Finite Group Databasebeta

← #28400972

Subgroups — #28400972

Order 14464.

392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 125 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#20299144C211yesmaximal, characteristic
2C2×#16813613C211yesmaximal, characteristic, complemented
3#20298965C212yesmaximal, complemented
4#20298961C212yesmaximal, complemented
5#20298954C212yesmaximal, complemented
6#20298951C212yesmaximal, complemented
7#20298600C211yesmaximal, characteristic, complemented
8#20298599C211yesmaximal, characteristic, complemented
9#20298597C211yesmaximal, characteristic, complemented
10M16×Dic113C211yesmaximal, characteristic, complemented
11#417×C113C211yesmaximal, characteristic, complemented
12C2×#14268647C2211yescharacteristic
13C2×#14268631C2211yescharacteristic
14#16813620C2211yescharacteristic
15#16813618C2211yescharacteristic
16#16813613—21no—
17#16813613—21no—
18#16813613C2212yes—
19#16813613C2212yes—
20#16813611C2211yescharacteristic
21#16813609C2211yescharacteristic
22#16813594—21no—
23#16813594—21no—
24C4×C22⋊D113—21no—
25C4×C22⋊D113—21no—
26C2×C4⋊Dic113—21no—
27C2×C4⋊Dic113C2211yescharacteristic
28C2×#14268626—21no—
29C2×C4×Dic113C2211yescharacteristic
30#16813547C2212yes—
31#16813546C2212yes—
32#16813545C2212yes—
33#16813544C2212yes—
34#16813543C2212yes—
35#16813542C2212yes—
36#16813532C2212yes—
37C8×Dic113C2212yes—
38C2×#41×C113C2211yescharacteristic
39C2×M16×C113C2211yescharacteristic
40C2×C4⋊C4×C113C2211yescharacteristic
41#103×C113C2212yes—
42#102×C113C2212yes—
43#14268647—22no—
44#14268647—22no—
45C2×Dic226C2311yescharacteristic
46C2×D452C2311yescharacteristic
47C2×C22⋊D113—21no—
48C2×C22⋊D113—21no—
49C2×C22⋊D113—21no—
50C22×Dic113—21no—
51C22×Dic113D411yescharacteristic
52C22×Dic113D411yescharacteristic
53C2×C4×D113—21no—
54#14268631—22no—
55C2×#11744751C2312yes—
56C4⋊Dic113—21no—
57C4⋊Dic113—22no—
58C4⋊Dic113—22no—
59C4⋊Dic113C2312yes—
60#14268626—22no—
61#14268626—22no—
62#14268626—21no—
63#14268626—21no—
64C22⋊Dic113—21no—
65C22⋊Dic113—21no—
66#14268624—21no—
67#14268624—21no—
68C4×Dic113D411yescharacteristic
69C4×Dic113D411yescharacteristic
70C4×Dic113C2311yescharacteristic
71C4×Dic113C2311yescharacteristic
72#41×C113—22no—
73#41×C113—22no—
74C2×Q8×C113C2311yescharacteristic
75C2×D4×C113—21no—
76C2×D4×C113C2311yescharacteristic
77C22×C4×C113—21no—
78C22×C4×C113—21no—
79C22×C4×C113C2311yescharacteristic
80M16×C113—22no—
81C2×C8×C113C2312yes—
82C4⋊C4×C113—21no—
83C4⋊C4×C113C2312yes—
84C23×C113—21no—
85C23×C113C2×D411yescharacteristic
86C22×D113—21no—
87Q8×C113—21no—
88Q8×C113—21no—
89D4×C113—21no—
90D4×C113—21no—
91D4×C113—42no—
92C2×C4×C113—22no—
93C2×C4×C113—21no—
94C2×C4×C113—42no—
95C2×C4×C113—42no—
96C2×C4×C113C2×D411yescharacteristic
97C2×C4×C113#4112yes—
98C2×C4×C113#4112yes—
99C2×C4×C113C2411yescharacteristic
100C22⋊D113—42no—
101C22⋊D113—42no—
102C22⋊D113—42no—
103C2×Dic113—21no—
104C2×Dic113—22no—
105C2×Dic113—41no—
106C2×Dic113—41no—
107C2×Dic113—42no—
108C2×Dic113C2×D411yescharacteristic
109C2×Dic113C2×D411yescharacteristic
110C2×Dic113C2×D411yescharacteristic
111C2×Dic113C2×D411yescharacteristic
112D452—21no—
113D452—21no—
114C4×D113—42no—
115Dic226—21no—
116Dic226—21no—
117C8×C113—22no—
118#11744751—22no—
119C22×C113—21no—
120C22×C113—21no—
121C22×C113—41no—
122C22×C113—41no—
123C22×C113—41no—
124C22×C113#12412yes—
125C22×C113C22×D411yescharacteristic
126C2×D113—41no—
127C2×D113—41no—
128C2×D113—41no—
129C4×C113—41no—
130C4×C113—42no—
131C4×C113#12412yes—
132C4×C113C2×#4111yescharacteristic
133C4×C113C2×#4111yescharacteristic
134Dic113—21no—
135Dic113—21no—
136Dic113—21no—
137Dic113—21no—
138Dic113—41no—
