Finite Group Databasebeta

← #34053975

Subgroups — #34053975

Order 19072.

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

normal subgroups only

This group has 732 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
1C2×#18011958C211yesmaximal, characteristic, complemented
2C2×#18011937C211yesmaximal, characteristic, complemented
3C22×#14558724C211yesmaximal, characteristic, complemented
4#23749768C214yesmaximal, complemented
5#23749763C214yesmaximal, complemented
6#23749633C211yesmaximal, characteristic, complemented
7#23749619C211yesmaximal, characteristic, complemented
8#23749592C211yesmaximal, characteristic, complemented
9#535×C149C211yesmaximal, characteristic, complemented
10#18011958—24no—
11#18011958—24no—
12C2×#14558736C2211yescharacteristic
13C2×#14558736C2212yescomplemented
14C2×#14558735—21no—
15C2×#14558735—22no—
16C22×Dic298C2211yescharacteristic
17C22×Dic298C2212yescomplemented
18C2×Q8×D149—21no—
19#18011937—24no—
20C2×#14558724—24no—
21C2×#14558724C2212yes—
22C2×#14558724C2214yes—
23C2×#14558721C2212yes—
24C2×#14558720C2211yescharacteristic
25C22×#11924746C2211yescharacteristic
26#18011834C2214yescomplemented
27#18011834C2212yescomplemented
28#18011831C2212yescomplemented
29C22⋊#11924746C2214yescomplemented
30C2×#41×C149C2211yescharacteristic
31C22×D4×C149C2211yescharacteristic
32#127×C149—21no—
33#124×C149—21no—
34#121×C149C2214yes—
35#120×C149—22no—
36#117×C149C2211yescharacteristic
37#14558736—24no—
38#14558736—24no—
39#14558736—22no—
40#14558736D414yescomplemented
41#14558735—216no—
42#14558735—28no—
43C2×Dic298—24no—
44C2×Dic298—24no—
45C2×Dic298—21no—
46C2×Dic298—22no—
47C2×Dic298—22no—
48C2×Dic298D414yescomplemented
49C2×Dic298C2312yes—
50C2×Dic298C2311yescharacteristic
51Q8×D149—28no—
52C2×D596C2311yescharacteristic
53C2×C22⋊D149—21no—
54C2×C22⋊D149—22no—
55C22×Dic149—21no—
56C22×Dic149—22no—
57C2×C4×D149—21no—
58C2×C4×D149—22no—
59#14558724—28no—
60#14558724—24no—
61#14558721—24no—
62#14558720—22no—
63C2×#11924746—22no—
64C2×#11924746C2312yes—
65C2×#11924746C2312yes—
66C24×C149—21no—
67#41×C149—22no—
68#41×C149—22no—
69C2×Q8×C149D411yescharacteristic
70C2×D4×C149—24no—
71C2×D4×C149—22no—
72C2×D4×C149—22no—
73C2×D4×C149—21no—
74C2×D4×C149D412yes—
75C2×D4×C149D411yescharacteristic
76C2×D4×C149C2312yes—
77C22×C4×C149C2312yes—
78C22×C4×C149C2311yescharacteristic
79C4⋊C4×C149C2312yes—
80C22⋊C4×C149—21no—
81C22⋊C4×C149—24no—
82C42×C149—21no—
83C22×D149—21no—
84Dic298—28no—
85Dic298—24no—
86Dic298—21no—
87Dic298—22no—
88Dic298C2×D412yes—
89Dic298C2×D414yes—
90D596—21no—
91D596C2×D412yes—
92C22⋊D149—28no—
93C22⋊D149—24no—
94C2×Dic149—28no—
95C2×Dic149—24no—
96C2×Dic149—21no—
97C2×Dic149—22no—
98C4×D149—28no—
99C4×D149—24no—
100#11924746—22no—
101#11924746—22no—
102C23×C149—22no—
103C23×C149—42no—
104C23×C149—82no—
105C23×C149C2×D412yes—
106C23×C149C2×D411yescharacteristic
107Q8×C149—22no—
108D4×C149—24no—
109D4×C149—22no—
110D4×C149—22no—
111D4×C149—22no—
112D4×C149—42no—
113D4×C149—84no—
114C2×C4×C149—22no—
115C2×C4×C149—22no—
116C2×C4×C149—22no—
117C2×C4×C149C2×D412yes—
118C2×C4×C149C2×D412yes—
119C2×C4×C149C2×D412yes—
120C2×C4×C149C2×D411yescharacteristic
121C2×C4×C149C2411yescharacteristic
122C22×C149—22no—
123C22×C149—22no—
124C22×C149—24no—
125C22×C149—42no—
126C22×C149—44no—
127C22×C149—84no—
128C22×C149#12012yes—
129C22×C149C22×D411yescharacteristic
130C2×D149—22no—
131C2×D149—42no—
132C4×C149—22no—
133C4×C149—42no—
134C4×C149#12012yes—
135C4×C149C22×D411yescharacteristic
136C4×C149C22×D411yescharacteristic
137Dic149—24no—
138Dic149—22no—
139C2×C149—22no—
140C2×C149—42no—
141C2×C149—82no—
