Finite Group Databasebeta

← #29651319

Subgroups — #29651319

Order 15616.

656 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454886C211yesmaximal, characteristic, complemented
2#21454854C211yesmaximal, characteristic, complemented
3#21444733C211yesmaximal, characteristic, complemented
4#21444704C211yesmaximal, characteristic, complemented
5#21444684C211yesmaximal, characteristic, complemented
6#21444684C211yesmaximal, characteristic, complemented
7#21444649C211yesmaximal, characteristic, complemented
8#21444649C211yesmaximal, characteristic, complemented
9#21444643C211yesmaximal, characteristic, complemented
10D8×#92418C211yesmaximal, characteristic, complemented
11#21444599C211yesmaximal, characteristic, complemented
12#21444288C211yesmaximal, characteristic, complemented
13#21444210C211yesmaximal, characteristic, complemented
14#21444119C211yesmaximal, characteristic, complemented
15C61×#3100C211yesmaximal, characteristic
16#16839840—21no—
17#16839840C2211yescharacteristic
18#16839840C2211yescharacteristic
19#16839840C2211yescharacteristic, complemented
20#16839840C2211yescharacteristic, complemented
21#16839834—21no—
22#16839834—21no—
23D4×#92418—21no—
24D4×#92418C2211yescharacteristic
25D4×#92418C2211yescharacteristic
26D4×#92418C2211yescharacteristic, complemented
27D4×#92418C2211yescharacteristic, complemented
28#16839819C2211yescharacteristic
29#16839815C2211yescharacteristic
30#16839815C2211yescharacteristic
31#16839815C2211yescharacteristic
32#16839729—21no—
33#16839729—21no—
34#16839726—21no—
35C2×C22⋊#92418—21no—
36#16839515C2211yescharacteristic, complemented
37#16839515C2211yescharacteristic, complemented
38#16839513C2211yescharacteristic, complemented
39#16839513C2211yescharacteristic, complemented
40D4⋊#92418C2211yescharacteristic
41D4⋊#92418C2211yescharacteristic
42D4⋊#92418C2211yescharacteristic
43D4⋊#92418C2211yescharacteristic
44D4⋊#92418C2211yescharacteristic, complemented
45D4⋊#92418C2211yescharacteristic, complemented
46D4⋊#92418C2211yescharacteristic, complemented
47D4⋊#92418C2211yescharacteristic, complemented
48#16839484C2211yescharacteristic, complemented
49#16839484C2211yescharacteristic, complemented
50#16839483C2211yescharacteristic, complemented
51C8×#92418C2211yescharacteristic, complemented
52C61×#532C2211yescharacteristic
53C2×C4×D4×C61C2211yescharacteristic
54C61×#480C411yescharacteristic
55C61×#480C411yescharacteristic
56C61×#474C411yescharacteristic
57C61×#474C411yescharacteristic
58C61×#459C411yescharacteristic
59C61×#459C411yescharacteristic
60C61×#447C411yescharacteristic
61C61×#447C411yescharacteristic
62C4×D8×C61C2211yescharacteristic
63C4×D8×C61C2211yescharacteristic
64C4×D8×C61C2211yescharacteristic
65C4×D8×C61C2211yescharacteristic
66C61×#431C2211yescharacteristic
67C2×#11758194—21no—
68C2×#11758194—21no—
69C2×#11758194—21no—
70C2×#11758194—21no—
71C22×#92418—21no—
72C22×#92418—21no—
73C22×#92418—21no—
74C22×#92418—21no—
75C4⋊#92418—21no—
76C4⋊#92418D411yescharacteristic
77C4⋊#92418D411yescharacteristic
78C4⋊#92418C2311yescharacteristic
79C4⋊#92418C2311yescharacteristic
80C4⋊#92418C2311yescharacteristic
81C4⋊#92418C2311yescharacteristic
82C22⋊#92418—21no—
83C22⋊#92418—21no—
84C22⋊#92418—21no—
85C22⋊#92418—21no—
86C22⋊#92418—21no—
87C22⋊#92418—21no—
88C22⋊#92418—21no—
89C22⋊#92418—21no—
90C22⋊#92418—21no—
91C22⋊#92418—21no—
92C22⋊#92418—21no—
93C22⋊#92418D411yescharacteristic
94C22⋊#92418D411yescharacteristic
95#14519688—21no—
96C4×#92418—21no—
97C4×#92418C2311yescharacteristic
98C4×#92418C2311yescharacteristic
99C4×#92418C2311yescharacteristic
