Finite Group Databasebeta

← #28400775

Subgroups — #28400775

Order 14464.

396 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#20299203C211yesmaximal, characteristic, complemented
2#20299078C211yesmaximal, characteristic, complemented
3#20298917C211yesmaximal, characteristic, complemented
4#20298912C211yesmaximal, characteristic, complemented
5#20298906C211yesmaximal, characteristic, complemented
6#20298899C211yesmaximal, characteristic, complemented
7#20298799C211yesmaximal, characteristic, complemented
8#20298794C211yesmaximal, characteristic, complemented
9#20298745C211yesmaximal, characteristic, complemented
10#20298745C211yesmaximal, characteristic, complemented
11#20298711C211yesmaximal, characteristic, complemented
12#20298700C211yesmaximal, characteristic, complemented
13C4×#14268636C211yesmaximal, characteristic, complemented
14C4×D904C211yesmaximal, characteristic, complemented
15#433×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17C2×#14268636C2211yescharacteristic
18C2×#14268636C2211yescharacteristic
19C2×D904C2211yescharacteristic
20C2×D904C2211yescharacteristic
21#16813619C2211yescharacteristic
22#16813614C2211yescharacteristic
23#16813607—21no—
24#16813607—21no—
25#16813596C2211yescharacteristic
26#16813596C2211yescharacteristic
27#16813595—21no—
28#16813595—21no—
29C4×Dic226C2211yescharacteristic
30C4×Dic226C2211yescharacteristic
31C4×D452C2211yescharacteristic
32C4×D452C2211yescharacteristic
33C4×D452C2211yescharacteristic
34C4×D452C2211yescharacteristic
35#16813582—21no—
36#16813582—21no—
37#16813580—21no—
38C2×C4⋊Dic113C2211yescharacteristic
39C4⋊C4×D113—21no—
40#16813556C2211yescharacteristic
41#16813556C2211yescharacteristic
42#16813554C2211yescharacteristic
43#16813554C2211yescharacteristic
44#16813547C2211yescharacteristic
45#16813547C2211yescharacteristic
46#16813544C2211yescharacteristic
47#16813544C2211yescharacteristic
48#16813544C2211yescharacteristic
49#16813544C2211yescharacteristic
50#16813544C2211yescharacteristic
51#16813544C2211yescharacteristic
52#117×C113C2211yescharacteristic
53C4⋊C8×C113C2211yescharacteristic
54C4⋊C8×C113C2211yescharacteristic
55C22⋊C8×C113C2211yescharacteristic
56C22⋊C8×C113C2211yescharacteristic
57#97×C113C2211yescharacteristic
58C4×C8×C113C2211yescharacteristic
59#14268647—22no—
60#14268647—22no—
61C2×Dic226C2311yescharacteristic
62C2×D452—21no—
63C2×D452—21no—
64C2×D452C2311yescharacteristic
65C2×D452C2311yescharacteristic
66C2×D452C2311yescharacteristic
67C2×C22⋊D113—21no—
68C2×C22⋊D113—21no—
69C2×C22⋊D113—21no—
70C22×Dic113—21no—
71C2×C4×D113—21no—
72C2×C4×D113—21no—
73C2×C4×D113—21no—
74C2×C4×D113—21no—
75C2×C4×D113—21no—
76#14268636—22no—
77#14268636—22no—
78D904—22no—
79D904—22no—
80C4⋊Dic113—21no—
81C4⋊Dic113C2311yescharacteristic
82C4⋊Dic113C2311yescharacteristic
83C4⋊Dic113C2311yescharacteristic
84C4⋊Dic113C2311yescharacteristic
85#14268626—21no—
86#14268626—21no—
87#14268626—21no—
88#14268626—21no—
89#14268624—21no—
90#14268624—21no—
91#14268624—21no—
92#14268624—21no—
93#14268624—21no—
94#14268624—21no—
95C4×Dic113—21no—
96C4×Dic113—21no—
97C22×C4×C113C2311yescharacteristic
