Finite Group Databasebeta

← #30610301

Subgroups — #30610301

Order 15616.

1002 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462508C212yesmaximal, complemented
2#21461095C212yesmaximal, complemented
3#21461090C212yesmaximal, complemented
4#21461088C212yesmaximal, complemented
5#21461077C211yesmaximal, characteristic, complemented
6#21461072C211yesmaximal, characteristic, complemented
7#21461071C211yesmaximal, characteristic, complemented
8#21461057C211yesmaximal, characteristic, complemented
9#21461052C211yesmaximal, characteristic, complemented
10#21461051C211yesmaximal, characteristic, complemented
11C2×#16840474C211yesmaximal, characteristic
12#16840786—22no—
13#16840786—22no—
14#16840783C2212yes—
15#16840782C2212yes—
16#16840779C2212yes—
17#16840778C2212yes—
18#16840768—22no—
19#16840732C2212yes—
20C2×C22⋊#92420C2212yes—
21#16840726—22no—
22#16840608C2211yescharacteristic
23#16840608C2211yescharacteristic
24#16840608C2211yescharacteristic
25#16840608C2211yescharacteristic
26#16840606C2212yes—
27#16840606C2212yes—
28#16840606C2212yes—
29#16840606C2212yes—
30#16840605C2212yes—
31#16840605C2212yes—
32#16840474—22no—
33#16840474—22no—
34#16840474—22no—
35#16840474—22no—
36C2×#14519775C411yescharacteristic
37C2×#14519766C2211yescharacteristic
38C2×#14519763C411yescharacteristic
39C2×#14519763C2211yescharacteristic
40C2×#14519750C411yescharacteristic
41C2×#14519750C411yescharacteristic
42C2×#14519749C411yescharacteristic
43C2×#14519749C2211yescharacteristic
44C2×#14519737C411yescharacteristic
45C2×#14519737C2211yescharacteristic
46C2×#14519734C411yescharacteristic
47C2×#14519734C2211yescharacteristic
48C2×#14519733C2211yescharacteristic
49C2×#14519733C2211yescharacteristic
50C2×#124×C61C411yescharacteristic
51C2×#11758217—22no—
52C22×#92420—22no—
53#14519844—22no—
54#14519844—22no—
55C4⋊#92420—22no—
56C4⋊#92420—22no—
57C22⋊#92420—22no—
58C22⋊#92420—22no—
59C22⋊#92420C2312yes—
60C22⋊#92420C2312yes—
61C22⋊#92420C2312yes—
62C22⋊#92420C2312yes—
63#14519832—22no—
64#14519832—22no—
65C4×#92420—22no—
66C4×#92420—22no—
67C22×Dic122C2×C411yescharacteristic
68C22×D244C2×C411yescharacteristic
69C22×C22⋊D61C2×C411yescharacteristic
70C22×C22⋊D61C2×C411yescharacteristic
71C22×C22⋊D61C2×C411yescharacteristic
72C22×C22⋊D61C2×C411yescharacteristic
73C23×Dic61C2×C411yescharacteristic
74C23×Dic61C2311yescharacteristic
75C22×C4×D61C2×C411yescharacteristic
76C22×C4×D61C2×C411yescharacteristic
77#14519775—22no—
78#14519775—22no—
79#14519766—22no—
80#14519766—22no—
81#14519763—22no—
82#14519763—22no—
83#14519763—22no—
84#14519763—22no—
85#14519750—22no—
86#14519750—22no—
87#14519750—22no—
88#14519750—22no—
89#14519749—22no—
90#14519749—22no—
91#14519749—22no—
92#14519749—22no—
93#14519737—22no—
94#14519737—22no—
95#14519737—21no—
96#14519737—21no—
97#14519737—21no—
98#14519737—21no—
99#14519734—21no—
100#14519734—21no—
101#14519734—21no—
102#14519734—21no—
103#14519734—22no—
104#14519734—22no—
105#14519733—22no—
106#14519733—22no—
107#14519733D412yes—
108#14519733D412yes—
109#14519733D412yes—
110#14519733D412yes—
