Finite Group Databasebeta

← #34080366

Subgroups — #34080366

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#23752818C211yesmaximal, characteristic
3#23752622C211yesmaximal, characteristic, complemented
4#23752578C211yesmaximal, characteristic, complemented
5#23752559C211yesmaximal, characteristic, complemented
6#23752539C211yesmaximal, characteristic, complemented
7#23752538C211yesmaximal, characteristic, complemented
8#23752532C211yesmaximal, characteristic, complemented
9#23752527C211yesmaximal, characteristic, complemented
10#23752515C211yesmaximal, characteristic, complemented
11#23752511C211yesmaximal, characteristic, complemented
12#23752501C211yesmaximal, characteristic, complemented
13#23752491C211yesmaximal, characteristic, complemented
14#23752271C211yesmaximal, characteristic, complemented
15#499×C151C211yesmaximal, characteristic, complemented
16#18012739C2211yescharacteristic
17#18012738—21no—
18#18012738C2211yescharacteristic
19#18012736C2211yescharacteristic
20#18012730C2211yescharacteristic
21#18012729—21no—
22#18012724—21no—
23#18012724—21no—
24#18012719—21no—
25#18012717—21no—
26#18012714—21no—
27#18012714—21no—
28#18012714C2211yescharacteristic
29#18012714C2211yescharacteristic
30#18012701C2211yescharacteristic
31#18012701C2211yescharacteristic
32#18012697C2211yescharacteristic
33#18012696C2211yescharacteristic
34C4⋊C4×D151C2211yescharacteristic
35#18012672C2211yescharacteristic
36#18012672C2211yescharacteristic
37#18012670C2211yescharacteristic
38#18012670C2211yescharacteristic
39Dic151⋊C8C2211yescharacteristic
40Dic151⋊C8C2211yescharacteristic
41#18012661C2211yescharacteristic
42#18012661C2211yescharacteristic
43#18012661C2211yescharacteristic
44#18012661C2211yescharacteristic
45#18012659C2211yescharacteristic
46#18012659C2211yescharacteristic
47#18012659C2211yescharacteristic
48#18012659C2211yescharacteristic
49(C2×D151)⋊C8C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51#18012650C2211yescharacteristic
52#125×C151C2211yescharacteristic
53#125×C151C2211yescharacteristic
54#107×C151C2211yescharacteristic
55#107×C151C2211yescharacteristic
56#106×C151C2211yescharacteristic
57#106×C151C2211yescharacteristic
58C4×C8×C151C2211yescharacteristic
59C2×Dic302—21no—
60C2×Dic302—21no—
61C2×D604—21no—
62C2×D604—21no—
63C2×D604—21no—
64C2×D604—21no—
65C2×D604C2311yescharacteristic
66C2×D604C2311yescharacteristic
67C2×C4×D151—21no—
68C2×C4×D151—21no—
69C2×C4×D151—21no—
70C2×C4×D151C2311yescharacteristic
71C2×C151⋊C8C2311yescharacteristic
72C2×C151⋊C8C2311yescharacteristic
73C4⋊Dic151—21no—
74C4⋊Dic151—21no—
75C4⋊Dic151C2311yescharacteristic
76C4⋊Dic151C2311yescharacteristic
77Dic151⋊C4—21no—
78Dic151⋊C4—21no—
79Dic151⋊C4—21no—
80Dic151⋊C4D411yescharacteristic
81Dic151⋊C4D411yescharacteristic
82(C2×D151)⋊C4—21no—
83(C2×D151)⋊C4—21no—
84(C2×D151)⋊C4—21no—
85(C2×D151)⋊C4—21no—
86(C2×D151)⋊C4—21no—
87(C2×D151)⋊C4D411yescharacteristic
88(C2×D151)⋊C4D411yescharacteristic
89C4×Dic151—21no—
90C4×Dic151C2311yescharacteristic
91C2×C8×C151C2311yescharacteristic
92C2×C8×C151C2311yescharacteristic
93C4⋊C4×C151—21no—
94C4⋊C4×C151—21no—
95C4⋊C4×C151—21no—
96C4⋊C4×C151—21no—
97C4⋊C4×C151C2311yescharacteristic
98C4⋊C4×C151C2311yescharacteristic
99C4⋊C4×C151C2311yescharacteristic
100C4⋊C4×C151C2311yescharacteristic
101C42×C151C2311yescharacteristic
102C22×D151—21no—
103C22×D151—21no—
104C22×D151C2×D411yescharacteristic
105Dic302—81no—
106Dic302—81no—
107D604—21no—
108D604—21no—
109D604—21no—
110D604—21no—
111D604—81no—
112D604—81no—
113D604—81no—
114D604—81no—
115C2×Dic151—21no—
116C2×Dic151—21no—
117C2×Dic151C2×D411yescharacteristic
118C2×Dic151C2×D411yescharacteristic
119C2×Dic151C2×D411yescharacteristic
120C4×D151—21no—
