Finite Group Databasebeta

← C107×#7653 #41033617

Subgroups — C107×#7653 #41033617

Order 27392.

456 conjugacy classes of subgroups; only the 170 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 170 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×C107C211yesmaximal, characteristic
2C107×#1831C212yesmaximal
3C107×#1272C214yesmaximal
4C2×C4⋊Q8×C107C411yescharacteristic
5C2×C4×Q8×C107C412yes—
6C2×C4⋊C8×C107—22no—
7#391×C107C2212yes—
8#389×C107—22no—
9#384×C107C411yescharacteristic
10C4×C4⋊C4×C107—22no—
11C43×C107C2211yescharacteristic
12#336×C107—22no—
13#336×C107C2214yes—
14C22×Q8×C107C2×C412yes—
15C22×C8×C107—24no—
16C4⋊Q8×C107—24no—
17C4×Q8×C107—44no—
18C2×C4⋊C4×C107—22no—
19C2×C4⋊C4×C107—22no—
20C2×C4⋊C4×C107—22no—
21C2×C4⋊C4×C107C2×C412yes—
22C2×C42×C107—22no—
23C2×C42×C107C2×C411yescharacteristic
24C2×C42×C107C2×C411yescharacteristic
25C2×C42×C107D412yes—
26C2×C42×C107D412yes—
27C2×C42×C107C2311yescharacteristic
28C4⋊C8×C107—44no—
29#95×C107—24no—
30C2×Q8×C107—22no—
31C2×Q8×C107—42no—
32C2×Q8×C107—42no—
33C2×Q8×C107M1614yes—
34C22×C4×C107—22no—
35C22×C4×C107—22no—
36C22×C4×C107C22⋊C411yescharacteristic
37C22×C4×C107C22⋊C412yes—
38C22×C4×C107C22⋊C411yescharacteristic
39C22×C4×C107C22×C411yescharacteristic
40C22×C4×C107C2×D412yes—
41C2×C8×C107—44no—
42C2×C8×C107—44no—
43C2×C8×C107—44no—
44C4⋊C4×C107—28no—
45C4⋊C4×C107—42no—
46C4⋊C4×C107—44no—
47C4⋊C4×C107—44no—
48C42×C107—22no—
49C42×C107—22no—
50C42×C107—42no—
51C42×C107—41no—
52C42×C107—44no—
53C42×C107SD1614yes—
54C42×C107Q1614yes—
55C23×C107C2×C22⋊C411yescharacteristic
56Q8×C107—44no—
57Q8×C107—44no—
58C2×C4×C107—22no—
59C2×C4×C107—22no—
60C2×C4×C107—21no—
61C2×C4×C107—21no—
62C2×C4×C107—22no—
63C2×C4×C107—22no—
64C2×C4×C107—24no—
65C2×C4×C107—21no—
66C2×C4×C107—22no—
67C2×C4×C107—42no—
68C2×C4×C107—42no—
69C2×C4×C107—42no—
70C2×C4×C107—44no—
71C2×C4×C107#10012yes—
72C2×C4×C107#10314yes—
73C2×C4×C107#10314yes—
74C2×C4×C107C2×M1612yes—
75C2×C4×C107C2×SD1612yes—
76C2×C4×C107C2×Q1612yes—
77C8×C107—84no—
78C22×C107#40711yescharacteristic
79C22×C107#41011yescharacteristic
80C22×C107C2×#10011yescharacteristic
81C22×C107C2×#10312yes—
82C22×C107#42112yes—
83C4×C107—22no—
84C4×C107—24no—
85C4×C107—22no—
86C4×C107—22no—
87C4×C107—41no—
88C4×C107—44no—
89C4×C107—82no—
90C4×C107#33314yes—
91#7653C10711yesmaximal, characteristic, direct product factor, Sylow
92C2×C107#146611yescharacteristic
93C2×C107#148712yes—
94C2×C107#151812yes—
95C2×C107#153611yescharacteristic
96C2×C107C2×#33311yescharacteristic
97C4×C4⋊Q8C2×C10711yescharacteristic
98#1831C2×C10712yes—
99#1272C2×C10714yes—
100C107#765311yescharacteristic, direct product factor, Sylow
101C2×C4⋊Q8C4×C10711yescharacteristic
102C2×C4×Q8C4×C10712yes—
103C2×C4⋊C8—22no—
104#391C22×C10712yes—
105#389—22no—
106#384C4×C10711yescharacteristic
107C4×C4⋊C4—22no—
108C43C22×C10711yescharacteristic
109#336—22no—
110#336C22×C10714yes—
111C22×Q8C2×C4×C10712yes—
112C22×C8—24no—
113C4⋊Q8—24no—
114C4×Q8—44no—
115C2×C4⋊C4—22no—
116C2×C4⋊C4—22no—
117C2×C4⋊C4—22no—
118C2×C4⋊C4C2×C4×C10712yes—
119C2×C42—22no—
120C2×C42C2×C4×C10711yescharacteristic
121C2×C42C2×C4×C10711yescharacteristic
122C2×C42D4×C10712yes—
123C2×C42D4×C10712yes—
124C2×C42C23×C10711yescharacteristic
125C4⋊C8—44no—
126#95—24no—
127C2×Q8—22no—
128C2×Q8—42no—
129C2×Q8—42no—
130C2×Q8M16×C10714yes—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4C22⋊C4×C10711yescharacteristic
134C22×C4C22⋊C4×C10712yes—
135C22×C4C22⋊C4×C10711yescharacteristic
136C22×C4C22×C4×C10711yescharacteristic
137C22×C4C2×D4×C10712yes—
138C2×C8—44no—
139C2×C8—44no—
140C2×C8—44no—
141C4⋊C4—28no—
142C4⋊C4—42no—
143C4⋊C4—44no—
144C4⋊C4—44no—
145C42—22no—
146C42—22no—
147C42—42no—
148C42—41no—
149C42—44no—
150C42SD16×C10714yes—
151C42Q16×C10714yes—
152C23C2×C22⋊C4×C10711yescharacteristic
153Q8—44no—
154Q8—44no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—24no—
162C2×C4—21no—
163C2×C4—22no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—44no—
168C2×C4#100×C10712yes—
169C2×C4#103×C10714yes—
170C2×C4#103×C10714yes—
171C2×C4C2×M16×C10712yes—
172C2×C4C2×SD16×C10712yes—
173C2×C4C2×Q16×C10712yes—
174C8—84no—
175C22#407×C10711yescharacteristic
176C22#410×C10711yescharacteristic
177C22C2×#100×C10711yescharacteristic
178C22C2×#103×C10712yes—
179C22#421×C10712yes—
180C4—22no—
181C4—24no—
182C4—22no—
183C4—22no—
184C4—44no—
185C4—41no—
186C4—82no—
187C4#333×C10714yes—
188C2C107×#146611yescharacteristic
189C2C107×#148712yes—
190C2C107×#151812yes—
191C2C107×#153611yescharacteristic
192C2C2×#333×C10711yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C107C2×C22⋊C4
commutatorC22×C4C22×C4×C107
Frattini, cosocleC2×C42C23×C107
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C107 ◁ C43×C107 ◁ G

Complements

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

NH ≅ G/Ntype
91. #7653C107direct (N × H)
100. C107#7653direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C4⋊Q8×C1072
C107×#18312
C107×#12722
#7653107