Finite Group Databasebeta

← #28406719

Subgroups — #28406719

Order 14464.

348 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 82 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×#16813690C211yesmaximal, characteristic, complemented
2C2×#16813685C211yesmaximal, characteristic, complemented
3C2×#16813684C211yesmaximal, characteristic
4C2×C8×#90673C211yesmaximal, characteristic, complemented
5(C2×#90673)⋊Q8C211yesmaximal, characteristic, complemented
6#20299550C211yesmaximal, characteristic
7C2×SD16×D113C211yesmaximal, characteristic
8C2×#14268655C2211yescharacteristic
9C2×C4⋊#90673C2211yescharacteristic
10C2×C4⋊#90673C2211yescharacteristic
11C2×C22⋊#90673—22no—
12C2×C4×#90673C2211yescharacteristic
13#16813690—22no—
14#16813685—22no—
15#16813684—22no—
16C8×#90673—22no—
17(C2×#90673)⋊C4—22no—
18C2×Q8×D113C2211yescharacteristic
19C2×D4×D113C2211yescharacteristic
20C2×#14268636C411yescharacteristic, complemented
21C2×#14268635C411yescharacteristic, complemented
22C2×#14268634C411yescharacteristic, complemented
23SD16×D113—22no—
24SD16×D113—22no—
25C2×C8×D113C2211yescharacteristic
26C2×SD16×C113C411yescharacteristic, complemented
27C22×#90673—21no—
28C22×#90673—21no—
29C22×#90673D412yes—
30#14268655—21no—
31#14268655D412yes—
32C2×#11744753—21no—
33C4⋊#90673—21no—
34C4⋊#90673—21no—
35C4⋊#90673—21no—
36C4⋊#90673—21no—
37C22⋊#90673—44no—
38C4×#90673—21no—
39C4×#90673—21no—
40C23×D113—21no—
41C2×Dic226—21no—
42C2×Dic226C2×C411yescharacteristic
43Q8×D113—21no—
44Q8×D113—21no—
45Q8×D113—21no—
46Q8×D113—21no—
47C2×D452C2×C411yescharacteristic
48C2×C22⋊D113—21no—
49D4×D113—21no—
50D4×D113—21no—
51D4×D113—21no—
52D4×D113—21no—
53C2×C4×D113—21no—
54C2×C4×D113C2311yescharacteristic
55#14268636—22no—
56#14268635—22no—
57#14268634—22no—
58C2×#11744751C2×C411yescharacteristic
59C8×D113D412yes—
60C8×D113D412yes—
61C2×Q8×C113C2×C411yescharacteristic
62C2×D4×C113C2×C411yescharacteristic
63SD16×C113—22no—
64C2×C8×C113C2×C411yescharacteristic
65C23×C113—21no—
66C22×D113—21no—
67C22×D113—41no—
68C22×D113—41no—
69C22×D113—42no—
70C22×D113—42no—
71C22×D113C2×D411yescharacteristic
72C2×#90673—22no—
73C2×#90673—22no—
74C2×#90673—41no—
75C2×#90673—41no—
76C2×#90673—42no—
77C2×#90673—42no—
78C2×#90673SD1614yescomplemented
79Q8×C113—21no—
80Q8×C113—21no—
81D4×C113—21no—
82D4×C113—21no—
83C2×C4×C113—21no—
84C2×C4×C113C22×C411yescharacteristic
85C22⋊D113—41no—
86C22⋊D113—41no—
87C2×Dic113—21no—
88C2×Dic113#4111yescharacteristic
89D452—21no—
90D452—21no—
91C4×D113—41no—
92C4×D113—41no—
93C4×D113C2×D411yescharacteristic
94C4×D113C2×D411yescharacteristic
95C4×D113C2×D411yescharacteristic
96C4×D113#4111yescharacteristic
97Dic226—21no—
98Dic226—21no—
99Dic226—41no—
100Dic226—41no—
101#11744753—22no—
102C8×C113C22⋊C412yescomplemented
103#11744751C22⋊C412yescomplemented
104C22×C113—41no—
105C22×C113—42no—
106C22×C113C4×D411yescharacteristic
107C2×D113—41no—
108C2×D113—42no—
109C2×D113—82no—
110C2×D113—81no—
111C2×D113—81no—
112C2×D113#12111yescharacteristic
113C2×D113#12711yescharacteristic
114C2×D113C2×SD1612yes—
115C2×D113#13512yes—
116#90673—24no—
117#90673—81no—
118#90673—81no—
119C4×C113—41no—
120C4×C113C2×C22⋊C411yescharacteristic
121C4×C113C4×D411yescharacteristic
122Dic113—41no—
123Dic113#12111yescharacteristic
124Dic113#12411yescharacteristic
125C2×C113—81no—
126C2×C113#39011yescharacteristic
127C2×C113C4×SD1612yes—
