Finite Group Databasebeta

← #29651237

Subgroups — #29651237

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#21455866C211yesmaximal, characteristic
2#21454975C211yesmaximal, characteristic, complemented
3#21454854C211yesmaximal, characteristic, complemented
4#21444730C211yesmaximal, characteristic, complemented
5#21444718C211yesmaximal, characteristic, complemented
6#21444665C211yesmaximal, characteristic, complemented
7#21444652C211yesmaximal, characteristic, complemented
8#21444651C211yesmaximal, characteristic, complemented
9#21444645C211yesmaximal, characteristic, complemented
10#21444640C211yesmaximal, characteristic, complemented
11#21444628C211yesmaximal, characteristic, complemented
12#21444602C211yesmaximal, characteristic, complemented
13#21444280C211yesmaximal, characteristic, complemented
14#21444111C211yesmaximal, characteristic, complemented
15C2×C61×D4⋊C8C211yesmaximal, characteristic, complemented
16#16840296C2211yescharacteristic
17#16840097C411yescharacteristic
18#16840080C411yescharacteristic
19#16840062C411yescharacteristic
20#16840062C411yescharacteristic
21#16839977C411yescharacteristic
22#16839977C411yescharacteristic
23#16839913C411yescharacteristic
24#16839896C411yescharacteristic
25#16839889C2211yescharacteristic, complemented
26#16839886C2211yescharacteristic, complemented
27C4×#11758200C2211yescharacteristic
28C4×#11758200C2211yescharacteristic
29C4×#11758199C2211yescharacteristic
30C4×#11758199C2211yescharacteristic
31#16839840C2211yescharacteristic
32#16839840C2211yescharacteristic
33#16839839C2211yescharacteristic, complemented
34#16839834—21no—
35#16839834—21no—
36#16839833—21no—
37D4×#92418C2211yescharacteristic
38D4×#92418C2211yescharacteristic
39#16839827C2211yescharacteristic, complemented
40C8×C22⋊D61—21no—
41#16839822—21no—
42#16839819C2211yescharacteristic
43#16839815C2211yescharacteristic
44#16839815C2211yescharacteristic
45#16839787—21no—
46#16839726—21no—
47C2×C22⋊#92418—21no—
48#16839514C2211yescharacteristic, complemented
49#16839514C2211yescharacteristic, complemented
50#16839512C2211yescharacteristic, complemented
51#16839512C2211yescharacteristic, complemented
52#16839494C2211yescharacteristic, complemented
53#16839494C2211yescharacteristic, complemented
54#16839491C2211yescharacteristic, complemented
55#16839491C2211yescharacteristic, complemented
56#16839484C2211yescharacteristic, complemented
57#16839484C2211yescharacteristic, complemented
58#16839484C2211yescharacteristic, complemented
59#16839484C2211yescharacteristic, complemented
60C2×C4×D4×C61C2211yescharacteristic
61C2×C4⋊C8×C61C2211yescharacteristic
62C2×C4×C8×C61C2211yescharacteristic
63C61×D4⋊C8C2211yescharacteristic
64C61×D4⋊C8C2211yescharacteristic
65C61×D4⋊C8C2211yescharacteristic
66C61×D4⋊C8C2211yescharacteristic
67C2×#11758200C2×C411yescharacteristic
68C2×#11758200C2×C411yescharacteristic
69C2×#11758199C2×C411yescharacteristic
70C2×#11758199C2×C411yescharacteristic
71C2×#11758194—21no—
72C2×#11758194—21no—
73C2×#11758189—21no—
74C22×#92418—21no—
75C22×#92418—21no—
76C2×C8×D61—21no—
77#14519771—21no—
78#14519769C2×C411yescharacteristic
79#14519765C2×C411yescharacteristic
80#14519760—21no—
81#14519756C2×C411yescharacteristic
82#14519751C2×C411yescharacteristic
83C4×Dic122C2311yescharacteristic
