Finite Group Databasebeta

← #29695948

Subgroups — #29695948

Order 15616.

1312 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840569C211yesmaximal, characteristic
2#21454736C211yesmaximal, characteristic, complemented
3#21454301C211yesmaximal, characteristic, complemented
4#21454297C211yesmaximal, characteristic, complemented
5#21446722C211yesmaximal, characteristic, complemented
6#21446720C211yesmaximal, characteristic, complemented
7#21446299C211yesmaximal, characteristic, complemented
8#21446297C211yesmaximal, characteristic, complemented
9#21446292C211yesmaximal, characteristic, complemented
10#21446290C211yesmaximal, characteristic, complemented
11#21445866C211yesmaximal, characteristic, complemented
12#21445793C211yesmaximal, characteristic, complemented
13#21445788C211yesmaximal, characteristic, complemented
14#21445620C211yesmaximal, characteristic, complemented
15C61×#2957C211yesmaximal, 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
29#16840529C2211yescharacteristic
30#16840529C2211yescharacteristic, complemented
31C2×#14519783C2211yescharacteristic
32#16839884—22no—
33#16839879—22no—
34C2×#14519713C2211yescharacteristic, complemented
35#16839779C2211yescharacteristic
36#16839779C2211yescharacteristic, complemented
37#16839772C2211yescharacteristic, complemented
38#16839770C2211yescharacteristic, complemented
39#16839768C2211yescharacteristic
40#16839766C2211yescharacteristic
41#16839744—22no—
42#16839744—22no—
43#16839744C2211yescharacteristic
44#16839744C2211yescharacteristic
45#16839744C2211yescharacteristic
46C2×#14519695—22no—
47C2×#14519695C2211yescharacteristic, complemented
48C2×#14519695C2211yescharacteristic, complemented
49C2×#14519693—22no—
50C2×#14519693C2211yescharacteristic
51C2×#14519693C2211yescharacteristic
52#16839735C2211yescharacteristic
53#16839717C2211yescharacteristic, complemented
54#16839534C2211yescharacteristic, complemented
55#16839532C2211yescharacteristic, complemented
56#16839520C2211yescharacteristic, complemented
57#16839520C2211yescharacteristic, complemented
58C2×#135×C61C2211yescharacteristic
59C61×#568C2211yescharacteristic
60C61×#568C2211yescharacteristic, complemented
61C61×#444—22no—
62C61×#443—22no—
63C2×#108×C61C2211yescharacteristic, complemented
64C61×#421C2211yescharacteristic
65C61×#421C2211yescharacteristic, complemented
66C61×#405C2211yescharacteristic, complemented
67#14519824—22no—
68#14519824—22no—
69#14519824—41no—
70#14519824—41no—
71#14519823—22no—
72#14519823—22no—
73#14519823—41no—
74#14519823—41no—
75C2×#11758226C2×C412yes—
76C2×#11758222—21no—
77C2×#11758222—21no—
78C2×#11758222C2311yescharacteristic
79C2×#11758224—22no—
80C2×#11758224C2×C412yes—
81C22×Dic122—21no—
82C22×Dic122C2311yescharacteristic
83C2×Q8×D61C2×C412yes—
84C22×D244—21no—
85C22×D244C2311yescharacteristic
86C2×D4×D61—22no—
87C2×D4×D61C2×C412yes—
88#14519809—24no—
89#14519809—24no—
90#14519807—22no—
91#14519807—22no—
92#14519802—22no—
93#14519802—22no—
94#14519801—24no—
95#14519801—24no—
96#14519798—24no—
97#14519798—24no—
98C2×#11758202C2×C412yes—
99C2×#11758190—21no—
