Finite Group Databasebeta

← #28336448

Subgroups — #28336448

Order 13696.

380 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 87 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×(C22⋊D107)⋊C4C211yesmaximal, characteristic
2C2×#16812023C212yesmaximal
3#20292485C212yesmaximal, complemented
4#20292394C211yesmaximal, characteristic, complemented
5#342×C107C211yesmaximal, characteristic, complemented
6C22×C22⋊D107C2211yescharacteristic
7C23×Dic107C2211yescharacteristic
8C22×C4×D107C411yescharacteristic, complemented
9(C22⋊D107)⋊C4—22no—
10(C22⋊D107)⋊C4—22no—
11C2×Dic107⋊C4—22no—
12C2×Dic107⋊C4C411yescharacteristic, complemented
13C2×C22⋊Dic107C2212yes—
14C2×(C2×D107)⋊C4C411yescharacteristic, complemented
15C2×C4×Dic107C411yescharacteristic, complemented
16#16812023—24no—
17C107⋊#95—22no—
18C2×C22⋊C4×C107C2212yes—
19C2×C22⋊C4×C107C2211yescharacteristic
20C23×D107C2×C411yescharacteristic
21C2×C22⋊D107—22no—
22C2×C22⋊D107—22no—
23C2×C22⋊D107D412yes—
24C2×C22⋊D107Q812yes—
25C22×Dic107—22no—
26C22×Dic107—42no—
27C22×Dic107C2×C411yescharacteristic
28C22×Dic107C2×C411yescharacteristic
29C22×Dic107C2×C411yescharacteristic
30C22×Dic107D412yes—
31C22×Dic107D412yes—
32C2×C4×D107—21no—
33C2×C4×D107—21no—
34C2×C4×D107—42no—
35Dic107⋊C4—22no—
36Dic107⋊C4—44no—
37C22⋊Dic107—22no—
38C22⋊Dic107—22no—
39(C2×D107)⋊C4—22no—
40C4×Dic107—21no—
41C4×Dic107—21no—
42C24×C107C2311yescharacteristic
43C22×C4×C107—22no—
44C22×C4×C107C2×C411yescharacteristic
45C22×C4×C107C2×C411yescharacteristic
46C22⋊C4×C107—22no—
47C22⋊C4×C107—22no—
48C22⋊C4×C107—22no—
49C23×C107—41no—
50C23×C107—41no—
51C23×C107C22×C411yescharacteristic
52C23×C107C2×D412yes—
53C23×C107C2×D411yescharacteristic
54C23×C107C2×Q811yescharacteristic
55C23×C107#4112yes—
56C22×D107—21no—
57C22×D107—21no—
58C22×D107—41no—
59C22×D107—41no—
60C22×D107C4⋊C412yescomplemented
61C2×C4×C107—21no—
62C2×C4×C107—21no—
63C2×C4×C107—41no—
64C2×C4×C107—41no—
65C2×C4×C107—42no—
66C2×C4×C107—42no—
67C2×C4×C107—42no—
68C22⋊D107—24no—
69C22⋊D107—24no—
70C2×Dic107—21no—
71C2×Dic107—21no—
72C2×Dic107—24no—
73C2×Dic107—22no—
74C2×Dic107—41no—
75C2×Dic107—42no—
76C2×Dic107—42no—
77C2×Dic107—42no—
78C2×Dic107—42no—
79C2×Dic107C22⋊C411yescharacteristic
80C2×Dic107C22⋊C412yes—
81C2×Dic107C22⋊C411yescharacteristic
82C2×Dic107C4⋊C412yescomplemented
83C4×D107—42no—
84C4×D107—42no—
85C22×C107—22no—
86C22×C107—21no—
87C22×C107—22no—
88C22×C107—21no—
89C22×C107—41no—
90C22×C107—41no—
91C22×C107—42no—
92C22×C107C2×C22⋊C411yescharacteristic
93C22×C107C2×C4⋊C411yescharacteristic
94C22×C107#11711yescharacteristic
95C22×C107#12112yes—
96C22×C107C22⋊Q812yes—
97C2×D107—22no—
98C2×D107—42no—
99C2×D107—41no—
100C2×D107—41no—
101C2×D107—42no—
102C4×C107—41no—
103C4×C107—41no—
104C4×C107—82no—
105Dic107—22no—
106Dic107—21no—
107Dic107—22no—
108Dic107—82no—
109Dic107#9912yescomplemented
110C2×C107—22no—
111C2×C107—21no—
112C2×C107—21no—
113C2×C107—22no—
114C2×C107#38011yescharacteristic
115C2×C107C2×#9911yescharacteristic