100C4×#92418C2311yescharacteristic
101C2×#41×C61—21no—
102C22×D4×C61C2×C411yescharacteristic
103C23×C4×C61—21no—
104C2×D8×C61C2×C411yescharacteristic
105C2×D8×C61C2×C411yescharacteristic
106C2×D8×C61C2×C411yescharacteristic
107C2×D8×C61C2×C411yescharacteristic
108C4⋊Q8×C61C2×C411yescharacteristic
109#127×C61C2×C411yescharacteristic
110#124×C61—21no—
111#121×C61—21no—
112#121×C61C2×C411yescharacteristic
113#121×C61C2×C411yescharacteristic
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
122C4×D4×C61C2311yescharacteristic
123C2×C4⋊C4×C61C2×C411yescharacteristic
124C2×C22⋊C4×C61—21no—
125C2×C42×C61C2311yescharacteristic
126#107×C61C2×C411yescharacteristic
127#107×C61C2×C411yescharacteristic
128#107×C61C2×C411yescharacteristic
129#107×C61C2×C411yescharacteristic
130C4⋊C8×C61C2×C411yescharacteristic
131C4⋊C8×C61C2×C411yescharacteristic
132#102×C61C2×C411yescharacteristic
133#102×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—
145#41×C61—81no—
146#41×C61—81no—
147C2×Q8×C61—21no—
148C2×D4×C61—22no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—41no—
155C2×D4×C61C22×C411yescharacteristic
156C2×D4×C61C22×C411yescharacteristic
157C2×D4×C61C22×C411yescharacteristic
158C2×D4×C61C22×C411yescharacteristic
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—81no—
167C22×C4×C61—81no—
168C22×C4×C61C22×C411yescharacteristic
169C22×C4×C61C2×D411yescharacteristic
170C22×C4×C61#4111yescharacteristic
171D8×C61—22no—
172D8×C61—22no—
173D8×C61—41no—
174D8×C61—41no—
175C2×C8×C61C22×C411yescharacteristic
176C2×C8×C61C22×C411yescharacteristic
177C2×C8×C61C22×C411yescharacteristic
178C2×C8×C61C22×C411yescharacteristic
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61C22×C411yescharacteristic
182C4⋊C4×C61C22×C411yescharacteristic
183C4⋊C4×C61C22×C411yescharacteristic
184C4⋊C4×C61C22×C411yescharacteristic
185C22⋊C4×C61—21no—
186C22⋊C4×C61—21no—
187C22⋊C4×C61—21no—
188C22⋊C4×C61—21no—
189C22⋊C4×C61—21no—
190C22⋊C4×C61—21no—
191C22⋊C4×C61—21no—
192C22⋊C4×C61—21no—
193C42×C61C22×C411yescharacteristic
194C42×C61C2×D411yescharacteristic
195C42×C61#4111yescharacteristic
196C42×C61C2411yescharacteristic
197#11758194—81no—
198#11758194—81no—
199#11758194—81no—
200#11758194—81no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—81no—
208C2×#92418—81no—
209C2×#92418—81no—
210C2×#92418—81no—
211C2×#92418C2×D411yescharacteristic
212C2×#92418C2×D411yescharacteristic
213C2×#92418C2×D411yescharacteristic
214C2×#92418C2×D411yescharacteristic
215C23×C61—21no—
216C23×C61—21no—
217C23×C61—21no—
218C23×C61—21no—
219C23×C61—42no—
220C23×C61—42no—
221C23×C61—81no—
222C23×C61C4×D411yescharacteristic
223Q8×C61—81no—
224D4×C61—21no—
225D4×C61—21no—
226D4×C61—21no—
227D4×C61—21no—
228D4×C61—21no—
229D4×C61—21no—
230D4×C61—21no—
231D4×C61—42no—
232D4×C61—42no—
233D4×C61—81no—
234D4×C61—81no—
235D4×C61—81no—
236D4×C61#13112yes—
237C2×C4×C61—21no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61—41no—
246C2×C4×C61—41no—
247C2×C4×C61—41no—
248C2×C4×C61—41no—
249C2×C4×C61—41no—
250C2×C4×C61—41no—
251C2×C4×C61—41no—
252C2×C4×C61—41no—
253C2×C4×C61—41no—
254C2×C4×C61—81no—
255C2×C4×C61—81no—
256C2×C4×C61—81no—
257C2×C4×C61C4×D411yescharacteristic
258C2×C4×C61C4×D411yescharacteristic
259C2×C4×C61C4×D411yescharacteristic
260C2×C4×C61C23×C411yescharacteristic
261C2×C4×C61C22×D411yescharacteristic
262C2×C4×C61C2×#4111yescharacteristic
263C8×C61—21no—
264C8×C61—21no—
265C8×C61—21no—
266C8×C61—21no—
267#92418—21no—
268#92418—21no—
269#92418—21no—
270#92418—21no—
271#92418—41no—
272#92418—41no—
