Finite Group Databasebeta

← #28406718

Subgroups — #28406718

Order 14464.

312 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 70 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#20299601C211yesmaximal, characteristic, complemented
2C2×#16813683C212yesmaximal, complemented
3C2×#16813682C212yesmaximal
4C4×#14268656C211yesmaximal, characteristic, complemented
5C2×#16813608C211yesmaximal, characteristic
6C2×#14268656C2212yes—
7C2×#14268656C2212yes—
8#16813689—21no—
9C4⋊#11744753—21no—
10#16813683—24no—
11#16813682—24no—
12#16813677—21no—
13C4×#11744753—21no—
14C22×Dic226C2211yescharacteristic
15C22×C22⋊D113C2211yescharacteristic
16#16813608—21no—
17#16813608—21no—
18#16813608—21no—
19#16813608—21no—
20C2×C22⋊Dic113C411yescharacteristic
21C2×#14268624C411yescharacteristic
22C2×#14268624C411yescharacteristic
23C2×C4×Dic113C2211yescharacteristic
24C2×C22⋊C4×C113C411yescharacteristic
25#14268656—22no—
26#14268656—22no—
27#14268656—22no—
28#14268656D414yes—
29C2×#11744753—22no—
30C2×#11744753—22no—
31C23×D113C2×C411yescharacteristic
32C2×Dic226—21no—
33C2×Dic226—21no—
34C2×Dic226—22no—
35C2×Dic226—22no—
36C2×C22⋊D113—21no—
37C2×C22⋊D113—21no—
38C2×C22⋊D113—22no—
39C2×C22⋊D113—22no—
40C22×Dic113C2×C411yescharacteristic
41C22×Dic113C2×C411yescharacteristic
42C22×Dic113C2311yescharacteristic
43C22⋊Dic113—21no—
44C22⋊Dic113—21no—
45#14268624—21no—
46#14268624—21no—
47#14268624—21no—
48#14268624—21no—
49C4×Dic113D411yescharacteristic
50C4×Dic113D411yescharacteristic
51C4×Dic113D411yescharacteristic
52C4×Dic113D411yescharacteristic
53C24×C113C2×C411yescharacteristic
54C22×C4×C113C2×C411yescharacteristic
55C22×C4×C113C2×C411yescharacteristic
56C22⋊C4×C113—21no—
57C22⋊C4×C113—21no—
58C23×C113—21no—
59C23×C113—22no—
60C23×C113—41no—
61C23×C113—41no—
62C23×C113C22×C411yescharacteristic
63C22×D113—21no—
64C22×D113—22no—
65C22×D113—41no—
66C22×D113—41no—
67C2×C4×C113—21no—
68C2×C4×C113—22no—
69C2×C4×C113—41no—
70C2×C4×C113C22⋊C411yescharacteristic
71C2×C4×C113C22⋊C411yescharacteristic
72C22⋊D113—42no—
73C22⋊D113—41no—
74C22⋊D113—41no—
75C2×Dic113—21no—
76C2×Dic113—22no—
77C2×Dic113—41no—
78C2×Dic113C22⋊C411yescharacteristic
79C2×Dic113C22⋊C411yescharacteristic
80C2×Dic113C2×D411yescharacteristic
81C2×Dic113C2×D412yes—
82C2×Dic113C2×D411yescharacteristic
83C2×Dic113#4112yes—
84Dic226—42no—
85Dic226—41no—
86Dic226—41no—
87#11744753—24no—
88#11744753—42no—
89C22×C113—21no—
90C22×C113—21no—
91C22×C113—41no—
92C22×C113—41no—
93C22×C113—41no—
94C22×C113—82no—
95C22×C113C2×C22⋊C411yescharacteristic
96C22×C113C4×D412yes—
97C2×D113—41no—
98C2×D113—41no—
99C2×D113—41no—
100C2×D113—82no—
101C4×C113—21no—
102C4×C113—21no—
103C4×C113—41no—
104Dic113—21no—
105Dic113—21no—
106Dic113—41no—
107Dic113#12112yes—
108Dic113#12411yescharacteristic
109Dic113#12711yescharacteristic
110C2×C113—22no—
111C2×C113—81no—
