Finite Group Databasebeta

← #29689155

Subgroups — #29689155

Order 15616.

1362 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459148C211yesmaximal, characteristic
2#21454262C211yesmaximal, characteristic, complemented
3#21448305C211yesmaximal, characteristic, complemented
4#21446264C212yesmaximal, complemented
5#21446259C212yesmaximal, complemented
6#21446118C212yesmaximal, complemented
7#21446118C212yesmaximal, complemented
8#21445919C211yesmaximal, characteristic, complemented
9#21445916C211yesmaximal, characteristic, complemented
10#21445763C211yesmaximal, characteristic, complemented
11C61×#1789C211yesmaximal, characteristic, complemented
12C22×#11758222C2211yescharacteristic
13C2×M16×D61C2212yescomplemented
14#16840340C412yescomplemented
15#16840340C412yescomplemented
16#16840336C412yescomplemented
17#16840333—21no—
18#16840329C412yescomplemented
19#16840326—21no—
20#16840321—21no—
21#16840321—21no—
22#16840308—22no—
23#16840273—22no—
24#16840269C2212yes—
25#16840269C2212yes—
26C2×#14519736C2211yescharacteristic
27C2×#14519734C2211yescharacteristic, complemented
28C2×C42×D61C2211yescharacteristic, complemented
29C2×#14519704C2212yes—
30C2×#14519704C2212yes—
31#16839727—22no—
32#16839727—22no—
33#16839726C2211yescharacteristic
34#16839725C2212yescomplemented
35#16839666—21no—
36#16839662—21no—
37#16839640—21no—
38#16839638—21no—
39C4×#11758198C2211yescharacteristic, complemented
40C4×#11758198C2211yescharacteristic, complemented
41C4×C22⋊Dic61C2211yescharacteristic
42#16839523C2212yescomplemented
43#16839523C2212yescomplemented
44#16839522C2212yescomplemented
45#16839522C2212yescomplemented
46C22×#41×C61C2211yescharacteristic
47C2×#104×C61C2212yes—
48C2×#104×C61C2212yes—
49C61×#407C2211yescharacteristic
50C4×C22⋊C4×C61C2211yescharacteristic
51C2×#11758222—42no—
52C2×#11758222—42no—
53C2×#11758222C2×C412yes—
54C2×#11758222C2×C412yes—
55C2×#11758222D412yes—
56C2×#11758222D412yes—
57C22×Dic122D411yescharacteristic
58C22×D244D411yescharacteristic
59C22×C22⋊D61D411yescharacteristic
60C22×C22⋊D61D411yescharacteristic
61C22×C4×D61—21no—
62C22×C4×D61C2311yescharacteristic
63C22×C4×D61C2311yescharacteristic
64C2×#11758194C2312yes—
65C2×#11758189—22no—
66M16×D61—42no—
67M16×D61—42no—
68C2×C8×D61—22no—
69#14519775—22no—
70#14519773—22no—
71#14519766—22no—
72#14519764—22no—
73#14519760—22no—
74#14519760—22no—
75#14519758—22no—
76#14519758—22no—
77#14519756—22no—
78#14519756—22no—
79#14519753C2×C412yes—
80#14519753C2×C412yes—
81#14519753C2×C412yescomplemented
82#14519753C2×C412yescomplemented
83#14519751—22no—
84#14519751—22no—
85#14519749—22no—
86#14519749—22no—
87#14519749—22no—
88#14519749—22no—
89#14519748C2×C412yes—
90#14519748C2×C412yes—
91#14519748C2×C412yescomplemented
92#14519748C2×C412yescomplemented
93#14519746—22no—
94#14519746—22no—
95#14519745—22no—
96#14519745—22no—
97C4×C22⋊D61—22no—
98C4×C22⋊D61—22no—
99C4×C22⋊D61—22no—
100C4×C22⋊D61—22no—
101#14519736—21no—
