Finite Group Databasebeta

← #28337621

Subgroups — #28337621

Order 13696.

246 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 67 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#20293255C211yesmaximal, characteristic
2#20292637C211yesmaximal, characteristic
3#20292635C211yesmaximal, characteristic
4#20292533C211yesmaximal, characteristic
5#20292395C211yesmaximal, characteristic
6#20292387C211yesmaximal, characteristic
7#339×C107C211yesmaximal, characteristic
8C22×Dic214C2211yescharacteristic
9C2×#13133802C2211yescharacteristic
10#16812109—21no—
11#16812108—21no—
12#16812101—21no—
13#16812100—21no—
14#16812086—22no—
15#16812068C2211yescharacteristic
16C2×C4⋊Dic107C2211yescharacteristic
17#16812034—21no—
18#16812034—21no—
19#16812032—21no—
20#16812032—21no—
21C107⋊#95—22no—
22C2×M16×C107C2211yescharacteristic
23#117×C107C2211yescharacteristic
24C2×C42×C107C2211yescharacteristic
25C2×Dic214—21no—
26C2×Dic214—21no—
27C2×Dic214—21no—
28C2×Dic214—21no—
29C2×Dic214—21no—
30C2×Dic214—22no—
31C2×Dic214Q812yescomplemented
32C22×Dic107—21no—
33C22×Dic107D412yes—
34#13133802—21no—
35#13133802—21no—
36C2×C107⋊C8—21no—
37C4⋊Dic107—22no—
38C4⋊Dic107—21no—
39C4⋊Dic107—21no—
40C4⋊Dic107D411yescharacteristic
41C4⋊Dic107D411yescharacteristic
42Dic107⋊C4—22no—
43Dic107⋊C4—22no—
44C22⋊Dic107—21no—
45C4×Dic107—21no—
46C22×C4×C107—21no—
47C22×C4×C107C2311yescharacteristic
48M16×C107—21no—
49M16×C107—21no—
50C2×C8×C107—21no—
51C4⋊C4×C107D411yescharacteristic
52C4⋊C4×C107D411yescharacteristic
53C22⋊C4×C107—21no—
54C42×C107—21no—
55C42×C107—21no—
56C42×C107—21no—
57C23×C107C2×D411yescharacteristic
58C2×C4×C107—22no—
59C2×C4×C107—21no—
60C2×C4×C107—21no—
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—22no—
73C2×Dic107—41no—
74C2×Dic107—41no—
75C2×Dic107—42no—
76Dic214—22no—
77Dic214—22no—
78Dic214—41no—
79Dic214—41no—
80Dic214—82no—
81C8×C107—41no—
82C107⋊C8—41no—
83C22×C107—21no—
84C22×C107—21no—
85C22×C107#12011yescharacteristic
86C22×C107C22⋊Q811yescharacteristic
87C22×C107#12411yescharacteristic
88C4×C107—42no—
89C4×C107—41no—
90C4×C107—41no—
91C4×C107C22⋊Q811yescharacteristic
92C4×C107C22⋊Q811yescharacteristic
93C4×C107#12411yescharacteristic
94C4×C107#12411yescharacteristic
95Dic107—42no—
96Dic107—41no—
97Dic107—42no—
98Dic107—41no—
99C2×C107—21no—
100C2×C107—21no—
101C2×C107#39311yescharacteristic
102C2×C107#45511yescharacteristic
103C2×C107#45611yescharacteristic
104#2028—1071nomaximal, Sylow
105C107#202811yescharacteristic, complemented, Sylow
106#544—1071no—
107#419—1071no—
108#419—1071no—
109#391—1071no—
110#343—1071no—
111#339—1071no—
112#339D10711yescharacteristic
113C22×Q8—1071no—
114C2×M16—1071no—
115C2×M16C2×D10711yescharacteristic
116C4⋊Q8—2141no—
117C4⋊Q8—2141no—
118#125—2141no—
119#125—2141no—
120C22⋊Q8—2142no—
121#117—1071no—
122#117C2×D10711yescharacteristic
123C2×C4⋊C4—1071no—
124C2×C42C2×D10711yescharacteristic
125#103—2141no—
126#103—2141no—
127#103—2141no—
128#103—2141no—
129#95—2142no—
130C2×Q8—1072no—
131C2×Q8—2142no—
132C2×Q8—2141no—
133C2×Q8—2141no—
134C2×Q8—2141no—
135C2×Q8—2141no—
136C2×Q8—2141no—
137C22×C4—21no—
138C22×C4—1072no—
139C22×C4—2141no—
140C22×C4C22×D10711yescharacteristic
141M16—21no—
142M16—21no—
143M16—2141no—
144M16—2141no—
145C2×C8—21no—
146C2×C8—2141no—
147C4⋊C4—1071no—
148C4⋊C4—1071no—
149C4⋊C4—2142no—
150C4⋊C4—2142no—
151C4⋊C4—2142no—
152C4⋊C4—2141no—
153C4⋊C4—2141no—
154C4⋊C4D42811yescharacteristic
155C4⋊C4D42811yescharacteristic
156C22⋊C4—21no—
157C22⋊C4—2141no—
158C42—21no—
159C42—21no—
160C42—21no—
161C42—2141no—
162C23D4×D10711yescharacteristic
163Q8—8562no—
164Q8—4281no—
165Q8—4281no—
166Q8—2142no—
167Q8—2142no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—4281no—
174C2×C4—4281no—
175C2×C4—4282no—
176C2×C4—2141no—
177C2×C4—2141no—
178C2×C4—2142no—
179C2×C4—2142no—
180C2×C4D4×D10711yescharacteristic
181C2×C4C2×D42811yescharacteristic
182C2×C4Q8×D10711yescharacteristic
183C2×C4#1313381711yescharacteristic
184C2×C4#1313381811yescharacteristic
185C2×C4#1313381811yescharacteristic
186C8—41no—
187C8—4281no—
188C22—21no—
189C22—21no—
190C22#1681207911yescharacteristic
191C22#1681208711yescharacteristic
192C22#1681209511yescharacteristic
193C4—42no—
194C4—41no—
195C4—41no—
196C4—4282no—
197C4—4282no—
198C4—4281no—
199C4—4281no—
200C4#1681208711yescharacteristic
201C4#1681208911yescharacteristic
202C4#1681209511yescharacteristic
203C4#1681209711yescharacteristic
204C2—21no—
205C2—21no—
206C2#2029254011yescharacteristic
207C2#2029280611yescharacteristic
208C2#2029281111yescharacteristic
subgroupG/H
centerC22#16812079
commutator, cosocleC22×C4×C107C23
FrattiniC22×C4C22×D107
Fitting#339×C107C2
socleC22×C107#120
prime radicalC23×C107C2×D4
hypercenter#339D107
hypocenterC107#2028
LCSG ▷ C22×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
31. C2×Dic214Q8semidirect
105. C107#2028semidirect

Maximal subgroups

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

subgroupindex
#202932552
#202926372
#202926352
#202925332
#202923952
#202923872
#339×C1072
#2028107