Finite Group Databasebeta

← #29695926

Subgroups — #29695926

Order 15616.

1336 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840569C211yesmaximal, characteristic
2#21454680C211yesmaximal, characteristic, complemented
3#21454677C211yesmaximal, characteristic, complemented
4#21454281C211yesmaximal, characteristic, complemented
5#21454278C211yesmaximal, characteristic, complemented
6#21446718C211yesmaximal, characteristic, complemented
7#21446316C211yesmaximal, characteristic, complemented
8#21446310C211yesmaximal, characteristic, complemented
9#21446309C211yesmaximal, characteristic, complemented
10#21446303C211yesmaximal, characteristic, complemented
11#21445862C211yesmaximal, characteristic, complemented
12#21445793C211yesmaximal, characteristic, complemented
13#21445788C211yesmaximal, characteristic, complemented
14#21445620C211yesmaximal, characteristic, complemented
15C61×#1976C211yesmaximal, characteristic, complemented
16C2×#14519824C2211yescharacteristic
17C2×#14519823C2211yescharacteristic
18#16840569—22no—
19#16840569—22no—
20#16840569—22no—
21#16840569—22no—
22C2×#14519809C412yescomplemented
23C2×#14519807C2211yescharacteristic
24C2×#14519802C2211yescharacteristic
25C2×#14519801C412yescomplemented
26C2×#14519798C412yescomplemented
27C22×#11758190C2211yescharacteristic
28C2×SD16×D61C412yescomplemented
29C2×#14519783C2211yescharacteristic
30#16840239C2211yescharacteristic, complemented
31#16840239C2211yescharacteristic, complemented
32#16840236C2211yescharacteristic
33#16840236C2211yescharacteristic
34#16839864—22no—
35#16839861—22no—
36C4×#11758190—22no—
37#16839849—22no—
38#16839800C2211yescharacteristic, complemented
39#16839779C2211yescharacteristic
40#16839779C2211yescharacteristic, complemented
41#16839772C2211yescharacteristic, complemented
42#16839770C2211yescharacteristic, complemented
43#16839768C2211yescharacteristic
44#16839766C2211yescharacteristic
45#16839744C2211yescharacteristic
46#16839736C2211yescharacteristic
47#16839736C2211yescharacteristic, complemented
48#16839735C2211yescharacteristic
49#16839735C2211yescharacteristic
50#16839735C2211yescharacteristic
51#16839734—24no—
52#99×D61—24no—
53#16839717C2211yescharacteristic, complemented
54#16839534C2211yescharacteristic, complemented
55#16839532C2211yescharacteristic, complemented
56#16839518C2211yescharacteristic, complemented
57#16839518C2211yescharacteristic, complemented
58C2×#135×C61C2211yescharacteristic
59C61×#427C2211yescharacteristic, complemented
60C61×#421C2211yescharacteristic
61C61×#421C2211yescharacteristic, complemented
62C61×#410C2211yescharacteristic
63C61×#410C2211yescharacteristic, complemented
64C61×#405C2211yescharacteristic, complemented
65#14519824—22no—
66#14519824—22no—
67#14519824—41no—
68#14519824—41no—
69#14519823—22no—
70#14519823—22no—
71#14519823—41no—
