Finite Group Databasebeta

← #28334777

Subgroups — #28334777

Order 13696.

332 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 97 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×C4×C22⋊D107C211yesmaximal, characteristic
2C2×C22⋊(C107⋊C8)C211yesmaximal, characteristic, complemented
3#20292352C212yesmaximal, complemented
4#20292350C212yesmaximal, complemented
5C2×C22⋊C8×C107C211yesmaximal, characteristic, complemented
6C22×C22⋊D107C411yescharacteristic
7C22×C4×D107C411yescharacteristic
8C22×C107⋊C8—21no—
9C4×C22⋊D107—21no—
10C4×C22⋊D107—21no—
11C4×C22⋊D107—21no—
12C4×C22⋊D107—21no—
13C2×Dic107⋊C4C2211yescharacteristic
14C2×C22⋊Dic107C411yescharacteristic
15C2×(C2×D107)⋊C4C2211yescharacteristic
16C2×C4×Dic107C411yescharacteristic
17C22⋊(C107⋊C8)—21no—
18C22⋊(C107⋊C8)C2212yes—
19C23×C4×C107C2211yescharacteristic
20C22×C8×C107—21no—
21C22⋊C8×C107—21no—
22C22⋊C8×C107C2212yes—
23C23×D107C2×C411yescharacteristic
24C2×C22⋊D107—21no—
25C2×C22⋊D107—21no—
26C2×C22⋊D107—22no—
27C2×C22⋊D107C814yescomplemented
28C22×Dic107C2×C411yescharacteristic
29C22×Dic107C2×C411yescharacteristic
30C22×Dic107C2×C411yescharacteristic
31C2×C4×D107—21no—
32C2×C4×D107—21no—
33C2×C4×D107—42no—
34C2×C107⋊C8—22no—
35C2×C107⋊C8—42no—
36Dic107⋊C4—21no—
37Dic107⋊C4—21no—
38C22⋊Dic107—21no—
39C22⋊Dic107—21no—
40(C2×D107)⋊C4—21no—
41(C2×D107)⋊C4—21no—
42C4×Dic107—21no—
43C4×Dic107—21no—
44C24×C107C2×C411yescharacteristic
45C22×C4×C107—42no—
46C22×C4×C107C2×C411yescharacteristic
47C22×C4×C107D411yescharacteristic
48C22×C4×C107D411yescharacteristic
49C22×C4×C107D411yescharacteristic
50C22×C4×C107D411yescharacteristic
51C22×C4×C107C2311yescharacteristic
52C2×C8×C107—22no—
53C2×C8×C107—42no—
54C23×C107—41no—
55C23×C107—41no—
56C23×C107C22⋊C411yescharacteristic
57C23×C107C22⋊C411yescharacteristic
58C23×C107C2×C812yes—
59C23×C107M1612yes—
60C23×C107C22×C411yescharacteristic
61C22×D107—21no—
62C22×D107—21no—
63C22×D107—41no—
64C22×D107—41no—
65C22×D107C2×C812yescomplemented
66C2×C4×C107—22no—
67C2×C4×C107—22no—
68C2×C4×C107—22no—
69C2×C4×C107—41no—
70C2×C4×C107—41no—
71C2×C4×C107—41no—
72C2×C4×C107C22⋊C411yescharacteristic
73C2×C4×C107C22⋊C411yescharacteristic
74C2×C4×C107C2×D411yescharacteristic
75C2×C4×C107C2×D411yescharacteristic
76C22⋊D107—24no—
77C22⋊D107—24no—
78C2×Dic107—21no—
79C2×Dic107—21no—
80C2×Dic107—21no—
81C2×Dic107—21no—
82C2×Dic107—41no—
83C2×Dic107—41no—
84C2×Dic107C2×C812yescomplemented
85C4×D107—42no—
86C4×D107—42no—
87C8×C107—42no—
88C107⋊C8—42no—
89C22×C107—21no—
90C22×C107—21no—
91C22×C107—21no—
92C22×C107—21no—
93C22×C107—21no—
94C22×C107—21no—
95C22×C107—42no—
96C22×C107—42no—
97C22×C107C22⋊C812yes—
98C22×C107C22⋊C812yes—
99C22×C107C2×C22⋊C411yescharacteristic
100C22×C107C22×C811yescharacteristic
101C22×C107C2×M1611yescharacteristic
102C2×D107—22no—
103C2×D107—42no—
104C2×D107—41no—
105C2×D107—41no—
106C2×D107—42no—
107C4×C107—21no—
108C4×C107—21no—
109C4×C107—21no—
110C4×C107#9912yes—
111Dic107—22no—
112Dic107—41no—
113Dic107—41no—
114C2×C107—21no—
115C2×C107—21no—
116C2×C107—22no—
117C2×C107—22no—
118C2×C107C2×C22⋊C811yescharacteristic
119C2×C107C2×#9911yescharacteristic
120C2×C107#41311yescharacteristic
