Finite Group Databasebeta

← #11882277

Subgroups — #11882277

Order 1152.

848 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593970C211yesmaximal, characteristic
2#10593873C211yesmaximal, characteristic, complemented
3#10592547C211yesmaximal, characteristic, complemented
4C3×#4851C211yesmaximal, characteristic, complemented
5C3×D3×C4⋊C8C211yesmaximal, characteristic, complemented
6#10590847C212yesmaximal, complemented
7#10590830C212yesmaximal, complemented
8#10590760C212yesmaximal, complemented
9#10590759C212yesmaximal, complemented
10#10590367C211yesmaximal, characteristic, complemented
11#10590307C211yesmaximal, characteristic, complemented
12#81002—31nomaximal
13#79027—31nomaximal
14C2×#3799—21no—
15C2×#3744C2212yes—
16#64083C2211yescharacteristic
17C4×#634C2211yescharacteristic
18C2×C3×D3×C8C2212yes—
19C3×C42×D3C2211yescharacteristic
20C3×#869C2211yescharacteristic
21C3×C4×Dic6C2211yescharacteristic
22#63918C2211yescharacteristic
23C4×#627—21no—
24#63909—21no—
25#63909C2212yes—
26#63894—21no—
27#63894C2212yes—
28#63867—21no—
29#63866C2211yescharacteristic
30#63864—21no—
31#63857C2211yescharacteristic
32#63856C2211yescharacteristic
33#63855—21no—
34#63851—21no—
35C2×#3717C2212yes—
36C32×C4⋊C8C2211yescharacteristic
37#63648C2212yes—
38C3×#817C2212yes—
39C3×#816C2212yes—
40C3×Dic3⋊C8C2212yes—
41C3×C4⋊(C3⋊C8)C2211yescharacteristic
42#63573C2212yes—
43#63567C2212yes—
44#63564C2212yes—
45#5725—31no—
46#5578—31no—
47#5477—31no—
48#5470—31no—
49C3×#475—31no—
50C2×C3×C4⋊C8—31no—
51#5114—32no—
52#5114—32no—
53#5094—31no—
54#5027—31no—
55#4870—32no—
56#4864—32no—
57#4851—31no—
58#4851D311yescharacteristic, complemented
59#4848—31no—
60#4848—31no—
61#4848—31no—
62#4848—61no—
63#4842—32no—
64#4841—32no—
65D3×C4⋊C8D311yescharacteristic, complemented
66#4818—32no—
67#4807—32no—
68C2×C4⋊(C3⋊D3)—21no—
69C2×C4⋊(C3⋊D3)—21no—
70C2×C4⋊(C3⋊D3)C2312yes—
71C2×#634C2311yescharacteristic
72C2×C3×C4×D3D411yescharacteristic
73C2×C3×C4×D3D411yescharacteristic
74C2×C3×C4×D3C2311yescharacteristic
75C2×C3×Dic6—21no—
76C2×C3×Dic6C2311yescharacteristic
77C2×#627—21no—
78C2×#626—22no—
79C2×#624—22no—
80#3799—44no—
81C2×C32×C8C2312yes—
82C32×C42C2311yescharacteristic
83C4⋊(C3⋊Dic3)C2311yescharacteristic
84#3750—21no—
85C4×C3⋊Dic3—21no—
86#3744—42no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3C2311yescharacteristic
89C3×C4⋊Dic3C2312yes—
90C3×Dic3⋊C4—21no—
91C3×C4×Dic3—21no—
92C3×C4×Dic3D411yescharacteristic
93C3×C4×Dic3D411yescharacteristic
94C3×C4×Dic3C2311yescharacteristic
