Finite Group Databasebeta

← #11774781

Subgroups — #11774781

Order 1152.

424 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 69 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
2#10593805C211yesmaximal, characteristic
3C2×#63553C211yesmaximal, characteristic
4#10590031C214yesmaximal, complemented
5C2×#3792—21no—
6C2×C4×C3⋊Dic3C2211yescharacteristic
7C3×#924—21no—
8C22×C3×C3⋊C8—21no—
9#63982C412yes—
10#63957—21no—
11#63919C411yescharacteristic
12#63873C411yescharacteristic
13#63870—21no—
14#63843—21no—
15#63838C2212yes—
16#63779C2212yes—
17C4⋊#622—21no—
18#63553—21no—
19#63553C2212yes—
20#5622—61no—
21C2×C8×Dic3—61no—
22C22×C32×C4D411yescharacteristic
23C22×C3⋊Dic3C2×C411yescharacteristic
24C22×C3⋊Dic3D411yescharacteristic
25C2×C3×Dic6—21no—
26C2×#627C2×C412yes—
27#3792—42no—
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—
36C2×C3×C3⋊C8—24no—
37C2×C3×C3⋊C8—22no—
38#3724—21no—
39#3724—21no—
40#3724C2×C412yes—
41Dic3⋊Dic3—22no—
42Dic32—22no—
43#1493—91nomaximal, Sylow
44C22×C3×C8—61no—
45C3×C22⋊Q8—61no—
46Q8×Dic3—61no—
47#944—61no—
48#924—21no—
49C2×C4×Dic3—61no—
50C2×C4×Dic3—61no—
51C22×C3⋊C8—21no—
52#889—62no—
53#888—61no—
54#887—62no—
55#887—61no—
56#878—62no—
57#877—62no—
58C8×Dic3—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⋊Dic3C22⋊C411yescharacteristic
66C2×C3⋊Dic3C22⋊C411yescharacteristic
67C2×C3⋊Dic3SD1612yes—
68C2×C3⋊Dic3Q1612yes—
69C2×C3⋊Dic3C22×C411yescharacteristic
70C2×C3⋊Dic3C2×D411yescharacteristic
71C2×C3×Dic3—22no—
72C2×C3×Dic3—22no—
73C3×Dic6—42no—
74#627—24no—
75#622—42no—
76C3×C3⋊C8—24no—
77#533—91no—
78#423—91no—
79C2×C4×C8—91no—
80Q8⋊C8—94no—
81C2×C3×Q8—61no—
82C22×C3×C4—21no—
83C22×C3×C4—21no—
84C22×Dic3—61no—
85C22×Dic3—61no—
86C22×Dic3—61no—
87C22×Dic3—61no—
88C2×Dic6—21no—
89C2×Dic6—62no—
90C2×C3×C8—62no—
91C2×C3×C8—64no—
92C3×C4⋊C4—61no—
93C3×C4⋊C4—62no—
94C3×C22⋊C4—62no—
95#217—22no—
96C4⋊Dic3—21no—
97C4⋊Dic3—62no—
98Dic3⋊C4—22no—
99Dic3⋊C4—62no—
100Dic3⋊C4—62no—
101Dic3⋊C4—62no—
102Dic3⋊C4—62no—
103C4×Dic3—61no—
104C4×Dic3—61no—
105C4×Dic3—61no—
106C4×Dic3—61no—
107C4×Dic3—61no—
108C4×Dic3—61no—
109C4×Dic3—61no—
110C4×Dic3—61no—
111C4×Dic3—62no—
112C4×Dic3—62no—
113C2×C3⋊C8—22no—
114C2×C3⋊C8—24no—
115C22×C32—21no—
116C22×C32—21no—
117C22×C32#10312yes—
118C22×C32C2×C22⋊C411yescharacteristic
119C32×C4—21no—
120C32×C4#10412yes—
121C3⋊Dic3—21no—
122C3⋊Dic3#10312yes—
123C3⋊Dic3#13112yes—
124C3⋊Dic3C2×SD1611yescharacteristic
125C3⋊Dic3C2×Q1611yescharacteristic
126C3×Dic3—42no—
127C3×Dic3—42no—
128C2×M16—181no—
129C22×C8—61no—
130C4⋊Q8—91no—
131C4⋊Q8—91no—
132#125—181no—
133C22⋊Q8—61no—
134C22⋊Q8—92no—
