Finite Group Databasebeta

← #34078716

Subgroups — #34078716

Order 19328.

500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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×#18012759C211yesmaximal, characteristic, complemented
2C22×#14558988C211yesmaximal, characteristic, complemented
3#23752723C211yesmaximal, characteristic, complemented
4#23752468C212yesmaximal, complemented
5#23752463C212yesmaximal, complemented
6#23752460C212yesmaximal, complemented
7#23752456C212yesmaximal, complemented
8#23752248C211yesmaximal, characteristic, complemented
9#23752208C211yesmaximal, characteristic, complemented
10#23752206C211yesmaximal, characteristic, complemented
11#525×C151C211yesmaximal, characteristic, complemented
12C2×#14559004C2211yescharacteristic
13#18012759—24no—
14C2×#14558994C2211yescharacteristic, complemented
15C2×#14558992C2211yescharacteristic, complemented
16C2×#14558991C2211yescharacteristic, complemented
17C2×#14558989C2211yescharacteristic, complemented
18C2×#14558988—24no—
19C2×#14558988C2212yes—
20C2×#14558988C2212yes—
21C22×C151⋊C8C2211yescharacteristic
22C22×C151⋊C8C2211yescharacteristic
23#18012722—21no—
24#18012718C2212yes—
25#18012713C2212yes—
26#18012708—21no—
27C4×C22⋊D151—22no—
28#18012698C2211yescharacteristic
29#18012672C2212yescomplemented
30#18012670C2212yescomplemented
31#18012663C2212yescomplemented
32#18012662C2212yescomplemented
33#18012660C2212yescomplemented
34#18012659C2212yescomplemented
35C2×#41×C151C2211yescharacteristic
36C23×C4×C151C2211yescharacteristic
37#123×C151—21no—
38C22⋊Q8×C151C2212yes—
39#121×C151C2212yes—
40#120×C151—21no—
41C4×D4×C151—22no—
42#117×C151C2211yescharacteristic
43#14559004—22no—
44#14559004—22no—
45C2×Dic302C2311yescharacteristic
46C2×D604C2311yescharacteristic
47C2×C22⋊D151—22no—
48C2×C22⋊D151—21no—
49C2×C4×D151—21no—
50#14558994—22no—
51#14558992—22no—
52#14558991—22no—
53#14558989—22no—
54#14558988—24no—
55#14558988—24no—
56C2×C151⋊C8—22no—
57C2×C151⋊C8D414yescomplemented
58C2×C151⋊C8C2312yes—
59C2×C151⋊C8C2311yescharacteristic
60C2×C151⋊C8C2311yescharacteristic
61C4⋊Dic151C2312yes—
62Dic151⋊C4—22no—
63C22⋊Dic151—21no—
64C22⋊Dic151—22no—
65(C2×D151)⋊C4—22no—
66C4×Dic151—21no—
67C24×C151D411yescharacteristic
68#41×C151—22no—
69#41×C151—22no—
70C2×Q8×C151C2311yescharacteristic
71C2×D4×C151—22no—
72C2×D4×C151—21no—
73C2×D4×C151C2311yescharacteristic
74C22×C4×C151—22no—
75C22×C4×C151—22no—
76C22×C4×C151—21no—
77C22×C4×C151D412yes—
78C22×C4×C151D411yescharacteristic
79C22×C4×C151C2312yes—
80C22×C4×C151C2311yescharacteristic
81C4⋊C4×C151—22no—
82C4⋊C4×C151C2312yes—
83C22⋊C4×C151—21no—
84C22⋊C4×C151—22no—
85C22⋊C4×C151—22no—
86C42×C151—21no—
87C22×D151—21no—
88Dic302—21no—
89Dic302—21no—
90D604—21no—
91D604—21no—
92C22⋊D151—44no—
93C22⋊D151—42no—
94C2×Dic151—22no—
95C2×Dic151—21no—
96C4×D151—42no—
97C151⋊C8—22no—
98C151⋊C8C2×D412yes—
99C151⋊C8C2×D412yes—
100C23×C151—22no—
101C23×C151—21no—
102C23×C151—42no—
103C23×C151C2×D412yes—
104C23×C151C2×D411yescharacteristic
105Q8×C151—21no—
106Q8×C151—21no—
107D4×C151—21no—
108D4×C151—21no—
109D4×C151—44no—
110D4×C151—42no—
111C2×C4×C151—22no—
112C2×C4×C151—24no—
113C2×C4×C151—22no—
114C2×C4×C151—22no—
115C2×C4×C151—21no—
116C2×C4×C151—22no—
117C2×C4×C151—42no—
118C2×C4×C151C2×D412yes—
119C2×C4×C151C2×D412yes—
120C2×C4×C151C2×D411yescharacteristic
121C2×C4×C151#4112yes—
122C2×C4×C151C2411yescharacteristic
123C22×C151—22no—
124C22×C151—22no—
125C22×C151—22no—
126C22×C151—22no—
127C22×C151—44no—
128C22×C151—41no—
129C22×C151—42no—
130C22×C151#12112yes—
131C22×C151C22×D411yescharacteristic
132C2×D151—41no—
133C2×D151—42no—
134C4×C151—22no—
135C4×C151—41no—
136C4×C151—42no—
137C4×C151#12112yes—
138C4×C151C22×D411yescharacteristic
139C4×C151C2×#4111yescharacteristic
140Dic151—41no—
141Dic151—42no—
142C2×C151—22no—
143C2×C151—42no—
144C2×C151—81no—
