Finite Group Databasebeta

← #28338858

Subgroups — #28338858

Order 13696.

568 conjugacy classes of subgroups; only the 197 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 197 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×C42×D107C211yesmaximal, characteristic
2#20292495C211yesmaximal, characteristic, complemented
3#20292491C212yesmaximal, complemented
4#20292489C212yesmaximal
5#20292486C212yesmaximal
6#20292478C212yesmaximal, complemented
7#20292474C212yesmaximal
8#20292472C212yesmaximal, complemented
9#383×C107C211yesmaximal, characteristic, complemented
10C22×C4×D107C2211yescharacteristic
11C22×C4×D107C2211yescharacteristic
12C22×C4×D107C2211yescharacteristic
13C2×Dic107⋊C4C2214yes—
14C2×(C2×D107)⋊C4C2214yes—
15C2×C4×Dic107C2214yes—
16C2×C4×Dic107C2211yescharacteristic
17C2×C4×Dic107C2211yescharacteristic
18C2×C4×Dic107C2211yescharacteristic
19C42×D107C418yescomplemented
20C107⋊#95C2212yes—
21C107⋊#95C2214yes—
22C107⋊#95C2212yes—
23C107⋊#95C2212yes—
24C2×C42×C107C2211yescharacteristic
25#95×C107C2212yes—
26#95×C107C2212yes—
27#95×C107C2212yes—
28C23×D107C2311yescharacteristic
29C22×Dic107C2314yes—
30C22×Dic107C2311yescharacteristic
31C22×Dic107C2311yescharacteristic
32C22×Dic107C2311yescharacteristic
33C2×C4×D107—24no—
34C2×C4×D107—24no—
35C2×C4×D107—24no—
36C2×C4×D107C2×C414yes—
37C2×C4×D107C2×C414yes—
38C2×C4×D107C2×C414yes—
39Dic107⋊C4—28no—
40(C2×D107)⋊C4—28no—
41C4×Dic107—28no—
42C4×Dic107C2×C414yes—
43C4×Dic107C2×C414yes—
44C4×Dic107C2×C414yes—
45C22×C4×C107C2314yes—
46C22×C4×C107C2311yescharacteristic
47C22×C4×C107C2311yescharacteristic
48C22×C4×C107C2311yescharacteristic
49C42×C107C2×C414yes—
50C23×C107C2411yescharacteristic
51C22×D107—22no—
52C22×D107—22no—
53C22×D107C22×C412yes—
54C22×D107#4114yes—
55C2×C4×C107—22no—
56C2×C4×C107—22no—
57C2×C4×C107—22no—
58C2×C4×C107—24no—
59C2×C4×C107—24no—
60C2×C4×C107—24no—
61C2×C4×C107C22×C412yes—
62C2×C4×C107C22×C412yes—
63C2×C4×C107C22×C412yes—
64C2×Dic107—22no—
65C2×Dic107—24no—
66C2×Dic107—24no—
67C2×Dic107—24no—
68C2×Dic107C22×C412yes—
69C2×Dic107C22×C412yes—
70C2×Dic107C22×C412yes—
71C2×Dic107#4114yes—
72C2×Dic107#4114yes—
73C4×D107—28no—
74C4×D107—28no—
75C4×D107—28no—
76C22×C107C23×C411yescharacteristic
77C22×C107C2×#4112yes—
78C22×C107C2×#4112yes—
79C22×C107C2×#4112yes—
80C2×D107—22no—
81C2×D107—22no—
82C2×D107—28no—
83C2×D107#11714yes—
84C4×C107—22no—
85C4×C107—22no—
86C4×C107—22no—
87C4×C107—44no—
88Dic107—22no—
89Dic107—44no—
90Dic107#11714yes—
91Dic107#11714yes—
92C2×C107C2×#11711yescharacteristic
93C2×C107C2×#11711yescharacteristic
94C2×C107C2×#11711yescharacteristic
95C2×C107#52914yes—
96D107—24no—
97#2283—1071nomaximal, Sylow
98C107#228311yescharacteristic, complemented, Sylow
99C22×C42—1071no—
100#383—1071no—
101#383D10711yescharacteristic, complemented
102#382—1072no—
103#381—1072no—
104#380—1072no—
105C4×C4⋊C4—1072no—
106C4×C22⋊C4—1072no—
107#376—1072no—
108C23×C4—1071no—
109C23×C4—1071no—
110C23×C4—1071no—
111C2×C4⋊C4—1074no—
112C2×C22⋊C4—1074no—
113C2×C42—1071no—
114C2×C42—1071no—
115C2×C42—1071no—
116C2×C42—1078no—
117C2×C42—1074no—
118C2×C42C2×D10711yescharacteristic
119#95—1072no—
120#95—1074no—
121#95—1072no—
122#95—1072no—
123#95C2×D10712yes—
124#95C2×D10712yes—
125#95C2×D10712yes—
126C24—1071no—
127C22×C4—1071no—
128C22×C4—1071no—
129C22×C4—1071no—
130C22×C4—1074no—
131C22×C4—1074no—
132C22×C4—1074no—
133C22×C4—1074no—
134C22×C4—2144no—
135C22×C4—2144no—
136C22×C4—2144no—
137C22×C4C22×D10714yes—
138C22×C4C22×D10711yescharacteristic
139C22×C4C22×D10711yescharacteristic
140C22×C4C22×D10711yescharacteristic
141C4⋊C4—2148no—
142C22⋊C4—2148no—
143C42—1074no—
144C42—1074no—
145C42—1074no—
146C42—2148no—
147C42C4×D10714yes—
148C23—1072no—
149C23—1074no—
150C23—2142no—
151C23—2142no—
152C23C23×D10711yescharacteristic
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—24no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—1072no—
160C2×C4—1072no—
161C2×C4—1074no—
162C2×C4—1074no—
163C2×C4—1072no—
164C2×C4—2148no—
165C2×C4—2148no—
166C2×C4—2148no—
167C2×C4—2144no—
168C2×C4—2144no—
169C2×C4—2144no—
170C2×C4—2142no—
171C2×C4C2×C4×D10712yes—
172C2×C4C2×C4×D10712yes—
173C2×C4C2×C4×D10712yes—
174C22—1074no—
175C22—2148no—
176C22—2142no—
177C22—2142no—
178C22C22×C4×D10711yescharacteristic
179C22#41×D10712yes—
180C22#41×D10712yes—
181C22#41×D10712yes—
182C4—22no—
183C4—22no—
184C4—22no—
185C4—44no—
186C4—1074no—
187C4—1074no—
188C4—4284no—
189C4—2142no—
190C2—2144no—
191C2#117×D10711yescharacteristic
192C2#117×D10711yescharacteristic
193C2#117×D10711yescharacteristic
194C2#2029316014yes—
subgroupG/H
center, FrattiniC23C23×D107
commutatorC22×C107C23×C4
Fitting#383×C107C2
socle, cosocleC23×C107C24
prime radicalC23×D107C23
hypercenter#383D107
hypocenterC107#2283
LCSG ▷ C22×C107 ▷ C107
UCSC1 ◁ C23 ◁ #383

Complements

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

NH ≅ G/Ntype
2. #20292495C2semidirect
3. #20292491C2semidirect
6. #20292478C2semidirect
8. #20292472C2semidirect
9. #383×C107C2semidirect
19. C42×D107C4semidirect
98. C107#2283semidirect
101. #383D107semidirect

Maximal subgroups

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

subgroupindex
C2×C42×D1072
#202924952
#202924912
#202924892
#202924862
#202924782
#202924742
#202924722
#383×C1072
#2283107