736—22no—
31#16839736—22no—
32#16839735—22no—
33#16839735—22no—
34C2×#14519692C2214yes—
35C2×#14519691C2214yes—
36#16839529C2214yes—
37#16839528C2214yes—
38C22×#41×C61C2211yescharacteristic
39C2×#117×C61C2211yescharacteristic
40C2×#117×C61C2211yescharacteristic
41C61×#410—22no—
42C61×#410—22no—
43C2×#99×C61C2214yes—
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×#11758222C2×C412yes—
53C2×#11758222C2×C412yes—
54C2×#11758222D412yes—
55C2×#11758222D412yes—
56C22×Dic122D411yescharacteristic
57C22×D244D411yescharacteristic
58C22×C22⋊D61C2312yes—
59C22×C4×D61D412yes—
60#14519775—22no—
61#14519773—22no—
62#14519766—22no—
63#14519764—22no—
64#14519760C2×C418yescomplemented
65#14519758—24no—
66#14519756—24no—
67#14519753—24no—
68#14519751—24no—
69#14519749—28no—
70#14519748—24no—
71#14519746C2×C418yescomplemented
72#14519745—24no—
73C4×Dic122—24no—
74#14519742—24no—
75C4×D244—24no—
76#14519739—24no—
77C4×C22⋊D61—28no—
78C4×C22⋊D61—28no—
79#14519737—28no—
80#14519736—21no—
81#14519736—21no—
82#14519736—21no—
83#14519736—21no—
84#14519736—21no—
85#14519736—21no—
86#14519736—21no—
87#14519736—21no—
88#14519736C2×C412yescomplemented
89#14519736C2×C412yescomplemented
90#14519736D412yescomplemented
91#14519736D412yescomplemented
92#14519735—24no—
93#14519734—24no—
94#14519733—24no—
95C2×C4⋊Dic61—21no—
96C2×C4⋊Dic61—21no—
97C2×C4⋊Dic61—21no—
98C4⋊C4×D61—24no—
99C2×C22⋊Dic61C2312yes—
100C2×C22⋊Dic61C2312yes—
101C2×C22⋊Dic61C2312yes—
102C22⋊C4×D61—24no—
103C2×C4×Dic61—21no—
104C2×C4×Dic61—21no—
105C2×C4×Dic61—21no—
106C42×D61—24no—
107#14519692—28no—
108#14519691—28no—
109C2×#41×C61—21no—
110C2×#41×C61—21no—
111C2×#41×C61—21no—
112C2×#41×C61—21no—
113C2×#41×C61—21no—
114C2×#41×C61—21no—
115C2×#41×C61—21no—
116C2×#41×C61—21no—
117C2×#41×C61—21no—
118C2×#41×C61—21no—
119C2×#41×C61—21no—
120C2×#41×C61—21no—
121C22×Q8×C61C2×C411yescharacteristic, complemented
122C22×D4×C61C2×C411yescharacteristic, complemented
123C22×D4×C61C2312yes—
124C23×C4×C61C2×C412yescomplemented
125C23×C4×C61C2311yescharacteristic
126#117×C61—21no—
127#117×C61—21no—
128#117×C61—21no—
129#117×C61—21no—
130#117×C61—21no—
131#117×C61—21no—
132#117×C61D412yescomplemented
133#117×C61D412yescomplemented
134C2×C4⋊C4×C61—21no—
135C2×C4⋊C4×C61—21no—
136C2×C22⋊C4×C61C2312yes—
137C2×C22⋊C4×C61C2312yes—
138C2×C42×C61—21no—
139C2×C42×C61—21no—
140#99×C61—28no—
141C24×C61C22×C412yes—
142C24×C61C2411yescharacteristic
143C23×D61C2×D412yes—
144#41×C61—41no—
145#41×C61—41no—
146#41×C61—41no—
147#41×C61—41no—
148#41×C61—41no—
149#41×C61—41no—
150#41×C61—41no—
151#41×C61—41no—
152#41×C61—41no—
153#41×C61—41no—
154#41×C61—41no—
155#41×C61—41no—
156#41×C61—41no—
157#41×C61—41no—
158#41×C61—41no—
159#41×C61—41no—
160C2×Q8×C61—21no—
161C2×Q8×C61—21no—
162C2×Q8×C61—21no—
163C2×Q8×C61—21no—
164C2×Q8×C61—21no—
