Finite Group Databasebeta

← #11882279

Subgroups — #11882279

Order 1152.

832 conjugacy classes of subgroups.

The subgroup lattice has 589 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593897C211yesmaximal, characteristic
2#10593873C211yesmaximal, characteristic, complemented
3#10592550C211yesmaximal, characteristic, complemented
4C3×#4848C211yesmaximal, characteristic, complemented
5C3×D3×C4⋊C8C211yesmaximal, characteristic, complemented
6#10590829C212yesmaximal, complemented
7#10590825C212yesmaximal, complemented
8#10590757C212yesmaximal, complemented
9#10590752C212yesmaximal, complemented
10#10590377C211yesmaximal, characteristic, complemented
11#10590301C211yesmaximal, characteristic, complemented
12#80366—31nomaximal
13#79027—31nomaximal
14C2×#3795—21no—
15#64078C2211yescharacteristic
16C4×#634C2211yescharacteristic
17C2×C3×#204C2212yes—
18C2×C3×D3×C8C2212yes—
19C3×#874C2211yescharacteristic
20C3×C42×D3C2211yescharacteristic
21C3×C4×Dic6C2211yescharacteristic
22#63918C2211yescharacteristic
23C4×#627—21no—
24#63908—21no—
25#63908C2212yes—
26Dic3×D12—21no—
27Dic3×D12C2212yes—
28#63867—21no—
29#63866C2211yescharacteristic
30#63860—21no—
31#63857C2211yescharacteristic
32#63856C2211yescharacteristic
33#63855—21no—
34#63851—21no—
35C2×#3716C2212yes—
36C32×C4⋊C8C2211yescharacteristic
37#63644C2212yes—
38#63643C2212yes—
39C3×#821C2212yes—
40C3×Dic3⋊C8C2212yes—
41C3×C4⋊(C3⋊C8)C2211yescharacteristic
42#63573C2212yes—
43#63566C2212yes—
44#63563C2212yes—
45#5716—31no—
46#5578—31no—
47#5477—31no—
48#5470—31no—
49C3×#460—31no—
50C2×C3×C4⋊C8—31no—
51#5171—32no—
52#5162—32no—
53#5114—32no—
54#5114—32no—
55#5075—31no—
56#5020—31no—
57#4851—31no—
58#4851—31no—
59#4851—31no—
60#4851—61no—
61#4848—31no—
62#4848D311yescharacteristic, complemented
63#4842—32no—
64#4841—32no—
65D3×C4⋊C8D311yescharacteristic, complemented
66#4778—32no—
67#4761—32no—
68C2×#634—21no—
69C2×#634C2311yescharacteristic
70C2×C3×D12—21no—
71C2×C3×D12—21no—
72C2×C3×D12C2312yes—
73C2×C3×C4×D3D411yescharacteristic
74C2×C3×C4×D3D411yescharacteristic
75C2×C3×C4×D3C2311yescharacteristic
76C2×C3×Dic6C2311yescharacteristic
77C2×#627—21no—
78C2×#625—22no—
79C2×D3×Dic3—22no—
80#3795—44no—
81C2×C32×C8C2312yes—
82C32×C42C2311yescharacteristic
83C4⋊(C3⋊Dic3)—21no—
84C4⋊(C3⋊Dic3)C2311yescharacteristic
85C4⋊(C3⋊Dic3)C2312yes—
86#3750—21no—
87C4×C3⋊Dic3—21no—
88C3×C4⋊Dic3C2311yescharacteristic
89C3×Dic3⋊C4—21no—
90C3×C4×Dic3—21no—
91C3×C4×Dic3D411yescharacteristic
92C3×C4×Dic3D411yescharacteristic
93C3×C4×Dic3C2311yescharacteristic
94C2×C3×C3⋊C8C2312yes—
95C3×#204—42no—
96C3×D3×C8—42no—
97#3724—21no—
98Dic3⋊Dic3—21no—
99Dic3⋊Dic3—21no—
100Dic3⋊Dic3—21no—
101Dic3⋊Dic3—21no—
102(C2×D3)⋊Dic3—21no—
103(C2×D3)⋊Dic3—21no—
104(C2×D3)⋊Dic3—22no—
105(C2×D3)⋊Dic3—22no—
106#3716—42no—
107#3246—91noSylow
108C2×#237—61no—
109C2×#235—61no—
110C2×C3×SD16—32no—
111C22×C3×C8—32no—
112C3×#127—31no—
113C3×C4×Q8—31no—
114C2×C3×C42—31no—
115#946—31no—
116#944—31no—
117#938—32no—
118#938—61no—
119#936—61no—
120D4×Dic3—32no—
121D4×Dic3—61no—
