Finite Group Databasebeta

← #28402465

Subgroups — #28402465

Order 14464.

386 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299290C211yesmaximal, characteristic, complemented
2#20299259C211yesmaximal, characteristic
3#20298954C211yesmaximal, characteristic, complemented
4#20298938C211yesmaximal, characteristic, complemented
5#20298912C211yesmaximal, characteristic, complemented
6#20298907C211yesmaximal, characteristic, complemented
7#20298836C211yesmaximal, characteristic, complemented
8#20298829C211yesmaximal, characteristic, complemented
9#20298822C211yesmaximal, characteristic, complemented
10#20298759C211yesmaximal, characteristic, complemented
11Q16×Dic113C211yesmaximal, characteristic, complemented
12#20298661C211yesmaximal, characteristic, complemented
13#20298593C211yesmaximal, characteristic, complemented
14C2×#16813546C211yesmaximal, characteristic, complemented
15#451×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×#14268634C2211yescharacteristic
18C22×#11744751C2211yescharacteristic
19C2×C8×D113C2211yescharacteristic
20#16813617—21no—
21#16813613—21no—
22#16813613C2211yescharacteristic
23#16813611—21no—
24#16813611C2211yescharacteristic
25#16813606—21no—
26#16813598—21no—
27#16813598C2211yescharacteristic
28#16813598C2211yescharacteristic
29#16813596—21no—
30#16813596C2211yescharacteristic
31Q8×Dic113C2211yescharacteristic
32Q8×Dic113C2211yescharacteristic
33C4×C22⋊D113—21no—
34C4×C22⋊D113C2211yescharacteristic
35#16813580C2211yescharacteristic
36#16813578—21no—
37C2×C4⋊Dic113C2211yescharacteristic
38#16813556C2211yescharacteristic
39#16813556C2211yescharacteristic
40#16813553C2211yescharacteristic
41#16813551C2211yescharacteristic
42#16813546C2211yescharacteristic
43#16813546C2211yescharacteristic
44#16813546C2211yescharacteristic
45#16813546C2211yescharacteristic
46#16813546C2211yescharacteristic
47#16813544C2211yescharacteristic
48#16813544C2211yescharacteristic
49#16813542C2211yescharacteristic
50#16813534C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C22×Q8×C113C2211yescharacteristic
53C2×Q16×C113C2211yescharacteristic
54C2×Q16×C113C2211yescharacteristic
55C22⋊Q8×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58C22⋊C8×C113C2211yescharacteristic
59#14268648—22no—
60#14268648—41no—
61C2×D452—21no—
62C2×D452C2311yescharacteristic
63C2×C22⋊D113—21no—
64C2×C22⋊D113D411yescharacteristic
65C22×Dic113—21no—
66C2×C4×D113—21no—
67C2×C4×D113C2311yescharacteristic
68#14268634—41no—
69C2×#11744751—41no—
70C2×#11744751C2311yescharacteristic
71C2×#11744751C2311yescharacteristic
72C8×D113—41no—
73C4⋊Dic113—21no—
74C4⋊Dic113—21no—
75C4⋊Dic113—21no—
76C4⋊Dic113—21no—
77C4⋊Dic113C2311yescharacteristic
78C4⋊Dic113C2311yescharacteristic
79C4⋊Dic113C2311yescharacteristic
80#14268626—21no—
81#14268626—21no—
82#14268626—21no—
83#14268626D411yescharacteristic
84C22⋊Dic113D411yescharacteristic
85#14268624—21no—
86#14268624—21no—
87#14268624—21no—
88#14268624—21no—
89#14268624—21no—
90#14268624—21no—
91#14268624D411yescharacteristic
92C4×Dic113—21no—
93C4×Dic113—21no—
