Finite Group Databasebeta

← #11895490

Subgroups — #11895490

Order 1152.

778 conjugacy classes of subgroups.

The subgroup lattice has 315 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#634C211yesmaximal, characteristic
2C3×#5570C211yesmaximal, characteristic
3C3×Q8×C3⋊C8C211yesmaximal, characteristic
4#10590388C213yesmaximal
5C4×#3719C213yesmaximal
6#10590287C213yesmaximal
7#10590283C213yesmaximal
8#83696—31nomaximal
9#79933—31nomaximal
10C32×C4×Q8C2211yescharacteristic
11Q8×C3⋊Dic3—21no—
12#64097—23no—
13#64078C2213yes—
14C4×#634C2213yes—
15C3×Q8×Dic3—21no—
16C3×#890—23no—
17C3×#869C2213yes—
18C3×C4×Dic6C2213yes—
19C2×#3719C2213yes—
20C3×C4⋊(C3⋊C8)C2213yes—
21C3×C4×C3⋊C8C2213yes—
22#63575C2213yes—
23#63567C2211yescharacteristic
24#63566C2216yes—
25#63566C2213yes—
26C3×#557—31no—
27#5570D311yescharacteristic
28Q8×Dic6—31no—
29Q8×Dic6—31no—
30Q8×Dic6—61no—
31C3×C8×Q8—31no—
32#5090—33no—
33#5079—33no—
34C4×#216—33no—
35Q8×C3⋊C8D311yescharacteristic
36#5021—33no—
37#4850—33no—
38#4849—33no—
39C4×Dic12—33no—
40#4681—33no—
41C2×C32×Q8D411yescharacteristic
42C2×#634—23no—
43C2×#634C2311yescharacteristic
44C2×C3×Dic6C2313yes—
45C32×C4⋊C4D413yes—
46C32×C42C2313yes—
47C4⋊(C3⋊Dic3)—23no—
48C4⋊(C3⋊Dic3)C2313yes—
49#3750—23no—
50C4×C3⋊Dic3—23no—
51C3×C4⋊Dic3—23no—
52C3×C4⋊Dic3—23no—
53C3×C4⋊Dic3C2311yescharacteristic
54C3×Dic3⋊C4—23no—
55C3×C4×Dic3—23no—
56C2×C3×C3⋊C8C2311yescharacteristic
57C2×C3×C3⋊C8C2313yes—
58#3719—26no—
59#3363—91noSylow
60C3×C4⋊Q8—33no—
61C3×#125—63no—
62C3×C4×Q8—21no—
63C3×C4×Q8—33no—
64C3×C4×Q8—61no—
65C3×C4×Q8C2×D311yescharacteristic
66C3×C4×Q8C2×D311yescharacteristic
67Q8×Dic3—21no—
68Q8×Dic3—62no—
69Q8×Dic3—61no—
70Q8×Dic3—61no—
71C2×#216—33no—
72C2×Dic12—33no—
73#890—23no—
74#888—66no—
75#888—63no—
76#888—63no—
77#869—33no—
78#869—33no—
79#869—63no—
80#869C2×D313yes—
81C4×Dic6—33no—
82C4×Dic6—33no—
83C4×Dic6—63no—
84C4×Dic6C2×D313yes—
85C3×C4⋊C8—33no—
86C3×C4×C8—33no—
87#835—36no—
88#835—33no—
89#818—33no—
90#816—33no—
91#816—36no—
92#816—31no—
93#810—31no—
94#807—33no—
95C4⋊(C3⋊C8)C2×D313yes—
96C4×C3⋊C8C2×D313yes—
97C32×Q8Q1614yescomplemented
98C2×C32×C4C2×D413yes—
99C2×C32×C4C2×D413yes—
100C2×C32×C4C2411yescharacteristic
101C2×C3⋊Dic3—21no—
102C2×C3⋊Dic3—23no—
103#634—21no—
104#634—83no—
105#634#4112yes—
106C2×C3×Dic3—21no—
107C2×C3×Dic3—23no—
108C3×Dic6—23no—
109C3×Dic6—23no—
110C3×C3⋊C8—23no—
111C3×C3⋊C8—21no—
112Q82—91no—
113#557—31no—
114#487—93no—
115#477—93no—
116#462—93no—
117C8×Q8—31no—
118C4×Q16—93no—
119C2×C3×Q8—21no—
120C2×C3×Q8—33no—
121C2×C3×Q8D1211yescharacteristic
122C2×C3×Q8#6711yescharacteristic
123C2×Dic6—31no—
124C2×Dic6—31no—
125C2×Dic6—61no—
126C2×Dic6—66no—
127C2×Dic6—63no—
128C2×Dic6—63no—
129C2×Dic6C22×D313yes—
130C2×C3×C8—31no—
131C2×C3×C8—33no—
132C3×C4⋊C4—23no—
133C3×C4⋊C4—31no—
134C3×C4⋊C4—63no—
135C3×C4⋊C4—63no—
136C3×C4⋊C4—63no—
137C3×C4⋊C4D1213yes—
138C3×C4⋊C4#6713yes—
139C3×C42—23no—
140C3×C42—63no—
141C3×C42C22×D313yes—
142C3×C42C22×D313yes—
143#216—66no—
144C4⋊Dic3—23no—
145C4⋊Dic3—23no—
146C4⋊Dic3—33no—
147C4⋊Dic3—33no—
148C4⋊Dic3—63no—
149C4⋊Dic3—66no—
150C4⋊Dic3—63no—
151C4⋊Dic3—63no—
152C4⋊Dic3C22×D311yescharacteristic
153Dic3⋊C4—23no—
154Dic3⋊C4—66no—
155Dic3⋊C4—63no—
156Dic3⋊C4—63no—
157C4×Dic3—23no—
158C4×Dic3—66no—
159C4×Dic3—63no—
160C4×Dic3—63no—
161C2×C3⋊C8C22×D311yescharacteristic
162C2×C3⋊C8C22×D313yes—
163Dic12—66no—
164C22×C32C22×D411yescharacteristic
165C32×C4—23no—
166C32×C4C2×Q1616yes—
