Finite Group Databasebeta

← #28335455

Subgroups — #28335455

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#20293222C211yesmaximal, characteristic
2#20292957C211yesmaximal, characteristic, complemented
3#20292558C211yesmaximal, characteristic, complemented
4#20292365C211yesmaximal, characteristic, complemented
5#20292361C211yesmaximal, characteristic
6#20292352C211yesmaximal, characteristic, complemented
7#480×C107C211yesmaximal, characteristic
8#16812102—21no—
9#16812099—21no—
10#16812090—21no—
11#16812090—21no—
12#16812088C2211yescharacteristic
13#16812086—21no—
14D4×Dic107—21no—
15C2×Dic107⋊C4—21no—
16C2×Dic107⋊C4C2211yescharacteristic
17#16812040—21no—
18#16812032—21no—
19C22⋊(C107⋊C8)C2211yescharacteristic
20C107⋊#95—21no—
21C107⋊#95C2211yescharacteristic
22#121×C107C2211yescharacteristic
23C2×C4⋊C4×C107C2211yescharacteristic
24#107×C107—21no—
25#102×C107—21no—
26C22⋊C8×C107C2211yescharacteristic
27C2×Dic214D411yescharacteristic
28C22×Dic107—21no—
29C22×Dic107—21no—
30C22×Dic107D411yescharacteristic
31C22×Dic107D411yescharacteristic
32C2×C107⋊C8—21no—
33C4⋊Dic107—21no—
34C4⋊Dic107D411yescharacteristic
35Dic107⋊C4—21no—
36Dic107⋊C4—21no—
37Dic107⋊C4—21no—
38Dic107⋊C4—21no—
39Dic107⋊C4—21no—
40Dic107⋊C4—42no—
41C22⋊Dic107—21no—
42C22⋊Dic107—21no—
43C22⋊Dic107—21no—
44C22⋊Dic107—21no—
45C4×Dic107—21no—
46C2×D4×C107—21no—
47C2×D4×C107D411yescharacteristic
48C22×C4×C107—21no—
49C22×C4×C107C2311yescharacteristic
50C2×C8×C107—21no—
51C4⋊C4×C107—21no—
52C4⋊C4×C107—21no—
53C4⋊C4×C107D411yescharacteristic
54C22⋊C4×C107—21no—
55C23×C107—21no—
56C23×C107C2×D411yescharacteristic
57D4×C107—41no—
58D4×C107—41no—
59D4×C107—41no—
60C2×C4×C107—21no—
61C2×C4×C107—41no—
62C2×C4×C107—41no—
63C2×C4×C107—41no—
64C2×C4×C107—41no—
65C2×C4×C107C2×D411yescharacteristic
66C2×C4×C107C2×D411yescharacteristic
67C2×Dic107—22no—
68C2×Dic107—21no—
69C2×Dic107—21no—
70C2×Dic107—21no—
71C2×Dic107—21no—
72C2×Dic107—21no—
73C2×Dic107—21no—
74C2×Dic107—41no—
75C2×Dic107—41no—
76C2×Dic107—41no—
77C2×Dic107—81no—
78Dic214—41no—
79C8×C107—41no—
80C107⋊C8—41no—
81C22×C107—21no—
82C22×C107—21no—
83C22×C107—41no—
84C22×C107—41no—
85C22×C107—41no—
86C22×C107#12011yescharacteristic
87C22×C107#13511yescharacteristic
88C22×C107AGL(1,ℤ/8)11yescharacteristic
89C4×C107—21no—
90C4×C107—21no—
91C4×C107—41no—
92C4×C107—81no—
93Dic107—42no—
94Dic107—41no—
95Dic107—41no—
96Dic107—41no—
97Dic107—41no—
98C2×C107—21no—
99C2×C107—21no—
100C2×C107—81no—
101C2×C107#44911yescharacteristic
102C2×C107#45611yescharacteristic
103C2×C107#45811yescharacteristic
104#1609—1071nomaximal, Sylow
105C107#160911yescharacteristic, complemented, Sylow
106#539—1071no—
107#483—1071no—
108#480D10711yescharacteristic
109#398—1071no—
110#328—1071no—
111#327—1071no—
112#324—1071no—
113#126—2141no—
114#125—2141no—
115#123—2141no—
116#123—2141no—
117C22⋊Q8—1071no—
118C22⋊Q8—2141no—
119#121C2×D10711yescharacteristic
120C4×D4—2141no—
121C2×C4⋊C4—1071no—
122C2×C4⋊C4—2141no—
123C2×C4⋊C4C2×D10711yescharacteristic
124#107—21no—
125#106—2141no—
126#103—2141no—
127#102—21no—
128C22⋊C8—1071no—
129C22⋊C8C2×D10711yescharacteristic
130#95—1071no—
131#95—2141no—
132C2×Q8—1071no—
133C2×D4—21no—
134C2×D4C22⋊D10711yescharacteristic
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—21no—
145C4⋊C4—1071no—
146C4⋊C4—4282no—
147C4⋊C4—2141no—
148C4⋊C4—2141no—
149C4⋊C4—2141no—
150C4⋊C4—2141no—
151C4⋊C4—2141no—
152C4⋊C4—2141no—
153C4⋊C4C22⋊D10711yescharacteristic
154C22⋊C4—21no—
155C22⋊C4—2141no—
156C22⋊C4—2141no—
157C22⋊C4—2141no—
158C22⋊C4—2141no—
159C42—2141no—
160C23—21no—
161C23D4×D10711yescharacteristic
162Q8—4281no—
163D4—41no—
164D4—41no—
165D4—41no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—8561no—
172C2×C4—4281no—
173C2×C4—4281no—
174C2×C4—4281no—
175C2×C4—2142no—
176C2×C4—2141no—
177C2×C4—2141no—
178C2×C4—2141no—
179C2×C4—2141no—
180C2×C4—2141no—
181C2×C4—2141no—
182C2×C4D4×D10711yescharacteristic
183C2×C4C2×C22⋊D10711yescharacteristic
184C8—41no—
185C8—4281no—
186C22—21no—
187C22—21no—
188C22—41no—
189C22—41no—
190C22—41no—
191C22#1681207711yescharacteristic
192C22#1681212811yescharacteristic
193C22#1681213311yescharacteristic
194C4—21no—
195C4—21no—
196C4—41no—
197C4—81no—
198C4—4282no—
199C4—4281no—
200C4—4281no—
201C4—4281no—
202C4—4281no—
203C2—21no—
204C2—21no—
205C2—81no—
206C2#2029276911yescharacteristic
207C2#2029280811yescharacteristic
208C2#2029281611yescharacteristic
subgroupG/H
centerC22#16812077
commutator, cosocleC22×C4×C107C23
FrattiniC22×C4C22×D107
Fitting#480×C107C2
socleC22×C107#120
prime radical#121×C107C22
hypercenter#480D107
hypocenterC107#1609
LCSG ▷ C22×C4×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. #20292957C2semidirect
3. #20292558C2semidirect
4. #20292365C2semidirect
6. #20292352C2semidirect
105. C107#1609semidirect

Maximal subgroups

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

subgroupindex
#202932222
#202929572
#202925582
#202923652
#202923612
#202923522
#480×C1072
#1609107