Finite Group Databasebeta

← #11773832

Subgroups — #11773832

Order 1152.

546 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 80 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×#634C211yesmaximal, characteristic
2#10593801C212yesmaximal
3#10590203C212yesmaximal
4#10590202C212yesmaximal
5C22×#634C411yescharacteristic
6C2×C32×C42C411yescharacteristic
7C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
8C2×#3750C411yescharacteristic
9C2×#3750C2211yescharacteristic
10C2×C4×C3⋊Dic3C411yescharacteristic
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C4×#634—22no—
13C4×#634—22no—
14C22⋊#622C2214yes—
15#63779—22no—
16C4×#622—22no—
17C2×C4×Dic6—62no—
18C22×C32×C4C2×C411yescharacteristic
19C22×C32×C4C2×C411yescharacteristic
20C22×C32×C4C2×C411yescharacteristic
21C22×C3⋊Dic3C2×C411yescharacteristic
22C22×C3⋊Dic3C2×C411yescharacteristic
23C22×C3⋊Dic3C2×C411yescharacteristic
24C22×C3⋊Dic3C2311yescharacteristic
25C2×#634—22no—
26C2×#634—22no—
27C2×#634C814yescomplemented
28C2×#622—24no—
29C32×C42—21no—
30C32×C42—21no—
31C4⋊(C3⋊Dic3)—22no—
32#3750—22no—
33#3750—22no—
34C4×C3⋊Dic3—21no—
35C4×C3⋊Dic3—21no—
36C4×C3⋊Dic3D412yes—
37C4×C3⋊Dic3D412yes—
38#1461—91nomaximal, Sylow
39C22×Dic6—62no—
40C2×C3×C42—22no—
41C2×C4⋊Dic3—62no—
42C2×Dic3⋊C4—62no—
43C2×Dic3⋊C4—62no—
44C2×C4×Dic3—62no—
45C2×C4×Dic3—62no—
46C4×Dic6—68no—
47C4×Dic6—68no—
48C23×C32C22×C411yescharacteristic
49C2×C32×C4—21no—
50C2×C32×C4—21no—
51C2×C32×C4—22no—
52C2×C32×C4—21no—
53C2×C32×C4—41no—
54C2×C32×C4C22⋊C411yescharacteristic
55C2×C32×C4C22⋊C411yescharacteristic
56C2×C32×C4C2×C812yes—
57C2×C3⋊Dic3—21no—
58C2×C3⋊Dic3—21no—
59C2×C3⋊Dic3—21no—
60C2×C3⋊Dic3—41no—
61C2×C3⋊Dic3—41no—
62C2×C3⋊Dic3C22⋊C412yes—
63C2×C3⋊Dic3C2×C812yes—
64C2×C3⋊Dic3C2×C812yes—
65C2×C3⋊Dic3M1612yes—
66C2×C3⋊Dic3C2×D412yes—
67#634—28no—
68#622—44no—
69C2×C4×Q8—91no—
70#431—92no—
71#324—92no—
72#324—92no—
73C22×C3×C4—22no—
74C22×C3×C4—22no—
75C22×C3×C4—22no—
76C22×Dic3—62no—
77C22×Dic3—62no—
78C22×Dic3—62no—
79C22×Dic3—62no—
80C2×Dic6—68no—
81C2×Dic6—68no—
82C2×Dic6—68no—
83C3×C42—24no—
84C3×C42—24no—
85C4⋊Dic3—68no—
86Dic3⋊C4—68no—
87Dic3⋊C4—68no—
88C4×Dic3—64no—
89C4×Dic3—64no—
90C4×Dic3—64no—
91C4×Dic3—64no—
92C22×C32—21no—
93C22×C32—21no—
94C22×C32C2×C22⋊C411yescharacteristic
95C22×C32C22×C811yescharacteristic
96C22×C32C2×M1611yescharacteristic
97C32×C4—22no—
98C32×C4—21no—
99C32×C4—41no—
100C32×C4#10112yes—
101C3⋊Dic3—22no—
102C3⋊Dic3—22no—
103C3⋊Dic3—41no—
104C3⋊Dic3C22⋊C814yes—
105C22×Q8—91no—
106C4×Q8—182no—
