Finite Group Databasebeta

← #34080178

Subgroups — #34080178

Order 19328.

396 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752822C211yesmaximal, characteristic, complemented
2#23752779C211yesmaximal, characteristic
3#23752603C211yesmaximal, characteristic, complemented
4#23752583C211yesmaximal, characteristic, complemented
5#23752575C211yesmaximal, characteristic, complemented
6#23752565C211yesmaximal, characteristic, complemented
7#23752433C211yesmaximal, characteristic, complemented
8#23752432C211yesmaximal, characteristic, complemented
9#23752411C211yesmaximal, characteristic, complemented
10#23752410C211yesmaximal, characteristic, complemented
11#23752376C211yesmaximal, characteristic, complemented
12#23752372C211yesmaximal, characteristic, complemented
13#23752363C211yesmaximal, characteristic, complemented
14#23752270C211yesmaximal, characteristic, complemented
15#450×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C2×Dic604C2211yescharacteristic, complemented
18C2×#14558994C2211yescharacteristic, complemented
19C2×#14558993C2211yescharacteristic, complemented
20C2×#14558992C2211yescharacteristic
21C2×#14558992C2211yescharacteristic
22C2×#14558991C2211yescharacteristic, complemented
23#18012737C2211yescharacteristic, complemented
24#18012735C2211yescharacteristic
25#18012735C2211yescharacteristic
26#18012732—21no—
27#18012732—21no—
28#18012730—21no—
29#18012730C2211yescharacteristic, complemented
30#18012729—21no—
31#18012726C2211yescharacteristic
32#18012726C2211yescharacteristic
33#18012718C2211yescharacteristic
34#18012710—21no—
35#18012710—21no—
36#18012708—21no—
37#18012708—21no—
38Q8×Dic151C2211yescharacteristic, complemented
39#18012704C2211yescharacteristic, complemented
40#18012698C2211yescharacteristic
41Dic151⋊C8C2211yescharacteristic, complemented
42Dic151⋊C8C2211yescharacteristic, complemented
43#18012664C2211yescharacteristic, complemented
44#18012662C2211yescharacteristic, complemented
45#18012661C2211yescharacteristic, complemented
46#18012660C2211yescharacteristic
47#18012660C2211yescharacteristic
48#18012659C2211yescharacteristic, complemented
49C22⋊(C151⋊C8)C2211yescharacteristic
50#18012649C2211yescharacteristic, complemented
51C8×Dic151C2211yescharacteristic, complemented
52C22×D4×C151C2211yescharacteristic
53C2×SD16×C151C2211yescharacteristic
54C2×SD16×C151C2211yescharacteristic
55C22⋊Q8×C151C2211yescharacteristic
56#102×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58C22⋊C8×C151C2211yescharacteristic
59#14559004—41no—
60#14559004—41no—
61C2×Dic302C2311yescharacteristic
62C2×Dic302C2311yescharacteristic
63C2×D604C2311yescharacteristic
64C2×C22⋊D151—21no—
65C2×C22⋊D151—21no—
66C2×C22⋊D151—21no—
67C2×C22⋊D151—21no—
68C2×C22⋊D151—21no—
69C2×C4×D151—21no—
70Dic604—41no—
71#14558994—41no—
72#14558993—41no—
73#14558992—41no—
74#14558992—41no—
75#14558991—41no—
76C2×C151⋊C8C2311yescharacteristic
77C2×C151⋊C8C2311yescharacteristic
78C4⋊Dic151—21no—
79C4⋊Dic151—21no—
80C4⋊Dic151D411yescharacteristic
81C4⋊Dic151D411yescharacteristic
82C4⋊Dic151C2311yescharacteristic
83Dic151⋊C4—21no—
84Dic151⋊C4—21no—
85Dic151⋊C4—21no—
86Dic151⋊C4—21no—
87Dic151⋊C4—21no—
88C22⋊Dic151—21no—
89C22⋊Dic151—21no—
90C22⋊Dic151—21no—
91C22⋊Dic151—21no—
92C22⋊Dic151—21no—
93C22⋊Dic151D411yescharacteristic
94C22⋊Dic151D411yescharacteristic
95C4×Dic151—21no—
96C4×Dic151—21no—
