Finite Group Databasebeta

← #11872788

Subgroups — #11872788

Order 1152.

1182 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596096C211yesmaximal, characteristic, complemented
2#10595992C211yesmaximal, characteristic
3C32×#485C211yesmaximal, characteristic, complemented
4#10592745C211yesmaximal, characteristic
5#10592695C211yesmaximal, characteristic, complemented
6#10592590C211yesmaximal, characteristic, complemented
7#10592588C211yesmaximal, characteristic, complemented
8#10592570C211yesmaximal, characteristic, complemented
9#10592551C211yesmaximal, characteristic, complemented
10#10592517C211yesmaximal, characteristic, complemented
11#10592517C211yesmaximal, characteristic, complemented
12#10592516C211yesmaximal, characteristic, complemented
13#10592487C211yesmaximal, characteristic, complemented
14#10592430C211yesmaximal, characteristic
15#10592419C211yesmaximal, characteristic, complemented
16#81498—34nomaximal
17C22×C4⋊(C3⋊D3)C2211yescharacteristic
18C32×C22⋊Q8C2211yescharacteristic
19C32×#117C2211yescharacteristic
20Q8×C3⋊Dic3C2211yescharacteristic, complemented
21#64153C2211yescharacteristic, complemented
22C2×#3755C2211yescharacteristic
23C2×#3755C2211yescharacteristic
24#64135C2211yescharacteristic
25#64133C2211yescharacteristic
26C2×#3744C2211yescharacteristic
27C2×#3744C2211yescharacteristic
28#64102C2211yescharacteristic
29#64102C2211yescharacteristic
30#64102C2211yescharacteristic
31#64102C2211yescharacteristic
32#64099—21no—
33#64099C2211yescharacteristic, complemented
34#64098—21no—
35#64096C2211yescharacteristic, complemented
36C22⋊C4×C3⋊D3—21no—
37C22⋊C4×C3⋊D3—21no—
38#64088—21no—
39#64088—21no—
40C4×C4⋊(C3⋊D3)—21no—
41C4×C4⋊(C3⋊D3)—21no—
42C32×#107C2211yescharacteristic, complemented
43C32×#106C2211yescharacteristic, complemented
44C32×#103C2211yescharacteristic, complemented
45C32×#103C2211yescharacteristic, complemented
46C32×C22⋊C8C2211yescharacteristic
47#63657C2211yescharacteristic
48#63648C2211yescharacteristic
49#63648C2211yescharacteristic
50#63642C2211yescharacteristic, complemented
51#63641C2211yescharacteristic, complemented
52#63641C2211yescharacteristic, complemented
53C8×C3⋊Dic3C2211yescharacteristic, complemented
54#63637C2211yescharacteristic, complemented
55#63637C2211yescharacteristic, complemented
56#63636C2211yescharacteristic
57#63636C2211yescharacteristic
58#63635C2211yescharacteristic, complemented
59#63634C2211yescharacteristic, complemented
60#5625—34no—
61#5521—34no—
62C3×#485D314yescomplemented
63#5046—34no—
