Finite Group Databasebeta

← #11772556

Subgroups — #11772556

Order 1152.

444 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 40 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#10593826C211yesmaximal, characteristic
2#10593825C211yesmaximal, characteristic
3C3⋊D3×#99C211yesmaximal, characteristic
4C23×#157C411yescharacteristic, complemented
5C2×D4×C3⋊D3C2211yescharacteristic
6C2×C22⋊#157—21no—
7C2×C22⋊#157C411yescharacteristic, complemented
8#64283—21no—
9C22⋊C4×C3⋊D3—21no—
10#63788—21no—
11#63788C412yescomplemented
12#63781—21no—
13C32×#99C411yescharacteristic, complemented
14#63661C411yescharacteristic, complemented
15#63633—21no—
16D3×#99—62no—
17C23×C3⋊D3C2×C411yescharacteristic
18C23×C3⋊D3D411yescharacteristic
19C22×#157—21no—
20C22×#157—21no—
21C22×#157—42no—
22C22×#157—41no—
23C2×C32×D4C2×C411yescharacteristic
24C2×#638C2×C411yescharacteristic
25C2×#638D411yescharacteristic
26D4×C3⋊D3—41no—
27D4×C3⋊D3—41no—
28C2×C4⋊(C3⋊D3)Q811yescharacteristic
29C2×C4×C3⋊D3—41no—
30C2×C4×C3⋊D3D411yescharacteristic
31C22⋊#157—42no—
32C22⋊#157—41no—
33#3792—22no—
34#3788—41no—
35#3787—41no—
36C32×C22⋊C4—21no—
37#3757—21no—
38#3752—41no—
39#1390—91nomaximal, Sylow
40C2×D3×D4—62no—
41D3×C22⋊C4—64no—
42C3×#99—22no—
43#834—62no—
44#806—64no—
45C23×C32C4211yescharacteristic
46C23×C32C22⋊C411yescharacteristic
47C22×C3⋊D3—21no—
48C22×C3⋊D3—21no—
49C22×C3⋊D3—21no—
50C22×C3⋊D3—21no—
51C22×C3⋊D3—41no—
52C22×C3⋊D3—41no—
53C22×C3⋊D3—41no—
54C22×C3⋊D3—41no—
55C22×C3⋊D3C22⋊C411yescharacteristic
56C22×C3⋊D3C4⋊C411yescharacteristic
57C22×C3⋊D3C4⋊C411yescharacteristic
58C2×#157—22no—
59C2×#157—41no—
60C2×#157—42no—
61C2×#157—41no—
62C2×#157—42no—
63C2×#157—41no—
64C2×#157—41no—
65C2×#157—41no—
66C32×D4—41no—
67C2×C32×C4—41no—
68C2×C32×C4C4⋊C411yescharacteristic
69#638—41no—
70#638—41no—
71C2×C3⋊Dic3—41no—
72C2×C3⋊Dic3C22⋊C411yescharacteristic
73C4⋊(C3⋊D3)—41no—
74C4×C3⋊D3—21no—
75C4×C3⋊D3—21no—
76C4×C3⋊D3—81no—
77C4×C3⋊D3—81no—
78#622—42no—
79C2×#100—91no—
80C2×#99—91no—
81#386—91no—
82C23×D3—62no—
83C23×D3—62no—
84C2×C3×D4—22no—
85C2×#67—62no—
86C2×#67—62no—
87D3×D4—124no—
88D3×D4—124no—
89C2×D12—62no—
90C2×C4×D3—62no—
91C2×C4×D3—124no—
92C3×C22⋊C4—24no—
93#217—64no—
94(C2×D3)⋊C4—124no—
95C22×C32—21no—
96C22×C32—21no—
97C22×C32—41no—
98C22×C32—41no—
99C22×C32#9511yescharacteristic
100C2×C3⋊D3—21no—
101C2×C3⋊D3—21no—
102C2×C3⋊D3—21no—
103C2×C3⋊D3—21no—
104C2×C3⋊D3—41no—
105C2×C3⋊D3—41no—
106C2×C3⋊D3—42no—
107C2×C3⋊D3—41no—
108C2×C3⋊D3—41no—
109C2×C3⋊D3—41no—
110C2×C3⋊D3—41no—
111C2×C3⋊D3—81no—
112C2×C3⋊D3#9911yescharacteristic
113C2×C3⋊D3#9911yescharacteristic
114#157—42no—
115#157—81no—
116C32×C4—21no—
117C32×C4—81no—
118C3⋊Dic3—21no—
119C3⋊Dic3—81no—
120C22×D4—91no—
121C23×C4—91no—
122C2×M16—181no—
123C2×C22⋊C4—91no—
124C2×C22⋊C4—181no—
125C2×C22⋊C4—181no—
126#100—92no—
127#100—181no—
128#99—91no—
129#99—181no—
130#99#15711yescharacteristic, complemented
131#95—181no—
132C23×C3—22no—
133C23×C3—22no—
134C22×D3—62no—
135C22×D3—62no—
136C22×D3—62no—
137C22×D3—64no—
138C22×D3—64no—
139C22×D3—122no—
140C22×D3—122no—
