Finite Group Databasebeta

← C2×#10590203 #11773735

Subgroups — C2×#10590203 #11773735

Order 1152.

746 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 746 conjugacy classes of subgroups — too many to draw. Only its 98 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×#3750C211yesmaximal, characteristic
2C2×C22⋊#622C212yesmaximal
3#10590203C214yesmaximal, direct product factor
4C23×C32×C4C411yescharacteristic
5C23×C3⋊Dic3C411yescharacteristic
6C23×C3⋊Dic3C2211yescharacteristic
7C22×#622—22no—
8C2×#3750—22no—
9C2×#3750—22no—
10C2×#3750C412yes—
11C2×#3750C2212yes—
12C22⋊#622—22no—
13C22⋊#622C2214yes—
14C22×Dic3⋊C4—62no—
15C24×C32C2×C411yescharacteristic
16C22×C32×C4—21no—
17C22×C32×C4—21no—
18C22×C32×C4—42no—
19C22×C32×C4C2×C412yes—
20C22×C3⋊Dic3—21no—
21C22×C3⋊Dic3—21no—
22C22×C3⋊Dic3—22no—
23C22×C3⋊Dic3—42no—
24C22×C3⋊Dic3C814yescomplemented
25C22×C3⋊Dic3C2×C412yes—
26C22×C3⋊Dic3C2×C411yescharacteristic
27C22×C3⋊Dic3D412yes—
28C22×C3⋊Dic3D412yes—
29C22×C3⋊Dic3C2311yescharacteristic
30C2×#622—24no—
31C2×#622—44no—
32#3750—24no—
33#3750—24no—
34C2×#324—91nomaximal, Sylow
35C23×C3×C4—22no—
36C23×Dic3—62no—
37C23×Dic3—62no—
38C2×Dic3⋊C4—64no—
39C2×Dic3⋊C4—64no—
40C2×Dic3⋊C4—68no—
41C2×Dic3⋊C4—68no—
42C23×C32—22no—
43C23×C32—22no—
44C23×C32C22⋊C411yescharacteristic
45C23×C32C22⋊C411yescharacteristic
46C23×C32C2×C812yes—
47C23×C32M1612yes—
48C23×C32C22×C411yescharacteristic
49C2×C32×C4—22no—
50C2×C32×C4—42no—
51C2×C32×C4—42no—
52C2×C32×C4—42no—
53C2×C3⋊Dic3—24no—
54C2×C3⋊Dic3—24no—
55C2×C3⋊Dic3—22no—
56C2×C3⋊Dic3—22no—
57C2×C3⋊Dic3—24no—
58C2×C3⋊Dic3—41no—
59C2×C3⋊Dic3—42no—
60C2×C3⋊Dic3—41no—
61C2×C3⋊Dic3C22⋊C412yes—
62C2×C3⋊Dic3C2×C814yescomplemented
63C2×C3⋊Dic3C2×D412yes—
64#622—44no—
65C22×C4⋊C4—91no—
66C2×C22⋊C8—92no—
67#324—94no—
68C24×C3—22no—
69C22×C3×C4—24no—
70C22×C3×C4—24no—
71C22×C3×C4—24no—
72C22×C3×C4—48no—
73C22×Dic3—64no—
74C22×Dic3—68no—
75C22×Dic3—62no—
76C22×Dic3—64no—
77C22×Dic3—64no—
78C22×Dic3—62no—
79C22×Dic3—64no—
80C22×Dic3—64no—
81C22×Dic3—68no—
82C22×Dic3—128no—
83Dic3⋊C4—616no—
84Dic3⋊C4—616no—
85C22×C32—24no—
86C22×C32—24no—
87C22×C32—21no—
88C22×C32—21no—
89C22×C32—21no—
90C22×C32—21no—
91C22×C32C22⋊C812yes—
92C22×C32C22⋊C812yes—
93C22×C32#9912yes—
94C22×C32#10112yes—
95C22×C32C2×C22⋊C411yescharacteristic
96C22×C32C22×C811yescharacteristic
97C22×C32C2×M1611yescharacteristic
98C32×C4—42no—
99C3⋊Dic3—24no—
100C3⋊Dic3—22no—
101C3⋊Dic3—22no—
102C23×C4—91no—
103C23×C4—91no—
104C23×C4#15711yescharacteristic
105C22×C8—182no—
106C2×C4⋊C4—92no—
107C2×C4⋊C4—92no—
108C2×C4⋊C4—182no—
109C2×C4⋊C4—182no—
110C22⋊C8—94no—
111C22⋊C8—182no—
112C23×C3—28no—
113C23×C3—28no—
114C23×C3—22no—
115C23×C3—24no—