64#4996—34no—
65#4891—34no—
66#4889—34no—
67#4871—34no—
68#4852—34no—
69#4818—34no—
70#4818—34no—
71#4817—34no—
72#4788—34no—
73#4731—34no—
74#4720—34no—
75C23×C3⋊D3—21no—
76C2×C32×Q8C2311yescharacteristic
77C22×C32×C4C2311yescharacteristic
78C2×C4⋊(C3⋊D3)—21no—
79C2×C4⋊(C3⋊D3)—22no—
80C2×C4⋊(C3⋊D3)—22no—
81C2×C4⋊(C3⋊D3)C2311yescharacteristic
82C2×C4⋊(C3⋊D3)C2311yescharacteristic
83C2×C4×C3⋊D3—21no—
84C2×C4×C3⋊D3—21no—
85C2×C4×C3⋊D3—21no—
86C2×C4×C3⋊D3—21no—
87C2×#634C2311yescharacteristic
88C2×C32×C8C2311yescharacteristic
89C2×C32×C8C2311yescharacteristic
90C32×C4⋊C4—21no—
91C32×C4⋊C4C2311yescharacteristic
92C32×C4⋊C4C2311yescharacteristic
93C32×C4⋊C4C2311yescharacteristic
94C32×C22⋊C4—21no—
95C32×C22⋊C4—21no—
96C32×C42—21no—
97#3757—21no—
98#3757D411yescharacteristic
99#3757D411yescharacteristic
100#3755—22no—
101#3755—22no—
102#3752—21no—
103#3752—21no—
104#3752—21no—
105#3752—21no—
106C4⋊(C3⋊Dic3)—21no—
107C4⋊(C3⋊Dic3)—21no—
108C4⋊(C3⋊Dic3)D411yescharacteristic
109C4⋊(C3⋊Dic3)D411yescharacteristic
110C4⋊(C3⋊Dic3)C2311yescharacteristic
111#3750—21no—
112#3750—21no—
113#3750—21no—
114#3750—21no—
115#3750—21no—
116C4×C3⋊Dic3—21no—
117C4×C3⋊Dic3—21no—
118C4×C3⋊Dic3C2311yescharacteristic
119C4×C3⋊Dic3C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122#3744—22no—
123#3744—22no—
124#3123—91noSylow
125C22×D12—34no—
126C3×C22⋊Q8C2×D314yes—
127C3×#117C2×D314yes—
128Q8×Dic3—34no—
129#944—34no—
130C2×#215—34no—
131C2×#215—34no—
132#926—34no—
133#924—34no—
134C2×#204—34no—
135C2×#204—34no—
136#893—34no—
137#893—34no—
138#893—34no—
139#893—34no—
140#890—34no—
141#890—64no—
142#889—64no—
143#887—34no—
144D3×C22⋊C4—64no—
145D3×C22⋊C4—64no—
146#879—64no—
147#879—64no—
148C4×D12—64no—
149C4×D12—64no—
150C3×#107C2×D314yescomplemented
151C3×#106C2×D314yescomplemented
152C3×#103C2×D314yescomplemented
153C3×#103C2×D314yescomplemented
154C3×C22⋊C8C2×D314yes—
155#830—34no—
156#821—34no—
157#821—34no—
158#815—34no—
159Dic3⋊C8—34no—
160Dic3⋊C8—34no—
161C8×Dic3—34no—
162#810—34no—
163#810—34no—
164#809—34no—
165#809—34no—
166#808—34no—
167#807—34no—
168C23×C32C2×D411yescharacteristic
169C22×C3⋊D3—21no—
170C22×C3⋊D3—21no—
171C22×C3⋊D3—24no—
172C22×C3⋊D3—81no—
173C22×C3⋊D3—81no—
174C32×Q8—21no—
175C32×Q8—21no—
176C2×C32×C4—21no—
177C2×C32×C4—21no—
178C2×C32×C4—21no—
179C2×C32×C4—21no—
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2411yescharacteristic
184C2×C3⋊Dic3—21no—
185C2×C3⋊Dic3—21no—
186C2×C3⋊Dic3C2×D411yescharacteristic
187C2×C3⋊Dic3C2×D411yescharacteristic
188C2×C3⋊Dic3C2×D411yescharacteristic
