Finite Group Databasebeta

← #30610281

Subgroups — #30610281

Order 15616.

1008 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462508C212yesmaximal, complemented
2#21461102C212yesmaximal, complemented
3#21461101C212yesmaximal, complemented
4#21461095C212yesmaximal, complemented
5#21461080C211yesmaximal, characteristic, complemented
6#21461078C211yesmaximal, characteristic, complemented
7#21461077C211yesmaximal, characteristic, complemented
8#21461060C211yesmaximal, characteristic, complemented
9#21461058C211yesmaximal, characteristic, complemented
10#21461057C211yesmaximal, characteristic, complemented
11C2×#16840457C211yesmaximal, 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#16840608C2212yes—
23#16840608C2212yes—
24#16840606C2211yescharacteristic
25#16840606C2211yescharacteristic
26#16840606C2211yescharacteristic
27#16840606C2211yescharacteristic
28#16840606C2212yes—
29#16840606C2212yes—
30#16840605C2212yes—
31#16840605C2212yes—
32#16840457—22no—
33#16840457—22no—
34#16840457—22no—
35#16840457—22no—
36C2×#14519772C2211yescharacteristic
37C2×#14519770C2211yescharacteristic
38C2×#14519767C411yescharacteristic
39C2×#14519759C411yescharacteristic
40C2×#14519750C411yescharacteristic
41C2×#14519750C411yescharacteristic
42C2×#14519749C2211yescharacteristic
43C2×#14519748C411yescharacteristic
44C2×#14519739C2211yescharacteristic
45C2×C4×C22⋊D61C411yescharacteristic
46C2×C4×C22⋊D61C2211yescharacteristic
47C2×#14519737C2211yescharacteristic
48C2×#14519733C2211yescharacteristic
49C2×C4⋊C4×D61C411yescharacteristic
50C2×#123×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×D244C2×C411yescharacteristic
68C22×C22⋊D61C2×C411yescharacteristic
69C22×C22⋊D61C2×C411yescharacteristic
70C22×C22⋊D61C2×C411yescharacteristic
71C22×C22⋊D61C2×C411yescharacteristic
72C23×Dic61C2311yescharacteristic
73C22×C4×D61C2×C411yescharacteristic
74C22×C4×D61C2×C411yescharacteristic
75C22×C4×D61C2×C411yescharacteristic
76C22×C4×D61C2×C411yescharacteristic
77#14519772—22no—
78#14519772—22no—
79#14519770—22no—
80#14519770—22no—
81#14519767—22no—
82#14519767—22no—
83#14519759—22no—
84#14519759—22no—
85#14519750—22no—
86#14519750—22no—
87#14519750—22no—
88#14519750—22no—
89#14519749—22no—
90#14519749—22no—
91#14519748—22no—
92#14519748—22no—
93#14519739—22no—
94#14519739—22no—
95C4×C22⋊D61—21no—
96C4×C22⋊D61—21no—
97C4×C22⋊D61—21no—
98C4×C22⋊D61—21no—
99C4×C22⋊D61—22no—
100C4×C22⋊D61—22no—
101#14519737—22no—
102#14519737—22no—
103#14519733D412yes—
104#14519733D412yes—
105#14519733D412yes—
106#14519733D412yes—
107C2×C4⋊Dic61C2×C411yescharacteristic
108C2×C4⋊Dic61C2×C411yescharacteristic
109C2×#11758196C2×C411yescharacteristic
110C2×#11758196C2×C411yescharacteristic
111C2×#11758196C2×C411yescharacteristic
112C2×#11758196C2×C411yescharacteristic
113C2×#11758196C2×C411yescharacteristic
114C2×#11758196C2311yescharacteristic
115C4⋊C4×D61—21no—
116C4⋊C4×D61—21no—
