Finite Group Databasebeta

← #28402756

Subgroups — #28402756

Order 14464.

392 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#20299311C211yesmaximal, characteristic, complemented
2#20299255C211yesmaximal, characteristic, complemented
3#20298956C211yesmaximal, characteristic, complemented
4#20298939C211yesmaximal, characteristic, complemented
5#20298921C211yesmaximal, characteristic, complemented
6#20298881C211yesmaximal, characteristic, complemented
7#20298850C211yesmaximal, characteristic, complemented
8#20298827C211yesmaximal, characteristic, complemented
9#20298812C211yesmaximal, characteristic, complemented
10#20298743C211yesmaximal, characteristic, complemented
11#20298738C211yesmaximal, characteristic, complemented
12#20298701C211yesmaximal, characteristic, complemented
13#20298669C211yesmaximal, characteristic, complemented
14#20298605C211yesmaximal, characteristic, complemented
15#416×C113C211yesmaximal, characteristic, complemented
16C2×Q8×D113C2211yescharacteristic
17C2×#14268636C2211yescharacteristic
18C2×#14268634C2211yescharacteristic
19C2×#14268632C2211yescharacteristic
20C2×#14268630C2211yescharacteristic
21#16813621C2211yescharacteristic
22#16813610—21no—
23#16813609—21no—
24#16813609C2211yescharacteristic
25#16813608—21no—
26#16813601—21no—
27#16813601C2211yescharacteristic
28#16813597C2211yescharacteristic
29#16813596C2211yescharacteristic
30#16813595—21no—
31#16813593—21no—
32#16813593C2211yescharacteristic
33Q8×Dic113C2211yescharacteristic
34#16813584C2211yescharacteristic
35C4×C22⋊D113—21no—
36C4×C22⋊D113C2211yescharacteristic
37#16813580C2211yescharacteristic
38#16813579—21no—
39#16813555C2211yescharacteristic
40#16813554C2211yescharacteristic
41#16813553C2211yescharacteristic
42#16813551C2211yescharacteristic
43#16813547C2211yescharacteristic
44#16813546C2211yescharacteristic
45#16813545C2211yescharacteristic
46#16813545C2211yescharacteristic
47#16813544C2211yescharacteristic
48#16813543C2211yescharacteristic
49C22⋊#11744751C2211yescharacteristic
50#16813534C2211yescharacteristic
51#16813532C2211yescharacteristic
52C2×#41×C113C2211yescharacteristic
53C22×C8×C113C2211yescharacteristic
54#117×C113C2211yescharacteristic
55#103×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58#102×C113C2211yescharacteristic
59C2×Dic226—21no—
60C2×Dic226—21no—
61C2×Dic226C2311yescharacteristic
62Q8×D113—22no—
63Q8×D113—41no—
64C2×D452—21no—
65C2×D452C2311yescharacteristic
66C2×C22⋊D113—21no—
67C2×C22⋊D113—21no—
68C2×C22⋊D113D411yescharacteristic
69C2×C4×D113—21no—
70C2×C4×D113—21no—
71C2×C4×D113C2311yescharacteristic
72#14268636—41no—
73#14268634—22no—
74#14268632—41no—
75#14268630—41no—
76C2×#11744751C2311yescharacteristic
77C2×#11744751C2311yescharacteristic
78C4⋊Dic113—21no—
79C4⋊Dic113C2311yescharacteristic
80C4⋊Dic113C2311yescharacteristic
81#14268626—21no—
82#14268626—21no—
83#14268626D411yescharacteristic
84C22⋊Dic113—21no—
85C22⋊Dic113—21no—
86C22⋊Dic113—21no—
87C22⋊Dic113—21no—
88C22⋊Dic113D411yescharacteristic
89#14268624—21no—
90#14268624—21no—
91#14268624—21no—
