Finite Group Databasebeta

← #28335487

Subgroups — #28335487

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#20292963C211yesmaximal, characteristic, complemented
3#20292960C211yesmaximal, characteristic, complemented
4#20292564C211yesmaximal, characteristic
5#20292363C211yesmaximal, characteristic, complemented
6#20292350C211yesmaximal, characteristic
7#328×C107C211yesmaximal, characteristic, complemented
8#16812089—21no—
9#16812088C2211yescharacteristic
10#16812087—21no—
11#16812087—21no—
12#16812086—21no—
13#16812085—21no—
14C2×C4⋊Dic107—21no—
15C2×C4⋊Dic107C2211yescharacteristic
16C2×(C2×D107)⋊C4—21no—
17C2×(C2×D107)⋊C4C2211yescharacteristic
18C22⋊C4×D107—21no—
19#16812043—21no—
20#16812042—21no—
21#16812034—21no—
22#16812033—21no—
23C22⋊(C107⋊C8)C2211yescharacteristic
24C22⋊Q8×C107C2211yescharacteristic
25C22⋊C8×C107C2211yescharacteristic
26#95×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⋊Dic107—21no—
37C4⋊Dic107—21no—
38C4⋊Dic107—42no—
39C4⋊Dic107D411yescharacteristic
40Dic107⋊C4—21no—
41Dic107⋊C4—21no—
42Dic107⋊C4—21no—
43C22⋊Dic107—21no—
44(C2×D107)⋊C4—21no—
45(C2×D107)⋊C4—21no—
46(C2×D107)⋊C4—21no—
47(C2×D107)⋊C4—21no—
48(C2×D107)⋊C4—42no—
49C2×Q8×C107D411yescharacteristic
50C22×C4×C107—21no—
51C22×C4×C107C2311yescharacteristic
52C2×C8×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—22no—
64C2×C4×C107—21no—
65C2×C4×C107—21no—
66C2×C4×C107—41no—
67C2×C4×C107—41no—
68C2×C4×C107—41no—
69C2×C4×C107C2×D411yescharacteristic
70C2×C4×C107C2×D411yescharacteristic
71C2×Dic107—21no—
72C2×Dic107—21no—
73C2×Dic107—21no—
74C2×Dic107—41no—
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—42no—
97C4×C107—41no—
98C4×C107—41no—
99Dic107—41no—
100Dic107—41no—
101Dic107—41no—
102Dic107—81no—
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#484—1071no—
114#399—1071no—
115#328—1071no—
116#328D10711yescharacteristic, complemented
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—1071no—
126C2×C4⋊C4—2141no—
127C2×C22⋊C4—1071no—
128C2×C22⋊C4—2141no—
129C2×C22⋊C4—2141no—
130#107—2141no—
131#107—2141no—
132#103—2141no—
133#103—2141no—
134C22⋊C8—1071no—
135C22⋊C8C2×D10711yescharacteristic
136#95C2×D10711yescharacteristic
137C24—1071no—
138C2×Q8—1071no—
139C2×Q8—2141no—
140C2×Q8D42811yescharacteristic
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—1071no—
151C4⋊C4—4282no—
152C4⋊C4—2141no—
153C4⋊C4—2141no—
154C4⋊C4—2141no—
155C4⋊C4—2141no—
156C4⋊C4—2141no—
157C4⋊C4—2141no—
158C4⋊C4D42811yescharacteristic
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—22no—
176C2×C4—21no—
177C2×C4—21no—
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—4281no—
187C2×C4—2141no—
188C2×C4—2141no—
189C2×C4—2141no—
190C2×C4D4×D10711yescharacteristic
191C2×C4C2×D42811yescharacteristic
192C8—41no—
193C8—4281no—
194C22—21no—
195C22—21no—
196C22—8561no—
197C22—4282no—
198C22—4281no—
199C22—4281no—
200C22—2142no—
201C22#1681207911yescharacteristic
202C22Q16×D10711yescharacteristic
203C22#1681213811yescharacteristic
204C4—21no—
205C4—21no—
206C4—42no—
207C4—41no—
208C4—41no—
209C4—8561no—
210C4—4281no—
211C4—4281no—
212C4—4281no—
213C2—21no—
214C2—21no—
215C2—4282no—
216C2#2029278411yescharacteristic
217C2#2029279611yescharacteristic
218C2#2029281811yescharacteristic
subgroupG/H
centerC22#16812079
commutator, cosocleC22×C4×C107C23
FrattiniC22×C4C22×D107
Fitting#328×C107C2
socleC22×C107#120
prime radicalC23×D107D4
hypercenter#328D107
hypocenterC107#1614
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
2. #20292963C2semidirect
3. #20292960C2semidirect
5. #20292363C2semidirect
7. #328×C107C2semidirect
110. C107#1614semidirect
116. #328D107semidirect

Maximal subgroups

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

subgroupindex
#202932522
#202929632
#202929602
#202925642
#202923632
#202923502
#328×C1072
#1614107