Finite Group Databasebeta

← #28335447

Subgroups — #28335447

Order 13696.

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

normal subgroups only

This group has 280 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#20292938C212yesmaximal, complemented
2#20292552C211yesmaximal, characteristic, complemented
3#20292361C212yesmaximal, complemented
4#20292351C211yesmaximal, characteristic, complemented
5#534×C107C211yesmaximal, characteristic
6C2×C4⋊Dic107C2211yescharacteristic, complemented
7C2×C22⋊Dic107—21no—
8#16812042—22no—
9#16812030—22no—
10C22⋊(C107⋊C8)C2212yescomplemented
11C107⋊#95—21no—
12C107⋊#95C2211yescharacteristic, complemented
13C22×D4×C107—21no—
14#123×C107—22no—
15#121×C107—21no—
16#121×C107C2212yes—
17#120×C107—22no—
18C2×C22⋊C4×C107C2211yescharacteristic
19C22×Dic107—21no—
20C22×Dic107—21no—
21C2×C107⋊C8—22no—
22C4⋊Dic107—22no—
23C22⋊Dic107—42no—
24C24×C107—21no—
25C24×C107D411yescharacteristic
26C2×D4×C107—22no—
27C2×D4×C107—22no—
28C2×D4×C107—21no—
29C2×D4×C107—42no—
30C2×D4×C107—42no—
31C2×D4×C107D412yes—
32C22×C4×C107—21no—
33C22×C4×C107D411yescharacteristic
34C22×C4×C107C2311yescharacteristic
35C4⋊C4×C107—21no—
36C4⋊C4×C107D412yes—
37C22⋊C4×C107—22no—
38C22⋊C4×C107—22no—
39C22⋊C4×C107—22no—
40C23×C107—21no—
41C23×C107—21no—
42C23×C107—22no—
43C23×C107—41no—
44C23×C107—41no—
45C23×C107—42no—
46C23×C107—81no—
47C23×C107—81no—
48C23×C107D812yes—
49C23×C107C2×D411yescharacteristic
50D4×C107—42no—
51D4×C107—44no—
52D4×C107—42no—
53D4×C107—42no—
54D4×C107—81no—
55C2×C4×C107—21no—
56C2×C4×C107—22no—
57C2×C4×C107—41no—
58C2×C4×C107—42no—
59C2×C4×C107—41no—
60C2×C4×C107C2×D412yes—
61C2×Dic107—41no—
62C2×Dic107—41no—
63C2×Dic107—41no—
64C2×Dic107—41no—
65C2×Dic107—41no—
66C2×Dic107—41no—
67C107⋊C8—42no—
68C22×C107—21no—
69C22×C107—21no—
70C22×C107—22no—
71C22×C107—42no—
72C22×C107—41no—
73C22×C107—41no—
74C22×C107—42no—
75C22×C107—42no—
76C22×C107—42no—
77C22×C107—81no—
78C22×C107—84no—
79C22×C107#12011yescharacteristic
80C22×C107C2×D811yescharacteristic
81C22×C107AGL(1,ℤ/8)11yescharacteristic
82C4×C107—22no—
83C4×C107—42no—
84C4×C107—41no—
85Dic107—81no—
86Dic107—81no—
87C2×C107—21no—
88C2×C107—21no—
89C2×C107—42no—
90C2×C107—82no—
91C2×C107#44711yescharacteristic
92C2×C107#45511yescharacteristic
93C2×C107#45811yescharacteristic
94#1607—1071nomaximal, Sylow
95C107#160711yescharacteristic, complemented, Sylow
96#534D10711yescharacteristic
97#480—1072no—
98#397—1071no—
99#327—1072no—
100#323—1071no—
101C22×D4—21no—
102#123—22no—
103#121—21no—
104#121C2×D10712yes—
105#120—22no—
106C2×C4⋊C4—1071no—
107C2×C22⋊C4—2141no—
108C2×C22⋊C4C2×D10711yescharacteristic
109#107—2142no—
110#102—2142no—
111C22⋊C8—1072no—
112#95—1071no—
113#95—2141no—
114C24—21no—
115C24C22⋊D10711yescharacteristic
116C2×D4—22no—
117C2×D4—22no—
118C2×D4—21no—
119C2×D4—42no—
120C2×D4—42no—
121C2×D4C22⋊D10712yes—
122C22×C4—21no—
123C22×C4—2141no—
124C22×C4—2141no—
125C22×C4C22⋊D10711yescharacteristic
126C22×C4C22×D10711yescharacteristic
127C2×C8—2142no—
128C4⋊C4—21no—
129C4⋊C4—2142no—
130C4⋊C4C22⋊D10712yes—
131C22⋊C4—22no—
132C22⋊C4—22no—
133C22⋊C4—22no—
134C22⋊C4—4282no—
135C23—21no—
136C23—21no—
137C23—22no—
138C23—41no—
139C23—41no—
140C23—42no—
141C23—81no—
142C23—81no—
143C23#1313380312yes—
144C23C2×C22⋊D10711yescharacteristic
145D4—42no—
146D4—44no—
147D4—42no—
148D4—42no—
149D4—81no—
150C2×C4—21no—
151C2×C4—22no—
152C2×C4—41no—
153C2×C4—42no—
154C2×C4—41no—
155C2×C4—4281no—
156C2×C4—4281no—
157C2×C4—4281no—
158C2×C4—4281no—
159C2×C4—4281no—
160C2×C4—4281no—
161C2×C4C2×C22⋊D10712yes—
162C8—4282no—
163C22—21no—
164C22—21no—
165C22—22no—
166C22—42no—
167C22—41no—
168C22—41no—
169C22—42no—
170C22—42no—
171C22—42no—
172C22—81no—
173C22—84no—
174C22#1681207811yescharacteristic
175C22C2×#1313380311yescharacteristic
176C22#1681213511yescharacteristic
177C4—22no—
178C4—42no—
179C4—41no—
180C4—8561no—
181C4—8561no—
182C2—21no—
183C2—21no—
184C2—42no—
185C2—82no—
186C2#2029276111yescharacteristic
187C2#2029280511yescharacteristic
188C2#2029281711yescharacteristic
subgroupG/H
centerC22#16812078
commutator, cosocleC22×C4×C107C23
FrattiniC22×C4C22×D107
Fitting, prime radical#534×C107C2
socleC22×C107#120
hypercenter#534D107
hypocenterC107#1607
LCSG ▷ C22×C4×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ #534

Complements

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

NH ≅ G/Ntype
1. #20292938C2semidirect
2. #20292552C2semidirect
3. #20292361C2semidirect
4. #20292351C2semidirect
6. C2×C4⋊Dic107C22semidirect
10. C22⋊(C107⋊C8)C22semidirect
12. C107⋊#95C22semidirect
95. C107#1607semidirect

Maximal subgroups

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

subgroupindex
#202929382
#202925522
#202923612
#202923512
#534×C1072
#1607107