Finite Group Databasebeta

← #28339792

Subgroups — #28339792

Order 13696.

864 conjugacy classes of subgroups; only the 185 normal subgroups are shown.

normal subgroups only

This group has 864 conjugacy classes of subgroups — too many to draw. Only its 185 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×#16812090C212yesmaximal, complemented
2C22×Dic107⋊C4C211yesmaximal, characteristic, complemented
3#20292546C212yesmaximal, complemented
4#20292541C212yesmaximal, complemented
5#20292507C212yesmaximal, complemented
6#20292500C214yesmaximal, complemented
7#20292490C211yesmaximal, characteristic, complemented
8C22×#41×C107C211yesmaximal, characteristic
9C23×Dic107C2211yescharacteristic
10C23×Dic107C2211yescharacteristic
11#16812090—28no—
12C2×Dic107⋊C4—24no—
13C2×Dic107⋊C4C2214yes—
14C2×Dic107⋊C4C2212yes—
15C2×Dic107⋊C4C2212yes—
16C2×C22⋊Dic107C2212yes—
17C2×C22⋊Dic107C2214yes—
18C2×C22⋊Dic107C2214yes—
19C107⋊#95C2212yes—
20C107⋊#95C2212yes—
21C107⋊#95C2214yes—
22C2×#41×C107—28no—
23C2×#41×C107—24no—
24C22×Q8×C107C2211yescharacteristic
25C22×D4×C107C2211yescharacteristic
26C22×D4×C107C2212yes—
27C23×C4×C107C2212yes—
28C23×C4×C107C2211yescharacteristic
29C22×Dic107—22no—
30C22×Dic107—24no—
31C22×Dic107—22no—
32C22×Dic107—24no—
33C22×Dic107C2314yes—
34C22×Dic107C2312yes—
35C22×Dic107C2312yes—
36Dic107⋊C4—24no—
37Dic107⋊C4—24no—
38Dic107⋊C4—28no—
39C22⋊Dic107—24no—
40C22⋊Dic107—28no—
41C22⋊Dic107—28no—
42C24×C107C2312yes—
43C24×C107C2311yescharacteristic
44#41×C107—232no—
45C2×Q8×C107—24no—
46C2×Q8×C107—22no—
47C2×D4×C107—24no—
48C2×D4×C107—24no—
49C2×D4×C107—24no—
50C2×D4×C107—22no—
51C2×D4×C107D418yes—
52C22×C4×C107—24no—
53C22×C4×C107—24no—
54C22×C4×C107—24no—
55C22×C4×C107—24no—
56C22×C4×C107D414yes—
57C22×C4×C107C2311yescharacteristic
58C22×C4×C107C2312yes—
59C22×C4×C107C2311yescharacteristic
60C23×C107—22no—
61C23×C107—22no—
62C23×C107—22no—
63C23×C107—22no—
64C23×C107—24no—
65C23×C107—24no—
66C23×C107C2×D414yes—
67C23×C107C2×D414yes—
68C23×C107C2×D412yes—
69C23×C107C2411yescharacteristic
70Q8×C107—28no—
71D4×C107—28no—
72D4×C107—216no—
73C2×C4×C107—216no—
74C2×C4×C107—28no—
75C2×C4×C107—22no—
76C2×C4×C107—22no—
77C2×C4×C107—22no—
78C2×C4×C107—22no—
79C2×C4×C107C2×D412yes—
80C2×C4×C107C2×D414yes—
81C2×C4×C107C2×D412yes—
82C2×Dic107—28no—
83C2×Dic107—22no—
84C2×Dic107—22no—
85C2×Dic107—24no—
86C2×Dic107—24no—
87C2×Dic107—22no—
88C2×Dic107—24no—
89C2×Dic107—24no—
90C2×Dic107—44no—
91C2×Dic107#4114yescomplemented
92C22×C107—22no—
93C22×C107—22no—
94C22×C107—28no—
95C22×C107—24no—
96C22×C107—28no—
97C22×C107—42no—
98C22×C107—42no—
99C22×C107—44no—
100C22×C107#12014yes—
101C22×C107C22×D411yescharacteristic
102C22×C107C22×D412yes—
103C22×C107C2×#4112yes—
104C22×C1072−1+412yes—
105C4×C107—22no—
106C4×C107—24no—
107C4×C107—22no—
108Dic107—24no—
109Dic107—42no—
110Dic107—44no—
111C2×C107—24no—
112C2×C107—44no—
113C2×C107C2×#12011yescharacteristic
114C2×C107#52511yescharacteristic
