Finite Group Databasebeta

← #28335461

Subgroups — #28335461

Order 13696.

216 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 49 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#20293226C211yesmaximal, characteristic
2#20292955C211yesmaximal, characteristic, complemented
3#20292941C211yesmaximal, characteristic
4#20292559C211yesmaximal, characteristic, complemented
5#20292360C211yesmaximal, characteristic
6#20292352C211yesmaximal, characteristic, complemented
7#328×C107C211yesmaximal, characteristic, complemented
8#16812104—21no—
9#16812100—21no—
10#16812094—21no—
11#16812093—21no—
12#16812085—21no—
13#16812083C2211yescharacteristic
14(C22⋊D107)⋊C4—21no—
15C2×C4⋊Dic107—21no—
16C2×C4⋊Dic107C2211yescharacteristic
17C2×Dic107⋊C4C2211yescharacteristic
18#16812043—21no—
19#16812040—21no—
20#16812033—21no—
21#16812031—21no—
22C22⋊(C107⋊C8)C2211yescharacteristic
23C107⋊#95—21no—
24C22⋊Q8×C107C2211yescharacteristic
25C22⋊C8×C107C2211yescharacteristic
26#95×C107C2211yescharacteristic
27C2×D428D411yescharacteristic
28C2×C22⋊D107—21no—
29C22×Dic107—21no—
30C22×Dic107D411yescharacteristic
31C22×Dic107D411yescharacteristic
32C2×C4×D107—21no—
33C2×C107⋊C8—21no—
34C4⋊Dic107—21no—
35C4⋊Dic107—21no—
36C4⋊Dic107—21no—
37C4⋊Dic107—21no—
38C4⋊Dic107—42no—
39C4⋊Dic107D411yescharacteristic
40Dic107⋊C4—21no—
41Dic107⋊C4—21no—
42Dic107⋊C4—21no—
43(C2×D107)⋊C4—21no—
44(C2×D107)⋊C4—21no—
45(C2×D107)⋊C4—21no—
46(C2×D107)⋊C4—21no—
47C4×Dic107—21no—
48C2×Q8×C107D411yescharacteristic
49C22×C4×C107—21no—
50C22×C4×C107C2311yescharacteristic
51C2×C8×C107—21no—
52C4⋊C4×C107—21no—
53C4⋊C4×C107D411yescharacteristic
54C22⋊C4×C107—21no—
55C23×C107C2×D411yescharacteristic
56C22×D107—21no—
57Q8×C107—41no—
58C2×C4×C107—22no—
59C2×C4×C107—21no—
60C2×C4×C107—21no—
61C2×C4×C107—41no—
62C2×C4×C107—41no—
63C2×C4×C107—41no—
64C2×C4×C107C2×D411yescharacteristic
65C2×C4×C107C2×D411yescharacteristic
66C22⋊D107—41no—
67C22⋊D107—41no—
68C2×Dic107—21no—
69C2×Dic107—21no—
70C2×Dic107—21no—
71C2×Dic107—21no—
72C2×Dic107—21no—
73C2×Dic107—41no—
74C2×Dic107—41no—
75C2×Dic107—41no—
76C2×Dic107—41no—
77D428—41no—
78C4×D107—81no—
79C8×C107—41no—
80C107⋊C8—41no—
81C22×C107—21no—
82C22×C107—21no—
83C22×C107#12011yescharacteristic
84C22×C107#13511yescharacteristic
85C22×C107AGL(1,ℤ/8)11yescharacteristic
86C2×D107—41no—
87C2×D107—41no—
88C2×D107—41no—
89C4×C107—21no—
90C4×C107—21no—
91C4×C107—42no—
92C4×C107—41no—
93C4×C107—41no—
94Dic107—41no—
95Dic107—41no—
96Dic107—41no—
97Dic107—81no—
98C2×C107—21no—
99C2×C107—21no—
100C2×C107#44911yescharacteristic
101C2×C107#45611yescharacteristic
102C2×C107#45811yescharacteristic
103D107—81no—
104#1609—1071nomaximal, Sylow
105C107#160911yescharacteristic, complemented, Sylow
106#539—1071no—
107#483—1071no—
108#480—1071no—
109#398—1071no—
110#328D10711yescharacteristic, complemented
111#327—1071no—
112#324—1071no—
113#126—2141no—
114#125—2141no—
115#123—2141no—
116#123—2141no—
117C22⋊Q8—2141no—
118C22⋊Q8C2×D10711yescharacteristic
119#121—1071no—
120C4×D4—2141no—
121C2×C4⋊C4—1071no—
122C2×C4⋊C4—1071no—
123C2×C4⋊C4—2141no—
124#107—2141no—
125#106—2141no—
126#103—2141no—
127#102—2141no—
128C22⋊C8—1071no—
129C22⋊C8C2×D10711yescharacteristic
130#95—2141no—
131#95C2×D10711yescharacteristic
132C2×Q8D42811yescharacteristic
133C2×D4—1071no—
134C2×D4—2141no—
135C22×C4—21no—
136C22×C4—1071no—
137C22×C4—1071no—
138C22×C4—2141no—
139C22×C4—2141no—
140C22×C4C22×D10711yescharacteristic
141C2×C8—21no—
142C2×C8—2141no—
143C4⋊C4—21no—
144C4⋊C4—1071no—
145C4⋊C4—4282no—
146C4⋊C4—2141no—
147C4⋊C4—2141no—
148C4⋊C4—2141no—
149C4⋊C4—2141no—
150C4⋊C4—2141no—
151C4⋊C4—2141no—
152C4⋊C4—2141no—
153C4⋊C4D42811yescharacteristic
154C22⋊C4—21no—
155C22⋊C4—2141no—
156C22⋊C4—2141no—
157C22⋊C4—2141no—
158C22⋊C4—2141no—
159C42—2141no—
160C23—2141no—
161C23D4×D10711yescharacteristic
162Q8—41no—
163D4—4281no—
164D4—4281no—
165D4—4281no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—8561no—
173C2×C4—4281no—
174C2×C4—4281no—
175C2×C4—4281no—
176C2×C4—4281no—
177C2×C4—2141no—
178C2×C4—2141no—
179C2×C4—2141no—
180C2×C4—2141no—
181C2×C4—2141no—
182C2×C4D4×D10711yescharacteristic
183C2×C4C2×D42811yescharacteristic
184C8—41no—
185C8—4281no—
186C22—21no—
187C22—21no—
188C22—4281no—
189C22—4281no—
190C22—4281no—
191C22#1681207911yescharacteristic
192C22#1681213211yescharacteristic
193C22#1681213611yescharacteristic
194C4—21no—
195C4—21no—
196C4—42no—
197C4—41no—
198C4—41no—
199C4—8561no—
200C4—4281no—
201C4—4281no—
202C4—4281no—
203C2—21no—
204C2—21no—
205C2—8561no—
206C2#2029277511yescharacteristic
207C2#2029281111yescharacteristic
208C2#2029281811yescharacteristic
subgroupG/H
centerC22#16812079
commutator, cosocleC22×C4×C107C23
FrattiniC22×C4C22×D107
Fitting#328×C107C2
socleC22×C107#120
prime radical#16812083C22
hypercenter#328D107
hypocenterC107#1609
LCSG ▷ C22×C4×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #20292955C2semidirect
4. #20292559C2semidirect
6. #20292352C2semidirect
7. #328×C107C2semidirect
105. C107#1609semidirect
110. #328D107semidirect

Maximal subgroups

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

subgroupindex
#202932262
#202929552
#202929412
#202925592
#202923602
#202923522
#328×C1072
#1609107