Finite Group Databasebeta

← #34078459

Subgroups — #34078459

Order 19328.

724 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 724 conjugacy classes of subgroups — too many to draw. Only its 161 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
1#23753010C212yesmaximal, complemented
2#23752758C211yesmaximal, characteristic, complemented
3#23752395C212yesmaximal, complemented
4#23752390C212yesmaximal, complemented
5#23752385C212yesmaximal, complemented
6#23752380C212yesmaximal, complemented
7C2×#18012666C212yesmaximal, complemented
8#23752196C211yesmaximal, characteristic, complemented
9#585×C151C211yesmaximal, characteristic, complemented
10C2×#14559004C2211yescharacteristic, complemented
11#18012770—22no—
12#18012769C2214yescomplemented
13#18012765—22no—
14#18012764C2214yescomplemented
15#18012759—24no—
16C2×#14558988C2212yescomplemented
17#18012737C2211yescharacteristic, complemented
18#18012735C2211yescharacteristic, complemented
19#18012728C2211yescharacteristic, complemented
20#18012726C2211yescharacteristic, complemented
21#18012711—22no—
22C4×C22⋊D151—22no—
23C2×C4×Dic151C2211yescharacteristic, complemented
24#18012666C2214yescomplemented
25#18012666C2214yescomplemented
26#18012658C2212yescomplemented
27#18012656C2212yescomplemented
282−1+4×C151—22no—
292−1+4×C151C2212yes—
30H(5,𝔽2)×C151—22no—
31H(5,𝔽2)×C151—22no—
32H(5,𝔽2)×C151C2212yes—
33C2×#41×C151—22no—
34C2×#41×C151—24no—
35C2×#41×C151C2212yes—
36C2×#41×C151C2211yescharacteristic
37#14559004—22no—
38#14559004—22no—
39C2×Dic302C2311yescharacteristic
40C2×D604C2311yescharacteristic
41C2×C22⋊D151—22no—
42C2×C22⋊D151—21no—
43C22×Dic151—21no—
44C2×C4×D151—21no—
45#14558994—24no—
46#14558992—24no—
47#14558991—24no—
48#14558989—24no—
49#14558988—22no—
50#14558988C2314yes—
51C2×C151⋊C8—22no—
52Dic151⋊C4—22no—
53C22⋊Dic151—22no—
54(C2×D151)⋊C4—22no—
55C4×Dic151—21no—
56C4×Dic151C2311yescharacteristic
57C4×Dic151C2311yescharacteristic
58#41×C151—24no—
59#41×C151—28no—
60#41×C151—24no—
61#41×C151—24no—
62#41×C151—24no—
63#41×C151—22no—
64#41×C151—22no—
65#41×C151—24no—
66#41×C151—22no—
67#41×C151—22no—
68#41×C151D414yescomplemented
69#41×C151C2314yes—
70C2×Q8×C151—22no—
71C2×Q8×C151—24no—
72C2×Q8×C151D412yescomplemented
73C2×Q8×C151C2311yescharacteristic
74C2×D4×C151—28no—
75C2×D4×C151—22no—
76C2×D4×C151—24no—
77C2×D4×C151—22no—
78C2×D4×C151—24no—
79C2×D4×C151D412yes—
80C2×D4×C151D412yescomplemented
81C2×D4×C151C2311yescharacteristic
82C22×C4×C151—24no—
83C22×C4×C151—22no—
84C22×C4×C151D412yes—
85C22×C4×C151C2311yescharacteristic
86C22×D151—21no—
87Dic302—22no—
88D604—22no—
89C22⋊D151—44no—
90C22⋊D151—42no—
91C2×Dic151—21no—
92C2×Dic151—21no—
93C2×Dic151—21no—
94C2×Dic151—42no—
95C4×D151—41no—
96C4×D151—41no—
97C151⋊C8—24no—
98C23×C151—24no—
99C23×C151—22no—
100C23×C151C2×D412yes—
101C23×C151C2×D411yescharacteristic
102Q8×C151—24no—
103Q8×C151—22no—
104Q8×C151—22no—
105Q8×C151C2×D414yes—
106D4×C151—28no—
107D4×C151—24no—
108D4×C151—24no—
109D4×C151—24no—
110D4×C151—24no—
111D4×C151—22no—
112D4×C151—22no—
113D4×C151C2×D414yes—
114C2×C4×C151—24no—
115C2×C4×C151—28no—
116C2×C4×C151—22no—
117C2×C4×C151—22no—
118C2×C4×C151—22no—
119C2×C4×C151—24no—
120C2×C4×C151—24no—
121C2×C4×C151C2×D412yes—
122C2×C4×C151C2×D411yescharacteristic
123C2×C4×C151C2×D412yes—
124C2×C4×C151C2×D412yes—
125C2×C4×C151C2411yescharacteristic
126C22×C151—22no—
127C22×C151—24no—
128C22×C151—41no—
129C22×C151—42no—
130C22×C151—82no—
131C22×C151—84no—
132C22×C151#12012yes—
133C22×C151C22×D411yescharacteristic
134C2×D151—42no—
135C2×D151—41no—
136C4×C151—24no—
137C4×C151—22no—
138C4×C151#12011yescharacteristic
139C4×C151#12011yescharacteristic
140C4×C151C22×D412yes—
141Dic151—22no—
142Dic151—41no—
143Dic151—41no—
144C2×C151—21no—
145C2×C151—22no—
146C2×C151—42no—
147C2×C151—44no—
148C2×C151C2×#12011yescharacteristic
149D151—81no—
150C151#301811yescharacteristic, complemented, Sylow
151#3018—1511nomaximal, Sylow
152#585D15111yescharacteristic, complemented
153#575—1512no—
154#532—1511no—
155#456—1512no—
156#455—1512no—
157#454—1512no—
158#453—1512no—
159C2×#104—1512no—
160#413—1511no—
1612−1+4—22no—
1622−1+4C2×D15112yes—
163H(5,𝔽2)—22no—
164H(5,𝔽2)—22no—
165H(5,𝔽2)C2×D15112yes—
166C2×#41—24no—
167C2×#41—22no—
168C2×#41—1511no—
169C2×#41C2×D15112yes—
170C2×#41C2×D15111yescharacteristic
171#137—3022no—
172#137—1514no—
173AGL(1,ℤ/8)—3022no—
174AGL(1,ℤ/8)—1514no—
175#135—3024no—
176C2×M16—1512no—
177C4⋊Q8—1511no—
178#127—1511no—
179#124—1511no—
180#124—1511no—
181#121—3022no—
182C4×D4—3022no—
183C2×C42—1511no—
184#104—1514no—
185#104—1514no—
186#101—1512no—
187#100—1512no—
188#41—24no—
189#41—28no—
190#41—24no—
191#41—24no—
192#41—24no—
193#41—22no—
194#41—22no—
195#41—24no—
196#41—22no—
197#41—22no—
198#41—3022no—
199#41—3022no—
200#41C22⋊D15114yescomplemented
201#41C22×D15114yes—
202C2×Q8—22no—
203C2×Q8—24no—
204C2×Q8—1511no—
205C2×Q8C22⋊D15112yescomplemented
206C2×Q8C22×D15111yescharacteristic
207C2×D4—28no—
208C2×D4—22no—
209C2×D4—24no—
210C2×D4—22no—
211C2×D4—24no—
212C2×D4—3022no—
213C2×D4—3021no—
214C2×D4—1511no—
215C2×D4C22⋊D15112yes—
216C2×D4C22⋊D15112yescomplemented
217C2×D4C22×D15111yescharacteristic
218C22×C4—24no—
219C22×C4—22no—
220C22×C4—3021no—
221C22×C4—3021no—
222C22×C4C22⋊D15112yes—
223C22×C4C22×D15111yescharacteristic
224Q16—3024no—
225SD16—3024no—
226SD16—3024no—
227D8—3024no—
228M16—3022no—
229M16—1514no—
230C2×C8—3022no—
231C4⋊C4—3022no—
232C22⋊C4—3022no—
233C22⋊C4—3022no—
234C42—3021no—
235C42—1511no—
236C42—1511no—
237C23—24no—
238C23—22no—
239C23—3021no—
240C23C2×C22⋊D15112yes—
241C23C2×C22⋊D15111yescharacteristic
242Q8—24no—
243Q8—22no—
244Q8—22no—
245Q8—3022no—
246Q8C2×C22⋊D15114yes—
247D4—28no—
248D4—24no—
249D4—24no—
250D4—24no—
251D4—24no—
252D4—22no—
253D4—22no—
254D4—3022no—
255D4—6044no—
256D4—6042no—
257D4C2×C22⋊D15114yes—
258C2×C4—24no—
259C2×C4—28no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—24no—
263C2×C4—22no—
264C2×C4—24no—
265C2×C4—3021no—
266C2×C4—3021no—
267C2×C4—3021no—
268C2×C4—6042no—
269C2×C4—6041no—
270C2×C4—6041no—
271C2×C4C2×C22⋊D15112yes—
272C2×C4C2×C22⋊D15111yescharacteristic
273C2×C4C2×C22⋊D15112yes—
274C2×C4C2×C22⋊D15112yes—
275C2×C4C23×D15111yescharacteristic
276C8—3024no—
277C22—22no—
278C22—24no—
279C22—41no—
280C22—42no—
281C22—82no—
282C22—84no—
283C22—6042no—
284C22—6041no—
285C22#1801270812yes—
286C22C22×C22⋊D15111yescharacteristic
287C4—24no—
288C4—22no—
289C4—3022no—
290C4—6041no—
291C4—6041no—
292C4#1801270811yescharacteristic
293C4#1801270811yescharacteristic
294C4C22×C22⋊D15112yes—
295C2—21no—
296C2—22no—
297C2—42no—
298C2—44no—
299C2—12081no—
300C2C2×#1801270811yescharacteristic
subgroupG/H
centerC4#18012708
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#585×C151C2
socleC2×C151C2×#120
hypercenter#585D151
hypocenterC151#3018
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C4 ◁ C22×C4 ◁ #585

