Finite Group Databasebeta

← #30622367

Subgroups — #30622367

Order 15616.

722 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462353C211yesmaximal, characteristic
2#21462338C211yesmaximal, characteristic
3#21462002C211yesmaximal, characteristic
4#21461931C211yesmaximal, characteristic
5#21461910C211yesmaximal, characteristic
6#21461908C211yesmaximal, characteristic
7#21461898C211yesmaximal, characteristic
8#21461898C211yesmaximal, characteristic
9#21461883C211yesmaximal, characteristic
10#21461882C211yesmaximal, characteristic
11#21461634C211yesmaximal, characteristic
12#106×#6923C211yesmaximal, characteristic
13#21461620C211yesmaximal, characteristic
14#21461591C211yesmaximal, characteristic
15#479×D61C211yesmaximal, characteristic
16C2×#14519845C2211yescharacteristic
17C2×#14519845C2211yescharacteristic
18C2×#14519840C2211yescharacteristic
19C2×#14519840C2211yescharacteristic
20#16840721C2211yescharacteristic
21C2×#14519831C2211yescharacteristic
22C2×C8×#6923C2211yescharacteristic
23(C2×#6923)⋊Q8C2211yescharacteristic
24(C2×#6923)⋊Q8C2211yescharacteristic
25#16840713—21no—
26#16840713C2211yescharacteristic
27#16840713C2211yescharacteristic
28#16840711—21no—
29#16840711—21no—
30#16840711—21no—
31#16840711—21no—
32#16840708C2211yescharacteristic
33#16840706—21no—
34C4⋊C4×#6923—21no—
35C4⋊C4×#6923C2211yescharacteristic
36C4⋊C4×#6923C2211yescharacteristic
37C4⋊C4×#6923C2211yescharacteristic
38C4⋊C4×#6923C2211yescharacteristic
39C4×C4⋊#6923—21no—
40C4×C4⋊#6923C2211yescharacteristic
41C4×C4⋊#6923C2211yescharacteristic
42#16840636C2211yescharacteristic
43#16840636C2211yescharacteristic
44#16840635C2211yescharacteristic
45#16840635C2211yescharacteristic
46#16840635C2211yescharacteristic
47#16840635C2211yescharacteristic
48#16840635C2211yescharacteristic
49#16840635C2211yescharacteristic
50(C2×#6923)⋊C8C2211yescharacteristic
51(C2×#6923)⋊C8C2211yescharacteristic
52#125×D61C2211yescharacteristic
53C4×Q8×D61C2211yescharacteristic
54#16840072C411yescharacteristic, complemented
55#16840071C411yescharacteristic, complemented
56#16840070C411yescharacteristic, complemented
57#16840069C411yescharacteristic, complemented
58#16840068C411yescharacteristic, complemented
59#16840067C411yescharacteristic, complemented
60#16840066C411yescharacteristic, complemented
61#107×D61C2211yescharacteristic
62#106×D61C2211yescharacteristic
63C4⋊C8×D61C2211yescharacteristic
64#103×D61C2211yescharacteristic
65#103×D61C2211yescharacteristic
66C61×#479C411yescharacteristic, complemented
67C2×D61⋊C8C2311yescharacteristic
68C2×D61⋊C8C2311yescharacteristic
69C2×C4⋊#6923—21no—
70C2×C4⋊#6923—21no—
71C2×C4⋊#6923—21no—
72C2×C4⋊#6923—21no—
