Finite Group Databasebeta

← #28402784

Subgroups — #28402784

Order 14464.

402 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299244C211yesmaximal, characteristic
2#20298955C211yesmaximal, characteristic, complemented
3#20298939C211yesmaximal, characteristic, complemented
4#20298916C211yesmaximal, characteristic, complemented
5#20298895C211yesmaximal, characteristic, complemented
6#20298854C211yesmaximal, characteristic, complemented
7#20298846C211yesmaximal, characteristic, complemented
8#20298820C211yesmaximal, characteristic, complemented
9#20298758C211yesmaximal, characteristic, complemented
10#20298748C211yesmaximal, characteristic, complemented
11C4×#14268634C211yesmaximal, characteristic, complemented
12#20298676C211yesmaximal, characteristic, complemented
13#20298602C211yesmaximal, characteristic, complemented
14#20298597C211yesmaximal, characteristic, complemented
15#552×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17C22×D452C2211yescharacteristic
18C2×#14268637C2211yescharacteristic, complemented
19C2×#14268634C2211yescharacteristic
20C2×#14268634C2211yescharacteristic
21C2×#14268631C2211yescharacteristic
22C2×#14268631C2211yescharacteristic, complemented
23#16813610C2211yescharacteristic
24#16813607—21no—
25#16813601C2211yescharacteristic
26#16813596C2211yescharacteristic
27#16813595—21no—
28#16813590—21no—
29C4×D452C2211yescharacteristic
30C22⋊C4×D113—21no—
31#16813555C2211yescharacteristic, complemented
32#16813553C2211yescharacteristic, complemented
33#16813553C2211yescharacteristic, complemented
34C4⋊#11744751C2211yescharacteristic, complemented
35#16813546C2211yescharacteristic, complemented
36#16813545C2211yescharacteristic, complemented
37#16813545C2211yescharacteristic, complemented
38#16813545C2211yescharacteristic, complemented
39#16813542C2211yescharacteristic
40#16813542C2211yescharacteristic
41#16813542C2211yescharacteristic
42#16813542C2211yescharacteristic
43#16813542C2211yescharacteristic
44#16813542C2211yescharacteristic
45C22⋊#11744751C2211yescharacteristic
46C22⋊#11744751C2211yescharacteristic, complemented
47C4×#11744751C2211yescharacteristic, complemented
48#126×C113—21no—
49#125×C113—21no—
50#125×C113C2211yescharacteristic, complemented
51#123×C113—21no—
52C22⋊Q8×C113C2211yescharacteristic
53C22⋊Q8×C113C2211yescharacteristic, complemented
54C4×Q8×C113C2211yescharacteristic, complemented
55C4×D4×C113C2211yescharacteristic
56#117×C113—21no—
57#117×C113C2211yescharacteristic
58C2×C4⋊C4×C113C2211yescharacteristic, complemented
59C23×D113—21no—
60#14268647—22no—
61#14268647—41no—
62C2×Dic226C2311yescharacteristic
63C2×D452—22no—
64C2×D452—21no—
65C2×D452—41no—
66C2×D452C2311yescharacteristic
67C2×D452C2311yescharacteristic
68C2×C22⋊D113—21no—
69C2×C22⋊D113—21no—
70C2×C4×D113—21no—
71C2×C4×D113—21no—
72#14268637—41no—
73#14268634—22no—
74#14268634—41no—
75#14268631—41no—
76#14268631—41no—
77C2×#11744751C2311yescharacteristic
78C2×#11744751C2311yescharacteristic
79C2×#11744751C2311yescharacteristic
80C2×#11744751C2311yescharacteristic
81C4⋊Dic113C2311yescharacteristic
82#14268626—21no—
83C22⋊Dic113—21no—
84#14268624—21no—
85#14268624—21no—
86#14268624—21no—
87#14268624—21no—
88C2×Q8×C113C2311yescharacteristic
89C2×D4×C113D411yescharacteristic
90C22×C4×C113—21no—
91C22×C4×C113C2311yescharacteristic
92C22×C4×C113C2311yescharacteristic
93C4⋊C4×C113—21no—
94C4⋊C4×C113—21no—
