Finite Group Databasebeta

← #28391714

Subgroups — #28391714

Order 14464.

290 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 87 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
1C2×#16813621C211yesmaximal, characteristic
2C2×#16813547C211yesmaximal, characteristic
3C2×#16813545C211yesmaximal, characteristic
4#20298503C211yesmaximal, characteristic
5#20298360C211yesmaximal, characteristic
6#20298352C211yesmaximal, characteristic
7#340×C113C211yesmaximal, characteristic
8C22×Dic226—21no—
9C22×Dic226C2211yescharacteristic
10C22×#11744751C2211yescharacteristic
11#16813621—22no—
12#16813621—22no—
13C2×C4⋊Dic113C2211yescharacteristic
14C2×#14268626—21no—
15C2×C4×Dic113C2211yescharacteristic
16#16813547—22no—
17#16813545—22no—
18#16813529—21no—
19#16813529—21no—
20C22×C8×C113C2211yescharacteristic
21C2×C4⋊C4×C113C2211yescharacteristic
22C2×C4⋊C4×C113C2211yescharacteristic
23C2×Dic226—21no—
24C2×Dic226—21no—
25C2×Dic226—21no—
26C2×Dic226—21no—
27C2×Dic226—24no—
28C2×Dic226—21no—
29C2×Dic226—42no—
30C2×Dic226—42no—
31C2×Dic226Q812yescomplemented
32C22×Dic113—21no—
33C22×Dic113—21no—
34C22×Dic113D411yescharacteristic
35C22×Dic113D411yescharacteristic
36C2×#11744751—21no—
37C2×#11744751—21no—
38C2×#11744751—21no—
39C4⋊Dic113—21no—
40C4⋊Dic113D412yes—
41#14268626—24no—
42C4×Dic113—21no—
43C4×Dic113—21no—
44C22×C4×C113—21no—
45C22×C4×C113—21no—
46C22×C4×C113C2311yescharacteristic
47C2×C8×C113—21no—
48C2×C8×C113—21no—
49C2×C8×C113—21no—
50C4⋊C4×C113—21no—
51C4⋊C4×C113—21no—
52C4⋊C4×C113—21no—
53C4⋊C4×C113D412yes—
54C23×C113C2×D411yescharacteristic
55C2×C4×C113—22no—
56C2×C4×C113—41no—
57C2×C4×C113—41no—
58C2×C4×C113—41no—
59C2×C4×C113—41no—
60C2×C4×C113—41no—
61C2×C4×C113C2×D411yescharacteristic
62C2×C4×C113C2×D411yescharacteristic
63C2×C4×C113C2×Q811yescharacteristic
64C2×C4×C113#4111yescharacteristic
65C2×C4×C113#4111yescharacteristic
66C2×C4×C113#4111yescharacteristic
67C2×Dic113—21no—
68C2×Dic113—21no—
69C2×Dic113—21no—
70C2×Dic113—21no—
71C2×Dic113—22no—
72C2×Dic113—22no—
73C2×Dic113—41no—
74C2×Dic113—41no—
75C2×Dic113—41no—
76C2×Dic113—41no—
77C2×Dic113SD1612yes—
78C2×Dic113Q1612yes—
79Dic226—22no—
80Dic226—22no—
81Dic226—48no—
82Dic226—41no—
83Dic226—41no—
84C8×C113—41no—
85#11744751—41no—
86C22×C113#12011yescharacteristic
87C22×C113C22⋊Q811yescharacteristic
88C22×C113#12411yescharacteristic
89C22×C113C2×SD1611yescharacteristic
90C22×C113C2×Q1611yescharacteristic
91C22×C113AGL(1,ℤ/8)11yescharacteristic
92C22×C113#13711yescharacteristic
93C4×C113—42no—
94C4×C113—81no—
95C4×C113C22⋊Q811yescharacteristic
96C4×C113C22⋊Q811yescharacteristic
97C4×C113#12411yescharacteristic
98C4×C113#12411yescharacteristic
99Dic113—22no—
100Dic113—22no—
101Dic113—42no—
102Dic113—42no—
103C2×C113#39311yescharacteristic
104C2×C113#45011yescharacteristic
105C2×C113#45111yescharacteristic
106C2×C113#47511yescharacteristic
107C2×C113#47711yescharacteristic
108C2×C113#48711yescharacteristic
