Finite Group Databasebeta

← #28389498

Subgroups — #28389498

Order 14464.

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

normal subgroups only

This group has 316 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#20299223C211yesmaximal, characteristic, complemented
2#20298751C211yesmaximal, characteristic, complemented
3#20298748C211yesmaximal, characteristic, complemented
4#20298508C211yesmaximal, characteristic
5#20298334C211yesmaximal, characteristic, complemented
6#20298321C211yesmaximal, characteristic, complemented
7#328×C113C211yesmaximal, characteristic, complemented
8C22×D452—21no—
9C22×D452C2211yescharacteristic
10C2×#14268636—21no—
11C2×#14268634—21no—
12#16813602—21no—
13#16813601C2211yescharacteristic
14#16813600—21no—
15#16813600—21no—
16#16813599—21no—
17#16813598—21no—
18C2×#14268624—21no—
19C2×#14268624C2211yescharacteristic
20C22⋊C4×D113—21no—
21#16813544—21no—
22#16813542—21no—
23C22⋊#11744751C2211yescharacteristic
24C22⋊Q8×C113C2211yescharacteristic
25C22⋊C8×C113C2211yescharacteristic
26#95×C113C2211yescharacteristic
27C23×D113—21no—
28C23×D113D411yescharacteristic
29C2×Dic226—21no—
30C2×Dic226D411yescharacteristic, complemented
31C2×D452—21no—
32C2×D452—21no—
33C2×D452—42no—
34C2×D452—42no—
35C2×D452—42no—
36C2×D452—42no—
37C22×Dic113D411yescharacteristic
38C2×C4×D113—21no—
39C2×C4×D113—21no—
40#14268636—42no—
41#14268634—42no—
42C2×#11744751—21no—
43C4⋊Dic113—21no—
44C4⋊Dic113D411yescharacteristic, complemented
45#14268626—21no—
46#14268626—21no—
47#14268626—21no—
48C22⋊Dic113—21no—
49#14268624—21no—
50#14268624—21no—
51#14268624—21no—
52#14268624—21no—
53#14268624—42no—
54C2×Q8×C113D411yescharacteristic, complemented
55C22×C4×C113—21no—
56C22×C4×C113C2311yescharacteristic
57C2×C8×C113—21no—
58C4⋊C4×C113—21no—
59C4⋊C4×C113D411yescharacteristic, complemented
60C22⋊C4×C113—21no—
61C23×C113C2×D411yescharacteristic
62C22×D113—21no—
63C22×D113—21no—
64C22×D113—22no—
65C22×D113—41no—
66C22×D113—41no—
67C22×D113—41no—
68C22×D113—41no—
69C22×D113—41no—
70C22×D113—41no—
71C22×D113—41no—
72C22×D113—41no—
73C22×D113SD1612yescomplemented
74Q8×C113—41no—
75C2×C4×C113—22no—
76C2×C4×C113—21no—
77C2×C4×C113—21no—
78C2×C4×C113—41no—
79C2×C4×C113—41no—
80C2×C4×C113—41no—
81C2×C4×C113C2×D411yescharacteristic
82C2×C4×C113C2×D411yescharacteristic
83C2×Dic113—21no—
84C2×Dic113—21no—
85C2×Dic113—21no—
86C2×Dic113—41no—
87D452—22no—
88D452—22no—
89D452—41no—
90D452—41no—
91D452—48no—
92C4×D113—81no—
93C4×D113—81no—
94Dic226—41no—
95Dic226—81no—
96C8×C113—41no—
97#11744751—41no—
98C22×C113—21no—
99C22×C113—21no—
100C22×C113#12011yescharacteristic
101C22×C113C2×SD1611yescharacteristic
102C22×C113#13711yescharacteristic
103C2×D113—22no—
104C2×D113—41no—
105C2×D113—41no—
106C2×D113—42no—
107C2×D113—42no—
108C2×D113—42no—
109C2×D113—42no—
110C2×D113—81no—
111C2×D113—81no—
112C2×D113—81no—
113C2×D113—81no—
114C2×D113—81no—
115C4×C113—21no—
116C4×C113—21no—
117C4×C113—42no—
118C4×C113—41no—
119C4×C113—41no—
120Dic113—41no—
121Dic113—41no—
122Dic113—41no—
123C2×C113—21no—
124C2×C113—21no—
125C2×C113#44811yescharacteristic
126C2×C113#45311yescharacteristic
127C2×C113B(4,𝔽2)11yescharacteristic
128D113—42no—
