Finite Group Databasebeta

← #11785762

Subgroups — #11785762

Order 1152.

762 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 762 conjugacy classes of subgroups — too many to draw. Only its 84 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⋊C4×C3⋊D3C211yesmaximal, characteristic
2#10593812C211yesmaximal, characteristic
3#10593800C211yesmaximal, characteristic
4#10590163C214yesmaximal, complemented
5C22×C4×C3⋊D3—21no—
6C22×C4×C3⋊D3C2211yescharacteristic
7C2×C22⋊#157—21no—
8C2×C4⋊#157C2212yes—
9C2×#3787C2212yes—
10C2×C32×C4⋊C4C411yescharacteristic, complemented
11C2×C4⋊(C3⋊Dic3)C411yescharacteristic, complemented
12C2×#3750—21no—
13C4⋊C4×C3⋊D3—21no—
14C4⋊C4×C3⋊D3—21no—
15C4⋊C4×C3⋊D3C412yescomplemented
16C4⋊C4×C3⋊D3C2212yes—
17C22⋊#622—21no—
18#63781—21no—
19#63778—21no—
20C2×D3×C4⋊C4—62no—
21C23×C3⋊D3D411yescharacteristic
22C22×#157—22no—
23C22×C32×C4—21no—
24C22×C32×C4C2×C411yescharacteristic
25C22×C3⋊Dic3—21no—
26C22×C3⋊Dic3D411yescharacteristic
27C2×C4×C3⋊D3—24no—
28C2×C4×C3⋊D3—22no—
29C2×C4×C3⋊D3—22no—
30C2×C4×C3⋊D3—42no—
31C2×C4×C3⋊D3—42no—
32C2×C4×C3⋊D3C2×C411yescharacteristic
33C2×C4×C3⋊D3D411yescharacteristic
34C2×C4×C3⋊D3D411yescharacteristic
35C2×C4×C3⋊D3C2311yescharacteristic
36C22⋊#157—42no—
37C2×#622—22no—
38C4⋊#157—24no—
39#3787—24no—
40C32×C4⋊C4—21no—
41C32×C4⋊C4C2×C412yes—
42C4⋊(C3⋊Dic3)—21no—
43C4⋊(C3⋊Dic3)C2×C412yes—
44#3750—22no—
45#3750—22no—
46#1823—91nomaximal, Sylow
47C22×C4×D3—62no—
48C22×C4×D3—64no—
49C2×C3×C4⋊C4—22no—
50C2×C4⋊Dic3—62no—
51C2×Dic3⋊C4—64no—
52D3×C4⋊C4—64no—
53D3×C4⋊C4—64no—
54D3×C4⋊C4—64no—
55D3×C4⋊C4—64no—
56C23×C32C22⋊C411yescharacteristic
57C22×C3⋊D3—22no—
58C22×C3⋊D3—22no—
59C22×C3⋊D3C22⋊C411yescharacteristic
60C22×C3⋊D3D812yes—
61C22×C3⋊D3SD1612yes—
62C22×C3⋊D3C2×D411yescharacteristic
63C2×#157—42no—
64C2×#157—42no—
65C2×#157—42no—
66C2×C32×C4—22no—
67C2×C32×C4—22no—
68C2×C32×C4—42no—
69C2×C32×C4C22⋊C411yescharacteristic
70C2×C32×C4C22×C411yescharacteristic
71C2×C3⋊Dic3—22no—
72C2×C3⋊Dic3—22no—
73C2×C3⋊Dic3—42no—
74C2×C3⋊Dic3C22⋊C411yescharacteristic
75C2×C3⋊Dic3C2×D411yescharacteristic
76C4×C3⋊D3—22no—
77C4×C3⋊D3—22no—
78C4×C3⋊D3—22no—
79C4×C3⋊D3—44no—
80C4×C3⋊D3—42no—
81C4×C3⋊D3—42no—
82C4×C3⋊D3#4114yes—
83#622—42no—
84C22×C4⋊C4—91no—
85C2×C22⋊C8—91no—
86#380—91no—
87#340—94no—
88C23×D3—62no—
89C22×C3×C4—24no—
90C22×C3×C4—22no—
91C22×Dic3—62no—
92C22×Dic3—64no—
93C2×C4×D3—62no—
94C2×C4×D3—62no—
95C2×C4×D3—62no—
96C2×C4×D3—62no—
97C2×C4×D3—616no—
98C2×C4×D3—68no—
99C2×C4×D3—68no—
100C2×C4×D3—128no—
101C2×C4×D3—128no—
102C3×C4⋊C4—24no—
103C3×C4⋊C4—24no—
104C4⋊Dic3—64no—
105C4⋊Dic3—64no—
106Dic3⋊C4—68no—
107Dic3⋊C4—68no—
108C22×C32—21no—
109C22×C32—21no—
110C22×C32#10212yes—
111C22×C32C2×C22⋊C411yescharacteristic
112C2×C3⋊D3—21no—
113C2×C3⋊D3—21no—
114C2×C3⋊D3—24no—
115C2×C3⋊D3—24no—
116C2×C3⋊D3#10212yes—
117C2×C3⋊D3#12312yes—
118C2×C3⋊D3C2×D811yescharacteristic
119C2×C3⋊D3C2×SD1611yescharacteristic
120C2×C3⋊D3#13712yes—
121#157—82no—
122C32×C4—21no—
123C32×C4—42no—
124C32×C4#11712yes—
125C3⋊Dic3—21no—
126C3⋊Dic3—42no—
127C3⋊Dic3#12312yes—
128C23×C4—91no—
129C23×C4—181no—
130C22×C8—92no—
