Finite Group Databasebeta

← #28400194

Subgroups — #28400194

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×#16813650C211yesmaximal, characteristic, complemented
2C2×M16×D113C211yesmaximal, characteristic, complemented
3#20299110C211yesmaximal, characteristic, complemented
4C2×#16813597C211yesmaximal, characteristic, complemented
5#20298852C212yesmaximal, complemented
6#20298845C212yesmaximal, complemented
7#20298835C212yesmaximal, complemented
8#20298828C212yesmaximal, complemented
9#20298602C211yesmaximal, characteristic, complemented
10#20298597C211yesmaximal, characteristic, complemented
11#428×C113C211yesmaximal, characteristic, complemented
12C2×#14268647C2211yescharacteristic
13C22×D452—21no—
14C22×D452C2211yescharacteristic
15C22×C4×D113C2211yescharacteristic
16#16813650—24no—
17C2×#14268636C2212yescomplemented
18C2×D904C2212yescomplemented
19C2×#14268631C2211yescharacteristic
20C2×#14268630C2212yescomplemented
21M16×D113—24no—
22C2×C8×D113C2212yescomplemented
23#16813606—21no—
24#16813602C2211yescharacteristic, complemented
25#16813602C2211yescharacteristic, complemented
26#16813597—21no—
27#16813597—21no—
28#16813597C2212yes—
29#16813597C2212yes—
30#16813597C2211yescharacteristic, complemented
31#16813597C2211yescharacteristic, complemented
32#16813592—21no—
33C4×D452—21no—
34C4×D452—21no—
35C2×#14268624—21no—
36#16813545C2212yescomplemented
37#16813542C2212yescomplemented
38#16813542C2212yescomplemented
39#16813542C2212yescomplemented
40C2×M16×C113C2211yescharacteristic
41#117×C113C2211yescharacteristic
42C2×C4⋊C4×C113C2211yescharacteristic
43#107×C113C2212yescomplemented
44#106×C113C2212yescomplemented
45C23×D113—21no—
46C23×D113D411yescharacteristic
47#14268647—22no—
48#14268647—22no—
49C2×Dic226C2311yescharacteristic
50C2×D452—22no—
51C2×D452—22no—
52C2×D452—21no—
53C2×D452—21no—
54C2×D452—22no—
55C2×D452—22no—
56C2×D452—21no—
57C2×D452—44no—
58C2×D452C2312yes—
59C2×D452C2311yescharacteristic
60C2×C22⋊D113—21no—
61C22×Dic113D411yescharacteristic
62C2×C4×D113—22no—
63C2×C4×D113—22no—
64C2×C4×D113—21no—
65C2×C4×D113D411yescharacteristic
66C2×C4×D113D411yescharacteristic
67C2×C4×D113C2311yescharacteristic
68C2×C4×D113C2311yescharacteristic
69#14268636—24no—
70D904—24no—
71#14268631—22no—
72#14268630—24no—
73C2×#11744751C2312yes—
74C8×D113—24no—
75C4⋊Dic113—21no—
76C4⋊Dic113—21no—
77#14268624—21no—
78#14268624—21no—
79#14268624—22no—
80#14268624—22no—
81#14268624—21no—
82#14268624—21no—
83C22×C4×C113—21no—
84C22×C4×C113C2311yescharacteristic
85M16×C113D414yescomplemented
86C2×C8×C113C2312yes—
87C4⋊C4×C113—21no—
88C4⋊C4×C113C2312yes—
89C4⋊C4×C113C2311yescharacteristic
90C4⋊C4×C113C2311yescharacteristic
91C22⋊C4×C113—21no—
92C42×C113—21no—
93C23×C113C2×D411yescharacteristic
94C22×D113—22no—
95C22×D113—22no—
96C22×D113—21no—
97C22×D113—22no—
98C22×D113—41no—
99C22×D113—42no—
100C22×D113—42no—
101C22×D113—42no—
102C22×D113C2×D411yescharacteristic
103C22×D113C2×D411yescharacteristic
104C2×C4×C113—21no—
105C2×C4×C113—21no—
106C2×C4×C113—22no—
107C2×C4×C113—42no—
108C2×C4×C113C2×D411yescharacteristic
109C2×C4×C113C2×D412yes—
110C2×C4×C113#4112yes—
111C2×C4×C113C2411yescharacteristic
112C22⋊D113—42no—
113C2×Dic113—22no—
114C2×Dic113—21no—
115C2×Dic113C2×D411yescharacteristic
116C2×Dic113C2×D411yescharacteristic
117D452—21no—
118D452—22no—
119D452—22no—
120D452—21no—
121D452—42no—
122D452—44no—
123D452—42no—
124D452—44no—
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×C113C2×D414yescomplemented
136#11744751—22no—
137C22×C113—21no—
138C22×C113—21no—
139C22×C113#12112yes—
140C22×C113C22×D411yescharacteristic
141C2×D113—21no—
142C2×D113—21no—
143C2×D113—21no—
144C2×D113—21no—
145C2×D113—21no—
146C2×D113—44no—
147C2×D113—41no—
148C2×D113—42no—
149C2×D113—42no—
150C2×D113—41no—
151C2×D113—41no—
152C2×D113—42no—
153C2×D113—84no—
154C2×D113AGL(1,ℤ/8)12yescomplemented
155C4×C113—42no—
156C4×C113—41no—
157C4×C113—41no—
158C4×C113#12112yes—
159C4×C113C22×D411yescharacteristic
160C4×C113C2×#4111yescharacteristic
161Dic113—21no—
162Dic113—21no—
163Dic113—41no—
164C2×C113—22no—