97C4×Dic151C2311yescharacteristic
98C4×Dic151C2311yescharacteristic
99C24×C151—21no—
100C2×Q8×C151C2311yescharacteristic
101C2×D4×C151—21no—
102C2×D4×C151—41no—
103C2×D4×C151—41no—
104C2×D4×C151C2311yescharacteristic
105C2×D4×C151C2311yescharacteristic
106C22×C4×C151C2311yescharacteristic
107SD16×C151—41no—
108SD16×C151—41no—
109C2×C8×C151C2311yescharacteristic
110C2×C8×C151C2311yescharacteristic
111C4⋊C4×C151—21no—
112C4⋊C4×C151C2311yescharacteristic
113C22⋊C4×C151—21no—
114C22×D151—21no—
115Dic302—21no—
116Dic302—21no—
117Dic302—21no—
118Dic302—21no—
119D604—21no—
120D604—21no—
121C22⋊D151—42no—
122C22⋊D151—81no—
123C22⋊D151—81no—
124C22⋊D151—81no—
125C22⋊D151—81no—
126C2×Dic151—21no—
127C2×Dic151—21no—
128C2×Dic151—21no—
129C2×Dic151C2×D411yescharacteristic
130C2×Dic151C2×D411yescharacteristic
131C2×Dic151C2×D411yescharacteristic
132C2×Dic151C2×D411yescharacteristic
133C4×D151—42no—
134C151⋊C8—21no—
135C151⋊C8—21no—
136C23×C151—21no—
137C23×C151—21no—
138C23×C151—42no—
139C23×C151—81no—
140C23×C151—81no—
141C23×C151C2×D411yescharacteristic
142Q8×C151—21no—
143Q8×C151—21no—
144D4×C151—21no—
145D4×C151—21no—
146D4×C151—21no—
147D4×C151—21no—
148D4×C151—42no—
149C2×C4×C151—21no—
150C2×C4×C151—21no—
151C2×C4×C151—21no—
152C2×C4×C151—21no—
153C2×C4×C151C2×D411yescharacteristic
154C2×C4×C151C2411yescharacteristic
155C8×C151—21no—
156C8×C151—21no—
157C22×C151—21no—
158C22×C151—21no—
159C22×C151—21no—
160C22×C151—41no—
161C22×C151—41no—
162C22×C151—41no—
163C22×C151—41no—
164C22×C151—41no—
165C22×C151—41no—
166C22×C151—84no—
167C22×C151C22×D411yescharacteristic
168C2×D151—41no—
169C2×D151—41no—
170C2×D151—41no—
171C4×C151—21no—
172C4×C151—41no—
173C4×C151—41no—
174C4×C151H(5,𝔽2)11yescharacteristic
175C4×C151H(5,𝔽2)11yescharacteristic
176Dic151—21no—
177Dic151—21no—
178Dic151—21no—
179Dic151—21no—
180Dic151—41no—
181Dic151—41no—
182Dic151—41no—
183C2×C151—41no—
184C2×C151—81no—
185C2×C151—81no—
186C2×C151#53511yescharacteristic
187C2×C151#57711yescharacteristic
188C2×C151#57711yescharacteristic
189D151—81no—
190C151#322211yescharacteristic, complemented, Sylow
191#3222—1511nomaximal, Sylow
192#541—1511no—
193#535—1511no—
194#497—1511no—
195#492—1511no—
196#490—1511no—
197#488—1511no—
198#464—1511no—
199#464—1511no—
200#460—1511no—
201#460—1511no—
202#452—1511no—
203#452—1511no—
204#450—1511no—
205#450D15111yescharacteristic, complemented
206#433—1511no—
207C2×#41—1511no—
208C22×D4C2×D15111yescharacteristic
209C2×Q16—1511no—
210C2×Q16—1511no—
211C2×SD16—1511no—
212C2×SD16—1511no—
213C2×SD16—1511no—
214C2×SD16—1511no—
215C2×SD16C2×D15111yescharacteristic
216C2×SD16C2×D15111yescharacteristic
217C4⋊Q8—1511no—
218#127—1511no—
219#127—1511no—
220#126—3021no—
221#126—3021no—
222#125—3021no—
223#125—3021no—
224#125—1511no—
225#124—1511no—
226#124—1511no—
227C22⋊Q8—1511no—
228C22⋊Q8C2×D15111yescharacteristic
229#121—3021no—
230#121—3021no—
231#120—3021no—
232#120—3021no—
233C4×Q8—1511no—
234C4×Q8—1511no—
235#117—1511no—
236C4⋊C8—1511no—
237C4⋊C8—1511no—
238#103—1511no—
239#103—1511no—
240#102—1511no—
241#102—1511no—
242#102—1511no—
243#102—1511no—
244#102C2×D15111yescharacteristic
245#102C2×D15111yescharacteristic
246C22⋊C8—1511no—
247C22⋊C8C2×D15111yescharacteristic
248#97—1511no—
249C4×C8—1511no—
250C24—21no—
251#41—6041no—
252#41—6041no—
253C2×Q8—1511no—
254C2×Q8—1511no—
255C2×Q8C22×D15111yescharacteristic
256C2×D4—21no—
