Finite Group Databasebeta

← #34053979

Subgroups — #34053979

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×#18011939C211yesmaximal, characteristic, complemented
3C22×#14558725C211yesmaximal, characteristic, complemented
4#23750189C211yesmaximal, characteristic, complemented
5#23749772C214yesmaximal, complemented
6#23749766C214yesmaximal, complemented
7#23749635C211yesmaximal, characteristic, complemented
8#23749622C211yesmaximal, characteristic, complemented
9#408×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—
19C22×D596C2211yescharacteristic
20#18011939—24no—
21C2×#14558725—24no—
22C2×#14558725C2212yes—
23C2×#14558725C2214yes—
24C2×D1192C2212yes—
25#18011907—21no—
26#18011900—21no—
27#18011885C2214yes—
28#18011879—22no—
29#18011870C2211yescharacteristic
30#18011836C2214yescomplemented
31#18011836C2212yescomplemented
32#18011833C2212yescomplemented
33C2×#41×C149C2211yescharacteristic
34C2×M16×C149C2211yescharacteristic
35C22×C8×C149C2211yescharacteristic
36C22⋊C8×C149C2214yescomplemented
37C23×D149—21no—
38#14558736—24no—
39#14558736—24no—
40#14558736—22no—
41#14558736D414yescomplemented
42#14558735—216no—
43#14558735—28no—
44C2×Dic298—24no—
45C2×Dic298—24no—
46C2×Dic298—21no—
47C2×Dic298—22no—
48C2×Dic298—22no—
49C2×Dic298D414yescomplemented
50C2×Dic298C2312yes—
51C2×Dic298C2311yescharacteristic
52Q8×D149—28no—
53C2×D596—22no—
54C2×D596—22no—
55C2×D596—21no—
56C2×D596C2312yes—
57C2×D596C2311yescharacteristic
58C2×C22⋊D149—21no—
59C2×C22⋊D149—22no—
60C2×C22⋊D149—24no—
61C22×Dic149—21no—
62C22×Dic149—22no—
63C2×C4×D149—21no—
64C2×C4×D149—22no—
65#14558725—28no—
66#14558725—24no—
67D1192—24no—
68C4⋊Dic149C2312yes—
69C22⋊Dic149—21no—
70#14558713—24no—
71C4×Dic149—21no—
72#41×C149—22no—
73#41×C149—22no—
74C2×Q8×C149D411yescharacteristic
75C2×D4×C149D411yescharacteristic
76C2×D4×C149D412yes—
77C22×C4×C149C2312yes—
78C22×C4×C149C2311yescharacteristic
79M16×C149—22no—
80C2×C8×C149—22no—
81C2×C8×C149C2312yes—
82C2×C8×C149C2312yes—
83C22×D149—21no—
84C22×D149—22no—
85C22×D149—42no—
86C22×D149—82no—
87Dic298—28no—
88Dic298—24no—
89Dic298—21no—
90Dic298—22no—
91Dic298C2×D412yes—
92Dic298C2×D414yes—
93D596—21no—
94D596—22no—
95D596—22no—
96D596—42no—
97D596C2×D412yes—
98C22⋊D149—28no—
99C22⋊D149—24no—
100C22⋊D149—84no—
101C2×Dic149—28no—
102C2×Dic149—24no—
103C2×Dic149—21no—
104C2×Dic149—22no—
105C2×Dic149—22no—
106C4×D149—28no—
107C4×D149—24no—
108C23×C149C2×D412yes—
109C23×C149C2×D411yescharacteristic
110Q8×C149—22no—
111D4×C149—24no—
112D4×C149—22no—
113C2×C4×C149—22no—
114C2×C4×C149—22no—
115C2×C4×C149C2×D412yes—
116C2×C4×C149C2×D412yes—
117C2×C4×C149C2×D412yes—
118C2×C4×C149C2×D411yescharacteristic
119C2×C4×C149C2411yescharacteristic
120C8×C149—22no—
121C8×C149—22no—
122C22×C149—22no—
123C22×C149—22no—
124C22×C149—24no—
125C22×C149#12012yes—
126C22×C149C22×D411yescharacteristic
127C2×D149—22no—
128C2×D149—42no—
129C2×D149—42no—
130C2×D149—44no—
131C2×D149—84no—
132C4×C149—22no—
133C4×C149#12012yes—
134C4×C149C22×D411yescharacteristic
135C4×C149C22×D411yescharacteristic
136Dic149—24no—
137Dic149—22no—
138Dic149—42no—
139C2×C149—22no—
140C2×C149—42no—
141C2×C149C2×#12011yescharacteristic
