Finite Group Databasebeta

← #28402464

Subgroups — #28402464

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#20299287C211yesmaximal, characteristic, complemented
2#20299258C211yesmaximal, characteristic
3#20298954C211yesmaximal, characteristic, complemented
4#20298913C211yesmaximal, characteristic, complemented
5#20298908C211yesmaximal, characteristic, complemented
6#20298837C211yesmaximal, characteristic, complemented
7#20298828C211yesmaximal, characteristic, complemented
8#20298823C211yesmaximal, characteristic, complemented
9#20298762C211yesmaximal, characteristic, complemented
10#20298755C211yesmaximal, characteristic, complemented
11#20298692C211yesmaximal, characteristic, complemented
12#20298661C211yesmaximal, characteristic, complemented
13#20298592C211yesmaximal, characteristic, complemented
14#103×D113C211yesmaximal, characteristic, complemented
15#485×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17C2×Q8×D113C2211yescharacteristic
18C2×Dic452C2211yescharacteristic
19C2×#14268637C2211yescharacteristic
20C2×#14268636C2211yescharacteristic
21C22×#11744751C2211yescharacteristic
22C2×C8×D113C2211yescharacteristic
23#16813615—21no—
24#16813614—21no—
25#16813613C2211yescharacteristic
26#16813611C2211yescharacteristic
27#16813608—21no—
28#16813604—21no—
29#16813602C2211yescharacteristic
30#16813601C2211yescharacteristic
31#16813600—21no—
32#16813597C2211yescharacteristic
33#16813595—21no—
34#16813587C2211yescharacteristic
35#16813587C2211yescharacteristic
36#16813584—21no—
37C4×C22⋊D113C2211yescharacteristic
38#16813579—21no—
39C4⋊C4×D113C2211yescharacteristic
40#16813555C2211yescharacteristic
41#16813551C2211yescharacteristic
42#16813547C2211yescharacteristic
43#16813546C2211yescharacteristic
44#16813545C2211yescharacteristic
45#16813545C2211yescharacteristic
46#16813545C2211yescharacteristic
47#16813544C2211yescharacteristic
48#16813542C2211yescharacteristic
49#16813542C2211yescharacteristic
50#16813534C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C22⋊Q8×C113C2211yescharacteristic
53#117×C113C2211yescharacteristic
54#107×C113C2211yescharacteristic
55#106×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58C22⋊C8×C113C2211yescharacteristic
59#14268647—22no—
60#14268647—41no—
61C2×Dic226—21no—
62C2×Dic226C2311yescharacteristic
63C2×Dic226C2311yescharacteristic
64Q8×D113—22no—
65Q8×D113—41no—
66C2×D452—21no—
67C2×D452C2311yescharacteristic
68C2×C22⋊D113—21no—
69C2×C22⋊D113D411yescharacteristic
70C2×C4×D113—21no—
71C2×C4×D113—21no—
72C2×C4×D113—21no—
73C2×C4×D113C2311yescharacteristic
74Dic452—22no—
75#14268637—41no—
76#14268636—41no—
77C2×#11744751—41no—
78C2×#11744751C2311yescharacteristic
79C2×#11744751C2311yescharacteristic
80C8×D113—41no—
81C4⋊Dic113—21no—
82C4⋊Dic113—21no—
83C4⋊Dic113C2311yescharacteristic
84#14268626—21no—
85#14268626—21no—
86#14268626—21no—
87#14268626—21no—
88#14268626—21no—
89#14268626D411yescharacteristic
90C22⋊Dic113—21no—
91C22⋊Dic113D411yescharacteristic
92#14268624—21no—
93#14268624—21no—
94#14268624—21no—
95#14268624—21no—
96#14268624D411yescharacteristic
97C4×Dic113—21no—
98C4×Dic113—21no—
99C4×Dic113C2311yescharacteristic
100C2×Q8×C113C2311yescharacteristic
101C22×C4×C113C2311yescharacteristic
102C2×C8×C113C2311yescharacteristic
103C2×C8×C113C2311yescharacteristic
104C4⋊C4×C113—21no—
105C4⋊C4×C113C2311yescharacteristic
106C4⋊C4×C113C2311yescharacteristic
107C4⋊C4×C113C2311yescharacteristic
108C22⋊C4×C113—21no—
109C22⋊C4×C113—21no—
110C42×C113—21no—
111C23×C113C2×D411yescharacteristic
112C22×D113—21no—
113C22×D113C2×D411yescharacteristic
114Q8×C113—21no—
115Q8×C113—21no—
116C2×C4×C113—21no—
117C2×C4×C113—21no—
118C2×C4×C113—21no—
119C2×C4×C113—21no—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113C2×D411yescharacteristic
123C2×C4×C113C2411yescharacteristic
124C22⋊D113—22no—
125C22⋊D113—42no—
126C2×Dic113—21no—
127C2×Dic113—21no—
128C2×Dic113—21no—
129C2×Dic113C2×D411yescharacteristic
130C2×Dic113C2×D411yescharacteristic
131C2×Dic113C2×D411yescharacteristic
