Finite Group Databasebeta

← #28400825

Subgroups — #28400825

Order 14464.

394 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299206C211yesmaximal, characteristic, complemented
2#20299070C211yesmaximal, characteristic
3#20298941C211yesmaximal, characteristic, complemented
4#20298938C211yesmaximal, characteristic, complemented
5#20298901C211yesmaximal, characteristic, complemented
6#20298896C211yesmaximal, characteristic, complemented
7#20298802C211yesmaximal, characteristic, complemented
8#20298801C211yesmaximal, characteristic, complemented
9#20298750C211yesmaximal, characteristic
10#20298747C211yesmaximal, characteristic
11#20298700C211yesmaximal, characteristic, complemented
12C4×#14268634C211yesmaximal, characteristic, complemented
13C4×#14268635C211yesmaximal, characteristic, complemented
14#20298660C211yesmaximal, characteristic, complemented
15#440×C113C211yesmaximal, characteristic, complemented
16C2×D4×D113C2211yescharacteristic
17C2×#14268636C2211yescharacteristic
18C2×#14268635C2211yescharacteristic
19C2×#14268634C2211yescharacteristic
20#16813620C2211yescharacteristic, complemented
21#16813617—21no—
22#16813616—21no—
23#16813614—21no—
24#16813613C2211yescharacteristic, complemented
25#16813612—21no—
26#16813602C2211yescharacteristic
27#16813598C2211yescharacteristic
28C4×Dic226C2211yescharacteristic, complemented
29C4×D452C2211yescharacteristic
30D4×Dic113C2211yescharacteristic
31#16813584C2211yescharacteristic
32C4×C22⋊D113—21no—
33#16813582—21no—
34#16813580C2211yescharacteristic
35#16813579C2211yescharacteristic
36C2×#14268624—21no—
37C22⋊C4×D113—21no—
38#16813556C2211yescharacteristic, complemented
39#16813553C2211yescharacteristic, complemented
40#16813553C2211yescharacteristic, complemented
41#16813551C2211yescharacteristic, complemented
42#16813551C2211yescharacteristic, complemented
43#16813547C2211yescharacteristic, complemented
44#16813546C2211yescharacteristic, complemented
45#16813545C2211yescharacteristic, complemented
46#16813544C2211yescharacteristic
47#16813543C2211yescharacteristic
48#16813542C2211yescharacteristic
49#16813534C2211yescharacteristic
50#16813534C2211yescharacteristic
51C4×#11744751C2211yescharacteristic, complemented
52C2×SD16×C113C2211yescharacteristic
53C4×Q8×C113C2211yescharacteristic, complemented
54C4×D4×C113C2211yescharacteristic
55#107×C113C2211yescharacteristic, complemented
56#103×C113C2211yescharacteristic, complemented
57#102×C113C2211yescharacteristic
58#97×C113C2211yescharacteristic, complemented
59C23×D113—21no—
60C2×Dic226C2311yescharacteristic
61C2×D452C2311yescharacteristic
62C2×C22⋊D113—21no—
63D4×D113—22no—
64D4×D113—22no—
65C22×Dic113—21no—
66C2×C4×D113—21no—
67C2×C4×D113—21no—
68C2×C4×D113C2311yescharacteristic
69#14268636—22no—
70#14268635—22no—
71#14268634—22no—
72C2×#11744751C2311yescharacteristic
73C2×#11744751C2311yescharacteristic
74C4⋊Dic113—21no—
75C4⋊Dic113—21no—
76C4⋊Dic113C2311yescharacteristic
77C4⋊Dic113C2311yescharacteristic
78#14268626—21no—
79#14268626—21no—
80#14268626—21no—
81#14268626—21no—
82#14268626—21no—
83#14268626D411yescharacteristic
84#14268626D411yescharacteristic
85C22⋊Dic113—21no—
86#14268624—21no—
87#14268624—21no—
88#14268624—21no—
89#14268624—21no—
90#14268624—21no—