95C2×C3×C3⋊C8C2312yes—
96C3×D3×C8—42no—
97#3724—21no—
98Dic3⋊Dic3—21no—
99Dic3⋊Dic3—21no—
100Dic3⋊Dic3—21no—
101Dic3⋊Dic3—21no—
102#3722—22no—
103#3722—22no—
104(C2×D3)⋊Dic3—21no—
105(C2×D3)⋊Dic3—21no—
106#3717—42no—
107#3246—91noSylow
108C2×#239—61no—
109C2×#235—61no—
110C22×C3×C8—32no—
111C3×C4⋊Q8—31no—
112C3×C4×Q8—31no—
113C2×C3×C42—31no—
114#947—61no—
115#946—31no—
116#944—31no—
117C2×#215—32no—
118#930—32no—
119#930—61no—
120#926—61no—
121#924—31no—
122#924—31no—
123#924—61no—
124C2×#204—32no—
125C2×#204—32no—
126C2×#204—32no—
127C2×#204—62no—
128C2×D3×C8C2×D312yes—
129#897—31no—
130#896—61no—
131#895—32no—
132#895—61no—
133#893—32no—
134#893—61no—
135#889—61no—
136#888—31no—
137#875—61no—
138#874—31no—
139#874—31no—
140#874—61no—
141C4×D12—32no—
142C4×D12—61no—
143#872—61no—
144C42×D3C2×D311yescharacteristic
145#870—61no—
146#869—31no—
147#869—31no—
148#869C2×D311yescharacteristic
149C4×Dic6—31no—
150C4×Dic6—31no—
151C4×Dic6—61no—
152C4×Dic6—61no—
153C4×Dic6—61no—
154C4×Dic6C2×D311yescharacteristic
155C3×#106—32no—
156C3×C4⋊C8—21no—
157C3×C4⋊C8—32no—
158C3×C4⋊C8—31no—
159C3×C4⋊C8C2×D311yescharacteristic
160C3×C4⋊C8C2×D311yescharacteristic
161C3×#103—32no—
162#821—32no—
163#821—32no—
164#821—32no—
165#821—62no—
166#817—32no—
167#817C2×D312yes—
168#816—32no—
169#816C2×D312yes—
170Dic3⋊C8C2×D312yes—
171#810—32no—
172#809—32no—
173#808—32no—
174C4⋊(C3⋊C8)C2×D311yescharacteristic
175C22×C3⋊D3—22no—
176C22×C3×D3C2×D411yescharacteristic
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2411yescharacteristic
180C2×C3⋊Dic3—21no—
181C2×C3⋊Dic3—21no—
182C4⋊(C3⋊D3)—22no—
183C4⋊(C3⋊D3)—22no—
184C4⋊(C3⋊D3)—42no—
185C4⋊(C3⋊D3)—42no—
186#634—21no—
187#634—21no—
188C2×C3×Dic3—21no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3C2×D411yescharacteristic
192C2×C3×Dic3C2×D411yescharacteristic
193C2×C3×Dic3C2×D411yescharacteristic
194C3×C4×D3—21no—
195C3×C4×D3—21no—
196C3×C4×D3—41no—
197C3×C4×D3SD1614yescomplemented
198C3×Dic6—21no—
199C3×Dic6—21no—
200C3×Dic6—42no—
201#627—42no—
202#626—44no—
203#624—44no—
204C32×C8—22no—
205C3×C3⋊C8—22no—
206#533—91no—
207#532—91no—
208#476—92no—
209#475—31no—
210#475—91no—
211#465—92no—
212#465—92no—
213#461—92no—
214#460—91no—
215#460—91no—
216C2×C4⋊C8—31no—
217C2×C3×Q8—31no—
218C2×C3×Q8—61no—
219C22×C3×C4—31no—
220C22×C3×C4—31no—
221C22×C3×C4—31no—
222C2×#67—62no—
223#239—124no—
224#235—124no—
225C2×D12—32no—
226C2×D12—32no—
227C2×D12—62no—
228C2×D12—62no—
229C2×D12—61no—
230C2×D12—61no—
231C2×D12—61no—
232C2×D12—61no—
233C2×D12—121no—
