Finite Group Databasebeta

← #28400803

Subgroups — #28400803

Order 14464.

370 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299219C211yesmaximal, characteristic
2#20298939C211yesmaximal, characteristic, complemented
3#20298922C211yesmaximal, characteristic
4#20298893C211yesmaximal, characteristic, complemented
5#20298883C211yesmaximal, characteristic, complemented
6#20298820C211yesmaximal, characteristic, complemented
7#20298820C211yesmaximal, characteristic, complemented
8#20298754C211yesmaximal, characteristic, complemented
9#20298737C211yesmaximal, characteristic
10#20298703C211yesmaximal, characteristic, complemented
11#20298696C211yesmaximal, characteristic, complemented
12C4×#14268637C211yesmaximal, characteristic, complemented
13C4×#14268634C211yesmaximal, characteristic, complemented
14#20298659C211yesmaximal, characteristic, complemented
15#519×C113C211yesmaximal, characteristic, complemented
16C2×#14268637C2211yescharacteristic
17C2×#14268637C2211yescharacteristic
18C2×#14268634C2211yescharacteristic
19C2×#14268634C2211yescharacteristic
20#16813622C2211yescharacteristic
21#16813617—21no—
22#16813610C2211yescharacteristic
23#16813608—21no—
24#16813604—21no—
25#16813601C2211yescharacteristic
26#16813600—21no—
27#16813596C2211yescharacteristic
28C4×Dic226C2211yescharacteristic
29C4×D452C2211yescharacteristic
30#16813555C2211yescharacteristic
31#16813555C2211yescharacteristic
32#16813553C2211yescharacteristic
33#16813553C2211yescharacteristic
34C4⋊#11744751C2211yescharacteristic
35C4⋊#11744751C2211yescharacteristic
36#16813546C2211yescharacteristic
37#16813546C2211yescharacteristic
38#16813546C2211yescharacteristic
39#16813546C2211yescharacteristic
40#16813545C2211yescharacteristic
41#16813545C2211yescharacteristic
42#16813542C2211yescharacteristic
43#16813542C2211yescharacteristic
44C22⋊#11744751C2211yescharacteristic
45C22⋊#11744751C2211yescharacteristic
46#16813533C2211yescharacteristic
47C4×#11744751C2211yescharacteristic
48C22×Q8×C113C2211yescharacteristic
49C4×Q8×C113—21no—
50C4×Q8×C113—21no—
51C4×Q8×C113C2211yescharacteristic
52C4×Q8×C113C2211yescharacteristic
53C4×Q8×C113C2211yescharacteristic
54C4×Q8×C113C2211yescharacteristic
55#117×C113—21no—
56#117×C113—21no—
57#117×C113C2211yescharacteristic
58#117×C113C2211yescharacteristic
59C2×Dic226—21no—
60C2×Dic226C2311yescharacteristic
61C2×D452C2311yescharacteristic
62C2×C22⋊D113—21no—
63C2×C4×D113—21no—
64#14268637—22no—
65#14268637—22no—
66#14268634—22no—
67#14268634—22no—
68C2×#11744751C2311yescharacteristic
69C2×#11744751C2311yescharacteristic
70C2×#11744751C2311yescharacteristic
71C2×#11744751C2311yescharacteristic
72C4⋊Dic113—21no—
73C4⋊Dic113C2311yescharacteristic
74C4⋊Dic113C2311yescharacteristic
75#14268626—21no—
76#14268626—21no—
77C22⋊Dic113—21no—
78#14268624—21no—
79#14268624—21no—
80#14268624—21no—
81#14268624—21no—
82C4×Dic113—21no—
83C2×Q8×C113—22no—
84C2×Q8×C113—22no—
85C2×Q8×C113—21no—
86C2×Q8×C113C2311yescharacteristic
87C2×Q8×C113C2311yescharacteristic
