Finite Group Databasebeta

← #28402487

Subgroups — #28402487

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#20299316C211yesmaximal, characteristic, complemented
2#20299247C211yesmaximal, characteristic
3#20298947C211yesmaximal, characteristic, complemented
4#20298939C211yesmaximal, characteristic, complemented
5#20298938C211yesmaximal, characteristic, complemented
6#20298876C211yesmaximal, characteristic, complemented
7#20298839C211yesmaximal, characteristic, complemented
8#20298838C211yesmaximal, characteristic, complemented
9#20298807C211yesmaximal, characteristic, complemented
10#20298761C211yesmaximal, characteristic, complemented
11#20298760C211yesmaximal, characteristic, complemented
12#20298689C211yesmaximal, characteristic, complemented
13C8×C22⋊D113C211yesmaximal, characteristic, complemented
14#20298591C211yesmaximal, characteristic, complemented
15#416×C113C211yesmaximal, characteristic, complemented
16C2×#14268646C2211yescharacteristic
17C2×Dic452C2211yescharacteristic
18C2×#14268637C2211yescharacteristic
19C2×#14268635C2211yescharacteristic
20C2×C8×D113C2211yescharacteristic
21#16813621C2211yescharacteristic
22#16813620C2211yescharacteristic
23#16813616—21no—
24#16813615—21no—
25#16813608—21no—
26#16813605—21no—
27#16813603—21no—
28#16813602C2211yescharacteristic
29#16813601C2211yescharacteristic
30#16813601C2211yescharacteristic
31#16813598C2211yescharacteristic
32#16813594—21no—
33C4×Dic226—21no—
34#16813587C2211yescharacteristic
35D4×Dic113C2211yescharacteristic
36C4×C22⋊D113C2211yescharacteristic
37#16813580C2211yescharacteristic
38C2×#14268626—21no—
39#16813556C2211yescharacteristic
40#16813555C2211yescharacteristic
41#16813553C2211yescharacteristic
42#16813551C2211yescharacteristic
43#16813547C2211yescharacteristic
44#16813547C2211yescharacteristic
45#16813546C2211yescharacteristic
46#16813545C2211yescharacteristic
47#16813545C2211yescharacteristic
48#16813543C2211yescharacteristic
49C22⋊#11744751C2211yescharacteristic
50#16813534C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C2×#41×C113C2211yescharacteristic
53C22×C8×C113C2211yescharacteristic
54#117×C113C2211yescharacteristic
55#103×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58#102×C113C2211yescharacteristic
59#14268646—22no—
60#14268646—41no—
61C2×Dic226—21no—
62C2×Dic226C2311yescharacteristic
63C2×Dic226C2311yescharacteristic
64C2×C22⋊D113—21no—
65C2×C22⋊D113D411yescharacteristic
66C22×Dic113—21no—
67C22×Dic113—21no—
68C2×C4×D113C2311yescharacteristic
69Dic452—41no—
70#14268637—41no—
71#14268635—22no—
72C2×#11744751C2311yescharacteristic
73C2×#11744751C2311yescharacteristic
74C8×D113—41no—
75C4⋊Dic113—21no—
76C4⋊Dic113C2311yescharacteristic
77C4⋊Dic113C2311yescharacteristic
78#14268626—21no—
79#14268626—21no—
80#14268626—21no—
81#14268626—21no—
82#14268626—21no—
83#14268626—21no—
84#14268626—21no—
85#14268626D411yescharacteristic
86C22⋊Dic113—21no—
87C22⋊Dic113—21no—
88C22⋊Dic113—21no—
89C22⋊Dic113D411yescharacteristic
90#14268624—21no—
91#14268624—21no—
92#14268624—21no—
93#14268624D411yescharacteristic
94C4×Dic113—21no—
95C4×Dic113—21no—
96C4×Dic113C2311yescharacteristic
97#41×C113—22no—
98#41×C113—41no—
99C2×Q8×C113C2311yescharacteristic
100C2×D4×C113—21no—
101C2×D4×C113C2311yescharacteristic
102C22×C4×C113—21no—
103C22×C4×C113C2311yescharacteristic
104C2×C8×C113—41no—
105C2×C8×C113C2311yescharacteristic
106C2×C8×C113C2311yescharacteristic
107C4⋊C4×C113C2311yescharacteristic
108C4⋊C4×C113C2311yescharacteristic
109C22⋊C4×C113—21no—
110C42×C113—21no—
111C23×C113—21no—
112C23×C113C2×D411yescharacteristic
113C22×D113C2×D411yescharacteristic
114Q8×C113—21no—
115Q8×C113—21no—
116D4×C113—21no—
117D4×C113—42no—
118D4×C113#4112yes—
119C2×C4×C113—21no—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113—21no—
124C2×C4×C113—42no—
125C2×C4×C113C2×D411yescharacteristic
126C2×C4×C113C2411yescharacteristic
127C22⋊D113—22no—
128C22⋊D113—42no—
129C2×Dic113—21no—
130C2×Dic113—21no—
131C2×Dic113—21no—
132C2×Dic113—21no—
133C2×Dic113—42no—
134C2×Dic113—42no—
135C2×Dic113C2×D411yescharacteristic
136C2×Dic113C2×D411yescharacteristic
137C2×Dic113C2×D411yescharacteristic
138C4×D113—21no—
139C4×D113—21no—
140Dic226—21no—
141Dic226—21no—
142Dic226—21no—
143Dic226—21no—
