Finite Group Databasebeta

← #28400037

Subgroups — #28400037

Order 14464.

548 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813650C211yesmaximal, characteristic, complemented
2C2×#16813647C211yesmaximal, characteristic, complemented
3#20299144C211yesmaximal, characteristic, complemented
4C2×#16813584C211yesmaximal, characteristic, complemented
5#20298816C212yesmaximal, complemented
6#20298812C212yesmaximal, complemented
7#20298802C212yesmaximal, complemented
8#20298792C212yesmaximal, complemented
9#20298621C211yesmaximal, characteristic, complemented
10#20298597C211yesmaximal, characteristic, complemented
11#417×C113C211yesmaximal, characteristic, complemented
12C2×#14268647C2211yescharacteristic
13C22×D452C2211yescharacteristic
14C22×C4×D113—21no—
15#16813650—24no—
16#16813647—24no—
17C2×#14268636C2212yes—
18C2×#14268634C2212yes—
19C2×D904C2212yes—
20C2×#14268632C2212yes—
21C2×#14268631C2211yescharacteristic
22#16813620C2211yescharacteristic, complemented
23#16813618C2211yescharacteristic, complemented
24#16813611C2211yescharacteristic, complemented
25#16813609C2211yescharacteristic, complemented
26#16813594—21no—
27#16813594—21no—
28#16813584—21no—
29#16813584—21no—
30#16813584C2212yes—
31#16813584C2212yes—
32C4×C22⋊D113—21no—
33C4×C22⋊D113—21no—
34C2×#14268624—21no—
35C2×C4×Dic113C2211yescharacteristic
36#16813551C2212yescomplemented
37#16813551C2212yescomplemented
38#16813545C2212yescomplemented
39#16813542C2212yescomplemented
40C2×#41×C113C2211yescharacteristic
41C2×M16×C113C2211yescharacteristic
42C2×C4⋊C4×C113C2211yescharacteristic
43#103×C113C2212yescomplemented
44#102×C113C2212yescomplemented
45C23×D113—21no—
46#14268647—22no—
47#14268647—22no—
48C2×Dic226C2311yescharacteristic
49C2×D452—21no—
50C2×D452—22no—
51C2×D452D414yescomplemented
52C2×D452C2311yescharacteristic
53C2×D452C2312yes—
54C2×C22⋊D113—21no—
55C2×C22⋊D113—21no—
56C2×C22⋊D113—21no—
57C22×Dic113D411yescharacteristic
58C22×Dic113D411yescharacteristic
59C2×C4×D113—21no—
60C2×C4×D113—22no—
61C2×C4×D113—22no—
62C2×C4×D113—44no—
63#14268636—24no—
64#14268634—24no—
65D904—24no—
66#14268632—24no—
67#14268631—22no—
68C2×#11744751C2312yes—
69#14268626—21no—
70#14268626—21no—
71C22⋊Dic113—21no—
72C22⋊Dic113—21no—
73#14268624—22no—
74#14268624—22no—
75#14268624—21no—
76#14268624—21no—
77C4×Dic113D411yescharacteristic
78C4×Dic113D411yescharacteristic
79C4×Dic113C2311yescharacteristic
80C4×Dic113C2311yescharacteristic
81#41×C113—22no—
82#41×C113—22no—
83C2×Q8×C113C2311yescharacteristic
84C2×D4×C113—21no—
85C2×D4×C113C2311yescharacteristic
86C22×C4×C113—21no—
87C22×C4×C113—21no—
88C22×C4×C113C2311yescharacteristic
89M16×C113—22no—
90C2×C8×C113C2312yes—
91C4⋊C4×C113—21no—
92C4⋊C4×C113C2312yes—
93C23×C113—21no—
94C23×C113C2×D411yescharacteristic
95C22×D113—24no—
96C22×D113—22no—
97C22×D113—21no—
