Finite Group Databasebeta

← #28406560

Subgroups — #28406560

Order 14464.

360 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 78 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×#16813701C211yesmaximal, characteristic
2C2×#16813685C212yesmaximal, complemented
3#20299566C211yesmaximal, characteristic
4#20299471C212yesmaximal, complemented
5C22⋊Q8×D113C211yesmaximal, characteristic
6C2×#14268655C2212yes—
7#16813701—24no—
8C2×C4⋊#90673C2212yes—
9C2×C22⋊#90673—21no—
10C2×C4×#90673—21no—
11#16813685—24no—
12#16813679—21no—
13C22⋊#11744753—21no—
14C2×Q8×D113C2211yescharacteristic
15C22×C4×D113C2211yescharacteristic
16#16813602C411yescharacteristic, complemented
17#16813601C411yescharacteristic, complemented
18#16813600—21no—
19#16813599—21no—
20#16813598C411yescharacteristic, complemented
21C4⋊C4×D113—21no—
22C4⋊C4×D113C2211yescharacteristic
23C22⋊C4×D113—21no—
24C22⋊Q8×C113C411yescharacteristic, complemented
25C22×#90673—22no—
26#14268655—22no—
27#14268655—22no—
28C2×#11744753—22no—
29C4⋊#90673—22no—
30C4⋊#90673D414yes—
31C22⋊#90673—24no—
32C4×#90673—24no—
33C23×D113D411yescharacteristic
34C2×Dic226—21no—
35C2×Dic226C2×C411yescharacteristic
36Q8×D113—22no—
37Q8×D113—22no—
38C22×Dic113D411yescharacteristic
39C2×C4×D113—22no—
40C2×C4×D113—22no—
41C2×C4×D113—21no—
42C2×C4×D113—21no—
43C2×C4×D113C2×C411yescharacteristic
44C2×C4×D113D411yescharacteristic
45C2×C4×D113D411yescharacteristic
46C2×C4×D113C2311yescharacteristic
47C4⋊Dic113—21no—
48C4⋊Dic113C2×C411yescharacteristic
49#14268626—21no—
50#14268626—21no—
51#14268626—21no—
52C22⋊Dic113—21no—
53#14268624—21no—
54#14268624—21no—
55C2×Q8×C113C2×C411yescharacteristic
56C22×C4×C113C2×C411yescharacteristic
57C4⋊C4×C113—21no—
58C4⋊C4×C113C2×C411yescharacteristic
59C22⋊C4×C113—21no—
60C23×C113C22⋊C411yescharacteristic
61C22×D113—21no—
62C22×D113—21no—
63C22×D113—22no—
64C22×D113—22no—
65C22×D113C22⋊C411yescharacteristic
66C22×D113C2×D411yescharacteristic
67C2×#90673—24no—
68C2×#90673—42no—
69C2×#90673—42no—
70Q8×C113—22no—
71C2×C4×C113—22no—
72C2×C4×C113—21no—
73C2×C4×C113—21no—
74C2×C4×C113C22⋊C411yescharacteristic
75C2×C4×C113C22×C411yescharacteristic
76C2×Dic113—22no—
77C2×Dic113—21no—
78C2×Dic113—21no—
79C2×Dic113C22⋊C411yescharacteristic
80C2×Dic113C2×D411yescharacteristic
81C4×D113—21no—
82C4×D113—21no—
83C4×D113—22no—
84C4×D113—22no—
85C4×D113—41no—
86C4×D113—41no—
87C4×D113—42no—
88C4×D113C2×D412yes—
89C4×D113#4112yes—
90Dic226—22no—
91Dic226—42no—
92#11744753—42no—
93C22×C113—21no—
94C22×C113—21no—
95C22×C113—21no—
96C22×C113C2×C22⋊C411yescharacteristic
97C2×D113—21no—
98C2×D113—21no—
99C2×D113—21no—
100C2×D113—42no—
101C2×D113—42no—
102C2×D113#12011yescharacteristic
103C2×D113#12311yescharacteristic
104C2×D113#13512yes—
105C2×D113#13712yes—
106#90673—44no—
107C4×C113—21no—
108C4×C113—41no—
109C4×C113—41no—
110C4×C113C4×D412yes—
111Dic113—21no—
112Dic113—41no—
113Dic113—41no—
114Dic113#12112yes—
115C2×C113—41no—
116C2×C113#38611yescharacteristic
117C2×C113#41611yescharacteristic
118C2×C113#41911yescharacteristic
