Finite Group Databasebeta

← #28402018

Subgroups — #28402018

Order 14464.

346 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299206C211yesmaximal, characteristic, complemented
2#20299202C211yesmaximal, characteristic
3#20298906C211yesmaximal, characteristic, complemented
4#20298905C211yesmaximal, characteristic, complemented
5#20298900C211yesmaximal, characteristic, complemented
6#20298896C211yesmaximal, characteristic, complemented
7#20298843C211yesmaximal, characteristic, complemented
8#20298841C211yesmaximal, characteristic, complemented
9#20298826C211yesmaximal, characteristic, complemented
10#20298824C211yesmaximal, characteristic, complemented
11#20298801C211yesmaximal, characteristic, complemented
12#20298801C211yesmaximal, characteristic, complemented
13#20298795C211yesmaximal, characteristic, complemented
14#20298623C211yesmaximal, characteristic, complemented
15#460×C113C211yesmaximal, characteristic, complemented
16C2×#14268635C2211yescharacteristic
17C2×#14268635C2211yescharacteristic
18C2×#14268630C2211yescharacteristic
19C2×C8×D113C2211yescharacteristic
20#16813620C2211yescharacteristic
21#16813617—21no—
22#16813616—21no—
23#16813614—21no—
24#16813614C2211yescharacteristic
25#16813613C2211yescharacteristic
26#16813612—21no—
27#16813603—21no—
28#16813603—21no—
29#16813602C2211yescharacteristic
30#16813598C2211yescharacteristic
31#16813594—21no—
32#16813594—21no—
33#16813593C2211yescharacteristic
34#16813593C2211yescharacteristic
35C4×Dic226C2211yescharacteristic
36D4×Dic113C2211yescharacteristic
37D4×Dic113C2211yescharacteristic
38#16813579C2211yescharacteristic
39#16813556C2211yescharacteristic
40#16813555C2211yescharacteristic
41#16813554C2211yescharacteristic
42#16813553C2211yescharacteristic
43C4⋊#11744751C2211yescharacteristic
44#16813551C2211yescharacteristic
45#16813551C2211yescharacteristic
46#16813547C2211yescharacteristic
47#16813547C2211yescharacteristic
48#16813546C2211yescharacteristic
49#16813546C2211yescharacteristic
50#16813543C2211yescharacteristic
51#16813543C2211yescharacteristic
52C2×SD16×C113C2211yescharacteristic
53C2×SD16×C113C2211yescharacteristic
54#127×C113C2211yescharacteristic
55C4×Q8×C113C2211yescharacteristic
56C4⋊C8×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58#102×C113C2211yescharacteristic
59C2×Dic226C2311yescharacteristic
60C2×C22⋊D113—21no—
61C2×C22⋊D113—21no—
62C22×Dic113—21no—
63C22×Dic113—21no—
64C2×C4×D113C2311yescharacteristic
65#14268635—41no—
66#14268635—41no—
67#14268630—41no—
68C2×#11744751C2311yescharacteristic
69C2×#11744751C2311yescharacteristic
70C8×D113—41no—
71C4⋊Dic113—21no—
72C4⋊Dic113—21no—
73C4⋊Dic113C2311yescharacteristic
74C4⋊Dic113C2311yescharacteristic
75C4⋊Dic113C2311yescharacteristic
76#14268626—21no—
77#14268626—21no—
78#14268626—21no—
79#14268626—21no—
80#14268626—21no—
81#14268626—21no—
82#14268626—21no—
83#14268626D411yescharacteristic
84#14268626D411yescharacteristic
85C22⋊Dic113—21no—
86C22⋊Dic113—21no—
87C22⋊Dic113—21no—
