Finite Group Databasebeta

← #11772566

Subgroups — #11772566

Order 1152.

352 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 39 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
3#10593817C211yesmaximal, characteristic
4C23×#157C411yescharacteristic, complemented
5C2×D4×C3⋊D3C2211yescharacteristic
6C2×C22⋊#157—21no—
7C2×C22⋊#157—21no—
8C2×C22⋊#157C411yescharacteristic, complemented
9#64283—21no—
10#63788—21no—
11#63788C412yescomplemented
12#63786—21no—
13#63781—21no—
14#63774C412yescomplemented
15C23×C3⋊D3C2×C411yescharacteristic
16C23×C3⋊D3D411yescharacteristic
17C22×#157—21no—
18C22×#157—21no—
19C22×#157—42no—
20C22×#157—41no—
21C22×#157—41no—
22C2×C32×D4Q811yescharacteristic
23C2×#638C2×C411yescharacteristic
24C2×#638D411yescharacteristic
25D4×C3⋊D3—41no—
26D4×C3⋊D3—41no—
27C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
28C2×C4×C3⋊D3D411yescharacteristic
29C22⋊#157—22no—
30C22⋊#157—42no—
31C22⋊#157—41no—
32C22⋊#157—41no—
33#3792—22no—
34#3788—41no—
35#3787—41no—
36#1390—91nomaximal, Sylow
37C2×D3×D4—121no—
38C23×C32C4⋊C411yescharacteristic
39C23×C32C4⋊C411yescharacteristic
40C22×C3⋊D3—21no—
41C22×C3⋊D3—21no—
42C22×C3⋊D3—21no—
43C22×C3⋊D3—21no—
44C22×C3⋊D3—41no—
45C22×C3⋊D3—41no—
46C22×C3⋊D3—41no—
47C22×C3⋊D3—41no—
48C22×C3⋊D3C4211yescharacteristic
49C22×C3⋊D3C22⋊C411yescharacteristic
50C22×C3⋊D3C22⋊C411yescharacteristic
51C2×#157—22no—
52C2×#157—41no—
53C2×#157—42no—
54C2×#157—41no—
55C2×#157—42no—
56C2×#157—41no—
57C2×#157—41no—
58C2×#157—42no—
59C2×#157—41no—
60C2×#157—81no—
61C2×#157—81no—
62C32×D4—41no—
63C2×C32×C4C4⋊C411yescharacteristic
64#638—41no—
65#638—41no—
66C2×C3⋊Dic3C22⋊C411yescharacteristic
67C4⋊(C3⋊D3)—41no—
68C4×C3⋊D3—21no—
69C4×C3⋊D3—21no—
70#622—42no—
71C2×#100—91no—
72C2×#99—91no—
73#386—91no—
74C23×D3—121no—
75C23×D3—121no—
76C2×C3×D4—41no—
77C2×#67—121no—
78C2×#67—121no—
79D3×D4—124no—
80D3×D4—124no—
81C2×D12—121no—
82C2×C4×D3—121no—
83C22×C32—21no—
84C22×C32—21no—
85C22×C32—41no—
86C22×C32—41no—
87C22×C32#9511yescharacteristic
88C2×C3⋊D3—21no—
89C2×C3⋊D3—21no—
90C2×C3⋊D3—21no—
91C2×C3⋊D3—21no—
92C2×C3⋊D3—42no—
93C2×C3⋊D3—41no—
94C2×C3⋊D3—41no—
95C2×C3⋊D3—41no—
96C2×C3⋊D3—41no—
97C2×C3⋊D3—41no—
98C2×C3⋊D3—41no—
99C2×C3⋊D3—81no—
100C2×C3⋊D3#9911yescharacteristic
101C2×C3⋊D3#9911yescharacteristic
102#157—42no—
103#157—81no—
104#157—82no—
105C32×C4—21no—
106C3⋊Dic3—21no—
107C22×D4—91no—
108C23×C4—91no—
109C2×M16—181no—
110C2×C22⋊C4—91no—
111C2×C22⋊C4—181no—
112C2×C22⋊C4—181no—
113#100—92no—
114#100—181no—
115#99—92no—
116#99—181no—
117#95—181no—
118C23×C3—41no—
119C23×C3—41no—
120C22×D3—121no—
121C22×D3—121no—
122C22×D3—121no—
123C22×D3—122no—
124C22×D3—122no—
125C22×D3—122no—
126C22×D3—122no—
127C22×D3—242no—
128C22×D3—242no—
129C22×D3—242no—