72#14519823—41no—
73C2×#11758226C2×C412yes—
74C2×#11758222—21no—
75C2×#11758222—21no—
76C2×#11758222C2311yescharacteristic
77C2×#11758224—22no—
78C2×#11758224C2×C412yescomplemented
79C22×Dic122—21no—
80C22×Dic122C2311yescharacteristic
81C2×Q8×D61C2×C412yescomplemented
82C22×D244—21no—
83C22×D244C2311yescharacteristic
84C2×D4×D61—22no—
85C2×D4×D61C2×C412yes—
86#14519809—24no—
87#14519809—24no—
88#14519807—22no—
89#14519807—22no—
90#14519802—22no—
91#14519802—22no—
92#14519801—24no—
93#14519801—24no—
94#14519798—24no—
95#14519798—24no—
96C2×#11758202C2×C412yescomplemented
97C2×#11758190C2×C412yes—
98C2×#11758190C2×C412yes—
99C2×#11758190D412yes—
100C2×#11758190D412yes—
101C2×#11758190D412yes—
102C2×#11758190D412yes—
103C2×#11758200C2×C412yescomplemented
104C2×#11758201C2×C412yes—
105SD16×D61—24no—
106SD16×D61—24no—
107C2×#11758199C2×C412yes—
108#14519783—21no—
109#14519783—21no—
110#14519783—21no—
111#14519783—21no—
112C2×#11758194C2311yescharacteristic
113C2×#11758194C2311yescharacteristic
114C2×#11758189C2×C412yescomplemented
115C2×C8×D61C2×C412yescomplemented
116C4×Dic122—22no—
117C4×Dic122—41no—
118#14519742—22no—
119#14519742—41no—
120C4×D244—22no—
121C4×D244—41no—
122#14519739—22no—
123#14519739—41no—
124#14519736C2311yescharacteristic
125#14519736C2311yescharacteristic
126#14519736C2311yescharacteristic
127#14519733—22no—
128#14519733—22no—
129C22⋊C4×D61—22no—
130C22⋊C4×D61—22no—
131#14519711—21no—
132#14519709—21no—
133#14519704—41no—
134#14519704—41no—
135#14519702—22no—
136#14519700—22no—
137#14519699—22no—
138#14519697—22no—
139#14519695—21no—
140#14519693—21no—
141#14519692—22no—
142#14519692—22no—
143#14519691—22no—
144#14519691—22no—
145#14519691D414yes—
146#14519687—21no—
147C8×Dic61—21no—
148C2×#41×C61C2311yescharacteristic
149C2×#41×C61C2311yescharacteristic
150#135×C61—21no—
151#135×C61—21no—
152#135×C61—21no—
153#135×C61—21no—
154C2×Q16×C61C2×C411yescharacteristic, complemented
155C2×SD16×C61C2×C411yescharacteristic, complemented
156C2×SD16×C61C2×C411yescharacteristic, complemented
157C2×D8×C61C2×C411yescharacteristic, complemented
158C2×M16×C61C2311yescharacteristic
159C22×C8×C61C2311yescharacteristic
160#117×C61C2311yescharacteristic
161#117×C61C2311yescharacteristic
162#117×C61C2311yescharacteristic
163#107×C61—21no—
164#106×C61—21no—
165#104×C61—41no—
166#104×C61—41no—
167#99×C61—22no—
168#99×C61—22no—
169#97×C61—21no—
170C4×C8×C61—21no—
171C23×D61—21no—
172C23×D61—22no—
173#41×C61—21no—
174#41×C61—21no—
175#41×C61—21no—
176#41×C61—21no—
177#41×C61—21no—
178#41×C61—21no—
179#41×C61—21no—
180#41×C61—21no—
181C2×Q8×C61C22×C411yescharacteristic
182C2×Q8×C61C22×C411yescharacteristic
183C2×D4×C61—21no—
184C2×D4×C61—21no—
185C2×D4×C61C22×C411yescharacteristic
186C2×D4×C61C22×C411yescharacteristic
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61C2411yescharacteristic