73C2×C4⋊#6923D411yescharacteristic
74C2×C4⋊#6923D411yescharacteristic
75C2×C4⋊#6923C2311yescharacteristic
76C2×C4⋊#6923C2311yescharacteristic
77C2×C4⋊#6923C2311yescharacteristic
78C2×C4⋊#6923C2311yescharacteristic
79C2×C4×#6923—21no—
80C2×C4×#6923—21no—
81C2×C4×#6923—21no—
82C2×C4×#6923—21no—
83C2×C4×#6923—21no—
84C2×C4×#6923C2311yescharacteristic
85C2×C4×#6923C2311yescharacteristic
86#14519845—22no—
87#14519845—22no—
88#14519840—22no—
89#14519840—22no—
90#14519832—21no—
91#14519832—21no—
92#14519831—22no—
93C8×#6923—22no—
94(C2×#6923)⋊C4—21no—
95(C2×#6923)⋊C4—21no—
96(C2×#6923)⋊C4—21no—
97(C2×#6923)⋊C4—21no—
98(C2×#6923)⋊C4—21no—
99(C2×#6923)⋊C4—21no—
100(C2×#6923)⋊C4—21no—
101(C2×#6923)⋊C4—21no—
102(C2×#6923)⋊C4—21no—
103(C2×#6923)⋊C4—21no—
104(C2×#6923)⋊C4—21no—
105(C2×#6923)⋊C4D411yescharacteristic
106(C2×#6923)⋊C4D411yescharacteristic
107C2×Q8×D61C2311yescharacteristic
108C2×C8×D61C2311yescharacteristic
109C2×C8×D61C2311yescharacteristic
110#14519769C2×C411yescharacteristic
111#14519768C2×C411yescharacteristic
112#14519768C2×C411yescharacteristic
113#14519767—21no—
114#14519767—21no—
115Q8×Dic61C2×C411yescharacteristic
116C4×Dic122—21no—
117C4×Dic122C2×C411yescharacteristic
118#14519742—21no—
119#14519742C2×C411yescharacteristic
120C4⋊C4×D61—21no—
121C4⋊C4×D61—21no—
122C4⋊C4×D61—21no—
123C4⋊C4×D61C2311yescharacteristic
124C4⋊C4×D61C2311yescharacteristic
125C4⋊C4×D61C2311yescharacteristic
126C42×D61—21no—
127C42×D61C2311yescharacteristic
128#14519711C2×C411yescharacteristic
129#14519710C2×C411yescharacteristic
130#14519710C2×C411yescharacteristic
131#14519709C2×C411yescharacteristic
132#14519708C2×C411yescharacteristic
133#14519708C2×C411yescharacteristic
134C4⋊#92418C2×C411yescharacteristic
135#14519706C2×C411yescharacteristic
136#14519706C2×C411yescharacteristic
137#14519702C2×C411yescharacteristic
138#14519702C2×C411yescharacteristic
139#14519701C2×C411yescharacteristic
140#14519701C2×C411yescharacteristic
141#14519700C2×C411yescharacteristic
142#14519700C2×C411yescharacteristic
143#125×C61C2×C411yescharacteristic
144C4×Q8×C61C2×C411yescharacteristic
145#107×C61C2×C411yescharacteristic
146#106×C61C2×C411yescharacteristic
147C4⋊C8×C61C2×C411yescharacteristic
148#103×C61C2×C411yescharacteristic
149#103×C61C2×C411yescharacteristic
150C22×#6923—21no—
151C22×#6923—21no—
152C22×#6923—21no—
153C22×#6923—21no—
154C22×#6923C2×D411yescharacteristic
155C22×#6923C2×D411yescharacteristic
156C22×#6923C2×D411yescharacteristic
157C22×#6923C2×D411yescharacteristic
158C2×Q8×C61C22×C411yescharacteristic
159Q8×D61—21no—
160Q8×D61—21no—
161Q8×D61—21no—
162Q8×D61—21no—
163C2×C4×D61—21no—
164C2×C4×D61—21no—
165C2×C4×D61—21no—
166C2×C4×D61—21no—