132D452—21no—
133D452—21no—
134D452—42no—
135C4×D113—21no—
136C4×D113—21no—
137C4×D113—42no—
138C4×D113—42no—
139C4×D113—42no—
140Dic226—21no—
141Dic226—21no—
142Dic226—21no—
143Dic226—42no—
144Dic226#4112yes—
145C8×C113—21no—
146C8×C113—21no—
147#11744751—21no—
148#11744751—21no—
149C22×C113—21no—
150C22×C113—21no—
151C22×C113—21no—
152C22×C113C22×D411yescharacteristic
153C2×D113—21no—
154C2×D113—21no—
155C2×D113—41no—
156C2×D113—41no—
157C2×D113—41no—
158C2×D113#13512yes—
159C4×C113—21no—
160C4×C113—41no—
161C4×C113—41no—
162C4×C113—41no—
163C4×C113—41no—
164C4×C113C2×#4111yescharacteristic
165C4×C113H(5,𝔽2)11yescharacteristic
166Dic113—22no—
167Dic113—21no—
168Dic113—21no—
169Dic113—21no—
170Dic113—41no—
171Dic113—41no—
172C2×C113—41no—
173C2×C113#54611yescharacteristic
174C2×C113C2×#13511yescharacteristic
175C2×C113#57811yescharacteristic
176D113—22no—
177D113—81no—
178#3300—1131nomaximal, Sylow
179C113#330011yescharacteristic, complemented, Sylow
180#552—1131no—
181#548—1131no—
182#488—1131no—
183#485D11311yescharacteristic, complemented
184#480—1131no—
185#479—1131no—
186#467—1131no—
187#465—1131no—
188#464—1131no—
189#452—1131no—
190#451—1131no—
191C4×Q16—1131no—
192C8×D4—1131no—
193#416—1131no—
194C2×#103—1131no—
195C2×#41—1131no—
196C22×Q8—1131no—
197C2×Q16—1131no—
198C2×Q16—1131no—
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—2261no—
219#117C2×D11311yescharacteristic
220C2×C4⋊C4—1131no—
221#107—1131no—
222#107C2×D11311yescharacteristic
223#106C2×D11311yescharacteristic
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—1131no—
241C2×Q8—1131no—
242C2×Q8—4521no—
243C2×Q8—2261no—
244C2×Q8—2262no—
245C2×Q8C22×D11311yescharacteristic
246C2×D4—1131no—
247C2×D4—1131no—
248C2×D4—2261no—
249C2×D4—2261no—
250C22×C4—1131no—
251C22×C4—2261no—
252C22×C4—2261no—
253C22×C4—2261no—
254C22×C4C22×D11311yescharacteristic
255Q16—4521no—
256Q16—2262no—
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—2261no—
268C4⋊C4—2261no—
269C4⋊C4—2261no—
270C4⋊C4—2261no—
271C4⋊C4—2261no—
272C4⋊C4—2261no—
273C4⋊C4—2261no—
274C4⋊C4C22×D11311yescharacteristic
275C4⋊C4C22×D11311yescharacteristic
276C4⋊C4C22×D11311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—1131no—
280C22⋊C4—1131no—
281C22⋊C4—2261no—
282C22⋊C4—2261no—
283C22⋊C4—2261no—
284C22⋊C4—2261no—
285C22⋊C4—2261no—
286C42—21no—
287C42—1131no—
288C42—2261no—
289C42—2261no—
290C23—1131no—
291C23—2261no—
292C23D4×D11311yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—1132no—
296Q8—4522no—
297Q8—2261no—
298Q8—2261no—
299Q8—2261no—
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—1131no—
312C2×C4—1131no—
313C2×C4—1131no—
314C2×C4—4522no—
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—21no—
331C22—1132no—
332C22—4521no—
333C22—4521no—
334C22—4521no—
335C22—2261no—
336C22—2261no—
337C22C2×D4×D11311yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—4521no—
344C4—4521no—
345C4—2261no—
346C4—2261no—
347C4—2261no—
348C4—2262no—
349C4#41×D11311yescharacteristic
350C4#1681366811yescharacteristic
351C2—41no—
352C2—9041no—
353C2—2262no—
354C2#2029924011yescharacteristic
355C2#135×D11311yescharacteristic
356C2#2029941411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#485×C113C2
socleC22×C113C22×D4
prime radical#20299258C2
hypercenter#485D113
hypocenterC113#3300
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #20299287C2semidirect
3. #20298954C2semidirect
4. #20298913C2semidirect
5. #20298908C2semidirect
6. #20298837C2semidirect
7. #20298828C2semidirect
8. #20298823C2semidirect
9. #20298762C2semidirect
10. #20298755C2semidirect
11. #20298692C2semidirect
12. #20298661C2semidirect
13. #20298592C2semidirect
14. #103×D113C2semidirect
15. #485×C113C2semidirect
179. C113#3300semidirect
183. #485D113semidirect

Maximal subgroups

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

subgroupindex
#202992872
#202992582
#202989542
#202989132
#202989082
#202988372
#202988282
#202988232
#202987622
#202987552
#202986922
#202986612
#202985922
#103×D1132
#485×C1132
#3300113