234C2×D12—121no—
235C2×C4×D3—62no—
236C2×C4×D3—62no—
237C2×C4×D3D1211yescharacteristic
238C2×C4×D3D1211yescharacteristic
239C2×C4×D3C22×D311yescharacteristic
240C2×Dic6—21no—
241C2×Dic6—31no—
242C2×Dic6—31no—
243C2×Dic6—61no—
244C2×Dic6—61no—
245C2×Dic6—61no—
246C2×Dic6C22×D311yescharacteristic
247C2×C3×C8—22no—
248C2×C3×C8—32no—
249C2×C3×C8—122no—
250C2×C3×C8C22×D312yes—
251C2×C3×C8C22×D312yes—
252C3×C4⋊C4—32no—
253C3×C4⋊C4—31no—
254C3×C4⋊C4—61no—
255C3×C4⋊C4—61no—
256C3×C42—21no—
257C3×C42—31no—
258C3×C42—31no—
259C3×C42—31no—
260C3×C42—61no—
261C3×C42C22×D311yescharacteristic
262C3×C42C22×D311yescharacteristic
263#217—61no—
264#217—61no—
265#215—122no—
266(C2×D3)⋊C4—62no—
267(C2×D3)⋊C4—62no—
268(C2×D3)⋊C4—61no—
269(C2×D3)⋊C4—61no—
270(C2×D3)⋊C4—62no—
271(C2×D3)⋊C4—62no—
272C4⋊Dic3—21no—
273C4⋊Dic3—31no—
274C4⋊Dic3—31no—
275C4⋊Dic3—61no—
276C4⋊Dic3—61no—
277C4⋊Dic3—61no—
278C4⋊Dic3—61no—
279C4⋊Dic3—61no—
280C4⋊Dic3C22×D312yes—
281C4⋊Dic3C22×D311yescharacteristic
282Dic3⋊C4—21no—
283Dic3⋊C4—61no—
284Dic3⋊C4—61no—
285Dic3⋊C4—61no—
286Dic3⋊C4—61no—
287Dic3⋊C4—61no—
288Dic3⋊C4—61no—
289Dic3⋊C4—61no—
290Dic3⋊C4—61no—
291Dic3⋊C4—121no—
292C4×Dic3—21no—
293C4×Dic3—61no—
294C4×Dic3—61no—
295C4×Dic3—121no—
296C4×Dic3D1211yescharacteristic
297C4×Dic3D1211yescharacteristic
298C4×Dic3C22×D311yescharacteristic
299C2×C3⋊C8C22×D312yes—
300#204—122no—
301#204—122no—
302#204—124no—
303#204—122no—
304D3×C8—42no—
305C22×C32C22×D411yescharacteristic
306C2×C3⋊D3—42no—
307C2×C3⋊D3—42no—
308C2×C3⋊D3—42no—
309C2×C3×D3—21no—
310C2×C3×D3—21no—
311C2×C3×D3C2×SD1612yes—
312C32×C4—21no—
313C32×C4C2×SD1612yes—
314C32×C4H(5,𝔽2)11yescharacteristic
315C32×C42−1+411yescharacteristic
316C3⋊Dic3—41no—
317C3⋊Dic3—41no—
318C3×Dic3—21no—
319C3×Dic3—21no—
320C3×Dic3—41no—
321C3×Dic3—42no—
322C3×Dic3—41no—
323C3×Dic3C2×SD1612yes—
324C2×#41—181no—
325C2×SD16—92no—
326C2×SD16—92no—
327C22×C8—32no—
328C4⋊Q8—31no—
329C4⋊Q8—91no—
330C4⋊Q8—91no—
331#127—91no—
332#125—181no—
333#124—181no—
334C22⋊Q8—91no—
335C22⋊Q8—91no—
336C22⋊Q8—181no—
337#121—92no—
338#121—181no—
339C4×Q8—31no—
340C4×Q8—91no—
341C4×Q8—181no—
342C4×D4—92no—
343C4×D4—181no—
344#117—181no—
345C2×C42—31no—
346#106—32no—
347#106—92no—
348C4⋊C8—32no—
349C4⋊C8—31no—
350C4⋊C8D3211yescharacteristic
351#103—32no—
352#103—92no—
353#102—92no—
354#102—92no—
355C23×C3—31no—
356C22×D3—62no—
357C22×D3—62no—
358C22×D3—122no—
359C22×D3C2×D1211yescharacteristic
360C3×Q8—61no—
361C3×Q8—61no—
362C3×Q8—122no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—31no—
