Finite Group Databasebeta

← #11790628

Subgroups — #11790628

Order 1152.

570 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 570 conjugacy classes of subgroups — too many to draw. Only its 107 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×#63919C211yesmaximal, characteristic
2C2×C4×#622C211yesmaximal, characteristic
3C2×#63740C214yesmaximal
4#10591359C211yesmaximal, characteristic
5C22×#627C2212yes—
6C22×#622C2212yes—
7C2×C4×C3⋊Dic3C2211yescharacteristic
8C2×C3×C4⋊Dic3—21no—
9C2×C3×C4⋊Dic3—21no—
10C2×#3724—21no—
11C2×#3724—21no—
12C2×#3724C2212yes—
13#63919—22no—
14#63919C414yescomplemented
15C4×#622—22no—
16#63740—28no—
17C2×#888—61no—
18#4975—61no—
19C22×C32×C4D411yescharacteristic
20C22×C3⋊Dic3D411yescharacteristic
21C22×C3⋊Dic3C2311yescharacteristic
22C22×C3×Dic3—22no—
23C22×C3×Dic3—22no—
24C2×#627—24no—
25C2×#627—24no—
26C2×#627—22no—
27C2×#627C2×C414yes—
28C2×#622—22no—
29C2×#622—22no—
30C2×#622D414yes—
31C4×C3⋊Dic3C2×C412yes—
32C4×C3⋊Dic3D412yes—
33C3×C4⋊Dic3—24no—
34C3×C4⋊Dic3—42no—
35#3724—24no—
36#3724—24no—
37#3724—42no—
38#1956—91nomaximal, Sylow
39C22×Dic6—62no—
40C2×C3×C4⋊C4—61no—
41C2×C3×C4⋊C4—61no—
42C2×C4⋊Dic3—21no—
43C2×C4⋊Dic3—21no—
44C2×Dic3⋊C4—62no—
45C2×Dic3⋊C4—62no—
46C2×Dic3⋊C4—62no—
47C2×C4×Dic3—61no—
48C2×C4×Dic3—61no—
49#888—64no—
50#888—64no—
51C23×C32C2×D411yescharacteristic
52C2×C32×C4C22⋊C412yes—
53C2×C32×C4SD1612yes—
54C2×C32×C4Q1612yes—
55C2×C3⋊Dic3C22⋊C412yes—
56C2×C3⋊Dic3SD1612yes—
57C2×C3⋊Dic3Q1612yes—
58C2×C3⋊Dic3C22×C411yescharacteristic
59C2×C3⋊Dic3C2×D412yes—
60C2×C3⋊Dic3C2×D411yescharacteristic
61C2×C3⋊Dic3#4112yes—
62C2×C3×Dic3—24no—
63C2×C3×Dic3—42no—
64C2×C3×Dic3—42no—
65C2×C3×Dic3—42no—
66C2×C3×Dic3—42no—
67C2×C3×Dic3—42no—
68#627—28no—
69#627—44no—
70#622—24no—
71C2×C4⋊Q8—91no—
72C2×#103—94no—
73C2×C4×C8—91no—
74#384—91no—
75C22×C3×C4—21no—
76C22×C3×C4—21no—
77C22×C3×C4—62no—
78C22×C3×C4—62no—
79C22×Dic3—22no—
80C22×Dic3—22no—
81C22×Dic3—61no—
82C22×Dic3—61no—
83C22×Dic3—61no—
84C22×Dic3—61no—
85C2×Dic6—64no—
86C2×Dic6—64no—
87C2×Dic6—124no—
88C2×Dic6—124no—
89C3×C4⋊C4—64no—
90C3×C4⋊C4—122no—
91C4⋊Dic3—24no—
92C4⋊Dic3—42no—
93Dic3⋊C4—68no—
94Dic3⋊C4—124no—
95Dic3⋊C4—124no—
96C4×Dic3—62no—
97C4×Dic3—62no—
98C4×Dic3—62no—
99C4×Dic3—62no—
100C22×C32C2×C22⋊C411yescharacteristic
101C22×C32#12411yescharacteristic
102C22×C32#12711yescharacteristic
103C22×C32C2×SD1611yescharacteristic
104C22×C32C2×SD1611yescharacteristic
105C22×C32C2×Q1611yescharacteristic
106C22×C32C2×Q1611yescharacteristic
107C32×C4#10314yescomplemented
108C3⋊Dic3#10314yescomplemented
109C3⋊Dic3C4×D412yes—
110C3⋊Dic3#12112yes—
111C3×Dic3—44no—
112C3×Dic3—82no—
113C22×Q8—92no—
114C22×C8—92no—
115C4⋊Q8—94no—
116C4⋊Q8—182no—
117C2×C4⋊C4—61no—
118C2×C4⋊C4—61no—
119C2×C4⋊C4—92no—
120C2×C4⋊C4—181no—
121C2×C4⋊C4—181no—
122C2×C42—91no—
123#103—188no—
124C4×C8—182no—
125C23×C3—21no—
126C23×C3—21no—
127C2×C3×C4—22no—
128C2×C3×C4—22no—
129C2×C3×C4—22no—
130C2×C3×C4—22no—
131C2×C3×C4—22no—
132C2×C3×C4—22no—
133C2×C3×C4—64no—
134C2×C3×C4—122no—
135C2×C3×C4—122no—
