Finite Group Databasebeta

← #28391658

Subgroups — #28391658

Order 14464.

406 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C22×#14268636C211yesmaximal, characteristic
2C22×#14268634C211yesmaximal, characteristic
3C2×#16813620C211yesmaximal, characteristic, complemented
4C2×#16813545C211yesmaximal, characteristic, complemented
5#20298499C211yesmaximal, characteristic
6#20298352C211yesmaximal, characteristic, complemented
7C2×#103×C113C211yesmaximal, characteristic, complemented
8C22×Dic226C2211yescharacteristic
9C22×D452C2211yescharacteristic
10C2×#14268636—22no—
11C2×#14268636—22no—
12C2×#14268636—22no—
13C2×#14268634—22no—
14C2×#14268634—22no—
15C2×#14268634—22no—
16C22×#11744751C2211yescharacteristic
17#16813620—22no—
18#16813620—22no—
19C2×#14268626—22no—
20C2×#14268624—22no—
21C2×C4×Dic113C2211yescharacteristic
22#16813545—22no—
23C22×Q8×C113C2211yescharacteristic
24C22×C8×C113C2211yescharacteristic
25C2×C4⋊C4×C113C2211yescharacteristic
26#103×C113—22no—
27C23×D113—21no—
28C2×Dic226—21no—
29C2×Dic226—21no—
30C2×Dic226—21no—
31C2×Dic226—21no—
32C2×Dic226—21no—
33C2×Dic226D412yes—
34C2×D452—21no—
35C2×D452—21no—
36C2×D452—21no—
37C2×D452—21no—
38C2×D452—21no—
39C2×D452D412yes—
40C22×Dic113—21no—
41C22×Dic113D412yes—
42#14268636—28no—
43#14268634—28no—
44C2×#11744751—21no—
45C2×#11744751—21no—
46C2×#11744751D412yes—
47#14268626—28no—
48#14268624—44no—
49C4×Dic113—21no—
50C4×Dic113—21no—
51C2×Q8×C113—21no—
52C2×Q8×C113—21no—
53C2×Q8×C113—21no—
54C2×Q8×C113—21no—
55C2×Q8×C113—21no—
56C2×Q8×C113D412yes—
57C22×C4×C113—21no—
58C22×C4×C113—21no—
59C22×C4×C113C2311yescharacteristic
60C2×C8×C113—21no—
61C2×C8×C113—21no—
62C2×C8×C113D412yes—
63C4⋊C4×C113—21no—
64C4⋊C4×C113—21no—
65C23×C113C2×D411yescharacteristic
66C22×D113—22no—
67C22×D113—41no—
68C22×D113—41no—
69C22×D113—42no—
70C22×D113—42no—
71Q8×C113—22no—
72Q8×C113—22no—
73Q8×C113—41no—
74Q8×C113—41no—
75C2×C4×C113—22no—
76C2×C4×C113—41no—
77C2×C4×C113—41no—
78C2×C4×C113—41no—
79C2×C4×C113—42no—
80C2×C4×C113C2×D411yescharacteristic
81C2×C4×C113C2×D411yescharacteristic
82C2×C4×C113C2×D411yescharacteristic
83C2×C4×C113C2×D411yescharacteristic
84C2×C4×C113C2×D411yescharacteristic
85C2×C4×C113#4111yescharacteristic
86C2×Dic113—22no—
87C2×Dic113—22no—
88C2×Dic113—22no—
89C2×Dic113—41no—
90C2×Dic113—41no—
91C2×Dic113SD1614yescomplemented
92D452—22no—
93D452—22no—
94D452—41no—
95D452—41no—
96Dic226—22no—
97Dic226—22no—
98Dic226—41no—
99Dic226—41no—
100C8×C113—22no—
101#11744751—22no—
102C22×C113#12011yescharacteristic
103C22×C113#12111yescharacteristic
104C22×C113#12711yescharacteristic
105C22×C113C2×SD1612yes—
106C22×C113#13712yes—
107C2×D113—42no—
108C2×D113—44no—
109C2×D113—82no—
110C2×D113—81no—
111C2×D113—81no—
112C4×C113—42no—
113C4×C113—81no—
114C4×C113#12011yescharacteristic
115C4×C113#12011yescharacteristic
116C4×C113#12111yescharacteristic
117C4×C113#12111yescharacteristic
118Dic113—24no—
119Dic113—42no—
120C2×C113#39211yescharacteristic
121C2×C113#44812yes—
122C2×C113#46112yes—
123C2×C113#49211yescharacteristic
124C2×C113#49711yescharacteristic
125D113—82no—
126#2013—1131nomaximal, Sylow
127C113#201311yescharacteristic, complemented, Sylow