84C4×D244C2311yescharacteristic
85C4×C22⋊D61—21no—
86#14519734—21no—
87#14519710C2×C411yescharacteristic
88#14519710C2×C411yescharacteristic
89#14519708C2×C411yescharacteristic
90#14519708C2×C411yescharacteristic
91C4⋊#92418C2×C411yescharacteristic
92C4⋊#92418C2×C411yescharacteristic
93C4⋊#92418D411yescharacteristic
94C4⋊#92418D411yescharacteristic
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97#14519706—21no—
98#14519706—21no—
99#14519700C2×C411yescharacteristic
100#14519700C2×C411yescharacteristic
101#14519698C2×C411yescharacteristic
102#14519698C2×C411yescharacteristic
103#14519698C2×C411yescharacteristic
104#14519698C2×C411yescharacteristic
105#14519697C2×C411yescharacteristic
106#14519697C2×C411yescharacteristic
107C22⋊#92418—21no—
108C22⋊#92418—21no—
109C22⋊#92418—21no—
110C22⋊#92418—21no—
111C22⋊#92418—21no—
112C22⋊#92418C2×C411yescharacteristic
113C22⋊#92418C2×C411yescharacteristic
114C22⋊#92418D411yescharacteristic
115C22⋊#92418D411yescharacteristic
116#14519689—21no—
117#14519689—21no—
118#14519688—21no—
119#14519687—21no—
120C4×#92418C2311yescharacteristic
121C4×#92418C2311yescharacteristic
122C4×#92418C2311yescharacteristic
123C4×#92418C2311yescharacteristic
124C8×Dic61—21no—
125C22×D4×C61C2×C411yescharacteristic
126C23×C4×C61—21no—
127C22×C8×C61—21no—
128C22×C8×C61—21no—
129C4×D4×C61—21no—
130C4×D4×C61—21no—
131C4×D4×C61C2×C411yescharacteristic
132C4×D4×C61C2×C411yescharacteristic
133C4×D4×C61C2311yescharacteristic
134C4×D4×C61C2311yescharacteristic
135C2×C4⋊C4×C61C2×C411yescharacteristic
136C2×C22⋊C4×C61—21no—
137C2×C42×C61C2311yescharacteristic
138C4⋊C8×C61—21no—
139C4⋊C8×C61C2311yescharacteristic
140C4⋊C8×C61C2311yescharacteristic
141C4×C8×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C24×C61—21no—
145C2×D4×C61—22no—
146C2×D4×C61—21no—
147C2×D4×C61—41no—
148C2×D4×C61C22×C411yescharacteristic
149C2×D4×C61C22×C411yescharacteristic
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—81no—
156C22×C4×C61—81no—
157C22×C4×C61C22×C411yescharacteristic
158C22×C4×C61C2×D411yescharacteristic
159C22×C4×C61#4111yescharacteristic
160C2×C22⋊D61—21no—
161C2×D244C22×C411yescharacteristic
162C2×C4×D61—21no—
163C2×Dic122C22×C411yescharacteristic
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—42no—
169C2×C8×C61—81no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61C22×C411yescharacteristic
172C4⋊C4×C61C22×C411yescharacteristic
173C22⋊C4×C61—21no—
174C22⋊C4×C61—21no—
175C22⋊C4×C61—21no—
176C22⋊C4×C61—21no—
177C42×C61C22×C411yescharacteristic
178C42×C61C2×D411yescharacteristic
179C42×C61#4111yescharacteristic
180C42×C61C2411yescharacteristic
181C22⋊Dic61—21no—
182#11758200—22no—
183#11758200—41no—
184#11758199—22no—
185#11758199—41no—
186#11758198—21no—
187#11758198—21no—
188#11758198—21no—
189#11758198—21no—
190C4⋊Dic61C22×C411yescharacteristic
191C4⋊Dic61C22×C411yescharacteristic
192#11758196—21no—
193#11758196—21no—
194#11758196—21no—
195#11758196—21no—
196C4×Dic61—21no—
197#11758194—81no—
198#11758194—81no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—81no—
202C2×#92418—81no—
203C2×#92418C22×C411yescharacteristic
204C2×#92418C22×C411yescharacteristic
205C2×#92418C22×C411yescharacteristic
206C2×#92418C22×C411yescharacteristic
207C2×#92418C2×D411yescharacteristic
208C2×#92418C2×D411yescharacteristic
