Finite Group Databasebeta

← #29651249

Subgroups — #29651249

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#21455862C211yesmaximal, characteristic
2#21454979C211yesmaximal, characteristic, complemented
3#21454856C211yesmaximal, characteristic, complemented
4#21444730C211yesmaximal, characteristic, complemented
5#21444724C211yesmaximal, characteristic, complemented
6#21444659C211yesmaximal, characteristic, complemented
7#21444658C211yesmaximal, characteristic, complemented
8#21444651C211yesmaximal, characteristic, complemented
9#21444645C211yesmaximal, characteristic, complemented
10#21444640C211yesmaximal, characteristic, complemented
11#21444634C211yesmaximal, characteristic, complemented
12#21444605C211yesmaximal, characteristic, complemented
13C2×#16839491C211yesmaximal, characteristic, complemented
14#21444111C211yesmaximal, characteristic, complemented
15C61×#1494C211yesmaximal, characteristic, complemented
16C2×C4×D244C2211yescharacteristic
17#16840095C411yescharacteristic
18#16840078C411yescharacteristic
19#16840059C411yescharacteristic
20#16840059C411yescharacteristic
21#16839974C411yescharacteristic
22#16839974C411yescharacteristic
23#16839912C411yescharacteristic
24#16839895C411yescharacteristic
25#16839893C2211yescharacteristic, complemented
26Q8×#92418C2211yescharacteristic, complemented
27C4×#11758201C2211yescharacteristic
28C4×#11758201C2211yescharacteristic
29C4×#11758199C2211yescharacteristic
30C4×#11758199C2211yescharacteristic
31#16839840C2211yescharacteristic, complemented
32#16839839C2211yescharacteristic
33#16839839C2211yescharacteristic
34#16839835—21no—
35#16839835—21no—
36#16839834—21no—
37D4×#92418—21no—
38D4×#92418C2211yescharacteristic, complemented
39#16839827C2211yescharacteristic
40#16839827C2211yescharacteristic
41#16839823—21no—
42#16839815C2211yescharacteristic
43#16839815C2211yescharacteristic
44#16839789—21no—
45C2×C4⋊#92418C2211yescharacteristic
46#16839724—21no—
47C22⋊C8×D61—21no—
48#16839514C2211yescharacteristic, complemented
49#16839514C2211yescharacteristic, complemented
50#16839512C2211yescharacteristic, complemented
51#16839512C2211yescharacteristic, complemented
52#16839491C2211yescharacteristic
53#16839491C2211yescharacteristic
54#16839491C2211yescharacteristic
55#16839491C2211yescharacteristic
56#16839484C2211yescharacteristic, complemented
57#16839484C2211yescharacteristic, complemented
58#16839484C2211yescharacteristic, complemented
59#16839484C2211yescharacteristic, complemented
60C61×#529C2211yescharacteristic
61C61×#432C2211yescharacteristic
62C2×C4×C8×C61C2211yescharacteristic
63C61×Q8⋊C8C2211yescharacteristic, complemented
64C61×Q8⋊C8C2211yescharacteristic, complemented
65C61×D4⋊C8C2211yescharacteristic, complemented
66C61×D4⋊C8C2211yescharacteristic, complemented
67C22×D244C2×C411yescharacteristic
68C22×C4×D61—21no—
69C2×#11758201C2×C411yescharacteristic
70C2×#11758201C2×C411yescharacteristic
71C2×#11758199C2×C411yescharacteristic
72C2×#11758199C2×C411yescharacteristic
73C2×#11758194—21no—
74C2×#11758189—21no—
75C2×#11758189—21no—
76C22×#92418—21no—
77C22×#92418—21no—
78C2×C8×D61—21no—
79C2×C8×D61—21no—
80C4×D244—21no—
81C4×D244—21no—
82C4×D244C2×C411yescharacteristic
83C4×D244C2×C411yescharacteristic
84C4×D244C2311yescharacteristic
85C4×D244C2311yescharacteristic
86C2×C4⋊Dic61C2×C411yescharacteristic
87C2×#11758198—21no—
88#14519710C2×C411yescharacteristic
89#14519710C2×C411yescharacteristic
