Finite Group Databasebeta

← #28336447

Subgroups — #28336447

Order 13696.

380 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 95 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×D4×Dic107C211yesmaximal, characteristic
2C2×#16812024C211yesmaximal, characteristic
3#20292485C212yesmaximal, complemented
4#20292393C212yesmaximal, complemented
5C2×#99×C107C211yesmaximal, characteristic
6C23×Dic107C411yescharacteristic, complemented
7C23×Dic107C2211yescharacteristic
8D4×Dic107—22no—
9D4×Dic107—22no—
10C2×C4⋊Dic107C411yescharacteristic, complemented
11C2×Dic107⋊C4—22no—
12C2×C22⋊Dic107C411yescharacteristic, complemented
13C2×C22⋊Dic107C2212yes—
14C2×C22⋊Dic107C2211yescharacteristic
15C2×C4×Dic107C411yescharacteristic, complemented
16#16812024—22no—
17C107⋊#95—22no—
18C22×D4×C107C2211yescharacteristic
19C2×C22⋊C4×C107C2212yes—
20#99×C107—22no—
21C22×Dic107—21no—
22C22×Dic107—21no—
23C22×Dic107—22no—
24C22×Dic107—42no—
25C22×Dic107—42no—
26C22×Dic107C2×C411yescharacteristic
27C22×Dic107C2×C411yescharacteristic
28C22×Dic107C2×C411yescharacteristic
29C22×Dic107C2×C411yescharacteristic
30C22×Dic107D412yes—
31C22×Dic107D412yes—
32C4⋊Dic107—22no—
33Dic107⋊C4—44no—
34C22⋊Dic107—22no—
35C22⋊Dic107—22no—
36C22⋊Dic107—22no—
37C22⋊Dic107—22no—
38C4×Dic107—21no—
39C4×Dic107—21no—
40C24×C107C2×C411yescharacteristic
41C24×C107C2311yescharacteristic
42C2×D4×C107—22no—
43C2×D4×C107—22no—
44C2×D4×C107D412yes—
45C2×D4×C107Q812yes—
46C22×C4×C107—22no—
47C22×C4×C107C2×C411yescharacteristic
48C22⋊C4×C107—22no—
49C22⋊C4×C107—22no—
50C23×C107—21no—
51C23×C107—21no—
52C23×C107—41no—
53C23×C107—41no—
54C23×C107—41no—
55C23×C107—41no—
56C23×C107C4⋊C412yescomplemented
57C23×C107C22×C411yescharacteristic
58C23×C107C2×D412yes—
59C23×C107C2×D411yescharacteristic
60C23×C107C2×Q811yescharacteristic
61C23×C107#4112yes—
62D4×C107—24no—
63D4×C107—24no—
64C2×C4×C107—21no—
65C2×C4×C107—21no—
66C2×C4×C107—42no—
67C2×C4×C107—42no—
68C2×C4×C107—42no—
69C2×C4×C107C4⋊C412yescomplemented
70C2×Dic107—24no—
71C2×Dic107—22no—
72C2×Dic107—21no—
73C2×Dic107—21no—
74C2×Dic107—41no—
75C2×Dic107—42no—
76C2×Dic107—42no—
77C2×Dic107—42no—
78C2×Dic107—41no—
79C2×Dic107—41no—
80C2×Dic107—42no—
81C2×Dic107—42no—
82C2×Dic107—42no—
83C2×Dic107C22⋊C411yescharacteristic
84C2×Dic107C22⋊C412yes—
85C2×Dic107C22⋊C411yescharacteristic
86C22×C107—22no—
87C22×C107—21no—
88C22×C107—22no—
89C22×C107—21no—
90C22×C107—22no—
91C22×C107—41no—
92C22×C107—41no—
93C22×C107—42no—
94C22×C107—42no—
95C22×C107—42no—
96C22×C107—41no—
97C22×C107—41no—
98C22×C107C2×C22⋊C411yescharacteristic
99C22×C107C2×C4⋊C411yescharacteristic
100C22×C107#11711yescharacteristic
101C22×C107#12112yes—
102C22×C107C22⋊Q812yes—
103C4×C107—22no—
104C4×C107—82no—
105Dic107—21no—
106Dic107—22no—
107Dic107—41no—
108Dic107—41no—
109Dic107—82no—
110Dic107#9912yescomplemented
111C2×C107—22no—
112C2×C107—21no—
113C2×C107—21no—
114C2×C107—22no—
115C2×C107—42no—
116C2×C107#38011yescharacteristic
117C2×C107C2×#9911yescharacteristic