209C2×#92418C2×D411yescharacteristic
210C2×#92418C2×D411yescharacteristic
211#11758189—81no—
212C8×D61—81no—
213C23×C61—21no—
214C23×C61—21no—
215C23×C61—42no—
216C23×C61—42no—
217C23×C61—81no—
218C23×C61C4×D411yescharacteristic
219C22×D61—21no—
220D4×C61—21no—
221D4×C61—21no—
222D4×C61—21no—
223D4×C61—42no—
224D4×C61#13112yes—
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—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—81no—
237C2×C4×C61—81no—
238C2×C4×C61—81no—
239C2×C4×C61C4×D411yescharacteristic
240C2×C4×C61C4×D411yescharacteristic
241C2×C4×C61C4×D411yescharacteristic
242C2×C4×C61C23×C411yescharacteristic
243C2×C4×C61C22×D411yescharacteristic
244C2×C4×C61C2×#4111yescharacteristic
245C22⋊D61—42no—
246C2×Dic61—21no—
247C2×Dic61—21no—
248C2×Dic61—21no—
249D244—21no—
250D244—21no—
251C4×D61—41no—
252C4×D61—41no—
253Dic122—21no—
254Dic122—21no—
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—22no—
273C22×C61—41no—
274C22×C61—41no—
275C22×C61—41no—
276C22×C61—41no—
277C22×C61—41no—
278C22×C61—84no—
279C22×C61#44412yes—
280C22×C61C2×C4×D411yescharacteristic
281C2×D61—41no—
282C2×D61—41no—
283C2×D61—41no—
284C4×C61—21no—
285C4×C61—21no—
286C4×C61—21no—
287C4×C61—21no—
288C4×C61—41no—
289C4×C61—41no—
290C4×C61C2×#13111yescharacteristic
291C4×C61#56811yescharacteristic
292C4×C61#57611yescharacteristic
293C4×C61#57711yescharacteristic
294Dic61—41no—
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#1494—611no—
310C2×D4⋊C8D6111yescharacteristic, complemented
311#1452—611no—
312C2×C61—22no—
313C2×C61—42no—
314C2×C61—81no—
315C2×C61#293311yescharacteristic
316C2×C61#294611yescharacteristic
317C2×C61C2×#44411yescharacteristic
318D61—81no—
319#529—611no—
320C2×C4×D4C2×D6111yescharacteristic
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#432—611no—
347#431—611no—
348#431—611no—
349#424—1221no—
350C2×C4⋊C8C2×D6111yescharacteristic
351#407—1221no—
352C2×C22⋊C8—1221no—
353C2×C4×C8C2×D6111yescharacteristic
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⋊C8C2×D6111yescharacteristic
363D4⋊C8C2×D6111yescharacteristic
364D4⋊C8C2×D6111yescharacteristic
365D4⋊C8C2×D6111yescharacteristic
366#322—611no—
367#322—611no—
368#322—611no—
369#322—611no—
370C61#1802011yescharacteristic, complemented, Sylow
371C22×D4C4×D6111yescharacteristic
372C23×C4—21no—
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—21no—
382C22×C8—1221no—
383C22×C8—1221no—
384C22×C8—1221no—
385#126—1221no—
386#125—611no—
387#124—611no—
388#123—1221no—
389C22⋊Q8—611no—
390#121—611no—
391C4×Q8—611no—
392C4×D4—21no—
393C4×D4—21no—
394C4×D4—611no—
395C4×D4—1221no—
396C4×D4C4×D6111yescharacteristic
397C4×D4C4×D6111yescharacteristic
398C4×D4C22×D6111yescharacteristic
399C4×D4C22×D6111yescharacteristic
400#117—1221no—
401C2×C4⋊C4C4×D6111yescharacteristic
402C2×C22⋊C4—21no—
403C2×C42C22×D6111yescharacteristic
404#107—611no—
405#107—611no—
406#106—611no—
407#106—611no—
408C4⋊C8—21no—
409C4⋊C8—611no—
410C4⋊C8—611no—
411C4⋊C8—611no—
412C4⋊C8—611no—
413C4⋊C8—611no—
414C4⋊C8—611no—
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—611no—
428C22⋊C8—611no—
429C22⋊C8—611no—
430C22⋊C8—611no—
431C22⋊C8—1221no—
432C22⋊C8—1221no—
433C22⋊C8—1221no—
434C22⋊C8—1221no—
435C22⋊C8—1221no—
436C22⋊C8—1221no—
437C22⋊C8—1221no—
438#97—1221no—