109C2×C113#48911yescharacteristic
110#2024—1131nomaximal, Sylow
111C113#202411yescharacteristic, complemented, Sylow
112C2×C4⋊Q8—1131no—
113C2×#103—1131no—
114C2×#103—1131no—
115#391—1131no—
116#340—1131no—
117#340D11311yescharacteristic
118#336—1131no—
119C22×Q8—1131no—
120C22×Q8—2261no—
121C22×C8—1131no—
122C22×C8C2×D11311yescharacteristic
123C4⋊Q8—2262no—
124C4⋊Q8—2262no—
125C2×C4⋊C4—1131no—
126C2×C4⋊C4—2261no—
127C2×C4⋊C4C2×D11311yescharacteristic
128C2×C4⋊C4C2×D11311yescharacteristic
129C2×C42—1131no—
130#103—2262no—
131#103—2262no—
132#95—2261no—
133#95—2261no—
134C2×Q8—1132no—
135C2×Q8—4522no—
136C2×Q8—4522no—
137C2×Q8—2264no—
138C2×Q8—2261no—
139C2×Q8—2261no—
140C2×Q8—2261no—
141C2×Q8—2261no—
142C2×Q8—2261no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—1131no—
146C22×C4—1131no—
147C22×C4—2261no—
148C22×C4—2261no—
149C22×C4C22×D11311yescharacteristic
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—2261no—
154C2×C8—2261no—
155C2×C8—2261no—
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—1132no—
160C4⋊C4—2264no—
161C4⋊C4—2261no—
162C4⋊C4D45212yes—
163C42—2261no—
164C42—2261no—
165C23D4×D11311yescharacteristic
166Q8—4528no—
167Q8—4521no—
168Q8—4521no—
169Q8—2262no—
170Q8—2262no—
171C2×C4—22no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—1132no—
178C2×C4—1132no—
179C2×C4—4521no—
180C2×C4—4521no—
181C2×C4—4521no—
182C2×C4—4521no—
183C2×C4—2262no—
184C2×C4—2262no—
185C2×C4—2261no—
186C2×C4—2261no—
187C2×C4—2261no—
188C2×C4—2261no—
189C2×C4D4×D11311yescharacteristic
190C2×C4C2×D45211yescharacteristic
191C2×C4Q8×D11311yescharacteristic
192C2×C4#1426864611yescharacteristic
193C2×C4#1426864711yescharacteristic
194C2×C4#1426864711yescharacteristic
195C8—41no—
196C8—4521no—
197C22#1681359211yescharacteristic
198C22#1681360011yescharacteristic
199C22#1681360811yescharacteristic
200C22SD16×D11311yescharacteristic
201C22Q16×D11311yescharacteristic
202C22#1681364611yescharacteristic
203C22#1681365111yescharacteristic
204C4—42no—
205C4—81no—
206C4—4522no—
207C4—4522no—
208C4—2262no—
209C4—2262no—
210C4#1681360011yescharacteristic
211C4#1681360211yescharacteristic
212C4#1681360811yescharacteristic
213C4#1681361011yescharacteristic
214C2#2029851111yescharacteristic
215C2#2029875011yescharacteristic
216C2#2029875511yescharacteristic
217C2#2029888211yescharacteristic
218C2#2029889211yescharacteristic
219C2#2029894711yescharacteristic
220C2#2029895611yescharacteristic
subgroupG/H
centerC23D4×D113
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#340×C113C2
socle, prime radicalC23×C113C2×D4
hypercenter#340D113
hypocenterC113#2024
LCSG ▷ C22×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
31. C2×Dic226Q8semidirect
111. C113#2024semidirect

Maximal subgroups

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

subgroupindex
C2×#168136212
C2×#168135472
C2×#168135452
#202985032
#202983602
#202983522
#340×C1132
#2024113