Finite Group Databasebeta

← #11774724

Subgroups — #11774724

Order 1152.

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

normal subgroups only

This group has 472 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
1C4×#3797C211yesmaximal, characteristic
2#10593731C211yesmaximal, characteristic
3#10590247C211yesmaximal, characteristic
4#10590031C214yesmaximal, complemented
5C2×#3797C411yescharacteristic
6C42×C3⋊D3C2211yescharacteristic
7C3×C4×Dic6—21no—
8C4×#627C412yes—
9#63900C411yescharacteristic
10#63883—21no—
11C4×#624—21no—
12#63843—21no—
13#63838C2212yes—
14C2×#3712—21no—
15#63779C2212yes—
16#63778—21no—
17#63777—21no—
18C3×#803—21no—
19#63553C2212yes—
20C4×D3×Q8—61no—
21#4707—61no—
22C2×C4×C3⋊D3C2×C411yescharacteristic
23C2×C4×C3⋊D3D411yescharacteristic
24C2×C4×C3⋊D3D411yescharacteristic
25C2×C3×Dic6—21no—
26C2×#627C2×C412yes—
27C2×#624—21no—
28C2×#624—21no—
29#3797—24no—
30C2×#622—22no—
31C32×C42D411yescharacteristic
32C4×C3⋊Dic3C2×C411yescharacteristic
33C4×C3⋊Dic3D411yescharacteristic
34C4×C3⋊Dic3C2311yescharacteristic
35C3×C4⋊Dic3—21no—
36C3×Dic3⋊C4—22no—
37C3×C4×Dic3—22no—
38C2×C3×C3⋊C8—22no—
39#3724C2×C412yes—
40Dic3⋊Dic3—22no—
41Dic32—22no—
42#3712—24no—
43#1491—91nomaximal, Sylow
44C2×D3×Q8—61no—
45C3×C4×Q8—61no—
46Q8×Dic3—61no—
47C2×ΓL(1,𝔽25)—62no—
48D3×C4⋊C4—61no—
49D3×C4⋊C4—62no—
50#887—62no—
51#887—61no—
52C42×D3—61no—
53C42×D3—61no—
54C42×D3—62no—
55C4×Dic6—21no—
56C4×Dic6—62no—
57C3×#97—61no—
58C8×Dic3—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—
72C3×Dic6—24no—
73#627—22no—
74#627M1614yescomplemented
75#624—24no—
76#624—42no—
77#622—42no—
78C3×C3⋊C8—24no—
79C2×C4×Q8—91no—
80#432—91no—
81C4×M16—91no—
82Q8⋊C8—94no—
83C2×C3×Q8—61no—
84D3×Q8—68no—
85C2×C4×D3—61no—
86C2×C4×D3—61no—
87C2×C4×D3—61no—
88C2×C4×D3—61no—
89C2×C4×D3—61no—
90C2×C4×D3—61no—
91C2×C4×D3—62no—
92C2×C4×D3—62no—
93C2×Dic6—21no—
94C2×Dic6—62no—
95C2×C3×C8—62no—
96C3×C4⋊C4—62no—
97C3×C4⋊C4—61no—
98C3×C42—21no—
99C3×C42—21no—
100C3×C42—62no—
101C4⋊Dic3—21no—
102C4⋊Dic3—62no—
103Dic3⋊C4—22no—
104Dic3⋊C4—62no—
105Dic3⋊C4—62no—
106C4×Dic3—22no—
107C4×Dic3—61no—
108C4×Dic3—61no—
109C4×Dic3—61no—
110C4×Dic3—61no—
111C4×Dic3—61no—
112C4×Dic3—61no—
113C4×Dic3—62no—
114C4×Dic3—62no—
115C2×C3⋊C8—22no—
116ΓL(1,𝔽25)—68no—
117C22×C32C2×C22⋊C411yescharacteristic
118C2×C3⋊D3—21no—
119C2×C3⋊D3—21no—
120C2×C3⋊D3#10412yes—
121C32×C4—21no—
122C32×C4—21no—
123C32×C4—21no—
124C3⋊Dic3—21no—
125C3⋊Dic3C2×M1612yes—
126C3⋊Dic3#13712yes—
127C3×Dic3—24no—
128C3×Dic3—42no—
129C22×Q8—91no—
130C2×M16—181no—
131C4×Q8—61no—
