Finite Group Databasebeta

← #11895438

Subgroups — #11895438

Order 1152.

890 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596193C211yesmaximal, characteristic, complemented
2#10593906C211yesmaximal, characteristic
3C3×#5088C211yesmaximal, characteristic, complemented
4C3×#5084C211yesmaximal, characteristic, complemented
5#10590553C212yesmaximal, complemented
6#10590552C212yesmaximal, complemented
7#10590472C212yesmaximal, complemented
8#10590460C212yesmaximal, complemented
9#10590377C211yesmaximal, characteristic, complemented
10C4×#3716C211yesmaximal, characteristic, complemented
11#10590254C211yesmaximal, characteristic, complemented
12#81588—31nomaximal
13#81090—31nomaximal
14C2×#3795—21no—
15C32×C4⋊Q8C2211yescharacteristic
16#64153—22no—
17#64097—21no—
18#64097C2212yes—
19#64096—21no—
20#64096C2212yes—
21C4×#634C2211yescharacteristic
22C4×#634C2211yescharacteristic
23C3×#874C2211yescharacteristic
24C3×C4×D12C2211yescharacteristic
25#63914C2212yes—
26#63908—21no—
27#63898C2212yes—
28#63885—22no—
29C2×#3716C2211yescharacteristic
30C2×#3716C2212yes—
31C3×#809C2212yes—
32C3×#809C2212yes—
33C3×#809C2212yes—
34C3×#808C2212yes—
35C3×C4⋊(C3⋊C8)C2211yescharacteristic
36C3×C4×C3⋊C8C2211yescharacteristic
37#63573C2211yescharacteristic
38#63572C2212yes—
39#63567C2211yescharacteristic
40#63563C2212yes—
41#63563C2211yescharacteristic
42#63553C2212yes—
43#5722—31no—
44#5722—31no—
45#5722—61no—
46#5718—31no—
47#5553—31no—
48C3×#486—31no—
49C3×#476—31no—
50#5088D311yescharacteristic, complemented
51#5084D311yescharacteristic, complemented
52#5075—31no—
53C4×#214—31no—
54#4870—32no—
55#4852—32no—
56#4848—31no—
57#4830—31no—
58#4762—32no—
59#4762—32no—
60#4761—32no—
61#4760—32no—
62#4760—32no—
63#4758—32no—
64C4×#204—31no—
65C8×Dic6—31no—
66C2×C32×Q8—21no—
67C2×#634—22no—
68C2×#634D411yescharacteristic
69C2×#634C2311yescharacteristic
70C2×C3×D12—21no—
71C2×C3×D12—21no—
72C2×C3×D12C2312yes—
73C2×C3×D12C2311yescharacteristic
74C2×C3×C4×D3—21no—
75C2×#625—22no—
76C2×#625—22no—
77C2×D3×Dic3—22no—
78#3795—44no—
79C32×C4⋊C4—21no—
80C32×C4⋊C4C2312yes—
81C32×C42C2311yescharacteristic
82C4⋊(C3⋊Dic3)D411yescharacteristic
83C4⋊(C3⋊Dic3)C2311yescharacteristic
84#3750—21no—
85#3750—22no—
86#3750—22no—
87#3750D412yes—
88C4×C3⋊Dic3—21no—
89C4×C3⋊Dic3—22no—
90C4×C3⋊Dic3C2312yes—
91C3×(C2×D3)⋊C4—21no—
92C3×C4⋊Dic3C2311yescharacteristic
93C2×C3×C3⋊C8C2311yescharacteristic
94C2×C3×C3⋊C8C2312yes—
95C2×C3×C3⋊C8C2311yescharacteristic
96(C2×D3)⋊Dic3—22no—
97#3716—22no—
98#3716—24no—
99#3362—91noSylow
100C2×#237—61no—
101C2×#235—61no—
102C3×C4⋊Q8—21no—
103C3×C4⋊Q8C2×D311yescharacteristic
104C3×C4⋊Q8C2×D311yescharacteristic
105C3×#127—31no—
106C3×C4×D4—31no—
107#944—62no—
108#944—62no—
109#944—64no—
110#940—32no—
111#940—32no—
112#939—62no—
113#938—61no—
114D4×Dic3—32no—
115C2×#214—32no—
116C2×#214—31no—
117#930—61no—
118C2×#204—31no—