189C2×C3⋊Dic3C2×D411yescharacteristic
190C4⋊(C3⋊D3)—24no—
191C4⋊(C3⋊D3)—21no—
192C4⋊(C3⋊D3)—21no—
193C4⋊(C3⋊D3)#4112yes—
194C4⋊(C3⋊D3)#4112yes—
195C4×C3⋊D3—81no—
196C4×C3⋊D3—81no—
197C4×C3⋊D3—81no—
198C4×C3⋊D3—81no—
199#634—21no—
200#634—21no—
201C32×C8—21no—
202C32×C8—21no—
203C3⋊(C3⋊C8)—21no—
204C3⋊(C3⋊C8)—21no—
205#541—91no—
206#518—91no—
207#485—91no—
208#485C3⋊D311yescharacteristic, complemented
209#478—91no—
210#478—91no—
211#461—91no—
212#461—91no—
213#450—91no—
214#450—91no—
215#440—91no—
216#440—91no—
217C4×SD16—91no—
218C4×SD16—91no—
219#433—91no—
220C23×D3—64no—
221C2×C3×Q8C22×D314yes—
222C22×C3×C4C22×D314yes—
223C2×D12—34no—
224C2×D12—34no—
225C2×D12—68no—
226C2×D12—68no—
227C2×D12—64no—
228C2×C4×D3—64no—
229C2×C4×D3—64no—
230C2×C4×D3—64no—
231C2×C4×D3—64no—
232C2×Dic6—34no—
233C2×C3×C8C22×D314yes—
234C2×C3×C8C22×D314yes—
235C3×C4⋊C4—24no—
236C3×C4⋊C4C22×D314yes—
237C3×C4⋊C4C22×D314yes—
238C3×C4⋊C4C22×D314yes—
239C3×C22⋊C4—24no—
240C3×C22⋊C4—24no—
241C3×C42—24no—
242#217—34no—
243#217—34no—
244#217—64no—
245#215—68no—
246#215—68no—
247(C2×D3)⋊C4—64no—
248(C2×D3)⋊C4—64no—
249(C2×D3)⋊C4—64no—
250(C2×D3)⋊C4—64no—
251C4⋊Dic3—34no—
252C4⋊Dic3—34no—
253C4⋊Dic3—34no—
254C4⋊Dic3—64no—
255C4⋊Dic3—64no—
256Dic3⋊C4—64no—
257Dic3⋊C4—64no—
258Dic3⋊C4—64no—
259Dic3⋊C4—64no—
260Dic3⋊C4—64no—
261C4×Dic3—34no—
262C4×Dic3—34no—
263C4×Dic3—64no—
264C4×Dic3—64no—
265C2×C3⋊C8—34no—
266C2×C3⋊C8—34no—
267#204—68no—
268#204—68no—
269C22×C32—21no—
270C22×C32—21no—
271C22×C32—21no—
272C22×C32C22×D411yescharacteristic
273C2×C3⋊D3—22no—
274C2×C3⋊D3—22no—
275C2×C3⋊D3—41no—
276C2×C3⋊D3—41no—
277C2×C3⋊D3—41no—
278C2×C3⋊D3—41no—
279C2×C3⋊D3—84no—
280C32×C4—21no—
281C32×C4—41no—
282C32×C4—41no—
283C32×C4—41no—
284C32×C4—41no—
285C32×C4C2×#4111yescharacteristic
286C32×C4C2×#4111yescharacteristic
287C3⋊Dic3—21no—
288C3⋊Dic3—21no—
289C3⋊Dic3—21no—
290C3⋊Dic3—21no—
291C3⋊Dic3—41no—
292C3⋊Dic3—41no—
293C22×D4—91no—
294C2×SD16—91no—
295C2×SD16—91no—
296C2×SD16—91no—
297C2×SD16—91no—
298C4⋊Q8—91no—
299#126—181no—
300#126—181no—
301#125—91no—
302#125—181no—
303#125—181no—
304C22⋊Q8—91no—
305C22⋊Q8C2×C3⋊D311yescharacteristic
306C4×Q8—91no—
307C4×Q8—91no—
308C4×D4—91no—
309C4×D4—91no—
310C4×D4—91no—
311C4×D4—91no—
312C4×D4—181no—
313C4×D4—181no—
314#117—91no—
315#117C2×C3⋊D311yescharacteristic
316C2×C22⋊C4—181no—
317C2×C22⋊C4—181no—
318#107—91no—
319#107C2×C3⋊D311yescharacteristic, complemented
320#106—91no—
321#106C2×C3⋊D311yescharacteristic, complemented
322C4⋊C8—91no—
323C4⋊C8—91no—