128D113—81no—
129D113#46512yes—
130D113#49211yescharacteristic
131D113#49511yescharacteristic
132#1968—1131nomaximal, Sylow
133C113#196811yescharacteristic, complemented, Sylow
134C22×SD16—1131no—
135C2×#106—1131no—
136C2×#103—1131no—
137C2×#102—1131no—
138C2×C4×C8—1131no—
139#391—1131no—
140#390—1131no—
141C22×Q8—1131no—
142C22×D4—1131no—
143C2×SD16—1131no—
144C2×SD16—1131no—
145C2×SD16—1131no—
146C2×SD16—2262no—
147C2×SD16—2262no—
148C2×SD16#9067311yescharacteristic, complemented
149C22×C8—1131no—
150C22×C8—1131no—
151C2×C4⋊C4—1131no—
152C2×C4⋊C4—1131no—
153C2×C22⋊C4—2262no—
154C2×C42—1131no—
155#106—2262no—
156#103—2262no—
157#102—2262no—
158C4×C8—2262no—
159#95—2262no—
160C24—2261no—
161C2×Q8—1131no—
162C2×Q8—2261no—
163C2×Q8—2261no—
164C2×Q8—2261no—
165C2×Q8—2261no—
166C2×Q8—2261no—
167C2×Q8C2×#9067311yescharacteristic
168C2×D4—1131no—
169C2×D4—2261no—
170C2×D4—2261no—
171C2×D4—2261no—
172C2×D4—2261no—
173C2×D4—2261no—
174C2×D4C2×#9067311yescharacteristic
175C22×C4—1131no—
176C22×C4—1132no—
177C22×C4—2261no—
178C22×C4—2261no—
179C22×C4—2261no—
180SD16—22no—
181SD16—2262no—
182SD16—2262no—
183SD16—2262no—
184C2×C8—1131no—
185C2×C8—1132no—
186C2×C8—1132no—
187C2×C8—1132no—
188C2×C8—2261no—
189C2×C8—2261no—
190C2×C8C2×#9067311yescharacteristic
191C4⋊C4—2261no—
192C4⋊C4—2261no—
193C4⋊C4—2261no—
194C4⋊C4—2261no—
195C22⋊C4—4524no—
196C42—2261no—
197C42—2261no—
198C23—21no—
199C23—1131no—
200C23—4522no—
201C23—4521no—
202C23—4521no—
203C23—4522no—
204C23—2261no—
205Q8—21no—
206Q8—21no—
207Q8—4521no—
208Q8—4521no—
209Q8—2261no—
210Q8—2261no—
211D4—21no—
212D4—21no—
213D4—4521no—
214D4—4521no—
215D4—2261no—
216D4—2261no—
217C2×C4—21no—
218C2×C4—1131no—
219C2×C4—1131no—
220C2×C4—1131no—
221C2×C4—1131no—
222C2×C4—1131no—
223C2×C4—1134no—
224C2×C4—4521no—
225C2×C4—4521no—
226C2×C4—4522no—
227C2×C4—4521no—
228C2×C4—4521no—
229C2×C4—4522no—
230C2×C4—2261no—
231C2×C4—2262no—
232C2×C4—2262no—
233C2×C4C22×#9067311yescharacteristic
234C8—1132no—
235C8—2262no—
236C8C22⋊#9067312yescomplemented
237C22—41no—
238C22—42no—
239C22—1131no—
240C22—1131no—
241C22—1132no—
242C22—1132no—
243C22—9041no—
244C22—9041no—
245C22—9042no—
246C22—4521no—
247C22—4522no—
248C22D4×#9067311yescharacteristic
249C4—41no—
250C4—1131no—
251C4—1131no—
252C4—9041no—
253C4—9041no—
254C4—4521no—
255C4—2264no—
256C4C2×C22⋊#9067311yescharacteristic
257C4D4×#9067311yescharacteristic
258C2—81no—
259C2—1131no—
260C2—1131no—
261C2—1132no—
262C2—9041no—
263C2#2029955011yescharacteristic
264C2SD16×#9067312yes—
subgroupG/H
centerC22D4×#90673
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
FittingC2×SD16×C113C4
socleC22×C113C4×D4
prime radicalC2×D4×D113C22
cosocleC2×C4×D113C23
hypercenterC2×SD16#90673
hypocenterC113#1968
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#16813690C2semidirect
2. C2×#16813685C2semidirect
4. C2×C8×#90673C2semidirect
5. (C2×#90673)⋊Q8C2semidirect
20. C2×#14268636C4semidirect
21. C2×#14268635C4semidirect
22. C2×#14268634C4semidirect
26. C2×SD16×C113C4semidirect
78. C2×#90673SD16semidirect
102. C8×C113C22⋊C4semidirect
103. #11744751C22⋊C4semidirect
133. C113#1968semidirect
148. C2×SD16#90673semidirect
236. C8C22⋊#90673semidirect

Maximal subgroups

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

subgroupindex
C2×#168136902
C2×#168136852
C2×#168136842
C2×C8×#906732
(C2×#90673)⋊Q82
#202995502
C2×SD16×D1132
#1968113