117C4⋊C4×D61—21no—
118C4⋊C4×D61—21no—
119C2×C22⋊Dic61C2×C411yescharacteristic
120C2×C22⋊Dic61C2×C411yescharacteristic
121C2×C22⋊Dic61C2311yescharacteristic
122C2×#11758198C2×C411yescharacteristic
123C2×#11758198C2×C411yescharacteristic
124C2×#11758198C2311yescharacteristic
125C2×#11758198C2311yescharacteristic
126C2×C4×Dic61C2×C411yescharacteristic
127C2×C4×Dic61C2311yescharacteristic
128C2×C4×Dic61C2311yescharacteristic
129C22×D4×C61C2×C411yescharacteristic
130C23×C4×C61C2×C411yescharacteristic
131#123×C61—22no—
132#123×C61—22no—
133C2×C4⋊C4×C61C2×C411yescharacteristic
134C2×C4⋊C4×C61C2×C411yescharacteristic
135C2×C22⋊C4×C61C2×C411yescharacteristic
136C2×C22⋊C4×C61C2×C411yescharacteristic
137C2×C22⋊C4×C61C2×C411yescharacteristic
138C24×C61C22×C411yescharacteristic
139C24×C61C22×C411yescharacteristic
140C23×D61C22×C411yescharacteristic
141C23×D61C22×C411yescharacteristic
142C2×D4×C61—22no—
143C2×D4×C61—81no—
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—81no—
147C22×C4×C61C22×C411yescharacteristic
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C22×C411yescharacteristic
150C22×C4×C61C22×C411yescharacteristic
151C22×C4×C61C22×C411yescharacteristic
152C2×C22⋊D61—22no—
153C2×C22⋊D61—22no—
154C2×C22⋊D61—22no—
155C2×C22⋊D61—22no—
156C2×C22⋊D61—22no—
157C2×C22⋊D61—21no—
158C2×C22⋊D61—21no—
159C2×C22⋊D61—41no—
160C2×C22⋊D61—41no—
161C2×C22⋊D61—42no—
162C2×C22⋊D61—81no—
163C22×Dic61—42no—
164C22×Dic61C22×C411yescharacteristic
165C22×Dic61C22×C411yescharacteristic
166C22×Dic61C22×C411yescharacteristic
167C22×Dic61C22×C411yescharacteristic
168C22×Dic61C22×C411yescharacteristic
169C22×Dic61C2×D412yes—
170C22×Dic61C2×D412yes—
171C22×Dic61C2411yescharacteristic
172C2×D244—22no—
173C2×D244—22no—
174C2×D244—41no—
175C2×C4×D61—21no—
176C2×C4×D61—21no—
177C2×C4×D61—21no—
178C2×C4×D61—21no—
179C2×C4×D61—21no—
180C2×C4×D61—21no—
181C2×C4×D61—21no—
182C2×C4×D61—21no—
183C2×C4×D61—42no—
184C2×C4×D61—81no—
185C2×C4×D61—81no—
186C2×C4×D61—81no—
187#11758217—44no—
188C2×#92420—22no—
189C2×#92420—22no—
190C2×#92420—22no—
191C2×#92420—22no—
192C2×#92420—44no—
193C4⋊C4×C61—21no—
194C4⋊C4×C61—21no—
195C4⋊C4×C61—22no—
196C22⋊C4×C61—22no—
197C22⋊C4×C61—22no—
198C22⋊C4×C61C22⋊C412yes—
199C22⋊C4×C61C22⋊C412yes—
200C22⋊Dic61—21no—
201C22⋊Dic61—21no—
202C22⋊Dic61—22no—
203C22⋊Dic61C22⋊C412yes—
204C22⋊Dic61C22⋊C412yes—
205#11758198—21no—
206#11758198—21no—
207#11758198—22no—
208#11758198—22no—
209#11758198—22no—
210C4⋊Dic61—21no—
211C4⋊Dic61—21no—
212C4⋊Dic61—22no—
213#11758196—22no—
214#11758196—21no—
215#11758196—21no—
216#11758196—22no—
217#11758196—22no—
218#11758196C22⋊C411yescharacteristic
219#11758196C22⋊C411yescharacteristic
220#11758196C22⋊C411yescharacteristic
221#11758196C22⋊C411yescharacteristic
222#11758196C22⋊C412yes—
223#11758196C22⋊C412yes—
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—41no—
247C22×D61—41no—
248C22×D61—41no—