100C2×#11758190—21no—
101C2×#11758190—21no—
102C2×#11758190—21no—
103C2×#11758190C2×C412yes—
104C2×#11758190C2×C412yes—
105C2×#11758200C2×C412yes—
106C2×#11758201C2×C412yes—
107SD16×D61—24no—
108SD16×D61—24no—
109C2×#11758199C2×C412yes—
110#14519784—22no—
111#14519784—22no—
112#14519784—41no—
113#14519784—41no—
114#14519783—21no—
115#14519783—21no—
116#14519783—21no—
117#14519783—21no—
118C2×#11758194—22no—
119C2×#11758194—22no—
120C2×#11758194C2311yescharacteristic
121C2×#11758194C2311yescharacteristic
122C2×#11758194C2311yescharacteristic
123C2×#11758194C2311yescharacteristic
124C2×#11758189C2×C412yes—
125C2×C8×D61C2×C412yes—
126#14519736C2311yescharacteristic
127#14519713—21no—
128#14519713—21no—
129#14519704—22no—
130#14519704—22no—
131#14519702—41no—
132#14519700—41no—
133#14519699—41no—
134#14519697—41no—
135#14519695—21no—
136#14519695—21no—
137#14519695—22no—
138#14519695—22no—
139#14519695D412yes—
140#14519693—21no—
141#14519693—21no—
142#14519693—22no—
143#14519693—22no—
144#14519693D412yes—
145#14519691—22no—
146#14519687—21no—
147C8×Dic61—21no—
148C2×#41×C61C2311yescharacteristic
149C2×#41×C61C2311yescharacteristic
150#135×C61D412yes—
151#135×C61D412yes—
152#135×C61D412yes—
153#135×C61D412yes—
154C2×Q16×C61C2×C411yescharacteristic
155C2×SD16×C61C2×C411yescharacteristic
156C2×SD16×C61C2×C411yescharacteristic
157C2×D8×C61C2×C411yescharacteristic
158#131×C61—22no—
159#131×C61—22no—
160#131×C61—41no—
161#131×C61—41no—
162C2×M16×C61—22no—
163C2×M16×C61—22no—
164C2×M16×C61C2311yescharacteristic
165C2×M16×C61C2311yescharacteristic
166C2×M16×C61C2311yescharacteristic
167C22×C8×C61C2311yescharacteristic
168#117×C61C2311yescharacteristic
169#108×C61—21no—
170#108×C61—21no—
171#104×C61—22no—
172#104×C61—22no—
173#97×C61—21no—
174C4×C8×C61—21no—
175C23×D61—21no—
176C23×D61—22no—
177#41×C61—21no—
178#41×C61—21no—
179#41×C61—21no—
180#41×C61—21no—
181#41×C61C2×D412yes—
182#41×C61C2×D412yes—
183#41×C61C2×D412yes—
184#41×C61C2×D412yes—
185C2×Q8×C61C22×C411yescharacteristic
186C2×Q8×C61C22×C411yescharacteristic
187C2×D4×C61—21no—
188C2×D4×C61—21no—
189C2×D4×C61C22×C411yescharacteristic
190C2×D4×C61C22×C411yescharacteristic
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61C2411yescharacteristic
194C2×C22⋊D61—22no—
195C2×C22⋊D61—22no—
196C2×C22⋊D61#4112yes—
197C22×Dic61—21no—
198C22×Dic61—22no—
199#11758226—24no—
200#11758226—42no—
201Q8×D61—24no—
202Q8×D61—42no—
203#11758224—24no—
204#11758224—42no—
205#11758224—44no—
206#11758224—44no—
207D4×D61—24no—
208D4×D61—42no—
209D4×D61—44no—
210D4×D61—44no—
211#11758222—21no—
212#11758222—21no—
213#11758222—21no—
214#11758222—21no—
215#11758222—42no—
216#11758222—42no—
217#11758222—42no—
218#11758222—42no—
219C2×D244—21no—
220C2×D244—21no—
221C2×D244—21no—
222C2×D244—21no—
223C2×D244—22no—
224C2×D244—21no—
225C2×D244—42no—
226C2×D244—42no—
227C2×D244C22×C412yes—
228C2×D244C2×D411yescharacteristic
229C2×C4×D61—22no—
230C2×C4×D61—22no—
231C2×C4×D61C22×C412yes—
232C2×Dic122—21no—
233C2×Dic122—21no—
234C2×Dic122—21no—
235C2×Dic122—21no—
236C2×Dic122—21no—
237C2×Dic122—22no—
238C2×Dic122—42no—
