Finite Group Databasebeta

← #28344646

Subgroups — #28344646

Order 13696.

372 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 117 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
1C107⋊#401C212yesmaximal, complemented
2#20292563C211yesmaximal, characteristic
3#20292561C212yesmaximal, complemented
4#20292559C212yesmaximal, complemented
5#20292557C212yesmaximal, complemented
6#20292555C212yesmaximal
7#20292502C212yesmaximal
8#20292499C211yesmaximal, characteristic
9#397×C107C211yesmaximal, characteristic
10C23×Dic107C2211yescharacteristic
11C2×C4⋊Dic107C2212yes—
12C2×C4⋊Dic107C2212yes—
13C2×C4⋊Dic107C2211yescharacteristic
14C2×Dic107⋊C4C2212yes—
15C2×Dic107⋊C4C2212yes—
16C2×Dic107⋊C4C2212yes—
17C2×C22⋊Dic107C2211yescharacteristic
18C2×C22⋊Dic107C2212yes—
19C107⋊#95C2212yes—
20C107⋊#95C2212yes—
21C107⋊#95C2212yes—
22C107⋊#95C2212yes—
23C107⋊#95C2212yes—
24C107⋊#95C2212yes—
25C107⋊#95C2211yescharacteristic
26C2×C4⋊C4×C107C2211yescharacteristic
27C2×C22⋊C4×C107C2212yes—
28C2×C22⋊C4×C107C2211yescharacteristic
29#95×C107C2212yes—
30#95×C107C2211yescharacteristic
31C22×Dic107—42no—
32C22×Dic107—41no—
33C22×Dic107C2312yes—
34C22×Dic107C2312yes—
35C22×Dic107C2312yes—
36C22×Dic107C2312yes—
37C4⋊Dic107—42no—
38C4⋊Dic107—41no—
39C4⋊Dic107—42no—
40Dic107⋊C4—42no—
41Dic107⋊C4—42no—
42Dic107⋊C4—42no—
43C22⋊Dic107—22no—
44C22⋊Dic107—42no—
45C24×C107C2311yescharacteristic
46C22×C4×C107C2311yescharacteristic
47C22×C4×C107C2312yes—
48C22×C4×C107C2311yescharacteristic
49C22×C4×C107C2312yes—
50C4⋊C4×C107—41no—
51C22⋊C4×C107—24no—
52C22⋊C4×C107—41no—
53C23×C107—21no—
54C23×C107—22no—
55C23×C107—22no—
56C23×C107—21no—
57C23×C107#4112yes—
58C23×C107C2411yescharacteristic
59C2×C4×C107—22no—
60C2×C4×C107—22no—
61C2×C4×C107—21no—
62C2×C4×C107—21no—
63C2×C4×C107—22no—
64C2×C4×C107—22no—
65C2×C4×C107—22no—
66C2×C4×C107—22no—
67C2×C4×C107—22no—
68C2×C4×C107—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—
79C2×Dic107—22no—
80C2×Dic107—22no—
81C2×Dic107—44no—
82C22×C107—24no—
83C22×C107—22no—
84C22×C107—41no—
85C22×C107—41no—
86C22×C107—42no—
87C22×C107C2×#4111yescharacteristic
88C22×C107H(5,𝔽2)11yescharacteristic
89C22×C107H(5,𝔽2)12yes—
90C22×C1072−1+412yes—
91C22×C1072−1+411yescharacteristic
92C4×C107—42no—
93C4×C107—42no—
94C4×C107—41no—
95C4×C107—41no—
96Dic107—42no—
97Dic107—42no—
98Dic107—42no—
99Dic107—42no—
100C2×C107—42no—
101C2×C107#53912yes—
102C2×C107#53911yescharacteristic
103C2×C107#56011yescharacteristic
104C2×C107#56311yescharacteristic
105C2×C107#56312yes—
106#2834—1071nomaximal, Sylow
107C107#283411yescharacteristic, complemented, Sylow
108#401—1072no—
109#399—1071no—
110#398—1072no—
111#398—1072no—
112#398—1072no—
113#397—1072no—
114#397D10711yescharacteristic
115#385—1071no—
116#385—1072no—
117C23×C4—1071no—
118C2×C4⋊C4—1072no—
119C2×C4⋊C4—1072no—
120C2×C4⋊C4—1072no—
121C2×C4⋊C4—1072no—
122C2×C4⋊C4—1072no—
123C2×C4⋊C4—1071no—
124C2×C4⋊C4C2×D10711yescharacteristic
125C2×C22⋊C4—1072no—
126C2×C22⋊C4—1071no—
127C2×C22⋊C4C2×D10712yes—
128C2×C22⋊C4C2×D10711yescharacteristic
129#95—1072no—
130#95—1072no—
131#95—1072no—
132#95—1072no—
133#95—1072no—
134#95—1072no—
135#95—1071no—
136#95C2×D10711yescharacteristic
137#95C2×D10712yes—
138C24C22×D10711yescharacteristic
139C22×C4—1072no—
140C22×C4—1072no—
141C22×C4—1072no—
142C22×C4—1072no—
143C22×C4—4281no—
144C22×C4—4282no—
145C22×C4C22×D10711yescharacteristic
146C22×C4C22×D10712yes—
147C22×C4C22×D10712yes—
148C22×C4C22×D10711yescharacteristic
149C4⋊C4—41no—
150C4⋊C4—4282no—
151C4⋊C4—4282no—
152C4⋊C4—4282no—
153C4⋊C4—4281no—
154C4⋊C4—4282no—
155C4⋊C4—4282no—
156C22⋊C4—24no—
157C22⋊C4—41no—
158C22⋊C4—4282no—
159C22⋊C4—2142no—
160C23—21no—
161C23—22no—
162C23—22no—
163C23—21no—
164C23#1313381712yes—
165C23C23×D10711yescharacteristic
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—4284no—
177C2×C4—2142no—
178C2×C4—2142no—
179C2×C4—2142no—
180C2×C4—2142no—
181C2×C4—2142no—
182C2×C4—2142no—
183C2×C4—2142no—
184C2×C4—2142no—
185C2×C4—2142no—
186C2×C4—2142no—
187C2×C4—2142no—
188C2×C4—2142no—
189C22—24no—
190C22—22no—
191C22—41no—
192C22—42no—
193C22—41no—
194C22C2×#1313381711yescharacteristic
195C22#1681215411yescharacteristic
196C22#1681215512yes—
197C22#1681215612yes—
198C22#1681215611yescharacteristic
199C4—41no—
200C4—42no—
201C4—42no—
202C4—41no—
203C4—4282no—
204C4—4282no—
205C4—4282no—
206C4—4282no—
207C2—42no—
208C2#2029322112yes—
209C2#2029322211yescharacteristic
210C2#2029336711yescharacteristic
211C2#2029337711yescharacteristic
212C2#2029337912yes—
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, cosocleC23×C107C24
Fitting#397×C107C2
prime radicalC24×C107C23
hypercenter#397D107
hypocenterC107#2834
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C107⋊#401C2semidirect
3. #20292561C2semidirect
4. #20292559C2semidirect
5. #20292557C2semidirect
107. C107#2834semidirect

Maximal subgroups

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

subgroupindex
C107⋊#4012
#202925632
#202925612
#202925592
#202925572
#202925552
#202925022
#202924992
#397×C1072
#2834107