165C2×Q8×C61—21no—
166C2×D4×C61—22no—
167C2×D4×C61—22no—
168C2×D4×C61—22no—
169C2×D4×C61—22no—
170C2×D4×C61—22no—
171C2×D4×C61—22no—
172C2×D4×C61—21no—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61—21no—
177C2×D4×C61—21no—
178C22×C4×C61—22no—
179C22×C4×C61—22no—
180C22×C4×C61—22no—
181C22×C4×C61—22no—
182C22×C4×C61—22no—
183C22×C4×C61—22no—
184C22×C4×C61—22no—
185C22×C4×C61—22no—
186C22×C4×C61C22×C412yes—
187C22×C4×C61C22×C411yescharacteristic
188C22×C4×C61C22×C411yescharacteristic
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61C2×D411yescharacteristic
193C22×C4×C61C2×D411yescharacteristic
194C22×C4×C61C2×D411yescharacteristic
195C22×C4×C61C2×D411yescharacteristic
196C22×C4×C61C2×D411yescharacteristic
197C22×C4×C61#4111yescharacteristic
198C22×C4×C61#4111yescharacteristic
199C22×C4×C61#4111yescharacteristic
200C22×C4×C61#4111yescharacteristic
201C2×C22⋊D61—22no—
202C2×C22⋊D61—22no—
203C2×C22⋊D61—22no—
204C2×C22⋊D61—22no—
205C2×C22⋊D61—28no—
206C2×C22⋊D61C22×C414yes—
207C2×C22⋊D61C2×D414yes—
208C22×Dic61—22no—
209C22×Dic61—22no—
210C22×Dic61—22no—
211C22×Dic61C2×D412yes—
212#11758222—22no—
213#11758222—22no—
214#11758222—22no—
215#11758222—22no—
216#11758222—22no—
217#11758222—22no—
218#11758222—22no—
219#11758222—22no—
220#11758222—22no—
221#11758222—22no—
222#11758222—22no—
223#11758222—22no—
224#11758222—22no—
225#11758222—22no—
226#11758222—22no—
227#11758222—22no—
228C2×D244—21no—
229C2×D244—21no—
230C2×D244—21no—
231C2×D244—21no—
232C2×D244C22⋊C412yes—
233C2×D244C22⋊C412yes—
234C2×C4×D61—22no—
235C2×C4×D61—22no—
236C2×C4×D61—22no—
237C2×C4×D61—22no—
238C2×C4×D61—28no—
239C2×C4×D61C22⋊C414yes—
240C2×C4×D61C22⋊C414yes—
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—41no—
250C4⋊C4×C61—41no—
251C22⋊C4×C61—22no—
252C22⋊C4×C61—22no—
253C22⋊C4×C61—22no—
254C22⋊C4×C61C2×D414yes—
255C42×C61—22no—
256C42×C61—22no—
257C42×C61—41no—
258C42×C61—41no—
259C22⋊Dic61—22no—
260C22⋊Dic61—22no—
261C22⋊Dic61—28no—
262C22⋊Dic61—22no—
263C22⋊Dic61—22no—
264C22⋊Dic61C22×C414yes—
265C22⋊Dic61C2×D414yes—
266#11758198—28no—
267#11758198—28no—
268C4⋊Dic61—22no—
269C4⋊Dic61—22no—
270C4⋊Dic61—22no—
271C4⋊Dic61—22no—
272C4⋊Dic61—41no—
273C4⋊Dic61—41no—
274#11758196—28no—
275#11758196—28no—
276C4×Dic61—28no—
277C4×Dic61—22no—
278C4×Dic61—22no—
279C4×Dic61—22no—
280C4×Dic61—22no—
281C4×Dic61—41no—
282C4×Dic61—41no—
283C23×C61—22no—
284C23×C61—22no—
285C23×C61—22no—
286C23×C61—81no—
287C23×C61—82no—
288C23×C61C23×C411yescharacteristic
289C23×C61C22×D411yescharacteristic
290C23×C61C22×D411yescharacteristic
291C23×C61C22×D411yescharacteristic
292C23×C61C22×D411yescharacteristic
293C23×C61C2×#4111yescharacteristic
294C23×C61C2×#4111yescharacteristic
295C22×D61—22no—
296C22×D61—22no—
297C22×D61—82no—
298C22×D61C2×C22⋊C414yes—
299Q8×C61—41no—
