Finite Group Databasebeta

← #11784334

Subgroups — #11784334

Order 1152.

410 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 102 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×#63767C211yesmaximal, characteristic
2C2×C8×#157C211yesmaximal, characteristic
3C4×C4⋊#157C211yesmaximal, characteristic
4#10593723C211yesmaximal, characteristic
5C3⋊D3×C4⋊C8C211yesmaximal, characteristic
6#10590181C211yesmaximal, characteristic
7#10590181C211yesmaximal, characteristic
8C2×C4⋊#157C412yes—
9C2×C4×#157C2211yescharacteristic
10C2×C4×#157C2211yescharacteristic
11C2×#3787C2211yescharacteristic
12C2×#3787C2211yescharacteristic
13C2×C8×C3⋊D3C2211yescharacteristic
14C2×C8×C3⋊D3C2211yescharacteristic
15C42×C3⋊D3C2211yescharacteristic
16#63781C412yes—
17#63777C412yescomplemented
18#63777C412yescomplemented
19#63767—22no—
20C8×#157—22no—
21C32×C4⋊C8C411yescharacteristic, complemented
22#63641C411yescharacteristic, complemented
23#63641C411yescharacteristic, complemented
24C4⋊(C3⋊(C3⋊C8))C411yescharacteristic, complemented
25D3×C4⋊C8—62no—
26C22×#157C2×C412yes—
27C22×#157C2×C412yes—
28C2×C4×C3⋊D3C2×C411yescharacteristic
29C2×C4×C3⋊D3C2×C411yescharacteristic
30C2×C4×C3⋊D3C2311yescharacteristic
31C2×#622C2×C412yes—
32C2×#622C2×C412yes—
33C4⋊#157—24no—
34C4×#157—21no—
35C4×#157—21no—
36C4×#157—21no—
37C4×#157—21no—
38#3787—21no—
39#3787—21no—
40#3787D412yes—
41#3787Q812yes—
42C2×C32×C8C2×C411yescharacteristic
43C2×C32×C8C2×C411yescharacteristic
44C32×C42C2×C411yescharacteristic
45C4×C3⋊Dic3C2×C411yescharacteristic
46C4×C3⋊Dic3C2×C411yescharacteristic
47C4×C3⋊Dic3C2×C411yescharacteristic
48C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
49C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
50C8×C3⋊D3—21no—
51C8×C3⋊D3—21no—
52C8×C3⋊D3—21no—
53C8×C3⋊D3—21no—
54#1771—91nomaximal, Sylow
55C2×D3×C8—62no—
56C2×D3×C8—62no—
57C42×D3—62no—
58C3×C4⋊C8—22no—
59Dic3⋊C8—62no—
60Dic3⋊C8—62no—
61C4⋊(C3⋊C8)—62no—
62C22×C3⋊D3C22×C411yescharacteristic
63C2×#157—22no—
64C2×#157—22no—
65C2×#157—22no—
66C2×#157—22no—
67C2×#157—22no—
68C2×#157M1614yes—
69C2×C32×C4C4211yescharacteristic
70C2×C32×C4C4211yescharacteristic
71C2×C32×C4C22×C411yescharacteristic
72C2×C3⋊Dic3C4211yescharacteristic
73C2×C3⋊Dic3C4211yescharacteristic
74C2×C3⋊Dic3C22×C411yescharacteristic
75C4×C3⋊D3—22no—
76C4×C3⋊D3—22no—
77C4×C3⋊D3C2×D411yescharacteristic
78C4×C3⋊D3C2×Q811yescharacteristic
79C4×C3⋊D3#4111yescharacteristic
80C4×C3⋊D3#4111yescharacteristic
81#622—22no—
82#622C4⋊C414yescomplemented
83C32×C8—21no—
84C32×C8—21no—
85C3⋊(C3⋊C8)—21no—
86C3⋊(C3⋊C8)—21no—
87C2×C4⋊C8—91no—
88C2×#97—91no—
89C2×#97—91no—
90C2×C4×C8—91no—
91C4×C4⋊C4—91no—
92#336—91no—
93#336—91no—
94C2×C4×D3—62no—
95C2×C4×D3—62no—
96C2×C4×D3—62no—
97C2×C3×C8—22no—
98C2×C3×C8—22no—
99C3×C42—22no—
100C4×Dic3—62no—
101C4×Dic3—62no—
102C4×Dic3—62no—
103C2×C3⋊C8—62no—
104C2×C3⋊C8—62no—
105D3×C8—122no—
106D3×C8—122no—
107D3×C8—122no—
108D3×C8—122no—
109C22×C32C2×C4211yescharacteristic
110C2×C3⋊D3C4×D411yescharacteristic
111C2×C3⋊D3C4×Q811yescharacteristic
112C2×C3⋊D3C2×M1612yes—
113C2×C3⋊D3#13112yes—
114#157—24no—
115#157—42no—
116C32×C4—21no—