190C2×C22⋊D61—22no—
191C2×C22⋊D61—22no—
192C2×C22⋊D61C2×D412yes—
193C22×Dic61—21no—
194C22×Dic61—22no—
195#11758226—24no—
196#11758226—42no—
197Q8×D61—24no—
198Q8×D61—42no—
199#11758224—24no—
200#11758224—42no—
201#11758224—44no—
202#11758224—44no—
203D4×D61—24no—
204D4×D61—42no—
205D4×D61—44no—
206D4×D61—44no—
207#11758222—21no—
208#11758222—21no—
209#11758222—21no—
210#11758222—21no—
211#11758222—42no—
212#11758222—42no—
213#11758222—42no—
214#11758222—42no—
215C2×D244—21no—
216C2×D244—21no—
217C2×D244—21no—
218C2×D244—22no—
219C2×D244—42no—
220C2×D244—42no—
221C2×D244C22×C412yes—
222C2×D244C2×D412yes—
223C2×D244C2×D412yes—
224C2×D244#4111yescharacteristic
225C2×C4×D61—22no—
226C2×C4×D61—22no—
227C2×C4×D61—42no—
228C2×C4×D61—42no—
229C2×C4×D61C22×C412yes—
230C2×Dic122—21no—
231C2×Dic122—21no—
232C2×Dic122—21no—
233C2×Dic122—22no—
234C2×Dic122—42no—
235C2×Dic122—42no—
236C2×Dic122C22×C412yes—
237C2×Dic122C2×D412yes—
238C2×Dic122C2×D412yes—
239C2×Dic122#4111yescharacteristic
240Q16×C61—21no—
241Q16×C61—21no—
242SD16×C61—21no—
243SD16×C61—21no—
244SD16×C61—21no—
245SD16×C61—21no—
246D8×C61—21no—
247D8×C61—21no—
248M16×C61—21no—
249M16×C61—21no—
250C2×C8×C61—21no—
251C2×C8×C61C22×C411yescharacteristic
252C2×C8×C61C22×C411yescharacteristic
253C2×C8×C61C2×D411yescharacteristic
254C2×C8×C61C2×D411yescharacteristic
255C2×C8×C61C2×D411yescharacteristic
256C2×C8×C61C2×D411yescharacteristic
257C4⋊C4×C61—21no—
258C4⋊C4×C61—21no—
259C4⋊C4×C61—21no—
260C22⋊C4×C61—21no—
261C22⋊C4×C61—21no—
262C22⋊C4×C61C2×D412yes—
263C42×C61—21no—
264C42×C61—21no—
265C42×C61—21no—
266C22⋊Dic61—21no—
267C22⋊Dic61—21no—
268C22⋊Dic61C2×D412yes—
269#11758202—24no—
270#11758201—24no—
271#11758200—24no—
272#11758199—24no—
273#11758198—42no—
274#11758198—42no—
275C4⋊Dic61—21no—
276C4⋊Dic61—21no—
277C4⋊Dic61—21no—
278#11758196—42no—
279#11758196—42no—
280C4×Dic61—21no—
281C4×Dic61—21no—
282C4×Dic61—21no—
283C4×Dic61—42no—
284C4×Dic61—42no—
285#11758194—21no—
286#11758194—21no—
287#11758194—21no—
288#11758194—21no—
289C2×#92418—21no—
290C2×#92418C22×C412yes—
291#11758190C22⋊C414yes—
292#11758190C22⋊C414yes—
293#11758190C22⋊C414yes—
294#11758190C22⋊C414yes—
295#11758189—22no—
296#11758189—22no—
297C8×D61—22no—
298C8×D61—22no—
299C23×C61—21no—
300C23×C61—21no—
301C23×C61C22×D411yescharacteristic
302C22×D61—22no—
303C22×D61—22no—
304C22×D61—22no—
305C22×D61—44no—
306C22×D61—162no—
307C22×D61—161no—
308C22×D61C4×D412yes—
309Q8×C61—21no—
310Q8×C61—21no—
311Q8×C61—21no—
312Q8×C61—21no—
313D4×C61—21no—
314D4×C61—21no—
315D4×C61—21no—
316D4×C61—21no—
317D4×C61—41no—
318D4×C61—41no—
319D4×C61—41no—
320D4×C61—41no—
321C2×C4×C61—21no—
322C2×C4×C61—21no—
323C2×C4×C61—22no—
324C2×C4×C61—41no—
325C2×C4×C61—41no—
326C2×C4×C61—41no—
327C2×C4×C61—41no—
328C2×C4×C61—41no—
329C2×C4×C61—41no—
