Finite Group Databasebeta

← #28334829

Subgroups — #28334829

Order 13696.

214 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 61 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×#16812104C211yesmaximal, characteristic
2#20292681C211yesmaximal, characteristic, complemented
3#20292677C211yesmaximal, characteristic, complemented
4#20292353C211yesmaximal, characteristic, complemented
5#20292350C211yesmaximal, characteristic
6#20292350C211yesmaximal, characteristic
7#324×C107C211yesmaximal, characteristic, complemented
8#16812104—21no—
9#16812104—21no—
10#16812104—21no—
11#16812104—21no—
12C2×C4⋊Dic107C411yescharacteristic
13C2×Dic107⋊C4C411yescharacteristic
14C2×(C2×D107)⋊C4C411yescharacteristic
15C2×(C2×D107)⋊C4C411yescharacteristic
16C2×(C2×D107)⋊C4C2211yescharacteristic
17C2×C4×Dic107C2211yescharacteristic
18Dic107⋊C8—21no—
19Dic107⋊C8—21no—
20C22⋊(C107⋊C8)C2211yescharacteristic
21C22⋊(C107⋊C8)C2211yescharacteristic
22#16812019—21no—
23C8×Dic107—21no—
24C2×C4⋊C4×C107C2211yescharacteristic
25C22⋊C8×C107C2211yescharacteristic
26C22⋊C8×C107C2211yescharacteristic
27C23×D107C2×C411yescharacteristic
28C22×Dic107C2×C411yescharacteristic
29C22×Dic107C2×C411yescharacteristic
30C22×Dic107C2×C411yescharacteristic
31C2×C107⋊C8—21no—
32C2×C107⋊C8—21no—
33C4⋊Dic107—21no—
34C4⋊Dic107—21no—
35Dic107⋊C4—21no—
36Dic107⋊C4—21no—
37(C2×D107)⋊C4—21no—
38(C2×D107)⋊C4—21no—
39(C2×D107)⋊C4—21no—
40(C2×D107)⋊C4—21no—
41(C2×D107)⋊C4—21no—
42(C2×D107)⋊C4—21no—
43C4×Dic107D411yescharacteristic
44C4×Dic107D411yescharacteristic
45C4×Dic107D411yescharacteristic
46C4×Dic107D411yescharacteristic
47C22×C4×C107C2×C411yescharacteristic
48C22×C4×C107C2×C411yescharacteristic
49C22×C4×C107C2311yescharacteristic
50C2×C8×C107—21no—
51C2×C8×C107—21no—
52C4⋊C4×C107—21no—
53C4⋊C4×C107—21no—
54C23×C107C22×C411yescharacteristic
55C22×D107—21no—
56C22×D107—21no—
57C22×D107—21no—
58C22×D107—41no—
59C22×D107—41no—
60C2×C4×C107—21no—
61C2×C4×C107—21no—
62C2×C4×C107—21no—
63C2×C4×C107—21no—
64C2×C4×C107—41no—
65C2×C4×C107—41no—
66C2×C4×C107C2×D411yescharacteristic
67C2×C4×C107C2×D411yescharacteristic
68C2×Dic107—21no—
69C2×Dic107—21no—
70C2×Dic107—21no—
71C2×Dic107—41no—
72C2×Dic107—41no—
73C2×Dic107C22⋊C411yescharacteristic
74C2×Dic107C22⋊C411yescharacteristic
75C2×Dic107C22⋊C411yescharacteristic
76C2×Dic107C22⋊C411yescharacteristic
77C8×C107—41no—
78C8×C107—41no—
79C107⋊C8—41no—
80C107⋊C8—41no—
81C22×C107—21no—
82C22×C107—21no—
83C22×C107C2×C22⋊C411yescharacteristic
84C22×C107#13111yescharacteristic
85C22×C107#13111yescharacteristic
86C2×D107—41no—
87C2×D107—41no—
88C2×D107—41no—
89C2×D107—81no—
90C2×D107—81no—
91C4×C107—21no—
92C4×C107—21no—
93C4×C107—41no—
94C4×C107—41no—
95Dic107—21no—
96Dic107—21no—
97Dic107—21no—
98Dic107—21no—
99Dic107—41no—
