Finite Group Databasebeta

← #30622366

Subgroups — #30622366

Order 15616.

730 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462352C211yesmaximal, characteristic
2#21462339C211yesmaximal, characteristic
3#21462003C211yesmaximal, characteristic
4#21461932C211yesmaximal, characteristic
5#21461910C211yesmaximal, characteristic
6#21461908C211yesmaximal, characteristic
7#21461899C211yesmaximal, characteristic
8#21461898C211yesmaximal, characteristic
9#21461882C211yesmaximal, characteristic
10#21461881C211yesmaximal, characteristic
11#21461635C211yesmaximal, characteristic
12#106×#6923C211yesmaximal, characteristic
13#21461620C211yesmaximal, characteristic
14#21461591C211yesmaximal, characteristic
15#475×D61C211yesmaximal, characteristic
16C2×#14519846C2211yescharacteristic
17C2×#14519845C2211yescharacteristic
18C2×#14519840C2211yescharacteristic
19C2×#14519840C2211yescharacteristic
20#16840721C2211yescharacteristic
21C2×#14519831C2211yescharacteristic
22C2×C8×#6923C2211yescharacteristic
23(C2×#6923)⋊Q8—21no—
24(C2×#6923)⋊Q8—21no—
25(C2×#6923)⋊Q8C2211yescharacteristic
26(C2×#6923)⋊Q8C2211yescharacteristic
27#16840713—21no—
28#16840713C2211yescharacteristic
29#16840713C2211yescharacteristic
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
52C4⋊Q8×D61C2211yescharacteristic
53C4×Q8×D61C2211yescharacteristic
54#16840048C411yescharacteristic, complemented
55#16840047C411yescharacteristic, complemented
56#16840046C411yescharacteristic, complemented
57#16840046C411yescharacteristic, complemented
58#16840045C411yescharacteristic, complemented
59#16840045C411yescharacteristic, complemented
60#16840044C411yescharacteristic, complemented
61#106×D61C2211yescharacteristic
62#106×D61C2211yescharacteristic
63C4⋊C8×D61C2211yescharacteristic
64#103×D61C2211yescharacteristic
65#103×D61C2211yescharacteristic
66C61×#475C411yescharacteristic, 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—
88#14519832—21no—
89#14519832—21no—
90#14519831—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×D61—21no—
108C2×Q8×D61C2311yescharacteristic
109C2×C8×D61C2311yescharacteristic
110C2×C8×D61C2311yescharacteristic
111#14519777C2×C411yescharacteristic
112#14519776—21no—
113#14519776C2×C411yescharacteristic
114#14519776C2×C411yescharacteristic
115#14519775—21no—
116Q8×Dic61C2×C411yescharacteristic
117C4×Dic122—21no—
118C4×Dic122C2×C411yescharacteristic
119#14519742—21no—
120#14519742C2×C411yescharacteristic
121C4⋊C4×D61—21no—
122C4⋊C4×D61—21no—
123C4⋊C4×D61C2311yescharacteristic
124C4⋊C4×D61C2311yescharacteristic
125C4⋊C4×D61C2311yescharacteristic
126C42×D61—21no—
127C42×D61C2311yescharacteristic
128#14519709C2×C411yescharacteristic
129#14519709C2×C411yescharacteristic
130#14519708C2×C411yescharacteristic
131#14519708C2×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
143C4⋊Q8×C61C2×C411yescharacteristic
144C4×Q8×C61C2×C411yescharacteristic
145#106×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×C61—21no—
159C2×Q8×C61C22×C411yescharacteristic
160Q8×D61—21no—
161Q8×D61—21no—
162Q8×D61—21no—
163Q8×D61—21no—
164Q8×D61—81no—
165Q8×D61—81no—
166C2×C4×D61—21no—
167C2×C4×D61—21no—
168C2×C4×D61—21no—
169C2×C4×D61—21no—
