Finite Group Databasebeta

← #28400808

Subgroups — #28400808

Order 14464.

370 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299222C211yesmaximal, characteristic
2#20299074C211yesmaximal, characteristic, complemented
3#20298941C211yesmaximal, characteristic, complemented
4#20298925C211yesmaximal, characteristic
5#20298880C211yesmaximal, characteristic, complemented
6#20298821C211yesmaximal, characteristic, complemented
7#20298820C211yesmaximal, characteristic, complemented
8#20298755C211yesmaximal, characteristic, complemented
9#20298738C211yesmaximal, characteristic
10#20298702C211yesmaximal, characteristic, complemented
11#20298697C211yesmaximal, characteristic, complemented
12#20298692C211yesmaximal, characteristic, complemented
13#20298683C211yesmaximal, characteristic, complemented
14#20298658C211yesmaximal, characteristic, complemented
15#477×C113C211yesmaximal, characteristic, complemented
16C2×Q8×D113C2211yescharacteristic
17C2×Dic452C2211yescharacteristic
18C2×#14268637C2211yescharacteristic
19C2×#14268636C2211yescharacteristic
20C2×#14268634C2211yescharacteristic
21#16813617—21no—
22#16813611—21no—
23#16813610C2211yescharacteristic
24#16813607—21no—
25#16813602C2211yescharacteristic
26#16813598—21no—
27#16813597C2211yescharacteristic
28Q8×Dic113C2211yescharacteristic
29C4×Dic226—21no—
30C4×Dic226C2211yescharacteristic
31#16813587—21no—
32#16813587C2211yescharacteristic
33#16813587C2211yescharacteristic
34#16813584C2211yescharacteristic
35#16813580—21no—
36#16813580C2211yescharacteristic
37#16813579—21no—
38#16813579C2211yescharacteristic
39#16813553C2211yescharacteristic
40#16813553C2211yescharacteristic
41C4⋊#11744751C2211yescharacteristic
42#16813547C2211yescharacteristic
43#16813545C2211yescharacteristic
44#16813545C2211yescharacteristic
45#16813545C2211yescharacteristic
46#16813544C2211yescharacteristic
47#16813542C2211yescharacteristic
48#16813534C2211yescharacteristic
49#16813534C2211yescharacteristic
50#16813532C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C4⋊Q8×C113C2211yescharacteristic
53C4×Q8×C113C2211yescharacteristic
54#107×C113C2211yescharacteristic
55#107×C113C2211yescharacteristic
56C4⋊C8×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58#103×C113C2211yescharacteristic
59C2×Dic226—21no—
60C2×Dic226C2311yescharacteristic
61C2×Dic226C2311yescharacteristic
62Q8×D113—22no—
63Q8×D113—22no—
64C2×D452—21no—
65C2×D452C2311yescharacteristic
66C2×C4×D113—21no—
67C2×C4×D113—21no—
68C2×C4×D113C2311yescharacteristic
69Dic452—22no—
70#14268637—22no—
71#14268636—22no—
72#14268634—22no—
73C2×#11744751C2311yescharacteristic
74C2×#11744751C2311yescharacteristic
75C4⋊Dic113—21no—
76C4⋊Dic113—21no—
77C4⋊Dic113C2311yescharacteristic
78#14268626—21no—
79#14268626—21no—
80#14268626—21no—
81#14268626D411yescharacteristic
82#14268626D411yescharacteristic
83#14268624—21no—
84#14268624—21no—
85#14268624—21no—
86#14268624—21no—
