Finite Group Databasebeta

← #29693905

Subgroups — #29693905

Order 15616.

826 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456262C211yesmaximal, characteristic
2#21454535C211yesmaximal, characteristic, complemented
3#21454534C211yesmaximal, characteristic, complemented
4#21446645C211yesmaximal, characteristic, complemented
5#21446645C211yesmaximal, characteristic, complemented
6#21446149C211yesmaximal, characteristic, complemented
7#21446148C211yesmaximal, characteristic, complemented
8#21446147C211yesmaximal, characteristic, complemented
9#21446146C211yesmaximal, characteristic, complemented
10#21446145C211yesmaximal, characteristic, complemented
11#21446144C211yesmaximal, characteristic, complemented
12#21446143C211yesmaximal, characteristic, complemented
13#21445958C211yesmaximal, characteristic, complemented
14#21445566C211yesmaximal, characteristic, complemented
15C61×#1876C211yesmaximal, characteristic, complemented
16C2×#14519799C2211yescharacteristic
17C2×#14519797C2211yescharacteristic
18C2×#14519797C2211yescharacteristic
19C2×#14519785C2211yescharacteristic
20C2×#14519784C2211yescharacteristic
21C2×#14519783C2211yescharacteristic
22#16840308C2211yescharacteristic
23#16840308C2211yescharacteristic
24#16840155C411yescharacteristic, complemented
25#16840155C411yescharacteristic, complemented
26#16840153C411yescharacteristic, complemented
27#16840153C411yescharacteristic, complemented
28#16840150C411yescharacteristic, complemented
29#16840150C411yescharacteristic, complemented
30#16840148C411yescharacteristic, complemented
31#16840148C411yescharacteristic, complemented
32#16839836—21no—
33#16839836—21no—
34#16839833—21no—
35#16839833—21no—
36#16839831—21no—
37#16839831—21no—
38#16839830—21no—
39#16839830—21no—
40#16839785C2211yescharacteristic
41#16839785C2211yescharacteristic
42C2×#14519705C2211yescharacteristic
43C2×#14519705C2211yescharacteristic
44C2×#14519704C2211yescharacteristic
45C2×#14519704C2211yescharacteristic
46C2×#14519703C2211yescharacteristic
47C2×#14519703C2211yescharacteristic
48#16839730C2211yescharacteristic
49#16839729C2211yescharacteristic
50#16839728C2211yescharacteristic
51C2×#14519687C2211yescharacteristic
52C2×#14519687C2211yescharacteristic
53C42×Dic61C2211yescharacteristic
54#16839527C2211yescharacteristic
55#16839526C2211yescharacteristic
56#16839526C2211yescharacteristic
57#16839517C2211yescharacteristic
58#16839516C2211yescharacteristic
59#16839516C2211yescharacteristic
60C2×#135×C61C2211yescharacteristic
61C2×#131×C61C2211yescharacteristic
62C2×#104×C61C2211yescharacteristic
63C2×#104×C61C2211yescharacteristic
64C61×#408C2211yescharacteristic
65C61×#341C2211yescharacteristic
66C61×#336C2211yescharacteristic
67C2×#11758222C2311yescharacteristic
68C2×#11758222C2311yescharacteristic
69#14519799—41no—
70#14519799—41no—
71#14519797—41no—
72#14519797—41no—
73#14519797—41no—
74#14519797—41no—
75C2×Dic244C2×C411yescharacteristic
76C2×#11758202C2×C411yescharacteristic
77C2×#11758202C2×C411yescharacteristic
78C2×#11758190C2×C411yescharacteristic
