Finite Group Databasebeta

← #28337632

Subgroups — #28337632

Order 13696.

244 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 63 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#20293180C211yesmaximal, characteristic, complemented
2#20292645C211yesmaximal, characteristic
3C2×#16812035C211yesmaximal, characteristic
4#20292600C211yesmaximal, characteristic
5#20292399C211yesmaximal, characteristic, complemented
6#20292386C211yesmaximal, characteristic, complemented
7H(3,ℤ/4)×C107C211yesmaximal, characteristic, complemented
8C2×#13133818C2211yescharacteristic
9C2×#13133802C2211yescharacteristic
10#16812108—21no—
11#16812100—21no—
12#16812086—22no—
13C4×Dic214—22no—
14#16812068C2211yescharacteristic
15C2×C4×Dic107C2211yescharacteristic
16#16812037—22no—
17#16812035—21no—
18#16812035—21no—
19#16812023—22no—
20C2×M16×C107C2211yescharacteristic
21#117×C107C2211yescharacteristic
22#117×C107C2211yescharacteristic
23#13133818—21no—
24#13133818—21no—
25#13133818—21no—
26#13133818—21no—
27C2×Dic214—22no—
28C2×Dic214Q811yescharacteristic, complemented
29C2×D428Q811yescharacteristic, complemented
30C2×C22⋊D107—21no—
31C22×Dic107—21no—
32C2×C4×D107—21no—
33#13133802—21no—
34#13133802—21no—
35C2×C107⋊C8—21no—
36C4⋊Dic107—22no—
37C4⋊Dic107—21no—
38Dic107⋊C4—22no—
39Dic107⋊C4—22no—
40C22⋊Dic107D412yes—
41C4×Dic107—21no—
42C4×Dic107—21no—
43C4×Dic107D411yescharacteristic
44C4×Dic107D411yescharacteristic
45C22×C4×C107C2311yescharacteristic
46M16×C107—21no—
47M16×C107—21no—
48C2×C8×C107—21no—
49C4⋊C4×C107—21no—
50C4⋊C4×C107—21no—
51C22⋊C4×C107—21no—
52C22⋊C4×C107—21no—
53C42×C107—21no—
54C42×C107D412yes—
55C23×C107C2×D411yescharacteristic
56C22×D107—21no—
57C2×C4×C107—22no—
58C2×C4×C107—41no—
59C2×C4×C107C2×D411yescharacteristic
60C2×C4×C107C2×D411yescharacteristic
61C2×C4×C107C2×Q811yescharacteristic
62C2×C4×C107#4111yescharacteristic
63C2×C4×C107#4111yescharacteristic
64C2×C4×C107#4111yescharacteristic
65C22⋊D107—41no—
66C22⋊D107—41no—
67C2×Dic107—21no—
68C2×Dic107—21no—
69C2×Dic107—22no—
70C2×Dic107—21no—
71C2×Dic107—42no—
72D428—21no—
73D428—21no—
74C4×D107—41no—
75C4×D107—41no—
76Dic214—21no—
77Dic214—21no—
78Dic214—44no—
79C8×C107—41no—
80C107⋊C8—41no—
81C22×C107—41no—
82C22×C107#12011yescharacteristic
83C22×C107C22⋊Q811yescharacteristic
84C22×C107#12411yescharacteristic
85C2×D107—41no—
86C2×D107—81no—
87C4×C107—42no—
88C4×C107—81no—
89C4×C107C22⋊Q811yescharacteristic
90C4×C107C22⋊Q811yescharacteristic
91C4×C107#12411yescharacteristic
92C4×C107#12411yescharacteristic
93Dic107—22no—
94Dic107—42no—
95Dic107—41no—
96Dic107—41no—
97C2×C107—21no—
98C2×C107—21no—
99C2×C107—21no—
100C2×C107#39311yescharacteristic
101D107—81no—
102#2031—1071nomaximal, Sylow
