Finite Group Databasebeta

← #11895252

Subgroups — #11895252

Order 1152.

814 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596050C211yesmaximal, characteristic, complemented
2C3×#5584C211yesmaximal, characteristic, complemented
3C3×Q8×C3⋊C8C211yesmaximal, characteristic, complemented
4#10590379C211yesmaximal, characteristic, complemented
5C4×#3717C212yesmaximal, complemented
6#10590356C212yesmaximal
7C4×#3714C211yesmaximal, characteristic
8#10590302C212yesmaximal, complemented
9#10590287C211yesmaximal, characteristic, complemented
10#10590274C212yesmaximal, complemented
11#10590268C211yesmaximal, characteristic, complemented
12#83667—31nomaximal
13#79926—31nomaximal
14C32×C4×Q8C2211yescharacteristic
15#64155—21no—
16#64105—22no—
17C4⋊C4×C3⋊D3—21no—
18C4×C4⋊(C3⋊D3)C2211yescharacteristic
19C4×C4⋊(C3⋊D3)C2212yes—
20#64079C2212yes—
21#64078C2211yescharacteristic
22C3×#946—21no—
23C3×#898—22no—
24C3×#892—21no—
25C3×#875C2212yes—
26C3×C4×D12C2211yescharacteristic
27C3×#869C2211yescharacteristic
28C3×C4×Dic6C2212yes—
29C2×#3717C2212yes—
30C2×#3714C2211yescharacteristic
31C3×C4⋊(C3⋊C8)C2211yescharacteristic
32C3×C4⋊(C3⋊C8)C2212yes—
33C3×C4×C3⋊C8C2212yes—
34C3×C4×C3⋊C8C2211yescharacteristic
35#63575C2211yescharacteristic
36#63573C2212yes—
37#63566C2212yes—
38#63566C2212yes—
39#63566C2212yes—
40#63564C2211yescharacteristic
41#63563C2212yes—
42#63563C2211yescharacteristic
43C3×#556—31no—
44#5584D311yescharacteristic, complemented
45#5579—31no—
46#5579—31no—
47#5579—61no—
48C3×C8×Q8—31no—
49#5083—31no—
50#5079—31no—
51#5057—32no—
52#5056—32no—
53C4×#215—32no—
54Q8×C3⋊C8D311yescharacteristic, complemented
55#5022—32no—
56C4×#213—31no—
57#5008—31no—
58#4844—32no—
59#4842—31no—
60#4841—31no—
61#4829—32no—
62#4697—32no—
63C4×D24—31no—
64C4×#204—32no—
65#4681—31no—
66C2×C32×Q8D411yescharacteristic
67C2×C4⋊(C3⋊D3)C2311yescharacteristic
68C2×C4×C3⋊D3—21no—
69C2×C4×C3⋊D3—22no—
70C2×#634—21no—
71C2×C3×D12C2311yescharacteristic
72C2×C3×C4×D3—21no—
73C2×C3×Dic6C2312yes—
74C32×C4⋊C4D411yescharacteristic
75C32×C4⋊C4D412yes—
76C32×C42C2311yescharacteristic
77C32×C42C2312yes—
78#3752—21no—
79#3752—22no—
80C4⋊(C3⋊Dic3)—21no—
81C4⋊(C3⋊Dic3)C2312yes—
82C4⋊(C3⋊Dic3)C2311yescharacteristic
83#3750—22no—
84#3750—22no—
85C3×(C2×D3)⋊C4—22no—
86C3×(C2×D3)⋊C4—21no—
87C3×(C2×D3)⋊C4—22no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3C2311yescharacteristic
91C3×Dic3⋊C4—22no—
92C3×C4×Dic3—22no—
93C2×C3×C3⋊C8C2311yescharacteristic
94C2×C3×C3⋊C8C2312yes—
95C2×C3×C3⋊C8C2311yescharacteristic
96#3717—24no—
97#3714—22no—
98#3360—91noSylow
99C3×C4⋊Q8—31no—
100C3×#126—62no—
101C3×#124—32no—
102C3×C22⋊Q8—61no—
103C3×C4×Q8—21no—
104C3×C4×Q8—32no—
105C3×C4×Q8C2×D311yescharacteristic
106C3×C4×Q8C2×D311yescharacteristic
107C3×C4×D4—31no—
108C3×#117—61no—
109#946—21no—
110#946—62no—
111#946—61no—
112#946—61no—
113C2×#215—32no—
114C2×#213—31no—
115C2×D24—31no—