300Q8×C61—41no—
301Q8×C61—41no—
302Q8×C61—41no—
303D4×C61—42no—
304D4×C61—42no—
305D4×C61—42no—
306D4×C61—42no—
307D4×C61—41no—
308D4×C61—41no—
309D4×C61—41no—
310D4×C61—41no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—24no—
315C2×C4×C61—42no—
316C2×C4×C61—42no—
317C2×C4×C61—42no—
318C2×C4×C61—42no—
319C2×C4×C61—42no—
320C2×C4×C61—82no—
321C2×C4×C61—82no—
322C2×C4×C61C2×C22⋊C411yescharacteristic
323C2×C4×C61C2×C22⋊C411yescharacteristic
324C2×C4×C61C2×C22⋊C411yescharacteristic
325C2×C4×C61C2×C22⋊C411yescharacteristic
326C2×C4×C61C4×D411yescharacteristic
327C2×C4×C61C4×D411yescharacteristic
328C2×C4×C61C4×D411yescharacteristic
329C2×C4×C61C4×D411yescharacteristic
330C2×C4×C61C4×D411yescharacteristic
331C2×C4×C61C4×D411yescharacteristic
332C2×C4×C61C4×D411yescharacteristic
333C2×C4×C61C4×D411yescharacteristic
334C2×C4×C61#12011yescharacteristic
335C2×C4×C61#12011yescharacteristic
336C2×C4×C61#12011yescharacteristic
337C2×C4×C61#12011yescharacteristic
338C2×C4×C61#12111yescharacteristic
339C2×C4×C61#12111yescharacteristic
340C2×C4×C61#12111yescharacteristic
341C2×C4×C61#12111yescharacteristic
342C2×C4×C61#12111yescharacteristic
343C2×C4×C61#12111yescharacteristic
344C2×C4×C61#12111yescharacteristic
345C2×C4×C61#12111yescharacteristic
346C2×C4×C61#12311yescharacteristic
347C2×C4×C61#12311yescharacteristic
348C2×C4×C61#12311yescharacteristic
349C2×C4×C61#12311yescharacteristic
350C22⋊D61—24no—
351C22⋊D61—24no—
352C22⋊D61—24no—
353C22⋊D61—24no—
354C22⋊D61—88no—
355C2×Dic61—22no—
356C2×Dic61—22no—
357C2×Dic61—24no—
358C2×Dic61—24no—
359C2×Dic61—42no—
360C2×Dic61—82no—
361C2×Dic61—82no—
362C2×Dic61—82no—
363C2×Dic61C2×C22⋊C414yes—
364D244—22no—
365D244—22no—
366D244—22no—
367D244—22no—
368C4×D61—24no—
369C4×D61—24no—
370C4×D61—24no—
371C4×D61—24no—
372C4×D61—88no—
373Dic122—22no—
374Dic122—22no—
375Dic122—22no—
376Dic122—22no—
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×C61—44no—
386C22×C61—42no—
387C22×C61—82no—
388C22×C61—82no—
389C22×C61C22×C22⋊C411yescharacteristic
390C22×C61C2×C4×D411yescharacteristic
391C22×C61C2×C4×D411yescharacteristic
392C22×C61C2×#12011yescharacteristic
393C22×C61C2×#12111yescharacteristic
394C22×C61C2×#12111yescharacteristic
395C22×C61C2×#12311yescharacteristic
396C2×D61—24no—
397C2×D61—44no—
398C2×D61—44no—
399C2×D61—82no—
400C4×C61—44no—
401C4×C61—42no—
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—44no—
414Dic61—82no—
415#3449—611no—
416#3428—611no—
417C2×#410—611no—
418C2×#410—611no—
419C2×#410D6111yescharacteristic, complemented
420#1913—618no—
421#1740—611no—
422#1740—611no—
423C2×C61—21no—
424C2×C61—21no—
425C2×C61—21no—
426C2×C61—21no—
427C2×C61—21no—
428C2×C61—21no—
429C2×C61—21no—
430C2×C61—82no—
431C2×C61C2×#38611yescharacteristic
432D61—44no—
433C22×#41—611no—
434C22×#41C2×D6111yescharacteristic