98C2×C8×C113C2311yescharacteristic
99C2×C8×C113C2311yescharacteristic
100C2×C8×C113C2311yescharacteristic
101C2×C8×C113C2311yescharacteristic
102C4⋊C4×C113D411yescharacteristic
103C4⋊C4×C113D411yescharacteristic
104C22⋊C4×C113D411yescharacteristic
105C22⋊C4×C113D411yescharacteristic
106C42×C113C2311yescharacteristic
107C42×C113C2311yescharacteristic
108C23×C113C2×D411yescharacteristic
109C22×D113—21no—
110C22×D113—21no—
111C22×D113—21no—
112C2×C4×C113—21no—
113C2×C4×C113—21no—
114C2×C4×C113C2×D411yescharacteristic
115C2×C4×C113C2×D411yescharacteristic
116C2×C4×C113C2×D411yescharacteristic
117C2×C4×C113C2×D411yescharacteristic
118C2×C4×C113C2×D411yescharacteristic
119C2×C4×C113C2411yescharacteristic
120C22⋊D113—24no—
121C22⋊D113—81no—
122C22⋊D113—81no—
123C2×Dic113—21no—
124C2×Dic113—21no—
125C2×Dic113—21no—
126C2×Dic113—21no—
127C2×Dic113—21no—
128C2×Dic113—81no—
129D452—21no—
130D452—21no—
131D452—21no—
132D452—21no—
133D452—21no—
134D452—81no—
135D452—81no—
136D452#4112yes—
137C4×D113—24no—
138C4×D113—81no—
139C4×D113—81no—
140C4×D113—81no—
141C4×D113—81no—
142Dic226—21no—
143Dic226#4112yes—
144C8×C113—21no—
145C8×C113—21no—
146C8×C113—21no—
147C8×C113—21no—
148C22×C113—21no—
149C22×C113—21no—
150C22×C113—21no—
151C22×C113C22×D411yescharacteristic
152C2×D113—22no—
153C2×D113—41no—
154C2×D113—41no—
155C2×D113—41no—
156C2×D113—41no—
157C2×D113—41no—
158C2×D113—41no—
159C2×D113—41no—
160C2×D113—41no—
161C4×C113—21no—
162C4×C113—21no—
163C4×C113—21no—
164C4×C113—21no—
165C4×C113—21no—
166C4×C113C2×#4111yescharacteristic
167C4×C113C2×#4111yescharacteristic
168Dic113—22no—
169Dic113—41no—
170Dic113—41no—
171Dic113—41no—
172Dic113—41no—
173C2×C113—41no—
174C2×C113#52511yescharacteristic
175C2×C113#57611yescharacteristic
176C2×C113#57711yescharacteristic
177D113—42no—
178D113—81no—
179D113—81no—
180#3119—1131nomaximal, Sylow
181C113#311911yescharacteristic, complemented, Sylow
182#540—1131no—
183#520—1131no—
184#481—1131no—
185#480—1131no—
186#479—1131no—
187#478—1131no—
188#460—1131no—
189#459—1131no—
190#449—1131no—
191#449—1131no—
192#442—1131no—
193#440—1131no—
194C4×SD16—1131no—
195C4×D8—1131no—
196#433D11311yescharacteristic, complemented
197C2×#41—1131no—
198C2×SD16—1131no—
199C2×SD16—1131no—
200C2×D8—1131no—
201C2×D8—1131no—
202#127—1131no—
203#125—1131no—
204#123—2261no—
205#123—2261no—
206#121—1131no—
207#121—1131no—
208#121—2261no—
209#121—2261no—
210C4×Q8—1131no—
211C4×Q8—1131no—
212C4×D4—1131no—
213C4×D4—1131no—
214C4×D4—1131no—
215C4×D4—1131no—
216C4×D4—2261no—
217C4×D4—2261no—
218#117—2261no—
219#117C2×D11311yescharacteristic
220C2×C4⋊C4—1131no—
221C2×C4⋊C4—2261no—
222#107—1131no—
223#107—1131no—
224#106—1131no—
225#106—1131no—
226C4⋊C8C2×D11311yescharacteristic
227C4⋊C8C2×D11311yescharacteristic
228#103—1131no—
229#103—1131no—
230#102—1131no—
231#102—1131no—
232#102—1131no—
233#102—1131no—
234#102—1131no—
235#102—1131no—
236C22⋊C8C2×D11311yescharacteristic
237C22⋊C8C2×D11311yescharacteristic
238#97C2×D11311yescharacteristic
239C4×C8C2×D11311yescharacteristic
240#41—2262no—
241#41—2262no—
242C2×Q8—1131no—
243C2×D4—1131no—
244C2×D4—1131no—