116C2×C107#41011yescharacteristic
117D107—42no—
118#1799—1071nomaximal, Sylow
119C107#179911yescharacteristic, complemented, Sylow
120C2×C4×D4—1071no—
121C2×#99—1072no—
122#380—1072no—
123#342—1071no—
124#342D10711yescharacteristic, complemented
125C22×D4—1071no—
126C23×C4—1071no—
127C23×C4—1071no—
128C4×D4—2142no—
129C4×D4—2142no—
130C2×C4⋊C4—1071no—
131C2×C4⋊C4—2142no—
132C2×C22⋊C4—1071no—
133C2×C22⋊C4—1072no—
134C2×C22⋊C4C2×D10712yes—
135C2×C22⋊C4C2×D10711yescharacteristic
136C2×C42—1071no—
137#99—2144no—
138#95—2142no—
139C24—1071no—
140C24C22×D10711yescharacteristic
141C2×D4—1072no—
142C2×D4—1072no—
143C2×D4—2142no—
144C2×D4—2142no—
145C22×C4—22no—
146C22×C4—1071no—
147C22×C4—1072no—
148C22×C4—1071no—
149C22×C4—1071no—
150C22×C4—1072no—
151C22×C4—4282no—
152C22×C4—4282no—
153C22×C4—2141no—
154C22×C4—2141no—
155C22×C4—2142no—
156C22×C4C4×D10711yescharacteristic
157C22×C4C4×D10711yescharacteristic
158C4⋊C4—4284no—
159C4⋊C4—2142no—
160C22⋊C4—22no—
161C22⋊C4—22no—
162C22⋊C4—22no—
163C22⋊C4—2142no—
164C22⋊C4—2142no—
165C22⋊C4—2142no—
166C42—2141no—
167C42—2141no—
168C23—41no—
169C23—41no—
170C23—1072no—
171C23—4281no—
172C23—4281no—
173C23—2141no—
174C23—2141no—
175C23C2×C4×D10711yescharacteristic
176C23D4×D10712yes—
177C23D4×D10711yescharacteristic
178C23Q8×D10711yescharacteristic
179C23#1313381812yes—
180D4—2144no—
181D4—2144no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—1071no—
190C2×C4—1071no—
191C2×C4—1072no—
192C2×C4—1072no—
193C2×C4—4282no—
194C2×C4—4282no—
195C2×C4—4282no—
196C2×C4—4282no—
197C2×C4—4282no—
198C2×C4—4282no—
199C2×C4—4281no—
200C2×C4—2144no—
201C2×C4—2142no—
202C2×C4—2141no—
203C2×C4—2141no—
204C22—22no—
205C22—21no—
206C22—22no—
207C22—21no—
208C22—41no—
209C22—41no—
210C22—42no—
211C22—4282no—
212C22—4282no—
213C22—4281no—
214C22—4281no—
215C22—2142no—
216C22C22⋊C4×D10711yescharacteristic
217C22C4⋊C4×D10711yescharacteristic
218C22#1681206611yescharacteristic
219C22#1681208212yes—
220C22#1681208712yes—
221C4—41no—
222C4—41no—
223C4—82no—
224C4—8562no—
225C4—1072no—
226C4—2142no—
227C4—2141no—
228C4—2142no—
229C2—22no—
230C2—21no—
231C2—21no—
232C2—22no—
233C2—4282no—
234C2#2029248611yescharacteristic
235C2#99×D10711yescharacteristic
236C2#2029259911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D107
commutatorC23×C107C22×C4
FrattiniC24C22×D107
Fitting#342×C107C2
socleC22×C107C2×C22⋊C4
prime radicalC22×C22⋊D107C22
cosocleC24×C107C23
hypercenter#342D107
hypocenterC107#1799
LCSG ▷ C23×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
3. #20292485C2semidirect
4. #20292394C2semidirect
5. #342×C107C2semidirect
8. C22×C4×D107C4semidirect
12. C2×Dic107⋊C4C4semidirect
14. C2×(C2×D107)⋊C4C4semidirect
15. C2×C4×Dic107C4semidirect
60. C22×D107C4⋊C4semidirect
82. C2×Dic107C4⋊C4semidirect
109. Dic107#99semidirect
119. C107#1799semidirect
124. #342D107semidirect

Maximal subgroups

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

subgroupindex
C2×(C22⋊D107)⋊C42
C2×#168120232
#202924852
#202923942
#342×C1072
#1799107