324#103—91no—
325#103—91no—
326#103C2×C3⋊D311yescharacteristic, complemented
327#103C2×C3⋊D311yescharacteristic, complemented
328#102—91no—
329#102—91no—
330#102—91no—
331#102—91no—
332C22⋊C8—91no—
333C22⋊C8C2×C3⋊D311yescharacteristic
334#97—91no—
335C4×C8—91no—
336C23×C3D3×D414yes—
337C22×D3—64no—
338C22×D3—64no—
339C22×D3—616no—
340C22×D3—244no—
341C22×D3—244no—
342C3×Q8—24no—
343C3×Q8—24no—
344C2×C3×C4—24no—
345C2×C3×C4—24no—
346C2×C3×C4—24no—
347C2×C3×C4—24no—
348C2×C3×C4—24no—
349C2×C3×C4—24no—
350C2×C3×C4D3×D414yes—
351C2×C3×C4C23×D314yes—
352C2×Dic3—34no—
353C2×Dic3—34no—
354C2×Dic3—34no—
355C2×Dic3—34no—
356C2×Dic3—64no—
357C2×Dic3—64no—
358D12—38no—
359D12—38no—
360D12—616no—
361D12—64no—
362D12—64no—
363C4×D3—244no—
364C4×D3—244no—
365C4×D3—244no—
366C4×D3—244no—
367Dic6—64no—
368Dic6—64no—
369C3×C8—24no—
370C3×C8—24no—
371C3⋊C8—64no—
372C3⋊C8—64no—
373C2×C32—41no—
374C2×C32#52511yescharacteristic
375C2×C32#57711yescharacteristic
376C2×C32#57711yescharacteristic
377C3⋊D3—42no—
378C3⋊D3—42no—
379C24—181no—
380C2×Q8—91no—
381C2×Q8C22×C3⋊D311yescharacteristic
382C2×D4—91no—
383C2×D4—91no—
384C2×D4—182no—
385C2×D4—182no—
386C2×D4—181no—
387C22×C4—181no—
388C22×C4—181no—
389C22×C4—181no—
390C22×C4—181no—
391C22×C4C22×C3⋊D311yescharacteristic
392SD16—182no—
393SD16—182no—
394SD16—182no—
395SD16—182no—
396C2×C8—91no—
397C2×C8—91no—
398C2×C8C22×C3⋊D311yescharacteristic
399C2×C8C22×C3⋊D311yescharacteristic
400C4⋊C4—21no—
401C4⋊C4—91no—
402C4⋊C4—91no—
403C4⋊C4—91no—
404C4⋊C4—181no—
405C4⋊C4—181no—
406C4⋊C4—181no—
407C4⋊C4—181no—
408C4⋊C4—181no—
409C4⋊C4—181no—
410C4⋊C4—181no—
411C4⋊C4C22×C3⋊D311yescharacteristic
412C4⋊C4C22×C3⋊D311yescharacteristic
413C4⋊C4C22×C3⋊D311yescharacteristic
414C22⋊C4—21no—
415C22⋊C4—21no—
416C22⋊C4—91no—
417C22⋊C4—91no—
418C22⋊C4—181no—
419C22⋊C4—181no—
420C22⋊C4—181no—
421C22⋊C4—181no—
422C22⋊C4—181no—
423C42—21no—
424C42—91no—
425C42—91no—
426C42—181no—
427C42—181no—
428C22×C3—24no—
429C22×C3—24no—
430C22×C3—24no—
431C22×C3C2×D3×D414yes—
432C2×D3—68no—
433C2×D3—68no—
434C2×D3—124no—
435C2×D3—124no—
436C2×D3—124no—
437C2×D3—124no—
438C2×D3—2416no—
439C3×C4—24no—
440C3×C4—44no—
441C3×C4—44no—
442C3×C4—44no—
443C3×C4—44no—
444C3×C4D3×#4114yes—
445C3×C4D3×#4114yes—
446Dic3—64no—
447Dic3—64no—
448Dic3—64no—
449Dic3—64no—
450Dic3—124no—
451Dic3—124no—
452C32#312311yescharacteristic, complemented, Sylow
453C23—184no—
454C23—181no—
455C23—181no—
456C23—721no—
457C23—721no—
458C23D4×C3⋊D311yescharacteristic
459Q8—21no—
460Q8—21no—
461Q8—181no—
