Finite Group Databasebeta

← #28335565

Subgroups — #28335565

Order 13696.

250 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 57 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#20293292C211yesmaximal, characteristic, complemented
2#20292975C211yesmaximal, characteristic, complemented
3#20292828C211yesmaximal, characteristic, complemented
4#20292823C211yesmaximal, characteristic
5#20292357C211yesmaximal, characteristic, complemented
6#20292354C211yesmaximal, characteristic, complemented
7#332×C107C211yesmaximal, characteristic, complemented
8C2×Q8×D107—21no—
9C2×#13133807—21no—
10C2×D856—21no—
11#16812108—21no—
12#16812106C2211yescharacteristic
13#16812087—22no—
14#16812085—21no—
15C4×Dic214C2211yescharacteristic
16C4×D428C2211yescharacteristic
17#16812071—21no—
18#16812031—21no—
19#16812031—21no—
20#16812029—22no—
21C4×C107⋊C8C2211yescharacteristic
22C4⋊Q8×C107C2211yescharacteristic
23C4⋊C8×C107C2211yescharacteristic
24C4⋊C8×C107C2211yescharacteristic
25C2×Dic214—22no—
26C2×Dic214D411yescharacteristic
27Q8×D107—42no—
28Q8×D107—42no—
29C2×D428—21no—
30C2×D428—21no—
31C2×D428—21no—
32C2×D428D411yescharacteristic
33C2×C4×D107—22no—
34C2×C4×D107—21no—
35#13133807—42no—
36D856—42no—
37C2×C107⋊C8—21no—
38C4⋊Dic107D411yescharacteristic
39C4⋊Dic107D411yescharacteristic
40Dic107⋊C4—22no—
41Dic107⋊C4—21no—
42(C2×D107)⋊C4—22no—
43(C2×D107)⋊C4—21no—
44C4×Dic107—21no—
45C2×Q8×C107—21no—
46C2×C8×C107—21no—
47C2×C8×C107—21no—
48C4⋊C4×C107—21no—
49C4⋊C4×C107D412yes—
50C42×C107C2311yescharacteristic
51C22×D107—21no—
52C22×D107—41no—
53Q8×C107—41no—
54Q8×C107—41no—
55C2×C4×C107—22no—
56C2×C4×C107C2×D411yescharacteristic
57C2×C4×C107C2×D411yescharacteristic
58C2×C4×C107C2×D411yescharacteristic
59C2×Dic107—21no—
60C2×Dic107—21no—
61C2×Dic107—21no—
62D428—21no—
63D428—42no—
64D428—41no—
65D428—41no—
66D428—41no—
67D428—41no—
68D428SD1612yescomplemented
69C4×D107—44no—
70C4×D107—41no—
71C4×D107—41no—
72Dic214—21no—
73Dic214—44no—
74Dic214D812yescomplemented
75C8×C107—41no—
76C8×C107—41no—
77C107⋊C8—41no—
78C22×C107#12011yescharacteristic
79C2×D107—22no—
80C2×D107—41no—
81C2×D107—41no—
82C2×D107—81no—
83C2×D107—81no—
84C2×D107—81no—
85C4×C107—21no—
86C4×C107—42no—
87C4×C107C2×D811yescharacteristic
88C4×C107C2×SD1611yescharacteristic
89C4×C107AGL(1,ℤ/8)11yescharacteristic
90C4×C107#13711yescharacteristic
91Dic107—22no—
92Dic107—41no—
93Dic107—41no—
94C2×C107#44711yescharacteristic
95C2×C107#44811yescharacteristic
96C2×C107#45411yescharacteristic
97D107—42no—
98D107—161no—
99#1627—1071nomaximal, Sylow
100C107#162711yescharacteristic, complemented, Sylow
101D4×Q8—1071no—
102#486—1071no—
103#460—1071no—
104#459—1071no—
105#332D10711yescharacteristic, complemented
106Q8⋊C8—1071no—
107D4⋊C8—1071no—
108C22×Q8—2141no—
109C2×SD16—2141no—
110C2×D8—2141no—
111C4⋊Q8—2141no—
112C4⋊Q8C2×D10711yescharacteristic
113#127—1071no—
114C22⋊Q8—2141no—
115C22⋊Q8—2142no—
116C4×Q8—1071no—
117C4×D4—1071no—
118C4×D4—2141no—
119C4⋊C8C2×D10711yescharacteristic
120C4⋊C8C2×D10711yescharacteristic
121#102—2141no—
122#102—2141no—
123#102—2142no—
124C4×C8—1071no—
125C2×Q8—21no—
126C2×Q8—1071no—
127C2×Q8—4282no—
128C2×Q8—4282no—
129C2×Q8—2142no—
130C2×D4—1071no—
131C2×D4—2141no—
132C2×D4—2141no—
133C2×D4—2141no—
134C22×C4—2142no—
135C22×C4—2141no—
136SD16—4282no—
137D8—4282no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—2141no—
141C4⋊C4—21no—
142C4⋊C4—1071no—
143C4⋊C4—1071no—
144C4⋊C4—2142no—
145C4⋊C4—2141no—
146C4⋊C4D42812yes—
147C22⋊C4—2142no—
148C22⋊C4—2141no—
149C42—2141no—
150C42C22×D10711yescharacteristic
151C23—4281no—
152C23—2141no—
153Q8—41no—
154Q8—41no—
155Q8—1072no—
156Q8—4284no—
157Q8—2141no—
158D4—1072no—
159D4—4282no—
160D4—4281no—
161D4—4281no—
162D4—4281no—
163D4—4281no—
164D4—2141no—
165C2×C4—22no—
166C2×C4—4284no—
167C2×C4—4281no—
168C2×C4—4281no—
169C2×C4—2141no—
170C2×C4—2141no—
171C2×C4—2141no—
172C2×C4D4×D10711yescharacteristic
173C2×C4D4×D10711yescharacteristic
174C2×C4C2×D42811yescharacteristic
175C8—41no—
176C8—41no—
177C8—4281no—
178C22—8561no—
179C22—8561no—
180C22—8561no—
181C22—4281no—
182C22—4281no—
183C22—2142no—
184C22#1681207911yescharacteristic
185C4—21no—
186C4—42no—
187C4—4281no—
188C4—4281no—
189C4—2142no—
190C4D8×D10711yescharacteristic
191C4SD16×D10711yescharacteristic
192C4#1681213611yescharacteristic
193C4#1681214111yescharacteristic
194C2—4282no—
195C2—17121no—
196C2#2029276211yescharacteristic
197C2#2029276711yescharacteristic
198C2#2029280211yescharacteristic
subgroupG/H
centerC22#16812079
commutator, cosocleC42×C107C23
FrattiniC42C22×D107
Fitting#332×C107C2
socleC22×C107#120
prime radical#20292823C2
hypercenter#332D107
hypocenterC107#1627
LCSG ▷ C42×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
1. #20293292C2semidirect
2. #20292975C2semidirect
3. #20292828C2semidirect
5. #20292357C2semidirect
6. #20292354C2semidirect
7. #332×C107C2semidirect
68. D428SD16semidirect
74. Dic214D8semidirect
100. C107#1627semidirect
105. #332D107semidirect

Maximal subgroups

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

subgroupindex
#202932922
#202929752
#202928282
#202928232
#202923572
#202923542
#332×C1072
#1627107