Finite Group Databasebeta

← #28401575

Subgroups — #28401575

Order 14464.

400 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299152C211yesmaximal, characteristic, complemented
2#124×D113C211yesmaximal, characteristic
3#20298991C211yesmaximal, characteristic, complemented
4#20298989C211yesmaximal, characteristic, complemented
5#20298959C211yesmaximal, characteristic, complemented
6#20298956C211yesmaximal, characteristic, complemented
7#20298821C211yesmaximal, characteristic, complemented
8#20298820C211yesmaximal, characteristic, complemented
9#20298817C211yesmaximal, characteristic, complemented
10#20298755C211yesmaximal, characteristic, complemented
11#20298752C211yesmaximal, characteristic, complemented
12#20298750C211yesmaximal, characteristic
13#20298747C211yesmaximal, characteristic
14#20298654C211yesmaximal, characteristic, complemented
15#464×C113C211yesmaximal, characteristic, complemented
16C2×Q8×D113C2211yescharacteristic
17C2×D4×D113C2211yescharacteristic
18C2×Dic452C2211yescharacteristic, complemented
19C2×#14268637C2211yescharacteristic, complemented
20C2×#14268637C2211yescharacteristic, complemented
21C2×#14268636C2211yescharacteristic
22C2×#14268635C2211yescharacteristic
23C2×#14268634C2211yescharacteristic
24#16813621C2211yescharacteristic, complemented
25#16813620C2211yescharacteristic, complemented
26#16813612—21no—
27#16813611C2211yescharacteristic
28#16813610C2211yescharacteristic
29#16813609C2211yescharacteristic
30#16813608—21no—
31#16813608—21no—
32#16813602C2211yescharacteristic
33#16813600—21no—
34#16813598C2211yescharacteristic
35C4×Dic226—21no—
36C4×Dic226C2211yescharacteristic, complemented
37#16813579—21no—
38C22⋊C4×D113—21no—
39C22⋊C4×D113—21no—
40C42×D113C2211yescharacteristic
41C4⋊#11744751C2211yescharacteristic, complemented
42#16813547C2211yescharacteristic, complemented
43#16813546C2211yescharacteristic, complemented
44#16813545C2211yescharacteristic, complemented
45#16813544C2211yescharacteristic
46#16813543C2211yescharacteristic
47#16813542C2211yescharacteristic
48#16813534C2211yescharacteristic
49#16813534C2211yescharacteristic
50#16813532C2211yescharacteristic, complemented
51#16813532C2211yescharacteristic, complemented
52C2×Q16×C113C2211yescharacteristic, complemented
53C2×SD16×C113C2211yescharacteristic
54#124×C113C2211yescharacteristic
55C4×Q8×C113C2211yescharacteristic, complemented
56C4⋊C8×C113C2211yescharacteristic, complemented
57#103×C113C2211yescharacteristic, complemented
58#102×C113C2211yescharacteristic
59C23×D113—21no—
60C2×Dic226—21no—
61C2×Dic226—21no—
62C2×Dic226C2311yescharacteristic
63C2×Dic226C2311yescharacteristic
64Q8×D113—41no—
65Q8×D113—41no—
66C2×D452C2311yescharacteristic
67C2×C22⋊D113—21no—
68D4×D113—41no—
69D4×D113—41no—
70C2×C4×D113—21no—
71C2×C4×D113D411yescharacteristic
72C2×C4×D113D411yescharacteristic
73C2×C4×D113C2311yescharacteristic
74Dic452—41no—
75#14268637—41no—
76#14268637—41no—
77#14268636—41no—
78#14268635—41no—
79#14268634—41no—
80C2×#11744751C2311yescharacteristic
81C2×#11744751C2311yescharacteristic
82C4⋊Dic113—21no—
83C4⋊Dic113C2311yescharacteristic
84#14268626—21no—
85#14268626—21no—
86#14268626—21no—
87#14268626—21no—
88#14268626—21no—
89C22⋊Dic113—21no—
90C22⋊Dic113—21no—
91#14268624—21no—
92#14268624—21no—
93#14268624—21no—
94#14268624—21no—
95#14268624—21no—
96#14268624—21no—
97C4×Dic113—21no—
98C4×Dic113D411yescharacteristic