102#14519736—21no—
103#14519736C2×C412yescomplemented
104#14519736C2312yes—
105#14519734—42no—
106C2×C4⋊Dic61C2×C411yescharacteristic, complemented
107C2×C4⋊Dic61C2×C411yescharacteristic, complemented
108C2×#11758196—21no—
109C2×C22⋊Dic61—21no—
110C2×C22⋊Dic61—21no—
111C2×#11758198—21no—
112C2×#11758198—21no—
113C2×#11758198—21no—
114C2×C4×Dic61—21no—
115C2×C4×Dic61—21no—
116C2×C4×Dic61C2311yescharacteristic
117C2×C4×Dic61C2311yescharacteristic
118C42×D61—42no—
119#14519704—42no—
120#14519704—42no—
121C22⋊#92418—21no—
122C22⋊#92418—21no—
123#14519689—24no—
124#14519684—21no—
125#14519684—21no—
126#14519684—21no—
127C2×#41×C61—21no—
128C2×#41×C61—21no—
129C2×#41×C61—42no—
130C2×#41×C61—42no—
131C2×#41×C61C2×C412yescomplemented
132C2×#41×C61C2312yes—
133C22×Q8×C61C2×C411yescharacteristic, complemented
134C22×D4×C61—21no—
135C22×D4×C61C2×C411yescharacteristic, complemented
136C23×C4×C61—21no—
137C23×C4×C61C2311yescharacteristic
138C2×M16×C61C2312yes—
139C2×C22⋊C4×C61—21no—
140C2×C42×C61C2311yescharacteristic
141C2×C42×C61C2311yescharacteristic
142#104×C61—42no—
143#104×C61—42no—
144C22⋊C8×C61—21no—
145C22⋊C8×C61—21no—
146#95×C61—21no—
147C24×C61—21no—
148C24×C61C2×D411yescharacteristic
149C23×D61C2×D411yescharacteristic
150C23×D61C2×D411yescharacteristic
151#41×C61—22no—
152#41×C61—22no—
153#41×C61—22no—
154#41×C61—22no—
155#41×C61—42no—
156#41×C61—42no—
157#41×C61—42no—
158#41×C61—42no—
159#41×C61—44no—
160C2×Q8×C61—21no—
161C2×Q8×C61—42no—
162C2×Q8×C61C22×C412yes—
163C2×D4×C61—22no—
164C2×D4×C61—22no—
165C2×D4×C61—21no—
166C2×D4×C61—42no—
167C2×D4×C61—42no—
168C2×D4×C61—42no—
169C2×D4×C61C22×C412yes—
170C22×C4×C61—22no—
171C22×C4×C61—22no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—22no—
175C22×C4×C61—22no—
176C22×C4×C61—21no—
177C22×C4×C61—44no—
178C22×C4×C61C22×C411yescharacteristic
179C22×C4×C61C22×C411yescharacteristic
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61C2×D411yescharacteristic
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61C2411yescharacteristic
184C2×C22⋊D61—22no—
185C2×C22⋊D61—22no—
186C2×C22⋊D61—22no—
187C2×C22⋊D61—22no—
188C2×C22⋊D61—41no—
189C2×C22⋊D61—41no—
190C2×C22⋊D61—41no—
191C2×C22⋊D61—41no—
192C2×C22⋊D61C22⋊C412yes—
193C2×C22⋊D61C22⋊C412yes—
194C2×C22⋊D61C22⋊C412yes—
195C2×C22⋊D61C22⋊C412yes—
196C22×Dic61—21no—
197C22×Dic61—21no—
198C22×Dic61—21no—
199C22×Dic61—21no—
200C22×Dic61C2×D411yescharacteristic
201C22×Dic61C2×D411yescharacteristic
202#11758222—44no—
203#11758222—44no—
204#11758222—42no—
205#11758222—42no—
206#11758222—42no—
207#11758222—42no—
208C2×D244—41no—
209C2×D244—41no—
210C2×D244C22⋊C412yes—
211C2×D244C22⋊C412yes—
212C2×C4×D61—22no—
213C2×C4×D61—22no—
214C2×C4×D61—22no—
215C2×C4×D61—22no—
216C2×C4×D61—42no—
217C2×C4×D61—42no—
218C2×C4×D61—42no—
219C2×C4×D61C22×C412yes—
220C2×C4×D61C22×C412yes—
221C2×C4×D61C2×D412yes—
222C2×C4×D61C2×D412yes—
223C2×Dic122—41no—
224C2×Dic122—41no—
225C2×Dic122C22⋊C412yes—
