Finite Group Databasebeta

← #28344433

Subgroups — #28344433

Order 13696.

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

normal subgroups only

This group has 408 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, complemented
2#20292563C211yesmaximal, characteristic
3#20292563C211yesmaximal, characteristic
4#20292560C212yesmaximal, complemented
5#20292524C212yesmaximal, complemented
6#20292523C212yesmaximal, complemented
7#20292520C212yesmaximal
8#20292500C212yesmaximal
9#385×C107C211yesmaximal, characteristic
10C2×C4⋊Dic107C2212yes—
11C2×C4⋊Dic107C2211yescharacteristic
12C2×C4⋊Dic107C2211yescharacteristic
13C2×Dic107⋊C4C2212yes—
14C2×Dic107⋊C4C2212yes—
15C2×Dic107⋊C4C2212yes—
16C2×Dic107⋊C4C2212yes—
17C2×C22⋊Dic107C2212yes—
18C2×C22⋊Dic107C2212yes—
19C2×C4×Dic107C2212yes—
20C107⋊#95C2212yes—
21C107⋊#95C2212yes—
22C107⋊#95C2212yes—
23C107⋊#95C2212yes—
24C107⋊#95C2211yescharacteristic
25C107⋊#95C2211yescharacteristic
26C23×C4×C107C2211yescharacteristic
27C2×C4⋊C4×C107C2212yes—
28C2×C22⋊C4×C107C2211yescharacteristic
29C2×C22⋊C4×C107C2211yescharacteristic
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—42no—
40Dic107⋊C4—42no—
41Dic107⋊C4—42no—
42C22⋊Dic107—24no—
43C22⋊Dic107—42no—
44C4×Dic107—42no—
45C24×C107C2311yescharacteristic
46C22×C4×C107—42no—
47C22×C4×C107—41no—
48C22×C4×C107C2311yescharacteristic
49C22×C4×C107C2311yescharacteristic
50C22×C4×C107C2312yes—
51C22×C4×C107C2312yes—
52C4⋊C4×C107—42no—
53C22⋊C4×C107—41no—
54C22⋊C4×C107Q814yes—
55C23×C107—22no—
56C23×C107—21no—
57C23×C107—22no—
58C23×C107—21no—
59C23×C107C2×Q812yes—
60C23×C107C2411yescharacteristic
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×C4×C107—44no—
71C2×C4×C107C2×Q814yes—
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—22no—
82C2×Dic107—22no—
83C2×Dic107#4114yes—
84C22×C107—22no—
85C22×C107—24no—
86C22×C107—42no—
87C22×C107—41no—
88C22×C107—41no—
89C22×C107C22×Q811yescharacteristic
90C22×C107C2×#4112yes—
91C22×C107H(5,𝔽2)12yes—
92C22×C107H(5,𝔽2)11yescharacteristic
93C22×C1072−1+411yescharacteristic
94C4×C107—24no—
95C4×C107—41no—
96C4×C107—41no—
97C4×C107—42no—
98Dic107—24no—
99Dic107—42no—
100Dic107—42no—
101Dic107—42no—
102C2×C107—42no—
103C2×C107#53912yes—
104C2×C107#54411yescharacteristic
105C2×C107#55412yes—
106C2×C107#55911yescharacteristic
107C2×C107#56011yescharacteristic
108#2807—1071nomaximal, Sylow
109C107#280711yescharacteristic, complemented, Sylow
110#400—1072no—
111#399—1071no—
112#399—1071no—
113#398—1072no—
114#389—1072no—
115#389—1072no—
116#388—1072no—
117#385—1072no—
118#385D10711yescharacteristic
119C23×C4C2×D10711yescharacteristic
120C2×C4⋊C4—1072no—
121C2×C4⋊C4—1072no—
122C2×C4⋊C4—1072no—
123C2×C4⋊C4—1071no—
124C2×C4⋊C4—1071no—
125C2×C4⋊C4—1072no—
126C2×C4⋊C4—1072no—
127C2×C4⋊C4C2×D10712yes—
128C2×C22⋊C4—1072no—
129C2×C22⋊C4—1072no—
130C2×C22⋊C4C2×D10711yescharacteristic
131C2×C22⋊C4C2×D10711yescharacteristic
132C2×C42—1072no—
133#95—1072no—
134#95—1072no—
135#95—1072no—
136#95—1072no—
137#95—1071no—
138#95—1071no—
139#95C2×D10712yes—
140C24C22×D10711yescharacteristic
141C22×C4—42no—
142C22×C4—41no—
143C22×C4—1072no—
144C22×C4—1072no—
145C22×C4—1072no—
146C22×C4—1072no—
147C22×C4C22×D10712yes—
148C22×C4C22×D10711yescharacteristic
149C22×C4C22×D10711yescharacteristic
150C22×C4C22×D10712yes—
151C4⋊C4—42no—
152C4⋊C4—4282no—
153C4⋊C4—4282no—
154C4⋊C4—4282no—
155C4⋊C4—4281no—
156C4⋊C4—4281no—
157C4⋊C4—2144no—
158C4⋊C4—2144no—
159C22⋊C4—41no—
160C22⋊C4—4282no—
161C22⋊C4—2144no—
162C22⋊C4Dic21414yes—
163C42—4282no—
164C23—22no—
165C23—21no—
166C23—22no—
167C23—21no—
168C23C2×Dic21412yes—
169C23C23×D10711yescharacteristic
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—44no—
180C2×C4—1074no—
181C2×C4—2142no—
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×C4C2×Dic21414yes—
193C22—22no—
194C22—24no—
195C22—42no—
196C22—41no—
197C22—41no—
198C22C22×Dic21411yescharacteristic
199C22#41×D10712yes—
200C22#1681215412yes—
201C22#1681215411yescharacteristic
202C22#1681215711yescharacteristic
203C4—24no—
204C4—41no—
205C4—42no—
206C4—41no—
207C4—4282no—
208C4—4282no—
209C4—4282no—
210C4—2144no—
211C2—42no—
212C2#2029322312yes—
213C2#2029325811yescharacteristic
214C2#2029333612yes—
215C2#2029336111yescharacteristic
216C2#2029336611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, cosocleC23×C107C24
Fitting#385×C107C2
prime radicalC24×C107C23
hypercenter#385D107
hypocenterC107#2807
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. #20292569C2semidirect
4. #20292560C2semidirect
5. #20292524C2semidirect
6. #20292523C2semidirect
109. C107#2807semidirect

Maximal subgroups

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

subgroupindex
#202925692
#202925632
#202925602
#202925242
#202925232
#202925202
#202925002
#385×C1072
#2807107