Finite Group Databasebeta

← #34080070

Subgroups — #34080070

Order 19328.

410 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#23752741C211yesmaximal, characteristic, complemented
2#124×D151C211yesmaximal, characteristic, complemented
3#23752594C211yesmaximal, characteristic, complemented
4#23752567C211yesmaximal, characteristic, complemented
5#23752566C211yesmaximal, characteristic, complemented
6#23752436C211yesmaximal, characteristic, complemented
7#23752432C211yesmaximal, characteristic, complemented
8#23752429C211yesmaximal, characteristic, complemented
9#23752425C211yesmaximal, characteristic, complemented
10#23752366C211yesmaximal, characteristic, complemented
11#23752361C211yesmaximal, characteristic, complemented
12#23752349C211yesmaximal, characteristic, complemented
13#23752344C211yesmaximal, characteristic
14#23752263C211yesmaximal, characteristic, complemented
15#495×C151C211yesmaximal, characteristic, complemented
16C2×Q8×D151C2211yescharacteristic
17C2×D4×D151C2211yescharacteristic
18C2×#14558994C2211yescharacteristic, complemented
19C2×#14558992C2211yescharacteristic, complemented
20C2×#14558991C2211yescharacteristic
21C2×#14558989C2211yescharacteristic
22#18012732—21no—
23#18012731C2211yescharacteristic, complemented
24#18012728C2211yescharacteristic
25#18012727C2211yescharacteristic
26#18012726C2211yescharacteristic
27#18012725—21no—
28#18012725—21no—
29#18012721—21no—
30#18012715C2211yescharacteristic
31#18012710C2211yescharacteristic
32Q8×Dic151C2211yescharacteristic, complemented
33D4×Dic151C2211yescharacteristic, complemented
34(C22⋊D151)⋊C4—21no—
35#18012695—21no—
36C22⋊C4×D151—21no—
37C22⋊C4×D151—21no—
38C42×D151C2211yescharacteristic
39Dic151⋊C8C2211yescharacteristic, complemented
40Dic151⋊C8C2211yescharacteristic, complemented
41#18012664C2211yescharacteristic, complemented
42#18012664C2211yescharacteristic, complemented
43#18012663C2211yescharacteristic, complemented
44#18012663C2211yescharacteristic, complemented
45#18012661C2211yescharacteristic
46#18012661C2211yescharacteristic
47#18012660C2211yescharacteristic
48#18012660C2211yescharacteristic
49(C2×D151)⋊C8C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51C4×C151⋊C8C2211yescharacteristic, complemented
52C2×Q16×C151C2211yescharacteristic, complemented
53C2×SD16×C151C2211yescharacteristic
54C2×SD16×C151C2211yescharacteristic, complemented
55C2×D8×C151C2211yescharacteristic
56#124×C151C2211yescharacteristic
57#124×C151C2211yescharacteristic, complemented
58C4×C8×C151C2211yescharacteristic, complemented
59C23×D151—21no—
60C2×Dic302—21no—
61C2×Dic302C2311yescharacteristic
62Q8×D151—41no—
63Q8×D151—41no—
64C2×D604C2311yescharacteristic
65C2×C22⋊D151—21no—
66C2×C22⋊D151—21no—
67D4×D151—41no—
68D4×D151—41no—
69C22×Dic151—21no—
70C2×C4×D151—21no—
71C2×C4×D151D411yescharacteristic
72C2×C4×D151D411yescharacteristic
73C2×C4×D151C2311yescharacteristic
74#14558994—41no—
75#14558992—41no—
76#14558991—41no—
77#14558989—41no—
78C2×C151⋊C8C2311yescharacteristic
79C2×C151⋊C8C2311yescharacteristic
80C4⋊Dic151—21no—
81C4⋊Dic151C2311yescharacteristic
82C4⋊Dic151C2311yescharacteristic
83Dic151⋊C4—21no—
84Dic151⋊C4—21no—
85Dic151⋊C4—21no—
86C22⋊Dic151—21no—
87C22⋊Dic151—21no—
88C22⋊Dic151—21no—
89C22⋊Dic151—21no—
90(C2×D151)⋊C4—21no—
91(C2×D151)⋊C4—21no—
92(C2×D151)⋊C4—21no—
93(C2×D151)⋊C4—21no—
94(C2×D151)⋊C4—21no—
95C4×Dic151—21no—
96C4×Dic151D411yescharacteristic
97C4×Dic151D411yescharacteristic