226C2×Dic122C22⋊C412yes—
227M16×C61—22no—
228M16×C61—22no—
229C2×C8×C61—22no—
230C22⋊C4×C61—42no—
231C42×C61—22no—
232C42×C61—22no—
233C22⋊Dic61—22no—
234C22⋊Dic61—22no—
235C22⋊Dic61—22no—
236C22⋊Dic61—22no—
237C22⋊Dic61—22no—
238C22⋊Dic61—22no—
239C22⋊Dic61—42no—
240#11758198—22no—
241#11758198—22no—
242#11758198—22no—
243#11758198—22no—
244#11758198—42no—
245#11758198—42no—
246#11758198—42no—
247C4⋊Dic61—21no—
248C4⋊Dic61—21no—
249C4⋊Dic61C22×C412yes—
250C4⋊Dic61C22×C412yes—
251#11758196—22no—
252#11758196—22no—
253#11758196—22no—
254#11758196—22no—
255#11758196—42no—
256C4×Dic61—22no—
257C4×Dic61—22no—
258C4×Dic61—22no—
259C4×Dic61—22no—
260C4×Dic61—42no—
261#11758194—22no—
262#11758194—22no—
263C2×#92418—22no—
264#11758189—44no—
265C8×D61—44no—
266C23×C61—21no—
267C23×C61—21no—
268C23×C61—22no—
269C23×C61—41no—
270C23×C61—41no—
271C23×C61—42no—
272C23×C61—81no—
273C23×C61—81no—
274C23×C61C2×C22⋊C411yescharacteristic
275C23×C61C2×C22⋊C411yescharacteristic
276C23×C61C22×D411yescharacteristic
277C22×D61—21no—
278C22×D61—21no—
279C22×D61—21no—
280C22×D61—21no—
281C22×D61—41no—
282C22×D61—41no—
283C22×D61—41no—
284C22×D61—41no—
285C22×D61C2×C22⋊C412yes—
286C22×D61C2×C22⋊C412yes—
287Q8×C61—22no—
288Q8×C61—22no—
289Q8×C61—42no—
290D4×C61—22no—
291D4×C61—22no—
292D4×C61—42no—
293D4×C61—44no—
294D4×C61—42no—
295D4×C61—42no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—44no—
305C2×C4×C61—41no—
306C2×C4×C61—42no—
307C2×C4×C61—41no—
308C2×C4×C61—42no—
309C2×C4×C61—42no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61C2×C22⋊C411yescharacteristic
314C2×C4×C61C2×C22⋊C411yescharacteristic
315C2×C4×C61C23×C411yescharacteristic
316C2×C4×C61C22×D411yescharacteristic
317C2×C4×C61H(5,𝔽2)12yes—
318C2×C4×C61H(5,𝔽2)12yes—
319C22⋊D61—42no—
320C22⋊D61—42no—
321C22⋊D61—42no—
322C22⋊D61—42no—
323C22⋊D61—82no—
324C22⋊D61—82no—
325C22⋊D61—82no—
326C22⋊D61—82no—
327C2×Dic61—21no—
328C2×Dic61—21no—
329C2×Dic61—21no—
330C2×Dic61—21no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61—41no—
339C2×Dic61—81no—
340C2×Dic61—81no—
341C2×Dic61C2×C22⋊C412yes—
342C2×Dic61C2×C22⋊C412yes—
343D244—42no—
344D244—42no—
345C4×D61—24no—
346C4×D61—24no—
347C4×D61—22no—
348C4×D61—22no—
349C4×D61—22no—
350C4×D61—22no—
351C4×D61—48no—
352Dic122—42no—
353Dic122—42no—
354C8×C61—42no—
355#92418—42no—
356#21775—611nomaximal, Sylow
357C22×C61—21no—
358C22×C61—21no—
359C22×C61—21no—
360C22×C61—21no—
361C22×C61—21no—
362C22×C61—21no—
363C22×C61—21no—
364C22×C61—21no—
365C22×C61—42no—
366C22×C61—42no—
367C22×C61—42no—
368C22×C61—81no—
369C22×C61—81no—
370C22×C61—84no—
371C22×C61C22×C22⋊C411yescharacteristic
372C22×C61#53411yescharacteristic
373C22×C61#53411yescharacteristic
374C2×D61—22no—
375C2×D61—22no—
376C2×D61—22no—
377C2×D61—22no—
378C2×D61—22no—
379C2×D61—22no—
380C2×D61—42no—
381C2×D61—42no—
382C2×D61—81no—
383C2×D61—81no—
384C4×C61—21no—
385C4×C61—21no—
386C4×C61—42no—
387C4×C61—42no—