130C22×D3—242no—
131C3×D4—44no—
132C2×C3×C4—41no—
133#67—124no—
134#67—124no—
135C2×Dic3—121no—
136D12—124no—
137C4×D3—122no—
138C4×D3—122no—
139C2×C32—21no—
140C2×C32—41no—
141C2×C32—41no—
142C2×C32#34211yescharacteristic
143C3⋊D3—21no—
144C3⋊D3—41no—
145C3⋊D3—41no—
146C3⋊D3AΣL(1,𝔽16)11yescharacteristic
147C3⋊D3#35211yescharacteristic
148C24—91no—
149C24—91no—
150C2×D4—91no—
151C2×D4—91no—
152C2×D4—91no—
153C2×D4—361no—
154C2×D4—361no—
155C2×D4PSU(3,𝔽2)11yescharacteristic
156C22×C4—91no—
157C22×C4—181no—
158C22×C4—181no—
159C22×C4—362no—
160C22×C4—361no—
161C22×C4—361no—
162M16—182no—
163M16—361no—
164C2×C8—361no—
165C22⋊C4—182no—
166C22⋊C4—362no—
167C22⋊C4—361no—
168C22⋊C4—361no—
169C22×C3—42no—
170C22×C3—42no—
171C22×C3—41no—
172C22×C3—82no—
173C22×C3—82no—
174C2×D3—121no—
175C2×D3—121no—
176C2×D3—122no—
177C2×D3—122no—
178C2×D3—122no—
179C2×D3—122no—
180C2×D3—242no—
181C2×D3—242no—
182C2×D3—242no—
183C2×D3—242no—
184C2×D3—244no—
185C2×D3—242no—
186C2×D3—242no—
187C2×D3—244no—
188C3×C4—42no—
189Dic3—122no—
190C32#139011yescharacteristic, complemented, Sylow
191C23—91no—
192C23—91no—
193C23—91no—
194C23—181no—
195C23—181no—
196C23—181no—
197C23—181no—
198C23—361no—
199C23—361no—
200C23—361no—
201C23—361no—
202C23#377711yescharacteristic
203C23#377711yescharacteristic
204D4—41no—
205D4—361no—
206D4—361no—
207D4—361no—
208C2×C4—91no—
209C2×C4—181no—
210C2×C4—181no—
211C2×C4—182no—
212C2×C4—361no—
213C2×C4—361no—
214C2×C4—362no—
215C2×C4—362no—
216C2×C4—361no—
217C2×C4—362no—
218C2×C4—361no—
219C2×C4—361no—
220C2×C4—721no—
221C2×C4—721no—
222C2×C4#377711yescharacteristic
223C8—362no—
224C2×C3—42no—
225C2×C3—41no—
226C2×C3—82no—
227C2×C3—82no—
228D3—121no—
229D3—121no—
230D3—122no—
231D3—242no—
232D3—242no—
233C22—21no—
234C22—21no—
235C22—41no—
236C22—41no—
237C22—91no—
238C22—91no—
239C22—181no—
240C22—181no—
241C22—181no—
242C22—181no—
243C22—361no—
244C22—361no—
245C22—361no—
246C22—361no—
247C22—361no—
248C22—361no—
249C22—362no—
250C22—721no—
251C22#6374711yescharacteristic
252C4—21no—
253C4—181no—
254C4—362no—
255C4—721no—
256C4—722no—
257C3—41no—
258C2—21no—
259C2—41no—
260C2—41no—
261C2—91no—
262C2—91no—
263C2—181no—
264C2—361no—
265C2—361no—
266C2#1059009811yescharacteristic
subgroupG/H
centerC2#10590098
commutatorC22×C3⋊D3C42
Frattini, hypercenterC2×D4PSU(3,𝔽2)
FittingC2×C32×D4Q8
socleC2×C32#342
prime radical, cosocleC2×D4×C3⋊D3C22
hypocenterC32#1390
LCSG ▷ C22×C3⋊D3 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
4. C23×#157C4semidirect
8. C2×C22⋊#157C4semidirect
11. #63788C4semidirect
14. #63774C4semidirect
190. C32#1390semidirect

Maximal subgroups

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

subgroupindex
#105938262
#105938252
#105938172
#13909