Finite Group Databasebeta

← #28336919

Subgroups — #28336919

Order 13696.

378 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 93 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×#16812092C211yesmaximal, characteristic
2C2×#16812023C212yesmaximal
3#20292490C211yesmaximal, characteristic, complemented
4#20292393C212yesmaximal, complemented
5C2×#117×C107C211yesmaximal, characteristic, complemented
6C22×C22⋊D107C2211yescharacteristic
7#16812092—22no—
8#16812092—21no—
9#16812092—21no—
10C2×Dic107⋊C4C412yescomplemented
11C2×C22⋊Dic107C2212yes—
12C2×C22⋊Dic107C2211yescharacteristic
13C2×(C2×D107)⋊C4C412yescomplemented
14#16812023—24no—
15C107⋊#95—22no—
16C23×C4×C107C2211yescharacteristic
17#117×C107—24no—
18C2×C4⋊C4×C107—21no—
19C2×C22⋊C4×C107C2212yes—
20C2×C42×C107—21no—
21C23×D107C2×C411yescharacteristic
22C2×C22⋊D107—21no—
23C2×C22⋊D107—21no—
24C2×C22⋊D107—22no—
25C2×C22⋊D107—22no—
26C22×Dic107—22no—
27C22×Dic107C2×C411yescharacteristic
28C22×Dic107C2×C412yes—
29Dic107⋊C4—22no—
30Dic107⋊C4—22no—
31C22⋊Dic107—21no—
32C22⋊Dic107—21no—
33C22⋊Dic107—22no—
34C22⋊Dic107—22no—
35(C2×D107)⋊C4—22no—
36(C2×D107)⋊C4—22no—
37C24×C107C2311yescharacteristic
38C22×C4×C107—22no—
39C22×C4×C107—22no—
40C22×C4×C107—22no—
41C22×C4×C107C2×C412yes—
42C22×C4×C107D412yes—
43C22×C4×C107D411yescharacteristic
44C22×C4×C107D411yescharacteristic
45C4⋊C4×C107—24no—
46C22⋊C4×C107—22no—
47C22⋊C4×C107D414yes—
48C42×C107—24no—
49C23×C107—42no—
50C23×C107C22×C411yescharacteristic
51C23×C107C2×D411yescharacteristic
52C23×C107C2×D412yes—
53C23×C107C2×D411yescharacteristic
54C23×C107#4112yes—
55C22×D107—21no—
56C22×D107—22no—
57C22×D107—42no—
58C2×C4×C107—24no—
59C2×C4×C107—21no—
60C2×C4×C107—21no—
61C2×C4×C107—24no—
62C2×C4×C107—21no—
63C2×C4×C107—21no—
64C2×C4×C107—24no—
65C2×C4×C107—44no—
66C2×C4×C107C22⋊C412yes—
67C2×C4×C107C22⋊C412yes—
68C22⋊D107—41no—
69C22⋊D107—42no—
70C22⋊D107—41no—
71C2×Dic107—22no—
72C2×Dic107—21no—
73C2×Dic107—22no—
74C2×Dic107—42no—
75C2×Dic107—44no—
76C2×Dic107—42no—
77C22×C107—22no—
78C22×C107—22no—
79C22×C107—22no—
80C22×C107—42no—
81C22×C107—42no—
82C22×C107C2×C22⋊C411yescharacteristic
83C22×C107C4×D412yes—
84C22×C107#12011yescharacteristic
85C22×C107#12112yes—
86C22×C107#12311yescharacteristic
87C2×D107—41no—
88C2×D107—42no—
89C2×D107—82no—
90C4×C107—22no—
91C4×C107—22no—
92C4×C107—44no—
93Dic107—41no—
94Dic107—42no—
95Dic107—82no—
96C2×C107—22no—
97C2×C107—21no—
98C2×C107—22no—
99C2×C107—21no—
100C2×C107#38611yescharacteristic
101C2×C107#41012yes—
102D107—81no—
103#1899—1071nomaximal, Sylow
104C107#189911yescharacteristic, complemented, Sylow
