Finite Group Databasebeta

← #11860464

Subgroups — #11860464

Order 1152.

1518 conjugacy classes of subgroups.

The subgroup lattice has 417 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#520C211yesmaximal, characteristic, complemented
2C2×#64158C211yesmaximal, characteristic
3#10595992C211yesmaximal, characteristic, complemented
4#10592932C211yesmaximal, characteristic, complemented
5#10592725C212yesmaximal, complemented
6C4×#3755C212yesmaximal, complemented
7#10592713C212yesmaximal, complemented
8C4×#3753C212yesmaximal, complemented
9#10592696C211yesmaximal, characteristic, complemented
10C2×#63636C211yesmaximal, characteristic, complemented
11#10592663C211yesmaximal, characteristic, complemented
12#82564—34nomaximal
13C2×C32×#41C2211yescharacteristic
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C32×C4×Q8C2212yescomplemented
16C32×C4×D4—22no—
17C32×C4×D4C2212yescomplemented
18C32×#117—21no—
19C32×#117C2211yescharacteristic
20C2×C32×C4⋊C4—21no—
21C2×C32×C4⋊C4C2211yescharacteristic
22#64158C418yescomplemented
23C2×#3755C2212yes—
24C2×#3753C2212yes—
25#64135C2211yescharacteristic
26C2×#3748C2211yescharacteristic
27C22×C3⋊(C3⋊C8)C2211yescharacteristic
28#64102—21no—
29#64102—21no—
30C22⋊C4×C3⋊D3—22no—
31C4×C4⋊(C3⋊D3)C2212yes—
32C4×C4⋊(C3⋊D3)C2212yes—
33#63662C2211yescharacteristic, complemented
34#63662C2211yescharacteristic, complemented
35#63659C2211yescharacteristic, complemented
36#63659C2211yescharacteristic, complemented
37#63636C2212yes—
38#63636C2212yes—
39#63635C2212yescomplemented
40#63634C2212yescomplemented
41#63630C2212yescomplemented
42C4×C3⋊(C3⋊C8)C2212yescomplemented
43C3×#520D314yescomplemented
44C2×#949—34no—
45#5521—34no—
46#5233—34no—
47#5026—38no—
48C4×#215—38no—
49#5014—38no—
50C4×#213—38no—
51#4997—34no—
52C2×#809—34no—
53#4964—34no—
54C23×C3⋊D3—21no—
55C32×#41—22no—
56C32×#41C2×C414yescomplemented
57C2×C32×Q8C2311yescharacteristic
58C2×C32×D4—21no—
59C2×C32×D4C2311yescharacteristic
60C22×C32×C4—21no—
61C22×C32×C4—21no—
62C22×C32×C4—22no—
63C22×C32×C4C2311yescharacteristic
64C2×C4⋊(C3⋊D3)—21no—
65C2×C4⋊(C3⋊D3)—22no—
66C2×C4⋊(C3⋊D3)C2×C414yescomplemented
67C2×C4⋊(C3⋊D3)C2312yes—
68C2×C4×C3⋊D3—22no—
69C2×C4×C3⋊D3—22no—
70C32×C4⋊C4—21no—
71C32×C4⋊C4—22no—
72C32×C4⋊C4D411yescharacteristic
73C32×C4⋊C4D411yescharacteristic
74C32×C4⋊C4C2312yes—
75C32×C22⋊C4—22no—
76C32×C22⋊C4D412yes—
77C32×C42—22no—
78C32×C42C2312yes—
79#3757—21no—
80#3755C2×C418yescomplemented
81#3753C2×C418yescomplemented
82#3752—22no—
83#3752—22no—
84C4⋊(C3⋊Dic3)C2311yescharacteristic
85C4⋊(C3⋊Dic3)C2311yescharacteristic
86C4×C3⋊Dic3—21no—
87#3748C2×C414yescomplemented
88C2×C3⋊(C3⋊C8)—22no—
89C2×C3⋊(C3⋊C8)C2311yescharacteristic
90C2×C3⋊(C3⋊C8)C2311yescharacteristic
91C2×C3⋊(C3⋊C8)C2312yes—
92#2946—91noSylow
93C2×C3×#41C2×D314yes—
94C22×D12—34no—
95C3×C4×Q8C2×D318yescomplemented
96C3×C4×D4—28no—
97C3×C4×D4C2×D318yescomplemented
98C3×#117—24no—
99C3×#117C2×D314yes—
100C2×C3×C4⋊C4—24no—
101C2×C3×C4⋊C4C2×D314yes—
102#949—332no—
103C2×#215—38no—
104C2×#213—38no—
105#926—34no—
106C2×#208—34no—
107C22×C3⋊C8—34no—
