Finite Group Databasebeta

← #28389600

Subgroups — #28389600

Order 14464.

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

normal subgroups only

This group has 236 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
2#20298934C211yesmaximal, characteristic, complemented
3#20298931C211yesmaximal, characteristic, complemented
4#20298535C211yesmaximal, characteristic
5#20298334C211yesmaximal, characteristic, complemented
6#20298321C211yesmaximal, characteristic
7#328×C113C211yesmaximal, characteristic, complemented
8#16813602—21no—
9#16813601C2211yescharacteristic
10#16813600—21no—
11#16813600—21no—
12#16813599—21no—
13#16813598—21no—
14C2×C4⋊Dic113—21no—
15C2×C4⋊Dic113C2211yescharacteristic
16C2×#14268624—21no—
17C2×#14268624C2211yescharacteristic
18C22⋊C4×D113—21no—
19#16813556—21no—
20#16813555—21no—
21#16813547—21no—
22#16813546—21no—
23C22⋊#11744751C2211yescharacteristic
24C22⋊Q8×C113C2211yescharacteristic
25C22⋊C8×C113C2211yescharacteristic
26#95×C113C2211yescharacteristic
27C23×D113D411yescharacteristic
28C2×Dic226—21no—
29C2×Dic226D411yescharacteristic
30C22×Dic113—21no—
31C22×Dic113D411yescharacteristic
32C2×C4×D113—21no—
33C2×C4×D113—21no—
34C2×#11744751—21no—
35C4⋊Dic113—21no—
36C4⋊Dic113—21no—
37C4⋊Dic113—21no—
38C4⋊Dic113—42no—
39C4⋊Dic113D411yescharacteristic
40#14268626—21no—
41#14268626—21no—
42#14268626—21no—
43C22⋊Dic113—21no—
44#14268624—21no—
45#14268624—21no—
46#14268624—21no—
47#14268624—21no—
48#14268624—42no—
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—41no—
60C22×D113—41no—
61C22×D113Q1612yes—
62Q8×C113—41no—
63C2×C4×C113—22no—
64C2×C4×C113—21no—
65C2×C4×C113—21no—
66C2×C4×C113—41no—
67C2×C4×C113—41no—
68C2×C4×C113—41no—
69C2×C4×C113C2×D411yescharacteristic
70C2×C4×C113C2×D411yescharacteristic
71C2×Dic113—21no—
72C2×Dic113—21no—
73C2×Dic113—21no—
74C2×Dic113—41no—
75C2×Dic113—41no—
76C2×Dic113—41no—
77C2×Dic113—41no—
78C4×D113—81no—
79C4×D113—81no—
80Dic226—41no—
81Dic226—81no—
82C8×C113—41no—
83#11744751—41no—
84C22×C113—21no—
85C22×C113—21no—
86C22×C113#12011yescharacteristic
87C22×C113C2×Q1611yescharacteristic
88C22×C113#13711yescharacteristic
89C2×D113—22no—
90C2×D113—41no—
91C2×D113—41no—
92C2×D113—42no—
93C2×D113—81no—
94C4×C113—21no—
95C4×C113—21no—
96C4×C113—42no—
97C4×C113—41no—
98C4×C113—41no—
99Dic113—41no—
100Dic113—41no—
101Dic113—41no—
102Dic113—81no—
103C2×C113—21no—
104C2×C113—21no—
105C2×C113#45111yescharacteristic
106C2×C113#45311yescharacteristic
107C2×C113#45811yescharacteristic
108D113—42no—
109#1614—1131nomaximal, Sylow
110C113#161411yescharacteristic, complemented, Sylow
111#543—1131no—
112#484—1131no—
113#484—1131no—
114#399—1131no—
115#328—1131no—
116#328D11311yescharacteristic, complemented
117#323—1131no—
118C22⋊Q8—1131no—
119C22⋊Q8—2261no—
120C22⋊Q8—2261no—
121C22⋊Q8—2261no—
122C22⋊Q8—2261no—
123C22⋊Q8—2261no—
124C22⋊Q8C2×D11311yescharacteristic
125C2×C4⋊C4—1131no—
126C2×C4⋊C4—2261no—
127C2×C22⋊C4—1131no—
128C2×C22⋊C4—2261no—
129C2×C22⋊C4—2261no—
130#107—2261no—
131#107—2261no—
132#103—2261no—
133#103—2261no—
134C22⋊C8—1131no—
135C22⋊C8C2×D11311yescharacteristic
136#95C2×D11311yescharacteristic
137C24—1131no—
138C2×Q8—1131no—
139C2×Q8—2261no—
140C2×Q8D45211yescharacteristic
141C22×C4—21no—
142C22×C4—1131no—
143C22×C4—2261no—
144C22×C4—2261no—
145C22×C4—2261no—
146C22×C4C22×D11311yescharacteristic
147C2×C8—21no—
148C2×C8—2261no—
149C4⋊C4—21no—
150C4⋊C4—1131no—
151C4⋊C4—4522no—
152C4⋊C4—2261no—
153C4⋊C4—2261no—
154C4⋊C4—2261no—
155C4⋊C4—2261no—
156C4⋊C4—2261no—
157C4⋊C4—2261no—
158C4⋊C4D45211yescharacteristic
159C22⋊C4—21no—
160C22⋊C4—4522no—
161C22⋊C4—2261no—
162C22⋊C4—2261no—
163C22⋊C4—2261no—
164C22⋊C4—2261no—
165C22⋊C4—2261no—
166C23—1132no—
167C23—4521no—
168C23—4521no—
169C23—2261no—
170C23—2261no—
171C23D4×D11311yescharacteristic
172Q8—41no—
173Q8—9041no—
174Q8—4521no—
175C2×C4—22no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—9041no—
182C2×C4—9041no—
183C2×C4—4521no—
184C2×C4—4521no—
185C2×C4—4521no—
186C2×C4—4521no—
187C2×C4—2261no—
188C2×C4—2261no—
189C2×C4—2261no—
190C2×C4D4×D11311yescharacteristic
191C2×C4C2×D45211yescharacteristic
192C8—41no—
193C8—4521no—
194C22—21no—
195C22—21no—
196C22—9041no—
197C22—4522no—
198C22—4521no—
199C22—4521no—
200C22—2262no—
201C22#1681359211yescharacteristic
202C22Q16×D11311yescharacteristic
203C22#1681365111yescharacteristic
204C4—21no—
205C4—21no—
206C4—42no—
207C4—41no—
208C4—41no—
209C4—9041no—
210C4—4521no—
211C4—4521no—
212C4—4521no—
213C2—21no—
214C2—21no—
215C2—4522no—
216C2#2029875511yescharacteristic
217C2#2029876711yescharacteristic
218C2#2029878911yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#328×C113C2
socleC22×C113#120
prime radicalC23×D113D4
hypercenter#328D113
hypocenterC113#1614
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. #20298934C2semidirect
3. #20298931C2semidirect
5. #20298334C2semidirect
7. #328×C113C2semidirect
110. C113#1614semidirect
116. #328D113semidirect

Maximal subgroups

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

subgroupindex
#202992232
#202989342
#202989312
#202985352
#202983342
#202983212
#328×C1132
#1614113