Finite Group Databasebeta

← #28389625

Subgroups — #28389625

Order 14464.

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

normal subgroups only

This group has 240 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#20299188C211yesmaximal, characteristic
2#20298931C211yesmaximal, characteristic, complemented
3#20298917C211yesmaximal, characteristic, complemented
4#20298535C211yesmaximal, characteristic, complemented
5#20298331C211yesmaximal, characteristic, complemented
6#20298321C211yesmaximal, characteristic, complemented
7#328×C113C211yesmaximal, characteristic, complemented
8#16813617—21no—
9#16813611—21no—
10#16813607—21no—
11#16813597—21no—
12#16813596C2211yescharacteristic
13#16813592—21no—
14#16813582—21no—
15C2×C4⋊Dic113—21no—
16C2×C4⋊Dic113C2211yescharacteristic
17C2×#14268624—21no—
18C2×#14268624C2211yescharacteristic
19#16813555—21no—
20#16813554—21no—
21#16813546—21no—
22#16813544—21no—
23C22⋊#11744751C2211yescharacteristic
24C22⋊Q8×C113C2211yescharacteristic
25C22⋊C8×C113C2211yescharacteristic
26#95×C113C2211yescharacteristic
27C23×D113D411yescharacteristic
28C2×D452—21no—
29C2×D452—21no—
30C2×D452D411yescharacteristic
31C2×C22⋊D113—21no—
32C22×Dic113—21no—
33C22×Dic113D411yescharacteristic
34C2×C4×D113—21no—
35C2×#11744751—21no—
36C4⋊Dic113—21no—
37C4⋊Dic113—21no—
38C4⋊Dic113—42no—
39C4⋊Dic113D411yescharacteristic
40#14268626—21no—
41#14268624—21no—
42#14268624—21no—
43#14268624—21no—
44#14268624—21no—
45#14268624—21no—
46#14268624—21no—
47#14268624—42no—
48C4×Dic113—21no—
49C2×Q8×C113D411yescharacteristic
50C22×C4×C113—21no—
51C22×C4×C113C2311yescharacteristic
52C2×C8×C113—21no—
53C4⋊C4×C113—21no—
54C4⋊C4×C113D411yescharacteristic
55C22⋊C4×C113—21no—
56C23×C113C2×D411yescharacteristic
57C22×D113—21no—
58C22×D113—21no—
59C22×D113—21no—
60C22×D113—21no—
61C22×D113—41no—
62C22×D113—41no—
63Q8×C113—41no—
64C2×C4×C113—22no—
65C2×C4×C113—21no—
66C2×C4×C113—21no—
67C2×C4×C113—41no—
68C2×C4×C113—41no—
69C2×C4×C113—41no—
70C2×C4×C113C2×D411yescharacteristic
71C2×C4×C113C2×D411yescharacteristic
72C22⋊D113—41no—
73C22⋊D113—41no—
74C2×Dic113—21no—
75C2×Dic113—21no—
76C2×Dic113—41no—
77C2×Dic113—41no—
78C2×Dic113—41no—
79C2×Dic113—41no—
80D452—41no—
81D452—81no—
82D452—81no—
83C4×D113—81no—
84C8×C113—41no—
85#11744751—41no—
86C22×C113—21no—
87C22×C113—21no—
88C22×C113#12011yescharacteristic
89C22×C113#13511yescharacteristic
90C22×C113#13711yescharacteristic
91C2×D113—42no—
92C2×D113—41no—
93C2×D113—41no—
94C2×D113—41no—
95C2×D113—41no—
96C2×D113—41no—
97C2×D113—41no—
98C2×D113—81no—
99C4×C113—21no—
100C4×C113—21no—
101C4×C113—42no—
102C4×C113—41no—
103C4×C113—41no—
104Dic113—41no—
105Dic113—41no—
106Dic113—81no—
107C2×C113—21no—
108C2×C113—21no—
109C2×C113#45211yescharacteristic
