Finite Group Databasebeta

← #29651245

Subgroups — #29651245

Order 15616.

642 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454979C211yesmaximal, characteristic, complemented
2#21454854C211yesmaximal, characteristic, complemented
3#21444733C211yesmaximal, characteristic, complemented
4#21444722C211yesmaximal, characteristic, complemented
5#21444663C211yesmaximal, characteristic, complemented
6#21444656C211yesmaximal, characteristic, complemented
7#21444649C211yesmaximal, characteristic, complemented
8#21444649C211yesmaximal, characteristic, complemented
9#21444643C211yesmaximal, characteristic, complemented
10SD16⋊#92418C211yesmaximal, characteristic, complemented
11#21444604C211yesmaximal, characteristic, complemented
12#21444279C211yesmaximal, characteristic, complemented
13C2×D4⋊#92418C211yesmaximal, characteristic, complemented
14#21444112C211yesmaximal, characteristic, complemented
15C61×#3105C211yesmaximal, characteristic
16#16839893C2211yescharacteristic, complemented
17Q8×#92418C2211yescharacteristic, complemented
18#16839840C2211yescharacteristic
19#16839840C2211yescharacteristic
20#16839840C2211yescharacteristic, complemented
21#16839834—21no—
22#16839834—21no—
23#16839834—21no—
24D4×#92418—21no—
25D4×#92418C2211yescharacteristic
26D4×#92418C2211yescharacteristic
27D4×#92418C2211yescharacteristic, complemented
28#16839823—21no—
29#16839819C2211yescharacteristic
30#16839815C2211yescharacteristic
31#16839789—21no—
32C2×C4⋊#92418C2211yescharacteristic
33#16839726—21no—
34C2×C22⋊#92418—21no—
35C2×C4×#92418C2211yescharacteristic
36#16839515C2211yescharacteristic, complemented
37#16839515C2211yescharacteristic, complemented
38#16839513C2211yescharacteristic, complemented
39#16839513C2211yescharacteristic, complemented
40Q8⋊#92418C2211yescharacteristic, complemented
41Q8⋊#92418C2211yescharacteristic, complemented
42D4⋊#92418C2211yescharacteristic
43D4⋊#92418C2211yescharacteristic
44D4⋊#92418C2211yescharacteristic
45D4⋊#92418C2211yescharacteristic
46D4⋊#92418C2211yescharacteristic, complemented
47D4⋊#92418C2211yescharacteristic, complemented
48#16839484C2211yescharacteristic, complemented
49#16839484C2211yescharacteristic, complemented
50#16839483C2211yescharacteristic, complemented
51#16839483C2211yescharacteristic, complemented
52C61×#529C2211yescharacteristic
53C2×C4×D4×C61C2211yescharacteristic
54C61×#484C411yescharacteristic
55C61×#481C411yescharacteristic
56C61×#478C411yescharacteristic
57C61×#478C411yescharacteristic
58C61×#463C411yescharacteristic
59C61×#463C411yescharacteristic
60C61×#450C411yescharacteristic
61C61×#447C411yescharacteristic
62C4×SD16×C61C2211yescharacteristic
63C4×SD16×C61C2211yescharacteristic
64C4×D8×C61C2211yescharacteristic
65C4×D8×C61C2211yescharacteristic
66C61×#431C2211yescharacteristic
67C2×#11758194—21no—
68C2×#11758194—21no—
69C2×#11758194—21no—
70C22×#92418—21no—
71C22×#92418—21no—
72C22×#92418—21no—
73C22×#92418—21no—
74C22×#92418—21no—
75C4⋊#92418—21no—
76C4⋊#92418—21no—
77C4⋊#92418—21no—
78C4⋊#92418D411yescharacteristic
79C4⋊#92418D411yescharacteristic
80C4⋊#92418C2311yescharacteristic
81C4⋊#92418C2311yescharacteristic
82C4⋊#92418C2311yescharacteristic
83C4⋊#92418C2311yescharacteristic
84C22⋊#92418—21no—
85C22⋊#92418—21no—
86C22⋊#92418—21no—
87C22⋊#92418—21no—
88C22⋊#92418—21no—
89C22⋊#92418—21no—
90C22⋊#92418—21no—
91C22⋊#92418D411yescharacteristic
92C22⋊#92418D411yescharacteristic
93#14519688—21no—
94#14519688—21no—
95C4×#92418—21no—
96C4×#92418—21no—
97C4×#92418C2311yescharacteristic
98C4×#92418C2311yescharacteristic
99C4×#92418C2311yescharacteristic
