Finite Group Databasebeta

← #30622353

Subgroups — #30622353

Order 15616.

726 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462353C211yesmaximal, characteristic
2#21462339C211yesmaximal, characteristic
3#21462001C211yesmaximal, characteristic
4#21461932C211yesmaximal, characteristic
5#21461908C211yesmaximal, characteristic
6#21461908C211yesmaximal, characteristic
7#21461899C211yesmaximal, characteristic
8#21461898C211yesmaximal, characteristic
9#21461882C211yesmaximal, characteristic
10#21461880C211yesmaximal, characteristic
11#107×#6923C211yesmaximal, characteristic
12#106×#6923C211yesmaximal, characteristic
13#21461612C211yesmaximal, characteristic
14C4×#14519840C211yesmaximal, characteristic
15#479×D61C211yesmaximal, characteristic
16C2×#14519846C2211yescharacteristic
17C2×#14519845C2211yescharacteristic
18C2×#14519840C2211yescharacteristic
19C2×#14519840C2211yescharacteristic
20C4×D61⋊C8C2211yescharacteristic
21C2×C8×#6923C2211yescharacteristic
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#16840707—21no—
33#16840706C2211yescharacteristic
34C4⋊C4×#6923—21no—
35C4⋊C4×#6923C2211yescharacteristic
36C4⋊C4×#6923C2211yescharacteristic
37C4⋊C4×#6923C2211yescharacteristic
38C4⋊C4×#6923C2211yescharacteristic
39C4×C4⋊#6923C2211yescharacteristic
40C4×C4⋊#6923C2211yescharacteristic
41#16840698—21no—
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⋊#6923D411yescharacteristic
72C2×C4⋊#6923D411yescharacteristic
73C2×C4⋊#6923C2311yescharacteristic
74C2×C4⋊#6923C2311yescharacteristic
75C2×C4⋊#6923C2311yescharacteristic
76C2×C4⋊#6923C2311yescharacteristic
77C2×C4×#6923—21no—
78C2×C4×#6923—21no—
79C2×C4×#6923—21no—
80C2×C4×#6923—21no—
81C2×C4×#6923—21no—
82C2×C4×#6923C2311yescharacteristic
83C2×C4×#6923C2311yescharacteristic
84#14519846—22no—
85#14519845—22no—
86#14519840—22no—
87#14519840—22no—
88C4×#92420—21no—
89C4×#92420—21no—
90C8×#6923—22no—
91C8×#6923—22no—
92(C2×#6923)⋊C4—21no—
93(C2×#6923)⋊C4—21no—
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—22no—
176C4⋊#6923—21no—
177C4⋊#6923—21no—
178C4⋊#6923—21no—
179C4⋊#6923—21no—
180C4⋊#6923—21no—
181C4⋊#6923—21no—
182C4⋊#6923—21no—
183C4⋊#6923—42no—
184C4⋊#6923—81no—
185C4⋊#6923#4112yes—
186C4×#6923—21no—
187C4×#6923—21no—
188C4×#6923—21no—
189C4×#6923—21no—
190C4×#6923—42no—
191C4×#6923—42no—
192C4×#6923—42no—
193C4×#6923—81no—
194C4×#6923—81no—
195D61⋊C8—21no—
196D61⋊C8—21no—
197D61⋊C8—21no—
198D61⋊C8#4112yes—
199C2×C8×C61C22×C411yescharacteristic
200C2×C8×C61C22×C411yescharacteristic
201C4⋊C4×C61—21no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61C22×C411yescharacteristic
205C4⋊C4×C61C22×C411yescharacteristic
206C4⋊C4×C61C22×C411yescharacteristic
207C42×C61—21no—
208C42×C61C22×C411yescharacteristic
209C4⋊Dic61—21no—
210C4⋊Dic61—21no—
211C4⋊Dic61—21no—
212C4⋊Dic61C22×C411yescharacteristic
213C4⋊Dic61C22×C411yescharacteristic