88C22×C4×C113—21no—
89C22×C4×C113C2311yescharacteristic
90C4⋊C4×C113—21no—
91C4⋊C4×C113—21no—
92C4⋊C4×C113—21no—
93C4⋊C4×C113—21no—
94C4⋊C4×C113D411yescharacteristic
95C4⋊C4×C113D411yescharacteristic
96C4⋊C4×C113C2311yescharacteristic
97C4⋊C4×C113C2311yescharacteristic
98C22⋊C4×C113—21no—
99C22⋊C4×C113D411yescharacteristic
100C22⋊C4×C113D411yescharacteristic
101C42×C113—21no—
102C42×C113—21no—
103C42×C113—21no—
104C42×C113—21no—
105C42×C113—21no—
106C42×C113C2311yescharacteristic
107C42×C113C2311yescharacteristic
108C23×C113C2×D411yescharacteristic
109C22×D113—21no—
110Q8×C113—24no—
111Q8×C113—21no—
112Q8×C113—21no—
113Q8×C113#4112yes—
114Q8×C113#4112yes—
115C2×C4×C113—24no—
116C2×C4×C113—21no—
117C2×C4×C113—21no—
118C2×C4×C113—21no—
119C2×C4×C113—21no—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113C2×D411yescharacteristic
123C2×C4×C113C2×D411yescharacteristic
124C2×C4×C113C2×D411yescharacteristic
125C2×C4×C113C2×D411yescharacteristic
126C2×C4×C113C2×D411yescharacteristic
127C2×C4×C113C2411yescharacteristic
128C22⋊D113—81no—
129C2×Dic113—21no—
130C2×Dic113—21no—
131C2×Dic113—21no—
132D452—21no—
133D452—21no—
134C4×D113—81no—
135Dic226—21no—
136Dic226—21no—
137Dic226—81no—
138#11744751—21no—
139#11744751—21no—
140#11744751—21no—
141#11744751—21no—
142C22×C113—21no—
143C22×C113—21no—
144C22×C113—21no—
145C22×C113C22×D411yescharacteristic
146C2×D113—41no—
147C2×D113—41no—
148C2×D113—41no—
149C4×C113—22no—
150C4×C113—22no—
151C4×C113—21no—
152C4×C113—21no—
153C4×C113—21no—
154C4×C113—21no—
155C4×C113—21no—
156C4×C113—41no—
157C4×C113—41no—
158C4×C113C2×#4111yescharacteristic
159C4×C113C2×#4111yescharacteristic
160Dic113—41no—
161Dic113—41no—
162Dic113—41no—
163C2×C113—41no—
164C2×C113#52511yescharacteristic
165C2×C113#57711yescharacteristic
166C2×C113#57811yescharacteristic
167D113—81no—
168#3121—1131nomaximal, Sylow
169C113#312111yescharacteristic, complemented, Sylow
170#542—1131no—
171#519D11311yescharacteristic, complemented
172#485—1131no—
173#482—1131no—
174#477—1131no—
175#475—1131no—
176#464—1131no—
177#464—1131no—
178#451—1131no—
179#448—1131no—
180#441—1131no—
181#440—1131no—
182C4×Q16—1131no—
183C4×SD16—1131no—
184#433—1131no—
185C22×Q8C2×D11311yescharacteristic
186C2×Q16—1131no—
187C2×Q16—1131no—
188C2×SD16—1131no—
189C2×SD16—1131no—
190C4⋊Q8—1131no—
191#126—2261no—
192#124—1131no—
193#124—2261no—
194#123—2261no—
195C22⋊Q8—1131no—
196C22⋊Q8—2261no—
197#121—1131no—
198C4×Q8—21no—
199C4×Q8—21no—
200C4×Q8—1131no—
201C4×Q8C2×D11311yescharacteristic
202C4×Q8C2×D11311yescharacteristic
203C4×Q8C2×D11311yescharacteristic
204C4×Q8C2×D11311yescharacteristic
205C4×D4—1131no—
206#117—21no—
207#117—21no—
208#117C2×D11311yescharacteristic
209#117C2×D11311yescharacteristic
210#107—1131no—
211#107—1131no—
212#106—1131no—
213#106—1131no—
214C4⋊C8—1131no—
215C4⋊C8—1131no—
216#103—1131no—
217#103—1131no—
218#103—1131no—
219#103—1131no—
220#103—1131no—
221#103—1131no—
222#102—1131no—
223#102—1131no—
224C22⋊C8—1131no—
225C22⋊C8—1131no—
226#97—1131no—
