Finite Group Databasebeta

← #28400191

Subgroups — #28400191

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×#16813648C211yesmaximal, characteristic, complemented
2C2×M16×D113C211yesmaximal, characteristic, complemented
3#20299110C211yesmaximal, characteristic, complemented
4C2×#16813593C211yesmaximal, characteristic, complemented
5#20298850C212yesmaximal, complemented
6#20298843C212yesmaximal, complemented
7#20298833C212yesmaximal, complemented
8#20298826C212yesmaximal, complemented
9#20298641C211yesmaximal, characteristic, complemented
10#20298600C211yesmaximal, characteristic, complemented
11#418×C113C211yesmaximal, characteristic, complemented
12C2×#14268647C2211yescharacteristic
13C22×C22⋊D113—21no—
14C22×C4×D113C2211yescharacteristic
15#16813648—24no—
16C2×#14268635C2212yescomplemented
17C2×#14268632C2212yescomplemented
18C2×#14268631C2211yescharacteristic
19C2×#14268630C2212yescomplemented
20M16×D113—24no—
21C2×C8×D113C2212yescomplemented
22#16813606—21no—
23#16813602C2211yescharacteristic, complemented
24#16813602C2211yescharacteristic, complemented
25#16813597C2211yescharacteristic, complemented
26#16813597C2211yescharacteristic, complemented
27#16813593—21no—
28#16813593—21no—
29#16813593C2212yes—
30#16813593C2212yes—
31#16813592—21no—
32C4×D452—21no—
33C4×D452—21no—
34C2×C4⋊Dic113C2211yescharacteristic
35C2×C22⋊Dic113—21no—
36#16813555C2212yescomplemented
37#16813553C2212yescomplemented
38#16813547C2212yescomplemented
39#16813544C2212yescomplemented
40C22×D4×C113C2211yescharacteristic
41C2×M16×C113C2211yescharacteristic
42#117×C113C2211yescharacteristic
43#102×C113C2212yescomplemented
44#102×C113C2212yescomplemented
45C23×D113D411yescharacteristic
46#14268647—22no—
47#14268647—22no—
48C2×Dic226C2311yescharacteristic
49C2×D452—21no—
50C2×D452—21no—
51C2×D452C2311yescharacteristic
52C2×C22⋊D113—21no—
53C2×C22⋊D113—22no—
54C2×C22⋊D113—22no—
55C2×C22⋊D113—44no—
56C22×Dic113—21no—
57C22×Dic113D411yescharacteristic
58C2×C4×D113—22no—
59C2×C4×D113—22no—
60C2×C4×D113—21no—
61C2×C4×D113D411yescharacteristic
62C2×C4×D113D411yescharacteristic
63C2×C4×D113C2311yescharacteristic
64C2×C4×D113C2311yescharacteristic
65#14268635—24no—
66#14268632—24no—
67#14268631D414yescomplemented
68#14268630—24no—
69C2×#11744751C2312yes—
70C8×D113—24no—
71C4⋊Dic113—21no—
72C4⋊Dic113—21no—
73C4⋊Dic113—21no—
74C4⋊Dic113C2312yes—
75C22⋊Dic113—22no—
76C22⋊Dic113—22no—
77#14268624—21no—
78#14268624—21no—
79#14268624—21no—
80#14268624—21no—
81C24×C113—21no—
82C2×D4×C113—22no—
83C2×D4×C113—21no—
84C2×D4×C113—22no—
85C2×D4×C113C2312yes—
86C22×C4×C113C2311yescharacteristic
87M16×C113—22no—
88C2×C8×C113C2312yes—
89C4⋊C4×C113C2311yescharacteristic
90C4⋊C4×C113C2311yescharacteristic
91C22⋊C4×C113—21no—
92C42×C113—21no—
93C23×C113—22no—
94C23×C113—42no—
95C23×C113—42no—
96C23×C113—42no—
97C23×C113C2×D411yescharacteristic
98C22×D113—22no—
99C22×D113—22no—
100C22×D113—21no—
101C22×D113—41no—
102C22×D113C2×D411yescharacteristic