99C4×Dic113D411yescharacteristic
100C4×Dic113C2311yescharacteristic
101C2×Q8×C113C2311yescharacteristic
102C2×Q8×C113C2311yescharacteristic
103C2×D4×C113C2311yescharacteristic
104Q16×C113—41no—
105SD16×C113—41no—
106C2×C8×C113C2311yescharacteristic
107C2×C8×C113C2311yescharacteristic
108C4⋊C4×C113—21no—
109C4⋊C4×C113C2311yescharacteristic
110C22⋊C4×C113—21no—
111C22⋊C4×C113—21no—
112C42×C113—21no—
113C42×C113C2311yescharacteristic
114C23×C113—21no—
115C22×D113—21no—
116C22×D113—42no—
117C22×D113—42no—
118C22×D113—42no—
119C22×D113C2×D411yescharacteristic
120Q8×C113—21no—
121Q8×C113—21no—
122Q8×C113—21no—
123Q8×C113—21no—
124D4×C113—21no—
125D4×C113—21no—
126C2×C4×C113—21no—
127C2×C4×C113—21no—
128C2×C4×C113—21no—
129C2×C4×C113C2×D411yescharacteristic
130C2×C4×C113C2×D411yescharacteristic
131C2×C4×C113C2411yescharacteristic
132C22⋊D113—42no—
133C2×Dic113—21no—
134C2×Dic113—21no—
135C2×Dic113—21no—
136C2×Dic113C2×D411yescharacteristic
137C2×Dic113C2×D411yescharacteristic
138C2×Dic113C2×D411yescharacteristic
139D452—21no—
140D452—21no—
141C4×D113—22no—
142C4×D113—21no—
143C4×D113—21no—
144C4×D113—41no—
145C4×D113—42no—
146Dic226—21no—
147Dic226—21no—
148Dic226—21no—
149Dic226—21no—
150Dic226—42no—
151Dic226—42no—
152C8×C113—21no—
153C8×C113—21no—
154#11744751—21no—
155#11744751—21no—
156C22×C113—41no—
157C22×C113—41no—
158C22×C113—41no—
159C22×C113C22×D411yescharacteristic
160C2×D113—21no—
161C2×D113—21no—
162C2×D113—41no—
163C2×D113—41no—
164C2×D113—41no—
165C2×D113—84no—
166C2×D113#13712yes—
167C4×C113—21no—
168C4×C113—21no—
169C4×C113—41no—
170C4×C113—41no—
171C4×C113—41no—
172C4×C113H(5,𝔽2)11yescharacteristic
173C4×C113H(5,𝔽2)11yescharacteristic
174Dic113—21no—
175Dic113—21no—
176Dic113—21no—
177Dic113—41no—
178Dic113—41no—
179Dic113—41no—
180C2×C113—81no—
181C2×C113#53511yescharacteristic
182C2×C113C2×#13711yescharacteristic
183C2×C113#57511yescharacteristic
184D113—22no—
185D113—81no—
186#3215—1131nomaximal, Sylow
187C113#321511yescharacteristic, complemented, Sylow
188#533—1131no—
189C2×#124—1131no—
190#497—1131no—
191#497—1131no—
192#489—1131no—
193#489—1131no—
194#464—1131no—
195#464—1131no—
196#464—1131no—
197#464D11311yescharacteristic, complemented
198#451—1131no—
199#451—1131no—
200#450—1131no—
201#450—1131no—
202#432—1131no—
203C22×Q8—1131no—
204C22×D4—1131no—
205C2×Q16—1131no—
206C2×Q16—1131no—
207C2×Q16—1131no—
208C2×Q16C2×D11311yescharacteristic, complemented
209C2×SD16—1131no—
210C2×SD16—1131no—
211C2×SD16—1131no—
212C2×SD16C2×D11311yescharacteristic
213C4⋊Q8—1131no—
214C4⋊Q8—1131no—
215#125—2261no—
216#124—1131no—
217#124—1131no—
218#124—1131no—
219#124—2261no—
220#124—2261no—
221#124C2×D11311yescharacteristic
222C22⋊Q8—1131no—
223C22⋊Q8—1131no—
224C22⋊Q8—2261no—
225C4×Q8—1131no—
226C4×Q8—2261no—
227C4×Q8C2×D11311yescharacteristic, complemented
228#117—2261no—
229C2×C22⋊C4—2261no—
230C2×C22⋊C4—2261no—
231C2×C42—1131no—
232C4⋊C8—1131no—
233C4⋊C8C2×D11311yescharacteristic, complemented
234#103—1131no—
235#103—1131no—
236#103—1131no—
237#103C2×D11311yescharacteristic, complemented
238#102—1131no—
239#102—1131no—
240#102—1131no—
241#102C2×D11311yescharacteristic
242C22⋊C8—1131no—
243C22⋊C8—1131no—
244#97—1131no—
245#97—1131no—
246C24—2261no—
247C2×Q8—1131no—
248C2×Q8—1131no—
249C2×Q8—4521no—
250C2×Q8—4521no—
251C2×Q8—2261no—
252C2×Q8—2261no—
253C2×Q8C22×D11311yescharacteristic
254C2×Q8C22×D11311yescharacteristic
