Finite Group Databasebeta

← #28401138

Subgroups — #28401138

Order 14464.

380 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#20299132C211yesmaximal, characteristic, complemented
2#20298997C211yesmaximal, characteristic, complemented
3#20298980C211yesmaximal, characteristic, complemented
4#20298955C211yesmaximal, characteristic, complemented
5#20298952C211yesmaximal, characteristic, complemented
6#20298837C211yesmaximal, characteristic, complemented
7#20298832C211yesmaximal, characteristic
8#20298829C211yesmaximal, characteristic, complemented
9#20298825C211yesmaximal, characteristic, complemented
10C4×#14268637C211yesmaximal, characteristic, complemented
11C4×#14268634C211yesmaximal, characteristic, complemented
12C4×#14268635C211yesmaximal, characteristic, complemented
13C4×#14268632C211yesmaximal, characteristic, complemented
14C2×C4×#11744751C211yesmaximal, characteristic, complemented
15#529×C113C211yesmaximal, characteristic, complemented
16C2×#14268637C2211yescharacteristic
17C2×#14268635C2211yescharacteristic
18C2×#14268634C2211yescharacteristic
19C2×#14268632C2211yescharacteristic
20C22×#11744751C2211yescharacteristic
21C22×#11744751C2211yescharacteristic
22#16813616—21no—
23#16813614C2211yescharacteristic
24#16813610C2211yescharacteristic
25#16813605—21no—
26#16813601C2211yescharacteristic
27#16813596C2211yescharacteristic
28C4×Dic226C2211yescharacteristic
29C4×D452C2211yescharacteristic
30C4×C22⋊D113—21no—
31#16813579—21no—
32#16813555C2211yescharacteristic
33#16813555C2211yescharacteristic
34#16813553C2211yescharacteristic
35#16813553C2211yescharacteristic
36#16813546C2211yescharacteristic
37#16813546C2211yescharacteristic
38#16813545C2211yescharacteristic
39#16813545C2211yescharacteristic
40#16813543C2211yescharacteristic
41#16813543C2211yescharacteristic
42#16813542C2211yescharacteristic
43#16813542C2211yescharacteristic
44C4×#11744751C2211yescharacteristic
45C4×#11744751C2211yescharacteristic
46C4×#11744751C2211yescharacteristic
47C4×#11744751C2211yescharacteristic
48#126×C113—21no—
49#125×C113C2211yescharacteristic
50#124×C113C2211yescharacteristic
51#123×C113—21no—
52C22⋊Q8×C113C2211yescharacteristic
53#121×C113C2211yescharacteristic
54C4×Q8×C113C2211yescharacteristic
55C4×D4×C113—21no—
56C4×D4×C113C2211yescharacteristic
57#117×C113—21no—
58C2×C42×C113C2211yescharacteristic
59C2×Dic226C2311yescharacteristic
60C2×D452C2311yescharacteristic
61C2×C22⋊D113—21no—
62C2×C4×D113—21no—
63#14268637—22no—
64#14268635—22no—
65#14268634—22no—
66#14268632—22no—
67C2×#11744751—22no—
68C2×#11744751—22no—
69C2×#11744751C2311yescharacteristic
70C2×#11744751C2311yescharacteristic
71C2×#11744751C2311yescharacteristic
72C2×#11744751C2311yescharacteristic
73C4⋊Dic113C2311yescharacteristic
74C4⋊Dic113C2311yescharacteristic
75#14268626—21no—
76#14268626—21no—
77#14268626—21no—
78#14268626—21no—
79C22⋊Dic113—21no—
80#14268624—21no—
81#14268624—21no—
82#14268624—21no—
83#14268624—21no—
84C4×Dic113—21no—
85C2×Q8×C113C2311yescharacteristic
86C2×D4×C113—21no—