367C2×C3×C4—34no—
368C2×C3×C4—31no—
369C2×C3×C4—31no—
370C2×C3×C4—61no—
371C2×C3×C4—61no—
372C2×C3×C4—61no—
373C2×C3×C4—61no—
374C2×C3×C4—62no—
375C2×C3×C4—121no—
376C2×C3×C4C2×D1211yescharacteristic
377C2×C3×C4C2×D1211yescharacteristic
378C2×C3×C4D3×D411yescharacteristic
379C2×C3×C4D3×D411yescharacteristic
380C2×C3×C4C23×D311yescharacteristic
381C2×C3×C4C23×D311yescharacteristic
382#67—124no—
383C2×Dic3—21no—
384C2×Dic3—21no—
385C2×Dic3—22no—
386C2×Dic3—61no—
387C2×Dic3—61no—
388C2×Dic3—61no—
389C2×Dic3—61no—
390C2×Dic3—121no—
391C2×Dic3—121no—
392C2×Dic3C2×D1211yescharacteristic
393C2×Dic3C2×D1211yescharacteristic
394C2×Dic3C2×D1211yescharacteristic
395D12—62no—
396D12—62no—
397D12—62no—
398D12—62no—
399D12—122no—
400D12—122no—
401D12—122no—
402D12—122no—
403D12—124no—
404D12—122no—
405D12—122no—
406D12—242no—
407D12—242no—
408C4×D3—21no—
409C4×D3—21no—
410C4×D3—41no—
411C4×D3—124no—
412C4×D3—124no—
413C4×D3#20414yescomplemented
414Dic6—21no—
415Dic6—21no—
416Dic6—42no—
417Dic6—62no—
418Dic6—61no—
419Dic6—61no—
420Dic6—61no—
421Dic6—61no—
422Dic6—121no—
423Dic6—122no—
424Dic6—122no—
425C3×C8—22no—
426C3×C8—22no—
427C3×C8—42no—
428C3×C8—62no—
429C3⋊C8—22no—
430C2×C32#53711yescharacteristic
431C2×C32C22×SD1611yescharacteristic
432C2×C32#57511yescharacteristic
433C3⋊D3—82no—
434C3×D3—22no—
435#41—364no—
436C2×Q8—31no—
437C2×Q8—61no—
438C2×Q8—91no—
439C2×Q8—181no—
440C2×D4—92no—
441C2×D4—182no—
442C2×D4—181no—
443C2×D4—181no—
444C22×C4—31no—
445C22×C4—31no—
446C22×C4—31no—
447C22×C4—182no—
448SD16—362no—
449SD16—362no—
450C2×C8—32no—
451C2×C8—122no—
452C2×C8C2×D3212yes—
453C4⋊C4—31no—
454C4⋊C4—32no—
455C4⋊C4—61no—
456C4⋊C4—61no—
457C4⋊C4—91no—
458C4⋊C4—181no—
459C4⋊C4—181no—
460C4⋊C4—181no—
461C4⋊C4—181no—
462C4⋊C4—181no—
463C4⋊C4—181no—
464C22⋊C4—182no—
465C22⋊C4—182no—
466C22⋊C4—181no—
467C22⋊C4—181no—
468C42—31no—
469C42—31no—
470C42—31no—
471C42—61no—
472C42—181no—
473C42C2×D3211yescharacteristic
474C22×C3—21no—
475C22×C3—32no—
476C22×C3—61no—
477C22×C3—61no—
478C22×C3C22×D1211yescharacteristic
479C22×C3C2×D3×D411yescharacteristic
480C2×D3—21no—
481C2×D3—21no—
482C2×D3—122no—
483C2×D3—122no—
484C2×D3—122no—
485C2×D3—122no—
486C2×D3—122no—
487C2×D3—122no—
488C2×D3—242no—
489C2×D3—242no—
490C2×D3—242no—
491C2×D3C2×#20412yes—
492C3×C4—21no—
493C3×C4—21no—
494C3×C4—22no—
495C3×C4—21no—
496C3×C4—21no—
497C3×C4—32no—
498C3×C4—41no—
499C3×C4—61no—
500C3×C4—61no—
501C3×C4—122no—
502C3×C4—121no—
503C3×C4—121no—
504C3×C4C2×#20412yes—
505C3×C4D3×SD1612yes—
