Finite Group Databasebeta

← #34080358

Subgroups — #34080358

Order 19328.

332 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752842C211yesmaximal, characteristic, complemented
2#23752816C211yesmaximal, characteristic
3#23752621C211yesmaximal, characteristic, complemented
4#23752611C211yesmaximal, characteristic, complemented
5#23752558C211yesmaximal, characteristic, complemented
6#23752535C211yesmaximal, characteristic, complemented
7#23752534C211yesmaximal, characteristic, complemented
8#23752529C211yesmaximal, characteristic, complemented
9#23752524C211yesmaximal, characteristic, complemented
10#23752514C211yesmaximal, characteristic, complemented
11#23752510C211yesmaximal, characteristic, complemented
12#23752500C211yesmaximal, characteristic, complemented
13#23752490C211yesmaximal, characteristic, complemented
14#23752274C211yesmaximal, characteristic, complemented
15#490×C151C211yesmaximal, characteristic, complemented
16#18012739C2211yescharacteristic
17#18012738—21no—
18#18012738C2211yescharacteristic
19#18012731C2211yescharacteristic
20#18012730C2211yescharacteristic
21#18012729—21no—
22#18012720—21no—
23#18012720—21no—
24#18012719—21no—
25#18012717—21no—
26#18012711—21no—
27#18012711—21no—
28#18012710C2211yescharacteristic
29#18012710C2211yescharacteristic
30D4×Dic151C2211yescharacteristic
31D4×Dic151C2211yescharacteristic
32#18012697C2211yescharacteristic
33#18012696C2211yescharacteristic
34C4⋊C4×D151C2211yescharacteristic
35#18012673C2211yescharacteristic
36#18012673C2211yescharacteristic
37#18012672C2211yescharacteristic
38#18012672C2211yescharacteristic
39#18012671C2211yescharacteristic
40#18012671C2211yescharacteristic
41#18012670C2211yescharacteristic
42#18012670C2211yescharacteristic
43Dic151⋊C8C2211yescharacteristic
44Dic151⋊C8C2211yescharacteristic
45#18012660C2211yescharacteristic
46#18012660C2211yescharacteristic
47#18012660C2211yescharacteristic
48#18012660C2211yescharacteristic
49(C2×D151)⋊C8C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51C4×C151⋊C8C2211yescharacteristic
52#127×C151C2211yescharacteristic
53#125×C151C2211yescharacteristic
54#102×C151C2211yescharacteristic
55#102×C151C2211yescharacteristic
56#102×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58#97×C151C2211yescharacteristic
59C2×Dic302—21no—
60C2×Dic302—21no—
61C2×C22⋊D151—21no—
62C2×C22⋊D151—21no—
63C22×Dic151—21no—
64C22×Dic151—21no—
65C2×C4×D151—21no—
66C2×C4×D151C2311yescharacteristic
67C2×C151⋊C8C2311yescharacteristic
68C2×C151⋊C8C2311yescharacteristic
69C4⋊Dic151—21no—
70C4⋊Dic151—21no—
71C4⋊Dic151C2311yescharacteristic
72C4⋊Dic151C2311yescharacteristic
73C4⋊Dic151C2311yescharacteristic
74C4⋊Dic151C2311yescharacteristic
75Dic151⋊C4—21no—
76Dic151⋊C4—21no—
77Dic151⋊C4—21no—
78Dic151⋊C4—21no—
79Dic151⋊C4—21no—
80Dic151⋊C4D411yescharacteristic
81Dic151⋊C4D411yescharacteristic
82C22⋊Dic151—21no—
83C22⋊Dic151—21no—
84C22⋊Dic151—21no—