273#92418—41no—
274#92418—41no—
275#92418—41no—
276#92418—41no—
277#18026—611nomaximal, Sylow
278C22×C61—21no—
279C22×C61—22no—
280C22×C61—21no—
281C22×C61—21no—
282C22×C61—41no—
283C22×C61—41no—
284C22×C61—41no—
285C22×C61—41no—
286C22×C61—41no—
287C22×C61—41no—
288C22×C61—41no—
289C22×C61—41no—
290C22×C61—41no—
291C22×C61—41no—
292C22×C61—41no—
293C22×C61—84no—
294C22×C61C2×C4×D411yescharacteristic
295C4×C61—21no—
296C4×C61—21no—
297C4×C61—21no—
298C4×C61—21no—
299C4×C61—41no—
300C4×C61—41no—
301C4×C61—41no—
302C4×C61—41no—
303C4×C61C2×#13111yescharacteristic
304C4×C61#56811yescharacteristic
305C4×C61#57611yescharacteristic
306C4×C61#57611yescharacteristic
307#3100D6111yescharacteristic
308#2979—611no—
309#2974—611no—
310#1594—611no—
311#1589—611no—
312#1586—611no—
313#1586—611no—
314#1581—611no—
315#1581—611no—
316#1580—611no—
317C8×D8—611no—
318#1572—611no—
319#1496—611no—
320#1478—611no—
321#1454—611no—
322C2×C61—41no—
323C2×C61—42no—
324C2×C61—81no—
325C2×C61—81no—
326C2×C61—81no—
327C2×C61#293311yescharacteristic
328C2×C61#294811yescharacteristic
329C2×C61#295511yescharacteristic
330#532C2×D6111yescharacteristic
331C2×C4×D4C2×D6111yescharacteristic
332#480Dic6111yescharacteristic
333#480Dic6111yescharacteristic
334#474Dic6111yescharacteristic
335#474Dic6111yescharacteristic
336#459Dic6111yescharacteristic
337#459Dic6111yescharacteristic
338#447Dic6111yescharacteristic
339#447Dic6111yescharacteristic
340C4×D8C2×D6111yescharacteristic
341C4×D8C2×D6111yescharacteristic
342C4×D8C2×D6111yescharacteristic
343C4×D8C2×D6111yescharacteristic
344#436—611no—
345#436—611no—
346#436—611no—
347#436—611no—
348#436—1221no—
349#435—1221no—
350#435—1221no—
351C8×D4—611no—
352C8×D4—611no—
353C8×D4—611no—
354C8×D4—611no—
355C8×D4—1221no—
356#432—611no—
357#431—611no—
358#431—611no—
359#431—611no—
360#431C2×D6111yescharacteristic
361#408—1221no—
362#408—1221no—
363#407—1221no—
364C2×C22⋊C8—1221no—
365#335—611no—
366#335—611no—
367#334—611no—
368#334—611no—
369D4⋊C8—611no—
370D4⋊C8—611no—
371D4⋊C8—611no—
372D4⋊C8—611no—
373D4⋊C8—611no—
374D4⋊C8—611no—
375D4⋊C8—611no—
376D4⋊C8—611no—
377#322—611no—
378#322—611no—
379#322—611no—
380C82—611no—
381C61#1802611yescharacteristic, complemented, Sylow
382C2×#41—21no—
383C22×D4C2×Dic6111yescharacteristic
384C23×C4—21no—
385C2×D8C2×Dic6111yescharacteristic
386C2×D8C2×Dic6111yescharacteristic
387C2×D8C2×Dic6111yescharacteristic
388C2×D8C2×Dic6111yescharacteristic
389C2×M16—1221no—
390C2×M16—1221no—
391C2×M16—1221no—
392C2×M16—1221no—
393C22×C8—1221no—
394C22×C8—1221no—
395C22×C8—1221no—
396C22×C8—1221no—
397C4⋊Q8C2×Dic6111yescharacteristic
398#127C2×Dic6111yescharacteristic
399#124—21no—
400#121—21no—
401#121C2×Dic6111yescharacteristic
402#121C2×Dic6111yescharacteristic
403C4×D4—21no—
404C4×D4—21no—
405C4×D4—21no—
406C4×D4C2×Dic6111yescharacteristic
407C4×D4C2×Dic6111yescharacteristic
408C4×D4C22×D6111yescharacteristic
409C4×D4C22×D6111yescharacteristic
410C4×D4C22×D6111yescharacteristic
411C4×D4C22×D6111yescharacteristic
412C2×C4⋊C4C2×Dic6111yescharacteristic
413C2×C22⋊C4—21no—
414C2×C42C22×D6111yescharacteristic
415#107C2×Dic6111yescharacteristic
416#107C2×Dic6111yescharacteristic
417#107C2×Dic6111yescharacteristic
418#107C2×Dic6111yescharacteristic
419C4⋊C8—611no—
420C4⋊C8—611no—
421C4⋊C8—611no—
422C4⋊C8—611no—
423C4⋊C8—611no—
424C4⋊C8—611no—
425C4⋊C8—1221no—
426C4⋊C8C2×Dic6111yescharacteristic
427C4⋊C8C2×Dic6111yescharacteristic
428#102C2×Dic6111yescharacteristic
429#102C2×Dic6111yescharacteristic
430#102C2×Dic6111yescharacteristic
431#102C2×Dic6111yescharacteristic