103C107#203111yescharacteristic, complemented, Sylow
104#533—1071no—
105#421—1071no—
106C2×#104—1071no—
107#410—1071no—
108#344—1071no—
109#339—1071no—
110H(3,ℤ/4)D10711yescharacteristic, complemented
111C2×#41—1071no—
112C2×M16—1071no—
113C2×M16C2×D10711yescharacteristic
114C4⋊Q8—2141no—
115#125—2141no—
116C22⋊Q8—2142no—
117C4×Q8—2142no—
118#117—1071no—
119#117C2×D10711yescharacteristic
120#117C2×D10711yescharacteristic
121C2×C42—1071no—
122#104—2141no—
123#104—2141no—
124#104—2142no—
125#99—2142no—
126#41—2141no—
127#41—2141no—
128#41—2141no—
129#41—2141no—
130C2×Q8—1071no—
131C2×Q8—2142no—
132C2×D4—1071no—
133C2×D4—2141no—
134C22×C4—2141no—
135C22×C4—2141no—
136C22×C4C22×D10711yescharacteristic
137M16—21no—
138M16—21no—
139M16—2141no—
140M16—2141no—
141C2×C8—21no—
142C2×C8—2141no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—2142no—
146C4⋊C4—2142no—
147C4⋊C4—2142no—
148C4⋊C4—2141no—
149C22⋊C4—21no—
150C22⋊C4—21no—
151C22⋊C4—1072no—
152C42—21no—
153C42—1071no—
154C42—1071no—
155C42—2141no—
156C42—2141no—
157C42D42812yes—
158C23—2141no—
159C23D4×D10711yescharacteristic
160Q8—4284no—
161Q8—2141no—
162Q8—2141no—
163D4—4281no—
164D4—4281no—
165D4—2141no—
166D4—2141no—
167C2×C4—22no—
168C2×C4—41no—
169C2×C4—4282no—
170C2×C4—4281no—
171C2×C4—4281no—
172C2×C4—2141no—
173C2×C4—2142no—
174C2×C4—2141no—
175C2×C4—2141no—
176C2×C4D4×D10711yescharacteristic
177C2×C4C2×D42811yescharacteristic
178C2×C4Q8×D10711yescharacteristic
179C2×C4#1313381711yescharacteristic
180C2×C4#1313381811yescharacteristic
181C2×C4#1313381811yescharacteristic
182C8—41no—
183C8—4281no—
184C22—41no—
185C22—8561no—
186C22—4281no—
187C22#1681207911yescharacteristic
188C22#1681208711yescharacteristic
189C22#1681209511yescharacteristic
190C4—42no—
191C4—81no—
192C4—4281no—
193C4—4282no—
194C4—4281no—
195C4—2142no—
196C4#1681208711yescharacteristic
197C4#1681208911yescharacteristic
198C4#1681209511yescharacteristic
199C4#1681209711yescharacteristic
200C2—21no—
201C2—21no—
202C2—21no—
203C2—8561no—
204C2#2029254011yescharacteristic
subgroupG/H
centerC4#16812097
commutator, cosocleC22×C4×C107C23
FrattiniC22×C4C22×D107
FittingH(3,ℤ/4)×C107C2
socleC2×C107#393
prime radicalC2×#13133818C22
hypercenterH(3,ℤ/4)D107
hypocenterC107#2031
LCSG ▷ C22×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C4 ◁ C22×C4 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
1. #20293180C2semidirect
5. #20292399C2semidirect
6. #20292386C2semidirect
7. H(3,ℤ/4)×C107C2semidirect
28. C2×Dic214Q8semidirect
29. C2×D428Q8semidirect
103. C107#2031semidirect
110. H(3,ℤ/4)D107semidirect

Maximal subgroups

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

subgroupindex
#202931802
#202926452
C2×#168120352
#202926002
#202923992
#202923862
H(3,ℤ/4)×C1072
#2031107