100C4×#92418C2311yescharacteristic
101C22×D4×C61C2×C411yescharacteristic
102C23×C4×C61—21no—
103C2×SD16×C61C2×C411yescharacteristic
104C2×SD16×C61C2×C411yescharacteristic
105C2×D8×C61C2×C411yescharacteristic
106C2×D8×C61C2×C411yescharacteristic
107#126×C61—21no—
108#125×C61C2×C411yescharacteristic
109#124×C61C2×C411yescharacteristic
110#123×C61—21no—
111C22⋊Q8×C61C2×C411yescharacteristic
112#121×C61C2×C411yescharacteristic
113C4×Q8×C61C2311yescharacteristic
114C4×D4×C61—21no—
115C4×D4×C61—21no—
116C4×D4×C61—21no—
117C4×D4×C61C2×C411yescharacteristic
118C4×D4×C61C2×C411yescharacteristic
119C4×D4×C61C2311yescharacteristic
120C4×D4×C61C2311yescharacteristic
121C4×D4×C61C2311yescharacteristic
122#117×C61—21no—
123C2×C4⋊C4×C61C2×C411yescharacteristic
124C2×C22⋊C4×C61—21no—
125C2×C42×C61C2311yescharacteristic
126#107×C61C2×C411yescharacteristic
127#107×C61C2×C411yescharacteristic
128#106×C61C2×C411yescharacteristic
129#106×C61C2×C411yescharacteristic
130C4⋊C8×C61C2×C411yescharacteristic
131C4⋊C8×C61C2×C411yescharacteristic
132#103×C61C2×C411yescharacteristic
133#103×C61C2×C411yescharacteristic
134#102×C61C2×C411yescharacteristic
135#102×C61C2×C411yescharacteristic
136#102×C61C2×C411yescharacteristic
137#102×C61C2×C411yescharacteristic
138#102×C61C2×C411yescharacteristic
139#102×C61C2×C411yescharacteristic
140C22⋊C8×C61C2×C411yescharacteristic
141C22⋊C8×C61C2×C411yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C24×C61—21no—
145C2×Q8×C61C22×C411yescharacteristic
146C2×D4×C61—22no—
147C2×D4×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61—41no—
150C2×D4×C61C22×C411yescharacteristic
151C2×D4×C61C22×C411yescharacteristic
152C2×D4×C61C22×C411yescharacteristic
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—81no—
160C22×C4×C61—81no—
161C22×C4×C61C22×C411yescharacteristic
162C22×C4×C61C2×D411yescharacteristic
163C22×C4×C61#4111yescharacteristic
164SD16×C61—22no—
165SD16×C61—41no—
166D8×C61—22no—
167D8×C61—41no—
168C2×C8×C61C22×C411yescharacteristic
169C2×C8×C61C22×C411yescharacteristic
170C2×C8×C61C22×C411yescharacteristic
171C2×C8×C61C22×C411yescharacteristic
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61C22×C411yescharacteristic
178C4⋊C4×C61C22×C411yescharacteristic
179C4⋊C4×C61C22×C411yescharacteristic
180C4⋊C4×C61C22×C411yescharacteristic
181C22⋊C4×C61—21no—
182C22⋊C4×C61—21no—
183C22⋊C4×C61—21no—
184C22⋊C4×C61—21no—
185C22⋊C4×C61—21no—
186C22⋊C4×C61—21no—
187C22⋊C4×C61—21no—
188C22⋊C4×C61—21no—
189C22⋊C4×C61—21no—
190C42×C61—21no—
191C42×C61C22×C411yescharacteristic
192C42×C61C2×D411yescharacteristic
193C42×C61#4111yescharacteristic
194C42×C61C2411yescharacteristic
195#11758194—81no—
196#11758194—81no—
197#11758194—81no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—42no—
205C2×#92418—81no—
206C2×#92418—81no—
207C2×#92418—81no—
208C2×#92418—81no—
209C2×#92418C2×D411yescharacteristic
210C2×#92418C2×D411yescharacteristic
211C2×#92418C2×D411yescharacteristic
212C2×#92418C2×D411yescharacteristic
213C23×C61—21no—
214C23×C61—21no—
215C23×C61—21no—
216C23×C61—42no—
217C23×C61—42no—
218C23×C61—81no—
219C23×C61C4×D411yescharacteristic
220Q8×C61—21no—
221Q8×C61—21no—
222D4×C61—21no—
223D4×C61—21no—
224D4×C61—21no—
225D4×C61—21no—
226D4×C61—21no—
227D4×C61—42no—
228D4×C61—42no—
229D4×C61#13112yes—
230C2×C4×C61—22no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—41no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—81no—
247C2×C4×C61—81no—
248C2×C4×C61—81no—
249C2×C4×C61C4×D411yescharacteristic
250C2×C4×C61C4×D411yescharacteristic
251C2×C4×C61C4×D411yescharacteristic
252C2×C4×C61C23×C411yescharacteristic