330C2×C4×C61C23×C411yescharacteristic
331C2×C4×C61C22×D411yescharacteristic
332C2×C4×C61C22×D411yescharacteristic
333C2×C4×C61C2×#4111yescharacteristic
334C2×C4×C61H(5,𝔽2)11yescharacteristic
335C2×C4×C61H(5,𝔽2)11yescharacteristic
336C22⋊D61—22no—
337C22⋊D61—22no—
338C22⋊D61—44no—
339C22⋊D61—44no—
340C2×Dic61—22no—
341C2×Dic61—22no—
342C2×Dic61—22no—
343C2×Dic61—22no—
344C2×Dic61—44no—
345C2×Dic61—41no—
346C2×Dic61—41no—
347C2×Dic61C4×D412yes—
348D244—22no—
349D244—22no—
350D244—22no—
351D244—21no—
352D244—21no—
353D244—44no—
354D244C2×C22⋊C414yes—
355C4×D61—22no—
356C4×D61—22no—
357C4×D61—44no—
358C4×D61—44no—
359C4×D61—162no—
360C4×D61—162no—
361Dic122—22no—
362Dic122—22no—
363Dic122—22no—
364Dic122—21no—
365Dic122—21no—
366Dic122—44no—
367Dic122C2×C22⋊C414yes—
368C8×C61—41no—
369C8×C61C2×C22⋊C411yescharacteristic
370C8×C61C2×C22⋊C411yescharacteristic
371C8×C61C2×C22⋊C411yescharacteristic
372C8×C61C2×C22⋊C411yescharacteristic
373#92418—22no—
374#92418—41no—
375#22456—611nomaximal, Sylow
376C22×C61—41no—
377C22×C61—41no—
378C22×C61—41no—
379C22×C61—81no—
380C22×C61—81no—
381C22×C61C2×C4×D411yescharacteristic
382C22×C61D4211yescharacteristic
383C22×C61D4211yescharacteristic
384C2×D61—22no—
385C2×D61—24no—
386C2×D61—42no—
387C2×D61—82no—
388C2×D61—82no—
389C2×D61—82no—
390C2×D61—164no—
391C4×C61—42no—
392C4×C61—41no—
393C4×C61—41no—
394C4×C61—81no—
395C4×C61—81no—
396C4×C61C22×C22⋊C411yescharacteristic
397C4×C61#51811yescharacteristic
398C4×C61#54611yescharacteristic
399C4×C61#54611yescharacteristic
400Dic61—24no—
401Dic61—22no—
402Dic61—42no—
403Dic61—81no—
404Dic61—81no—
405C2×#577—611no—
406#2949—611no—
407#2949—611no—
408#2884—611no—
409#2883—611no—
410#1976—611no—
411#1976D6111yescharacteristic, complemented
412#1905—611no—
413#1905—611no—
414#1904—611no—
415#1904—611no—
416#1812—611no—
417#1796—611no—
418#1795—611no—
419#1757—611no—
420C2×C61—21no—
421C2×C61—21no—
422C2×C61—21no—
423C2×C61—81no—
424C2×C61—81no—
425C2×C61D4×C22⋊C411yescharacteristic
426D61—42no—
427D61—44no—
428C2×2−1+4—611no—
429C2×H(5,𝔽2)—611no—
430#577—1222no—
431#577—1222no—
432#577—1222no—
433#577—1222no—
434C2×#137—611no—
435C2×#137—612no—
436C2×AGL(1,ℤ/8)—611no—
437C2×AGL(1,ℤ/8)—612no—
438C2×#135—612no—
439C2×#135C2×D6111yescharacteristic
440C22×SD16—612no—
441C22×SD16—611no—
442C2×#131—611no—
443#519—611no—
444#519—611no—
445#518—611no—
446#518—611no—
447#440—1222no—
448#440—1222no—
449C4×SD16—1222no—
450C4×SD16—1222no—
451#427—611no—
452#427C2×D6111yescharacteristic, complemented
453#421—611no—
454#421—611no—
455#421C2×D6111yescharacteristic
456#421C2×D6111yescharacteristic, complemented
457#419—611no—
458#419—611no—
459#418—611no—
460#418—611no—
461#413—611no—
462#410—611no—
463#410—611no—
464#410—611no—
465#410—611no—
466#410—611no—
467#410—1224no—
468#410C2×D6111yescharacteristic
