Finite Group Databasebeta

← #28402003

Subgroups — #28402003

Order 14464.

334 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299221C211yesmaximal, characteristic
2#20299208C211yesmaximal, characteristic, complemented
3#20298903C211yesmaximal, characteristic, complemented
4#20298901C211yesmaximal, characteristic, complemented
5#20298892C211yesmaximal, characteristic, complemented
6#20298881C211yesmaximal, characteristic, complemented
7#20298854C211yesmaximal, characteristic, complemented
8#20298846C211yesmaximal, characteristic
9#20298827C211yesmaximal, characteristic
10#20298823C211yesmaximal, characteristic, complemented
11#20298822C211yesmaximal, characteristic, complemented
12#20298806C211yesmaximal, characteristic, complemented
13#20298802C211yesmaximal, characteristic, complemented
14#20298624C211yesmaximal, characteristic, complemented
15#467×C113C211yesmaximal, characteristic, complemented
16C2×#14268637C2211yescharacteristic
17C2×#14268636C2211yescharacteristic
18C2×#14268634C2211yescharacteristic
19C2×#14268631C2211yescharacteristic
20#16813621C2211yescharacteristic
21#16813620C2211yescharacteristic
22#16813617—21no—
23#16813615—21no—
24#16813615—21no—
25#16813613—21no—
26#16813613C2211yescharacteristic
27#16813612—21no—
28#16813611C2211yescharacteristic
29#16813608—21no—
30#16813604—21no—
31#16813602—21no—
32#16813601C2211yescharacteristic
33#16813596C2211yescharacteristic
34Q8×Dic113C2211yescharacteristic
35Q8×Dic113C2211yescharacteristic
36#16813587C2211yescharacteristic
37#16813584C2211yescharacteristic
38#16813581C2211yescharacteristic
39#16813555C2211yescharacteristic
40#16813554C2211yescharacteristic
41#16813553C2211yescharacteristic
42#16813551C2211yescharacteristic
43#16813551C2211yescharacteristic
44#16813551C2211yescharacteristic
45#16813551C2211yescharacteristic
46#16813547C2211yescharacteristic
47#16813546C2211yescharacteristic
48#16813546C2211yescharacteristic
49#16813545C2211yescharacteristic
50#16813544C2211yescharacteristic
51#16813542C2211yescharacteristic
52C2×Q16×C113C2211yescharacteristic
53C22×C8×C113C2211yescharacteristic
54C22⋊Q8×C113C2211yescharacteristic
55C22⋊Q8×C113C2211yescharacteristic
56#107×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58#103×C113C2211yescharacteristic
59C2×Dic226—21no—
60C2×Dic226C2311yescharacteristic
61C2×D452C2311yescharacteristic
62C2×C22⋊D113—21no—
63C2×C4×D113—21no—
64#14268637—41no—
65#14268636—41no—
66#14268634—41no—
67#14268631—41no—
68C2×#11744751C2311yescharacteristic
69C2×#11744751C2311yescharacteristic
70C4⋊Dic113—21no—
71C4⋊Dic113—21no—
72C4⋊Dic113—21no—
73C4⋊Dic113D411yescharacteristic
74C4⋊Dic113D411yescharacteristic
75C4⋊Dic113C2311yescharacteristic
76C4⋊Dic113C2311yescharacteristic
77#14268626—21no—
78#14268626—21no—
79#14268626—21no—
80#14268626—21no—
81#14268626—21no—
82#14268626—21no—
83C22⋊Dic113—21no—
84C22⋊Dic113D411yescharacteristic
85C22⋊Dic113D411yescharacteristic
86#14268624—21no—
87#14268624—21no—
88#14268624—21no—
89#14268624—21no—
90C4×Dic113—21no—
91C4×Dic113—21no—
92C4×Dic113—21no—
93C4×Dic113C2311yescharacteristic
94C4×Dic113C2311yescharacteristic
95C2×Q8×C113C2311yescharacteristic
96C2×Q8×C113C2311yescharacteristic
97C22×C4×C113C2311yescharacteristic
98Q16×C113—41no—
99C2×C8×C113—41no—
100C2×C8×C113C2311yescharacteristic
101C2×C8×C113C2311yescharacteristic
102C4⋊C4×C113—21no—
103C4⋊C4×C113—21no—
104C4⋊C4×C113C2311yescharacteristic
105C4⋊C4×C113C2311yescharacteristic
106C22⋊C4×C113—21no—
107C22⋊C4×C113—21no—
108C23×C113C2×D411yescharacteristic
109C22×D113—21no—
110Q8×C113—21no—
111Q8×C113—21no—
112Q8×C113—21no—
113Q8×C113—21no—
114C2×C4×C113—21no—
115C2×C4×C113—21no—
116C2×C4×C113—21no—
117C2×C4×C113—21no—
118C2×C4×C113—21no—
119C2×C4×C113—21no—
120C2×C4×C113C2×D411yescharacteristic
121C2×C4×C113C2411yescharacteristic
122C22⋊D113—81no—
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—81no—
133Dic226—21no—
134Dic226—21no—
135Dic226—81no—
136C8×C113—21no—
137C8×C113—21no—
138#11744751—21no—
139#11744751—21no—
140C22×C113—21no—
141C22×C113—21no—
142C22×C113—21no—
143C22×C113C22×D411yescharacteristic
144C2×D113—41no—
145C2×D113—41no—
146C2×D113—41no—
147C4×C113—21no—
148C4×C113—41no—
149C4×C113—41no—
150C4×C113—41no—
151C4×C113—41no—