253C2×C4×C61C22×D411yescharacteristic
254C2×C4×C61C2×#4111yescharacteristic
255C8×C61—21no—
256C8×C61—21no—
257C8×C61—21no—
258C8×C61—21no—
259#92418—21no—
260#92418—21no—
261#92418—21no—
262#92418—21no—
263#92418—41no—
264#92418—41no—
265#92418—41no—
266#92418—41no—
267#92418—41no—
268#92418—41no—
269#18020—611nomaximal, Sylow
270C22×C61—21no—
271C22×C61—21no—
272C22×C61—22no—
273C22×C61—41no—
274C22×C61—41no—
275C22×C61—41no—
276C22×C61—41no—
277C22×C61—41no—
278C22×C61—41no—
279C22×C61—41no—
280C22×C61—41no—
281C22×C61—84no—
282C22×C61#44412yes—
283C22×C61C2×C4×D411yescharacteristic
284C4×C61—21no—
285C4×C61—21no—
286C4×C61—21no—
287C4×C61—21no—
288C4×C61—41no—
289C4×C61—41no—
290C4×C61—41no—
291C4×C61—41no—
292C4×C61—41no—
293C4×C61C2×#13111yescharacteristic
294C4×C61#56811yescharacteristic
295C4×C61#57611yescharacteristic
296C4×C61#57711yescharacteristic
297#3105D6111yescharacteristic
298#2994—611no—
299#2974—611no—
300#1594—611no—
301#1592—611no—
302#1583—611no—
303#1582—611no—
304#1581—611no—
305#1581—611no—
306#1580—611no—
307SD16⋊C8—611no—
308#1573—611no—
309#1494—611no—
310C2×D4⋊C8—611no—
311#1452—611no—
312C2×C61—22no—
313C2×C61—42no—
314C2×C61—81no—
315C2×C61—81no—
316C2×C61#293311yescharacteristic
317C2×C61#294611yescharacteristic
318C2×C61C2×#44411yescharacteristic
319#529C2×D6111yescharacteristic
320C2×C4×D4C2×D6111yescharacteristic
321#484Dic6111yescharacteristic
322#481Dic6111yescharacteristic
323#478Dic6111yescharacteristic
324#478Dic6111yescharacteristic
325#463Dic6111yescharacteristic
326#463Dic6111yescharacteristic
327#450Dic6111yescharacteristic
328#447Dic6111yescharacteristic
329#446—611no—
330C8×Q8—611no—
331C4×SD16C2×D6111yescharacteristic
332C4×SD16C2×D6111yescharacteristic
333C4×D8C2×D6111yescharacteristic
334C4×D8C2×D6111yescharacteristic
335#436—611no—
336#436—611no—
337#436—611no—
338#435—1221no—
339#435—1221no—
340#435—1221no—
341C8×D4—611no—
342C8×D4—611no—
343C8×D4—611no—
344C8×D4—1221no—
345#433—1221no—
346#432—611no—
347#431—611no—
348#431C2×D6111yescharacteristic
349#424—1221no—
350C2×C4⋊C8—611no—
351#407—1221no—
352C2×C22⋊C8—1221no—
353C2×C4×C8—611no—
354#335—611no—
355#335—611no—
356#334—611no—
357#334—611no—
358Q8⋊C8—611no—
359Q8⋊C8—611no—
360D4⋊C8—611no—
361D4⋊C8—611no—
362D4⋊C8—611no—
363D4⋊C8—611no—
364D4⋊C8—611no—
365D4⋊C8—611no—
366#322—611no—
367#322—611no—
368#322—611no—
369#322—611no—
370C61#1802011yescharacteristic, complemented, Sylow
371C22×D4C2×Dic6111yescharacteristic
372C23×C4—21no—
373C2×SD16C2×Dic6111yescharacteristic
374C2×SD16C2×Dic6111yescharacteristic
375C2×D8C2×Dic6111yescharacteristic
376C2×D8C2×Dic6111yescharacteristic
377C2×M16—1221no—
378C2×M16—1221no—
379C2×M16—1221no—
380C22×C8—1221no—
381C22×C8—1221no—
382C22×C8—1221no—
383C22×C8—1221no—
384C22×C8—1221no—
385#126—21no—
386#125C2×Dic6111yescharacteristic
387#124C2×Dic6111yescharacteristic
388#123—21no—
389C22⋊Q8C2×Dic6111yescharacteristic
390#121C2×Dic6111yescharacteristic
391C4×Q8C22×D6111yescharacteristic
392C4×D4—21no—
393C4×D4—21no—
394C4×D4—21no—
395C4×D4C2×Dic6111yescharacteristic
396C4×D4C2×Dic6111yescharacteristic
397C4×D4C22×D6111yescharacteristic
398C4×D4C22×D6111yescharacteristic
399C4×D4C22×D6111yescharacteristic
400#117—21no—
401C2×C4⋊C4C2×Dic6111yescharacteristic
402C2×C22⋊C4—21no—
403C2×C42C22×D6111yescharacteristic
404#107C2×Dic6111yescharacteristic
405#107C2×Dic6111yescharacteristic
406#106C2×Dic6111yescharacteristic
407#106C2×Dic6111yescharacteristic
408C4⋊C8—611no—
409C4⋊C8—611no—
410C4⋊C8—611no—
411C4⋊C8—611no—
412C4⋊C8—611no—
413C4⋊C8—611no—
414C4⋊C8—1221no—
415C4⋊C8—1221no—
