Finite Group Databasebeta

← C2×#10590212 #11796456

Subgroups — C2×#10590212 #11796456

Order 1152.

590 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 590 conjugacy classes of subgroups — too many to draw. Only its 58 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×#64145C211yesmaximal, characteristic
2C2×#63780C212yesmaximal, complemented
3#10590212C214yesmaximal, direct product factor
4C22×C32×D4C411yescharacteristic
5C22×#634C2211yescharacteristic
6C2×#3792—22no—
7C2×#3757—22no—
8#64145—22no—
9#64145C412yes—
10#64145C2212yes—
11C2×C4×C3⋊Dic3C411yescharacteristic
12#63780—22no—
13#63780C2214yescomplemented
14C2×#936—62no—
15C24×C32—21no—
16C2×C32×D4—21no—
17C2×C32×D4—41no—
18C2×C32×D4—41no—
19C2×C32×D4C2×C412yes—
20C22×C32×C4C2×C411yescharacteristic
21C22×C3⋊Dic3—21no—
22C22×C3⋊Dic3D412yes—
23C2×#634—41no—
24C2×#634—41no—
25C2×#634C2×C411yescharacteristic
26C2×#634D412yes—
27C2×#634C2311yescharacteristic
28#3792—24no—
29#3792—42no—
30C2×#622—42no—
31#3757—24no—
32#3757—24no—
33C4×C3⋊Dic3—21no—
34C4×C3⋊Dic3C2×C412yes—
35C2×#355—91nomaximal, Sylow
36C22×C3×D4—22no—
37C22×Dic6—62no—
38C2×#217—68no—
39#936—64no—
40#936—64no—
41#936—68no—
42C2×C4×Dic3—62no—
43C23×C32—22no—
44C23×C32—44no—
45C23×C32—41no—
46C23×C32—41no—
47C23×C32C22⋊C411yescharacteristic
48C32×D4—42no—
49C32×D4—42no—
50C2×C32×C4—21no—
51C2×C32×C4—21no—
52C2×C32×C4C22⋊C411yescharacteristic
53C2×C32×C4C22×C411yescharacteristic
54C2×C3⋊Dic3—22no—
55C2×C3⋊Dic3—22no—
56C2×C3⋊Dic3—22no—
57C2×C3⋊Dic3—42no—
58C2×C3⋊Dic3C22⋊C412yes—
59C2×C3⋊Dic3C2×D412yes—
60#634—41no—
61#634—42no—
62#634—41no—
63#622—44no—
64C2×#124—91no—
65C2×#101—92no—
66#355—94no—
67C24×C3—24no—
68C2×C3×D4—24no—
69C2×C3×D4—24no—
70C2×C3×D4—44no—
71C2×C3×D4—44no—
72C22×C3×C4—22no—
73C22×Dic3—64no—
74C22×Dic3—64no—
75C2×Dic6—62no—
76C2×Dic6—64no—
77C2×Dic6—62no—
78C2×Dic6—124no—
79C2×Dic6—124no—
80#217—616no—
81#217—616no—
82C4×Dic3—64no—
83C4×Dic3—64no—
84C22×C32—22no—
85C22×C32—44no—
86C22×C32—42no—
87C22×C32—82no—
88C22×C32—82no—
89C22×C32#9911yescharacteristic
90C22×C32#9911yescharacteristic
91C22×C32C2×C22⋊C411yescharacteristic
92C32×C4—21no—
93C32×C4—21no—
94C3⋊Dic3—22no—
95C3⋊Dic3—22no—
96C3⋊Dic3—42no—
97C22×Q8—91no—
98C22×D4#15711yescharacteristic
99C2×M16—182no—
100#124—92no—
101#124—92no—
102#124—182no—
103C2×C22⋊C4—182no—
104C2×C42—91no—
105#101—94no—
106#101—182no—
107C23×C3—28no—
108C23×C3—22no—
109C23×C3—44no—
110C23×C3—44no—
111C23×C3—416no—
112C3×D4—48no—
113C3×D4—48no—
114C2×C3×C4—24no—
115C2×C3×C4—24no—
116C2×C3×C4—22no—
117C2×C3×C4—22no—
118C2×Dic3—64no—
119C2×Dic3—64no—
120C2×Dic3—68no—
121C2×Dic3—124no—
122C2×Dic3—124no—
123C2×Dic3—128no—
124Dic6—124no—
125Dic6—128no—
126Dic6—124no—
127C2×C32—21no—
128C2×C32—21no—
129C2×C32—82no—
130C2×C32#35512yescomplemented
131C2×C32C2×#9911yescharacteristic
132C24—21no—
133C2×Q8—91no—
134C2×Q8—91no—
135C2×Q8—92no—
136C2×Q8—361no—
137C2×Q8—361no—
138C2×D4—21no—
139C2×D4—41no—
140C2×D4—41no—
141C2×D4C2×#15712yes—
142C22×C4—92no—
143C22×C4—181no—
144C22×C4C2×#15711yescharacteristic
145M16—184no—
146M16—362no—
147C2×C8—362no—
148C22⋊C4—184no—
149C22⋊C4—184no—
150C42—92no—
151C42—181no—
152C22×C3—28no—
153C22×C3—22no—
154C22×C3—22no—
155C22×C3—22no—
156C22×C3—48no—
157C22×C3—416no—
158C22×C3—88no—
159C22×C3—88no—
160C3×C4—24no—
161C3×C4—24no—
162Dic3—124no—
163Dic3—124no—
164Dic3—128no—
165C32C2×#35511yescharacteristic, complemented, Sylow
166C23—22no—
167C23—44no—
168C23—41no—
169C23—41no—
170C23C22⋊#15711yescharacteristic
171Q8—361no—
172Q8—361no—
173Q8—362no—
174D4—42no—
175D4—42no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—92no—
179C2×C4—92no—
180C2×C4—182no—
181C2×C4—182no—
182C2×C4—182no—
183C2×C4—362no—
184C2×C4C22⋊#15711yescharacteristic
185C2×C4C22×#15711yescharacteristic
186C8—364no—
187C2×C3—24no—
188C2×C3—24no—
189C2×C3—24no—
190C2×C3—22no—
191C2×C3—88no—
192C22—22no—
193C22—44no—
194C22—42no—
195C22—82no—
196C22—82no—
197C22#6378611yescharacteristic
198C22#6378611yescharacteristic
199C22C2×C22⋊#15711yescharacteristic
200C4—21no—
201C4—21no—
202C4—182no—
203C4—182no—
204C4—362no—
205C3—22no—
206C2—21no—
207C2—21no—
208C2—82no—
209C2#1059021212yesdirect product factor
210C2C2×#6378611yescharacteristic
subgroupG/H
centerC22#63786
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
Fitting, prime radicalC22×C32×D4C4
socleC22×C32#99
cosocleC2×#634C23
hypercenterC22×D4#157
hypocenterC32C2×#355
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#63780C2semidirect
3. #10590212C2direct (N × H)
13. #63780C22semidirect
130. C2×C32#355semidirect
165. C32C2×#355semidirect
209. C2#10590212direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641452
C2×#637802
#105902122
C2×#3559