214C4⋊Dic61C22×C411yescharacteristic
215#11758196—21no—
216#11758196—21no—
217#11758196—21no—
218#11758196—21no—
219#11758196—21no—
220#11758196—21no—
221#11758196—21no—
222#11758196—21no—
223#11758196—21no—
224C4×Dic61—21no—
225C4×Dic61—21no—
226C4×Dic61—21no—
227C4×Dic61C22×C411yescharacteristic
228C4×Dic61#4111yescharacteristic
229C4×Dic61#4111yescharacteristic
230C2×#92418C22×C411yescharacteristic
231C2×#92418C22×C411yescharacteristic
232C8×D61—21no—
233C8×D61—21no—
234C8×D61—21no—
235C8×D61—21no—
236C22×D61C22×D411yescharacteristic
237C2×#6923—21no—
238C2×#6923—21no—
239C2×#6923—21no—
240C2×#6923—21no—
241C2×#6923—21no—
242C2×#6923—21no—
243C2×#6923—22no—
244C2×#6923—21no—
245C2×#6923—21no—
246C2×#6923—21no—
247C2×#6923—21no—
248C2×#6923—41no—
249C2×#6923—41no—
250C2×#6923—41no—
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#13512yes—
260C2×#6923#13512yes—
261Q8×C61—21no—
262Q8×C61—21no—
263C2×C4×C61—21no—
264C2×C4×C61—21no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61C4×D411yescharacteristic
268C2×C4×C61C4×D411yescharacteristic
269C2×C4×C61C23×C411yescharacteristic
270C2×Dic61—21no—
271C2×Dic61—21no—
272C2×Dic61—21no—
273C2×Dic61—21no—
274C2×Dic61C4×D411yescharacteristic
275C2×Dic61C4×D411yescharacteristic
276C2×Dic61C2×#4111yescharacteristic
277C4×D61—21no—
278C4×D61—21no—
279C4×D61—21no—
280C4×D61—21no—
281C4×D61—41no—
282C4×D61—41no—
283C4×D61—41no—
284C4×D61—41no—
285C4×D61—41no—
286C4×D61—41no—
287C4×D61—41no—
288C4×D61—41no—
289C4×D61C2×#4111yescharacteristic
290C4×D61C2×#4111yescharacteristic
291C4×D612−1+411yescharacteristic
292C4×D612−1+411yescharacteristic
293Dic122—21no—
294Dic122—21no—
295Dic122—41no—
296Dic122—41no—
297#92420—22no—
298#92420—41no—
299C8×C61—21no—
300C8×C61—21no—
301#92418—21no—
302#92418—21no—
303#23064—611nomaximal, Sylow
304C22×C61C2×C4×D411yescharacteristic
305C2×D61#54711yescharacteristic
306C2×D61#54811yescharacteristic
307C2×D61C2×#13511yescharacteristic
308C2×D61C2×#13511yescharacteristic
309C2×D61#57711yescharacteristic
310C2×D61#57811yescharacteristic
311#6923—22no—
312#6923—22no—
313#6923—41no—
314#6923—41no—
315#6923—42no—
316#6923—81no—
317#6923—81no—
318#6923—81no—
319C4×C61—21no—
320C4×C61—21no—
321C4×C61—41no—
322C4×C61—41no—
323C4×C61—41no—
324C4×C61—41no—
325C4×C61C4×#4111yescharacteristic
326C4×C61#51911yescharacteristic
327Dic61—21no—
328Dic61—21no—
329Dic61—41no—
330Dic61—41no—
331Dic61—41no—
332Dic61—41no—
333Dic61#55211yescharacteristic
334Dic61#55611yescharacteristic
335C2×#479—611no—
336#2370—611no—
337#2356—611no—
338#1991—611no—
339#1949—611no—
340#1933—611no—
341#1933—611no—
342#1928—611no—
343#1927—611no—
344#1920—611no—
345#1918—611no—
346C4×#107—611no—
347C4×#106—611no—
348C8×C4⋊C4—611no—
349C4×#103—611no—
350C2×C61#236211yescharacteristic
351C2×C61C4×#13511yescharacteristic
352C2×C61#294711yescharacteristic
353D61#333611yescharacteristic
