Finite Group Databasebeta

← #28335484

Subgroups — #28335484

Order 13696.

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

normal subgroups only

This group has 236 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#20293252C211yesmaximal, characteristic
2#20292962C211yesmaximal, characteristic, complemented
3#20292562C211yesmaximal, characteristic
4#20292365C211yesmaximal, characteristic, complemented
5#20292364C211yesmaximal, characteristic, complemented
6#20292350C211yesmaximal, characteristic
7#484×C107C211yesmaximal, characteristic, complemented
8#16812089—21no—
9#16812088C2211yescharacteristic
10#16812087—21no—
11#16812087—21no—
12#16812086—21no—
13#16812085—21no—
14C2×Dic107⋊C4—21no—
15C2×(C2×D107)⋊C4—21no—
16C2×(C2×D107)⋊C4C2211yescharacteristic
17C22⋊C4×D107—21no—
18#16812042—21no—
19#16812032—21no—
20C22⋊(C107⋊C8)C2211yescharacteristic
21C107⋊#95C2211yescharacteristic
22C22⋊Q8×C107C2211yescharacteristic
23C2×C4⋊C4×C107C2211yescharacteristic
24#107×C107—21no—
25#103×C107—21no—
26C22⋊C8×C107C2211yescharacteristic
27C23×D107D411yescharacteristic
28C2×Dic214—21no—
29C2×Dic214D411yescharacteristic
30C22×Dic107—21no—
31C22×Dic107D411yescharacteristic
32C2×C4×D107—21no—
33C2×C4×D107—21no—
34C2×C107⋊C8—21no—
35C4⋊Dic107—21no—
36C4⋊Dic107D411yescharacteristic
37Dic107⋊C4—21no—
38Dic107⋊C4—21no—
39Dic107⋊C4—21no—
40Dic107⋊C4—42no—
41C22⋊Dic107—21no—
42(C2×D107)⋊C4—21no—
43(C2×D107)⋊C4—21no—
44(C2×D107)⋊C4—21no—
45(C2×D107)⋊C4—21no—
46(C2×D107)⋊C4—42no—
47C2×Q8×C107D411yescharacteristic
48C22×C4×C107—21no—
49C22×C4×C107C2311yescharacteristic
50C2×C8×C107—21no—
51C4⋊C4×C107—21no—
52C4⋊C4×C107—21no—
53C4⋊C4×C107—21no—
54C4⋊C4×C107D411yescharacteristic
55C22⋊C4×C107—21no—
56C23×C107C2×D411yescharacteristic
57C22×D107—21no—
58C22×D107—21no—
59C22×D107—41no—
60C22×D107—41no—
61C22×D107Q1612yes—
62Q8×C107—41no—
63C2×C4×C107—21no—
64C2×C4×C107—21no—
65C2×C4×C107—41no—
66C2×C4×C107—41no—
67C2×C4×C107—41no—
68C2×C4×C107—41no—
69C2×C4×C107C2×D411yescharacteristic
70C2×C4×C107C2×D411yescharacteristic
71C2×Dic107—22no—
72C2×Dic107—21no—
73C2×Dic107—21no—
74C2×Dic107—21no—
75C2×Dic107—41no—
76C2×Dic107—41no—
77C2×Dic107—41no—
78C4×D107—81no—
79C4×D107—81no—
80Dic214—41no—
81Dic214—81no—
82C8×C107—41no—
83C107⋊C8—41no—
84C22×C107—21no—
85C22×C107—21no—
86C22×C107#12011yescharacteristic
87C22×C107C2×Q1611yescharacteristic
88C22×C107#13711yescharacteristic
89C2×D107—22no—
90C2×D107—41no—
91C2×D107—41no—
92C2×D107—42no—
93C2×D107—81no—
94C4×C107—21no—
95C4×C107—21no—
96C4×C107—41no—
97C4×C107—41no—
98C4×C107—81no—
99Dic107—42no—
100Dic107—41no—
101Dic107—41no—
102Dic107—41no—
103C2×C107—21no—
104C2×C107—21no—
105C2×C107#45111yescharacteristic
106C2×C107#45311yescharacteristic