118C2×C107#41011yescharacteristic
119#1799—1071nomaximal, Sylow
120C107#179911yescharacteristic, complemented, Sylow
121C2×C4×D4—1071no—
122C2×#99—1071no—
123C2×#99D10711yescharacteristic
124#380—1072no—
125#342—1072no—
126C22×D4C2×D10711yescharacteristic
127C23×C4—1071no—
128C23×C4—1071no—
129C4×D4—2142no—
130C4×D4—2142no—
131C2×C4⋊C4—1071no—
132C2×C4⋊C4—2142no—
133C2×C22⋊C4—1071no—
134C2×C22⋊C4—1071no—
135C2×C22⋊C4—1072no—
136C2×C22⋊C4C2×D10712yes—
137C2×C42—1071no—
138#99—22no—
139#99—2142no—
140#95—2142no—
141C24C4×D10711yescharacteristic
142C24C22×D10711yescharacteristic
143C2×D4—22no—
144C2×D4—22no—
145C2×D4Dic21412yes—
146C2×D4C22⋊D10712yes—
147C22×C4—22no—
148C22×C4—1071no—
149C22×C4—1072no—
150C22×C4—1071no—
151C22×C4—1072no—
152C22×C4—1071no—
153C22×C4—1071no—
154C22×C4—4282no—
155C22×C4—4282no—
156C22×C4—2141no—
157C22×C4—2141no—
158C22×C4—2142no—
159C22×C4C4×D10711yescharacteristic
160C4⋊C4—4284no—
161C4⋊C4—2142no—
162C22⋊C4—22no—
163C22⋊C4—22no—
164C22⋊C4—2142no—
165C22⋊C4—2142no—
166C22⋊C4—2142no—
167C22⋊C4—2142no—
168C42—2141no—
169C42—2141no—
170C23—21no—
171C23—21no—
172C23—41no—
173C23—41no—
174C23—41no—
175C23—41no—
176C23Dic107⋊C412yescomplemented
177C23C2×C4×D10711yescharacteristic
178C23D4×D10712yes—
179C23C2×C22⋊D10711yescharacteristic
180C23C2×Dic21411yescharacteristic
181C23#1313381712yes—
182D4—24no—
183D4—24no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—1071no—
190C2×C4—1071no—
191C2×C4—1072no—
192C2×C4—4282no—
193C2×C4—4282no—
194C2×C4—4282no—
195C2×C4—4282no—
196C2×C4—4282no—
197C2×C4—4281no—
198C2×C4—4281no—
199C2×C4—4282no—
200C2×C4—4281no—
201C2×C4—2144no—
202C2×C4—2142no—
203C2×C4—2141no—
204C2×C4—2141no—
205C2×C4Dic107⋊C412yescomplemented
206C22—22no—
207C22—21no—
208C22—22no—
209C22—21no—
210C22—22no—
211C22—41no—
212C22—41no—
213C22—42no—
214C22—42no—
215C22—42no—
216C22—41no—
217C22—41no—
218C22C22⋊C4×D10711yescharacteristic
219C22C2×Dic107⋊C411yescharacteristic
220C22#1681206511yescharacteristic
221C22#1681208112yes—
222C22#1681208612yes—
223C4—22no—
224C4—82no—
225C4—8562no—
226C4—1072no—
227C4—4281no—
228C4—4281no—
229C4—2141no—
230C4—2142no—
231C2—22no—
232C2—21no—
233C2—21no—
234C2—22no—
235C2—42no—
236C2#2029248511yescharacteristic
237C2#99×D10711yescharacteristic
238C2#2029259911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D107
commutatorC23×C107C22×C4
FrattiniC24C22×D107
FittingC2×#99×C107C2
socleC22×C107C2×C22⋊C4
prime radicalC22×D4×C107C22
cosocleC24×C107C23
hypercenterC2×#99D107
hypocenterC107#1799
LCSG ▷ C23×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
3. #20292485C2semidirect
4. #20292393C2semidirect
6. C23×Dic107C4semidirect
10. C2×C4⋊Dic107C4semidirect
12. C2×C22⋊Dic107C4semidirect
15. C2×C4×Dic107C4semidirect
56. C23×C107C4⋊C4semidirect
69. C2×C4×C107C4⋊C4semidirect
110. Dic107#99semidirect
120. C107#1799semidirect
176. C23Dic107⋊C4semidirect
205. C2×C4Dic107⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic1072
C2×#168120242
#202924852
#202923932
C2×#99×C1072
#1799107