119C2×#204—32no—
120#893—32no—
121#888—32no—
122#888—32no—
123#888—62no—
124#888—61no—
125#888—61no—
126#888—62no—
127#887—32no—
128#887—32no—
129#887—62no—
130#887—61no—
131#887—61no—
132#887—62no—
133#884—62no—
134#874C2×D311yescharacteristic
135C4×D12C2×D311yescharacteristic
136C4×Dic6—31no—
137C4×Dic6—31no—
138C4×Dic6—31no—
139C4×Dic6—31no—
140C4×Dic6—61no—
141C4×Dic6—61no—
142C3×#106—32no—
143C3×C4⋊C8—31no—
144C3×#102—32no—
145C3×#102—32no—
146C3×#102—32no—
147C3×C4×C8—31no—
148#832—31no—
149#832—32no—
150#821—32no—
151#821—31no—
152#817—31no—
153#816—31no—
154Dic3⋊C8—32no—
155Dic3⋊C8—32no—
156C8×Dic3—32no—
157C8×Dic3—32no—
158#810—31no—
159#809C2×D312yes—
160#809C2×D312yes—
161#809C2×D312yes—
162#808—31no—
163#808C2×D312yes—
164C4⋊(C3⋊C8)C2×D311yescharacteristic
165C4×C3⋊C8C2×D311yescharacteristic
166C22×C3×D3—22no—
167C22×C3×D3—21no—
168C32×Q8—81no—
169C2×C32×C4—22no—
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2411yescharacteristic
173C2×C3⋊Dic3—21no—
174C2×C3⋊Dic3—21no—
175C2×C3⋊Dic3C2×D412yes—
176C2×C3⋊Dic3C2×D412yes—
177#634—21no—
178#634—82no—
179#634SD1614yescomplemented
180#634#4112yescomplemented
181C2×C3×Dic3—21no—
182C3×D12—22no—
183C3×D12—21no—
184C3×D12—21no—
185C3×D12—22no—
186C3×D12—42no—
187C3×D12—81no—
188C3×C4×D3—42no—
189#625—44no—
190#625—82no—
191D3×Dic3—44no—
192C3×C3⋊C8—22no—
193C3×C3⋊C8—21no—
194C3×C3⋊C8—21no—
195Q82—91no—
196#550—91no—
197#486—31no—
198#486—92no—
199#476—31no—
200#476—92no—
201#460—92no—
202#460—91no—
203C8×Q8—91no—
204C4×SD16—91no—
205C4×SD16—92no—
206C2×C3×Q8—22no—
207C2×C3×Q8—21no—
208C2×C3×Q8—21no—
209C2×C3×D4—32no—
210C2×C3×D4—31no—
211C2×C3×D4—61no—
212C2×C3×D4—61no—
213C22×C3×C4—61no—
214C2×#67—62no—
215C2×#67—62no—
216C2×#67—62no—
217C2×#67—62no—
218C22×Dic3—62no—
219#237—124no—
220#235—124no—
221C2×D12—21no—
222C2×D12—21no—
223C2×D12C22×D311yescharacteristic
224C2×D12C22×D312yes—
225C2×C4×D3—21no—
226C2×C4×D3—62no—
227C2×Dic6—31no—
228C2×Dic6—31no—
229C2×Dic6—31no—
230C2×Dic6—31no—
231C2×Dic6—61no—
232C2×Dic6—61no—
233C2×Dic6—62no—
234C2×Dic6—62no—
235C2×Dic6—64no—
236C2×C3×C8—31no—
237C2×C3×C8—32no—
238C2×C3×C8—31no—
239C3×C4⋊C4—22no—
240C3×C4⋊C4—21no—
241C3×C4⋊C4—21no—
242C3×C4⋊C4—22no—
243C3×C4⋊C4—31no—
244C3×C4⋊C4C22×D312yes—
245C3×C4⋊C4C22×D312yes—
246C3×C22⋊C4—61no—
247C3×C42—21no—
248C3×C42C22×D311yescharacteristic
249C3×C42C22×D311yescharacteristic
250#217—62no—
251#214—62no—
252#214—64no—
253(C2×D3)⋊C4—21no—
254(C2×D3)⋊C4—62no—
255C4⋊Dic3—31no—
256C4⋊Dic3—31no—
257C4⋊Dic3—31no—
258C4⋊Dic3—31no—
259C4⋊Dic3—61no—
260C4⋊Dic3—61no—
261C4⋊Dic3C22×D311yescharacteristic
262Dic3⋊C4—32no—
263Dic3⋊C4—32no—
264Dic3⋊C4—62no—
265Dic3⋊C4—62no—
266Dic3⋊C4—62no—
267Dic3⋊C4—62no—
268Dic3⋊C4—62no—
269Dic3⋊C4—62no—
270Dic3⋊C4—64no—
271Dic3⋊C4—64no—
272Dic3⋊C4—61no—
273Dic3⋊C4—61no—
274C4×Dic3—32no—
275C4×Dic3—32no—
276C4×Dic3—62no—
277C4×Dic3—62no—