98C4×Dic151C2311yescharacteristic
99C2×Q8×C151C2311yescharacteristic
100C2×Q8×C151C2311yescharacteristic
101C2×D4×C151C2311yescharacteristic
102C2×D4×C151C2311yescharacteristic
103Q16×C151—41no—
104SD16×C151—41no—
105SD16×C151—41no—
106D8×C151—41no—
107C2×C8×C151C2311yescharacteristic
108C2×C8×C151C2311yescharacteristic
109C22⋊C4×C151—21no—
110C22⋊C4×C151—21no—
111C22⋊C4×C151—21no—
112C22⋊C4×C151—21no—
113C42×C151C2311yescharacteristic
114C22×D151—21no—
115C22×D151—42no—
116C22×D151—42no—
117C22×D151—42no—
118C22×D151C2×D411yescharacteristic
119Dic302—21no—
120Dic302—21no—
121Dic302—42no—
122D604—21no—
123D604—21no—
124C22⋊D151—42no—
125C22⋊D151—42no—
126C2×Dic151—21no—
127C2×Dic151—21no—
128C2×Dic151—21no—
129C2×Dic151—42no—
130C2×Dic151C2×D411yescharacteristic
131C2×Dic151C2×D411yescharacteristic
132C2×Dic151C2×D411yescharacteristic
133C4×D151—22no—
134C4×D151—21no—
135C4×D151—21no—
136C4×D151—41no—
137C4×D151—42no—
138C151⋊C8—21no—
139C151⋊C8—21no—
140C23×C151—21no—
141C23×C151—21no—
142Q8×C151—21no—
143Q8×C151—21no—
144Q8×C151—21no—
145Q8×C151—21no—
146D4×C151—21no—
147D4×C151—21no—
148D4×C151—21no—
149D4×C151—21no—
150C2×C4×C151—21no—
151C2×C4×C151—21no—
152C2×C4×C151C2×D411yescharacteristic
153C2×C4×C151C2×D411yescharacteristic
154C2×C4×C151C2411yescharacteristic
155C8×C151—21no—
156C8×C151—21no—
157C22×C151—41no—
158C22×C151—41no—
159C22×C151—41no—
160C22×C151—41no—
161C22×C151—41no—
162C22×C151—41no—
163C22×C151C22×D411yescharacteristic
164C2×D151—21no—
165C2×D151—21no—
166C2×D151—41no—
167C2×D151—41no—
168C2×D151—41no—
169C2×D151—84no—
170C2×D151#13512yes—
171C4×C151—21no—
172C4×C151—21no—
173C4×C151—41no—
174C4×C151—41no—
175C4×C151H(5,𝔽2)11yescharacteristic
176C4×C151H(5,𝔽2)11yescharacteristic
177Dic151—21no—
178Dic151—21no—
179Dic151—21no—
180Dic151—41no—
181Dic151—41no—
182Dic151—41no—
183C2×C151—81no—
184C2×C151—81no—
185C2×C151#53511yescharacteristic
186C2×C151C2×#13511yescharacteristic
187C2×C151#57511yescharacteristic
188D151—22no—
189D151—81no—
190C151#321111yescharacteristic, complemented, Sylow
191#3211—1511nomaximal, Sylow
192#529—1511no—
193C2×#124—1511no—
194#495—1511no—
195#495D15111yescharacteristic, complemented
196#488—1511no—
197#488—1511no—
198#464—1511no—
199#464—1511no—
200#463—1511no—
201#463—1511no—
202#451—1511no—
203#450—1511no—
204#448—1511no—
205#447—1511no—
206#431—1511no—
207C22×Q8—1511no—
208C22×D4—1511no—
209C2×Q16—1511no—
210C2×Q16C2×D15111yescharacteristic, complemented
211C2×SD16—1511no—
212C2×SD16—1511no—
213C2×SD16C2×D15111yescharacteristic
214C2×SD16C2×D15111yescharacteristic, complemented
215C2×D8—1511no—
216C2×D8C2×D15111yescharacteristic
217#126—3021no—
218#125—1511no—
219#124—3021no—
220#124—3021no—
221#124—1511no—
222#124—1511no—
223#124—1511no—
224#124C2×D15111yescharacteristic
225#124C2×D15111yescharacteristic, complemented
226#123—3021no—
227C22⋊Q8—1511no—
228#121—1511no—
229C4×Q8—1511no—
230C4×D4—3021no—
231C4×D4—1511no—
232#117—3021no—
233C2×C22⋊C4—3021no—
234C2×C22⋊C4—3021no—
235C2×C42—1511no—
236C4⋊C8—1511no—
237C4⋊C8—1511no—
238#103—1511no—
239#103—1511no—
240#103—1511no—
241#103—1511no—
242#102—1511no—
243#102—1511no—
244#102—1511no—
245#102—1511no—
246C22⋊C8—1511no—
247C22⋊C8—1511no—
248C4×C8—1511no—
249C4×C8C2×D15111yescharacteristic, complemented
250C24—3021no—
251C2×Q8—3021no—
252C2×Q8—6041no—
253C2×Q8—6041no—
254C2×Q8—1511no—
255C2×Q8C22×D15111yescharacteristic
256C2×Q8C22×D15111yescharacteristic
257C2×D4—3021no—