142C2×C149C2×#12011yescharacteristic
143C2×C149#57712yes—
144D149—42no—
145C149#301011yescharacteristic, complemented, Sylow
146#3010—1491nomaximal, Sylow
147C2×2−1+4—1491no—
148C2×AGL(1,ℤ/8)—1491no—
149C22×SD16—1491no—
150#535D14911yescharacteristic, complemented
151#449—1494no—
152#448—1494no—
153#419—1491no—
154#416—1491no—
155#408—1491no—
1562−1+4—2984no—
1572−1+4—2984no—
158C2×#41—2982no—
159C2×#41—2981no—
160C2×#41—1492no—
161C2×#41—1491no—
162C2×#41C2×D14911yescharacteristic
163C22×Q8—2981no—
164C22×Q8—1492no—
165C22×Q8—1491no—
166C22×D4C2×D14911yescharacteristic
167AGL(1,ℤ/8)—2984no—
168C2×SD16—2984no—
169C2×SD16—1494no—
170C2×SD16—1492no—
171C2×D8—1492no—
172C2×M16—1491no—
173C22×C8—1491no—
174#127—21no—
175#124—21no—
176#121C2×D14914yes—
177#120—22no—
178#117C2×D14911yescharacteristic
179#103—1492no—
180#103—1494no—
181#102—1492no—
182C22⋊C8—1494no—
183C24—21no—
184#41—22no—
185#41—22no—
186#41—2984no—
187#41—2984no—
188#41—29816no—
189#41—2988no—
190#41—2982no—
191#41—1494no—
192C2×Q8—2984no—
193C2×Q8—2984no—
194C2×Q8—2988no—
195C2×Q8—2982no—
196C2×Q8—2982no—
197C2×Q8—2981no—
198C2×Q8—1494no—
199C2×Q8—1491no—
200C2×Q8—1492no—
201C2×Q8C22⋊D14911yescharacteristic
202C2×D4—24no—
203C2×D4—22no—
204C2×D4—22no—
205C2×D4—21no—
206C2×D4—2982no—
207C2×D4—2981no—
208C2×D4—1491no—
209C2×D4C22⋊D14912yes—
210C2×D4C22⋊D14911yescharacteristic
211C2×D4C22×D14912yes—
212C22×C4—2982no—
213C22×C4—2981no—
214C22×C4—2982no—
215C22×C4—2981no—
216C22×C4C22×D14912yes—
217C22×C4C22×D14911yescharacteristic
218SD16—2988no—
219SD16—2984no—
220D8—2984no—
221M16—2982no—
222C2×C8—2982no—
223C2×C8—1492no—
224C2×C8—1492no—
225C4⋊C4C22×D14912yes—
226C22⋊C4—21no—
227C22⋊C4—24no—
228C42—21no—
229C23—22no—
230C23—42no—
231C23—82no—
232C23—2981no—
233C23C2×C22⋊D14912yes—
234C23C2×C22⋊D14911yescharacteristic
235Q8—22no—
236Q8—2988no—
237Q8—2981no—
238Q8—2982no—
239Q8—2984no—
240Q8—1492no—
241Q8—1494no—
242D4—24no—
243D4—22no—
244D4—22no—
245D4—22no—
246D4—42no—
247D4—84no—
248D4—2988no—
249D4—2984no—
250D4—2981no—
251D4—1492no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—2988no—
256C2×C4—2988no—
257C2×C4—2982no—
258C2×C4—2981no—
259C2×C4—2984no—
260C2×C4—2984no—
261C2×C4D4×D14912yes—
262C2×C4D4×D14912yes—
263C2×C4C2×C22⋊D14912yes—
264C2×C4C2×C22⋊D14911yescharacteristic
265C2×C4C23×D14911yescharacteristic
266C8—2982no—
267C8—2982no—
268C22—22no—
269C22—24no—
270C22—22no—
271C22—44no—
272C22—42no—
273C22—84no—
274C22—2982no—
275C22—5962no—
276C22#1801187912yes—
277C22C22×C22⋊D14911yescharacteristic
278C4—22no—
279C4—42no—
280C4—2984no—
281C4—2982no—
282C4#1801187912yes—
283C4C2×D4×D14911yescharacteristic
284C4C2×D4×D14911yescharacteristic
285C2—22no—
286C2—42no—
287C2—82no—
288C2—5962no—
289C2C2×#1801187911yescharacteristic
290C2#2375043612yes—
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#535×C149C2
socleC22×C149C22×D4
hypercenter#535D149
hypocenterC149#3010
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C2×#18011958C2semidirect
2. C2×#18011937C2semidirect
3. C22×#14558724C2semidirect
4. #23749768C2semidirect
5. #23749763C2semidirect
6. #23749633C2semidirect
7. #23749619C2semidirect
8. #23749592C2semidirect
9. #535×C149C2semidirect
13. C2×#14558736C22semidirect
17. C22×Dic298C22semidirect
26. #18011834C22semidirect
27. #18011834C22semidirect
28. #18011831C22semidirect
29. C22⋊#11924746C22semidirect
40. #14558736D4semidirect
48. C2×Dic298D4semidirect
145. C149#3010semidirect
150. #535D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119582
C2×#180119372
C22×#145587242
#237497682
#237497632
#237496332
#237496192
#237495922
#535×C1492
#3010149