Finite Group Databasebeta

← #11790082

Subgroups — #11790082

Order 1152.

386 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 77 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
2C4×#3773C211yesmaximal, characteristic
3C2×#63732C211yesmaximal, characteristic
4#10590658C212yesmaximal
5#10590043C212yesmaximal
6C2×C4×#157C2211yescharacteristic
7C2×#3787C2211yescharacteristic
8C2×#3773C412yes—
9C2×C8×C3⋊D3C2211yescharacteristic
10C4×#624C2212yes—
11C2×#3710C2212yes—
12#63767—22no—
13#63737C411yescharacteristic
14#63737C411yescharacteristic
15#63732—22no—
16C3×Dic3⋊C8—22no—
17Dic3⋊(C3⋊C8)—22no—
18D3×C4⋊C8—62no—
19C22×#157C2×C411yescharacteristic
20C22×#157C2×C411yescharacteristic
21C2×C4×C3⋊D3C2311yescharacteristic
22C2×#624C2×C412yes—
23C2×#624C2×C412yes—
24C2×#622—21no—
25C4×#157D412yes—
26C4×#157Q812yes—
27#3787—21no—
28#3787Q812yes—
29#3773—24no—
30C2×C32×C8D411yescharacteristic
31C2×C3⋊(C3⋊C8)D411yescharacteristic
32C8×C3⋊D3—21no—
33C8×C3⋊D3—21no—
34C3×C4×Dic3—22no—
35C2×C3×C3⋊C8—22no—
36Dic32—22no—
37#3710—22no—
38#3710—22no—
39#1940—91nomaximal, Sylow
40C2×D3×C8—62no—
41C2×D3×C8—62no—
42C42×D3—62no—
43C3×C4⋊C8—62no—
44Dic3⋊C8—22no—
45Dic3⋊C8—62no—
46C4⋊(C3⋊C8)—62no—
47C22×C3⋊D3C22×C411yescharacteristic
48C2×#157—22no—
49C2×#157—22no—
50C2×#157C4⋊C412yes—
51C2×#157C4⋊C412yes—
52C2×C32×C4C2×D411yescharacteristic
53C2×C3⋊Dic3#4111yescharacteristic
54C4×C3⋊D3C2×D411yescharacteristic
55C4×C3⋊D3C2×Q811yescharacteristic
56C4×C3⋊D3C2×Q811yescharacteristic
57C4×C3⋊D3#4111yescharacteristic
58C2×C3×Dic3—22no—
59C2×C3×Dic3—22no—
60#624—22no—
61#624—22no—
62#624—22no—
63#624M1614yes—
64#622—22no—
65C32×C8—21no—
66C3⋊(C3⋊C8)—21no—
67C3×C3⋊C8—42no—
68C2×C4⋊C8—92no—
69C2×C4⋊C8—91no—
70C2×#97—91no—
71C4×C4⋊C4—91no—
72#336—92no—
73C2×C4×D3—62no—
74C2×C4×D3—62no—
75C2×C4×D3—62no—
76C2×C3×C8—22no—
77C2×C3×C8—62no—
78C3×C42—62no—
79C4×Dic3—22no—
80C4×Dic3—62no—
81C4×Dic3—62no—
82C2×C3⋊C8—22no—
83C2×C3⋊C8—62no—
84D3×C8—122no—
85D3×C8—122no—
86D3×C8—122no—
87D3×C8—122no—
88C22×C32C4×D411yescharacteristic
89C2×C3⋊D3C2×C4⋊C411yescharacteristic
90C2×C3⋊D3C4×Q811yescharacteristic
91C2×C3⋊D3C2×M1612yes—
92C2×C3⋊D3#13112yes—
93#157—22no—
94#157—22no—
95C32×C4#12111yescharacteristic
96C32×C4C4⋊Q811yescharacteristic
97C3⋊Dic3C22⋊Q811yescharacteristic
98C3⋊Dic3#12511yescharacteristic
99C3×Dic3—24no—
100C3×Dic3—42no—
101C22×C8—92no—
102C22×C8—91no—