122C2×#214—32no—
123#930—32no—
124#930—61no—
125#926—61no—
126#924—31no—
127#924—31no—
128#924—61no—
129C2×#204—32no—
130C2×#204C2×D312yes—
131C2×D3×C8C2×D312yes—
132#897—31no—
133#896—61no—
134#889—61no—
135#888—31no—
136#875—61no—
137#874C2×D311yescharacteristic
138C4×D12—32no—
139C4×D12—61no—
140#872—61no—
141C42×D3C2×D311yescharacteristic
142#870—61no—
143#869—31no—
144#869—31no—
145#869—31no—
146#869—31no—
147#869—61no—
148C4×Dic6—31no—
149C4×Dic6—31no—
150C4×Dic6—61no—
151C4×Dic6—61no—
152C4×Dic6—61no—
153C4×Dic6C2×D311yescharacteristic
154C3×C4⋊C8—21no—
155C3×C4⋊C8—32no—
156C3×C4⋊C8—31no—
157C3×C4⋊C8C2×D311yescharacteristic
158C3×C4⋊C8C2×D311yescharacteristic
159C3×#102—32no—
160#835—32no—
161#832—32no—
162#821—32no—
163#821C2×D312yes—
164#817—32no—
165#817—32no—
166#817—32no—
167#817—62no—
168#816—32no—
169#816—32no—
170#816—32no—
171#816—62no—
172Dic3⋊C8C2×D312yes—
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—22no—
181C2×C3⋊Dic3—21no—
182C2×C3⋊Dic3—21no—
183#634—21no—
184#634—21no—
185#634—42no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3C2×D411yescharacteristic
189C2×C3×Dic3C2×D411yescharacteristic
190C2×C3×Dic3C2×D411yescharacteristic
191C3×D12—22no—
192C3×D12—22no—
193C3×D12—42no—
194C3×D12—42no—
195C3×C4×D3—21no—
196C3×C4×D3—21no—
197C3×C4×D3—41no—
198C3×C4×D3SD1614yescomplemented
199C3×Dic6—21no—
200C3×Dic6—21no—
201#627—42no—
202#625—44no—
203D3×Dic3—44no—
204C32×C8—22no—
205C3×C3⋊C8—22no—
206#533—91no—
207#532—91no—
208#476—92no—
209#475—91no—
210#475—91no—
211#465—92no—
212#465—92no—
213#461—92no—
214#460—31no—
215#460—91no—
216C2×C4⋊C8—31no—
217C2×C3×Q8—31no—
218C2×C3×D4—32no—
219C2×C3×D4—61no—
220C2×C3×D4—61no—
221C22×C3×C4—31no—
222C22×C3×C4—31no—
223C22×C3×C4—31no—
224C2×#67—62no—
225C2×#67—62no—
226C22×Dic3—62no—
227#237—124no—
228#235—124no—
229C2×D12—21no—
230C2×D12—21no—
231C2×D12C22×D312yes—
232C2×C4×D3—62no—
233C2×C4×D3D1211yescharacteristic
234C2×C4×D3D1211yescharacteristic
235C2×C4×D3C22×D311yescharacteristic
236C2×Dic6—31no—
237C2×Dic6—31no—
238C2×Dic6—61no—
239C2×Dic6—61no—
240C2×Dic6—61no—
241C2×Dic6—61no—
242C2×Dic6—61no—
243C2×Dic6—121no—
244C2×Dic6C22×D311yescharacteristic
245C3×SD16—122no—
246C2×C3×C8—22no—
247C2×C3×C8—32no—
248C2×C3×C8—122no—
249C2×C3×C8C22×D312yes—
250C2×C3×C8C22×D312yes—
251C3×C4⋊C4—31no—
252C3×C4⋊C4—61no—
253C3×C42—21no—
254C3×C42—31no—
255C3×C42—31no—
256C3×C42—31no—
257C3×C42—61no—
258C3×C42C22×D311yescharacteristic
259C3×C42C22×D311yescharacteristic
260#217—61no—
261#217—61no—
262#217—62no—
263#217—62no—
264#214—122no—
265(C2×D3)⋊C4—62no—
266(C2×D3)⋊C4—62no—
267(C2×D3)⋊C4—61no—
268(C2×D3)⋊C4—61no—
269C4⋊Dic3—32no—
270C4⋊Dic3—32no—
271C4⋊Dic3—31no—
272C4⋊Dic3—31no—
273C4⋊Dic3—62no—
274C4⋊Dic3—61no—
275C4⋊Dic3—61no—
276C4⋊Dic3—61no—
277C4⋊Dic3—61no—
278C4⋊Dic3—61no—
279C4⋊Dic3—61no—
280C4⋊Dic3—61no—
281C4⋊Dic3—121no—
282C4⋊Dic3C22×D311yescharacteristic
283Dic3⋊C4—21no—
284Dic3⋊C4—61no—
285Dic3⋊C4—61no—
286Dic3⋊C4—61no—
287Dic3⋊C4—61no—
288Dic3⋊C4—61no—
289Dic3⋊C4—61no—
290Dic3⋊C4—61no—