91#14268624D411yescharacteristic
92#14268624D411yescharacteristic
93C4×Dic113—21no—
94C4×Dic113—21no—
95C4×Dic113C2311yescharacteristic
96C2×Q8×C113C2311yescharacteristic
97C2×D4×C113C2311yescharacteristic
98C22×C4×C113—21no—
99SD16×C113—22no—
100C2×C8×C113C2311yescharacteristic
101C2×C8×C113C2311yescharacteristic
102C4⋊C4×C113—21no—
103C4⋊C4×C113C2311yescharacteristic
104C4⋊C4×C113C2311yescharacteristic
105C22⋊C4×C113—21no—
106C42×C113—21no—
107C42×C113C2311yescharacteristic
108C23×C113—21no—
109C22×D113—21no—
110C22×D113—24no—
111C22×D113—81no—
112C22×D113—81no—
113C22×D113C2×D411yescharacteristic
114Q8×C113—21no—
115Q8×C113—21no—
116D4×C113—21no—
117D4×C113#4112yes—
118C2×C4×C113—21no—
119C2×C4×C113—21no—
120C2×C4×C113—21no—
121C2×C4×C113—81no—
122C2×C4×C113C2×D411yescharacteristic
123C2×C4×C113C2×D411yescharacteristic
124C2×C4×C113C2411yescharacteristic
125C22⋊D113—24no—
126C2×Dic113—21no—
127C2×Dic113—21no—
128C2×Dic113—21no—
129C2×Dic113—81no—
130C2×Dic113C2×D411yescharacteristic
131C2×Dic113C2×D411yescharacteristic
132C2×Dic113C2×D411yescharacteristic
133D452—21no—
134D452#4112yes—
135C4×D113—21no—
136C4×D113—21no—
137C4×D113—81no—
138C4×D113—81no—
139Dic226—21no—
140Dic226—21no—
141C8×C113—21no—
142C8×C113—21no—
143#11744751—21no—
144#11744751—21no—
145C22×C113—22no—
146C22×C113—41no—
147C22×C113—41no—
148C22×C113C22×D411yescharacteristic
149C2×D113—21no—
150C2×D113—22no—
151C2×D113—21no—
152C2×D113—21no—
153C2×D113—41no—
154C2×D113—41no—
155C2×D113—84no—
156C4×C113—21no—
157C4×C113—21no—
158C4×C113—41no—
159C4×C113—41no—
160C4×C113—41no—
161C4×C113C2×#4111yescharacteristic
162C4×C113C2×#4111yescharacteristic
163Dic113—21no—
164Dic113—21no—
165Dic113—21no—
166Dic113—41no—
167Dic113—41no—
168Dic113—41no—
169C2×C113—42no—
170C2×C113#52511yescharacteristic
171C2×C113#57711yescharacteristic
172C2×C113#57711yescharacteristic
173D113—41no—
174D113—42no—
175#3123—1131nomaximal, Sylow
176C113#312311yescharacteristic, complemented, Sylow
177#541—1131no—
178#518—1131no—
179#485—1131no—
180#485—1131no—
181#478—1131no—
182#478—1131no—
183#461—1131no—
184#461—1131no—
185#450—1131no—
186#450—1131no—
187#440—1131no—
188#440D11311yescharacteristic, complemented
189C4×SD16—1131no—
190C4×SD16—1131no—
191#433—1131no—
192C22×D4—1131no—
193C2×SD16—1131no—
194C2×SD16—1131no—
195C2×SD16—1131no—
196C2×SD16C2×D11311yescharacteristic
197C4⋊Q8—1131no—
198#126—2261no—
199#126—2261no—
200#125—1131no—
201#125—2261no—
202#125—2261no—
203C22⋊Q8—1131no—
204C22⋊Q8—1131no—
205C4×Q8—1131no—
206C4×Q8C2×D11311yescharacteristic, complemented
207C4×D4—1131no—
208C4×D4—1131no—
209C4×D4—1131no—
210C4×D4—2261no—
211C4×D4—2261no—
212C4×D4C2×D11311yescharacteristic
213#117—1131no—
214#117—1131no—
215C2×C22⋊C4—2261no—
216C2×C22⋊C4—2261no—
217#107—1131no—
218#107C2×D11311yescharacteristic, complemented
219#106—1131no—
220#106—1131no—
221C4⋊C8—1131no—
222C4⋊C8—1131no—
223#103—1131no—
224#103—1131no—
225#103—1131no—
226#103C2×D11311yescharacteristic, complemented
227#102—1131no—
228#102—1131no—
229#102—1131no—
230#102C2×D11311yescharacteristic
231C22⋊C8—1131no—
232C22⋊C8—1131no—
233#97C2×D11311yescharacteristic, complemented
234C4×C8—1131no—
235C24—2261no—
236C2×Q8—1131no—
237C2×Q8C22×D11311yescharacteristic