388C4×C61—81no—
389C4×C61#51812yes—
390C4×C61#53412yes—
391Dic61—22no—
392Dic61—22no—
393Dic61—42no—
394Dic61—42no—
395Dic61—42no—
396Dic61—81no—
397#3449—611no—
398#2879—611no—
399#2297—611no—
400#1897—612no—
401#1896—612no—
402#1871—612no—
403#1871—612no—
404#1826—611no—
405#1826—611no—
406#1789—611no—
407#1789D6111yescharacteristic, complemented
408C2×C61—21no—
409C2×C61—21no—
410C2×C61—41no—
411C2×C61—41no—
412C2×C61—82no—
413C2×C61#230811yescharacteristic
414C2×C61#290111yescharacteristic
415C2×C61#290111yescharacteristic
416D61—42no—
417D61—42no—
418C22×#41—611no—
419C22×#41C2×D6111yescharacteristic
420C22×M16—612no—
421#537—612no—
422#537—612no—
423#536—612no—
424#536—1221no—
425#535—612no—
426#535—1221no—
427#534—1221no—
428#534—1221no—
429#532—1222no—
430#525—612no—
431#525—612no—
432#525—1222no—
433C2×#117—611no—
434C2×#117—611no—
435C22×C42—611no—
436C2×#104—612no—
437C2×#104—612no—
438C2×#104C2×D6112yes—
439C2×#104C2×D6112yes—
440#408—1222no—
441#408—1222no—
442#407—611no—
443#407—612no—
444#407C2×D6111yescharacteristic
445#391—1221no—
446#390—1221no—
447#386—1221no—
448#386—1221no—
449C4×C22⋊C4—611no—
450C4×C22⋊C4—611no—
451C4×C22⋊C4—611no—
452C4×C22⋊C4C2×D6111yescharacteristic
453#339—612no—
454#339—612no—
455#339—612no—
456#339—612no—
457C61#2177511yescharacteristic, complemented, Sylow
458C2×#41—21no—
459C2×#41—21no—
460C2×#41—42no—
461C2×#41—42no—
462C2×#41—612no—
463C2×#41—612no—
464C2×#41—612no—
465C2×#41—612no—
466C2×#41—2442no—
467C2×#41—2442no—
468C2×#41C4×D6112yescomplemented
469C2×#41C22×D6112yes—
470C22×Q8—611no—
471C22×Q8C4×D6111yescharacteristic, complemented
472C22×D4—21no—
473C22×D4—611no—
474C22×D4—611no—
475C22×D4—611no—
476C22×D4C4×D6111yescharacteristic, complemented
477C23×C4—21no—
478C23×C4—611no—
479C23×C4—611no—
480C23×C4—1221no—
481C23×C4C22×D6111yescharacteristic
482C2×M16—612no—
483C2×M16—1222no—
484C2×M16—2442no—
485C2×M16—2442no—
486C2×M16C22×D6112yes—
487C22×C8—1222no—
488C4⋊Q8—1222no—
489#127—1222no—
490#124—1222no—
491#124—1222no—
492#123—1222no—
493#123—1222no—
494#123—1222no—
495#123—1222no—
496C22⋊Q8—612no—
497C22⋊Q8—612no—
498C22⋊Q8—612no—
499C22⋊Q8—612no—
500C22⋊Q8—1222no—
501C22⋊Q8—1222no—
502#121—612no—
503#121—612no—
504#121—612no—
505#121—612no—
506#121—1222no—
507#121—1222no—
508#121—1222no—
509#121—1222no—
510#121—1222no—
511#121—1222no—
512#120—1222no—
513#120—1222no—
514#120—1222no—
515#120—1222no—
516C4×D4—1222no—
517C4×D4—1222no—
518C4×D4—1222no—
519C4×D4—1222no—
520#117—612no—
521#117—612no—
522#117—1221no—
523#117—1221no—
524#117—2442no—
525C2×C4⋊C4—611no—
526C2×C4⋊C4—611no—
527C2×C4⋊C4—1221no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—1221no—
530C2×C22⋊C4—1221no—
531C2×C22⋊C4—1221no—
532C2×C22⋊C4—1221no—
533C2×C22⋊C4—1221no—
534C2×C42—611no—
535C2×C42—611no—
536C2×C42—1221no—
537C2×C42—1221no—
538C2×C42—2442no—
539C2×C42C22×D6111yescharacteristic
540C2×C42C22×D6111yescharacteristic
541#104—42no—