144Dic226—42no—
145C8×C113—21no—
146C8×C113—21no—
147#11744751—21no—
148#11744751—21no—
149C22×C113—22no—
150C22×C113—21no—
151C22×C113—21no—
152C22×C113—21no—
153C22×C113—41no—
154C22×C113—41no—
155C22×C113C22×D411yescharacteristic
156C2×D113—21no—
157C2×D113—21no—
158C2×D113—21no—
159C4×C113—21no—
160C4×C113—41no—
161C4×C113—41no—
162C4×C113—41no—
163C4×C113C2×#4111yescharacteristic
164C4×C113H(5,𝔽2)11yescharacteristic
165Dic113—21no—
166Dic113—21no—
167Dic113—41no—
168Dic113—41no—
169Dic113—41no—
170Dic113—41no—
171Dic113#13512yes—
172C2×C113—41no—
173C2×C113—42no—
174C2×C113#54611yescharacteristic
175C2×C113C2×#13511yescharacteristic
176C2×C113#57811yescharacteristic
177D113—41no—
178#3302—1131nomaximal, Sylow
179C113#330211yescharacteristic, complemented, Sylow
180#556—1131no—
181#547—1131no—
182#487—1131no—
183#485—1131no—
184#485—1131no—
185#474—1131no—
186#467—1131no—
187#467—1131no—
188#462—1131no—
189#452—1131no—
190#452—1131no—
191C4×SD16—1131no—
192C8×D4—1131no—
193#416—1131no—
194#416D11311yescharacteristic, complemented
195C2×#41—1131no—
196C2×#41C2×D11311yescharacteristic
197C2×Q16—1131no—
198C2×Q16—1131no—
199C2×SD16—1131no—
200C22×C8—1131no—
201C22×C8C2×D11311yescharacteristic
202C4⋊Q8—1131no—
203C4⋊Q8—1131no—
204#126—2261no—
205#126—2261no—
206#124—2261no—
207#123—2261no—
208#123—2261no—
209C22⋊Q8—1131no—
210C22⋊Q8—1131no—
211C22⋊Q8—1131no—
212C22⋊Q8—1131no—
213#121—2261no—
214C4×Q8—1131no—
215C4×Q8—2261no—
216C4×D4—1131no—
217C4×D4—1131no—
218#117—1131no—
219#117C2×D11311yescharacteristic
220C2×C4⋊C4—2261no—
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#102C2×D11311yescharacteristic
234#102C2×D11311yescharacteristic
235C22⋊C8—1131no—
236C22⋊C8—1131no—
237C4×C8—1131no—
238#41—22no—
239#41—41no—
240#41—4521no—
241#41—2262no—
242C2×Q8—1131no—
243C2×Q8—1131no—
244C2×Q8—2261no—
245C2×Q8C22×D11311yescharacteristic
246C2×D4—21no—
247C2×D4—1131no—
248C2×D4—2261no—
249C2×D4C22×D11311yescharacteristic
250C22×C4—21no—
251C22×C4—1131no—
252C22×C4—2261no—
253C22×C4—2261no—
254C22×C4C22×D11311yescharacteristic
255Q16—4521no—
256Q16—4521no—
257SD16—2262no—
258C2×C8—41no—
259C2×C8—1131no—
260C2×C8—1131no—
261C2×C8—4521no—
262C2×C8C22×D11311yescharacteristic
263C2×C8C22×D11311yescharacteristic
264C4⋊C4—1131no—
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⋊C4—2261no—
275C4⋊C4C22×D11311yescharacteristic
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—21no—
287C42—1131no—
288C42—2261no—
289C42—2261no—
290C23—21no—
291C23—1131no—
292C23D4×D11311yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—4522no—
296Q8—2261no—
297Q8—2261no—
298Q8—2261no—
299Q8—2261no—
300D4—21no—
301D4—42no—
302D4—4522no—
303D4—2262no—
304D4#1426864712yes—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—42no—
311C2×C4—1131no—
312C2×C4—1131no—
313C2×C4—1131no—
314C2×C4—4522no—
315C2×C4—4522no—
316C2×C4—2261no—
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—22no—
332C22—41no—
333C22—41no—
334C22—2261no—
335C22—2261no—
336C22—2261no—
337C22C2×D4×D11311yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—1132no—
343C4—4521no—
344C4—4521no—
345C4—4521no—
346C4—4521no—
347C4—2261no—
348C4—2261no—
349C4C2×#1426864711yescharacteristic
350C4#1681366711yescharacteristic
351C2—41no—
352C2—42no—
353C2—4521no—
354C2#2029923811yescharacteristic
355C2#135×D11311yescharacteristic
356C2#2029941211yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#416×C113C2
socleC22×C113C22×D4
prime radical#20299247C2
hypercenter#416D113
hypocenterC113#3302
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #20299316C2semidirect
3. #20298947C2semidirect
4. #20298939C2semidirect
5. #20298938C2semidirect
6. #20298876C2semidirect
7. #20298839C2semidirect
8. #20298838C2semidirect
9. #20298807C2semidirect
10. #20298761C2semidirect
11. #20298760C2semidirect
12. #20298689C2semidirect
13. C8×C22⋊D113C2semidirect
14. #20298591C2semidirect
15. #416×C113C2semidirect
179. C113#3302semidirect
194. #416D113semidirect

Maximal subgroups

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

subgroupindex
#202993162
#202992472
#202989472
#202989392
#202989382
#202988762
#202988392
#202988382
#202988072
#202987612
#202987602
#202986892
C8×C22⋊D1132
#202985912
#416×C1132
#3302113