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—611no—
454C2×#117—1222no—
455C2×#117C2×D6111yescharacteristic
456C2×#117C2×D6111yescharacteristic
457#410—22no—
458#410—22no—
459#410—1222no—
460#410—1222no—
461#410—1222no—
462#410—1222no—
463C2×#99—614no—
464C2×#99—614no—
465C2×#99C2×D6114yes—
466#342—614no—
467#342—614no—
468C61#2101411yescharacteristic, complemented, Sylow
469C2×#41—21no—
470C2×#41—21no—
471C2×#41—21no—
472C2×#41—21no—
473C2×#41—21no—
474C2×#41—21no—
475C2×#41—21no—
476C2×#41—21no—
477C2×#41—21no—
478C2×#41—21no—
479C2×#41—21no—
480C2×#41—21no—
481C2×#41—612no—
482C2×#41—612no—
483C2×#41—612no—
484C2×#41—612no—
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×Q8C4×D6111yescharacteristic, complemented
495C22×D4—612no—
496C22×D4—611no—
497C22×D4C4×D6111yescharacteristic, complemented
498C22×D4C22×D6112yes—
499C23×C4—612no—
500C23×C4C4×D6112yescomplemented
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—1224no—
518C4×D4—1228no—
519C4×D4—1224no—
520C4×D4—1228no—
521C4×D4—1228no—
522#117—21no—
523#117—21no—
524#117—21no—
525#117—21no—
526#117—21no—
527#117—21no—
528#117—612no—
529#117—612no—
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#117—1221no—
542#117—1221no—
543#117C22⋊D6112yescomplemented
544#117C22⋊D6112yescomplemented
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—1224no—
548C2×C4⋊C4—1221no—
549C2×C4⋊C4—1221no—
550C2×C4⋊C4—1221no—
551C2×C22⋊C4—612no—
552C2×C22⋊C4—612no—
553C2×C22⋊C4—612no—
554C2×C22⋊C4—1224no—
555C2×C22⋊C4C22×D6112yes—
556C2×C22⋊C4C22×D6112yes—
557C2×C42—21no—
558C2×C42—21no—
559C2×C42—1224no—
560C2×C42—1221no—
561C2×C42—1221no—
562C2×C42—1221no—
563#99—28no—
564#99—1228no—
565#99—1228no—
566C24—612no—
567C24C2×C4×D6112yes—
568C24C23×D6111yescharacteristic
569#41—41no—
570#41—41no—
571#41—41no—
572#41—41no—
573#41—41no—
574#41—41no—
575#41—41no—
576#41—41no—
577#41—41no—
578#41—41no—
579#41—41no—
580#41—41no—
581#41—41no—
582#41—41no—
583#41—41no—
584#41—41no—
585#41—1222no—
586#41—1222no—
587#41—1222no—
588#41—1222no—
589#41—1222no—
590#41—1222no—
591#41—1222no—
592#41—1222no—
593#41—1222no—
594#41—1222no—
595#41—1222no—
596#41—1222no—
597#41—1222no—
598#41—1222no—
599#41—1222no—
600#41—1222no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—612no—
608C2×Q8—612no—
609C2×Q8—1221no—
610C2×Q8—1221no—
611C2×Q8—1221no—
612C2×Q8—1221no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—22no—
618C2×D4—22no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—614no—
626C2×D4—614no—
627C2×D4—612no—
628C2×D4—612no—
629C2×D4—1222no—
630C2×D4—1222no—
631C2×D4—1222no—
632C2×D4—1222no—
633C2×D4—1228no—
634C2×D4—1221no—
635C2×D4—1221no—
636C2×D4—1221no—
637C2×D4—1221no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—612no—
647C22×C4—614no—
648C22×C4—614no—