94C4×Dic113—21no—
95C4×Dic113C2311yescharacteristic
96C2×Q8×C113—21no—
97C2×Q8×C113—22no—
98C2×Q8×C113—41no—
99C2×Q8×C113C2311yescharacteristic
100C2×Q8×C113C2311yescharacteristic
101C2×Q8×C113C2311yescharacteristic
102C22×C4×C113—21no—
103C22×C4×C113C2311yescharacteristic
104Q16×C113—22no—
105Q16×C113—41no—
106C2×C8×C113C2311yescharacteristic
107C2×C8×C113C2311yescharacteristic
108C4⋊C4×C113—21no—
109C4⋊C4×C113C2311yescharacteristic
110C22⋊C4×C113—21no—
111C23×C113C2×D411yescharacteristic
112C22×D113—21no—
113C22×D113C2×D411yescharacteristic
114Q8×C113—21no—
115Q8×C113—21no—
116Q8×C113—21no—
117Q8×C113—21no—
118Q8×C113—21no—
119Q8×C113—42no—
120Q8×C113#4112yes—
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113—21no—
124C2×C4×C113—21no—
125C2×C4×C113—21no—
126C2×C4×C113—21no—
127C2×C4×C113—42no—
128C2×C4×C113C2×D411yescharacteristic
129C2×C4×C113C2411yescharacteristic
130C22⋊D113—22no—
131C22⋊D113—42no—
132C2×Dic113—21no—
133C2×Dic113—21no—
134C2×Dic113—21no—
135C2×Dic113—42no—
136C2×Dic113C2×D411yescharacteristic
137C2×Dic113C2×D411yescharacteristic
138C2×Dic113C2×D411yescharacteristic
139D452—21no—
140D452—21no—
141D452—42no—
142C4×D113—21no—
143C4×D113—21no—
144C4×D113—42no—
145C8×C113—21no—
146C8×C113—21no—
147#11744751—21no—
148#11744751—21no—
149C22×C113—21no—
150C22×C113—21no—
151C22×C113#13512yes—
152C22×C113C22×D411yescharacteristic
153C2×D113—21no—
154C2×D113—21no—
155C2×D113—21no—
156C2×D113—41no—
157C2×D113—41no—
158C2×D113—41no—
159C4×C113—22no—
160C4×C113—21no—
161C4×C113—41no—
162C4×C113—41no—
163C4×C113—41no—
164C4×C113C2×#4111yescharacteristic
165C4×C113H(5,𝔽2)11yescharacteristic
166Dic113—21no—
167Dic113—21no—
168Dic113—21no—
169Dic113—41no—
170Dic113—41no—
171Dic113—41no—
172C2×C113—22no—
173C2×C113#54611yescharacteristic
174C2×C113C2×#13511yescharacteristic
175C2×C113#57811yescharacteristic
176D113—41no—
177D113—81no—
178#3300—1131nomaximal, Sylow
179C113#330011yescharacteristic, complemented, Sylow
180#552—1131no—
181#548—1131no—
182#488—1131no—
183#485—1131no—
184#480—1131no—
185#479—1131no—
186#467—1131no—
187#465—1131no—
188#464—1131no—
189#452—1131no—
190#451D11311yescharacteristic, complemented
191C4×Q16—1131no—
192C8×D4—1131no—
193#416—1131no—
194C2×#103—1131no—
195C2×#41—1131no—
196C22×Q8C2×D11311yescharacteristic
197C2×Q16C2×D11311yescharacteristic
198C2×Q16C2×D11311yescharacteristic
199C2×SD16—1131no—
200C22×C8—1131no—
201C22×C8—1131no—
202#126—2261no—
203#125—1131no—
204#125—2261no—
205#124—1131no—
206#124—2261no—
207#123—2261no—
208C22⋊Q8—1131no—
209C22⋊Q8—1131no—
210C22⋊Q8—2261no—
211C22⋊Q8C2×D11311yescharacteristic
212#121—1131no—
213#121—2261no—
214C4×Q8—1131no—
215C4×Q8—1131no—
216C4×D4—1131no—
217C4×D4—2261no—
218#117—1131no—
219#117—2261no—
220C2×C4⋊C4—1131no—
221#107—1131no—
222#107—1131no—
223#106—1131no—
224C4⋊C8—1131no—
225#103—1131no—
226#103—1131no—
227#103—1131no—
228#103—1131no—
229#103—1131no—
230#103C2×D11311yescharacteristic
231#103C2×D11311yescharacteristic
232#102—1131no—
233#102—1131no—
234#102—1131no—
235C22⋊C8—1131no—