92#14268624—21no—
93#14268624D411yescharacteristic
94C4×Dic113—21no—
95C4×Dic113—21no—
96C4×Dic113C2311yescharacteristic
97#41×C113—22no—
98#41×C113—41no—
99C2×Q8×C113C2311yescharacteristic
100C2×D4×C113—21no—
101C2×D4×C113C2311yescharacteristic
102C22×C4×C113—21no—
103C22×C4×C113C2311yescharacteristic
104C2×C8×C113—41no—
105C2×C8×C113C2311yescharacteristic
106C2×C8×C113C2311yescharacteristic
107C4⋊C4×C113C2311yescharacteristic
108C4⋊C4×C113C2311yescharacteristic
109C22⋊C4×C113—21no—
110C42×C113—21no—
111C23×C113—21no—
112C23×C113C2×D411yescharacteristic
113C22×D113—21no—
114C22×D113C2×D411yescharacteristic
115Q8×C113—21no—
116Q8×C113#4112yes—
117D4×C113—21no—
118D4×C113—21no—
119D4×C113—42no—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113—21no—
124C2×C4×C113—21no—
125C2×C4×C113—42no—
126C2×C4×C113C2×D411yescharacteristic
127C2×C4×C113C2411yescharacteristic
128C22⋊D113—41no—
129C22⋊D113—42no—
130C22⋊D113—81no—
131C2×Dic113—21no—
132C2×Dic113—21no—
133C2×Dic113—21no—
134C2×Dic113C2×D411yescharacteristic
135C2×Dic113C2×D411yescharacteristic
136C2×Dic113C2×D411yescharacteristic
137D452—21no—
138D452—21no—
139D452—81no—
140C4×D113—21no—
141C4×D113—21no—
142C4×D113—42no—
143C4×D113—42no—
144Dic226—21no—
145Dic226—21no—
146Dic226—42no—
147Dic226—81no—
148C8×C113—21no—
149C8×C113—21no—
150#11744751—21no—
151#11744751—21no—
152C22×C113—21no—
153C22×C113—21no—
154C22×C113—21no—
155C22×C113—41no—
156C22×C113—41no—
157C22×C113—41no—
158C22×C113C22×D411yescharacteristic
159C2×D113—21no—
160C2×D113—21no—
161C2×D113—21no—
162C2×D113—41no—
163C2×D113—41no—
164C2×D113—41no—
165C4×C113—22no—
166C4×C113—21no—
167C4×C113—41no—
168C4×C113—41no—
169C4×C113C2×#4111yescharacteristic
170C4×C113H(5,𝔽2)11yescharacteristic
171Dic113—21no—
172Dic113—21no—
173Dic113—21no—
174Dic113—41no—
175Dic113—41no—
176Dic113—41no—
177C2×C113—41no—
178C2×C113—81no—
179C2×C113#54611yescharacteristic
180C2×C113#57511yescharacteristic
181C2×C113#57711yescharacteristic
182D113—41no—
183D113—81no—
184#3321—1131nomaximal, Sylow
185C113#332111yescharacteristic, complemented, Sylow
186#555—1131no—
187#548—1131no—
188#489—1131no—
189#485—1131no—
190#482—1131no—
191#475—1131no—
192#469—1131no—
193#465—1131no—
194#463—1131no—
195#449—1131no—
196#448—1131no—
197#440—1131no—
198#435—1131no—
199#419—1131no—
200#416D11311yescharacteristic, complemented
201C2×#41C2×D11311yescharacteristic
202C22×Q8—1131no—
203C2×SD16—1131no—
204C2×SD16—1131no—
205C2×D8—1131no—
206C2×M16—1131no—
207C22×C8C2×D11311yescharacteristic
208C4⋊Q8—1131no—
209#124—1131no—
210#124—2261no—
211#124—2261no—
212#124—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—1131no—
223C4×D4—2261no—
224#117—1131no—
225#117—2261no—
226#117C2×D11311yescharacteristic
227#107—1131no—
228#106—1131no—
229#106—1131no—
230C4⋊C8—1131no—
231#103—1131no—
232#103—1131no—
233#103—1131no—
234#103—1131no—
235#103C2×D11311yescharacteristic
236#103C2×D11311yescharacteristic
237#102—1131no—
238#102—1131no—
239#102C2×D11311yescharacteristic
240#102C2×D11311yescharacteristic
241C22⋊C8—1131no—
