Finite Group Databasebeta

← #28389515

Subgroups — #28389515

Order 14464.

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

normal subgroups only

This group has 266 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#20299227C211yesmaximal, characteristic, complemented
2#20298751C211yesmaximal, characteristic
3#20298748C211yesmaximal, characteristic
4#20298516C211yesmaximal, characteristic
5#20298334C211yesmaximal, characteristic, complemented
6#20298323C211yesmaximal, characteristic, complemented
7#328×C113C211yesmaximal, characteristic, complemented
8C22×D452C2211yescharacteristic
9C2×#14268636—21no—
10C2×#14268634—21no—
11#16813621—21no—
12#16813620—21no—
13#16813612—21no—
14#16813612—21no—
15#16813601C2211yescharacteristic
16#16813599—21no—
17#16813578—21no—
18C2×#14268626C2211yescharacteristic
19C2×#14268624—21no—
20C2×#14268624—21no—
21#16813544—21no—
22#16813542—21no—
23C22⋊#11744751C2211yescharacteristic
24C22⋊Q8×C113C2211yescharacteristic
25C22⋊C8×C113C2211yescharacteristic
26#95×C113C2211yescharacteristic
27C23×D113—21no—
28C2×Dic226—21no—
29C2×Dic226D411yescharacteristic
30C2×D452—21no—
31C2×D452—21no—
32C2×D452—42no—
33C22×Dic113D411yescharacteristic
34C22×Dic113D411yescharacteristic
35#14268636—42no—
36#14268634—42no—
37C2×#11744751—21no—
38C4⋊Dic113—21no—
39C4⋊Dic113D411yescharacteristic
40#14268626—21no—
41#14268626—21no—
42#14268626—21no—
43#14268626—21no—
44#14268626—21no—
45#14268626—21no—
46#14268626—21no—
47C22⋊Dic113—21no—
48#14268624—42no—
49#14268624—42no—
50C4×Dic113—21no—
51C4×Dic113—21no—
52C2×Q8×C113D411yescharacteristic
53C22×C4×C113—21no—
54C22×C4×C113C2311yescharacteristic
55C2×C8×C113—21no—
56C4⋊C4×C113—21no—
57C4⋊C4×C113D411yescharacteristic
58C22⋊C4×C113—21no—
59C23×C113C2×D411yescharacteristic
60C22×D113—22no—
61C22×D113—41no—
62C22×D113—41no—
63C22×D113—41no—
64C22×D113—41no—
65C22×D113—41no—
66C22×D113—41no—
67Q8×C113—41no—
68C2×C4×C113—21no—
69C2×C4×C113—21no—
70C2×C4×C113—41no—
71C2×C4×C113—41no—
72C2×C4×C113—41no—
73C2×C4×C113—41no—
74C2×C4×C113C2×D411yescharacteristic
75C2×C4×C113C2×D411yescharacteristic
76C2×Dic113—21no—
77C2×Dic113—21no—
78C2×Dic113—21no—
79C2×Dic113—21no—
80C2×Dic113—21no—
81C2×Dic113—41no—
82C2×Dic113SD1612yescomplemented
83D452—22no—
84D452—22no—
85D452—41no—
86D452—41no—
87Dic226—41no—
88Dic226—81no—
89C8×C113—41no—
90#11744751—41no—
91C22×C113—21no—
92C22×C113—21no—
93C22×C113#12011yescharacteristic
94C22×C113C2×SD1611yescharacteristic
95C22×C113#13711yescharacteristic
96C2×D113—42no—
97C2×D113—42no—
98C2×D113—42no—
99C2×D113—81no—
100C2×D113—81no—
101C2×D113—81no—
102C2×D113—81no—
103C4×C113—21no—
104C4×C113—21no—
105C4×C113—41no—
106C4×C113—41no—
107C4×C113—81no—
108Dic113—22no—
109Dic113—41no—
110Dic113—41no—
111Dic113—41no—
112C2×C113—21no—
113C2×C113—21no—
114C2×C113#44811yescharacteristic
