Finite Group Databasebeta

← #11895419

Subgroups — #11895419

Order 1152.

848 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593902C211yesmaximal, characteristic
2#10593856C211yesmaximal, characteristic, complemented
3#10592547C211yesmaximal, characteristic, complemented
4C3×#4842C211yesmaximal, characteristic, complemented
5C3×#4830C211yesmaximal, characteristic, complemented
6#10590879C212yesmaximal, complemented
7#10590878C212yesmaximal, complemented
8#10590759C212yesmaximal, complemented
9#10590758C212yesmaximal, complemented
10C4×#3716C211yesmaximal, characteristic, complemented
11#10590281C211yesmaximal, characteristic, complemented
12#81090—31nomaximal
13#79932—31nomaximal
14C2×#3799—21no—
15C2×#3744C2212yes—
16#64083C2211yescharacteristic
17C4×#634C2211yescharacteristic
18C3×C4×D12C2211yescharacteristic
19C3×#869C2211yescharacteristic
20C3×C4×Dic6C2211yescharacteristic
21#63919—21no—
22#63918C2212yes—
23#63911C2212yes—
24#63910—22no—
25#63909—21no—
26#63894C2212yes—
27#63844C2212yes—
28#63843—21no—
29#63839—22no—
30C2×#3716C2211yescharacteristic
31C32×C4⋊C8C2211yescharacteristic
32#63648C2212yes—
33C3×#821C2212yes—
34C3×#817C2212yes—
35C3×Dic3⋊C8C2212yes—
36C3×C8×Dic3C2212yes—
37C3×C4×C3⋊C8C2211yescharacteristic
38#63573C2211yescharacteristic
39#63567C2211yescharacteristic
40#63564C2212yes—
41#63564C2212yes—
42#63563C2211yescharacteristic
43#5722—31no—
44#5577—31no—
45Q8×Dic6—31no—
46#5553—31no—
47C3×#476—31no—
48C3×C8×Q8—31no—
49#5088—31no—
50C4×#214—31no—
51#4870—32no—
52#4852—32no—
53#4848—31no—
54#4848—31no—
55#4848—32no—
56#4848—61no—
57#4842—32no—
58#4842D311yescharacteristic, complemented
59#4830D311yescharacteristic, complemented
60#4762—32no—
61#4760—32no—
62#4694—31no—
63#4694—32no—
64C4×#204—31no—
65C4×#204—32no—
66C2×C4⋊(C3⋊D3)—21no—
67C2×C4⋊(C3⋊D3)—21no—
68C2×C4⋊(C3⋊D3)C2312yes—
69C2×#634C2311yescharacteristic
70C2×C3×D12C2311yescharacteristic
71C2×C3×C4×D3—21no—
72C2×C3×Dic6—21no—
73C2×C3×Dic6D411yescharacteristic
74C2×#627—22no—
75C2×#626—22no—
76C2×#626—22no—
77C2×#624—22no—
78#3799—44no—
79C2×C32×C8C2312yes—
80C32×C42C2311yescharacteristic
81C4⋊(C3⋊Dic3)C2311yescharacteristic
82#3750—21no—
83C4×C3⋊Dic3—21no—
84#3744—24no—
85C3×(C2×D3)⋊C4—21no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3D411yescharacteristic
88C3×C4⋊Dic3C2312yes—
89C3×C4⋊Dic3C2311yescharacteristic
90C3×Dic3⋊C4D412yes—
91C3×C4×Dic3C2312yes—
92C2×C3×C3⋊C8C2311yescharacteristic
93C2×C3×C3⋊C8C2311yescharacteristic
94#3724—22no—
95Dic3⋊Dic3—22no—
96#3722—22no—
97Dic32—22no—
98#3716—22no—
99#3362—91noSylow
100C2×#239—61no—
101C2×#235—61no—
102C3×C4⋊Q8—31no—
103C3×C4×Q8—31no—
104C3×C4×D4—31no—
105Q8×Dic3—61no—
106#944—62no—
107#940—32no—
108C2×#214—31no—
109#930—61no—
110C2×#204—31no—
111C2×#204—32no—
112C2×#204—32no—
113C2×#204—62no—
114#895—62no—
115#895—61no—
116#893—32no—
117#888—32no—
118#888—61no—
119#888—62no—
120#888—61no—