121C4×D151—21no—
122C4×D151—81no—
123C4×D151—81no—
124C4×D151—81no—
125C151⋊C8—21no—
126C151⋊C8—21no—
127C2×C4×C151—21no—
128C2×C4×C151—21no—
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×C151C22×D411yescharacteristic
137C2×D151—21no—
138C2×D151—21no—
139C2×D151—21no—
140C2×D151—41no—
141C2×D151—41no—
142C2×D151—41no—
143C2×D151—41no—
144C2×D151—41no—
145C2×D151—41no—
146C4×C151—21no—
147C4×C151—21no—
148C4×C151—41no—
149C4×C151—41no—
150C4×C151—41no—
151C4×C151—41no—
152C4×C1512−1+411yescharacteristic
153C4×C1512−1+411yescharacteristic
154Dic151—21no—
155Dic151—21no—
156Dic151—21no—
157Dic151—41no—
158Dic151—41no—
159C2×C151#53611yescharacteristic
160C2×C151#57611yescharacteristic
161C2×C151#57711yescharacteristic
162D151—41no—
163D151—81no—
164D151—81no—
165C151#324111yescharacteristic, complemented, Sylow
166#3241—1511nomaximal, Sylow
167#544—1511no—
168#540—1511no—
169#501—1511no—
170#499D15111yescharacteristic, complemented
171#490—1511no—
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#127—1511no—
186#125—3021no—
187#125—1511no—
188#125C2×D15111yescharacteristic
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#107C2×D15111yescharacteristic
206#107C2×D15111yescharacteristic
207#106—1511no—
208#106—1511no—
209#106C2×D15111yescharacteristic
210#106C2×D15111yescharacteristic
211C4⋊C8—1511no—
212C4⋊C8—1511no—
213#102—1511no—
214#102—1511no—
215#102—1511no—
216#102—1511no—
217#102—1511no—
218#102—1511no—
219#102—1511no—
220#102—1511no—
221C22⋊C8—1511no—
222C22⋊C8—1511no—
223#97—1511no—
224C4×C8C2×D15111yescharacteristic
225C2×Q8—3021no—
226C2×Q8—3021no—
227C2×D4—3021no—
228C2×D4—3021no—
229C2×D4—3021no—
230C2×D4—3021no—
231C2×D4—1511no—
232C2×D4—1511no—
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—21no—
244C4⋊C4—21no—
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⋊C4C22×D15111yescharacteristic
255C4⋊C4C22×D15111yescharacteristic
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—3021no—
269C23—3021no—
270C23—1511no—
271Q8—12081no—
272Q8—12081no—
273D4—3021no—
274D4—3021no—
275D4—3021no—
276D4—3021no—
277D4—12081no—
278D4—12081no—
279D4—12081no—
280D4—12081no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
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—3021no—
303C22—3021no—
304C22—3021no—
305C22—6041no—
306C22—6041no—
307C22—6041no—
308C22—6041no—
309C22—6041no—
310C22—6041no—
311C22C2×D4×D15111yescharacteristic
312C4—21no—
313C4—21no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—3021no—
319C4—3021no—
320C4—3021no—
321C4—6041no—
322C4—6041no—
323C4#1801278711yescharacteristic
324C4#1801278711yescharacteristic
325C2—6041no—
326C2—12081no—
327C2—12081no—
328C2#2375278711yescharacteristic
329C2#2375301411yescharacteristic
330C2#2375301911yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#499×C151C2
socleC22×C151C22×D4
prime radical#23752818C2
hypercenter#499D151
hypocenterC151#3241
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #499

Complements

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

NH ≅ G/Ntype
1. #23752842C2semidirect
3. #23752622C2semidirect
4. #23752578C2semidirect
5. #23752559C2semidirect
6. #23752539C2semidirect
7. #23752538C2semidirect
8. #23752532C2semidirect
9. #23752527C2semidirect
10. #23752515C2semidirect
11. #23752511C2semidirect
12. #23752501C2semidirect
13. #23752491C2semidirect
14. #23752271C2semidirect
15. #499×C151C2semidirect
165. C151#3241semidirect
170. #499D151semidirect

Maximal subgroups

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

subgroupindex
#237528422
#237528182
#237526222
#237525782
#237525592
#237525392
#237525382
#237525322
#237525272
#237525152
#237525112
#237525012
#237524912
#237522712
#499×C1512
#3241151