79C2×#11758190C2×C411yescharacteristic
80C2×#11758200C2×C411yescharacteristic
81C2×#11758200C2×C411yescharacteristic
82C2×#11758201C2×C411yescharacteristic
83C2×#11758201C2×C411yescharacteristic
84C2×D488C2×C411yescharacteristic
85C2×#11758199C2×C411yescharacteristic
86C2×#11758199C2×C411yescharacteristic
87#14519785—41no—
88#14519785—41no—
89#14519784—41no—
90#14519784—41no—
91#14519783—41no—
92#14519783—41no—
93C2×#11758194—21no—
94C2×#11758194C2311yescharacteristic
95C2×#11758194C2311yescharacteristic
96C2×#11758189—21no—
97C2×#11758189—21no—
98C22×#92418—21no—
99C22×#92418C2311yescharacteristic
100C22×#92418C2311yescharacteristic
101C2×C8×D61—21no—
102C2×C8×D61—21no—
103#14519775C2×C411yescharacteristic
104#14519775C2×C411yescharacteristic
105#14519773C2×C411yescharacteristic
106#14519773C2×C411yescharacteristic
107#14519766C2×C411yescharacteristic
108#14519766C2×C411yescharacteristic
109#14519764C2×C411yescharacteristic
110#14519764C2×C411yescharacteristic
111#14519749—21no—
112#14519749—21no—
113#14519749—21no—
114#14519749—21no—
115C4×C22⋊D61—21no—
116C4×C22⋊D61—21no—
117C4×C22⋊D61—21no—
118C4×C22⋊D61—21no—
119C2×C4×Dic61—21no—
120C2×C4×Dic61—21no—
121C2×C4×Dic61C2311yescharacteristic
122C2×C4×Dic61C2311yescharacteristic
123#14519706—21no—
124#14519706—21no—
125#14519706—21no—
126#14519706—21no—
127#14519705—41no—
128#14519705—41no—
129#14519704—41no—
130#14519704—41no—
131#14519703—41no—
132#14519703—41no—
133C22⋊#92418—21no—
134C22⋊#92418—21no—
135#14519689—21no—
136#14519689—21no—
137#14519689—21no—
138#14519689—21no—
139#14519687C2×C411yescharacteristic
140#14519687C2×C411yescharacteristic
141#14519687C2×C411yescharacteristic
142#14519687C2×C411yescharacteristic
143#14519687D411yescharacteristic
144#14519687D411yescharacteristic
145#14519687D411yescharacteristic
146#14519687D411yescharacteristic
147C2×#41×C61C2311yescharacteristic
148C2×#41×C61C2311yescharacteristic
149#135×C61—41no—
150#135×C61—41no—
151C2×Q16×C61C2×C411yescharacteristic
152C2×SD16×C61C2×C411yescharacteristic
153C2×SD16×C61C2×C411yescharacteristic
154C2×D8×C61C2×C411yescharacteristic
155#131×C61—41no—
156#131×C61—41no—
157C2×M16×C61—21no—
158C2×M16×C61C2311yescharacteristic
159C2×M16×C61C2311yescharacteristic
160C22×C8×C61—21no—
161C22×C8×C61C2311yescharacteristic
162C22×C8×C61C2311yescharacteristic
163C2×C42×C61C2311yescharacteristic
164#104×C61—41no—
165#104×C61—41no—
166C22⋊C8×C61—21no—
167C22⋊C8×C61—21no—
168#41×C61—21no—
169#41×C61—21no—
170#41×C61—21no—
171#41×C61—21no—
172#41×C61—21no—
173#41×C61—21no—
174#41×C61—21no—
175#41×C61—21no—
176C2×Q8×C61C22×C411yescharacteristic
177C2×Q8×C61C22×C411yescharacteristic
178C2×D4×C61—21no—
179C2×D4×C61—21no—
180C2×D4×C61C22×C411yescharacteristic
181C2×D4×C61C22×C411yescharacteristic
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61C2411yescharacteristic
186C2×C22⋊D61—21no—
187C2×C22⋊D61—21no—
188C2×C22⋊D61—21no—
189C2×C22⋊D61—21no—
190C2×C22⋊D61—21no—
191C2×C22⋊D61—21no—
192C22×Dic61—21no—
193C22×Dic61#4111yescharacteristic
194C22×Dic61#4111yescharacteristic
195#11758222—21no—
