Finite Group Databasebeta

← #28334966

Subgroups — #28334966

Order 13696.

334 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 77 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
1#20293138C211yesmaximal, characteristic
2C2×C107⋊#95C211yesmaximal, characteristic, complemented
3#20292365C212yesmaximal, complemented
4#20292362C212yesmaximal, complemented
5#407×C107C211yesmaximal, characteristic, complemented
6C2×#13133818C411yescharacteristic, complemented
7C23×Dic107—21no—
8#16812092—21no—
9#16812088C411yescharacteristic, complemented
10#16812088C2211yescharacteristic
11#16812083C411yescharacteristic, complemented
12#16812083C2211yescharacteristic
13#16812078—21no—
14C4×C22⋊D107—21no—
15C4×C22⋊D107—21no—
16#16812068C411yescharacteristic, complemented
17C107⋊#95—21no—
18C107⋊#95C2212yes—
19C23×C4×C107C2211yescharacteristic
20C2×M16×C107—21no—
21C22⋊C8×C107—21no—
22C22⋊C8×C107C2212yes—
23#13133818—42no—
24C2×Dic214C2×C411yescharacteristic, complemented
25C2×D428C2×C411yescharacteristic, complemented
26C2×C22⋊D107—21no—
27C2×C22⋊D107—21no—
28C2×C22⋊D107—21no—
29C22×Dic107—24no—
30C22×Dic107—22no—
31C22×Dic107—42no—
32C22×Dic107—42no—
33C2×C4×D107—21no—
34C4⋊Dic107C2×C411yescharacteristic, complemented
35C4⋊Dic107C2×C411yescharacteristic, complemented
36Dic107⋊C4—21no—
37Dic107⋊C4—21no—
38C22⋊Dic107—21no—
39C22⋊Dic107—21no—
40C22⋊Dic107—21no—
41(C2×D107)⋊C4—21no—
42(C2×D107)⋊C4—21no—
43C4×Dic107—21no—
44C24×C107D411yescharacteristic
45C22×C4×C107—42no—
46C22×C4×C107C2×C411yescharacteristic
47C22×C4×C107C2×C411yescharacteristic
48C22×C4×C107D411yescharacteristic
49C22×C4×C107D411yescharacteristic
50C22×C4×C107D411yescharacteristic
51C22×C4×C107C2311yescharacteristic
52M16×C107—42no—
53C2×C8×C107—22no—
54C23×C107—22no—
55C23×C107—22no—
56C23×C107—21no—
57C23×C107—21no—
58C23×C107C22⋊C411yescharacteristic
59C23×C107C22⋊C411yescharacteristic
60C23×C107C2×D411yescharacteristic
61C22×D107—21no—
62C2×C4×C107—22no—
63C2×C4×C107—22no—
64C2×C4×C107—41no—
65C2×C4×C107—41no—
66C2×C4×C107—41no—
67C2×C4×C107—41no—
68C2×C4×C107C22⋊C411yescharacteristic
69C2×C4×C107C22⋊C411yescharacteristic
70C2×C4×C107C22×C411yescharacteristic
71C2×C4×C107C2×D411yescharacteristic
72C22⋊D107—42no—
73C22⋊D107—42no—
74C22⋊D107—41no—
75C22⋊D107—41no—
76C2×Dic107—24no—
77C2×Dic107—21no—
78C2×Dic107—21no—
79C2×Dic107—21no—
80C2×Dic107—48no—
81C2×Dic107—42no—
82C2×Dic107—42no—
83D428—41no—
84C4×D107—42no—
85Dic214—41no—
86C8×C107—42no—
87C22×C107—24no—
88C22×C107—24no—
89C22×C107—21no—
90C22×C107—21no—
91C22×C107—21no—
92C22×C107—21no—
93C22×C107—21no—
94C22×C107—21no—
95C22×C107#9912yes—
96C22×C107#10412yes—
97C22×C107C2×C22⋊C411yescharacteristic
98C22×C107AGL(1,ℤ/8)11yescharacteristic
99C22×C107#13711yescharacteristic
100C2×D107—41no—
101C2×D107—41no—
102C2×D107—41no—
103C4×C107—21no—
104C4×C107—21no—
105C4×C107—21no—
106C4×C107—21no—
107Dic107—44no—
108Dic107—41no—
109Dic107—41no—
110Dic107—41no—
111C2×C107—21no—
112C2×C107—22no—
113C2×C107—22no—
114C2×C107—21no—
115C2×C107C2×#9911yescharacteristic
116C2×C107#41711yescharacteristic
117C2×C107C2×#10411yescharacteristic
118D107—81no—
