Finite Group Databasebeta

← #34047672

Subgroups — #34047672

Order 19072.

928 conjugacy classes of subgroups; only the 209 normal subgroups are shown.

normal subgroups only

This group has 928 conjugacy classes of subgroups — too many to draw. Only its 209 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×#18011879C211yesmaximal, characteristic
2C2×#18011871C212yesmaximal, complemented
3C2×C22⋊C4×D149C212yesmaximal, complemented
4#23749513C212yesmaximal, complemented
5#23749505C211yesmaximal, characteristic, complemented
6#23749501C212yesmaximal, complemented
7#23749496C212yesmaximal, complemented
8C4×#14558713C212yesmaximal, complemented
9#390×C149C211yesmaximal, characteristic, complemented
10C24×D149C2211yescharacteristic
11C22×C22⋊D149C2212yes—
12C23×Dic149C2211yescharacteristic, complemented
13C22×C4×D149C2212yes—
14C22×C4×D149C2212yes—
15#18011879C418yescomplemented
16#18011871—28no—
17C2×#14558715C2212yescomplemented
18C2×C22⋊Dic149C2212yes—
19C2×C22⋊Dic149C2211yescharacteristic
20C2×C22⋊Dic149C2211yescharacteristic, complemented
21C2×#14558713C2212yes—
22C2×#14558713C2212yes—
23C2×#14558713C2212yes—
24C22⋊C4×D149—28no—
25C2×C4×Dic149C2212yescomplemented
26#18011818C2212yescomplemented
27#18011818C2212yescomplemented
28#18011818C2212yescomplemented
29C22×D4×C149C2211yescharacteristic
30C2×C4⋊C4×C149C2211yescharacteristic, complemented
31C2×C22⋊C4×C149C2212yes—
32C2×C22⋊C4×C149C2212yescomplemented
33C2×C42×C149C2211yescharacteristic, complemented
34C23×D149—24no—
35C23×D149—24no—
36C23×D149—41no—
37C23×D149—41no—
38C23×D149C2×C414yescomplemented
39C23×D149C2312yes—
40C2×C22⋊D149—24no—
41C2×C22⋊D149—24no—
42C2×C22⋊D149C2×C418yescomplemented
43C22×Dic149—24no—
44C22×Dic149—41no—
45C22×Dic149C2312yes—
46C22×Dic149C2312yes—
47C22×Dic149C2312yes—
48C2×C4×D149—24no—
49C2×C4×D149—24no—
50C2×C4×D149—24no—
51C2×C4×D149—24no—
52C2×C4×D149—42no—
53C2×C4×D149—42no—
54#14558715—24no—
55C22⋊Dic149—24no—
56C22⋊Dic149—41no—
57C22⋊Dic149C2×C414yescomplemented
58#14558713—24no—
59#14558713C2×C418yescomplemented
60#14558713D418yescomplemented
61C4×Dic149—24no—
62C24×C149C2311yescharacteristic
63C24×C149C2311yescharacteristic
64C2×D4×C149—41no—
65C2×D4×C149—41no—
66C2×D4×C149C2×C414yescomplemented
67C22×C4×C149C2312yes—
68C22×C4×C149C2311yescharacteristic
69C22×C4×C149C2312yes—
70C4⋊C4×C149—41no—
71C22⋊C4×C149—24no—
72C22⋊C4×C149—24no—
73C42×C149—41no—
74C22×D149—22no—
75C22×D149—22no—
76C22×D149—22no—
77C22×D149—22no—
78C22×D149—216no—
79C22×D149—44no—
80C22×D149—44no—
81C22×D149—48no—
82C22×D149—44no—
83C22×D149C22×C414yes—
84C22×D149C2×D414yes—
85C22×D149#4114yes—
86C22⋊D149—216no—
87C2×Dic149—22no—
88C2×Dic149—22no—
89C2×Dic149—22no—
90C2×Dic149—22no—
91C2×Dic149—22no—
92C2×Dic149—22no—
93C2×Dic149—22no—
