Finite Group Databasebeta

← #11775694

Subgroups — #11775694

Order 1152.

418 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 61 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#10593948C211yesmaximal, characteristic
2#10593723C211yesmaximal, characteristic
3#10590322C211yesmaximal, characteristic
4#10590036C214yesmaximal, complemented
5C2×#3787—21no—
6C42×C3⋊D3C2211yescharacteristic
7C3×#870—21no—
8#63900C411yescharacteristic
9#63900C411yescharacteristic
10#63883—21no—
11#63883—21no—
12#63872—21no—
13#63870C412yes—
14#63870C2212yes—
15C2×#3710—21no—
16#63777—21no—
17#63777C2212yes—
18C3×#803—21no—
19#63555C2212yes—
20D3×#125—61no—
21D3×#97—61no—
22C2×C4×C3⋊D3C2×C411yescharacteristic
23C2×C4×C3⋊D3D411yescharacteristic
24C2×C4×C3⋊D3D411yescharacteristic
25C2×#624—21no—
26C2×#624—21no—
27C2×#622—22no—
28#3787—24no—
29C32×C42D411yescharacteristic
30C4×C3⋊Dic3C2×C411yescharacteristic
31C4×C3⋊Dic3D411yescharacteristic
32C4×C3⋊Dic3C2311yescharacteristic
33C3×C4⋊Dic3—21no—
34C3×C4⋊Dic3—21no—
35C3×Dic3⋊C4—22no—
36C3×Dic3⋊C4—22no—
37C2×C3×C3⋊C8—22no—
38#3724C2×C412yes—
39#3724C2×C412yes—
40Dic3⋊Dic3—22no—
41Dic3⋊Dic3—22no—
42#3710—24no—
43C2×#330—91nomaximal, Sylow
44C3×#125—61no—
45C2×D3×C8—62no—
46D3×C4⋊C4—61no—
47D3×C4⋊C4—61no—
48D3×C4⋊C4—62no—
49D3×C4⋊C4—62no—
50#890—61no—
51#890—61no—
52#889—62no—
53#889—62no—
54C42×D3—61no—
55C42×D3—61no—
56#870—21no—
57C3×#97—61no—
58#815—62no—
59#803—21no—
60C22×C3⋊D3C22⋊C411yescharacteristic
61C2×C32×C4C22⋊C411yescharacteristic
62C2×C32×C4C22⋊C411yescharacteristic
63C2×C32×C4C2×D411yescharacteristic
64C2×C3⋊Dic3C22⋊C411yescharacteristic
65C2×C3⋊Dic3C22×C411yescharacteristic
66C2×C3⋊Dic3C2×D411yescharacteristic
67C4×C3⋊D3—22no—
68C4×C3⋊D3—22no—
69C4×C3⋊D3—22no—
70C2×C3×Dic3—22no—
71C2×C3×Dic3—22no—
72#624—42no—
73#624—42no—
74#622—24no—
75C3×C3⋊C8—24no—
76C2×#125—91no—
77C2×#97—91no—
78C2×#97—91no—
79#330—94no—
80C2×C4×D3—61no—
81C2×C4×D3—61no—
82C2×C4×D3—61no—
83C2×C4×D3—61no—
84C2×C4×D3—61no—
85C2×C4×D3—61no—
86C2×C4×D3—62no—
87C2×C4×D3—62no—
88C2×C3×C8—62no—
89C3×C4⋊C4—62no—
90C3×C4⋊C4—62no—
91C3×C4⋊C4—61no—
92C3×C4⋊C4—61no—
93C3×C42—21no—
94C3×C42—21no—
95C4⋊Dic3—21no—
96C4⋊Dic3—21no—
97C4⋊Dic3—62no—
98C4⋊Dic3—62no—
99Dic3⋊C4—22no—
100Dic3⋊C4—22no—
101Dic3⋊C4—62no—
102Dic3⋊C4—62no—
103Dic3⋊C4—62no—
104Dic3⋊C4—62no—
105C4×Dic3—61no—
106C4×Dic3—61no—
107C4×Dic3—61no—
108C4×Dic3—61no—
109C4×Dic3—61no—
110C4×Dic3—61no—
111C2×C3⋊C8—22no—
112D3×C8—68no—
113C22×C32C2×C22⋊C411yescharacteristic
114C2×C3⋊D3#10112yes—
115C2×C3⋊D3#10412yes—
116C2×C3⋊D3#10412yes—
117C32×C4—21no—
118C32×C4—21no—
119C32×C4—21no—
120C3⋊Dic3—21no—
121C3⋊Dic3—21no—
122C3⋊Dic3—21no—
123C3×Dic3—42no—
124C3×Dic3—42no—
125C22×C8—181no—