245C2×D4—1131no—
246C2×D4—2261no—
247C2×D4—2261no—
248C2×D4—2261no—
249C2×D4—2261no—
250C2×D4—2261no—
251C22×C4—2261no—
252C22×C4—2261no—
253C22×C4—2261no—
254C22×C4—2261no—
255C22×C4—2261no—
256C22×C4—2261no—
257C22×C4C22×D11311yescharacteristic
258SD16—2262no—
259SD16—2262no—
260D8—2262no—
261D8—2262no—
262C2×C8C22×D11311yescharacteristic
263C2×C8C22×D11311yescharacteristic
264C2×C8C22×D11311yescharacteristic
265C2×C8C22×D11311yescharacteristic
266C4⋊C4—1131no—
267C4⋊C4—1131no—
268C4⋊C4—1131no—
269C4⋊C4—1131no—
270C4⋊C4—2261no—
271C4⋊C4—2261no—
272C4⋊C4—2261no—
273C4⋊C4—2261no—
274C4⋊C4—2261no—
275C4⋊C4D45211yescharacteristic
276C4⋊C4D45211yescharacteristic
277C22⋊C4—2261no—
278C22⋊C4—2261no—
279C22⋊C4—2261no—
280C22⋊C4—2261no—
281C22⋊C4—2261no—
282C22⋊C4—2261no—
283C22⋊C4D45211yescharacteristic
284C22⋊C4D45211yescharacteristic
285C42—2261no—
286C42—2261no—
287C42C22×D11311yescharacteristic
288C42C22×D11311yescharacteristic
289C23—2261no—
290C23—2261no—
291C23—2261no—
292C23C2×D45211yescharacteristic
293Q8—1132no—
294Q8—2261no—
295D4—1132no—
296D4—9041no—
297D4—9041no—
298D4—9041no—
299D4—9041no—
300D4—2264no—
301D4—2261no—
302D4—2261no—
303D4—2261no—
304D4—2261no—
305D4—2261no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—9041no—
309C2×C4—9041no—
310C2×C4—9041no—
311C2×C4—9041no—
312C2×C4—9041no—
313C2×C4—2264no—
314C2×C4—2261no—
315C2×C4—2261no—
316C2×C4—2261no—
317C2×C4—2261no—
318C2×C4—2261no—
319C2×C4C2×D45211yescharacteristic
320C2×C4C2×D45211yescharacteristic
321C2×C4C2×D45211yescharacteristic
322C2×C4C2×D45211yescharacteristic
323C2×C4C2×D45211yescharacteristic
324C2×C4C23×D11311yescharacteristic
325C8—21no—
326C8—21no—
327C8—21no—
328C8—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—4521no—
333C22—4521no—
334C22—4521no—
335C22—4521no—
336C22—4521no—
337C22—4521no—
338C22—4521no—
339C22—4521no—
340C22—2262no—
341C22C22×D45211yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—4521no—
348C4—4521no—
349C4—4521no—
350C4—4521no—
351C4—2262no—
352C4#41×D11311yescharacteristic
353C4#41×D11311yescharacteristic
354C2—41no—
355C2—9041no—
356C2—9041no—
357C2—4522no—
358C2#2029911011yescharacteristic
359C2#2029940311yescharacteristic
360C2#2029941011yescharacteristic
subgroupG/H
centerC22C22×D452
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#433×C113C2
socleC22×C113C22×D4
hypercenter#433D113
hypocenterC113#3119
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #20299203C2semidirect
2. #20299078C2semidirect
3. #20298917C2semidirect
4. #20298912C2semidirect
5. #20298906C2semidirect
6. #20298899C2semidirect
7. #20298799C2semidirect
8. #20298794C2semidirect
9. #20298745C2semidirect
10. #20298745C2semidirect
11. #20298711C2semidirect
12. #20298700C2semidirect
13. C4×#14268636C2semidirect
14. C4×D904C2semidirect
15. #433×C113C2semidirect
181. C113#3119semidirect
196. #433D113semidirect

Maximal subgroups

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

subgroupindex
#202992032
#202990782
#202989172
#202989122
#202989062
#202988992
#202987992
#202987942
#202987452
#202987112
#202987002
C4×#142686362
C4×D9042
#433×C1132
#3119113