Finite Group Databasebeta

← #28400750

Subgroups — #28400750

Order 14464.

386 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299133C211yesmaximal, characteristic
2C4×Q8×D113C211yesmaximal, characteristic, complemented
3#20298935C211yesmaximal, characteristic, complemented
4#20298918C211yesmaximal, characteristic
5#20298902C211yesmaximal, characteristic, complemented
6#20298821C211yesmaximal, characteristic, complemented
7#20298820C211yesmaximal, characteristic, complemented
8#20298755C211yesmaximal, characteristic, complemented
9#20298738C211yesmaximal, characteristic
10#20298704C211yesmaximal, characteristic, complemented
11#20298702C211yesmaximal, characteristic, complemented
12#20298701C211yesmaximal, characteristic, complemented
13#20298697C211yesmaximal, characteristic, complemented
14#20298654C211yesmaximal, characteristic, complemented
15#479×C113C211yesmaximal, characteristic, complemented
16C2×Q8×D113C2211yescharacteristic
17C2×Dic452C2211yescharacteristic
18C2×#14268637C2211yescharacteristic
19C2×#14268636C2211yescharacteristic
20C2×#14268634C2211yescharacteristic
21#16813617—21no—
22#16813610C2211yescharacteristic
23#16813607—21no—
24#16813602C2211yescharacteristic
25#16813597C2211yescharacteristic
26Q8×Dic113C2211yescharacteristic
27C4×Dic226—21no—
28C4×Dic226C2211yescharacteristic
29#16813587—21no—
30#16813587C2211yescharacteristic
31#16813587C2211yescharacteristic
32#16813584—21no—
33#16813584C2211yescharacteristic
34#16813580—21no—
35C4⋊C4×D113—21no—
36C4⋊C4×D113C2211yescharacteristic
37C42×D113—21no—
38C42×D113C2211yescharacteristic
39#16813555C2211yescharacteristic
40#16813553C2211yescharacteristic
41C4⋊#11744751C2211yescharacteristic
42#16813547C2211yescharacteristic
43#16813545C2211yescharacteristic
44#16813545C2211yescharacteristic
45#16813545C2211yescharacteristic
46#16813544C2211yescharacteristic
47#16813542C2211yescharacteristic
48#16813534C2211yescharacteristic
49#16813534C2211yescharacteristic
50#16813532C2211yescharacteristic
51#16813532C2211yescharacteristic
52#125×C113C2211yescharacteristic
53C4×Q8×C113C2211yescharacteristic
54#107×C113C2211yescharacteristic
55#106×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×D113—21no—
69C2×C4×D113D411yescharacteristic
70C2×C4×D113D411yescharacteristic
71C2×C4×D113C2311yescharacteristic
72Dic452—22no—
73#14268637—22no—
74#14268636—22no—
75#14268634—22no—
76C2×#11744751C2311yescharacteristic
77C2×#11744751C2311yescharacteristic
78C4⋊Dic113—21no—
79C4⋊Dic113—21no—
80C4⋊Dic113C2311yescharacteristic
81#14268626—21no—
82#14268626—21no—
83#14268626—21no—
84#14268626—21no—
85#14268624—21no—
86#14268624—21no—
87#14268624—21no—
88#14268624—21no—
89#14268624—21no—
90C4×Dic113—21no—
91C4×Dic113—21no—
92C4×Dic113—21no—
93C4×Dic113—21no—
94C4×Dic113D411yescharacteristic
95C4×Dic113D411yescharacteristic
96C4×Dic113C2311yescharacteristic
97C2×Q8×C113C2311yescharacteristic
98C2×C8×C113C2311yescharacteristic
99C2×C8×C113C2311yescharacteristic
100C4⋊C4×C113—21no—
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#4112yes—
112C2×C4×C113—21no—
113C2×C4×C113—21no—
114C2×C4×C113—21no—
115C2×C4×C113—21no—
116C2×C4×C113C2×D411yescharacteristic
117C2×C4×C113C2×D411yescharacteristic
118C2×C4×C113C2411yescharacteristic
119C2×Dic113—21no—
120C2×Dic113—21no—
121C2×Dic113—21no—
122C2×Dic113C2×D411yescharacteristic
123C2×Dic113C2×D411yescharacteristic
124C2×Dic113C2×D411yescharacteristic
125D452—21no—
126D452—21no—
127D452—42no—
128C4×D113—24no—
129C4×D113—22no—
130C4×D113—21no—
131C4×D113—21no—
132C4×D113—41no—
133C4×D113—42no—
134C4×D113—42no—
135Dic226—24no—
136Dic226—21no—
137Dic226—21no—
138Dic226—21no—
139Dic226#4112yes—
140C8×C113—21no—
141C8×C113—21no—
142#11744751—21no—
143#11744751—21no—
144C22×C113C22×D411yescharacteristic
145C2×D113—21no—
146C2×D113—21no—
147C2×D113—41no—
148C2×D113—41no—
149C2×D113—41no—
150C2×D113#13712yes—
151C4×C113—22no—
152C4×C113—21no—
153C4×C113—21no—
154C4×C113—41no—
155C4×C113—41no—
156C4×C113—41no—
157C4×C113C2×#4111yescharacteristic
158C4×C113C2×#4111yescharacteristic
159Dic113—21no—
160Dic113—22no—
161Dic113—21no—
