Finite Group Databasebeta

← #28400835

Subgroups — #28400835

Order 14464.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299217C211yesmaximal, characteristic, complemented
2#20299080C211yesmaximal, characteristic, complemented
3#20298932C211yesmaximal, characteristic, complemented
4#20298910C211yesmaximal, characteristic, complemented
5#20298893C211yesmaximal, characteristic, complemented
6#20298879C211yesmaximal, characteristic, complemented
7#20298810C211yesmaximal, characteristic, complemented
8#20298759C211yesmaximal, characteristic, complemented
9#20298742C211yesmaximal, characteristic
10#20298701C211yesmaximal, characteristic, complemented
11#20298699C211yesmaximal, characteristic, complemented
12Q16×Dic113C211yesmaximal, characteristic, complemented
13#20298678C211yesmaximal, characteristic, complemented
14#20298658C211yesmaximal, characteristic, complemented
15#464×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×#14268634C2211yescharacteristic
18C2×#14268632C2211yescharacteristic
19#16813622C2211yescharacteristic
20#16813615—21no—
21#16813608—21no—
22#16813606—21no—
23#16813599—21no—
24#16813598C2211yescharacteristic
25#16813593C2211yescharacteristic
26Q8×Dic113C2211yescharacteristic
27Q8×Dic113C2211yescharacteristic
28C4×D452—21no—
29C4×D452C2211yescharacteristic
30D4×Dic113C2211yescharacteristic
31#16813584—21no—
32#16813584C2211yescharacteristic
33#16813579—21no—
34#16813579C2211yescharacteristic
35C4⋊C4×D113—21no—
36C4⋊C4×D113C2211yescharacteristic
37#16813556C2211yescharacteristic
38#16813556C2211yescharacteristic
39#16813555C2211yescharacteristic
40#16813555C2211yescharacteristic
41C4⋊#11744751C2211yescharacteristic
42#16813546C2211yescharacteristic
43#16813546C2211yescharacteristic
44#16813546C2211yescharacteristic
45#16813544C2211yescharacteristic
46#16813544C2211yescharacteristic
47#16813543C2211yescharacteristic
48#16813534C2211yescharacteristic
49#16813534C2211yescharacteristic
50#16813532C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C2×Q16×C113C2211yescharacteristic
53C2×SD16×C113C2211yescharacteristic
54#124×C113C2211yescharacteristic
55C4×Q8×C113C2211yescharacteristic
56C4⋊C8×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58#102×C113C2211yescharacteristic
59#14268648—22no—
60#14268648—22no—
61C2×Dic226—21no—
62C2×D452—21no—
63C2×D452C2311yescharacteristic
64C2×C22⋊D113—21no—
65C22×Dic113—21no—
66C2×C4×D113—21no—
67C2×C4×D113—21no—
68C2×C4×D113—21no—
69C2×C4×D113—21no—
70C2×C4×D113C2311yescharacteristic
71#14268634—22no—
72#14268632—22no—
73C2×#11744751C2311yescharacteristic
74C2×#11744751C2311yescharacteristic
75C4⋊Dic113—21no—
76C4⋊Dic113—21no—
77C4⋊Dic113—21no—
78C4⋊Dic113C2311yescharacteristic
79C4⋊Dic113C2311yescharacteristic
80C4⋊Dic113C2311yescharacteristic
81#14268626—21no—
82#14268626—21no—
83#14268626D411yescharacteristic
84#14268626D411yescharacteristic
85C22⋊Dic113—21no—
86C22⋊Dic113—21no—
87#14268624—21no—
88#14268624—21no—
89#14268624—21no—
90#14268624D411yescharacteristic
