Finite Group Databasebeta

← #28402872

Subgroups — #28402872

Order 14464.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299248C211yesmaximal, characteristic, complemented
2#20299247C211yesmaximal, characteristic, complemented
3#20298947C211yesmaximal, characteristic, complemented
4#20298934C211yesmaximal, characteristic, complemented
5#20298932C211yesmaximal, characteristic, complemented
6#20298876C211yesmaximal, characteristic, complemented
7#20298842C211yesmaximal, characteristic, complemented
8#20298841C211yesmaximal, characteristic, complemented
9#20298801C211yesmaximal, characteristic, complemented
10#20298740C211yesmaximal, characteristic, complemented
11D8×Dic113C211yesmaximal, characteristic, complemented
12#20298673C211yesmaximal, characteristic, complemented
13#20298599C211yesmaximal, characteristic, complemented
14#20298596C211yesmaximal, characteristic, complemented
15#449×C113C211yesmaximal, characteristic, complemented
16C2×#14268646—21no—
17C2×#14268646C2211yescharacteristic
18C2×#14268635C2211yescharacteristic
19C2×#14268631C2211yescharacteristic
20C2×#14268630C2211yescharacteristic
21#16813621C2211yescharacteristic
22#16813620C2211yescharacteristic
23#16813605—21no—
24#16813604—21no—
25#16813603—21no—
26#16813603—21no—
27#16813601C2211yescharacteristic
28#16813599—21no—
29#16813598C2211yescharacteristic
30#16813594—21no—
31#16813593C2211yescharacteristic
32D4×Dic113C2211yescharacteristic
33D4×Dic113C2211yescharacteristic
34C4×C22⋊D113C2211yescharacteristic
35C2×C4⋊Dic113C2211yescharacteristic
36C2×#14268626—21no—
37C4⋊C4×D113C2211yescharacteristic
38#16813556C2211yescharacteristic
39#16813556C2211yescharacteristic
40#16813555C2211yescharacteristic
41#16813551C2211yescharacteristic
42#16813547C2211yescharacteristic
43#16813547C2211yescharacteristic
44#16813546C2211yescharacteristic
45#16813546C2211yescharacteristic
46#16813545C2211yescharacteristic
47#16813543C2211yescharacteristic
48#16813543C2211yescharacteristic
49#16813543C2211yescharacteristic
50#16813534C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C2×#41×C113C2211yescharacteristic
53C2×SD16×C113C2211yescharacteristic
54C2×D8×C113C2211yescharacteristic
55#121×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58C22⋊C8×C113C2211yescharacteristic
59#14268646—22no—
60#14268646—41no—
61#14268646—44no—
62C2×Dic226—21no—
63C2×Dic226C2311yescharacteristic
64C2×C22⋊D113—21no—
65C2×C22⋊D113—21no—
66C2×C22⋊D113D411yescharacteristic
67C22×Dic113—21no—
68C22×Dic113—21no—
69C22×Dic113—21no—
70C22×Dic113—21no—
71C2×C4×D113—21no—
72C2×C4×D113C2311yescharacteristic
73#14268635—41no—
74#14268631—41no—
75#14268630—41no—
76C2×#11744751C2311yescharacteristic
77C2×#11744751C2311yescharacteristic
78C4⋊Dic113—21no—
79C4⋊Dic113C2311yescharacteristic
80C4⋊Dic113C2311yescharacteristic
81C4⋊Dic113C2311yescharacteristic
82#14268626—21no—
83#14268626—21no—
84#14268626—21no—
85#14268626—21no—
86#14268626—21no—
87#14268626—21no—
88#14268626D411yescharacteristic
89C22⋊Dic113—21no—
90C22⋊Dic113—21no—
91C22⋊Dic113—21no—
92C22⋊Dic113—21no—
93C22⋊Dic113D411yescharacteristic
94#14268624—21no—
95#14268624D411yescharacteristic
96C4×Dic113C2311yescharacteristic
97#41×C113—22no—
