Finite Group Databasebeta

← #28389591

Subgroups — #28389591

Order 14464.

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

normal subgroups only

This group has 232 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#20298926C211yesmaximal, characteristic, complemented
3#20298912C211yesmaximal, characteristic, complemented
4#20298525C211yesmaximal, 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⋊Dic113C2211yescharacteristic
16C2×#14268624—21no—
17C2×#14268624C2211yescharacteristic
18#16813556—21no—
19#16813553—21no—
20#16813546—21no—
21#16813544—21no—
22C22⋊#11744751C2211yescharacteristic
23#16813529—21no—
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⋊Dic113D411yescharacteristic
39#14268626—21no—
40#14268624—21no—
41#14268624—21no—
42#14268624—21no—
43#14268624—21no—
44#14268624—21no—
45#14268624—21no—
46#14268624—42no—
47C4×Dic113—21no—
48C2×Q8×C113D411yescharacteristic
49C22×C4×C113—21no—
50C22×C4×C113C2311yescharacteristic
51C2×C8×C113—21no—
52C4⋊C4×C113—21no—
53C4⋊C4×C113D411yescharacteristic
54C22⋊C4×C113—21no—
55C23×C113C2×D411yescharacteristic
56C22×D113—21no—
57C22×D113—21no—
58C22×D113—21no—
59C22×D113—21no—
60C22×D113—41no—
61C22×D113—41no—
62Q8×C113—41no—
63C2×C4×C113—21no—
64C2×C4×C113—21no—
65C2×C4×C113—41no—
66C2×C4×C113—41no—
67C2×C4×C113—41no—
68C2×C4×C113—41no—
69C2×C4×C113C2×D411yescharacteristic
70C2×C4×C113C2×D411yescharacteristic
71C22⋊D113—41no—
72C22⋊D113—41no—
73C2×Dic113—21no—
74C2×Dic113—21no—
75C2×Dic113—41no—
76C2×Dic113—41no—
77C2×Dic113—41no—
78C2×Dic113—41no—
79D452—41no—
80D452—81no—
81D452—81no—
82C4×D113—81no—
83C8×C113—41no—
84#11744751—41no—
85C22×C113—21no—
86C22×C113—21no—
87C22×C113#12011yescharacteristic
88C22×C113#13511yescharacteristic
89C22×C113AGL(1,ℤ/8)11yescharacteristic
90C2×D113—42no—
91C2×D113—41no—
92C2×D113—41no—
93C2×D113—41no—
94C2×D113—41no—
95C2×D113—41no—
96C2×D113—41no—
97C2×D113—81no—
98C4×C113—21no—
99C4×C113—21no—
100C4×C113—41no—
101C4×C113—41no—
102C4×C113—81no—
103Dic113—41no—
104Dic113—41no—
105Dic113—81no—
106C2×C113—21no—
107C2×C113—21no—
108C2×C113#44911yescharacteristic
109C2×C113#45511yescharacteristic
110C2×C113#45811yescharacteristic
111D113—81no—
112D113—81no—
113#1612—1131nomaximal, Sylow
114C113#161211yescharacteristic, complemented, Sylow
115#538—1131no—
116#483—1131no—
117#480—1131no—
118#397—1131no—
119#328D11311yescharacteristic, complemented
120#327—1131no—
121#323—1131no—
122#126—2261no—
123#124—2261no—
124#123—2261no—
125C22⋊Q8C2×D11311yescharacteristic
126#121—1131no—
127#121—2261no—
128#120—2261no—
129C4×D4—2261no—
130C2×C4⋊C4—1131no—
131C2×C22⋊C4—1131no—
132C2×C22⋊C4—2261no—
133#107—2261no—
134#106—2261no—
135#103—2261no—
136#102—2261no—
137C22⋊C8—1131no—
138C22⋊C8C2×D11311yescharacteristic
139#95—2261no—
140#95C2×D11311yescharacteristic
141C24—1131no—
142C2×Q8D45211yescharacteristic
143C2×D4—1131no—
144C2×D4—2261no—
145C2×D4—2261no—
146C2×D4—2261no—
147C22×C4—21no—
148C22×C4—1131no—
149C22×C4—2261no—
150C22×C4—2261no—
151C22×C4C22×D11311yescharacteristic
152C2×C8—21no—
153C2×C8—2261no—
154C4⋊C4—21no—
155C4⋊C4—1131no—
156C4⋊C4—2261no—
157C4⋊C4—2261no—
158C4⋊C4—2261no—
159C4⋊C4D45211yescharacteristic
160C22⋊C4—21no—
161C22⋊C4—4522no—
162C22⋊C4—2261no—
163C22⋊C4—2261no—
164C22⋊C4—2261no—
165C22⋊C4—2261no—
166C22⋊C4—2261no—
167C22⋊C4—2261no—
168C42—2261no—
169C23—4521no—
170C23—4521no—
171C23—2261no—
172C23—2261no—
173C23—2261no—
174C23—2261no—
175C23D4×D11311yescharacteristic
176Q8—41no—
177D4—9041no—
178D4—9041no—
179D4—4521no—
180D4—4521no—
181D4—4521no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—9041no—
189C2×C4—4521no—
190C2×C4—4521no—
191C2×C4—4521no—
192C2×C4—4521no—
193C2×C4—2261no—
194C2×C4—2261no—
195C2×C4D4×D11311yescharacteristic
196C2×C4C2×D45211yescharacteristic
197C8—41no—
198C8—4521no—
199C22—21no—
200C22—21no—
201C22—9041no—
202C22—4522no—
203C22—4521no—
204C22—4521no—
205C22—4521no—
206C22—4521no—
207C22—4521no—
208C22—4521no—
209C22#1681359211yescharacteristic
210C22#1681364511yescharacteristic
211C22#1681364911yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—41no—
216C4—81no—
217C4—9041no—
218C4—4521no—
219C4—4521no—
220C2—21no—
221C2—21no—
222C2—9041no—
223C2—9041no—
224C2#2029874611yescharacteristic
225C2#2029877711yescharacteristic
226C2#2029878911yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#328×C113C2
socleC22×C113#120
prime radical#20299188C2
hypercenter#328D113
hypocenterC113#1612
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. #20298926C2semidirect
3. #20298912C2semidirect
4. #20298525C2semidirect
5. #20298331C2semidirect
6. #20298321C2semidirect
7. #328×C113C2semidirect
114. C113#1612semidirect
119. #328D113semidirect

Maximal subgroups

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

subgroupindex
#202991882
#202989262
#202989122
#202985252
#202983312
#202983212
#328×C1132
#1612113