Finite Group Databasebeta

← #28343888

Subgroups — #28343888

Order 13696.

400 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 121 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, complemented
2#20292560C212yesmaximal, complemented
3#20292539C211yesmaximal, characteristic
4#20292531C212yesmaximal, complemented
5#20292520C212yesmaximal
6#20292499C212yesmaximal
7#20292494C212yesmaximal, complemented
8#20292488C211yesmaximal, characteristic
9#397×C107C211yesmaximal, characteristic
10C22×Dic214C2211yescharacteristic
11C23×Dic107C2211yescharacteristic
12C2×C4⋊Dic107C2212yes—
13C2×Dic107⋊C4C2212yes—
14C2×Dic107⋊C4C2212yes—
15C2×C22⋊Dic107C2212yes—
16C2×C22⋊Dic107C2211yescharacteristic
17C2×C4×Dic107C2212yes—
18C107⋊#95C2212yes—
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×C107C2211yescharacteristic
30#95×C107C2212yes—
31C2×Dic214—24no—
32C2×Dic214—41no—
33C22×Dic107—22no—
34C22×Dic107—41no—
35C22×Dic107—41no—
36C22×Dic107C2312yes—
37C22×Dic107C2312yes—
38C22×Dic107C2312yes—
39C22×Dic107C2312yes—
40C4⋊Dic107—42no—
41Dic107⋊C4—42no—
42Dic107⋊C4—42no—
43C22⋊Dic107—24no—
44C22⋊Dic107—41no—
45C4×Dic107—24no—
46C24×C107C2311yescharacteristic
47C22×C4×C107C2312yes—
48C22×C4×C107C2312yes—
49C22×C4×C107C2311yescharacteristic
50C22×C4×C107C2311yescharacteristic
51C4⋊C4×C107—41no—
52C22⋊C4×C107—24no—
53C22⋊C4×C107—41no—
54C23×C107—22no—
55C23×C107—21no—
56C23×C107—21no—
57C23×C107—22no—
58C23×C107#4112yes—
59C23×C107C2411yescharacteristic
60C2×C4×C107—22no—
61C2×C4×C107—22no—
62C2×C4×C107—22no—
63C2×C4×C107—22no—
64C2×C4×C107—21no—
65C2×C4×C107—21no—
66C2×C4×C107—22no—
67C2×C4×C107—22no—
68C2×C4×C107—22no—
69C2×C4×C107—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—
82C2×Dic107#4114yes—
83Dic214—44no—
84C22×C107—22no—
85C22×C107—24no—
86C22×C107—42no—
87C22×C107—41no—
88C22×C107—41no—
89C22×C107C2×#4112yes—
90C22×C107C2×#4111yescharacteristic
91C22×C107H(5,𝔽2)11yescharacteristic
92C22×C107H(5,𝔽2)11yescharacteristic
93C22×C1072−1+412yes—
94C4×C107—42no—
95C4×C107—41no—
96C4×C107—42no—
97C4×C107—41no—
98Dic107—24no—
99Dic107—42no—
100Dic107—42no—
101Dic107—42no—
102C2×C107—42no—
103C2×C107#53811yescharacteristic
104C2×C107#54212yes—
105C2×C107#55111yescharacteristic
106C2×C107#55212yes—
107C2×C107#56311yescharacteristic
108#2764—1071nomaximal, Sylow
109C107#276411yescharacteristic, complemented, Sylow
110#400—1072no—
111#398—1072no—
112#397D10711yescharacteristic
113#393—1071no—
114#391—1072no—
115#388—1072no—
116#385—1072no—
117#383—1072no—
118#381—1071no—
119C22×Q8—1071no—
120C23×C4—1071no—
121C2×C4⋊C4—1072no—
122C2×C4⋊C4—1072no—
123C2×C4⋊C4—1072no—
124C2×C4⋊C4C2×D10711yescharacteristic
125C2×C22⋊C4—1071no—
126C2×C22⋊C4—1072no—
127C2×C22⋊C4C2×D10712yes—
128C2×C22⋊C4C2×D10711yescharacteristic
129C2×C42—1072no—
130#95—1072no—
131#95—1072no—
132#95—1072no—
133#95—1072no—
134#95—1072no—
135#95—1072no—
136#95—1072no—
137#95—1071no—
138#95C2×D10711yescharacteristic
139#95C2×D10712yes—
140C24C22×D10711yescharacteristic
141C2×Q8—4281no—
142C2×Q8—2144no—
143C22×C4—1072no—
144C22×C4—1072no—
145C22×C4—1072no—
146C22×C4—1072no—
147C22×C4—4281no—
148C22×C4—4281no—
149C22×C4—2142no—
150C22×C4C22×D10711yescharacteristic
151C22×C4C22×D10712yes—
152C22×C4C22×D10711yescharacteristic
153C22×C4C22×D10712yes—
154C4⋊C4—41no—
155C4⋊C4—4282no—
156C4⋊C4—4282no—
157C4⋊C4—4282no—
158C22⋊C4—24no—
159C22⋊C4—41no—
160C22⋊C4—4281no—
161C22⋊C4—2144no—
162C42—2144no—
163C23—22no—
164C23—21no—
165C23—21no—
166C23—22no—
167C23#1313381712yes—
168C23C23×D10711yescharacteristic
169Q8—4284no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—1074no—
181C2×C4—4284no—
182C2×C4—2142no—
183C2×C4—2142no—
184C2×C4—2142no—
185C2×C4—2142no—
186C2×C4—2142no—
187C2×C4—2142no—
188C2×C4—2142no—
189C2×C4—2142no—
190C2×C4—2142no—
191C2×C4—2142no—
192C2×C4—2142no—
193C22—22no—
194C22—24no—
195C22—41no—
196C22—42no—
197C22—41no—
198C22#41×D10712yes—
199C22C2×#1313381711yescharacteristic
200C22#1681215411yescharacteristic
201C22#1681215511yescharacteristic
202C22#1681215612yes—
203C4—41no—
204C4—42no—
205C4—41no—
206C4—42no—
207C4—4282no—
208C4—4282no—
209C4—4282no—
210C4—2144no—
211C2—42no—
212C2#2029321411yescharacteristic
213C2#2029324312yes—
214C2#2029330711yescharacteristic
215C2#2029331412yes—
216C2#2029338011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, cosocleC23×C107C24
Fitting#397×C107C2
prime radicalC24×C107C23
hypercenter#397D107
hypocenterC107#2764
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. #20292567C2semidirect
2. #20292560C2semidirect
4. #20292531C2semidirect
7. #20292494C2semidirect
109. C107#2764semidirect

Maximal subgroups

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

subgroupindex
#202925672
#202925602
#202925392
#202925312
#202925202
#202924992
#202924942
#202924882
#397×C1072
#2764107