87#14268624—21no—
88#14268624—21no—
89#14268624D411yescharacteristic
90#14268624D411yescharacteristic
91C4×Dic113—21no—
92C4×Dic113—21no—
93C4×Dic113—21no—
94C4×Dic113—21no—
95C4×Dic113—21no—
96C4×Dic113C2311yescharacteristic
97C2×Q8×C113—21no—
98C2×Q8×C113C2311yescharacteristic
99C2×C8×C113C2311yescharacteristic
100C2×C8×C113C2311yescharacteristic
101C4⋊C4×C113—21no—
102C4⋊C4×C113—21no—
103C4⋊C4×C113C2311yescharacteristic
104C4⋊C4×C113C2311yescharacteristic
105C4⋊C4×C113C2311yescharacteristic
106C42×C113—21no—
107C42×C113C2311yescharacteristic
108C22×D113—21no—
109C22×D113C2×D411yescharacteristic
110Q8×C113—21no—
111Q8×C113—81no—
112Q8×C113#4112yes—
113C2×C4×C113—21no—
114C2×C4×C113—21no—
115C2×C4×C113—21no—
116C2×C4×C113—21no—
117C2×C4×C113C2×D411yescharacteristic
118C2×C4×C113C2×D411yescharacteristic
119C2×C4×C113C2411yescharacteristic
120C2×Dic113—21no—
121C2×Dic113—21no—
122C2×Dic113—21no—
123C2×Dic113C2×D411yescharacteristic
124C2×Dic113C2×D411yescharacteristic
125C2×Dic113C2×D411yescharacteristic
126D452—21no—
127D452—21no—
128D452—81no—
129C4×D113—24no—
130C4×D113—21no—
131C4×D113—21no—
132C4×D113—81no—
133Dic226—24no—
134Dic226—21no—
135Dic226—21no—
136Dic226—21no—
137Dic226#4112yes—
138C8×C113—21no—
139C8×C113—21no—
140#11744751—21no—
141#11744751—21no—
142C22×C113C22×D411yescharacteristic
143C2×D113—21no—
144C2×D113—21no—
145C2×D113—21no—
146C2×D113—41no—
147C2×D113—41no—
148C2×D113—41no—
149C4×C113—22no—
150C4×C113—21no—
151C4×C113—21no—
152C4×C113—41no—
153C4×C113—41no—
154C4×C113—41no—
155C4×C113C2×#4111yescharacteristic
156C4×C113C2×#4111yescharacteristic
157Dic113—21no—
158Dic113—22no—
159Dic113—21no—
160Dic113—21no—
161Dic113—41no—
162Dic113—41no—
163C2×C113#52511yescharacteristic
164C2×C113#57711yescharacteristic
165C2×C113#57811yescharacteristic
166D113—41no—
167D113—81no—
168#3121—1131nomaximal, Sylow
169C113#312111yescharacteristic, complemented, Sylow
170#542—1131no—
171#519—1131no—
172#485—1131no—
173#482—1131no—
174#477D11311yescharacteristic, complemented
175#475—1131no—
176#464—1131no—
177#464—1131no—
178#451—1131no—
179#448—1131no—
180#441—1131no—
181#440—1131no—
182C4×Q16—1131no—
183C4×SD16—1131no—
184#433—1131no—
185C22×Q8—1131no—
186C2×Q16—1131no—
187C2×Q16—1131no—
188C2×SD16—1131no—
189C2×SD16—1131no—
190C4⋊Q8C2×D11311yescharacteristic
191#126—2261no—
192#124—1131no—
193#124—2261no—
194#123—2261no—
195C22⋊Q8—1131no—
196C22⋊Q8—2261no—
197#121—1131no—
198C4×Q8—1131no—
199C4×Q8—1131no—
200C4×Q8—1131no—
201C4×Q8—1131no—
202C4×Q8—2261no—
203C4×Q8—2261no—
204C4×Q8C2×D11311yescharacteristic
205C4×D4—1131no—
206#117—1131no—
207#117—1131no—
208#117—2261no—
209#117—2261no—
210#107C2×D11311yescharacteristic
211#107C2×D11311yescharacteristic
212#106—1131no—
213#106—1131no—
214C4⋊C8—1131no—
215C4⋊C8C2×D11311yescharacteristic
216#103—1131no—
217#103—1131no—
218#103—1131no—
219#103—1131no—
220#103C2×D11311yescharacteristic
221#103C2×D11311yescharacteristic