98#41×C113—41no—
99C2×Q8×C113C2311yescharacteristic
100C2×D4×C113—21no—
101C2×D4×C113—21no—
102C2×D4×C113C2311yescharacteristic
103C2×D4×C113C2311yescharacteristic
104C22×C4×C113—21no—
105C22×C4×C113C2311yescharacteristic
106SD16×C113—41no—
107D8×C113—22no—
108C2×C8×C113C2311yescharacteristic
109C2×C8×C113C2311yescharacteristic
110C4⋊C4×C113C2311yescharacteristic
111C22⋊C4×C113—21no—
112C23×C113—21no—
113C23×C113—21no—
114C23×C113C2×D411yescharacteristic
115C22×D113C2×D411yescharacteristic
116Q8×C113—21no—
117Q8×C113—21no—
118D4×C113—21no—
119D4×C113—21no—
120D4×C113—21no—
121D4×C113—42no—
122D4×C113—42no—
123D4×C113#4112yescomplemented
124C2×C4×C113—21no—
125C2×C4×C113—21no—
126C2×C4×C113—21no—
127C2×C4×C113—21no—
128C2×C4×C113—42no—
129C2×C4×C113C2×D411yescharacteristic
130C2×C4×C113C2411yescharacteristic
131C22⋊D113—22no—
132C22⋊D113—42no—
133C22⋊D113—42no—
134C2×Dic113—21no—
135C2×Dic113—21no—
136C2×Dic113—21no—
137C2×Dic113—21no—
138C2×Dic113—42no—
139C2×Dic113—42no—
140C2×Dic113—42no—
141C2×Dic113—42no—
142C2×Dic113C2×D411yescharacteristic
143C2×Dic113C2×D411yescharacteristic
144C2×Dic113C2×D411yescharacteristic
145C4×D113—21no—
146C4×D113—21no—
147C4×D113—42no—
148Dic226—21no—
149Dic226—21no—
150Dic226—42no—
151C8×C113—21no—
152C8×C113—21no—
153#11744751—21no—
154#11744751—21no—
155C22×C113—22no—
156C22×C113—21no—
157C22×C113—21no—
158C22×C113—21no—
159C22×C113—41no—
160C22×C113—41no—
161C22×C113—41no—
162C22×C113—41no—
163C22×C113—41no—
164C22×C113C22×D411yescharacteristic
165C2×D113—21no—
166C2×D113—21no—
167C2×D113—21no—
168C4×C113—21no—
169C4×C113—41no—
170C4×C113—41no—
171C4×C113C2×#4111yescharacteristic
172C4×C113H(5,𝔽2)11yescharacteristic
173Dic113—21no—
174Dic113—21no—
175Dic113—41no—
176Dic113—41no—
177Dic113—41no—
178Dic113—41no—
179Dic113AGL(1,ℤ/8)12yes—
180C2×C113—41no—
181C2×C113—42no—
182C2×C113—81no—
183C2×C113#54611yescharacteristic
184C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
185C2×C113#57811yescharacteristic
186D113—41no—
187#3330—1131nomaximal, Sylow
188C113#333011yescharacteristic, complemented, Sylow
189#547—1131no—
190#547—1131no—
191#487—1131no—
192#484—1131no—
193#484—1131no—
194#474—1131no—
195#468—1131no—
196#468—1131no—
197#461—1131no—
198#449—1131no—
199#449D11311yescharacteristic, complemented
200C4×D8—1131no—
201#436—1131no—
202#417—1131no—
203#417—1131no—
204C2×#41—1131no—
205C2×#41—2261no—
206C2×#41C2×D11311yescharacteristic
207C2×SD16—1131no—
208C2×SD16C2×D11311yescharacteristic
209C2×D8C2×D11311yescharacteristic
210C2×M16—1131no—
211C2×M16—1131no—
212C4⋊Q8—1131no—
213C4⋊Q8—1131no—
214#123—2261no—
215#123—2261no—
216#123—2261no—
217#123—2261no—
218C22⋊Q8—1131no—
219C22⋊Q8—1131no—
220C22⋊Q8—2261no—
221#121—1131no—
222#121—2261no—
223#121C2×D11311yescharacteristic
224C4×D4—1131no—
225C4×D4—1131no—
226C4×D4—1131no—
227C2×C4⋊C4—1131no—
228C2×C4⋊C4—1131no—
229C2×C4⋊C4—2261no—
230#107—1131no—
231#107—1131no—
232#107—1131no—
233C4⋊C8—1131no—
234#103—1131no—
235#103—1131no—
236#103—1131no—
237#103—1131no—
238#103—1131no—
239#103C2×D11311yescharacteristic
240#102—1131no—
241#102—1131no—
242#102—1131no—
243#102C2×D11311yescharacteristic
244C22⋊C8—1131no—
245C22⋊C8C2×D11311yescharacteristic
