Finite Group Databasebeta

← #28400685

Subgroups — #28400685

Order 14464.

392 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299132C211yesmaximal, characteristic, complemented
2C4×#14268647C211yesmaximal, characteristic, complemented
3#20298940C211yesmaximal, characteristic, complemented
4#20298923C211yesmaximal, characteristic, complemented
5#20298906C211yesmaximal, characteristic, complemented
6#20298899C211yesmaximal, characteristic, complemented
7#20298821C211yesmaximal, characteristic, complemented
8#20298814C211yesmaximal, characteristic, complemented
9#20298762C211yesmaximal, characteristic, complemented
10#20298745C211yesmaximal, characteristic
11#20298711C211yesmaximal, characteristic, complemented
12#20298706C211yesmaximal, characteristic, complemented
13#20298700C211yesmaximal, characteristic, complemented
14#20298700C211yesmaximal, characteristic, complemented
15#432×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17C2×Dic452C2211yescharacteristic
18C2×#14268636C2211yescharacteristic
19C2×#14268636C2211yescharacteristic
20C2×D904C2211yescharacteristic
21#16813616—21no—
22#16813614C2211yescharacteristic
23#16813610C2211yescharacteristic
24#16813605—21no—
25#16813601C2211yescharacteristic
26#16813596C2211yescharacteristic
27C4×Dic226C2211yescharacteristic
28C4×Dic226C2211yescharacteristic
29C4×Dic226C2211yescharacteristic
30C4×D452C2211yescharacteristic
31C4×D452C2211yescharacteristic
32C4×D452C2211yescharacteristic
33C4×C22⋊D113—21no—
34C4×C22⋊D113—21no—
35C4×C22⋊D113—21no—
36#16813581C2211yescharacteristic
37#16813579—21no—
38#16813579—21no—
39C42×D113—21no—
40#16813556C2211yescharacteristic
41#16813556C2211yescharacteristic
42#16813554C2211yescharacteristic
43#16813554C2211yescharacteristic
44#16813547C2211yescharacteristic
45#16813547C2211yescharacteristic
46#16813547C2211yescharacteristic
47#16813547C2211yescharacteristic
48#16813544C2211yescharacteristic
49#16813544C2211yescharacteristic
50#16813544C2211yescharacteristic
51#16813544C2211yescharacteristic
52C2×C42×C113C2211yescharacteristic
53C4⋊C8×C113C2211yescharacteristic
54C4⋊C8×C113C2211yescharacteristic
55C22⋊C8×C113C2211yescharacteristic
56C22⋊C8×C113C2211yescharacteristic
57#97×C113C2211yescharacteristic
58#97×C113C2211yescharacteristic
59#14268647—22no—
60#14268647—22no—
61C2×Dic226C2311yescharacteristic
62C2×Dic226C2311yescharacteristic
63C2×D452C2311yescharacteristic
64C2×D452C2311yescharacteristic
65C2×C22⋊D113—21no—
66C2×C22⋊D113—21no—
67C2×C4×D113—21no—
68C2×C4×D113—21no—
69C2×C4×D113—21no—
70C2×C4×D113—21no—
71Dic452—22no—
72#14268636—22no—
73#14268636—22no—
74D904—22no—
75C4⋊Dic113C2311yescharacteristic
76C4⋊Dic113C2311yescharacteristic
77C4⋊Dic113C2311yescharacteristic
78C4⋊Dic113C2311yescharacteristic
79#14268626—21no—
80#14268626—21no—
81#14268626—21no—
82#14268626—21no—
83#14268626—21no—
84#14268626—21no—
85C22⋊Dic113—21no—
86C22⋊Dic113—21no—
87#14268624—21no—
88#14268624—21no—
89#14268624—21no—
90#14268624—21no—
91#14268624—21no—
92#14268624—21no—
93C4×Dic113—21no—
94C4×Dic113—21no—
