Finite Group Databasebeta

← #34081765

Subgroups — #34081765

Order 19328.

362 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752944C211yesmaximal, characteristic, complemented
2#23752921C211yesmaximal, characteristic, complemented
3#23752568C211yesmaximal, characteristic, complemented
4#23752566C211yesmaximal, characteristic, complemented
5#23752557C211yesmaximal, characteristic, complemented
6#23752514C211yesmaximal, characteristic, complemented
7#23752513C211yesmaximal, characteristic, complemented
8#23752505C211yesmaximal, characteristic, complemented
9#23752429C211yesmaximal, characteristic, complemented
10#23752405C211yesmaximal, characteristic
11#23752336C211yesmaximal, characteristic, complemented
12SD16×Dic151C211yesmaximal, characteristic, complemented
13D8×Dic151C211yesmaximal, characteristic, complemented
14C4×#14558989C211yesmaximal, characteristic, complemented
15#463×C151C211yesmaximal, characteristic, complemented
16C2×#14558989C2211yescharacteristic
17#18012738C2211yescharacteristic
18#18012735C2211yescharacteristic
19#18012731C2211yescharacteristic
20#18012730C2211yescharacteristic
21#18012728C2211yescharacteristic
22#18012725—21no—
23#18012723—21no—
24#18012721—21no—
25#18012718—21no—
26#18012716—21no—
27#18012716—21no—
28Q8×Dic151C2211yescharacteristic
29C4×Dic302C2211yescharacteristic
30C4×D604C2211yescharacteristic
31D4×Dic151C2211yescharacteristic
32D4×Dic151C2211yescharacteristic
33D4×Dic151C2211yescharacteristic
34(C22⋊D151)⋊C4—21no—
35C2×Dic151⋊C4—21no—
36#18012673C2211yescharacteristic
37#18012672C2211yescharacteristic
38#18012671C2211yescharacteristic
39Dic151⋊C8C2211yescharacteristic
40Dic151⋊C8C2211yescharacteristic
41#18012663C2211yescharacteristic
42#18012663C2211yescharacteristic
43#18012661C2211yescharacteristic
44#18012661C2211yescharacteristic
45#18012660C2211yescharacteristic
46#18012660C2211yescharacteristic
47#18012660C2211yescharacteristic
48#18012659C2211yescharacteristic
49C4×C151⋊C8C2211yescharacteristic
50C8×Dic151C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52C2×SD16×C151C2211yescharacteristic
53C2×D8×C151C2211yescharacteristic
54#124×C151C2211yescharacteristic
55C4×D4×C151C2211yescharacteristic
56C4⋊C8×C151C2211yescharacteristic
57#103×C151C2211yescharacteristic
58#102×C151C2211yescharacteristic
59C2×Dic302—21no—
60C2×Dic302D411yescharacteristic
61C2×D604C2311yescharacteristic
62C2×C22⋊D151—21no—
63C2×C22⋊D151—21no—
64C22×Dic151—21no—
65C22×Dic151—21no—
66C22×Dic151—21no—
67C2×C4×D151—21no—
68#14558989—22no—
69C2×C151⋊C8C2311yescharacteristic
70C2×C151⋊C8C2311yescharacteristic
71C4⋊Dic151—21no—
72C4⋊Dic151—21no—
73C4⋊Dic151D411yescharacteristic
74C4⋊Dic151C2311yescharacteristic
75C4⋊Dic151C2311yescharacteristic
76C4⋊Dic151C2311yescharacteristic
77Dic151⋊C4—21no—
78Dic151⋊C4—21no—
79Dic151⋊C4—21no—
80Dic151⋊C4—21no—
81Dic151⋊C4D411yescharacteristic
82Dic151⋊C4D411yescharacteristic
83C22⋊Dic151—21no—
84C22⋊Dic151—21no—
85C22⋊Dic151—21no—
86(C2×D151)⋊C4—21no—
