Finite Group Databasebeta

← #28389555

Subgroups — #28389555

Order 14464.

260 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 260 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#20299185C211yesmaximal, characteristic
2#20298756C211yesmaximal, characteristic, complemented
3#20298736C211yesmaximal, characteristic, complemented
4#20298511C211yesmaximal, characteristic, complemented
5#20298334C211yesmaximal, characteristic, complemented
6#20298321C211yesmaximal, characteristic, complemented
7#327×C113C211yesmaximal, characteristic, complemented
8C22×Dic226C2211yescharacteristic
9C2×Dic452—21no—
10C2×#14268635—21no—
11#16813617—21no—
12#16813608—21no—
13#16813606—21no—
14#16813601C2211yescharacteristic
15#16813594—21no—
16#16813590—21no—
17D4×Dic113—21no—
18C2×#14268624—21no—
19C2×#14268624C2211yescharacteristic
20#16813547—21no—
21#16813545—21no—
22C22⋊#11744751C2211yescharacteristic
23#16813529—21no—
24#121×C113C2211yescharacteristic
25C22⋊C8×C113C2211yescharacteristic
26#95×C113C2211yescharacteristic
27C23×D113D411yescharacteristic
28C2×Dic226—21no—
29C2×Dic226—21no—
30C2×Dic226—42no—
31C2×Dic226D411yescharacteristic
32C2×C22⋊D113—21no—
33C2×C22⋊D113—21no—
34C22×Dic113—21no—
35C22×Dic113—21no—
36C22×Dic113D411yescharacteristic
37Dic452—42no—
38#14268635—42no—
39C2×#11744751—21no—
40C4⋊Dic113—21no—
41C4⋊Dic113D411yescharacteristic
42#14268626—21no—
43C22⋊Dic113—21no—
44C22⋊Dic113—21no—
45#14268624—21no—
46#14268624—21no—
47#14268624—21no—
48#14268624—21no—
49#14268624—42no—
50C4×Dic113—21no—
51C2×D4×C113—21no—
52C2×D4×C113D411yescharacteristic
53C22×C4×C113—21no—
54C22×C4×C113C2311yescharacteristic
55C2×C8×C113—21no—
56C4⋊C4×C113D411yescharacteristic
57C22⋊C4×C113—21no—
58C23×C113—21no—
59C23×C113C2×D411yescharacteristic
60C22×D113—21no—
61C22×D113—21no—
62C22×D113—21no—
63C22×D113—41no—
64C22×D113—41no—
65D4×C113—41no—
66D4×C113—41no—
67D4×C113—41no—
68C2×C4×C113—21no—
69C2×C4×C113—41no—
70C2×C4×C113—41no—
71C2×C4×C113—41no—
72C2×C4×C113—41no—
73C2×C4×C113C2×D411yescharacteristic
74C2×C4×C113C2×D411yescharacteristic
75C22⋊D113—81no—
76C22⋊D113—81no—
77C2×Dic113—22no—
78C2×Dic113—21no—
79C2×Dic113—21no—
80C2×Dic113—21no—
81C2×Dic113—41no—
82C2×Dic113—41no—
83C2×Dic113—41no—
84C2×Dic113—81no—
85Dic226—22no—
86Dic226—22no—
87Dic226—41no—
88Dic226—41no—
89Dic226—41no—
90C8×C113—41no—
91#11744751—41no—
92C22×C113—21no—
93C22×C113—21no—
94C22×C113—41no—
95C22×C113—41no—
96C22×C113—41no—
97C22×C113#12011yescharacteristic
98C22×C113#13511yescharacteristic
99C22×C113#13711yescharacteristic
100C2×D113—42no—
101C2×D113—41no—
102C2×D113—41no—
103C2×D113—41no—
104C2×D113—81no—
105C4×C113—21no—
106C4×C113—21no—
107C4×C113—41no—
108C4×C113—81no—
109Dic113—41no—
110Dic113—41no—
111Dic113—42no—
112Dic113—41no—
113C2×C113—21no—
114C2×C113—21no—
115C2×C113—81no—
116C2×C113#45211yescharacteristic
