Finite Group Databasebeta

← #28335436

Subgroups — #28335436

Order 13696.

238 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 51 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#20293256C211yesmaximal, characteristic
2#20292785C211yesmaximal, characteristic
3#20292782C211yesmaximal, characteristic
4#20292548C211yesmaximal, characteristic
5#20292363C211yesmaximal, characteristic
6#20292352C211yesmaximal, characteristic
7#328×C107C211yesmaximal, characteristic
8C22×Dic214C2211yescharacteristic
9C2×Dic428—21no—
10C2×#13133808—21no—
11#16812108—21no—
12#16812107—21no—
13#16812099—21no—
14#16812099—21no—
15#16812088C2211yescharacteristic
16#16812086—21no—
17#16812065—21no—
18C2×C4⋊Dic107—21no—
19C2×Dic107⋊C4C2211yescharacteristic
20#16812034—21no—
21#16812032—21no—
22C22⋊(C107⋊C8)C2211yescharacteristic
23C107⋊#95—21no—
24C22⋊Q8×C107C2211yescharacteristic
25C22⋊C8×C107C2211yescharacteristic
26#95×C107C2211yescharacteristic
27C2×Dic214—21no—
28C2×Dic214—21no—
29C2×Dic214—21no—
30C2×Dic214—42no—
31C2×Dic214D411yescharacteristic
32C22×Dic107—21no—
33C22×Dic107D411yescharacteristic
34C22×Dic107D411yescharacteristic
35Dic428—42no—
36#13133808—42no—
37C2×C107⋊C8—21no—
38C4⋊Dic107—21no—
39C4⋊Dic107—42no—
40C4⋊Dic107D411yescharacteristic
41Dic107⋊C4—21no—
42Dic107⋊C4—21no—
43Dic107⋊C4—21no—
44Dic107⋊C4—21no—
45Dic107⋊C4—21no—
46Dic107⋊C4—21no—
47Dic107⋊C4—21no—
48C22⋊Dic107—21no—
49C4×Dic107—21no—
50C4×Dic107—21no—
51C2×Q8×C107D411yescharacteristic
52C22×C4×C107—21no—
53C22×C4×C107C2311yescharacteristic
54C2×C8×C107—21no—
55C4⋊C4×C107—21no—
56C4⋊C4×C107D411yescharacteristic
57C22⋊C4×C107—21no—
58C23×C107C2×D411yescharacteristic
59Q8×C107—41no—
60C2×C4×C107—22no—
61C2×C4×C107—21no—
62C2×C4×C107—21no—
63C2×C4×C107—41no—
64C2×C4×C107—41no—
65C2×C4×C107—41no—
66C2×C4×C107C2×D411yescharacteristic
67C2×C4×C107C2×D411yescharacteristic
68C2×Dic107—21no—
69C2×Dic107—21no—
70C2×Dic107—22no—
71C2×Dic107—21no—
72C2×Dic107—21no—
73C2×Dic107—21no—
74C2×Dic107—41no—
75C2×Dic107—41no—
76C2×Dic107—41no—
77C2×Dic107Q1612yescomplemented
78Dic214—22no—
79Dic214—22no—
80Dic214—41no—
81Dic214—41no—
82Dic214—41no—
83Dic214—81no—
84C8×C107—41no—
85C107⋊C8—41no—
86C22×C107—21no—
87C22×C107—21no—
88C22×C107#12011yescharacteristic
89C22×C107C2×Q1611yescharacteristic
90C22×C107#13711yescharacteristic
91C4×C107—21no—
92C4×C107—21no—
93C4×C107—42no—
94C4×C107—41no—
95C4×C107—41no—
96Dic107—22no—
97Dic107—41no—
98Dic107—42no—
99Dic107—41no—
100Dic107—41no—
101C2×C107—21no—
102C2×C107—21no—
103C2×C107#45111yescharacteristic
104C2×C107#45611yescharacteristic
105C2×C107B(4,𝔽2)11yescharacteristic
106#1605—1071nomaximal, Sylow
107C107#160511yescharacteristic, complemented, Sylow
108#544—1071no—
109#451—1071no—
110#451—1071no—
111#395—1071no—
112#328—1071no—
113#328D10711yescharacteristic
114#324—1071no—
115C22×Q8—1071no—
116C2×Q16—2141no—
117C2×Q16—2141no—
118C4⋊Q8—2141no—
119C4⋊Q8—2141no—
120#125—2141no—
121#125—2141no—
122C22⋊Q8—1071no—
123C22⋊Q8—2141no—
124C22⋊Q8C2×D10711yescharacteristic
125#117—2141no—
126C2×C4⋊C4—1071no—
127C2×C4⋊C4—2141no—
128#103—2141no—
129#103—2141no—
130C22⋊C8—1071no—
131C22⋊C8C2×D10711yescharacteristic
132#95—2141no—
133#95C2×D10711yescharacteristic
134C2×Q8—1071no—
135C2×Q8—4282no—
136C2×Q8—2141no—
137C2×Q8—2141no—
138C2×Q8—2141no—
139C2×Q8D42811yescharacteristic
140C22×C4—21no—
141C22×C4—1071no—
142C22×C4—1071no—
143C22×C4—2141no—
144C22×C4C22×D10711yescharacteristic
145Q16—4282no—
146Q16—4282no—
147C2×C8—21no—
148C2×C8—2141no—
149C4⋊C4—21no—
150C4⋊C4—1071no—
151C4⋊C4—4282no—
152C4⋊C4—2141no—
153C4⋊C4—2141no—
154C4⋊C4—2141no—
155C4⋊C4—2141no—
156C4⋊C4—2141no—
157C4⋊C4—2141no—
158C4⋊C4—2141no—
159C4⋊C4—2141no—
160C4⋊C4D42811yescharacteristic
161C22⋊C4—21no—
162C22⋊C4—2141no—
163C42—2141no—
164C42—2141no—
165C23D4×D10711yescharacteristic
166Q8—41no—
167Q8—8561no—
168Q8—4281no—
169Q8—4281no—
170Q8—4281no—
171Q8—2142no—
172Q8—2142no—
173C2×C4—22no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—1072no—
180C2×C4—4281no—
181C2×C4—4281no—
182C2×C4—4281no—
183C2×C4—2142no—
184C2×C4—2141no—
185C2×C4—2141no—
186C2×C4—2141no—
187C2×C4—2141no—
188C2×C4—2141no—
189C2×C4D4×D10711yescharacteristic
190C2×C4C2×D42811yescharacteristic
191C8—41no—
192C8—4281no—
193C22—21no—
194C22—21no—
195C22#1681207911yescharacteristic
196C22Q16×D10711yescharacteristic
197C22#1681213811yescharacteristic
198C4—21no—
199C4—21no—
200C4—42no—
201C4—41no—
202C4—41no—
203C4—4281no—
204C4—4282no—
205C4—4281no—
206C4—4281no—
207C4—2142no—
208C2—21no—
209C2—21no—
210C2#2029278411yescharacteristic
211C2#2029281111yescharacteristic
212C2#2029281511yescharacteristic
subgroupG/H
centerC22#16812079
commutator, cosocleC22×C4×C107C23
FrattiniC22×C4C22×D107
Fitting#328×C107C2
socleC22×C107#120
prime radicalC23×C107C2×D4
hypercenter#328D107
hypocenterC107#1605
LCSG ▷ C22×C4×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
77. C2×Dic107Q16semidirect
107. C107#1605semidirect

Maximal subgroups

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

subgroupindex
#202932562
#202927852
#202927822
#202925482
#202923632
#202923522
#328×C1072
#1605107