Finite Group Databasebeta

← #28335690

Subgroups — #28335690

Order 13696.

212 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 53 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#20293343C211yesmaximal, characteristic
2#20292977C211yesmaximal, characteristic, complemented
3#20292908C211yesmaximal, characteristic, complemented
4#20292833C211yesmaximal, characteristic, complemented
5#20292354C211yesmaximal, characteristic, complemented
6#20292354C211yesmaximal, characteristic, complemented
7#333×C107C211yesmaximal, characteristic, complemented
8C2×#13133807—21no—
9#16812109C2211yescharacteristic
10#16812098—22no—
11#16812084—21no—
12#16812084—21no—
13C4×D428C2211yescharacteristic
14C4×D428C2211yescharacteristic
15#16812067—21no—
16#16812067—21no—
17#16812043—21no—
18#16812034—21no—
19#16812033—22no—
20#16812031—21no—
21C4×C107⋊C8C2211yescharacteristic
22C4⋊Q8×C107C2211yescharacteristic
23C4⋊C8×C107C2211yescharacteristic
24C4⋊C8×C107C2211yescharacteristic
25C2×Dic214—21no—
26C2×D428—22no—
27C2×D428D411yescharacteristic
28C2×D428D411yescharacteristic
29C2×C4×D107—21no—
30C2×C4×D107—21no—
31#13133807—42no—
32C2×C107⋊C8—21no—
33C4⋊Dic107—21no—
34C4⋊Dic107—21no—
35C4⋊Dic107D411yescharacteristic
36C4⋊Dic107D411yescharacteristic
37(C2×D107)⋊C4—22no—
38(C2×D107)⋊C4—22no—
39(C2×D107)⋊C4—21no—
40(C2×D107)⋊C4—21no—
41C4×Dic107—22no—
42C2×Q8×C107D412yes—
43C2×C8×C107—21no—
44C2×C8×C107—21no—
45C4⋊C4×C107—21no—
46C4⋊C4×C107—21no—
47C42×C107C2311yescharacteristic
48C22×D107—21no—
49C22×D107—21no—
50Q8×C107—42no—
51C2×C4×C107—22no—
52C2×C4×C107C2×D411yescharacteristic
53C2×C4×C107C2×D411yescharacteristic
54C2×C4×C107C2×D411yescharacteristic
55C2×Dic107—21no—
56C2×Dic107—21no—
57C2×Dic107—41no—
58D428—21no—
59D428—21no—
60D428—21no—
61D428—21no—
62D428—82no—
63C4×D107—41no—
64C4×D107—41no—
65C4×D107—41no—
66C4×D107—41no—
67Dic214—41no—
68Dic214—41no—
69C8×C107—41no—
70C8×C107—41no—
71C107⋊C8—41no—
72C22×C107#12011yescharacteristic
73C2×D107—41no—
74C2×D107—41no—
75C2×D107—41no—
76C2×D107—41no—
77C2×D107—41no—
78C2×D107—41no—
79C4×C107—21no—
80C4×C107—42no—
81C4×C107#13511yescharacteristic
82C4×C107#13511yescharacteristic
83C4×C107AGL(1,ℤ/8)11yescharacteristic
84C4×C107#13711yescharacteristic
85Dic107—41no—
86Dic107—41no—
87Dic107—81no—
88C2×C107#44911yescharacteristic
89C2×C107#45211yescharacteristic
90C2×C107#45511yescharacteristic
91D107—81no—
92D107—81no—
93#1646—1071nomaximal, Sylow
94C107#164611yescharacteristic, complemented, Sylow
95#555—1071no—
96#487—1071no—
97#474—1071no—
98#461—1071no—
99#333D10711yescharacteristic, complemented
100D4⋊C8—1071no—
101D4⋊C8—1071no—
102C2×SD16—2141no—
103C4⋊Q8—1071no—
104C4⋊Q8C2×D10711yescharacteristic
105#124—2142no—
106#121—2141no—
107#121—2141no—
108C4×D4—1071no—
109C4×D4—1071no—
110#117—2141no—
111#117—2141no—
112#107—2141no—
113C4⋊C8C2×D10711yescharacteristic
114C4⋊C8C2×D10711yescharacteristic
115#103—2141no—
116#103—2142no—
117#102—2141no—
118C4×C8—1071no—
119C2×Q8—2141no—
120C2×Q8D42812yes—
121C2×D4—1071no—
122C2×D4—1071no—
123C2×D4—2142no—
124C22×C4—2141no—
125C22×C4—2141no—
126SD16—4282no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—2141no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—1071no—
133C4⋊C4—1071no—
134C4⋊C4—2141no—
135C4⋊C4—2141no—
136C22⋊C4—2142no—
137C22⋊C4—2142no—
138C22⋊C4—2141no—
139C22⋊C4—2141no—
140C42—2142no—
141C42C22×D10711yescharacteristic
142C23—2141no—
143C23—2141no—
144Q8—42no—
145Q8—4281no—
146Q8—4281no—
147D4—8562no—
148D4—2141no—
149D4—2141no—
150D4—2141no—
151D4—2141no—
152C2×C4—22no—
153C2×C4—4281no—
154C2×C4—4281no—
155C2×C4—4281no—
156C2×C4—4281no—
157C2×C4—4281no—
158C2×C4—2141no—
159C2×C4—2141no—
160C2×C4D4×D10711yescharacteristic
161C2×C4D4×D10711yescharacteristic
162C2×C4C2×D42811yescharacteristic
163C8—41no—
164C8—41no—
165C8—4281no—
166C22—4281no—
167C22—4281no—
168C22—4281no—
169C22—4281no—
170C22—4281no—
171C22—4281no—
172C22#1681207911yescharacteristic
173C4—21no—
174C4—42no—
175C4—8561no—
176C4—4281no—
177C4—4281no—
178C4#1681213011yescharacteristic
179C4#1681213211yescharacteristic
180C4#1681213611yescharacteristic
181C4#1681214111yescharacteristic
182C2—8561no—
183C2—8561no—
184C2#2029277511yescharacteristic
185C2#2029279211yescharacteristic
186C2#2029280711yescharacteristic
subgroupG/H
centerC22#16812079
commutator, cosocleC42×C107C23
FrattiniC42C22×D107
Fitting#333×C107C2
socleC22×C107#120
prime radical#20293343C2
hypercenter#333D107
hypocenterC107#1646
LCSG ▷ C42×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #20292977C2semidirect
3. #20292908C2semidirect
4. #20292833C2semidirect
5. #20292354C2semidirect
6. #20292354C2semidirect
7. #333×C107C2semidirect
94. C107#1646semidirect
99. #333D107semidirect

Maximal subgroups

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

subgroupindex
#202933432
#202929772
#202929082
#202928332
#202923542
#333×C1072
#1646107