278C4×Dic3—62no—
279C4×Dic3—62no—
280C4×Dic3—64no—
281C4×Dic3—61no—
282C4×Dic3—61no—
283C2×C3⋊C8C22×D311yescharacteristic
284C2×C3⋊C8C22×D311yescharacteristic
285C2×C3⋊C8C22×D312yes—
286#204—64no—
287#204—62no—
288C22×C32C22×D411yescharacteristic
289C2×C3×D3—41no—
290C2×C3×D3—42no—
291C2×C3×D3—42no—
292C2×C3×D3—41no—
293C2×C3×D3—41no—
294C2×C3×D3—42no—
295C32×C4—21no—
296C32×C4—42no—
297C32×C4C2×SD1612yes—
298C32×C4C2×#4111yescharacteristic
299C32×C42−1+411yescharacteristic
300C3⋊Dic3—22no—
301C3⋊Dic3—22no—
302C3⋊Dic3—41no—
303C3⋊Dic3C2×SD1614yes—
304C3×Dic3—41no—
305C2×#41—181no—
306C2×SD16—91no—
307C2×SD16—92no—
308C4⋊Q8—92no—
309C4⋊Q8—181no—
310C4⋊Q8—182no—
311C4⋊Q8D3211yescharacteristic
312#127—31no—
313#127—92no—
314#121—182no—
315#121—181no—
316C4×Q8—91no—
317C4×Q8—92no—
318C4×Q8—91no—
319C4×Q8—181no—
320C4×D4—31no—
321C4×D4—92no—
322#106—32no—
323#106—91no—
324C4⋊C8—31no—
325C4⋊C8—92no—
326#103—91no—
327#102—32no—
328#102—32no—
329#102—32no—
330#102—91no—
331#102—92no—
332C4×C8—31no—
333C4×C8—92no—
334C23×C3—62no—
335C23×C3—61no—
336C22×D3—21no—
337C22×D3—22no—
338C3×Q8—81no—
339C3×Q8—81no—
340C3×Q8—82no—
341C3×D4—62no—
342C3×D4—62no—
343C3×D4—61no—
344C3×D4—61no—
345C3×D4—122no—
346C3×D4—241no—
347C2×C3×C4—24no—
348C2×C3×C4—22no—
349C2×C3×C4—22no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—61no—
354C2×C3×C4—122no—
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4C23×D311yescharacteristic
360C2×C3×C4C23×D311yescharacteristic
361#67—124no—
362#67—124no—
363#67—242no—
364#67—242no—
365C2×Dic3—21no—
366C2×Dic3—32no—
367C2×Dic3—32no—
368C2×Dic3—32no—
369C2×Dic3—32no—
370C2×Dic3—62no—
371C2×Dic3—62no—
372C2×Dic3—62no—
373C2×Dic3—61no—
374C2×Dic3—61no—
375C2×Dic3—62no—
376C2×Dic3—61no—
377C2×Dic3—61no—
378C2×Dic3—124no—
379D12—21no—
380D12—21no—
381D12—22no—
382D12—22no—
383D12—42no—
384D12—81no—
385C4×D3—42no—
386C4×D3—124no—
387Dic6—34no—
388Dic6—34no—
389Dic6—32no—
390Dic6—32no—
391Dic6—64no—
392Dic6—62no—
393Dic6—62no—
394Dic6—61no—
395Dic6—61no—
396Dic6—242no—
397Dic6—242no—
398Dic6—244no—
399C3×C8—61no—
400C3×C8—61no—
401C3×C8—62no—
402C3⋊C8—22no—
403C3⋊C8—21no—
404C3⋊C8—21no—
405C2×C32#54811yescharacteristic
406C2×C32C22×SD1611yescharacteristic
407C2×C32#57611yescharacteristic
408C3×D3—82no—
409C3×D3—81no—
410#41—364no—
411C2×Q8—21no—
412C2×Q8—91no—
413C2×Q8—91no—
414C2×Q8—182no—
415C2×D4—31no—
416C2×D4—32no—
417C2×D4—61no—
418C2×D4—61no—
419C2×D4—182no—
420C2×D4—182no—
421C22×C4—61no—
422C22×C4—182no—
423SD16—182no—
424SD16—184no—
425C2×C8—31no—
426C2×C8—31no—
427C2×C8—32no—
428C4⋊C4—21no—
429C4⋊C4—31no—
430C4⋊C4—92no—
431C4⋊C4—91no—
432C4⋊C4—91no—
433C4⋊C4—182no—
434C4⋊C4—182no—
435C4⋊C4—181no—
436C4⋊C4C2×D3212yes—
437C22⋊C4—61no—
438C22⋊C4—182no—
439C42—92no—
440C42—182no—
441C42—181no—
442C42C2×D3211yescharacteristic
443C22×C3—21no—
444C22×C3—122no—
445C22×C3—121no—
