Finite Group Databasebeta

← #28337610

Subgroups — #28337610

Order 13696.

258 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 85 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×#16812100C211yesmaximal, characteristic
2C2×#16812033C211yesmaximal, characteristic
3#20292534C211yesmaximal, characteristic
4#20292390C211yesmaximal, characteristic
5#20292389C211yesmaximal, characteristic
6#20292381C211yesmaximal, characteristic
7C2×#103×C107C211yesmaximal, characteristic
8C22×C107⋊C8C2211yescharacteristic
9#16812100—22no—
10#16812100—22no—
11C2×C4⋊Dic107—21no—
12C2×C4⋊Dic107C2211yescharacteristic
13C2×C4⋊Dic107C2211yescharacteristic
14C2×Dic107⋊C4—21no—
15C2×C4×Dic107C2211yescharacteristic
16#16812033—22no—
17C107⋊#95—21no—
18C107⋊#95—21no—
19C22×Q8×C107C2211yescharacteristic
20C22×C8×C107C2211yescharacteristic
21C2×C4⋊C4×C107C2211yescharacteristic
22#103×C107—22no—
23C22×Dic107—21no—
24C22×Dic107—21no—
25C22×Dic107D411yescharacteristic
26C22×Dic107D411yescharacteristic
27C2×C107⋊C8—21no—
28C2×C107⋊C8—21no—
29C2×C107⋊C8—21no—
30C4⋊Dic107—24no—
31C4⋊Dic107—21no—
32C4⋊Dic107—21no—
33C4⋊Dic107—21no—
34C4⋊Dic107D412yes—
35Dic107⋊C4—24no—
36C4×Dic107—21no—
37C4×Dic107—21no—
38C2×Q8×C107—21no—
39C2×Q8×C107—21no—
40C2×Q8×C107—21no—
41C2×Q8×C107—21no—
42C2×Q8×C107—21no—
43C2×Q8×C107Q812yes—
44C22×C4×C107—21no—
45C22×C4×C107—21no—
46C22×C4×C107C2311yescharacteristic
47C2×C8×C107—21no—
48C2×C8×C107—21no—
49C2×C8×C107—21no—
50C4⋊C4×C107—21no—
51C4⋊C4×C107D412yes—
52C23×C107C2×D411yescharacteristic
53Q8×C107—22no—
54Q8×C107—22no—
55Q8×C107—41no—
56Q8×C107—41no—
57C2×C4×C107—22no—
58C2×C4×C107—22no—
59C2×C4×C107—41no—
60C2×C4×C107—41no—
61C2×C4×C107—41no—
62C2×C4×C107—41no—
63C2×C4×C107C2×D411yescharacteristic
64C2×C4×C107C2×D411yescharacteristic
65C2×C4×C107C2×Q811yescharacteristic
66C2×C4×C107#4111yescharacteristic
67C2×C4×C107#4111yescharacteristic
68C2×C4×C107#4111yescharacteristic
69C2×Dic107—21no—
70C2×Dic107—21no—
71C2×Dic107—22no—
72C2×Dic107—21no—
73C2×Dic107—21no—
74C2×Dic107—21no—
75C2×Dic107—21no—
76C2×Dic107—41no—
77C2×Dic107—41no—
78C2×Dic107—41no—
79C2×Dic107—41no—
80C2×Dic107—41no—
81C8×C107—41no—
82C107⋊C8—41no—
83C22×C107#12011yescharacteristic
84C22×C107C22⋊Q811yescharacteristic
85C22×C107#12411yescharacteristic
86C22×C107#13511yescharacteristic
87C22×C107#13511yescharacteristic
88C22×C107#13711yescharacteristic
89C22×C107#13711yescharacteristic
90C4×C107—42no—
91C4×C107—42no—
92C4×C107C22⋊Q811yescharacteristic
93C4×C107C22⋊Q811yescharacteristic
94C4×C107#12411yescharacteristic
95C4×C107#12411yescharacteristic
96Dic107—41no—
97Dic107—41no—
98Dic107—42no—
99Dic107—81no—
100C2×C107#39311yescharacteristic
101C2×C107#45211yescharacteristic
102C2×C107#45211yescharacteristic
103C2×C107#47911yescharacteristic
104C2×C107#47911yescharacteristic
105C2×C107#48811yescharacteristic
