Finite Group Databasebeta

← #28344527

Subgroups — #28344527

Order 13696.

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

normal subgroups only

This group has 380 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
1C2×#16812099C212yesmaximal
2#20292569C212yesmaximal
3#20292568C212yesmaximal
4#20292561C212yesmaximal
5#20292560C212yesmaximal
6#20292560C212yesmaximal
7#20292557C211yesmaximal, characteristic
8#20292492C211yesmaximal, characteristic
9#398×C107C211yesmaximal, characteristic
10#16812099—28no—
11C2×C4⋊Dic107C2212yes—
12C2×C4⋊Dic107C2211yescharacteristic
13C2×C4⋊Dic107C2211yescharacteristic
14C2×Dic107⋊C4C2212yes—
15C2×Dic107⋊C4C2212yes—
16C2×Dic107⋊C4C2212yes—
17C2×Dic107⋊C4C2212yes—
18C2×Dic107⋊C4C2212yes—
19C2×C4×Dic107C2211yescharacteristic
20C107⋊#95C2212yes—
21C107⋊#95C2212yes—
22C107⋊#95C2212yes—
23C107⋊#95C2211yescharacteristic
24C107⋊#95C2212yes—
25C107⋊#95C2212yes—
26C107⋊#95C2212yes—
27C2×C4⋊C4×C107C2212yes—
28C2×C4⋊C4×C107C2211yescharacteristic
29C2×C4⋊C4×C107C2211yescharacteristic
30#95×C107C2212yes—
31#95×C107C2211yescharacteristic
32C22×Dic107C2312yes—
33C22×Dic107C2312yes—
34C22×Dic107C2312yes—
35C22×Dic107C2312yes—
36C4⋊Dic107—24no—
37C4⋊Dic107—41no—
38C4⋊Dic107—41no—
39Dic107⋊C4—24no—
40Dic107⋊C4—24no—
41Dic107⋊C4—24no—
42Dic107⋊C4—24no—
43Dic107⋊C4—42no—
44C4×Dic107D414yes—
45C22×C4×C107C2312yes—
46C22×C4×C107C2312yes—
47C22×C4×C107C2311yescharacteristic
48C22×C4×C107C2311yescharacteristic
49C22×C4×C107C2311yescharacteristic
50C4⋊C4×C107—24no—
51C4⋊C4×C107—41no—
52C4⋊C4×C107—41no—
53C23×C107C2411yescharacteristic
54C2×C4×C107—21no—
55C2×C4×C107—21no—
56C2×C4×C107—22no—
57C2×C4×C107—22no—
58C2×C4×C107—21no—
59C2×C4×C107—22no—
60C2×C4×C107—21no—
61C2×C4×C107—22no—
62C2×C4×C107—22no—
63C2×C4×C107—22no—
64C2×C4×C107—22no—
65C2×C4×C107—22no—
66C2×C4×C107C2×D412yes—
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—24no—
77C2×Dic107C2×D414yes—
78C22×C107C22×D411yescharacteristic
79C22×C107H(5,𝔽2)11yescharacteristic
80C22×C1072−1+412yes—
81C22×C1072−1+411yescharacteristic
82C22×C1072−1+412yes—
83C4×C107—22no—
84C4×C107—42no—
85C4×C107—42no—
86C4×C107—41no—
87C4×C107—41no—
88Dic107—24no—
89Dic107—42no—
90Dic107—42no—
91Dic107—42no—
92C2×C107#53612yes—
93C2×C107#53711yescharacteristic
94C2×C107#56311yescharacteristic
95C2×C107#56311yescharacteristic
96C2×C107#56412yes—
97#2822—1071nomaximal, Sylow
98C107#282211yescharacteristic, complemented, Sylow
99C2×#125—1072no—
100#400—1072no—
101#400—1072no—
102#398—1071no—
103#398—1072no—
104#398—1072no—
105#398—1072no—
106#398D10711yescharacteristic
107#382—1071no—
108#125—2148no—
109C2×C4⋊C4—1072no—
110C2×C4⋊C4—1071no—
111C2×C4⋊C4—1071no—
112C2×C4⋊C4—1072no—
113C2×C4⋊C4—1072no—
114C2×C4⋊C4—1072no—
115C2×C4⋊C4—1072no—
116C2×C4⋊C4—1072no—
117C2×C4⋊C4C2×D10712yes—
118C2×C4⋊C4C2×D10711yescharacteristic
119C2×C4⋊C4C2×D10711yescharacteristic
120C2×C42—1071no—
121#95—1072no—
122#95—1072no—
123#95—1072no—
124#95—1072no—
125#95—1072no—
126#95—1072no—
127#95—1071no—
128#95C2×D10712yes—
129#95C2×D10711yescharacteristic
130C22×C4—1072no—
131C22×C4—1072no—
132C22×C4—1072no—
133C22×C4—1072no—
134C22×C4C22×D10711yescharacteristic
135C22×C4C22×D10711yescharacteristic
136C22×C4C22×D10712yes—
137C22×C4C22×D10712yes—
138C22×C4C22×D10711yescharacteristic
139C4⋊C4—24no—
140C4⋊C4—41no—
141C4⋊C4—41no—
142C4⋊C4—4282no—
143C4⋊C4—4281no—
144C4⋊C4—4281no—
145C4⋊C4—2144no—
146C4⋊C4—2144no—
147C4⋊C4—2144no—
148C4⋊C4—2144no—
149C4⋊C4—2144no—
150C42—1074no—
151C23C23×D10711yescharacteristic
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—1074no—
165C2×C4—2142no—
166C2×C4—2142no—
167C2×C4—2142no—
168C2×C4—2142no—
169C2×C4—2142no—
170C2×C4—2142no—
171C2×C4—2144no—
172C2×C4—2142no—
173C2×C4—2142no—
174C2×C4—2142no—
175C2×C4D4×D10712yes—
176C22C2×D4×D10711yescharacteristic
177C22#1681215411yescharacteristic
178C22#1681215612yes—
179C22#1681215611yescharacteristic
180C22#1681215712yes—
181C4—22no—
182C4—41no—
183C4—41no—
184C4—42no—
185C4—42no—
186C4—4282no—
187C4—4282no—
188C4—4282no—
189C4—2144no—
190C2#2029320012yes—
191C2#2029320411yescharacteristic
192C2#2029337611yescharacteristic
193C2#2029338011yescharacteristic
194C2C107⋊#56412yes—
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, prime radical, cosocleC23×C107C24
Fitting#398×C107C2
hypercenter#398D107
hypocenterC107#2822
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
98. C107#2822semidirect

Maximal subgroups

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

subgroupindex
C2×#168120992
#202925692
#202925682
#202925612
#202925602
#202925572
#202924922
#398×C1072
#2822107