Finite Group Databasebeta

← C107×#7602 #41033566

Subgroups — C107×#7602 #41033566

Order 27392.

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

normal subgroups only

This group has 408 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×#125×C107C211yesmaximal, characteristic
2C107×#1831C212yesmaximal
3C107×#1271C214yesmaximal
4C2×#125×C107C411yescharacteristic
5C2×C4⋊C8×C107—22no—
6#389×C107C2212yes—
7#387×C107—22no—
8#382×C107C411yescharacteristic
9C4×C4⋊C4×C107—22no—
10C4×C4⋊C4×C107C412yes—
11C43×C107C2211yescharacteristic
12#336×C107—22no—
13#336×C107C2214yes—
14C22×C8×C107—24no—
15#125×C107—22no—
16#125×C107C814yescomplemented
17C2×C4⋊C4×C107—22no—
18C2×C4⋊C4×C107—22no—
19C2×C4⋊C4×C107C2×C412yes—
20C2×C4⋊C4×C107C2×C412yes—
21C2×C42×C107—22no—
22C2×C42×C107C2×C411yescharacteristic
23C2×C42×C107C2×C411yescharacteristic
24C2×C42×C107D412yes—
25C2×C42×C107D412yes—
26C2×C42×C107C2311yescharacteristic
27C4⋊C8×C107—44no—
28#95×C107—22no—
29#95×C107—22no—
30#95×C107—22no—
31C22×C4×C107—22no—
32C22×C4×C107—22no—
33C22×C4×C107C22⋊C411yescharacteristic
34C22×C4×C107C22⋊C412yes—
35C22×C4×C107C22⋊C411yescharacteristic
36C22×C4×C107C22×C411yescharacteristic
37C22×C4×C107C2×D412yes—
38C2×C8×C107—44no—
39C2×C8×C107—44no—
40C2×C8×C107—44no—
41C4⋊C4×C107—28no—
42C4⋊C4×C107—22no—
43C4⋊C4×C107—42no—
44C4⋊C4×C107—42no—
45C4⋊C4×C107—42no—
46C4⋊C4×C107C2×C814yes—
47C42×C107—22no—
48C42×C107—22no—
49C42×C107—22no—
50C42×C107—42no—
51C42×C107—41no—
52C42×C107—44no—
53C42×C107C2×C812yes—
54C42×C107M1612yes—
55C23×C107C2×C22⋊C411yescharacteristic
56C2×C4×C107—21no—
57C2×C4×C107—22no—
58C2×C4×C107—21no—
59C2×C4×C107—22no—
60C2×C4×C107—22no—
61C2×C4×C107—22no—
62C2×C4×C107—22no—
63C2×C4×C107—24no—
64C2×C4×C107—21no—
65C2×C4×C107—22no—
66C2×C4×C107—42no—
67C2×C4×C107—42no—
68C2×C4×C107—42no—
69C2×C4×C107—42no—
70C2×C4×C107—42no—
71C2×C4×C107C22⋊C814yes—
72C2×C4×C107#10112yes—
73C2×C4×C107C22×C811yescharacteristic
74C2×C4×C107C2×M1611yescharacteristic
75C2×C4×C107AGL(1,ℤ/8)12yes—
76C2×C4×C107#13712yes—
77C8×C107—84no—
78C22×C107C2×C22⋊C811yescharacteristic
79C22×C107#41011yescharacteristic
80C22×C107C2×#10111yescharacteristic
81C22×C107#41712yes—
82C22×C107#42112yes—
83C4×C107—21no—
84C4×C107—21no—
85C4×C107—24no—
86C4×C107—22no—
87C4×C107—22no—
88C4×C107—22no—
89C4×C107—41no—
90C4×C107—44no—
91C4×C107—82no—
92#7602C10711yesmaximal, characteristic, direct product factor, Sylow
93C2×C107#146111yescharacteristic
94C2×C107#147712yes—
95C2×C107#151212yes—
96C2×C107#153411yescharacteristic
97C2×C107#156111yescharacteristic
98C4×#125C2×C10711yescharacteristic
99#1831C2×C10712yes—
100#1271C2×C10714yes—
101C107#760211yescharacteristic, direct product factor, Sylow
102C2×#125C4×C10711yescharacteristic
103C2×C4⋊C8—22no—
104#389C22×C10712yes—
105#387—22no—
106#382C4×C10711yescharacteristic
107C4×C4⋊C4—22no—
108C4×C4⋊C4C4×C10712yes—
109C43C22×C10711yescharacteristic
110#336—22no—
111#336C22×C10714yes—
112C22×C8—24no—
113#125—22no—
114#125C8×C10714yescomplemented
115C2×C4⋊C4—22no—
116C2×C4⋊C4—22no—
117C2×C4⋊C4C2×C4×C10712yes—
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—22no—
127#95—22no—
128#95—22no—
129C22×C4—22no—
130C22×C4—22no—
131C22×C4C22⋊C4×C10711yescharacteristic
132C22×C4C22⋊C4×C10712yes—
133C22×C4C22⋊C4×C10711yescharacteristic
134C22×C4C22×C4×C10711yescharacteristic
135C22×C4C2×D4×C10712yes—
136C2×C8—44no—
137C2×C8—44no—
138C2×C8—44no—
139C4⋊C4—28no—
140C4⋊C4—22no—
141C4⋊C4—42no—
142C4⋊C4—42no—
143C4⋊C4—42no—
144C4⋊C4C2×C8×C10714yes—
145C42—22no—
146C42—22no—
147C42—22no—
148C42—42no—
149C42—41no—
150C42—44no—
151C42C2×C8×C10712yes—
152C42M16×C10712yes—
153C23C2×C22⋊C4×C10711yescharacteristic
154C2×C4—21no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—22no—
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—42no—
168C2×C4—42no—
169C2×C4C22⋊C8×C10714yes—
170C2×C4#101×C10712yes—
171C2×C4C22×C8×C10711yescharacteristic
172C2×C4C2×M16×C10711yescharacteristic
173C2×C4AGL(1,ℤ/8)×C10712yes—
174C2×C4#137×C10712yes—
175C8—84no—
176C22C2×C22⋊C8×C10711yescharacteristic
177C22#410×C10711yescharacteristic
178C22C2×#101×C10711yescharacteristic
179C22#417×C10712yes—
180C22#421×C10712yes—
181C4—21no—
182C4—21no—
183C4—24no—
184C4—22no—
185C4—22no—
186C4—22no—
187C4—44no—
188C4—41no—
189C4—82no—
190C2C107×#146111yescharacteristic
191C2C107×#147712yes—
192C2C107×#151212yes—
193C2C107×#153411yescharacteristic
194C2C107×#156111yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C107C2×C22⋊C4
commutatorC2×C4C22×C8×C107
Frattini, cosocleC2×C42C23×C107
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C107 ◁ C43×C107 ◁ G

Complements

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

NH ≅ G/Ntype
16. #125×C107C8semidirect
92. #7602C107direct (N × H)
101. C107#7602direct (N × H)
114. #125C8×C107semidirect

Maximal subgroups

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

subgroupindex
C4×#125×C1072
C107×#18312
C107×#12712
#7602107