Finite Group Databasebeta

← #11791015

Subgroups — #11791015

Order 1152.

522 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 79 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×#63802C211yesmaximal, characteristic
2C2×#63769C211yesmaximal, characteristic
3#10593341C212yesmaximal
4C2×#63730C212yesmaximal
5C8×#624C211yesmaximal, characteristic
6C2×#3797C2212yes—
7C2×C4⋊#157C2212yes—
8C2×C8×C3⋊D3C2211yescharacteristic
9C2×C3×Dic12—21no—
10C4×#624C2211yescharacteristic
11C2×#3718—21no—
12C2×#3710C2211yescharacteristic
13#63802—22no—
14#63802C414yescomplemented
15#63769—22no—
16#63737—24no—
17#63730—24no—
18C3×C8×Dic3—21no—
19Dic3×C3⋊C8—21no—
20C2×D3×Q16—61no—
21C4×D3×C8—61no—
22C22×#157—22no—
23C2×C4×C3⋊D3C2311yescharacteristic
24C2×C3×Dic6—22no—
25C2×#627—22no—
26C2×#624—22no—
27C2×#624D412yes—
28#3797—22no—
29#3797—22no—
30#3797—22no—
31#3797C2×C414yes—
32C4⋊#157—22no—
33C4⋊#157—22no—
34C2×C32×C8D411yescharacteristic
35C2×C3⋊(C3⋊C8)D411yescharacteristic
36C8×C3⋊D3C2×C412yes—
37C8×C3⋊D3D412yes—
38C3×C4×Dic3—21no—
39C2×C3×C3⋊C8—21no—
40C3×Dic12—24no—
41Dic32—21no—
42#3718—24no—
43#3710—21no—
44#3710D412yes—
45#1969—91nomaximal, Sylow
46C2×D3×Q8—62no—
47C2×C3×Q16—61no—
48C2×#216—62no—
49D3×Q16—64no—
50D3×Q16—64no—
51C2×Dic12—21no—
52C2×D3×C8—61no—
53C2×D3×C8—61no—
54C2×D3×C8—61no—
55C42×D3—61no—
56C3×C4×C8—61no—
57C8×Dic3—21no—
58C8×Dic3—61no—
59C4×C3⋊C8—61no—
60C22×C3⋊D3C2×D411yescharacteristic
61C2×#157—42no—
62C2×#157—44no—
63C2×C32×C4C2×D411yescharacteristic
64C2×C3⋊Dic3#4111yescharacteristic
65C4×C3⋊D3C22×C411yescharacteristic
66C4×C3⋊D3C2×D411yescharacteristic
67C4×C3⋊D3C2×D411yescharacteristic
68C4×C3⋊D3#4111yescharacteristic
69C2×C3×Dic3—22no—
70C2×C3×Dic3—42no—
71C3×Dic6—24no—
72C3×Dic6—42no—
73#627—24no—
74#627—42no—
75#624—22no—
76#624—24no—
77#624—42no—
78#624Q1614yescomplemented
79C32×C8C22⋊C412yes—
80C3⋊(C3⋊C8)C22⋊C412yes—
81C3×C3⋊C8—22no—
82C22×Q16—91no—
83C2×#107—91no—
84C2×#103—92no—
85C2×C4×C8—91no—
86#391—92no—
87C2×C3×Q8—62no—
88D3×Q8—64no—
89D3×Q8—64no—
90D3×Q8—122no—
91D3×Q8—122no—
92C2×C4×D3—62no—
93C2×C4×D3—61no—
94C2×C4×D3—61no—
95C2×C4×D3—122no—
96C2×Dic6—22no—
97C2×Dic6—122no—
98C3×Q16—64no—
99C2×C3×C8—21no—
100C2×C3×C8—21no—
101C2×C3×C8—61no—
102C3×C42—61no—
103#216—68no—
104C4×Dic3—21no—
105C4×Dic3—62no—
106C2×C3⋊C8—21no—
107C2×C3⋊C8—61no—
108C2×C3⋊C8—61no—
109Dic12—24no—
110D3×C8—62no—
111D3×C8—62no—
112D3×C8—62no—
113D3×C8—62no—
114D3×C8—62no—
115D3×C8—62no—
116C22×C32#12111yescharacteristic
117C2×C3⋊D3C4×D411yescharacteristic
118C2×C3⋊D3#12711yescharacteristic
119C2×C3⋊D3C2×Q1612yes—
120C2×C3⋊D3#13512yes—
121#157—82no—
122C32×C4C2×C22⋊C411yescharacteristic
123C32×C4#12111yescharacteristic
124C3⋊Dic3C4×D411yescharacteristic
125C3⋊Dic3#12411yescharacteristic
126C3×Dic3—24no—
127C3×Dic3—44no—
128C22×Q8—92no—
129C2×Q16—61no—
130C2×Q16—94no—
131C2×Q16—182no—
132C2×Q16—181no—