117C32×C4—21no—
118C32×C4C4×D411yescharacteristic
119C32×C4C4×Q811yescharacteristic
120C3⋊Dic3—21no—
121C3⋊Dic3—21no—
122C3⋊Dic3C2×C4⋊C411yescharacteristic
123C3⋊Dic3#11711yescharacteristic
124C22×C8—91no—
125C22×C8—91no—
126C22×C8—91no—
127C22×C8—91no—
128C2×C4⋊C4—92no—
129C2×C42—91no—
130C2×C42—91no—
131C2×C42—91no—
132C4⋊C8—91no—
133C4⋊C8—91no—
134C4⋊C8—91no—
135C4⋊C8#15711yescharacteristic, complemented
136#97—92no—
137#97—92no—
138#97—182no—
139C4×C8—182no—
140#95—92no—
141C22×D3—62no—
142C2×C3×C4—22no—
143C2×C3×C4—22no—
144C2×C3×C4—22no—
145C2×Dic3—62no—
146C2×Dic3—62no—
147C2×Dic3—62no—
148C4×D3—62no—
149C4×D3—62no—
150C4×D3—62no—
151C4×D3—62no—
152C4×D3—68no—
153C4×D3—124no—
154C3×C8—42no—
155C3×C8—42no—
156C3⋊C8—122no—
157C3⋊C8—122no—
158C2×C32C4×C4⋊C411yescharacteristic
159C2×C32C4×M1611yescharacteristic
160C2×C32#40511yescharacteristic
161C3⋊D3#43512yes—
162C3⋊D3#44612yes—
163C22×C4—91no—
164C22×C4—92no—
165C22×C4—91no—
166C22×C4—91no—
167C22×C4—92no—
168C2×C8—92no—
169C2×C8—92no—
170C2×C8—92no—
171C2×C8—92no—
172C2×C8—91no—
173C2×C8—91no—
174C2×C8—181no—
175C2×C8—181no—
176C2×C8—181no—
177C2×C8—181no—
178C2×C8—181no—
179C2×C8—181no—
180C2×C8C2×#15711yescharacteristic
181C2×C8C2×#15711yescharacteristic
182C4⋊C4—184no—
183C42—91no—
184C42—91no—
185C42—91no—
186C42—181no—
187C42—181no—
188C42—181no—
189C42—181no—
190C42C2×#15711yescharacteristic
191C22×C3—22no—
192C2×D3—62no—
193C2×D3—62no—
194C2×D3—64no—
195C2×D3—64no—
196C3×C4—24no—
197C3×C4—22no—
198C3×C4—22no—
199C3×C4—42no—
200Dic3—62no—
201Dic3—62no—
202Dic3—64no—
203Dic3—122no—
204C32#177111yescharacteristic, complemented, Sylow
205C23—91no—
206C2×C4—91no—
207C2×C4—91no—
208C2×C4—91no—
209C2×C4—91no—
210C2×C4—91no—
211C2×C4—94no—
212C2×C4—91no—
213C2×C4—91no—
214C2×C4—182no—
215C2×C4—182no—
216C2×C4—182no—
217C2×C4—182no—
218C2×C4—182no—
219C2×C4—182no—
220C2×C4—182no—
221C2×C4C4×#15711yescharacteristic
222C2×C4C4×#15711yescharacteristic
223C2×C4C22×#15711yescharacteristic
224C8—21no—
225C8—21no—
226C8—94no—
227C8—182no—
228C8—181no—
229C8—181no—
230C2×C3—22no—
231C2×C3—22no—
232C2×C3—22no—
233D3—64no—
234D3—64no—
235C22—91no—
236C22—91no—
237C22—92no—
238C22—92no—
239C22C2×C4×#15711yescharacteristic
240C4—21no—
241C4—21no—
242C4—91no—
243C4—91no—
244C4—184no—
245C4—181no—
246C4—181no—
247C4—362no—
248C4D4×#15711yescharacteristic
249C4Q8×#15711yescharacteristic
250C3—22no—
251C2—92no—
252C2—92no—
253C2C4⋊C4×#15711yescharacteristic
254C2#1059376511yescharacteristic
255C2M16×#15711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×#157
commutator, socleC22×C32C2×C42
FittingC32×C4⋊C8C4
prime radicalC22×C3⋊D3C22×C4
cosocleC2×C4×C3⋊D3C23
hypercenterC4⋊C8#157
hypocenterC32#1771
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
17. #63777C4semidirect
18. #63777C4semidirect
21. C32×C4⋊C8C4semidirect
22. #63641C4semidirect
23. #63641C4semidirect
24. C4⋊(C3⋊(C3⋊C8))C4semidirect
82. #622C4⋊C4semidirect
135. C4⋊C8#157semidirect
204. C32#1771semidirect

Maximal subgroups

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

subgroupindex
C2×#637672
C2×C8×#1572
C4×C4⋊#1572
#105937232
C3⋊D3×C4⋊C82
#105901812
#17719