Finite Group Databasebeta

← #11770810

Subgroups — #11770810

Order 1152.

594 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 82 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×C22⋊#622C212yesmaximal
2C2×#63658C211yesmaximal, characteristic
3C23×C32×C4C411yescharacteristic
4C23×C3⋊Dic3C411yescharacteristic
5C23×C3⋊Dic3C2211yescharacteristic
6C22×#622—22no—
7C22⋊#622—22no—
8C22⋊#622C414yescomplemented
9#63658—22no—
10C2×C3⋊#95—62no—
11C24×C32C2×C411yescharacteristic
12C22×C32×C4—21no—
13C22×C32×C4—21no—
14C22×C32×C4—41no—
15C22×C32×C4—41no—
16C22×C32×C4C812yescomplemented
17C22×C3⋊Dic3—21no—
18C22×C3⋊Dic3—21no—
19C22×C3⋊Dic3—41no—
20C22×C3⋊Dic3—41no—
21C22×C3⋊Dic3—41no—
22C22×C3⋊Dic3—41no—
23C22×C3⋊Dic3C812yescomplemented
24C22×C3⋊Dic3C2×C412yes—
25C22×C3⋊Dic3D412yes—
26C22×C3⋊Dic3D411yescharacteristic
27C22×C3⋊Dic3Q811yescharacteristic
28C2×#622—24no—
29C2×#622—42no—
30C2×#622—42no—
31#1280—91nomaximal, Sylow
32C23×C3×C4—22no—
33C23×Dic3—62no—
34C23×Dic3—62no—
35C3⋊#95—68no—
36C23×C32—21no—
37C23×C32—21no—
38C23×C32—21no—
39C23×C32—21no—
40C23×C32C4211yescharacteristic
41C23×C32C22⋊C411yescharacteristic
42C23×C32C4⋊C411yescharacteristic
43C23×C32C2×C811yescharacteristic
44C23×C32C2×C811yescharacteristic
45C23×C32M1611yescharacteristic
46C23×C32M1611yescharacteristic
47C2×C32×C4—22no—
48C2×C32×C4—42no—
49C2×C32×C4—41no—
50C2×C32×C4—41no—
51C2×C32×C4—42no—
52C2×C3⋊Dic3—22no—
53C2×C3⋊Dic3—22no—
54C2×C3⋊Dic3—22no—
55C2×C3⋊Dic3—42no—
56C2×C3⋊Dic3—41no—
57C2×C3⋊Dic3—41no—
58C2×C3⋊Dic3—42no—
59C2×C3⋊Dic3—41no—
60C2×C3⋊Dic3—41no—
61C2×C3⋊Dic3—42no—
62C2×C3⋊Dic3C22⋊C412yes—
63C2×C3⋊Dic3C4⋊C412yes—
64#622—44no—
65C2×C22⋊C8—92no—
66C2×#95—91no—
67C24×C3—22no—
68C22×C3×C4—24no—
69C22×C3×C4—24no—
70C22×C3×C4—24no—
71C22×C3×C4—44no—
72C22×C3×C4—44no—
73C22×Dic3—64no—
74C22×Dic3—64no—
75C22×Dic3—64no—
76C22×Dic3—62no—
77C22×Dic3—62no—
78C22×Dic3—64no—
79C22×Dic3—64no—
80C22×Dic3—124no—
81C22×Dic3—124no—
82C22×Dic3—124no—
83C22×Dic3—124no—
84C22×C32—21no—
85C22×C32—21no—
86C22×C32—21no—
87C22×C32—21no—
88C22×C32—21no—
89C22×C32—21no—
90C22×C32—21no—
91C22×C32—21no—
92C22×C32—21no—
93C22×C32—21no—
94C22×C32—21no—
95C22×C32—21no—
96C22×C32#9511yescharacteristic
97C22×C32C4×C811yescharacteristic
98C22×C32#9711yescharacteristic
99C22×C32C22⋊C811yescharacteristic
100C22×C32C22⋊C811yescharacteristic
101C22×C32#9911yescharacteristic
102C22×C32#9911yescharacteristic
103C22×C32#10011yescharacteristic
104C22×C32#10111yescharacteristic
105C22×C32C4⋊C811yescharacteristic
106C22×C32C4⋊C811yescharacteristic
107C32×C4—42no—
108C3⋊Dic3—22no—
109C3⋊Dic3—22no—
110C3⋊Dic3—42no—
111C23×C4—91no—
112C23×C4—91no—
113C23×C4#15711yescharacteristic
114C22×C8—182no—
115C22⋊C8—94no—
116C22⋊C8—182no—
117#95—182no—
118C23×C3—24no—
119C23×C3—24no—
120C23×C3—24no—
121C23×C3—24no—
122C23×C3—22no—
123C23×C3—22no—
124C23×C3—22no—
125C23×C3—22no—
126C23×C3—22no—
127C23×C3—22no—
128C23×C3—22no—
129C2×C3×C4—28no—
130C2×C3×C4—48no—
131C2×C3×C4—44no—
132C2×C3×C4—44no—
133C2×C3×C4—48no—
134C2×Dic3—64no—
135C2×Dic3—64no—
136C2×Dic3—68no—
137C2×Dic3—124no—
138C2×Dic3—124no—
139C2×Dic3—128no—
140C2×Dic3—124no—
141C2×Dic3—124no—
142C2×Dic3—128no—
143C2×Dic3—124no—
144C2×Dic3—124no—
