Finite Group Databasebeta

← #11773464

Subgroups — #11773464

Order 1152.

938 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 938 conjugacy classes of subgroups — too many to draw. Only its 130 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×C4⋊C4×C3⋊D3C211yesmaximal, characteristic
2C2×#63781C211yesmaximal, characteristic
3C2×#63781C211yesmaximal, characteristic
4C2×#63781C214yesmaximal
5C23×#157C2212yes—
6C23×#157C2212yes—
7C22×C4×C3⋊D3C2212yes—
8C22×C4×C3⋊D3C2211yescharacteristic
9C2×C32×C4⋊C4C411yescharacteristic, complemented
10C2×C4⋊(C3⋊Dic3)C411yescharacteristic, complemented
11C2×#3750C412yescomplemented
12C4⋊C4×C3⋊D3—22no—
13C4⋊C4×C3⋊D3—22no—
14#63781—22no—
15#63781—22no—
16#63781—28no—
17C2×D3×C4⋊C4—62no—
18C23×C3⋊D3C2311yescharacteristic
19C22×#157—22no—
20C22×#157—24no—
21C22×#157—22no—
22C22×#157—22no—
23C22×#157—24no—
24C22×#157—22no—
25C22×#157—24no—
26C22×#157—24no—
27C22×#157D414yes—
28C22×#157Q814yes—
29C22×C32×C4C2×C412yes—
30C22×C32×C4C2×C411yescharacteristic
31C22×C3⋊Dic3C2×C412yes—
32C22×C3⋊Dic3C2×C411yescharacteristic
33C2×C4×C3⋊D3—24no—
34C2×C4×C3⋊D3—22no—
35C2×C4×C3⋊D3—22no—
36C2×C4×C3⋊D3—24no—
37C2×C4×C3⋊D3—24no—
38C2×C4×C3⋊D3D412yes—
39C2×C4×C3⋊D3D412yes—
40C32×C4⋊C4—22no—
41C4⋊(C3⋊Dic3)—22no—
42#3750—24no—
43#1445—91nomaximal, Sylow
44C22×C4×D3—62no—
45C22×C4×D3—64no—
46C2×C3×C4⋊C4—22no—
47C2×C4⋊Dic3—62no—
48C2×Dic3⋊C4—64no—
49D3×C4⋊C4—68no—
50D3×C4⋊C4—68no—
51C23×C32C22×C411yescharacteristic
52C22×C3⋊D3C2×D411yescharacteristic
53C22×C3⋊D3C2×D412yes—
54C22×C3⋊D3C2×D411yescharacteristic
55C22×C3⋊D3C2×Q812yes—
56C22×C3⋊D3#4112yes—
57C22×C3⋊D3#4114yes—
58C22×C3⋊D3#4112yes—
59C2×#157—24no—
60C2×#157—28no—
61C2×#157—24no—
62C2×#157—28no—
63C2×#157—42no—
64C2×#157—44no—
65C2×#157—42no—
66C2×#157—42no—
67C2×#157—44no—
68C2×#157—42no—
69C2×C32×C4—22no—
70C2×C32×C4—22no—
71C2×C32×C4—24no—
72C2×C32×C4C22⋊C412yes—
73C2×C3⋊Dic3—22no—
74C2×C3⋊Dic3—22no—
75C2×C3⋊Dic3—24no—
76C2×C3⋊Dic3C22⋊C412yes—
77C4×C3⋊D3—24no—
78C4×C3⋊D3—24no—
79C4×C3⋊D3—44no—
80C4×C3⋊D3—42no—
81C4×C3⋊D3—42no—
82C22×C4⋊C4—91no—
83C2×#95—91no—
84C2×#95—91no—
85C2×#95—94no—
86C23×D3—62no—
87C22×C3×C4—22no—
88C22×C3×C4—24no—
89C22×Dic3—62no—
90C22×Dic3—64no—
91C2×C4×D3—64no—
92C2×C4×D3—64no—
93C2×C4×D3—616no—
94C2×C4×D3—68no—
95C2×C4×D3—68no—
96C2×C4×D3—128no—
97C2×C4×D3—128no—
98C3×C4⋊C4—28no—
99C4⋊Dic3—68no—
100Dic3⋊C4—616no—
101C22×C32C2×C22⋊C411yescharacteristic
102C22×C32#11712yes—
103C22×C32C4×D412yes—
104C22×C32C4×Q812yes—
105C2×C3⋊D3#12112yes—
106C2×C3⋊D3C22⋊Q814yes—
107C2×C3⋊D3C22⋊Q812yes—
108C2×C3⋊D3#12312yes—
109C2×C3⋊D3#12314yes—
110C2×C3⋊D3#12312yes—
111C2×C3⋊D3#12411yescharacteristic
112C2×C3⋊D3#12411yescharacteristic
113C2×C3⋊D3#12514yes—
114C2×C3⋊D3#12614yes—
115C2×C3⋊D3#12711yescharacteristic
116C2×C3⋊D3C4⋊Q811yescharacteristic
117#157—44no—
118#157—44no—
119C32×C4—22no—
120C32×C4—42no—
121C3⋊Dic3—22no—
122C3⋊Dic3—42no—
123C23×C4—91no—
124C23×C4—92no—
125C23×C4—92no—
126C23×C4—92no—
127C2×C4⋊C4—92no—
128C2×C4⋊C4—91no—
129C2×C4⋊C4—182no—