95C4×Dic113—21no—
96C4×Dic113—21no—
97C22×C4×C113D411yescharacteristic
98C22×C4×C113D411yescharacteristic
99C22×C4×C113C2311yescharacteristic
100C2×C8×C113C2311yescharacteristic
101C2×C8×C113C2311yescharacteristic
102C2×C8×C113C2311yescharacteristic
103C2×C8×C113C2311yescharacteristic
104C42×C113D411yescharacteristic
105C42×C113D411yescharacteristic
106C42×C113C2311yescharacteristic
107C42×C113C2311yescharacteristic
108C23×C113C2×D411yescharacteristic
109C22×D113—21no—
110C22×D113—21no—
111C2×C4×C113—21no—
112C2×C4×C113—21no—
113C2×C4×C113—41no—
114C2×C4×C113—41no—
115C2×C4×C113C2×D411yescharacteristic
116C2×C4×C113C2×D411yescharacteristic
117C2×C4×C113C2×D411yescharacteristic
118C2×C4×C113C2×D411yescharacteristic
119C2×C4×C113C2×D411yescharacteristic
120C2×C4×C113C2411yescharacteristic
121C22⋊D113—24no—
122C22⋊D113—42no—
123C2×Dic113—21no—
124C2×Dic113—21no—
125C2×Dic113—21no—
126C2×Dic113—21no—
127C2×Dic113—21no—
128C2×Dic113—21no—
129D452—21no—
130D452—21no—
131D452—21no—
132D452#4112yes—
133C4×D113—24no—
134C4×D113—42no—
135C4×D113—42no—
136C4×D113—42no—
137Dic226—21no—
138Dic226—21no—
139Dic226—21no—
140Dic226#4112yes—
141C8×C113—21no—
142C8×C113—21no—
143C8×C113—21no—
144C8×C113—21no—
145C22×C113—21no—
146C22×C113—21no—
147C22×C113—21no—
148C22×C113C22×D411yescharacteristic
149C2×D113—22no—
150C2×D113—41no—
151C2×D113—41no—
152C2×D113—41no—
153C2×D113—41no—
154C2×D113—41no—
155C4×C113—21no—
156C4×C113—21no—
157C4×C113—21no—
158C4×C113—21no—
159C4×C113—21no—
160C4×C113C2×#4111yescharacteristic
161C4×C113C2×#4111yescharacteristic
162Dic113—22no—
163Dic113—41no—
164Dic113—41no—
165Dic113—41no—
166Dic113—41no—
167Dic113—41no—
168C2×C113—41no—
169C2×C113#52511yescharacteristic
170C2×C113#57511yescharacteristic
171C2×C113#57511yescharacteristic
172D113—42no—
173D113—81no—
174#3111—1131nomaximal, Sylow
175C113#311111yescharacteristic, complemented, Sylow
176#529—1131no—
177C4×#41—1131no—
178#485—1131no—
179#482—1131no—
180#479—1131no—
181#478—1131no—
182#464—1131no—
183#463—1131no—
184#452—1131no—
185#449—1131no—
186#442—1131no—
187#441—1131no—
188#440—1131no—
189#440—1131no—
190#432D11311yescharacteristic, complemented
191C2×#41—1131no—
192C2×Q16—1131no—
193C2×SD16—1131no—
194C2×SD16—1131no—
195C2×D8—1131no—
196#126—2261no—
197#125—1131no—
198#124—1131no—
199#123—2261no—
200C22⋊Q8—1131no—
201#121—1131no—
202C4×Q8—1131no—
203C4×Q8—1131no—
204C4×Q8—1131no—
205C4×D4—1131no—
206C4×D4—1131no—
207C4×D4—1131no—
208C4×D4—2261no—
209C4×D4—2261no—
210C4×D4—2261no—
211#117—1131no—
212#117—2261no—
213#117—2261no—
214C2×C42—2261no—
215C2×C42C2×D11311yescharacteristic
216#107—1131no—
217#107—1131no—
218#106—1131no—
219#106—1131no—
220C4⋊C8C2×D11311yescharacteristic
221C4⋊C8C2×D11311yescharacteristic
222#103—1131no—
223#103—1131no—
224#103—1131no—
225#103—1131no—
226#102—1131no—
227#102—1131no—
228#102—1131no—
229#102—1131no—
230C22⋊C8C2×D11311yescharacteristic
231C22⋊C8C2×D11311yescharacteristic
232#97C2×D11311yescharacteristic
233#97C2×D11311yescharacteristic
234#41—2262no—
235#41—2262no—