87(C2×D151)⋊C4—21no—
88(C2×D151)⋊C4—21no—
89C4×Dic151—21no—
90C4×Dic151C2311yescharacteristic
91C4×Dic151C2311yescharacteristic
92C2×Q8×C151C2311yescharacteristic
93C2×D4×C151C2311yescharacteristic
94C2×D4×C151C2311yescharacteristic
95C22×C4×C151—21no—
96SD16×C151—22no—
97D8×C151—22no—
98C2×C8×C151C2311yescharacteristic
99C2×C8×C151C2311yescharacteristic
100C4⋊C4×C151C2311yescharacteristic
101C22⋊C4×C151—21no—
102C22⋊C4×C151—21no—
103C22⋊C4×C151—21no—
104C42×C151C2311yescharacteristic
105C22×D151—21no—
106Dic302—22no—
107Dic302—81no—
108D604—21no—
109D604—21no—
110C22⋊D151—42no—
111C22⋊D151—81no—
112C2×Dic151—21no—
113C2×Dic151—21no—
114C2×Dic151—21no—
115C2×Dic151—42no—
116C2×Dic151—81no—
117C2×Dic151—81no—
118C2×Dic151C2×D411yescharacteristic
119C2×Dic151C2×D411yescharacteristic
120C2×Dic151C2×D411yescharacteristic
121C2×Dic151C2×D411yescharacteristic
122C4×D151—81no—
123C151⋊C8—21no—
124C151⋊C8—21no—
125C23×C151—21no—
126C23×C151—21no—
127Q8×C151—21no—
128Q8×C151—21no—
129D4×C151—21no—
130D4×C151—21no—
131D4×C151—21no—
132D4×C151#4112yes—
133C2×C4×C151—21no—
134C2×C4×C151—21no—
135C2×C4×C151—81no—
136C2×C4×C151C2×D411yescharacteristic
137C2×C4×C151C2×D411yescharacteristic
138C2×C4×C151C2411yescharacteristic
139C8×C151—21no—
140C8×C151—21no—
141C22×C151—22no—
142C22×C151—41no—
143C22×C151—41no—
144C22×C151—41no—
145C22×C151—41no—
146C22×C151—41no—
147C22×C151C22×D411yescharacteristic
148C2×D151—41no—
149C2×D151—41no—
150C2×D151—41no—
151C4×C151—21no—
152C4×C151—21no—
153C4×C151—41no—
154C4×C151—41no—
155C4×C151C2×#4111yescharacteristic
156C4×C1512−1+411yescharacteristic
157Dic151—21no—
158Dic151—21no—
159Dic151—21no—
160Dic151—41no—
161Dic151—41no—
162Dic151—41no—
163Dic151#13512yes—
164C2×C151—42no—
165C2×C151—81no—
166C2×C151#54811yescharacteristic
167C2×C151C2×#13511yescharacteristic
168C2×C151#57611yescharacteristic
169D151—81no—
170C151#336111yescharacteristic, complemented, Sylow
171#3361—1511nomaximal, Sylow
172#559—1511no—
173#554—1511no—
174#488—1511no—
175#488—1511no—
176#486—1511no—
177#478—1511no—
178#478—1511no—
179#477—1511no—
180#463—1511no—
181#463D15111yescharacteristic, complemented
182#459—1511no—
183C8×Q8—1511no—
184C4×SD16—1511no—
185C4×D8—1511no—
186C4×D8—1511no—
187C2×SD16C2×D15111yescharacteristic
188C2×D8—1511no—
189C2×D8C2×D15111yescharacteristic
190C4⋊Q8—1511no—
191#127—1511no—
192#125—1511no—
193#125—1511no—
194#124—3021no—
195#124—1511no—
196#124C2×D15111yescharacteristic
197#123—3021no—
198#123—3021no—
199C22⋊Q8—3021no—
200C22⋊Q8—3021no—
201C22⋊Q8—3021no—
202C4×Q8—1511no—
203C4×Q8—1511no—
204C4×D4—3021no—
205C4×D4—1511no—
206C4×D4—1511no—
207C4×D4—1511no—
208C4×D4—1511no—
209C4×D4C2×D15111yescharacteristic
210C2×C4⋊C4—3021no—
211#107—1511no—
212#107—1511no—
213#106—1511no—
214C4⋊C8—1511no—
215C4⋊C8—1511no—
216C4⋊C8C2×D15111yescharacteristic
217#103—1511no—
218#103—1511no—
219#103C2×D15111yescharacteristic
220#102—1511no—
221#102—1511no—
222#102—1511no—
223#102—1511no—
224#102—1511no—
225#102—1511no—
