Finite Group Databasebeta

← #28401165

Subgroups — #28401165

Order 14464.

408 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299145C211yesmaximal, characteristic, complemented
2#20299135C211yesmaximal, characteristic, complemented
3#20299005C211yesmaximal, characteristic, complemented
4#20298984C211yesmaximal, characteristic, complemented
5#20298961C211yesmaximal, characteristic, complemented
6#20298959C211yesmaximal, characteristic, complemented
7#20298852C211yesmaximal, characteristic, complemented
8#20298850C211yesmaximal, characteristic, complemented
9#20298847C211yesmaximal, characteristic, complemented
10#20298841C211yesmaximal, characteristic, complemented
11C4×#14268634C211yesmaximal, characteristic, complemented
12C4×D904C211yesmaximal, characteristic, complemented
13C4×#14268632C211yesmaximal, characteristic, complemented
14C4×#14268630C211yesmaximal, characteristic, complemented
15C4×SD16×C113C211yesmaximal, characteristic, complemented
16C2×#14268647—21no—
17C2×#14268634C2211yescharacteristic
18C2×D904C2211yescharacteristic
19C2×#14268632C2211yescharacteristic
20C2×#14268630C2211yescharacteristic
21C2×#14268630C2211yescharacteristic
22#16813621C2211yescharacteristic
23#16813618C2211yescharacteristic
24#16813617—21no—
25#16813613C2211yescharacteristic
26#16813611C2211yescharacteristic
27#16813608—21no—
28#16813607—21no—
29#16813598C2211yescharacteristic
30#16813597C2211yescharacteristic
31#16813597C2211yescharacteristic
32#16813595—21no—
33#16813593C2211yescharacteristic
34C4×D452—21no—
35C4×D452C2211yescharacteristic
36C4×D452C2211yescharacteristic
37C4×C22⋊D113—21no—
38#16813579—21no—
39C42×D113C2211yescharacteristic
40#16813556C2211yescharacteristic
41#16813555C2211yescharacteristic
42#16813553C2211yescharacteristic
43#16813546C2211yescharacteristic
44#16813544C2211yescharacteristic
45#16813544C2211yescharacteristic
46#16813543C2211yescharacteristic
47#16813542C2211yescharacteristic
48#16813542C2211yescharacteristic
49#16813532C2211yescharacteristic
50#16813532C2211yescharacteristic
51C4×#11744751C2211yescharacteristic
52C2×SD16×C113C2211yescharacteristic
53C4×Q8×C113C2211yescharacteristic
54C4×D4×C113C2211yescharacteristic
55#106×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58C4×C8×C113C2211yescharacteristic
59#14268647—44no—
60C2×Dic226—21no—
61C2×D452—21no—
62C2×D452—21no—
63C2×D452C2311yescharacteristic
64C2×D452C2311yescharacteristic
65C2×C22⋊D113—21no—
66C2×C22⋊D113—21no—
67C2×C22⋊D113—21no—
68C2×C4×D113—21no—
69C2×C4×D113—21no—
70C2×C4×D113D411yescharacteristic
71C2×C4×D113D411yescharacteristic
72C2×C4×D113C2311yescharacteristic
73#14268634—22no—
74D904—22no—
75#14268632—22no—
76#14268630—22no—
77#14268630—22no—
78C2×#11744751C2311yescharacteristic
79C2×#11744751C2311yescharacteristic
80C4⋊Dic113—21no—
81C4⋊Dic113C2311yescharacteristic
82C4⋊Dic113C2311yescharacteristic
83#14268626—21no—
84#14268626—21no—
85#14268626—21no—
86C22⋊Dic113—21no—
87#14268624—21no—
88#14268624—21no—
89#14268624—21no—
90#14268624—21no—
91#14268624—21no—
92#14268624—21no—
93#14268624—21no—
94C4×Dic113D411yescharacteristic
95C4×Dic113D411yescharacteristic
96C4×Dic113C2311yescharacteristic
