Finite Group Databasebeta

← #11783678

Subgroups — #11783678

Order 1152.

562 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 562 conjugacy classes of subgroups — too many to draw. Only its 108 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
1C22×#3787C211yesmaximal, characteristic
2C4×C22⋊#157C211yesmaximal, characteristic
3C2×#63767C212yesmaximal, complemented
4C3⋊D3×C22⋊C8C211yesmaximal, characteristic
5#10590181C212yesmaximal, complemented
6C22×C4×C3⋊D3C2211yescharacteristic
7C2×C22⋊#157C412yes—
8C22×#622C412yescomplemented
9C2×C4×#157C2212yes—
10C2×#3787—24no—
11C2×#3787C412yescomplemented
12C2×#3787C2211yescharacteristic
13C2×#3787C2211yescharacteristic
14C2×C8×C3⋊D3C2212yes—
15#63781C412yes—
16#63767—24no—
17C32×C22⋊C8C411yescharacteristic, complemented
18#63657C411yescharacteristic, complemented
19#63647C412yescomplemented
20D3×C22⋊C8—62no—
21C23×C3⋊D3C2×C411yescharacteristic
22C22×#157C2×C414yes—
23C22×C32×C4C2×C411yescharacteristic
24C22×C3⋊Dic3C2×C411yescharacteristic
25C2×C4×C3⋊D3—22no—
26C2×C4×C3⋊D3—22no—
27C2×C4×C3⋊D3C2×C411yescharacteristic
28C2×C4×C3⋊D3C2×C411yescharacteristic
29C2×C4×C3⋊D3C2×C411yescharacteristic
30C2×C4×C3⋊D3C2311yescharacteristic
31C22⋊#157—24no—
32C2×#622—24no—
33C2×#622C2×C412yes—
34C2×#622C2×C412yes—
35C4×#157—22no—
36C4×#157—22no—
37#3787—22no—
38#3787—24no—
39#3787D414yes—
40C2×C32×C8C2×C412yes—
41C2×C3⋊(C3⋊C8)C2×C412yes—
42C8×C3⋊D3—22no—
43C8×C3⋊D3—22no—
44#1752—91nomaximal, Sylow
45C22×C4×D3—62no—
46C2×D3×C8—64no—
47C3×C22⋊C8—22no—
48#830—62no—
49(C2×D3)⋊C8—64no—
50C23×C32C4211yescharacteristic
51C22×C3⋊D3—22no—
52C22×C3⋊D3—22no—
53C22×C3⋊D3C4211yescharacteristic
54C22×C3⋊D3M1614yes—
55C22×C3⋊D3C22×C411yescharacteristic
56C2×#157—24no—
57C2×#157—24no—
58C2×#157—24no—
59C2×C32×C4—22no—
60C2×C32×C4C4211yescharacteristic
61C2×C32×C4C22×C411yescharacteristic
62C2×C3⋊Dic3—21no—
63C2×C3⋊Dic3—21no—
64C2×C3⋊Dic3C4211yescharacteristic
65C2×C3⋊Dic3C22×C411yescharacteristic
66C4×C3⋊D3—22no—
67C4×C3⋊D3—22no—
68C4×C3⋊D3—21no—
69C4×C3⋊D3—21no—
70C4×C3⋊D3C2×D412yes—
71C4×C3⋊D3#4112yes—
72#622—22no—
73#622C22⋊C414yescomplemented
74C32×C8—22no—
75C3⋊(C3⋊C8)—22no—
76C23×C8—91no—
77C2×C22⋊C8—91no—
78C2×#97—92no—
79C4×C22⋊C4—91no—
80#336—92no—
81C23×D3—62no—
82C22×C3×C4—22no—
83C22×Dic3—62no—
84C2×C4×D3—62no—
85C2×C4×D3—62no—
86C2×C4×D3—62no—
87C2×C4×D3—62no—
88C2×C4×D3—124no—
89C2×C4×D3—124no—
90C2×C3×C8—24no—
91C2×C3⋊C8—64no—
92D3×C8—124no—
93D3×C8—124no—
94C22×C32—21no—
95C22×C32—21no—
96C22×C32#9712yescomplemented
97C22×C32C2×C4211yescharacteristic
98C2×C3⋊D3—21no—
99C2×C3⋊D3—21no—
100C2×C3⋊D3—28no—
101C2×C3⋊D3#9712yescomplemented
102C2×C3⋊D3C4×D412yes—
103C2×C3⋊D3C2×M1612yes—
104C2×C3⋊D3#13112yes—
105#157—44no—
106C32×C4—21no—
107C32×C4C4×D412yes—
108C3⋊Dic3—21no—
109C3⋊Dic3C2×C22⋊C411yescharacteristic
110C3⋊Dic3#11711yescharacteristic
111C23×C4—91no—
112C22×C8—91no—
113C22×C8—92no—
114C22×C8—91no—
115C22×C8—92no—
116C22×C8—92no—
117C22×C8—184no—
118C2×C22⋊C4—92no—