249C22×D61—41no—
250C22×D61#13112yes—
251D4×C61—82no—
252C2×C4×C61—21no—
253C2×C4×C61—21no—
254C2×C4×C61—21no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—41no—
258C2×C4×C61—41no—
259C2×C4×C61—41no—
260C2×C4×C61—41no—
261C2×C4×C61—81no—
262C2×C4×C61—81no—
263C2×C4×C61C2×C22⋊C412yes—
264C2×C4×C61C2×C22⋊C411yescharacteristic
265C2×C4×C61C2×C22⋊C411yescharacteristic
266C22⋊D61—44no—
267C22⋊D61—42no—
268C22⋊D61—44no—
269C22⋊D61—42no—
270C22⋊D61—82no—
271C2×Dic61—21no—
272C2×Dic61—21no—
273C2×Dic61—24no—
274C2×Dic61—22no—
275C2×Dic61—21no—
276C2×Dic61—21no—
277C2×Dic61—21no—
278C2×Dic61—21no—
279C2×Dic61—41no—
280C2×Dic61—42no—
281C2×Dic61—41no—
282C2×Dic61—41no—
283C2×Dic61C2×C22⋊C411yescharacteristic
284C2×Dic61C2×C22⋊C412yes—
285C2×Dic61C2×C22⋊C411yescharacteristic
286C2×Dic61C2×C22⋊C411yescharacteristic
287C2×Dic61C2×C22⋊C411yescharacteristic
288C2×Dic61C22×D412yes—
289D244—44no—
290C4×D61—42no—
291C4×D61—42no—
292C4×D61—81no—
293C4×D61—81no—
294C4×D61—81no—
295C4×D61—81no—
296C4×D61—81no—
297C4×D61—81no—
298#92420—42no—
299#92420—42no—
300#92420—42no—
301#92420—42no—
302#17415—611nomaximal, Sylow
303C22×C61—21no—
304C22×C61—21no—
305C22×C61—22no—
306C22×C61—22no—
307C22×C61—22no—
308C22×C61—41no—
309C22×C61—41no—
310C22×C61—41no—
311C22×C61—81no—
312C22×C61—81no—
313C22×C61—81no—
314C22×C61—81no—
315C22×C61C22×C22⋊C411yescharacteristic
316C22×C61C2×#13111yescharacteristic
317C22×C61#56811yescharacteristic
318C2×D61—22no—
319C2×D61—42no—
320C2×D61—41no—
321C2×D61—41no—
322C2×D61—42no—
323C2×D61—41no—
324C2×D61—41no—
325C2×D61—41no—
326C2×D61—81no—
327C2×D61—81no—
328C4×C61—22no—
329C4×C61—21no—
330C4×C61—21no—
331C4×C61—41no—
332C4×C61—41no—
333C4×C61—41no—
334Dic61—22no—
335Dic61—22no—
336Dic61—21no—
337Dic61—21no—
338Dic61—21no—
339Dic61—41no—
340Dic61—41no—
341Dic61#41012yes—
342C2×#553—611no—
343#2924—612no—
344#1473—612no—
345#1473—612no—
346#1471—612no—
347#1466—611no—
348#1466—611no—
349#1465—611no—
350#1460—611no—
351#1460—611no—
352#1459—611no—
353C2×C61—21no—
354C2×C61—21no—
355C2×C61—42no—
356C2×C61—81no—
357C2×C61#288011yescharacteristic
358C2×C61C2×#41011yescharacteristic
359C2×C61#288811yescharacteristic
360D61—42no—
361D61—81no—
362#553—1222no—
363#553—1222no—
364#553—1222no—
365#553—1222no—
366C2×#126—611no—
367C2×#126—611no—
368C2×#125—611no—
369C2×#123—611no—
370C2×#123#692311yescharacteristic
371C2×#121—611no—
372C2×#121—611no—
373C2×#121—611no—
374C2×#121—611no—
375C2×C4×D4—611no—
376C2×C4×D4—611no—
377C2×C4×D4—611no—
378C2×C4×D4—611no—
379C2×#117—611no—
380C22×C4⋊C4—611no—
381#433—1222no—
382#433—1222no—
383#432—612no—
384#432—612no—
385#431—612no—
386#431—612no—
387#424—1222no—
388#407—612no—
389C2×C22⋊C8—612no—
390#405—1222no—
391#324—612no—
392#324—612no—
393#323—612no—
394#323—612no—
395#323—611no—
396#323—611no—
397#323—611no—
398#323—611no—
399#323—612no—
400#323—612no—
401C61#1741511yescharacteristic, complemented, Sylow