162Dic113—21no—
163Dic113—41no—
164Dic113—41no—
165C2×C113#52511yescharacteristic
166C2×C113C2×#13711yescharacteristic
167C2×C113#57511yescharacteristic
168D113—22no—
169D113—81no—
170#3117—1131nomaximal, Sylow
171C113#311711yescharacteristic, complemented, Sylow
172#529—1131no—
173C2×C4×Q8—1131no—
174#484—1131no—
175#481—1131no—
176#479—1131no—
177#479D11311yescharacteristic, complemented
178#464—1131no—
179#464—1131no—
180#451—1131no—
181#448—1131no—
182#441—1131no—
183#441—1131no—
184#440—1131no—
185#440—1131no—
186#432—1131no—
187C22×Q8—1131no—
188C2×Q16—1131no—
189C2×Q16—1131no—
190C2×SD16—1131no—
191C2×SD16—1131no—
192#126—2261no—
193#125C2×D11311yescharacteristic
194#124—1131no—
195#123—2261no—
196C22⋊Q8—1131no—
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—
206C4×D4—2261no—
207#117—2261no—
208C2×C4⋊C4—1131no—
209C2×C4⋊C4—2261no—
210C2×C42—1131no—
211C2×C42—2261no—
212#107—1131no—
213#107C2×D11311yescharacteristic
214#106—1131no—
215#106C2×D11311yescharacteristic
216C4⋊C8—1131no—
217C4⋊C8C2×D11311yescharacteristic
218#103—1131no—
219#103—1131no—
220#103—1131no—
221#103—1131no—
222#103C2×D11311yescharacteristic
223#103C2×D11311yescharacteristic
224#102—1131no—
225#102—1131no—
226C22⋊C8—1131no—
227C22⋊C8—1131no—
228#97—1131no—
229#97—1131no—
230C2×Q8—1131no—
231C2×Q8—1131no—
232C2×Q8—2261no—
233C2×Q8—2262no—
234C2×Q8—2262no—
235C2×Q8C22×D11311yescharacteristic
236C2×D4—1131no—
237C2×D4—2261no—
238C22×C4—1131no—
239C22×C4—1131no—
240C22×C4—1131no—
241C22×C4—2261no—
242C22×C4—2261no—
243C22×C4—2261no—
244Q16—2262no—
245Q16—2262no—
246SD16—2262no—
247SD16—2262no—
248C2×C8—1131no—
249C2×C8—1131no—
250C2×C8C22×D11311yescharacteristic
251C2×C8C22×D11311yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—1131no—
256C4⋊C4—2261no—
257C4⋊C4—2261no—
258C4⋊C4—2261no—
259C4⋊C4—2261no—
260C4⋊C4—2261no—
261C4⋊C4—2261no—
262C4⋊C4C22×D11311yescharacteristic
263C4⋊C4C22×D11311yescharacteristic
264C4⋊C4C22×D11311yescharacteristic
265C22⋊C4—2261no—
266C22⋊C4—2261no—
267C22⋊C4—2261no—
268C22⋊C4—2261no—
269C22⋊C4—2261no—
270C42—21no—
271C42—1131no—
272C42—1131no—
273C42—1131no—
274C42—2261no—
275C42—2261no—
276C42—2261no—
277C42—2261no—
278C42C22×D11311yescharacteristic
279C23—1131no—
280C23—2261no—
281Q8—21no—
282Q8—1132no—
283Q8—2264no—
284Q8—2261no—
285Q8—2261no—
286Q8—2261no—
287Q8#1426864812yes—
288D4—4522no—
289D4—2261no—
290D4—2261no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—1131no—
296C2×C4—1131no—
297C2×C4—1131no—
298C2×C4—4521no—
299C2×C4—4522no—
300C2×C4—4522no—
301C2×C4—2262no—
302C2×C4—2264no—
303C2×C4—2261no—
304C2×C4—2261no—
305C2×C4—2261no—
306C2×C4—2261no—
307C2×C4—2261no—
308C2×C4D4×D11311yescharacteristic
309C2×C4D4×D11311yescharacteristic
310C2×C4C23×D11311yescharacteristic
311C8—21no—
312C8—21no—
313C8—2261no—
314C8—2261no—
315C22—1132no—
316C22—4521no—
317C22—4521no—
318C22—4521no—
319C22—2261no—
320C22—2261no—
321C22C2×D4×D11311yescharacteristic
322C4—22no—
323C4—21no—
324C4—21no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—4521no—
329C4—4521no—
330C4—2261no—
331C4—2262no—
332C4—2261no—
333C4—2261no—
334C4#41×D11311yescharacteristic
335C4C2×#1426864811yescharacteristic
336C2—9041no—
337C2—2262no—
338C2#2029911111yescharacteristic
339C2#137×D11311yescharacteristic
340C2#2029939511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#479×C113C2
socleC22×C113C22×D4
prime radical#16813597C22
hypercenter#479D113
hypocenterC113#3117
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D113C2semidirect
3. #20298935C2semidirect
5. #20298902C2semidirect
6. #20298821C2semidirect
7. #20298820C2semidirect
8. #20298755C2semidirect
10. #20298704C2semidirect
11. #20298702C2semidirect
12. #20298701C2semidirect
13. #20298697C2semidirect
14. #20298654C2semidirect
15. #479×C113C2semidirect
171. C113#3117semidirect
177. #479D113semidirect

Maximal subgroups

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

subgroupindex
#202991332
C4×Q8×D1132
#202989352
#202989182
#202989022
#202988212
#202988202
#202987552
#202987382
#202987042
#202987022
#202987012
#202986972
#202986542
#479×C1132
#3117113