236C22⋊C8C2×D11311yescharacteristic
237C4×C8—1131no—
238#41—4521no—
239#41—2262no—
240C2×Q8—21no—
241C2×Q8—22no—
242C2×Q8—41no—
243C2×Q8C22×D11311yescharacteristic
244C2×Q8C22×D11311yescharacteristic
245C2×Q8C22×D11311yescharacteristic
246C2×D4—1131no—
247C2×D4—1131no—
248C2×D4—2261no—
249C2×D4—2261no—
250C22×C4—21no—
251C22×C4—1131no—
252C22×C4—2261no—
253C22×C4—2261no—
254C22×C4C22×D11311yescharacteristic
255Q16—22no—
256Q16—41no—
257SD16—4521no—
258C2×C8—1131no—
259C2×C8—1131no—
260C2×C8—4521no—
261C2×C8—4521no—
262C2×C8C22×D11311yescharacteristic
263C2×C8C22×D11311yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—1131no—
266C4⋊C4—1131no—
267C4⋊C4—1131no—
268C4⋊C4—1131no—
269C4⋊C4—2261no—
270C4⋊C4—2261no—
271C4⋊C4—2261no—
272C4⋊C4—2261no—
273C4⋊C4—2261no—
274C4⋊C4—2261no—
275C4⋊C4—2261no—
276C4⋊C4C22×D11311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—1131no—
279C22⋊C4—1131no—
280C22⋊C4—2261no—
281C22⋊C4—2261no—
282C22⋊C4—2261no—
283C22⋊C4—2261no—
284C22⋊C4—2261no—
285C22⋊C4—2261no—
286C42—1131no—
287C42—2261no—
288C42—2261no—
289C42—2261no—
290C23—1131no—
291C23—2261no—
292C23D4×D11311yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—42no—
299Q8#1426864612yes—
300D4—4522no—
301D4—4522no—
302D4—2262no—
303D4—2261no—
304D4—2261no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—42no—
312C2×C4—1131no—
313C2×C4—1131no—
314C2×C4—1131no—
315C2×C4—4522no—
316C2×C4—4522no—
317C2×C4—2261no—
318C2×C4—2261no—
319C2×C4—2261no—
320C2×C4—2261no—
321C2×C4—2261no—
322C2×C4D4×D11311yescharacteristic
323C2×C4C23×D11311yescharacteristic
324C8—21no—
325C8—21no—
326C8—2261no—
327C8—2261no—
328C22—21no—
329C22—21no—
330C22—4521no—
331C22—4521no—
332C22—4521no—
333C22—2261no—
334C22—2261no—
335C22—2261no—
336C22#1681364512yes—
337C22C2×D4×D11311yescharacteristic
338C4—21no—
339C4—22no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—4521no—
344C4—4521no—
345C4—4521no—
346C4—2261no—
347C4—2261no—
348C4—2261no—
349C4C2×#1426864611yescharacteristic
350C4#1681366711yescharacteristic
351C2—22no—
352C2—9041no—
353C2—4521no—
354C2#2029923511yescharacteristic
355C2C2×#1681364511yescharacteristic
356C2#2029941411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#451×C113C2
socleC22×C113C22×D4
prime radical#20299259C2
hypercenter#451D113
hypocenterC113#3300
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
1. #20299290C2semidirect
3. #20298954C2semidirect
4. #20298938C2semidirect
5. #20298912C2semidirect
6. #20298907C2semidirect
7. #20298836C2semidirect
8. #20298829C2semidirect
9. #20298822C2semidirect
10. #20298759C2semidirect
11. Q16×Dic113C2semidirect
12. #20298661C2semidirect
13. #20298593C2semidirect
14. C2×#16813546C2semidirect
15. #451×C113C2semidirect
179. C113#3300semidirect
190. #451D113semidirect

Maximal subgroups

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

subgroupindex
#202992902
#202992592
#202989542
#202989382
#202989122
#202989072
#202988362
#202988292
#202988222
#202987592
Q16×Dic1132
#202986612
#202985932
C2×#168135462
#451×C1132
#3300113