432#102C2×Dic6111yescharacteristic
433#102C2×Dic6111yescharacteristic
434#102C2×Dic6111yescharacteristic
435#102C2×Dic6111yescharacteristic
436C22⋊C8—611no—
437C22⋊C8—611no—
438C22⋊C8—1221no—
439C22⋊C8—1221no—
440C22⋊C8—1221no—
441C22⋊C8—1221no—
442C22⋊C8—1221no—
443C22⋊C8—1221no—
444C22⋊C8—1221no—
445C22⋊C8—1221no—
446C22⋊C8—1221no—
447C22⋊C8—1221no—
448C22⋊C8—1221no—
449C22⋊C8C2×Dic6111yescharacteristic
450C22⋊C8C2×Dic6111yescharacteristic
451#97—1221no—
452C4×C8—611no—
453C4×C8—611no—
454C4×C8—611no—
455C4×C8—611no—
456C4×C8—1221no—
457C4×C8C22×D6111yescharacteristic
458C4×C8C22×D6111yescharacteristic
459C24—21no—
460#41—81no—
461#41—81no—
462C2×Q8—21no—
463C2×D4—22no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—41no—
470C2×D4C22×Dic6111yescharacteristic
471C2×D4C22×Dic6111yescharacteristic
472C2×D4C22×Dic6111yescharacteristic
473C2×D4C22×Dic6111yescharacteristic
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—81no—
482C22×C4—81no—
483C22×C4D4×D6111yescharacteristic
484C22×C4#1175822411yescharacteristic
485C22×C4C22×Dic6111yescharacteristic
486D8—22no—
487D8—22no—
488D8—41no—
489D8—41no—
490M16—4881no—
491M16—4881no—
492M16—4881no—
493M16—4881no—
494C2×C8—611no—
495C2×C8—611no—
496C2×C8—611no—
497C2×C8—611no—
498C2×C8—1221no—
499C2×C8—1221no—
500C2×C8—1221no—
501C2×C8—1221no—
502C2×C8—1221no—
503C2×C8—1221no—
504C2×C8—4881no—
505C2×C8—4881no—
506C2×C8—4881no—
507C2×C8—4881no—
508C2×C8C22×Dic6111yescharacteristic
509C2×C8C22×Dic6111yescharacteristic
510C2×C8C22×Dic6111yescharacteristic
511C2×C8C22×Dic6111yescharacteristic
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4C22×Dic6111yescharacteristic
515C4⋊C4C22×Dic6111yescharacteristic
516C4⋊C4C22×Dic6111yescharacteristic
517C4⋊C4C22×Dic6111yescharacteristic
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—21no—
524C22⋊C4—21no—
525C22⋊C4—21no—
526C42D4×D6111yescharacteristic
527C42#1175822411yescharacteristic
528C42C22×Dic6111yescharacteristic
529C42C23×D6111yescharacteristic
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—42no—
535C23—42no—
536C23—81no—
537C23D4×Dic6111yescharacteristic
538Q8—81no—
539D4—21no—
540D4—21no—
541D4—21no—
542D4—21no—
543D4—21no—
544D4—21no—
545D4—21no—
546D4—42no—
547D4—42no—
548D4—81no—
549D4—81no—
550D4—81no—
551D4#1451978412yes—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—81no—
570C2×C4—81no—
571C2×C4—81no—
572C2×C4D4×Dic6111yescharacteristic
573C2×C4D4×Dic6111yescharacteristic
574C2×C4D4×Dic6111yescharacteristic
575C2×C4C23×Dic6111yescharacteristic
576C2×C4C2×D4×D6111yescharacteristic
577C2×C4C2×#1175822411yescharacteristic
578C8—21no—
579C8—21no—
580C8—21no—
581C8—21no—
582C8—1221no—
583C8—1221no—
584C8—1221no—
585C8—1221no—
586C8—2441no—
587C8—2441no—
588C8—2441no—
589C8—2441no—
590C8—2441no—
591C8—2441no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—22no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—84no—
608C22C2×D4×Dic6111yescharacteristic
609C4—21no—
610C4—21no—
611C4—21no—
612C4—21no—
613C4—41no—
614C4—41no—
615C4—41no—
616C4—41no—
617C4C2×#1451978411yescharacteristic
618C4#1684052911yescharacteristic
619C4#1684056311yescharacteristic
620C4#1684056311yescharacteristic
621C2—41no—
622C2—42no—
623C2—81no—
624C2—81no—
625C2—81no—
626C2#2145454611yescharacteristic
627C2#2145467111yescharacteristic
628C2#2145472211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
Fitting, prime radicalC61×#3100C2
socleC22×C61C2×C4×D4
cosocleC42×C61C24
hypercenter#3100D61
hypocenterC61#18026
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3100