116C23×C3—24no—
117C23×C3—22no—
118C23×C3—22no—
119C2×C3×C4—28no—
120C2×C3×C4—48no—
121C2×C3×C4—48no—
122C2×C3×C4—48no—
123C2×Dic3—68no—
124C2×Dic3—64no—
125C2×Dic3—64no—
126C2×Dic3—68no—
127C2×Dic3—68no—
128C2×Dic3—616no—
129C2×Dic3—616no—
130C2×Dic3—128no—
131C2×Dic3—124no—
132C2×Dic3—128no—
133C2×Dic3—124no—
134C2×C32—22no—
135C2×C32—21no—
136C2×C32—21no—
137C2×C32#32414yescomplemented
138C2×C32C2×C22⋊C811yescharacteristic
139C2×C32C2×#9911yescharacteristic
140C2×C32C2×#10111yescharacteristic
141C24C2×#15711yescharacteristic
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—42no—
145C22×C4—92no—
146C22×C4—94no—
147C22×C4—92no—
148C22×C4—91no—
149C22×C4—91no—
150C22×C4—92no—
151C22×C4—182no—
152C22×C4—181no—
153C22×C4—181no—
154C22×C4—362no—
155C22×C4C2×#15712yes—
156C2×C8—184no—
157C2×C8—364no—
158C4⋊C4—184no—
159C4⋊C4—184no—
160C22×C3—24no—
161C22×C3—24no—
162C22×C3—24no—
163C22×C3—24no—
164C22×C3—216no—
165C22×C3—216no—
166C22×C3—22no—
167C22×C3—22no—
168C22×C3—24no—
169C22×C3—24no—
170C22×C3—24no—
171C22×C3—22no—
172C22×C3—24no—
173C3×C4—48no—
174Dic3—616no—
175Dic3—124no—
176Dic3—124no—
177C32C2×#32411yescharacteristic, complemented, Sylow
178C23—22no—
179C23—22no—
180C23#378712yes—
181C23#378812yes—
182C23C22⋊#15711yescharacteristic
183C23C22⋊#15711yescharacteristic
184C23C22×#15711yescharacteristic
185C2×C4—22no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—94no—
190C2×C4—92no—
191C2×C4—92no—
192C2×C4—182no—
193C2×C4—184no—
194C2×C4—184no—
195C2×C4—182no—
196C2×C4—184no—
197C2×C4—361no—
198C2×C4—362no—
199C2×C4—361no—
200C8—364no—
201C2×C3—24no—
202C2×C3—24no—
203C2×C3—28no—
204C2×C3—22no—
205C2×C3—22no—
206C2×C3—22no—
207C2×C3—28no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22—24no—
213C22—24no—
214C22#6377812yes—
215C22#6377812yes—
216C22#6378012yes—
217C22#6378612yes—
218C22C2×#378711yescharacteristic
219C22C2×#378811yescharacteristic
220C22C2×C22⋊#15711yescharacteristic
221C4—42no—
222C4—184no—
223C4—182no—
224C4—182no—
225C3—22no—
226C2—21no—
227C2—21no—
228C2—22no—
229C2#1059020314yesdirect product factor
230C2C2×#6377811yescharacteristic
231C2C2×#6378011yescharacteristic
232C2C2×#6378611yescharacteristic
subgroupG/H
centerC23C22⋊#157
commutatorC22×C32C22×C8
FrattiniC23C22×#157
FittingC23×C32×C4C4
socleC23×C32C22⋊C4
prime radicalC24×C32C2×C4
cosocleC22×C3⋊Dic3C23
hypercenterC23×C4#157
hypocenterC32C2×#324
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
3. #10590203C2direct (N × H)
24. C22×C3⋊Dic3C8semidirect
62. C2×C3⋊Dic3C2×C8semidirect
137. C2×C32#324semidirect
177. C32C2×#324semidirect
229. C2#10590203direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37502
C2×C22⋊#6222
#105902032
C2×#3249