242C22⋊C8—1131no—
243#97—1131no—
244#41—22no—
245#41—41no—
246C2×Q8—1131no—
247C2×Q8—4521no—
248C2×Q8—2261no—
249C2×Q8—2261no—
250C2×Q8—2262no—
251C2×Q8C22×D11311yescharacteristic
252C2×D4—21no—
253C2×D4—1131no—
254C2×D4—1131no—
255C2×D4—2261no—
256C2×D4—2261no—
257C2×D4—2261no—
258C2×D4C22×D11311yescharacteristic
259C22×C4—21no—
260C22×C4—1131no—
261C22×C4—2261no—
262C22×C4—2261no—
263C22×C4C22×D11311yescharacteristic
264SD16—4521no—
265SD16—2262no—
266D8—4521no—
267M16—4521no—
268C2×C8—41no—
269C2×C8—1131no—
270C2×C8—1131no—
271C2×C8C22×D11311yescharacteristic
272C2×C8C22×D11311yescharacteristic
273C4⋊C4—1131no—
274C4⋊C4—1131no—
275C4⋊C4—1131no—
276C4⋊C4—2261no—
277C4⋊C4—2261no—
278C4⋊C4—2261no—
279C4⋊C4C22×D11311yescharacteristic
280C4⋊C4C22×D11311yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—1131no—
283C22⋊C4—1131no—
284C22⋊C4—2261no—
285C22⋊C4—2261no—
286C22⋊C4—2261no—
287C22⋊C4—2261no—
288C22⋊C4—2261no—
289C22⋊C4—2261no—
290C22⋊C4—2261no—
291C22⋊C4—2261no—
292C42—21no—
293C42—1131no—
294C42—2261no—
295C42—2261no—
296C23—21no—
297C23—1131no—
298C23—2261no—
299C23D4×D11311yescharacteristic
300Q8—21no—
301Q8—9041no—
302Q8—4522no—
303Q8—2261no—
304Q8—2261no—
305Q8#1426864712yes—
306D4—21no—
307D4—21no—
308D4—42no—
309D4—9041no—
310D4—9041no—
311D4—4522no—
312D4—4521no—
313D4—2261no—
314D4—2261no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—42no—
321C2×C4—1131no—
322C2×C4—1131no—
323C2×C4—1131no—
324C2×C4—4522no—
325C2×C4—4522no—
326C2×C4—2261no—
327C2×C4—2261no—
328C2×C4—2261no—
329C2×C4—2261no—
330C2×C4—2261no—
331C2×C4D4×D11311yescharacteristic
332C2×C4C23×D11311yescharacteristic
333C8—21no—
334C8—21no—
335C8—2261no—
336C8—2261no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—4521no—
344C22—4521no—
345C22—4521no—
346C22—2261no—
347C22—2261no—
348C22—2261no—
349C22C2×D4×D11311yescharacteristic
350C4—21no—
351C4—22no—
352C4—41no—
353C4—41no—
354C4—4521no—
355C4—4521no—
356C4—4521no—
357C4—2261no—
358C4—2261no—
359C4—2261no—
360C4C2×#1426864711yescharacteristic
361C4#1681366711yescharacteristic
362C2—41no—
363C2—81no—
364C2—9041no—
365C2—4521no—
366C2#2029923811yescharacteristic
367C2#2029939511yescharacteristic
368C2#2029940511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#416×C113C2
socleC22×C113C22×D4
hypercenter#416D113
hypocenterC113#3321
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #20299311C2semidirect
2. #20299255C2semidirect
3. #20298956C2semidirect
4. #20298939C2semidirect
5. #20298921C2semidirect
6. #20298881C2semidirect
7. #20298850C2semidirect
8. #20298827C2semidirect
9. #20298812C2semidirect
10. #20298743C2semidirect
11. #20298738C2semidirect
12. #20298701C2semidirect
13. #20298669C2semidirect
14. #20298605C2semidirect
15. #416×C113C2semidirect
185. C113#3321semidirect
200. #416D113semidirect

Maximal subgroups

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

subgroupindex
#202993112
#202992552
#202989562
#202989392
#202989212
#202988812
#202988502
#202988272
#202988122
#202987432
#202987382
#202987012
#202986692
#202986052
#416×C1132
#3321113