246C4×C8—1131no—
247#41—22no—
248#41—41no—
249#41—4524no—
250#41—4521no—
251#41—2262no—
252C2×Q8—1131no—
253C2×Q8—2261no—
254C2×Q8C22×D11311yescharacteristic
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—1131no—
258C2×D4—2261no—
259C2×D4—2261no—
260C2×D4C22×D11311yescharacteristic
261C2×D4C22×D11311yescharacteristic
262C22×C4—21no—
263C22×C4—1131no—
264C22×C4—2261no—
265C22×C4—2261no—
266C22×C4—2261no—
267C22×C4—2261no—
268C22×C4—2261no—
269C22×C4C22×D11311yescharacteristic
270SD16—41no—
271SD16—4521no—
272D8—22no—
273M16—4521no—
274M16—4521no—
275C2×C8—1131no—
276C2×C8—1131no—
277C2×C8C22×D11311yescharacteristic
278C2×C8C22×D11311yescharacteristic
279C4⋊C4—1131no—
280C4⋊C4—1131no—
281C4⋊C4—1131no—
282C4⋊C4—1131no—
283C4⋊C4—2261no—
284C4⋊C4—2261no—
285C4⋊C4—2261no—
286C4⋊C4—2261no—
287C4⋊C4—2261no—
288C4⋊C4—2261no—
289C4⋊C4—2261no—
290C4⋊C4C22×D11311yescharacteristic
291C22⋊C4—21no—
292C22⋊C4—1131no—
293C22⋊C4—1131no—
294C22⋊C4—2261no—
295C22⋊C4—2261no—
296C22⋊C4—2261no—
297C22⋊C4—2261no—
298C22⋊C4—2261no—
299C42—1131no—
300C23—21no—
301C23—21no—
302C23—1131no—
303C23D4×D11311yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—4522no—
307Q8—2261no—
308Q8—2261no—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—42no—
313D4—42no—
314D4—4522no—
315D4—4522no—
316D4—2262no—
317D4#1426864612yescomplemented
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—1131no—
324C2×C4—1131no—
325C2×C4—1131no—
326C2×C4—4522no—
327C2×C4—4522no—
328C2×C4—4522no—
329C2×C4—4522no—
330C2×C4—4522no—
331C2×C4—2261no—
332C2×C4—2261no—
333C2×C4—2261no—
334C2×C4—2261no—
335C2×C4—2261no—
336C2×C4—2261no—
337C2×C4D4×D11311yescharacteristic
338C2×C4C23×D11311yescharacteristic
339C8—21no—
340C8—21no—
341C8—2261no—
342C8—2261no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—22no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—2261no—
353C22—2261no—
354C22—2261no—
355C22C2×D4×D11311yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—1132no—
360C4—4521no—
361C4—4521no—
362C4—4521no—
363C4—4521no—
364C4—2261no—
365C4—2261no—
366C4C2×#1426864611yescharacteristic
367C4#1681366711yescharacteristic
368C2—41no—
369C2—42no—
370C2—81no—
371C2—4521no—
372C2#2029923511yescharacteristic
373C2AGL(1,ℤ/8)×D11311yescharacteristic
374C2#2029941211yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#449×C113C2
socleC22×C113C22×D4
hypercenter#449D113
hypocenterC113#3330
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #20299248C2semidirect
2. #20299247C2semidirect
3. #20298947C2semidirect
4. #20298934C2semidirect
5. #20298932C2semidirect
6. #20298876C2semidirect
7. #20298842C2semidirect
8. #20298841C2semidirect
9. #20298801C2semidirect
10. #20298740C2semidirect
11. D8×Dic113C2semidirect
12. #20298673C2semidirect
13. #20298599C2semidirect
14. #20298596C2semidirect
15. #449×C113C2semidirect
123. D4×C113#41semidirect
188. C113#3330semidirect
199. #449D113semidirect
317. D4#14268646semidirect

Maximal subgroups

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

subgroupindex
#202992482
#202992472
#202989472
#202989342
#202989322
#202988762
#202988422
#202988412
#202988012
#202987402
D8×Dic1132
#202986732
#202985992
#202985962
#449×C1132
#3330113