Finite Group Databasebeta

← #28401641

Subgroups — #28401641

Order 14464.

396 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 109 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#20299209C211yesmaximal, characteristic, complemented
2#20299166C211yesmaximal, characteristic
3#20298972C211yesmaximal, characteristic, complemented
4#20298963C211yesmaximal, characteristic, complemented
5#20298952C211yesmaximal, characteristic, complemented
6#20298822C212yesmaximal, complemented
7#20298796C212yesmaximal, complemented
8#20298759C212yesmaximal, complemented
9#20298747C212yesmaximal, complemented
10#20298660C211yesmaximal, characteristic, complemented
11#497×C113C211yesmaximal, characteristic, complemented
12C2×#14268648C2211yescharacteristic
13C2×D4×D113C2211yescharacteristic
14C2×#14268634C2212yes—
15C2×#14268634C2212yescomplemented
16#16813619C2211yescharacteristic
17#16813618C2211yescharacteristic
18#16813617—22no—
19#16813614C2211yescharacteristic, complemented
20#16813612—22no—
21#16813611C2211yescharacteristic
22#16813598C2212yes—
23#16813595—22no—
24#16813592—22no—
25Q8×Dic113C2212yescomplemented
26#16813579C2211yescharacteristic
27#16813551C2212yescomplemented
28#16813546C2212yescomplemented
29#16813544C2212yes—
30#16813544C2212yescomplemented
31#16813543C2212yes—
32#16813534C2212yes—
33C4×#11744751C2211yescharacteristic, complemented
34C2×Q16×C113C2212yescomplemented
35C2×SD16×C113C2212yes—
36C4⋊Q8×C113C2211yescharacteristic, complemented
37#124×C113C2211yescharacteristic
38#97×C113C2211yescharacteristic, complemented
39C23×D113—21no—
40#14268648—42no—
41C2×D452—21no—
42C2×D452—22no—
43C2×D452C2311yescharacteristic
44C2×D452C2311yescharacteristic
45C2×C22⋊D113—21no—
46C2×C22⋊D113—22no—
47D4×D113—42no—
48C2×C4×D113—21no—
49C2×C4×D113C2311yescharacteristic
50#14268634—42no—
51#14268634—42no—
52C2×#11744751C2312yes—
53C4⋊Dic113—22no—
54C4⋊Dic113C2312yes—
55#14268626—22no—
56#14268626—22no—
57#14268626D412yes—
58#14268624—22no—
59#14268624—22no—
60#14268624D412yes—
61C4×Dic113—22no—
62C4×Dic113C2311yescharacteristic
63C2×Q8×C113C2312yes—
64C2×Q8×C113C2311yescharacteristic
65C2×D4×C113C2311yescharacteristic
66Q16×C113—42no—
67SD16×C113—42no—
68C2×C8×C113C2312yes—
69C4⋊C4×C113—22no—
70C22⋊C4×C113—22no—
71C42×C113C2311yescharacteristic
72C23×C113—21no—
73C22×D113—21no—
74C22×D113—21no—
75C22×D113—42no—
76C22×D113—82no—
77C22×D113C2×D411yescharacteristic
78Q8×C113—22no—
79Q8×C113—22no—
80Q8×C113—22no—
81D4×C113—22no—
82C2×C4×C113—21no—
83C2×C4×C113—22no—
84C2×C4×C113C2×D412yes—
85C2×C4×C113C2411yescharacteristic
86C22⋊D113—42no—
87C22⋊D113—82no—
88C2×Dic113—22no—
89C2×Dic113C2×D412yes—
90C2×Dic113C2×D411yescharacteristic
91D452—22no—
92D452—22no—
93D452—42no—
94D452—82no—
95C4×D113—22no—
96C4×D113—42no—
97C8×C113—22no—
98#11744751—22no—
99C22×C113—41no—
100C22×C113—42no—
101C22×C113C22×D411yescharacteristic
102C2×D113—21no—
103C2×D113—22no—
104C2×D113—41no—
105C2×D113—41no—
106C2×D113—42no—
107C2×D113—42no—
108C2×D113—84no—
109C4×C113—22no—
110C4×C113—41no—
111C4×C113—42no—
112C4×C113H(5,𝔽2)12yes—
113Dic113—21no—
114Dic113—22no—
115Dic113—42no—
116C2×C113—81no—
117C2×C113#53511yescharacteristic
118C2×C113#57712yes—
119D113—41no—
120D113—81no—
121D113—81no—
122#3222—1131nomaximal, Sylow