116C2×#204—32no—
117#898—22no—
118#896—64no—
119#896—62no—
120#896—62no—
121#892—21no—
122D3×C4⋊C4—62no—
123D3×C4⋊C4—61no—
124D3×C4⋊C4—61no—
125#875C2×D312yes—
126C4×D12—32no—
127C4×D12—31no—
128C4×D12—31no—
129C4×D12—32no—
130C4×D12—61no—
131C4×D12—62no—
132C4×D12C2×D311yescharacteristic
133#870—32no—
134#870—32no—
135#870—62no—
136#869—31no—
137#869—31no—
138#869—61no—
139#869C2×D311yescharacteristic
140C4×Dic6C2×D312yes—
141C3×C4⋊C8—32no—
142C3×C4⋊C8—31no—
143C3×C4×C8—31no—
144C3×C4×C8—32no—
145#835—32no—
146#835—32no—
147#835—32no—
148#832—32no—
149#832—31no—
150#821—31no—
151#821—32no—
152#821—31no—
153#818—31no—
154#817—32no—
155#816—32no—
156#816—32no—
157#816—32no—
158#809—31no—
159#808—32no—
160#807—31no—
161C4⋊(C3⋊C8)C2×D311yescharacteristic
162C4⋊(C3⋊C8)C2×D312yes—
163C4×C3⋊C8C2×D311yescharacteristic
164C4×C3⋊C8C2×D312yes—
165C22×C3⋊D3—21no—
166C22×C3×D3—21no—
167C32×Q8—22no—
168C2×C32×C4C2×D412yes—
169C2×C32×C4C2×D412yes—
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2411yescharacteristic
173C2×C3⋊Dic3—21no—
174C2×C3⋊Dic3—22no—
175C4⋊(C3⋊D3)—21no—
176C4⋊(C3⋊D3)#4112yes—
177C4×C3⋊D3—42no—
178C4×C3⋊D3—82no—
179#634—81no—
180C2×C3×Dic3—21no—
181C2×C3×Dic3—22no—
182C3×D12—21no—
183C3×D12—21no—
184C3×C4×D3—42no—
185C3×Dic6—22no—
186C3×Dic6—22no—
187C3×C3⋊C8—21no—
188C3×C3⋊C8—22no—
189C3×C3⋊C8—21no—
190#556—31no—
191#554—91no—
192#488—92no—
193#487—91no—
194#479—92no—
195#476—91no—
196#463—92no—
197#461—91no—
198C8×Q8—31no—
199C4×SD16—92no—
200C4×D8—91no—
201C2×C3×Q8—21no—
202C2×C3×Q8—32no—
203C2×C3×Q8D1211yescharacteristic
204C2×C3×Q8#6711yescharacteristic
205C2×C3×D4—31no—
206C22×C3×C4—61no—
207C2×D12—31no—
208C2×D12—31no—
209C2×D12—61no—
210C2×D12C22×D311yescharacteristic
211C2×C4×D3—21no—
212C2×C4×D3—62no—
213C2×C4×D3—61no—
214C2×C4×D3—61no—
215C2×C4×D3—64no—
216C2×C4×D3—62no—
217C2×C4×D3—62no—
218C2×Dic6—62no—
219C2×Dic6—61no—
220C2×Dic6—61no—
221C2×Dic6C22×D312yes—
222C2×C3×C8—31no—
223C2×C3×C8—31no—
224C2×C3×C8—32no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—22no—
227C3×C4⋊C4—31no—
228C3×C4⋊C4—62no—
229C3×C4⋊C4—61no—
230C3×C4⋊C4—61no—
231C3×C4⋊C4D1211yescharacteristic
232C3×C4⋊C4D1212yes—
233C3×C4⋊C4#6711yescharacteristic
234C3×C4⋊C4#6712yes—
235C3×C22⋊C4—62no—
236C3×C22⋊C4—61no—
237C3×C22⋊C4—62no—
238C3×C42—21no—
239C3×C42—22no—
240C3×C42—62no—
241C3×C42C22×D311yescharacteristic
242C3×C42C22×D312yes—
243C3×C42C22×D312yes—
244C3×C42C22×D311yescharacteristic
245#215—64no—
246#213—62no—
247(C2×D3)⋊C4—21no—
248(C2×D3)⋊C4—22no—
249(C2×D3)⋊C4—22no—
250(C2×D3)⋊C4—62no—
251(C2×D3)⋊C4—64no—
252(C2×D3)⋊C4—61no—
253(C2×D3)⋊C4—62no—
254(C2×D3)⋊C4—61no—
255(C2×D3)⋊C4—62no—
256C4⋊Dic3—21no—
257C4⋊Dic3—21no—
258C4⋊Dic3—31no—
259C4⋊Dic3—32no—
260C4⋊Dic3—32no—
261C4⋊Dic3—31no—
262C4⋊Dic3—62no—
263C4⋊Dic3—61no—
264C4⋊Dic3—62no—
265C4⋊Dic3—61no—
266C4⋊Dic3—61no—
267C4⋊Dic3C22×D311yescharacteristic
