Finite Group Databasebeta

← #28344447

Subgroups — #28344447

Order 13696.

368 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 137 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
1#20292569C212yesmaximal
2#20292561C212yesmaximal
3#20292560C212yesmaximal
4#20292534C211yesmaximal, characteristic
5#20292534C211yesmaximal, characteristic
6#20292524C212yesmaximal
7#20292511C212yesmaximal
8#20292510C212yesmaximal
9#391×C107C211yesmaximal, characteristic
10C2×C4⋊Dic107C2212yes—
11C2×C4⋊Dic107C2211yescharacteristic
12C2×C4⋊Dic107C2211yescharacteristic
13C2×Dic107⋊C4C2212yes—
14C2×Dic107⋊C4C2212yes—
15C2×Dic107⋊C4C2212yes—
16C2×Dic107⋊C4C2212yes—
17C2×C4×Dic107C2211yescharacteristic
18C2×C4×Dic107C2211yescharacteristic
19C107⋊#95C2212yes—
20C107⋊#95C2212yes—
21C107⋊#95C2212yes—
22C107⋊#95C2212yes—
23C107⋊#95C2212yes—
24C107⋊#95C2212yes—
25C107⋊#95C2212yes—
26C22×Q8×C107C2211yescharacteristic
27C2×C4⋊C4×C107C2211yescharacteristic
28C2×C42×C107C2211yescharacteristic
29#95×C107C2212yes—
30#95×C107C2212yes—
31C22×Dic107C2312yes—
32C22×Dic107C2312yes—
33C22×Dic107C2312yes—
34C22×Dic107C2312yes—
35C4⋊Dic107—24no—
36C4⋊Dic107—41no—
37C4⋊Dic107—41no—
38Dic107⋊C4—24no—
39Dic107⋊C4—24no—
40Dic107⋊C4—42no—
41Dic107⋊C4—42no—
42C4×Dic107—41no—
43C4×Dic107—41no—
44C2×Q8×C107—41no—
45C2×Q8×C107—41no—
46C2×Q8×C107Q814yes—
47C22×C4×C107C2312yes—
48C22×C4×C107C2312yes—
49C22×C4×C107C2311yescharacteristic
50C22×C4×C107C2311yescharacteristic
51C22×C4×C107C2311yescharacteristic
52C4⋊C4×C107—41no—
53C42×C107—41no—
54C23×C107C2411yescharacteristic
55Q8×C107—44no—
56C2×C4×C107—21no—
57C2×C4×C107—21no—
58C2×C4×C107—21no—
59C2×C4×C107—21no—
60C2×C4×C107—21no—
61C2×C4×C107—21no—
62C2×C4×C107—22no—
63C2×C4×C107—22no—
64C2×C4×C107—22no—
65C2×C4×C107—22no—
66C2×C4×C107—22no—
67C2×C4×C107—22no—
68C2×C4×C107C2×Q812yes—
69C2×C4×C107C2×Q812yes—
70C2×C4×C107C2×Q812yes—
71C2×Dic107—22no—
72C2×Dic107—22no—
73C2×Dic107—22no—
74C2×Dic107—22no—
75C2×Dic107—22no—
76C2×Dic107—22no—
77C2×Dic107—22no—
78C2×Dic107—22no—
79C2×Dic107—22no—
80C2×Dic107—24no—
81C2×Dic107#4114yes—
82C22×C107C22×Q811yescharacteristic
83C22×C107C2×#4112yes—
84C22×C107H(5,𝔽2)11yescharacteristic
85C22×C107H(5,𝔽2)11yescharacteristic
86C22×C1072−1+412yes—
87C4×C107—22no—
88C4×C107—22no—
89C4×C107—22no—
90C4×C107—42no—
91C4×C107—42no—
92Dic107—24no—
93Dic107—42no—
94Dic107—42no—
95Dic107—42no—
96C2×C107#53912yes—
97C2×C107#54311yescharacteristic
98C2×C107#55511yescharacteristic
99C2×C107#55712yes—
100C2×C107#56311yescharacteristic
101#2809—1071nomaximal, Sylow
102C107#280911yescharacteristic, complemented, Sylow
103#400—1072no—
104#398—1072no—
105#398—1072no—
106#391—1071no—
107#391—1071no—
108#391D10711yescharacteristic
109#389—1072no—
110#387—1072no—
111#387—1072no—
112C22×Q8C2×D10711yescharacteristic
113C2×C4⋊C4—1072no—
114C2×C4⋊C4—1072no—
115C2×C4⋊C4—1071no—
116C2×C4⋊C4—1071no—
117C2×C4⋊C4—1072no—
118C2×C4⋊C4—1072no—
119C2×C4⋊C4—1072no—
120C2×C4⋊C4C2×D10711yescharacteristic
121C2×C42—1071no—
122C2×C42—1071no—
123C2×C42C2×D10711yescharacteristic
124#95—1072no—
125#95—1072no—
126#95—1072no—
127#95—1072no—
128#95—1072no—
129#95—1072no—
130#95—1072no—
131#95C2×D10712yes—
132#95C2×D10712yes—
133C2×Q8—41no—
134C2×Q8—41no—
135C2×Q8Dic21414yes—
136C22×C4—1072no—
137C22×C4—1072no—
138C22×C4—1072no—
139C22×C4—1072no—
140C22×C4C22×D10712yes—
141C22×C4C22×D10712yes—
142C22×C4C22×D10711yescharacteristic
143C22×C4C22×D10711yescharacteristic
144C22×C4C22×D10711yescharacteristic
145C4⋊C4—41no—
146C4⋊C4—4282no—
147C4⋊C4—4282no—
148C4⋊C4—4281no—
149C4⋊C4—4281no—
150C4⋊C4—2144no—
151C4⋊C4—2144no—
152C4⋊C4—2144no—
153C42—41no—
154C42—4281no—
155C42—4281no—
156C23C23×D10711yescharacteristic
157Q8—44no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—1074no—
171C2×C4—2142no—
172C2×C4—2142no—
173C2×C4—2142no—
174C2×C4—2142no—
175C2×C4—2142no—
176C2×C4—2142no—
177C2×C4—2144no—
178C2×C4—2142no—
179C2×C4—2142no—
180C2×C4—2142no—
181C2×C4C2×Dic21412yes—
182C2×C4C2×Dic21412yes—
183C2×C4C2×Dic21412yes—
184C22C22×Dic21411yescharacteristic
185C22#41×D10712yes—
186C22#1681215411yescharacteristic
187C22#1681215411yescharacteristic
188C22#1681215712yes—
189C4—22no—
190C4—22no—
191C4—22no—
192C4—42no—
193C4—42no—
194C4—4282no—
195C4—4282no—
196C4—4282no—
197C4—2144no—
198C2#2029322312yes—
199C2#2029325311yescharacteristic
200C2#2029333911yescharacteristic
201C2#2029335312yes—
202C2#2029337611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, prime radical, cosocleC23×C107C24
Fitting#391×C107C2
hypercenter#391D107
hypocenterC107#2809
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
102. C107#2809semidirect

Maximal subgroups

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

subgroupindex
#202925692
#202925612
#202925602
#202925342
#202925242
#202925112
#202925102
#391×C1072
#2809107