90#14519708C2×C411yescharacteristic
91#14519708C2×C411yescharacteristic
92C4⋊#92418—21no—
93C4⋊#92418—21no—
94C4⋊#92418—21no—
95C4⋊#92418C2×C411yescharacteristic
96C4⋊#92418C2×C411yescharacteristic
97C4⋊#92418D411yescharacteristic
98C4⋊#92418D411yescharacteristic
99C4⋊#92418C2311yescharacteristic
100C4⋊#92418C2311yescharacteristic
101#14519701C2×C411yescharacteristic
102#14519701C2×C411yescharacteristic
103#14519698C2×C411yescharacteristic
104#14519698C2×C411yescharacteristic
105#14519697C2×C411yescharacteristic
106#14519697C2×C411yescharacteristic
107#14519697C2×C411yescharacteristic
108#14519697C2×C411yescharacteristic
109C22⋊#92418—21no—
110C22⋊#92418—21no—
111C22⋊#92418C2×C411yescharacteristic
112C22⋊#92418C2×C411yescharacteristic
113C22⋊#92418D411yescharacteristic
114C22⋊#92418D411yescharacteristic
115#14519689—21no—
116#14519689—21no—
117#14519689—21no—
118#14519689—21no—
119#14519688—21no—
120C4×#92418—21no—
121C4×#92418C2311yescharacteristic
122C4×#92418C2311yescharacteristic
123C4×#92418C2311yescharacteristic
124C4×#92418C2311yescharacteristic
125C22×C8×C61—21no—
126#126×C61—21no—
127#125×C61C2×C411yescharacteristic
128#124×C61C2×C411yescharacteristic
129#123×C61—21no—
130C22⋊Q8×C61C2×C411yescharacteristic
131#121×C61C2×C411yescharacteristic
132C4×Q8×C61C2311yescharacteristic
133C4×D4×C61—21no—
134C4×D4×C61C2311yescharacteristic
135#117×C61—21no—
136C2×C42×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138C4⋊C8×C61C2311yescharacteristic
139C22⋊C8×C61—21no—
140#97×C61—21no—
141C4×C8×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C23×D61—21no—
145C2×Q8×C61C22×C411yescharacteristic
146C2×D4×C61—21no—
147C2×D4×C61C22×C411yescharacteristic
148C22×C4×C61—21no—
149C22×C4×C61C22×C411yescharacteristic
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61#4111yescharacteristic
152C22×Dic61—21no—
153C2×D244—22no—
154C2×D244—21no—
155C2×D244—41no—
156C2×D244C22×C411yescharacteristic
157C2×D244C22×C411yescharacteristic
158C2×C4×D61—21no—
159C2×C4×D61—21no—
160C2×C4×D61—21no—
161C2×C4×D61—21no—
162C2×C4×D61—81no—
163C2×C4×D61—81no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—42no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61C22×C411yescharacteristic
174C4⋊C4×C61C22×C411yescharacteristic
175C22⋊C4×C61—21no—
176C22⋊C4×C61—21no—
177C22⋊C4×C61—21no—
178C22⋊C4×C61—21no—
179C22⋊C4×C61—21no—
180C42×C61—21no—
181C42×C61C22×C411yescharacteristic
182C42×C61C2×D411yescharacteristic
183C42×C61#4111yescharacteristic
184C42×C61C2411yescharacteristic
185#11758201—22no—
186#11758201—41no—
187#11758199—22no—
188#11758199—41no—
189#11758198—21no—
190#11758198—21no—
191#11758198—21no—
192#11758198—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61C22×C411yescharacteristic
195C4⋊Dic61C22×C411yescharacteristic
196#11758194—81no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—81no—
200C2×#92418—81no—
201C2×#92418C22×C411yescharacteristic
202C2×#92418C22×C411yescharacteristic
203C2×#92418C22×C411yescharacteristic
204C2×#92418C22×C411yescharacteristic
205C2×#92418C2×D411yescharacteristic
206C2×#92418C2×D411yescharacteristic
207C2×#92418C2×D411yescharacteristic
208C2×#92418C2×D411yescharacteristic
209#11758189—81no—
210#11758189—81no—
211C8×D61—81no—
212C8×D61—81no—
213C23×C61—21no—
214C23×C61C4×D411yescharacteristic
215C22×D61—21no—
216C22×D61—21no—
217C22×D61—42no—
218C22×D61—42no—
219C22×D61—81no—
220Q8×C61—21no—
221Q8×C61—21no—
222D4×C61—21no—
223D4×C61—21no—
