Finite Group Databasebeta

← C113×#8335 #43276355

Subgroups — C113×#8335 #43276355

Order 28928.

826 conjugacy classes of subgroups; only the 182 normal subgroups are shown.

normal subgroups only

This group has 826 conjugacy classes of subgroups — too many to draw. Only its 182 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×#125×C113C211yesmaximal, characteristic
2C113×#1749C212yesmaximal
3C2×#330×C113C214yesmaximal, complemented
4C2×#125×C113—28no—
5C2×#125×C113—22no—
6C2×#125×C113C412yes—
7C2×#125×C113C2212yes—
8C22×C4⋊C4×C113—22no—
9C22×C4⋊C4×C113C412yes—
10C22×C42×C113C2211yescharacteristic
11C2×C22⋊C8×C113—22no—
12C2×#97×C113C2214yes—
13#336×C113—22no—
14#330×C113—28no—
15C23×C4×C113—22no—
16C23×C4×C113C2×C411yescharacteristic
17C23×C4×C113D412yes—
18C22×C8×C113—24no—
19#125×C113—216no—
20#125×C113—28no—
21#125×C113—24no—
22#125×C113D418yes—
23C2×C4⋊C4×C113—216no—
24C2×C4⋊C4×C113—24no—
25C2×C4⋊C4×C113—22no—
26C2×C4⋊C4×C113—24no—
27C2×C4⋊C4×C113—28no—
28C2×C4⋊C4×C113C2×C414yes—
29C2×C42×C113—24no—
30C2×C42×C113C2×C411yescharacteristic
31C2×C42×C113D412yes—
32C2×C42×C113C2311yescharacteristic
33C22⋊C8×C113—28no—
34#97×C113—28no—
35C24×C113C22⋊C411yescharacteristic
36C22×C4×C113—22no—
37C22×C4×C113—22no—
38C22×C4×C113—22no—
39C22×C4×C113—28no—
40C22×C4×C113—24no—
41C22×C4×C113—24no—
42C22×C4×C113—24no—
43C22×C4×C113—42no—
44C22×C4×C113—44no—
45C22×C4×C113—44no—
46C22×C4×C113C22⋊C412yes—
47C22×C4×C113C22⋊C411yescharacteristic
48C22×C4×C113C22×C411yescharacteristic
49C22×C4×C113C2×D412yes—
50C2×C8×C113—28no—
51C2×C8×C113—44no—
52C2×C8×C113—44no—
53C4⋊C4×C113—28no—
54C4⋊C4×C113—216no—
55C4⋊C4×C113—24no—
56C4⋊C4×C113—216no—
57C4⋊C4×C113C22⋊C418yes—
58C42×C113—22no—
59C42×C113—24no—
60C42×C113C2×D414yes—
61C23×C113—21no—
62C23×C113—21no—
63C23×C113—22no—
64C23×C113#10112yes—
65C23×C113#10414yes—
66C23×C113C2×C22⋊C411yescharacteristic
67C2×C4×C113—28no—
68C2×C4×C113—21no—
69C2×C4×C113—21no—
70C2×C4×C113—21no—
71C2×C4×C113—21no—
72C2×C4×C113—22no—
73C2×C4×C113—22no—
74C2×C4×C113—22no—
75C2×C4×C113—28no—
76C2×C4×C113—22no—
77C2×C4×C113—22no—
78C2×C4×C113—48no—
79C2×C4×C113—416no—
80C2×C4×C113—44no—
81C2×C4×C113—44no—
82C2×C4×C113#10112yes—
83C2×C4×C113C2×C22⋊C412yes—
84C2×C4×C113#12014yes—
85C8×C113—48no—
86C22×C113—24no—
87C22×C113—22no—
88C22×C113—24no—
89C22×C113—22no—
90C22×C113#33014yescomplemented
91C22×C113#37911yescharacteristic
92C22×C113C2×#10111yescharacteristic
93C22×C113C2×#10111yescharacteristic
94C22×C113C2×#10412yes—
95C22×C113#42112yes—
96C4×C113—22no—
97C4×C113—22no—
98C4×C113—24no—
99C4×C113—42no—
100C4×C113—48no—
101#8335C11311yesmaximal, characteristic, direct product factor, Sylow
102C2×C113—24no—
103C2×C113C2×#33011yescharacteristic
104C2×C113#152812yes—
105C2×C113#153411yescharacteristic
106C2×C113#178411yescharacteristic