227C4×C8—1131no—
228C2×Q8—22no—
229C2×Q8—22no—
230C2×Q8—21no—
231C2×Q8—1131no—
232C2×Q8—2261no—
233C2×Q8C22×D11311yescharacteristic
234C2×Q8C22×D11311yescharacteristic
235C2×D4—1131no—
236C2×D4—2261no—
237C22×C4—21no—
238C22×C4—2261no—
239C22×C4C22×D11311yescharacteristic
240Q16—2262no—
241Q16—2262no—
242SD16—2262no—
243SD16—2262no—
244C2×C8—1131no—
245C2×C8—1131no—
246C2×C8—1131no—
247C2×C8—1131no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—1131no—
253C4⋊C4—1131no—
254C4⋊C4—2261no—
255C4⋊C4—2261no—
256C4⋊C4—2261no—
257C4⋊C4C22⋊D11311yescharacteristic
258C4⋊C4C22⋊D11311yescharacteristic
259C4⋊C4C22×D11311yescharacteristic
260C4⋊C4C22×D11311yescharacteristic
261C22⋊C4—21no—
262C22⋊C4—2261no—
263C22⋊C4—2261no—
264C22⋊C4—2261no—
265C22⋊C4—2261no—
266C22⋊C4—2261no—
267C22⋊C4C22⋊D11311yescharacteristic
268C22⋊C4C22⋊D11311yescharacteristic
269C42—21no—
270C42—21no—
271C42—21no—
272C42—21no—
273C42—21no—
274C42—2261no—
275C42C22×D11311yescharacteristic
276C42C22×D11311yescharacteristic
277C23—2261no—
278C23C2×C22⋊D11311yescharacteristic
279Q8—24no—
280Q8—21no—
281Q8—21no—
282Q8—9041no—
283Q8—2261no—
284Q8—2261no—
285Q8#1426864712yes—
286Q8#1426864712yes—
287D4—9041no—
288D4—2261no—
289D4—2261no—
290C2×C4—24no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—9041no—
298C2×C4—2261no—
299C2×C4—2261no—
300C2×C4—2261no—
301C2×C4C2×C22⋊D11311yescharacteristic
302C2×C4C2×C22⋊D11311yescharacteristic
303C2×C4C2×C22⋊D11311yescharacteristic
304C2×C4C2×C22⋊D11311yescharacteristic
305C2×C4C2×C22⋊D11311yescharacteristic
306C2×C4C23×D11311yescharacteristic
307C8—2261no—
308C8—2261no—
309C8—2261no—
310C8—2261no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—4521no—
315C22—4521no—
316C22—4521no—
317C22C22×C22⋊D11311yescharacteristic
318C4—22no—
319C4—22no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—41no—
326C4—41no—
327C4—4521no—
328C4—4521no—
329C4—4521no—
330C4C2×#1426864711yescharacteristic
331C4C2×#1426864711yescharacteristic
332C2—41no—
333C2—9041no—
334C2#2029910911yescharacteristic
335C2#2029940611yescharacteristic
336C2#2029941311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#519×C113C2
socleC22×C113C22×D4
prime radical#16813596C22
hypercenter#519D113
hypocenterC113#3121
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ #117 ◁ #519

Complements

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

NH ≅ G/Ntype
2. #20298939C2semidirect
4. #20298893C2semidirect
5. #20298883C2semidirect
6. #20298820C2semidirect
7. #20298820C2semidirect
8. #20298754C2semidirect
10. #20298703C2semidirect
11. #20298696C2semidirect
12. C4×#14268637C2semidirect
13. C4×#14268634C2semidirect
14. #20298659C2semidirect
15. #519×C113C2semidirect
169. C113#3121semidirect
171. #519D113semidirect

Maximal subgroups

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

subgroupindex
#202992192
#202989392
#202989222
#202988932
#202988832
#202988202
#202987542
#202987372
#202987032
#202986962
C4×#142686372
C4×#142686342
#202986592
#519×C1132
#3121113