Finite Group Databasebeta

← #28334950

Subgroups — #28334950

Order 13696.

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

normal subgroups only

This group has 304 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×C22⋊(C107⋊C8)C211yesmaximal, characteristic, complemented
3#20292363C212yesmaximal, complemented
4#20292360C212yesmaximal, complemented
5C4×C22⋊C4×C107C211yesmaximal, characteristic, complemented
6C2×#13133818C411yescharacteristic, complemented
7C22×C107⋊C8—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
17C22⋊(C107⋊C8)—21no—
18C22⋊(C107⋊C8)C2212yes—
19C23×C4×C107C2211yescharacteristic
20C2×C22⋊C4×C107—21no—
21C2×C42×C107—21no—
22#95×C107C2212yes—
23#13133818—42no—
24C2×Dic214C2×C411yescharacteristic
25C2×D428C2×C411yescharacteristic
26C2×C22⋊D107—21no—
27C2×C22⋊D107—21no—
28C2×C22⋊D107—21no—
29C2×C4×D107—21no—
30C2×C107⋊C8—22no—
31C2×C107⋊C8—42no—
32C4⋊Dic107C2×C411yescharacteristic
33C4⋊Dic107C2×C411yescharacteristic
34Dic107⋊C4—21no—
35Dic107⋊C4—21no—
36C22⋊Dic107—21no—
37C22⋊Dic107—21no—
38C22⋊Dic107—21no—
39(C2×D107)⋊C4—21no—
40(C2×D107)⋊C4—21no—
41C4×Dic107—21no—
42C24×C107D411yescharacteristic
43C22×C4×C107—22no—
44C22×C4×C107—42no—
45C22×C4×C107C2×C411yescharacteristic
46C22×C4×C107C2×C411yescharacteristic
47C22×C4×C107D411yescharacteristic
48C22×C4×C107D411yescharacteristic
49C22×C4×C107D411yescharacteristic
50C22×C4×C107C2311yescharacteristic
51C22⋊C4×C107—24no—
52C42×C107—42no—
53C23×C107—22no—
54C23×C107—22no—
55C23×C107—41no—
56C23×C107C22⋊C411yescharacteristic
57C23×C107C22⋊C411yescharacteristic
58C23×C107C2×D411yescharacteristic
59C22×D107—21no—
60C2×C4×C107—22no—
61C2×C4×C107—22no—
62C2×C4×C107—22no—
63C2×C4×C107—24no—
64C2×C4×C107—41no—
65C2×C4×C107—41no—
66C2×C4×C107—41no—
67C2×C4×C107—42no—
68C2×C4×C107—42no—
69C2×C4×C107C22⋊C411yescharacteristic
70C2×C4×C107C22⋊C411yescharacteristic
71C2×C4×C107C22×C411yescharacteristic
72C2×C4×C107C2×D411yescharacteristic
73C22⋊D107—42no—
74C22⋊D107—42no—
75C22⋊D107—42no—
76C2×Dic107—21no—
77C2×Dic107—21no—
78C2×Dic107—21no—
79D428—41no—
80C4×D107—42no—
81Dic214—41no—
82C107⋊C8—42no—
83C22×C107—21no—
84C22×C107—21no—
85C22×C107—21no—
86C22×C107—21no—
87C22×C107—21no—
88C22×C107—21no—
89C22×C107—21no—
90C22×C107—44no—
91C22×C107#10412yes—
92C22×C107C2×C22⋊C411yescharacteristic
93C22×C107#13512yes—
94C2×D107—41no—
95C2×D107—41no—
96C2×D107—41no—
97C4×C107—21no—
98C4×C107—21no—
99C4×C107—21no—
100C4×C107—44no—
101C4×C107#9912yes—
102Dic107—41no—
103Dic107—41no—
104Dic107—41no—
105C2×C107—22no—
106C2×C107—22no—
107C2×C107—41no—
108C2×C107C2×#9911yescharacteristic
109C2×C107#41611yescharacteristic
110C2×C107C2×#10411yescharacteristic
111D107—81no—
112#1501—1071nomaximal, Sylow
113C107#150111yescharacteristic, complemented, Sylow
114#525—1071no—
115C2×C22⋊C8—1071no—