85C22⋊Dic151—21no—
86(C2×D151)⋊C4—21no—
87(C2×D151)⋊C4D411yescharacteristic
88(C2×D151)⋊C4D411yescharacteristic
89C4×Dic151—21no—
90C4×Dic151C2311yescharacteristic
91C2×D4×C151—21no—
92C2×D4×C151—21no—
93C2×D4×C151C2311yescharacteristic
94C2×D4×C151C2311yescharacteristic
95C2×C8×C151C2311yescharacteristic
96C2×C8×C151C2311yescharacteristic
97C4⋊C4×C151—21no—
98C4⋊C4×C151—21no—
99C4⋊C4×C151C2311yescharacteristic
100C4⋊C4×C151C2311yescharacteristic
101C42×C151C2311yescharacteristic
102C22×D151C2×D411yescharacteristic
103Dic302—81no—
104Dic302—81no—
105C22⋊D151—81no—
106C22⋊D151—81no—
107C2×Dic151—21no—
108C2×Dic151—21no—
109C2×Dic151—21no—
110C2×Dic151—21no—
111C2×Dic151—81no—
112C2×Dic151—81no—
113C2×Dic151C2×D411yescharacteristic
114C2×Dic151C2×D411yescharacteristic
115C2×Dic151C2×D411yescharacteristic
116C4×D151—21no—
117C4×D151—21no—
118C4×D151—81no—
119C151⋊C8—21no—
120C151⋊C8—21no—
121C23×C151—21no—
122C23×C151—21no—
123D4×C151—21no—
124D4×C151—21no—
125D4×C151—21no—
126D4×C151—21no—
127D4×C151—81no—
128D4×C151—81no—
129C2×C4×C151—21no—
130C2×C4×C151—21no—
131C2×C4×C151C2×D411yescharacteristic
132C2×C4×C151C2×D411yescharacteristic
133C2×C4×C151C2411yescharacteristic
134C8×C151—21no—
135C8×C151—21no—
136C22×C151—41no—
137C22×C151—41no—
138C22×C151—41no—
139C22×C151—41no—
140C22×C151—41no—
141C22×C151—41no—
142C22×C151C22×D411yescharacteristic
143C2×D151—21no—
144C2×D151—21no—
145C2×D151—21no—
146C4×C151—21no—
147C4×C151—21no—
148C4×C151—41no—
149C4×C151—41no—
150C4×C1512−1+411yescharacteristic
151C4×C1512−1+411yescharacteristic
152Dic151—21no—
153Dic151—21no—
154Dic151—21no—
155Dic151—41no—
156Dic151—41no—
157Dic151—41no—
158Dic151—41no—
159C2×C151—81no—
160C2×C151—81no—
161C2×C151#53611yescharacteristic
162C2×C151#57611yescharacteristic
163C2×C151#57711yescharacteristic
164D151—41no—
165C151#324111yescharacteristic, complemented, Sylow
166#3241—1511nomaximal, Sylow
167#544—1511no—
168#540—1511no—
169#501—1511no—
170#499—1511no—
171#490D15111yescharacteristic, complemented
172#486—1511no—
173#482—1511no—
174#482—1511no—
175#481—1511no—
176#480—1511no—
177#478—1511no—
178#478—1511no—
179#476—1511no—
180#474—1511no—
181#433—1511no—
182C4⋊Q8—3021no—
183C4⋊Q8—1511no—
184C4⋊Q8—1511no—
185#127C2×D15111yescharacteristic
186#125—3021no—
187#125—1511no—
188#125—1511no—
189#125C2×D15111yescharacteristic
190#123—3021no—
191#123—3021no—
192C22⋊Q8—3021no—
193C22⋊Q8—3021no—
194#121—3021no—
195#121—3021no—
196#121—1511no—
197#121—1511no—
198C4×D4—1511no—
199C4×D4—1511no—
200#117—1511no—
201#117—1511no—
202C2×C4⋊C4—1511no—
203#107—1511no—
204#107—1511no—
205#107—1511no—
206#107—1511no—
207#106—1511no—
208#106—1511no—
209#106—1511no—
210#106—1511no—
211C4⋊C8—1511no—
212C4⋊C8—1511no—
213#102—1511no—
214#102—1511no—
215#102—1511no—
216#102—1511no—
217#102C2×D15111yescharacteristic
218#102C2×D15111yescharacteristic
219#102C2×D15111yescharacteristic
220#102C2×D15111yescharacteristic
