Finite Group Databasebeta

← #11772557

Subgroups — #11772557

Order 1152.

520 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 44 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
1C2×#63788C211yesmaximal, characteristic
2C2×#63786C211yesmaximal, characteristic
3#10592912C211yesmaximal, characteristic
4C23×C32×C4C411yescharacteristic, complemented
5C22×#638C2211yescharacteristic
6C2×C22⋊#157—21no—
7C2×#3792—21no—
8C2×#3757C411yescharacteristic, complemented
9C2×#3752—21no—
10#63788—21no—
11#63788C412yescomplemented
12#63786—21no—
13#63786C412yescomplemented
14#63658—21no—
15#5213—62no—
16C24×C32C2×C411yescharacteristic
17C23×C3⋊D3D411yescharacteristic
18C22×#157—41no—
19C22×C32×C4—21no—
20C22×C32×C4—42no—
21C22×C32×C4—41no—
22C2×#638—41no—
23C2×#638—41no—
24C2×#638C2×C411yescharacteristic
25C2×#638C2×C411yescharacteristic
26C2×#638D411yescharacteristic
27C2×#638Q811yescharacteristic
28C22×C3⋊Dic3—21no—
29C22×C3⋊Dic3D411yescharacteristic
30C22⋊#157—22no—
31C22⋊#157—41no—
32#3792—22no—
33#3792—41no—
34C2×#622—41no—
35#3757—41no—
36#3752—42no—
37#1390—91nomaximal, Sylow
38C23×C3×C4—22no—
39C22×#67—62no—
40C2×#217—62no—
41C2×(C2×D3)⋊C4—64no—
42C3⋊#95—64no—
43C23×C32—21no—
44C23×C32—21no—
45C23×C32—41no—
46C23×C32—41no—
47C23×C32C4211yescharacteristic
48C23×C32C22⋊C411yescharacteristic
49C23×C32C4⋊C411yescharacteristic
50C22×C3⋊D3—21no—
51C22×C3⋊D3—21no—
52C22×C3⋊D3—41no—
53C22×C3⋊D3—41no—
54C22×C3⋊D3C22⋊C411yescharacteristic
55C22×C3⋊D3C4⋊C411yescharacteristic
56C2×#157—42no—
57C2×#157—81no—
58C2×#157—81no—
59C2×C32×C4—22no—
60C2×C32×C4—41no—
61C2×C32×C4—42no—
62C2×C32×C4—41no—
63C2×C32×C4—42no—
64#638—41no—
65#638—41no—
66#638—41no—
67#638—41no—
68C2×C3⋊Dic3—21no—
69C2×C3⋊Dic3—21no—
70C2×C3⋊Dic3—41no—
71C2×C3⋊Dic3—41no—
72C2×C3⋊Dic3—41no—
73C2×C3⋊Dic3C22⋊C411yescharacteristic
74C2×C3⋊Dic3C4⋊C411yescharacteristic
75#622—42no—
76C2×#100—91no—
77C2×#99—91no—
78#386—91no—
79C24×C3—22no—
80C23×D3—62no—
81C22×C3×C4—24no—
82C22×C3×C4—48no—
83C22×C3×C4—44no—
84C2×#67—62no—
85C2×#67—62no—
86C2×#67—62no—
87C2×#67—62no—
88C2×#67—124no—
89C2×#67—124no—
90C22×Dic3—62no—
91C22×Dic3—64no—
92#217—124no—
93(C2×D3)⋊C4—128no—
94C22×C32—21no—
95C22×C32—21no—
96C22×C32—21no—
97C22×C32—21no—
98C22×C32—41no—
99C22×C32—41no—
100C22×C32—42no—
101C22×C32—41no—
102C22×C32—41no—
103C22×C32#9511yescharacteristic
104C22×C32#9911yescharacteristic
105C22×C32#9911yescharacteristic
106C2×C3⋊D3—21no—
107C2×C3⋊D3—21no—
108C2×C3⋊D3—41no—
109C2×C3⋊D3—41no—
110C2×C3⋊D3—41no—
111C2×C3⋊D3—41no—
112C2×C3⋊D3—81no—
113#157—82no—
114C32×C4—42no—
115C3⋊Dic3—21no—
116C3⋊Dic3—21no—
117C3⋊Dic3—81no—
118C22×D4—91no—
119C23×C4#15711yescharacteristic, complemented
120C2×M16—181no—
121C2×C22⋊C4—91no—
122C2×C22⋊C4—181no—
123C2×C22⋊C4—181no—
124#100—92no—
125#100—181no—
126#99—92no—
127#99—181no—
128#95—181no—
129C23×C3—24no—
130C23×C3—24no—
131C23×C3—22no—
132C23×C3—22no—
133C23×C3—22no—
134C23×C3—44no—
135C23×C3—44no—
136C22×D3—62no—
137C22×D3—62no—
138C22×D3—122no—
139C22×D3—122no—
140C22×D3—124no—