291Dic3⋊C4—61no—
292Dic3⋊C4—121no—
293C4×Dic3—21no—
294C4×Dic3—61no—
295C4×Dic3—61no—
296C4×Dic3—121no—
297C4×Dic3D1211yescharacteristic
298C4×Dic3D1211yescharacteristic
299C4×Dic3C22×D311yescharacteristic
300C2×C3⋊C8C22×D312yes—
301#204—42no—
302#204—122no—
303D3×C8—42no—
304C22×C32C22×D411yescharacteristic
305C2×C3×D3—21no—
306C2×C3×D3—21no—
307C2×C3×D3—42no—
308C2×C3×D3—42no—
309C2×C3×D3—42no—
310C2×C3×D3C2×SD1612yes—
311C32×C4—21no—
312C32×C4C2×SD1612yes—
313C32×C4H(5,𝔽2)11yescharacteristic
314C32×C42−1+411yescharacteristic
315C3⋊Dic3—41no—
316C3⋊Dic3—42no—
317C3⋊Dic3—41no—
318C3×Dic3—21no—
319C3×Dic3—21no—
320C3×Dic3—41no—
321C3×Dic3—41no—
322C3×Dic3C2×SD1612yes—
323C2×#41—181no—
324C2×SD16—32no—
325C2×SD16—92no—
326C22×C8—32no—
327C4⋊Q8—91no—
328C4⋊Q8—91no—
329C4⋊Q8—91no—
330#127—31no—
331#125—181no—
332#124—181no—
333C22⋊Q8—91no—
334C22⋊Q8—91no—
335C22⋊Q8—181no—
336#121—92no—
337#121—181no—
338C4×Q8—31no—
339C4×Q8—91no—
340C4×Q8—181no—
341C4×D4—92no—
342C4×D4—181no—
343#117—181no—
344C2×C42—31no—
345#106—92no—
346#106—92no—
347C4⋊C8—32no—
348C4⋊C8—31no—
349C4⋊C8D3211yescharacteristic
350#103—92no—
351#103—92no—
352#102—32no—
353#102—92no—
354C23×C3—31no—
355C23×C3—62no—
356C22×D3—22no—
357C22×D3C2×D1211yescharacteristic
358C3×Q8—61no—
359C3×Q8—61no—
360C3×D4—62no—
361C3×D4—62no—
362C3×D4—122no—
363C3×D4—122no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—31no—
368C2×C3×C4—34no—
369C2×C3×C4—31no—
370C2×C3×C4—31no—
371C2×C3×C4—61no—
372C2×C3×C4—61no—
373C2×C3×C4—61no—
374C2×C3×C4—61no—
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—
383#67—124no—
384C2×Dic3—21no—
385C2×Dic3—21no—
386C2×Dic3—61no—
387C2×Dic3—61no—
388C2×Dic3—62no—
389C2×Dic3—61no—
390C2×Dic3—61no—
391C2×Dic3—62no—
392C2×Dic3—121no—
393C2×Dic3—121no—
394C2×Dic3—122no—
395C2×Dic3—124no—
396C2×Dic3C2×D1211yescharacteristic
397C2×Dic3C2×D1211yescharacteristic
398C2×Dic3C2×D1211yescharacteristic
399D12—22no—
400D12—22no—
401D12—42no—
402D12—42no—
403C4×D3—21no—
404C4×D3—21no—
405C4×D3—41no—
406C4×D3—124no—
407C4×D3#20414yescomplemented
408Dic6—21no—
409Dic6—21no—
410Dic6—62no—
411Dic6—61no—
412Dic6—61no—
413Dic6—61no—
414Dic6—61no—
415Dic6—121no—
416Dic6—122no—
417Dic6—122no—
418Dic6—122no—
419Dic6—122no—
420Dic6—242no—
421C3×C8—22no—
422C3×C8—22no—
423C3×C8—42no—
424C3×C8—62no—
425C3⋊C8—22no—
426C2×C32#53711yescharacteristic
427C2×C32C22×SD1611yescharacteristic
428C2×C32#57511yescharacteristic
429C3×D3—22no—
430C3×D3—82no—
431#41—364no—
432C2×Q8—31no—
433C2×Q8—91no—
434C2×Q8—181no—
435C2×Q8—181no—
436C2×D4—32no—
437C2×D4—61no—
438C2×D4—61no—
439C2×D4—182no—
440C22×C4—31no—
441C22×C4—31no—
442C22×C4—31no—
443C22×C4—182no—
444SD16—122no—
445SD16—362no—
446C2×C8—32no—
447C2×C8—122no—
448C2×C8C2×D3212yes—
449C4⋊C4—31no—
450C4⋊C4—61no—
451C4⋊C4—91no—
452C4⋊C4—92no—
453C4⋊C4—181no—
454C4⋊C4—181no—
455C4⋊C4—181no—
456C4⋊C4—181no—
457C4⋊C4—181no—
458C4⋊C4—181no—
459C4⋊C4—181no—
460C22⋊C4—182no—
461C22⋊C4—182no—
462C22⋊C4—181no—
463C22⋊C4—181no—
464C42—31no—
465C42—31no—
466C42—31no—
467C42—61no—