100C2×C107—21no—
101C2×C107—21no—
102C2×C107#40811yescharacteristic
103C2×C107#41011yescharacteristic
104C2×C107#41311yescharacteristic
105D107—81no—
106#1473—1071nomaximal, Sylow
107C107#147311yescharacteristic, complemented, Sylow
108C2×#126—1071no—
109#432—1071no—
110#431—1071no—
111#324—1071no—
112#324D10711yescharacteristic, complemented
113#323—1071no—
114#323—1071no—
115#126—2141no—
116#126—2141no—
117#126—2141no—
118#126—2141no—
119C2×C4⋊C4—1071no—
120C2×C4⋊C4—1071no—
121C2×C4⋊C4C2×D10711yescharacteristic
122C2×C22⋊C4—1071no—
123C2×C22⋊C4—1071no—
124C2×C22⋊C4—1071no—
125C2×C42—1071no—
126C4⋊C8—2141no—
127C4⋊C8—2141no—
128C22⋊C8—1071no—
129C22⋊C8—1071no—
130C22⋊C8C2×D10711yescharacteristic
131C22⋊C8C2×D10711yescharacteristic
132#97—2141no—
133C4×C8—2141no—
134C24—1071no—
135C22×C4—1071no—
136C22×C4—1071no—
137C22×C4—1071no—
138C22×C4C4×D10711yescharacteristic
139C22×C4C4×D10711yescharacteristic
140C22×C4C22×D10711yescharacteristic
141C2×C8—21no—
142C2×C8—21no—
143C2×C8—2141no—
144C2×C8—2141no—
145C4⋊C4—21no—
146C4⋊C4—21no—
147C4⋊C4—2141no—
148C4⋊C4—2141no—
149C4⋊C4—2141no—
150C4⋊C4—2141no—
151C22⋊C4—2141no—
152C22⋊C4—2141no—
153C22⋊C4—2141no—
154C22⋊C4—2141no—
155C22⋊C4—2141no—
156C22⋊C4—2141no—
157C42—1071no—
158C42—1071no—
159C42—1071no—
160C42—1071no—
161C23—4281no—
162C23—4281no—
163C23—2141no—
164C23—2141no—
165C23—2141no—
166C23C2×C4×D10711yescharacteristic
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—1071no—
174C2×C4—1071no—
175C2×C4—1071no—
176C2×C4—1071no—
177C2×C4—4281no—
178C2×C4—4281no—
179C2×C4—2141no—
180C2×C4—2141no—
181C2×C4—2141no—
182C2×C4D4×D10711yescharacteristic
183C2×C4D4×D10711yescharacteristic
184C8—41no—
185C8—41no—
186C8—4281no—
187C8—4281no—
188C22—21no—
189C22—21no—
190C22—8561no—
191C22—8561no—
192C22—4281no—
193C22—4281no—
194C22—4281no—
195C22C22⋊C4×D10711yescharacteristic
196C22#1681211511yescharacteristic
197C22#1681211711yescharacteristic
198C4—21no—
199C4—21no—
200C4—41no—
201C4—41no—
202C4—4281no—
203C4—2141no—
204C4—2141no—
205C4—2141no—
206C4—2141no—
207C2—21no—
208C2—21no—
209C2—8561no—
210C2#2029259211yescharacteristic
211C2#2029259911yescharacteristic
212C2#2029261011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D107
commutatorC23×C107C22×C4
FrattiniC22×C4C22×D107
Fitting#324×C107C2
socleC22×C107C2×C22⋊C4
prime radicalC23×D107C2×C4
cosocleC22×C4×C107C23
hypercenter#324D107
hypocenterC107#1473
LCSG ▷ C23×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #20292681C2semidirect
3. #20292677C2semidirect
4. #20292353C2semidirect
7. #324×C107C2semidirect
107. C107#1473semidirect
112. #324D107semidirect

Maximal subgroups

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

subgroupindex
C2×#168121042
#202926812
#202926772
#202923532
#202923502
#324×C1072
#1473107