224D4×C61—42no—
225C2×C4×C61—22no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61C4×D411yescharacteristic
236C2×C4×C61C4×D411yescharacteristic
237C2×C4×C61C4×D411yescharacteristic
238C2×C4×C61C23×C411yescharacteristic
239C2×C4×C61C22×D411yescharacteristic
240C2×C4×C61C2×#4111yescharacteristic
241C2×Dic61—21no—
242C2×Dic61—21no—
243C2×Dic61—81no—
244D244—21no—
245D244—21no—
246D244—21no—
247D244—42no—
248D244#13112yes—
249C4×D61—41no—
250C4×D61—41no—
251C4×D61—41no—
252C4×D61—41no—
253C4×D61—81no—
254C4×D61—81no—
255C8×C61—41no—
256C8×C61—41no—
257C8×C61—41no—
258C8×C61—41no—
259#92418—21no—
260#92418—21no—
261#92418—21no—
262#92418—21no—
263#92418—21no—
264#92418—21no—
265#92418—21no—
266#92418—21no—
267#92418—41no—
268#92418—41no—
269#18020—611nomaximal, Sylow
270C22×C61—21no—
271C22×C61—21no—
272C22×C61—41no—
273C22×C61—41no—
274C22×C61—41no—
275C22×C61#44412yes—
276C22×C61C2×C4×D411yescharacteristic
277C2×D61—22no—
278C2×D61—41no—
279C2×D61—41no—
280C2×D61—41no—
281C2×D61—41no—
282C2×D61—41no—
283C2×D61—84no—
284C4×C61—21no—
285C4×C61—21no—
286C4×C61—21no—
287C4×C61—21no—
288C4×C61—41no—
289C4×C61—41no—
290C4×C61—41no—
291C4×C61C2×#13111yescharacteristic
292C4×C61#56811yescharacteristic
293C4×C61#57611yescharacteristic
294C4×C61#57711yescharacteristic
295Dic61—41no—
296Dic61—41no—
297#3105—611no—
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#1494D6111yescharacteristic, complemented
310C2×D4⋊C8—611no—
311#1452—611no—
312C2×C61—22no—
313C2×C61—81no—
314C2×C61#293311yescharacteristic
315C2×C61#294611yescharacteristic
316C2×C61C2×#44411yescharacteristic
317D61—42no—
318D61—81no—
319#529C2×D6111yescharacteristic
320C2×C4×D4—611no—
321#484—611no—
322#481—611no—
323#478—611no—
324#478—611no—
325#463—611no—
326#463—611no—
327#450—611no—
328#447—611no—
329#446—611no—
330C8×Q8—611no—
331C4×SD16—611no—
332C4×SD16—611no—
333C4×D8—611no—
334C4×D8—611no—
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#432C2×D6111yescharacteristic
347#431—611no—
348#431—611no—
349#424—1221no—
350C2×C4⋊C8—611no—
351#407—1221no—
352C2×C22⋊C8—1221no—
353C2×C4×C8C2×D6111yescharacteristic
354#335—611no—
355#335—611no—
356#334—611no—
357#334—611no—
358Q8⋊C8C2×D6111yescharacteristic, complemented
359Q8⋊C8C2×D6111yescharacteristic, complemented
360D4⋊C8—611no—
361D4⋊C8—611no—
362D4⋊C8—611no—
363D4⋊C8—611no—
364D4⋊C8C2×D6111yescharacteristic, complemented
365D4⋊C8C2×D6111yescharacteristic, complemented
366#322—611no—
367#322—611no—
368#322—611no—
369#322—611no—
370C61#1802011yescharacteristic, complemented, Sylow
371C22×D4—611no—
372C23×C4—1221no—
373C2×SD16—611no—
374C2×SD16—611no—
375C2×D8—611no—
376C2×D8—611no—
377C2×M16—1221no—
378C2×M16—1221no—
379C2×M16—1221no—
380C22×C8—21no—
381C22×C8—1221no—
382C22×C8—1221no—
383C22×C8—1221no—
384C22×C8—1221no—
385#126—21no—
386#125C4×D6111yescharacteristic
387#124C4×D6111yescharacteristic
388#123—21no—
389C22⋊Q8C4×D6111yescharacteristic
390#121C4×D6111yescharacteristic
391C4×Q8C22×D6111yescharacteristic
392C4×D4—21no—
393C4×D4—611no—
394C4×D4—611no—
395C4×D4—611no—
396C4×D4—611no—
397C4×D4—1221no—
398C4×D4—1221no—
399C4×D4C22×D6111yescharacteristic
400#117—21no—
401C2×C4⋊C4—611no—
402C2×C22⋊C4—1221no—
403C2×C42C22×D6111yescharacteristic
404#107—611no—
405#107—611no—
406#106—611no—
407#106—611no—
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⋊C8C22×D6111yescharacteristic
418C4⋊C8C22×D6111yescharacteristic
419#103—611no—
420#103—611no—