196#11758222—21no—
197#11758222—21no—
198#11758222—21no—
199#11758222—21no—
200#11758222—21no—
201#11758222—21no—
202#11758222—21no—
203C2×D244C22×C411yescharacteristic
204C2×D244C22×C411yescharacteristic
205C2×C4×D61—21no—
206C2×C4×D61—21no—
207C2×Dic122C22×C411yescharacteristic
208C2×Dic122C22×C411yescharacteristic
209Q16×C61—41no—
210SD16×C61—41no—
211SD16×C61—41no—
212D8×C61—41no—
213M16×C61—21no—
214M16×C61—21no—
215M16×C61—21no—
216M16×C61—21no—
217M16×C61—42no—
218C2×C8×C61—21no—
219C2×C8×C61—21no—
220C2×C8×C61—21no—
221C2×C8×C61—21no—
222C2×C8×C61—21no—
223C2×C8×C61—21no—
224C2×C8×C61—42no—
225C2×C8×C61C22×C411yescharacteristic
226C2×C8×C61C22×C411yescharacteristic
227C2×C8×C61C2×D411yescharacteristic
228C2×C8×C61C2×D411yescharacteristic
229C42×C61—21no—
230C42×C61—21no—
231C22⋊Dic61—21no—
232C22⋊Dic61—21no—
233C22⋊Dic61—21no—
234C22⋊Dic61—21no—
235#11758202—41no—
236#11758202—41no—
237#11758201—41no—
238#11758201—41no—
239#11758200—41no—
240#11758200—41no—
241#11758199—41no—
242#11758199—41no—
243#11758198—21no—
244#11758198—21no—
245#11758198—21no—
246#11758198—21no—
247#11758196—21no—
248#11758196—21no—
249#11758196—21no—
250#11758196—21no—
251C4×Dic61—21no—
252C4×Dic61—21no—
253C4×Dic61—42no—
254C4×Dic61—42no—
255C4×Dic61C22×C411yescharacteristic
256C4×Dic61C22×C411yescharacteristic
257C4×Dic61C2×D411yescharacteristic
258C4×Dic61C2×D411yescharacteristic
259#11758194—21no—
260#11758194—21no—
261#11758194—21no—
262#11758194—21no—
263#11758194—42no—
264C2×#92418—21no—
265C2×#92418—21no—
266C2×#92418—21no—
267C2×#92418—21no—
268C2×#92418—21no—
269C2×#92418—21no—
270C2×#92418—42no—
271C2×#92418C22×C411yescharacteristic
272C2×#92418C22×C411yescharacteristic
273C2×#92418C2×D411yescharacteristic
274C2×#92418C2×D411yescharacteristic
275Dic244—41no—
276D488—41no—
277#11758190—41no—
278#11758190—41no—
279#11758189—42no—
280#11758189—42no—
281C8×D61—42no—
282C8×D61—42no—
283C23×C61—21no—
284C23×C61—21no—
285C23×C61C2×#4111yescharacteristic
286C22×D61—21no—
287C22×D61—21no—
288Q8×C61—21no—
289Q8×C61—21no—
290Q8×C61—21no—
291Q8×C61—21no—
292D4×C61—21no—
293D4×C61—21no—
294D4×C61—21no—
295D4×C61—21no—
296D4×C61—41no—
297D4×C61—41no—
298D4×C61—41no—
299D4×C61—41no—
300C2×C4×C61—22no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—41no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61C23×C411yescharacteristic
310C2×C4×C61C22×D411yescharacteristic
311C2×C4×C61H(5,𝔽2)11yescharacteristic
312C2×C4×C61H(5,𝔽2)11yescharacteristic
313C2×C4×C61H(5,𝔽2)11yescharacteristic
314C2×C4×C61H(5,𝔽2)11yescharacteristic
315C22⋊D61—41no—
316C22⋊D61—41no—
317C22⋊D61—41no—
318C22⋊D61—41no—
319C22⋊D61—81no—
320C22⋊D61—81no—
321C22⋊D61—81no—
322C22⋊D61—81no—
323C2×Dic61—22no—
324C2×Dic61—21no—
325C2×Dic61—21no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330C2×Dic61C4×D411yescharacteristic
331C2×Dic61C4×D411yescharacteristic
332C2×Dic61C4×D411yescharacteristic
333C2×Dic61C4×D411yescharacteristic
334D244—21no—
335D244—21no—
336D244—21no—
337D244—21no—
338C4×D61—41no—
339C4×D61—41no—
340C4×D61—41no—
341C4×D61—41no—
