Finite Group Databasebeta

← #28335504

Subgroups — #28335504

Order 13696.

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

normal subgroups only

This group has 202 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#20292963C211yesmaximal, characteristic
3#20292960C211yesmaximal, characteristic
4#20292567C211yesmaximal, 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⋊Dic107C2211yescharacteristic
16C2×Dic107⋊C4C2211yescharacteristic
17#16812043—21no—
18#16812042—21no—
19#16812034—21no—
20#16812033—21no—
21C22⋊(C107⋊C8)C2211yescharacteristic
22C107⋊#95—21no—
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⋊Dic107D411yescharacteristic
37Dic107⋊C4—21no—
38Dic107⋊C4—21no—
39Dic107⋊C4—21no—
40Dic107⋊C4—21no—
41Dic107⋊C4—21no—
42Dic107⋊C4—21no—
43Dic107⋊C4—21no—
44C22⋊Dic107—21no—
45C4×Dic107—21no—
46C4×Dic107—21no—
47C2×Q8×C107D411yescharacteristic
48C22×C4×C107—21no—
49C22×C4×C107C2311yescharacteristic
50C2×C8×C107—21no—
51C4⋊C4×C107—21no—
52C4⋊C4×C107D411yescharacteristic
53C22⋊C4×C107—21no—
54C23×C107C2×D411yescharacteristic
55Q8×C107—41no—
56C2×C4×C107—21no—
57C2×C4×C107—21no—
58C2×C4×C107—41no—
59C2×C4×C107—41no—
60C2×C4×C107—41no—
61C2×C4×C107—41no—
62C2×C4×C107C2×D411yescharacteristic
63C2×C4×C107C2×D411yescharacteristic
64C2×Dic107—21no—
65C2×Dic107—21no—
66C2×Dic107—21no—
67C2×Dic107—21no—
68C2×Dic107—21no—
69C2×Dic107—41no—
70C2×Dic107—42no—
71C2×Dic107—41no—
72C2×Dic107Q1612yes—
73Dic214—41no—
74Dic214—81no—
75C8×C107—41no—
76C107⋊C8—41no—
77C22×C107—21no—
78C22×C107—21no—
79C22×C107#12011yescharacteristic
80C22×C107C2×Q1611yescharacteristic
81C22×C107#13711yescharacteristic
82C4×C107—21no—
83C4×C107—21no—
84C4×C107—41no—
85C4×C107—41no—
86C4×C107—81no—
87Dic107—22no—
88Dic107—41no—
89Dic107—41no—
90Dic107—41no—
91Dic107—81no—
92C2×C107—21no—
93C2×C107—21no—
94C2×C107#45111yescharacteristic
95C2×C107#45411yescharacteristic
96C2×C107#45811yescharacteristic
97#1617—1071nomaximal, Sylow
98C107#161711yescharacteristic, complemented, Sylow
99#544—1071no—
100#484—1071no—
101#484—1071no—
102#400—1071no—
103#328—1071no—
104#328D10711yescharacteristic
105#324—1071no—
106C4⋊Q8—2141no—
107C4⋊Q8—2141no—
108#125—2141no—
109#125—2141no—
110C22⋊Q8—1071no—
111C22⋊Q8—2141no—
112C22⋊Q8C2×D10711yescharacteristic
113#117—2141no—
114C2×C4⋊C4—1071no—
115C2×C4⋊C4—1071no—
116#107—2141no—
117#107—2141no—
118#103—2141no—
119#103—2141no—
120C22⋊C8—1071no—
121C22⋊C8C2×D10711yescharacteristic
122#95—2141no—
123#95—2141no—
124#95C2×D10711yescharacteristic
125C2×Q8—1071no—
126C2×Q8—2141no—
127C2×Q8D42811yescharacteristic
128C22×C4—21no—
129C22×C4—1071no—
130C22×C4—1071no—
131C22×C4—2141no—
132C22×C4C22×D10711yescharacteristic
133C2×C8—21no—
134C2×C8—2141no—
135C4⋊C4—21no—
136C4⋊C4—1071no—
137C4⋊C4—2141no—
138C4⋊C4—2141no—
139C4⋊C4—2141no—
140C4⋊C4—2141no—
141C4⋊C4—2141no—
142C4⋊C4—2141no—
143C4⋊C4—2141no—
144C4⋊C4—2141no—
145C4⋊C4—2141no—
146C4⋊C4—2141no—
147C4⋊C4D42811yescharacteristic
148C22⋊C4—21no—
149C22⋊C4—2141no—
150C42—2141no—
151C42—2141no—
152C23D4×D10711yescharacteristic
153Q8—41no—
154Q8—8561no—
155Q8—4281no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—1072no—
163C2×C4—4282no—
164C2×C4—4281no—
165C2×C4—4281no—
166C2×C4—2141no—
167C2×C4—2141no—
168C2×C4—2141no—
169C2×C4—2141no—
170C2×C4—2141no—
171C2×C4D4×D10711yescharacteristic
172C2×C4C2×D42811yescharacteristic
173C8—41no—
174C8—4281no—
175C22—21no—
176C22—21no—
177C22#1681207911yescharacteristic
178C22Q16×D10711yescharacteristic
179C22#1681213811yescharacteristic
180C4—21no—
181C4—21no—
182C4—41no—
183C4—41no—
184C4—81no—
185C4—8561no—
186C4—4281no—
187C4—4281no—
188C4—4281no—
189C4—2142no—
190C2—21no—
191C2—21no—
192C2#2029278411yescharacteristic
193C2#2029280111yescharacteristic
194C2#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#1617
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
98. C107#1617semidirect

Maximal subgroups

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

subgroupindex
#202932562
#202929632
#202929602
#202925672
#202923632
#202923522
#328×C1072
#1617107