Finite Group Databasebeta

← #28344452

Subgroups — #28344452

Order 13696.

344 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 125 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#20292567C212yesmaximal
2#20292566C212yesmaximal
3#20292565C212yesmaximal
4#20292525C211yesmaximal, characteristic
5#20292525C211yesmaximal, characteristic
6#20292514C212yesmaximal
7#20292513C212yesmaximal
8#20292508C212yesmaximal
9#389×C107C211yesmaximal, characteristic
10C2×C4⋊Dic107C2211yescharacteristic
11C2×C4⋊Dic107C2211yescharacteristic
12C2×C4⋊Dic107C2211yescharacteristic
13C2×C4⋊Dic107C2211yescharacteristic
14C2×Dic107⋊C4C2212yes—
15C2×Dic107⋊C4C2212yes—
16C2×C4×Dic107C2212yes—
17C107⋊#95C2212yes—
18C107⋊#95C2212yes—
19C107⋊#95C2212yes—
20C107⋊#95C2212yes—
21C107⋊#95C2212yes—
22C107⋊#95C2212yes—
23C107⋊#95C2212yes—
24C107⋊#95C2212yes—
25C107⋊#95C2212yes—
26C2×C4⋊C4×C107C2212yes—
27C2×C4⋊C4×C107C2211yescharacteristic
28C2×C4⋊C4×C107C2211yescharacteristic
29C2×C42×C107C2211yescharacteristic
30#95×C107C2212yes—
31C22×Dic107C2312yes—
32C22×Dic107C2312yes—
33C22×Dic107C2312yes—
34C22×Dic107C2312yes—
35C4⋊Dic107—22no—
36C4⋊Dic107—22no—
37C4⋊Dic107—41no—
38C4⋊Dic107—41no—
39Dic107⋊C4—24no—
40Dic107⋊C4—24no—
41C4×Dic107—42no—
42C22×C4×C107C2312yes—
43C22×C4×C107C2312yes—
44C22×C4×C107C2311yescharacteristic
45C22×C4×C107C2311yescharacteristic
46C22×C4×C107C2311yescharacteristic
47C4⋊C4×C107—24no—
48C4⋊C4×C107—22no—
49C4⋊C4×C107—41no—
50C42×C107—41no—
51C23×C107C2411yescharacteristic
52C2×C4×C107—21no—
53C2×C4×C107—21no—
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—22no—
61C2×C4×C107—22no—
62C2×C4×C107—22no—
63C2×C4×C107—22no—
64C2×C4×C107#4112yes—
65C2×C4×C107#4112yes—
66C2×C4×C107#4112yes—
67C2×Dic107—22no—
68C2×Dic107—22no—
69C2×Dic107—22no—
70C2×Dic107—22no—
71C2×Dic107—22no—
72C2×Dic107—22no—
73C2×Dic107—22no—
74C2×Dic107—22no—
75C2×Dic107—22no—
76C2×Dic107—22no—
77C2×Dic107—22no—
78C2×Dic107—22no—
79C22×C107C2×#4111yescharacteristic
80C22×C107C2×#4111yescharacteristic
81C22×C107C2×#4111yescharacteristic
82C22×C107H(5,𝔽2)11yescharacteristic
83C22×C1072−1+411yescharacteristic
84C22×C1072−1+411yescharacteristic
85C22×C1072−1+411yescharacteristic
86C4×C107—22no—
87C4×C107—22no—
88C4×C107—22no—
89C4×C107—42no—
90C4×C107—42no—
91Dic107—42no—
92Dic107—42no—
93Dic107—42no—
94Dic107—42no—
95C2×C107#53911yescharacteristic
96C2×C107#53911yescharacteristic
97C2×C107#53911yescharacteristic
98C2×C107#55611yescharacteristic
99C2×C107#55611yescharacteristic
100C2×C107#55611yescharacteristic
101C2×C107#56411yescharacteristic
102#2810—1071nomaximal, Sylow
103C107#281011yescharacteristic, complemented, Sylow
104#400—1072no—
105#400—1072no—
106#400—1072no—
107#389—1071no—
108#389—1071no—
109#389D10711yescharacteristic
110#387—1072no—
111#387—1072no—
112#387—1072no—
113C2×C4⋊C4—1071no—
114C2×C4⋊C4—1071no—
115C2×C4⋊C4—1072no—
116C2×C4⋊C4—1072no—
117C2×C4⋊C4—1071no—
118C2×C4⋊C4—1071no—
119C2×C4⋊C4C2×D10712yes—
120C2×C4⋊C4C2×D10711yescharacteristic
121C2×C4⋊C4C2×D10711yescharacteristic
122C2×C42—1072no—
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#95—1072no—
132#95—1072no—
133#95C2×D10712yes—
134C22×C4—1072no—
135C22×C4—1072no—
136C22×C4—1072no—
137C22×C4—1072no—
138C22×C4C22×D10712yes—
139C22×C4C22×D10712yes—
140C22×C4C22×D10711yescharacteristic
141C22×C4C22×D10711yescharacteristic
142C22×C4C22×D10711yescharacteristic
143C4⋊C4—24no—
144C4⋊C4—22no—
145C4⋊C4—41no—
146C4⋊C4—4281no—
147C4⋊C4—4281no—
148C4⋊C4—2142no—
149C4⋊C4—2144no—
150C4⋊C4—2144no—
151C4⋊C4—2142no—
152C42—41no—
153C42—4282no—
154C23C23×D10711yescharacteristic
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—2142no—
168C2×C4—2142no—
169C2×C4—2142no—
170C2×C4—2142no—
171C2×C4—2142no—
172C2×C4—2142no—
173C2×C4—2142no—
174C2×C4—2142no—
175C2×C4—2142no—
176C2×C4—2142no—
177C2×C4—2142no—
178C2×C4—2142no—
179C2×C4#1313381712yes—
180C2×C4#1313381812yes—
181C2×C4#1313381912yes—
182C22C2×#1313381711yescharacteristic
183C22C2×#1313381811yescharacteristic
184C22C2×#1313381911yescharacteristic
185C22#1681215411yescharacteristic
186C22#1681215611yescharacteristic
187C22#1681215611yescharacteristic
188C22#1681215711yescharacteristic
189C4—22no—
190C4—22no—
191C4—22no—
192C4—42no—
193C4—42no—
194C4—4282no—
195C4—4282no—
196C4—4282no—
197C4—4282no—
198C2#2029322211yescharacteristic
199C2#2029322411yescharacteristic
200C2#2029322611yescharacteristic
201C2#2029334711yescharacteristic
202C2#2029335011yescharacteristic
203C2#2029335111yescharacteristic
204C2C107⋊#56411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, prime radical, cosocleC23×C107C24
Fitting#389×C107C2
hypercenter#389D107
hypocenterC107#2810
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
103. C107#2810semidirect

Maximal subgroups

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

subgroupindex
#202925672
#202925662
#202925652
#202925252
#202925142
#202925132
#202925082
#389×C1072
#2810107