170C2×C4×D61C2×D411yescharacteristic
171C2×C4×D61C2×D411yescharacteristic
172C2×C4×D61C2411yescharacteristic
173C2×Dic122—21no—
174C2×Dic122—21no—
175C2×Dic122—21no—
176C2×Dic122—21no—
177C2×Dic122C22×C411yescharacteristic
178C2×#92420—21no—
179C2×#92420—21no—
180C4⋊#6923—22no—
181C4⋊#6923—21no—
182C4⋊#6923—21no—
183C4⋊#6923—21no—
184C4⋊#6923—21no—
185C4⋊#6923—21no—
186C4⋊#6923—21no—
187C4⋊#6923—21no—
188C4⋊#6923—41no—
189C4⋊#6923—81no—
190C4⋊#6923—81no—
191C4⋊#6923#4112yes—
192C4×#6923—21no—
193C4×#6923—21no—
194C4×#6923—21no—
195C4×#6923—21no—
196C4×#6923—42no—
197C4×#6923—42no—
198C4×#6923—42no—
199C4×#6923—81no—
200C4×#6923—81no—
201D61⋊C8—21no—
202D61⋊C8—21no—
203D61⋊C8—21no—
204D61⋊C8#4112yes—
205C2×C8×C61C22×C411yescharacteristic
206C2×C8×C61C22×C411yescharacteristic
207C4⋊C4×C61—21no—
208C4⋊C4×C61—21no—
209C4⋊C4×C61C22×C411yescharacteristic
210C4⋊C4×C61C22×C411yescharacteristic
211C4⋊C4×C61C22×C411yescharacteristic
212C42×C61—21no—
213C42×C61C22×C411yescharacteristic
214C4⋊Dic61—21no—
215C4⋊Dic61—21no—
216C4⋊Dic61C22×C411yescharacteristic
217C4⋊Dic61C22×C411yescharacteristic
218C4⋊Dic61C22×C411yescharacteristic
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—
265Q8×C61—81no—
266C2×C4×C61—21no—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61C4×D411yescharacteristic
271C2×C4×C61C4×D411yescharacteristic
272C2×C4×C61C23×C411yescharacteristic
273C2×Dic61—21no—
274C2×Dic61—21no—
275C2×Dic61—21no—
276C2×Dic61—21no—
277C2×Dic61C4×D411yescharacteristic
278C2×Dic61C4×D411yescharacteristic
279C2×Dic61C2×#4111yescharacteristic
280C4×D61—21no—
281C4×D61—21no—
282C4×D61—21no—
283C4×D61—21no—
284C4×D61—41no—
285C4×D61—41no—
286C4×D61—41no—
287C4×D61—41no—
288C4×D61—41no—
289C4×D61—41no—
290C4×D61—41no—
291C4×D61—41no—
292C4×D61C2×#4111yescharacteristic
293C4×D61C2×#4111yescharacteristic
294C4×D612−1+411yescharacteristic
295C4×D612−1+411yescharacteristic
296Dic122—21no—
297Dic122—21no—
298Dic122—41no—
299Dic122—41no—
300Dic122—81no—
301Dic122—81no—
302Dic122—81no—
303#92420—22no—
304#92420—41no—
305C8×C61—21no—
306C8×C61—21no—
307#92418—21no—
308#92418—21no—
309#23077—611nomaximal, Sylow
310C22×C61C2×C4×D411yescharacteristic
311C2×D61#54711yescharacteristic
312C2×D61#54811yescharacteristic
313C2×D61C2×#13711yescharacteristic
314C2×D61#57511yescharacteristic
315C2×D61#57711yescharacteristic
316C2×D61#57711yescharacteristic
317#6923—22no—
318#6923—41no—
319#6923—41no—
320#6923—41no—
321#6923—42no—
322#6923—81no—
323#6923—81no—
324#6923—81no—
325C4×C61—21no—
326C4×C61—21no—
327C4×C61—41no—
328C4×C61—41no—
329C4×C61—41no—
330C4×C61—41no—
331C4×C61C4×#4111yescharacteristic
332C4×C61#51911yescharacteristic
333Dic61—21no—
334Dic61—21no—
335Dic61—41no—
336Dic61—41no—
337Dic61—41no—
338Dic61—41no—
339Dic61#55211yescharacteristic
340Dic61#55611yescharacteristic
341C2×#475—611no—
342#2369—611no—
343#2356—611no—
344#1993—611no—
345#1949—611no—
346#1935—611no—
347#1933—611no—
348#1928—611no—
349#1927—611no—
350#1920—611no—
351#1919—611no—
352#1776—611no—
353C4×#106—611no—
354#1771—611no—
355#1763—611no—
356C2×C61#236211yescharacteristic
357C2×C61C4×#13711yescharacteristic
358C2×C61#294911yescharacteristic
359D61#334411yescharacteristic