103C22×C8—91no—
104C2×C4⋊C4—92no—
105C2×C42—92no—
106C2×C42—91no—
107C4⋊C8—62no—
108C4⋊C8—182no—
109C4⋊C8—182no—
110#97—182no—
111#95—91no—
112#95—91no—
113C22×D3—62no—
114C2×C3×C4—22no—
115C2×C3×C4—62no—
116C2×C3×C4—62no—
117C2×Dic3—22no—
118C2×Dic3—22no—
119C2×Dic3—62no—
120C4×D3—64no—
121C4×D3—62no—
122C4×D3—62no—
123C4×D3—62no—
124C4×D3—62no—
125C4×D3—64no—
126C4×D3—122no—
127C4×D3—122no—
128C3×C8—42no—
129C3×C8—122no—
130C3⋊C8—42no—
131C3⋊C8—122no—
132C2×C32#38911yescharacteristic
133C2×C32#43512yes—
134C3⋊D3#42311yescharacteristic
135C3⋊D3#42411yescharacteristic
136C3⋊D3#44612yes—
137C22×C4—92no—
138C22×C4—92no—
139C22×C4—91no—
140C22×C4—91no—
141C22×C4—91no—
142C2×C8—62no—
143C2×C8—92no—
144C2×C8—91no—
145C2×C8—181no—
146C2×C8—181no—
147C2×C8—182no—
148C2×C8—182no—
149C2×C8—181no—
150C2×C8—181no—
151C2×C8GO+(4,𝔽2)11yescharacteristic
152C4⋊C4—184no—
153C42—62no—
154C42—92no—
155C42—92no—
156C42—182no—
157C22×C3—22no—
158C2×D3—62no—
159C2×D3—62no—
160C2×D3—62no—
161C2×D3—62no—
162C2×D3—62no—
163C2×D3—62no—
164C3×C4—22no—
165C3×C4—22no—
166C3×C4—64no—
167C3×C4—122no—
168Dic3—24no—
169Dic3—42no—
170Dic3—62no—
171Dic3—62no—
172C32#194011yescharacteristic, complemented, Sylow
173C23—91no—
174C2×C4—62no—
175C2×C4—62no—
176C2×C4—94no—
177C2×C4—91no—
178C2×C4—91no—
179C2×C4—91no—
180C2×C4—91no—
181C2×C4—91no—
182C2×C4—92no—
183C2×C4—92no—
184C2×C4—182no—
185C2×C4—182no—
186C2×C4—182no—
187C2×C4—182no—
188C2×C4—182no—
189C2×C4C2×GO+(4,𝔽2)11yescharacteristic
190C8—21no—
191C8—122no—
192C8—182no—
193C8—181no—
194C2×C3—22no—
195C2×C3—22no—
196C2×C3—22no—
197D3—62no—
198D3—62no—
199D3—62no—
200D3—62no—
201C22—92no—
202C22—92no—
203C22—91no—
204C22—91no—
205C22C4×GO+(4,𝔽2)11yescharacteristic
206C4—64no—
207C4—91no—
208C4—91no—
209C4—122no—
210C4—182no—
211C4—182no—
212C4#6422211yescharacteristic
213C4#6424211yescharacteristic
214C3—22no—
215C2—91no—
216C2—91no—
217C2—92no—
218C2#1059328212yes—
219C2#1059341011yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutator, prime radicalC22×C3⋊D3C22×C4
FittingC2×C32×C8D4
socleC22×C32C4×D4
cosocleC2×C4×C3⋊D3C23
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#1940
LCSG ▷ C22×C3⋊D3 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
172. C32#1940semidirect

Maximal subgroups

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

subgroupindex
C2×#637672
C4×#37732
C2×#637322
#105906582
#105900432
#19409