Complements

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

NH ≅ G/Ntype
1. #23753010C2semidirect
2. #23752758C2semidirect
3. #23752395C2semidirect
4. #23752390C2semidirect
5. #23752385C2semidirect
6. #23752380C2semidirect
7. C2×#18012666C2semidirect
8. #23752196C2semidirect
9. #585×C151C2semidirect
10. C2×#14559004C22semidirect
12. #18012769C22semidirect
14. #18012764C22semidirect
16. C2×#14558988C22semidirect
17. #18012737C22semidirect
18. #18012735C22semidirect
19. #18012728C22semidirect
20. #18012726C22semidirect
23. C2×C4×Dic151C22semidirect
24. #18012666C22semidirect
25. #18012666C22semidirect
26. #18012658C22semidirect
27. #18012656C22semidirect
68. #41×C151D4semidirect
72. C2×Q8×C151D4semidirect
80. C2×D4×C151D4semidirect
150. C151#3018semidirect
152. #585D151semidirect
200. #41C22⋊D151semidirect
205. C2×Q8C22⋊D151semidirect
216. C2×D4C22⋊D151semidirect

Maximal subgroups

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

subgroupindex
#237530102
#237527582
#237523952
#237523902
#237523852
#237523802
C2×#180126662
#237521962
#585×C1512
#3018151