Finite Group Databasebeta

← #28403606

Subgroups — #28403606

Order 14464.

350 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299326C211yesmaximal, characteristic, complemented
2#20299320C211yesmaximal, characteristic
3#20298992C211yesmaximal, characteristic
4#20298991C211yesmaximal, characteristic
5#20298976C211yesmaximal, characteristic, complemented
6#20298823C211yesmaximal, characteristic
7#20298820C211yesmaximal, characteristic
8#20298808C211yesmaximal, characteristic, complemented
9#20298807C211yesmaximal, characteristic, complemented
10#20298807C211yesmaximal, characteristic, complemented
11#20298802C211yesmaximal, characteristic
12#20298726C211yesmaximal, characteristic, complemented
13#20298704C211yesmaximal, characteristic, complemented
14#20298685C211yesmaximal, characteristic
15#441×C113C211yesmaximal, characteristic, complemented
16C2×Dic452C2211yescharacteristic
17C2×Dic452C2211yescharacteristic
18C2×#14268637C2211yescharacteristic
19C2×#14268637C2211yescharacteristic
20C2×#14268637C2211yescharacteristic
21C2×#14268636C2211yescharacteristic
22C2×#14268636C2211yescharacteristic
23C2×#14268634C2211yescharacteristic
24#16813622C2211yescharacteristic
25#16813620C2211yescharacteristic
26#16813620C2211yescharacteristic
27#16813620C2211yescharacteristic
28#16813617—21no—
29#16813616—21no—
30#16813614—21no—
31#16813612—21no—
32#16813612—21no—
33#16813611C2211yescharacteristic
34#16813610C2211yescharacteristic
35#16813600—21no—
36C4×Dic226—21no—
37C4×Dic226C2211yescharacteristic
38#16813587C2211yescharacteristic
39#16813587C2211yescharacteristic
40#16813587C2211yescharacteristic
41#16813584C2211yescharacteristic
42#16813579—21no—
43C4⋊#11744751C2211yescharacteristic
44#16813551C2211yescharacteristic
45#16813551C2211yescharacteristic
46#16813545C2211yescharacteristic
47#16813545C2211yescharacteristic
48#16813545C2211yescharacteristic
49#16813542C2211yescharacteristic
50#16813532C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C2×Q16×C113C2211yescharacteristic
53C4×Q8×C113C2211yescharacteristic
54C4×Q8×C113C2211yescharacteristic
55#106×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58#97×C113C2211yescharacteristic
59C2×Dic226D411yescharacteristic
60C2×Dic226C2311yescharacteristic
61C2×Dic226C2311yescharacteristic
62C2×Dic226C2311yescharacteristic
63C2×D452C2311yescharacteristic
64C2×C4×D113—21no—
65Dic452—22no—
66Dic452—41no—
67#14268637—41no—
68#14268637—41no—
69#14268637—41no—
70#14268636—22no—
71#14268636—41no—
72#14268634—41no—
73C2×#11744751C2311yescharacteristic
74C2×#11744751C2311yescharacteristic
75C4⋊Dic113—21no—
76C4⋊Dic113—21no—
77C4⋊Dic113D411yescharacteristic
78#14268626—21no—
79#14268626—21no—
80#14268626—21no—
81#14268626—21no—
82#14268626—21no—
83#14268626—21no—
84#14268626—21no—
85#14268626—21no—
86#14268626—21no—
87#14268626D411yescharacteristic
88#14268626D411yescharacteristic
89#14268624—21no—
90#14268624—21no—
91#14268624—21no—
92#14268624—21no—
93#14268624—21no—
94C4×Dic113—21no—
95C4×Dic113—21no—
96C4×Dic113—21no—
97C4×Dic113C2311yescharacteristic
98C4×Dic113C2311yescharacteristic
99C2×Q8×C113C2311yescharacteristic
100C2×Q8×C113C2311yescharacteristic
101Q16×C113—22no—
102C2×C8×C113C2311yescharacteristic
103C2×C8×C113C2311yescharacteristic
104C4⋊C4×C113—21no—
105C4⋊C4×C113—21no—
106C4⋊C4×C113C2311yescharacteristic
107C4⋊C4×C113C2311yescharacteristic
108C42×C113—21no—
109C42×C113—21no—
110C42×C113C2311yescharacteristic
111C22×D113—21no—
112Q8×C113—21no—
113Q8×C113—21no—
114Q8×C113—21no—
115Q8×C113—21no—
116C2×C4×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
123C2×Dic113—21no—
124C2×Dic113—21no—
125C2×Dic113—21no—
126C2×Dic113C2×D411yescharacteristic
127C2×Dic113C2×D411yescharacteristic
128C2×Dic113C2×D411yescharacteristic
129C2×Dic113C2×D411yescharacteristic
130D452—21no—
131D452—21no—
132C4×D113—42no—
133Dic226—22no—
134Dic226—21no—
135Dic226—21no—
136Dic226—21no—
137Dic226—21no—
138Dic226—21no—
139Dic226—21no—
140C8×C113—21no—
141C8×C113#4112yes—
142#11744751—21no—
143#11744751—21no—
144C22×C113C22×D411yescharacteristic
145C2×D113—41no—
146C2×D113—41no—
147C2×D113—41no—
148C4×C113—21no—
149C4×C113—21no—
150C4×C113—41no—
151C4×C113—41no—
152C4×C113—41no—