131C2×C4⋊C4—91no—
132C2×C4⋊C4—92no—
133C2×C4⋊C4—92no—
134C2×C4⋊C4—92no—
135C2×C4⋊C4—181no—
136C2×C4⋊C4—181no—
137C2×C4⋊C4—181no—
138C2×C4⋊C4#15711yescharacteristic, complemented
139C2×C22⋊C4—181no—
140C22⋊C8—181no—
141C22⋊C8—181no—
142#95—181no—
143C23×C3—22no—
144C22×D3—62no—
145C22×D3—64no—
146C22×D3—64no—
147C22×D3—62no—
148C22×D3—68no—
149C22×D3—68no—
150C2×C3×C4—28no—
151C2×C3×C4—28no—
152C2×C3×C4—22no—
153C2×C3×C4—22no—
154C2×C3×C4—48no—
155C2×Dic3—62no—
156C2×Dic3—62no—
157C2×Dic3—68no—
158C2×Dic3—68no—
159C2×Dic3—128no—
160C4×D3—68no—
161C4×D3—68no—
162C4×D3—68no—
163C4×D3—68no—
164C4×D3—1216no—
165C4×D3—128no—
166C4×D3—128no—
167C2×C32—22no—
168C2×C32#38111yescharacteristic
169C2×C32C2×#10211yescharacteristic
170C2×C32#41911yescharacteristic
171C3⋊D3—22no—
172C3⋊D3#48012yes—
173C3⋊D3#48312yes—
174C24—91no—
175C22×C4—21no—
176C22×C4—91no—
177C22×C4—91no—
178C22×C4—91no—
179C22×C4—91no—
180C22×C4—91no—
181C22×C4—184no—
182C22×C4—182no—
183C22×C4—182no—
184C22×C4—181no—
185C22×C4—182no—
186C22×C4—362no—
187C22×C4—362no—
188C22×C4C2×#15711yescharacteristic
189C2×C8—182no—
190C2×C8—184no—
191C4⋊C4—21no—
192C4⋊C4—92no—
193C4⋊C4—182no—
194C4⋊C4—182no—
195C4⋊C4—184no—
196C4⋊C4—181no—
197C4⋊C4C2×#15712yes—
198C22⋊C4—362no—
199C22×C3—24no—
200C22×C3—24no—
201C22×C3—22no—
202C22×C3—24no—
203C2×D3—64no—
204C2×D3—64no—
205C2×D3—62no—
206C2×D3—62no—
207C2×D3—64no—
208C2×D3—64no—
209C2×D3—616no—
210C2×D3—616no—
211C2×D3—64no—
212C3×C4—24no—
213C3×C4—24no—
214C3×C4—48no—
215Dic3—64no—
216Dic3—64no—
217Dic3—128no—
218C32#182311yescharacteristic, complemented, Sylow
219C23—91no—
220C23—91no—
221C23—92no—
222C23—92no—
223C23—182no—
224C23—182no—
225C23C22⋊#15711yescharacteristic
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—42no—
229C2×C4—91no—
230C2×C4—94no—
231C2×C4—91no—
232C2×C4—182no—
233C2×C4—182no—
234C2×C4—182no—
235C2×C4—182no—
236C2×C4—182no—
237C2×C4—362no—
238C2×C4—362no—
239C2×C4—364no—
240C2×C4—362no—
241C2×C4—362no—
242C2×C4—362no—
243C2×C4—362no—
244C2×C4C22⋊#15711yescharacteristic
245C2×C4C22×#15711yescharacteristic
246C8—362no—
247C2×C3—28no—
248C2×C3—22no—
249C2×C3—22no—
250C2×C3—22no—
251D3—64no—
252D3—64no—
253D3—68no—
254C22—21no—
255C22—21no—
256C22—92no—
257C22—91no—
258C22—91no—
259C22—92no—
260C22—92no—
261C22—184no—
262C22—184no—
263C22—181no—
264C22—181no—
265C22#6378212yes—
266C22C2×C22⋊#15711yescharacteristic
267C4—21no—
268C4—42no—
269C4—92no—
270C4—181no—
271C4—362no—
272C4—722no—
273C4#6428612yes—
274C3—22no—
275C2—22no—
276C2—92no—
277C2—92no—
278C2—182no—
279C2#1059381111yescharacteristic
280C2C2×#6378211yescharacteristic
281C2#1059382911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC2×C32×C4⋊C4C4
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3D4
cosocleC2×C4×C3⋊D3C23
hypercenterC2×C4⋊C4#157
hypocenterC32#1823
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #10590163C2semidirect
10. C2×C32×C4⋊C4C4semidirect
11. C2×C4⋊(C3⋊Dic3)C4semidirect
15. C4⋊C4×C3⋊D3C4semidirect
138. C2×C4⋊C4#157semidirect
218. C32#1823semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×C3⋊D32
#105938122
#105938002
#105901632
#18239