Finite Group Databasebeta

← #11774725

Subgroups — #11774725

Order 1152.

472 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 63 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
1C2×#63838C211yesmaximal, characteristic
2#10593804C211yesmaximal, characteristic
3#10591060C211yesmaximal, characteristic
4#10590031C214yesmaximal, complemented
5C22×#627C411yescharacteristic
6C2×C4×C3⋊Dic3C2211yescharacteristic
7C2×C3×Dic3⋊C4—21no—
8C2×C3×#208—21no—
9C2×#3724C411yescharacteristic
10C2×Dic32—21no—
11#63838—21no—
12#63838—21no—
13#63838C412yes—
14#63838C2212yes—
15C22⋊#622—21no—
16#63779C2212yes—
17#63777—21no—
18#63555—21no—
19#63553C2212yes—
20C2×#887—61no—
21Dic3×M16—61no—
22C22×C32×C4D411yescharacteristic
23C22×C3⋊Dic3C2×C411yescharacteristic
24C22×C3⋊Dic3D411yescharacteristic
25C22×C3×Dic3—21no—
26C22×C3×Dic3—21no—
27C2×#627—21no—
28C2×#627—24no—
29C2×#627C2×C412yes—
30C2×#622—22no—
31C4×C3⋊Dic3C2×C411yescharacteristic
32C4×C3⋊Dic3D411yescharacteristic
33C4×C3⋊Dic3D411yescharacteristic
34C4×C3⋊Dic3C2311yescharacteristic
35C3×Dic3⋊C4—22no—
36C3×Dic3⋊C4—22no—
37C3×#208—24no—
38C2×C3×C3⋊C8—22no—
39#3724—21no—
40#3724C2×C412yes—
41Dic32—22no—
42Dic32—22no—
43#1491—91nomaximal, Sylow
44C22×Dic6—61no—
45C2×C3×M16—61no—
46C2×C3×C4⋊C4—61no—
47C2×Dic3⋊C4—21no—
48C2×Dic3⋊C4—61no—
49C2×C4×Dic3—61no—
50C2×C4×Dic3—61no—
51C2×C4×Dic3—61no—
52C2×C4×Dic3—61no—
53C2×#208—21no—
54#887—62no—
55#887—62no—
56#887—62no—
57#887—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—24no—
71C2×C3×Dic3—22no—
72C2×C3×Dic3—22no—
73C2×C3×Dic3—42no—
74#627—24no—
75#627—22no—
76#627M1614yescomplemented
77#622—42no—
78C3×C3⋊C8—24no—
79C2×C4×Q8—91no—
80#432—91no—
81C4×M16—91no—
82Q8⋊C8—94no—
83C22×C3×C4—21no—
84C22×C3×C4—21no—
85C22×C3×C4—61no—
86C22×C3×C4—61no—
87C22×Dic3—21no—
88C22×Dic3—21no—
89C22×Dic3—61no—
90C22×Dic3—61no—
91C22×Dic3—61no—
92C22×Dic3—61no—
93C2×Dic6—62no—
94C2×Dic6—62no—
95C2×Dic6—68no—
96C3×M16—64no—
97C2×C3×C8—62no—
98C3×C4⋊C4—62no—
99C3×C4⋊C4—62no—
100Dic3⋊C4—22no—
101Dic3⋊C4—22no—
102Dic3⋊C4—62no—
103Dic3⋊C4—62no—
104C4×Dic3—61no—
105C4×Dic3—61no—
106C4×Dic3—61no—
107C4×Dic3—61no—
108C4×Dic3—61no—
109C4×Dic3—61no—
110C4×Dic3—61no—
111C4×Dic3—61no—
112C4×Dic3—62no—
113C4×Dic3—62no—
114C4×Dic3—62no—
115C4×Dic3—62no—
116#208—24no—
117C2×C3⋊C8—22no—
118C22×C32—21no—
119C22×C32—21no—
120C22×C32#10412yes—
121C22×C32C2×C22⋊C411yescharacteristic
122C32×C4—21no—
123C32×C4—21no—
124C3⋊Dic3—21no—
125C3⋊Dic3—21no—
126C3⋊Dic3C2×M1612yes—
127C3⋊Dic3#13712yes—
128C3×Dic3—24no—
129C3×Dic3—42no—
130C22×Q8—91no—
131C2×M16—61no—
132C4×Q8—92no—
133C4×Q8—92no—
134C4×Q8—181no—
135C4×Q8—181no—
136C2×C4⋊C4—61no—