117C2×C113#45511yescharacteristic
118C2×C113B(4,𝔽2)11yescharacteristic
119D113—81no—
120#1606—1131nomaximal, Sylow
121C113#160611yescharacteristic, complemented, Sylow
122#538—1131no—
123#451—1131no—
124#448—1131no—
125#393—1131no—
126#328—1131no—
127#327D11311yescharacteristic, complemented
128#323—1131no—
129C22×Q8—1131no—
130C2×Q16—2261no—
131C2×SD16—2261no—
132#126—2261no—
133#124—2261no—
134#123—2261no—
135C22⋊Q8—1131no—
136#121—2261no—
137#121C2×D11311yescharacteristic
138#120—2261no—
139C4×D4—2261no—
140C2×C22⋊C4—1131no—
141C2×C22⋊C4—2261no—
142#103—2261no—
143#103—2261no—
144C22⋊C8—1131no—
145C22⋊C8C2×D11311yescharacteristic
146#95—2261no—
147#95C2×D11311yescharacteristic
148C24—1131no—
149C2×Q8—1131no—
150C2×Q8—4522no—
151C2×Q8—2261no—
152C2×Q8—2261no—
153C2×D4—21no—
154C2×D4—2261no—
155C2×D4—2261no—
156C2×D4D45211yescharacteristic
157C22×C4—21no—
158C22×C4—1131no—
159C22×C4—2261no—
160C22×C4—2261no—
161C22×C4C22×D11311yescharacteristic
162Q16—4522no—
163SD16—4522no—
164C2×C8—21no—
165C2×C8—2261no—
166C4⋊C4—1131no—
167C4⋊C4—2261no—
168C4⋊C4—2261no—
169C4⋊C4D45211yescharacteristic
170C22⋊C4—21no—
171C22⋊C4—4522no—
172C22⋊C4—2261no—
173C22⋊C4—2261no—
174C22⋊C4—2261no—
175C22⋊C4—2261no—
176C22⋊C4—2261no—
177C22⋊C4—2261no—
178C42—2261no—
179C23—21no—
180C23—4521no—
181C23—4521no—
182C23—2261no—
183C23—2261no—
184C23—2261no—
185C23D4×D11311yescharacteristic
186Q8—4521no—
187Q8—4521no—
188Q8—4521no—
189Q8—2262no—
190Q8—2262no—
191D4—41no—
192D4—41no—
193D4—41no—
194D4—9041no—
195D4—9041no—
196C2×C4—21no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—9041no—
202C2×C4—4521no—
203C2×C4—4521no—
204C2×C4—4521no—
205C2×C4—2262no—
206C2×C4—2261no—
207C2×C4—2261no—
208C2×C4—2261no—
209C2×C4D4×D11311yescharacteristic
210C2×C4C2×D45211yescharacteristic
211C8—41no—
212C8—4521no—
213C22—21no—
214C22—21no—
215C22—41no—
216C22—41no—
217C22—41no—
218C22—9041no—
219C22—4522no—
220C22—4521no—
221C22—4521no—
222C22—4521no—
223C22#1681359211yescharacteristic
224C22#1681364111yescharacteristic
225C22#1681365111yescharacteristic
226C4—21no—
227C4—21no—
228C4—41no—
229C4—81no—
230C4—4521no—
231C4—4521no—
232C4—4522no—
233C4—4521no—
234C2—21no—
235C2—21no—
236C2—81no—
237C2—9041no—
238C2#2029876111yescharacteristic
239C2#2029877711yescharacteristic
240C2#2029878611yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#327×C113C2
socleC22×C113#120
prime radical#20299185C2
hypercenter#327D113
hypocenterC113#1606
LCSG ▷ C22×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #20298756C2semidirect
3. #20298736C2semidirect
4. #20298511C2semidirect
5. #20298334C2semidirect
6. #20298321C2semidirect
7. #327×C113C2semidirect
121. C113#1606semidirect
127. #327D113semidirect

Maximal subgroups

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

subgroupindex
#202991852
#202987562
#202987362
#202985112
#202983342
#202983212
#327×C1132
#1606113