167C2×C4×D61C2×D411yescharacteristic
168C2×C4×D61C2×D411yescharacteristic
169C2×C4×D61C2411yescharacteristic
170C2×Dic122—21no—
171C2×Dic122C22×C411yescharacteristic
172C2×#92420—21no—
173C2×#92420—21no—
174C4⋊#6923—22no—
175C4⋊#6923—21no—
176C4⋊#6923—21no—
177C4⋊#6923—21no—
178C4⋊#6923—21no—
179C4⋊#6923—21no—
180C4⋊#6923—21no—
181C4⋊#6923—21no—
182C4⋊#6923—41no—
183C4⋊#6923—42no—
184C4⋊#6923—42no—
185C4⋊#6923—81no—
186C4⋊#6923—81no—
187C4⋊#6923#4112yes—
188C4×#6923—21no—
189C4×#6923—21no—
190C4×#6923—21no—
191C4×#6923—21no—
192C4×#6923—42no—
193C4×#6923—81no—
194C4×#6923—81no—
195C4×#6923—81no—
196C4×#6923—81no—
197D61⋊C8—21no—
198D61⋊C8—21no—
199D61⋊C8—21no—
200D61⋊C8#4112yes—
201C2×C8×C61C22×C411yescharacteristic
202C2×C8×C61C22×C411yescharacteristic
203C4⋊C4×C61—21no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61C22×C411yescharacteristic
207C4⋊C4×C61C22×C411yescharacteristic
208C4⋊C4×C61C22×C411yescharacteristic
209C42×C61—21no—
210C42×C61C22×C411yescharacteristic
211C4⋊Dic61—21no—
212C4⋊Dic61—21no—
213C4⋊Dic61—21no—
214C4⋊Dic61C22×C411yescharacteristic
215C4⋊Dic61C22×C411yescharacteristic
216C4⋊Dic61C22×C411yescharacteristic
217#11758196—21no—
218#11758196—21no—
219#11758196—21no—
220#11758196—21no—
221#11758196—21no—
222#11758196—21no—
223#11758196—21no—
224#11758196—21no—
225#11758196—21no—
226C4×Dic61—21no—
227C4×Dic61—21no—
228C4×Dic61—21no—
229C4×Dic61C22×C411yescharacteristic
230C4×Dic61#4111yescharacteristic
231C4×Dic61#4111yescharacteristic
232C2×#92418C22×C411yescharacteristic
233C2×#92418C22×C411yescharacteristic
234C8×D61—21no—
235C8×D61—21no—
236C8×D61—21no—
237C8×D61—21no—
238C22×D61C22×D411yescharacteristic
239C2×#6923—21no—
240C2×#6923—21no—
241C2×#6923—21no—
242C2×#6923—21no—
243C2×#6923—21no—
244C2×#6923—22no—
245C2×#6923—21no—
246C2×#6923—21no—
247C2×#6923—21no—
248C2×#6923—21no—
249C2×#6923—21no—
250C2×#6923—21no—
251C2×#6923—41no—
252C2×#6923—41no—
253C2×#6923—41no—
254C2×#6923—41no—
255C2×#6923—41no—
256C2×#6923—41no—
257C2×#6923—41no—
258C2×#6923—41no—
259C2×#6923—41no—
260C2×#6923—41no—
261C2×#6923—41no—
262C2×#6923#13712yes—
263Q8×C61—21no—
264Q8×C61—21no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61C4×D411yescharacteristic
270C2×C4×C61C4×D411yescharacteristic
271C2×C4×C61C23×C411yescharacteristic
272C2×Dic61—21no—
273C2×Dic61—21no—
274C2×Dic61—21no—
275C2×Dic61—21no—
276C2×Dic61C4×D411yescharacteristic
277C2×Dic61C4×D411yescharacteristic
278C2×Dic61C2×#4111yescharacteristic
279C4×D61—21no—
280C4×D61—21no—
281C4×D61—21no—
282C4×D61—21no—
283C4×D61—41no—
284C4×D61—41no—
285C4×D61—41no—
286C4×D61—41no—
287C4×D61—41no—
288C4×D61—41no—
289C4×D61—41no—
290C4×D61—41no—