542#104—42no—
543#104—2442no—
544#104—2442no—
545C22⋊C8—21no—
546C22⋊C8—21no—
547C22⋊C8—1224no—
548C22⋊C8—1221no—
549C22⋊C8—1221no—
550#95—21no—
551#95—1221no—
552#95—1221no—
553#95—1221no—
554C24—21no—
555C24—611no—
556C24—611no—
557C24D4×D6111yescharacteristic
558#41—22no—
559#41—22no—
560#41—22no—
561#41—22no—
562#41—42no—
563#41—42no—
564#41—42no—
565#41—42no—
566#41—44no—
567#41—2444no—
568#41—2444no—
569#41—2442no—
570#41—2442no—
571#41—2442no—
572#41—2442no—
573C2×Q8—21no—
574C2×Q8—42no—
575C2×Q8—612no—
576C2×Q8—612no—
577C2×Q8—2441no—
578C2×Q8—2441no—
579C2×Q8C2×C4×D6112yes—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—21no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—612no—
587C2×D4—612no—
588C2×D4—612no—
589C2×D4—612no—
590C2×D4—612no—
591C2×D4—612no—
592C2×D4—1222no—
593C2×D4—1222no—
594C2×D4—1222no—
595C2×D4—1222no—
596C2×D4—2441no—
597C2×D4—2441no—
598C2×D4—2441no—
599C2×D4—2441no—
600C2×D4—2441no—
601C2×D4—2441no—
602C2×D4C2×C4×D6112yes—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—21no—
610C22×C4—44no—
611C22×C4—611no—
612C22×C4—611no—
613C22×C4—612no—
614C22×C4—612no—
615C22×C4—612no—
616C22×C4—612no—
617C22×C4—1222no—
618C22×C4—1222no—
619C22×C4—1222no—
620C22×C4—1222no—
621C22×C4—1221no—
622C22×C4—1221no—
623C22×C4—1221no—
624C22×C4—1221no—
625C22×C4—2442no—
626C22×C4—2442no—
627C22×C4—2442no—
628C22×C4C2×C4×D6111yescharacteristic
629C22×C4C2×C4×D6111yescharacteristic
630C22×C4D4×D6111yescharacteristic
631C22×C4D4×D6111yescharacteristic
632C22×C4D4×D6111yescharacteristic
633C22×C4C23×D6111yescharacteristic
634M16—22no—
635M16—22no—
636M16—1222no—
637M16—1222no—
638M16—2444no—
639C2×C8—22no—
640C2×C8—1222no—
641C2×C8—2444no—
642C4⋊C4—612no—
643C4⋊C4—612no—
644C4⋊C4—1222no—
645C4⋊C4—1222no—
646C4⋊C4—1222no—
647C4⋊C4—1222no—
648C4⋊C4—1221no—
649C4⋊C4—1221no—
650C4⋊C4—2442no—
651C22⋊C4—42no—
652C22⋊C4—1222no—
653C22⋊C4—1222no—
654C22⋊C4—1222no—
655C22⋊C4—1222no—
656C22⋊C4—1222no—
657C22⋊C4—1222no—
658C22⋊C4—1222no—
659C22⋊C4—1222no—
660C22⋊C4—1222no—
661C22⋊C4—1222no—
662C22⋊C4—2442no—
663C22⋊C4—2442no—
664C22⋊C4—2442no—
665C22⋊C4—2442no—
666C42—22no—
667C42—22no—
668C42—1222no—
669C42—1222no—
670C42—1222no—
671C42—1222no—
672C42—2442no—
673C23—21no—
674C23—21no—
675C23—22no—
676C23—41no—
677C23—41no—
678C23—42no—
679C23—81no—
680C23—81no—
681C23—612no—
682C23—612no—
683C23—1221no—
684C23—1221no—
685C23—1221no—
686C23—1221no—
687C23—2441no—
688C23—2441no—
689C23—2441no—
690C23—2441no—
691C23C22⋊C4×D6111yescharacteristic
692C23C22⋊C4×D6111yescharacteristic
693C23C2×D4×D6111yescharacteristic
694Q8—22no—
695Q8—22no—
696Q8—42no—
697Q8—2442no—
698Q8—2442no—
699D4—22no—
700D4—22no—
701D4—42no—
702D4—44no—
703D4—42no—
704D4—42no—
705D4—4882no—
706D4—4882no—
707D4—4882no—
708D4—4882no—
709D4—2442no—
710D4—2442no—
711D4—2442no—
712D4—2442no—
713D4—2442no—
714D4—2442no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—44no—