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—
412C23×C4—611no—
413C23×C4C2×#692311yescharacteristic
414C2×M16—1222no—
415C22×C8—1222no—
416#126—1222no—
417#126—1222no—
418#126—1222no—
419#126—1222no—
420#125—1222no—
421#125—1222no—
422#123—22no—
423#123—22no—
424#123—1222no—
425#123—1222no—
426#121—1222no—
427#121—1222no—
428#121—1222no—
429#121—1222no—
430#121—1222no—
431#121—1222no—
432#121—1222no—
433#121—1222no—
434C4×D4—1222no—
435C4×D4—1222no—
436C4×D4—1222no—
437C4×D4—1222no—
438C4×D4—1222no—
439C4×D4—1222no—
440C4×D4—1221no—
441C4×D4—1221no—
442C4×D4—1221no—
443C4×D4—1221no—
444#117—612no—
445#117—612no—
446#117—612no—
447#117—612no—
448C2×C4⋊C4—611no—
449C2×C4⋊C4—611no—
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×C4⋊C4—1221no—
457C2×C4⋊C4—1221no—
458C2×C4⋊C4—1221no—
459C2×C4⋊C4—1221no—
460C2×C4⋊C4C2×#692311yescharacteristic
461C2×C4⋊C4C2×#692311yescharacteristic
462C2×C22⋊C4—611no—
463C2×C22⋊C4—611no—
464C2×C22⋊C4—611no—
465C2×C22⋊C4—611no—
466C2×C22⋊C4—611no—
467C2×C22⋊C4—611no—
468C2×C22⋊C4—611no—
469C2×C22⋊C4C2×#692311yescharacteristic
470C2×C22⋊C4C2×#692311yescharacteristic
471C2×C22⋊C4C2×#692311yescharacteristic
472C2×C42—611no—
473C2×C42—611no—
474C2×C42—611no—
475C4⋊C8—1222no—
476C4⋊C8—1222no—
477C4⋊C8—1222no—
478C4⋊C8—1222no—
479C22⋊C8—612no—
480C22⋊C8—612no—
481C22⋊C8—612no—
482C22⋊C8—612no—
483C22⋊C8—1222no—
484C22⋊C8—1222no—
485#97—1222no—
486#97—1222no—
487C4×C8—1222no—
488C4×C8—1222no—
489C24—611no—
490C24—611no—
491C24C22×#692311yescharacteristic
492C24C22×#692311yescharacteristic
493C2×D4—22no—
494C2×D4—81no—
495C2×D4—1222no—
496C2×D4—1221no—
497C2×D4—1222no—
498C2×D4—1221no—
499C2×D4—1222no—
500C2×D4—1222no—
501C2×D4—1222no—
502C2×D4—1222no—
503C2×D4—1222no—
504C2×D4—4881no—
505C2×D4—2441no—
506C2×D4—2441no—
507C2×D4—2441no—
508C2×D4—2442no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—81no—
512C22×C4—612no—
513C22×C4—611no—
514C22×C4—611no—
515C22×C4—612no—
516C22×C4—611no—
517C22×C4—611no—
518C22×C4—611no—
519C22×C4—611no—
520C22×C4—1221no—
521C22×C4—1221no—
522C22×C4—1221no—
523C22×C4—1221no—
524C22×C4—1221no—
525C22×C4—1221no—
526C22×C4—1221no—
527C22×C4—1221no—
528C22×C4—4881no—
529C22×C4—4881no—
530C22×C4—4881no—
531C22×C4—2442no—
532C22×C4—2442no—
533C22×C4C22×#692311yescharacteristic
534C22×C4C22×#692311yescharacteristic
535C22×C4C22×#692311yescharacteristic
536C22×C4C22×#692311yescharacteristic
537C22×C4C22×#692311yescharacteristic
538M16—2444no—
539C2×C8—1222no—
540C2×C8—1222no—
541C2×C8—1222no—
542C2×C8—1222no—
543C2×C8—2444no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—22no—
547C4⋊C4—611no—
548C4⋊C4—611no—
549C4⋊C4—611no—
550C4⋊C4—611no—
551C4⋊C4—612no—
552C4⋊C4—612no—
553C4⋊C4—1221no—
554C4⋊C4—1221no—
555C4⋊C4—1221no—
556C4⋊C4—1221no—
557C4⋊C4—1222no—
558C4⋊C4—1222no—
559C4⋊C4—1222no—
560C4⋊C4—1222no—
561C22⋊C4—22no—
562C22⋊C4—22no—