121#887—32no—
122#887—61no—
123#884—62no—
124#874—32no—
125#874—31no—
126#874—31no—
127#874—61no—
128C4×D12—32no—
129C4×D12C2×D311yescharacteristic
130#869—32no—
131#869C2×D311yescharacteristic
132C4×Dic6—31no—
133C4×Dic6—31no—
134C4×Dic6—32no—
135C4×Dic6—61no—
136C4×Dic6C2×D311yescharacteristic
137C3×#106—32no—
138C3×C4⋊C8—21no—
139C3×C4⋊C8—32no—
140C3×C4⋊C8C2×D311yescharacteristic
141C3×C4⋊C8C2×D311yescharacteristic
142C3×#102—32no—
143C3×C4×C8—32no—
144C3×C4×C8—31no—
145#832—31no—
146#821—31no—
147#821—32no—
148#821—32no—
149#821—32no—
150#821—32no—
151#821—62no—
152#821C2×D312yes—
153#817—31no—
154#817C2×D312yes—
155#816—31no—
156Dic3⋊C8C2×D312yes—
157C8×Dic3C2×D312yes—
158#810—31no—
159#809—32no—
160#809—32no—
161#808—31no—
162C4×C3⋊C8C2×D311yescharacteristic
163C22×C3⋊D3—22no—
164C22×C3×D3—21no—
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2411yescharacteristic
168C2×C3⋊Dic3—21no—
169C2×C3⋊Dic3—21no—
170C4⋊(C3⋊D3)—22no—
171C4⋊(C3⋊D3)—22no—
172C4⋊(C3⋊D3)—42no—
173C4⋊(C3⋊D3)—81no—
174#634—21no—
175#634#4112yescomplemented
176C2×C3×Dic3—22no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3C2×D412yes—
179C2×C3×Dic3C2×D412yes—
180C3×D12—21no—
181C3×D12—21no—
182C3×C4×D3—42no—
183C3×Dic6—81no—
184C3×Dic6SD1614yescomplemented
185#627—82no—
186#626—44no—
187#626—82no—
188#624—44no—
189C32×C8—22no—
190C3×C3⋊C8—21no—
191C3×C3⋊C8—21no—
192Q82—91no—
193#550—91no—
194#486—92no—
195#486—91no—
196#476—31no—
197#476—92no—
198#460—92no—
199#460—91no—
200C8×Q8—31no—
201C4×SD16—92no—
202C4×SD16—91no—
203C2×C3×Q8—31no—
204C2×C3×Q8—61no—
205C2×C3×D4—31no—
206C22×C3×C4—61no—
207C2×#67—62no—
208C2×#67—62no—
209#239—124no—
210#235—124no—
211C2×D12—32no—
212C2×D12—32no—
213C2×D12—62no—
214C2×D12—62no—
215C2×D12—61no—
216C2×D12—61no—
217C2×D12—62no—
218C2×D12—61no—
219C2×D12—61no—
220C2×D12—121no—
221C2×D12—121no—
222C2×D12C22×D311yescharacteristic
223C2×C4×D3—21no—
224C2×C4×D3—62no—
225C2×C4×D3—62no—
226C2×Dic6—21no—
227C2×Dic6—31no—
228C2×Dic6—31no—
229C2×Dic6—61no—
230C2×Dic6—62no—
231C2×Dic6—62no—
232C2×Dic6D1211yescharacteristic
233C2×C3×C8—22no—
234C2×C3×C8—31no—
235C2×C3×C8—31no—
236C2×C3×C8C22×D312yes—
237C2×C3×C8C22×D312yes—
238C3×C4⋊C4—32no—
239C3×C4⋊C4—31no—
240C3×C4⋊C4—31no—
241C3×C4⋊C4—32no—
242C3×C4⋊C4—61no—
243C3×C22⋊C4—61no—
244C3×C42—21no—
245C3×C42—32no—
246C3×C42C22×D311yescharacteristic
247C3×C42C22×D311yescharacteristic
248#214—62no—
249(C2×D3)⋊C4—21no—
250(C2×D3)⋊C4—62no—
251(C2×D3)⋊C4—62no—
252C4⋊Dic3—21no—
253C4⋊Dic3—31no—
254C4⋊Dic3—31no—
255C4⋊Dic3—61no—
256C4⋊Dic3—62no—
257C4⋊Dic3D1211yescharacteristic
258C4⋊Dic3C22×D311yescharacteristic
259C4⋊Dic3C22×D312yes—
260Dic3⋊C4—62no—
261Dic3⋊C4—61no—
262Dic3⋊C4—61no—
263Dic3⋊C4—62no—
264Dic3⋊C4—62no—
265Dic3⋊C4—121no—
266Dic3⋊C4D1212yes—
267C4×Dic3—62no—
268C4×Dic3—61no—
269C4×Dic3—61no—
270C4×Dic3—62no—
271C4×Dic3—121no—
272C4×Dic3C22×D312yes—