88C22⋊Dic113—21no—
89#14268624—21no—
90#14268624—21no—
91#14268624D411yescharacteristic
92#14268624D411yescharacteristic
93C4×Dic113—21no—
94C4×Dic113C2311yescharacteristic
95C2×Q8×C113C2311yescharacteristic
96C2×D4×C113—21no—
97C2×D4×C113—21no—
98C2×D4×C113C2311yescharacteristic
99C2×D4×C113C2311yescharacteristic
100SD16×C113—41no—
101SD16×C113—41no—
102C2×C8×C113C2311yescharacteristic
103C2×C8×C113C2311yescharacteristic
104C4⋊C4×C113—21no—
105C4⋊C4×C113C2311yescharacteristic
106C42×C113—21no—
107C42×C113C2311yescharacteristic
108C23×C113—21no—
109C23×C113—21no—
110C22×D113C2×D411yescharacteristic
111Q8×C113—21no—
112Q8×C113—21no—
113D4×C113—21no—
114D4×C113—21no—
115D4×C113—21no—
116D4×C113—21no—
117D4×C113—81no—
118D4×C113—81no—
119C2×C4×C113—21no—
120C2×C4×C113—21no—
121C2×C4×C113C2×D411yescharacteristic
122C2×C4×C113C2×D411yescharacteristic
123C2×C4×C113C2411yescharacteristic
124C22⋊D113—81no—
125C22⋊D113—81no—
126C2×Dic113—21no—
127C2×Dic113—21no—
128C2×Dic113—21no—
129C2×Dic113—21no—
130C2×Dic113—81no—
131C2×Dic113—81no—
132C2×Dic113C2×D411yescharacteristic
133C2×Dic113C2×D411yescharacteristic
134C2×Dic113C2×D411yescharacteristic
135C4×D113—21no—
136C4×D113—21no—
137Dic226—21no—
138Dic226—21no—
139C8×C113—21no—
140C8×C113—21no—
141#11744751—21no—
142#11744751—21no—
143C22×C113—41no—
144C22×C113—41no—
145C22×C113—41no—
146C22×C113—41no—
147C22×C113—41no—
148C22×C113—41no—
149C22×C113C22×D411yescharacteristic
150C2×D113—21no—
151C2×D113—21no—
152C2×D113—21no—
153C4×C113—21no—
154C4×C113—21no—
155C4×C113—41no—
156C4×C113—41no—
157C4×C113H(5,𝔽2)11yescharacteristic
158C4×C1132−1+411yescharacteristic
159Dic113—21no—
160Dic113—21no—
161Dic113—21no—
162Dic113—41no—
163Dic113—41no—
164Dic113—41no—
165Dic113—41no—
166C2×C113—81no—
167C2×C113—81no—
168C2×C113#53711yescharacteristic
169C2×C113#57711yescharacteristic
170C2×C113#57711yescharacteristic
171D113—41no—
172#3260—1131nomaximal, Sylow
173C113#326011yescharacteristic, complemented, Sylow
174#541—1131no—
175#540—1131no—
176#479—1131no—
177#479—1131no—
178#478—1131no—
179#478—1131no—
180#468—1131no—
181#468—1131no—
182#465—1131no—
183#465—1131no—
184#461—1131no—
185#461—1131no—
186#460—1131no—
187#460D11311yescharacteristic, complemented
188#424—1131no—
189C2×SD16—1131no—
190C2×SD16—1131no—
191C2×SD16C2×D11311yescharacteristic
192C2×SD16C2×D11311yescharacteristic
193C2×M16—1131no—
194C22×C8—1131no—
195C4⋊Q8—1131no—
196#127C2×D11311yescharacteristic
197#126—2261no—
198#126—2261no—
199#125—1131no—
200#125—1131no—
201#125—2261no—
202#125—2261no—
203#123—2261no—
204#123—2261no—
205C22⋊Q8—1131no—
206C22⋊Q8—1131no—
207#121—1131no—
208#121—1131no—
209#121—2261no—
210#121—2261no—
211C4×Q8—1131no—
212C4×Q8C2×D11311yescharacteristic
213C4×D4—1131no—
214C4×D4—1131no—
215#117—1131no—
216#107—1131no—
217#107—1131no—
218#106—1131no—
219#106—1131no—
220C4⋊C8—1131no—
221C4⋊C8—1131no—
222C4⋊C8—1131no—
223C4⋊C8C2×D11311yescharacteristic
224#103—1131no—
225#103—1131no—
226#103—1131no—