421#102—611no—
422#102—611no—
423#102—611no—
424#102—611no—
425#102—611no—
426#102—611no—
427C22⋊C8—21no—
428C22⋊C8—611no—
429C22⋊C8—611no—
430C22⋊C8—611no—
431C22⋊C8—611no—
432C22⋊C8—1221no—
433C22⋊C8—1221no—
434C22⋊C8—1221no—
435C22⋊C8—1221no—
436C22⋊C8—1221no—
437C22⋊C8—1221no—
438#97—21no—
439#97—1221no—
440C4×C8—21no—
441C4×C8—611no—
442C4×C8—611no—
443C4×C8—611no—
444C4×C8—611no—
445C4×C8—1221no—
446C4×C8C22×D6111yescharacteristic
447C4×C8C22×D6111yescharacteristic
448C24—1221no—
449C2×Q8C2×C4×D6111yescharacteristic
450C2×D4—21no—
451C2×D4—611no—
452C2×D4—611no—
453C2×D4—1222no—
454C2×D4—1221no—
455C2×D4—2441no—
456C2×D4C2×C4×D6111yescharacteristic
457C22×C4—21no—
458C22×C4—1221no—
459C22×C4—1221no—
460C22×C4—1221no—
461C22×C4—1221no—
462C22×C4—1221no—
463C22×C4—4881no—
464C22×C4—4881no—
465C22×C4C2×C4×D6111yescharacteristic
466C22×C4D4×D6111yescharacteristic
467C22×C4#1175822411yescharacteristic
468SD16—1222no—
469SD16—2441no—
470D8—1222no—
471D8—2441no—
472M16—4881no—
473M16—4881no—
474M16—4881no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—42no—
480C2×C8—611no—
481C2×C8—611no—
482C2×C8—611no—
483C2×C8—611no—
484C2×C8—611no—
485C2×C8—611no—
486C2×C8—611no—
487C2×C8—611no—
488C2×C8—1221no—
489C2×C8—1221no—
490C2×C8—4881no—
491C2×C8—4881no—
492C2×C8—4881no—
493C2×C8—4881no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—611no—
499C4⋊C4—611no—
500C4⋊C4—1221no—
501C4⋊C4C2×C4×D6111yescharacteristic
502C4⋊C4C2×C4×D6111yescharacteristic
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—1221no—
509C22⋊C4—1221no—
510C22⋊C4—1221no—
511C22⋊C4—1221no—
512C42—21no—
513C42C2×C4×D6111yescharacteristic
514C42D4×D6111yescharacteristic
515C42#1175822411yescharacteristic
516C42C23×D6111yescharacteristic
517C23—21no—
518C23—1221no—
519C23—1221no—
520C23—4881no—
521C23—2442no—
522C23—2442no—
523C23#1451973711yescharacteristic
524Q8—21no—
525Q8—21no—
526D4—21no—
527D4—21no—
528D4—42no—
529D4—612no—
530D4—1221no—
531D4—1221no—
532D4—1221no—
533D4—2442no—
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—41no—
543C2×C4—41no—
544C2×C4—1221no—
545C2×C4—1221no—
546C2×C4—4881no—
547C2×C4—4881no—
548C2×C4—4881no—
549C2×C4—2441no—
550C2×C4—2441no—
551C2×C4—2441no—
552C2×C4—2441no—
553C2×C4#1451973711yescharacteristic
554C2×C4#1451973711yescharacteristic
555C2×C4#1451973711yescharacteristic
556C2×C4C22×C4×D6111yescharacteristic
557C2×C4C2×D4×D6111yescharacteristic
558C2×C4C2×#1175822411yescharacteristic
559C8—41no—
560C8—41no—
561C8—41no—
562C8—41no—
563C8—1221no—
564C8—1221no—
565C8—1221no—
566C8—1221no—
567C8—1221no—
568C8—1221no—
569C8—1221no—
570C8—1221no—
571C8—2441no—
572C8—2441no—
573C22—21no—
574C22—21no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—1222no—
579C22—4884no—
580C22—2441no—
581C22—2441no—
582C22—2441no—
583C22—2441no—
584C22—2441no—
585C22#1683988112yes—
586C22C2×#1451973711yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—2441no—
595C4—2441no—
596C4#131×D6111yescharacteristic
597C4#1684052711yescharacteristic
598C4#1684056411yescharacteristic
599C4#1684056911yescharacteristic
600C2—22no—
601C2—81no—
602C2—4881no—
603C2—2442no—
604C2#2145454911yescharacteristic
605C2#2145465411yescharacteristic
606C2C2×#1683988111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1494C2
socleC22×C61C2×C4×D4
prime radical#16839895C4
cosocleC42×C61C24
hypercenter#1494D61
hypocenterC61#18020
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1494

