Finite Group Databasebeta

← #28400035

Subgroups — #28400035

Order 14464.

548 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 143 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×#16813648C211yesmaximal, characteristic, complemented
2#20299144C211yesmaximal, characteristic, complemented
3C2×D4×Dic113C211yesmaximal, characteristic, complemented
4#20298815C212yesmaximal, complemented
5#20298811C212yesmaximal, complemented
6#20298801C212yesmaximal, complemented
7#20298791C212yesmaximal, complemented
8#20298621C211yesmaximal, characteristic, complemented
9#20298600C211yesmaximal, characteristic, complemented
10#20298599C211yesmaximal, characteristic, complemented
11C2×AGL(1,ℤ/8)×C113C211yesmaximal, characteristic, complemented
12C2×#14268647C2211yescharacteristic
13C23×Dic113—21no—
14#16813648—24no—
15C2×#14268635C2212yes—
16C2×#14268632C2212yes—
17C2×#14268631C2211yescharacteristic
18#16813620C2211yescharacteristic, complemented
19#16813618C2211yescharacteristic, complemented
20#16813611C2211yescharacteristic, complemented
21#16813609C2211yescharacteristic, complemented
22#16813594—21no—
23#16813594—21no—
24D4×Dic113—21no—
25D4×Dic113—21no—
26D4×Dic113C2212yes—
27D4×Dic113C2212yes—
28C4×C22⋊D113—21no—
29C4×C22⋊D113—21no—
30C2×C4⋊Dic113C2211yescharacteristic
31C2×C22⋊Dic113—21no—
32C2×C4×Dic113C2211yescharacteristic
33#16813551C2212yescomplemented
34#16813551C2212yescomplemented
35#16813547C2212yescomplemented
36#16813546C2212yescomplemented
37#16813544C2212yescomplemented
38#16813543C2212yescomplemented
39C2×#41×C113C2211yescharacteristic
40C22×D4×C113C2211yescharacteristic
41AGL(1,ℤ/8)×C113—24no—
42C2×SD16×C113C2212yes—
43C2×D8×C113C2212yes—
44C2×M16×C113C2211yescharacteristic
45#14268647—22no—
46#14268647—22no—
47C2×Dic226C2311yescharacteristic
48C2×D452C2311yescharacteristic
49C2×C22⋊D113—21no—
50C2×C22⋊D113—21no—
51C2×C22⋊D113—21no—
52C22×Dic113—21no—
53C22×Dic113—22no—
54C22×Dic113—22no—
55C22×Dic113—44no—
56C22×Dic113D411yescharacteristic
57C22×Dic113D411yescharacteristic
58C2×C4×D113—21no—
59#14268635—24no—
60#14268632—24no—
61#14268631—22no—
62C2×#11744751C2312yes—
63C4⋊Dic113—21no—
64C4⋊Dic113C2312yes—
65#14268626—21no—
66#14268626—21no—
67C22⋊Dic113—22no—
68C22⋊Dic113—22no—
69C22⋊Dic113—21no—
70C22⋊Dic113—21no—
71#14268624—21no—
72#14268624—21no—
73C4×Dic113D411yescharacteristic
74C4×Dic113D411yescharacteristic
75C4×Dic113C2311yescharacteristic
76C4×Dic113C2311yescharacteristic
77C24×C113—21no—
78#41×C113—22no—
79#41×C113—22no—
80C2×Q8×C113C2311yescharacteristic
81C2×D4×C113—21no—
82C2×D4×C113—21no—
83C2×D4×C113—22no—
84C2×D4×C113D414yescomplemented
85C2×D4×C113C2311yescharacteristic
86C2×D4×C113C2312yes—
87C22×C4×C113—21no—
88C22×C4×C113C2311yescharacteristic
89SD16×C113—24no—