360D61#334811yescharacteristic
361D61#336911yescharacteristic
362D61#337611yescharacteristic
363C2×C4⋊Q8—611no—
364C2×C4×Q8—611no—
365#475—611no—
366#475—611no—
367#475—611no—
368#475—611no—
369#475—611no—
370#475—611no—
371#475—611no—
372#475#692311yescharacteristic, complemented
373C2×#107—611no—
374C2×#106—611no—
375C2×#106—611no—
376C2×#106—611no—
377C2×C4⋊C8—611no—
378C2×#103—611no—
379C2×#103—611no—
380C2×#103—611no—
381C2×#103—611no—
382C2×#97—611no—
383C2×#97—611no—
384C2×C4×C8—611no—
385#391—611no—
386#391—611no—
387#391—1221no—
388#391—1221no—
389#389—611no—
390#389—611no—
391#389—1221no—
392#387—1221no—
393#387—1221no—
394#383—1221no—
395#382—611no—
396C4×C4⋊C4—611no—
397C4×C4⋊C4—611no—
398C4×C4⋊C4—611no—
399C4×C4⋊C4—611no—
400C4×C4⋊C4—611no—
401C4×C4⋊C4—611no—
402C4×C4⋊C4—1221no—
403#376—1221no—
404#340—611no—
405#340—611no—
406#340—611no—
407#340—611no—
408#340—611no—
409#340—611no—
410#340—611no—
411#340—611no—
412#336—611no—
413#336—611no—
414C61#2307711yescharacteristic, complemented, Sylow
415C22×Q8—611no—
416C22×Q8—1221no—
417C22×C8—611no—
418C22×C8—611no—
419C22×C8—611no—
420C22×C8—611no—
421C4⋊Q8—611no—
422C4⋊Q8—611no—
423C4⋊Q8—611no—
424C4⋊Q8—1221no—
425C4⋊Q8—1221no—
426C4⋊Q8C2×#692311yescharacteristic
427C4×Q8—611no—
428C4×Q8—611no—
429C4×Q8—611no—
430C4×Q8—1221no—
431C4×Q8—1221no—
432C4×Q8C2×#692311yescharacteristic
433C2×C4⋊C4—611no—
434C2×C4⋊C4—611no—
435C2×C4⋊C4—611no—
436C2×C4⋊C4—611no—
437C2×C4⋊C4—611no—
438C2×C4⋊C4—611no—
439C2×C4⋊C4—611no—
440C2×C4⋊C4—611no—
441C2×C4⋊C4—611no—
442C2×C4⋊C4—1221no—
443C2×C4⋊C4—1221no—
444C2×C4⋊C4—1221no—
445C2×C4⋊C4—1221no—
446C2×C42—611no—
447C2×C42—611no—
448C2×C42—611no—
449C2×C42—1221no—
450C2×C42—1221no—
451C2×C42—1221no—
452C2×C42—1221no—
453C2×C42—1221no—
454C2×C42—1221no—
455#107—1222no—
456#106—611no—
457#106—611no—
458#106—611no—
459#106—611no—
460#106—611no—
461#106—611no—
462#106—1222no—
463#106C2×#692311yescharacteristic
464#106C2×#692311yescharacteristic
465C4⋊C8—611no—
466C4⋊C8—611no—
467C4⋊C8—611no—
468C4⋊C8C2×#692311yescharacteristic
469#103—611no—
470#103—611no—
471#103—611no—
472#103—611no—
473#103—611no—
474#103—611no—
475#103—1222no—
476#103—1222no—
477#103C2×#692311yescharacteristic
478#103C2×#692311yescharacteristic
479#97—1221no—
480#97—1221no—
481#97—1222no—
482C4×C8—1222no—
483#95—611no—
484#95—611no—
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—
494#95—1221no—
495#95—1221no—
496#95—1221no—
497#95—1221no—
498C2×Q8—21no—
499C2×Q8—611no—
500C2×Q8—1221no—
501C2×Q8—1221no—
502C2×Q8—1221no—
503C2×Q8—1221no—
504C2×Q8—1221no—
505C2×Q8—1221no—
506C2×Q8—1221no—
507C2×Q8—1221no—
508C2×Q8—4881no—
509C2×Q8—4881no—
510C2×Q8C22×#692311yescharacteristic
511C22×C4—611no—
512C22×C4—611no—
513C22×C4—611no—
514C22×C4—611no—
515C22×C4—611no—
516C22×C4—611no—
517C22×C4—611no—
518C22×C4—1221no—
519C22×C4—1221no—
520C22×C4—1221no—
521C22×C4—1221no—
522C22×C4—1221no—
523C22×C4—1221no—
524C22×C4—1221no—
525C22×C4—1221no—
526C2×C8—612no—
527C2×C8—611no—
528C2×C8—611no—
529C2×C8—1221no—
530C2×C8—1221no—
531C2×C8—1221no—
532C2×C8—1221no—
533C2×C8—1221no—
534C2×C8—1221no—
535C2×C8—1221no—
536C2×C8—1221no—
537C2×C8—1221no—
538C2×C8C22×#692311yescharacteristic