126C22×C8—181no—
127#125—61no—
128#125—92no—
129#125—92no—
130#125—181no—
131C2×C4⋊C4—91no—
132C2×C4⋊C4—91no—
133C2×C4⋊C4—181no—
134C2×C4⋊C4—181no—
135C2×C42—91no—
136#97—61no—
137#97—92no—
138#97—92no—
139#97—181no—
140C22×D3—61no—
141C22×D3—61no—
142C2×C3×C4—21no—
143C2×C3×C4—21no—
144C2×C3×C4—21no—
145C2×C3×C4—21no—
146C2×C3×C4—21no—
147C2×C3×C4—21no—
148C2×C3×C4—62no—
149C2×C3×C4—62no—
150C2×Dic3—22no—
151C2×Dic3—22no—
152C2×Dic3—61no—
153C2×Dic3—61no—
154C2×Dic3—61no—
155C2×Dic3—61no—
156C2×Dic3—61no—
157C2×Dic3—61no—
158C4×D3—64no—
159C4×D3—64no—
160C4×D3—122no—
161C4×D3—122no—
162C4×D3—122no—
163C4×D3—122no—
164C4×D3—124no—
165C4×D3—124no—
166C3×C8—64no—
167C3⋊C8—24no—
168C2×C32C2×#10111yescharacteristic
169C2×C32C2×#10411yescharacteristic
170C2×C32C2×#10411yescharacteristic
171C3⋊D3#33014yescomplemented
172C22×C4—91no—
173C22×C4—91no—
174C22×C4—91no—
175C22×C4—181no—
176C22×C4—181no—
177C2×C8—62no—
178C2×C8—184no—
179C2×C8—182no—
180C2×C8—184no—
181C4⋊C4—62no—
182C4⋊C4—61no—
183C4⋊C4—61no—
184C4⋊C4—62no—
185C4⋊C4—92no—
186C4⋊C4—92no—
187C4⋊C4—182no—
188C4⋊C4—182no—
189C42—91no—
190C42—91no—
191C42—91no—
192C42GO+(4,𝔽2)11yescharacteristic
193C22×C3—21no—
194C22×C3—21no—
195C2×D3—62no—
196C2×D3—62no—
197C2×D3—62no—
198C2×D3—62no—
199C2×D3—62no—
200C2×D3—62no—
201C3×C4—22no—
202C3×C4—22no—
203C3×C4—41no—
204C3×C4—41no—
205C3×C4—41no—
206C3×C4—41no—
207C3×C4—122no—
208C3×C4—122no—
209Dic3—42no—
210Dic3—42no—
211Dic3—62no—
212Dic3—62no—
213Dic3—121no—
214Dic3—121no—
215Dic3—121no—
216Dic3—121no—
217C32C2×#33011yescharacteristic, complemented, Sylow
218C23—91no—
219C2×C4—62no—
220C2×C4—62no—
221C2×C4—91no—
222C2×C4—91no—
223C2×C4—91no—
224C2×C4—182no—
225C2×C4—182no—
226C2×C4—182no—
227C2×C4—362no—
228C2×C4—362no—
229C2×C4D32⋊C411yescharacteristic
230C2×C4D32⋊C411yescharacteristic
231C2×C4C2×GO+(4,𝔽2)11yescharacteristic
232C8—64no—
233C8—184no—
234C2×C3—21no—
235C2×C3—21no—
236C2×C3—21no—
237C2×C3—21no—
238C2×C3—21no—
239C2×C3—21no—
240D3—64no—
241D3—64no—
242C22—92no—
243C22—92no—
244C22—92no—
245C22C2×D32⋊C411yescharacteristic
246C4—21no—
247C4—21no—
248C4—21no—
249C4—122no—
250C4—122no—
251C4—181no—
252C4—181no—
253C4—181no—
254C3—21no—
255C3—21no—
256C2—94no—
257C2#1059331511yescharacteristic
258C2#1059332511yescharacteristic
259C2#1059338011yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C22⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32C2×#330
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
4. #10590036C2semidirect
171. C3⋊D3#330semidirect
217. C32C2×#330semidirect

Maximal subgroups

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

subgroupindex
#105939482
#105937232
#105903222
#105900362
C2×#3309