Finite Group Databasebeta

← C107×#7650 #41033614

Subgroups — C107×#7650 #41033614

Order 27392.

384 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 130 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×#125×C107C211yesmaximal, characteristic
2C107×#1839C212yesmaximal
3C107×#1271C214yesmaximal
4C2×#125×C107C411yescharacteristic
5#389×C107C2212yes—
6#387×C107—22no—
7#382×C107C411yescharacteristic
8C4×C4⋊C4×C107—22no—
9C4×C4⋊C4×C107C412yes—
10C43×C107C2211yescharacteristic
11#336×C107—22no—
12#336×C107—22no—
13#336×C107C2214yes—
14C22×C8×C107—24no—
15#125×C107—24no—
16C2×C4⋊C4×C107—22no—
17C2×C4⋊C4×C107—22no—
18C2×C4⋊C4×C107C2×C412yes—
19C2×C4⋊C4×C107C2×C412yes—
20C2×C42×C107—22no—
21C2×C42×C107C2×C411yescharacteristic
22C2×C42×C107C2×C411yescharacteristic
23C2×C42×C107D412yes—
24C2×C42×C107D412yes—
25C2×C42×C107C2311yescharacteristic
26#95×C107—22no—
27#95×C107—22no—
28#95×C107—22no—
29C22×C4×C107—22no—
30C22×C4×C107—22no—
31C22×C4×C107C22⋊C411yescharacteristic
32C22×C4×C107C22⋊C412yes—
33C22×C4×C107C22⋊C411yescharacteristic
34C22×C4×C107C22×C411yescharacteristic
35C22×C4×C107C2×D412yes—
36C2×C8×C107—44no—
37C2×C8×C107—44no—
38C2×C8×C107—44no—
39C4⋊C4×C107—28no—
40C4⋊C4×C107—22no—
41C4⋊C4×C107—42no—
42C4⋊C4×C107—44no—
43C4⋊C4×C107M1614yes—
44C42×C107—22no—
45C42×C107—22no—
46C42×C107—24no—
47C42×C107—42no—
48C42×C107—41no—
49C42×C107—44no—
50C23×C107C2×C22⋊C411yescharacteristic
51C2×C4×C107—21no—
52C2×C4×C107—22no—
53C2×C4×C107—21no—
54C2×C4×C107—22no—
55C2×C4×C107—22no—
56C2×C4×C107—22no—
57C2×C4×C107—24no—
58C2×C4×C107—21no—
59C2×C4×C107—22no—
60C2×C4×C107—22no—
61C2×C4×C107—22no—
62C2×C4×C107—42no—
63C2×C4×C107—42no—
64C2×C4×C107—42no—
65C2×C4×C107—42no—
66C2×C4×C107—42no—
67C2×C4×C107#10112yes—
68C2×C4×C107C2×M1612yes—
69C2×C4×C107#13514yes—
70C8×C107—84no—
71C22×C107#40711yescharacteristic
72C22×C107#41011yescharacteristic
73C22×C107C2×#10111yescharacteristic
74C22×C107#41612yes—
75C22×C107#42112yes—
76C4×C107—22no—
77C4×C107—24no—
78C4×C107—22no—
79C4×C107—41no—
80C4×C107—42no—
81C4×C107—44no—
82C4×C107—82no—
83#7650C10711yesmaximal, characteristic, direct product factor, Sylow
84C2×C107#146711yescharacteristic
85C2×C107#148812yes—
86C2×C107#152112yes—
87C2×C107#153411yescharacteristic
88C2×C107#154411yescharacteristic
89C4×#125C2×C10711yescharacteristic
90#1839C2×C10712yes—
91#1271C2×C10714yes—
92C107#765011yescharacteristic, direct product factor, Sylow
93C2×#125C4×C10711yescharacteristic
94#389C22×C10712yes—
95#387—22no—
96#382C4×C10711yescharacteristic
97C4×C4⋊C4—22no—
98C4×C4⋊C4C4×C10712yes—
99C43C22×C10711yescharacteristic
100#336—22no—
101#336—22no—
102#336C22×C10714yes—
103C22×C8—24no—
104#125—24no—
105C2×C4⋊C4—22no—
106C2×C4⋊C4—22no—
107C2×C4⋊C4C2×C4×C10712yes—
108C2×C4⋊C4C2×C4×C10712yes—
109C2×C42—22no—
110C2×C42C2×C4×C10711yescharacteristic
111C2×C42C2×C4×C10711yescharacteristic
112C2×C42D4×C10712yes—
113C2×C42D4×C10712yes—
114C2×C42C23×C10711yescharacteristic
115#95—22no—
116#95—22no—
117#95—22no—
118C22×C4—22no—
119C22×C4—22no—
120C22×C4C22⋊C4×C10711yescharacteristic
121C22×C4C22⋊C4×C10712yes—
122C22×C4C22⋊C4×C10711yescharacteristic
123C22×C4C22×C4×C10711yescharacteristic
124C22×C4C2×D4×C10712yes—
125C2×C8—44no—
126C2×C8—44no—
127C2×C8—44no—
128C4⋊C4—28no—
129C4⋊C4—22no—
130C4⋊C4—42no—
131C4⋊C4—44no—
132C4⋊C4M16×C10714yes—
133C42—22no—
134C42—22no—
135C42—24no—
136C42—42no—
137C42—41no—
138C42—44no—
139C23C2×C22⋊C4×C10711yescharacteristic
140C2×C4—21no—
141C2×C4—22no—
142C2×C4—21no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—22no—
146C2×C4—24no—
147C2×C4—21no—
148C2×C4—22no—
149C2×C4—22no—
150C2×C4—22no—
151C2×C4—42no—
152C2×C4—42no—
153C2×C4—42no—
154C2×C4—42no—
155C2×C4—42no—
156C2×C4#101×C10712yes—
157C2×C4C2×M16×C10712yes—
158C2×C4#135×C10714yes—
159C8—84no—
160C22#407×C10711yescharacteristic
161C22#410×C10711yescharacteristic
162C22C2×#101×C10711yescharacteristic
163C22#416×C10712yes—
164C22#421×C10712yes—
165C4—22no—
166C4—24no—
167C4—22no—
168C4—42no—
169C4—44no—
170C4—41no—
171C4—82no—
172C2C107×#146711yescharacteristic
173C2C107×#148812yes—
174C2C107×#152112yes—
175C2C107×#153411yescharacteristic
176C2C107×#154411yescharacteristic
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
83. #7650C107direct (N × H)
92. C107#7650direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#125×C1072
C107×#18392
C107×#12712
#7650107