Finite Group Databasebeta

← #34053936

Subgroups — #34053936

Order 19072.

758 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 758 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C22×#14558736C211yesmaximal, characteristic, complemented
2C2×#18011944C211yesmaximal, characteristic, complemented
3C2×#18011939C211yesmaximal, characteristic, complemented
4#23750136C211yesmaximal, characteristic, complemented
5#23749789C214yesmaximal, complemented
6#23749772C214yesmaximal, complemented
7#23749635C211yesmaximal, characteristic, complemented
8#23749631C211yesmaximal, characteristic, complemented
9#407×C149C211yesmaximal, characteristic, complemented
10C2×#14558736—22no—
11C2×#14558736—24no—
12C2×#14558736—24no—
13C2×#14558736C2211yescharacteristic
14C2×#14558736C2214yes—
15C22×Dic298C2211yescharacteristic
16C22×D596C2211yescharacteristic
17C22×C22⋊D149—21no—
18C22×C4×D149—21no—
19#18011944—24no—
20#18011939—24no—
21C2×Dic596C2212yescomplemented
22C2×#14558725C2212yescomplemented
23C2×#14558725C2212yescomplemented
24C2×D1192C2212yescomplemented
25#18011894—21no—
26#18011890C2212yescomplemented
27#18011885C2212yescomplemented
28#18011880—21no—
29C4×C22⋊D149—22no—
30#18011870C2211yescharacteristic
31#18011836C2214yescomplemented
32#18011833C2214yescomplemented
33C23×C4×C149C2211yescharacteristic
34C2×M16×C149C2211yescharacteristic
35C2×M16×C149C2211yescharacteristic
36C22⋊C8×C149C2214yescomplemented
37C23×D149—21no—
38#14558736—216no—
39#14558736—28no—
40#14558736—28no—
41#14558736—22no—
42#14558736—22no—
43C2×Dic298—22no—
44C2×Dic298—21no—
45C2×Dic298D414yescomplemented
46C2×Dic298C2311yescharacteristic
47C2×Dic298C2312yes—
48C2×D596—22no—
49C2×D596—21no—
50C2×D596D414yescomplemented
51C2×D596C2311yescharacteristic
52C2×D596C2312yes—
53C2×C22⋊D149—28no—
54C2×C22⋊D149—24no—
55C2×C22⋊D149—21no—
56C2×C22⋊D149—22no—
57C22×Dic149—21no—
58C2×C4×D149—28no—
59C2×C4×D149—24no—
60C2×C4×D149—21no—
61Dic596—24no—
62#14558725—24no—
63#14558725—24no—
64D1192—24no—
65C4⋊Dic149C2312yes—
66#14558715—22no—
67C22⋊Dic149—21no—
68C22⋊Dic149—22no—
69#14558713—22no—
70C4×Dic149—21no—
71C24×C149D411yescharacteristic
72C22×C4×C149—22no—
73C22×C4×C149—22no—
74C22×C4×C149D411yescharacteristic
75C22×C4×C149D412yes—
76C22×C4×C149C2312yes—
77C22×C4×C149C2311yescharacteristic
78M16×C149—22no—
79M16×C149—22no—
80C2×C8×C149C2312yes—
81C2×C8×C149C2312yes—
82C22×D149—24no—
83C22×D149—22no—
84C22×D149—21no—
85C22×D149—44no—
86Dic298—24no—
87Dic298—22no—
88Dic298—21no—
89Dic298—21no—
90Dic298C2×D414yes—
91D596—24no—
92D596—22no—
93D596—21no—
94D596—21no—
95D596C2×D414yes—
96C22⋊D149—216no—
97C22⋊D149—44no—
98C22⋊D149—42no—
99C2×Dic149—24no—
100C2×Dic149—22no—
101C2×Dic149—21no—
102C2×Dic149—22no—
103C4×D149—216no—
104C4×D149—42no—
105C23×C149—22no—
106C23×C149—42no—
107C23×C149C2×D412yes—
108C23×C149C2×D411yescharacteristic
109C2×C4×C149—22no—
110C2×C4×C149—24no—
111C2×C4×C149—22no—
112C2×C4×C149—22no—
113C2×C4×C149C2×D412yes—
114C2×C4×C149C2×D412yes—
115C2×C4×C149C2×D412yes—
116C2×C4×C149C2×D411yescharacteristic
117C2×C4×C149C2411yescharacteristic
118C8×C149—22no—
119C8×C149—22no—
120C22×C149—22no—
121C22×C149—22no—
122C22×C149—22no—
123C22×C149—22no—
124C22×C149—44no—
125C22×C149#12012yes—
126C22×C149C22×D411yescharacteristic
127C2×D149—24no—
128C2×D149—48no—
129C2×D149—44no—
130C2×D149—41no—
131C2×D149—42no—
132C4×C149—22no—
133C4×C149#12012yes—
134C4×C149C22×D411yescharacteristic
135C4×C149C22×D411yescharacteristic
136Dic149—24no—
137Dic149—41no—
138Dic149—42no—
139C2×C149—22no—
140C2×C149—42no—
141C2×C149C2×#12011yescharacteristic
142C2×C149#57512yes—
143D149—44no—
144D149—81no—
145C149#300511yescharacteristic, complemented, Sylow