226#102C2×D15111yescharacteristic
227C4×C8—1511no—
228C4×C8—1511no—
229C4×C8—1511no—
230C2×Q8—3021no—
231C2×Q8—1511no—
232C2×Q8C22×D15111yescharacteristic
233C2×D4—3021no—
234C2×D4—3021no—
235C2×D4—1511no—
236C2×D4C22×D15111yescharacteristic
237C2×D4C22×D15111yescharacteristic
238C22×C4—21no—
239C22×C4—3021no—
240C22×C4—3021no—
241C22×C4—3021no—
242C22×C4—3021no—
243SD16—22no—
244D8—22no—
245D8—3022no—
246C2×C8—1511no—
247C2×C8—1511no—
248C2×C8C22×D15111yescharacteristic
249C2×C8C22×D15111yescharacteristic
250C4⋊C4—3021no—
251C4⋊C4—3021no—
252C4⋊C4—3021no—
253C4⋊C4—3021no—
254C4⋊C4—3021no—
255C4⋊C4—3021no—
256C4⋊C4—1511no—
257C4⋊C4—1511no—
258C4⋊C4—1511no—
259C4⋊C4—1511no—
260C4⋊C4—1511no—
261C4⋊C4—1511no—
262C4⋊C4C22×D15111yescharacteristic
263C22⋊C4—21no—
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—3021no—
267C22⋊C4—3021no—
268C22⋊C4—3021no—
269C22⋊C4—3021no—
270C22⋊C4—3021no—
271C22⋊C4—3021no—
272C42—3021no—
273C42—1511no—
274C42—1511no—
275C42C22×D15111yescharacteristic
276C23—21no—
277C23—21no—
278C23—3021no—
279Q8—21no—
280Q8—21no—
281Q8—3022no—
282Q8—12081no—
283D4—21no—
284D4—21no—
285D4—21no—
286D4—3021no—
287D4—3021no—
288D4—6042no—
289D4—12081no—
290D4#1455900312yes—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—81no—
294C2×C4—3021no—
295C2×C4—3021no—
296C2×C4—3021no—
297C2×C4—6042no—
298C2×C4—1511no—
299C2×C4—1511no—
300C2×C4—1511no—
301C2×C4—1511no—
302C2×C4—12081no—
303C2×C4—12081no—
304C2×C4—12081no—
305C2×C4D4×D15111yescharacteristic
306C2×C4D4×D15111yescharacteristic
307C2×C4C23×D15111yescharacteristic
308C8—21no—
309C8—21no—
310C8—3021no—
311C8—3021no—
312C22—22no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—6041no—
319C22—6041no—
320C22—6041no—
321C22C2×D4×D15111yescharacteristic
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—3021no—
327C4—3021no—
328C4—3021no—
329C4—6041no—
330C4—6041no—
331C4—6041no—
332C4—1512no—
333C4C2×#1455900311yescharacteristic
334C4#1801278611yescharacteristic
335C2—42no—
336C2—81no—
337C2—12081no—
338C2#2375286811yescharacteristic
339C2#135×D15111yescharacteristic
340C2#2375301611yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#463×C151C2
socleC22×C151C22×D4
prime radical#23752405C2
hypercenter#463D151
hypocenterC151#3361
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #23752944C2semidirect
2. #23752921C2semidirect
3. #23752568C2semidirect
4. #23752566C2semidirect
5. #23752557C2semidirect
6. #23752514C2semidirect
7. #23752513C2semidirect
8. #23752505C2semidirect
9. #23752429C2semidirect
11. #23752336C2semidirect
12. SD16×Dic151C2semidirect
13. D8×Dic151C2semidirect
14. C4×#14558989C2semidirect
15. #463×C151C2semidirect
170. C151#3361semidirect
181. #463D151semidirect

Maximal subgroups

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

subgroupindex
#237529442
#237529212
#237525682
#237525662
#237525572
#237525142
#237525132
#237525052
#237524292
#237524052
#237523362
SD16×Dic1512
D8×Dic1512
C4×#145589892
#463×C1512
#3361151