446C22×C3—121no—
447C22×C3—122no—
448C22×C3—121no—
449C22×C3—122no—
450C22×C3C2×D3×D411yescharacteristic
451C22×C3C2×D3×D411yescharacteristic
452C2×D3—41no—
453C2×D3—42no—
454C2×D3—42no—
455C2×D3—41no—
456C2×D3—42no—
457C2×D3—41no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—21no—
461C3×C4—21no—
462C3×C4—22no—
463C3×C4—41no—
464C3×C4—44no—
465C3×C4—42no—
466C3×C4—42no—
467C3×C4—121no—
468C3×C4D3×SD1612yes—
469C3×C4D3×SD1612yes—
470C3×C4#100711yescharacteristic
471C3×C4D3×#4111yescharacteristic
472C3×C4D3×#4111yescharacteristic
473C3×C4#101011yescharacteristic
474Dic3—34no—
475Dic3—34no—
476Dic3—41no—
477Dic3—64no—
478Dic3—64no—
479Dic3—62no—
480Dic3—62no—
481Dic3—62no—
482Dic3—62no—
483Dic3—122no—
484Dic3—122no—
485Dic3—121no—
486Dic3—121no—
487C32#336211yescharacteristic, complemented, Sylow
488C23—61no—
489C23—62no—
490Q8—81no—
491Q8—94no—
492Q8—92no—
493Q8—181no—
494Q8—722no—
495D4—61no—
496D4—62no—
497D4—61no—
498D4—62no—
499D4—122no—
500D4—241no—
501D4—364no—
502D4—722no—
503C2×C4—22no—
504C2×C4—61no—
505C2×C4—92no—
506C2×C4—92no—
507C2×C4—122no—
508C2×C4—181no—
509C2×C4—181no—
510C2×C4—364no—
511C2×C4#381111yescharacteristic
512C2×C4#381111yescharacteristic
513C2×C4C22×D3211yescharacteristic
514C8—61no—
515C8—61no—
516C8—62no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—241no—
521C2×C3—242no—
522C2×C3#563311yescharacteristic
523C2×C3#567711yescharacteristic
524C2×C3#575711yescharacteristic
525C2×C3C2×D3×SD1611yescharacteristic
526C2×C3C2×D3×SD1611yescharacteristic
527C2×C3#577411yescharacteristic
528D3—82no—
529D3—81no—
530C22—122no—
531C22—121no—
532C22—121no—
533C22—122no—
534C22—121no—
535C22—122no—
536C22C2×#381111yescharacteristic
537C4—21no—
538C4—42no—
539C4—94no—
540C4—121no—
541C4—182no—
542C4—182no—
543C4—361no—
544C4#6394012yes—
545C4#6431511yescharacteristic
546C4#6431911yescharacteristic
547C3—21no—
548C3#8109011yescharacteristic, complemented
549C3#8158811yescharacteristic, complemented
550C2—242no—
551C2—241no—
552C2#1059510211yescharacteristic
553C2C2×#6394011yescharacteristic
554C2#1059536211yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radical#10593906C2
hypercenterC4⋊Q8D32
hypocenterC32#3362
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596193C2semidirect
3. C3×#5088C2semidirect
4. C3×#5084C2semidirect
5. #10590553C2semidirect
6. #10590552C2semidirect
7. #10590472C2semidirect
8. #10590460C2semidirect
9. #10590377C2semidirect
10. C4×#3716C2semidirect
11. #10590254C2semidirect
50. #5088D3semidirect
51. #5084D3semidirect
179. #634SD16semidirect
180. #634#41semidirect
487. C32#3362semidirect
548. C3#81090semidirect
549. C3#81588semidirect

Maximal subgroups

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

subgroupindex
#105961932
#105939062
C3×#50882
C3×#50842
#105905532
#105905522
#105904722
#105904602
#105903772
C4×#37162
#105902542
#815883
#810903