87C2×D4×C113C2311yescharacteristic
88C22×C4×C113—21no—
89C22×C4×C113D411yescharacteristic
90C22×C4×C113D411yescharacteristic
91C22×C4×C113C2311yescharacteristic
92C4⋊C4×C113—21no—
93C4⋊C4×C113—21no—
94C4⋊C4×C113—21no—
95C4⋊C4×C113—21no—
96C4⋊C4×C113C2311yescharacteristic
97C4⋊C4×C113C2311yescharacteristic
98C22⋊C4×C113—21no—
99C22⋊C4×C113—21no—
100C22⋊C4×C113—21no—
101C22⋊C4×C113—21no—
102C22⋊C4×C113—21no—
103C42×C113—21no—
104C42×C113D411yescharacteristic
105C42×C113D411yescharacteristic
106C42×C113C2311yescharacteristic
107C42×C113C2311yescharacteristic
108C23×C113—21no—
109C23×C113C2×D411yescharacteristic
110C22×D113—21no—
111Q8×C113—21no—
112Q8×C113—21no—
113D4×C113—21no—
114D4×C113—21no—
115D4×C113—42no—
116C2×C4×C113—22no—
117C2×C4×C113—22no—
118C2×C4×C113—21no—
119C2×C4×C113—21no—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113—42no—
124C2×C4×C113C2×D411yescharacteristic
125C2×C4×C113C2×D411yescharacteristic
126C2×C4×C113C2×D411yescharacteristic
127C2×C4×C113C2×D411yescharacteristic
128C2×C4×C113C2×D411yescharacteristic
129C2×C4×C113C2411yescharacteristic
130C22⋊D113—42no—
131C2×Dic113—21no—
132C2×Dic113—21no—
133C2×Dic113—21no—
134D452—21no—
135D452—21no—
136C4×D113—42no—
137Dic226—21no—
138Dic226—21no—
139#11744751—21no—
140#11744751—21no—
141#11744751#4112yes—
142#11744751#4112yes—
143C22×C113—21no—
144C22×C113—21no—
145C22×C113—41no—
146C22×C113—41no—
147C22×C113—41no—
148C22×C113#13512yes—
149C22×C113C22×D411yescharacteristic
150C2×D113—41no—
151C2×D113—41no—
152C2×D113—41no—
153C4×C113—21no—
154C4×C113—21no—
155C4×C113—21no—
156C4×C113—21no—
157C4×C113—41no—
158C4×C113—41no—
159C4×C113—41no—
160C4×C113#13512yes—
161C4×C113C2×#4111yescharacteristic
162C4×C113C2×#4111yescharacteristic
163Dic113—41no—
164Dic113—41no—
165Dic113—41no—
166C2×C113—22no—
167C2×C113—81no—
168C2×C113#53211yescharacteristic
169C2×C113C2×#13511yescharacteristic
170C2×C113C2×#13511yescharacteristic
171D113—81no—
172#3168—1131nomaximal, Sylow
173C113#316811yescharacteristic, complemented, Sylow
174#529—1131no—
175#529D11311yescharacteristic, complemented
176#499—1131no—
177#495—1131no—
178#488—1131no—
179#488—1131no—
180#467—1131no—
181#466—1131no—
182#465—1131no—
183#465—1131no—
184C4×Q16—1131no—
185C4×SD16—1131no—
186C4×SD16—1131no—
187C4×D8—1131no—
188C2×C4×C8—1131no—
189C2×Q16—1131no—
190C2×SD16—1131no—
191C2×SD16—1131no—
192C2×D8—1131no—
193C22×C8—1131no—
194C22×C8—1131no—
195#126—21no—
196#126—2261no—
197#125—1131no—
198#125C2×D11311yescharacteristic
199#124—1131no—
200#124C2×D11311yescharacteristic
201#123—21no—
202#123—2261no—
203C22⋊Q8—1131no—
204C22⋊Q8C2×D11311yescharacteristic
205#121—1131no—
206#121C2×D11311yescharacteristic
207C4×Q8—1131no—
208C4×Q8C2×D11311yescharacteristic
209C4×D4—21no—
210C4×D4—1131no—
211C4×D4—2261no—
212C4×D4C2×D11311yescharacteristic
213#117—21no—
214#117—2261no—
215C2×C42C2×D11311yescharacteristic
216#107—1131no—
217#107—1131no—
218#106—1131no—
219#106—1131no—
220#103—1131no—
221#103—1131no—
222#103—1131no—
223#103—1131no—
224#102—1131no—
225#102—1131no—