107C2×C113#178912yes—
108C22×#125C2×C11311yescharacteristic
109#1749C2×C11312yes—
110C2×#330C2×C11314yescomplemented
111C113#833511yescharacteristic, direct product factor, Sylow
112C2×#125—28no—
113C2×#125—22no—
114C2×#125C4×C11312yes—
115C2×#125C22×C11312yes—
116C22×C4⋊C4—22no—
117C22×C4⋊C4C4×C11312yes—
118C22×C42C22×C11311yescharacteristic
119C2×C22⋊C8—22no—
120C2×#97C22×C11314yes—
121#336—22no—
122#330—28no—
123C23×C4—22no—
124C23×C4C2×C4×C11311yescharacteristic
125C23×C4D4×C11312yes—
126C22×C8—24no—
127#125—216no—
128#125—28no—
129#125—24no—
130#125D4×C11318yes—
131C2×C4⋊C4—216no—
132C2×C4⋊C4—24no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—24no—
135C2×C4⋊C4—28no—
136C2×C4⋊C4C2×C4×C11314yes—
137C2×C42—24no—
138C2×C42C2×C4×C11311yescharacteristic
139C2×C42D4×C11312yes—
140C2×C42C23×C11311yescharacteristic
141C22⋊C8—28no—
142#97—28no—
143C24C22⋊C4×C11311yescharacteristic
144C22×C4—22no—
145C22×C4—22no—
146C22×C4—22no—
147C22×C4—28no—
148C22×C4—24no—
149C22×C4—24no—
150C22×C4—24no—
151C22×C4—42no—
152C22×C4—44no—
153C22×C4—44no—
154C22×C4C22⋊C4×C11312yes—
155C22×C4C22⋊C4×C11311yescharacteristic
156C22×C4C22×C4×C11311yescharacteristic
157C22×C4C2×D4×C11312yes—
158C2×C8—28no—
159C2×C8—44no—
160C2×C8—44no—
161C4⋊C4—28no—
162C4⋊C4—216no—
163C4⋊C4—24no—
164C4⋊C4—216no—
165C4⋊C4C22⋊C4×C11318yes—
166C42—22no—
167C42—24no—
168C42C2×D4×C11314yes—
169C23—21no—
170C23—21no—
171C23—22no—
172C23#101×C11312yes—
173C23#104×C11314yes—
174C23C2×C22⋊C4×C11311yescharacteristic
175C2×C4—28no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—28no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—48no—
187C2×C4—416no—
188C2×C4—44no—
189C2×C4—44no—
190C2×C4#101×C11312yes—
191C2×C4C2×C22⋊C4×C11312yes—
192C2×C4#120×C11314yes—
193C8—48no—
194C22—24no—
195C22—22no—
196C22—24no—
197C22—22no—
198C22#330×C11314yescomplemented
199C22#379×C11311yescharacteristic
200C22C2×#101×C11311yescharacteristic
201C22C2×#101×C11311yescharacteristic
202C22C2×#104×C11312yes—
203C22#421×C11312yes—
204C4—22no—
205C4—22no—
206C4—24no—
207C4—42no—
208C4—48no—
209C2—24no—
210C2C2×#330×C11311yescharacteristic
211C2C113×#152812yes—
212C2C113×#153411yescharacteristic
213C2C113×#178411yescharacteristic
214C2C113×#178912yes—
subgroupG/H
center, socleC23×C113C2×C22⋊C4
commutatorC22×C4C22×C4×C113
Frattini, cosocleC2×C42C23×C113
prime radicalC24×C113C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C113 ◁ C22×C42×C113 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#330×C113C2semidirect
90. C22×C113#330semidirect
101. #8335C113direct (N × H)
110. C2×#330C2×C113semidirect
111. C113#8335direct (N × H)
198. C22#330×C113semidirect

Maximal subgroups

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

subgroupindex
C22×#125×C1132
C113×#17492
C2×#330×C1132
#8335113