91#14268624D411yescharacteristic
92C4×Dic113—21no—
93C4×Dic113—21no—
94C4×Dic113C2311yescharacteristic
95C2×Q8×C113C2311yescharacteristic
96C2×Q8×C113C2311yescharacteristic
97C2×D4×C113C2311yescharacteristic
98Q16×C113—22no—
99SD16×C113—22no—
100C2×C8×C113C2311yescharacteristic
101C2×C8×C113C2311yescharacteristic
102C4⋊C4×C113—21no—
103C4⋊C4×C113C2311yescharacteristic
104C22⋊C4×C113—21no—
105C22⋊C4×C113—21no—
106C42×C113—21no—
107C42×C113C2311yescharacteristic
108C23×C113—21no—
109C22×D113—21no—
110C22×D113C2×D411yescharacteristic
111Q8×C113—21no—
112Q8×C113—21no—
113Q8×C113—21no—
114Q8×C113#4112yes—
115D4×C113—21no—
116D4×C113—21no—
117C2×C4×C113—21no—
118C2×C4×C113—21no—
119C2×C4×C113—21no—
120C2×C4×C113C2×D411yescharacteristic
121C2×C4×C113C2×D411yescharacteristic
122C2×C4×C113C2411yescharacteristic
123C22⋊D113—81no—
124C2×Dic113—21no—
125C2×Dic113—21no—
126C2×Dic113—21no—
127C2×Dic113—81no—
128C2×Dic113C2×D411yescharacteristic
129C2×Dic113C2×D411yescharacteristic
130C2×Dic113C2×D411yescharacteristic
131D452—24no—
132D452—21no—
133D452#4112yes—
134C4×D113—24no—
135C4×D113—21no—
136C4×D113—21no—
137C4×D113—81no—
138C4×D113—81no—
139C4×D113—81no—
140Dic226—81no—
141C8×C113—21no—
142C8×C113—21no—
143#11744751—21no—
144#11744751—21no—
145C22×C113—41no—
146C22×C113—41no—
147C22×C113—41no—
148C22×C113C22×D411yescharacteristic
149C2×D113—21no—
150C2×D113—22no—
151C2×D113—21no—
152C2×D113—21no—
153C2×D113—41no—
154C2×D113—41no—
155C4×C113—22no—
156C4×C113—21no—
157C4×C113—21no—
158C4×C113—41no—
159C4×C113—41no—
160C4×C113C2×#4111yescharacteristic
161C4×C113C2×#4111yescharacteristic
162Dic113—21no—
163Dic113—21no—
164Dic113—21no—
165Dic113—41no—
166Dic113—41no—
167Dic113—41no—
168C2×C113—81no—
169C2×C113#52511yescharacteristic
170C2×C113#57611yescharacteristic
171C2×C113#57811yescharacteristic
172D113—41no—
173D113—42no—
174#3124—1131nomaximal, Sylow
175C113#312411yescharacteristic, complemented, Sylow
176#542—1131no—
177#520—1131no—
178#484—1131no—
179#480—1131no—
180#477—1131no—
181#474—1131no—
182#464D11311yescharacteristic, complemented
183#463—1131no—
184#452—1131no—
185#449—1131no—
186#440—1131no—
187#440—1131no—
188C4×Q16—1131no—
189C4×D8—1131no—
190#433—1131no—
191C2×#41—1131no—
192C2×Q16C2×D11311yescharacteristic
193C2×SD16—1131no—
194C2×SD16C2×D11311yescharacteristic
195C2×D8—1131no—
196C4⋊Q8—1131no—
197#126—2261no—
198#124—2261no—
199#124C2×D11311yescharacteristic
200#123—2261no—
201C22⋊Q8—1131no—
202C22⋊Q8—2261no—
203#121—1131no—
204C4×Q8—1131no—
205C4×Q8—1131no—
206C4×Q8C2×D11311yescharacteristic
207C4×D4—1131no—
208C4×D4—1131no—
209C4×D4—1131no—
210C4×D4—2261no—
211C4×D4—2261no—
212#117—1131no—
213#117—2261no—
214C2×C4⋊C4—1131no—
215C2×C4⋊C4—2261no—
216#107—1131no—
217#107—1131no—
218#107—1131no—
219#107—1131no—
220C4⋊C8—1131no—
221C4⋊C8C2×D11311yescharacteristic
222#103—1131no—
223#103—1131no—
224#103—1131no—
225#103C2×D11311yescharacteristic
226#102—1131no—
227#102—1131no—
228#102—1131no—
229#102C2×D11311yescharacteristic
230C22⋊C8—1131no—