108#893—64no—
109#893—64no—
110D3×C22⋊C4—68no—
111C4×D12—38no—
112C4×D12—38no—
113#835—34no—
114#835—34no—
115#832—34no—
116#832—34no—
117#809—38no—
118#809—38no—
119#808—38no—
120#807—38no—
121#803—38no—
122C4×C3⋊C8—38no—
123C23×C32—21no—
124C23×C32C2×D411yescharacteristic
125C22×C3⋊D3—22no—
126C22×C3⋊D3—24no—
127C22×C3⋊D3—81no—
128C22×C3⋊D3—81no—
129C32×Q8—21no—
130C32×Q8C22×C412yes—
131C32×D4—24no—
132C32×D4—21no—
133C32×D4C22×C412yes—
134C2×C32×C4—21no—
135C2×C32×C4—24no—
136C2×C32×C4—22no—
137C2×C32×C4—82no—
138C2×C32×C4—81no—
139C2×C32×C4C22×C412yes—
140C2×C32×C4C2×D412yes—
141C2×C32×C4C2×D412yes—
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4#4112yes—
144C2×C32×C4C2411yescharacteristic
145C2×C3⋊Dic3—21no—
146C2×C3⋊Dic3—21no—
147C4⋊(C3⋊D3)—24no—
148C4⋊(C3⋊D3)—22no—
149C4⋊(C3⋊D3)C22×C414yes—
150C4×C3⋊D3—82no—
151C4×C3⋊D3—82no—
152C3⋊(C3⋊C8)—21no—
153C3⋊(C3⋊C8)—21no—
154C3⋊(C3⋊C8)C22×C414yes—
155C2×AGL(1,ℤ/8)—91no—
156#520C3⋊D311yescharacteristic, complemented
157#518—91no—
158#442—92no—
159#440—92no—
160C4×SD16—92no—
161C4×D8—92no—
162#428—91no—
163#416—91no—
164C2×#102—91no—
165#405—91no—
166C23×D3—64no—
167C3×#41—28no—
168C3×#41C4×D3116yescomplemented
169C2×C3×Q8C22×D314yes—
170C2×C3×D4—24no—
171C2×C3×D4C22×D314yes—
172C22×C3×C4—24no—
173C22×C3×C4—24no—
174C22×C3×C4—28no—
175C22×C3×C4C22×D314yes—
176C2×D12—316no—
177C2×D12—38no—
178C2×D12—68no—
179C2×D12—64no—
180C2×C4×D3—68no—
181C2×C4×D3—68no—
182C3×C4⋊C4—24no—
183C3×C4⋊C4—28no—
184C3×C4⋊C4#6714yes—
185C3×C4⋊C4#6714yes—
186C3×C4⋊C4C22×D318yes—
187C3×C22⋊C4—28no—
188C3×C22⋊C4#6718yes—
189C3×C42—28no—
190C3×C42C22×D318yes—
191#217—64no—
192#215—332no—
193#213—332no—
194(C2×D3)⋊C4—68no—
195(C2×D3)⋊C4—68no—
196C4⋊Dic3—34no—
197C4⋊Dic3—34no—
198C4×Dic3—64no—
199#208—316no—
200C2×C3⋊C8—38no—
201C2×C3⋊C8—34no—
202C2×C3⋊C8—34no—
203C2×C3⋊C8—68no—
204C22×C32—21no—
205C22×C32—21no—
206C22×C32—22no—
207C22×C32—41no—
208C22×C32—41no—
209C22×C32C4×D412yes—
210C22×C32C22×D411yescharacteristic
211C2×C3⋊D3—24no—
212C2×C3⋊D3—42no—
213C2×C3⋊D3—42no—
214C2×C3⋊D3—84no—
215C32×C4—22no—
216C32×C4—22no—
217C32×C4—22no—
218C32×C4—42no—
219C32×C4C4×D412yes—
220C32×C4C23×C411yescharacteristic
221C32×C4C2×#4111yescharacteristic
222C3⋊Dic3—41no—
223C3⋊Dic3—41no—
224C2×#41C2×C3⋊D311yescharacteristic
225C22×D4—91no—
226AGL(1,ℤ/8)—98no—
227C2×SD16—92no—
228C2×D8—92no—
229C2×M16—91no—
230C22×C8—91no—
231C4×Q8C2×C3⋊D312yescomplemented
232C4×D4—22no—
233C4×D4—92no—
234C4×D4—92no—
235C4×D4—181no—
236C4×D4—181no—
237C4×D4C2×C3⋊D312yescomplemented
238#117—21no—
239#117—91no—
240#117C2×C3⋊D311yescharacteristic
241C2×C4⋊C4—21no—
242C2×C4⋊C4C2×C3⋊D311yescharacteristic
243C2×C22⋊C4—182no—
244#107—92no—
245#106—92no—
246#103—91no—
247#103—91no—
248#102—91no—
249#102—91no—
250#102—92no—
251#102—92no—
252#97—92no—
253C4×C8—92no—
254C23×C3—24no—
255C23×C3C2×#6714yes—
256C22×D3—68no—
257C22×D3—616no—
258C22×D3—244no—
259C22×D3—244no—
260C3×Q8—24no—
261C3×Q8C2×C4×D318yes—
262C3×D4—216no—
263C3×D4—24no—
264C3×D4C2×C4×D318yes—
265C2×C3×C4—24no—
266C2×C3×C4—216no—
267C2×C3×C4—28no—
