Finite Group Databasebeta

← #11773214

Subgroups — #11773214

Order 1152.

1074 conjugacy classes of subgroups; only the 199 normal subgroups are shown.

normal subgroups only

This group has 1074 conjugacy classes of subgroups — too many to draw. Only its 199 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
1C22×C4×#157C211yesmaximal, characteristic
2C2×#63900C212yesmaximal
3C2×#63737C214yesmaximal
4C23×#157C2212yes—
5C22×C4×C3⋊D3C2211yescharacteristic
6C22×#624C2214yes—
7C2×C4×#157—24no—
8C2×C4×#157C414yescomplemented
9C2×C3×C4⋊Dic3—22no—
10C2×#3724—22no—
11#63900—24no—
12#63900C418yescomplemented
13#63737—28no—
14C2×D3×C4⋊C4—62no—
15C23×C3⋊D3C2311yescharacteristic
16C22×#157—24no—
17C22×#157—24no—
18C22×#157C2×C414yes—
19C22×#157D414yes—
20C22×#157Q814yes—
21C22×C32×C4D411yescharacteristic
22C22×C3⋊Dic3D411yescharacteristic
23C2×C4×C3⋊D3C2×C412yes—
24C2×C4×C3⋊D3C2×C414yes—
25C2×C4×C3⋊D3D414yes—
26C2×C4×C3⋊D3Q812yes—
27C22×C3×Dic3—24no—
28C2×#624—28no—
29C2×#624—28no—
30C2×#624—24no—
31C2×#624C2×C418yes—
32C4×#157—28no—
33C3×C4⋊Dic3—28no—
34#3724—28no—
35C4⋊#95—91nomaximal, Sylow
36C22×C4×D3—62no—
37C22×C4×D3—64no—
38C2×C3×C4⋊C4—62no—
39C2×C4⋊Dic3—22no—
40C2×Dic3⋊C4—64no—
41D3×C4⋊C4—68no—
42D3×C4⋊C4—68no—
43C23×C32C2×D411yescharacteristic
44C22×C3⋊D3C22×C411yescharacteristic
45C22×C3⋊D3C22×C412yes—
46C22×C3⋊D3C2×D412yes—
47C22×C3⋊D3C2×D412yes—
48C22×C3⋊D3C2×Q811yescharacteristic
49C22×C3⋊D3C2×Q812yes—
50C22×C3⋊D3#4114yes—
51C2×#157—24no—
52C2×#157—24no—
53C2×#157—28no—
54C2×#157—28no—
55C2×#157C4⋊C418yescomplemented
56C2×C32×C4C22⋊C414yes—
57C2×C32×C4C4⋊C412yes—
58C2×C3⋊Dic3C22⋊C414yes—
59C2×C3⋊Dic3C4⋊C412yes—
60C4×C3⋊D3C4214yes—
61C4×C3⋊D3C22⋊C414yes—
62C4×C3⋊D3C4⋊C418yes—
63C2×C3×Dic3—28no—
64C2×C3×Dic3—44no—
65C2×C3×Dic3—44no—
66#624—216no—
67#624—48no—
68C22×C4⋊C4—92no—
69C22×C42—91no—
70C2×#95—94no—
71C23×D3—62no—
72C22×C3×C4—22no—
73C22×C3×C4—64no—
74C22×Dic3—24no—
75C22×Dic3—62no—
76C2×C4×D3—64no—
77C2×C4×D3—64no—
78C2×C4×D3—64no—
79C2×C4×D3—64no—
80C2×C4×D3—64no—
81C2×C4×D3—64no—
82C2×C4×D3—68no—
83C2×C4×D3—68no—
84C2×C4×D3—128no—
85C2×C4×D3—128no—
86C3×C4⋊C4—68no—
87C4⋊Dic3—28no—
88Dic3⋊C4—616no—
89C22×C32C2×C22⋊C412yes—
90C22×C32C2×C4⋊C411yescharacteristic
91C22×C32#12412yes—
92C22×C32#12711yescharacteristic
93C22×C32C4⋊Q811yescharacteristic
94C2×C3⋊D3C2×C4211yescharacteristic
95C2×C3⋊D3C2×C22⋊C411yescharacteristic
96C2×C3⋊D3C2×C4⋊C412yes—
97C2×C3⋊D3C2×C4⋊C412yes—
98C2×C3⋊D3#11712yes—
99C2×C3⋊D3C4×D414yes—
100C2×C3⋊D3C4×Q814yes—
101C2×C3⋊D3#12114yes—
102C2×C3⋊D3C22⋊Q814yes—
103C2×C3⋊D3#12512yes—
104C2×C3⋊D3C4⋊Q812yes—
105#157—28no—
106C32×C4#9514yescomplemented
107C3⋊Dic3#9514yescomplemented
108C3×Dic3—48no—
109C23×C4—94no—
110C23×C4—91no—
111C23×C4—92no—
112C2×C4⋊C4—62no—
113C2×C4⋊C4—98no—
114C2×C4⋊C4—184no—
115C2×C4⋊C4—182no—
116C2×C42—94no—
117C2×C42—184no—
118#95—188no—
119C23×C3—22no—
120C22×D3—62no—
121C22×D3—62no—
122C22×D3—62no—
123C22×D3—62no—
124C22×D3—62no—
125C22×D3—64no—
126C22×D3—62no—
127C22×D3—64no—