136C2×C3×C4—122no—
137C2×C3×C4—122no—
138C2×C3×C4—122no—
139C2×Dic3—24no—
140C2×Dic3—42no—
141C2×Dic3—42no—
142C2×Dic3—42no—
143C2×Dic3—42no—
144C2×Dic3—42no—
145C2×Dic3—62no—
146C2×Dic3—62no—
147C2×Dic3—62no—
148C2×Dic3—62no—
149C2×Dic3—62no—
150C2×Dic3—62no—
151C2×Dic3—61no—
152C2×Dic3—61no—
153C2×Dic3—61no—
154C2×Dic3—61no—
155C2×Dic3—62no—
156C2×Dic3—62no—
157C2×Dic3—62no—
158C2×Dic3—62no—
159Dic6—128no—
160Dic6—128no—
161C2×C32#39011yescharacteristic
162C2×C32C2×#10311yescharacteristic
163C2×C32C2×#10311yescharacteristic
164C2×C32#48711yescharacteristic
165C2×C32#48711yescharacteristic
166C2×C32#49211yescharacteristic
167C2×C32#49411yescharacteristic
168C2×Q8—94no—
169C2×Q8—182no—
170C2×Q8—184no—
171C2×Q8—184no—
172C22×C4—62no—
173C22×C4—62no—
174C22×C4—91no—
175C22×C4—91no—
176C22×C4GO+(4,𝔽2)11yescharacteristic
177C2×C8—94no—
178C2×C8—182no—
179C2×C8—182no—
180C4⋊C4—64no—
181C4⋊C4—122no—
182C4⋊C4—184no—
183C4⋊C4—184no—
184C4⋊C4—362no—
185C42—92no—
186C42—92no—
187C22×C3—21no—
188C22×C3—21no—
189C22×C3—21no—
190C22×C3—21no—
191C22×C3—21no—
192C22×C3—21no—
193C22×C3—21no—
194C22×C3—21no—
195C22×C3—21no—
196C22×C3—21no—
197C22×C3—21no—
198C22×C3—21no—
199C22×C3—21no—
200C22×C3—21no—
201C3×C4—24no—
202C3×C4—24no—
203C3×C4—124no—
204C3×C4—242no—
205Dic3—44no—
206Dic3—62no—
207Dic3—62no—
208Dic3—64no—
209Dic3—64no—
210Dic3—62no—
211Dic3—62no—
212Dic3—82no—
213C32#195611yescharacteristic, complemented, Sylow
214C23C2×GO+(4,𝔽2)11yescharacteristic
215Q8—188no—
216Q8—364no—
217C2×C4—64no—
218C2×C4—92no—
219C2×C4—92no—
220C2×C4—92no—
221C2×C4—92no—
222C2×C4—92no—
223C2×C4—91no—
224C2×C4—91no—
225C2×C4—122no—
226C2×C4—122no—
227C2×C4—122no—
228C2×C4—122no—
229C2×C4—122no—
230C2×C4D32⋊C412yes—
231C2×C4#377512yes—
232C2×C4#377612yes—
233C8—184no—
234C2×C3—21no—
235C2×C3—21no—
236C2×C3—21no—
237C2×C3—21no—
238C2×C3—21no—
239C2×C3—21no—
240C2×C3—21no—
241C2×C3—21no—
242C2×C3—21no—
243C2×C3—21no—
244C2×C3—21no—
245C2×C3—21no—
246C2×C3—21no—
247C2×C3—21no—
248C22#6422111yescharacteristic
249C22#6422711yescharacteristic
250C22#6422811yescharacteristic
251C22#6423111yescharacteristic
252C22C2×D32⋊C411yescharacteristic
253C22C2×#377511yescharacteristic
254C22C2×#377611yescharacteristic
255C4—94no—
256C4—92no—
257C4—92no—
258C4—124no—
259C4—242no—
260C4#6374014yescomplemented
261C3—21no—
262C3—21no—
263C2#1059337511yescharacteristic
264C2#1059337711yescharacteristic
265C2#1059337911yescharacteristic
266C2#1059340711yescharacteristic
267C2#1059344211yescharacteristic
268C2#1059345011yescharacteristic
269C2C2×#6374011yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC22×C32×C4D4
socle, prime radicalC23×C32C2×D4
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1956
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
14. #63919C4semidirect
107. C32×C4#103semidirect
108. C3⋊Dic3#103semidirect
213. C32#1956semidirect
260. C4#63740semidirect

Maximal subgroups

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

subgroupindex
C2×#639192
C2×C4×#6222
C2×#637402
#105913592
#19569