115C2×C113#45411yescharacteristic
116C2×C113B(4,𝔽2)11yescharacteristic
117D113—82no—
118#1599—1131nomaximal, Sylow
119C113#159911yescharacteristic, complemented, Sylow
120#544—1131no—
121#450—1131no—
122#450—1131no—
123#394—1131no—
124#328—1131no—
125#328D11311yescharacteristic, complemented
126#324—1131no—
127C22×D4—1131no—
128C2×SD16—2261no—
129C2×SD16—2261no—
130C4⋊Q8—2261no—
131C4⋊Q8—2261no—
132#125—2261no—
133#125—2261no—
134C22⋊Q8—1131no—
135C22⋊Q8—2261no—
136C22⋊Q8C2×D11311yescharacteristic
137#117—2261no—
138C2×C4⋊C4—1131no—
139C2×C22⋊C4—2261no—
140C2×C22⋊C4—2261no—
141#102—2261no—
142#102—2261no—
143C22⋊C8—1131no—
144C22⋊C8C2×D11311yescharacteristic
145#95C2×D11311yescharacteristic
146C24—2261no—
147C2×Q8—1131no—
148C2×Q8—2261no—
149C2×Q8D45211yescharacteristic
150C2×D4—4522no—
151C2×D4—2261no—
152C2×D4—2261no—
153C22×C4—21no—
154C22×C4—1131no—
155C22×C4—1131no—
156C22×C4C22×D11311yescharacteristic
157SD16—4522no—
158SD16—4522no—
159C2×C8—21no—
160C2×C8—2261no—
161C4⋊C4—21no—
162C4⋊C4—1131no—
163C4⋊C4—2261no—
164C4⋊C4—2261no—
165C4⋊C4—2261no—
166C4⋊C4—2261no—
167C4⋊C4—2261no—
168C4⋊C4—2261no—
169C4⋊C4—2261no—
170C4⋊C4—2261no—
171C4⋊C4D45211yescharacteristic
172C22⋊C4—21no—
173C22⋊C4—4522no—
174C22⋊C4—4522no—
175C22⋊C4—2261no—
176C42—2261no—
177C42—2261no—
178C23—4521no—
179C23—4521no—
180C23—4521no—
181C23—4521no—
182C23—4521no—
183C23—4521no—
184C23—2262no—
185C23D4×D11311yescharacteristic
186Q8—41no—
187Q8—9041no—
188Q8—4521no—
189D4—4521no—
190D4—4521no—
191D4—2262no—
192D4—2262no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—1132no—
200C2×C4—4521no—
201C2×C4—2261no—
202C2×C4—2261no—
203C2×C4—2261no—
204C2×C4—2261no—
205C2×C4—2261no—
206C2×C4D4×D11311yescharacteristic
207C2×C4C2×D45211yescharacteristic
208C8—41no—
209C8—4521no—
210C22—21no—
211C22—21no—
212C22—9041no—
213C22—9041no—
214C22—9041no—
215C22—9041no—
216C22—4522no—
217C22—4522no—
218C22—4522no—
219C22#1681359211yescharacteristic
220C22SD16×D11311yescharacteristic
221C22#1681365411yescharacteristic
222C4—21no—
223C4—21no—
224C4—41no—
225C4—41no—
226C4—81no—
227C4—4521no—
228C4—4521no—
229C4—4521no—
230C4—2262no—
231C2—21no—
232C2—21no—
233C2—9042no—
234C2#2029873811yescharacteristic
235C2#2029877211yescharacteristic
236C2#2029878611yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#328×C113C2
socleC22×C113#120
prime radicalC22×D452C22
hypercenter#328D113
hypocenterC113#1599
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. #20299227C2semidirect
5. #20298334C2semidirect
6. #20298323C2semidirect
7. #328×C113C2semidirect
82. C2×Dic113SD16semidirect
119. C113#1599semidirect
125. #328D113semidirect

Maximal subgroups

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

subgroupindex
#202992272
#202987512
#202987482
#202985162
#202983342
#202983232
#328×C1132
#1599113