273C2×C3⋊C8C22×D311yescharacteristic
274C2×C3⋊C8C22×D311yescharacteristic
275#204—64no—
276#204—64no—
277#204—62no—
278#204—124no—
279C22×C32C22×D411yescharacteristic
280C2×C3⋊D3—42no—
281C2×C3⋊D3—42no—
282C2×C3⋊D3—42no—
283C2×C3×D3—41no—
284C2×C3×D3—41no—
285C2×C3×D3—41no—
286C32×C4—21no—
287C32×C4C2×SD1612yes—
288C32×C4C2×#4111yescharacteristic
289C32×C42−1+411yescharacteristic
290C3⋊Dic3—22no—
291C3⋊Dic3—41no—
292C3×Dic3—22no—
293C3×Dic3—41no—
294C3×Dic3—42no—
295C3×Dic3C2×SD1614yes—
296C2×#41—181no—
297C2×SD16—91no—
298C2×SD16—92no—
299C4⋊Q8—31no—
300C4⋊Q8—92no—
301C4⋊Q8—181no—
302C4⋊Q8—182no—
303#127—92no—
304#127—91no—
305#121—182no—
306#121—181no—
307C4×Q8—31no—
308C4×Q8—92no—
309C4×Q8—91no—
310C4×Q8—181no—
311C4×D4—31no—
312C4×D4—92no—
313#106—32no—
314#106—91no—
315C4⋊C8—32no—
316C4⋊C8D3211yescharacteristic
317#103—91no—
318#102—32no—
319#102—92no—
320#102—92no—
321#102—91no—
322#102—92no—
323C4×C8—32no—
324C4×C8—31no—
325C23×C3—61no—
326C22×D3—21no—
327C22×D3—62no—
328C22×D3—62no—
329C22×D3—122no—
330C3×Q8—34no—
331C3×Q8—241no—
332C3×D4—61no—
333C3×D4—61no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—32no—
338C2×C3×C4—32no—
339C2×C3×C4—62no—
340C2×C3×C4—61no—
341C2×C3×C4—122no—
342C2×C3×C4C2×D1211yescharacteristic
343C2×C3×C4C2×D1211yescharacteristic
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4C23×D311yescharacteristic
347C2×C3×C4C23×D311yescharacteristic
348#67—124no—
349#67—242no—
350C2×Dic3—22no—
351C2×Dic3—21no—
352C2×Dic3—61no—
353C2×Dic3—61no—
354C2×Dic3—61no—
355C2×Dic3—61no—
356C2×Dic3—121no—
357C2×Dic3—121no—
358C2×Dic3C2×D1212yes—
359C2×Dic3C2×D1212yes—
360D12—21no—
361D12—21no—
362D12—62no—
363D12—62no—
364D12—62no—
365D12—62no—
366D12—122no—
367D12—122no—
368D12—124no—
369D12—122no—
370D12—122no—
371D12—242no—
372D12—241no—
373D12—241no—
374D12—242no—
375D12—242no—
376C4×D3—42no—
377C4×D3—124no—
378C4×D3—124no—
379Dic6—32no—
380Dic6—32no—
381Dic6—62no—
382Dic6—61no—
383Dic6—61no—
384Dic6—81no—
385Dic6—121no—
386Dic6—242no—
387Dic6—242no—
388Dic6#20414yescomplemented
389C3×C8—22no—
390C3×C8—22no—
391C3×C8—42no—
392C3×C8—61no—
393C3×C8—61no—
394C3⋊C8—21no—
395C3⋊C8—21no—
396C2×C32#54811yescharacteristic
397C2×C32C22×SD1611yescharacteristic
398C2×C32#57611yescharacteristic
399C3⋊D3—82no—
400C3×D3—81no—
401#41—364no—
402C2×Q8—31no—
403C2×Q8—61no—
404C2×Q8—91no—
405C2×Q8—182no—
406C2×D4—31no—
407C2×D4—92no—
408C2×D4—182no—
409C2×D4—182no—
410C2×D4—181no—
411C2×D4—181no—
412C22×C4—61no—
413C22×C4—182no—
414SD16—184no—
415SD16—182no—
416C2×C8—31no—
417C2×C8—31no—
418C2×C8C2×D3212yes—
419C4⋊C4—32no—
420C4⋊C4—31no—
421C4⋊C4—32no—
422C4⋊C4—31no—
423C4⋊C4—61no—
424C4⋊C4—91no—
425C4⋊C4—182no—
426C4⋊C4—182no—
427C4⋊C4—181no—
428C22⋊C4—61no—
429C22⋊C4—182no—
430C42—32no—
431C42—182no—
432C42—181no—
433C42C2×D3211yescharacteristic
434C22×C3—21no—
435C22×C3—121no—
436C22×C3—121no—
437C22×C3—121no—
438C22×C3C22×D1211yescharacteristic