133C22×C8—91no—
134C22×C8—91no—
135C2×C4⋊C4—92no—
136C2×C42—91no—
137#107—182no—
138#103—184no—
139C4×C8—61no—
140C4×C8—181no—
141#95—184no—
142C22×D3—61no—
143C22×D3—61no—
144C3×Q8—64no—
145C3×Q8—122no—
146C2×C3×C4—21no—
147C2×C3×C4—21no—
148C2×C3×C4—62no—
149C2×C3×C4—122no—
150C2×Dic3—22no—
151C2×Dic3—42no—
152C2×Dic3—61no—
153C2×Dic3—61no—
154C4×D3—64no—
155C4×D3—61no—
156C4×D3—61no—
157C4×D3—61no—
158C4×D3—61no—
159C4×D3—61no—
160C4×D3—61no—
161C4×D3—61no—
162C4×D3—61no—
163C4×D3—64no—
164C4×D3—124no—
165C4×D3—124no—
166Dic6—24no—
167Dic6—42no—
168Dic6—124no—
169Dic6—124no—
170C3×C8—22no—
171C3×C8—22no—
172C3×C8—62no—
173C3⋊C8—22no—
174C3⋊C8—62no—
175C3⋊C8—62no—
176C2×C32#39011yescharacteristic
177C2×C32#46712yes—
178C3⋊D3C4×Q1612yes—
179C3⋊D3#49411yescharacteristic
180C3⋊D3#49511yescharacteristic
181C2×Q8—62no—
182C2×Q8—94no—
183C2×Q8—182no—
184C2×Q8—182no—
185C2×Q8—182no—
186C2×Q8—182no—
187C22×C4—92no—
188C22×C4—91no—
189C22×C4—182no—
190C22×C4—182no—
191Q16—64no—
192Q16—184no—
193C2×C8—61no—
194C2×C8—92no—
195C2×C8—91no—
196C2×C8—92no—
197C2×C8—92no—
198C2×C8—181no—
199C2×C8GO+(4,𝔽2)11yescharacteristic
200C4⋊C4—182no—
201C4⋊C4—182no—
202C42—61no—
203C42—181no—
204C22×C3—21no—
205C22×C3—21no—
206C2×D3—61no—
207C2×D3—61no—
208C2×D3—61no—
209C2×D3—61no—
210C2×D3—62no—
211C2×D3—62no—
212C2×D3—62no—
213C2×D3—62no—
214C3×C4—21no—
215C3×C4—21no—
216C3×C4—21no—
217C3×C4—21no—
218C3×C4—64no—
219C3×C4—124no—
220Dic3—24no—
221Dic3—44no—
222Dic3—61no—
223Dic3—61no—
224Dic3—61no—
225Dic3—61no—
226C32#196911yescharacteristic, complemented, Sylow
227C23—91no—
228Q8—64no—
229Q8—122no—
230Q8—184no—
231Q8—362no—
232C2×C4—62no—
233C2×C4—94no—
234C2×C4—91no—
235C2×C4—91no—
236C2×C4—91no—
237C2×C4—91no—
238C2×C4—91no—
239C2×C4—122no—
240C2×C4—182no—
241C2×C4—184no—
242C2×C4—362no—
243C2×C4—362no—
244C2×C4—364no—
245C2×C4C2×GO+(4,𝔽2)11yescharacteristic
246C8—62no—
247C8—92no—
248C8D32⋊C412yes—
249C2×C3—22no—
250C2×C3—22no—
251C2×C3—21no—
252C2×C3—21no—
253D3—62no—
254D3—62no—
255D3—61no—
256D3—61no—
257D3—61no—
258D3—61no—
259C22—92no—
260C22—92no—
261C22—91no—
262C22—91no—
263C22#6423011yescharacteristic
264C4—64no—
265C4—91no—
266C4—91no—
267C4—124no—
268C4—722no—
269C4#6423011yescharacteristic
270C4C2×D32⋊C411yescharacteristic
271C3—21no—
272C3—21no—
273C2—91no—
274C2—91no—
275C2—92no—
276C2#1059328812yes—
277C2#1059340511yescharacteristic
subgroupG/H
centerC22#64230
commutatorC4×C3⋊D3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC22×C32#121
prime radicalC22×C3⋊D3C2×D4
cosocleC2×C4×C3⋊D3C23
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#1969
LCSG ▷ C4×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
14. #63802C4semidirect
78. #624Q16semidirect
226. C32#1969semidirect

Maximal subgroups

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

subgroupindex
C2×#638022
C2×#637692
#105933412
C2×#637302
C8×#6242
#19699