724C2×C4—42no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—612no—
733C2×C4—612no—
734C2×C4—1221no—
735C2×C4—1221no—
736C2×C4—1221no—
737C2×C4—1221no—
738C2×C4—1224no—
739C2×C4—1224no—
740C2×C4—1222no—
741C2×C4—1222no—
742C2×C4—1222no—
743C2×C4—1222no—
744C2×C4—1222no—
745C2×C4—1222no—
746C2×C4—1222no—
747C2×C4—4881no—
748C2×C4—4881no—
749C2×C4—2448no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4—2441no—
755C2×C4C22⋊C4×D6111yescharacteristic
756C2×C4C22⋊C4×D6111yescharacteristic
757C2×C4C22×C4×D6111yescharacteristic
758C2×C4C2×D4×D6111yescharacteristic
759C2×C4#1451982212yes—
760C2×C4#1451982212yes—
761C8—42no—
762C8—2442no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—81no—
775C22—81no—
776C22—84no—
777C22—1222no—
778C22—1222no—
779C22—1222no—
780C22—1222no—
781C22—1222no—
782C22—1222no—
783C22—4881no—
784C22—4881no—
785C22—2442no—
786C22—2442no—
787C22C2×C22⋊C4×D6111yescharacteristic
788C22#1684032211yescharacteristic
789C22#1684032211yescharacteristic
790C4—21no—
791C4—21no—
792C4—42no—
793C4—42no—
794C4—81no—
795C4—1222no—
796C4—1222no—
797C4—4881no—
798C4—2442no—
799C4—2442no—
800C4—2442no—
801C4#1684023512yes—
802C4#1684032212yes—
803C2—21no—
804C2—21no—
805C2—41no—
806C2—41no—
807C2—82no—
808C2—2442no—
809C2—2442no—
810C2#2144839511yescharacteristic
811C2#2145436311yescharacteristic
812C2#2145436511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1789C2
socleC22×C61C22×C22⋊C4
prime radical#21459148C2
cosocleC22×C4×C61C24
hypercenter#1789D61
hypocenterC61#21775
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1789

Complements

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

NH ≅ G/Ntype
2. #21454262C2semidirect
3. #21448305C2semidirect
4. #21446264C2semidirect
5. #21446259C2semidirect
6. #21446118C2semidirect
7. #21446118C2semidirect
8. #21445919C2semidirect
9. #21445916C2semidirect
10. #21445763C2semidirect
11. C61×#1789C2semidirect
13. C2×M16×D61C22semidirect
14. #16840340C4semidirect
15. #16840340C4semidirect
16. #16840336C4semidirect
18. #16840329C4semidirect
27. C2×#14519734C22semidirect
28. C2×C42×D61C22semidirect
34. #16839725C22semidirect
39. C4×#11758198C22semidirect
40. C4×#11758198C22semidirect
42. #16839523C22semidirect
43. #16839523C22semidirect
44. #16839522C22semidirect
45. #16839522C22semidirect
81. #14519753C2×C4semidirect
82. #14519753C2×C4semidirect
91. #14519748C2×C4semidirect
92. #14519748C2×C4semidirect
103. #14519736C2×C4semidirect
106. C2×C4⋊Dic61C2×C4semidirect
107. C2×C4⋊Dic61C2×C4semidirect
131. C2×#41×C61C2×C4semidirect
133. C22×Q8×C61C2×C4semidirect
135. C22×D4×C61C2×C4semidirect
407. #1789D61semidirect
457. C61#21775semidirect
468. C2×#41C4×D61semidirect
471. C22×Q8C4×D61semidirect
476. C22×D4C4×D61semidirect

Maximal subgroups

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

subgroupindex
#214591482
#214542622
#214483052
#214462642
#214462592
#214461182
#214459192
#214459162
#214457632
C61×#17892
#2177561