98C22×D113—42no—
99C22×D113—42no—
100Q8×C113—21no—
101Q8×C113—21no—
102D4×C113—21no—
103D4×C113—21no—
104D4×C113—42no—
105C2×C4×C113—22no—
106C2×C4×C113—21no—
107C2×C4×C113—42no—
108C2×C4×C113—42no—
109C2×C4×C113C2×D411yescharacteristic
110C2×C4×C113C2×D412yes—
111C2×C4×C113#4112yes—
112C2×C4×C113C2411yescharacteristic
113C22⋊D113—42no—
114C22⋊D113—42no—
115C22⋊D113—42no—
116C2×Dic113—22no—
117C2×Dic113—21no—
118C2×Dic113—41no—
119C2×Dic113C2×D411yescharacteristic
120C2×Dic113C2×D411yescharacteristic
121C2×Dic113C2×D411yescharacteristic
122C2×Dic113C2×D411yescharacteristic
123D452—24no—
124D452—21no—
125D452—22no—
126D452—21no—
127D452C2×D414yes—
128C4×D113—44no—
129C4×D113—42no—
130C4×D113—44no—
131Dic226—21no—
132Dic226—21no—
133C8×C113—22no—
134#11744751—22no—
135C22×C113—21no—
136C22×C113—21no—
137C22×C113—41no—
138C22×C113—41no—
139C22×C113—41no—
140C22×C113#12112yes—
141C22×C113C22×D411yescharacteristic
142C2×D113—24no—
143C2×D113—48no—
144C2×D113—42no—
145C2×D113—42no—
146C2×D113—41no—
147C2×D113—41no—
148C2×D113—41no—
149C4×C113—41no—
150C4×C113—42no—
151C4×C113#12112yes—
152C4×C113C22×D411yescharacteristic
153C4×C113C2×#4111yescharacteristic
154Dic113—21no—
155Dic113—21no—
156Dic113—21no—
157Dic113—41no—
158Dic113AGL(1,ℤ/8)12yescomplemented
159C2×C113—22no—
160C2×C113—81no—
161C2×C113C2×#12111yescharacteristic
162C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
163C2×C113#57511yescharacteristic
164D113—44no—
165D113—81no—
166#3036—1131nomaximal, Sylow
167C113#303611yescharacteristic, complemented, Sylow
168C2×AGL(1,ℤ/8)—1131no—
169C2×AGL(1,ℤ/8)—1131no—
170#532—1131no—
171C2×C4×D4—1131no—
172#463—1132no—
173#463—1132no—
174#461—1132no—
175#459—1132no—
176#423—1131no—
177#417—1131no—
178#417D11311yescharacteristic, complemented
179C2×#41—1131no—
180C2×#41C2×D11311yescharacteristic
181C22×D4—1131no—
182C23×C4—2261no—
183AGL(1,ℤ/8)—2264no—
184AGL(1,ℤ/8)—2264no—
185C2×SD16—1132no—
186C2×SD16—1132no—
187C2×D8—1132no—
188C2×D8—1132no—
189C2×M16—1131no—
190C2×M16C2×D11311yescharacteristic
191C4⋊Q8—1131no—
192#127—1131no—
193#124—1131no—
194#124—1131no—
195#121—2261no—
196#121—2261no—
197C4×D4—1132no—
198C4×D4—1132no—
199C4×D4—2261no—
200C4×D4—2261no—
201C4×D4—2261no—
202C4×D4—2261no—
203C2×C4⋊C4C2×D11311yescharacteristic
204C2×C22⋊C4—2261no—
205C2×C42—1131no—
206C4⋊C8—1132no—
207C4⋊C8—1132no—
208#103—1132no—
209#103C2×D11312yescomplemented
210#102—1132no—
211#102C2×D11312yescomplemented
212C24—2261no—
213#41—22no—
214#41—22no—
215#41—2262no—
216#41—2262no—
217C2×Q8—1131no—
218C2×Q8C22×D11311yescharacteristic
219C2×D4—21no—
220C2×D4—1134no—
221C2×D4—1132no—
222C2×D4—1131no—
223C2×D4—2261no—
224C2×D4—2261no—
225C2×D4—2261no—
226C2×D4—2261no—
227C2×D4—2262no—
228C2×D4C22×D11311yescharacteristic
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—1131no—
