Finite Group Databasebeta

← #28402886

Subgroups — #28402886

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#20299303C211yesmaximal, characteristic, complemented
2#20299247C211yesmaximal, characteristic
3#20298947C211yesmaximal, characteristic, complemented
4#20298928C211yesmaximal, characteristic, complemented
5#20298927C211yesmaximal, characteristic, complemented
6#20298886C211yesmaximal, characteristic, complemented
7#20298856C211yesmaximal, characteristic, complemented
8#20298855C211yesmaximal, characteristic, complemented
9#20298807C211yesmaximal, characteristic, complemented
10#20298761C211yesmaximal, characteristic, complemented
11#20298760C211yesmaximal, characteristic, complemented
12#20298689C211yesmaximal, characteristic, complemented
13#20298674C211yesmaximal, characteristic, complemented
14#20298596C211yesmaximal, characteristic, complemented
15#417×C113C211yesmaximal, characteristic, complemented
16C2×#14268646C2211yescharacteristic
17C2×Dic452C2211yescharacteristic
18C2×#14268637C2211yescharacteristic
19C2×#14268635C2211yescharacteristic
20C2×#14268630C2211yescharacteristic
21#16813621C2211yescharacteristic
22#16813620C2211yescharacteristic
23#16813612—21no—
24#16813605—21no—
25#16813603—21no—
26#16813602C2211yescharacteristic
27#16813601—21no—
28#16813601C2211yescharacteristic
29#16813601C2211yescharacteristic
30#16813600—21no—
31#16813598C2211yescharacteristic
32#16813594—21no—
33#16813587C2211yescharacteristic
34D4×Dic113C2211yescharacteristic
35C4×C22⋊D113—21no—
36C4×C22⋊D113C2211yescharacteristic
37C2×#14268626—21no—
38C4⋊C4×D113C2211yescharacteristic
39#16813554C2211yescharacteristic
40#16813553C2211yescharacteristic
41#16813553C2211yescharacteristic
42#16813551C2211yescharacteristic
43#16813547C2211yescharacteristic
44#16813547C2211yescharacteristic
45#16813546C2211yescharacteristic
46#16813545C2211yescharacteristic
47#16813545C2211yescharacteristic
48#16813543C2211yescharacteristic
49C22⋊#11744751C2211yescharacteristic
50#16813534C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C2×#41×C113C2211yescharacteristic
53C2×M16×C113C2211yescharacteristic
54C2×C4⋊C4×C113C2211yescharacteristic
55#103×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58#102×C113C2211yescharacteristic
59#14268646—22no—
60#14268646—41no—
61C2×Dic226—21no—
62C2×Dic226C2311yescharacteristic
63C2×Dic226C2311yescharacteristic
64C2×C22⋊D113—21no—
65C2×C22⋊D113D411yescharacteristic
66C22×Dic113—21no—
67C22×Dic113—21no—
68C2×C4×D113—21no—
69C2×C4×D113C2311yescharacteristic
70Dic452—41no—
71#14268637—41no—
72#14268635—22no—
73#14268630—41no—
74C2×#11744751C2311yescharacteristic
75C2×#11744751C2311yescharacteristic
76C4⋊Dic113—21no—
77C4⋊Dic113C2311yescharacteristic
78C4⋊Dic113C2311yescharacteristic
79#14268626—21no—
80#14268626—21no—
81#14268626—21no—
82#14268626—21no—
83#14268626—21no—
84#14268626—21no—
85#14268626—21no—
86#14268626—21no—
87#14268626D411yescharacteristic
88C22⋊Dic113—21no—
89C22⋊Dic113—21no—
90C22⋊Dic113—21no—
91C22⋊Dic113D411yescharacteristic
92#14268624—21no—
93#14268624—21no—
94#14268624D411yescharacteristic
95C4×Dic113—21no—
96C4×Dic113C2311yescharacteristic
97#41×C113—22no—
98#41×C113—41no—
99C2×Q8×C113C2311yescharacteristic
100C2×D4×C113—21no—
101C2×D4×C113C2311yescharacteristic
102C22×C4×C113—21no—
103C22×C4×C113—21no—
104C22×C4×C113C2311yescharacteristic
105M16×C113—41no—
106C2×C8×C113C2311yescharacteristic
107C2×C8×C113C2311yescharacteristic
108C4⋊C4×C113—21no—
109C4⋊C4×C113C2311yescharacteristic
110C4⋊C4×C113C2311yescharacteristic
111C23×C113—21no—
112C23×C113C2×D411yescharacteristic
113C22×D113C2×D411yescharacteristic
114Q8×C113—21no—
115Q8×C113—21no—
116D4×C113—21no—
117D4×C113—42no—
118D4×C113#4112yes—
119C2×C4×C113—21no—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113—21no—
124C2×C4×C113—42no—
125C2×C4×C113—81no—
126C2×C4×C113C2×D411yescharacteristic
127C2×C4×C113C2411yescharacteristic
128C22⋊D113—22no—
129C22⋊D113—42no—
130C2×Dic113—21no—
131C2×Dic113—21no—
132C2×Dic113—21no—
133C2×Dic113—21no—
134C2×Dic113—42no—
135C2×Dic113—42no—
136C2×Dic113C2×D411yescharacteristic
137C2×Dic113C2×D411yescharacteristic
138C2×Dic113C2×D411yescharacteristic
139C4×D113—21no—
140C4×D113—21no—
141C4×D113—81no—
142Dic226—21no—
143Dic226—21no—
144Dic226—21no—