129D113—82no—
130#1596—1131nomaximal, Sylow
131C113#159611yescharacteristic, complemented, Sylow
132#543—1131no—
133#450—1131no—
134#450—1131no—
135#392—1131no—
136#328—1131no—
137#328D11311yescharacteristic, complemented
138#323—1131no—
139C22×D4—1131no—
140C22×D4—2261no—
141C2×SD16—2261no—
142C2×SD16—2261no—
143C22⋊Q8—1131no—
144C22⋊Q8—2261no—
145C22⋊Q8—2261no—
146C22⋊Q8—2261no—
147C22⋊Q8—2261no—
148C22⋊Q8—2261no—
149C22⋊Q8C2×D11311yescharacteristic
150C2×C22⋊C4—1131no—
151C2×C22⋊C4—2261no—
152C2×C22⋊C4—2261no—
153#102—2261no—
154#102—2261no—
155C22⋊C8—1131no—
156C22⋊C8C2×D11311yescharacteristic
157#95C2×D11311yescharacteristic
158C24—1131no—
159C24—2261no—
160C2×Q8—1131no—
161C2×Q8—2261no—
162C2×Q8D45211yescharacteristic, complemented
163C2×D4—4522no—
164C2×D4—4522no—
165C2×D4—4522no—
166C2×D4—4522no—
167C2×D4—2261no—
168C2×D4—2261no—
169C22×C4—21no—
170C22×C4—1131no—
171C22×C4—2261no—
172C22×C4—2261no—
173C22×C4C22×D11311yescharacteristic
174SD16—4522no—
175SD16—4522no—
176C2×C8—21no—
177C2×C8—2261no—
178C4⋊C4—21no—
179C4⋊C4—1131no—
180C4⋊C4—2261no—
181C4⋊C4—2261no—
182C4⋊C4—2261no—
183C4⋊C4—2261no—
184C4⋊C4D45211yescharacteristic, complemented
185C22⋊C4—21no—
186C22⋊C4—4522no—
187C22⋊C4—2261no—
188C22⋊C4—2261no—
189C22⋊C4—2261no—
190C22⋊C4—2261no—
191C22⋊C4—2261no—
192C23—1132no—
193C23—4521no—
194C23—4521no—
195C23—4521no—
196C23—4521no—
197C23—4521no—
198C23—4521no—
199C23—4521no—
200C23—4521no—
201C23—2262no—
202C23—2261no—
203C23—2261no—
204C23D4×D11311yescharacteristic
205Q8—41no—
206Q8—9041no—
207Q8—4521no—
208D4—4521no—
209D4—4521no—
210D4—4528no—
211D4—2262no—
212D4—2262no—
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—9041no—
220C2×C4—9041no—
221C2×C4—4521no—
222C2×C4—2261no—
223C2×C4—2261no—
224C2×C4—2261no—
225C2×C4D4×D11311yescharacteristic
226C2×C4C2×D45211yescharacteristic
227C8—41no—
228C8—4521no—
229C22—21no—
230C22—21no—
231C22—9041no—
232C22—9041no—
233C22—9041no—
234C22—9041no—
235C22—9041no—
236C22—4522no—
237C22—4522no—
238C22—4522no—
239C22—4522no—
240C22—4521no—
241C22—4521no—
242C22—2262no—
243C22#1681359211yescharacteristic
244C22SD16×D11311yescharacteristic
245C22#1681365411yescharacteristic
246C4—21no—
247C4—21no—
248C4—42no—
249C4—41no—
250C4—41no—
251C4—4521no—
252C4—4521no—
253C4—4521no—
254C2—21no—
255C2—21no—
256C2—9042no—
257C2—4522no—
258C2#2029873811yescharacteristic
259C2#2029876711yescharacteristic
260C2#2029878611yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#328×C113C2
socleC22×C113#120
prime radical#20298508C2
hypercenter#328D113
hypocenterC113#1596
LCSG ▷ C22×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
1. #20299223C2semidirect
2. #20298751C2semidirect
3. #20298748C2semidirect
5. #20298334C2semidirect
6. #20298321C2semidirect
7. #328×C113C2semidirect
30. C2×Dic226D4semidirect
44. C4⋊Dic113D4semidirect
54. C2×Q8×C113D4semidirect
59. C4⋊C4×C113D4semidirect
73. C22×D113SD16semidirect
131. C113#1596semidirect
137. #328D113semidirect
162. C2×Q8D452semidirect
184. C4⋊C4D452semidirect

Maximal subgroups

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

subgroupindex
#202992232
#202987512
#202987482
#202985082
#202983342
#202983212
#328×C1132
#1596113