354D61#333711yescharacteristic
355D61#336011yescharacteristic
356D61#336411yescharacteristic
357C2×#125—611no—
358C2×C4×Q8—611no—
359#479—611no—
360#479—611no—
361#479—611no—
362#479—611no—
363#479—611no—
364#479—611no—
365#479—611no—
366#479#692311yescharacteristic, complemented
367C2×#107—611no—
368C2×#107—611no—
369C2×#106—611no—
370C2×#106—611no—
371C2×C4⋊C8—611no—
372C2×#103—611no—
373C2×#103—611no—
374C2×#103—611no—
375C2×#103—611no—
376C2×C4×C8—611no—
377C2×C4×C8—611no—
378C2×C4×C8—611no—
379#391—611no—
380#391—611no—
381#389—611no—
382#389—611no—
383#389—1221no—
384#387—1221no—
385#387—1221no—
386#387—1221no—
387#387—1221no—
388#383—1221no—
389#382—611no—
390C4×C4⋊C4—611no—
391C4×C4⋊C4—611no—
392C4×C4⋊C4—611no—
393C4×C4⋊C4—611no—
394C4×C4⋊C4—611no—
395C4×C4⋊C4—611no—
396C4×C4⋊C4—1221no—
397#376—1221no—
398#340—611no—
399#340—611no—
400#340—611no—
401#340—611no—
402#340—611no—
403#340—611no—
404#340—611no—
405#340—611no—
406#336—611no—
407#336—611no—
408C61#2306411yescharacteristic, complemented, Sylow
409C22×Q8—611no—
410C22×C8—611no—
411C22×C8—611no—
412C22×C8—611no—
413C22×C8—611no—
414#125—611no—
415#125—611no—
416#125—611no—
417#125—1221no—
418#125—1221no—
419#125C2×#692311yescharacteristic
420C4×Q8—611no—
421C4×Q8—611no—
422C4×Q8—611no—
423C4×Q8—1221no—
424C4×Q8—1221no—
425C4×Q8C2×#692311yescharacteristic
426C2×C4⋊C4—611no—
427C2×C4⋊C4—611no—
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—1221no—
436C2×C4⋊C4—1221no—
437C2×C4⋊C4—1221no—
438C2×C4⋊C4—1221no—
439C2×C4⋊C4—1221no—
440C2×C42—611no—
441C2×C42—611no—
442C2×C42—611no—
443C2×C42—1221no—
444C2×C42—1221no—
445C2×C42—1221no—
446C2×C42—1221no—
447C2×C42—1221no—
448C2×C42—1221no—
449#107—611no—
450#107—611no—
451#107—611no—
452#107—1222no—
453#107C2×#692311yescharacteristic
454#106—611no—
455#106—611no—
456#106—611no—
457#106—1222no—
458#106C2×#692311yescharacteristic
459C4⋊C8—611no—
460C4⋊C8—611no—
461C4⋊C8—611no—
462C4⋊C8C2×#692311yescharacteristic
463#103—611no—
464#103—611no—
465#103—611no—
466#103—611no—
467#103—611no—
468#103—611no—
469#103—1222no—
470#103—1222no—
471#103C2×#692311yescharacteristic
472#103C2×#692311yescharacteristic
473C4×C8—1221no—
474C4×C8—1221no—
475C4×C8—1222no—
476C4×C8—1222no—
477#95—611no—
478#95—611no—
479#95—1221no—
480#95—1221no—
481#95—1221no—
482#95—1221no—
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—
492C2×Q8—611no—
493C2×Q8—1221no—
494C2×Q8—1221no—
495C2×Q8—1221no—
496C2×Q8—1221no—
497C2×Q8—1221no—
498C2×Q8C22×#692311yescharacteristic
499C22×C4—611no—
500C22×C4—611no—
501C22×C4—611no—
502C22×C4—611no—
503C22×C4—611no—
504C22×C4—611no—
505C22×C4—611no—
506C22×C4—1221no—
507C22×C4—1221no—
508C22×C4—1221no—
509C22×C4—1221no—
510C22×C4—1221no—
511C22×C4—1221no—
512C22×C4—1221no—
513C22×C4—1221no—
514C2×C8—612no—
515C2×C8—611no—
516C2×C8—611no—
517C2×C8—1221no—
518C2×C8—1221no—