257C2×D4—41no—
258C2×D4—41no—
259C2×D4—3021no—
260C2×D4—3021no—
261C2×D4—3021no—
262C2×D4—3021no—
263C2×D4—3021no—
264C2×D4—1511no—
265C2×D4C22×D15111yescharacteristic
266C2×D4C22×D15111yescharacteristic
267C22×C4—3021no—
268C22×C4C22×D15111yescharacteristic
269Q16—6041no—
270Q16—6041no—
271SD16—41no—
272SD16—41no—
273SD16—6041no—
274SD16—6041no—
275SD16—6041no—
276SD16—6041no—
277C2×C8—1511no—
278C2×C8—1511no—
279C2×C8C22×D15111yescharacteristic
280C2×C8C22×D15111yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—3021no—
283C4⋊C4—3021no—
284C4⋊C4—3021no—
285C4⋊C4—3021no—
286C4⋊C4—3021no—
287C4⋊C4—3021no—
288C4⋊C4—3021no—
289C4⋊C4—1511no—
290C4⋊C4—1511no—
291C4⋊C4—1511no—
292C4⋊C4C22×D15111yescharacteristic
293C22⋊C4—21no—
294C22⋊C4—3021no—
295C22⋊C4—3021no—
296C22⋊C4—3021no—
297C22⋊C4—3021no—
298C22⋊C4—3021no—
299C22⋊C4—1511no—
300C22⋊C4—1511no—
301C42—3021no—
302C42—3021no—
303C42—1511no—
304C42—1511no—
305C23—21no—
306C23—21no—
307C23—42no—
308C23—81no—
309C23—81no—
310C23—3021no—
311C23D4×D15111yescharacteristic
312Q8—21no—
313Q8—21no—
314Q8—3021no—
315Q8—3021no—
316Q8—3021no—
317Q8—3021no—
318D4—21no—
319D4—21no—
320D4—21no—
321D4—21no—
322D4—42no—
323D4—3021no—
324D4—3021no—
325D4—6042no—
326D4—12081no—
327D4—12081no—
328D4—12081no—
329D4—12081no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—3021no—
335C2×C4—3021no—
336C2×C4—3021no—
337C2×C4—6042no—
338C2×C4—1511no—
339C2×C4—1511no—
340C2×C4—1511no—
341C2×C4—1511no—
342C2×C4D4×D15111yescharacteristic
343C2×C4C23×D15111yescharacteristic
344C8—21no—
345C8—21no—
346C8—3021no—
347C8—3021no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—84no—
358C22—6041no—
359C22—6041no—
360C22—6041no—
361C22C2×D4×D15111yescharacteristic
362C4—21no—
363C4—41no—
364C4—41no—
365C4—3021no—
366C4—3021no—
367C4—3021no—
368C4—3021no—
369C4—6041no—
370C4—6041no—
371C4—6041no—
372C4#1801278411yescharacteristic
373C4#1801278411yescharacteristic
374C2—41no—
375C2—81no—
376C2—81no—
377C2—12081no—
378C2#2375277711yescharacteristic
379C2#2375301811yescharacteristic
380C2#2375302211yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#450×C151C2
socleC22×C151C22×D4
prime radical#23752779C2
hypercenter#450D151
hypocenterC151#3222
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #23752822C2semidirect
3. #23752603C2semidirect
4. #23752583C2semidirect
5. #23752575C2semidirect
6. #23752565C2semidirect
7. #23752433C2semidirect
8. #23752432C2semidirect
9. #23752411C2semidirect
10. #23752410C2semidirect
11. #23752376C2semidirect
12. #23752372C2semidirect
13. #23752363C2semidirect
14. #23752270C2semidirect
15. #450×C151C2semidirect
17. C2×Dic604C22semidirect
18. C2×#14558994C22semidirect
19. C2×#14558993C22semidirect
22. C2×#14558991C22semidirect
23. #18012737C22semidirect
29. #18012730C22semidirect
38. Q8×Dic151C22semidirect
39. #18012704C22semidirect
41. Dic151⋊C8C22semidirect
42. Dic151⋊C8C22semidirect
43. #18012664C22semidirect
44. #18012662C22semidirect
45. #18012661C22semidirect
48. #18012659C22semidirect
50. #18012649C22semidirect
51. C8×Dic151C22semidirect
190. C151#3222semidirect
205. #450D151semidirect

Maximal subgroups

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

subgroupindex
#237528222
#237527792
#237526032
#237525832
#237525752
#237525652
#237524332
#237524322
#237524112
#237524102
#237523762
#237523722
#237523632
#237522702
#450×C1512
#3222151