111C2×#11758196C2×C411yescharacteristic
112C2×#11758196C2×C411yescharacteristic
113C2×#11758196C2×C411yescharacteristic
114C2×#11758196C2×C411yescharacteristic
115C2×#11758196C2×C411yescharacteristic
116C2×#11758196C2311yescharacteristic
117C2×C22⋊Dic61C2×C411yescharacteristic
118C2×C22⋊Dic61C2311yescharacteristic
119C2×#11758198C2×C411yescharacteristic
120C2×#11758198C2×C411yescharacteristic
121C2×#11758198C2×C411yescharacteristic
122C2×#11758198C2×C411yescharacteristic
123C2×#11758198C2311yescharacteristic
124C2×#11758198C2311yescharacteristic
125C2×C4×Dic61C2×C411yescharacteristic
126C2×C4×Dic61C2×C411yescharacteristic
127C2×C4×Dic61C2311yescharacteristic
128C2×C4×Dic61C2311yescharacteristic
129C22×Q8×C61C2×C411yescharacteristic
130C22×D4×C61C2×C411yescharacteristic
131#124×C61—22no—
132#124×C61—22no—
133C2×C22⋊C4×C61C2×C411yescharacteristic
134C2×C22⋊C4×C61C2×C411yescharacteristic
135C2×C22⋊C4×C61C2×C411yescharacteristic
136C2×C22⋊C4×C61C2×C411yescharacteristic
137C2×C42×C61C2×C411yescharacteristic
138C24×C61C22×C411yescharacteristic
139C24×C61C22×C411yescharacteristic
140C23×D61C22×C411yescharacteristic
141C23×D61C22×C411yescharacteristic
142C2×Q8×C61—22no—
143C2×Q8×C61—81no—
144C2×D4×C61—22no—
145C2×D4×C61—81no—
146C22×C4×C61C22×C411yescharacteristic
147C22×C4×C61C22×C411yescharacteristic
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C22×C411yescharacteristic
150C22×C4×C61C22×C411yescharacteristic
151C2×C22⋊D61—22no—
152C2×C22⋊D61—22no—
153C2×C22⋊D61—21no—
154C2×C22⋊D61—21no—
155C2×C22⋊D61—22no—
156C2×C22⋊D61—22no—
157C2×C22⋊D61—41no—
158C2×C22⋊D61—42no—
159C2×C22⋊D61—81no—
160C2×C22⋊D61—81no—
161C22×Dic61—21no—
162C22×Dic61—21no—
163C22×Dic61—22no—
164C22×Dic61—42no—
165C22×Dic61—41no—
166C22×Dic61C22×C411yescharacteristic
167C22×Dic61C22×C411yescharacteristic
168C22×Dic61C22×C411yescharacteristic
169C22×Dic61C22×C411yescharacteristic
170C22×Dic61C22×C411yescharacteristic
171C22×Dic61C2×D412yes—
172C22×Dic61C2×D412yes—
173C22×Dic61C2411yescharacteristic
174C2×D244—22no—
175C2×D244—81no—
176C2×C4×D61—21no—
177C2×C4×D61—21no—
178C2×C4×D61—21no—
179C2×C4×D61—21no—
180C2×C4×D61—22no—
181C2×C4×D61—41no—
182C2×C4×D61—42no—
183C2×Dic122—22no—
184C2×Dic122—81no—
185#11758217—44no—
186C2×#92420—22no—
187C2×#92420—22no—
188C2×#92420—22no—
189C2×#92420—22no—
190C2×#92420—44no—
191C22⋊C4×C61—22no—
192C22⋊C4×C61—22no—
193C22⋊C4×C61—21no—
194C22⋊C4×C61—21no—
195C22⋊C4×C61C22⋊C412yes—
196C22⋊C4×C61C22⋊C412yes—
197C42×C61—21no—
198C42×C61—21no—
199C22⋊Dic61—22no—
200C22⋊Dic61C22⋊C412yes—
201C22⋊Dic61C22⋊C412yes—
202#11758198—21no—
203#11758198—21no—
204#11758198—21no—
205#11758198—21no—
206#11758198—22no—
207#11758198—21no—
208#11758198—21no—
209#11758198—22no—
210#11758198—22no—
211#11758196—22no—
212#11758196—22no—
213#11758196—21no—
214#11758196—21no—
215#11758196—22no—
216#11758196C22⋊C411yescharacteristic
217#11758196C22⋊C411yescharacteristic
218#11758196C22⋊C411yescharacteristic
219#11758196C22⋊C411yescharacteristic
220#11758196C22⋊C412yes—
221#11758196C22⋊C412yes—
222C4×Dic61—21no—
223C4×Dic61—21no—
224C4×Dic61—21no—