107C4×Q8—182no—
108C2×C4⋊C4—91no—
109C2×C4⋊C4—91no—
110C2×C4⋊C4—91no—
111C2×C42—91no—
112C2×C42—91no—
113C2×C42#15711yescharacteristic
114C4⋊C8—182no—
115C22⋊C8—94no—
116C4×C8—182no—
117C23×C3—22no—
118C2×C3×C4—24no—
119C2×C3×C4—24no—
120C2×C3×C4—28no—
121C2×C3×C4—24no—
122C2×C3×C4—24no—
123C2×C3×C4—22no—
124C2×C3×C4—22no—
125C2×C3×C4—44no—
126C2×Dic3—64no—
127C2×Dic3—64no—
128C2×Dic3—64no—
129C2×Dic3—64no—
130C2×Dic3—64no—
131C2×Dic3—64no—
132C2×Dic3—64no—
133C2×Dic3—64no—
134C2×Dic3—124no—
135C2×Dic3—124no—
136Dic6—632no—
137C2×C32—21no—
138C2×C32—21no—
139C2×C32C2×C22⋊C811yescharacteristic
140C2×C32#41011yescharacteristic
141C2×C32C2×#10111yescharacteristic
142C2×Q8—94no—
143C2×Q8—182no—
144C2×Q8—182no—
145C22×C4—91no—
146C22×C4—91no—
147C22×C4—91no—
148C22×C4—91no—
149C22×C4C2×#15711yescharacteristic
150C22×C4C2×#15711yescharacteristic
151C22×C4C2×#15711yescharacteristic
152C2×C8—184no—
153C4⋊C4—182no—
154C4⋊C4—182no—
155C4⋊C4—182no—
156C42—21no—
157C42—21no—
158C42—92no—
159C42—92no—
160C42—181no—
161C42—181no—
162C22×C3—24no—
163C22×C3—24no—
164C22×C3—22no—
165C22×C3—22no—
166C22×C3—22no—
167C3×C4—28no—
168C3×C4—24no—
169C3×C4—24no—
170C3×C4—44no—
171Dic3—68no—
172Dic3—68no—
173Dic3—124no—
174Dic3—124no—
175C32#146111yescharacteristic, complemented, Sylow
176C23C22×#15711yescharacteristic
177Q8—188no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—21no—
182C2×C4—41no—
183C2×C4—92no—
184C2×C4—92no—
185C2×C4—92no—
186C2×C4—92no—
187C2×C4—92no—
188C2×C4—181no—
189C2×C4—181no—
190C2×C4—181no—
191C2×C4—361no—
192C2×C4—361no—
193C2×C4#378712yes—
194C2×C4C22⋊#15711yescharacteristic
195C2×C4C22⋊#15711yescharacteristic
196C8—364no—
197C2×C3—24no—
198C2×C3—24no—
199C2×C3—22no—
200C2×C3—22no—
201C2×C3—22no—
202C22—21no—
203C22—21no—
204C22C2×#378711yescharacteristic
205C22#6428311yescharacteristic
206C22C2×C22⋊#15711yescharacteristic
207C4—22no—
208C4—21no—
209C4—41no—
210C4—94no—
211C4—182no—
212C4—182no—
213C4—361no—
214C4#6378012yes—
215C3—22no—
216C2—21no—
217C2—21no—
218C2#1059379211yescharacteristic
219C2#1059380011yescharacteristic
220C2C2×#6378011yescharacteristic
subgroupG/H
centerC2×C4C22⋊#157
commutatorC22×C32C22×C8
FrattiniC23C22×#157
FittingC2×C32×C42C4
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C22×C4
cosocleC22×C3⋊Dic3C23
hypercenterC2×C42#157
hypocenterC32#1461
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
27. C2×#634C8semidirect
175. C32#1461semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6342
#105938012
#105902032
#105902022
#14619