103C22×D113C2×D411yescharacteristic
104D4×C113—22no—
105D4×C113—22no—
106D4×C113—42no—
107C2×C4×C113—21no—
108C2×C4×C113—21no—
109C2×C4×C113C2×D411yescharacteristic
110C2×C4×C113C2×D412yes—
111C2×C4×C113#4112yes—
112C2×C4×C113C2411yescharacteristic
113C22⋊D113—44no—
114C22⋊D113—42no—
115C22⋊D113—44no—
116C2×Dic113—22no—
117C2×Dic113—21no—
118C2×Dic113—22no—
119C2×Dic113—42no—
120C2×Dic113C2×D411yescharacteristic
121C2×Dic113C2×D411yescharacteristic
122D452—21no—
123D452—21no—
124D452—42no—
125D452—42no—
126C4×D113—22no—
127C4×D113—22no—
128C4×D113—21no—
129C4×D113—21no—
130C4×D113—21no—
131C4×D113—21no—
132C4×D113—42no—
133Dic226—21no—
134Dic226—21no—
135C8×C113—22no—
136#11744751C2×D414yescomplemented
137C22×C113—21no—
138C22×C113—21no—
139C22×C113—42no—
140C22×C113—42no—
141C22×C113—42no—
142C22×C113—84no—
143C22×C113#12112yes—
144C22×C113C22×D411yescharacteristic
145C2×D113—21no—
146C2×D113—21no—
147C2×D113—21no—
148C2×D113—21no—
149C2×D113—21no—
150C2×D113—44no—
151C2×D113—41no—
152C2×D113—41no—
153C2×D113—41no—
154C2×D113AGL(1,ℤ/8)12yescomplemented
155C4×C113—41no—
156C4×C113—41no—
157C4×C113#12112yes—
158C4×C113C22×D411yescharacteristic
159C4×C113C2×#4111yescharacteristic
160Dic113—21no—
161Dic113—21no—
162Dic113—41no—
163Dic113—42no—
164C2×C113—22no—
165C2×C113—82no—
166C2×C113C2×#12111yescharacteristic
167C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
168C2×C113#57511yescharacteristic
169D113—22no—
170D113—41no—
171D113—81no—
172#3055—1131nomaximal, Sylow
173C113#305511yescharacteristic, complemented, Sylow
174C2×AGL(1,ℤ/8)—1131no—
175C22×M16—1131no—
176#525—1131no—
177C2×#121—1131no—
178#469—1132no—
179#468—1132no—
180#466—1132no—
181#465—1132no—
182#428—1131no—
183#418D11311yescharacteristic, complemented
184#417—1131no—
185C2×#41—1131no—
186C22×D4—2261no—
187C22×D4C2×D11311yescharacteristic
188C23×C4—1131no—
189AGL(1,ℤ/8)—2264no—
190C2×SD16—1132no—
191C2×D8—1132no—
192C2×M16—1131no—
193C2×M16—1132no—
194C2×M16—2264no—
195C2×M16C2×D11311yescharacteristic
196C22×C8—1132no—
197#123—2261no—
198C22⋊Q8—1131no—
199C22⋊Q8—1131no—
200#121—1132no—
201#121—1132no—
202#121—1131no—
203#121—1131no—
204#121—2261no—
205#121—2261no—
206#120—2261no—
207C4×D4—2261no—
208C4×D4—2261no—
209#117C2×D11311yescharacteristic
210C2×C4⋊C4—1131no—
211C2×C22⋊C4—2261no—
212#107—1132no—
213#106—1132no—
214#103—1132no—
215#102—1132no—
216#102C2×D11312yescomplemented
217#102C2×D11312yescomplemented
218C24—21no—
219C24—1131no—
220#41—2262no—
221#41—2262no—
222C2×Q8—1131no—
223C2×D4—22no—
224C2×D4—21no—
225C2×D4—22no—
226C2×D4—1131no—
227C2×D4—4524no—
228C2×D4—2261no—
229C2×D4—2261no—
230C2×D4—2262no—
231C2×D4—2262no—
232C2×D4—2261no—
233C2×D4C22×D11312yes—
234C22×C4—1131no—
235C22×C4—1131no—
236C22×C4—1131no—
237C22×C4—1131no—
238C22×C4—1131no—
239C22×C4—2261no—
240C22×C4—2261no—
241C22×C4—2262no—
242C22×C4—2262no—
243C22×C4C22×D11311yescharacteristic
244SD16—2264no—
245D8—2264no—
246M16—22no—