649C22×C4—1228no—
650C22×C4—1222no—
651C22×C4—1222no—
652C22×C4—1222no—
653C22×C4—1222no—
654C22×C4—1222no—
655C22×C4—1222no—
656C22×C4—1222no—
657C22×C4C2×C4×D6112yes—
658C22×C4C2×C4×D6111yescharacteristic
659C22×C4C2×C4×D6111yescharacteristic
660C22×C4#1175822211yescharacteristic
661C22×C4#1175822211yescharacteristic
662C22×C4D4×D6111yescharacteristic
663C22×C4D4×D6111yescharacteristic
664C22×C4D4×D6111yescharacteristic
665C22×C4D4×D6111yescharacteristic
666C22×C4D4×D6111yescharacteristic
667C22×C4D4×D6111yescharacteristic
668C22×C4#1175822411yescharacteristic
669C22×C4#1175822411yescharacteristic
670C22×C4C2×C22⋊D6111yescharacteristic
671C22×C4C2×C22⋊D6111yescharacteristic
672C4⋊C4—22no—
673C4⋊C4—22no—
674C4⋊C4—41no—
675C4⋊C4—41no—
676C4⋊C4—1228no—
677C4⋊C4—1228no—
678C4⋊C4—1222no—
679C4⋊C4—1222no—
680C4⋊C4—1222no—
681C4⋊C4—1222no—
682C4⋊C4—2441no—
683C4⋊C4—2441no—
684C22⋊C4—22no—
685C22⋊C4—22no—
686C22⋊C4—22no—
687C22⋊C4—614no—
688C22⋊C4—614no—
689C22⋊C4—1228no—
690C22⋊C4—1228no—
691C22⋊C4—1228no—
692C22⋊C4—1222no—
693C22⋊C4—1222no—
694C22⋊C4—1222no—
695C22⋊C4—1222no—
696C22⋊C4C2×C22⋊D6114yes—
697C42—22no—
698C42—22no—
699C42—41no—
700C42—41no—
701C42—1228no—
702C42—1222no—
703C42—1222no—
704C42—1222no—
705C42—1222no—
706C42—2441no—
707C42—2441no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—81no—
712C23—82no—
713C23—614no—
714C23—1222no—
715C23—1222no—
716C23—4882no—
717C23C22×C4×D6111yescharacteristic
718C23C2×D4×D6111yescharacteristic
719C23C2×D4×D6111yescharacteristic
720C23C2×D4×D6111yescharacteristic
721C23C22×C22⋊D6111yescharacteristic
722C23C2×#1175822411yescharacteristic
723C23C2×#1175822211yescharacteristic
724Q8—41no—
725Q8—41no—
726Q8—41no—
727Q8—41no—
728Q8—1222no—
729Q8—1222no—
730Q8—1222no—
731Q8—1222no—
732D4—42no—
733D4—42no—
734D4—42no—
735D4—42no—
736D4—41no—
737D4—41no—
738D4—41no—
739D4—41no—
740D4—1224no—
741D4—1224no—
742D4—1224no—
743D4—1224no—
744D4—1222no—
745D4—1222no—
746D4—1222no—
747D4—1222no—
748D4—4888no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—24no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—82no—
759C2×C4—82no—
760C2×C4—614no—
761C2×C4—1222no—
762C2×C4—1222no—
763C2×C4—1224no—
764C2×C4—1224no—
765C2×C4—1224no—
766C2×C4—1224no—
767C2×C4—1224no—
768C2×C4—1224no—
769C2×C4—4888no—
770C2×C4—4882no—
771C2×C4—4882no—
772C2×C4—4882no—
773C2×C4—2442no—
774C2×C4C22⋊C4×D6111yescharacteristic
775C2×C4C22⋊C4×D6111yescharacteristic
776C2×C4C22⋊C4×D6111yescharacteristic
777C2×C4C22⋊C4×D6111yescharacteristic
778C2×C4#1451973711yescharacteristic
779C2×C4#1451973711yescharacteristic
780C2×C4#1451973711yescharacteristic
781C2×C4#1451973711yescharacteristic
782C2×C4C4×C22⋊D6111yescharacteristic
783C2×C4C4×C22⋊D6111yescharacteristic
784C2×C4C4×C22⋊D6111yescharacteristic
785C2×C4C4×C22⋊D6111yescharacteristic