539C2×C8C22×#692311yescharacteristic
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—612no—
543C4⋊C4—611no—
544C4⋊C4—611no—
545C4⋊C4—611no—
546C4⋊C4—1221no—
547C4⋊C4—1221no—
548C4⋊C4—1221no—
549C4⋊C4—1221no—
550C4⋊C4—1221no—
551C4⋊C4—1221no—
552C4⋊C4—1221no—
553C4⋊C4—1221no—
554C4⋊C4—1222no—
555C4⋊C4—1221no—
556C4⋊C4—1221no—
557C4⋊C4—1221no—
558C4⋊C4—1221no—
559C4⋊C4—1221no—
560C4⋊C4—1221no—
561C4⋊C4—1221no—
562C4⋊C4—1221no—
563C4⋊C4—4881no—
564C4⋊C4—4881no—
565C4⋊C4—2441no—
566C4⋊C4C22×#692311yescharacteristic
567C4⋊C4C22×#692311yescharacteristic
568C4⋊C4C22×#692311yescharacteristic
569C42—21no—
570C42—611no—
571C42—611no—
572C42—611no—
573C42—1221no—
574C42—1221no—
575C42—1221no—
576C42—1221no—
577C42—1221no—
578C42—1221no—
579C42—1221no—
580C42—4881no—
581C42—4881no—
582C42—2442no—
583C42—2442no—
584C42—2442no—
585C42C22×#692311yescharacteristic
586C23—611no—
587Q8—21no—
588Q8—21no—
589Q8—81no—
590Q8—1221no—
591Q8—1221no—
592Q8—4881no—
593Q8—4881no—
594Q8—4881no—
595Q8—2441no—
596Q8—2441no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—611no—
602C2×C4—611no—
603C2×C4—611no—
604C2×C4—611no—
605C2×C4—611no—
606C2×C4—612no—
607C2×C4—611no—
608C2×C4—611no—
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—1221no—
618C2×C4—1221no—
619C2×C4—1221no—
620C2×C4—1222no—
621C2×C4—1221no—
622C2×C4—1221no—
623C2×C4—1221no—
624C2×C4—1221no—
625C2×C4—1221no—
626C2×C4—1221no—
627C2×C4—1221no—
628C2×C4—1221no—
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×C4—2441no—
641C2×C4—2441no—
642C2×C4—2441no—
643C2×C4—2441no—
644C2×C4—2441no—
645C2×C4—2441no—
646C2×C4—2441no—
647C2×C4—2441no—
648C2×C4D4×#692311yescharacteristic
649C2×C4D4×#692311yescharacteristic
650C2×C4C23×#692311yescharacteristic
651C8—21no—
652C8—21no—
653C8—1222no—
654C8—1221no—
655C8—1221no—
656C8—2441no—
657C22—611no—
658C22—611no—
659C22—611no—
660C22—611no—
661C22—611no—
662C22—611no—
663C22C2×D4×#692311yescharacteristic
664C4—21no—
665C4—21no—
666C4—41no—
667C4—41no—
668C4—41no—
669C4—41no—
670C4—611no—
671C4—611no—
672C4—1222no—
673C4—1221no—
674C4—1221no—
675C4—4881no—
676C4—4881no—
677C4—4881no—
678C4—2441no—
679C4—2441no—
680C4—2441no—
681C4—2442no—
682C4—2441no—
683C4—2441no—
684C4—2441no—
685C4—2441no—
686C4#41×#692311yescharacteristic
687C4#1684083011yescharacteristic
688C2—611no—
689C2—611no—
690C2—611no—
691C2—611no—
692C2#2146234511yescharacteristic
693C2#137×#692311yescharacteristic
694C2#2146257911yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#475C4
socleC22×C61C2×C4×D4
prime radicalC22×D61C22×D4
cosocleC2×C4×D61C24
hypercenter#475#6923
hypocenterC61#23077
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
54. #16840048C4semidirect
55. #16840047C4semidirect
56. #16840046C4semidirect
57. #16840046C4semidirect
58. #16840045C4semidirect
59. #16840045C4semidirect
60. #16840044C4semidirect
66. C61×#475C4semidirect
372. #475#6923semidirect
414. C61#23077semidirect

Maximal subgroups

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

subgroupindex
#214623522
#214623392
#214620032
#214619322
#214619102
#214619082
#214618992
#214618982
#214618822
#214618812
#214616352
#106×#69232
#214616202
#214615912
#475×D612
#2307761