232C22×C4—1131no—
233C22×C4—4524no—
234C22×C4—2262no—
235C22×C4—2262no—
236C22×C4—2261no—
237C22×C4C22×D11311yescharacteristic
238SD16—2264no—
239SD16—2264no—
240D8—2264no—
241D8—2264no—
242M16—22no—
243M16—2262no—
244C2×C8—1132no—
245C2×C8C22×D11312yes—
246C4⋊C4—21no—
247C4⋊C4—2261no—
248C4⋊C4—2261no—
249C4⋊C4C22×D11312yes—
250C22⋊C4—2262no—
251C22⋊C4—2262no—
252C22⋊C4—2261no—
253C22⋊C4—2261no—
254C22⋊C4—2261no—
255C22⋊C4—2261no—
256C42—1131no—
257C42—1131no—
258C42—1131no—
259C42—1131no—
260C23—21no—
261C23—4522no—
262C23—4522no—
263C23—2261no—
264C23—2264no—
265C23—2262no—
266C23D4×D11311yescharacteristic
267Q8—21no—
268Q8—21no—
269Q8—2261no—
270Q8—2261no—
271D4—21no—
272D4—21no—
273D4—42no—
274D4—1134no—
275D4—4522no—
276D4—4522no—
277D4—4522no—
278D4—2264no—
279D4—2261no—
280D4—2261no—
281D4—2262no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—1131no—
287C2×C4—1131no—
288C2×C4—1131no—
289C2×C4—1131no—
290C2×C4—4524no—
291C2×C4—4524no—
292C2×C4—4522no—
293C2×C4—4521no—
294C2×C4—2262no—
295C2×C4—2261no—
296C2×C4D4×D11311yescharacteristic
297C2×C4D4×D11312yes—
298C2×C4#1426864712yes—
299C2×C4C23×D11311yescharacteristic
300C8—22no—
301C8—2262no—
302C22—21no—
303C22—21no—
304C22—41no—
305C22—41no—
306C22—41no—
307C22—4528no—
308C22—4521no—
309C22—4521no—
310C22—4521no—
311C22—4522no—
312C22—4522no—
313C22—2264no—
314C22#1681359512yes—
315C22C2×D4×D11311yescharacteristic
316C4—41no—
317C4—42no—
318C4—1132no—
319C4—4521no—
320C4—2261no—
321C4—2261no—
322C4—2261no—
323C4#1681359512yes—
324C4C2×D4×D11311yescharacteristic
325C4C2×#1426864711yescharacteristic
326C2—22no—
327C2—81no—
328C2—9041no—
329C2—4524no—
330C2C2×#1681359511yescharacteristic
331C2AGL(1,ℤ/8)×D11311yescharacteristic
332C2#2029939711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#417×C113C2
socleC22×C113C22×D4
hypercenter#417D113
hypocenterC113#3036
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. C2×#16813650C2semidirect
2. C2×#16813647C2semidirect
3. #20299144C2semidirect
4. C2×#16813584C2semidirect
5. #20298816C2semidirect
6. #20298812C2semidirect
7. #20298802C2semidirect
8. #20298792C2semidirect
9. #20298621C2semidirect
10. #20298597C2semidirect
11. #417×C113C2semidirect
22. #16813620C22semidirect
23. #16813618C22semidirect
24. #16813611C22semidirect
25. #16813609C22semidirect
36. #16813551C22semidirect
37. #16813551C22semidirect
38. #16813545C22semidirect
39. #16813542C22semidirect
43. #103×C113C22semidirect
44. #102×C113C22semidirect
51. C2×D452D4semidirect
158. Dic113AGL(1,ℤ/8)semidirect
167. C113#3036semidirect
178. #417D113semidirect
209. #103C2×D113semidirect
211. #102C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136502
C2×#168136472
#202991442
C2×#168135842
#202988162
#202988122
#202988022
#202987922
#202986212
#202985972
#417×C1132
#3036113