Finite Group Databasebeta

← #11774723

Subgroups — #11774723

Order 1152.

456 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 65 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×C4×#627C211yesmaximal, characteristic
2C4×#3792C211yesmaximal, characteristic
3#10591066C211yesmaximal, characteristic
4#10590032C214yesmaximal, complemented
5C22×#627C411yescharacteristic
6C2×#3792—21no—
7C2×C4×C3⋊Dic3C2211yescharacteristic
8C2×C3×C4×Dic3—21no—
9C2×#3724C411yescharacteristic
10C2×Dic3⋊Dic3—21no—
11C4×#627—21no—
12C4×#627—21no—
13C4×#627C412yes—
14C4×#627C2212yes—
15#63777—21no—
16C4×#622C2212yes—
17C3×#830—21no—
18#63572C2212yes—
19#63555—21no—
20C2×C4×Dic6—61no—
21#4719—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—
30#3792—24no—
31C2×#622—22no—
32C4×C3⋊Dic3C2×C411yescharacteristic
33C4×C3⋊Dic3D411yescharacteristic
34C4×C3⋊Dic3D411yescharacteristic
35C4×C3⋊Dic3C2311yescharacteristic
36C3×C4×Dic3—22no—
37C3×C4×Dic3—22no—
38C2×C3×C3⋊C8—22no—
39#3724—21no—
40#3724C2×C412yes—
41Dic3⋊Dic3—22no—
42Dic3⋊Dic3—22no—
43#1491—91nomaximal, Sylow
44C22×Dic6—61no—
45C2×C3×C42—61no—
46C2×C4⋊Dic3—61no—
47C2×Dic3⋊C4—61no—
48C2×Dic3⋊C4—61no—
49C2×C4×Dic3—21no—
50C2×C4×Dic3—61no—
51C2×C4×Dic3—61no—
52C4×Dic6—62no—
53C4×Dic6—62no—
54C4×Dic6—62no—
55C4×Dic6—62no—
56C3×C22⋊C8—61no—
57#830—21no—
58#815—62no—
59Dic3⋊C8—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—24no—
78C3×C3⋊C8—42no—
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—
96C2×C3×C8—62no—
97C3×C42—62no—
98C3×C42—62no—
99C4⋊Dic3—62no—
100C4⋊Dic3—62no—
101Dic3⋊C4—62no—
102Dic3⋊C4—62no—
103Dic3⋊C4—62no—
104Dic3⋊C4—62no—
105C4×Dic3—22no—
106C4×Dic3—22no—
107C4×Dic3—61no—
108C4×Dic3—61no—
109C4×Dic3—61no—
110C4×Dic3—61no—
111C4×Dic3—61no—
112C4×Dic3—61no—
113C4×Dic3—61no—
114C4×Dic3—61no—
115C2×C3⋊C8—22no—
116C22×C32—21no—
117C22×C32—21no—
118C22×C32#10412yes—
119C22×C32C2×C22⋊C411yescharacteristic
120C32×C4—21no—
121C32×C4#13712yes—
122C3⋊Dic3—21no—
123C3⋊Dic3—21no—
124C3⋊Dic3—21no—
125C3⋊Dic3C2×M1612yes—
126C3×Dic3—24no—
127C3×Dic3—42no—
128C22×Q8—91no—
129C2×M16—181no—
130C4×Q8—92no—
131C4×Q8—92no—
132C4×Q8—181no—
133C4×Q8—181no—
134C2×C4⋊C4—91no—
135C2×C4⋊C4—181no—
136C2×C42—61no—
137C2×C42—91no—
138C4⋊C8—92no—
139C22⋊C8—61no—
140#97—181no—
141#97—181no—
142C4×C8—92no—
143C23×C3—21no—
144C23×C3—21no—
145C2×C3×C4—24no—
146C2×C3×C4—21no—
147C2×C3×C4—21no—
148C2×C3×C4—21no—
149C2×C3×C4—21no—
150C2×C3×C4—42no—
151C2×C3×C4—62no—
152C2×C3×C4—64no—
153C2×C3×C4—62no—
154C2×C3×C4—122no—
155C2×Dic3—22no—
156C2×Dic3—24no—
157C2×Dic3—22no—
158C2×Dic3—42no—
159C2×Dic3—61no—
160C2×Dic3—61no—
161C2×Dic3—61no—
162C2×Dic3—61no—
163C2×Dic3—61no—
164C2×Dic3—61no—
165C2×Dic3—61no—
166C2×Dic3—61no—
167C2×Dic3—64no—
168C2×Dic3—122no—
169C2×Dic3—122no—
170C2×Dic3—122no—
171Dic6—64no—
172Dic6—64no—
173Dic6—68no—
174C3×C8—122no—
175C3⋊C8—42no—
176C2×C32—22no—
177C2×C32#40711yescharacteristic
178C2×C32#41911yescharacteristic
179C2×C32C2×#10411yescharacteristic
180C2×Q8—92no—
181C2×Q8—181no—
182C2×Q8—184no—
183C22×C4—61no—
184C22×C4—61no—
185C22×C4—91no—
186C22×C4—91no—
187C22×C4GO+(4,𝔽2)11yescharacteristic
188M16—184no—
189C2×C8—62no—
190C2×C8—182no—
191C4⋊C4—92no—
192C4⋊C4—181no—
193C4⋊C4—182no—
194C4⋊C4—182no—
195C42—62no—
196C42—62no—
197C42—91no—
198C42—91no—
199C42—91no—
200C42—91no—
201C22×C3—22no—
202C22×C3—22no—
203C22×C3—21no—
204C22×C3—21no—
205C22×C3—22no—
206C22×C3—22no—
207C22×C3—41no—
208C22×C3—41no—
209C3×C4—22no—
210C3×C4—22no—
211C3×C4—22no—
212C3×C4—41no—
213C3×C4—64no—
214C3×C4—122no—
215Dic3—24no—
216Dic3—42no—
217Dic3—62no—
218Dic3—62no—
219Dic3—62no—
220Dic3—121no—
221Dic3—121no—
222Dic3—121no—
223Dic3—121no—
224Dic3—121no—
225C32#149111yescharacteristic, complemented, Sylow
226C23D32⋊C411yescharacteristic
227Q8—94no—
228Q8—182no—
229Q8—184no—
230C2×C4—22no—
231C2×C4—64no—
232C2×C4—62no—
233C2×C4—62no—
234C2×C4—91no—
235C2×C4—91no—
236C2×C4—91no—
237C2×C4—91no—
238C2×C4—122no—
239C2×C4—182no—
240C2×C4—182no—
241C2×C4D32⋊C411yescharacteristic
242C2×C4C2×GO+(4,𝔽2)11yescharacteristic
243C8—122no—
244C8—184no—
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#6373112yes—
256C22C2×D32⋊C411yescharacteristic
257C4—21no—
258C4—64no—
259C4—92no—
260C4—122no—
261C4—181no—
262C4—181no—
263C4—181no—
264C4#6423912yes—
265C3—21no—
266C3—21no—
267C2—22no—
268C2#1059330711yescharacteristic
269C2C2×#6373111yescharacteristic
270C2#1059350311yescharacteristic
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#1491
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
76. #627M16semidirect
225. C32#1491semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6272
C4×#37922
#105910662
#105900322
#14919