123C113#322211yescharacteristic, complemented, Sylow
124#541—1131no—
125#535—1131no—
126#497D11311yescharacteristic, complemented
127#492—1131no—
128#490—1131no—
129#488—1131no—
130#464—1132no—
131#460—1132no—
132#452—1132no—
133#450—1132no—
134#433—1131no—
135C2×#41—1131no—
136C22×D4—1131no—
137C2×Q16C2×D11312yescomplemented
138C2×SD16—1132no—
139C2×SD16—1132no—
140C2×SD16C2×D11312yes—
141C4⋊Q8C2×D11311yescharacteristic, complemented
142#127—1131no—
143#127—1131no—
144#126—2262no—
145#125—1131no—
146#125—2262no—
147#124—1131no—
148#124C2×D11311yescharacteristic
149C22⋊Q8—1132no—
150#121—2262no—
151#120—2262no—
152C4×Q8—1132no—
153#117—1131no—
154C4⋊C8—1132no—
155#103—1132no—
156#102—1132no—
157#102—1132no—
158#102—1132no—
159C22⋊C8—1132no—
160#97C2×D11311yescharacteristic, complemented
161C4×C8—1131no—
162C24—2261no—
163#41—4522no—
164C2×Q8C22×D11311yescharacteristic
165C2×Q8C22×D11312yes—
166C2×D4—1131no—
167C2×D4—1131no—
168C2×D4—4522no—
169C2×D4—2261no—
170C2×D4—2262no—
171C2×D4—2261no—
172C2×D4—2262no—
173C2×D4C22×D11311yescharacteristic
174C22×C4—1131no—
175C22×C4—2261no—
176Q16—42no—
177SD16—42no—
178SD16—4522no—
179SD16—4522no—
180C2×C8—1132no—
181C2×C8C22×D11312yes—
182C4⋊C4—22no—
183C4⋊C4—1132no—
184C4⋊C4—1132no—
185C4⋊C4—2262no—
186C4⋊C4—2262no—
187C4⋊C4—2262no—
188C22⋊C4—22no—
189C22⋊C4—1132no—
190C22⋊C4—2262no—
191C22⋊C4—2262no—
192C42—1131no—
193C42—2262no—
194C42C22×D11311yescharacteristic
195C23—21no—
196C23—1131no—
197C23—9042no—
198C23—4522no—
199C23—2261no—
200C23—2261no—
201Q8—22no—
202Q8—22no—
203Q8—22no—
204D4—22no—
205D4—9042no—
206D4—9042no—
207D4—4522no—
208D4—4522no—
209D4—2262no—
210D4—2262no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—1132no—
214C2×C4—1131no—
215C2×C4—4522no—
216C2×C4—2262no—
217C2×C4—2262no—
218C2×C4D4×D11312yes—
219C2×C4C23×D11311yescharacteristic
220C8—22no—
221C8—2262no—
222C22—42no—
223C22—41no—
224C22—9044no—
225C22—4522no—
226C22—4522no—
227C22—4521no—
228C22—4521no—
229C22—2262no—
230C22—2261no—
231C22C2×D4×D11311yescharacteristic
232C4—22no—
233C4—41no—
234C4—42no—
235C4—4522no—
236C4—2262no—
237C4—2261no—
238C4#1681366712yes—
239C2—81no—
240C2—9041no—
241C2—9041no—
242C2—4521no—
243C2#2029916111yescharacteristic
244C2#2029940712yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#497×C113C2
socleC22×C113C22×D4
prime radical#20299166C2
hypercenter#497D113
hypocenterC113#3222
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. #20299209C2semidirect
3. #20298972C2semidirect
4. #20298963C2semidirect
5. #20298952C2semidirect
6. #20298822C2semidirect
7. #20298796C2semidirect
8. #20298759C2semidirect
9. #20298747C2semidirect
10. #20298660C2semidirect
11. #497×C113C2semidirect
15. C2×#14268634C22semidirect
19. #16813614C22semidirect
25. Q8×Dic113C22semidirect
27. #16813551C22semidirect
28. #16813546C22semidirect
30. #16813544C22semidirect
33. C4×#11744751C22semidirect
34. C2×Q16×C113C22semidirect
36. C4⋊Q8×C113C22semidirect
38. #97×C113C22semidirect
123. C113#3222semidirect
126. #497D113semidirect
137. C2×Q16C2×D113semidirect
141. C4⋊Q8C2×D113semidirect
160. #97C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202992092
#202991662
#202989722
#202989632
#202989522
#202988222
#202987962
#202987592
#202987472
#202986602
#497×C1132
#3222113