139Dic113—42no—
140C2×C113—22no—
141C2×C113—81no—
142C2×C113C2×#12411yescharacteristic
143C2×C113#57511yescharacteristic
144C2×C113#57511yescharacteristic
145D113—81no—
146#3142—1131nomaximal, Sylow
147C113#314211yescharacteristic, complemented, Sylow
148#532—1131no—
149C2×#125—1131no—
150#491—1132no—
151#490—1132no—
152#488—1132no—
153#488—1132no—
154#417—1131no—
155#417—1131no—
156#417—1131no—
157#417D11311yescharacteristic, complemented
158C4×M16—1131no—
159C2×#41—1131no—
160C2×#41C2×D11311yescharacteristic
161C2×M16—1131no—
162C2×M16C2×D11311yescharacteristic
163C4⋊Q8—1131no—
164#127—1131no—
165#125—1132no—
166#125—1132no—
167#125—2261no—
168#125—2261no—
169#124—1131no—
170#124—1131no—
171#121—2261no—
172#121—2261no—
173C4×D4—2261no—
174C4×D4—2261no—
175C2×C4⋊C4—1131no—
176C2×C4⋊C4—2261no—
177C2×C4⋊C4—2261no—
178C2×C4⋊C4C2×D11311yescharacteristic
179C2×C42—1131no—
180#103—1132no—
181#103—1132no—
182#103—1132no—
183#103C2×D11312yes—
184#102—1132no—
185#102—1132no—
186#102—1132no—
187#102C2×D11312yes—
188#97—1132no—
189C4×C8—1132no—
190#41—22no—
191#41—22no—
192#41—2262no—
193#41—2262no—
194C2×Q8—1131no—
195C2×Q8C22×D11311yescharacteristic
196C2×D4—21no—
197C2×D4—1131no—
198C2×D4—2261no—
199C2×D4—2261no—
200C2×D4—2261no—
201C2×D4C22×D11311yescharacteristic
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—1131no—
205C22×C4—1131no—
206C22×C4—2261no—
207C22×C4—2261no—
208C22×C4C22×D11311yescharacteristic
209M16—22no—
210M16—2262no—
211C2×C8—1132no—
212C2×C8C22×D11312yes—
213C4⋊C4—21no—
214C4⋊C4—1132no—
215C4⋊C4—2262no—
216C4⋊C4—2262no—
217C4⋊C4—2262no—
218C4⋊C4—2262no—
219C4⋊C4—2261no—
220C4⋊C4—2261no—
221C4⋊C4—2261no—
222C4⋊C4C22×D11312yes—
223C22⋊C4—2261no—
224C22⋊C4—2261no—
225C22⋊C4—2261no—
226C22⋊C4—2261no—
227C42—1131no—
228C42—1131no—
229C42—1131no—
230C42—1131no—
231C23—21no—
232C23—2261no—
233C23D4×D11311yescharacteristic
234Q8—21no—
235Q8—21no—
236Q8—2261no—
237Q8—2261no—
238D4—21no—
239D4—21no—
240D4—42no—
241D4—4522no—
242D4—4522no—
243D4—4522no—
244D4—2261no—
245D4—2261no—
246C2×C4—21no—
247C2×C4—22no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—1131no—
251C2×C4—1131no—
252C2×C4—1131no—
253C2×C4—1131no—
254C2×C4—4522no—
255C2×C4—4522no—
256C2×C4—4521no—
257C2×C4—4521no—
258C2×C4—2261no—
259C2×C4—2262no—
260C2×C4D4×D11311yescharacteristic
261C2×C4#1426864612yes—
262C2×C4#1426864712yes—
263C2×C4C23×D11311yescharacteristic
264C8—22no—
265C8—2262no—
266C22—21no—
267C22—21no—
268C22—41no—
269C22—41no—
270C22—41no—
271C22—4521no—
272C22—4521no—
273C22—4521no—
274C22#1681360812yes—
275C22C2×D4×D11311yescharacteristic
276C4—41no—
277C4—42no—
278C4—4521no—
279C4—4522no—
280C4—2261no—
281C4—2261no—
282C4—2261no—
283C4—2261no—
284C4#1681360812yes—
285C4C2×#1426864611yescharacteristic
286C4C2×#1426864711yescharacteristic
287C2—22no—
288C2—81no—
289C2—9041no—
290C2C2×#1681360811yescharacteristic
291C2#2029939411yescharacteristic
292C2#2029939711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#417×C113C2
socleC22×C113C22×D4
prime radical#20299144C2
hypercenter#417D113
hypocenterC113#3142
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
2. C2×#16813613C2semidirect
3. #20298965C2semidirect
4. #20298961C2semidirect
5. #20298954C2semidirect
6. #20298951C2semidirect
7. #20298600C2semidirect
8. #20298599C2semidirect
9. #20298597C2semidirect
10. M16×Dic113C2semidirect
11. #417×C113C2semidirect
147. C113#3142semidirect
157. #417D113semidirect

Maximal subgroups

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

subgroupindex
#202991442
C2×#168136132
#202989652
#202989612
#202989542
#202989512
#202986002
#202985992
#202985972
M16×Dic1132
#417×C1132
#3142113