786C2×C4#1451974511yescharacteristic
787C2×C4#1451974511yescharacteristic
788C2×C4#1451974511yescharacteristic
789C2×C4#1451974511yescharacteristic
790C2×C4#1451974811yescharacteristic
791C2×C4#1451974811yescharacteristic
792C2×C4#1451974811yescharacteristic
793C2×C4#1451974811yescharacteristic
794C2×C4#1451975011yescharacteristic
795C2×C4#1451975011yescharacteristic
796C2×C4#1451975011yescharacteristic
797C2×C4#1451975011yescharacteristic
798C2×C4#1451975911yescharacteristic
799C2×C4#1451975911yescharacteristic
800C2×C4#1451975911yescharacteristic
801C2×C4#1451975911yescharacteristic
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—44no—
810C22—42no—
811C22—82no—
812C22—82no—
813C22—1224no—
814C22—4882no—
815C22—2444no—
816C22—2444no—
817C22C2×C22⋊C4×D6111yescharacteristic
818C22C2×#1451973711yescharacteristic
819C22C2×C4×C22⋊D6111yescharacteristic
820C22C2×#1451974511yescharacteristic
821C22C2×#1451974811yescharacteristic
822C22C2×#1451975011yescharacteristic
823C22C2×#1451975911yescharacteristic
824C4—44no—
825C4—42no—
826C4—82no—
827C4—1224no—
828C4—4882no—
829C4—2444no—
830C4—2444no—
831C4#1683963811yescharacteristic
832C4#1683963811yescharacteristic
833C4#1683963811yescharacteristic
834C4#1683963811yescharacteristic
835C4#1683963811yescharacteristic
836C4#1683963811yescharacteristic
837C4#1683963811yescharacteristic
838C4#1683963811yescharacteristic
839C2—21no—
840C2—21no—
841C2—21no—
842C2—21no—
843C2—21no—
844C2—21no—
845C2—21no—
846C2—82no—
847C2—2444no—
848C2C2×#1683963811yescharacteristic
subgroupG/H
centerC4#16839638
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC2×C61×#410C2
socleC2×C61C2×#386
prime radical#21459148C2
cosocleC24×C61C24
hypercenterC2×#410D61
hypocenterC61#21014
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#410

Complements

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

NH ≅ G/Ntype
2. #21459020C2semidirect
3. C2×#16839736C2semidirect
4. C2×#16839735C2semidirect
5. #21446358C2semidirect
6. #21445552C2semidirect
7. #21445551C2semidirect
8. C2×C61×#410C2semidirect
11. #16840336C4semidirect
13. #16840329C4semidirect
17. #16840273C4semidirect
64. #14519760C2×C4semidirect
71. #14519746C2×C4semidirect
88. #14519736C2×C4semidirect
89. #14519736C2×C4semidirect
90. #14519736D4semidirect
91. #14519736D4semidirect
121. C22×Q8×C61C2×C4semidirect
122. C22×D4×C61C2×C4semidirect
124. C23×C4×C61C2×C4semidirect
132. #117×C61D4semidirect
133. #117×C61D4semidirect
419. C2×#410D61semidirect
468. C61#21014semidirect
494. C22×Q8C4×D61semidirect
497. C22×D4C4×D61semidirect
500. C23×C4C4×D61semidirect
543. #117C22⋊D61semidirect
544. #117C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214591482
#214590202
C2×#168397362
C2×#168397352
#214463582
#214455522
#214455512
C2×C61×#4102
#2101461