142C2×C149#57712yes—
143D149—42no—
144D149—82no—
145C149#301011yescharacteristic, complemented, Sylow
146#3010—1491nomaximal, Sylow
147C2×2−1+4—1491no—
148C2×AGL(1,ℤ/8)—1491no—
149C22×SD16—1491no—
150#535—1491no—
151#449—1494no—
152#448—1494no—
153#419—1491no—
154#416—1491no—
155#408D14911yescharacteristic, complemented
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×D4—1491no—
167AGL(1,ℤ/8)—2984no—
168C2×SD16—2984no—
169C2×SD16—1494no—
170C2×SD16—1492no—
171C2×D8—1492no—
172C2×M16C2×D14911yescharacteristic
173C22×C8C2×D14911yescharacteristic
174#127—2981no—
175#124—2981no—
176#121—1494no—
177#120—2982no—
178#117—1491no—
179#103—1492no—
180#103—1494no—
181#102—1492no—
182C22⋊C8C2×D14914yescomplemented
183C24—2981no—
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×Q8D59611yescharacteristic
202C2×D4—2982no—
203C2×D4—2981no—
204C2×D4—2984no—
205C2×D4—2982no—
206C2×D4—2982no—
207C2×D4—2981no—
208C2×D4—1492no—
209C2×D4—1491no—
210C2×D4D59612yes—
211C2×D4D59611yescharacteristic
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—22no—
222C2×C8—22no—
223C2×C8C22×D14912yes—
224C2×C8C22×D14912yes—
225C4⋊C4—1492no—
226C22⋊C4—2981no—
227C22⋊C4—2984no—
228C42—2981no—
229C23—2981no—
230C23—2982no—
231C23—5962no—
232C23—11922no—
233C23C2×D59612yes—
234C23C2×D59611yescharacteristic
235Q8—22no—
236Q8—2988no—
237Q8—2981no—
238Q8—2982no—
239Q8—2984no—
240Q8—1492no—
241Q8—1494no—
242D4—24no—
243D4—22no—
244D4—2988no—
245D4—2984no—
246D4—2981no—
247D4—2982no—
248D4—2982no—
249D4—5962no—
250D4—1492no—
251D4—11924no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—2988no—
255C2×C4—2988no—
256C2×C4—2982no—
257C2×C4—2981no—
258C2×C4—2984no—
259C2×C4—2984no—
260C2×C4—2982no—
261C2×C4D4×D14912yes—
262C2×C4D4×D14912yes—
263C2×C4C2×D59612yes—
264C2×C4C2×D59611yescharacteristic
265C2×C4C23×D14911yescharacteristic
266C8—22no—
267C8—22no—
268C22—22no—
269C22—24no—
270C22—22no—
271C22—2982no—
272C22—5962no—
273C22—5964no—
274C22—5962no—
275C22—11924no—
276C22#1801188112yes—
277C22C22×D59611yescharacteristic
278C4—22no—
279C4—2984no—
280C4—2982no—
281C4—5962no—
282C4#1801188112yes—
283C4C2×D4×D14911yescharacteristic
284C4C2×D4×D14911yescharacteristic
285C2—22no—
286C2—42no—
287C2—5962no—
288C2—11922no—
289C2C2×#1801188111yescharacteristic
290C2#2375043712yes—
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#408×C149C2
socleC22×C149C22×D4
hypercenter#408D149
hypocenterC149#3010
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
1. C2×#18011958C2semidirect
2. C2×#18011939C2semidirect
3. C22×#14558725C2semidirect
4. #23750189C2semidirect
5. #23749772C2semidirect
6. #23749766C2semidirect
7. #23749635C2semidirect
8. #23749622C2semidirect
9. #408×C149C2semidirect
13. C2×#14558736C22semidirect
17. C22×Dic298C22semidirect
30. #18011836C22semidirect
31. #18011836C22semidirect
32. #18011833C22semidirect
36. C22⋊C8×C149C22semidirect
41. #14558736D4semidirect
49. C2×Dic298D4semidirect
145. C149#3010semidirect
155. #408D149semidirect
182. C22⋊C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119582
C2×#180119392
C22×#145587252
#237501892
#237497722
#237497662
#237496352
#237496222
#408×C1492
#3010149