239C2×Dic122—42no—
240C2×Dic122C22×C412yes—
241C2×Dic122C2×D411yescharacteristic
242Q16×C61C22⋊C412yes—
243Q16×C61C22⋊C412yes—
244SD16×C61C22⋊C412yes—
245SD16×C61C22⋊C412yes—
246SD16×C61C22⋊C412yes—
247SD16×C61C22⋊C412yes—
248D8×C61C22⋊C412yes—
249D8×C61C22⋊C412yes—
250M16×C61—21no—
251M16×C61—21no—
252M16×C61—21no—
253M16×C61—21no—
254M16×C61—21no—
255M16×C61—42no—
256M16×C61—42no—
257M16×C61C2×D412yes—
258C2×C8×C61—21no—
259C2×C8×C61—21no—
260C2×C8×C61—21no—
261C2×C8×C61—42no—
262C2×C8×C61—42no—
263C2×C8×C61C22×C411yescharacteristic
264C2×C8×C61C22×C411yescharacteristic
265C2×C8×C61C2×D411yescharacteristic
266C2×C8×C61C2×D411yescharacteristic
267C2×C8×C61C2×D411yescharacteristic
268C2×C8×C61C2×D411yescharacteristic
269C4⋊C4×C61—21no—
270C22⋊C4×C61—21no—
271C42×C61—21no—
272C22⋊Dic61—21no—
273#11758202—24no—
274#11758201—24no—
275#11758200—24no—
276#11758199—24no—
277C4⋊Dic61—21no—
278C4×Dic61—21no—
279#11758194—21no—
280#11758194—21no—
281#11758194—21no—
282#11758194—21no—
283#11758194—21no—
284#11758194—21no—
285#11758194—21no—
286#11758194—42no—
287#11758194—42no—
288#11758194C2×D412yes—
289C2×#92418—21no—
290C2×#92418—21no—
291C2×#92418—21no—
292C2×#92418—42no—
293C2×#92418—42no—
294C2×#92418C22×C412yes—
295#11758190—22no—
296#11758190—22no—
297#11758190—22no—
298#11758190—22no—
299#11758189—22no—
300#11758189—22no—
301C8×D61—22no—
302C8×D61—22no—
303C23×C61—21no—
304C23×C61—21no—
305C23×C61C2×#4111yescharacteristic
306C22×D61—22no—
307C22×D61—44no—
308C22×D61—41no—
309C22×D61—41no—
310C22×D61—162no—
311C22×D61—161no—
312C22×D61C4×D412yes—
313Q8×C61—21no—
314Q8×C61—21no—
315Q8×C61C2×C22⋊C412yes—
316Q8×C61C2×C22⋊C412yes—
317D4×C61—22no—
318D4×C61—22no—
319D4×C61—22no—
320D4×C61—22no—
321D4×C61—21no—
322D4×C61—21no—
323D4×C61C2×C22⋊C412yes—
324D4×C61C2×C22⋊C412yes—
325C2×C4×C61—21no—
326C2×C4×C61—21no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—41no—
332C2×C4×C61C23×C411yescharacteristic
333C2×C4×C61C22×D411yescharacteristic
334C2×C4×C61C22×D411yescharacteristic
335C2×C4×C61C22×D411yescharacteristic
336C2×C4×C61H(5,𝔽2)11yescharacteristic
337C2×C4×C61H(5,𝔽2)11yescharacteristic
338C22⋊D61—22no—
339C22⋊D61—22no—
340C22⋊D61—44no—
341C22⋊D61—44no—
342C2×Dic61—22no—
343C2×Dic61—44no—
344C2×Dic61—41no—
345C2×Dic61—41no—
346C2×Dic61—41no—
347C2×Dic61C4×D412yes—
348D244—22no—
349D244—22no—
350D244—21no—
351D244—21no—
352D244—44no—
353D244—41no—
354D244—41no—
355C4×D61—22no—
356C4×D61—22no—
357C4×D61—44no—
358C4×D61—44no—
359Dic122—21no—
360Dic122—21no—
361Dic122—22no—
362Dic122—22no—
363Dic122—44no—
364Dic122—41no—
365Dic122—41no—
366C8×C61—22no—
367C8×C61—41no—
368C8×C61—41no—
369C8×C61C2×C22⋊C411yescharacteristic
370C8×C61C2×C22⋊C411yescharacteristic
371C8×C61C2×C22⋊C411yescharacteristic
372C8×C61C2×C22⋊C411yescharacteristic
373#92418—22no—
374#92418—22no—
375#92418—41no—
376#92418—41no—
377#22459—611nomaximal, Sylow
378C22×C61—22no—
379C22×C61—22no—
380C22×C61—41no—
381C22×C61—81no—
382C22×C61—81no—
383C22×C61C2×C4×D411yescharacteristic
384C22×C61#54611yescharacteristic
385C22×C61#54611yescharacteristic
386C2×D61—22no—