145C2×C151C2×#12111yescharacteristic
146C2×C151#57512yes—
147D151—81no—
148C151#305411yescharacteristic, complemented, Sylow
149#3054—1511nomaximal, Sylow
150C2×#135—1511no—
151C22×M16—1511no—
152#525—1511no—
153#525D15111yescharacteristic, complemented
154#470—1512no—
155#469—1512no—
156#468—1512no—
157#468—1512no—
158#427—1511no—
159#416—1511no—
160#416—1511no—
161C2×#41—1511no—
162C2×#41C2×D15111yescharacteristic
163C23×C4C2×D15111yescharacteristic
164#135—3024no—
165C2×Q16—1511no—
166C2×SD16—1511no—
167C2×SD16—1511no—
168C2×D8—1511no—
169C2×M16—3024no—
170C2×M16—1512no—
171C2×M16—1512no—
172C22×C8—1511no—
173C22×C8—1511no—
174#123—21no—
175#123—3021no—
176C22⋊Q8—1512no—
177C22⋊Q8C2×D15112yes—
178#121—1512no—
179#121C2×D15112yes—
180#120—21no—
181#120—3021no—
182C4×D4—22no—
183C4×D4—3022no—
184#117—1511no—
185#117C2×D15111yescharacteristic
186#107—1512no—
187#106—1512no—
188#103—1512no—
189#103—1512no—
190#102—1512no—
191#102—1512no—
192C24C22⋊D15111yescharacteristic
193#41—22no—
194#41—22no—
195#41—3022no—
196#41—3022no—
197C2×Q8—1511no—
198C2×Q8C22×D15111yescharacteristic
199C2×D4—22no—
200C2×D4—21no—
201C2×D4—3022no—
202C2×D4—3021no—
203C2×D4—1511no—
204C2×D4C22×D15111yescharacteristic
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—21no—
208C22×C4—3021no—
209C22×C4C22⋊D15111yescharacteristic
210C22×C4C22⋊D15112yes—
211C22×C4C22×D15112yes—
212C22×C4C22×D15111yescharacteristic
213Q16—3022no—
214SD16—3022no—
215SD16—3022no—
216D8—3022no—
217M16—3024no—
218M16—3024no—
219C2×C8—3022no—
220C2×C8—1512no—
221C2×C8—1514no—
222C2×C8—1511no—
223C2×C8—1511no—
224C4⋊C4—22no—
225C4⋊C4—3022no—
226C4⋊C4—1512no—
227C4⋊C4C22×D15112yes—
228C22⋊C4—21no—
229C22⋊C4—22no—
230C22⋊C4—22no—
231C22⋊C4—3021no—
232C22⋊C4—3022no—
233C22⋊C4—3022no—
234C42—21no—
235C42—3021no—
236C23—22no—
237C23—21no—
238C23—42no—
239C23—3021no—
240C23C2×C22⋊D15112yes—
241C23C2×C22⋊D15111yescharacteristic
242Q8—21no—
243Q8—21no—
244Q8—3021no—
245Q8—3021no—
246D4—21no—
247D4—21no—
248D4—44no—
249D4—42no—
250D4—3021no—
251D4—3021no—
252D4—6044no—
253D4—6042no—
254C2×C4—22no—
255C2×C4—24no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—42no—
261C2×C4—3022no—
262C2×C4—3021no—
263C2×C4—6042no—
264C2×C4D4×D15112yes—
265C2×C4C2×C22⋊D15112yes—
266C2×C4C2×C22⋊D15111yescharacteristic
267C2×C4#1455900312yes—
268C2×C4C23×D15111yescharacteristic
269C8—3022no—
270C8—1512no—
271C8—1512no—
272C22—22no—
273C22—22no—
274C22—22no—
275C22—22no—
276C22—44no—
277C22—42no—
278C22—41no—
279C22—6042no—
280C22—6041no—
281C22#1801271112yes—
282C22C22×C22⋊D15111yescharacteristic
283C4—22no—
284C4—42no—
285C4—41no—
286C4—6042no—
287C4—6041no—
288C4#1801271112yes—
289C4C2×D4×D15111yescharacteristic
290C4C2×#1455900311yescharacteristic
291C2—22no—
292C2—42no—
293C2—81no—
294C2—12081no—
295C2C2×#1801271111yescharacteristic
296C2#2375301012yes—
subgroupG/H
centerC2×C4C2×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#525×C151C2
socleC22×C151C22×D4
hypercenter#525D151
hypocenterC151#3054
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C2×#18012759C2semidirect
2. C22×#14558988C2semidirect
3. #23752723C2semidirect
4. #23752468C2semidirect
5. #23752463C2semidirect
6. #23752460C2semidirect
7. #23752456C2semidirect
8. #23752248C2semidirect
9. #23752208C2semidirect
10. #23752206C2semidirect
11. #525×C151C2semidirect
14. C2×#14558994C22semidirect
15. C2×#14558992C22semidirect
16. C2×#14558991C22semidirect
17. C2×#14558989C22semidirect
29. #18012672C22semidirect
30. #18012670C22semidirect
31. #18012663C22semidirect
32. #18012662C22semidirect
33. #18012660C22semidirect
34. #18012659C22semidirect
57. C2×C151⋊C8D4semidirect
148. C151#3054semidirect
153. #525D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127592
C22×#145589882
#237527232
#237524682
#237524632
#237524602
#237524562
#237522482
#237522082
#237522062
#525×C1512
#3054151