153C4×C113—41no—
154C4×C113C2×#4111yescharacteristic
155C4×C113H(5,𝔽2)11yescharacteristic
156Dic113—21no—
157Dic113—21no—
158Dic113—21no—
159Dic113—41no—
160Dic113—41no—
161Dic113—41no—
162Dic113#13712yes—
163C2×C113#55011yescharacteristic
164C2×C113C2×#13711yescharacteristic
165C2×C113#57811yescharacteristic
166D113—81no—
167#3398—1131nomaximal, Sylow
168C113#339811yescharacteristic, complemented, Sylow
169#557—1131no—
170#556—1131no—
171#497—1131no—
172#497—1131no—
173#494—1131no—
174#464—1131no—
175#464—1131no—
176#462—1131no—
177#462—1131no—
178#462—1131no—
179#461—1131no—
180#446—1131no—
181#441—1131no—
182#441D11311yescharacteristic, complemented
183C4×SD16—1131no—
184C2×Q16—1131no—
185C2×Q16—1131no—
186C2×Q16—1131no—
187C2×Q16—1131no—
188C2×Q16—1131no—
189C2×Q16C2×D11311yescharacteristic
190C2×SD16—1131no—
191C2×SD16—1131no—
192C2×SD16—1131no—
193C4⋊Q8—1131no—
194C4⋊Q8—1131no—
195C4⋊Q8—1131no—
196C4⋊Q8—1131no—
197#126—2261no—
198#126—2261no—
199#125—2261no—
200#125—2261no—
201#125—2261no—
202#124—1131no—
203#124—1131no—
204C22⋊Q8—2261no—
205C4×Q8—1131no—
206C4×Q8—1131no—
207C4×Q8—1131no—
208C4×Q8—1131no—
209C4×Q8—2261no—
210C4×Q8C2×D11311yescharacteristic
211C4×Q8C2×D11311yescharacteristic
212C4×D4—1131no—
213#117—2261no—
214#106C2×D11311yescharacteristic
215C4⋊C8—1131no—
216C4⋊C8—1131no—
217C4⋊C8—1131no—
218#103—1131no—
219#103—1131no—
220#103—1131no—
221#103C2×D11311yescharacteristic
222#103C2×D11311yescharacteristic
223#102—1131no—
224#97—1131no—
225#97C2×D11311yescharacteristic
226C4×C8—1131no—
227C2×Q8—1131no—
228C2×Q8—1131no—
229C2×Q8—1131no—
230C2×Q8—1131no—
231C2×Q8C22×D11311yescharacteristic
232C2×Q8C22×D11311yescharacteristic
233C2×D4—1131no—
234C22×C4—2261no—
235Q16—22no—
236Q16—4521no—
237Q16—4521no—
238Q16—4521no—
239Q16—4521no—
240Q16—2262no—
241SD16—4521no—
242SD16—4521no—
243SD16—2262no—
244C2×C8—1131no—
245C2×C8—1131no—
246C2×C8C22×D11311yescharacteristic
247C2×C8C22×D11311yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—1131no—
251C4⋊C4—1131no—
252C4⋊C4—1131no—
253C4⋊C4—2261no—
254C4⋊C4—2261no—
255C4⋊C4—2261no—
256C4⋊C4—2261no—
257C4⋊C4—2261no—
258C4⋊C4—2261no—
259C4⋊C4—2261no—
260C4⋊C4—2261no—
261C4⋊C4—2261no—
262C4⋊C4—2261no—
263C4⋊C4—2261no—
264C4⋊C4C22×D11311yescharacteristic
265C4⋊C4C22×D11311yescharacteristic
266C22⋊C4—2261no—
267C22⋊C4—2261no—
268C22⋊C4—2261no—
269C22⋊C4—2261no—
270C22⋊C4—2261no—
271C42—21no—
272C42—21no—
273C42—1131no—
274C42—1131no—
275C42—2261no—
276C42—2261no—
277C42—2261no—
278C42C22×D11311yescharacteristic
279C23—2261no—
280Q8—21no—
281Q8—21no—
282Q8—21no—
283Q8—21no—
284Q8—2262no—
285Q8—2261no—
286Q8—2261no—
287Q8—2261no—
288Q8—2261no—
289Q8—2261no—
290Q8—2261no—
291D4—2261no—
292D4—2261no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—1131no—
298C2×C4—1131no—
299C2×C4—1131no—
300C2×C4—1131no—
301C2×C4—4522no—
302C2×C4—2261no—
303C2×C4—2261no—
304C2×C4—2261no—
305C2×C4D4×D11311yescharacteristic
306C2×C4D4×D11311yescharacteristic
307C2×C4C23×D11311yescharacteristic
308C8—21no—
309C8—2261no—
310C8—2261no—
311C8#1426864712yes—
312C22—4521no—
313C22—4521no—
314C22—4521no—
315C22C2×D4×D11311yescharacteristic
316C4—21no—
317C4—21no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—1132no—
323C4—4521no—
324C4—4521no—
325C4—4521no—
326C4—2261no—
327C4—2261no—
328C4—2261no—
329C4C2×#1426864711yescharacteristic
330C4#1681366811yescharacteristic
331C2—9041no—
332C2#2029926911yescharacteristic
333C2#137×D11311yescharacteristic
334C2#2029941411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#441×C113C2
socleC22×C113C22×D4
prime radicalC2×D452C23
hypercenter#441D113
hypocenterC113#3398
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
1. #20299326C2semidirect
5. #20298976C2semidirect
8. #20298808C2semidirect
9. #20298807C2semidirect
10. #20298807C2semidirect
12. #20298726C2semidirect
13. #20298704C2semidirect
15. #441×C113C2semidirect
168. C113#3398semidirect
182. #441D113semidirect

Maximal subgroups

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

subgroupindex
#202993262
#202993202
#202989922
#202989912
#202989762
#202988232
#202988202
#202988082
#202988072
#202988022
#202987262
#202987042
#202986852
#441×C1132
#3398113