268C2×C3×C4—88no—
269C2×C3×C4—84no—
270C2×C3×C4C2×C4×D318yes—
271C2×C3×C4#23518yes—
272C2×C3×C4C2×#6718yes—
273C2×C3×C4C2×#6718yes—
274C2×C3×C4C2×#6714yes—
275C2×C3×C4C23×D314yes—
276C2×Dic3—64no—
277C2×Dic3—64no—
278D12—316no—
279D12—616no—
280D12—68no—
281C4×D3—248no—
282C4×D3—248no—
283C3⋊C8—316no—
284C3⋊C8—64no—
285C3⋊C8—64no—
286C2×C32—22no—
287C2×C32—42no—
288C2×C32C2×C4×D411yescharacteristic
289C2×C32#57611yescharacteristic
290C2×C32#57711yescharacteristic
291C3⋊D3—44no—
292C24—181no—
293#41—22no—
294#41C4×C3⋊D314yescomplemented
295C2×Q8C22×C3⋊D311yescharacteristic
296C2×D4—21no—
297C2×D4—92no—
298C2×D4—94no—
299C2×D4—182no—
300C2×D4—181no—
301C2×D4C22×C3⋊D311yescharacteristic
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—22no—
305C22×C4—182no—
306C22×C4—182no—
307C22×C4C22×C3⋊D311yescharacteristic
308SD16—98no—
309D8—98no—
310M16—94no—
311C2×C8—92no—
312C2×C8—91no—
313C2×C8—91no—
314C2×C8—182no—
315C4⋊C4—21no—
316C4⋊C4—22no—
317C4⋊C4—91no—
318C4⋊C4—91no—
319C4⋊C4#63811yescharacteristic
320C4⋊C4#63811yescharacteristic
321C4⋊C4C22×C3⋊D312yes—
322C22⋊C4—22no—
323C22⋊C4—181no—
324C22⋊C4—182no—
325C22⋊C4—182no—
326C22⋊C4#63812yes—
327C42—22no—
328C42—181no—
329C42C22×C3⋊D312yes—
330C22×C3—24no—
331C22×C3—24no—
332C22×C3—28no—
333C22×C3—44no—
334C22×C3—44no—
335C22×C3C4×#6718yes—
336C22×C3C22×#6714yes—
337C2×D3—616no—
338C2×D3—128no—
339C2×D3—128no—
340C2×D3—2416no—
341C3×C4—28no—
342C3×C4—28no—
343C3×C4—28no—
344C3×C4—48no—
345C3×C4C4×#6718yes—
346C3×C4C22×C4×D314yes—
347C3×C4C2×#23514yes—
348Dic3—124no—
349Dic3—124no—
350C32#294611yescharacteristic, complemented, Sylow
351C23—21no—
352C23—182no—
353C23—184no—
354C23—721no—
355C23—721no—
356C23C2×#63811yescharacteristic
357Q8—21no—
358Q8C2×C4×C3⋊D312yes—
359D4—24no—
360D4—21no—
361D4—94no—
362D4—182no—
363D4—184no—
364D4C2×C4×C3⋊D312yes—
365C2×C4—21no—
366C2×C4—24no—
367C2×C4—22no—
368C2×C4—82no—
369C2×C4—81no—
370C2×C4—181no—
371C2×C4—181no—
372C2×C4—722no—
373C2×C4—722no—
374C2×C4C2×C4×C3⋊D312yes—
375C2×C4#382812yes—
376C2×C4C2×#63812yes—
377C2×C4C2×#63812yes—
378C2×C4C2×#63811yescharacteristic
379C2×C4C23×C3⋊D311yescharacteristic
380C8—94no—
381C8—181no—
382C8—181no—
383C2×C3—28no—
384C2×C3—48no—
385C2×C3C2×C4×#6714yes—
386C2×C3#583514yes—
387C2×C3#583714yes—
388D3—1216no—
389C22—21no—
390C22—21no—
391C22—22no—
392C22—41no—
393C22—41no—
394C22—184no—
395C22—362no—
396C22—362no—
397C22—724no—
398C22C4×#63812yes—
399C22C22×#63811yescharacteristic
400C4—22no—
401C4—22no—
402C4—22no—
403C4—42no—
404C4—361no—
405C4—361no—
406C4C4×#63812yes—
407C4C22×C4×C3⋊D311yescharacteristic
408C4C2×#382811yescharacteristic
409C3#8256414yescomplemented
410C2—22no—
411C2—42no—
412C2—364no—
413C2C2×C4×#63811yescharacteristic
414C2#1059630611yescharacteristic
415C2#1059630811yescharacteristic
subgroupG/H
centerC22C22×#638
commutatorC32×C4C23×C4
FrattiniC2×C4C23×C3⋊D3
FittingC32×#520C2
socleC22×C32C22×D4
prime radicalC2×#64158C2
cosocleC2×C32×C4C24
hypercenter#520C3⋊D3
hypocenterC32#2946
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117 ◁ #520