225C4×Dic61—21no—
226C4×Dic61C2×D412yes—
227C4×Dic61C2×D412yes—
228C4×Dic61C2×D412yes—
229C4×Dic61C2×D412yes—
230C23×C61—21no—
231C23×C61—21no—
232C23×C61—21no—
233C23×C61—21no—
234C23×C61—21no—
235C23×C61—41no—
236C23×C61—41no—
237C23×C61—41no—
238C23×C61—41no—
239C23×C61C2×C22⋊C412yes—
240C23×C61C23×C411yescharacteristic
241C22×D61—21no—
242C22×D61—21no—
243C22×D61—21no—
244C22×D61—21no—
245C22×D61—21no—
246C22×D61—21no—
247C22×D61—41no—
248C22×D61—41no—
249C22×D61—41no—
250C22×D61—41no—
251Q8×C61—82no—
252D4×C61—82no—
253C2×C4×C61—21no—
254C2×C4×C61—21no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—41no—
259C2×C4×C61—41no—
260C2×C4×C61—41no—
261C2×C4×C61—41no—
262C2×C4×C61C2×C22⋊C412yes—
263C2×C4×C61C2×C22⋊C411yescharacteristic
264C2×C4×C61C2×C22⋊C411yescharacteristic
265C22⋊D61—44no—
266C22⋊D61—42no—
267C22⋊D61—42no—
268C22⋊D61—82no—
269C22⋊D61—82no—
270C2×Dic61—21no—
271C2×Dic61—21no—
272C2×Dic61—21no—
273C2×Dic61—21no—
274C2×Dic61—24no—
275C2×Dic61—22no—
276C2×Dic61—21no—
277C2×Dic61—41no—
278C2×Dic61—42no—
279C2×Dic61—41no—
280C2×Dic61—42no—
281C2×Dic61—42no—
282C2×Dic61—41no—
283C2×Dic61C2×C22⋊C411yescharacteristic
284C2×Dic61C2×C22⋊C411yescharacteristic
285C2×Dic61C2×C22⋊C411yescharacteristic
286C2×Dic61C2×C22⋊C412yes—
287C2×Dic61C2×C22⋊C411yescharacteristic
288C2×Dic61#13112yes—
289C2×Dic61C22×D412yes—
290D244—82no—
291C4×D61—42no—
292C4×D61—42no—
293C4×D61—42no—
294C4×D61—42no—
295Dic122—82no—
296#92420—42no—
297#92420—42no—
298#92420—42no—
299#92420—42no—
300#17418—611nomaximal, Sylow
301C22×C61—21no—
302C22×C61—21no—
303C22×C61—22no—
304C22×C61—22no—
305C22×C61—22no—
306C22×C61—41no—
307C22×C61—41no—
308C22×C61—41no—
309C22×C61—81no—
310C22×C61—81no—
311C22×C61—81no—
312C22×C61—81no—
313C22×C61C22×C22⋊C411yescharacteristic
314C22×C61C2×#13111yescharacteristic
315C22×C61#56811yescharacteristic
316C2×D61—41no—
317C2×D61—41no—
318C2×D61—41no—
319C2×D61—41no—
320C2×D61—41no—
321C2×D61—41no—
322C2×D61—81no—
323C2×D61—81no—
324C2×D61—81no—
325C2×D61—81no—
326C4×C61—21no—
327C4×C61—21no—
328C4×C61—22no—
329C4×C61—41no—
330C4×C61—41no—
331C4×C61—41no—
332Dic61—22no—
333Dic61—21no—
334Dic61—21no—
335Dic61—22no—
336Dic61—21no—
337Dic61—22no—
338Dic61—41no—
339Dic61#41012yes—
340C2×#555—611no—
341#2924—612no—
342#1471—612no—
343#1469—612no—
344#1469—612no—
345#1465—611no—
346#1464—611no—
347#1464—611no—
348#1459—611no—
349#1458—611no—
350#1458—611no—
351C2×C61—21no—
352C2×C61—21no—
353C2×C61—42no—
354C2×C61—81no—
355C2×C61#288011yescharacteristic
356C2×C61C2×#41011yescharacteristic
357C2×C61#288811yescharacteristic
358D61—81no—
359D61—81no—
360#555—1222no—
361#555—1222no—
362#555—1222no—
363#555—1222no—
364C2×C4⋊Q8—611no—
365C2×#124—611no—
366C2×#124—611no—
367C2×#124—611no—
368C2×#124#692311yescharacteristic
369C2×#121—611no—
370C2×#121—611no—
371C2×#121—611no—
372C2×#121—611no—
373C2×C4×D4—611no—
374C2×C4×D4—611no—
375C2×#117—611no—
376C2×#117—611no—
377C2×#117—611no—
378C2×#117—611no—
379#433—1222no—
380#433—1222no—
381#432—612no—
382#432—612no—
383#431—612no—
384#431—612no—
385#424—1222no—