112C2×C113#39011yescharacteristic
113C2×C113#41311yescharacteristic
114C2×C113#41311yescharacteristic
115D113—81no—
116#1967—1131nomaximal, Sylow
117C113#196711yescharacteristic, complemented, Sylow
118C2×#124—1131no—
119#423—1131no—
120C2×#101—1132no—
121C2×#100—1132no—
122C4×M16—1131no—
123C22×Q8—1131no—
124C22×D4—1131no—
125C2×M16—1132no—
126C2×M16—1132no—
127#124—2261no—
128#124—2261no—
129#124—2261no—
130#124—2261no—
131C2×C22⋊C4—1131no—
132C2×C22⋊C4—1131no—
133C2×C22⋊C4—1131no—
134C2×C22⋊C4#9067311yescharacteristic
135C2×C42—1131no—
136C4⋊C8—2261no—
137C4⋊C8—2261no—
138#101—2264no—
139#100—2264no—
140#97—2261no—
141C4×C8—2261no—
142C24—1131no—
143C24C2×#9067311yescharacteristic
144C2×Q8—2262no—
145C2×Q8—2261no—
146C2×Q8—2261no—
147C2×Q8—2262no—
148C2×D4—2262no—
149C2×D4—2261no—
150C2×D4—2261no—
151C2×D4—2262no—
152C22×C4—1131no—
153C22×C4—1131no—
154C22×C4—1131no—
155C22×C4C2×#9067311yescharacteristic
156C22×C4C2×#9067311yescharacteristic
157M16—1134no—
158M16—2262no—
159M16—2262no—
160M16—2262no—
161C2×C8—2262no—
162C2×C8—2262no—
163C22⋊C4—21no—
164C22⋊C4—21no—
165C22⋊C4—2261no—
166C22⋊C4—2261no—
167C22⋊C4—2261no—
168C22⋊C4—2261no—
169C22⋊C4—2261no—
170C22⋊C4—2261no—
171C42—1131no—
172C42—1131no—
173C42—1131no—
174C42—1131no—
175C23—21no—
176C23—22no—
177C23—41no—
178C23—41no—
179C23—4521no—
180C23—4521no—
181C23—2262no—
182C23—2261no—
183C23C22×#9067311yescharacteristic
184Q8—4521no—
185Q8—4522no—
186Q8—4521no—
187D4—4521no—
188D4—4522no—
189D4—4521no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—41no—
193C2×C4—1131no—
194C2×C4—1131no—
195C2×C4—1132no—
196C2×C4—1132no—
197C2×C4—1131no—
198C2×C4—1131no—
199C2×C4—4521no—
200C2×C4—2261no—
201C2×C4—2262no—
202C2×C4C22⋊#9067311yescharacteristic
203C2×C4C22⋊#9067311yescharacteristic
204C8—4522no—
205C8—2264no—
206C22—21no—
207C22—21no—
208C22—41no—
209C22—41no—
210C22—41no—
211C22—82no—
212C22—9042no—
213C22—4521no—
214C22—4521no—
215C22—4521no—
216C22C2×C22⋊#9067311yescharacteristic
217C22D4×#9067312yes—
218C4—21no—
219C4—21no—
220C4—41no—
221C4—1131no—
222C4—1132no—
223C4—1131no—
224C4—4521no—
225C4—2261no—
226C4—2261no—
227C2—22no—
228C2—81no—
229C2—9041no—
230C2#2029955011yescharacteristic
231C2#2029958411yescharacteristic
232C2#2029958511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#90673
commutatorC23×C113C22×C4
FrattiniC23C22×#90673
FittingC2×C22⋊C4×C113C4
socleC22×C113C2×C22⋊C4
prime radicalC22×C22⋊D113C22
cosocleC22×Dic113C23
hypercenterC2×C22⋊C4#90673
hypocenterC113#1967
LCSG ▷ C23×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #20299601C2semidirect
2. C2×#16813683C2semidirect
4. C4×#14268656C2semidirect
117. C113#1967semidirect

Maximal subgroups

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

subgroupindex
#202996012
C2×#168136832
C2×#168136822
C4×#142686562
C2×#168136082
#1967113