95C4⋊C4×C113—21no—
96C4⋊C4×C113—21no—
97C4⋊C4×C113—21no—
98C4⋊C4×C113—21no—
99C4⋊C4×C113D411yescharacteristic
100C4⋊C4×C113C2311yescharacteristic
101C4⋊C4×C113C2311yescharacteristic
102C4⋊C4×C113C2311yescharacteristic
103C22⋊C4×C113—21no—
104C22⋊C4×C113—21no—
105C22⋊C4×C113—21no—
106C22⋊C4×C113D411yescharacteristic
107C22⋊C4×C113D411yescharacteristic
108C42×C113—21no—
109C42×C113—21no—
110C42×C113C2311yescharacteristic
111C23×C113C2×D411yescharacteristic
112C23×C113C2×D411yescharacteristic
113C22×D113—21no—
114C22×D113—21no—
115C22×D113—42no—
116C22×D113—42no—
117C22×D113—81no—
118Q8×C113—21no—
119Q8×C113—21no—
120D4×C113—41no—
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113—21no—
124C2×C4×C113—21no—
125C2×C4×C113—21no—
126C2×C4×C113—21no—
127C2×C4×C113—21no—
128C2×C4×C113—21no—
129C2×C4×C113—42no—
130C2×C4×C113C2×D411yescharacteristic
131C2×C4×C113C2×D411yescharacteristic
132C2×C4×C113C2×D411yescharacteristic
133C2×C4×C113C2×D411yescharacteristic
134C2×C4×C113C2411yescharacteristic
135C22⋊D113—42no—
136C22⋊D113—81no—
137C2×Dic113—21no—
138C2×Dic113—21no—
139D452—21no—
140D452—21no—
141D452—21no—
142D452—42no—
143D452#4112yes—
144C4×D113—42no—
145C4×D113—81no—
146Dic226—21no—
147Dic226—21no—
148#11744751—21no—
149#11744751—21no—
150#11744751—21no—
151#11744751—21no—
152C22×C113—21no—
153C22×C113—21no—
154C22×C113—21no—
155C22×C113—21no—
156C22×C113—21no—
157C22×C113—21no—
158C22×C113C22×D411yescharacteristic
159C2×D113—22no—
160C2×D113—41no—
161C2×D113—41no—
162C2×D113—41no—
163C2×D113—41no—
164C2×D113—41no—
165C2×D113—84no—
166C4×C113—21no—
167C4×C113—21no—
168C4×C113—21no—
169C4×C113—21no—
170C4×C113—41no—
171C4×C113—41no—
172C4×C113—41no—
173C4×C113—41no—
174C4×C113C2×#4111yescharacteristic
175C4×C113H(5,𝔽2)11yescharacteristic
176Dic113—41no—
177Dic113—41no—
178C2×C113—41no—
179C2×C113—41no—
180C2×C113#54611yescharacteristic
181C2×C113#57511yescharacteristic
182C2×C113#57711yescharacteristic
183D113—42no—
184D113—81no—
185#3323—1131nomaximal, Sylow
186C113#332311yescharacteristic, complemented, Sylow
187#552D11311yescharacteristic, complemented
188#546—1131no—
189#488—1131no—
190#485—1131no—
191#481—1131no—
192#478—1131no—
193#470—1131no—
194#468—1131no—
195#464—1131no—
196#452—1131no—
197#450—1131no—
198C4×SD16—1131no—
199#436—1131no—
200#418—1131no—
201#417—1131no—
202C2×#41—1131no—
203C22×D4—1131no—
204C2×Q16—1131no—
205C2×SD16—1131no—
206C2×SD16—1131no—
207C2×M16—1131no—
208C2×M16—1131no—
209#126—21no—
210#125—21no—
211#125C2×D11311yescharacteristic, complemented
212#124—1131no—
213#123—21no—
214#123—2261no—
215C22⋊Q8—1131no—
216C22⋊Q8C2×D11311yescharacteristic
217C22⋊Q8C2×D11311yescharacteristic, complemented
218#121—1131no—
219#121—2261no—
220#120—2261no—
221C4×Q8C2×D11311yescharacteristic, complemented
222C4×D4—1131no—
223C4×D4C2×D11311yescharacteristic
224#117—21no—
225#117C2×D11311yescharacteristic
226C2×C4⋊C4C2×D11311yescharacteristic, complemented
227C2×C22⋊C4—2261no—
228#107—1131no—
229#106—1131no—
230#106—1131no—
231C4⋊C8—1131no—
232#103—1131no—
233#103—1131no—
234#103—1131no—
235#103—1131no—
236#102—1131no—
237#102—1131no—
238#102—1131no—
239#102—1131no—
240#102—1131no—
241#102—1131no—
242C22⋊C8—1131no—
243C22⋊C8—1131no—
244C4×C8—1131no—
245C24—2261no—
246#41—4521no—
247#41—2262no—
248C2×Q8—1131no—
249C2×Q8C22×D11311yescharacteristic
250C2×D4—1131no—
251C2×D4—1131no—
252C2×D4—4521no—