236C2×Q8—1131no—
237C2×Q8—1131no—
238C2×D4—1131no—
239C2×D4—1131no—
240C2×D4—2261no—
241C2×D4—2261no—
242C22×C4—2261no—
243C22×C4—2261no—
244C22×C4—2261no—
245C22×C4—2261no—
246C22×C4D45211yescharacteristic
247C22×C4D45211yescharacteristic
248C22×C4C22×D11311yescharacteristic
249Q16—2262no—
250SD16—2262no—
251SD16—2262no—
252D8—2262no—
253C2×C8C22×D11311yescharacteristic
254C2×C8C22×D11311yescharacteristic
255C2×C8C22×D11311yescharacteristic
256C2×C8C22×D11311yescharacteristic
257C4⋊C4—1131no—
258C4⋊C4—1131no—
259C4⋊C4—1131no—
260C4⋊C4—1131no—
261C4⋊C4—2261no—
262C4⋊C4—2261no—
263C4⋊C4—2261no—
264C4⋊C4—2261no—
265C4⋊C4—2261no—
266C4⋊C4—2261no—
267C22⋊C4—2261no—
268C22⋊C4—2261no—
269C22⋊C4—2261no—
270C22⋊C4—2261no—
271C22⋊C4—2261no—
272C22⋊C4—2261no—
273C22⋊C4—2261no—
274C22⋊C4—2261no—
275C42—2261no—
276C42—2261no—
277C42—2261no—
278C42—2261no—
279C42D45211yescharacteristic
280C42D45211yescharacteristic
281C42C22×D11311yescharacteristic
282C42C22×D11311yescharacteristic
283C23—2261no—
284C23—2261no—
285C23C2×D45211yescharacteristic
286Q8—1132no—
287Q8—2261no—
288Q8—2261no—
289Q8—2261no—
290D4—1132no—
291D4—4522no—
292D4—2264no—
293D4—2261no—
294D4—2261no—
295D4—2261no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—4522no—
301C2×C4—4522no—
302C2×C4—4522no—
303C2×C4—2264no—
304C2×C4—2261no—
305C2×C4—2261no—
306C2×C4—2261no—
307C2×C4—2261no—
308C2×C4—2261no—
309C2×C4—2261no—
310C2×C4C2×D45211yescharacteristic
311C2×C4C2×D45211yescharacteristic
312C2×C4C2×D45211yescharacteristic
313C2×C4C2×D45211yescharacteristic
314C2×C4C2×D45211yescharacteristic
315C2×C4C23×D11311yescharacteristic
316C8—21no—
317C8—21no—
318C8—21no—
319C8—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—4521no—
324C22—4521no—
325C22—4521no—
326C22—4521no—
327C22—4521no—
328C22—2262no—
329C22C22×D45211yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—4521no—
336C4—4521no—
337C4—4521no—
338C4—4521no—
339C4—4521no—
340C4—2262no—
341C4#41×D11311yescharacteristic
342C4#41×D11311yescharacteristic
343C2—41no—
344C2—9041no—
345C2—4522no—
346C2#2029911011yescharacteristic
347C2#2029939811yescharacteristic
348C2#2029939811yescharacteristic
subgroupG/H
centerC22C22×D452
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#432×C113C2
socleC22×C113C22×D4
prime radical#20298745C2
hypercenter#432D113
hypocenterC113#3111
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. #20299132C2semidirect
2. C4×#14268647C2semidirect
3. #20298940C2semidirect
4. #20298923C2semidirect
5. #20298906C2semidirect
6. #20298899C2semidirect
7. #20298821C2semidirect
8. #20298814C2semidirect
9. #20298762C2semidirect
11. #20298711C2semidirect
12. #20298706C2semidirect
13. #20298700C2semidirect
14. #20298700C2semidirect
15. #432×C113C2semidirect
175. C113#3111semidirect
190. #432D113semidirect

Maximal subgroups

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

subgroupindex
#202991322
C4×#142686472
#202989402
#202989232
#202989062
#202988992
#202988212
#202988142
#202987622
#202987452
#202987112
#202987062
#202987002
#432×C1132
#3111113