Finite Group Databasebeta

← #11797762

Subgroups — #11797762

Order 1152.

387 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 387 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592571C211yesmaximal, characteristic
2#10590818C211yesmaximal, characteristic, complemented
3C2×#63549C211yesmaximal, characteristic
4C3×#4492C211yesmaximal, characteristic, complemented
5C3×#4489C211yesmaximal, characteristic, complemented
6#10589116C211yesmaximal, characteristic
7#10589104C211yesmaximal, characteristic, complemented
8#69319—31nomaximal
9#69208—31nomaximal
10C2×#3745C2211yescharacteristic
11#64102—21no—
12C2×C3×Dic12C2211yescharacteristic
13#63843—21no—
14C32×#107C2211yescharacteristic
15C8×C3⋊Dic3C2211yescharacteristic
16#63636—21no—
17C3×#818C2211yescharacteristic
18C2×C3×C3⋊C16C2211yescharacteristic
19C2×C3×C3⋊C16C2211yescharacteristic
20#63565—21no—
21#63549C414yescomplemented
22Dic3×Q16—31no—
23C2×#828—31no—
24C2×#800—31no—
25#4873—31no—
26#4872—31no—
27#4872—31no—
28#4872—61no—
29C3×#366—31no—
30C3×#358—31no—
31#4509—31no—
32#4502—31no—
33#4502—31no—
34#4492D311yescharacteristic, complemented
35#4491—31no—
36#4489D311yescharacteristic, complemented
37C2×C4⋊(C3⋊D3)—21no—
38C2×C4×C3⋊D3—41no—
39C2×C3×Dic6—21no—
40C2×C32×C8C2311yescharacteristic
41C32×C4⋊C4—21no—
42#3752—41no—
43C4×C3⋊Dic3D411yescharacteristic
44C2×C3⋊(C3⋊C8)D411yescharacteristic
45#3745—21no—
46#3745C2×C412yes—
47C3×C4⋊Dic3—21no—
48C3×Dic12—21no—
49C3×Dic12C2×C412yescomplemented
50Dic3⋊Dic3—41no—
51Dic32—41no—
52C3×C3⋊C16—21no—
53C3×C3⋊C16C2×C412yescomplemented
54#2175—91noSylow
55C2×C3×Q16—31no—
56Q8×Dic3—61no—
57C2×Dic12C2×D311yescharacteristic
58C2×D24—31no—
59C2×D24—31no—
60C2×D24—61no—
61#893—61no—
62#893—61no—
63#893—62no—
64#887—61no—
65C2×C3×C16—31no—
66C2×C3×C16—31no—
67C3×#107—21no—
68C3×#107—31no—
69C3×#107C2×D311yescharacteristic
70C3×#107C2×D311yescharacteristic
71#835—61no—
72#828—34no—
73#818C2×D311yescharacteristic
74C8×Dic3—31no—
75C8×Dic3—31no—
76C8×Dic3—61no—
77C2×C3⋊C16C2×D311yescharacteristic
78C2×C3⋊C16C2×D311yescharacteristic
79#810—61no—
80#809—61no—
81#809—61no—
82#809—62no—
83#800—34no—
84C22×C3⋊D3—41no—
85C2×C32×C4—41no—
86C2×C32×C4C2×D411yescharacteristic
87C2×C3⋊Dic3D811yescharacteristic
88C2×C3⋊Dic3D811yescharacteristic
89C4⋊(C3⋊D3)—22no—
90C4⋊(C3⋊D3)—41no—
91C4×C3⋊D3—82no—
92C2×C3×Dic3—41no—
93C2×C3×Dic3—41no—
94C3×Dic6—22no—
95C3×Dic6—41no—
96C32×C8C22×C411yescharacteristic
97C32×C8#4111yescharacteristic
98C3⋊(C3⋊C8)—21no—
99C2×SD32—91no—
100C4×Q16—91no—
101C4×D8—91no—
102#366—31no—
103#358—31no—
104#357—91no—
105#346—91no—
106C2×C3×Q8—61no—
107C2×D12—62no—
108C2×D12—61no—
109C2×D12—61no—
110C2×C4×D3—121no—
111C2×C4×D3—121no—
112C2×C4×D3—122no—
113C2×Dic6—21no—
114C3×Q16—32no—
115C3×Q16—61no—
116C2×C3×C8—21no—
117C2×C3×C8C22×D311yescharacteristic
118C2×C3×C8C22×D311yescharacteristic
119C3×C4⋊C4—22no—
120C3×C4⋊C4—21no—
121C3×C4⋊C4—21no—
122C3×C4⋊C4—61no—
123(C2×D3)⋊C4—121no—
124(C2×D3)⋊C4—121no—
125(C2×D3)⋊C4—122no—
126C4⋊Dic3—21no—
127C4⋊Dic3—121no—
128Dic3⋊C4—121no—
129C4×Dic3—31no—
130C4×Dic3—31no—
131C4×Dic3—61no—
132C4×Dic3—121no—
133C4×Dic3—121no—
134C2×C3⋊C8—31no—
135C2×C3⋊C8—31no—
136C2×C3⋊C8—61no—
137Dic12—21no—
138Dic12C4×D312yescomplemented
139D24—32no—
140D24—32no—
141D24—62no—
142D24—62no—
143D24—61no—
144D24—61no—
145C3×C16—32no—
146C3×C16—61no—
147C3⋊C16—21no—
148C3⋊C16C4×D312yescomplemented
149C22×C32C2×D811yescharacteristic
150C2×C3⋊D3—42no—
151C2×C3⋊D3—81no—
152C2×C3⋊D3—81no—
153C32×C4—81no—
154C32×C4C4×D411yescharacteristic
155C32×C4#13511yescharacteristic
156C3⋊Dic3—21no—
157C3⋊Dic3—21no—
158C3×Dic3—42no—
159C3×Dic3—81no—
160C2×Q16—31no—
161C2×D8—91no—
162C4×Q8—181no—
163C4×D4—181no—
164SD32—94no—
165C2×C16—31no—