105C2×#123—1071no—
106C2×#117D10711yescharacteristic, complemented
107C2×#99—1072no—
108#381—1071no—
109#342—1072no—
110C22×D4—1071no—
111C23×C4C2×D10711yescharacteristic
112#123—2142no—
113#123—2141no—
114#123—2141no—
115#117—24no—
116C2×C4⋊C4—21no—
117C2×C4⋊C4—1072no—
118C2×C22⋊C4—1071no—
119C2×C22⋊C4—1072no—
120C2×C22⋊C4—1072no—
121C2×C22⋊C4C2×D10712yes—
122C2×C42—21no—
123#99—2144no—
124#95—2142no—
125C24—1071no—
126C24C22×D10711yescharacteristic
127C2×D4—2142no—
128C2×D4—2141no—
129C2×D4—2141no—
130C2×D4—2142no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—22no—
134C22×C4—1072no—
135C22×C4—1071no—
136C22×C4—2142no—
137C22×C4C4×D10712yes—
138C22×C4D42812yes—
139C22×C4C22⋊D10711yescharacteristic
140C22×C4C22⋊D10711yescharacteristic
141C4⋊C4—24no—
142C4⋊C4—2142no—
143C4⋊C4—2142no—
144C22⋊C4—22no—
145C22⋊C4—2142no—
146C22⋊C4—2142no—
147C22⋊C4—2141no—
148C22⋊C4—2141no—
149C22⋊C4—2142no—
150C22⋊C4—2142no—
151C22⋊C4C22⋊D10714yes—
152C42—24no—
153C23—42no—
154C23—4282no—
155C23—2142no—
156C23—2141no—
157C23C2×C4×D10711yescharacteristic
158C23C2×C22⋊D10711yescharacteristic
159C23C2×C22⋊D10712yes—
160C23C2×D42811yescharacteristic
161C23#1313381812yes—
162D4—4281no—
163D4—4282no—
164D4—4281no—
165C2×C4—24no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—24no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—24no—
172C2×C4—44no—
173C2×C4—4284no—
174C2×C4—4282no—
175C2×C4—4282no—
176C2×C4—2142no—
177C2×C4—2141no—
178C2×C4—2142no—
179C2×C4(C2×D107)⋊C412yes—
180C2×C4(C2×D107)⋊C412yes—
181C22—22no—
182C22—22no—
183C22—22no—
184C22—42no—
185C22—42no—
186C22—8562no—
187C22—4281no—
188C22—4282no—
189C22C2×(C2×D107)⋊C411yescharacteristic
190C22C4×C22⋊D10712yes—
191C22#1681207811yescharacteristic
192C22#1681208312yes—
193C22#1681209211yescharacteristic
194C4—22no—
195C4—22no—
196C4—44no—
197C4—8562no—
198C4—4281no—
199C4—4282no—
200C2—21no—
201C2—22no—
202C2—22no—
203C2—21no—
204C2—8561no—
205C2#2029250611yescharacteristic
206C2#2029260012yes—
subgroupG/H
centerC22C2×(C2×D107)⋊C4
commutatorC23×C107C22×C4
FrattiniC24C22×D107
FittingC2×#117×C107C2
socleC22×C107C2×C22⋊C4
prime radicalC22×C22⋊D107C22
cosocleC24×C107C23
hypercenterC2×#117D107
hypocenterC107#1899
LCSG ▷ C23×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
3. #20292490C2semidirect
4. #20292393C2semidirect
5. C2×#117×C107C2semidirect
10. C2×Dic107⋊C4C4semidirect
13. C2×(C2×D107)⋊C4C4semidirect
104. C107#1899semidirect
106. C2×#117D107semidirect

Maximal subgroups

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

subgroupindex
C2×#168120922
C2×#168120232
#202924902
#202923932
C2×#117×C1072
#1899107