468C42—181no—
469C42C2×D3211yescharacteristic
470C22×C3—21no—
471C22×C3—32no—
472C22×C3—61no—
473C22×C3—61no—
474C22×C3—122no—
475C22×C3—122no—
476C22×C3—122no—
477C22×C3C22×D1211yescharacteristic
478C22×C3C2×D3×D411yescharacteristic
479C2×D3—21no—
480C2×D3—21no—
481C2×D3—42no—
482C2×D3—42no—
483C2×D3—42no—
484C2×D3C2×#20412yes—
485C3×C4—21no—
486C3×C4—21no—
487C3×C4—22no—
488C3×C4—21no—
489C3×C4—21no—
490C3×C4—32no—
491C3×C4—41no—
492C3×C4—61no—
493C3×C4—61no—
494C3×C4—121no—
495C3×C4—121no—
496C3×C4C2×#20412yes—
497C3×C4D3×SD1612yes—
498C3×C4#100411yescharacteristic
499C3×C4#100411yescharacteristic
500C3×C4#100711yescharacteristic
501C3×C4#101011yescharacteristic
502Dic3—21no—
503Dic3—21no—
504Dic3—41no—
505Dic3—41no—
506Dic3—122no—
507Dic3—122no—
508Dic3—121no—
509Dic3—122no—
510Dic3—121no—
511Dic3—121no—
512Dic3—121no—
513Dic3—242no—
514Dic3—241no—
515Dic3C2×#20412yes—
516C32#324611yescharacteristic, complemented, Sylow
517C23—31no—
518C23—62no—
519Q8—61no—
520Q8—61no—
521Q8—181no—
522Q8—181no—
523Q8—362no—
524Q8—362no—
525D4—62no—
526D4—62no—
527D4—122no—
528D4—122no—
529D4—364no—
530C2×C4—31no—
531C2×C4—34no—
532C2×C4—31no—
533C2×C4—31no—
534C2×C4—61no—
535C2×C4—61no—
536C2×C4—61no—
537C2×C4—61no—
538C2×C4—121no—
539C2×C4—181no—
540C2×C4—181no—
541C2×C4—182no—
542C2×C4—364no—
543C2×C4D3×D1211yescharacteristic
544C2×C4D3×D1211yescharacteristic
545C2×C4C22×D3211yescharacteristic
546C8—22no—
547C8—62no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—21no—
551C2×C3—62no—
552C2×C3—242no—
553C2×C3#551011yescharacteristic
554C2×C3#560811yescharacteristic
555C2×C3C22×#20411yescharacteristic
556C2×C3#574811yescharacteristic
557C2×C3C2×D3×SD1611yescharacteristic
558C2×C3#577311yescharacteristic
559D3—22no—
560D3—82no—
561C22—32no—
562C22—61no—
563C22—61no—
564C22—122no—
565C22—122no—
566C22—122no—
567C22C2×D3×D1211yescharacteristic
568C4—21no—
569C4—32no—
570C4—61no—
571C4—61no—
572C4—121no—
573C4—121no—
574C4—362no—
575C4—361no—
576C4—361no—
577C4D3×#20412yes—
578C4#6431311yescharacteristic
579C4#6431511yescharacteristic
580C3—21no—
581C3#7902711yescharacteristic, complemented
582C3#8036611yescharacteristic, complemented
583C2—62no—
584C2—242no—
585C2#1059452211yescharacteristic
586C2C2×D3×#20411yescharacteristic
587C2#1059471211yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radical#10593897C2
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. #10592550C2semidirect
4. C3×#4848C2semidirect
5. C3×D3×C4⋊C8C2semidirect
6. #10590829C2semidirect
7. #10590825C2semidirect
8. #10590757C2semidirect
9. #10590752C2semidirect
10. #10590377C2semidirect
11. #10590301C2semidirect
62. #4848D3semidirect
65. D3×C4⋊C8D3semidirect
198. C3×C4×D3SD16semidirect
407. C4×D3#204semidirect
516. C32#3246semidirect
581. C3#79027semidirect
582. C3#80366semidirect

Maximal subgroups

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

subgroupindex
#105938972
#105938732
#105925502
C3×#48482
C3×D3×C4⋊C82
#105908292
#105908252
#105907572
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