469#410C2×D6111yescharacteristic, complemented
470C2×#99—1224no—
471#405—611no—
472#405C2×D6111yescharacteristic, complemented
473#344—611no—
474#344—611no—
475H(3,ℤ/4)—611no—
476H(3,ℤ/4)—611no—
477C61#2245611yescharacteristic, complemented, Sylow
4782−1+4—1222no—
4792−1+4—1222no—
4802−1+4—2441no—
4812−1+4—2441no—
482H(5,𝔽2)—1222no—
483H(5,𝔽2)—1222no—
484H(5,𝔽2)—2441no—
485H(5,𝔽2)—2441no—
486C2×#41—611no—
487C2×#41—612no—
488C2×#41—612no—
489C2×#41—1221no—
490C2×#41—1221no—
491C2×#41—1222no—
492C2×#41C22×D6111yescharacteristic
493C2×#41C22×D6111yescharacteristic
494C22×Q8—612no—
495C22×Q8—611no—
496C22×Q8—1221no—
497C22×D4—612no—
498C22×D4—611no—
499C22×D4—1221no—
500C22×D4—1222no—
501#137—1224no—
502#137—1224no—
503#137—1222no—
504#137—1222no—
505AGL(1,ℤ/8)—1224no—
506AGL(1,ℤ/8)—1224no—
507AGL(1,ℤ/8)—1222no—
508AGL(1,ℤ/8)—1222no—
509#135—21no—
510#135—21no—
511#135—21no—
512#135—21no—
513#135—1224no—
514#135—1224no—
515C2×Q16—612no—
516C2×Q16C4×D6111yescharacteristic, complemented
517C2×SD16—612no—
518C2×SD16—612no—
519C2×SD16—612no—
520C2×SD16—612no—
521C2×SD16—612no—
522C2×SD16—612no—
523C2×SD16—612no—
524C2×SD16—612no—
525C2×SD16—1224no—
526C2×SD16—1224no—
527C2×SD16C4×D6111yescharacteristic, complemented
528C2×SD16C4×D6111yescharacteristic, complemented
529C2×D8—612no—
530C2×D8C4×D6111yescharacteristic, complemented
531#131—1221no—
532#131—1221no—
533#131—1221no—
534#131—1221no—
535C2×M16—611no—
536C2×M16—612no—
537C2×M16—611no—
538C2×M16C22×D6111yescharacteristic
539C22×C8—612no—
540C22×C8C22×D6111yescharacteristic
541C4×Q8—1222no—
542C4×Q8—1222no—
543C4×Q8—2441no—
544C4×Q8—2441no—
545C4×D4—1222no—
546C4×D4—1222no—
547C4×D4—2441no—
548C4×D4—2441no—
549#117—611no—
550#117—611no—
551#117—611no—
552#117—1222no—
553#117—1222no—
554#117C22×D6111yescharacteristic
555#117C22×D6111yescharacteristic
556#117C22×D6111yescharacteristic
557C2×C22⋊C4—1222no—
558C2×C22⋊C4—1222no—
559#107—21no—
560#107—1221no—
561#106—21no—
562#106—1221no—
563#104—41no—
564#104—41no—
565#104—2441no—
566#104—2441no—
567#103—1222no—
568#103—1222no—
569#102—1222no—
570#102—1222no—
571#101—1221no—
572#100—1221no—
573#99—22no—
574#99—22no—
575#99—614no—
576#99—1222no—
577#99—1222no—
578#99—1222no—
579#99—1222no—
580#97—21no—
581#97—1221no—
582C4×C8—21no—
583C4×C8—1221no—
584C24—1222no—
585C24—1221no—
586#41—21no—
587#41—21no—
588#41—21no—
589#41—21no—
590#41—21no—
591#41—21no—
592#41—21no—
593#41—21no—
594#41—1221no—
595#41—1221no—
596#41—1221no—
597#41—1221no—
598#41—1224no—
599#41—1224no—
600#41—2442no—
601#41—2442no—
602#41—2442no—
603#41—2442no—
604#41—2442no—
605#41—2444no—
606#41—2444no—
607#41—2442no—
608C2×Q8—611no—
609C2×Q8—612no—
610C2×Q8—612no—
611C2×Q8—612no—
612C2×Q8—1222no—
613C2×Q8—1221no—
614C2×Q8—1221no—
615C2×Q8—1221no—
616C2×Q8—1224no—
617C2×Q8—2442no—
618C2×Q8—2442no—
619C2×Q8—2442no—