Complements

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

NH ≅ G/Ntype
1. C32×#520C2semidirect
3. #10595992C2semidirect
4. #10592932C2semidirect
5. #10592725C2semidirect
6. C4×#3755C2semidirect
7. #10592713C2semidirect
8. C4×#3753C2semidirect
9. #10592696C2semidirect
10. C2×#63636C2semidirect
11. #10592663C2semidirect
15. C32×C4×Q8C22semidirect
17. C32×C4×D4C22semidirect
22. #64158C4semidirect
33. #63662C22semidirect
34. #63662C22semidirect
35. #63659C22semidirect
36. #63659C22semidirect
39. #63635C22semidirect
40. #63634C22semidirect
41. #63630C22semidirect
42. C4×C3⋊(C3⋊C8)C22semidirect
43. C3×#520D3semidirect
56. C32×#41C2×C4semidirect
66. C2×C4⋊(C3⋊D3)C2×C4semidirect
80. #3755C2×C4semidirect
81. #3753C2×C4semidirect
87. #3748C2×C4semidirect
95. C3×C4×Q8C2×D3semidirect
97. C3×C4×D4C2×D3semidirect
156. #520C3⋊D3semidirect
168. C3×#41C4×D3semidirect
231. C4×Q8C2×C3⋊D3semidirect
237. C4×D4C2×C3⋊D3semidirect
294. #41C4×C3⋊D3semidirect
350. C32#2946semidirect
409. C3#82564semidirect

Maximal subgroups

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

subgroupindex
C32×#5202
C2×#641582
#105959922
#105929322
#105927252
C4×#37552
#105927132
C4×#37532
#105926962
C2×#636362
#105926632
#825643