258C2×D4—3021no—
259C2×D4—6041no—
260C2×D4—6041no—
261C2×D4—1511no—
262C2×D4C22×D15111yescharacteristic
263C2×D4C22×D15111yescharacteristic
264C22×C4—3021no—
265C22×C4—3021no—
266C22×C4—1511no—
267C22×C4—1511no—
268C22×C4—1511no—
269Q16—41no—
270Q16—6041no—
271SD16—41no—
272SD16—41no—
273SD16—6041no—
274SD16—6041no—
275D8—41no—
276D8—6041no—
277C2×C8—1511no—
278C2×C8—1511no—
279C2×C8C22×D15111yescharacteristic
280C2×C8C22×D15111yescharacteristic
281C4⋊C4—3021no—
282C4⋊C4—3021no—
283C4⋊C4—3021no—
284C4⋊C4—3021no—
285C4⋊C4—1511no—
286C4⋊C4—1511no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—3021no—
292C22⋊C4—3021no—
293C22⋊C4—3021no—
294C22⋊C4—3021no—
295C22⋊C4—3021no—
296C22⋊C4—3021no—
297C22⋊C4—3021no—
298C22⋊C4—3021no—
299C22⋊C4—3021no—
300C42—3021no—
301C42—1511no—
302C42—1511no—
303C42—1511no—
304C42C22×D15111yescharacteristic
305C23—21no—
306C23—21no—
307C23—3021no—
308C23—6042no—
309C23—6042no—
310C23—6042no—
311C23—1511no—
312Q8—21no—
313Q8—21no—
314Q8—21no—
315Q8—21no—
316Q8—3021no—
317Q8—3021no—
318Q8—6042no—
319D4—21no—
320D4—21no—
321D4—21no—
322D4—21no—
323D4—3021no—
324D4—3021no—
325D4—6042no—
326D4—6042no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—3022no—
330C2×C4—3021no—
331C2×C4—3021no—
332C2×C4—3021no—
333C2×C4—3021no—
334C2×C4—3021no—
335C2×C4—6041no—
336C2×C4—6042no—
337C2×C4—6042no—
338C2×C4—1511no—
339C2×C4—1511no—
340C2×C4—1511no—
341C2×C4D4×D15111yescharacteristic
342C2×C4D4×D15111yescharacteristic
343C2×C4C23×D15111yescharacteristic
344C8—21no—
345C8—21no—
346C8—3021no—
347C8—3021no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—3021no—
355C22—3021no—
356C22—6041no—
357C22—6041no—
358C22—6041no—
359C22—1512no—
360C22—12084no—
361C22C2×D4×D15111yescharacteristic
362C4—21no—
363C4—21no—
364C4—41no—
365C4—41no—
366C4—3021no—
367C4—3021no—
368C4—3021no—
369C4—6041no—
370C4—6041no—
371C4—6041no—
372C4#1801278411yescharacteristic
373C4#1801278411yescharacteristic
374C2—81no—
375C2—81no—
376C2—3022no—
377C2—12081no—
378C2#2375277511yescharacteristic
379C2#135×D15111yescharacteristic
380C2#2375300911yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#495×C151C2
socleC22×C151C22×D4
prime radical#23752344C2
hypercenter#495D151
hypocenterC151#3211
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #23752741C2semidirect
2. #124×D151C2semidirect
3. #23752594C2semidirect
4. #23752567C2semidirect
5. #23752566C2semidirect
6. #23752436C2semidirect
7. #23752432C2semidirect
8. #23752429C2semidirect
9. #23752425C2semidirect
10. #23752366C2semidirect
11. #23752361C2semidirect
12. #23752349C2semidirect
14. #23752263C2semidirect
15. #495×C151C2semidirect
18. C2×#14558994C22semidirect
19. C2×#14558992C22semidirect
23. #18012731C22semidirect
32. Q8×Dic151C22semidirect
33. D4×Dic151C22semidirect
39. Dic151⋊C8C22semidirect
40. Dic151⋊C8C22semidirect
41. #18012664C22semidirect
42. #18012664C22semidirect
43. #18012663C22semidirect
44. #18012663C22semidirect
51. C4×C151⋊C8C22semidirect
52. C2×Q16×C151C22semidirect
54. C2×SD16×C151C22semidirect
57. #124×C151C22semidirect
58. C4×C8×C151C22semidirect
190. C151#3211semidirect
195. #495D151semidirect
210. C2×Q16C2×D151semidirect
214. C2×SD16C2×D151semidirect
225. #124C2×D151semidirect
249. C4×C8C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527412
#124×D1512
#237525942
#237525672
#237525662
#237524362
#237524322
#237524292
#237524252
#237523662
#237523612
#237523492
#237523442
#237522632
#495×C1512
#3211151