Finite Group Databasebeta

← #11860232

Subgroups — #11860232

Order 1152.

1057 conjugacy classes of subgroups.

The subgroup lattice has 351 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594958C212yesmaximal, complemented
2C2×#63822C211yesmaximal, characteristic
3C2×#63642C211yesmaximal, characteristic, complemented
4C3×#5113C212yesmaximal, complemented
5#10591138C211yesmaximal, characteristic, complemented
6#10590791C212yesmaximal, complemented
7#10590743C214yesmaximal, complemented
8#10590741C212yesmaximal, complemented
9#78819—32nomaximal
10C2×C3×#235C2212yes—
11C22×C32×C8C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C3×#926C2212yes—
15#67⋊Dic3—24no—
16#63898C2214yes—
17C4×D3×Dic3—22no—
18#63855—22no—
19#63843C2214yes—
20C2×#3718C2211yescharacteristic
21C2×#3715C2212yes—
22#63822C418yescomplemented
23C2×#3713C2211yescharacteristic
24#63642C2212yes—
25#63642C2212yes—
26C3×#821C2214yes—
27C3×#816C2214yes—
28#63576C2212yes—
29#63574C2212yes—
30Dic3×#41—32no—
31C2×#950—32no—
32#5522—32no—
33C3×#416—32no—
34#5113D312yescomplemented
35C2×#815—32no—
36C2×#815—61no—
37#4998—32no—
38#4817—34no—
39#4789—34no—
40#4785—34no—
41#4757—34no—
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3D412yes—
44C2×C3×#67—22no—
45C3×#235—24no—
46C3×#235C2×C418yescomplemented
47C2×C3×D12C2312yes—
48C2×C3×C4×D3—22no—
49C2×C3×Dic6C2312yes—
50C2×D3×Dic3—24no—
51C2×C32×C8—22no—
52C2×C32×C8C2312yes—
53C4×C3⋊Dic3D412yes—
54C4×C3⋊Dic3C2312yes—
55C2×C3⋊(C3⋊C8)C2×C414yescomplemented
56C2×C3⋊(C3⋊C8)C2311yescharacteristic
57C2×C3⋊(C3⋊C8)C2311yescharacteristic
58C3×#217—22no—
59C3×C4⋊Dic3C2314yes—
60C3×C4×Dic3—22no—
61Dic3⋊Dic3—24no—
62(C2×D3)⋊Dic3—24no—
63Dic32—24no—
64#3718C2×C414yescomplemented
65#3715C2×C418yescomplemented
66#3713C2×C414yescomplemented
67#2943—91noSylow
68C2×C3×#41—32no—
69C2×#235C2×D312yes—
70C22×C3×C8—21no—
71C22×C3×C8C2×D312yes—
72C3×#117—32no—
73#950—316no—
74Q8×Dic3—34no—
75C2×#216—32no—
76C2×#215—32no—
77D4×Dic3—34no—
78D4×Dic3—64no—
79C2×#214—32no—
80C2×#213—32no—
81#926—62no—
82#926C2×D312yes—
83C2×C4×Dic3—32no—
84C2×C4×Dic3—61no—
85C2×C4×Dic3—62no—
86C22×C3⋊C8—32no—
87C22×C3⋊C8—61no—
88#893—34no—
89#887—34no—
90#67⋊C4—64no—
91#872—62no—
92C42×D3—62no—
93C3×#103—34no—
94C3×#102—34no—
95#821C2×D314yes—
96#816C2×D314yes—
97#815—34no—
98#815—34no—
99#815—62no—
100#815—62no—
101#808—34no—
102#807—34no—
103C23×C32C2×D411yescharacteristic
104C22×C3×D3—22no—
105C2×C32×C4C22×C412yes—
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4#4112yes—
108C2×C32×C4C2411yescharacteristic
109C2×C3⋊Dic3—42no—