222#102—1131no—
223#102—1131no—
224C22⋊C8—1131no—
225C22⋊C8—1131no—
226#97—1131no—
227C4×C8—1131no—
228C2×Q8—21no—
229C2×Q8—1131no—
230C2×Q8—1131no—
231C2×Q8—2261no—
232C2×Q8—2262no—
233C2×Q8—2262no—
234C2×Q8C22×D11311yescharacteristic
235C2×D4—1131no—
236C2×D4—2261no—
237C22×C4—1131no—
238C22×C4—2261no—
239C22×C4—2261no—
240Q16—2262no—
241Q16—2262no—
242SD16—2262no—
243SD16—2262no—
244C2×C8—1131no—
245C2×C8—1131no—
246C2×C8C22×D11311yescharacteristic
247C2×C8C22×D11311yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—1131no—
251C4⋊C4—1131no—
252C4⋊C4—1131no—
253C4⋊C4—2261no—
254C4⋊C4—2261no—
255C4⋊C4—2261no—
256C4⋊C4—2261no—
257C4⋊C4—2261no—
258C4⋊C4C22×D11311yescharacteristic
259C4⋊C4C22×D11311yescharacteristic
260C4⋊C4C22×D11311yescharacteristic
261C22⋊C4—1131no—
262C22⋊C4—1131no—
263C22⋊C4—2261no—
264C22⋊C4—2261no—
265C22⋊C4—2261no—
266C22⋊C4—2261no—
267C22⋊C4—2261no—
268C22⋊C4—2261no—
269C42—21no—
270C42—1131no—
271C42—2261no—
272C42—2261no—
273C42—2261no—
274C42—2261no—
275C42—2261no—
276C42C22×D11311yescharacteristic
277C23—1131no—
278C23—2261no—
279Q8—21no—
280Q8—81no—
281Q8—1132no—
282Q8—2264no—
283Q8—2261no—
284Q8—2261no—
285Q8—2261no—
286Q8#1426864812yes—
287D4—9041no—
288D4—2261no—
289D4—2261no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—1131no—
295C2×C4—1131no—
296C2×C4—1131no—
297C2×C4—9041no—
298C2×C4—2264no—
299C2×C4—2261no—
300C2×C4—2261no—
301C2×C4—2261no—
302C2×C4—2261no—
303C2×C4—2261no—
304C2×C4D4×D11311yescharacteristic
305C2×C4D4×D11311yescharacteristic
306C2×C4C23×D11311yescharacteristic
307C8—21no—
308C8—21no—
309C8—2261no—
310C8—2261no—
311C22—4521no—
312C22—4521no—
313C22—4521no—
314C22—2261no—
315C22—2261no—
316C22—2261no—
317C22C2×D4×D11311yescharacteristic
318C4—22no—
319C4—21no—
320C4—21no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—4521no—
325C4—4521no—
326C4—2261no—
327C4—2262no—
328C4—2261no—
329C4—2261no—
330C4#41×D11311yescharacteristic
331C4C2×#1426864811yescharacteristic
332C2—9041no—
333C2—4521no—
334C2#2029911111yescharacteristic
335C2#2029940811yescharacteristic
336C2#2029941111yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#477×C113C2
socleC22×C113C22×D4
prime radical#16813597C22
hypercenter#477D113
hypocenterC113#3121
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
2. #20299074C2semidirect
3. #20298941C2semidirect
5. #20298880C2semidirect
6. #20298821C2semidirect
7. #20298820C2semidirect
8. #20298755C2semidirect
10. #20298702C2semidirect
11. #20298697C2semidirect
12. #20298692C2semidirect
13. #20298683C2semidirect
14. #20298658C2semidirect
15. #477×C113C2semidirect
169. C113#3121semidirect
174. #477D113semidirect

Maximal subgroups

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

subgroupindex
#202992222
#202990742
#202989412
#202989252
#202988802
#202988212
#202988202
#202987552
#202987382
#202987022
#202986972
#202986922
#202986832
#202986582
#477×C1132
#3121113