Finite Group Databasebeta

← #28336440

Subgroups — #28336440

Order 13696.

400 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 129 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
2C2×Dic107⋊C8C212yesmaximal, complemented
3C2×(C2×D107)⋊C8C212yesmaximal
4#20292382C211yesmaximal, characteristic, complemented
5#336×C107C211yesmaximal, characteristic, complemented
6C22×C4×D107C411yescharacteristic
7C22×C4×D107C411yescharacteristic
8C22×C4×D107C2211yescharacteristic
9C22×C107⋊C8C2212yes—
10C2×C4×Dic107C411yescharacteristic
11C2×C4×Dic107C411yescharacteristic
12C2×C4×Dic107C2211yescharacteristic
13C42×D107—24no—
14Dic107⋊C8—24no—
15(C2×D107)⋊C8—24no—
16C22×C8×C107C2212yes—
17C2×C42×C107C2211yescharacteristic
18C23×D107C2×C411yescharacteristic
19C22×Dic107C2×C411yescharacteristic
20C22×Dic107C2×C411yescharacteristic
21C22×Dic107C2×C411yescharacteristic
22C2×C4×D107—22no—
23C2×C4×D107—22no—
24C2×C4×D107—22no—
25C2×C4×D107—22no—
26C2×C4×D107—22no—
27C2×C4×D107—22no—
28C2×C4×D107—22no—
29C2×C4×D107C814yescomplemented
30C2×C4×D107D412yes—
31C2×C4×D107Q812yes—
32C2×C107⋊C8—22no—
33C2×C107⋊C8—22no—
34C2×C107⋊C8—22no—
35C4×Dic107—22no—
36C4×Dic107—22no—
37C4×Dic107D414yes—
38C22×C4×C107C2×C411yescharacteristic
39C22×C4×C107C2×C411yescharacteristic
40C22×C4×C107C2311yescharacteristic
41C2×C8×C107—22no—
42C2×C8×C107—22no—
43C2×C8×C107—22no—
44C42×C107—22no—
45C23×C107C22×C411yescharacteristic
46C22×D107—21no—
47C22×D107—21no—
48C22×D107—21no—
49C22×D107—21no—
50C22×D107C4⋊C412yes—
51C22×D107C2×C812yes—
52C22×D107M1612yes—
53C2×C4×C107—21no—
54C2×C4×C107—21no—
55C2×C4×C107—21no—
56C2×C4×C107—21no—
57C2×C4×C107C2×C812yes—
58C2×C4×C107M1612yes—
59C2×C4×C107C2×D411yescharacteristic
60C2×C4×C107C2×D412yes—
61C2×C4×C107C2×Q811yescharacteristic
62C2×C4×C107#4112yes—
63C2×Dic107—21no—
64C2×Dic107—21no—
65C2×Dic107—21no—
66C2×Dic107—21no—
67C2×Dic107C22⋊C412yes—
68C2×Dic107C22⋊C412yes—
69C2×Dic107C4⋊C412yes—
70C2×Dic107C2×C812yes—
71C2×Dic107M1612yes—
72C4×D107—28no—
73C4×D107—24no—
74C4×D107—24no—
75C4×D107—28no—
76C8×C107—42no—
77C107⋊C8—42no—
78C22×C107C2×C22⋊C411yescharacteristic
79C22×C107C2×C4⋊C411yescharacteristic
80C22×C107#11711yescharacteristic
81C22×C107C22×C811yescharacteristic
82C22×C107C2×M1611yescharacteristic
83C22×C107C2×M1611yescharacteristic
84C22×C107C2×M1611yescharacteristic
85C2×D107—22no—
86C2×D107—22no—
87C2×D107—22no—
88C2×D107—22no—
89C2×D107—22no—
90C2×D107—22no—
91C2×D107C4⋊C814yescomplemented
92C4×C107—22no—
93C4×C107—22no—
94C4×C107#12112yes—
95C4×C107C22⋊Q812yes—
96Dic107—22no—
97Dic107—22no—
98Dic107C22⋊C814yescomplemented
99C2×C107#38011yescharacteristic
100C2×C107C2×C22⋊C811yescharacteristic
101C2×C107#40711yescharacteristic
102C2×C107C2×C4⋊C811yescharacteristic
103C2×C107#42311yescharacteristic
104C2×C107#43111yescharacteristic
105C2×C107#43211yescharacteristic
106D107—24no—
107#1797—1071nomaximal, Sylow