342Dic122—21no—
343Dic122—21no—
344Dic122—21no—
345Dic122—21no—
346C8×C61—21no—
347C8×C61—21no—
348C8×C61—21no—
349C8×C61—21no—
350C8×C61—41no—
351C8×C61—41no—
352#92418—21no—
353#92418—21no—
354#92418—21no—
355#92418—21no—
356#92418—41no—
357#92418—41no—
358#22283—611nomaximal, Sylow
359C22×C61—21no—
360C22×C61—21no—
361C22×C61—41no—
362C22×C61—41no—
363C22×C61—41no—
364C22×C61—41no—
365C22×C61—41no—
366C22×C61—41no—
367C22×C61C2×C4×D411yescharacteristic
368C22×C61#54011yescharacteristic
369C22×C61#54011yescharacteristic
370C2×D61—41no—
371C2×D61—41no—
372C2×D61—41no—
373C2×D61—41no—
374C2×D61—41no—
375C2×D61—41no—
376C4×C61—42no—
377C4×C61—41no—
378C4×C61—41no—
379C4×C61#51811yescharacteristic
380C4×C61#51811yescharacteristic
381C4×C61#53511yescharacteristic
382C4×C61#53511yescharacteristic
383Dic61—21no—
384Dic61—21no—
385Dic61—21no—
386Dic61—21no—
387Dic61—42no—
388Dic61—41no—
389Dic61—41no—
390#3150—611no—
391#2932—611no—
392#2932—611no—
393#1962—611no—
394#1962—611no—
395#1876—611no—
396#1876—611no—
397#1876—611no—
398#1876—611no—
399#1876—611no—
400#1876—611no—
401#1876—611no—
402#1876D6111yescharacteristic, complemented
403#1838—611no—
404#1745—611no—
405C2×C61—21no—
406C2×C61—21no—
407C2×C61—81no—
408C2×C61—81no—
409C2×C61#232811yescharacteristic
410C2×C61#295611yescharacteristic
411C2×C61#295611yescharacteristic
412D61—81no—
413D61—81no—
414C2×#135—611no—
415C2×#135—611no—
416C2×#135—611no—
417C2×#135C2×D6111yescharacteristic
418C2×#131—611no—
419C2×#131—611no—
420C2×#131—611no—
421C2×#131C2×D6111yescharacteristic
422#532—611no—
423#532—611no—
424#497—611no—
425#497—611no—
426#497—611no—
427#497—611no—
428#496—611no—
429#496—611no—
430#496—611no—
431#496—611no—
432#435—1221no—
433#435—1221no—
434#435—1221no—
435#435—1221no—
436#435—1221no—
437#435—1221no—
438#435—1221no—
439#435—1221no—
440#423—611no—
441#423—611no—
442C2×#104—611no—
443C2×#104—611no—
444C2×#104—611no—
445C2×#104—611no—
446C2×#104—611no—
447C2×#104—611no—
448C2×#104C2×D6111yescharacteristic
449C2×#104C2×D6111yescharacteristic
450#408—611no—
451#408—611no—
452#408—611no—
453#408C2×D6111yescharacteristic
454C2×#97—611no—
455C2×#97—611no—
456C43—611no—
457#341—611no—
458#341—611no—
459#341—611no—
460#341C2×D6111yescharacteristic
461#336—611no—
462#336—611no—
463#336—611no—
464#336C2×D6111yescharacteristic
465C61#2228311yescharacteristic, complemented, Sylow
466C2×#41—611no—
467C2×#41—611no—
468C2×#41C22×D6111yescharacteristic
469C2×#41C22×D6111yescharacteristic
470#135—41no—
471#135—41no—
472#135—2441no—
473#135—2441no—
474#135—2441no—
475#135—2441no—
476#135—2441no—
477#135—2441no—
478C2×Q16—611no—
479C2×Q16—611no—
480C2×Q16—611no—
481C2×Q16C4×D6111yescharacteristic
482C2×SD16—611no—
483C2×SD16—611no—
484C2×SD16—611no—
485C2×SD16—611no—
486C2×SD16—611no—
487C2×SD16—611no—
488C2×SD16C4×D6111yescharacteristic
489C2×SD16C4×D6111yescharacteristic
490C2×D8—611no—
491C2×D8—611no—
492C2×D8—611no—
493C2×D8C4×D6111yescharacteristic
494#131—41no—
495#131—41no—
496#131—2441no—
497#131—2441no—
498#131—2441no—
499#131—2441no—
500#131—2441no—