226#102—1131no—
227#102—1131no—
228C4×C8—1131no—
229C4×C8—1131no—
230C4×C8—1131no—
231C4×C8—1131no—
232C2×Q8—1131no—
233C2×Q8C22×D11311yescharacteristic
234C2×D4—21no—
235C2×D4—1131no—
236C2×D4—2261no—
237C2×D4C22×D11311yescharacteristic
238C22×C4—21no—
239C22×C4—2261no—
240C22×C4C22⋊D11311yescharacteristic
241C22×C4C22⋊D11311yescharacteristic
242C22×C4C22×D11311yescharacteristic
243Q16—2262no—
244SD16—2262no—
245SD16—2262no—
246D8—2262no—
247C2×C8—1131no—
248C2×C8—1131no—
249C2×C8—1131no—
250C2×C8—1131no—
251C2×C8—2262no—
252C2×C8—2262no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—1131no—
258C4⋊C4—1131no—
259C4⋊C4—2261no—
260C4⋊C4—2261no—
261C4⋊C4—2261no—
262C4⋊C4—2261no—
263C4⋊C4C22×D11311yescharacteristic
264C4⋊C4C22×D11311yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—2261no—
271C22⋊C4—2261no—
272C22⋊C4—2261no—
273C22⋊C4—2261no—
274C22⋊C4—2261no—
275C42—21no—
276C42—2261no—
277C42C22⋊D11311yescharacteristic
278C42C22⋊D11311yescharacteristic
279C42C22×D11311yescharacteristic
280C42C22×D11311yescharacteristic
281C23—21no—
282C23—2261no—
283C23C2×C22⋊D11311yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—2261no—
287Q8—2261no—
288D4—21no—
289D4—21no—
290D4—42no—
291D4—4522no—
292D4—2261no—
293D4—2261no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—42no—
302C2×C4—4522no—
303C2×C4—2261no—
304C2×C4—2261no—
305C2×C4—2261no—
306C2×C4C2×C22⋊D11311yescharacteristic
307C2×C4C2×C22⋊D11311yescharacteristic
308C2×C4C2×C22⋊D11311yescharacteristic
309C2×C4C2×C22⋊D11311yescharacteristic
310C2×C4C2×C22⋊D11311yescharacteristic
311C2×C4C23×D11311yescharacteristic
312C8—1132no—
313C8—1132no—
314C8—2261no—
315C8—2261no—
316C22—21no—
317C22—21no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—4521no—
322C22—4521no—
323C22—4521no—
324C22#1681364212yes—
325C22C22×C22⋊D11311yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—4521no—
334C4—4521no—
335C4—4521no—
336C4#1681364212yes—
337C4#41×D11311yescharacteristic
338C4#41×D11311yescharacteristic
339C2—22no—
340C2—81no—
341C2—9041no—
342C2#2029914411yescharacteristic
343C2C2×#1681364211yescharacteristic
344C2C2×#1681364211yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#529×C113C2
socleC22×C113C22×D4
prime radical#20298832C2
hypercenter#529D113
hypocenterC113#3168
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. #20299132C2semidirect
2. #20298997C2semidirect
3. #20298980C2semidirect
4. #20298955C2semidirect
5. #20298952C2semidirect
6. #20298837C2semidirect
8. #20298829C2semidirect
9. #20298825C2semidirect
10. C4×#14268637C2semidirect
11. C4×#14268634C2semidirect
12. C4×#14268635C2semidirect
13. C4×#14268632C2semidirect
14. C2×C4×#11744751C2semidirect
15. #529×C113C2semidirect
173. C113#3168semidirect
175. #529D113semidirect

Maximal subgroups

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

subgroupindex
#202991322
#202989972
#202989802
#202989552
#202989522
#202988372
#202988322
#202988292
#202988252
C4×#142686372
C4×#142686342
C4×#142686352
C4×#142686322
C2×C4×#117447512
#529×C1132
#3168113