Finite Group Databasebeta

← #28402747

Subgroups — #28402747

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#20299294C211yesmaximal, characteristic
2D4×Dic226C211yesmaximal, characteristic, complemented
3#20298967C211yesmaximal, characteristic, complemented
4#20298940C211yesmaximal, characteristic, complemented
5#20298934C211yesmaximal, characteristic, complemented
6#20298906C211yesmaximal, characteristic, complemented
7#20298844C211yesmaximal, characteristic, complemented
8#20298827C211yesmaximal, characteristic, complemented
9#20298804C211yesmaximal, characteristic, complemented
10#20298739C211yesmaximal, characteristic, complemented
11#20298739C211yesmaximal, characteristic, complemented
12#20298700C211yesmaximal, characteristic, complemented
13#20298608C211yesmaximal, characteristic, complemented
14C2×#16813547C211yesmaximal, characteristic, complemented
15#435×C113C211yesmaximal, characteristic, complemented
16C22×Dic226C2211yescharacteristic
17C22×Dic226C2211yescharacteristic
18C2×#14268636C2211yescharacteristic
19C2×#14268636C2211yescharacteristic
20C2×#14268636C2211yescharacteristic
21#16813622C2211yescharacteristic
22#16813621—21no—
23#16813617—21no—
24#16813614C2211yescharacteristic
25#16813604—21no—
26#16813601C2211yescharacteristic
27#16813601C2211yescharacteristic
28#16813599—21no—
29#16813599—21no—
30#16813596C2211yescharacteristic
31#16813596C2211yescharacteristic
32#16813594—21no—
33C4×Dic226C2211yescharacteristic
34C4×D452C2211yescharacteristic
35D4×Dic113—21no—
36#16813582—21no—
37#16813581C2211yescharacteristic
38C2×C4⋊Dic113C2211yescharacteristic
39#16813556C2211yescharacteristic
40#16813556C2211yescharacteristic
41#16813554C2211yescharacteristic
42#16813547C2211yescharacteristic
43#16813547C2211yescharacteristic
44#16813547C2211yescharacteristic
45#16813547C2211yescharacteristic
46#16813547C2211yescharacteristic
47#16813547C2211yescharacteristic
48#16813547C2211yescharacteristic
49#16813547C2211yescharacteristic
50#16813547C2211yescharacteristic
51#16813544C2211yescharacteristic
52C2×M16×C113C2211yescharacteristic
53C22×C8×C113C2211yescharacteristic
54C4×D4×C113C2211yescharacteristic
55C4⋊C8×C113C2211yescharacteristic
56C22⋊C8×C113C2211yescharacteristic
57C22⋊C8×C113C2211yescharacteristic
58#97×C113C2211yescharacteristic
59C2×Dic226—22no—
60C2×Dic226—22no—
61C2×Dic226—21no—
62C2×Dic226—21no—
63C2×Dic226—41no—
64C2×Dic226—41no—
65C2×Dic226C2311yescharacteristic
66C2×Dic226C2311yescharacteristic
67C2×Dic226C2311yescharacteristic
68C2×D452C2311yescharacteristic
69C2×C22⋊D113—21no—
70C2×C22⋊D113—21no—
71C22×Dic113—21no—
72C22×Dic113—21no—
73C22×Dic113—21no—
74C2×C4×D113—21no—
75#14268636—22no—
76#14268636—41no—
77#14268636—41no—
78C4⋊Dic113—21no—
79C4⋊Dic113—21no—
80C4⋊Dic113—21no—
81C4⋊Dic113C2311yescharacteristic
82C4⋊Dic113C2311yescharacteristic
83C4⋊Dic113C2311yescharacteristic
84C4⋊Dic113C2311yescharacteristic
85#14268626—21no—
86#14268626—21no—
87#14268626—21no—
88#14268626—21no—
89#14268626—21no—
90C22⋊Dic113—21no—