387C2×D61—42no—
388C2×D61—42no—
389C2×D61—82no—
390C2×D61—164no—
391C2×D61—161no—
392C2×D61—161no—
393C4×C61—22no—
394C4×C61—22no—
395C4×C61—81no—
396C4×C61C22×C22⋊C411yescharacteristic
397C4×C61#51811yescharacteristic
398C4×C61D4211yescharacteristic
399C4×C61D4211yescharacteristic
400Dic61—22no—
401Dic61—42no—
402Dic61—81no—
403C2×#577—611no—
404#2957—611no—
405#2957D6111yescharacteristic, complemented
406#2889—611no—
407#2888—611no—
408#1977—611no—
409#1977—611no—
410#1903—611no—
411#1903—611no—
412#1902—611no—
413#1902—611no—
414#1813—611no—
415#1796—611no—
416#1795—611no—
417#1757—611no—
418C2×C61—21no—
419C2×C61—21no—
420C2×C61—21no—
421C2×C61—42no—
422C2×C61—42no—
423C2×C61D4×C22⋊C411yescharacteristic
424D61—42no—
425D61—82no—
426C2×2−1+4—611no—
427C2×H(5,𝔽2)—611no—
428#577—1222no—
429#577—1222no—
430#577—1222no—
431#577—1222no—
432C2×#137—611no—
433C2×#137—612no—
434C2×AGL(1,ℤ/8)—611no—
435C2×AGL(1,ℤ/8)—612no—
436C2×#135—612no—
437C2×#135C2×D6111yescharacteristic
438C22×SD16—612no—
439C22×SD16—611no—
440#568—611no—
441#568—611no—
442#568C2×D6111yescharacteristic
443#568C2×D6111yescharacteristic, complemented
444C2×#131—611no—
445#444—22no—
446#444—1222no—
447#443—22no—
448#443—1222no—
449C2×#108—611no—
450C2×#108C2×D6111yescharacteristic, complemented
451#421—611no—
452#421—611no—
453#421C2×D6111yescharacteristic
454#421C2×D6111yescharacteristic, complemented
455#419—611no—
456#419—611no—
457#418—611no—
458#418—611no—
459#413—611no—
460#413—611no—
461#413—611no—
462#413—1222no—
463#413—1222no—
464C2×#101—611no—
465C2×#101—611no—
466C2×#101—1222no—
467C2×#100—611no—
468C2×#100—611no—
469C2×#100—1222no—
470#410—611no—
471#405—611no—
472#405C2×D6111yescharacteristic, complemented
473#344—611no—
474#344—611no—
475#338—611no—
476#338—611no—
477C61#2245911yescharacteristic, 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—1222no—
502#137—1222no—
503#137—1224no—
504#137—1224no—
505AGL(1,ℤ/8)—1222no—
506AGL(1,ℤ/8)—1222no—
507AGL(1,ℤ/8)—1224no—
508AGL(1,ℤ/8)—1224no—
509#135—1224no—
510#135—1224no—
511#135D24412yes—
512#135D24412yes—
513#135C22⋊D6112yes—
514#135C22⋊D6112yes—
515C2×Q16—612no—
516C2×Q16C4×D6111yescharacteristic
517C2×SD16—612no—
518C2×SD16—612no—
519C2×SD16—612no—
520C2×SD16—612no—
521C2×SD16—1224no—
522C2×SD16—1224no—
523C2×SD16—1221no—
524C2×SD16—1221no—
525C2×SD16—1221no—
526C2×SD16—1221no—
527C2×SD16C4×D6111yescharacteristic
528C2×SD16C4×D6111yescharacteristic
529C2×D8—612no—
530C2×D8C4×D6111yescharacteristic
531#131—22no—
532#131—22no—
533#131—41no—
534#131—41no—
535#131—1221no—
536#131—1221no—
537#131—1221no—
538#131—1221no—
539#131—1222no—
540#131—1222no—
541#131—2441no—
542#131—2441no—
543C2×M16—22no—
544C2×M16—22no—
545C2×M16—611no—
546C2×M16—612no—
547C2×M16—611no—
548C2×M16—611no—
549C2×M16—611no—
550C2×M16—1222no—
551C2×M16—1222no—
552C2×M16C22×D6111yescharacteristic
553C2×M16C22×D6111yescharacteristic
554C2×M16C22×D6111yescharacteristic
555C22×C8—612no—
556C22×C8C22×D6111yescharacteristic
557#117—611no—
558#117C22×D6111yescharacteristic
559#108—21no—
560#108—21no—
561#108—1221no—
562#108—1221no—