108C107#179711yescharacteristic, complemented, Sylow
109C22×C42—1071no—
110C2×C4⋊C8—1072no—
111C2×C22⋊C8—1072no—
112#336—1071no—
113#336D10711yescharacteristic, complemented
114C23×C4—1071no—
115C23×C4—1071no—
116C23×C4—1071no—
117C22×C8—1072no—
118C22×C8C2×D10712yes—
119C2×C42—1071no—
120C2×C42—1071no—
121C2×C42—1071no—
122C2×C42—2144no—
123C2×C42C2×D10711yescharacteristic
124C4⋊C8—2144no—
125C22⋊C8—2144no—
126C24—1071no—
127C22×C4—1071no—
128C22×C4—1071no—
129C22×C4—1071no—
130C22×C4—1074no—
131C22×C4—1072no—
132C22×C4—1072no—
133C22×C4—2142no—
134C22×C4—2142no—
135C22×C4—2142no—
136C22×C4—2142no—
137C22×C4—2142no—
138C22×C4—2142no—
139C22×C4—2142no—
140C22×C4C4×D10711yescharacteristic
141C22×C4C4×D10711yescharacteristic
142C22×C4C22×D10711yescharacteristic
143C2×C8—22no—
144C2×C8—22no—
145C2×C8—22no—
146C2×C8—2142no—
147C2×C8—2142no—
148C2×C8—2142no—
149C42—22no—
150C42—1074no—
151C42—2142no—
152C42—2142no—
153C23—1072no—
154C23—1072no—
155C23—1072no—
156C23—2141no—
157C23—2141no—
158C23—2141no—
159C23—2141no—
160C23C2×C4×D10711yescharacteristic
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—1072no—
166C2×C4—1072no—
167C2×C4—1072no—
168C2×C4—1072no—
169C2×C4—1072no—
170C2×C4—2148no—
171C2×C4—2148no—
172C2×C4—2141no—
173C2×C4—2141no—
174C2×C4—2141no—
175C2×C4—2141no—
176C2×C4—2144no—
177C2×C4—2144no—
178C2×C4C8×D10712yes—
179C2×C4#1313380112yes—
180C2×C4D4×D10711yescharacteristic
181C2×C4D4×D10712yes—
182C2×C4Q8×D10711yescharacteristic
183C2×C4#1313381812yes—
184C8—42no—
185C8—4282no—
186C22—1074no—
187C22—2142no—
188C22—2142no—
189C22—2142no—
190C22—2142no—
191C22—2142no—
192C22—2142no—
193C22C22⋊C4×D10711yescharacteristic
194C22C4⋊C4×D10711yescharacteristic
195C22#1681206611yescharacteristic
196C22C2×C8×D10711yescharacteristic
197C22M16×D10711yescharacteristic
198C22M16×D10711yescharacteristic
199C22C2×#1313380111yescharacteristic
200C4—22no—
201C4—22no—
202C4—1074no—
203C4—2142no—
204C4—2142no—
205C4#1681208212yes—
206C4#1681208712yes—
207C2—2144no—
208C2#2029248611yescharacteristic
209C2C22⋊C8×D10711yescharacteristic
210C2#2029258911yescharacteristic
211C2C4⋊C8×D10711yescharacteristic
212C2#2029264911yescharacteristic
213C2#2029267811yescharacteristic
214C2#2029268211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C22×D107
commutatorC22×C107C22×C8
Fitting#336×C107C2
socleC23×C107C22×C4
prime radicalC23×D107C2×C4
cosocleC22×C4×C107C23
hypercenter#336D107
hypocenterC107#1797
LCSG ▷ C22×C107 ▷ C107
UCSC1 ◁ C22×C4 ◁ #336

Complements

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

NH ≅ G/Ntype
2. C2×Dic107⋊C8C2semidirect
4. #20292382C2semidirect
5. #336×C107C2semidirect
29. C2×C4×D107C8semidirect
91. C2×D107C4⋊C8semidirect
98. Dic107C22⋊C8semidirect
108. C107#1797semidirect
113. #336D107semidirect

Maximal subgroups

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

subgroupindex
C2×C42×D1072
C2×Dic107⋊C82
C2×(C2×D107)⋊C82
#202923822
#336×C1072
#1797107