231C22⋊C8—1131no—
232#97—1131no—
233C4×C8—1131no—
234#41—2262no—
235#41—2262no—
236C2×Q8—2261no—
237C2×Q8C22×D11311yescharacteristic
238C2×Q8C22×D11311yescharacteristic
239C2×D4—1131no—
240C2×D4—2261no—
241C2×D4—2261no—
242C2×D4C22×D11311yescharacteristic
243C22×C4—1131no—
244C22×C4—2261no—
245C22×C4—2261no—
246C22×C4—2261no—
247C22×C4—2261no—
248C22×C4—2261no—
249Q16—22no—
250SD16—22no—
251SD16—2262no—
252D8—2262no—
253C2×C8—1131no—
254C2×C8—1131no—
255C2×C8C22×D11311yescharacteristic
256C2×C8C22×D11311yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—1131no—
259C4⋊C4—1131no—
260C4⋊C4—1131no—
261C4⋊C4—1131no—
262C4⋊C4—1131no—
263C4⋊C4—2261no—
264C4⋊C4—2261no—
265C4⋊C4—2261no—
266C4⋊C4—2261no—
267C4⋊C4—2261no—
268C4⋊C4C22×D11311yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—1131no—
272C22⋊C4—1131no—
273C22⋊C4—2261no—
274C22⋊C4—2261no—
275C22⋊C4—2261no—
276C22⋊C4—2261no—
277C22⋊C4—2261no—
278C42—21no—
279C42—1131no—
280C42—2261no—
281C42—2261no—
282C42C22×D11311yescharacteristic
283C23—21no—
284C23—1131no—
285C23—2261no—
286Q8—21no—
287Q8—21no—
288Q8—21no—
289Q8—9041no—
290Q8#1426864612yes—
291D4—21no—
292D4—21no—
293D4—1132no—
294D4—9041no—
295D4—2264no—
296D4—2261no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—1131no—
301C2×C4—1131no—
302C2×C4—1131no—
303C2×C4—9041no—
304C2×C4—9041no—
305C2×C4—9041no—
306C2×C4—9041no—
307C2×C4—2264no—
308C2×C4—2261no—
309C2×C4—2261no—
310C2×C4—2261no—
311C2×C4—2261no—
312C2×C4—2261no—
313C2×C4D4×D11311yescharacteristic
314C2×C4D4×D11311yescharacteristic
315C2×C4C23×D11311yescharacteristic
316C8—21no—
317C8—21no—
318C8—2261no—
319C8—2261no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—4521no—
324C22—4521no—
325C22—2262no—
326C22—2261no—
327C22—2261no—
328C22—2261no—
329C22C2×D4×D11311yescharacteristic
330C4—22no—
331C4—21no—
332C4—21no—
333C4—41no—
334C4—41no—
335C4—4521no—
336C4—4521no—
337C4—4521no—
338C4—2261no—
339C4—2261no—
340C4—2261no—
341C4#41×D11311yescharacteristic
342C4C2×#1426864611yescharacteristic
343C2—81no—
344C2—4522no—
345C2—4521no—
346C2#2029910811yescharacteristic
347C2#2029940011yescharacteristic
348C2#2029941411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#464×C113C2
socleC22×C113C22×D4
prime radical#20298742C2
hypercenter#464D113
hypocenterC113#3124
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #20299217C2semidirect
2. #20299080C2semidirect
3. #20298932C2semidirect
4. #20298910C2semidirect
5. #20298893C2semidirect
6. #20298879C2semidirect
7. #20298810C2semidirect
8. #20298759C2semidirect
10. #20298701C2semidirect
11. #20298699C2semidirect
12. Q16×Dic113C2semidirect
13. #20298678C2semidirect
14. #20298658C2semidirect
15. #464×C113C2semidirect
175. C113#3124semidirect
182. #464D113semidirect

Maximal subgroups

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

subgroupindex
#202992172
#202990802
#202989322
#202989102
#202988932
#202988792
#202988102
#202987592
#202987422
#202987012
#202986992
Q16×Dic1132
#202986782
#202986582
#464×C1132
#3124113