Finite Group Databasebeta

← #11785473

Subgroups — #11785473

Order 1152.

462 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 71 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×#64283C211yesmaximal, characteristic
2C2×#63733C212yesmaximal, complemented
3#10591159C212yesmaximal
4#10590051C212yesmaximal, complemented
5C22×C4×C3⋊D3C2211yescharacteristic
6C2×#3792C412yes—
7#64283—24no—
8C2×#3788C412yes—
9C2×#3787C2211yescharacteristic
10C2×#3787C2211yescharacteristic
11C2×#3712C2214yes—
12#63733—24no—
13C3×#830—22no—
14#63557—22no—
15#4726—62no—
16C23×C3⋊D3Q811yescharacteristic
17C22×C32×C4D411yescharacteristic
18C22×C3⋊Dic3C2×C411yescharacteristic
19C2×C4×C3⋊D3—22no—
20C2×C4×C3⋊D3—22no—
21C2×C4×C3⋊D3C2×C411yescharacteristic
22C2×C4×C3⋊D3D411yescharacteristic
23C2×C4×C3⋊D3Q811yescharacteristic
24C2×C4×C3⋊D3C2311yescharacteristic
25#3792—24no—
26C2×#622C2×C412yes—
27C2×#622C2×C412yes—
28#3788—24no—
29#3787—22no—
30#3787D414yes—
31C2×C3×C3⋊C8—24no—
32#3712—24no—
33#3712—24no—
34#1811—91nomaximal, Sylow
35C22×C4×D3—62no—
36C2×ΓL(1,𝔽25)—64no—
37C3×C22⋊C8—62no—
38#830—22no—
39(C2×D3)⋊C8—64no—
40C23×C32C4⋊C411yescharacteristic
41C22×C3⋊D3—22no—
42C22×C3⋊D3—42no—
43C22×C3⋊D3C4⋊C411yescharacteristic
44C22×C3⋊D3C2×Q811yescharacteristic
45C2×C32×C4—22no—
46C2×C32×C4C4⋊C411yescharacteristic
47C2×C32×C4C2×D411yescharacteristic
48C2×C3⋊Dic3—21no—
49C2×C3⋊Dic3—21no—
50C2×C3⋊Dic3C4⋊C411yescharacteristic
51C2×C3⋊Dic3C22×C411yescharacteristic
52C4×C3⋊D3—22no—
53C4×C3⋊D3—22no—
54C4×C3⋊D3—21no—
55C4×C3⋊D3—21no—
56C4×C3⋊D3C2×D412yes—
57C4×C3⋊D3#4112yes—
58#622—22no—
59#622C22⋊C414yes—
60C3×C3⋊C8—44no—
61C22×M16—91no—
62C2×#108—92no—
63#407—92no—
64#341—92no—
65C23×D3—62no—
66C22×C3×C4—22no—
67C22×Dic3—62no—
68C2×C4×D3—62no—
69C2×C4×D3—62no—
70C2×C4×D3—62no—
71C2×C4×D3—62no—
72C2×C4×D3—124no—
73C2×C4×D3—124no—
74C2×C3×C8—64no—
75C2×C3⋊C8—24no—
76ΓL(1,𝔽25)—124no—
77ΓL(1,𝔽25)—124no—
78C22×C32—22no—
79C22×C32—21no—
80C22×C32C2×C4⋊C411yescharacteristic
81C2×C3⋊D3—22no—
82C2×C3⋊D3—22no—
83C2×C3⋊D3—21no—
84C2×C3⋊D3—44no—
85C2×C3⋊D3C22⋊Q812yes—
86C32×C4—21no—
87C32×C4#12112yes—
88C3⋊Dic3—21no—
89C3⋊Dic3C2×C22⋊C411yescharacteristic
90C3⋊Dic3#11711yescharacteristic
91C23×C4—91no—
92C2×M16—94no—
93C2×M16—92no—
94C2×M16—92no—
95C2×M16—184no—
96C22×C8—91no—
97C22×C8—91no—
98#108—184no—
99C22⋊C8—62no—
100C22⋊C8—182no—
101C23×C3—22no—
102C22×D3—62no—
103C22×D3—62no—
104C22×D3—124no—
105C22×D3—124no—
106C22×D3—124no—
107C2×C3×C4—22no—
108C2×C3×C4—22no—
109C2×C3×C4—44no—
110C2×Dic3—62no—
111C2×Dic3—62no—
112C2×Dic3—122no—
113C2×Dic3—122no—
114C4×D3—64no—
115C4×D3—64no—
116C4×D3—122no—
117C4×D3—122no—
118C4×D3—124no—
119C4×D3—124no—
120C3×C8—124no—
121C3⋊C8—44no—
122C2×C32—41no—
123C2×C32#38011yescharacteristic
124C2×C32#43012yes—
125C3⋊D3—22no—
126C3⋊D3—41no—
127C24—91no—
128C22×C4—91no—
129C22×C4—91no—
130C22×C4—91no—
131C22×C4—91no—
132C22×C4—91no—
133C22×C4—182no—
134C22×C4—182no—
135C22×C4GO+(4,𝔽2)11yescharacteristic
136M16—184no—
137M16—184no—
138M16—184no—
139M16—184no—
140C2×C8—64no—
141C2×C8—94no—
142C2×C8—92no—
143C2×C8—92no—
144C2×C8—182no—
145C22×C3—24no—
146C22×C3—22no—
147C22×C3—42no—
148C22×C3—42no—
149C2×D3—64no—
150C2×D3—64no—
151C2×D3—122no—
152C2×D3—122no—
153C2×D3—122no—
154C2×D3—122no—
155C2×D3—1216no—
156C3×C4—24no—
157C3×C4—42no—
158Dic3—62no—
159Dic3—62no—
160Dic3—122no—
161C32#181111yescharacteristic, complemented, Sylow
162C23—91no—
163C23—91no—
164C23—182no—
165C23—362no—
166C23#377311yescharacteristic
167C2×C4—22no—
168C2×C4—91no—
169C2×C4—92no—
170C2×C4—92no—
171C2×C4—91no—
172C2×C4—181no—
173C2×C4—181no—
174C2×C4—182no—
175C2×C4—181no—
176C2×C4—181no—
177C2×C4—182no—
178C2×C4#377311yescharacteristic
179C2×C4C2×GO+(4,𝔽2)11yescharacteristic
180C8—94no—
181C8—124no—
182C8—182no—
183C2×C3—22no—
184C2×C3—22no—
185C2×C3—22no—
186C2×C3—44no—
187D3—124no—
188D3—124no—
189C22—22no—
190C22—21no—
191C22—92no—
192C22—182no—
193C22—182no—
194C22—181no—
195C22—364no—
196C22C2×#377311yescharacteristic
197C4—21no—
198C4—91no—
199C4—91no—
200C4—181no—
201C4#6424212yes—
202C3—22no—
203C2—41no—
204C2—182no—
205C2—361no—
206C2#1059333012yes—
207C2#1059351611yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC22×C32×C4D4
socleC22×C32C2×C4⋊C4
prime radicalC23×C3⋊D3Q8
cosocleC2×C4×C3⋊D3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1811
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×#63733C2semidirect
4. #10590051C2semidirect
161. C32#1811semidirect

Maximal subgroups

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

subgroupindex
C2×#642832
C2×#637332
#105911592
#105900512
#18119