97C2×Q8×C113C2311yescharacteristic
98C2×D4×C113C2311yescharacteristic
99C22×C4×C113—21no—
100SD16×C113—22no—
101C2×C8×C113C2311yescharacteristic
102C2×C8×C113C2311yescharacteristic
103C4⋊C4×C113—21no—
104C4⋊C4×C113C2311yescharacteristic
105C4⋊C4×C113C2311yescharacteristic
106C22⋊C4×C113—21no—
107C42×C113—21no—
108C42×C113C2311yescharacteristic
109C23×C113—21no—
110C22×D113—21no—
111C22×D113—21no—
112C22×D113C2×D411yescharacteristic
113Q8×C113—21no—
114Q8×C113—21no—
115D4×C113—21no—
116D4×C113—21no—
117C2×C4×C113—21no—
118C2×C4×C113—21no—
119C2×C4×C113—21no—
120C2×C4×C113—42no—
121C2×C4×C113C2×D411yescharacteristic
122C2×C4×C113C2×D411yescharacteristic
123C2×C4×C113C2411yescharacteristic
124C22⋊D113—42no—
125C22⋊D113—42no—
126C22⋊D113—42no—
127C2×Dic113—21no—
128C2×Dic113—21no—
129C2×Dic113C2×D411yescharacteristic
130C2×Dic113C2×D411yescharacteristic
131C2×Dic113C2×D411yescharacteristic
132D452—21no—
133D452—21no—
134D452—21no—
135D452—21no—
136D452—42no—
137D452—42no—
138C4×D113—22no—
139C4×D113—21no—
140C4×D113—21no—
141C4×D113—41no—
142C4×D113—42no—
143C4×D113—42no—
144Dic226—42no—
145C8×C113—21no—
146C8×C113#4112yescomplemented
147#11744751—21no—
148#11744751#4112yescomplemented
149C22×C113—41no—
150C22×C113—41no—
151C22×C113—41no—
152C22×C113C22×D411yescharacteristic
153C2×D113—21no—
154C2×D113—21no—
155C2×D113—21no—
156C2×D113—41no—
157C2×D113—41no—
158C2×D113—41no—
159C2×D113—41no—
160C2×D113—41no—
161C2×D113—41no—
162C4×C113—21no—
163C4×C113—41no—
164C4×C113—41no—
165C4×C113—41no—
166C4×C113AGL(1,ℤ/8)12yes—
167C4×C113C2×#4111yescharacteristic
168C4×C113C2×#4111yescharacteristic
169Dic113—21no—
170Dic113—21no—
171Dic113—21no—
172Dic113—41no—
173Dic113—41no—
174C2×C113—81no—
175C2×C113#53211yescharacteristic
176C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
177C2×C113#57511yescharacteristic
178D113—41no—
179D113—81no—
180D113—81no—
181#3171—1131nomaximal, Sylow
182C113#317111yescharacteristic, complemented, Sylow
183#532—1131no—
184#529—1131no—
185#501—1131no—
186#496—1131no—
187#490—1131no—
188#489—1131no—
189#469—1131no—
190#469—1131no—
191#468—1131no—
192#468—1131no—
193C4×SD16—1131no—
194C4×SD16D11311yescharacteristic, complemented
195C4×D8—1131no—
196C4×D8—1131no—
197C4×M16—1131no—
198C2×#41—2261no—
199C2×SD16—1131no—
200C2×SD16C2×D11311yescharacteristic
201C2×D8—1131no—
202C2×D8—1131no—
203C2×M16—1131no—
204C2×M16—1131no—
205C4⋊Q8—1131no—
206#127—1131no—
207#126—2261no—
208#125—1131no—
209#124—1131no—
210#124—2261no—
211#123—2261no—
212C22⋊Q8—1131no—
213#121—1131no—
214#121—1131no—
215#121—1131no—
216#121—2261no—
217C4×Q8C2×D11311yescharacteristic
218C4×D4—1131no—
219C4×D4—1131no—
220C4×D4—2261no—
221C4×D4—2261no—
222C4×D4C2×D11311yescharacteristic
223#117—2261no—
224C2×C42—1131no—
225#107—1131no—
226#107—1131no—
227#106—1131no—
228#106C2×D11311yescharacteristic
229#103—1131no—
230#103C2×D11311yescharacteristic
231#102—1131no—
232#102—1131no—
233#102—1131no—
234#102—1131no—
235#102—1131no—
236#102C2×D11311yescharacteristic
237#97—1131no—
238#97—1131no—
239C4×C8—1131no—
240C4×C8C2×D11311yescharacteristic
241#41—4524no—
242C2×Q8—2261no—
243C2×Q8C22×D11311yescharacteristic