152C4×C113H(5,𝔽2)11yescharacteristic
153C4×C1132−1+411yescharacteristic
154Dic113—21no—
155Dic113—21no—
156Dic113—21no—
157Dic113—21no—
158Dic113—41no—
159Dic113—41no—
160Dic113—41no—
161C2×C113—41no—
162C2×C113#53711yescharacteristic
163C2×C113#57711yescharacteristic
164C2×C113#57811yescharacteristic
165D113—81no—
166#3258—1131nomaximal, Sylow
167C113#325811yescharacteristic, complemented, Sylow
168#542—1131no—
169#541—1131no—
170#479—1131no—
171#478—1131no—
172#477—1131no—
173#475—1131no—
174#470—1131no—
175#468—1131no—
176#467D11311yescharacteristic, complemented
177#465—1131no—
178#464—1131no—
179#464—1131no—
180#462—1131no—
181#461—1131no—
182#424—1131no—
183C2×Q16—1131no—
184C2×Q16C2×D11311yescharacteristic
185C2×SD16—1131no—
186C2×SD16—1131no—
187C2×M16—1131no—
188C22×C8C2×D11311yescharacteristic
189C4⋊Q8—1131no—
190C4⋊Q8—1131no—
191#126—2261no—
192#126—2261no—
193#126—2261no—
194#125—1131no—
195#125—2261no—
196#125—2261no—
197#124—1131no—
198#124—2261no—
199#123—2261no—
200C22⋊Q8—1131no—
201C22⋊Q8—2261no—
202C22⋊Q8C2×D11311yescharacteristic
203C22⋊Q8C2×D11311yescharacteristic
204#121—1131no—
205C4×Q8—1131no—
206C4×Q8—1131no—
207C4×Q8—1131no—
208C4×D4—1131no—
209#117—1131no—
210#107—1131no—
211#107C2×D11311yescharacteristic
212#106—1131no—
213#106—1131no—
214C4⋊C8—1131no—
215C4⋊C8—1131no—
216C4⋊C8—1131no—
217C4⋊C8—1131no—
218#103—1131no—
219#103—1131no—
220#103—1131no—
221#103—1131no—
222#103C2×D11311yescharacteristic
223#103C2×D11311yescharacteristic
224#102—1131no—
225#102—1131no—
226C2×Q8—1131no—
227C2×Q8—2261no—
228C2×Q8C22×D11311yescharacteristic
229C2×Q8C22×D11311yescharacteristic
230C2×D4—1131no—
231C2×D4—2261no—
232C22×C4—2261no—
233C22×C4C22×D11311yescharacteristic
234Q16—41no—
235Q16—4521no—
236SD16—4521no—
237SD16—4521no—
238M16—4521no—
239C2×C8—41no—
240C2×C8—1131no—
241C2×C8—1131no—
242C2×C8C22×D11311yescharacteristic
243C2×C8C22×D11311yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—1131no—
247C4⋊C4—1131no—
248C4⋊C4—1131no—
249C4⋊C4—1131no—
250C4⋊C4—2261no—
251C4⋊C4—2261no—
252C4⋊C4—2261no—
253C4⋊C4—2261no—
254C4⋊C4—2261no—
255C4⋊C4—2261no—
256C4⋊C4—2261no—
257C4⋊C4—2261no—
258C4⋊C4—2261no—
259C4⋊C4C22×D11311yescharacteristic
260C4⋊C4C22×D11311yescharacteristic
261C22⋊C4—21no—
262C22⋊C4—21no—
263C22⋊C4—1131no—
264C22⋊C4—1131no—
265C22⋊C4—2261no—
266C22⋊C4—2261no—
267C22⋊C4—2261no—
268C22⋊C4—2261no—
269C22⋊C4—2261no—
270C42—1131no—
271C42—1131no—
272C42—2261no—
273C42—2261no—
274C42—2261no—
275C23—2261no—
276C23D4×D11311yescharacteristic
277Q8—21no—
278Q8—21no—
279Q8—21no—
280Q8—21no—
281Q8—9041no—
282Q8—2261no—
283Q8—2261no—
284D4—9041no—
285D4—2261no—
286D4—2261no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—1131no—
294C2×C4—1131no—
295C2×C4—1131no—
296C2×C4—1131no—
297C2×C4—9041no—
298C2×C4—2261no—
299C2×C4—2261no—
300C2×C4—2261no—
301C2×C4D4×D11311yescharacteristic
302C2×C4C23×D11311yescharacteristic
303C8—21no—
304C8—21no—
305C8—2261no—
306C8—2261no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—4521no—
311C22—4521no—
312C22—4521no—
313C22C2×D4×D11311yescharacteristic
314C4—21no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—4521no—
320C4—4521no—
321C4—4521no—
322C4—2261no—
323C4—2261no—
324C4—2261no—
325C4—2261no—
326C4#1681366711yescharacteristic
327C4#1681366911yescharacteristic
328C2—41no—
329C2—9041no—
330C2#2029917511yescharacteristic
331C2#2029940511yescharacteristic
332C2#2029941111yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#467×C113C2
socleC22×C113C22×D4
prime radical#16813596C22
hypercenter#467D113
hypocenterC113#3258
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
2. #20299208C2semidirect
3. #20298903C2semidirect
4. #20298901C2semidirect
5. #20298892C2semidirect
6. #20298881C2semidirect
7. #20298854C2semidirect
10. #20298823C2semidirect
11. #20298822C2semidirect
12. #20298806C2semidirect
13. #20298802C2semidirect
14. #20298624C2semidirect
15. #467×C113C2semidirect
167. C113#3258semidirect
176. #467D113semidirect

Maximal subgroups

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

subgroupindex
#202992212
#202992082
#202989032
#202989012
#202988922
#202988812
#202988542
#202988462
#202988272
#202988232
#202988222
#202988062
#202988022
#202986242
#467×C1132
#3258113