Finite Group Databasebeta

← C107×#7499 #41033463

Subgroups — C107×#7499 #41033463

Order 27392.

272 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 70 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
1C2×#356×C107C212yesmaximal
2C107×#1956C211yesmaximal, characteristic
3C2×C4⋊Q8×C107C2211yescharacteristic
4C2×#103×C107—22no—
5C2×#101×C107—22no—
6C2×C4×C8×C107C411yescharacteristic
7#384×C107C411yescharacteristic
8#356×C107—22no—
9#356×C107C414yescomplemented
10C22×Q8×C107D412yes—
11C2×M16×C107—42no—
12C22×C8×C107—21no—
13C4⋊Q8×C107—41no—
14C4⋊Q8×C107C2×C412yes—
15C4⋊Q8×C107D411yescharacteristic
16C4⋊Q8×C107Q811yescharacteristic
17C2×C4⋊C4×C107—21no—
18C2×C4⋊C4×C107—41no—
19C2×C4⋊C4×C107—41no—
20C2×C42×C107C2×C411yescharacteristic
21#103×C107—44no—
22#101×C107—24no—
23#101×C107—42no—
24C4×C8×C107—41no—
25C2×Q8×C107—22no—
26C2×Q8×C107—42no—
27C2×Q8×C107—42no—
28C2×Q8×C107C22⋊C412yes—
29C2×Q8×C107C4⋊C412yes—
30C22×C4×C107—21no—
31C22×C4×C107—22no—
32C22×C4×C107—41no—
33C22×C4×C107C22⋊C411yescharacteristic
34M16×C107—44no—
35M16×C107—82no—
36C2×C8×C107—22no—
37C2×C8×C107—41no—
38C2×C8×C107—41no—
39C2×C8×C107—82no—
40C4⋊C4×C107—42no—
41C4⋊C4×C107—41no—
42C4⋊C4×C107—41no—
43C4⋊C4×C107—42no—
44C4⋊C4×C107—82no—
45C42×C107—21no—
46C42×C107C4211yescharacteristic
47C42×C107C4⋊C411yescharacteristic
48C23×C107#9911yescharacteristic
49Q8×C107—42no—
50Q8×C107—42no—
51Q8×C107—82no—
52C2×C4×C107—22no—
53C2×C4×C107—22no—
54C2×C4×C107—21no—
55C2×C4×C107—21no—
56C2×C4×C107—21no—
57C2×C4×C107—21no—
58C2×C4×C107—22no—
59C2×C4×C107—22no—
60C2×C4×C107—42no—
61C2×C4×C107—42no—
62C2×C4×C107—82no—
63C2×C4×C107—81no—
64C2×C4×C107#9511yescharacteristic
65C2×C4×C107#9911yescharacteristic
66C8×C107—42no—
67C8×C107—84no—
68C22×C107—21no—
69C22×C107—21no—
70C22×C107#34211yescharacteristic
71C22×C107#35311yescharacteristic
72C22×C107#35411yescharacteristic
73C4×C107—22no—
74C4×C107—22no—
75C4×C107—21no—
76C4×C107—21no—
77C4×C107—42no—
78C4×C107—42no—
79C4×C107—161no—
80#7499C10711yesmaximal, characteristic, direct product factor, Sylow
81C2×C107—21no—
82C2×C107—21no—
83C2×C107#139311yescharacteristic
84C2×C107#141011yescharacteristic
85C2×C107#141111yescharacteristic
86C2×#356C2×C10712yes—
87#1956C2×C10711yescharacteristic
88C107#749911yescharacteristic, direct product factor, Sylow
89C2×C4⋊Q8C22×C10711yescharacteristic
90C2×#103—22no—
91C2×#101—22no—
92C2×C4×C8C4×C10711yescharacteristic
93#384C4×C10711yescharacteristic
94#356—22no—
95#356C4×C10714yescomplemented
96C22×Q8D4×C10712yes—
97C2×M16—42no—
98C22×C8—21no—
99C4⋊Q8—41no—
100C4⋊Q8C2×C4×C10712yes—
101C4⋊Q8D4×C10711yescharacteristic
102C4⋊Q8Q8×C10711yescharacteristic
103C2×C4⋊C4—21no—
104C2×C4⋊C4—41no—
105C2×C4⋊C4—41no—
106C2×C42C2×C4×C10711yescharacteristic
107#103—44no—
108#101—24no—
109#101—42no—
110C4×C8—41no—
111C2×Q8—22no—
112C2×Q8—42no—
113C2×Q8—42no—
114C2×Q8C22⋊C4×C10712yes—
115C2×Q8C4⋊C4×C10712yes—
116C22×C4—21no—
117C22×C4—22no—
118C22×C4—41no—
119C22×C4C22⋊C4×C10711yescharacteristic
120M16—44no—
121M16—82no—
122C2×C8—22no—
123C2×C8—41no—
124C2×C8—41no—
125C2×C8—82no—
126C4⋊C4—42no—
127C4⋊C4—41no—
128C4⋊C4—41no—
129C4⋊C4—42no—
130C4⋊C4—82no—
131C42—21no—
132C42C42×C10711yescharacteristic
133C42C4⋊C4×C10711yescharacteristic
134C23#99×C10711yescharacteristic
135Q8—42no—
136Q8—42no—
137Q8—82no—
138C2×C4—22no—
139C2×C4—22no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—22no—
145C2×C4—22no—
146C2×C4—42no—
147C2×C4—42no—
148C2×C4—82no—
149C2×C4—81no—
150C2×C4#95×C10711yescharacteristic
151C2×C4#99×C10711yescharacteristic
152C8—42no—
153C8—84no—
154C22—21no—
155C22—21no—
156C22#342×C10711yescharacteristic
157C22#353×C10711yescharacteristic
158C22#354×C10711yescharacteristic
159C4—22no—
160C4—22no—
161C4—21no—
162C4—21no—
163C4—42no—
164C4—42no—
165C4—161no—
166C2—21no—
167C2—21no—
168C2C107×#139311yescharacteristic
169C2C107×#141011yescharacteristic
170C2C107×#141111yescharacteristic
subgroupG/H
center, socleC22×C107#353
commutatorC42C42×C107
Frattini, cosocleC2×C4⋊Q8C22×C107
prime radicalC23×C107#99
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C107 ◁ C23×C107 ◁ C22×C4×C107 ◁ C2×C4⋊Q8×C107 ◁ G

Complements

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

NH ≅ G/Ntype
9. #356×C107C4semidirect
80. #7499C107direct (N × H)
88. C107#7499direct (N × H)
95. #356C4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#356×C1072
C107×#19562
#7499107