145C2×Dic3—128no—
146C2×C32—21no—
147C2×C32—21no—
148C2×C32—21no—
149C2×C32—21no—
150C2×C32#32311yescharacteristic
151C2×C32#32311yescharacteristic
152C2×C32#32411yescharacteristic
153C2×C32#32411yescharacteristic
154C2×C32#33611yescharacteristic
155C2×C32#34211yescharacteristic
156C2×C32#34311yescharacteristic
157C24C2×#15711yescharacteristic
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—41no—
161C22×C4—41no—
162C22×C4—92no—
163C22×C4—92no—
164C22×C4—91no—
165C22×C4—91no—
166C22×C4—92no—
167C22×C4—181no—
168C22×C4—181no—
169C22×C4—361no—
170C22×C4—361no—
171C22×C4—361no—
172C22×C4—361no—
173C22×C4#62212yescomplemented
174C2×C8—184no—
175C2×C8—362no—
176C2×C8—362no—
177C22×C3—24no—
178C22×C3—24no—
179C22×C3—24no—
180C22×C3—24no—
181C22×C3—24no—
182C22×C3—24no—
183C22×C3—24no—
184C22×C3—24no—
185C22×C3—24no—
186C22×C3—24no—
187C22×C3—24no—
188C22×C3—24no—
189C22×C3—22no—
190C22×C3—22no—
191C22×C3—22no—
192C22×C3—22no—
193C22×C3—22no—
194C22×C3—22no—
195C22×C3—22no—
196C22×C3—22no—
197C22×C3—22no—
198C22×C3—22no—
199C22×C3—22no—
200C3×C4—48no—
201Dic3—124no—
202Dic3—124no—
203Dic3—128no—
204C32#128011yescharacteristic, complemented, Sylow
205C23—21no—
206C23—21no—
207C23—21no—
208C23—21no—
209C23#378711yescharacteristic
210C23#378811yescharacteristic
211C23C4×#15711yescharacteristic
212C23C4⋊#15711yescharacteristic
213C23C2×#62211yescharacteristic
214C23#379211yescharacteristic
215C23C22⋊#15711yescharacteristic
216C2×C4—22no—
217C2×C4—42no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—42no—
221C2×C4—92no—
222C2×C4—92no—
223C2×C4—182no—
224C2×C4—182no—
225C2×C4—182no—
226C2×C4—361no—
227C2×C4—362no—
228C2×C4—361no—
229C2×C4—362no—
230C2×C4—361no—
231C2×C4—361no—
232C2×C4—362no—
233C8—364no—
234C2×C3—24no—
235C2×C3—24no—
236C2×C3—24no—
237C2×C3—24no—
238C2×C3—22no—
239C2×C3—22no—
240C2×C3—22no—
241C2×C3—22no—
242C2×C3—22no—
243C2×C3—22no—
244C2×C3—22no—
245C22—21no—
246C22—21no—
247C22—21no—
248C22—21no—
249C22—21no—
250C22—21no—
251C22—21no—
252C22—21no—
253C22—21no—
254C22—21no—
255C22—21no—
256C22—21no—
257C22#6377411yescharacteristic
258C22C4×#62211yescharacteristic
259C22C4⋊#62211yescharacteristic
260C22#6377711yescharacteristic
261C22#6377811yescharacteristic
262C22#6377911yescharacteristic
263C22#6378011yescharacteristic
264C22#6378111yescharacteristic
265C22#6378611yescharacteristic
266C22C22⋊#62211yescharacteristic
267C22#6378811yescharacteristic
268C4—42no—
269C4—182no—
270C4—182no—
271C4—362no—
272C3—22no—
273C2—21no—
274C2—21no—
275C2—21no—
276C2—21no—
277C2#1059020211yescharacteristic
278C2#1059020311yescharacteristic
279C2#1059020411yescharacteristic
280C2#1059020611yescharacteristic
281C2#1059020711yescharacteristic
282C2#1059020811yescharacteristic
283C2#1059022211yescharacteristic
subgroupG/H
centerC23C22⋊#157
commutatorC22×C32C4×C8
FrattiniC24C2×#157
FittingC23×C32×C4C4
socleC23×C32C22⋊C4
prime radicalC24×C32C2×C4
cosocleC23×C3⋊Dic3C22
hypercenterC23×C4#157
hypocenterC32#1280
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
8. C22⋊#622C4semidirect
16. C22×C32×C4C8semidirect
23. C22×C3⋊Dic3C8semidirect
173. C22×C4#622semidirect
204. C32#1280semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊#6222
C2×#636582
#12809