Finite Group Databasebeta

← C113×#7605 #43275625

Subgroups — C113×#7605 #43275625

Order 28928.

440 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 154 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
1C4×C4⋊Q8×C113C211yesmaximal, characteristic
2C113×#1839C212yesmaximal
3C113×#1272C214yesmaximal
4C2×C4⋊Q8×C113C411yescharacteristic
5C2×C4×Q8×C113C412yes—
6#391×C113C2212yes—
7#389×C113—22no—
8#384×C113C411yescharacteristic
9C4×C4⋊C4×C113—22no—
10C43×C113C2211yescharacteristic
11#336×C113—22no—
12#336×C113—22no—
13#336×C113C2214yes—
14C22×Q8×C113C2×C412yes—
15C22×C8×C113—24no—
16C4⋊Q8×C113—22no—
17C4⋊Q8×C113C814yescomplemented
18C4×Q8×C113—44no—
19C2×C4⋊C4×C113—22no—
20C2×C4⋊C4×C113—22no—
21C2×C4⋊C4×C113—22no—
22C2×C4⋊C4×C113C2×C412yes—
23C2×C42×C113—22no—
24C2×C42×C113C2×C411yescharacteristic
25C2×C42×C113C2×C411yescharacteristic
26C2×C42×C113D412yes—
27C2×C42×C113D412yes—
28C2×C42×C113C2311yescharacteristic
29#95×C113—24no—
30C2×Q8×C113—22no—
31C2×Q8×C113—42no—
32C2×Q8×C113—42no—
33C2×Q8×C113C2×C814yes—
34C22×C4×C113—22no—
35C22×C4×C113—22no—
36C22×C4×C113C22⋊C411yescharacteristic
37C22×C4×C113C22⋊C412yes—
38C22×C4×C113C22⋊C411yescharacteristic
39C22×C4×C113C22×C411yescharacteristic
40C22×C4×C113C2×D412yes—
41C2×C8×C113—44no—
42C2×C8×C113—44no—
43C2×C8×C113—44no—
44C4⋊C4×C113—28no—
45C4⋊C4×C113—42no—
46C4⋊C4×C113—44no—
47C4⋊C4×C113—44no—
48C42×C113—22no—
49C42×C113—24no—
50C42×C113—42no—
51C42×C113—41no—
52C42×C113—44no—
53C42×C113C2×C812yes—
54C42×C113M1612yes—
55C23×C113C2×C22⋊C411yescharacteristic
56Q8×C113—44no—
57Q8×C113—44no—
58C2×C4×C113—22no—
59C2×C4×C113—21no—
60C2×C4×C113—21no—
61C2×C4×C113—22no—
62C2×C4×C113—22no—
63C2×C4×C113—22no—
64C2×C4×C113—22no—
65C2×C4×C113—24no—
66C2×C4×C113—21no—
67C2×C4×C113—22no—
68C2×C4×C113—42no—
69C2×C4×C113—42no—
70C2×C4×C113—42no—
71C2×C4×C113—44no—
72C2×C4×C113C22⋊C814yes—
73C2×C4×C113#10012yes—
74C2×C4×C113C22×C811yescharacteristic
75C2×C4×C113C2×M1611yescharacteristic
76C2×C4×C113#13714yes—
77C8×C113—84no—
78C22×C113C2×C22⋊C811yescharacteristic
79C22×C113#41011yescharacteristic
80C22×C113C2×#10011yescharacteristic
81C22×C113#41912yes—
82C22×C113#42112yes—
83C4×C113—22no—
84C4×C113—21no—
85C4×C113—21no—
86C4×C113—24no—
87C4×C113—24no—
88C4×C113—41no—
89C4×C113—44no—
90C4×C113—82no—
91#7605C11311yesmaximal, characteristic, direct product factor, Sylow
92C2×C113#146011yescharacteristic
93C2×C113#147912yes—
94C2×C113#151512yes—
95C2×C113#153611yescharacteristic
96C2×C113#155811yescharacteristic
97C4×C4⋊Q8C2×C11311yescharacteristic
98#1839C2×C11312yes—
99#1272C2×C11314yes—
100C113#760511yescharacteristic, direct product factor, Sylow
101C2×C4⋊Q8C4×C11311yescharacteristic
102C2×C4×Q8C4×C11312yes—
103#391C22×C11312yes—
104#389—22no—
105#384C4×C11311yescharacteristic
106C4×C4⋊C4—22no—
107C43C22×C11311yescharacteristic
108#336—22no—
109#336—22no—
110#336C22×C11314yes—
111C22×Q8C2×C4×C11312yes—
112C22×C8—24no—
113C4⋊Q8—22no—
114C4⋊Q8C8×C11314yescomplemented
115C4×Q8—44no—
116C2×C4⋊C4—22no—
117C2×C4⋊C4—22no—
118C2×C4⋊C4—22no—
119C2×C4⋊C4C2×C4×C11312yes—
120C2×C42—22no—
121C2×C42C2×C4×C11311yescharacteristic
122C2×C42C2×C4×C11311yescharacteristic
123C2×C42D4×C11312yes—
124C2×C42D4×C11312yes—
125C2×C42C23×C11311yescharacteristic
126#95—24no—
127C2×Q8—22no—
128C2×Q8—42no—
129C2×Q8—42no—
130C2×Q8C2×C8×C11314yes—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4C22⋊C4×C11311yescharacteristic
134C22×C4C22⋊C4×C11312yes—
135C22×C4C22⋊C4×C11311yescharacteristic
136C22×C4C22×C4×C11311yescharacteristic
137C22×C4C2×D4×C11312yes—
138C2×C8—44no—
139C2×C8—44no—
140C2×C8—44no—
141C4⋊C4—28no—
142C4⋊C4—42no—
143C4⋊C4—44no—
144C4⋊C4—44no—
145C42—22no—
146C42—24no—
147C42—42no—
148C42—41no—
149C42—44no—
150C42C2×C8×C11312yes—
151C42M16×C11312yes—
152C23C2×C22⋊C4×C11311yescharacteristic
153Q8—44no—
154Q8—44no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—24no—
163C2×C4—21no—
164C2×C4—22no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—42no—
168C2×C4—44no—
169C2×C4C22⋊C8×C11314yes—
170C2×C4#100×C11312yes—
171C2×C4C22×C8×C11311yescharacteristic
172C2×C4C2×M16×C11311yescharacteristic
173C2×C4#137×C11314yes—
174C8—84no—
175C22C2×C22⋊C8×C11311yescharacteristic
176C22#410×C11311yescharacteristic
177C22C2×#100×C11311yescharacteristic
178C22#419×C11312yes—
179C22#421×C11312yes—
180C4—24no—
181C4—22no—
182C4—21no—
183C4—21no—
184C4—24no—
185C4—41no—
186C4—44no—
187C4—82no—
188C2C113×#146011yescharacteristic
189C2C113×#147912yes—
190C2C113×#151512yes—
191C2C113×#153611yescharacteristic
192C2C113×#155811yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C113C2×C22⋊C4
commutatorC2×C4C22×C8×C113
Frattini, cosocleC2×C42C23×C113
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C113 ◁ C43×C113 ◁ G

Complements

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

NH ≅ G/Ntype
17. C4⋊Q8×C113C8semidirect
91. #7605C113direct (N × H)
100. C113#7605direct (N × H)
114. C4⋊Q8C8×C113semidirect

Maximal subgroups

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

subgroupindex
C4×C4⋊Q8×C1132
C113×#18392
C113×#12722
#7605113