462Q8—181no—
463D4—92no—
464D4—92no—
465D4—184no—
466D4—181no—
467D4—181no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—91no—
475C2×C4—91no—
476C2×C4—91no—
477C2×C4—91no—
478C2×C4—181no—
479C2×C4—181no—
480C2×C4—721no—
481C2×C4—721no—
482C2×C4—721no—
483C2×C4—721no—
484C2×C4D4×C3⋊D311yescharacteristic
485C2×C4C23×C3⋊D311yescharacteristic
486C8—21no—
487C8—21no—
488C8—181no—
489C8—181no—
490C2×C3—44no—
491C2×C3#565614yes—
492C2×C3#577014yes—
493C2×C3#577814yes—
494D3—128no—
495D3—128no—
496C22—21no—
497C22—21no—
498C22—21no—
499C22—182no—
500C22—182no—
501C22—361no—
502C22—361no—
503C22—361no—
504C22—361no—
505C22—724no—
506C22C2×D4×C3⋊D311yescharacteristic
507C4—21no—
508C4—41no—
509C4—41no—
510C4—41no—
511C4—41no—
512C4—181no—
513C4—181no—
514C4—181no—
515C4—181no—
516C4—361no—
517C4—361no—
518C4#41×C3⋊D311yescharacteristic
519C4#41×C3⋊D311yescharacteristic
520C3#8149814yescomplemented
521C2—41no—
522C2—362no—
523C2—362no—
524C2#1059612711yescharacteristic
525C2#1059624111yescharacteristic
526C2#1059624911yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#485C2
socleC22×C32C22×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenter#485C3⋊D3
hypocenterC32#3123
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #10596096C2semidirect
3. C32×#485C2semidirect
5. #10592695C2semidirect
6. #10592590C2semidirect
7. #10592588C2semidirect
8. #10592570C2semidirect
9. #10592551C2semidirect
10. #10592517C2semidirect
11. #10592517C2semidirect
12. #10592516C2semidirect
13. #10592487C2semidirect
15. #10592419C2semidirect
20. Q8×C3⋊Dic3C22semidirect
21. #64153C22semidirect
33. #64099C22semidirect
35. #64096C22semidirect
42. C32×#107C22semidirect
43. C32×#106C22semidirect
44. C32×#103C22semidirect
45. C32×#103C22semidirect
50. #63642C22semidirect
51. #63641C22semidirect
52. #63641C22semidirect
53. C8×C3⋊Dic3C22semidirect
54. #63637C22semidirect
55. #63637C22semidirect
58. #63635C22semidirect
59. #63634C22semidirect
62. C3×#485D3semidirect
150. C3×#107C2×D3semidirect
151. C3×#106C2×D3semidirect
152. C3×#103C2×D3semidirect
153. C3×#103C2×D3semidirect
208. #485C3⋊D3semidirect
319. #107C2×C3⋊D3semidirect
321. #106C2×C3⋊D3semidirect
326. #103C2×C3⋊D3semidirect
327. #103C2×C3⋊D3semidirect
452. C32#3123semidirect
520. C3#81498semidirect

Maximal subgroups

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

subgroupindex
#105960962
#105959922
C32×#4852
#105927452
#105926952
#105925902
#105925882
#105925702
#105925512
#105925172
#105925162
#105924872
#105924302
#105924192
#814983