Complements

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

NH ≅ G/Ntype
2. #21454979C2semidirect
3. #21454856C2semidirect
4. #21444730C2semidirect
5. #21444724C2semidirect
6. #21444659C2semidirect
7. #21444658C2semidirect
8. #21444651C2semidirect
9. #21444645C2semidirect
10. #21444640C2semidirect
11. #21444634C2semidirect
12. #21444605C2semidirect
13. C2×#16839491C2semidirect
14. #21444111C2semidirect
15. C61×#1494C2semidirect
25. #16839893C22semidirect
26. Q8×#92418C22semidirect
31. #16839840C22semidirect
38. D4×#92418C22semidirect
48. #16839514C22semidirect
49. #16839514C22semidirect
50. #16839512C22semidirect
51. #16839512C22semidirect
56. #16839484C22semidirect
57. #16839484C22semidirect
58. #16839484C22semidirect
59. #16839484C22semidirect
63. C61×Q8⋊C8C22semidirect
64. C61×Q8⋊C8C22semidirect
65. C61×D4⋊C8C22semidirect
66. C61×D4⋊C8C22semidirect
309. #1494D61semidirect
358. Q8⋊C8C2×D61semidirect
359. Q8⋊C8C2×D61semidirect
364. D4⋊C8C2×D61semidirect
365. D4⋊C8C2×D61semidirect
370. C61#18020semidirect

Maximal subgroups

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

subgroupindex
#214558622
#214549792
#214548562
#214447302
#214447242
#214446592
#214446582
#214446512
#214446452
#214446402
#214446342
#214446052
C2×#168394912
#214441112
C61×#14942
#1802061