107C2×C107#45811yescharacteristic
108D107—42no—
109#1614—1071nomaximal, Sylow
110C107#161411yescharacteristic, complemented, Sylow
111#543—1071no—
112#484—1071no—
113#484D10711yescharacteristic, complemented
114#399—1071no—
115#328—1071no—
116#328—1071no—
117#323—1071no—
118C22⋊Q8—1071no—
119C22⋊Q8—2141no—
120C22⋊Q8—2141no—
121C22⋊Q8—2141no—
122C22⋊Q8—2141no—
123C22⋊Q8—2141no—
124C22⋊Q8C2×D10711yescharacteristic
125C2×C4⋊C4—2141no—
126C2×C4⋊C4C2×D10711yescharacteristic
127C2×C22⋊C4—1071no—
128C2×C22⋊C4—2141no—
129C2×C22⋊C4—2141no—
130#107—21no—
131#107—2141no—
132#103—21no—
133#103—2141no—
134C22⋊C8—1071no—
135C22⋊C8C2×D10711yescharacteristic
136#95—1071no—
137C24—1071no—
138C2×Q8—1071no—
139C2×Q8—2141no—
140C2×Q8C22⋊D10711yescharacteristic
141C22×C4—21no—
142C22×C4—1071no—
143C22×C4—2141no—
144C22×C4—2141no—
145C22×C4—2141no—
146C22×C4C22×D10711yescharacteristic
147C2×C8—21no—
148C2×C8—2141no—
149C4⋊C4—21no—
150C4⋊C4—21no—
151C4⋊C4—21no—
152C4⋊C4—1071no—
153C4⋊C4—4282no—
154C4⋊C4—2141no—
155C4⋊C4—2141no—
156C4⋊C4—2141no—
157C4⋊C4—2141no—
158C4⋊C4C22⋊D10711yescharacteristic
159C22⋊C4—21no—
160C22⋊C4—4282no—
161C22⋊C4—2141no—
162C22⋊C4—2141no—
163C22⋊C4—2141no—
164C22⋊C4—2141no—
165C22⋊C4—2141no—
166C23—1072no—
167C23—4281no—
168C23—4281no—
169C23—2141no—
170C23—2141no—
171C23D4×D10711yescharacteristic
172Q8—41no—
173Q8—8561no—
174Q8—4281no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—8561no—
182C2×C4—8561no—
183C2×C4—4281no—
184C2×C4—4281no—
185C2×C4—4281no—
186C2×C4—2142no—
187C2×C4—2141no—
188C2×C4—2141no—
189C2×C4—2141no—
190C2×C4D4×D10711yescharacteristic
191C2×C4C2×C22⋊D10711yescharacteristic
192C8—41no—
193C8—4281no—
194C22—21no—
195C22—21no—
196C22—8561no—
197C22—4282no—
198C22—4281no—
199C22—4281no—
200C22—2142no—
201C22#1681207711yescharacteristic
202C22Q16×D10711yescharacteristic
203C22#1681214111yescharacteristic
204C4—21no—
205C4—21no—
206C4—41no—
207C4—41no—
208C4—81no—
209C4—4282no—
210C4—4281no—
211C4—4281no—
212C4—4281no—
213C2—21no—
214C2—21no—
215C2—4282no—
216C2#2029278111yescharacteristic
217C2#2029279311yescharacteristic
218C2#2029281611yescharacteristic
subgroupG/H
centerC22#16812077
commutator, cosocleC22×C4×C107C23
FrattiniC22×C4C22×D107
Fitting#484×C107C2
socleC22×C107#120
prime radicalC23×D107D4
hypercenter#484D107
hypocenterC107#1614
LCSG ▷ C22×C4×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
2. #20292962C2semidirect
4. #20292365C2semidirect
5. #20292364C2semidirect
7. #484×C107C2semidirect
110. C107#1614semidirect
113. #484D107semidirect

Maximal subgroups

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

subgroupindex
#202932522
#202929622
#202925622
#202923652
#202923642
#202923502
#484×C1072
#1614107