Complements

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

NH ≅ G/Ntype
1. #21454886C2semidirect
2. #21454854C2semidirect
3. #21444733C2semidirect
4. #21444704C2semidirect
5. #21444684C2semidirect
6. #21444684C2semidirect
7. #21444649C2semidirect
8. #21444649C2semidirect
9. #21444643C2semidirect
10. D8×#92418C2semidirect
11. #21444599C2semidirect
12. #21444288C2semidirect
13. #21444210C2semidirect
14. #21444119C2semidirect
19. #16839840C22semidirect
20. #16839840C22semidirect
26. D4×#92418C22semidirect
27. D4×#92418C22semidirect
36. #16839515C22semidirect
37. #16839515C22semidirect
38. #16839513C22semidirect
39. #16839513C22semidirect
44. D4⋊#92418C22semidirect
45. D4⋊#92418C22semidirect
46. D4⋊#92418C22semidirect
47. D4⋊#92418C22semidirect
48. #16839484C22semidirect
49. #16839484C22semidirect
50. #16839483C22semidirect
51. C8×#92418C22semidirect
381. C61#18026semidirect

Maximal subgroups

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

subgroupindex
#214548862
#214548542
#214447332
#214447042
#214446842
#214446492
#214446432
D8×#924182
#214445992
#214442882
#214442102
#214441192
C61×#31002
#1802661