166C2×C16—31no—
167#107—31no—
168#107D3211yescharacteristic
169#103—181no—
170#102—181no—
171C4×C8—91no—
172C22×D3—122no—
173C22×D3—121no—
174C22×D3—121no—
175C3×Q8—62no—
176C3×Q8—121no—
177C2×C3×C4—21no—
178C2×C3×C4—42no—
179C2×C3×C4—41no—
180C2×C3×C4—41no—
181C2×C3×C4—121no—
182C2×C3×C4—121no—
183C2×C3×C4D3×D411yescharacteristic
184C2×C3×C4D3×D411yescharacteristic
185C2×Dic3—31no—
186C2×Dic3—31no—
187C2×Dic3—31no—
188C2×Dic3—31no—
189C2×Dic3—41no—
190C2×Dic3—41no—
191C2×Dic3—61no—
192C2×Dic3—61no—
193D12—64no—
194D12—62no—
195D12—62no—
196D12—122no—
197D12—121no—
198D12—121no—
199C4×D3—244no—
200C4×D3—242no—
201C4×D3—242no—
202Dic6—22no—
203Dic6—41no—
204C3×C8—21no—
205C3×C8—21no—
206C3×C8C2×C4×D311yescharacteristic
207C3×C8C2×C4×D311yescharacteristic
208C3×C8#23711yescharacteristic
209C3×C8#23911yescharacteristic
210C3⋊C8—61no—
211C3⋊C8—61no—
212C3⋊C8—121no—
213C2×C32C4×D811yescharacteristic
214C2×C32#50911yescharacteristic
215C2×C32#51011yescharacteristic
216C3⋊D3—82no—
217C2×Q8—61no—
218C2×D4—181no—
219C22×C4—361no—
220Q16—32no—
221Q16—61no—
222D8—92no—
223D8—181no—
224C2×C8—91no—
225C2×C8C2×D3211yescharacteristic
226C4⋊C4—21no—
227C4⋊C4—61no—
228C4⋊C4—361no—
229C22⋊C4—361no—
230C42—91no—
231C42—361no—
232C16—32no—
233C16—61no—
234C22×C3—21no—
235C22×C3D3×D811yescharacteristic
236C22×C3D3×D811yescharacteristic
237C2×D3—124no—
238C2×D3—122no—
239C2×D3—122no—
240C2×D3—242no—
241C2×D3—242no—
242C2×D3—241no—
243C2×D3—241no—
244C2×D3—241no—
245C2×D3—241no—
246C3×C4—21no—
247C3×C4—21no—
248C3×C4—82no—
249C3×C4—81no—
250C3×C4—81no—
251C3×C4—122no—
252C3×C4—241no—
253C3×C4#67⋊C411yescharacteristic
254C3×C4#89311yescharacteristic
255C3×C4#91611yescharacteristic
256C3×C4#91911yescharacteristic
257Dic3—42no—
258Dic3—62no—
259Dic3—61no—
260Dic3—61no—
261Dic3—61no—
262Dic3—61no—
263Dic3—81no—
264Dic3—121no—
265C32#217511yescharacteristic, complemented, Sylow
266C23—361no—
267Q8—62no—
268Q8—121no—
269D4—182no—
270D4—361no—
271C2×C4—41no—
272C2×C4—91no—
273C2×C4—91no—
274C2×C4—121no—
275C2×C4—121no—
276C2×C4—722no—
277C2×C4#381111yescharacteristic
278C8—181no—
279C8#379611yescharacteristic
280C8C4×D3211yescharacteristic
281C2×C3—21no—
282C2×C3—21no—
283C2×C3—21no—
284C2×C3#475611yescharacteristic
285C2×C3#487211yescharacteristic
286C2×C3#491111yescharacteristic
287C2×C3#491411yescharacteristic
288C2×C3#491811yescharacteristic
289C2×C3#491811yescharacteristic
290D3—244no—
291D3—242no—
292D3—242no—
293C22—362no—
294C22—721no—
295C22—721no—
296C22#6392611yescharacteristic
297C4—81no—
298C4—122no—
299C4—181no—
300C4—181no—
301C4—241no—
302C4#6388111yescharacteristic
303C4#6395011yescharacteristic
304C3—21no—
305C3#6920811yescharacteristic, complemented
306C3#6931911yescharacteristic, complemented
307C2—722no—
308C2#1059045911yescharacteristic
309C2#1059103611yescharacteristic
310C2#1059104411yescharacteristic
subgroupG/H
centerC22#63926
commutatorC32×C8C22×C4
FrattiniC2×C8C2×D32
FittingC32×#107C22
socleC22×C32C2×D8
prime radicalC2×#3745C22
cosocleC2×C32×C8C23
hypercenter#107D32
hypocenterC32#2175
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #107

Complements

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

NH ≅ G/Ntype
2. #10590818C2semidirect
4. C3×#4492C2semidirect
5. C3×#4489C2semidirect
7. #10589104C2semidirect
21. #63549C4semidirect
34. #4492D3semidirect
36. #4489D3semidirect
49. C3×Dic12C2×C4semidirect
53. C3×C3⋊C16C2×C4semidirect
138. Dic12C4×D3semidirect
148. C3⋊C16C4×D3semidirect
265. C32#2175semidirect
305. C3#69208semidirect
306. C3#69319semidirect

Maximal subgroups

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

subgroupindex
#105925712
#105908182
C2×#635492
C3×#44922
C3×#44892
#105891162
#105891042
#693193
#692083