253C2×D4—2262no—
254C2×D4—2261no—
255C2×D4—2261no—
256C2×D4—2261no—
257C2×D4C22⋊D11311yescharacteristic
258C22×C4—21no—
259C22×C4—2261no—
260C22×C4—2261no—
261C22×C4C22×D11311yescharacteristic
262C22×C4C22×D11311yescharacteristic
263Q16—4521no—
264SD16—4521no—
265SD16—2262no—
266M16—4521no—
267M16—4521no—
268C2×C8—1131no—
269C2×C8—1131no—
270C2×C8—1131no—
271C2×C8—1131no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—1131no—
279C4⋊C4—2261no—
280C4⋊C4C22⋊D11311yescharacteristic
281C4⋊C4C22×D11311yescharacteristic
282C4⋊C4C22×D11311yescharacteristic
283C4⋊C4C22×D11311yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—2261no—
288C22⋊C4—2261no—
289C22⋊C4—2261no—
290C22⋊C4—2261no—
291C22⋊C4—2261no—
292C22⋊C4C22⋊D11311yescharacteristic
293C22⋊C4C22⋊D11311yescharacteristic
294C42—21no—
295C42—21no—
296C42C22×D11311yescharacteristic
297C23—9041no—
298C23—4522no—
299C23—4522no—
300C23—2261no—
301C23—2261no—
302C23C2×C22⋊D11311yescharacteristic
303C23C2×C22⋊D11311yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—2261no—
307Q8—2261no—
308D4—41no—
309D4—1132no—
310D4—9041no—
311D4—4522no—
312D4—4522no—
313D4—2261no—
314D4—2261no—
315D4—2261no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—42no—
325C2×C4—9041no—
326C2×C4—4522no—
327C2×C4—2261no—
328C2×C4—2261no—
329C2×C4C2×C22⋊D11311yescharacteristic
330C2×C4C2×C22⋊D11311yescharacteristic
331C2×C4C2×C22⋊D11311yescharacteristic
332C2×C4C2×C22⋊D11311yescharacteristic
333C2×C4C23×D11311yescharacteristic
334C8—2261no—
335C8—2261no—
336C8—2261no—
337C8—2261no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—9044no—
345C22—4521no—
346C22—4521no—
347C22—4521no—
348C22—4521no—
349C22—4521no—
350C22—2262no—
351C22C22×C22⋊D11311yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—4521no—
361C4—4521no—
362C4#41×D11311yescharacteristic
363C4#1681366811yescharacteristic
364C2—41no—
365C2—41no—
366C2—9041no—
367C2—4522no—
368C2#2029923611yescharacteristic
369C2#2029939611yescharacteristic
370C2#2029940611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#552×C113C2
socleC22×C113C22×D4
prime radical#20299244C2
hypercenter#552D113
hypocenterC113#3323
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
2. #20298955C2semidirect
3. #20298939C2semidirect
4. #20298916C2semidirect
5. #20298895C2semidirect
6. #20298854C2semidirect
7. #20298846C2semidirect
8. #20298820C2semidirect
9. #20298758C2semidirect
10. #20298748C2semidirect
11. C4×#14268634C2semidirect
12. #20298676C2semidirect
13. #20298602C2semidirect
14. #20298597C2semidirect
15. #552×C113C2semidirect
18. C2×#14268637C22semidirect
22. C2×#14268631C22semidirect
31. #16813555C22semidirect
32. #16813553C22semidirect
33. #16813553C22semidirect
34. C4⋊#11744751C22semidirect
35. #16813546C22semidirect
36. #16813545C22semidirect
37. #16813545C22semidirect
38. #16813545C22semidirect
46. C22⋊#11744751C22semidirect
47. C4×#11744751C22semidirect
50. #125×C113C22semidirect
53. C22⋊Q8×C113C22semidirect
54. C4×Q8×C113C22semidirect
58. C2×C4⋊C4×C113C22semidirect
186. C113#3323semidirect
187. #552D113semidirect
211. #125C2×D113semidirect
217. C22⋊Q8C2×D113semidirect
221. C4×Q8C2×D113semidirect
226. C2×C4⋊C4C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202992442
#202989552
#202989392
#202989162
#202988952
#202988542
#202988462
#202988202
#202987582
#202987482
C4×#142686342
#202986762
#202986022
#202985972
#552×C1132
#3323113