Finite Group Databasebeta

← #28402751

Subgroups — #28402751

Order 14464.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299300C211yesmaximal, characteristic
2#20299261C211yesmaximal, characteristic, complemented
3#20298965C211yesmaximal, characteristic, complemented
4#20298942C211yesmaximal, characteristic, complemented
5#20298931C211yesmaximal, characteristic, complemented
6#20298908C211yesmaximal, characteristic, complemented
7#20298843C211yesmaximal, characteristic, complemented
8#20298801C211yesmaximal, characteristic, complemented
9#20298736C211yesmaximal, characteristic, complemented
10#20298735C211yesmaximal, characteristic, complemented
11#20298695C211yesmaximal, characteristic, complemented
12#20298669C211yesmaximal, characteristic, complemented
13#20298605C211yesmaximal, characteristic, complemented
14C2×#16813547C211yesmaximal, characteristic, complemented
15#465×C113C211yesmaximal, characteristic, complemented
16C22×Dic226C2211yescharacteristic
17C2×Q8×D113C2211yescharacteristic
18C2×#14268635C2211yescharacteristic
19C2×#14268635C2211yescharacteristic
20C2×#14268630C2211yescharacteristic
21#16813621—21no—
22#16813620C2211yescharacteristic
23#16813615—21no—
24#16813613C2211yescharacteristic
25#16813606—21no—
26#16813602C2211yescharacteristic
27#16813600—21no—
28#16813599—21no—
29#16813594—21no—
30#16813593C2211yescharacteristic
31#16813587C2211yescharacteristic
32D4×Dic113—21no—
33D4×Dic113C2211yescharacteristic
34C4×C22⋊D113C2211yescharacteristic
35#16813582—21no—
36#16813580C2211yescharacteristic
37C2×C4⋊Dic113C2211yescharacteristic
38#16813555C2211yescharacteristic
39#16813555C2211yescharacteristic
40#16813551C2211yescharacteristic
41#16813547C2211yescharacteristic
42#16813547C2211yescharacteristic
43#16813547C2211yescharacteristic
44#16813547C2211yescharacteristic
45#16813546C2211yescharacteristic
46#16813546C2211yescharacteristic
47#16813545C2211yescharacteristic
48#16813545C2211yescharacteristic
49C22⋊#11744751C2211yescharacteristic
50#16813534C2211yescharacteristic
51#16813532C2211yescharacteristic
52C2×SD16×C113C2211yescharacteristic
53C22×C8×C113C2211yescharacteristic
54C22⋊Q8×C113C2211yescharacteristic
55#121×C113C2211yescharacteristic
56#106×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58#102×C113C2211yescharacteristic
59C2×Dic226—22no—
60C2×Dic226—21no—
61C2×Dic226—21no—
62C2×Dic226—41no—
63C2×Dic226C2311yescharacteristic
64C2×Dic226C2311yescharacteristic
65Q8×D113—22no—
66Q8×D113—41no—
67C2×C22⋊D113—21no—
68C2×C22⋊D113D411yescharacteristic
69C22×Dic113—21no—
70C22×Dic113—21no—
71C22×Dic113—21no—
72C2×C4×D113—21no—
73C2×C4×D113C2311yescharacteristic
74#14268635—22no—
75#14268635—41no—
76#14268630—41no—
77C2×#11744751C2311yescharacteristic
78C2×#11744751C2311yescharacteristic
79C4⋊Dic113—21no—
80C4⋊Dic113—21no—
81C4⋊Dic113—21no—
82C4⋊Dic113C2311yescharacteristic
83C4⋊Dic113C2311yescharacteristic
84#14268626—21no—
85#14268626—21no—
86#14268626—21no—
87#14268626—21no—
88#14268626D411yescharacteristic
89C22⋊Dic113—21no—
90C22⋊Dic113—21no—
91C22⋊Dic113D411yescharacteristic
92#14268624—21no—