238C2×D4—1131no—
239C2×D4—2261no—
240C2×D4—2262no—
241C2×D4—2262no—
242C2×D4C22×D11311yescharacteristic
243C22×C4—21no—
244C22×C4—1131no—
245C22×C4—2261no—
246C22×C4—2261no—
247C22×C4—2261no—
248SD16—22no—
249SD16—2262no—
250SD16—2262no—
251SD16—2262no—
252C2×C8—1131no—
253C2×C8—1131no—
254C2×C8C22×D11311yescharacteristic
255C2×C8C22×D11311yescharacteristic
256C4⋊C4—21no—
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—
267C4⋊C4—2261no—
268C4⋊C4C22×D11311yescharacteristic
269C4⋊C4C22×D11311yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—1131no—
272C22⋊C4—1131no—
273C22⋊C4—2261no—
274C22⋊C4—2261no—
275C22⋊C4—2261no—
276C22⋊C4—2261no—
277C22⋊C4—2261no—
278C22⋊C4—2261no—
279C42—21no—
280C42—1131no—
281C42—2261no—
282C42—2261no—
283C42C22×D11311yescharacteristic
284C23—21no—
285C23—1131no—
286C23—9041no—
287C23—9041no—
288C23—2264no—
289C23—2261no—
290Q8—21no—
291Q8—21no—
292Q8—2261no—
293Q8—2261no—
294D4—21no—
295D4—1132no—
296D4—2264no—
297D4—2261no—
298D4#1426864712yes—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—1131no—
304C2×C4—1131no—
305C2×C4—1131no—
306C2×C4—9041no—
307C2×C4—9041no—
308C2×C4—9041no—
309C2×C4—2261no—
310C2×C4—2261no—
311C2×C4—2261no—
312C2×C4—2261no—
313C2×C4—2261no—
314C2×C4D4×D11311yescharacteristic
315C2×C4D4×D11311yescharacteristic
316C2×C4C23×D11311yescharacteristic
317C8—21no—
318C8—21no—
319C8—2261no—
320C8—2261no—
321C22—22no—
322C22—41no—
323C22—41no—
324C22—9044no—
325C22—4521no—
326C22—4521no—
327C22—2261no—
328C22—2262no—
329C22—2261no—
330C22—2261no—
331C22C2×D4×D11311yescharacteristic
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—4521no—
338C4—4521no—
339C4—4521no—
340C4—2261no—
341C4—2261no—
342C4—2261no—
343C4#41×D11311yescharacteristic
344C4C2×#1426864711yescharacteristic
345C2—42no—
346C2—4521no—
347C2—4522no—
348C2#2029910711yescharacteristic
349C2#2029940711yescharacteristic
350C2#2029940811yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#440×C113C2
socleC22×C113C22×D4
prime radicalC2×D4×D113C22
hypercenter#440D113
hypocenterC113#3123
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #20299206C2semidirect
3. #20298941C2semidirect
4. #20298938C2semidirect
5. #20298901C2semidirect
6. #20298896C2semidirect
7. #20298802C2semidirect
8. #20298801C2semidirect
11. #20298700C2semidirect
12. C4×#14268634C2semidirect
13. C4×#14268635C2semidirect
14. #20298660C2semidirect
15. #440×C113C2semidirect
20. #16813620C22semidirect
24. #16813613C22semidirect
28. C4×Dic226C22semidirect
38. #16813556C22semidirect
39. #16813553C22semidirect
40. #16813553C22semidirect
41. #16813551C22semidirect
42. #16813551C22semidirect
43. #16813547C22semidirect
44. #16813546C22semidirect
45. #16813545C22semidirect
51. C4×#11744751C22semidirect
53. C4×Q8×C113C22semidirect
55. #107×C113C22semidirect
56. #103×C113C22semidirect
58. #97×C113C22semidirect
176. C113#3123semidirect
188. #440D113semidirect
206. C4×Q8C2×D113semidirect
218. #107C2×D113semidirect
226. #103C2×D113semidirect
233. #97C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202992062
#202990702
#202989412
#202989382
#202989012
#202988962
#202988022
#202988012
#202987502
#202987472
#202987002
C4×#142686342
C4×#142686352
#202986602
#440×C1132
#3123113