135C4×Q8—92no—
136C4×Q8—181no—
137#117—181no—
138C2×C42—91no—
139C4⋊C8—92no—
140C4⋊C8—181no—
141C4×C8—92no—
142C4×C8—181no—
143C23×C3—21no—
144C23×C3—21no—
145C3×Q8—122no—
146C2×C3×C4—22no—
147C2×C3×C4—22no—
148C2×C3×C4—21no—
149C2×C3×C4—21no—
150C2×C3×C4—21no—
151C2×C3×C4—21no—
152C2×C3×C4—42no—
153C2×C3×C4—62no—
154C2×C3×C4—62no—
155C2×Dic3—22no—
156C2×Dic3—22no—
157C2×Dic3—61no—
158C2×Dic3—61no—
159C2×Dic3—61no—
160C2×Dic3—62no—
161C2×Dic3—62no—
162C2×Dic3—62no—
163C2×Dic3—62no—
164C2×Dic3—61no—
165C2×Dic3—61no—
166C2×Dic3—61no—
167C2×Dic3—61no—
168C2×Dic3—61no—
169C2×Dic3—64no—
170C2×Dic3—122no—
171Dic6—42no—
172Dic6—124no—
173C3×C8—64no—
174C3⋊C8—24no—
175C2×C32—22no—
176C2×C32#40811yescharacteristic
177C2×C32C2×#10311yescharacteristic
178C2×C32C2×#10411yescharacteristic
179C2×Q8—61no—
180C2×Q8—92no—
181C22×C4—91no—
182C22×C4—91no—
183C22×C4GO+(4,𝔽2)11yescharacteristic
184M16—362no—
185C2×C8—64no—
186C2×C8—62no—
187C2×C8—182no—
188C4⋊C4—62no—
189C4⋊C4—61no—
190C4⋊C4—92no—
191C4⋊C4—181no—
192C4⋊C4—181no—
193C4⋊C4—182no—
194C22⋊C4—62no—
195C42—91no—
196C42—91no—
197C42—91no—
198C42—91no—
199C42—182no—
200C22×C3—22no—
201C22×C3—22no—
202C22×C3—21no—
203C22×C3—21no—
204C22×C3—22no—
205C22×C3—22no—
206C22×C3—41no—
207C22×C3—41no—
208C3×C4—21no—
209C3×C4—21no—
210C3×C4—22no—
211C3×C4—22no—
212C3×C4—41no—
213C3×C4—122no—
214C3×C4—122no—
215Dic3—42no—
216Dic3—42no—
217Dic3—62no—
218Dic3—62no—
219Dic3—62no—
220Dic3—62no—
221Dic3—61no—
222Dic3—61no—
223Dic3—61no—
224Dic3—61no—
225Dic3—62no—
226Dic3—121no—
227C32#149311yescharacteristic, complemented, Sylow
228C23D32⋊C411yescharacteristic
229Q8—122no—
230Q8—184no—
231C2×C4—22no—
232C2×C4—62no—
233C2×C4—62no—
234C2×C4—91no—
235C2×C4—91no—
236C2×C4—91no—
237C2×C4—92no—
238C2×C4—92no—
239C2×C4—91no—
240C2×C4—182no—
241C2×C4D32⋊C411yescharacteristic
242C2×C4C2×GO+(4,𝔽2)11yescharacteristic
243C8—64no—
244C8—362no—
245C2×C3—24no—
246C2×C3—21no—
247C2×C3—21no—
248C2×C3—21no—
249C2×C3—21no—
250C2×C3—21no—
251C2×C3—21no—
252C2×C3—42no—
253C22—21no—
254C22—21no—
255C22#6373012yes—
256C22C2×D32⋊C411yescharacteristic
257C4—21no—
258C4—92no—
259C4—91no—
260C4—91no—
261C4—92no—
262C4—122no—
263C4—122no—
264C4—181no—
265C4#6374112yes—
266C3—21no—
267C3—21no—
268C2—22no—
269C2#1059330811yescharacteristic
270C2C2×#6373011yescharacteristic
271C2C2×#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#1493
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #10590031C2semidirect
227. C32#1493semidirect

Maximal subgroups

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

subgroupindex
#105948102
#105938052
C2×#635532
#105900312
#14939