247M16—1134no—
248M16—2264no—
249C2×C8—1132no—
250C2×C8—2264no—
251C2×C8C22×D11312yes—
252C4⋊C4—1132no—
253C4⋊C4—2261no—
254C4⋊C4—2261no—
255C4⋊C4—2261no—
256C4⋊C4C22×D11311yescharacteristic
257C4⋊C4C22×D11311yescharacteristic
258C22⋊C4—21no—
259C22⋊C4—2261no—
260C22⋊C4—2261no—
261C22⋊C4—2261no—
262C22⋊C4—2261no—
263C22⋊C4—2262no—
264C22⋊C4—2262no—
265C42—21no—
266C23—22no—
267C23—42no—
268C23—42no—
269C23—42no—
270C23—1131no—
271C23—1131no—
272C23—4521no—
273C23—2262no—
274C23—2261no—
275C23—2262no—
276C23D4×D11311yescharacteristic
277Q8—2261no—
278Q8—2261no—
279D4—22no—
280D4—22no—
281D4—42no—
282D4—4522no—
283D4—4522no—
284D4—4524no—
285D4—4524no—
286D4—4522no—
287D4—2261no—
288D4—2261no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—1131no—
292C2×C4—1131no—
293C2×C4—4522no—
294C2×C4—4522no—
295C2×C4—2262no—
296C2×C4—2261no—
297C2×C4—2262no—
298C2×C4—2262no—
299C2×C4—2262no—
300C2×C4—2261no—
301C2×C4—2261no—
302C2×C4—2261no—
303C2×C4—2261no—
304C2×C4D4×D11311yescharacteristic
305C2×C4D4×D11312yes—
306C2×C4#1426864712yes—
307C2×C4C23×D11311yescharacteristic
308C8—22no—
309C8—1134no—
310C22—21no—
311C22—21no—
312C22—42no—
313C22—42no—
314C22—42no—
315C22—84no—
316C22—1132no—
317C22—4524no—
318C22—4521no—
319C22—4521no—
320C22—4521no—
321C22—2261no—
322C22—2261no—
323C22—2261no—
324C22—2261no—
325C22—2261no—
326C22#1681359512yes—
327C22C2×D4×D11311yescharacteristic
328C4—41no—
329C4—41no—
330C4—4521no—
331C4—4522no—
332C4—2261no—
333C4—2261no—
334C4#1681359512yes—
335C4C2×D4×D11311yescharacteristic
336C4C2×#1426864711yescharacteristic
337C2—22no—
338C2—82no—
339C2—9041no—
340C2—4521no—
341C2—2262no—
342C2C2×#1681359511yescharacteristic
343C2AGL(1,ℤ/8)×D11311yescharacteristic
344C2#2029939411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#418×C113C2
socleC22×C113C22×D4
hypercenter#418D113
hypocenterC113#3055
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. C2×#16813648C2semidirect
2. C2×M16×D113C2semidirect
3. #20299110C2semidirect
4. C2×#16813593C2semidirect
5. #20298850C2semidirect
6. #20298843C2semidirect
7. #20298833C2semidirect
8. #20298826C2semidirect
9. #20298641C2semidirect
10. #20298600C2semidirect
11. #418×C113C2semidirect
16. C2×#14268635C22semidirect
17. C2×#14268632C22semidirect
19. C2×#14268630C22semidirect
21. C2×C8×D113C22semidirect
23. #16813602C22semidirect
24. #16813602C22semidirect
25. #16813597C22semidirect
26. #16813597C22semidirect
36. #16813555C22semidirect
37. #16813553C22semidirect
38. #16813547C22semidirect
39. #16813544C22semidirect
43. #102×C113C22semidirect
44. #102×C113C22semidirect
67. #14268631D4semidirect
136. #11744751C2×D4semidirect
154. C2×D113AGL(1,ℤ/8)semidirect
173. C113#3055semidirect
183. #418D113semidirect
216. #102C2×D113semidirect
217. #102C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136482
C2×M16×D1132
#202991102
C2×#168135932
#202988502
#202988432
#202988332
#202988262
#202986412
#202986002
#418×C1132
#3055113