165C2×C113C2×#12111yescharacteristic
166C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
167C2×C113#57511yescharacteristic
168D113—22no—
169D113—41no—
170D113—81no—
171D113—82no—
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#428D11311yescharacteristic, complemented
183#418—1131no—
184#417—1131no—
185C2×#41—1131no—
186C22×D4—1131no—
187C22×D4—2261no—
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⋊C4C2×D11311yescharacteristic
211C2×C22⋊C4—2261no—
212#107C2×D11312yescomplemented
213#106C2×D11312yescomplemented
214#103—1132no—
215#102—1132no—
216#102—1132no—
217#102—1132no—
218C24—1131no—
219C24—2261no—
220#41—2262no—
221#41—2262no—
222C2×Q8—1131no—
223C2×D4—1131no—
224C2×D4—1132no—
225C2×D4—4524no—
226C2×D4—2261no—
227C2×D4—2261no—
228C2×D4—2262no—
229C2×D4—2262no—
230C2×D4—2261no—
231C2×D4—2261no—
232C2×D4—2262no—
233C2×D4—2262no—
234C22×C4—21no—
235C22×C4—1131no—
236C22×C4—1131no—
237C22×C4—1131no—
238C22×C4—1131no—
239C22×C4—1131no—
240C22×C4—2261no—
241C22×C4—2262no—
242C22×C4—2262no—
243C22×C4C22×D11311yescharacteristic
244SD16—2264no—
245D8—2264no—
246M16—2262no—
247M16—2264no—
248M16D45214yescomplemented
249C2×C8—1132no—
250C2×C8—2264no—
251C2×C8C22×D11312yes—
252C4⋊C4—21no—
253C4⋊C4—2261no—
254C4⋊C4—2261no—
255C4⋊C4C22×D11311yescharacteristic
256C4⋊C4C22×D11311yescharacteristic
257C4⋊C4C22×D11312yes—
258C22⋊C4—21no—
259C22⋊C4—2262no—
260C22⋊C4—2262no—
261C22⋊C4—2261no—
262C22⋊C4—2261no—
263C22⋊C4—2261no—
264C22⋊C4—2261no—
265C42—21no—
266C23—1131no—
267C23—1131no—
268C23—4522no—
269C23—4522no—
270C23—4521no—
271C23—4522no—
272C23—2262no—
273C23—2261no—
274C23—2262no—
275C23—2262no—
276C23D4×D11311yescharacteristic
277Q8—2261no—
278Q8—2261no—
279D4—4524no—
280D4—4522no—
281D4—4524no—
282D4—4522no—
283D4—4522no—
284D4—4522no—
285D4—2261no—
286D4—2262no—
287D4—2262no—
288D4—2261no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—22no—
292C2×C4—42no—
293C2×C4—1131no—
294C2×C4—1131no—
295C2×C4—4522no—
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×C4C2×D45212yes—
306C2×C4#1426864812yes—
307C2×C4C23×D11311yescharacteristic
308C8—2262no—
309C8C2×D45214yescomplemented
310C22—21no—
311C22—21no—
312C22—1132no—
313C22—9044no—
314C22—4524no—
315C22—4521no—
316C22—4522no—
317C22—4522no—
318C22—4521no—
319C22—4521no—
320C22—4522no—
321C22—2261no—
322C22—2261no—
323C22—2261no—
324C22—2261no—
325C22—2261no—
326C22#1681359712yes—
327C22C2×D4×D11311yescharacteristic
328C4—42no—
329C4—41no—
330C4—41no—
331C4—4521no—
332C4—2261no—
333C4—2261no—
334C4#1681359712yes—
335C4C22×D45211yescharacteristic
336C4C2×#1426864811yescharacteristic
337C2—22no—
338C2—9042no—
339C2—9041no—
340C2—4521no—
341C2—2262no—
342C2C2×#1681359711yescharacteristic
343C2AGL(1,ℤ/8)×D11311yescharacteristic
344C2#2029939711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#428×C113C2
socleC22×C113C22×D4
hypercenter#428D113
hypocenterC113#3055
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
1. C2×#16813650C2semidirect
2. C2×M16×D113C2semidirect
3. #20299110C2semidirect
4. C2×#16813597C2semidirect
5. #20298852C2semidirect
6. #20298845C2semidirect
7. #20298835C2semidirect
8. #20298828C2semidirect
9. #20298602C2semidirect
10. #20298597C2semidirect
11. #428×C113C2semidirect
17. C2×#14268636C22semidirect
18. C2×D904C22semidirect
20. C2×#14268630C22semidirect
22. C2×C8×D113C22semidirect
24. #16813602C22semidirect
25. #16813602C22semidirect
30. #16813597C22semidirect
31. #16813597C22semidirect
36. #16813545C22semidirect
37. #16813542C22semidirect
38. #16813542C22semidirect
39. #16813542C22semidirect
43. #107×C113C22semidirect
44. #106×C113C22semidirect
85. M16×C113D4semidirect
135. C8×C113C2×D4semidirect
154. C2×D113AGL(1,ℤ/8)semidirect
173. C113#3055semidirect
182. #428D113semidirect
212. #107C2×D113semidirect
213. #106C2×D113semidirect
248. M16D452semidirect
309. C8C2×D452semidirect

Maximal subgroups

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

subgroupindex
C2×#168136502
C2×M16×D1132
#202991102
C2×#168135972
#202988522
#202988452
#202988352
#202988282
#202986022
#202985972
#428×C1132
#3055113