291C4×D61C2×#4111yescharacteristic
292C4×D61C2×#4111yescharacteristic
293C4×D612−1+411yescharacteristic
294C4×D612−1+411yescharacteristic
295Dic122—21no—
296Dic122—21no—
297Dic122—41no—
298Dic122—41no—
299#92420—22no—
300#92420—41no—
301C8×C61—21no—
302C8×C61—21no—
303#92418—21no—
304#92418—21no—
305#23078—611nomaximal, Sylow
306C22×C61C2×C4×D411yescharacteristic
307C2×D61#54711yescharacteristic
308C2×D61#54811yescharacteristic
309C2×D61C2×#13711yescharacteristic
310C2×D61#57511yescharacteristic
311C2×D61#57711yescharacteristic
312C2×D61#57711yescharacteristic
313#6923—22no—
314#6923—41no—
315#6923—41no—
316#6923—41no—
317#6923—42no—
318#6923—81no—
319#6923—81no—
320#6923—81no—
321C4×C61—21no—
322C4×C61—21no—
323C4×C61—41no—
324C4×C61—41no—
325C4×C61—41no—
326C4×C61—41no—
327C4×C61C4×#4111yescharacteristic
328C4×C61#51911yescharacteristic
329Dic61—21no—
330Dic61—21no—
331Dic61—41no—
332Dic61—41no—
333Dic61—41no—
334Dic61—41no—
335Dic61#55211yescharacteristic
336Dic61#55611yescharacteristic
337C2×#479—611no—
338#2370—611no—
339#2355—611no—
340#1992—611no—
341#1948—611no—
342#1935—611no—
343#1933—611no—
344#1927—611no—
345#1927—611no—
346#1921—611no—
347#1920—611no—
348#1776—611no—
349C4×#106—611no—
350#1771—611no—
351#1763—611no—
352C2×C61#236211yescharacteristic
353C2×C61C4×#13711yescharacteristic
354C2×C61#295211yescharacteristic
355D61#334411yescharacteristic
356D61#335011yescharacteristic
357D61#337111yescharacteristic
358D61#337211yescharacteristic
359C2×#125—611no—
360C2×C4×Q8—611no—
361#479—611no—
362#479—611no—
363#479—611no—
364#479—611no—
365#479—611no—
366#479—611no—
367#479—611no—
368#479#692311yescharacteristic, complemented
369C2×#107—611no—
370C2×#106—611no—
371C2×#106—611no—
372C2×#106—611no—
373C2×C4⋊C8—611no—
374C2×#103—611no—
375C2×#103—611no—
376C2×#103—611no—
377C2×#103—611no—
378C2×#97—611no—
379C2×#97—611no—
380C2×C4×C8—611no—
381#391—611no—
382#391—611no—
383#389—611no—
384#389—611no—
385#389—1221no—
386#387—1221no—
387#387—1221no—
388#387—1221no—
389#387—1221no—
390#384—611no—
391#382—1221no—
392C4×C4⋊C4—611no—
393C4×C4⋊C4—611no—
394C4×C4⋊C4—611no—
395C4×C4⋊C4—611no—
396C4×C4⋊C4—611no—
397C4×C4⋊C4—611no—
398C4×C4⋊C4—1221no—
399C4×C4⋊C4—1221no—
400#340—611no—
401#340—611no—
402#340—611no—
403#340—611no—
404#340—611no—
405#340—611no—
406#340—611no—
407#340—611no—
408#336—611no—
409#336—611no—
410C61#2307811yescharacteristic, complemented, Sylow
411C22×Q8—611no—
412C22×C8—611no—
413C22×C8—611no—
414C22×C8—611no—
415C22×C8—611no—
416#125—611no—
417#125—611no—
418#125—611no—
419#125—1221no—
420#125—1221no—
421#125C2×#692311yescharacteristic
422C4×Q8—611no—
423C4×Q8—611no—
424C4×Q8—611no—