137C2×C4⋊C4—91no—
138C2×C42—91no—
139C2×C42—181no—
140C4⋊C8—92no—
141C22⋊C8—181no—
142#97—181no—
143#97—181no—
144C4×C8—92no—
145C23×C3—21no—
146C23×C3—21no—
147C2×C3×C4—22no—
148C2×C3×C4—22no—
149C2×C3×C4—21no—
150C2×C3×C4—21no—
151C2×C3×C4—21no—
152C2×C3×C4—21no—
153C2×C3×C4—42no—
154C2×C3×C4—62no—
155C2×C3×C4—64no—
156C2×C3×C4—62no—
157C2×C3×C4—122no—
158C2×Dic3—22no—
159C2×Dic3—24no—
160C2×Dic3—22no—
161C2×Dic3—42no—
162C2×Dic3—61no—
163C2×Dic3—61no—
164C2×Dic3—61no—
165C2×Dic3—61no—
166C2×Dic3—61no—
167C2×Dic3—61no—
168C2×Dic3—61no—
169C2×Dic3—61no—
170C2×Dic3—64no—
171C2×Dic3—64no—
172C2×Dic3—122no—
173C2×Dic3—122no—
174Dic6—64no—
175Dic6—64no—
176Dic6—68no—
177C3×C8—64no—
178C3⋊C8—24no—
179C2×C32—22no—
180C2×C32#40711yescharacteristic
181C2×C32#41911yescharacteristic
182C2×C32C2×#10411yescharacteristic
183C2×Q8—92no—
184C2×Q8—181no—
185C2×Q8—184no—
186C22×C4—61no—
187C22×C4—61no—
188C22×C4—91no—
189C22×C4—91no—
190C22×C4GO+(4,𝔽2)11yescharacteristic
191M16—64no—
192C2×C8—62no—
193C2×C8—182no—
194C4⋊C4—62no—
195C4⋊C4—62no—
196C4⋊C4—92no—
197C4⋊C4—181no—
198C42—91no—
199C42—91no—
200C42—91no—
201C42—91no—
202C42—182no—
203C42—182no—
204C22×C3—22no—
205C22×C3—22no—
206C22×C3—21no—
207C22×C3—21no—
208C22×C3—22no—
209C22×C3—22no—
210C22×C3—41no—
211C22×C3—41no—
212C3×C4—21no—
213C3×C4—21no—
214C3×C4—22no—
215C3×C4—41no—
216C3×C4—41no—
217C3×C4—64no—
218C3×C4—122no—
219Dic3—24no—
220Dic3—42no—
221Dic3—62no—
222Dic3—62no—
223Dic3—62no—
224Dic3—62no—
225Dic3—62no—
226Dic3—62no—
227Dic3—121no—
228Dic3—121no—
229C32#149111yescharacteristic, complemented, Sylow
230C23D32⋊C411yescharacteristic
231Q8—94no—
232Q8—182no—
233Q8—184no—
234C2×C4—22no—
235C2×C4—64no—
236C2×C4—62no—
237C2×C4—62no—
238C2×C4—91no—
239C2×C4—91no—
240C2×C4—91no—
241C2×C4—91no—
242C2×C4—122no—
243C2×C4—182no—
244C2×C4—182no—
245C2×C4D32⋊C411yescharacteristic
246C2×C4C2×GO+(4,𝔽2)11yescharacteristic
247C8—64no—
248C8—362no—
249C2×C3—24no—
250C2×C3—21no—
251C2×C3—21no—
252C2×C3—21no—
253C2×C3—21no—
254C2×C3—21no—
255C2×C3—21no—
256C2×C3—42no—
257C22—21no—
258C22—21no—
259C22#6374112yes—
260C22C2×D32⋊C411yescharacteristic
261C4—21no—
262C4—21no—
263C4—64no—
264C4—92no—
265C4—92no—
266C4—122no—
267C4—181no—
268C4—181no—
269C3—21no—
270C3—21no—
271C2—22no—
272C2#1059330711yescharacteristic
273C2#1059332111yescharacteristic
274C2C2×#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#1491
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
76. #627M16semidirect
229. C32#1491semidirect

Maximal subgroups

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

subgroupindex
C2×#638382
#105938042
#105910602
#105900312
#14919