Finite Group Databasebeta

← #28335470

Subgroups — #28335470

Order 13696.

210 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 51 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#20293256C211yesmaximal, characteristic
2#20292958C211yesmaximal, characteristic
3#20292955C211yesmaximal, characteristic
4#20292559C211yesmaximal, characteristic
5#20292363C211yesmaximal, characteristic
6#20292352C211yesmaximal, characteristic
7#328×C107C211yesmaximal, characteristic
8#16812108—21no—
9#16812107—21no—
10#16812099—21no—
11#16812099—21no—
12#16812088C2211yescharacteristic
13#16812086—21no—
14#16812065—21no—
15C2×C4⋊Dic107—21no—
16C2×C4⋊Dic107C2211yescharacteristic
17C2×Dic107⋊C4C2211yescharacteristic
18#16812041—21no—
19#16812040—21no—
20#16812034—21no—
21#16812033—21no—
22C22⋊(C107⋊C8)C2211yescharacteristic
23C107⋊#95—21no—
24C22⋊Q8×C107C2211yescharacteristic
25C22⋊C8×C107C2211yescharacteristic
26#95×C107C2211yescharacteristic
27C2×Dic214—21no—
28C2×Dic214D411yescharacteristic
29C22×Dic107—21no—
30C22×Dic107D411yescharacteristic
31C22×Dic107D411yescharacteristic
32C2×C107⋊C8—21no—
33C4⋊Dic107—21no—
34C4⋊Dic107—21no—
35C4⋊Dic107—21no—
36C4⋊Dic107—42no—
37C4⋊Dic107D411yescharacteristic
38Dic107⋊C4—21no—
39Dic107⋊C4—21no—
40Dic107⋊C4—21no—
41Dic107⋊C4—21no—
42Dic107⋊C4—21no—
43Dic107⋊C4—21no—
44Dic107⋊C4—21no—
45C22⋊Dic107—21no—
46C4×Dic107—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
56Q8×C107—41no—
57C2×C4×C107—22no—
58C2×C4×C107—21no—
59C2×C4×C107—21no—
60C2×C4×C107—41no—
61C2×C4×C107—41no—
62C2×C4×C107—41no—
63C2×C4×C107C2×D411yescharacteristic
64C2×C4×C107C2×D411yescharacteristic
65C2×Dic107—21no—
66C2×Dic107—21no—
67C2×Dic107—21no—
68C2×Dic107—21no—
69C2×Dic107—21no—
70C2×Dic107—41no—
71C2×Dic107—41no—
72C2×Dic107—41no—
73C2×Dic107—41no—
74C2×Dic107SD1612yes—
75Dic214—41no—
76Dic214—81no—
77C8×C107—41no—
78C107⋊C8—41no—
79C22×C107—21no—
80C22×C107—21no—
81C22×C107#12011yescharacteristic
82C22×C107C2×SD1611yescharacteristic
83C22×C107#13711yescharacteristic
84C4×C107—21no—
85C4×C107—21no—
86C4×C107—42no—
87C4×C107—41no—
88C4×C107—41no—
89Dic107—22no—
90Dic107—41no—
91Dic107—41no—
92Dic107—41no—
93Dic107—81no—
94C2×C107—21no—
95C2×C107—21no—
96C2×C107#44811yescharacteristic
97C2×C107#45611yescharacteristic
98C2×C107#45811yescharacteristic
99#1611—1071nomaximal, Sylow
100C107#161111yescharacteristic, complemented, Sylow
101#544—1071no—
102#483—1071no—
103#483—1071no—
104#398—1071no—
105#328—1071no—
106#328D10711yescharacteristic
107#324—1071no—
108C4⋊Q8—2141no—
109C4⋊Q8—2141no—
110#125—2141no—
111#125—2141no—
112C22⋊Q8—1071no—
113C22⋊Q8—2141no—
114C22⋊Q8C2×D10711yescharacteristic
115#117—2141no—
116C2×C4⋊C4—1071no—
117C2×C4⋊C4—1071no—
118C2×C4⋊C4—2141no—
119#106—2141no—
120#106—2141no—
121#103—2141no—
122#103—2141no—
123C22⋊C8—1071no—
124C22⋊C8C2×D10711yescharacteristic
125#95—2141no—
126#95C2×D10711yescharacteristic
127C2×Q8—1071no—
128C2×Q8—2141no—
129C2×Q8D42811yescharacteristic
130C22×C4—21no—
131C22×C4—1071no—
132C22×C4—1071no—
133C22×C4—2141no—
134C22×C4C22×D10711yescharacteristic
135C2×C8—21no—
136C2×C8—2141no—
137C4⋊C4—21no—
138C4⋊C4—1071no—
139C4⋊C4—4282no—
140C4⋊C4—2141no—
141C4⋊C4—2141no—
142C4⋊C4—2141no—
143C4⋊C4—2141no—
144C4⋊C4—2141no—
145C4⋊C4—2141no—
146C4⋊C4—2141no—
147C4⋊C4—2141no—
148C4⋊C4—2141no—
149C4⋊C4—2141no—
150C4⋊C4D42811yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—2141no—
153C42—2141no—
154C42—2141no—
155C23D4×D10711yescharacteristic
156Q8—41no—
157Q8—8561no—
158Q8—4281no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—1072no—
166C2×C4—4281no—
167C2×C4—4281no—
168C2×C4—4281no—
169C2×C4—4281no—
170C2×C4—2141no—
171C2×C4—2141no—
172C2×C4—2141no—
173C2×C4—2141no—
174C2×C4—2141no—
175C2×C4D4×D10711yescharacteristic
176C2×C4C2×D42811yescharacteristic
177C8—41no—
178C8—4281no—
179C22—21no—
180C22—21no—
181C22#1681207911yescharacteristic
182C22SD16×D10711yescharacteristic
183C22#1681214111yescharacteristic
184C4—21no—
185C4—21no—
186C4—42no—
187C4—41no—
188C4—41no—
189C4—8561no—
190C4—4281no—
191C4—4281no—
192C4—4281no—
193C4—2142no—
194C2—21no—
195C2—21no—
196C2#2029276711yescharacteristic
197C2#2029281111yescharacteristic
198C2#2029281811yescharacteristic
subgroupG/H
centerC22#16812079
commutator, cosocleC22×C4×C107C23
FrattiniC22×C4C22×D107
Fitting#328×C107C2
socleC22×C107#120
prime radicalC23×C107C2×D4
hypercenter#328D107
hypocenterC107#1611
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
100. C107#1611semidirect

Maximal subgroups

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

subgroupindex
#202932562
#202929582
#202929552
#202925592
#202923632
#202923522
#328×C1072
#1611107