110C2×C113#45311yescharacteristic
111C2×C113#45811yescharacteristic
112D113—81no—
113D113—81no—
114#1618—1131nomaximal, Sylow
115C113#161811yescharacteristic, complemented, Sylow
116#538—1131no—
117#484—1131no—
118#481—1131no—
119#399—1131no—
120#328D11311yescharacteristic, complemented
121#327—1131no—
122#323—1131no—
123#126—2261no—
124#124—2261no—
125#123—2261no—
126C22⋊Q8C2×D11311yescharacteristic
127#121—1131no—
128#121—2261no—
129#120—2261no—
130C4×D4—2261no—
131C2×C4⋊C4—1131no—
132C2×C4⋊C4—2261no—
133C2×C22⋊C4—1131no—
134C2×C22⋊C4—2261no—
135#107—2261no—
136#106—2261no—
137#103—2261no—
138#102—2261no—
139C22⋊C8—1131no—
140C22⋊C8C2×D11311yescharacteristic
141#95C2×D11311yescharacteristic
142C24—1131no—
143C2×Q8D45211yescharacteristic
144C2×D4—1131no—
145C2×D4—2261no—
146C2×D4—2261no—
147C2×D4—2261no—
148C22×C4—21no—
149C22×C4—1131no—
150C22×C4—2261no—
151C22×C4—2261no—
152C22×C4C22×D11311yescharacteristic
153C2×C8—21no—
154C2×C8—2261no—
155C4⋊C4—21no—
156C4⋊C4—1131no—
157C4⋊C4—4522no—
158C4⋊C4—2261no—
159C4⋊C4—2261no—
160C4⋊C4—2261no—
161C4⋊C4D45211yescharacteristic
162C22⋊C4—21no—
163C22⋊C4—4522no—
164C22⋊C4—2261no—
165C22⋊C4—2261no—
166C22⋊C4—2261no—
167C22⋊C4—2261no—
168C22⋊C4—2261no—
169C22⋊C4—2261no—
170C42—2261no—
171C23—4521no—
172C23—4521no—
173C23—2261no—
174C23—2261no—
175C23—2261no—
176C23—2261no—
177C23D4×D11311yescharacteristic
178Q8—41no—
179D4—9041no—
180D4—9041no—
181D4—4521no—
182D4—4521no—
183D4—4521no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—9041no—
191C2×C4—4521no—
192C2×C4—4521no—
193C2×C4—4521no—
194C2×C4—4521no—
195C2×C4—2261no—
196C2×C4—2261no—
197C2×C4D4×D11311yescharacteristic
198C2×C4C2×D45211yescharacteristic
199C8—41no—
200C8—4521no—
201C22—21no—
202C22—21no—
203C22—9041no—
204C22—4522no—
205C22—4521no—
206C22—4521no—
207C22—4521no—
208C22—4521no—
209C22—4521no—
210C22—4521no—
211C22#1681359211yescharacteristic
212C22#1681364311yescharacteristic
213C22#1681365411yescharacteristic
214C4—21no—
215C4—21no—
216C4—42no—
217C4—41no—
218C4—41no—
219C4—9041no—
220C4—4521no—
221C4—4521no—
222C2—21no—
223C2—21no—
224C2—9041no—
225C2—9041no—
226C2#2029876311yescharacteristic
227C2#2029876711yescharacteristic
228C2#2029878911yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#328×C113C2
socleC22×C113#120
prime radical#20299188C2
hypercenter#328D113
hypocenterC113#1618
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
2. #20298931C2semidirect
3. #20298917C2semidirect
4. #20298535C2semidirect
5. #20298331C2semidirect
6. #20298321C2semidirect
7. #328×C113C2semidirect
115. C113#1618semidirect
120. #328D113semidirect

Maximal subgroups

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

subgroupindex
#202991882
#202989312
#202989172
#202985352
#202983312
#202983212
#328×C1132
#1618113