115C2×C107#53611yescharacteristic
116C2×C107#54714yes—
117#2406—1071nomaximal, Sylow
118C107#240611yescharacteristic, complemented, Sylow
119C22×#41D10711yescharacteristic
120C2×#123—1072no—
121C22×C4⋊C4—1071no—
122#395—1072no—
123#394—1072no—
124#386—1072no—
125#385—1074no—
126#381—1071no—
127C2×#41—28no—
128C2×#41—24no—
129C22×Q8C2×D10711yescharacteristic
130C22×D4C2×D10711yescharacteristic
131C22×D4C2×D10712yes—
132C23×C4—1071no—
133C23×C4—1071no—
134C23×C4C2×D10712yes—
135C23×C4C2×D10711yescharacteristic
136#123—2148no—
137C2×C4⋊C4—1072no—
138C2×C4⋊C4—1072no—
139C2×C4⋊C4—1074no—
140C2×C4⋊C4—2144no—
141C2×C22⋊C4—1072no—
142C2×C22⋊C4—1074no—
143C2×C22⋊C4—1074no—
144#95—1072no—
145#95—1072no—
146#95—1074no—
147C24C22×D10712yes—
148C24C22×D10711yescharacteristic
149#41—232no—
150C2×Q8—24no—
151C2×Q8—22no—
152C2×D4—24no—
153C2×D4—24no—
154C2×D4—24no—
155C2×D4—22no—
156C2×D4C22⋊D10718yes—
157C22×C4—24no—
158C22×C4—24no—
159C22×C4—24no—
160C22×C4—24no—
161C22×C4—1072no—
162C22×C4—1074no—
163C22×C4—1072no—
164C22×C4—2144no—
165C22×C4—2142no—
166C22×C4—2144no—
167C22×C4—2142no—
168C22×C4C22⋊D10714yes—
169C22×C4C22×D10711yescharacteristic
170C22×C4C22×D10712yes—
171C22×C4C22×D10711yescharacteristic
172C4⋊C4—2144no—
173C4⋊C4—2144no—
174C4⋊C4—2148no—
175C22⋊C4—2148no—
176C22⋊C4—2144no—
177C22⋊C4—2148no—
178C23—22no—
179C23—22no—
180C23—22no—
181C23—22no—
182C23—24no—
183C23—24no—
184C23C2×C22⋊D10714yes—
185C23C2×C22⋊D10714yes—
186C23C2×C22⋊D10712yes—
187C23C23×D10711yescharacteristic
188Q8—28no—
189D4—28no—
190D4—216no—
191C2×C4—216no—
192C2×C4—28no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—1074no—
198C2×C4—4284no—
199C2×C4—2144no—
200C2×C4—2144no—
201C2×C4—2142no—
202C2×C4—2144no—
203C2×C4—2144no—
204C2×C4—2148no—
205C2×C4—2142no—
206C2×C4—2142no—
207C2×C4C2×C22⋊D10712yes—
208C2×C4C2×C22⋊D10714yes—
209C2×C4C2×C22⋊D10712yes—
210C22—22no—
211C22—22no—
212C22—28no—
213C22—28no—
214C22—24no—
215C22—42no—
216C22—42no—
217C22—44no—
218C22#1681207814yes—
219C22C22×C22⋊D10711yescharacteristic
220C22C22×C22⋊D10712yes—
221C22#41×D10712yes—
222C22#1681215612yes—
223C4—22no—
224C4—24no—
225C4—22no—
226C4—4284no—
227C4—4282no—
228C4—2144no—
229C2—24no—
230C2—44no—
231C2C2×#1681207811yescharacteristic
232C2#2029313411yescharacteristic
233C2#2029319811yescharacteristic
234C2#2029327614yes—
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, cosocleC23×C107C24
Fitting, prime radicalC22×#41×C107C2
hypercenterC22×#41D107
hypocenterC107#2406
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C2×#16812090C2semidirect
2. C22×Dic107⋊C4C2semidirect
3. #20292546C2semidirect
4. #20292541C2semidirect
5. #20292507C2semidirect
6. #20292500C2semidirect
7. #20292490C2semidirect
91. C2×Dic107#41semidirect
118. C107#2406semidirect

Maximal subgroups

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

subgroupindex
C2×#168120902
C22×Dic107⋊C42
#202925462
#202925412
#202925072
#202925002
#202924902
C22×#41×C1072
#2406107