255C2×D4—1131no—
256C2×D4—4521no—
257C2×D4—4521no—
258C2×D4—2261no—
259C2×D4C22×D11311yescharacteristic
260C22×C4—1131no—
261C22×C4—1131no—
262C22×C4—1131no—
263C22×C4—2261no—
264Q16—41no—
265Q16—4521no—
266Q16—4521no—
267Q16—4521no—
268SD16—41no—
269SD16—4521no—
270SD16—4521no—
271SD16—4521no—
272C2×C8—1131no—
273C2×C8—1131no—
274C2×C8C22×D11311yescharacteristic
275C2×C8C22×D11311yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—1131no—
278C4⋊C4—2261no—
279C4⋊C4—2261no—
280C4⋊C4—2261no—
281C4⋊C4—2261no—
282C4⋊C4—2261no—
283C4⋊C4—2261no—
284C4⋊C4C22×D11311yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—2261no—
288C22⋊C4—2261no—
289C22⋊C4—2261no—
290C22⋊C4—2261no—
291C22⋊C4—2261no—
292C22⋊C4—2261no—
293C22⋊C4—2261no—
294C22⋊C4—2261no—
295C42—21no—
296C42—1131no—
297C42—1131no—
298C42—1131no—
299C42—2261no—
300C42C22×D11311yescharacteristic
301C23—21no—
302C23—1131no—
303C23—4522no—
304C23—4522no—
305C23—4522no—
306C23—2261no—
307Q8—21no—
308Q8—21no—
309Q8—21no—
310Q8—21no—
311Q8—4522no—
312Q8—4522no—
313Q8—2261no—
314Q8—2261no—
315Q8—2261no—
316Q8—2261no—
317D4—21no—
318D4—21no—
319D4—4522no—
320D4—2261no—
321D4—2261no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—1131no—
326C2×C4—1131no—
327C2×C4—1131no—
328C2×C4—4521no—
329C2×C4—4522no—
330C2×C4—2262no—
331C2×C4—2261no—
332C2×C4—2261no—
333C2×C4—2261no—
334C2×C4—2261no—
335C2×C4—2261no—
336C2×C4D4×D11311yescharacteristic
337C2×C4D4×D11311yescharacteristic
338C2×C4C23×D11311yescharacteristic
339C8—21no—
340C8—21no—
341C8—2261no—
342C8—2261no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—1132no—
347C22—9044no—
348C22—4521no—
349C22—4521no—
350C22—4521no—
351C22—2261no—
352C22—2261no—
353C22C2×D4×D11311yescharacteristic
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—4521no—
360C4—4521no—
361C4—4521no—
362C4—2261no—
363C4—2261no—
364C4—2261no—
365C4#1681366711yescharacteristic
366C4#1681366811yescharacteristic
367C2—81no—
368C2—9041no—
369C2—2262no—
370C2#2029916411yescharacteristic
371C2#137×D11311yescharacteristic
372C2#2029939511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#464×C113C2
socleC22×C113C22×D4
prime radicalC2×D4×D113C22
hypercenter#464D113
hypocenterC113#3215
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #20299152C2semidirect
3. #20298991C2semidirect
4. #20298989C2semidirect
5. #20298959C2semidirect
6. #20298956C2semidirect
7. #20298821C2semidirect
8. #20298820C2semidirect
9. #20298817C2semidirect
10. #20298755C2semidirect
11. #20298752C2semidirect
14. #20298654C2semidirect
15. #464×C113C2semidirect
18. C2×Dic452C22semidirect
19. C2×#14268637C22semidirect
20. C2×#14268637C22semidirect
24. #16813621C22semidirect
25. #16813620C22semidirect
36. C4×Dic226C22semidirect
41. C4⋊#11744751C22semidirect
42. #16813547C22semidirect
43. #16813546C22semidirect
44. #16813545C22semidirect
50. #16813532C22semidirect
51. #16813532C22semidirect
52. C2×Q16×C113C22semidirect
55. C4×Q8×C113C22semidirect
56. C4⋊C8×C113C22semidirect
57. #103×C113C22semidirect
187. C113#3215semidirect
197. #464D113semidirect
208. C2×Q16C2×D113semidirect
227. C4×Q8C2×D113semidirect
233. C4⋊C8C2×D113semidirect
237. #103C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991522
#124×D1132
#202989912
#202989892
#202989592
#202989562
#202988212
#202988202
#202988172
#202987552
#202987522
#202987502
#202987472
#202986542
#464×C1132
#3215113