116C4×C22⋊C4D10711yescharacteristic, complemented
117#328—1072no—
118#327—1072no—
119C2×#41—1071no—
120C23×C4C2×D10711yescharacteristic
121C22×C8—2141no—
122#123—2141no—
123C22⋊Q8—1071no—
124C22⋊Q8—1071no—
125#121—1071no—
126#121—1071no—
127#120—2141no—
128C4×D4—2141no—
129C4×D4—2141no—
130#117—1071no—
131C2×C22⋊C4—21no—
132C2×C42—21no—
133C22⋊C8—1072no—
134C22⋊C8—2141no—
135#95C2×D10712yes—
136C24C22⋊D10711yescharacteristic
137#41—4282no—
138C2×Q8—1071no—
139C2×D4—1071no—
140C2×D4—2141no—
141C2×D4—2141no—
142C2×D4—2141no—
143C22×C4—22no—
144C22×C4—42no—
145C22×C4—2141no—
146C22×C4C4×D10711yescharacteristic
147C22×C4C4×D10711yescharacteristic
148C22×C4D42811yescharacteristic
149C22×C4D42811yescharacteristic
150C22×C4C22⋊D10711yescharacteristic
151C22×C4C22×D10711yescharacteristic
152C2×C8—4282no—
153C2×C8—2142no—
154C4⋊C4—1071no—
155C4⋊C4—1071no—
156C4⋊C4—2141no—
157C4⋊C4—2141no—
158C22⋊C4—24no—
159C22⋊C4—2141no—
160C22⋊C4—2141no—
161C22⋊C4—2141no—
162C22⋊C4—2141no—
163C22⋊C4—2141no—
164C42—42no—
165C42—2141no—
166C23—22no—
167C23—22no—
168C23—41no—
169C23—2141no—
170C23(C2×D107)⋊C411yescharacteristic
171C23(C2×D107)⋊C411yescharacteristic
172C23C2×C22⋊D10711yescharacteristic
173Q8—4281no—
174D4—4281no—
175D4—4282no—
176D4—4282no—
177D4—4282no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—24no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—4282no—
188C2×C4—2141no—
189C2×C4—2141no—
190C2×C4—2141no—
191C2×C4(C2×D107)⋊C411yescharacteristic
192C2×C4(C2×D107)⋊C411yescharacteristic
193C2×C4C2×C4×D10711yescharacteristic
194C2×C4C2×D42811yescharacteristic
195C8—4282no—
196C22—21no—
197C22—21no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—44no—
204C22—4281no—
205C22—4281no—
206C22—4281no—
207C22#1681203712yes—
208C22C2×(C2×D107)⋊C411yescharacteristic
209C22#1681212912yes—
210C4—21no—
211C4—21no—
212C4—21no—
213C4—44no—
214C4—4281no—
215C4—4281no—
216C4—4281no—
217C4#1681202312yes—
218C2—22no—
219C2—22no—
220C2—41no—
221C2—8561no—
222C2C2×#1681202311yescharacteristic
223C2#2029262111yescharacteristic
224C2C2×#1681203711yescharacteristic
subgroupG/H
centerC2×C4(C2×D107)⋊C4
commutatorC2×C4×C107C22×C4
FrattiniC22×C4C22×D107
FittingC4×C22⋊C4×C107C2
socleC22×C107C2×C22⋊C4
prime radical#20293138C2
cosocleC22×C4×C107C23
hypercenterC4×C22⋊C4D107
hypocenterC107#1501
LCSG ▷ C2×C4×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊(C107⋊C8)C2semidirect
3. #20292363C2semidirect
4. #20292360C2semidirect
5. C4×C22⋊C4×C107C2semidirect
6. C2×#13133818C4semidirect
9. #16812088C4semidirect
11. #16812083C4semidirect
16. #16812068C4semidirect
113. C107#1501semidirect
116. C4×C22⋊C4D107semidirect

Maximal subgroups

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

subgroupindex
#202931382
C2×C22⋊(C107⋊C8)2
#202923632
#202923602
C4×C22⋊C4×C1072
#1501107