94C2×Dic149—44no—
95C2×Dic149C22×C414yes—
96C2×Dic149C2×D414yes—
97C4×D149—48no—
98C4×D149—48no—
99C23×C149—22no—
100C23×C149—22no—
101C23×C149—22no—
102C23×C149—22no—
103C23×C149—21no—
104C23×C149—21no—
105C23×C149—21no—
106C23×C149—21no—
107C23×C149C22×C412yes—
108C23×C149C22×C412yes—
109C23×C149C2411yescharacteristic
110D4×C149—44no—
111C2×C4×C149—22no—
112C2×C4×C149—22no—
113C2×C4×C149—21no—
114C2×C4×C149—21no—
115C2×C4×C149—22no—
116C2×C4×C149—22no—
117C2×C4×C149—22no—
118C2×C4×C149C22×C412yes—
119C2×C4×C149C2×D414yes—
120C22×C149—24no—
121C22×C149—24no—
122C22×C149—22no—
123C22×C149—22no—
124C22×C149—41no—
125C22×C149—41no—
126C22×C149—42no—
127C22×C149—42no—
128C22×C149—41no—
129C22×C149—41no—
130C22×C149C23×C411yescharacteristic
131C22×C149C22×D412yes—
132C22×C149C2×#4112yes—
133C22×C149H(5,𝔽2)11yescharacteristic
134C22×C149H(5,𝔽2)11yescharacteristic
135C2×D149—24no—
136C2×D149—24no—
137C2×D149—24no—
138C2×D149—24no—
139C2×D149—24no—
140C2×D149—24no—
141C2×D149—416no—
142C2×D149C4×D418yescomplemented
143C4×C149—22no—
144C4×C149—24no—
145C4×C149—42no—
146Dic149—24no—
147Dic149—24no—
148Dic149—42no—
149C2×C149—42no—
150C2×C149—42no—
151C2×C149C2×C4×D412yes—
152C2×C149#51811yescharacteristic
153C2×C149D4211yescharacteristic
154C2×C149#54612yes—
155C2×C149#55111yescharacteristic
156D149—28no—
157C149#235811yescharacteristic, complemented, Sylow
158#2358—1491nomaximal, Sylow
159C2×#120—1491no—
160C2×C4×D4—1492no—
161C22×C22⋊C4—1492no—
162#390D14911yescharacteristic, complemented
163#388—1492no—
164#386—1491no—
165#386—1492no—
166#385—1492no—
167C4×C22⋊C4—1492no—
168C25—1491no—
169C22×D4—1492no—
170C22×D4C2×D14911yescharacteristic
171C23×C4—1491no—
172C23×C4—1492no—
173C23×C4—1492no—
174#120—1498no—
175C4×D4—2988no—
176C2×C4⋊C4—1492no—
177C2×C4⋊C4C2×D14911yescharacteristic, complemented
178C2×C22⋊C4—2988no—
179C2×C22⋊C4—1492no—
180C2×C22⋊C4—1492no—
181C2×C22⋊C4—1491no—
182C2×C22⋊C4—1491no—
183C2×C22⋊C4—1492no—
184C2×C22⋊C4—1492no—
185C2×C22⋊C4C2×D14912yes—
186C2×C22⋊C4C2×D14912yescomplemented
187C2×C42—1492no—
188C2×C42C2×D14911yescharacteristic, complemented
189#95—1492no—
190#95—1492no—
191#95—1492no—
192C24—2984no—
193C24—2984no—
194C24—5961no—
195C24—5961no—
196C24—1494no—
197C24—1492no—
198C24C22×D14911yescharacteristic
199C24C22×D14911yescharacteristic
200C2×D4—41no—
201C2×D4—41no—
202C2×D4—2984no—
203C2×D4—2984no—
204C2×D4—1498no—
205C2×D4C4×D14914yescomplemented
206C22×C4—2984no—
207C22×C4—2984no—
208C22×C4—2984no—
209C22×C4—2984no—
210C22×C4—2984no—
211C22×C4—5962no—
212C22×C4—5962no—
213C22×C4—5961no—
214C22×C4—1492no—
215C22×C4—1492no—
216C22×C4—1492no—
217C22×C4C22×D14912yes—
218C22×C4C22×D14911yescharacteristic
219C22×C4C22×D14912yes—
220C4⋊C4—41no—
221C4⋊C4—2984no—
222C22⋊C4—24no—
223C22⋊C4—24no—
