Finite Group Databasebeta

← #28335494

Subgroups — #28335494

Order 13696.

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

normal subgroups only

This group has 208 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#20292963C211yesmaximal, characteristic, complemented
3#20292946C211yesmaximal, characteristic
4#20292566C211yesmaximal, 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
17#16812043—21no—
18#16812041—21no—
19#16812034—21no—
20#16812031—21no—
21C107⋊#95—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—
41C22⋊Dic107—21no—
42(C2×D107)⋊C4—21no—
43(C2×D107)⋊C4—21no—
44(C2×D107)⋊C4—21no—
45(C2×D107)⋊C4—21no—
46C4×Dic107—21no—
47C22×C4×C107D411yescharacteristic
48C22×C4×C107D411yescharacteristic
49C22×C4×C107C2311yescharacteristic
50C2×C8×C107—21no—
51C2×C8×C107—21no—
52C4⋊C4×C107—21no—
53C4⋊C4×C107—21no—
54C23×C107C2×D411yescharacteristic
55C22×D107—21no—
56C2×C4×C107—21no—
57C2×C4×C107—21no—
58C2×C4×C107—21no—
59C2×C4×C107—21no—
60C2×C4×C107—41no—
61C2×C4×C107—41no—
62C2×C4×C107C2×D411yescharacteristic
63C2×C4×C107C2×D411yescharacteristic
64C22⋊D107—41no—
65C22⋊D107—41no—
66C2×Dic107—21no—
67C2×Dic107—21no—
68C2×Dic107—21no—
69C2×Dic107—41no—
70C2×Dic107—41no—
71C2×Dic107—42no—
72C2×Dic107—41no—
73C2×Dic107—41no—
74D428—41no—
75C4×D107—81no—
76Dic214—41no—
77C8×C107—41no—
78C8×C107—41no—
79C22×C107—21no—
80C22×C107—21no—
81C22×C107#12011yescharacteristic
82C22×C107#13511yescharacteristic
83C22×C107#13711yescharacteristic
84C2×D107—41no—
85C2×D107—41no—
86C2×D107—41no—
87C4×C107—21no—
88C4×C107—21no—
89C4×C107—41no—
90C4×C107—41no—
91Dic107—41no—
92Dic107—41no—
93Dic107—41no—
94Dic107—81no—
95Dic107—81no—
96C2×C107—21no—
97C2×C107—21no—
98C2×C107#45211yescharacteristic
99C2×C107#45411yescharacteristic
100C2×C107#45811yescharacteristic
101D107—81no—
102#1615—1071nomaximal, Sylow
103C107#161511yescharacteristic, complemented, Sylow
104#539—1071no—
105#484—1071no—
106#481—1071no—
107#400—1071no—
108#328—1071no—
109#327—1071no—
110#324D10711yescharacteristic, complemented
111#126—2141no—
112#125—2141no—
113#123—2141no—
114#123—2141no—
115C22⋊Q8—1071no—
116C22⋊Q8—2141no—
117#121—1071no—
118C4×D4—2141no—
119C2×C4⋊C4—1071no—
120C2×C4⋊C4C2×D10711yescharacteristic
121#107—2141no—
122#106—2141no—
123#103—2141no—
124#102—2141no—
125C22⋊C8C2×D10711yescharacteristic
126C22⋊C8C2×D10711yescharacteristic
127#95—1071no—
128#95—2141no—
129#95—2141no—
130C2×Q8—1071no—
131C2×D4—1071no—
132C2×D4—2141no—
133C22×C4—2141no—
134C22×C4—2141no—
135C22×C4—2141no—
136C22×C4D42811yescharacteristic
137C22×C4D42811yescharacteristic
138C22×C4C22×D10711yescharacteristic
139C2×C8—21no—
140C2×C8—21no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—1071no—
144C4⋊C4—1071no—
145C4⋊C4—2141no—
146C4⋊C4—2141no—
147C4⋊C4—2141no—
148C4⋊C4—2141no—
149C4⋊C4—2141no—
150C4⋊C4—2141no—
151C22⋊C4—2141no—
152C22⋊C4—2141no—
153C22⋊C4—2141no—
154C22⋊C4—2141no—
155C22⋊C4—2141no—
156C42—2141no—
157C23—2141no—
158C23C2×D42811yescharacteristic
159Q8—4281no—
160D4—4281no—
161D4—4281no—
162D4—4281no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—8561no—
170C2×C4—4281no—
171C2×C4—4281no—
172C2×C4—4282no—
173C2×C4—4281no—
174C2×C4—4281no—
175C2×C4—2141no—
176C2×C4—2141no—
177C2×C4—2141no—
178C2×C4D4×D10711yescharacteristic
179C2×C4D4×D10711yescharacteristic
180C8—41no—
181C8—41no—
182C22—21no—
183C22—21no—
184C22—4281no—
185C22—4281no—
186C22—4281no—
187C22#1681207911yescharacteristic
188C22#1681213111yescharacteristic
189C22#1681214211yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—8561no—
195C4—8561no—
196C4—4281no—
197C4—4281no—
198C4—4281no—
199C2—21no—
200C2—21no—
201C2—8561no—
202C2#2029279111yescharacteristic
203C2#2029280211yescharacteristic
204C2#2029281811yescharacteristic
subgroupG/H
centerC22#16812079
commutator, cosocleC22×C4×C107C23
FrattiniC22×C4C22×D107
Fitting#324×C107C2
socleC22×C107#120
prime radical#16812083C22
hypercenter#324D107
hypocenterC107#1615
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. #20292963C2semidirect
4. #20292566C2semidirect
5. #20292365C2semidirect
7. #324×C107C2semidirect
103. C107#1615semidirect
110. #324D107semidirect

Maximal subgroups

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

subgroupindex
#202932242
#202929632
#202929462
#202925662
#202923652
#202923622
#324×C1072
#1615107