501#131—2441no—
502C2×M16—21no—
503C2×M16—611no—
504C2×M16—611no—
505C2×M16—1221no—
506C2×M16—1221no—
507C2×M16—1221no—
508C2×M16C22×D6111yescharacteristic
509C2×M16C22×D6111yescharacteristic
510C22×C8—21no—
511C22×C8—611no—
512C22×C8—611no—
513C22×C8—1221no—
514C22×C8—1221no—
515C22×C8—1221no—
516C22×C8C22×D6111yescharacteristic
517C22×C8C22×D6111yescharacteristic
518C4⋊Q8—611no—
519C4⋊Q8—611no—
520#127—611no—
521#127—611no—
522#124—611no—
523#124—611no—
524#124—611no—
525#124—611no—
526#121—1221no—
527#121—1221no—
528#121—1221no—
529#121—1221no—
530C4×D4—1221no—
531C4×D4—1221no—
532C4×D4—1221no—
533C4×D4—1221no—
534C2×C42—611no—
535C2×C42—611no—
536C2×C42—1221no—
537C2×C42—1221no—
538C2×C42C22×D6111yescharacteristic
539C4⋊C8—1221no—
540C4⋊C8—1221no—
541C4⋊C8—1221no—
542C4⋊C8—1221no—
543#104—41no—
544#104—41no—
545#104—2441no—
546#104—2441no—
547#104—2441no—
548#104—2441no—
549#104—2441no—
550#104—2441no—
551C22⋊C8—21no—
552C22⋊C8—21no—
553C22⋊C8—1221no—
554C22⋊C8—1221no—
555C22⋊C8—1221no—
556C22⋊C8—1221no—
557C22⋊C8—1221no—
558C22⋊C8—1221no—
559#97—611no—
560#97—611no—
561#97—611no—
562#97—611no—
563#97—611no—
564#97—611no—
565#97—611no—
566#97—611no—
567#41—21no—
568#41—21no—
569#41—21no—
570#41—21no—
571#41—21no—
572#41—21no—
573#41—21no—
574#41—21no—
575#41—1221no—
576#41—1221no—
577#41—1221no—
578#41—1221no—
579#41—1221no—
580#41—1221no—
581#41—1221no—
582#41—1221no—
583C2×Q8—611no—
584C2×Q8—611no—
585C2×Q8C2×C4×D6111yescharacteristic
586C2×Q8C2×C4×D6111yescharacteristic
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—611no—
590C2×D4—611no—
591C2×D4—1221no—
592C2×D4—1221no—
593C2×D4—1221no—
594C2×D4—1221no—
595C2×D4—1221no—
596C2×D4—1221no—
597C2×D4C2×C4×D6111yescharacteristic
598C2×D4C2×C4×D6111yescharacteristic
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—611no—
603C22×C4—611no—
604C22×C4—1221no—
605C22×C4—1221no—
606C22×C4—1221no—
607C22×C4C23×D6111yescharacteristic
608Q16—41no—
609Q16—2441no—
610Q16—2441no—
611Q16—2441no—
612SD16—41no—
613SD16—41no—
614SD16—2441no—
615SD16—2441no—
616SD16—2441no—
617SD16—2441no—
618SD16—2441no—
619SD16—2441no—
620D8—41no—
621D8—2441no—
622D8—2441no—
623D8—2441no—
624M16—21no—
625M16—21no—
626M16—21no—
627M16—21no—
628M16—42no—
629M16—1221no—
630M16—1221no—
631M16—1221no—
632M16—1221no—
633M16—2442no—
634M16—2442no—
635M16—2442no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—42no—
643C2×C8—611no—
644C2×C8—611no—
645C2×C8—611no—
646C2×C8—611no—
647C2×C8—1221no—
648C2×C8—1221no—
649C2×C8—1221no—
650C2×C8—1221no—
651C2×C8—1221no—
652C2×C8—1221no—
653C2×C8—2442no—
654C2×C8—2442no—
655C2×C8—2442no—
656C2×C8C2×C4×D6111yescharacteristic
657C2×C8C2×C4×D6111yescharacteristic
658C2×C8D4×D6111yescharacteristic
659C2×C8D4×D6111yescharacteristic
660C4⋊C4—1221no—
661C4⋊C4—1221no—
662C4⋊C4—1221no—
663C4⋊C4—1221no—
664C22⋊C4—1221no—
665C22⋊C4—1221no—
666C22⋊C4—1221no—
667C22⋊C4—1221no—
668C22⋊C4—1221no—
669C22⋊C4—1221no—
670C22⋊C4—1221no—
671C22⋊C4—1221no—
672C42—21no—
673C42—21no—
674C42—611no—
675C42—611no—
676C42—611no—
677C42—611no—
678C42—1221no—
