Finite Group Databasebeta

← #11774779

Subgroups — #11774779

Order 1152.

406 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 75 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#10595050C211yesmaximal, characteristic
2C2×C4×#622C211yesmaximal, characteristic
3#10591120C211yesmaximal, characteristic
4#10590032C214yesmaximal, complemented
5C22×#622—21no—
6C2×C4×C3⋊Dic3C2211yescharacteristic
7C3×#926—21no—
8C2×C3×#208—21no—
9#63982—21no—
10#63982C412yes—
11#63919C411yescharacteristic
12#63919C411yescharacteristic
13C4×#627—21no—
14C4×#627C2212yes—
15#63872—21no—
16C4×#622—21no—
17C4×#622C2212yes—
18#63572—21no—
19#63572C2212yes—
20#5517—61no—
21#5118—61no—
22C22×C32×C4D411yescharacteristic
23C22×C3⋊Dic3C2×C411yescharacteristic
24C22×C3⋊Dic3D411yescharacteristic
25C2×#627—21no—
26C2×#627C2×C412yes—
27C2×#622—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×C4⋊Dic3—21no—
36C3×C4×Dic3—22no—
37C3×#208—42no—
38C2×C3×C3⋊C8—22no—
39#3724—21no—
40#3724C2×C412yes—
41Dic3⋊Dic3—22no—
42Dic3⋊Dic3—22no—
43#1493—91nomaximal, Sylow
44C2×C3×M16—61no—
45C3×#117—61no—
46#926—21no—
47C2×C4×Dic3—61no—
48C2×C4×Dic3—61no—
49C2×#208—21no—
50#890—61no—
51#890—61no—
52#888—61no—
53#888—61no—
54#878—62no—
55#878—62no—
56C4×Dic6—62no—
57C4×Dic6—62no—
58Dic3⋊C8—62no—
59Dic3⋊C8—62no—
60C23×C32C22⋊C411yescharacteristic
61C2×C32×C4C22⋊C411yescharacteristic
62C2×C32×C4SD1612yes—
63C2×C32×C4Q1612yes—
64C2×C32×C4C2×D411yescharacteristic
65C2×C3⋊Dic3—22no—
66C2×C3⋊Dic3—22no—
67C2×C3⋊Dic3C22⋊C411yescharacteristic
68C2×C3⋊Dic3C22⋊C411yescharacteristic
69C2×C3⋊Dic3C22×C411yescharacteristic
70C2×C3⋊Dic3C2×D411yescharacteristic
71C2×C3×Dic3—22no—
72C2×C3×Dic3—22no—
73#627—24no—
74#627—42no—
75#622—24no—
76C3×C3⋊C8—42no—
77#533—91no—
78#423—91no—
79C2×C4×C8—91no—
80Q8⋊C8—94no—
81C22×C3×C4—21no—
82C22×C3×C4—21no—
83C22×Dic3—61no—
84C22×Dic3—61no—
85C22×Dic3—61no—
86C22×Dic3—61no—
87C2×Dic6—62no—
88C2×Dic6—62no—
89C3×M16—122no—
90C2×C3×C8—62no—
91C3×C4⋊C4—61no—
92C3×C4⋊C4—61no—
93C3×C22⋊C4—62no—
94C3×C42—62no—
95#217—22no—
96C4⋊Dic3—21no—
97C4⋊Dic3—21no—
98C4⋊Dic3—62no—
99C4⋊Dic3—62no—
100Dic3⋊C4—62no—
101Dic3⋊C4—62no—
102Dic3⋊C4—62no—
103Dic3⋊C4—62no—
104C4×Dic3—22no—
105C4×Dic3—61no—
106C4×Dic3—61no—
107C4×Dic3—61no—
108C4×Dic3—61no—
109C4×Dic3—61no—
110C4×Dic3—61no—
111C4×Dic3—61no—
112C4×Dic3—61no—
113#208—42no—
114C2×C3⋊C8—22no—
115C22×C32—21no—
116C22×C32—21no—
117C22×C32#10312yes—
118C22×C32C2×C22⋊C411yescharacteristic
119C32×C4#10312yes—
120C32×C4C2×SD1611yescharacteristic
121C32×C4C2×Q1611yescharacteristic
122C3⋊Dic3—21no—
123C3⋊Dic3—21no—
124C3⋊Dic3#10412yes—
125C3⋊Dic3#13112yes—
126C3×Dic3—42no—
127C3×Dic3—42no—
128C2×M16—61no—
129C22×C8—181no—