128C22×D3—64no—
129C22×D3—64no—
130C2×C3×C4—24no—
131C2×C3×C4—24no—
132C2×C3×C4—24no—
133C2×C3×C4—68no—
134C2×C3×C4—124no—
135C2×C3×C4—124no—
136C2×Dic3—28no—
137C2×Dic3—44no—
138C2×Dic3—44no—
139C2×Dic3—64no—
140C2×Dic3—64no—
141C2×Dic3—64no—
142C4×D3—68no—
143C4×D3—68no—
144C4×D3—68no—
145C4×D3—68no—
146C4×D3—1216no—
147C4×D3—1216no—
148C2×C32C2×#9511yescharacteristic
149C2×C32#38211yescharacteristic
150C2×C32#38411yescharacteristic
151C2×C32#39012yes—
152C2×C32#39112yes—
153C3⋊D3C4×C4⋊C412yes—
154C3⋊D3#38012yes—
155C3⋊D3#38914yes—
156C24—91no—
157C22×C4—64no—
158C22×C4—98no—
159C22×C4—91no—
160C22×C4—94no—
161C22×C4—94no—
162C22×C4—92no—
163C22×C4—92no—
164C22×C4—94no—
165C22×C4—94no—
166C22×C4—94no—
167C22×C4—184no—
168C22×C4—188no—
169C22×C4—188no—
170C22×C4—184no—
171C22×C4—184no—
172C22×C4GO+(4,𝔽2)11yescharacteristic
173C4⋊C4—68no—
174C4⋊C4—188no—
175C42—188no—
176C22×C3—22no—
177C22×C3—22no—
178C22×C3—22no—
179C22×C3—22no—
180C22×C3—22no—
181C22×C3—22no—
182C22×C3—22no—
183C2×D3—62no—
184C2×D3—62no—
185C2×D3—62no—
186C2×D3—62no—
187C2×D3—64no—
188C2×D3—64no—
189C2×D3—64no—
190C2×D3—64no—
191C2×D3—64no—
192C2×D3—64no—
193C2×D3—64no—
194C2×D3—64no—
195C2×D3—64no—
196C2×D3—64no—
197C2×D3—64no—
198C2×D3—64no—
199C3×C4—28no—
200C3×C4—128no—
201Dic3—48no—
202Dic3—68no—
203C32C4⋊#9511yescharacteristic, complemented, Sylow
204C23—94no—
205C23—92no—
206C23—92no—
207C23—92no—
208C23—92no—
209C23—91no—
210C23—91no—
211C23C2×GO+(4,𝔽2)11yescharacteristic
212C2×C4—68no—
213C2×C4—94no—
214C2×C4—92no—
215C2×C4—94no—
216C2×C4—98no—
217C2×C4—94no—
218C2×C4—98no—
219C2×C4—124no—
220C2×C4—124no—
221C2×C4—1816no—
222C2×C4—184no—
223C2×C4—188no—
224C2×C4—184no—
225C2×C4—188no—
226C2×C4—368no—
227C2×C4D32⋊C414yes—
228C2×C4#377312yes—
229C2×C3—22no—
230C2×C3—22no—
231C2×C3—22no—
232C2×C3—22no—
233C2×C3—22no—
234C2×C3—22no—
235C2×C3—22no—
236D3—64no—
237D3—64no—
238D3—64no—
239D3—64no—
240C22—94no—
241C22—94no—
242C22—92no—
243C22—92no—
244C22—94no—
245C22—94no—
246C22—92no—
247C22—92no—
248C22—91no—
249C22—91no—
250C22—92no—
251C22#6422112yes—
252C22#6422211yescharacteristic
253C22#6423111yescharacteristic
254C22C2×D32⋊C412yes—
255C22C2×#377311yescharacteristic
256C4—94no—
257C4—128no—
258C4—188no—
259C4#6373714yescomplemented
260C3—22no—
261C2—92no—
262C2—94no—
263C2—92no—
264C2#1059334212yes—
265C2#1059334411yescharacteristic
266C2#1059340712yes—
267C2#1059341311yescharacteristic
268C2C2×#6373711yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC2×C3⋊D3C2×C42
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radical, cosocleC23×C3⋊D3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C4⋊#95
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
8. C2×C4×#157C4semidirect
12. #63900C4semidirect
55. C2×#157C4⋊C4semidirect
106. C32×C4#95semidirect
107. C3⋊Dic3#95semidirect
203. C32C4⋊#95semidirect
259. C4#63737semidirect

Maximal subgroups

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

subgroupindex
C22×C4×#1572
C2×#639002
C2×#637372
C4⋊#959