Finite Group Databasebeta

← #28335460

Subgroups — #28335460

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#20293224C211yesmaximal, characteristic
2#20292958C211yesmaximal, characteristic, complemented
3#20292941C211yesmaximal, characteristic
4#20292557C211yesmaximal, characteristic, complemented
5#20292365C211yesmaximal, characteristic, complemented
6#20292362C211yesmaximal, characteristic
7#324×C107C211yesmaximal, characteristic, complemented
8#16812104—21no—
9#16812099—21no—
10#16812094—21no—
11#16812092—21no—
12#16812088C2211yescharacteristic
13#16812087—21no—
14#16812083C2211yescharacteristic
15C4×C22⋊D107—21no—
16C2×C4⋊Dic107C2211yescharacteristic
17C2×Dic107⋊C4—21no—
18#16812043—21no—
19#16812041—21no—
20#16812034—21no—
21#16812031—21no—
22C107⋊#95—21no—
23C107⋊#95C2211yescharacteristic
24C2×C4⋊C4×C107C2211yescharacteristic
25C22⋊C8×C107C2211yescharacteristic
26C22⋊C8×C107C2211yescharacteristic
27C2×Dic214D411yescharacteristic
28C2×D428D411yescharacteristic
29C2×C22⋊D107—21no—
30C22×Dic107—21no—
31C22×Dic107—21no—
32C2×C4×D107—21no—
33C4⋊Dic107—21no—
34C4⋊Dic107—21no—
35C4⋊Dic107D411yescharacteristic
36C4⋊Dic107D411yescharacteristic
37Dic107⋊C4—21no—
38Dic107⋊C4—21no—
39Dic107⋊C4—21no—
40Dic107⋊C4—21no—
41Dic107⋊C4—42no—
42C22⋊Dic107—21no—
43(C2×D107)⋊C4—21no—
44(C2×D107)⋊C4—21no—
45(C2×D107)⋊C4—21no—
46(C2×D107)⋊C4—21no—
47C4×Dic107—21no—
48C22×C4×C107D411yescharacteristic
49C22×C4×C107D411yescharacteristic
50C22×C4×C107C2311yescharacteristic
51C2×C8×C107—21no—
52C2×C8×C107—21no—
53C4⋊C4×C107—21no—
54C4⋊C4×C107—21no—
55C23×C107C2×D411yescharacteristic
56C22×D107—21no—
57C2×C4×C107—21no—
58C2×C4×C107—21no—
59C2×C4×C107—21no—
60C2×C4×C107—21no—
61C2×C4×C107—41no—
62C2×C4×C107—41no—
63C2×C4×C107C2×D411yescharacteristic
64C2×C4×C107C2×D411yescharacteristic
65C22⋊D107—41no—
66C22⋊D107—41no—
67C2×Dic107—22no—
68C2×Dic107—21no—
69C2×Dic107—21no—
70C2×Dic107—21no—
71C2×Dic107—41no—
72C2×Dic107—41no—
73C2×Dic107—41no—
74C2×Dic107—41no—
75C2×Dic107—41no—
76D428—41no—
77C4×D107—81no—
78Dic214—41no—
79C8×C107—41no—
80C8×C107—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—41no—
92C4×C107—41no—
93Dic107—42no—
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#328—1071no—
111#327—1071no—
112#324D10711yescharacteristic, complemented
113#126—2141no—
114#125—2141no—
115#123—2141no—
116#123—2141no—
117C22⋊Q8—1071no—
118C22⋊Q8—2141no—
119#121—1071no—
120C4×D4—2141no—
121C2×C4⋊C4—1071no—
122C2×C4⋊C4—2141no—
123C2×C4⋊C4C2×D10711yescharacteristic
124#107—2141no—
125#106—2141no—
126#103—2141no—
127#102—2141no—
128C22⋊C8C2×D10711yescharacteristic
129C22⋊C8C2×D10711yescharacteristic
130#95—1071no—
131#95—2141no—
132C2×Q8—1071no—
133C2×D4—1071no—
134C2×D4—2141no—
135C22×C4—2141no—
136C22×C4—2141no—
137C22×C4—2141no—
138C22×C4D42811yescharacteristic
139C22×C4D42811yescharacteristic
140C22×C4C22×D10711yescharacteristic
141C2×C8—21no—
142C2×C8—21no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—1071no—
146C4⋊C4—1071no—
147C4⋊C4—4282no—
148C4⋊C4—2141no—
149C4⋊C4—2141no—
150C4⋊C4—2141no—
151C4⋊C4—2141no—
152C4⋊C4—2141no—
153C4⋊C4—2141no—
154C22⋊C4—2141no—
155C22⋊C4—2141no—
156C22⋊C4—2141no—
157C22⋊C4—2141no—
158C22⋊C4—2141no—
159C42—2141no—
160C23—2141no—
161C23C2×D42811yescharacteristic
162Q8—4281no—
163D4—4281no—
164D4—4281no—
165D4—4281no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—8561no—
173C2×C4—4281no—
174C2×C4—4281no—
175C2×C4—4281no—
176C2×C4—4281no—
177C2×C4—4281no—
178C2×C4—2142no—
179C2×C4—2141no—
180C2×C4—2141no—
181C2×C4—2141no—
182C2×C4D4×D10711yescharacteristic
183C2×C4D4×D10711yescharacteristic
184C8—41no—
185C8—41no—
186C22—21no—
187C22—21no—
188C22—4281no—
189C22—4281no—
190C22—4281no—
191C22#1681207911yescharacteristic
192C22#1681213111yescharacteristic
193C22#1681213711yescharacteristic
194C4—21no—
195C4—21no—
196C4—41no—
197C4—41no—
198C4—8561no—
199C4—4282no—
200C4—4281no—
201C4—4281no—
202C4—4281no—
203C2—21no—
204C2—21no—
205C2—8561no—
206C2#2029277411yescharacteristic
207C2#2029281211yescharacteristic
208C2#2029281811yescharacteristic
subgroupG/H
centerC22#16812079
commutator, cosocleC22×C4×C107C23
FrattiniC22×C4C22×D107
Fitting#324×C107C2
socleC22×C107#120
prime radical#16812083C22
hypercenter#324D107
hypocenterC107#1609
LCSG ▷ C22×C4×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #20292958C2semidirect
4. #20292557C2semidirect
5. #20292365C2semidirect
7. #324×C107C2semidirect
105. C107#1609semidirect
112. #324D107semidirect

Maximal subgroups

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

subgroupindex
#202932242
#202929582
#202929412
#202925572
#202923652
#202923622
#324×C1072
#1609107