130C4⋊Q8—91no—
131C4⋊Q8—91no—
132#125—181no—
133C22⋊Q8—92no—
134C22⋊Q8—181no—
135C4×Q8—92no—
136C4×Q8—181no—
137#117—61no—
138C2×C42—91no—
139C4⋊C8—92no—
140C4⋊C8—181no—
141C4×C8—92no—
142C4×C8—181no—
143C23×C3—21no—
144C23×C3—21no—
145C2×C3×C4—21no—
146C2×C3×C4—21no—
147C2×C3×C4—21no—
148C2×C3×C4—21no—
149C2×C3×C4—22no—
150C2×C3×C4—22no—
151C2×C3×C4—22no—
152C2×C3×C4—22no—
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—61no—
161C2×Dic3—61no—
162C2×Dic3—61no—
163C2×Dic3—61no—
164C2×Dic3—61no—
165C2×Dic3—122no—
166C2×Dic3—122no—
167C2×Dic3—122no—
168C2×Dic3—122no—
169Dic6—124no—
170Dic6—124no—
171C3×C8—122no—
172C3⋊C8—42no—
173C2×C32—22no—
174C2×C32#40811yescharacteristic
175C2×C32C2×#10311yescharacteristic
176C2×C32C2×#10411yescharacteristic
177C2×Q8—92no—
178C2×Q8—181no—
179C22×C4—91no—
180C22×C4—91no—
181C22×C4GO+(4,𝔽2)11yescharacteristic
182M16—122no—
183C2×C8—62no—
184C2×C8—182no—
185C2×C8—184no—
186C4⋊C4—61no—
187C4⋊C4—61no—
188C4⋊C4—92no—
189C4⋊C4—182no—
190C4⋊C4—182no—
191C4⋊C4—181no—
192C22⋊C4—62no—
193C42—62no—
194C42—91no—
195C42—91no—
196C42—91no—
197C42—91no—
198C22×C3—21no—
199C22×C3—21no—
200C22×C3—22no—
201C22×C3—22no—
202C22×C3—41no—
203C22×C3—41no—
204C22×C3—41no—
205C22×C3—41no—
206C3×C4—21no—
207C3×C4—21no—
208C3×C4—21no—
209C3×C4—21no—
210C3×C4—22no—
211C3×C4—22no—
212C3×C4—122no—
213C3×C4—122no—
214Dic3—42no—
215Dic3—42no—
216Dic3—62no—
217Dic3—62no—
218Dic3—62no—
219Dic3—62no—
220Dic3—121no—
221Dic3—121no—
222Dic3—121no—
223Dic3—121no—
224C32#149311yescharacteristic, complemented, Sylow
225C23D32⋊C411yescharacteristic
226Q8—184no—
227Q8—362no—
228C2×C4—62no—
229C2×C4—62no—
230C2×C4—91no—
231C2×C4—91no—
232C2×C4—91no—
233C2×C4—91no—
234C2×C4—182no—
235C2×C4—182no—
236C2×C4D32⋊C411yescharacteristic
237C2×C4#377512yes—
238C2×C4#377612yes—
239C2×C4C2×GO+(4,𝔽2)11yescharacteristic
240C8—122no—
241C8—184no—
242C2×C3—21no—
243C2×C3—21no—
244C2×C3—21no—
245C2×C3—21no—
246C2×C3—21no—
247C2×C3—21no—
248C2×C3—42no—
249C2×C3—42no—
250C22—21no—
251C22—21no—
252C22#6374012yes—
253C22C2×D32⋊C411yescharacteristic
254C4—92no—
255C4—92no—
256C4—122no—
257C4—122no—
258C4—181no—
259C4—181no—
260C4#6374012yes—
261C4C2×#377511yescharacteristic
262C4C2×#377611yescharacteristic
263C3—21no—
264C3—21no—
265C2—22no—
266C2#1059330911yescharacteristic
267C2#1059332511yescharacteristic
268C2C2×#6374011yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
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 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #10590032C2semidirect
224. C32#1493semidirect

Maximal subgroups

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

subgroupindex
#105950502
C2×C4×#6222
#105911202
#105900322
#14939