110C2×C3⋊Dic3C2×D414yes—
111C3×#67—28no—
112C2×C3×Dic3—22no—
113C2×C3×Dic3—24no—
114C3×D12—22no—
115C3×D12C22×C414yes—
116C3×C4×D3—28no—
117C3×Dic6—22no—
118C3×Dic6C22×C414yes—
119D3×Dic3—48no—
120C32×C8—22no—
121C3⋊(C3⋊C8)C22×C412yes—
122C3⋊(C3⋊C8)C22×C412yes—
123C2×#135—91no—
124C4×#41—92no—
125#442—92no—
126#441—92no—
127#440—94no—
128#427—91no—
129#416—32no—
130C2×#97—91no—
131C3×#41—38no—
132C3×#41—64no—
133C2×C3×Q8—32no—
134C2×C3×D4—32no—
135C2×C3×D4—62no—
136C22×C3×C4—21no—
137C22×C3×C4—62no—
138C22×C3×C4C22×D312yes—
139C2×#67—22no—
140C22×Dic3—34no—
141C22×Dic3—62no—
142C22×Dic3—64no—
143#235—24no—
144#235C4×D318yescomplemented
145C2×D12C22×D312yes—
146C2×C4×D3—22no—
147C2×C4×D3—64no—
148C2×Dic6C22×D312yes—
149C2×C3×C8—24no—
150C2×C3×C8—24no—
151C2×C3×C8—22no—
152C2×C3×C8C22×D314yes—
153C3×C4⋊C4—34no—
154C3×C22⋊C4—62no—
155C3×C42—62no—
156#217—22no—
157#217—64no—
158#216—38no—
159#215—38no—
160#214—38no—
161#213—38no—
162(C2×D3)⋊C4—64no—
163C4⋊Dic3—64no—
164C4⋊Dic3C22×D314yes—
165Dic3⋊C4—64no—
166C4×Dic3—22no—
167C4×Dic3—32no—
168C4×Dic3—32no—
169C4×Dic3—34no—
170C4×Dic3—62no—
171C4×Dic3—62no—
172C4×Dic3—64no—
173C4×Dic3—64no—
174C2×C3⋊C8—38no—
175C2×C3⋊C8—32no—
176C2×C3⋊C8—32no—
177C2×C3⋊C8—61no—
178C2×C3⋊C8—61no—
179C2×C3⋊C8—64no—
180C22×C32—22no—
181C22×C32C4×D412yes—
182C22×C32C22×D411yescharacteristic
183C2×C3×D3—24no—
184C2×C3×D3—44no—
185C32×C4C4×D412yes—
186C32×C4C23×C411yescharacteristic
187C32×C4C2×#4111yescharacteristic
188C3⋊Dic3—24no—
189C3×Dic3—24no—
190C3×Dic3—44no—
191C2×#41—32no—
192#135—98no—
193C2×Q16—91no—
194C2×SD16—92no—
195C2×D8—91no—
196C22×C8—91no—
197C22×C8D3211yescharacteristic
198C4×Q8—94no—
199C4×D4—94no—
200C4×D4—184no—
201#117—32no—
202#117—182no—
203C2×C42—91no—
204C2×C42—182no—
205#107—92no—
206#106—92no—
207#103—34no—
208#102—34no—
209#97—92no—
210#97—92no—
211C23×C3—21no—
212C23×C3—62no—
213C23×C3D3×D412yes—
214C22×D3—22no—
215C3×Q8—34no—
216C3×Q8—62no—
217C3×D4—34no—
218C3×D4—68no—
219C3×D4—62no—
220C2×C3×C4—21no—
221C2×C3×C4—22no—
222C2×C3×C4—21no—
223C2×C3×C4—22no—
224C2×C3×C4—62no—
225C2×C3×C4—68no—
226C2×C3×C4—64no—
227C2×C3×C4C2×C4×D314yes—
228C2×C3×C4D3×D412yes—
229C2×C3×C4#23714yes—
230C2×C3×C4C23×D312yes—
231#67—28no—
232C2×Dic3—22no—
233C2×Dic3—24no—
234C2×Dic3—34no—
235C2×Dic3—34no—
236C2×Dic3—64no—
237C2×Dic3—128no—
238C2×Dic3—124no—
239C2×Dic3—124no—
240D12—22no—
241D12C2×C4×D314yes—
242C4×D3—28no—
243C4×D3—128no—
244Dic6—22no—
245Dic6C2×C4×D314yes—
246C3×C8—24no—
247C3×C8—24no—
248C3⋊C8—34no—
249C3⋊C8—34no—
250C3⋊C8—62no—
251C3⋊C8—62no—
252C2×C32—22no—