416C4⋊C8—1221no—
417C4⋊C8C2×Dic6111yescharacteristic
418C4⋊C8C2×Dic6111yescharacteristic
419#103C2×Dic6111yescharacteristic
420#103C2×Dic6111yescharacteristic
421#102C2×Dic6111yescharacteristic
422#102C2×Dic6111yescharacteristic
423#102C2×Dic6111yescharacteristic
424#102C2×Dic6111yescharacteristic
425#102C2×Dic6111yescharacteristic
426#102C2×Dic6111yescharacteristic
427C22⋊C8—611no—
428C22⋊C8—611no—
429C22⋊C8—1221no—
430C22⋊C8—1221no—
431C22⋊C8—1221no—
432C22⋊C8—1221no—
433C22⋊C8—1221no—
434C22⋊C8—1221no—
435C22⋊C8—1221no—
436C22⋊C8C2×Dic6111yescharacteristic
437C22⋊C8C2×Dic6111yescharacteristic
438#97—1221no—
439#97—1221no—
440C4×C8—611no—
441C4×C8—611no—
442C4×C8—611no—
443C4×C8—611no—
444C4×C8—1221no—
445C4×C8—1221no—
446C4×C8C22×D6111yescharacteristic
447C4×C8C22×D6111yescharacteristic
448C24—21no—
449C2×Q8C22×Dic6111yescharacteristic
450C2×D4—22no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—41no—
454C2×D4C22×Dic6111yescharacteristic
455C2×D4C22×Dic6111yescharacteristic
456C2×D4C22×Dic6111yescharacteristic
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—81no—
464C22×C4—81no—
465C22×C4D4×D6111yescharacteristic
466C22×C4#1175822411yescharacteristic
467C22×C4C22×Dic6111yescharacteristic
468SD16—22no—
469SD16—41no—
470D8—22no—
471D8—41no—
472M16—4881no—
473M16—4881no—
474M16—4881no—
475C2×C8—611no—
476C2×C8—611no—
477C2×C8—611no—
478C2×C8—611no—
479C2×C8—1221no—
480C2×C8—1221no—
481C2×C8—1221no—
482C2×C8—1221no—
483C2×C8—1221no—
484C2×C8—1221no—
485C2×C8—4881no—
486C2×C8—4881no—
487C2×C8—4881no—
488C2×C8—4881no—
489C2×C8—2442no—
490C2×C8C22×Dic6111yescharacteristic
491C2×C8C22×Dic6111yescharacteristic
492C2×C8C22×Dic6111yescharacteristic
493C2×C8C22×Dic6111yescharacteristic
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4C22×Dic6111yescharacteristic
500C4⋊C4C22×Dic6111yescharacteristic
501C4⋊C4C22×Dic6111yescharacteristic
502C4⋊C4C22×Dic6111yescharacteristic
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—21no—
511C22⋊C4—21no—
512C42—21no—
513C42D4×D6111yescharacteristic
514C42#1175822411yescharacteristic
515C42C22×Dic6111yescharacteristic
516C42C23×D6111yescharacteristic
517C23—21no—
518C23—21no—
519C23—21no—
520C23—42no—
521C23—42no—
522C23—81no—
523C23D4×Dic6111yescharacteristic
524Q8—21no—
525Q8—21no—
526D4—21no—
527D4—21no—
528D4—21no—
529D4—21no—
530D4—21no—
531D4—42no—
532D4—42no—
533D4#1451978412yes—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—81no—
551C2×C4—81no—
552C2×C4—81no—
553C2×C4D4×Dic6111yescharacteristic
554C2×C4D4×Dic6111yescharacteristic
555C2×C4D4×Dic6111yescharacteristic
556C2×C4C23×Dic6111yescharacteristic
557C2×C4C2×D4×D6111yescharacteristic
558C2×C4C2×#1175822411yescharacteristic
559C8—21no—
560C8—21no—
561C8—21no—
562C8—21no—
563C8—1221no—
564C8—1221no—
565C8—1221no—
566C8—1221no—
567C8—2441no—
568C8—2441no—
569C8—2441no—
570C8—2441no—
571C8—2441no—
572C8—2441no—
573C22—21no—
574C22—21no—
575C22—22no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—84no—
585C22#1683988412yes—
586C22C2×D4×Dic6111yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—41no—
595C4—41no—
596C4C2×#1451978411yescharacteristic
597C4#1684052911yescharacteristic
598C4#1684056611yescharacteristic
599C4#1684057211yescharacteristic
600C2—22no—
601C2—42no—
602C2—81no—
603C2—81no—
604C2#2145454611yescharacteristic
605C2#2145465211yescharacteristic
606C2C2×#1683988411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#3105C2
socleC22×C61C2×C4×D4
prime radicalC61×#447C4
cosocleC42×C61C24
hypercenter#3105D61
hypocenterC61#18020
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3105

