Finite Group Databasebeta

← #28349068

Subgroups — #28349068

Order 13696.

360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 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#20293327C212yesmaximal, complemented
2#20293029C211yesmaximal, characteristic, complemented
3#20292949C212yesmaximal, complemented
4#20292939C212yesmaximal, complemented
5#20292927C212yesmaximal, complemented
6#20292877C212yesmaximal, complemented
7#20292706C211yesmaximal, characteristic, complemented
8#20292668C212yesmaximal, complemented
9C4×D8×C107C211yesmaximal, characteristic, complemented
10C2×#13133801C2212yes—
11#16812102—22no—
12#16812101C2212yes—
13#16812092—22no—
14#16812082—22no—
15#16812080C2212yes—
16#16812080C2212yes—
17C4×D428C2211yescharacteristic
18C4×C22⋊D107—22no—
19#16812067C2212yes—
20C4⋊C4×D107C2212yes—
21#16812043C2211yescharacteristic
22#16812043C2211yescharacteristic
23#16812042C2212yes—
24#16812041C2212yes—
25#16812040C2212yes—
26C4⋊(C107⋊C8)C2211yescharacteristic
27#16812030C2212yes—
28#16812030C2212yes—
29(C2×D107)⋊C8C2212yes—
30C2×D8×C107C2211yescharacteristic
31C4×D4×C107C2212yes—
32#107×C107C2211yescharacteristic
33#102×C107C2212yes—
34C4×C8×C107C2211yescharacteristic
35C2×D428D411yescharacteristic
36C2×C22⋊D107—22no—
37C2×C22⋊D107—22no—
38C2×C4×D107—22no—
39C2×C4×D107C2312yes—
40#13133801—24no—
41C2×C107⋊C8C2312yes—
42C4⋊Dic107D411yescharacteristic
43C4⋊Dic107C2312yes—
44C4⋊Dic107C2312yes—
45Dic107⋊C4—22no—
46Dic107⋊C4—22no—
47Dic107⋊C4—22no—
48C22⋊Dic107—22no—
49C22⋊Dic107—22no—
50(C2×D107)⋊C4—22no—
51(C2×D107)⋊C4D412yes—
52C4×Dic107—22no—
53C2×D4×C107C2312yes—
54C22×C4×C107—22no—
55D8×C107—22no—
56C2×C8×C107C2311yescharacteristic
57C2×C8×C107C2311yescharacteristic
58C4⋊C4×C107C2312yes—
59C22⋊C4×C107—22no—
60C42×C107C2311yescharacteristic
61C23×C107—22no—
62C22×D107C2×D412yes—
63D4×C107—22no—
64D4×C107—22no—
65C2×C4×C107—22no—
66C2×C4×C107—82no—
67C2×C4×C107C2×D411yescharacteristic
68C2×C4×C107C2×D411yescharacteristic
69C2×C4×C107C2411yescharacteristic
70C22⋊D107—44no—
71C22⋊D107—82no—
72C2×Dic107—22no—
73C2×Dic107—22no—
74C2×Dic107C2×D412yes—
75D428—41no—
76C4×D107—22no—
77C4×D107—22no—
78C4×D107—82no—
79C8×C107—21no—
80C8×C107#4112yes—
81C107⋊C8—22no—
82C22×C107—42no—
83C22×C107—42no—
84C22×C107—42no—
85C22×C107C22×D411yescharacteristic
86C2×D107—22no—
87C2×D107—22no—
88C2×D107—22no—
89C4×C107—21no—
90C4×C107—21no—
91C4×C107—42no—
92C4×C107C2×#4111yescharacteristic
93C4×C1072−1+411yescharacteristic
94Dic107—22no—
95Dic107—42no—
96Dic107—42no—
97C2×C107—82no—
98C2×C107#54711yescharacteristic
99C2×C107#57511yescharacteristic
100C2×C107#57611yescharacteristic
101D107—42no—
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×D8D10711yescharacteristic, complemented
111#436—1071no—
112#428—1072no—
113C2×D8C2×D10711yescharacteristic
114C2×M16—1072no—
115#126—2142no—
116#125—1072no—
117#123—2142no—
118#121—1072no—
119#121—1072no—
120#121—2142no—
121C4×D4—1071no—
122C4×D4—2142no—
123C4×D4C2×D10712yes—
124#117—1072no—
125C2×C4⋊C4—1072no—
126#107—1071no—
127#107—1071no—
128#107—1072no—
129#107C2×D10711yescharacteristic
130#106—1072no—
131#106—1072no—
132C4⋊C8—1071no—
133#102—1072no—
134#102—1072no—
135#102C2×D10712yes—
136C22⋊C8—1072no—
137C4×C8C2×D10711yescharacteristic
138C2×D4—1071no—
139C2×D4—2142no—
140C2×D4—2142no—
141C2×D4C22×D10712yes—
142C22×C4—22no—
143C22×C4—1072no—
144C22×C4—2142no—
145D8—22no—
146M16—2144no—
147C2×C8—1072no—
148C2×C8C22×D10711yescharacteristic
149C2×C8C22×D10711yescharacteristic
150C4⋊C4—1071no—
151C4⋊C4—1072no—
152C4⋊C4—1072no—
153C4⋊C4—2142no—
154C4⋊C4—2142no—
155C4⋊C4—2142no—
156C4⋊C4C22×D10712yes—
157C22⋊C4—22no—
158C22⋊C4—1072no—
159C22⋊C4—2142no—
160C22⋊C4—2142no—
161C22⋊C4—2142no—
162C42—2142no—
163C42C22×D10711yescharacteristic
164C23—22no—
165C23—1072no—
166D4—22no—
167D4—22no—
168D4—8562no—
169D4—4281no—
170D4—4284no—
171C2×C4—22no—
172C2×C4—82no—
173C2×C4—8562no—
174C2×C4—1072no—
175C2×C4—2142no—
176C2×C4—2142no—
177C2×C4—2142no—
178C2×C4—2142no—
179C2×C4D4×D10711yescharacteristic
180C2×C4D4×D10711yescharacteristic
181C2×C4C23×D10711yescharacteristic
182C8—21no—
183C8—2142no—
184C8#1313381812yes—
185C22—42no—
186C22—42no—
187C22—42no—
188C22—2142no—
189C22—2142no—
190C22—2142no—
191C22C2×D4×D10711yescharacteristic
192C4—21no—
193C4—21no—
194C4—42no—
195C4—4282no—
196C4—4282no—
197C4—2142no—
198C4C2×#1313381811yescharacteristic
199C4#1681215611yescharacteristic
200C2—82no—
201C2—4282no—
202C2#2029328211yescharacteristic
203C2#2029342411yescharacteristic
204C2#2029342811yescharacteristic
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
FittingC4×D8×C107C2
socleC22×C107C22×D4
hypercenterC4×D8D107
hypocenterC107#3355
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #20293327C2semidirect
2. #20293029C2semidirect
3. #20292949C2semidirect
4. #20292939C2semidirect
5. #20292927C2semidirect
6. #20292877C2semidirect
7. #20292706C2semidirect
8. #20292668C2semidirect
9. C4×D8×C107C2semidirect
103. C107#3355semidirect
110. C4×D8D107semidirect

Maximal subgroups

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

subgroupindex
#202933272
#202930292
#202929492
#202929392
#202929272
#202928772
#202927062
#202926682
C4×D8×C1072
#3355107