119C2×C42—92no—
120C22⋊C8—91no—
121C22⋊C8—92no—
122C22⋊C8#15711yescharacteristic, complemented
123#97—184no—
124#95—92no—
125C23×C3—22no—
126C22×D3—62no—
127C22×D3—62no—
128C22×D3—68no—
129C22×D3—124no—
130C22×D3—124no—
131C2×C3×C4—22no—
132C2×C3×C4—22no—
133C2×C3×C4—44no—
134C2×Dic3—62no—
135C2×Dic3—62no—
136C2×Dic3—122no—
137C2×Dic3—122no—
138C4×D3—64no—
139C4×D3—64no—
140C4×D3—122no—
141C4×D3—122no—
142C4×D3—124no—
143C4×D3—124no—
144C3×C8—44no—
145C3⋊C8—124no—
146C2×C32—22no—
147C2×C32C4×C22⋊C411yescharacteristic
148C2×C32C2×#9711yescharacteristic
149C2×C32#40511yescharacteristic
150C3⋊D3—22no—
151C3⋊D3#43514yes—
152C24—91no—
153C22×C4—91no—
154C22×C4—91no—
155C22×C4—91no—
156C22×C4—91no—
157C22×C4—91no—
158C22×C4—94no—
159C22×C4—182no—
160C22×C4—182no—
161C22×C4C2×#15711yescharacteristic
162C2×C8—94no—
163C2×C8—92no—
164C2×C8—92no—
165C2×C8—92no—
166C2×C8—182no—
167C2×C8—182no—
168C2×C8—184no—
169C2×C8—184no—
170C2×C8—182no—
171C2×C8C2×#15712yes—
172C22⋊C4—184no—
173C42—182no—
174C42—182no—
175C22×C3—24no—
176C22×C3—22no—
177C22×C3—42no—
178C22×C3—42no—
179C2×D3—64no—
180C2×D3—64no—
181C2×D3—64no—
182C2×D3—64no—
183C2×D3—1216no—
184C2×D3—122no—
185C2×D3—122no—
186C3×C4—24no—
187C3×C4—42no—
188Dic3—62no—
189Dic3—62no—
190Dic3—122no—
191C32#175211yescharacteristic, complemented, Sylow
192C23—91no—
193C23—94no—
194C23—91no—
195C23—182no—
196C23—182no—
197C23C4×#15711yescharacteristic
198C2×C4—22no—
199C2×C4—91no—
200C2×C4—92no—
201C2×C4—92no—
202C2×C4—91no—
203C2×C4—181no—
204C2×C4—181no—
205C2×C4—182no—
206C2×C4—181no—
207C2×C4—181no—
208C2×C4—182no—
209C2×C4—184no—
210C2×C4—184no—
211C2×C4—184no—
212C2×C4C4×#15711yescharacteristic
213C2×C4C22×#15711yescharacteristic
214C8—22no—
215C8—94no—
216C8—182no—
217C8—182no—
218C2×C3—22no—
219C2×C3—22no—
220C2×C3—22no—
221C2×C3—44no—
222D3—68no—
223D3—124no—
224C22—21no—
225C22—21no—
226C22—92no—
227C22—92no—
228C22—92no—
229C22—92no—
230C22—188no—
231C22—181no—
232C22—181no—
233C22#6376712yescomplemented
234C22C2×C4×#15711yescharacteristic
235C4—21no—
236C4—91no—
237C4—91no—
238C4—181no—
239C4—364no—
240C4D4×#15712yes—
241C3—22no—
242C2—22no—
243C2—94no—
244C2—182no—
245C2C22⋊C4×#15711yescharacteristic
246C2C2×#6376711yescharacteristic
247C2#1059377511yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×#157
commutator, socleC22×C32C2×C42
FittingC32×C22⋊C8C4
prime radicalC23×C3⋊D3C2×C4
cosocleC2×C4×C3⋊D3C23
hypercenterC22⋊C8#157
hypocenterC32#1752
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
3. C2×#63767C2semidirect
5. #10590181C2semidirect
8. C22×#622C4semidirect
11. C2×#3787C4semidirect
17. C32×C22⋊C8C4semidirect
18. #63657C4semidirect
19. #63647C4semidirect
73. #622C22⋊C4semidirect
96. C22×C32#97semidirect
101. C2×C3⋊D3#97semidirect
122. C22⋊C8#157semidirect
191. C32#1752semidirect
233. C22#63767semidirect

Maximal subgroups

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

subgroupindex
C22×#37872
C4×C22⋊#1572
C2×#637672
C3⋊D3×C22⋊C82
#105901812
#17529