Complements

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

NH ≅ G/Ntype
1. #21454979C2semidirect
2. #21454854C2semidirect
3. #21444733C2semidirect
4. #21444722C2semidirect
5. #21444663C2semidirect
6. #21444656C2semidirect
7. #21444649C2semidirect
8. #21444649C2semidirect
9. #21444643C2semidirect
10. SD16⋊#92418C2semidirect
11. #21444604C2semidirect
12. #21444279C2semidirect
13. C2×D4⋊#92418C2semidirect
14. #21444112C2semidirect
16. #16839893C22semidirect
17. Q8×#92418C22semidirect
20. #16839840C22semidirect
27. D4×#92418C22semidirect
36. #16839515C22semidirect
37. #16839515C22semidirect
38. #16839513C22semidirect
39. #16839513C22semidirect
40. Q8⋊#92418C22semidirect
41. Q8⋊#92418C22semidirect
46. D4⋊#92418C22semidirect
47. D4⋊#92418C22semidirect
48. #16839484C22semidirect
49. #16839484C22semidirect
50. #16839483C22semidirect
51. #16839483C22semidirect
370. C61#18020semidirect

Maximal subgroups

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

subgroupindex
#214549792
#214548542
#214447332
#214447222
#214446632
#214446562
#214446492
#214446432
SD16⋊#924182
#214446042
#214442792
C2×D4⋊#924182
#214441122
C61×#31052
#1802061