145Dic226—21no—
146Dic226—81no—
147C8×C113—21no—
148C8×C113—21no—
149#11744751—21no—
150#11744751—21no—
151C22×C113—22no—
152C22×C113—21no—
153C22×C113—21no—
154C22×C113—21no—
155C22×C113—41no—
156C22×C113—41no—
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—21no—
168Dic113—21no—
169Dic113—41no—
170Dic113—41no—
171Dic113—41no—
172Dic113—41no—
173Dic113#13712yes—
174C2×C113—41no—
175C2×C113—42no—
176C2×C113#54611yescharacteristic
177C2×C113C2×#13711yescharacteristic
178C2×C113#57711yescharacteristic
179D113—41no—
180#3331—1131nomaximal, Sylow
181C113#333111yescharacteristic, complemented, Sylow
182#554—1131no—
183#547—1131no—
184#487—1131no—
185#483—1131no—
186#483—1131no—
187#476—1131no—
188#470—1131no—
189#470—1131no—
190#462—1131no—
191#452—1131no—
192#452—1131no—
193C4×SD16—1131no—
194#436—1131no—
195#417—1131no—
196#417D11311yescharacteristic, complemented
197C2×#41—1131no—
198C2×#41C2×D11311yescharacteristic
199C2×Q16—1131no—
200C2×Q16—1131no—
201C2×SD16—1131no—
202C2×M16—1131no—
203C2×M16C2×D11311yescharacteristic
204C4⋊Q8—1131no—
205C4⋊Q8—1131no—
206#125—2261no—
207#123—2261no—
208#123—2261no—
209C22⋊Q8—1131no—
210C22⋊Q8—1131no—
211C22⋊Q8—1131no—
212C22⋊Q8—1131no—
213C22⋊Q8—2261no—
214C22⋊Q8—2261no—
215#121—2261no—
216C4×Q8—1131no—
217C4×D4—1131no—
218C4×D4—1131no—
219C4×D4—2261no—
220C2×C4⋊C4—1131no—
221C2×C4⋊C4—2261no—
222C2×C4⋊C4C2×D11311yescharacteristic
223#106—1131no—
224#106—1131no—
225#106—1131no—
226C4⋊C8—1131no—
227#103—1131no—
228#103—1131no—
229#103—1131no—
230#103—1131no—
231#103—1131no—
232#103C2×D11311yescharacteristic
233#103C2×D11311yescharacteristic
234#102—1131no—
235#102C2×D11311yescharacteristic
236#102C2×D11311yescharacteristic
237C22⋊C8—1131no—
238C22⋊C8—1131no—
239C4×C8—1131no—
240#41—22no—
241#41—41no—
242#41—4521no—
243#41—2262no—
244C2×Q8—1131no—
245C2×Q8—1131no—
246C2×Q8—2261no—
247C2×Q8C22×D11311yescharacteristic
248C2×D4—21no—
249C2×D4—1131no—
250C2×D4—2261no—
251C2×D4C22×D11311yescharacteristic
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—1131no—
255C22×C4—2261no—
256C22×C4—2261no—
257C22×C4—2261no—
258C22×C4C22×D11311yescharacteristic
259Q16—4521no—
260Q16—4521no—
261SD16—2262no—
262M16—41no—
263M16—4521no—
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⋊C4—2261no—
280C4⋊C4—2261no—
281C4⋊C4C22×D11311yescharacteristic
282C4⋊C4C22×D11311yescharacteristic
283C22⋊C4—1131no—
284C22⋊C4—1131no—
285C22⋊C4—2261no—
286C22⋊C4—2261no—
287C22⋊C4—2261no—
288C22⋊C4—2261no—
289C22⋊C4—2261no—
290C42—1131no—
291C42—2261no—
292C23—21no—
293C23—1131no—
294C23D4×D11311yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—9041no—
298Q8—2261no—
299Q8—2261no—
300Q8—2261no—
301Q8—2261no—
302D4—21no—
303D4—42no—
304D4—4522no—
305D4—2262no—
306D4#1426864712yes—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—42no—
313C2×C4—81no—
314C2×C4—1131no—
315C2×C4—1131no—
316C2×C4—1131no—
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—21no—
335C22—22no—
336C22—41no—
337C22—41no—
338C22—2261no—
339C22—2261no—
340C22—2261no—
341C22C2×D4×D11311yescharacteristic
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—1132no—
347C4—4521no—
348C4—4521no—
349C4—4521no—
350C4—4521no—
351C4—2261no—
352C4—2261no—
353C4C2×#1426864711yescharacteristic
354C4#1681366711yescharacteristic
355C2—41no—
356C2—42no—
357C2—4521no—
358C2#2029923811yescharacteristic
359C2#137×D11311yescharacteristic
360C2#2029940811yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#417×C113C2
socleC22×C113C22×D4
prime radical#20299247C2
hypercenter#417D113
hypocenterC113#3331
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #20299303C2semidirect
3. #20298947C2semidirect
4. #20298928C2semidirect
5. #20298927C2semidirect
6. #20298886C2semidirect
7. #20298856C2semidirect
8. #20298855C2semidirect
9. #20298807C2semidirect
10. #20298761C2semidirect
11. #20298760C2semidirect
12. #20298689C2semidirect
13. #20298674C2semidirect
14. #20298596C2semidirect
15. #417×C113C2semidirect
181. C113#3331semidirect
196. #417D113semidirect

Maximal subgroups

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

subgroupindex
#202993032
#202992472
#202989472
#202989282
#202989272
#202988862
#202988562
#202988552
#202988072
#202987612
#202987602
#202986892
#202986742
#202985962
#417×C1132
#3331113