119D113—41no—
120D113#45212yes—
121D113#48512yes—
122#1873—1131nomaximal, Sylow
123C113#187311yescharacteristic, complemented, Sylow
124C2×C22⋊Q8—1131no—
125C2×#117—1131no—
126C2×#103—1132no—
127C2×C22⋊C8—1131no—
128#340—1132no—
129C22×Q8—1131no—
130C23×C4—1131no—
131C22×C8—1132no—
132C22⋊Q8—1131no—
133C22⋊Q8—1131no—
134C22⋊Q8—1131no—
135C22⋊Q8—2261no—
136C22⋊Q8—2261no—
137C22⋊Q8#9067311yescharacteristic, complemented
138#117—2264no—
139C2×C4⋊C4—1132no—
140C2×C4⋊C4—1131no—
141C2×C4⋊C4—2261no—
142C2×C22⋊C4—2261no—
143C2×C22⋊C4—2261no—
144C2×C42—2261no—
145#103—2264no—
146C22⋊C8—2261no—
147C22⋊C8—2261no—
148C24—1131no—
149C2×Q8—1131no—
150C2×Q8—2261no—
151C2×Q8—2262no—
152C2×Q8—2262no—
153C2×Q8C2×#9067311yescharacteristic
154C22×C4—1131no—
155C22×C4—1131no—
156C22×C4—1131no—
157C22×C4—1131no—
158C22×C4—1131no—
159C22×C4—2262no—
160C22×C4—2262no—
161C22×C4—2261no—
162C22×C4—2261no—
163C22×C4—2262no—
164C22×C4C2×#9067311yescharacteristic
165C2×C8—2262no—
166C2×C8—2262no—
167C2×C8—2262no—
168C4⋊C4—21no—
169C4⋊C4—1134no—
170C4⋊C4—1131no—
171C4⋊C4—2261no—
172C4⋊C4—2261no—
173C4⋊C4—2261no—
174C4⋊C4—2262no—
175C4⋊C4—2261no—
176C4⋊C4C2×#9067311yescharacteristic
177C22⋊C4—21no—
178C22⋊C4—2261no—
179C22⋊C4—2261no—
180C22⋊C4—2264no—
181C22⋊C4—2261no—
182C42—2264no—
183C23—1131no—
184C23—1131no—
185C23—2261no—
186C23—2261no—
187C23—2262no—
188C23—2262no—
189C23C22⋊#9067311yescharacteristic
190Q8—22no—
191Q8—4522no—
192Q8—2262no—
193C2×C4—22no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—1131no—
197C2×C4—1132no—
198C2×C4—1132no—
199C2×C4—1131no—
200C2×C4—4521no—
201C2×C4—4521no—
202C2×C4—4522no—
203C2×C4—4522no—
204C2×C4—4522no—
205C2×C4—2262no—
206C2×C4—2261no—
207C2×C4—2261no—
208C2×C4—2262no—
209C2×C4—2264no—
210C2×C4—2261no—
211C2×C4—2261no—
212C2×C4—2262no—
213C2×C4C22⋊#9067311yescharacteristic
214C2×C4C22×#9067311yescharacteristic
215C8—4522no—
216C22—21no—
217C22—21no—
218C22—21no—
219C22—1131no—
220C22—1131no—
221C22—1132no—
222C22—1132no—
223C22—4522no—
224C22—4522no—
225C22—2261no—
226C22—2261no—
227C22—2261no—
228C22C2×C22⋊#9067311yescharacteristic
229C4—21no—
230C4—41no—
231C4—41no—
232C4—1132no—
233C4—4524no—
234C4—4521no—
235C4—4521no—
236C4—2261no—
237C4D4×#9067312yes—
238C2—41no—
239C2—1132no—
240C2—1132no—
241C2—4521no—
242C2#2029954611yescharacteristic
243C2#2029958811yescharacteristic
244C2#2029959111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#90673
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
FittingC22⋊Q8×C113C4
socleC22×C113C2×C22⋊C4
prime radicalC23×D113D4
cosocleC2×C4×D113C23
hypercenterC22⋊Q8#90673
hypocenterC113#1873
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#16813685C2semidirect
4. #20299471C2semidirect
16. #16813602C4semidirect
17. #16813601C4semidirect
20. #16813598C4semidirect
24. C22⋊Q8×C113C4semidirect
123. C113#1873semidirect
137. C22⋊Q8#90673semidirect

Maximal subgroups

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

subgroupindex
C2×#168137012
C2×#168136852
#202995662
#202994712
C22⋊Q8×D1132
#1873113