Finite Group Databasebeta

← #28402478

Subgroups — #28402478

Order 14464.

398 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299294C211yesmaximal, characteristic, complemented
2#20299257C211yesmaximal, characteristic, complemented
3#20298953C211yesmaximal, characteristic, complemented
4#20298940C211yesmaximal, characteristic, complemented
5#20298917C211yesmaximal, characteristic, complemented
6#20298906C211yesmaximal, characteristic, complemented
7#20298834C211yesmaximal, characteristic, complemented
8#20298827C211yesmaximal, characteristic, complemented
9#20298814C211yesmaximal, characteristic, complemented
10#20298745C211yesmaximal, characteristic, complemented
11#20298739C211yesmaximal, characteristic, complemented
12C4×#14268636C211yesmaximal, characteristic, complemented
13#20298595C211yesmaximal, characteristic, complemented
14C2×#16813547C211yesmaximal, characteristic, complemented
15C8×D4×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17C22×Dic226C2211yescharacteristic
18C2×#14268636C2211yescharacteristic
19C2×#14268636C2211yescharacteristic
20C2×D904C2211yescharacteristic
21#16813617—21no—
22#16813614C2211yescharacteristic
23#16813610C2211yescharacteristic
24#16813608—21no—
25#16813604—21no—
26#16813601C2211yescharacteristic
27#16813600—21no—
28#16813596C2211yescharacteristic
29#16813596C2211yescharacteristic
30#16813596C2211yescharacteristic
31#16813594—21no—
32#16813594—21no—
33C4×Dic226C2211yescharacteristic
34C4×D452C2211yescharacteristic
35#16813582—21no—
36#16813582—21no—
37#16813581C2211yescharacteristic
38C2×C4⋊Dic113C2211yescharacteristic
39#16813556C2211yescharacteristic
40#16813554C2211yescharacteristic
41#16813554C2211yescharacteristic
42#16813547C2211yescharacteristic
43#16813547C2211yescharacteristic
44#16813547C2211yescharacteristic
45#16813547C2211yescharacteristic
46#16813547C2211yescharacteristic
47#16813547C2211yescharacteristic
48#16813544C2211yescharacteristic
49#16813544C2211yescharacteristic
50#16813544C2211yescharacteristic
51#16813544C2211yescharacteristic
52C22×C8×C113C2211yescharacteristic
53C22×C8×C113C2211yescharacteristic
54C4×D4×C113C2211yescharacteristic
55C4⋊C8×C113C2211yescharacteristic
56C22⋊C8×C113C2211yescharacteristic
57C22⋊C8×C113C2211yescharacteristic
58C4×C8×C113C2211yescharacteristic
59#14268647—22no—
60#14268647—41no—
61C2×Dic226—22no—
62C2×Dic226—21no—
63C2×Dic226—41no—
64C2×Dic226C2311yescharacteristic
65C2×Dic226C2311yescharacteristic
66C2×D452C2311yescharacteristic
67C2×D452C2311yescharacteristic
68C2×C22⋊D113—21no—
69C2×C22⋊D113—21no—
70C2×C22⋊D113—21no—
71C2×C22⋊D113—21no—
72C22×Dic113—21no—
73C22×Dic113—21no—
74C2×C4×D113—21no—
75C2×C4×D113—21no—
76#14268636—22no—
77#14268636—41no—
78D904—41no—
79C4⋊Dic113—21no—
80C4⋊Dic113C2311yescharacteristic
81C4⋊Dic113C2311yescharacteristic
82C4⋊Dic113C2311yescharacteristic
83C4⋊Dic113C2311yescharacteristic
84#14268626—21no—
85#14268626—21no—
86#14268626—21no—
87#14268626—21no—
88C22⋊Dic113—21no—
89C22⋊Dic113—21no—
90#14268624—21no—
91#14268624—21no—
92#14268624—21no—
93#14268624—21no—
94#14268624—21no—
95#14268624—21no—
96C4×Dic113—21no—
97C4×Dic113—21no—
98C2×D4×C113D411yescharacteristic
99C22×C4×C113C2311yescharacteristic