563C22⋊C4—612no—
564C22⋊C4—612no—
565C22⋊C4—1222no—
566C22⋊C4—1222no—
567C22⋊C4—1222no—
568C22⋊C4—1221no—
569C22⋊C4—1221no—
570C22⋊C4—1222no—
571C22⋊C4—1221no—
572C22⋊C4—1221no—
573C22⋊C4C22⋊#692312yes—
574C22⋊C4C22⋊#692312yes—
575C42—612no—
576C42—612no—
577C42—612no—
578C42—612no—
579C42—1221no—
580C42—1221no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—612no—
591C23—1221no—
592C23—1221no—
593C23—1221no—
594C23—1221no—
595C23—1221no—
596C23—2441no—
597C23—2441no—
598C23—2441no—
599C23—2441no—
600C23C2×C22⋊#692312yes—
601C23C23×#692311yescharacteristic
602D4—82no—
603D4—4882no—
604D4—2444no—
605D4—2442no—
606D4—2444no—
607D4—2442no—
608D4—2444no—
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—81no—
619C2×C4—81no—
620C2×C4—611no—
621C2×C4—612no—
622C2×C4—611no—
623C2×C4—611no—
624C2×C4—611no—
625C2×C4—612no—
626C2×C4—1224no—
627C2×C4—1222no—
628C2×C4—1221no—
629C2×C4—1221no—
630C2×C4—1221no—
631C2×C4—1221no—
632C2×C4—1221no—
633C2×C4—1221no—
634C2×C4—4881no—
635C2×C4—4881no—
636C2×C4—4881no—
637C2×C4—4881no—
638C2×C4—4881no—
639C2×C4—4881no—
640C2×C4—2442no—
641C2×C4—2442no—
642C2×C4—2441no—
643C2×C4—2441no—
644C2×C4—2442no—
645C2×C4—2441no—
646C2×C4C2×C22⋊#692312yes—
647C2×C4C2×C22⋊#692311yescharacteristic
648C2×C4C2×C22⋊#692311yescharacteristic
649C8—2442no—
650C8—2442no—
651C8—2442no—
652C8—2442no—
653C22—21no—
654C22—21no—
655C22—22no—
656C22—22no—
657C22—22no—
658C22—41no—
659C22—41no—
660C22—41no—
661C22—81no—
662C22—81no—
663C22—81no—
664C22—81no—
665C22—1222no—
666C22—4881no—
667C22—4881no—
668C22—2442no—
669C22—2442no—
670C22—2441no—
671C22—2441no—
672C22—2441no—
673C22—2441no—
674C22—2441no—
675C22C22×C22⋊#692311yescharacteristic
676C22D61⋊#13111yescharacteristic
677C22#1684084111yescharacteristic
678C4—22no—
679C4—21no—
680C4—21no—
681C4—41no—
682C4—41no—
683C4—41no—
684C4—612no—
685C4—1222no—
686C4—1222no—
687C4—1221no—
688C4—1221no—
689C4—1221no—
690C4—2441no—
691C4—2441no—
692C2—21no—
693C2—21no—
694C2—42no—
695C2—81no—
696C2—4881no—
697C2—2442no—
698C2#2146240911yescharacteristic
699C2D61⋊#41011yescharacteristic
700C2#2146242911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×#123×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840457C2
cosocleC22×Dic61C24
hypercenterC2×#123#6923
hypocenterC61#17415
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C22⋊C4 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. #21462508C2semidirect
2. #21461102C2semidirect
3. #21461101C2semidirect
4. #21461095C2semidirect
5. #21461080C2semidirect
6. #21461078C2semidirect
7. #21461077C2semidirect
8. #21461060C2semidirect
9. #21461058C2semidirect
10. #21461057C2semidirect
401. C61#17415semidirect

Maximal subgroups

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

subgroupindex
#214625082
#214611022
#214611012
#214610952
#214610802
#214610782
#214610772
#214610602
#214610582
#214610572
C2×#168404572
#1741561