Finite Group Databasebeta

← #34054271

Subgroups — #34054271

Order 19072.

520 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 137 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×#18011931C211yesmaximal, characteristic, complemented
2C22×C8×D149C211yesmaximal, characteristic, complemented
3#23750137C211yesmaximal, characteristic, complemented
4#23750132C211yesmaximal, characteristic, complemented
5#23749865C212yesmaximal, complemented
6#23749860C212yesmaximal, complemented
7#23749857C212yesmaximal, complemented
8#23749853C212yesmaximal, complemented
9#23749661C211yesmaximal, characteristic, complemented
10#23749622C211yesmaximal, characteristic, complemented
11#416×C149C211yesmaximal, characteristic, complemented
12C2×#14558736C2211yescharacteristic
13C22×C4×D149C2211yescharacteristic
14#18011931—24no—
15C2×#14558726C2211yescharacteristic, complemented
16C2×#14558724C2211yescharacteristic, complemented
17C2×#14558723C2211yescharacteristic, complemented
18C2×#14558721C2211yescharacteristic, complemented
19C22×#11924746C2211yescharacteristic
20C2×C8×D149—24no—
21C2×C8×D149C2212yes—
22C2×C8×D149C2212yes—
23#18011895—21no—
24#18011892—21no—
25#18011891C2212yes—
26#18011887C2212yes—
27#18011886C2212yes—
28#18011882C2212yes—
29#18011881—21no—
30#18011879—21no—
31C4×D596—22no—
32C4×C22⋊D149—22no—
33#18011870C2211yescharacteristic
34#18011844C2212yescomplemented
35#18011842C2212yescomplemented
36#18011836C2212yescomplemented
37#18011833C2212yescomplemented
38C2×#41×C149C2211yescharacteristic
39C22×C8×C149C2211yescharacteristic
40#117×C149C2211yescharacteristic
41#103×C149C2212yescomplemented
42#102×C149C2212yescomplemented
43C23×D149D411yescharacteristic
44#14558736—22no—
45#14558736—22no—
46C2×Dic298C2311yescharacteristic
47C2×D596—22no—
48C2×D596C2311yescharacteristic
49C2×C22⋊D149—22no—
50C2×C22⋊D149—21no—
51C22×Dic149D411yescharacteristic
52C2×C4×D149—22no—
53C2×C4×D149—21no—
54C2×C4×D149—22no—
55C2×C4×D149D412yes—
56C2×C4×D149C2312yes—
57#14558726—22no—
58#14558724—22no—
59#14558723—22no—
60#14558721—22no—
61C2×#11924746D414yescomplemented
62C2×#11924746C2311yescharacteristic
63C2×#11924746C2311yescharacteristic
64C8×D149—24no—
65C8×D149—24no—
66C4⋊Dic149—22no—
67C4⋊Dic149C2312yes—
68#14558715—22no—
69C22⋊Dic149—22no—
70C22⋊Dic149—21no—
71#14558713—22no—
72#14558713—22no—
73#14558713—22no—
74C4×Dic149—21no—
75#41×C149—22no—
76#41×C149—22no—
77C2×Q8×C149C2311yescharacteristic
78C2×D4×C149—21no—
79C2×D4×C149C2311yescharacteristic
80C22×C4×C149—21no—
81C22×C4×C149C2311yescharacteristic
82C2×C8×C149—22no—
83C2×C8×C149C2312yes—
84C4⋊C4×C149C2312yes—
85C22⋊C4×C149—21no—
86C42×C149—21no—
87C22×D149—22no—
88C22×D149—24no—
89C22×D149—21no—
90C22×D149C2×D412yes—
91Dic298—21no—
92Dic298—21no—
93D596—21no—
94D596—21no—
95D596—44no—
96C22⋊D149—42no—
97C22⋊D149—44no—
98C2×Dic149—22no—
99C2×Dic149—21no—
100C2×Dic149—22no—
101C2×Dic149C2×D412yes—
102C4×D149—24no—
103C4×D149—22no—
104C4×D149—22no—
105C4×D149—42no—
106#11924746C2×D412yes—
107#11924746C2×D412yes—
108C23×C149—21no—
109C23×C149C2×D411yescharacteristic
110Q8×C149—21no—
111Q8×C149—21no—
112D4×C149—21no—
113D4×C149—21no—
114D4×C149—42no—
115C2×C4×C149—22no—
116C2×C4×C149—21no—
117C2×C4×C149—42no—
118C2×C4×C149C2×D412yes—
119C2×C4×C149C2×D411yescharacteristic
120C2×C4×C149#4112yes—
121C2×C4×C149C2411yescharacteristic
122C8×C149—22no—
123C22×C149—22no—
124C22×C149—41no—
125C22×C149—42no—
126C22×C149#12112yes—
127C22×C149C22×D411yescharacteristic
128C2×D149—28no—
129C2×D149—22no—
130C2×D149—22no—
131C2×D149—41no—
132C2×D149—42no—
133C2×D149#13514yescomplemented
134C4×C149—41no—
135C4×C149—42no—
136C4×C149#12112yes—
137C4×C149C22×D411yescharacteristic
138C4×C149C2×#4111yescharacteristic
139Dic149—22no—
140Dic149—41no—
141Dic149—42no—
142C2×C149—22no—
143C2×C149—81no—
144C2×C149C2×#12111yescharacteristic
145C2×C149C2×#13512yes—
146D149—24no—
147D149—81no—