100C22×C4×C113C2311yescharacteristic
101C2×C8×C113—41no—
102C2×C8×C113—41no—
103C2×C8×C113C2311yescharacteristic
104C2×C8×C113C2311yescharacteristic
105C2×C8×C113C2311yescharacteristic
106C2×C8×C113C2311yescharacteristic
107C4⋊C4×C113D411yescharacteristic
108C22⋊C4×C113D411yescharacteristic
109C22⋊C4×C113D411yescharacteristic
110C42×C113C2311yescharacteristic
111C23×C113C2×D411yescharacteristic
112C23×C113C2×D411yescharacteristic
113C22×D113—21no—
114C22×D113—21no—
115D4×C113—22no—
116C2×C4×C113—21no—
117C2×C4×C113—21no—
118C2×C4×C113—21no—
119C2×C4×C113—21no—
120C2×C4×C113C2×D411yescharacteristic
121C2×C4×C113C2×D411yescharacteristic
122C2×C4×C113C2×D411yescharacteristic
123C2×C4×C113C2×D411yescharacteristic
124C2×C4×C113C2411yescharacteristic
125C22⋊D113—42no—
126C22⋊D113—42no—
127C22⋊D113—42no—
128C22⋊D113—81no—
129C2×Dic113—21no—
130C2×Dic113—21no—
131C2×Dic113—21no—
132C2×Dic113—21no—
133C2×Dic113—21no—
134C2×Dic113—21no—
135C2×Dic113—42no—
136C2×Dic113—81no—
137D452—21no—
138D452—21no—
139D452—21no—
140D452—21no—
141C4×D113—42no—
142C4×D113—81no—
143Dic226—21no—
144Dic226—21no—
145Dic226—21no—
146Dic226—42no—
147Dic226#4112yes—
148C8×C113—21no—
149C8×C113—21no—
150C8×C113—21no—
151C8×C113—21no—
152C22×C113—21no—
153C22×C113—21no—
154C22×C113—21no—
155C22×C113—21no—
156C22×C113—21no—
157C22×C113#13512yes—
158C22×C113C22×D411yescharacteristic
159C2×D113—41no—
160C2×D113—41no—
161C2×D113—41no—
162C2×D113—41no—
163C2×D113—41no—
164C2×D113—41no—
165C4×C113—21no—
166C4×C113—21no—
167C4×C113—21no—
168C4×C113—21no—
169C4×C113C2×#4111yescharacteristic
170C4×C113H(5,𝔽2)11yescharacteristic
171Dic113—22no—
172Dic113—41no—
173Dic113—41no—
174Dic113—41no—
175Dic113—41no—
176Dic113—41no—
177C2×C113—22no—
178C2×C113—41no—
179C2×C113#54611yescharacteristic
180C2×C113C2×#13511yescharacteristic
181C2×C113#57711yescharacteristic
182D113—81no—
183D113—81no—
184#3301—1131nomaximal, Sylow
185C113#330111yescharacteristic, complemented, Sylow
186#553—1131no—
187#548—1131no—
188#488—1131no—
189#485—1131no—
190#481—1131no—
191#479—1131no—
192#466—1131no—
193#465—1131no—
194#463—1131no—
195#449—1131no—
196#448—1131no—
197C4×SD16—1131no—
198C8×D4D11311yescharacteristic, complemented
199#416—1131no—
200C2×#103—1131no—
201C2×#41—1131no—
202C22×Q8—1131no—
203C2×SD16—1131no—
204C2×SD16—1131no—
205C2×D8—1131no—
206C22×C8C2×D11311yescharacteristic
207C22×C8C2×D11311yescharacteristic
208#126—2261no—
209#125—1131no—
210#124—1131no—
211#124—2261no—
212#123—2261no—
213C22⋊Q8—1131no—
214C22⋊Q8—2261no—
215#121—1131no—
216#121—1131no—
217#121—1131no—
218#121—2261no—
219#121—2261no—
220C4×Q8—1131no—
221C4×D4—1131no—
222C4×D4—2261no—
223C4×D4—2261no—
224C4×D4C2×D11311yescharacteristic
225#117—1131no—
226C2×C4⋊C4—1131no—
227#107—1131no—
228#106—1131no—
229#106—1131no—
230C4⋊C8C2×D11311yescharacteristic
231#103—1131no—
232#103—1131no—
233#103—1131no—
234#103—1131no—
235#103—1131no—
236#103—1131no—
237#102—1131no—
238#102—1131no—
239#102—1131no—
240#102—1131no—
241C22⋊C8C2×D11311yescharacteristic
242C22⋊C8C2×D11311yescharacteristic
243C4×C8C2×D11311yescharacteristic
244#41—4521no—
245#41—2262no—
246C2×Q8—1131no—
247C2×Q8—1131no—
248C2×Q8—4521no—