227#103—1131no—
228#102—1131no—
229#102—1131no—
230#102C2×D11311yescharacteristic
231#102C2×D11311yescharacteristic
232C2×Q8—1131no—
233C2×Q8C22×D11311yescharacteristic
234C2×D4—21no—
235C2×D4—21no—
236C2×D4—2261no—
237C2×D4—2261no—
238C2×D4C22×D11311yescharacteristic
239C2×D4C22×D11311yescharacteristic
240C22×C4—1131no—
241C22×C4—2261no—
242C22×C4—2261no—
243SD16—41no—
244SD16—41no—
245SD16—4521no—
246SD16—4521no—
247M16—4521no—
248C2×C8—1131no—
249C2×C8—1131no—
250C2×C8—4521no—
251C2×C8C22×D11311yescharacteristic
252C2×C8C22×D11311yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—1131no—
255C4⋊C4—1131no—
256C4⋊C4—1131no—
257C4⋊C4—1131no—
258C4⋊C4—1131no—
259C4⋊C4—2261no—
260C4⋊C4—2261no—
261C4⋊C4—2261no—
262C4⋊C4—2261no—
263C4⋊C4—2261no—
264C4⋊C4—2261no—
265C4⋊C4—2261no—
266C4⋊C4—2261no—
267C4⋊C4—2261no—
268C4⋊C4C22×D11311yescharacteristic
269C22⋊C4—1131no—
270C22⋊C4—1131no—
271C22⋊C4—2261no—
272C22⋊C4—2261no—
273C22⋊C4—2261no—
274C22⋊C4—2261no—
275C22⋊C4—2261no—
276C22⋊C4—2261no—
277C42—21no—
278C42—1131no—
279C42—2261no—
280C42C22×D11311yescharacteristic
281C23—21no—
282C23—21no—
283C23—1131no—
284Q8—21no—
285Q8—21no—
286Q8—2261no—
287Q8—2261no—
288D4—21no—
289D4—21no—
290D4—21no—
291D4—21no—
292D4—81no—
293D4—81no—
294D4—9041no—
295D4—9041no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—1131no—
299C2×C4—1131no—
300C2×C4—1131no—
301C2×C4—9041no—
302C2×C4—9041no—
303C2×C4—2261no—
304C2×C4—2261no—
305C2×C4—2261no—
306C2×C4—2261no—
307C2×C4—2261no—
308C2×C4—2261no—
309C2×C4D4×D11311yescharacteristic
310C2×C4D4×D11311yescharacteristic
311C2×C4C23×D11311yescharacteristic
312C8—21no—
313C8—21no—
314C8—2261no—
315C8—2261no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—2261no—
323C22—2261no—
324C22—2261no—
325C22C2×D4×D11311yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—4521no—
331C4—4521no—
332C4—4521no—
333C4—4521no—
334C4—2261no—
335C4—2261no—
336C4—2261no—
337C4#1681366711yescharacteristic
338C4#1681366911yescharacteristic
339C2—81no—
340C2—81no—
341C2—4521no—
342C2#2029917711yescharacteristic
343C2#2029940411yescharacteristic
344C2#2029940811yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#460×C113C2
socleC22×C113C22×D4
prime radical#20299202C2
hypercenter#460D113
hypocenterC113#3260
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #20299206C2semidirect
3. #20298906C2semidirect
4. #20298905C2semidirect
5. #20298900C2semidirect
6. #20298896C2semidirect
7. #20298843C2semidirect
8. #20298841C2semidirect
9. #20298826C2semidirect
10. #20298824C2semidirect
11. #20298801C2semidirect
12. #20298801C2semidirect
13. #20298795C2semidirect
14. #20298623C2semidirect
15. #460×C113C2semidirect
173. C113#3260semidirect
187. #460D113semidirect

Maximal subgroups

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

subgroupindex
#202992062
#202992022
#202989062
#202989052
#202989002
#202988962
#202988432
#202988412
#202988262
#202988242
#202988012
#202987952
#202986232
#460×C1132
#3260113