563#104—22no—
564#104—22no—
565#104—1222no—
566#104—1222no—
567#103—2441no—
568#103—2441no—
569#102—2441no—
570#102—2441no—
571#101—612no—
572#101—1222no—
573#101—1221no—
574#101—1221no—
575#101—1222no—
576#100—612no—
577#100—1222no—
578#100—1221no—
579#100—1221no—
580#100—1222no—
581#99—1222no—
582#97—21no—
583#97—1221no—
584C4×C8—21no—
585C4×C8—1221no—
586C24—1222no—
587C24—1221no—
588#41—21no—
589#41—21no—
590#41—21no—
591#41—21no—
592#41—1221no—
593#41—1221no—
594#41—1221no—
595#41—1221no—
596#41—1224no—
597#41—1224no—
598#41—2442no—
599#41—2442no—
600#41—2442no—
601#41—2442no—
602#41—2442no—
603#41—2442no—
604#41—2444no—
605#41—2444no—
606#41C2×D24412yes—
607#41C2×D24412yes—
608#41C2×C22⋊D6112yes—
609#41C2×C22⋊D6112yes—
610C2×Q8—611no—
611C2×Q8—612no—
612C2×Q8—1222no—
613C2×Q8—1221no—
614C2×Q8—1224no—
615C2×Q8—1221no—
616C2×Q8—1221no—
617C2×Q8—1221no—
618C2×Q8—1221no—
619C2×Q8—2442no—
620C2×Q8—2442no—
621C2×Q8—2442no—
622C2×Q8C2×C4×D6111yescharacteristic
623C2×Q8C2×C4×D6111yescharacteristic
624C2×D4—21no—
625C2×D4—21no—
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—1221no—
637C2×D4—1221no—
638C2×D4—2442no—
639C2×D4—2442no—
640C2×D4—2442no—
641C2×D4—2444no—
642C2×D4—2444no—
643C2×D4C2×C4×D6111yescharacteristic
644C2×D4C2×C4×D6111yescharacteristic
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—612no—
648C22×C4—1222no—
649C22×C4—1222no—
650C22×C4—1222no—
651C22×C4—1221no—
652C22×C4C23×D6111yescharacteristic
653Q16—1224no—
654Q16#1175819812yes—
655Q16#1175819812yes—
656SD16—1224no—
657SD16—1224no—
658SD16—1222no—
659SD16—1222no—
660SD16—1222no—
661SD16—1222no—
662SD16#1175819812yes—
663SD16#1175819812yes—
664SD16#1175819812yes—
665SD16#1175819812yes—
666D8—1224no—
667D8#1175819812yes—
668D8#1175819812yes—
669M16—21no—
670M16—21no—
671M16—21no—
672M16—21no—
673M16—21no—
674M16—42no—
675M16—42no—
676M16—612no—
677M16—1221no—
678M16—1221no—
679M16—1221no—
680M16—1222no—
681M16—1222no—
682M16—1221no—
683M16—1221no—
684M16—1221no—
685M16—1221no—
686M16—2442no—
687M16—2442no—
688M16D4×D6112yes—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—42no—
693C2×C8—42no—
694C2×C8—612no—
695C2×C8—1221no—
696C2×C8—1222no—
697C2×C8—1222no—
698C2×C8—1221no—
699C2×C8—1221no—
700C2×C8—2442no—
701C2×C8—2442no—
702C2×C8C2×C4×D6111yescharacteristic
703C2×C8C2×C4×D6111yescharacteristic
704C2×C8C2×D24411yescharacteristic
705C2×C8C2×D24411yescharacteristic
706C2×C8C2×C22⋊D6111yescharacteristic
707C2×C8C2×C22⋊D6111yescharacteristic
708C4⋊C4—21no—
709C4⋊C4—1221no—
710C22⋊C4—21no—
711C22⋊C4—1221no—
712C42—21no—
713C42—1221no—
714C23—21no—
715C23—21no—
716C23—612no—
717C23—1222no—
718C23—9761no—
719C23—9762no—
720C23—2444no—
721C23—2441no—
722C23—2441no—
723C23#41×D6111yescharacteristic
724Q8—21no—
725Q8—21no—
726Q8—1221no—
727Q8—1221no—
728Q8—1222no—
729Q8—1222no—
730Q8—2444no—
731Q8—2441no—
732Q8—2441no—
733Q8C2×#1175819812yes—
734Q8C2×#1175819812yes—
735D4—22no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—21no—
740D4—21no—
741D4—1222no—
742D4—1222no—
743D4—1222no—
744D4—1222no—
745D4—1221no—
746D4—1221no—
747D4—2444no—
748D4—2444no—