386#407—612no—
387C2×C22⋊C8—612no—
388#405—1222no—
389#324—611no—
390#324—611no—
391#324—611no—
392#324—611no—
393#323—612no—
394#323—612no—
395#323—612no—
396#323—612no—
397#323—612no—
398#323—612no—
399C61#1741811yescharacteristic, complemented, Sylow
400C22×Q8—611no—
401C22×Q8C2×#692311yescharacteristic
402C22×D4—611no—
403C22×D4—611no—
404C22×D4—611no—
405C22×D4—611no—
406C22×D4—611no—
407C22×D4C2×#692311yescharacteristic
408C23×C4—611no—
409C23×C4—611no—
410C23×C4—611no—
411C23×C4—611no—
412C2×M16—1222no—
413C22×C8—1222no—
414C4⋊Q8—1222no—
415C4⋊Q8—1222no—
416#124—22no—
417#124—22no—
418#124—1222no—
419#124—1222no—
420#124—1222no—
421#124—1222no—
422#124—1222no—
423#124—1222no—
424#121—1222no—
425#121—1222no—
426#121—1222no—
427#121—1222no—
428#121—1222no—
429#121—1222no—
430#121—1222no—
431#121—1222no—
432C4×D4—1221no—
433C4×D4—1221no—
434C4×D4—1221no—
435C4×D4—1221no—
436C4×D4—1222no—
437C4×D4—1222no—
438#117—612no—
439#117—612no—
440#117—612no—
441#117—612no—
442#117—1222no—
443#117—1222no—
444#117—1221no—
445#117—1221no—
446#117—1221no—
447#117—1221no—
448#117—1222no—
449#117—1222no—
450C2×C4⋊C4—611no—
451C2×C4⋊C4—611no—
452C2×C4⋊C4—611no—
453C2×C4⋊C4—611no—
454C2×C4⋊C4—611no—
455C2×C4⋊C4—611no—
456C2×C22⋊C4—611no—
457C2×C22⋊C4—611no—
458C2×C22⋊C4—611no—
459C2×C22⋊C4—611no—
460C2×C22⋊C4—611no—
461C2×C22⋊C4—611no—
462C2×C22⋊C4—611no—
463C2×C22⋊C4—611no—
464C2×C22⋊C4C2×#692311yescharacteristic
465C2×C22⋊C4C2×#692311yescharacteristic
466C2×C22⋊C4C2×#692311yescharacteristic
467C2×C22⋊C4C2×#692311yescharacteristic
468C2×C42—611no—
469C2×C42—611no—
470C2×C42—611no—
471C2×C42—611no—
472C2×C42C2×#692311yescharacteristic
473C4⋊C8—1222no—
474C4⋊C8—1222no—
475C4⋊C8—1222no—
476C4⋊C8—1222no—
477C22⋊C8—612no—
478C22⋊C8—612no—
479C22⋊C8—612no—
480C22⋊C8—612no—
481C22⋊C8—1222no—
482C22⋊C8—1222no—
483#97—1222no—
484#97—1222no—
485C4×C8—1222no—
486C4×C8—1222no—
487C24—611no—
488C24—611no—
489C24C22×#692311yescharacteristic
490C24C22×#692311yescharacteristic
491C2×Q8—22no—
492C2×Q8—81no—
493C2×Q8—1222no—
494C2×Q8—4881no—
495C2×D4—22no—
496C2×D4—81no—
497C2×D4—1222no—
498C2×D4—1221no—
499C2×D4—1221no—
500C2×D4—1222no—
501C2×D4—1222no—
502C2×D4—1222no—
503C2×D4—1222no—
504C2×D4—4881no—
505C2×D4—4881no—
506C2×D4—4881no—
507C2×D4—2441no—
508C2×D4—2442no—
509C22×C4—612no—
510C22×C4—611no—
511C22×C4—611no—
512C22×C4—611no—
513C22×C4—612no—
514C22×C4—611no—
515C22×C4—611no—
516C22×C4—611no—
517C22×C4—1221no—
518C22×C4—1221no—
519C22×C4—1222no—
520C22×C4—1221no—
521C22×C4—1221no—
522C22×C4—1222no—
523C22×C4—1221no—
524C22×C4—1221no—
525C22×C4—2441no—
526C22×C4—2442no—
527C22×C4—2442no—
528C22×C4—2441no—
529C22×C4C22×#692311yescharacteristic
530C22×C4C22×#692311yescharacteristic
531C22×C4C22×#692311yescharacteristic
532C22×C4C22×#692311yescharacteristic
533C22×C4C22×#692311yescharacteristic
534M16—2444no—
535C2×C8—1222no—
536C2×C8—1222no—
537C2×C8—1222no—
538C2×C8—1222no—
539C2×C8—2444no—
540C4⋊C4—611no—
541C4⋊C4—611no—
542C4⋊C4—611no—
543C4⋊C4—611no—
544C4⋊C4—612no—
545C4⋊C4—612no—
546C4⋊C4—1222no—
547C4⋊C4—1221no—
