Finite Group Databasebeta

← #28403642

Subgroups — #28403642

Order 14464.

368 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299333C211yesmaximal, characteristic, complemented
2#20299321C211yesmaximal, characteristic, complemented
3#20298992C211yesmaximal, characteristic, complemented
4#20298987C211yesmaximal, characteristic
5#20298982C211yesmaximal, characteristic, complemented
6#20298821C211yesmaximal, characteristic, complemented
7#20298821C211yesmaximal, characteristic, complemented
8#20298814C211yesmaximal, characteristic, complemented
9#20298814C211yesmaximal, characteristic, complemented
10#20298804C211yesmaximal, characteristic, complemented
11#20298799C211yesmaximal, characteristic, complemented
12#20298711C211yesmaximal, characteristic, complemented
13#20298706C211yesmaximal, characteristic, complemented
14C4×#14268636C211yesmaximal, characteristic, complemented
15#446×C113C211yesmaximal, characteristic, complemented
16C2×Dic452C2211yescharacteristic
17C2×Dic452C2211yescharacteristic
18C2×#14268636C2211yescharacteristic
19C2×#14268636C2211yescharacteristic
20C2×#14268636C2211yescharacteristic
21C2×#14268636C2211yescharacteristic
22C2×#14268636C2211yescharacteristic
23C2×D904C2211yescharacteristic
24C2×D904C2211yescharacteristic
25#16813622C2211yescharacteristic
26#16813619C2211yescharacteristic
27#16813617—21no—
28#16813617—21no—
29#16813611—21no—
30#16813610C2211yescharacteristic
31#16813610C2211yescharacteristic
32#16813610C2211yescharacteristic
33#16813610C2211yescharacteristic
34#16813607—21no—
35#16813607—21no—
36#16813598—21no—
37C4×Dic226C2211yescharacteristic
38C4×Dic226C2211yescharacteristic
39C4×Dic226C2211yescharacteristic
40C4×D452C2211yescharacteristic
41C4×D452C2211yescharacteristic
42C4×D452C2211yescharacteristic
43#16813584—21no—
44#16813580—21no—
45#16813554C2211yescharacteristic
46#16813547C2211yescharacteristic
47#16813547C2211yescharacteristic
48#16813547C2211yescharacteristic
49#16813544C2211yescharacteristic
50#16813544C2211yescharacteristic
51#16813544C2211yescharacteristic
52C4×Q8×C113C2211yescharacteristic
53C4⋊C8×C113C2211yescharacteristic
54C4⋊C8×C113C2211yescharacteristic
55C4⋊C8×C113C2211yescharacteristic
56#97×C113C2211yescharacteristic
57#97×C113C2211yescharacteristic
58C4×C8×C113C2211yescharacteristic
59C2×Dic226C2311yescharacteristic
60C2×Dic226C2311yescharacteristic
61C2×Dic226C2311yescharacteristic
62C2×D452—21no—
63C2×D452—21no—
64C2×D452C2311yescharacteristic
65C2×D452C2311yescharacteristic
66C2×D452C2311yescharacteristic
67C2×C4×D113—21no—
68C2×C4×D113—21no—
69C2×C4×D113—21no—
70Dic452—22no—
71Dic452—41no—
72#14268636—22no—
73#14268636—41no—
74#14268636—41no—
75#14268636—41no—
76#14268636—41no—
77D904—22no—
78D904—41no—
79C4⋊Dic113—21no—
80C4⋊Dic113—21no—
81C4⋊Dic113C2311yescharacteristic
82C4⋊Dic113C2311yescharacteristic
83#14268626—21no—
84#14268626—21no—
85#14268626—21no—
86#14268624—21no—
87#14268624—21no—
88#14268624—21no—
89#14268624—21no—
90#14268624—21no—
91#14268624—21no—
92#14268624—21no—
93#14268624—21no—
94#14268624—21no—
95#14268624—21no—