268Dic3⋊C4—22no—
269Dic3⋊C4—64no—
270Dic3⋊C4—64no—
271Dic3⋊C4—62no—
272Dic3⋊C4—62no—
273Dic3⋊C4—62no—
274Dic3⋊C4—62no—
275C4×Dic3—22no—
276C2×C3⋊C8C22×D311yescharacteristic
277C2×C3⋊C8C22×D311yescharacteristic
278C2×C3⋊C8C22×D312yes—
279D24—62no—
280#204—64no—
281C22×C32C22×D411yescharacteristic
282C2×C3⋊D3—22no—
283C2×C3⋊D3—41no—
284C2×C3⋊D3—41no—
285C2×C3×D3—41no—
286C2×C3×D3—41no—
287C2×C3×D3—41no—
288C32×C4—22no—
289C32×C4—21no—
290C32×C4—22no—
291C32×C4#13512yes—
292C32×C4C2×#4111yescharacteristic
293C32×C42−1+411yescharacteristic
294C3⋊Dic3—41no—
295C3⋊Dic3—42no—
296C3×Dic3—42no—
297C3×Dic3—41no—
298C2×SD16—92no—
299C2×D8—91no—
300C4⋊Q8—31no—
301C4⋊Q8—91no—
302#126—62no—
303#125—92no—
304#124—32no—
305C22⋊Q8—61no—
306C22⋊Q8—181no—
307C22⋊Q8—182no—
308C4×Q8—32no—
309C4×Q8D3211yescharacteristic
310C4×D4—31no—
311C4×D4—91no—
312C4×D4—92no—
313#117—61no—
314C2×C4⋊C4—181no—
315#107—91no—
316#106—92no—
317C4⋊C8—31no—
318C4⋊C8—32no—
319#103—92no—
320#103—92no—
321#103—92no—
322#102—91no—
323#102—91no—
324#102—92no—
325C4×C8—31no—
326C4×C8—32no—
327C23×C3—61no—
328C22×D3—21no—
329C22×D3—62no—
330C22×D3—61no—
331C22×D3—61no—
332C3×Q8—22no—
333C3×Q8—22no—
334C3×Q8—42no—
335C3×Q8—62no—
336C3×Q8—62no—
337C3×D4—61no—
338C3×D4—61no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—22no—
342C2×C3×C4—22no—
343C2×C3×C4—21no—
344C2×C3×C4—61no—
345C2×C3×C4—62no—
346C2×C3×C4—122no—
347C2×C3×C4C2×D1212yes—
348C2×C3×C4C2×D1212yes—
349C2×C3×C4C2×D1211yescharacteristic
350C2×C3×C4C2×D1211yescharacteristic
351C2×C3×C4C2×#6712yes—
352C2×C3×C4C2×#6712yes—
353C2×C3×C4C2×#6711yescharacteristic
354C2×C3×C4C2×#6711yescharacteristic
355C2×C3×C4C23×D311yescharacteristic
356C2×C3×C4C23×D311yescharacteristic
357C2×Dic3—21no—
358C2×Dic3—22no—
359C2×Dic3—62no—
360C2×Dic3—64no—
361C2×Dic3—61no—
362C2×Dic3—62no—
363C2×Dic3—61no—
364C2×Dic3—62no—
365D12—21no—
366D12—21no—
367D12—32no—
368D12—32no—
369D12—62no—
370D12—62no—
371D12—61no—
372D12—61no—
373C4×D3—42no—
374C4×D3—124no—
375C4×D3—122no—
376C4×D3—122no—
377C4×D3—242no—
378C4×D3—242no—
379C4×D3—244no—
380Dic6—22no—
381Dic6—22no—
382Dic6—241no—
383Dic6—241no—
384Dic6—242no—
385C3×C8—62no—
386C3×C8—61no—
387C3×C8—61no—
388C3⋊C8—21no—
389C3⋊C8—21no—
390C3⋊C8—22no—
391C2×C32#54811yescharacteristic
392C2×C32C2×#13511yescharacteristic
393C2×C32#57711yescharacteristic
394C3⋊D3—42no—
395C3×D3—81no—
396C2×Q8—32no—
397C2×Q8—181no—
398C2×Q8#62611yescharacteristic
399C2×D4—31no—
400C2×D4—91no—
401C22×C4—61no—
402C22×C4—181no—
403C22×C4—182no—
404SD16—184no—
405D8—182no—
406C2×C8—31no—
407C2×C8—32no—
408C2×C8—31no—
409C4⋊C4—31no—
410C4⋊C4—61no—
411C4⋊C4—62no—
412C4⋊C4—61no—
413C4⋊C4—92no—
414C4⋊C4—91no—
415C4⋊C4—182no—
416C4⋊C4—181no—
417C4⋊C4—182no—
418C4⋊C4#62611yescharacteristic
419C4⋊C4#62612yes—
420C22⋊C4—62no—
421C22⋊C4—61no—
422C22⋊C4—62no—
423C22⋊C4—181no—
424C22⋊C4—182no—
425C42—62no—