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—21no—
449C2×Q8—611no—
450C2×D4—22no—
451C2×D4—21no—
452C2×D4—41no—
453C2×D4—611no—
454C2×D4—1221no—
455C2×D4C2×C4×D6111yescharacteristic
456C2×D4C2×C4×D6111yescharacteristic
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—81no—
463C22×C4—81no—
464C22×C4—1221no—
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—81no—
481C2×C8—611no—
482C2×C8—611no—
483C2×C8—611no—
484C2×C8—611no—
485C2×C8—611no—
486C2×C8—611no—
487C2×C8—611no—
488C2×C8—611no—
489C2×C8—1221no—
490C2×C8—1221no—
491C2×C8—4881no—
492C2×C8—4881no—
493C2×C8—4881no—
494C4⋊C4—21no—
495C4⋊C4—611no—
496C4⋊C4—611no—
497C4⋊C4—1221no—
498C4⋊C4—1221no—
499C4⋊C4—1221no—
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—1221no—
508C22⋊C4—1221no—
509C22⋊C4—1221no—
510C22⋊C4—1221no—
511C22⋊C4—1221no—
512C42—1221no—
513C42C2×C4×D6111yescharacteristic
514C42D4×D6111yescharacteristic
515C42#1175822411yescharacteristic
516C42C23×D6111yescharacteristic
517C23—21no—
518C23—21no—
519C23—42no—
520C23—42no—
521C23—81no—
522C23—1221no—
523C23#1451973711yescharacteristic
524Q8—1221no—
525Q8—1221no—
526D4—21no—
527D4—21no—
528D4—21no—
529D4—42no—
530D4—1221no—
531D4—1221no—
532D4—2442no—
533D4#1451978312yes—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—81no—
546C2×C4—81no—
547C2×C4—81no—
548C2×C4—1221no—
549C2×C4—1221no—
550C2×C4—1221no—
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—22no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—84no—
582C22—2441no—
583C22—2441no—
584C22—2441no—
585C22#1683988112yes—
586C22C2×#1451973711yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—41no—
592C4—41no—
593C4—2441no—
594C4—2441no—
595C4—2441no—
596C4C2×#1451978311yescharacteristic
597C4#1684052811yescharacteristic
598C4#1684056311yescharacteristic
599C4#1684056811yescharacteristic
600C2—22no—
601C2—42no—
602C2—81no—
603C2—4881no—
604C2#2145454011yescharacteristic
605C2#2145464511yescharacteristic
606C2C2×#1683988111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC2×C61×D4⋊C8C2
socleC22×C61C2×C4×D4
prime radical#16839896C4
cosocleC42×C61C24
hypercenterC2×D4⋊C8D61
hypocenterC61#18020
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #21454975C2semidirect
3. #21454854C2semidirect
4. #21444730C2semidirect
5. #21444718C2semidirect
6. #21444665C2semidirect
7. #21444652C2semidirect
8. #21444651C2semidirect
9. #21444645C2semidirect
10. #21444640C2semidirect
11. #21444628C2semidirect
12. #21444602C2semidirect
13. #21444280C2semidirect
14. #21444111C2semidirect
15. C2×C61×D4⋊C8C2semidirect
25. #16839889C22semidirect
26. #16839886C22semidirect
33. #16839839C22semidirect
39. #16839827C22semidirect
48. #16839514C22semidirect
49. #16839514C22semidirect
50. #16839512C22semidirect
51. #16839512C22semidirect
52. #16839494C22semidirect
53. #16839494C22semidirect
54. #16839491C22semidirect
55. #16839491C22semidirect
56. #16839484C22semidirect
57. #16839484C22semidirect
58. #16839484C22semidirect
59. #16839484C22semidirect
310. C2×D4⋊C8D61semidirect
370. C61#18020semidirect

Maximal subgroups

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

subgroupindex
#214558662
#214549752
#214548542
#214447302
#214447182
#214446652
#214446522
#214446512
#214446452
#214446402
#214446282
#214446022
#214442802
#214441112
C2×C61×D4⋊C82
#1802061