221C22⋊C8—1511no—
222C22⋊C8—1511no—
223#97C2×D15111yescharacteristic
224C4×C8—1511no—
225C2×Q8—3021no—
226C2×Q8—3021no—
227C2×D4—21no—
228C2×D4—21no—
229C2×D4—3021no—
230C2×D4—3021no—
231C2×D4C22×D15111yescharacteristic
232C2×D4C22×D15111yescharacteristic
233C22×C4—3021no—
234C22×C4—3021no—
235C22×C4—3021no—
236C22×C4—1511no—
237C2×C8—1511no—
238C2×C8—1511no—
239C2×C8C22×D15111yescharacteristic
240C2×C8C22×D15111yescharacteristic
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—3021no—
244C4⋊C4—3021no—
245C4⋊C4—3021no—
246C4⋊C4—3021no—
247C4⋊C4—3021no—
248C4⋊C4—3021no—
249C4⋊C4—3021no—
250C4⋊C4—1511no—
251C4⋊C4—1511no—
252C4⋊C4—1511no—
253C4⋊C4—1511no—
254C4⋊C4—1511no—
255C4⋊C4—1511no—
256C4⋊C4C22×D15111yescharacteristic
257C4⋊C4C22×D15111yescharacteristic
258C22⋊C4—3021no—
259C22⋊C4—3021no—
260C22⋊C4—3021no—
261C22⋊C4—3021no—
262C22⋊C4—3021no—
263C22⋊C4—1511no—
264C22⋊C4—1511no—
265C42—3021no—
266C42—1511no—
267C42C22×D15111yescharacteristic
268C23—21no—
269C23—21no—
270C23—1511no—
271Q8—12081no—
272Q8—12081no—
273D4—21no—
274D4—21no—
275D4—21no—
276D4—21no—
277D4—81no—
278D4—81no—
279D4—12081no—
280D4—12081no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—3021no—
284C2×C4—3021no—
285C2×C4—3021no—
286C2×C4—3021no—
287C2×C4—3021no—
288C2×C4—3021no—
289C2×C4—1511no—
290C2×C4—1511no—
291C2×C4—1511no—
292C2×C4—12081no—
293C2×C4—12081no—
294C2×C4—12081no—
295C2×C4D4×D15111yescharacteristic
296C2×C4D4×D15111yescharacteristic
297C2×C4C23×D15111yescharacteristic
298C8—21no—
299C8—21no—
300C8—3021no—
301C8—3021no—
302C22—41no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—3021no—
309C22—3021no—
310C22—3021no—
311C22C2×D4×D15111yescharacteristic
312C4—21no—
313C4—21no—
314C4—41no—
315C4—41no—
316C4—3021no—
317C4—3021no—
318C4—3021no—
319C4—6041no—
320C4—6041no—
321C4—6041no—
322C4—6041no—
323C4#1801278611yescharacteristic
324C4#1801278611yescharacteristic
325C2—81no—
326C2—81no—
327C2—6041no—
328C2#2375278211yescharacteristic
329C2#2375301611yescharacteristic
330C2#2375302211yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#490×C151C2
socleC22×C151C22×D4
prime radical#23752816C2
hypercenter#490D151
hypocenterC151#3241
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #23752842C2semidirect
3. #23752621C2semidirect
4. #23752611C2semidirect
5. #23752558C2semidirect
6. #23752535C2semidirect
7. #23752534C2semidirect
8. #23752529C2semidirect
9. #23752524C2semidirect
10. #23752514C2semidirect
11. #23752510C2semidirect
12. #23752500C2semidirect
13. #23752490C2semidirect
14. #23752274C2semidirect
15. #490×C151C2semidirect
165. C151#3241semidirect
171. #490D151semidirect

Maximal subgroups

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

subgroupindex
#237528422
#237528162
#237526212
#237526112
#237525582
#237525352
#237525342
#237525292
#237525242
#237525142
#237525102
#237525002
#237524902
#237522742
#490×C1512
#3241151