96#14268624—21no—
97C4×Dic113—21no—
98C4×Dic113—21no—
99C4×Dic113—21no—
100C2×Q8×C113D411yescharacteristic
101C2×C8×C113C2311yescharacteristic
102C2×C8×C113C2311yescharacteristic
103C2×C8×C113C2311yescharacteristic
104C2×C8×C113C2311yescharacteristic
105C4⋊C4×C113D411yescharacteristic
106C4⋊C4×C113D411yescharacteristic
107C4⋊C4×C113D411yescharacteristic
108C42×C113C2311yescharacteristic
109C42×C113C2311yescharacteristic
110C42×C113C2311yescharacteristic
111C22×D113—21no—
112C22×D113—21no—
113C22×D113—21no—
114Q8×C113—41no—
115C2×C4×C113C2×D411yescharacteristic
116C2×C4×C113C2×D411yescharacteristic
117C2×C4×C113C2×D411yescharacteristic
118C2×C4×C113C2×D411yescharacteristic
119C2×C4×C113C2×D411yescharacteristic
120C2×C4×C113C2×D411yescharacteristic
121C2×C4×C113C2411yescharacteristic
122C2×Dic113—21no—
123C2×Dic113—21no—
124C2×Dic113—21no—
125C2×Dic113—21no—
126C2×Dic113—21no—
127D452—21no—
128D452—21no—
129D452—21no—
130D452—21no—
131D452—21no—
132D452—21no—
133D452—42no—
134D452—81no—
135C4×D113—42no—
136C4×D113—81no—
137C4×D113—81no—
138Dic226—21no—
139Dic226—21no—
140Dic226—21no—
141Dic226—21no—
142Dic226—21no—
143Dic226—21no—
144C8×C113—21no—
145C8×C113—21no—
146C8×C113—21no—
147C8×C113#4112yes—
148C22×C113C22×D411yescharacteristic
149C2×D113—41no—
150C2×D113—41no—
151C2×D113—41no—
152C2×D113—41no—
153C2×D113—41no—
154C2×D113—41no—
155C2×D113—41no—
156C2×D113—41no—
157C2×D113—41no—
158C4×C113—21no—
159C4×C113—21no—
160C4×C113—21no—
161C4×C113—21no—
162C4×C113—21no—
163C4×C113—21no—
164C4×C113C2×#4111yescharacteristic
165C4×C113H(5,𝔽2)11yescharacteristic
166Dic113—41no—
167Dic113—41no—
168Dic113—41no—
169Dic113—41no—
170Dic113—41no—
171C2×C113#55011yescharacteristic
172C2×C113#57511yescharacteristic
173C2×C113#57711yescharacteristic
174D113—81no—
175D113—81no—
176D113—81no—
177#3401—1131nomaximal, Sylow
178C113#340111yescharacteristic, complemented, Sylow
179#559—1131no—
180#556—1131no—
181#497—1131no—
182#496—1131no—
183#495—1131no—
184#464—1131no—
185#464—1131no—
186#463—1131no—
187#463—1131no—
188#461—1131no—
189#460—1131no—
190#446D11311yescharacteristic, complemented
191#442—1131no—
192#441—1131no—
193C4×SD16—1131no—
194C2×Q16—1131no—
195C2×Q16—1131no—
196C2×SD16—1131no—
197C2×SD16—1131no—
198C2×SD16—1131no—
199C2×SD16—1131no—
200C2×SD16—1131no—
201C2×D8—1131no—
202C2×D8—1131no—
203C4⋊Q8—1131no—
204#127—1131no—
205#126—2261no—
206#126—2261no—
207#124—1131no—
208#124—1131no—
209#124—1131no—
210#124—1131no—
211#124—2261no—
212#123—2261no—
213#123—2261no—
214C22⋊Q8—2261no—
215C4×Q8—1131no—
216C4×Q8—1131no—
217C4×Q8—1131no—
218C4×Q8C2×D11311yescharacteristic
219C4×D4—1131no—
220C4×D4—1131no—
221C4×D4—1131no—
222C4×D4—2261no—
223#117—2261no—
224#106—1131no—
225C4⋊C8C2×D11311yescharacteristic
226C4⋊C8C2×D11311yescharacteristic
227C4⋊C8C2×D11311yescharacteristic
228#103—1131no—
229#103—1131no—
230#103—1131no—
231#102—1131no—
232#102—1131no—
233#102—1131no—
234#97C2×D11311yescharacteristic
235#97C2×D11311yescharacteristic
236C4×C8C2×D11311yescharacteristic
237C2×Q8—1131no—
238C2×Q8—1131no—
239C2×Q8—1131no—