121D107—42no—
122#1459—1071nomaximal, Sylow
123C107#145911yescharacteristic, complemented, Sylow
124C2×C4×D4—1071no—
125C2×C22⋊C8—1071no—
126C2×C22⋊C8D10711yescharacteristic, complemented
127#324—1072no—
128#323—1072no—
129C22×D4—1071no—
130C23×C4—1071no—
131C23×C4C2×D10711yescharacteristic
132C22×C8—21no—
133C22×C8—2141no—
134C4×D4—2141no—
135C4×D4—2141no—
136C4×D4—2141no—
137C4×D4—2141no—
138C2×C4⋊C4—1071no—
139C2×C22⋊C4—1071no—
140C2×C22⋊C4—1071no—
141C2×C42—1071no—
142C22⋊C8—21no—
143C22⋊C8—1072no—
144C22⋊C8—2141no—
145C22⋊C8C2×D10712yes—
146C24—1071no—
147C24C4×D10711yescharacteristic
148C2×D4—1074no—
149C2×D4—2141no—
150C2×D4—2141no—
151C2×D4—2142no—
152C22×C4—42no—
153C22×C4—1071no—
154C22×C4—1071no—
155C22×C4—1071no—
156C22×C4—4282no—
157C22×C4—2141no—
158C22×C4—2141no—
159C22×C4C4×D10711yescharacteristic
160C22×C4D42811yescharacteristic
161C22×C4D42811yescharacteristic
162C22×C4C22⋊D10711yescharacteristic
163C22×C4C22⋊D10711yescharacteristic
164C22×C4C22×D10711yescharacteristic
165C2×C8—22no—
166C2×C8—42no—
167C2×C8—4282no—
168C2×C8—2142no—
169C4⋊C4—2141no—
170C4⋊C4—2141no—
171C22⋊C4—2141no—
172C22⋊C4—2141no—
173C22⋊C4—2141no—
174C22⋊C4—2141no—
175C42—2141no—
176C42—2141no—
177C23—41no—
178C23—41no—
179C23—1072no—
180C23—4281no—
181C23—4281no—
182C23—2141no—
183C23—2141no—
184C23(C2×D107)⋊C411yescharacteristic
185C23(C2×D107)⋊C411yescharacteristic
186C23C8×D10712yes—
187C23#1313380112yes—
188C23C2×C4×D10711yescharacteristic
189D4—2144no—
190D4—2144no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—1072no—
198C2×C4—4282no—
199C2×C4—4282no—
200C2×C4—4281no—
201C2×C4—4281no—
202C2×C4—2141no—
203C2×C4—2141no—
204C2×C4—2141no—
205C2×C4—2141no—
206C2×C4(C2×D107)⋊C411yescharacteristic
207C2×C4(C2×D107)⋊C411yescharacteristic
208C2×C4C2×C22⋊D10711yescharacteristic
209C2×C4C2×D42811yescharacteristic
210C8—42no—
211C8—4282no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—21no—
216C22—21no—
217C22—21no—
218C22—42no—
219C22—42no—
220C22—4282no—
221C22—4282no—
222C22—4281no—
223C22—4281no—
224C22—2142no—
225C22(C2×D107)⋊C812yes—
226C22(C2×D107)⋊C812yes—
227C22C2×(C2×D107)⋊C411yescharacteristic
228C22C2×C8×D10711yescharacteristic
229C22C2×#1313380111yescharacteristic
230C4—21no—
231C4—21no—
232C4—21no—
233C4—4281no—
234C4—4281no—
235C4—2142no—
236C4#1681202312yes—
237C2—21no—
238C2—21no—
239C2—22no—
240C2—22no—
241C2—4282no—
242C2C2×(C2×D107)⋊C811yescharacteristic
243C2C2×#1681202311yescharacteristic
244C2#2029260911yescharacteristic
subgroupG/H
centerC2×C4(C2×D107)⋊C4
commutatorC22×C107C22×C8
FrattiniC22×C4C22×D107
FittingC2×C22⋊C8×C107C2
socleC22×C107C2×C22⋊C4
prime radicalC22×C22⋊D107C4
cosocleC22×C4×C107C23
hypercenterC2×C22⋊C8D107
hypocenterC107#1459
LCSG ▷ C22×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊(C107⋊C8)C2semidirect
3. #20292352C2semidirect
4. #20292350C2semidirect
5. C2×C22⋊C8×C107C2semidirect
27. C2×C22⋊D107C8semidirect
65. C22×D107C2×C8semidirect
84. C2×Dic107C2×C8semidirect
123. C107#1459semidirect
126. C2×C22⋊C8D107semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊D1072
C2×C22⋊(C107⋊C8)2
#202923522
#202923502
C2×C22⋊C8×C1072
#1459107