146#3005—1491nomaximal, Sylow
147C22×#41—1491no—
148C2×#137—1491no—
149C2×AGL(1,ℤ/8)—1491no—
150#525—1491no—
151#452—1494no—
152#449—1494no—
153#419—1491no—
154#418—1491no—
155#407D14911yescharacteristic, complemented
156C2×#41—2984no—
157C2×#41—2984no—
158C2×#41—2982no—
159C2×#41—1491no—
160C2×#41—1494no—
161C22×Q8—1491no—
162C22×D4—2981no—
163C22×D4—1491no—
164C23×C4—2981no—
165C23×C4C2×D14911yescharacteristic
166#137—2984no—
167AGL(1,ℤ/8)—2984no—
168C2×Q16—1492no—
169C2×SD16—1492no—
170C2×SD16—1492no—
171C2×D8—1492no—
172C2×M16C2×D14911yescharacteristic
173C2×M16C2×D14911yescharacteristic
174#123—2981no—
175C22⋊Q8—1492no—
176#121—1492no—
177#120—2981no—
178C4×D4—2982no—
179#117—1491no—
180#103—1494no—
181#102—1494no—
182C22⋊C8C2×D14914yescomplemented
183C24—2981no—
184C24D59611yescharacteristic
185#41—29816no—
186#41—2988no—
187#41—2988no—
188#41—2982no—
189#41—2982no—
190C2×Q8—2982no—
191C2×Q8—2981no—
192C2×Q8—1494no—
193C2×Q8—1491no—
194C2×Q8—1492no—
195C2×D4—2988no—
196C2×D4—2984no—
197C2×D4—2982no—
198C2×D4—2981no—
199C2×D4—2982no—
200C2×D4—2981no—
201C2×D4—1494no—
202C2×D4—1491no—
203C2×D4—1492no—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—2988no—
207C22×C4—2981no—
208C22×C4—2984no—
209C22×C4—2981no—
210C22×C4D59612yes—
211C22×C4D59611yescharacteristic
212C22×C4C22×D14912yes—
213C22×C4C22×D14911yescharacteristic
214Q16—2984no—
215SD16—2984no—
216SD16—2984no—
217D8—2984no—
218M16—22no—
219M16—22no—
220C2×C8C22×D14912yes—
221C2×C8C22×D14912yes—
222C4⋊C4—2982no—
223C4⋊C4—1492no—
224C22⋊C4—2981no—
225C22⋊C4—2982no—
226C22⋊C4—2982no—
227C42—2981no—
228C23—22no—
229C23—42no—
230C23—2982no—
231C23—2984no—
232C23—2981no—
233C23—5964no—
234C23C2×D59612yes—
235C23C2×D59611yescharacteristic
236Q8—2982no—
237Q8—2984no—
238Q8—2981no—
239Q8—2981no—
240Q8—1494no—
241D4—29816no—
242D4—2982no—
243D4—2981no—
244D4—2981no—
245D4—2984no—
246D4—5964no—
247D4—5962no—
248D4—1494no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—24no—
253C2×C4—29816no—
254C2×C4—2982no—
255C2×C4—2984no—
256C2×C4—2982no—
257C2×C4—2981no—
258C2×C4—5962no—
259C2×C4D4×D14912yes—
260C2×C4D4×D14912yes—
261C2×C4C2×D59612yes—
262C2×C4C2×D59611yescharacteristic
263C2×C4C23×D14911yescharacteristic
264C8—22no—
265C8—22no—
266C22—22no—
267C22—22no—
268C22—22no—
269C22—22no—
270C22—44no—
271C22—2984no—
272C22—5968no—
273C22—5964no—
274C22—5962no—
275C22—5961no—
276C22#1801188112yes—
277C22C22×D59611yescharacteristic
278C4—22no—
279C4—2984no—
280C4—5962no—
281C4—5961no—
282C4#1801188112yes—
283C4C2×D4×D14911yescharacteristic
284C4C2×D4×D14911yescharacteristic
285C2—22no—
286C2—42no—
287C2—5964no—
288C2—11921no—
289C2C2×#1801188111yescharacteristic
290C2#2375042512yes—
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#407×C149C2
socleC22×C149C22×D4
hypercenter#407D149
hypocenterC149#3005
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. C22×#14558736C2semidirect
2. C2×#18011944C2semidirect
3. C2×#18011939C2semidirect
4. #23750136C2semidirect
5. #23749789C2semidirect
6. #23749772C2semidirect
7. #23749635C2semidirect
8. #23749631C2semidirect
9. #407×C149C2semidirect
21. C2×Dic596C22semidirect
22. C2×#14558725C22semidirect
23. C2×#14558725C22semidirect
24. C2×D1192C22semidirect
26. #18011890C22semidirect
27. #18011885C22semidirect
31. #18011836C22semidirect
32. #18011833C22semidirect
36. C22⋊C8×C149C22semidirect
45. C2×Dic298D4semidirect
50. C2×D596D4semidirect
145. C149#3005semidirect
155. #407D149semidirect
182. C22⋊C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
C22×#145587362
C2×#180119442
C2×#180119392
#237501362
#237497892
#237497722
#237496352
#237496312
#407×C1492
#3005149