132C4×Q8—92no—
133C4×Q8—92no—
134C4×Q8—181no—
135C2×C4⋊C4—91no—
136C2×C4⋊C4—181no—
137C2×C42—91no—
138C2×C42—181no—
139C4⋊C8—92no—
140C22⋊C8—181no—
141#97—61no—
142#97—181no—
143C4×C8—92no—
144C22×D3—61no—
145C22×D3—61no—
146C3×Q8—64no—
147C2×C3×C4—21no—
148C2×C3×C4—21no—
149C2×C3×C4—21no—
150C2×C3×C4—21no—
151C2×C3×C4—21no—
152C2×C3×C4—21no—
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—
163C4×D3—68no—
164C4×D3—64no—
165C4×D3—64no—
166C4×D3—64no—
167C4×D3—122no—
168C4×D3—122no—
169C4×D3—122no—
170C4×D3—124no—
171Dic6—24no—
172Dic6—64no—
173Dic6—64no—
174C3×C8—64no—
175C3⋊C8—24no—
176C2×C32#40711yescharacteristic
177C2×C32#41911yescharacteristic
178C2×C32C2×#10411yescharacteristic
179C3⋊D3—22no—
180C2×Q8—61no—
181C2×Q8—92no—
182C2×Q8—184no—
183C22×C4—91no—
184C22×C4—91no—
185C22×C4—91no—
186C22×C4—181no—
187C22×C4—181no—
188M16—184no—
189C2×C8—62no—
190C2×C8—182no—
191C4⋊C4—62no—
192C4⋊C4—61no—
193C4⋊C4—92no—
194C4⋊C4—182no—
195C42—62no—
196C42—91no—
197C42—91no—
198C42—91no—
199C42—182no—
200C42GO+(4,𝔽2)11yescharacteristic
201C22×C3—21no—
202C22×C3—21no—
203C2×D3—62no—
204C2×D3—62no—
205C2×D3—62no—
206C2×D3—62no—
207C2×D3—121no—
208C2×D3—121no—
209C3×C4—22no—
210C3×C4—22no—
211C3×C4—22no—
212C3×C4—41no—
213C3×C4—41no—
214C3×C4—41no—
215C3×C4—64no—
216C3×C4—122no—
217Dic3—24no—
218Dic3—42no—
219Dic3—62no—
220Dic3—62no—
221Dic3—62no—
222Dic3—62no—
223Dic3—62no—
224Dic3—121no—
225C32#149111yescharacteristic, complemented, Sylow
226C23—91no—
227Q8—64no—
228Q8—94no—
229Q8—182no—
230C2×C4—62no—
231C2×C4—62no—
232C2×C4—91no—
233C2×C4—91no—
234C2×C4—91no—
235C2×C4—182no—
236C2×C4—182no—
237C2×C4—182no—
238C2×C4—184no—
239C2×C4—362no—
240C2×C4D32⋊C411yescharacteristic
241C2×C4D32⋊C411yescharacteristic
242C2×C4C2×GO+(4,𝔽2)11yescharacteristic
243C8—64no—
244C8—362no—
245C2×C3—21no—
246C2×C3—21no—
247C2×C3—21no—
248C2×C3—21no—
249C2×C3—21no—
250C2×C3—21no—
251D3—64no—
252D3—122no—
253C22—92no—
254C22—181no—
255C22—181no—
256C22C2×D32⋊C411yescharacteristic
257C4—21no—
258C4—21no—
259C4—21no—
260C4—64no—
261C4—92no—
262C4—92no—
263C4—122no—
264C4—181no—
265C3—21no—
266C3—21no—
267C2—182no—
268C2#1059330711yescharacteristic
269C2#1059332111yescharacteristic
270C2#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)
hypocenterC32#1491
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
4. #10590031C2semidirect
74. #627M16semidirect
225. C32#1491semidirect

Maximal subgroups

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

subgroupindex
C4×#37972
#105937312
#105902472
#105900312
#14919