106C2×C107#49111yescharacteristic
107#2026—1071nomaximal, Sylow
108C107#202611yescharacteristic, complemented, Sylow
109C2×#125—1071no—
110C2×#103—1071no—
111C2×#103D10711yescharacteristic
112#391—1071no—
113#340—1071no—
114#340—1071no—
115#336—1071no—
116C22×Q8C2×D10711yescharacteristic
117C22×C8—1071no—
118C22×C8C2×D10711yescharacteristic
119#125—2142no—
120#125—2142no—
121C2×C4⋊C4—1071no—
122C2×C4⋊C4—1071no—
123C2×C4⋊C4—2141no—
124C2×C4⋊C4—2141no—
125C2×C4⋊C4C2×D10711yescharacteristic
126C2×C42—1071no—
127#103—22no—
128#103—2142no—
129#95—2141no—
130#95—2141no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—21no—
135C2×Q8—21no—
136C2×Q8Dic21412yes—
137C22×C4—21no—
138C22×C4—21no—
139C22×C4—1071no—
140C22×C4—1071no—
141C22×C4—2141no—
142C22×C4—2141no—
143C22×C4C22×D10711yescharacteristic
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—21no—
147C2×C8—2141no—
148C2×C8—2141no—
149C2×C8—2141no—
150C4⋊C4—21no—
151C4⋊C4—1072no—
152C4⋊C4—2144no—
153C4⋊C4—2144no—
154C4⋊C4—2141no—
155C4⋊C4—2141no—
156C4⋊C4—2141no—
157C4⋊C4C22⋊D10712yes—
158C42—2141no—
159C42—2141no—
160C23D4×D10711yescharacteristic
161Q8—22no—
162Q8—22no—
163Q8—41no—
164Q8—41no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—4281no—
172C2×C4—4281no—
173C2×C4—4281no—
174C2×C4—4281no—
175C2×C4—4281no—
176C2×C4—2141no—
177C2×C4—2141no—
178C2×C4—2142no—
179C2×C4—2141no—
180C2×C4—2141no—
181C2×C4—2141no—
182C2×C4—2141no—
183C2×C4D4×D10711yescharacteristic
184C2×C4C2×C22⋊D10711yescharacteristic
185C2×C4C2×Dic21411yescharacteristic
186C2×C4#1313381711yescharacteristic
187C2×C4#1313381711yescharacteristic
188C2×C4#1313381811yescharacteristic
189C8—41no—
190C8—4281no—
191C22#1681207711yescharacteristic
192C22#1681208611yescharacteristic
193C22#1681209511yescharacteristic
194C22#1681213011yescharacteristic
195C22#1681213211yescharacteristic
196C22#1681213811yescharacteristic
197C22#1681214111yescharacteristic
198C4—42no—
199C4—42no—
200C4—8561no—
201C4—4281no—
202C4—4282no—
203C4—4281no—
204C4#1681208611yescharacteristic
205C4#1681208811yescharacteristic
206C4#1681209511yescharacteristic
207C4#1681209611yescharacteristic
208C2#2029253911yescharacteristic
209C2#2029278611yescharacteristic
210C2#2029278811yescharacteristic
211C2#2029293211yescharacteristic
212C2#2029293611yescharacteristic
213C2#2029298311yescharacteristic
214C2#2029299411yescharacteristic
subgroupG/H
centerC23D4×D107
commutator, cosocleC22×C4×C107C23
FrattiniC22×C4C22×D107
FittingC2×#103×C107C2
socle, prime radicalC23×C107C2×D4
hypercenterC2×#103D107
hypocenterC107#2026
LCSG ▷ C22×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
108. C107#2026semidirect

Maximal subgroups

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

subgroupindex
C2×#168121002
C2×#168120332
#202925342
#202923902
#202923892
#202923812
C2×#103×C1072
#2026107