244C2×D4—1131no—
245C2×D4—1131no—
246C2×D4—2261no—
247C2×D4—2261no—
248C2×D4—2261no—
249C2×D4—2261no—
250C2×D4—2261no—
251C2×D4C22×D11311yescharacteristic
252C22×C4—21no—
253C22×C4—1131no—
254C22×C4—1131no—
255C22×C4—1131no—
256C22×C4—2261no—
257C22×C4—2261no—
258SD16—22no—
259SD16—2262no—
260D8—2262no—
261D8—2262no—
262M16—2262no—
263M16—2262no—
264C2×C8—1131no—
265C2×C8—1131no—
266C2×C8C22×D11311yescharacteristic
267C2×C8C22×D11311yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—1131no—
270C4⋊C4—1131no—
271C4⋊C4—2261no—
272C4⋊C4—2261no—
273C4⋊C4—2261no—
274C4⋊C4—2261no—
275C4⋊C4C22×D11311yescharacteristic
276C4⋊C4C22×D11311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—2261no—
279C22⋊C4—2261no—
280C22⋊C4—2261no—
281C22⋊C4—2261no—
282C22⋊C4—2261no—
283C22⋊C4—2261no—
284C22⋊C4—2261no—
285C22⋊C4—2261no—
286C42—21no—
287C42—1131no—
288C42—1131no—
289C42—1131no—
290C42C22×D11311yescharacteristic
291C23—21no—
292C23—1131no—
293C23—2261no—
294C23—2261no—
295Q8—21no—
296Q8—21no—
297Q8—4522no—
298D4—21no—
299D4—21no—
300D4—4522no—
301D4—4522no—
302D4—4522no—
303D4—4522no—
304D4—4522no—
305D4—2261no—
306D4—2261no—
307D4—2261no—
308D4—2261no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—42no—
313C2×C4—1131no—
314C2×C4—1131no—
315C2×C4—1131no—
316C2×C4—4521no—
317C2×C4—4522no—
318C2×C4—4522no—
319C2×C4—2261no—
320C2×C4—2261no—
321C2×C4—2262no—
322C2×C4—2261no—
323C2×C4—2261no—
324C2×C4D4×D11311yescharacteristic
325C2×C4D4×D11311yescharacteristic
326C2×C4C23×D11311yescharacteristic
327C8—21no—
328C8—1132no—
329C8—2261no—
330C8#1426864712yescomplemented
331C22—41no—
332C22—41no—
333C22—41no—
334C22—4521no—
335C22—4521no—
336C22—4521no—
337C22—4521no—
338C22—4521no—
339C22—4521no—
340C22—2261no—
341C22—2261no—
342C22—2261no—
343C22C2×D4×D11311yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—4521no—
349C4—4521no—
350C4—2261no—
351C4—2261no—
352C4—2261no—
353C4#1681364912yes—
354C4#41×D11311yescharacteristic
355C4C2×#1426864711yescharacteristic
356C2—81no—
357C2—9041no—
358C2—9041no—
359C2—4521no—
360C2#2029914511yescharacteristic
361C2C2×#1681364911yescharacteristic
362C2#2029939511yescharacteristic
subgroupG/H
centerC2×C4D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC4×SD16×C113C2
socleC22×C113C22×D4
hypercenterC4×SD16D113
hypocenterC113#3171
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #20299145C2semidirect
2. #20299135C2semidirect
3. #20299005C2semidirect
4. #20298984C2semidirect
5. #20298961C2semidirect
6. #20298959C2semidirect
7. #20298852C2semidirect
8. #20298850C2semidirect
9. #20298847C2semidirect
10. #20298841C2semidirect
11. C4×#14268634C2semidirect
12. C4×D904C2semidirect
13. C4×#14268632C2semidirect
14. C4×#14268630C2semidirect
15. C4×SD16×C113C2semidirect
146. C8×C113#41semidirect
148. #11744751#41semidirect
182. C113#3171semidirect
194. C4×SD16D113semidirect
330. C8#14268647semidirect

Maximal subgroups

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

subgroupindex
#202991452
#202991352
#202990052
#202989842
#202989612
#202989592
#202988522
#202988502
#202988472
#202988412
C4×#142686342
C4×D9042
C4×#142686322
C4×#142686302
C4×SD16×C1132
#3171113