Finite Group Databasebeta

← #11775769

Subgroups — #11775769

Order 1152.

408 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 59 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#10594810C211yesmaximal, characteristic
2C4×#3792C211yesmaximal, characteristic
3#10591060C211yesmaximal, characteristic
4#10590036C214yesmaximal, complemented
5C2×#3792—21no—
6C2×C4×C3⋊Dic3C2211yescharacteristic
7C3×#924—21no—
8C2×C3×#208—21no—
9#63982—21no—
10#63957C412yes—
11#63919C411yescharacteristic
12#63873C411yescharacteristic
13#63870C2212yes—
14#63843—21no—
15#63838—21no—
16#63777C2212yes—
17C4×#622—21no—
18#63555C2212yes—
19#63553—21no—
20#5622—61no—
21Dic3×M16—61no—
22C22×C32×C4D411yescharacteristic
23C22×C3⋊Dic3C2×C411yescharacteristic
24C22×C3⋊Dic3D411yescharacteristic
25C2×C3×Dic6—21no—
26C2×#627—21no—
27#3792—24no—
28C2×#622—22no—
29C4×C3⋊Dic3C2×C411yescharacteristic
30C4×C3⋊Dic3D411yescharacteristic
31C4×C3⋊Dic3D411yescharacteristic
32C4×C3⋊Dic3C2311yescharacteristic
33C3×#217—22no—
34C3×C4⋊Dic3—21no—
35C3×Dic3⋊C4—22no—
36C3×#208—24no—
37C2×C3×C3⋊C8—22no—
38#3724—21no—
39#3724C2×C412yes—
40#3724C2×C412yes—
41Dic3⋊Dic3—22no—
42Dic32—22no—
43#1526—91nomaximal, Sylow
44C2×C3×M16—61no—
45C3×C22⋊Q8—61no—
46Q8×Dic3—61no—
47#944—61no—
48#924—21no—
49C2×C4×Dic3—61no—
50C2×C4×Dic3—61no—
51C2×#208—21no—
52#889—62no—
53#888—61no—
54#887—62no—
55#887—61no—
56#878—62no—
57#877—62no—
58#815—62no—
59C8×Dic3—62no—
60C23×C32C22⋊C411yescharacteristic
61C2×C32×C4—22no—
62C2×C32×C4C22⋊C411yescharacteristic
63C2×C32×C4C2×D411yescharacteristic
64C2×C3⋊Dic3—22no—
65C2×C3⋊Dic3—22no—
66C2×C3⋊Dic3C22⋊C411yescharacteristic
67C2×C3⋊Dic3C22⋊C411yescharacteristic
68C2×C3⋊Dic3C22×C411yescharacteristic
69C2×C3⋊Dic3C2×D411yescharacteristic
70C2×C3×Dic3—22no—
71C2×C3×Dic3—22no—
72C3×Dic6—42no—
73#627—42no—
74#622—24no—
75C3×C3⋊C8—24no—
76#533—91no—
77C4×M16—91no—
78C4×M16—91no—
79#330—94no—
80C2×C3×Q8—61no—
81C22×C3×C4—21no—
82C22×C3×C4—21no—
83C22×Dic3—61no—
84C22×Dic3—61no—
85C22×Dic3—61no—
86C22×Dic3—61no—
87C2×Dic6—21no—
88C2×Dic6—62no—
89C3×M16—64no—
90C2×C3×C8—62no—
91C3×C4⋊C4—61no—
92C3×C4⋊C4—62no—
93C3×C22⋊C4—62no—
94#217—22no—
95C4⋊Dic3—21no—
96C4⋊Dic3—62no—
97Dic3⋊C4—22no—
98Dic3⋊C4—62no—
99Dic3⋊C4—62no—
100Dic3⋊C4—62no—
101Dic3⋊C4—62no—
102C4×Dic3—61no—
103C4×Dic3—61no—
104C4×Dic3—61no—
105C4×Dic3—61no—
106C4×Dic3—61no—
107C4×Dic3—61no—
108C4×Dic3—61no—
109C4×Dic3—61no—
110C4×Dic3—62no—
111C4×Dic3—62no—
112#208—24no—
113C2×C3⋊C8—22no—
114C22×C32—21no—
115C22×C32—21no—
116C22×C32—21no—
117C22×C32C2×C22⋊C411yescharacteristic
118C32×C4—21no—
119C32×C4#10412yes—
120C3⋊Dic3—21no—
121C3⋊Dic3—21no—
122C3⋊Dic3#10112yes—
123C3⋊Dic3#10412yes—
124C3×Dic3—42no—
125C3×Dic3—42no—