620C2×Q8C2×C4×D6111yescharacteristic
621C2×Q8C2×C4×D6111yescharacteristic
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—612no—
625C2×D4—612no—
626C2×D4—612no—
627C2×D4—612no—
628C2×D4—611no—
629C2×D4—1222no—
630C2×D4—1222no—
631C2×D4—1224no—
632C2×D4—1222no—
633C2×D4—1221no—
634C2×D4—1221no—
635C2×D4—1221no—
636C2×D4—2442no—
637C2×D4—2442no—
638C2×D4—2442no—
639C2×D4—2444no—
640C2×D4—2444no—
641C2×D4C2×C4×D6111yescharacteristic
642C2×D4C2×C4×D6111yescharacteristic
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—612no—
646C22×C4—1222no—
647C22×C4—1222no—
648C22×C4—1222no—
649C22×C4—1221no—
650C22×C4—2442no—
651C22×C4—2442no—
652C22×C4C23×D6111yescharacteristic
653Q16—21no—
654Q16—21no—
655Q16—1224no—
656SD16—21no—
657SD16—21no—
658SD16—21no—
659SD16—21no—
660SD16—614no—
661SD16—614no—
662SD16—614no—
663SD16—614no—
664SD16—1224no—
665SD16—1224no—
666D8—21no—
667D8—21no—
668D8—1224no—
669M16—21no—
670M16—21no—
671M16—1221no—
672M16—1221no—
673M16—1222no—
674M16—1222no—
675M16—1221no—
676M16—1221no—
677C2×C8—21no—
678C2×C8—612no—
679C2×C8—1222no—
680C2×C8—1222no—
681C2×C8—1221no—
682C2×C8C2×C4×D6111yescharacteristic
683C2×C8C2×C4×D6111yescharacteristic
684C2×C8D4×D6111yescharacteristic
685C2×C8D4×D6111yescharacteristic
686C2×C8D4×D6111yescharacteristic
687C2×C8D4×D6111yescharacteristic
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—1221no—
692C4⋊C4—1221no—
693C4⋊C4—1221no—
694C4⋊C4—2442no—
695C4⋊C4—2442no—
696C22⋊C4—21no—
697C22⋊C4—21no—
698C22⋊C4—612no—
699C22⋊C4—1221no—
700C22⋊C4—1221no—
701C22⋊C4—2442no—
702C22⋊C4—2442no—
703C22⋊C4D4×D6112yes—
704C42—21no—
705C42—21no—
706C42—21no—
707C42—1221no—
708C42—1221no—
709C42—1221no—
710C42—2442no—
711C42—2442no—
712C23—21no—
713C23—21no—
714C23—612no—
715C23—1222no—
716C23—1222no—
717C23—1222no—
718C23—9761no—
719C23—9762no—
720C23—2444no—
721C23C2×D4×D6111yescharacteristic
722Q8—21no—
723Q8—21no—
724Q8—21no—
725Q8—21no—
726Q8—614no—
727Q8—1222no—
728Q8—1222no—
729Q8—1221no—
730Q8—1222no—
731Q8—1221no—
732Q8—2444no—
733D4—21no—
734D4—21no—
735D4—21no—
736D4—21no—
737D4—41no—
738D4—41no—
739D4—41no—
740D4—41no—
741D4—614no—
742D4—1222no—
743D4—1222no—
744D4—1222no—
745D4—1222no—
746D4—1221no—
747D4—1222no—
748D4—1221no—
749D4—2444no—
750D4—2444no—
751D4—2444no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—612no—
762C2×C4—1222no—
763C2×C4—1222no—
764C2×C4—1222no—
765C2×C4—1222no—
766C2×C4—1222no—
767C2×C4—1222no—
768C2×C4—9762no—
769C2×C4—9762no—
770C2×C4—2444no—
771C2×C4—2444no—
772C2×C4—2444no—
773C2×C4—2441no—
774C2×C4—2441no—
775C2×C4C22×C4×D6111yescharacteristic
776C2×C4C2×D4×D6111yescharacteristic
777C2×C4C2×D4×D6111yescharacteristic
778C2×C4#41×D6111yescharacteristic
779C2×C4#1451982211yescharacteristic
780C2×C4#1451982311yescharacteristic
781C8—41no—
782C8—1222no—
783C8—2441no—
784C8C22⋊C4×D6111yescharacteristic