119#1504—1071nomaximal, Sylow
120C107#150411yescharacteristic, complemented, Sylow
121#525—1071no—
122#407D10711yescharacteristic, complemented
123C2×#95—1071no—
124#328—1072no—
125#327—1072no—
126C2×#41—1071no—
127C23×C4—2141no—
128C23×C4C2×D10711yescharacteristic
129C2×M16—21no—
130#123—2141no—
131C22⋊Q8—1071no—
132C22⋊Q8—1071no—
133#121—1071no—
134#121—1071no—
135#120—2141no—
136C4×D4—2141no—
137C4×D4—2141no—
138#117—1071no—
139C22⋊C8—21no—
140C22⋊C8C2×D10712yes—
141#95—1072no—
142#95—2141no—
143C24D42811yescharacteristic
144#41—4282no—
145C2×Q8—1071no—
146C2×D4—1071no—
147C2×D4—2141no—
148C2×D4—2141no—
149C2×D4—2141no—
150C22×C4—42no—
151C22×C4—4282no—
152C22×C4—4282no—
153C22×C4—2144no—
154C22×C4—2142no—
155C22×C4—2141no—
156C22×C4C4×D10711yescharacteristic
157C22×C4C4×D10711yescharacteristic
158C22×C4D42811yescharacteristic
159C22×C4C22⋊D10711yescharacteristic
160C22×C4C22⋊D10711yescharacteristic
161C22×C4C22×D10711yescharacteristic
162M16—42no—
163C2×C8—22no—
164C4⋊C4—1071no—
165C4⋊C4—1071no—
166C4⋊C4—2141no—
167C4⋊C4—2141no—
168C22⋊C4—2141no—
169C22⋊C4—2141no—
170C22⋊C4—2141no—
171C22⋊C4—2141no—
172C22⋊C4—2141no—
173C42—2141no—
174C23—22no—
175C23—21no—
176C23—21no—
177C23—22no—
178C23—2141no—
179C23(C2×D107)⋊C411yescharacteristic
180C23(C2×D107)⋊C411yescharacteristic
181C23C2×D42811yescharacteristic
182Q8—4281no—
183D4—4281no—
184D4—4282no—
185D4—4281no—
186D4—4281no—
187D4—4282no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—4282no—
195C2×C4—4288no—
196C2×C4—4282no—
197C2×C4—4282no—
198C2×C4—2144no—
199C2×C4—2141no—
200C2×C4—2141no—
201C2×C4—2141no—
202C2×C4(C2×D107)⋊C411yescharacteristic
203C2×C4(C2×D107)⋊C411yescharacteristic
204C2×C4C2×C4×D10711yescharacteristic
205C2×C4C2×C22⋊D10711yescharacteristic
206C8—42no—
207C22—24no—
208C22—24no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—4281no—
216C22—4281no—
217C22—4281no—
218C22#1681202312yes—
219C22#1681203512yes—
220C22C2×(C2×D107)⋊C411yescharacteristic
221C22#1681213711yescharacteristic
222C22#1681214211yescharacteristic
223C4—21no—
224C4—21no—
225C4—21no—
226C4—21no—
227C4—4284no—
228C4—4281no—
229C4—4281no—
230C4—4281no—
231C2—21no—
232C2—22no—
233C2—21no—
234C2—22no—
235C2—8561no—
236C2C2×#1681202311yescharacteristic
237C2#2029262911yescharacteristic
238C2C2×#1681203511yescharacteristic
subgroupG/H
centerC22C2×(C2×D107)⋊C4
commutatorC2×C4×C107C22×C4
FrattiniC22×C4C22×D107
Fitting#407×C107C2
socleC22×C107C2×C22⋊C4
prime radical#20293138C2
cosocleC22×C4×C107C23
hypercenter#407D107
hypocenterC107#1504
LCSG ▷ C2×C4×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C2×C107⋊#95C2semidirect
3. #20292365C2semidirect
4. #20292362C2semidirect
5. #407×C107C2semidirect
6. C2×#13133818C4semidirect
9. #16812088C4semidirect
11. #16812083C4semidirect
16. #16812068C4semidirect
24. C2×Dic214C2×C4semidirect
25. C2×D428C2×C4semidirect
34. C4⋊Dic107C2×C4semidirect
35. C4⋊Dic107C2×C4semidirect
120. C107#1504semidirect
122. #407D107semidirect

Maximal subgroups

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

subgroupindex
#202931382
C2×C107⋊#952
#202923652
#202923622
#407×C1072
#1504107