519C2×C8—1221no—
520C2×C8—1221no—
521C2×C8—1221no—
522C2×C8—1221no—
523C2×C8—1221no—
524C2×C8—1221no—
525C2×C8—1221no—
526C2×C8C22×#692311yescharacteristic
527C2×C8C22×#692311yescharacteristic
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—612no—
532C4⋊C4—611no—
533C4⋊C4—611no—
534C4⋊C4—611no—
535C4⋊C4—1221no—
536C4⋊C4—1221no—
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—1222no—
546C4⋊C4—1222no—
547C4⋊C4—1221no—
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—4881no—
557C4⋊C4—2442no—
558C4⋊C4C22×#692311yescharacteristic
559C4⋊C4C22×#692311yescharacteristic
560C4⋊C4C22×#692311yescharacteristic
561C42—21no—
562C42—611no—
563C42—611no—
564C42—611no—
565C42—1221no—
566C42—1221no—
567C42—1221no—
568C42—1221no—
569C42—1221no—
570C42—1221no—
571C42—1221no—
572C42—4881no—
573C42—4881no—
574C42—2442no—
575C42—2442no—
576C42—2442no—
577C42C22×#692311yescharacteristic
578C23—611no—
579Q8—21no—
580Q8—21no—
581Q8—1221no—
582Q8—1221no—
583Q8—2441no—
584Q8—2441no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—611no—
590C2×C4—611no—
591C2×C4—611no—
592C2×C4—611no—
593C2×C4—611no—
594C2×C4—612no—
595C2×C4—612no—
596C2×C4—611no—
597C2×C4—611no—
598C2×C4—1221no—
599C2×C4—1221no—
600C2×C4—1221no—
601C2×C4—1221no—
602C2×C4—1221no—
603C2×C4—1221no—
604C2×C4—1221no—
605C2×C4—1221no—
606C2×C4—1221no—
607C2×C4—1221no—
608C2×C4—1222no—
609C2×C4—1221no—
610C2×C4—1221no—
611C2×C4—1221no—
612C2×C4—1221no—
613C2×C4—1221no—
614C2×C4—1221no—
615C2×C4—1221no—
616C2×C4—1221no—
617C2×C4—2441no—
618C2×C4—2441no—
619C2×C4—2441no—
620C2×C4—2441no—
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×C4D4×#692311yescharacteristic
637C2×C4D4×#692311yescharacteristic
638C2×C4C23×#692311yescharacteristic
639C8—21no—
640C8—21no—
641C8—1222no—
642C8—1221no—
643C8—1221no—
644C8—2441no—
645C22—611no—
646C22—611no—
647C22—611no—
648C22—611no—
649C22—611no—
650C22—611no—
651C22C2×D4×#692311yescharacteristic
652C4—21no—
653C4—21no—
654C4—41no—
655C4—41no—
656C4—41no—
657C4—41no—
658C4—611no—
659C4—611no—
660C4—1222no—
661C4—1222no—
662C4—1221no—
663C4—1221no—
664C4—4881no—
665C4—4881no—
666C4—4881no—
667C4—2441no—
668C4—2441no—
669C4—2442no—
670C4—2441no—
671C4—2441no—
672C4—2441no—
673C4—2441no—
674C4#41×#692311yescharacteristic
675C4#1684083011yescharacteristic
676C2—611no—
677C2—611no—
678C2—611no—
679C2—611no—
680C2#2146234511yescharacteristic
681C2#135×#692311yescharacteristic
682C2#2146257711yescharacteristic
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#23064
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
366. #479#6923semidirect
408. C61#23064semidirect

Maximal subgroups

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

subgroupindex
#214623532
#214623392
#214620012
#214619322
#214619082
#214618992
#214618982
#214618822
#214618802
#107×#69232
#106×#69232
#214616122
C4×#145198402
#479×D612
#2306461