240C2×Q8D45211yescharacteristic
241C2×D4—1131no—
242C2×D4—1131no—
243C2×D4—1131no—
244C2×D4—2261no—
245C2×D4—2261no—
246C22×C4—2261no—
247C22×C4—2261no—
248C22×C4—2261no—
249Q16—4521no—
250Q16—2262no—
251SD16—4521no—
252SD16—4521no—
253SD16—4521no—
254SD16—4521no—
255SD16—2262no—
256D8—4521no—
257D8—2262no—
258C2×C8C22×D11311yescharacteristic
259C2×C8C22×D11311yescharacteristic
260C2×C8C22×D11311yescharacteristic
261C2×C8C22×D11311yescharacteristic
262C4⋊C4—1131no—
263C4⋊C4—1131no—
264C4⋊C4—2261no—
265C4⋊C4—2261no—
266C4⋊C4—2261no—
267C4⋊C4—2261no—
268C4⋊C4—2261no—
269C4⋊C4D45211yescharacteristic
270C4⋊C4D45211yescharacteristic
271C4⋊C4D45211yescharacteristic
272C22⋊C4—2261no—
273C22⋊C4—2261no—
274C22⋊C4—2261no—
275C22⋊C4—2261no—
276C22⋊C4—2261no—
277C22⋊C4—2261no—
278C22⋊C4—2261no—
279C22⋊C4—2261no—
280C22⋊C4—2261no—
281C22⋊C4—2261no—
282C22⋊C4—2261no—
283C42—2261no—
284C42—2261no—
285C42—2261no—
286C42C22×D11311yescharacteristic
287C42C22×D11311yescharacteristic
288C42C22×D11311yescharacteristic
289C23—2261no—
290C23—2261no—
291C23—2261no—
292Q8—41no—
293Q8—2261no—
294Q8—2261no—
295Q8—2261no—
296Q8—2261no—
297Q8—2261no—
298Q8—2261no—
299D4—9041no—
300D4—4522no—
301D4—2261no—
302D4—2261no—
303D4—2261no—
304D4—2261no—
305D4—2261no—
306D4—2261no—
307C2×C4—9041no—
308C2×C4—9041no—
309C2×C4—4522no—
310C2×C4—2261no—
311C2×C4—2261no—
312C2×C4—2261no—
313C2×C4—2261no—
314C2×C4—2261no—
315C2×C4C2×D45211yescharacteristic
316C2×C4C2×D45211yescharacteristic
317C2×C4C2×D45211yescharacteristic
318C2×C4C2×D45211yescharacteristic
319C2×C4C2×D45211yescharacteristic
320C2×C4C2×D45211yescharacteristic
321C2×C4C23×D11311yescharacteristic
322C8—21no—
323C8—21no—
324C8—21no—
325C8#1426864812yes—
326C22—4521no—
327C22—4521no—
328C22—4521no—
329C22—4521no—
330C22—4521no—
331C22—4521no—
332C22—4521no—
333C22—4521no—
334C22—4521no—
335C22C22×D45211yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—4521no—
343C4—4521no—
344C4—4521no—
345C4—4521no—
346C4—4521no—
347C4C2×#1426864811yescharacteristic
348C4#1681366811yescharacteristic
349C2—9041no—
350C2—9041no—
351C2—9041no—
352C2#2029927011yescharacteristic
353C2#2029939811yescharacteristic
354C2#2029941011yescharacteristic
subgroupG/H
centerC22C22×D452
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#446×C113C2
socleC22×C113C22×D4
prime radical#20298987C2
hypercenter#446D113
hypocenterC113#3401
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
1. #20299333C2semidirect
2. #20299321C2semidirect
3. #20298992C2semidirect
5. #20298982C2semidirect
6. #20298821C2semidirect
7. #20298821C2semidirect
8. #20298814C2semidirect
9. #20298814C2semidirect
10. #20298804C2semidirect
11. #20298799C2semidirect
12. #20298711C2semidirect
13. #20298706C2semidirect
14. C4×#14268636C2semidirect
15. #446×C113C2semidirect
178. C113#3401semidirect
190. #446D113semidirect

Maximal subgroups

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

subgroupindex
#202993332
#202993212
#202989922
#202989872
#202989822
#202988212
#202988142
#202988042
#202987992
#202987112
#202987062
C4×#142686362
#446×C1132
#3401113