749D4—2444no—
750D4—2441no—
751D4—2441no—
752D4C2×#1175819812yes—
753D4C2×#1175819812yes—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—41no—
761C2×C4—612no—
762C2×C4—1222no—
763C2×C4—1222no—
764C2×C4—1222no—
765C2×C4—2444no—
766C2×C4—2444no—
767C2×C4—2444no—
768C2×C4—2441no—
769C2×C4—2441no—
770C2×C4—2441no—
771C2×C4C22×C4×D6111yescharacteristic
772C2×C4C2×D4×D6111yescharacteristic
773C2×C4C22×C22⋊D6111yescharacteristic
774C2×C4C22×D24411yescharacteristic
775C2×C4#1451982211yescharacteristic
776C2×C4#1451982311yescharacteristic
777C8—22no—
778C8—41no—
779C8—41no—
780C8—1222no—
781C8—1222no—
782C8—2441no—
783C8—2441no—
784C8C2×#1175819811yescharacteristic
785C8C2×#1175819811yescharacteristic
786C8C2×#1175819811yescharacteristic
787C8C2×#1175819811yescharacteristic
788C22—22no—
789C22—22no—
790C22—41no—
791C22—81no—
792C22—81no—
793C22—1222no—
794C22—9761no—
795C22—9761no—
796C22—9764no—
797C22—4882no—
798C22—2442no—
799C22—2442no—
800C22C4×D4×D6111yescharacteristic
801C22#1684040011yescharacteristic
802C22#1684040711yescharacteristic
803C4—22no—
804C4—22no—
805C4—81no—
806C4—1222no—
807C4—4881no—
808C4—2442no—
809C4C22×#1175819811yescharacteristic
810C4#1684023411yescharacteristic
811C4D4×C22⋊D6111yescharacteristic
812C4D4×D24411yescharacteristic
813C2—21no—
814C2—21no—
815C2—21no—
816C2—42no—
817C2—42no—
818C2—4882no—
819C2—2442no—
820C2D4×#1175819811yescharacteristic
subgroupG/H
centerC2D4×#11758198
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2957C2
socleC2×C61D4×C22⋊C4
prime radicalC2×#16840569C2
cosocleC22×C4×C61C24
hypercenter#2957D61
hypocenterC61#22459
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ #2957

Complements

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

NH ≅ G/Ntype
2. #21454736C2semidirect
3. #21454301C2semidirect
4. #21454297C2semidirect
5. #21446722C2semidirect
6. #21446720C2semidirect
7. #21446299C2semidirect
8. #21446297C2semidirect
9. #21446292C2semidirect
10. #21446290C2semidirect
11. #21445866C2semidirect
12. #21445793C2semidirect
13. #21445788C2semidirect
14. #21445620C2semidirect
15. C61×#2957C2semidirect
22. C2×#14519809C4semidirect
25. C2×#14519801C4semidirect
26. C2×#14519798C4semidirect
28. C2×SD16×D61C4semidirect
30. #16840529C22semidirect
34. C2×#14519713C22semidirect
36. #16839779C22semidirect
37. #16839772C22semidirect
38. #16839770C22semidirect
47. C2×#14519695C22semidirect
48. C2×#14519695C22semidirect
53. #16839717C22semidirect
54. #16839534C22semidirect
55. #16839532C22semidirect
56. #16839520C22semidirect
57. #16839520C22semidirect
60. C61×#568C22semidirect
63. C2×#108×C61C22semidirect
65. C61×#421C22semidirect
66. C61×#405C22semidirect
405. #2957D61semidirect
443. #568C2×D61semidirect
450. C2×#108C2×D61semidirect
454. #421C2×D61semidirect
472. #405C2×D61semidirect
477. C61#22459semidirect

Maximal subgroups

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

subgroupindex
C2×#168405692
#214547362
#214543012
#214542972
#214467222
#214467202
#214462992
#214462972
#214462922
#214462902
#214458662
#214457932
#214457882
#214456202
C61×#29572
#2245961