130C2×C4⋊C4—182no—
131C2×C4⋊C4#15711yescharacteristic, complemented
132#95—182no—
133#95—182no—
134#95—188no—
135C23×C3—22no—
136C22×D3—62no—
137C22×D3—62no—
138C22×D3—64no—
139C22×D3—64no—
140C22×D3—68no—
141C22×D3—64no—
142C22×D3—64no—
143C2×C3×C4—28no—
144C2×C3×C4—28no—
145C2×C3×C4—24no—
146C2×C3×C4—48no—
147C2×Dic3—64no—
148C2×Dic3—68no—
149C2×Dic3—68no—
150C2×Dic3—128no—
151C4×D3—616no—
152C4×D3—616no—
153C4×D3—1216no—
154C4×D3—128no—
155C4×D3—128no—
156C2×C32#38111yescharacteristic
157C2×C32#38714yes—
158C2×C32#39011yescharacteristic
159C2×C32#39111yescharacteristic
160C3⋊D3#39712yes—
161C3⋊D3#39812yes—
162C3⋊D3#39912yes—
163C3⋊D3#40012yes—
164C24—91no—
165C22×C4—91no—
166C22×C4—92no—
167C22×C4—92no—
168C22×C4—94no—
169C22×C4—94no—
170C22×C4—92no—
171C22×C4—184no—
172C22×C4—184no—
173C22×C4—182no—
174C22×C4—182no—
175C22×C4—184no—
176C22×C4—184no—
177C22×C4—182no—
178C22×C4—182no—
179C22×C4—184no—
180C22×C4—184no—
181C22×C4—182no—
182C22×C4—182no—
183C22×C4—184no—
184C22×C4C2×#15712yes—
185C22×C4C2×#15711yescharacteristic
186C4⋊C4—22no—
187C4⋊C4—184no—
188C4⋊C4—182no—
189C22×C3—24no—
190C22×C3—24no—
191C22×C3—24no—
192C22×C3—22no—
193C2×D3—64no—
194C2×D3—64no—
195C2×D3—64no—
196C2×D3—62no—
197C2×D3—62no—
198C2×D3—64no—
199C2×D3—68no—
200C2×D3—68no—
201C2×D3—62no—
202C2×D3—68no—
203C2×D3—68no—
204C2×D3—62no—
205C3×C4—28no—
206C3×C4—48no—
207Dic3—68no—
208Dic3—128no—
209C32#144511yescharacteristic, complemented, Sylow
210C23—94no—
211C23—92no—
212C23—92no—
213C23—92no—
214C23—92no—
215C23—91no—
216C23—91no—
217C23C22×#15711yescharacteristic
218C2×C4—22no—
219C2×C4—24no—
220C2×C4—22no—
221C2×C4—92no—
222C2×C4—184no—
223C2×C4—184no—
224C2×C4—182no—
225C2×C4—184no—
226C2×C4—184no—
227C2×C4—188no—
228C2×C4—188no—
229C2×C4—184no—
230C2×C4—182no—
231C2×C4—364no—
232C2×C4—362no—
233C2×C4—362no—
234C2×C4—362no—
235C2×C4—362no—
236C2×C4—362no—
237C2×C4—362no—
238C2×C4—364no—
239C2×C4—364no—
240C2×C4C22⋊#15712yes—
241C2×C3—22no—
242C2×C3—22no—
243C2×C3—22no—
244C2×C3—28no—
245D3—64no—
246D3—64no—
247D3—64no—
248D3—64no—
249C22—92no—
250C22—92no—
251C22—92no—
252C22—91no—
253C22—91no—
254C22—92no—
255C22—91no—
256C22—91no—
257C22—94no—
258C22—94no—
259C22—94no—
260C22—94no—
261C22#6428612yes—
262C22D4×#15712yes—
263C22Q8×#15712yes—
264C22C2×C22⋊#15711yescharacteristic
265C4—22no—
266C4—42no—
267C4—182no—
268C4—364no—
269C4—364no—
270C4—362no—
271C3—22no—
272C2—92no—
273C2—92no—
274C2—92no—
275C2—92no—
276C2#1059375814yes—
277C2#1059381111yescharacteristic
278C2#1059382711yescharacteristic
279C2#1059383711yescharacteristic
subgroupG/H
center, FrattiniC23C22×#157
commutator, socleC23×C32C22×C4
FittingC2×C32×C4⋊C4C4
prime radical, cosocleC23×C3⋊D3C23
hypercenterC2×C4⋊C4#157
hypocenterC32#1445
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
9. C2×C32×C4⋊C4C4semidirect
10. C2×C4⋊(C3⋊Dic3)C4semidirect
11. C2×#3750C4semidirect
131. C2×C4⋊C4#157semidirect
209. C32#1445semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×C3⋊D32
C2×#637812
#14459