425C4×Q8—1221no—
426C4×Q8—1221no—
427C4×Q8C2×#692311yescharacteristic
428C2×C4⋊C4—611no—
429C2×C4⋊C4—611no—
430C2×C4⋊C4—611no—
431C2×C4⋊C4—611no—
432C2×C4⋊C4—611no—
433C2×C4⋊C4—611no—
434C2×C4⋊C4—611no—
435C2×C4⋊C4—611no—
436C2×C4⋊C4—611no—
437C2×C4⋊C4—1221no—
438C2×C4⋊C4—1221no—
439C2×C4⋊C4—1221no—
440C2×C4⋊C4—1221no—
441C2×C4⋊C4—1221no—
442C2×C4⋊C4—1221no—
443C2×C4⋊C4—1221no—
444C2×C42—611no—
445C2×C42—611no—
446C2×C42—611no—
447C2×C42—1221no—
448C2×C42—1221no—
449C2×C42—1221no—
450C2×C42—1221no—
451C2×C42—1221no—
452C2×C42—1221no—
453#107—611no—
454#107—611no—
455#107—611no—
456#107C2×#692311yescharacteristic
457#106—611no—
458#106—611no—
459#106—611no—
460#106—1222no—
461#106—1222no—
462#106C2×#692311yescharacteristic
463C4⋊C8—611no—
464C4⋊C8—611no—
465C4⋊C8—611no—
466C4⋊C8C2×#692311yescharacteristic
467#103—611no—
468#103—611no—
469#103—611no—
470#103—611no—
471#103—611no—
472#103—611no—
473#103—1222no—
474#103—1222no—
475#103C2×#692311yescharacteristic
476#103C2×#692311yescharacteristic
477#97—1221no—
478#97—1221no—
479#97—1222no—
480C4×C8—1222no—
481#95—611no—
482#95—611no—
483#95—1221no—
484#95—1221no—
485#95—1221no—
486#95—1221no—
487#95—1221no—
488#95—1221no—
489#95—1221no—
490#95—1221no—
491#95—1221no—
492#95—1221no—
493#95—1221no—
494C2×Q8—611no—
495C2×Q8—1221no—
496C2×Q8—1221no—
497C2×Q8—1221no—
498C2×Q8—1221no—
499C2×Q8—1221no—
500C2×Q8C22×#692311yescharacteristic
501C22×C4—611no—
502C22×C4—611no—
503C22×C4—611no—
504C22×C4—611no—
505C22×C4—611no—
506C22×C4—611no—
507C22×C4—611no—
508C22×C4—1221no—
509C22×C4—1221no—
510C22×C4—1221no—
511C22×C4—1221no—
512C22×C4—1221no—
513C22×C4—1221no—
514C22×C4—1221no—
515C22×C4—1221no—
516C2×C8—612no—
517C2×C8—611no—
518C2×C8—611no—
519C2×C8—1221no—
520C2×C8—1221no—
521C2×C8—1221no—
522C2×C8—1221no—
523C2×C8—1221no—
524C2×C8—1221no—
525C2×C8—1221no—
526C2×C8—1221no—
527C2×C8—1221no—
528C2×C8C22×#692311yescharacteristic
529C2×C8C22×#692311yescharacteristic
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—612no—
534C4⋊C4—611no—
535C4⋊C4—611no—
536C4⋊C4—611no—
537C4⋊C4—1221no—
538C4⋊C4—1221no—
539C4⋊C4—1221no—
540C4⋊C4—1221no—
541C4⋊C4—1221no—
542C4⋊C4—1221no—
543C4⋊C4—1221no—
544C4⋊C4—1221no—
545C4⋊C4—1221no—
546C4⋊C4—1221no—
547C4⋊C4—1222no—
548C4⋊C4—1221no—
549C4⋊C4—1221no—
550C4⋊C4—1221no—
551C4⋊C4—1221no—
552C4⋊C4—1221no—
553C4⋊C4—1221no—
554C4⋊C4—1221no—
555C4⋊C4—1221no—
556C4⋊C4—1221no—
557C4⋊C4—4881no—
558C4⋊C4—4881no—
559C4⋊C4—2441no—
560C4⋊C4—2442no—
561C4⋊C4—2442no—
562C4⋊C4C22×#692311yescharacteristic
563C4⋊C4C22×#692311yescharacteristic
564C4⋊C4C22×#692311yescharacteristic
565C42—21no—
566C42—611no—
567C42—611no—
568C42—611no—
569C42—1221no—
570C42—1221no—
