Finite Group Databasebeta

← #28349066

Subgroups — #28349066

Order 13696.

360 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 121 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#20293323C212yesmaximal, complemented
2#20293029C211yesmaximal, characteristic, complemented
3#20292952C212yesmaximal, complemented
4#20292941C212yesmaximal, complemented
5#20292928C212yesmaximal, complemented
6#20292880C212yesmaximal, complemented
7C4×D856C211yesmaximal, characteristic, complemented
8#20292669C212yesmaximal, complemented
9#436×C107C211yesmaximal, characteristic, complemented
10C2×D856C2211yescharacteristic
11#16812104—22no—
12#16812101C2212yes—
13#16812091—22no—
14#16812083C2212yes—
15#16812083C2212yes—
16#16812081—22no—
17C4×D428C2212yes—
18(C22⋊D107)⋊C4—22no—
19#16812068C2212yes—
20C2×C4⋊Dic107C2212yes—
21#16812043C2211yescharacteristic
22#16812043C2212yes—
23#16812043C2211yescharacteristic
24#16812043C2211yescharacteristic
25#16812041C2212yes—
26#16812041C2212yes—
27#16812031C2212yes—
28#16812031C2212yes—
29#16812031C2212yes—
30C2×M16×C107C2212yes—
31C4×D4×C107C2211yescharacteristic
32C4⋊C8×C107C2211yescharacteristic
33C22⋊C8×C107C2212yes—
34C4×C8×C107C2211yescharacteristic
35C2×D428C2312yes—
36C2×C22⋊D107—22no—
37C2×C22⋊D107—22no—
38C22×Dic107—22no—
39C2×C4×D107—22no—
40D856—22no—
41C4⋊Dic107—22no—
42C4⋊Dic107C2312yes—
43C4⋊Dic107C2312yes—
44C4⋊Dic107C2312yes—
45Dic107⋊C4—22no—
46Dic107⋊C4—22no—
47C22⋊Dic107—22no—
48(C2×D107)⋊C4—22no—
49(C2×D107)⋊C4—22no—
50(C2×D107)⋊C4—22no—
51C4×Dic107—22no—
52C2×D4×C107D411yescharacteristic
53C22×C4×C107C2312yes—
54M16×C107—24no—
55C2×C8×C107C2312yes—
56C2×C8×C107C2311yescharacteristic
57C2×C8×C107C2311yescharacteristic
58C4⋊C4×C107D411yescharacteristic
59C22⋊C4×C107D412yes—
60C42×C107C2311yescharacteristic
61C23×C107C2×D412yes—
62C22×D107—22no—
63D4×C107—41no—
64C2×C4×C107—22no—
65C2×C4×C107—22no—
66C2×C4×C107C2×D411yescharacteristic
67C2×C4×C107C2×D411yescharacteristic
68C2×C4×C107C2×D412yes—
69C2×C4×C107C2411yescharacteristic
70C22⋊D107—44no—
71C22⋊D107—82no—
72C2×Dic107—22no—
73C2×Dic107—22no—
74C2×Dic107—22no—
75C2×Dic107—82no—
76D428—22no—
77D428—22no—
78C4×D107—82no—
79C8×C107—22no—
80C8×C107—21no—
81C8×C107#4112yes—
82C22×C107—22no—
83C22×C107—22no—
84C22×C107—22no—
85C22×C107C22×D411yescharacteristic
86C2×D107—42no—
87C2×D107—42no—
88C2×D107—42no—
89C4×C107—22no—
90C4×C107—21no—
91C4×C107—21no—
92C4×C107C2×#4111yescharacteristic
93C4×C1072−1+411yescharacteristic
94Dic107—42no—
95Dic107—42no—
96Dic107—42no—
97C2×C107—42no—
98C2×C107#54711yescharacteristic
99C2×C107#57511yescharacteristic
100C2×C107#57611yescharacteristic
101D107—82no—
102#3355—1071nomaximal, Sylow
103C107#335511yescharacteristic, complemented, Sylow
104#553—1072no—
105#499—1071no—
106#482—1072no—
107#480—1072no—
108#478—1072no—
109#469—1072no—
110C4×D8—1071no—
111#436D10711yescharacteristic, complemented
112#428—1072no—
113C2×D8—1071no—
114C2×M16C2×D10712yes—
115#126—2142no—
116#125—1072no—
117#123—2142no—
118#121—1072no—
119#121—1072no—
120#121—2142no—
121C4×D4—1072no—
122C4×D4—2142no—
123C4×D4C2×D10711yescharacteristic
124#117—1072no—
125C2×C4⋊C4—1072no—
126#107—1071no—
127#107—1072no—
128#107—1071no—
129#107—1071no—
130#106—1072no—
131#106—1072no—
132C4⋊C8C2×D10711yescharacteristic
133#102—1072no—
134#102—1072no—
135#102—1072no—
136C22⋊C8C2×D10712yes—
137C4×C8C2×D10711yescharacteristic
138C2×D4—1072no—
139C2×D4—2142no—
140C2×D4—2142no—
141C2×D4D42811yescharacteristic
142C22×C4—2142no—
143C22×C4—2142no—
144C22×C4C22×D10712yes—
145D8—2142no—
146M16—24no—
147C2×C8C22×D10711yescharacteristic
148C2×C8C22×D10712yes—
149C2×C8C22×D10711yescharacteristic
150C4⋊C4—1072no—
151C4⋊C4—1072no—
152C4⋊C4—1072no—
153C4⋊C4—2142no—
154C4⋊C4—2142no—
155C4⋊C4—2142no—
156C4⋊C4D42811yescharacteristic
157C22⋊C4—2142no—
158C22⋊C4—2142no—
159C22⋊C4—2142no—
160C22⋊C4—2142no—
161C22⋊C4D42812yes—
162C42—2142no—
163C42C22×D10711yescharacteristic
164C23—2142no—
165C23C2×D42812yes—
166D4—41no—
167D4—8562no—
168D4—4284no—
169D4—2142no—
170D4—2142no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—8562no—
174C2×C4—8562no—
175C2×C4—2142no—
176C2×C4—2142no—
177C2×C4—2142no—
178C2×C4C2×D42812yes—
179C2×C4C2×D42811yescharacteristic
180C2×C4C2×D42811yescharacteristic
181C2×C4C23×D10711yescharacteristic
182C8—22no—
183C8—21no—
184C8#1313381712yes—
185C22—22no—
186C22—22no—
187C22—22no—
188C22—4282no—
189C22—4282no—
190C22—4282no—
191C22C22×D42811yescharacteristic
192C4—21no—
193C4—21no—
194C4—22no—
195C4—4282no—
196C4—4282no—
197C4—4282no—
198C4C2×#1313381711yescharacteristic
199C4#1681215611yescharacteristic
200C2—42no—
201C2—8562no—
202C2#2029328111yescharacteristic
203C2#2029342711yescharacteristic
204C2#2029343211yescharacteristic
subgroupG/H
centerC22C22×D428
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#436×C107C2
socleC22×C107C22×D4
hypercenter#436D107
hypocenterC107#3355
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
1. #20293323C2semidirect
2. #20293029C2semidirect
3. #20292952C2semidirect
4. #20292941C2semidirect
5. #20292928C2semidirect
6. #20292880C2semidirect
7. C4×D856C2semidirect
8. #20292669C2semidirect
9. #436×C107C2semidirect
103. C107#3355semidirect
111. #436D107semidirect

Maximal subgroups

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

subgroupindex
#202933232
#202930292
#202929522
#202929412
#202929282
#202928802
C4×D8562
#202926692
#436×C1072
#3355107