785C8C22⋊C4×D6111yescharacteristic
786C8C22⋊C4×D6111yescharacteristic
787C8C22⋊C4×D6111yescharacteristic
788C22—41no—
789C22—41no—
790C22—41no—
791C22—81no—
792C22—81no—
793C22—1222no—
794C22—1224no—
795C22—9764no—
796C22—4882no—
797C22—4882no—
798C22—4882no—
799C22—2442no—
800C22C4×D4×D6111yescharacteristic
801C22#1684039611yescharacteristic
802C22#1684039711yescharacteristic
803C4—42no—
804C4—41no—
805C4—41no—
806C4—81no—
807C4—81no—
808C4—1222no—
809C4—1224no—
810C4—4881no—
811C4—4881no—
812C4—2442no—
813C4C2×C22⋊C4×D6111yescharacteristic
814C4#1684023411yescharacteristic
815C4#1684040511yescharacteristic
816C4#1684040911yescharacteristic
817C2—21no—
818C2—21no—
819C2—21no—
820C2—81no—
821C2—81no—
822C2—2442no—
823C2—2444no—
824C2#2144864011yescharacteristic
subgroupG/H
centerC2#21448640
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1976C2
socleC2×C61D4×C22⋊C4
prime radicalC2×#16840569C2
cosocleC22×C4×C61C24
hypercenter#1976D61
hypocenterC61#22456
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ #1976

Complements

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

NH ≅ G/Ntype
2. #21454680C2semidirect
3. #21454677C2semidirect
4. #21454281C2semidirect
5. #21454278C2semidirect
6. #21446718C2semidirect
7. #21446316C2semidirect
8. #21446310C2semidirect
9. #21446309C2semidirect
10. #21446303C2semidirect
11. #21445862C2semidirect
12. #21445793C2semidirect
13. #21445788C2semidirect
14. #21445620C2semidirect
15. C61×#1976C2semidirect
22. C2×#14519809C4semidirect
25. C2×#14519801C4semidirect
26. C2×#14519798C4semidirect
28. C2×SD16×D61C4semidirect
30. #16840239C22semidirect
31. #16840239C22semidirect
38. #16839800C22semidirect
40. #16839779C22semidirect
41. #16839772C22semidirect
42. #16839770C22semidirect
47. #16839736C22semidirect
53. #16839717C22semidirect
54. #16839534C22semidirect
55. #16839532C22semidirect
56. #16839518C22semidirect
57. #16839518C22semidirect
59. C61×#427C22semidirect
61. C61×#421C22semidirect
63. C61×#410C22semidirect
64. C61×#405C22semidirect
78. C2×#11758224C2×C4semidirect
81. C2×Q8×D61C2×C4semidirect
96. C2×#11758202C2×C4semidirect
103. C2×#11758200C2×C4semidirect
114. C2×#11758189C2×C4semidirect
115. C2×C8×D61C2×C4semidirect
154. C2×Q16×C61C2×C4semidirect
155. C2×SD16×C61C2×C4semidirect
156. C2×SD16×C61C2×C4semidirect
157. C2×D8×C61C2×C4semidirect
411. #1976D61semidirect
452. #427C2×D61semidirect
456. #421C2×D61semidirect
469. #410C2×D61semidirect
472. #405C2×D61semidirect
477. C61#22456semidirect
516. C2×Q16C4×D61semidirect
527. C2×SD16C4×D61semidirect
528. C2×SD16C4×D61semidirect
530. C2×D8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168405692
#214546802
#214546772
#214542812
#214542782
#214467182
#214463162
#214463102
#214463092
#214463032
#214458622
#214457932
#214457882
#214456202
C61×#19762
#2245661