141C22×D3—124no—
142C2×C3×C4—28no—
143C2×C3×C4—44no—
144C2×C3×C4—44no—
145C2×C3×C4—48no—
146C2×C3×C4—48no—
147#67—124no—
148#67—124no—
149#67—124no—
150#67—124no—
151C2×Dic3—62no—
152C2×Dic3—62no—
153C2×Dic3—122no—
154C2×Dic3—122no—
155C2×Dic3—124no—
156C2×Dic3—124no—
157C2×Dic3—124no—
158C2×C32—21no—
159C2×C32—21no—
160C2×C32—41no—
161C2×C32—41no—
162C2×C32#34211yescharacteristic
163C2×C32AΣL(1,𝔽16)11yescharacteristic
164C2×C32#35211yescharacteristic
165C3⋊D3—41no—
166C3⋊D3—41no—
167C24—91no—
168C24C2×#15711yescharacteristic
169C2×D4—91no—
170C2×D4—91no—
171C2×D4—91no—
172C2×D4—91no—
173C2×D4—361no—
174C2×D4—361no—
175C22×C4—21no—
176C22×C4—42no—
177C22×C4—41no—
178C22×C4—91no—
179C22×C4—181no—
180C22×C4—361no—
181M16—182no—
182M16—361no—
183C2×C8—361no—
184C22⋊C4—182no—
185C22⋊C4—362no—
186C22⋊C4—361no—
187C22⋊C4—361no—
188C22×C3—24no—
189C22×C3—24no—
190C22×C3—24no—
191C22×C3—24no—
192C22×C3—22no—
193C22×C3—22no—
194C22×C3—22no—
195C22×C3—44no—
196C22×C3—44no—
197C22×C3—44no—
198C22×C3—48no—
199C22×C3—44no—
200C2×D3—122no—
201C2×D3—122no—
202C2×D3—124no—
203C2×D3—124no—
204C2×D3—242no—
205C2×D3—242no—
206C2×D3—244no—
207C3×C4—48no—
208Dic3—122no—
209Dic3—122no—
210Dic3—244no—
211C32#139011yescharacteristic, complemented, Sylow
212C23—21no—
213C23—21no—
214C23—41no—
215C23—41no—
216C23—91no—
217C23—91no—
218C23—181no—
219C23—181no—
220C23—361no—
221C23—361no—
222C23C4×#15711yescharacteristic
223C23C4⋊#15711yescharacteristic
224C23C22⋊#15711yescharacteristic
225D4—361no—
226D4—361no—
227D4—361no—
228D4—361no—
229C2×C4—22no—
230C2×C4—41no—
231C2×C4—42no—
232C2×C4—41no—
233C2×C4—42no—
234C2×C4—91no—
235C2×C4—91no—
236C2×C4—181no—
237C2×C4—181no—
238C2×C4—361no—
239C2×C4—361no—
240C2×C4—362no—
241C2×C4—361no—
242C2×C4—721no—
243C2×C4—721no—
244C8—362no—
245C2×C3—24no—
246C2×C3—24no—
247C2×C3—22no—
248C2×C3—22no—
249C2×C3—22no—
250C2×C3—44no—
251C2×C3—44no—
252D3—242no—
253D3—242no—
254C22—21no—
255C22—21no—
256C22—21no—
257C22—21no—
258C22—41no—
259C22—41no—
260C22—42no—
261C22—41no—
262C22—41no—
263C22—181no—
264C22—181no—
265C22—361no—
266C22—361no—
267C22—361no—
268C22—361no—
269C22—721no—
270C22#6377411yescharacteristic
271C22#6378111yescharacteristic
272C22#6378611yescharacteristic
273C4—42no—
274C4—181no—
275C4—181no—
276C4—721no—
277C4—722no—
278C3—22no—
279C2—21no—
280C2—21no—
281C2—41no—
282C2—41no—
283C2—361no—
284C2—361no—
285C2#1059020511yescharacteristic
286C2#1059020611yescharacteristic
287C2#1059022311yescharacteristic
subgroupG/H
centerC22#63786
commutatorC23×C32C42
FrattiniC24C2×#157
FittingC23×C32×C4C4
socleC22×C32#99
prime radical, cosocleC22×#638C22
hypercenterC23×C4#157
hypocenterC32#1390
LCSG ▷ C23×C32 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
4. C23×C32×C4C4semidirect
8. C2×#3757C4semidirect
11. #63788C4semidirect
13. #63786C4semidirect
119. C23×C4#157semidirect
211. C32#1390semidirect

Maximal subgroups

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

subgroupindex
C2×#637882
C2×#637862
#105929122
#13909