126C2×M16—61no—
127C2×M16—181no—
128C4⋊Q8—91no—
129C4⋊Q8—91no—
130#125—92no—
131C22⋊Q8—61no—
132C22⋊Q8—181no—
133C4×Q8—181no—
134C4×Q8—181no—
135#117—92no—
136C2×C42—91no—
137#97—92no—
138#97—92no—
139C4×C8—181no—
140C4×C8—181no—
141C23×C3—21no—
142C23×C3—21no—
143C3×Q8—122no—
144C2×C3×C4—22no—
145C2×C3×C4—22no—
146C2×C3×C4—21no—
147C2×C3×C4—21no—
148C2×C3×C4—21no—
149C2×C3×C4—21no—
150C2×C3×C4—42no—
151C2×C3×C4—62no—
152C2×C3×C4—62no—
153C2×Dic3—22no—
154C2×Dic3—22no—
155C2×Dic3—61no—
156C2×Dic3—61no—
157C2×Dic3—61no—
158C2×Dic3—61no—
159C2×Dic3—61no—
160C2×Dic3—61no—
161C2×Dic3—61no—
162C2×Dic3—61no—
163C2×Dic3—64no—
164C2×Dic3—122no—
165C2×Dic3—122no—
166C2×Dic3—122no—
167Dic6—42no—
168Dic6—124no—
169C3×C8—64no—
170C3⋊C8—24no—
171C2×C32—41no—
172C2×C32C2×#10111yescharacteristic
173C2×C32C2×#10411yescharacteristic
174C2×C32C2×#10411yescharacteristic
175C2×Q8—61no—
176C2×Q8—181no—
177C22×C4—91no—
178C22×C4—91no—
179C22×C4GO+(4,𝔽2)11yescharacteristic
180M16—64no—
181M16—184no—
182C2×C8—62no—
183C2×C8—182no—
184C4⋊C4—62no—
185C4⋊C4—61no—
186C4⋊C4—92no—
187C4⋊C4—92no—
188C4⋊C4—182no—
189C4⋊C4—181no—
190C22⋊C4—62no—
191C42—91no—
192C42—91no—
193C42—91no—
194C42—91no—
195C42—182no—
196C22×C3—22no—
197C22×C3—22no—
198C22×C3—21no—
199C22×C3—21no—
200C22×C3—41no—
201C22×C3—41no—
202C22×C3—41no—
203C22×C3—41no—
204C3×C4—21no—
205C3×C4—21no—
206C3×C4—22no—
207C3×C4—22no—
208C3×C4—41no—
209C3×C4—122no—
210C3×C4—122no—
211Dic3—42no—
212Dic3—42no—
213Dic3—62no—
214Dic3—62no—
215Dic3—62no—
216Dic3—62no—
217Dic3—62no—
218Dic3—121no—
219Dic3—121no—
220Dic3—121no—
221C32#152611yescharacteristic, complemented, Sylow
222C23D32⋊C411yescharacteristic
223Q8—122no—
224Q8—362no—
225C2×C4—22no—
226C2×C4—62no—
227C2×C4—62no—
228C2×C4—91no—
229C2×C4—91no—
230C2×C4—91no—
231C2×C4—91no—
232C2×C4—182no—
233C2×C4—182no—
234C2×C4D32⋊C411yescharacteristic
235C2×C4C2×GO+(4,𝔽2)11yescharacteristic
236C8—64no—
237C8—184no—
238C2×C3—21no—
239C2×C3—21no—
240C2×C3—21no—
241C2×C3—21no—
242C2×C3—21no—
243C2×C3—21no—
244C2×C3—42no—
245C2×C3—42no—
246C22—21no—
247C22—21no—
248C22—21no—
249C22C2×D32⋊C411yescharacteristic
250C4—21no—
251C4—92no—
252C4—92no—
253C4—122no—
254C4—122no—
255C4—181no—
256C4—181no—
257C4#6374112yes—
258C3—21no—
259C3—21no—
260C2—41no—
261C2#1059331511yescharacteristic
262C2#1059332511yescharacteristic
263C2C2×#6374111yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C22⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1526
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #10590036C2semidirect
221. C32#1526semidirect

Maximal subgroups

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

subgroupindex
#105948102
C4×#37922
#105910602
#105900362
#15269