148C149#305011yescharacteristic, complemented, Sylow
149#3050—1491nomaximal, Sylow
150C2×#135—1491no—
151C23×C8—1491no—
152#525—1491no—
153#525—1491no—
154#467—1492no—
155#466—1492no—
156#465—1492no—
157#465—1492no—
158#427—1491no—
159#416—1491no—
160#416D14911yescharacteristic, complemented
161C2×#41—1491no—
162C2×#41C2×D14911yescharacteristic
163C23×C4—1491no—
164#135—2984no—
165C2×Q16—1491no—
166C2×SD16—1491no—
167C2×SD16—1491no—
168C2×D8—1491no—
169C22×C8—2984no—
170C22×C8—1492no—
171C22×C8—1492no—
172C22×C8—1491no—
173C22×C8C2×D14911yescharacteristic
174#123—2981no—
175#123—2981no—
176C22⋊Q8—1492no—
177C22⋊Q8—1492no—
178#121—1492no—
179#121—1492no—
180#120—2981no—
181#120—2981no—
182C4×D4—2982no—
183C4×D4—2982no—
184#117—1491no—
185#117C2×D14911yescharacteristic
186#107—1492no—
187#106—1492no—
188#103—1492no—
189#103C2×D14912yescomplemented
190#102—1492no—
191#102C2×D14912yescomplemented
192C24—1491no—
193#41—22no—
194#41—22no—
195#41—2982no—
196#41—2982no—
197C2×Q8—1491no—
198C2×Q8C22×D14911yescharacteristic
199C2×D4—21no—
200C2×D4—2982no—
201C2×D4—2982no—
202C2×D4—2981no—
203C2×D4—1491no—
204C2×D4C22×D14911yescharacteristic
205C22×C4—21no—
206C22×C4—2982no—
207C22×C4—2982no—
208C22×C4—2981no—
209C22×C4—1491no—
210C22×C4—1492no—
211C22×C4—1492no—
212C22×C4C22×D14911yescharacteristic
213Q16—2982no—
214SD16—2982no—
215SD16—2982no—
216D8—2982no—
217C2×C8—22no—
218C2×C8—2984no—
219C2×C8—2984no—
220C2×C8—1494no—
221C2×C8—1491no—
222C2×C8—1491no—
223C2×C8C22×D14912yes—
224C4⋊C4—2982no—
225C4⋊C4—2982no—
226C4⋊C4—1492no—
227C4⋊C4C22×D14912yes—
228C22⋊C4—21no—
229C22⋊C4—2982no—
230C22⋊C4—2982no—
231C22⋊C4—2982no—
232C22⋊C4—2981no—
233C22⋊C4—2982no—
234C42—21no—
235C42—2981no—
236C23—21no—
237C23—2984no—
238C23—2982no—
239C23—2981no—
240C23—1492no—
241C23D4×D14911yescharacteristic
242Q8—21no—
243Q8—21no—
244Q8—2981no—
245Q8—2981no—
246D4—21no—
247D4—21no—
248D4—42no—
249D4—2981no—
250D4—2981no—
251D4—5964no—
252D4—5964no—
253D4—5962no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—42no—
257C2×C4—2982no—
258C2×C4—2982no—
259C2×C4—2982no—
260C2×C4—2984no—
261C2×C4—2982no—
262C2×C4—2981no—
263C2×C4—5962no—
264C2×C4—1492no—
265C2×C4D4×D14912yes—
266C2×C4D4×D14911yescharacteristic
267C2×C4#1455873612yes—
268C2×C4C23×D14911yescharacteristic
269C8—22no—
270C8—1492no—
271C8—1492no—
272C22—22no—
273C22—42no—
274C22—41no—
275C22—2988no—
276C22—2982no—
277C22—2982no—
278C22—5962no—
279C22—5961no—
280C22—1494no—
281C22#1801188412yes—
282C22C2×D4×D14911yescharacteristic
283C4—42no—
284C4—41no—
285C4—2982no—
286C4—5962no—
287C4—5961no—
288C4#1801188412yes—
289C4C2×D4×D14911yescharacteristic
290C4C2×#1455873611yescharacteristic
291C2—22no—
292C2—81no—
293C2—2984no—
294C2—11921no—
295C2C2×#1801188411yescharacteristic
296C2#135×D14912yes—
subgroupG/H
centerC2×C4D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#416×C149C2
socleC22×C149C22×D4
hypercenter#416D149
hypocenterC149#3050
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. C2×#18011931C2semidirect
2. C22×C8×D149C2semidirect
3. #23750137C2semidirect
4. #23750132C2semidirect
5. #23749865C2semidirect
6. #23749860C2semidirect
7. #23749857C2semidirect
8. #23749853C2semidirect
9. #23749661C2semidirect
10. #23749622C2semidirect
11. #416×C149C2semidirect
15. C2×#14558726C22semidirect
16. C2×#14558724C22semidirect
17. C2×#14558723C22semidirect
18. C2×#14558721C22semidirect
34. #18011844C22semidirect
35. #18011842C22semidirect
36. #18011836C22semidirect
37. #18011833C22semidirect
41. #103×C149C22semidirect
42. #102×C149C22semidirect
61. C2×#11924746D4semidirect
133. C2×D149#135semidirect
148. C149#3050semidirect
160. #416D149semidirect
189. #103C2×D149semidirect
191. #102C2×D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119312
C22×C8×D1492
#237501372
#237501322
#237498652
#237498602
#237498572
#237498532
#237496612
#237496222
#416×C1492
#3050149