90D8×C113—24no—
91M16×C113—22no—
92C2×C8×C113C2312yes—
93C23×C113—24no—
94C23×C113—22no—
95C23×C113—21no—
96C23×C113—42no—
97C23×C113—42no—
98C23×C113C2×D411yescharacteristic
99C22×D113—21no—
100Q8×C113—21no—
101Q8×C113—21no—
102D4×C113—24no—
103D4×C113—21no—
104D4×C113—22no—
105D4×C113—21no—
106D4×C113—42no—
107D4×C113C2×D414yes—
108C2×C4×C113—21no—
109C2×C4×C113—42no—
110C2×C4×C113C2×D411yescharacteristic
111C2×C4×C113C2×D412yes—
112C2×C4×C113#4112yes—
113C2×C4×C113C2411yescharacteristic
114C22⋊D113—42no—
115C22⋊D113—42no—
116C22⋊D113—42no—
117C2×Dic113—22no—
118C2×Dic113—21no—
119C2×Dic113—22no—
120C2×Dic113—41no—
121C2×Dic113—44no—
122C2×Dic113—42no—
123C2×Dic113—44no—
124C2×Dic113C2×D411yescharacteristic
125C2×Dic113C2×D411yescharacteristic
126C2×Dic113C2×D411yescharacteristic
127C2×Dic113C2×D411yescharacteristic
128D452—21no—
129D452—21no—
130C4×D113—42no—
131Dic226—21no—
132Dic226—21no—
133C8×C113—22no—
134#11744751—22no—
135C22×C113—21no—
136C22×C113—21no—
137C22×C113—24no—
138C22×C113—48no—
139C22×C113—42no—
140C22×C113—42no—
141C22×C113—41no—
142C22×C113—41no—
143C22×C113—41no—
144C22×C113#12112yes—
145C22×C113C22×D411yescharacteristic
146C2×D113—41no—
147C2×D113—41no—
148C2×D113—41no—
149C4×C113—41no—
150C4×C113#12112yes—
151C4×C113C22×D411yescharacteristic
152C4×C113C2×#4111yescharacteristic
153Dic113—21no—
154Dic113—21no—
155Dic113—21no—
156Dic113—41no—
157Dic113—42no—
158Dic113AGL(1,ℤ/8)12yescomplemented
159C2×C113—22no—
160C2×C113—44no—
161C2×C113—81no—
162C2×C113C2×#12111yescharacteristic
163C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
164C2×C113#57511yescharacteristic
165D113—81no—
166#3036—1131nomaximal, Sylow
167C113#303611yescharacteristic, complemented, Sylow
168C2×AGL(1,ℤ/8)—1131no—
169C2×AGL(1,ℤ/8)D11311yescharacteristic, complemented
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#417—1131no—
179C2×#41—1131no—
180C2×#41C2×D11311yescharacteristic
181C22×D4C2×D11311yescharacteristic
182C23×C4—2261no—
183AGL(1,ℤ/8)—24no—
184AGL(1,ℤ/8)—2264no—
185C2×SD16—1132no—
186C2×SD16C2×D11312yes—
187C2×D8—1132no—
188C2×D8C2×D11312yes—
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⋊C4—1131no—
204C2×C22⋊C4—2261no—
205C2×C42—1131no—
206C4⋊C8—1132no—
207C4⋊C8—1132no—
208#103—1132no—
209#103—1132no—
210#102—1132no—
211#102—1132no—
212C24—21no—
213#41—22no—
214#41—22no—
215#41—2262no—
216#41—2262no—
217C2×Q8—1131no—
218C2×Q8C22×D11311yescharacteristic
219C2×D4—21no—
220C2×D4—21no—
221C2×D4—22no—
222C2×D4—1131no—
223C2×D4—2261no—
224C2×D4—2261no—
225C2×D4—2261no—
226C2×D4C22⋊D11314yescomplemented
227C2×D4C22×D11311yescharacteristic
228C2×D4C22×D11312yes—
229C22×C4—21no—
230C22×C4—1131no—
231C22×C4—1131no—
232C22×C4—4524no—
233C22×C4—2262no—
234C22×C4—2262no—
235C22×C4—2261no—