93#14268624—21no—
94#14268624D411yescharacteristic
95C4×Dic113—21no—
96C4×Dic113—21no—
97C4×Dic113C2311yescharacteristic
98C2×Q8×C113C2311yescharacteristic
99C2×D4×C113—21no—
100C2×D4×C113C2311yescharacteristic
101C22×C4×C113C2311yescharacteristic
102SD16×C113—41no—
103C2×C8×C113—41no—
104C2×C8×C113C2311yescharacteristic
105C2×C8×C113C2311yescharacteristic
106C4⋊C4×C113—21no—
107C4⋊C4×C113C2311yescharacteristic
108C4⋊C4×C113C2311yescharacteristic
109C22⋊C4×C113—21no—
110C22⋊C4×C113—21no—
111C23×C113—21no—
112C23×C113C2×D411yescharacteristic
113C22×D113C2×D411yescharacteristic
114Q8×C113—21no—
115Q8×C113—21no—
116D4×C113—21no—
117D4×C113—21no—
118D4×C113—42no—
119C2×C4×C113—21no—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113—21no—
124C2×C4×C113C2×D411yescharacteristic
125C2×C4×C113C2411yescharacteristic
126C22⋊D113—22no—
127C22⋊D113—81no—
128C2×Dic113—21no—
129C2×Dic113—21no—
130C2×Dic113—21no—
131C2×Dic113—21no—
132C2×Dic113—42no—
133C2×Dic113—81no—
134C2×Dic113—81no—
135C2×Dic113C2×D411yescharacteristic
136C2×Dic113C2×D411yescharacteristic
137C2×Dic113C2×D411yescharacteristic
138C4×D113—21no—
139C4×D113—21no—
140C4×D113—42no—
141Dic226—21no—
142Dic226—21no—
143Dic226—21no—
144Dic226—42no—
145Dic226—42no—
146Dic226#4112yes—
147C8×C113—21no—
148C8×C113—21no—
149#11744751—21no—
150#11744751—21no—
151C22×C113—21no—
152C22×C113—21no—
153C22×C113—41no—
154C22×C113—41no—
155C22×C113—41no—
156C22×C113#13712yes—
157C22×C113C22×D411yescharacteristic
158C2×D113—21no—
159C2×D113—21no—
160C2×D113—21no—
161C4×C113—21no—
162C4×C113—41no—
163C4×C113—41no—
164C4×C113—41no—
165C4×C113C2×#4111yescharacteristic
166C4×C113H(5,𝔽2)11yescharacteristic
167Dic113—22no—
168Dic113—21no—
169Dic113—21no—
170Dic113—21no—
171Dic113—41no—
172Dic113—41no—
173Dic113—41no—
174C2×C113—22no—
175C2×C113—81no—
176C2×C113#54611yescharacteristic
177C2×C113C2×#13711yescharacteristic
178C2×C113#57711yescharacteristic
179D113—41no—
180#3320—1131nomaximal, Sylow
181C113#332011yescharacteristic, complemented, Sylow
182#553—1131no—
183D4×Q8—1131no—
184#491—1131no—
185#485—1131no—
186#484—1131no—
187#479—1131no—
188#468—1131no—
189#465D11311yescharacteristic, complemented
190#461—1131no—
191#448—1131no—
192#448—1131no—
193#440—1131no—
194#435—1131no—
195#419—1131no—
196C2×#103—1131no—
197C22×Q8—1131no—
198C22×Q8—1131no—
199C2×SD16—1131no—
200C2×SD16—1131no—
201C2×SD16C2×D11311yescharacteristic
202C2×M16—1131no—
203C22×C8C2×D11311yescharacteristic
204C4⋊Q8—1131no—
205C4⋊Q8—2261no—
206#126—2261no—
207#125—1131no—
208#123—2261no—
209C22⋊Q8—1131no—
210C22⋊Q8—2261no—
211C22⋊Q8—2261no—
212C22⋊Q8C2×D11311yescharacteristic
213#121—1131no—
214#121—2261no—
215#121C2×D11311yescharacteristic
216C4×Q8—1131no—
217C4×D4—1131no—
218C4×D4—1131no—
219C4×D4—2261no—
220C4×D4—2261no—
221#117—1131no—
222C2×C4⋊C4—1131no—
223#107—1131no—
224#107—1131no—
225#106C2×D11311yescharacteristic
226C4⋊C8—1131no—
227#103—1131no—
228#103—1131no—
229#103—1131no—
230#103—1131no—
231#103—1131no—
232#103—1131no—
233#103—1131no—
234#103—1131no—
235#103C2×D11311yescharacteristic
236#102C2×D11311yescharacteristic