91C22⋊Dic113—21no—
92C22⋊Dic113—21no—
93#14268624—21no—
94#14268624—21no—
95#14268624—21no—
96C4×Dic113—21no—
97C4×Dic113—21no—
98C2×D4×C113D411yescharacteristic
99C22×C4×C113C2311yescharacteristic
100C22×C4×C113C2311yescharacteristic
101M16×C113—41no—
102C2×C8×C113—41no—
103C2×C8×C113C2311yescharacteristic
104C2×C8×C113C2311yescharacteristic
105C2×C8×C113C2311yescharacteristic
106C2×C8×C113C2311yescharacteristic
107C4⋊C4×C113D411yescharacteristic
108C22⋊C4×C113D411yescharacteristic
109C22⋊C4×C113D411yescharacteristic
110C42×C113C2311yescharacteristic
111C23×C113C2×D411yescharacteristic
112C23×C113C2×D411yescharacteristic
113C22×D113—21no—
114D4×C113—22no—
115C2×C4×C113—21no—
116C2×C4×C113—21no—
117C2×C4×C113—21no—
118C2×C4×C113—21no—
119C2×C4×C113C2×D411yescharacteristic
120C2×C4×C113C2×D411yescharacteristic
121C2×C4×C113C2×D411yescharacteristic
122C2×C4×C113C2×D411yescharacteristic
123C2×C4×C113C2411yescharacteristic
124C22⋊D113—42no—
125C22⋊D113—81no—
126C2×Dic113—21no—
127C2×Dic113—21no—
128C2×Dic113—21no—
129C2×Dic113—21no—
130C2×Dic113—21no—
131C2×Dic113—21no—
132C2×Dic113—21no—
133C2×Dic113—42no—
134C2×Dic113—42no—
135C2×Dic113—81no—
136D452—21no—
137D452—21no—
138C4×D113—81no—
139Dic226—21no—
140Dic226—21no—
141Dic226—21no—
142Dic226—21no—
143Dic226—21no—
144Dic226—42no—
145Dic226—42no—
146Dic226#4112yes—
147C8×C113—21no—
148C8×C113—21no—
149C8×C113—21no—
150C8×C113—21no—
151C22×C113—21no—
152C22×C113—21no—
153C22×C113—21no—
154C22×C113—21no—
155C22×C113—21no—
156C22×C113#13712yes—
157C22×C113C22×D411yescharacteristic
158C2×D113—41no—
159C2×D113—41no—
160C2×D113—41no—
161C4×C113—21no—
162C4×C113—21no—
163C4×C113—21no—
164C4×C113—21no—
165C4×C113C2×#4111yescharacteristic
166C4×C113H(5,𝔽2)11yescharacteristic
167Dic113—22no—
168Dic113—41no—
169Dic113—41no—
170Dic113—41no—
171Dic113—41no—
172Dic113—41no—
173Dic113—41no—
174C2×C113—22no—
175C2×C113—41no—
176C2×C113#54611yescharacteristic
177C2×C113C2×#13711yescharacteristic
178C2×C113#57711yescharacteristic
179D113—81no—
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#465—1131no—
190#461—1131no—
191#448—1131no—
192#448—1131no—
193#440—1131no—
194#435D11311yescharacteristic, complemented
195#419—1131no—
196C2×#103—1131no—
197C22×Q8—1131no—
198C22×Q8—1131no—
199C2×SD16—1131no—
200C2×SD16—1131no—
201C2×SD16—1131no—
202C2×M16C2×D11311yescharacteristic
203C22×C8C2×D11311yescharacteristic
204C4⋊Q8—1131no—
205C4⋊Q8—2261no—
206#126—2261no—
207#125—1131no—
208#123—2261no—
209C22⋊Q8—1131no—
210C22⋊Q8—1131no—
211C22⋊Q8—2261no—
212C22⋊Q8—2261no—
213#121—1131no—
214#121—1131no—
215#121—2261no—
216C4×Q8—1131no—
217C4×D4—1131no—
218C4×D4—2261no—
219C4×D4—2261no—
220C4×D4C2×D11311yescharacteristic
221#117—1131no—
222C2×C4⋊C4—1131no—
223#107—1131no—
224#107—1131no—
225#106—1131no—
226C4⋊C8C2×D11311yescharacteristic
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#103—1131no—
236#102—1131no—
237C22⋊C8C2×D11311yescharacteristic
238C22⋊C8C2×D11311yescharacteristic
239#97C2×D11311yescharacteristic
240C2×Q8—1131no—
