Finite Group Databasebeta

← #28337602

Subgroups — #28337602

Order 13696.

290 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 93 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×#16812109C211yesmaximal, characteristic
2C2×#16812033C212yesmaximal
3#20292389C212yesmaximal
4#20292382C211yesmaximal, characteristic
5#391×C107C211yesmaximal, characteristic
6C22×Dic214—21no—
7C22×C107⋊C8C2212yes—
8#16812109—24no—
9C2×C4⋊Dic107—21no—
10C2×C4⋊Dic107C2212yes—
11#16812033—24no—
12C22×Q8×C107C2211yescharacteristic
13C2×C4⋊C4×C107C2211yescharacteristic
14C2×C42×C107C2211yescharacteristic
15#95×C107—21no—
16#95×C107—21no—
17C2×Dic214—24no—
18C2×Dic214—42no—
19C2×Dic214—42no—
20C22×Dic107—22no—
21C2×C107⋊C8—22no—
22C2×C107⋊C8—22no—
23C2×C107⋊C8—22no—
24C4⋊Dic107—24no—
25C4⋊Dic107—22no—
26C4⋊Dic107D414yes—
27C2×Q8×C107—21no—
28C2×Q8×C107—22no—
29C2×Q8×C107—22no—
30C2×Q8×C107Q812yescomplemented
31C22×C4×C107—21no—
32C22×C4×C107—21no—
33C22×C4×C107D411yescharacteristic
34C22×C4×C107D411yescharacteristic
35C22×C4×C107C2311yescharacteristic
36C4⋊C4×C107—22no—
37C42×C107—22no—
38C23×C107C2×D411yescharacteristic
39Q8×C107—24no—
40Q8×C107—42no—
41C2×C4×C107—21no—
42C2×C4×C107—21no—
43C2×C4×C107—21no—
44C2×C4×C107—21no—
45C2×C4×C107—22no—
46C2×C4×C107—41no—
47C2×C4×C107—41no—
48C2×C4×C107—41no—
49C2×C4×C107—41no—
50C2×C4×C107—41no—
51C2×C4×C107SD1612yes—
52C2×C4×C107Q1612yes—
53C2×C4×C107C2×D412yes—
54C2×C4×C107C2×Q811yescharacteristic
55C2×C4×C107#4112yes—
56C2×C4×C107#4111yescharacteristic
57C2×Dic107—24no—
58C2×Dic107—42no—
59C2×Dic107—42no—
60Dic214—48no—
61C107⋊C8—42no—
62C22×C107#12011yescharacteristic
63C22×C107C22⋊Q811yescharacteristic
64C22×C107#12411yescharacteristic
65C22×C107C2×SD1611yescharacteristic
66C22×C107C2×Q1611yescharacteristic
67C22×C107AGL(1,ℤ/8)11yescharacteristic
68C22×C107#13711yescharacteristic
69C4×C107—22no—
70C4×C107—22no—
71C4×C107—42no—
72C4×C107—81no—
73C4×C107C22⋊Q812yes—
74C4×C107#12412yes—
75Dic107—44no—
76C2×C107#39311yescharacteristic
77C2×C107#45011yescharacteristic
78C2×C107#45111yescharacteristic
79C2×C107#47511yescharacteristic
80C2×C107#47711yescharacteristic
81C2×C107#48711yescharacteristic
82C2×C107#48911yescharacteristic
83#2024—1071nomaximal, Sylow
84C107#202411yescharacteristic, complemented, Sylow
85C2×C4⋊Q8—1071no—
86C2×#103—1072no—
87#391D10711yescharacteristic
88#340—1072no—
89#336—1071no—
90C22×Q8—2141no—
91C22×Q8C2×D10711yescharacteristic
92C22×C8—1072no—
93C4⋊Q8—2144no—
94C2×C4⋊C4—1072no—
95C2×C4⋊C4—2141no—
96C2×C4⋊C4C2×D10711yescharacteristic
97C2×C42C2×D10711yescharacteristic
98#103—2144no—
99#95—21no—
100#95—21no—
101C2×Q8—21no—
102C2×Q8—22no—
103C2×Q8—22no—
104C2×Q8—4282no—
105C2×Q8—4282no—
106C2×Q8—2144no—
107C2×Q8Dic21412yescomplemented
108C22×C4—21no—
109C22×C4—21no—
110C22×C4—2142no—
111C22×C4C22⋊D10711yescharacteristic
112C22×C4C22⋊D10711yescharacteristic
113C22×C4C22×D10711yescharacteristic
114C2×C8—2142no—
115C2×C8—2142no—
116C2×C8—2142no—
117C4⋊C4—22no—
118C4⋊C4—1074no—
119C4⋊C4—2144no—
120C4⋊C4—2142no—
121C42—22no—
122C23C2×C22⋊D10711yescharacteristic
123Q8—24no—
124Q8—42no—
125Q8—4288no—
126C2×C4—21no—
127C2×C4—21no—
128C2×C4—21no—
129C2×C4—21no—
130C2×C4—22no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—41no—
136C2×C4—4282no—
137C2×C4—4282no—
138C2×C4—2144no—
139C2×C4#1313380512yes—
140C2×C4#1313380812yes—
141C2×C4D4×D10712yes—
142C2×C4C2×Dic21411yescharacteristic
143C2×C4#1313381712yes—
144C2×C4#1313381811yescharacteristic
145C8—4282no—
146C22#1681207711yescharacteristic
147C22#1681208811yescharacteristic
148C22#1681209611yescharacteristic
149C22C2×#1313380511yescharacteristic
150C22C2×#1313380811yescharacteristic
151C22#1681213411yescharacteristic
152C22#1681213911yescharacteristic
153C4—22no—
154C4—22no—
155C4—42no—
156C4—81no—
157C4—4284no—
158C4#1681208612yes—
159C4#1681209512yes—
160C2#2029253911yescharacteristic
161C2#2029277711yescharacteristic
162C2#2029278211yescharacteristic
163C2#2029291211yescharacteristic
164C2#2029292211yescharacteristic
165C2#2029297711yescharacteristic
166C2#2029298611yescharacteristic
subgroupG/H
centerC23C2×C22⋊D107
commutator, cosocleC22×C4×C107C23
FrattiniC22×C4C22×D107
Fitting#391×C107C2
socle, prime radicalC23×C107C2×D4
hypercenter#391D107
hypocenterC107#2024
LCSG ▷ C22×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
30. C2×Q8×C107Q8semidirect
84. C107#2024semidirect
107. C2×Q8Dic214semidirect

Maximal subgroups

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

subgroupindex
C2×#168121092
C2×#168120332
#202923892
#202923822
#391×C1072
#2024107