224C22⋊C4—2984no—
225C22⋊C4—2984no—
226C22⋊C4—5961no—
227C22⋊C4—1494no—
228C22⋊C4—1498no—
229C22⋊C4—1498no—
230C42—41no—
231C42—2984no—
232C23—22no—
233C23—22no—
234C23—22no—
235C23—22no—
236C23—21no—
237C23—21no—
238C23—21no—
239C23—21no—
240C23—29816no—
241C23—2982no—
242C23—2982no—
243C23—2982no—
244C23—2982no—
245C23—5964no—
246C23—5964no—
247C23—5968no—
248C23—5964no—
249C23—1494no—
250C23—1494no—
251C23—1494no—
252C23C2×C4×D14912yes—
253C23C2×C4×D14912yes—
254C23C23×D14911yescharacteristic
255D4—44no—
256D4—29816no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—2982no—
265C2×C4—2982no—
266C2×C4—2982no—
267C2×C4—2982no—
268C2×C4—2982no—
269C2×C4—2982no—
270C2×C4—2982no—
271C2×C4—5968no—
272C2×C4—5968no—
273C2×C4—5964no—
274C2×C4—1494no—
275C2×C4—1494no—
276C2×C4C2×C4×D14912yes—
277C2×C4D4×D14914yes—
278C22—24no—
279C22—24no—
280C22—22no—
281C22—22no—
282C22—41no—
283C22—41no—
284C22—42no—
285C22—42no—
286C22—41no—
287C22—41no—
288C22—2984no—
289C22—2984no—
290C22—2984no—
291C22—2984no—
292C22—2984no—
293C22—2984no—
294C22—59616no—
295C22—1498no—
296C22C22×C4×D14911yescharacteristic
297C22C2×D4×D14912yes—
298C22#41×D14912yes—
299C22#1801195611yescharacteristic
300C22#1801195611yescharacteristic
301C4—24no—
302C4—22no—
303C4—42no—
304C4—2984no—
305C4—2984no—
306C4—5962no—
307C2—42no—
308C2—42no—
309C2—2988no—
310C2C4×D4×D14912yes—
311C2#2375009811yescharacteristic
312C2#2375026011yescharacteristic
313C2#2375026412yes—
314C2#2375030511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D149
commutatorC22×C149C23×C4
Fitting#390×C149C2
socle, cosocleC23×C149C24
prime radicalC2×#18011879C2
hypercenter#390D149
hypocenterC149#2358
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×#18011871C2semidirect
3. C2×C22⋊C4×D149C2semidirect
4. #23749513C2semidirect
5. #23749505C2semidirect
6. #23749501C2semidirect
7. #23749496C2semidirect
8. C4×#14558713C2semidirect
9. #390×C149C2semidirect
12. C23×Dic149C22semidirect
15. #18011879C4semidirect
17. C2×#14558715C22semidirect
20. C2×C22⋊Dic149C22semidirect
25. C2×C4×Dic149C22semidirect
26. #18011818C22semidirect
27. #18011818C22semidirect
28. #18011818C22semidirect
30. C2×C4⋊C4×C149C22semidirect
32. C2×C22⋊C4×C149C22semidirect
33. C2×C42×C149C22semidirect
38. C23×D149C2×C4semidirect
42. C2×C22⋊D149C2×C4semidirect
57. C22⋊Dic149C2×C4semidirect
59. #14558713C2×C4semidirect
60. #14558713D4semidirect
66. C2×D4×C149C2×C4semidirect
142. C2×D149C4×D4semidirect
157. C149#2358semidirect
162. #390D149semidirect
177. C2×C4⋊C4C2×D149semidirect
186. C2×C22⋊C4C2×D149semidirect
188. C2×C42C2×D149semidirect
205. C2×D4C4×D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180118792
C2×#180118712
C2×C22⋊C4×D1492
#237495132
#237495052
#237495012
#237494962
C4×#145587132
#390×C1492
#2358149