506C3×C4#100411yescharacteristic
507C3×C4#100711yescharacteristic
508C3×C4#100711yescharacteristic
509C3×C4#100911yescharacteristic
510Dic3—21no—
511Dic3—21no—
512Dic3—42no—
513Dic3—41no—
514Dic3—41no—
515Dic3—122no—
516Dic3—121no—
517Dic3—121no—
518Dic3—121no—
519Dic3—121no—
520Dic3—241no—
521Dic3C2×#20412yes—
522C32#324611yescharacteristic, complemented, Sylow
523C23—31no—
524C23—182no—
525Q8—61no—
526Q8—61no—
527Q8—122no—
528Q8—181no—
529Q8—181no—
530Q8—362no—
531D4—182no—
532D4—182no—
533D4—362no—
534D4—364no—
535D4—362no—
536C2×C4—31no—
537C2×C4—34no—
538C2×C4—31no—
539C2×C4—31no—
540C2×C4—61no—
541C2×C4—61no—
542C2×C4—61no—
543C2×C4—61no—
544C2×C4—62no—
545C2×C4—121no—
546C2×C4—181no—
547C2×C4—181no—
548C2×C4—364no—
549C2×C4D3×D1211yescharacteristic
550C2×C4D3×D1211yescharacteristic
551C2×C4C22×D3211yescharacteristic
552C8—22no—
553C8—62no—
554C2×C3—21no—
555C2×C3—21no—
556C2×C3—21no—
557C2×C3—62no—
558C2×C3#551011yescharacteristic
559C2×C3#562911yescharacteristic
560C2×C3C22×#20411yescharacteristic
561C2×C3#574811yescharacteristic
562C2×C3C2×D3×SD1611yescharacteristic
563C2×C3#577711yescharacteristic
564D3—22no—
565D3—242no—
566D3—242no—
567D3—482no—
568C22—32no—
569C22—61no—
570C22—61no—
571C22—362no—
572C22—362no—
573C22—362no—
574C22C2×D3×D1211yescharacteristic
575C4—21no—
576C4—32no—
577C4—61no—
578C4—61no—
579C4—122no—
580C4—121no—
581C4—121no—
582C4—361no—
583C4—361no—
584C4D3×#20412yes—
585C4#6431411yescharacteristic
586C4#6431611yescharacteristic
587C3—21no—
588C3#7902711yescharacteristic, complemented
589C3#8100211yescharacteristic, complemented
590C2—62no—
591C2—722no—
592C2#1059452311yescharacteristic
593C2C2×D3×#20411yescharacteristic
594C2#1059471111yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radical#10593970C2
hypercenterC4⋊C8D32
hypocenterC32#3246
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10593873C2semidirect
3. #10592547C2semidirect
4. C3×#4851C2semidirect
5. C3×D3×C4⋊C8C2semidirect
6. #10590847C2semidirect
7. #10590830C2semidirect
8. #10590760C2semidirect
9. #10590759C2semidirect
10. #10590367C2semidirect
11. #10590307C2semidirect
58. #4851D3semidirect
65. D3×C4⋊C8D3semidirect
197. C3×C4×D3SD16semidirect
413. C4×D3#204semidirect
522. C32#3246semidirect
588. C3#79027semidirect
589. C3#81002semidirect

Maximal subgroups

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

subgroupindex
#105939702
#105938732
#105925472
C3×#48512
C3×D3×C4⋊C82
#105908472
#105908302
#105907602
#105907592
#105903672
#105903072
#810023
#790273