679C42—1221no—
680C42—2442no—
681C42—2442no—
682C23—21no—
683C23—21no—
684C23—1221no—
685C23—1221no—
686C23#41×D6111yescharacteristic
687Q8—21no—
688Q8—21no—
689Q8—21no—
690Q8—21no—
691Q8—1221no—
692Q8—1221no—
693Q8—1221no—
694Q8—1221no—
695D4—21no—
696D4—21no—
697D4—21no—
698D4—21no—
699D4—41no—
700D4—41no—
701D4—41no—
702D4—41no—
703D4—1221no—
704D4—1221no—
705D4—1221no—
706D4—1221no—
707D4—4881no—
708D4—4881no—
709D4—4881no—
710D4—4881no—
711D4—2441no—
712D4—2441no—
713D4—2441no—
714D4—2441no—
715C2×C4—22no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—611no—
725C2×C4—611no—
726C2×C4—611no—
727C2×C4—611no—
728C2×C4—1222no—
729C2×C4—1221no—
730C2×C4—1221no—
731C2×C4—2441no—
732C2×C4—2441no—
733C2×C4—2441no—
734C2×C4—2441no—
735C2×C4—2441no—
736C2×C4—2441no—
737C2×C4—2441no—
738C2×C4—2441no—
739C2×C4C22×C4×D6111yescharacteristic
740C2×C4C2×D4×D6111yescharacteristic
741C2×C4#1451982211yescharacteristic
742C2×C4#1451982211yescharacteristic
743C2×C4#1451982211yescharacteristic
744C2×C4#1451982311yescharacteristic
745C8—21no—
746C8—21no—
747C8—21no—
748C8—21no—
749C8—41no—
750C8—41no—
751C8—1221no—
752C8—1221no—
753C8—1221no—
754C8—1221no—
755C8—2441no—
756C8—2441no—
757C22—21no—
758C22—21no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—2441no—
766C22—2441no—
767C22—2441no—
768C22—2441no—
769C22—2441no—
770C22—2441no—
771C22C4×D4×D6111yescharacteristic
772C22#1684036211yescharacteristic
773C22#1684036411yescharacteristic
774C4—42no—
775C4—41no—
776C4—41no—
777C4—1221no—
778C4—1221no—
779C4—1221no—
780C4—1221no—
781C4—2442no—
782C4—2441no—
783C4—2441no—
784C4#1684023411yescharacteristic
785C4#1684023511yescharacteristic
786C4#1684032711yescharacteristic
787C4#1684032811yescharacteristic
788C2—21no—
789C2—21no—
790C2—81no—
791C2—81no—
792C2—4881no—
793C2—4881no—
794C2#2144854011yescharacteristic
795C2#2145472411yescharacteristic
796C2#2145472711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1876C2
socleC22×C61C2×C4×D4
prime radical#21456262C2
cosocleC22×C4×C61C24
hypercenter#1876D61
hypocenterC61#22283
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1876

Complements

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

NH ≅ G/Ntype
2. #21454535C2semidirect
3. #21454534C2semidirect
4. #21446645C2semidirect
5. #21446645C2semidirect
6. #21446149C2semidirect
7. #21446148C2semidirect
8. #21446147C2semidirect
9. #21446146C2semidirect
10. #21446145C2semidirect
11. #21446144C2semidirect
12. #21446143C2semidirect
13. #21445958C2semidirect
14. #21445566C2semidirect
15. C61×#1876C2semidirect
24. #16840155C4semidirect
25. #16840155C4semidirect
26. #16840153C4semidirect
27. #16840153C4semidirect
28. #16840150C4semidirect
29. #16840150C4semidirect
30. #16840148C4semidirect
31. #16840148C4semidirect
402. #1876D61semidirect
465. C61#22283semidirect

Maximal subgroups

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

subgroupindex
#214562622
#214545352
#214545342
#214466452
#214461492
#214461482
#214461472
#214461462
#214461452
#214461442
#214461432
#214459582
#214455662
C61×#18762
#2228361