548C4⋊C4—1222no—
549C4⋊C4—1221no—
550C4⋊C4—1222no—
551C22⋊C4—22no—
552C22⋊C4—22no—
553C22⋊C4—21no—
554C22⋊C4—21no—
555C22⋊C4—612no—
556C22⋊C4—612no—
557C22⋊C4—1222no—
558C22⋊C4—1221no—
559C22⋊C4—1221no—
560C22⋊C4—1222no—
561C22⋊C4—1221no—
562C22⋊C4—1221no—
563C22⋊C4—1222no—
564C22⋊C4—1222no—
565C22⋊C4—1221no—
566C22⋊C4—1221no—
567C22⋊C4C22⋊#692312yes—
568C22⋊C4C22⋊#692312yes—
569C42—21no—
570C42—21no—
571C42—612no—
572C42—612no—
573C42—612no—
574C42—612no—
575C42—1221no—
576C42—1221no—
577C42—1221no—
578C42—1221no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—1221no—
589C23—1221no—
590C23—1221no—
591C23—1221no—
592C23—1221no—
593C23—1221no—
594C23—2441no—
595C23—2441no—
596C23—2441no—
597C23—2441no—
598C23C2×C22⋊#692312yes—
599C23C23×#692311yescharacteristic
600Q8—82no—
601Q8—4882no—
602D4—82no—
603D4—4882no—
604D4—4882no—
605D4—4882no—
606D4—2442no—
607D4—2444no—
608D4—2442no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—611no—
619C2×C4—611no—
620C2×C4—611no—
621C2×C4—612no—
622C2×C4—611no—
623C2×C4—612no—
624C2×C4—612no—
625C2×C4—1224no—
626C2×C4—1222no—
627C2×C4—1221no—
628C2×C4—1221no—
629C2×C4—1221no—
630C2×C4—1221no—
631C2×C4—1221no—
632C2×C4—2442no—
633C2×C4—2442no—
634C2×C4—2442no—
635C2×C4—2442no—
636C2×C4—2441no—
637C2×C4—2442no—
638C2×C4—2441no—
639C2×C4—2442no—
640C2×C4—2442no—
641C2×C4—2441no—
642C2×C4C2×C22⋊#692311yescharacteristic
643C2×C4C2×C22⋊#692311yescharacteristic
644C2×C4C2×C22⋊#692312yes—
645C8—2442no—
646C8—2442no—
647C8—2442no—
648C8—2442no—
649C22—21no—
650C22—21no—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—41no—
655C22—41no—
656C22—41no—
657C22—81no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22—4881no—
662C22—4881no—
663C22—4881no—
664C22—4881no—
665C22—2441no—
666C22—2441no—
667C22—2441no—
668C22—2441no—
669C22—2441no—
670C22—2441no—
671C22C22×C22⋊#692311yescharacteristic
672C22D61⋊#13111yescharacteristic
673C22#1684084111yescharacteristic
674C4—21no—
675C4—21no—
676C4—22no—
677C4—41no—
678C4—41no—
679C4—41no—
680C4—612no—
681C4—1221no—
682C4—1221no—
683C4—1222no—
684C4—1222no—
685C4—1221no—
686C4—1222no—
687C4—2441no—
688C2—21no—
689C2—21no—
690C2—42no—
691C2—81no—
692C2—4881no—
693C2—4881no—
694C2#2146240911yescharacteristic
695C2D61⋊#41011yescharacteristic
696C2#2146242911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×#124×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840474C2
cosocleC22×Dic61C24
hypercenterC2×#124#6923
hypocenterC61#17418
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C22⋊C4 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. #21462508C2semidirect
2. #21461095C2semidirect
3. #21461090C2semidirect
4. #21461088C2semidirect
5. #21461077C2semidirect
6. #21461072C2semidirect
7. #21461071C2semidirect
8. #21461057C2semidirect
9. #21461052C2semidirect
10. #21461051C2semidirect
399. C61#17418semidirect

Maximal subgroups

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

subgroupindex
#214625082
#214610952
#214610902
#214610882
#214610772
#214610722
#214610712
#214610572
#214610522
#214610512
C2×#168404742
#1741861