237C22⋊C8—1131no—
238C22⋊C8—1131no—
239#97—1131no—
240C2×Q8—1131no—
241C2×Q8—1131no—
242C2×Q8—4521no—
243C2×Q8—4521no—
244C2×Q8—2261no—
245C2×Q8—2262no—
246C2×Q8—2262no—
247C2×Q8—2261no—
248C2×Q8C22×D11311yescharacteristic
249C2×D4—21no—
250C2×D4—1131no—
251C2×D4—2261no—
252C2×D4C22×D11311yescharacteristic
253C22×C4—1131no—
254C22×C4—2261no—
255C22×C4—2261no—
256C22×C4—2261no—
257C22×C4—2261no—
258C22×C4C22×D11311yescharacteristic
259SD16—41no—
260SD16—4521no—
261SD16—2262no—
262M16—4521no—
263C2×C8—41no—
264C2×C8—1131no—
265C2×C8—1131no—
266C2×C8C22×D11311yescharacteristic
267C2×C8C22×D11311yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—1131no—
270C4⋊C4—1131no—
271C4⋊C4—1131no—
272C4⋊C4—2261no—
273C4⋊C4—2261no—
274C4⋊C4—2261no—
275C4⋊C4—2261no—
276C4⋊C4—2261no—
277C4⋊C4—2261no—
278C4⋊C4—2261no—
279C4⋊C4C22×D11311yescharacteristic
280C4⋊C4C22×D11311yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—1131no—
284C22⋊C4—1131no—
285C22⋊C4—2261no—
286C22⋊C4—2261no—
287C22⋊C4—2261no—
288C22⋊C4—2261no—
289C42—1131no—
290C42—2261no—
291C42—2261no—
292C23—21no—
293C23—1131no—
294C23D4×D11311yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—1132no—
298Q8—4522no—
299Q8—4522no—
300Q8—2261no—
301Q8—2261no—
302Q8—2261no—
303D4—21no—
304D4—21no—
305D4—42no—
306D4—9041no—
307D4—2262no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—1131no—
314C2×C4—1131no—
315C2×C4—1131no—
316C2×C4—9041no—
317C2×C4—9041no—
318C2×C4—4522no—
319C2×C4—4522no—
320C2×C4—2261no—
321C2×C4—2261no—
322C2×C4—2261no—
323C2×C4—2261no—
324C2×C4—2261no—
325C2×C4—2261no—
326C2×C4D4×D11311yescharacteristic
327C2×C4C23×D11311yescharacteristic
328C8—21no—
329C8—21no—
330C8—2261no—
331C8—2261no—
332C22—21no—
333C22—21no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—2261no—
338C22—2261no—
339C22—2261no—
340C22#1681365112yes—
341C22C2×D4×D11311yescharacteristic
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—4521no—
347C4—4521no—
348C4—4521no—
349C4—2261no—
350C4—2261no—
351C4—2261no—
352C4—2262no—
353C4#41×D11311yescharacteristic
354C4#1681366711yescharacteristic
355C2—22no—
356C2—81no—
357C2—4521no—
358C2#2029923711yescharacteristic
359C2C2×#1681365111yescharacteristic
360C2#2029940511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#465×C113C2
socleC22×C113C22×D4
prime radical#20299300C2
hypercenter#465D113
hypocenterC113#3320
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
2. #20299261C2semidirect
3. #20298965C2semidirect
4. #20298942C2semidirect
5. #20298931C2semidirect
6. #20298908C2semidirect
7. #20298843C2semidirect
8. #20298801C2semidirect
9. #20298736C2semidirect
10. #20298735C2semidirect
11. #20298695C2semidirect
12. #20298669C2semidirect
13. #20298605C2semidirect
14. C2×#16813547C2semidirect
15. #465×C113C2semidirect
181. C113#3320semidirect
189. #465D113semidirect

Maximal subgroups

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

subgroupindex
#202993002
#202992612
#202989652
#202989422
#202989312
#202989082
#202988432
#202988012
#202987362
#202987352
#202986952
#202986692
#202986052
C2×#168135472
#465×C1132
#3320113