253C2×C32C2×C4×D411yescharacteristic
254C2×C32#57512yes—
255C3×D3—44no—
256#41—38no—
257#41—64no—
258C2×Q8—32no—
259C2×D4—32no—
260C2×D4—62no—
261C22×C4—62no—
262C22×C4—92no—
263C22×C4—184no—
264C22×C4C2×D3211yescharacteristic
265Q16—94no—
266SD16—98no—
267D8—94no—
268C2×C8—22no—
269C2×C8—91no—
270C2×C8—91no—
271C2×C8—94no—
272C2×C8C2×D3212yes—
273C4⋊C4—34no—
274C4⋊C4—184no—
275C22⋊C4—62no—
276C22⋊C4—184no—
277C42—62no—
278C42—92no—
279C42—92no—
280C42—184no—
281C22×C3—24no—
282C22×C3—24no—
283C22×C3—21no—
284C22×C3—22no—
285C22×C3—64no—
286C22×C3—124no—
287C22×C3#67⋊C414yes—
288C22×C3C2×D3×D412yes—
289C2×D3—24no—
290C2×D3—44no—
291C3×C4—21no—
292C3×C4—21no—
293C3×C4—22no—
294C3×C4—64no—
295C3×C4—124no—
296C3×C4#67⋊C414yes—
297C3×C4C22×C4×D312yes—
298C3×C4C2×#23712yes—
299Dic3—24no—
300Dic3—44no—
301Dic3—64no—
302Dic3—64no—
303Dic3—124no—
304C32#294311yescharacteristic, complemented, Sylow
305C23—62no—
306C23#380211yescharacteristic
307Q8—34no—
308Q8—62no—
309D4—34no—
310D4—68no—
311D4—62no—
312C2×C4—62no—
313C2×C4—68no—
314C2×C4—64no—
315C2×C4—94no—
316C2×C4—368no—
317C2×C4—362no—
318C2×C4C4×D3212yes—
319C2×C4#380211yescharacteristic
320C2×C4#380512yes—
321C2×C4C22×D3211yescharacteristic
322C8—22no—
323C8—92no—
324C8—92no—
325C2×C3—24no—
326C2×C3—24no—
327C2×C3—22no—
328C2×C3—21no—
329C2×C3—124no—
330C2×C3C2×#67⋊C412yes—
331C2×C3#576814yes—
332D3—44no—
333C22—22no—
334C22—64no—
335C22—124no—
336C22#6390212yes—
337C22C2×#380211yescharacteristic
338C4—64no—
339C4—124no—
340C4—184no—
341C4#6390212yes—
342C4C2×C4×D3211yescharacteristic
343C4C2×#380511yescharacteristic
344C3—21no—
345C3#7881912yescomplemented
346C2—22no—
347C2—124no—
348C2#1059468512yes—
349C2C2×#6390211yescharacteristic
subgroupG/H
centerC2×C4#3802
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
prime radicalC2×#63822C2
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32#2943
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. #10594958C2semidirect
3. C2×#63642C2semidirect
4. C3×#5113C2semidirect
5. #10591138C2semidirect
6. #10590791C2semidirect
7. #10590743C2semidirect
8. #10590741C2semidirect
22. #63822C4semidirect
34. #5113D3semidirect
46. C3×#235C2×C4semidirect
55. C2×C3⋊(C3⋊C8)C2×C4semidirect
64. #3718C2×C4semidirect
65. #3715C2×C4semidirect
66. #3713C2×C4semidirect
144. #235C4×D3semidirect
304. C32#2943semidirect
345. C3#78819semidirect

Maximal subgroups

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

subgroupindex
#105949582
C2×#638222
C2×#636422
C3×#51132
#105911382
#105907912
#105907432
#105907412
#788193