249C2×Q8—2262no—
250C2×Q8—2261no—
251C2×D4—1131no—
252C2×D4—1131no—
253C2×D4—2261no—
254C2×D4—2261no—
255C2×D4—2261no—
256C2×D4—2261no—
257C2×D4D45211yescharacteristic
258C22×C4—2261no—
259C22×C4—2261no—
260C22×C4—2261no—
261C22×C4—2261no—
262C22×C4C22×D11311yescharacteristic
263C22×C4C22×D11311yescharacteristic
264SD16—4521no—
265SD16—2262no—
266D8—4521no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8C22×D11311yescharacteristic
270C2×C8C22×D11311yescharacteristic
271C2×C8C22×D11311yescharacteristic
272C2×C8C22×D11311yescharacteristic
273C4⋊C4—1131no—
274C4⋊C4—1131no—
275C4⋊C4—1131no—
276C4⋊C4—1131no—
277C4⋊C4—2261no—
278C4⋊C4—2261no—
279C4⋊C4—2261no—
280C4⋊C4—2261no—
281C4⋊C4—2261no—
282C4⋊C4D45211yescharacteristic
283C22⋊C4—2261no—
284C22⋊C4—2261no—
285C22⋊C4—2261no—
286C22⋊C4—2261no—
287C22⋊C4—2261no—
288C22⋊C4—2261no—
289C22⋊C4—2261no—
290C22⋊C4—2261no—
291C22⋊C4D45211yescharacteristic
292C22⋊C4D45211yescharacteristic
293C42—2261no—
294C42—2261no—
295C42C22×D11311yescharacteristic
296C23—2261no—
297C23—2261no—
298C23C2×D45211yescharacteristic
299C23C2×D45211yescharacteristic
300Q8—1132no—
301Q8—4522no—
302Q8—2261no—
303Q8—2261no—
304Q8—2261no—
305D4—22no—
306D4—9041no—
307D4—4522no—
308D4—4522no—
309D4—4522no—
310D4—2261no—
311D4—2261no—
312D4—2261no—
313D4—2261no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—9041no—
319C2×C4—9041no—
320C2×C4—4522no—
321C2×C4—4522no—
322C2×C4—2261no—
323C2×C4—2261no—
324C2×C4—2261no—
325C2×C4—2261no—
326C2×C4—2261no—
327C2×C4—2261no—
328C2×C4C2×D45211yescharacteristic
329C2×C4C2×D45211yescharacteristic
330C2×C4C2×D45211yescharacteristic
331C2×C4C2×D45211yescharacteristic
332C2×C4C23×D11311yescharacteristic
333C8—21no—
334C8—21no—
335C8—21no—
336C8—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—4521no—
343C22—4521no—
344C22—4521no—
345C22—4521no—
346C22—4521no—
347C22—4521no—
348C22#1681364412yes—
349C22C22×D45211yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—4521no—
355C4—4521no—
356C4—4521no—
357C4—4521no—
358C4—4521no—
359C4—2262no—
360C4#41×D11311yescharacteristic
361C4#1681366711yescharacteristic
362C2—22no—
363C2—41no—
364C2—9041no—
365C2—9041no—
366C2#2029924311yescharacteristic
367C2C2×#1681364411yescharacteristic
368C2#2029941011yescharacteristic
subgroupG/H
centerC22C22×D452
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC8×D4×C113C2
socleC22×C113C22×D4
hypercenterC8×D4D113
hypocenterC113#3301
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #20299294C2semidirect
2. #20299257C2semidirect
3. #20298953C2semidirect
4. #20298940C2semidirect
5. #20298917C2semidirect
6. #20298906C2semidirect
7. #20298834C2semidirect
8. #20298827C2semidirect
9. #20298814C2semidirect
10. #20298745C2semidirect
11. #20298739C2semidirect
12. C4×#14268636C2semidirect
13. #20298595C2semidirect
14. C2×#16813547C2semidirect
15. C8×D4×C113C2semidirect
185. C113#3301semidirect
198. C8×D4D113semidirect

Maximal subgroups

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

subgroupindex
#202992942
#202992572
#202989532
#202989402
#202989172
#202989062
#202988342
#202988272
#202988142
#202987452
#202987392
C4×#142686362
#202985952
C2×#168135472
C8×D4×C1132
#3301113