439C22×C3C2×D3×D411yescharacteristic
440C2×D3—41no—
441C2×D3—41no—
442C2×D3—41no—
443C2×D3—122no—
444C2×D3—122no—
445C2×D3—122no—
446C2×D3—122no—
447C2×D3—122no—
448C2×D3—122no—
449C2×D3—242no—
450C2×D3—242no—
451C2×D3—242no—
452C3×C4—21no—
453C3×C4—21no—
454C3×C4—22no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—34no—
458C3×C4—41no—
459C3×C4—62no—
460C3×C4—121no—
461C3×C4—122no—
462C3×C4C2×#20412yes—
463C3×C4D3×SD1612yes—
464C3×C4#100711yescharacteristic
465C3×C4#100711yescharacteristic
466C3×C4D3×#4111yescharacteristic
467C3×C4D3×#4111yescharacteristic
468Dic3—22no—
469Dic3—41no—
470Dic3—42no—
471Dic3—62no—
472Dic3—62no—
473Dic3—122no—
474Dic3—121no—
475Dic3—121no—
476Dic3—241no—
477Dic3C2×#20414yes—
478C32#336211yescharacteristic, complemented, Sylow
479C23—61no—
480C23—182no—
481Q8—34no—
482Q8—92no—
483Q8—181no—
484Q8—241no—
485Q8—722no—
486D4—61no—
487D4—61no—
488D4—182no—
489D4—182no—
490D4—364no—
491D4—362no—
492D4—721no—
493D4—722no—
494C2×C4—32no—
495C2×C4—32no—
496C2×C4—62no—
497C2×C4—61no—
498C2×C4—122no—
499C2×C4—181no—
500C2×C4—181no—
501C2×C4—364no—
502C2×C4D3×D1211yescharacteristic
503C2×C4D3×D1211yescharacteristic
504C2×C4C22×D3211yescharacteristic
505C8—22no—
506C8—61no—
507C8—61no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—241no—
512C2×C3#557611yescharacteristic
513C2×C3#563311yescharacteristic
514C2×C3C22×#20411yescharacteristic
515C2×C3#575211yescharacteristic
516C2×C3C2×D3×SD1611yescharacteristic
517C2×C3#577411yescharacteristic
518D3—81no—
519D3—242no—
520D3—242no—
521D3—482no—
522C22—121no—
523C22—121no—
524C22—121no—
525C22—362no—
526C22—362no—
527C22—362no—
528C22C2×D3×D1211yescharacteristic
529C4—21no—
530C4—34no—
531C4—62no—
532C4—121no—
533C4—122no—
534C4—182no—
535C4—361no—
536C4D3×#20412yes—
537C4#6431211yescharacteristic
538C4#6431611yescharacteristic
539C3—21no—
540C3#7993211yescharacteristic, complemented
541C3#8109011yescharacteristic, complemented
542C2—241no—
543C2—722no—
544C2#1059432911yescharacteristic
545C2C2×D3×#20411yescharacteristic
546C2#1059471411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radical#10593902C2
hypercenterC4⋊C8D32
hypocenterC32#3362
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. #10593856C2semidirect
3. #10592547C2semidirect
4. C3×#4842C2semidirect
5. C3×#4830C2semidirect
6. #10590879C2semidirect
7. #10590878C2semidirect
8. #10590759C2semidirect
9. #10590758C2semidirect
10. C4×#3716C2semidirect
11. #10590281C2semidirect
58. #4842D3semidirect
59. #4830D3semidirect
175. #634#41semidirect
184. C3×Dic6SD16semidirect
388. Dic6#204semidirect
478. C32#3362semidirect
540. C3#79932semidirect
541. C3#81090semidirect

Maximal subgroups

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

subgroupindex
#105939022
#105938562
#105925472
C3×#48422
C3×#48302
#105908792
#105908782
#105907592
#105907582
C4×#37162
#105902812
#810903
#799323