141C22×D3—242no—
142C22×D3—242no—
143C22×D3—242no—
144C22×D3—242no—
145C3×D4—44no—
146C2×C3×C4—22no—
147C2×C3×C4—44no—
148#67—124no—
149#67—124no—
150C2×Dic3—62no—
151C2×Dic3—124no—
152D12—124no—
153C4×D3—122no—
154C4×D3—122no—
155C4×D3—244no—
156C4×D3—244no—
157C2×C32—21no—
158C2×C32—41no—
159C2×C32—41no—
160C2×C32#34211yescharacteristic
161C3⋊D3—21no—
162C3⋊D3—41no—
163C3⋊D3—41no—
164C3⋊D3AΣL(1,𝔽16)11yescharacteristic
165C3⋊D3#35211yescharacteristic
166C24—91no—
167C24—91no—
168C2×D4—91no—
169C2×D4—91no—
170C2×D4—91no—
171C2×D4—361no—
172C2×D4—361no—
173C2×D4C2×#15711yescharacteristic
174C22×C4—91no—
175C22×C4—181no—
176C22×C4—181no—
177C22×C4—361no—
178C22×C4—362no—
179C22×C4—361no—
180M16—182no—
181M16—361no—
182C2×C8—361no—
183C22⋊C4—21no—
184C22⋊C4—181no—
185C22⋊C4—361no—
186C22⋊C4—362no—
187C22⋊C4—361no—
188C22×C3—24no—
189C22×C3—22no—
190C22×C3—42no—
191C22×C3—82no—
192C22×C3—82no—
193C2×D3—62no—
194C2×D3—62no—
195C2×D3—64no—
196C2×D3—122no—
197C2×D3—122no—
198C2×D3—122no—
199C2×D3—124no—
200C2×D3—124no—
201C2×D3—242no—
202C2×D3—242no—
203C2×D3—242no—
204C2×D3—244no—
205C2×D3—242no—
206C2×D3—244no—
207C3×C4—42no—
208C3×C4—84no—
209Dic3—122no—
210Dic3—244no—
211C32#139011yescharacteristic, complemented, Sylow
212C23—91no—
213C23—91no—
214C23—91no—
215C23—181no—
216C23—181no—
217C23—181no—
218C23—181no—
219C23—361no—
220C23—361no—
221C23—361no—
222C23—361no—
223C23C4×#15711yescharacteristic
224C23C22⋊#15711yescharacteristic
225D4—41no—
226D4—361no—
227D4—361no—
228D4—361no—
229C2×C4—41no—
230C2×C4—91no—
231C2×C4—181no—
232C2×C4—181no—
233C2×C4—182no—
234C2×C4—361no—
235C2×C4—361no—
236C2×C4—362no—
237C2×C4—362no—
238C2×C4—361no—
239C2×C4—361no—
240C2×C4—361no—
241C2×C4—361no—
242C2×C4—721no—
243C2×C4—721no—
244C2×C4C4⋊#15711yescharacteristic
245C8—362no—
246C2×C3—22no—
247C2×C3—42no—
248C2×C3—44no—
249C2×C3—82no—
250D3—62no—
251D3—62no—
252D3—122no—
253D3—124no—
254D3—242no—
255C22—21no—
256C22—21no—
257C22—41no—
258C22—41no—
259C22—91no—
260C22—91no—
261C22—181no—
262C22—181no—
263C22—181no—
264C22—181no—
265C22—361no—
266C22—361no—
267C22—361no—
268C22—361no—
269C22—361no—
270C22—361no—
271C22—362no—
272C22—721no—
273C22#6378111yescharacteristic
274C4—21no—
275C4—81no—
276C4—181no—
277C4—362no—
278C4—721no—
279C4—721no—
280C3—22no—
281C2—21no—
282C2—41no—
283C2—41no—
284C2—91no—
285C2—91no—
286C2—181no—
287C2—361no—
288C2—361no—
289C2#1059015511yescharacteristic
subgroupG/H
centerC2#10590155
commutatorC23×C32C42
FrattiniC2×D4C2×#157
FittingC32×#99C4
socleC2×C32#342
prime radical, cosocleC2×D4×C3⋊D3C22
hypercenter#99#157
hypocenterC32#1390
LCSG ▷ C23×C32 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #99

Complements

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

NH ≅ G/Ntype
4. C23×#157C4semidirect
7. C2×C22⋊#157C4semidirect
11. #63788C4semidirect
13. C32×#99C4semidirect
14. #63661C4semidirect
130. #99#157semidirect
211. C32#1390semidirect

Maximal subgroups

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

subgroupindex
#105938262
#105938252
C3⋊D3×#992
#13909