236C22×C4—2261no—
237C22×C4C22×D11311yescharacteristic
238SD16—24no—
239SD16—2264no—
240D8—24no—
241D8—2264no—
242M16—22no—
243M16—2262no—
244C2×C8—1132no—
245C2×C8C22×D11312yes—
246C4⋊C4—1132no—
247C4⋊C4—2261no—
248C4⋊C4—2261no—
249C4⋊C4—2261no—
250C22⋊C4—2261no—
251C22⋊C4—2261no—
252C22⋊C4—2262no—
253C22⋊C4—2262no—
254C22⋊C4—2261no—
255C22⋊C4—2261no—
256C42—1131no—
257C42—1131no—
258C42—1131no—
259C42—1131no—
260C23—24no—
261C23—22no—
262C23—21no—
263C23—42no—
264C23—42no—
265C23—2261no—
266C23D4×D11311yescharacteristic
267Q8—21no—
268Q8—21no—
269Q8—2261no—
270Q8—2261no—
271D4—24no—
272D4—21no—
273D4—22no—
274D4—21no—
275D4—42no—
276D4—4522no—
277D4—4522no—
278D4—4522no—
279D4—2261no—
280D4—2261no—
281D4C2×C22⋊D11314yes—
282C2×C4—21no—
283C2×C4—42no—
284C2×C4—1131no—
285C2×C4—1131no—
286C2×C4—1131no—
287C2×C4—1131no—
288C2×C4—4524no—
289C2×C4—4522no—
290C2×C4—4524no—
291C2×C4—4522no—
292C2×C4—4521no—
293C2×C4—2262no—
294C2×C4—2262no—
295C2×C4—2261no—
296C2×C4D4×D11311yescharacteristic
297C2×C4C2×C22⋊D11312yes—
298C2×C4#1426864612yes—
299C2×C4C23×D11311yescharacteristic
300C8—22no—
301C8—2262no—
302C22—21no—
303C22—21no—
304C22—24no—
305C22—48no—
306C22—42no—
307C22—42no—
308C22—41no—
309C22—41no—
310C22—41no—
311C22—4521no—
312C22—4521no—
313C22—4521no—
314C22#1681359412yes—
315C22C2×D4×D11311yescharacteristic
316C4—41no—
317C4—1132no—
318C4—4521no—
319C4—4522no—
320C4—2261no—
321C4—2261no—
322C4—2261no—
323C4#1681359412yes—
324C4C22×C22⋊D11311yescharacteristic
325C4C2×#1426864611yescharacteristic
326C2—22no—
327C2—44no—
328C2—81no—
329C2—9041no—
330C2C2×#1681359411yescharacteristic
331C2AGL(1,ℤ/8)×D11311yescharacteristic
332C2#2029939411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×AGL(1,ℤ/8)×C113C2
socleC22×C113C22×D4
hypercenterC2×AGL(1,ℤ/8)D113
hypocenterC113#3036
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×#16813648C2semidirect
2. #20299144C2semidirect
3. C2×D4×Dic113C2semidirect
4. #20298815C2semidirect
5. #20298811C2semidirect
6. #20298801C2semidirect
7. #20298791C2semidirect
8. #20298621C2semidirect
9. #20298600C2semidirect
10. #20298599C2semidirect
11. C2×AGL(1,ℤ/8)×C113C2semidirect
18. #16813620C22semidirect
19. #16813618C22semidirect
20. #16813611C22semidirect
21. #16813609C22semidirect
33. #16813551C22semidirect
34. #16813551C22semidirect
35. #16813547C22semidirect
36. #16813546C22semidirect
37. #16813544C22semidirect
38. #16813543C22semidirect
84. C2×D4×C113D4semidirect
158. Dic113AGL(1,ℤ/8)semidirect
167. C113#3036semidirect
169. C2×AGL(1,ℤ/8)D113semidirect
226. C2×D4C22⋊D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136482
#202991442
C2×D4×Dic1132
#202988152
#202988112
#202988012
#202987912
#202986212
#202986002
#202985992
C2×AGL(1,ℤ/8)×C1132
#3036113