167C32×C4C2×#4111yescharacteristic
168C32×C42−1+411yescharacteristic
169C3⋊Dic3—22no—
170C3⋊Dic3—43no—
171C3×Dic3—43no—
172C3×Dic3—41no—
173C2×Q16—93no—
174C4⋊Q8—33no—
175C4⋊Q8—93no—
176C4⋊Q8—183no—
177#125—63no—
178C4×Q8—33no—
179C4×Q8—61no—
180C4×Q8—93no—
181C4×Q8—181no—
182C4×Q8D3211yescharacteristic
183#107—93no—
184C4⋊C8—33no—
185#103—91no—
186#103—93no—
187#103—96no—
188C4×C8—33no—
189C3×Q8—24no—
190C3×Q8—63no—
191C3×Q8—63no—
192C3×Q8Dic1214yescomplemented
193C3×Q8#21614yescomplemented
194C2×C3×C4—21no—
195C2×C3×C4—23no—
196C2×C3×C4—23no—
197C2×C3×C4—61no—
198C2×C3×C4—63no—
199C2×C3×C4C2×D1213yes—
200C2×C3×C4C2×D1213yes—
201C2×C3×C4C2×#6713yes—
202C2×C3×C4C2×#6713yes—
203C2×C3×C4C23×D311yescharacteristic
204C2×C3×C4C23×D311yescharacteristic
205C2×Dic3—21no—
206C2×Dic3—23no—
207C2×Dic3—62no—
208C2×Dic3—61no—
209C2×Dic3—61no—
210C2×Dic3—66no—
211C2×Dic3—63no—
212C2×Dic3—63no—
213Dic6—23no—
214Dic6—23no—
215Dic6—32no—
216Dic6—32no—
217Dic6—62no—
218Dic6—62no—
219Dic6—61no—
220Dic6—61no—
221Dic6—243no—
222Dic6—243no—
223Dic6—246no—
224C3×C8—63no—
225C3×C8—61no—
226C3⋊C8—21no—
227C3⋊C8—23no—
228C2×C32#54811yescharacteristic
229C2×C32C22×Q1611yescharacteristic
230C2×C32#57711yescharacteristic
231C2×Q8—33no—
232C2×Q8—91no—
233C2×Q8—183no—
234C2×Q8#62611yescharacteristic
235Q16—186no—
236C2×C8—31no—
237C2×C8—33no—
238C4⋊C4—31no—
239C4⋊C4—63no—
240C4⋊C4—63no—
241C4⋊C4—63no—
242C4⋊C4—93no—
243C4⋊C4—183no—
244C4⋊C4—183no—
245C4⋊C4#62613yes—
246C42—63no—
247C42—183no—
248C42C2×D3213yes—
249C22×C3—21no—
250C22×C3C22×D1211yescharacteristic
251C22×C3C22×#6711yescharacteristic
252C3×C4—23no—
253C3×C4—23no—
254C3×C4—21no—
255C3×C4—21no—
256C3×C4—26no—
257C3×C4—43no—
258C3×C4—121no—
259C3×C4—123no—
260C3×C4C2×Dic1216yes—
261C3×C4C2×#21616yes—
262C3×C4#100711yescharacteristic
263C3×C4D3×#4111yescharacteristic
264C3×C4D3×#4111yescharacteristic
265C3×C4#101011yescharacteristic
266Dic3—43no—
267Dic3—41no—
268Dic3—64no—
269Dic3—62no—
270Dic3—62no—
271Dic3—126no—
272Dic3—123no—
273Dic3—123no—
274C32#336311yescharacteristic, complemented, Sylow
275Q8—63no—
276Q8—63no—
277Q8—92no—
278Q8—181no—
279Q8—723no—
280Q8#371914yescomplemented
281C2×C4—61no—
282C2×C4—63no—
283C2×C4—181no—
284C2×C4—183no—
285C2×C4C2×#62613yes—
286C2×C4C2×#62613yes—
287C2×C4C22×D3211yescharacteristic
288C8—61no—
289C8—63no—
290C2×C3—21no—
291C2×C3—21no—
292C2×C3—21no—
293C2×C3#557611yescharacteristic
294C2×C3C22×Dic1211yescharacteristic
295C2×C3#575111yescharacteristic
296C2×C3C22×#21611yescharacteristic
297C2×C3#583111yescharacteristic
298C2×C3#583711yescharacteristic
299C22C22×#62611yescharacteristic
300C4—23no—
301C4—123no—
302C4—121no—
303C4—182no—
304C4—363no—
305C4C2×#371916yes—
306C4#6431511yescharacteristic
307C4#6431911yescharacteristic
308C3—21no—
309C3#7993311yescharacteristic, complemented
310C3#8369611yescharacteristic, complemented
311C2C22×#371911yescharacteristic
312C2#1059541411yescharacteristic
313C2#1059544811yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socle, prime radicalC22×C32C22×D4
hypercenterC4×Q8D32
hypocenterC32#3363
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
97. C32×Q8Q16semidirect
192. C3×Q8Dic12semidirect
193. C3×Q8#216semidirect
274. C32#3363semidirect
280. Q8#3719semidirect
309. C3#79933semidirect
310. C3#83696semidirect

Maximal subgroups

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

subgroupindex
Q8×#6342
C3×#55702
C3×Q8×C3⋊C82
#105903882
C4×#37192
#105902872
#105902832
#836963
#799333