241C2×Q8—1131no—
242C2×Q8—1131no—
243C2×Q8—4521no—
244C2×Q8—4521no—
245C2×Q8—2262no—
246C2×Q8—2262no—
247C2×Q8—2261no—
248C2×Q8—2261no—
249C2×D4—1131no—
250C2×D4—2261no—
251C2×D4—2261no—
252C2×D4D45211yescharacteristic
253C22×C4—2261no—
254C22×C4—2261no—
255C22×C4—2261no—
256C22×C4—2261no—
257C22×C4C22×D11311yescharacteristic
258C22×C4C22×D11311yescharacteristic
259SD16—4521no—
260SD16—4521no—
261SD16—2262no—
262M16—41no—
263C2×C8—41no—
264C2×C8C22×D11311yescharacteristic
265C2×C8C22×D11311yescharacteristic
266C2×C8C22×D11311yescharacteristic
267C2×C8C22×D11311yescharacteristic
268C4⋊C4—1131no—
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⋊C4D45211yescharacteristic
281C22⋊C4—2261no—
282C22⋊C4—2261no—
283C22⋊C4—2261no—
284C22⋊C4—2261no—
285C22⋊C4—2261no—
286C22⋊C4—2261no—
287C22⋊C4D45211yescharacteristic
288C22⋊C4D45211yescharacteristic
289C42—2261no—
290C42—2261no—
291C42C22×D11311yescharacteristic
292C23—2261no—
293C23C2×D45211yescharacteristic
294C23C2×D45211yescharacteristic
295Q8—1132no—
296Q8—4522no—
297Q8—4522no—
298Q8—2261no—
299Q8—2261no—
300Q8—2261no—
301Q8—2261no—
302Q8—2261no—
303D4—22no—
304D4—9041no—
305D4—4522no—
306D4—2261no—
307D4—2261no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—9041no—
313C2×C4—9041no—
314C2×C4—4522no—
315C2×C4—4522no—
316C2×C4—2261no—
317C2×C4—2261no—
318C2×C4—2261no—
319C2×C4—2261no—
320C2×C4—2261no—
321C2×C4—2261no—
322C2×C4—2261no—
323C2×C4C2×D45211yescharacteristic
324C2×C4C2×D45211yescharacteristic
325C2×C4C2×D45211yescharacteristic
326C2×C4C2×D45211yescharacteristic
327C2×C4C23×D11311yescharacteristic
328C8—21no—
329C8—21no—
330C8—21no—
331C8—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—4521no—
338C22—4521no—
339C22—4521no—
340C22#1681365512yes—
341C22C22×D45211yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—4521no—
347C4—4521no—
348C4—4521no—
349C4—4521no—
350C4—4521no—
351C4—4521no—
352C4—2262no—
353C4#41×D11311yescharacteristic
354C4#1681366711yescharacteristic
355C2—22no—
356C2—41no—
357C2—9041no—
358C2#2029924311yescharacteristic
359C2C2×#1681365511yescharacteristic
360C2#2029941011yescharacteristic
subgroupG/H
centerC22C22×D452
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#435×C113C2
socleC22×C113C22×D4
prime radical#20299294C2
hypercenter#435D113
hypocenterC113#3320
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
2. D4×Dic226C2semidirect
3. #20298967C2semidirect
4. #20298940C2semidirect
5. #20298934C2semidirect
6. #20298906C2semidirect
7. #20298844C2semidirect
8. #20298827C2semidirect
9. #20298804C2semidirect
10. #20298739C2semidirect
11. #20298739C2semidirect
12. #20298700C2semidirect
13. #20298608C2semidirect
14. C2×#16813547C2semidirect
15. #435×C113C2semidirect
181. C113#3320semidirect
194. #435D113semidirect

Maximal subgroups

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

subgroupindex
#202992942
D4×Dic2262
#202989672
#202989402
#202989342
#202989062
#202988442
#202988272
#202988042
#202987392
#202987002
#202986082
C2×#168135472
#435×C1132
#3320113