571C42—1221no—
572C42—1221no—
573C42—1221no—
574C42—1221no—
575C42—1221no—
576C42—4881no—
577C42—4881no—
578C42—4881no—
579C42—4881no—
580C42—2442no—
581C42C22×#692311yescharacteristic
582C23—611no—
583Q8—21no—
584Q8—21no—
585Q8—1221no—
586Q8—1221no—
587Q8—2441no—
588Q8—2441no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—611no—
594C2×C4—611no—
595C2×C4—611no—
596C2×C4—611no—
597C2×C4—611no—
598C2×C4—612no—
599C2×C4—611no—
600C2×C4—611no—
601C2×C4—1221no—
602C2×C4—1221no—
603C2×C4—1221no—
604C2×C4—1221no—
605C2×C4—1221no—
606C2×C4—1221no—
607C2×C4—1221no—
608C2×C4—1221no—
609C2×C4—1221no—
610C2×C4—1221no—
611C2×C4—1221no—
612C2×C4—1222no—
613C2×C4—1221no—
614C2×C4—1221no—
615C2×C4—1221no—
616C2×C4—1221no—
617C2×C4—1221no—
618C2×C4—1221no—
619C2×C4—1221no—
620C2×C4—1221no—
621C2×C4—2441no—
622C2×C4—2441no—
623C2×C4—2441no—
624C2×C4—2441no—
625C2×C4—2441no—
626C2×C4—2441no—
627C2×C4—2441no—
628C2×C4—2441no—
629C2×C4—2441no—
630C2×C4—2441no—
631C2×C4—2441no—
632C2×C4—2441no—
633C2×C4—2441no—
634C2×C4—2441no—
635C2×C4—2441no—
636C2×C4—2441no—
637C2×C4—2441no—
638C2×C4—2441no—
639C2×C4—2441no—
640C2×C4D4×#692311yescharacteristic
641C2×C4D4×#692311yescharacteristic
642C2×C4C23×#692311yescharacteristic
643C8—21no—
644C8—21no—
645C8—1222no—
646C8—1221no—
647C8—1221no—
648C8—2441no—
649C22—611no—
650C22—611no—
651C22—611no—
652C22—611no—
653C22—611no—
654C22—611no—
655C22C2×D4×#692311yescharacteristic
656C4—21no—
657C4—21no—
658C4—41no—
659C4—41no—
660C4—41no—
661C4—41no—
662C4—611no—
663C4—611no—
664C4—1222no—
665C4—1221no—
666C4—1221no—
667C4—4881no—
668C4—4881no—
669C4—4881no—
670C4—2441no—
671C4—2441no—
672C4—2441no—
673C4—2442no—
674C4—2441no—
675C4—2441no—
676C4—2441no—
677C4—2441no—
678C4#41×#692311yescharacteristic
679C4#1684083011yescharacteristic
680C2—611no—
681C2—611no—
682C2—611no—
683C2—611no—
684C2#2146234511yescharacteristic
685C2#137×#692311yescharacteristic
686C2#2146258211yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#479C4
socleC22×C61C2×C4×D4
prime radicalC22×D61C22×D4
cosocleC2×C4×D61C24
hypercenter#479#6923
hypocenterC61#23078
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
54. #16840072C4semidirect
55. #16840071C4semidirect
56. #16840070C4semidirect
57. #16840069C4semidirect
58. #16840068C4semidirect
59. #16840067C4semidirect
60. #16840066C4semidirect
66. C61×#479C4semidirect
368. #479#6923semidirect
410. C61#23078semidirect

Maximal subgroups

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

subgroupindex
#214623532
#214623382
#214620022
#214619312
#214619102
#214619082
#214618982
#214618832
#214618822
#214616342
#106×#69232
#214616202
#214615912
#479×D612
#2307861