426C42C2×D3211yescharacteristic
427C42C2×D3212yes—
428C22×C3—21no—
429C22×C3—121no—
430C22×C3—121no—
431C22×C3—121no—
432C22×C3C22×D1211yescharacteristic
433C22×C3C22×#6711yescharacteristic
434C2×D3—41no—
435C2×D3—41no—
436C2×D3—41no—
437C2×D3—64no—
438C2×D3—62no—
439C2×D3—62no—
440C2×D3—122no—
441C2×D3—122no—
442C2×D3—121no—
443C2×D3—121no—
444C2×D3—121no—
445C2×D3—121no—
446C3×C4—22no—
447C3×C4—21no—
448C3×C4—22no—
449C3×C4—22no—
450C3×C4—21no—
451C3×C4—22no—
452C3×C4—21no—
453C3×C4—21no—
454C3×C4—22no—
455C3×C4—41no—
456C3×C4—42no—
457C3×C4—42no—
458C3×C4—121no—
459C3×C4—122no—
460C3×C4#90412yes—
461C3×C4#95012yes—
462C3×C4#100711yescharacteristic
463C3×C4D3×#4111yescharacteristic
464C3×C4D3×#4111yescharacteristic
465C3×C4#101011yescharacteristic
466Dic3—41no—
467Dic3—42no—
468Dic3—124no—
469Dic3—122no—
470Dic3—121no—
471Dic3—122no—
472Dic3—121no—
473Dic3—122no—
474C32#336011yescharacteristic, complemented, Sylow
475C23—61no—
476C23—181no—
477Q8—22no—
478Q8—62no—
479Q8—62no—
480Q8—721no—
481D4—61no—
482D4—61no—
483D4—92no—
484D4—181no—
485C2×C4—61no—
486C2×C4—62no—
487C2×C4—122no—
488C2×C4—181no—
489C2×C4—182no—
490C2×C4—362no—
491C2×C4—722no—
492C2×C4C2×#62612yes—
493C2×C4C2×#62612yes—
494C2×C4C2×#62611yescharacteristic
495C2×C4C2×#62611yescharacteristic
496C2×C4C22×D3211yescharacteristic
497C8—61no—
498C8—61no—
499C8—62no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—241no—
504C2×C3#557611yescharacteristic
505C2×C3C2×#90411yescharacteristic
506C2×C3#575111yescharacteristic
507C2×C3C2×#95011yescharacteristic
508C2×C3#583111yescharacteristic
509C2×C3#583711yescharacteristic
510D3—81no—
511D3—124no—
512D3—122no—
513D3—122no—
514C22—121no—
515C22—121no—
516C22—121no—
517C22—182no—
518C22—361no—
519C22—361no—
520C22C22×#62611yescharacteristic
521C4—22no—
522C4—21no—
523C4—22no—
524C4—122no—
525C4—121no—
526C4—362no—
527C4—361no—
528C4#6382912yes—
529C4#6431511yescharacteristic
530C4#6431911yescharacteristic
531C3—21no—
532C3#7992611yescharacteristic, complemented
533C3#8366711yescharacteristic, complemented
534C2—241no—
535C2—362no—
536C2C2×#6382911yescharacteristic
537C2#1059541411yescharacteristic
538C2#1059544811yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×#3714C22
hypercenterC4×Q8D32
hypocenterC32#3360
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #10596050C2semidirect
2. C3×#5584C2semidirect
3. C3×Q8×C3⋊C8C2semidirect
4. #10590379C2semidirect
5. C4×#3717C2semidirect
8. #10590302C2semidirect
9. #10590287C2semidirect
10. #10590274C2semidirect
11. #10590268C2semidirect
44. #5584D3semidirect
54. Q8×C3⋊C8D3semidirect
474. C32#3360semidirect
532. C3#79926semidirect
533. C3#83667semidirect

Maximal subgroups

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

subgroupindex
#105960502
C3×#55842
C3×Q8×C3⋊C82
#105903792
C4×#37172
#105903562
C4×#37142
#105903022
#105902872
#105902742
#105902682
#836673
#799263