128C22×SD16—1131no—
129C22×SD16—1131no—
130C2×C4⋊Q8—1131no—
131C2×#103—1131no—
132C2×#103D11311yescharacteristic, complemented
133#390—1131no—
134#336—1131no—
135C22×Q8—1131no—
136C22×Q8C2×D11311yescharacteristic
137C22×D4—1131no—
138C2×SD16—2262no—
139C2×SD16—2262no—
140C2×SD16—2262no—
141C2×SD16—2262no—
142C2×SD16—2262no—
143C2×SD16—2262no—
144C22×C8—1131no—
145C22×C8C2×D11311yescharacteristic
146C4⋊Q8—2262no—
147C4⋊Q8—2262no—
148C2×C4⋊C4—2262no—
149C2×C4⋊C4C2×D11311yescharacteristic
150C2×C22⋊C4—2262no—
151C2×C42—1131no—
152#103—22no—
153#103—2262no—
154C24—2261no—
155C2×Q8—21no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—21no—
159C2×Q8—21no—
160C2×Q8—1132no—
161C2×Q8—2261no—
162C2×Q8—2261no—
163C2×Q8—2261no—
164C2×Q8—2261no—
165C2×Q8—2261no—
166C2×Q8D45212yes—
167C2×D4—1132no—
168C2×D4—2261no—
169C2×D4—2261no—
170C2×D4—2261no—
171C2×D4—2261no—
172C2×D4—2261no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—1132no—
176C22×C4—2261no—
177C22×C4C22×D11311yescharacteristic
178SD16—2268no—
179SD16—2268no—
180C2×C8—21no—
181C2×C8—21no—
182C2×C8—1132no—
183C2×C8—2261no—
184C2×C8—2261no—
185C2×C8C22⋊D11312yes—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—2268no—
189C22⋊C4—4524no—
190C42—2261no—
191C42—2261no—
192C23—4521no—
193C23—4521no—
194C23—4522no—
195C23—4522no—
196C23—2262no—
197C23D4×D11311yescharacteristic
198Q8—22no—
199Q8—22no—
200Q8—41no—
201Q8—41no—
202Q8—4521no—
203Q8—4521no—
204Q8—2262no—
205Q8—2262no—
206D4—4521no—
207D4—4521no—
208D4—2262no—
209D4—2262no—
210C2×C4—22no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—1134no—
216C2×C4—4521no—
217C2×C4—4521no—
218C2×C4—2262no—
219C2×C4—2262no—
220C2×C4—2262no—
221C2×C4D4×D11311yescharacteristic
222C2×C4D4×D11311yescharacteristic
223C2×C4D4×D11311yescharacteristic
224C2×C4C2×C22⋊D11311yescharacteristic
225C2×C4C2×D45211yescharacteristic
226C2×C4#1426864711yescharacteristic
227C8—22no—
228C8—2262no—
229C22—9041no—
230C22—9041no—
231C22—9042no—
232C22—4522no—
233C22—4524no—
234C22#1681359211yescharacteristic
235C22#1681359511yescharacteristic
236C22#1681361811yescharacteristic
237C22SD16×D11312yes—
238C22#1681365412yes—
239C4—42no—
240C4—81no—
241C4—4522no—
242C4—2264no—
243C4#1681359011yescharacteristic
244C4#1681359211yescharacteristic
245C4#1681359511yescharacteristic
246C4#1681359611yescharacteristic
247C2—9042no—
248C2#2029850711yescharacteristic
249C2#2029873812yes—
250C2#2029880212yes—
251C2#2029896911yescharacteristic
252C2#2029899111yescharacteristic
subgroupG/H
centerC23D4×D113
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
FittingC2×#103×C113C2
socleC23×C113C2×D4
prime radicalC22×D452C22
hypercenterC2×#103D113
hypocenterC113#2013
LCSG ▷ C22×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
3. C2×#16813620C2semidirect
4. C2×#16813545C2semidirect
6. #20298352C2semidirect
7. C2×#103×C113C2semidirect
91. C2×Dic113SD16semidirect
127. C113#2013semidirect
132. C2×#103D113semidirect

Maximal subgroups

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

subgroupindex
C22×#142686362
C22×#142686342
C2×#168136202
C2×#168135452
#202984992
#202983522
C2×#103×C1132
#2013113