Finite Group Databasebeta

← #34079895

Subgroups — #34079895

Order 19328.

420 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752724C211yesmaximal, characteristic
2C22⋊Q8×D151C211yesmaximal, characteristic, complemented
3#23752553C211yesmaximal, characteristic, complemented
4#23752544C211yesmaximal, characteristic, complemented
5#23752527C211yesmaximal, characteristic, complemented
6#23752454C211yesmaximal, characteristic, complemented
7#23752452C211yesmaximal, characteristic, complemented
8#23752444C211yesmaximal, characteristic, complemented
9#23752442C211yesmaximal, characteristic, complemented
10#23752376C211yesmaximal, characteristic, complemented
11#23752372C211yesmaximal, characteristic, complemented
12#23752369C211yesmaximal, characteristic, complemented
13#23752352C211yesmaximal, characteristic, complemented
14C22⋊C8×D151C211yesmaximal, characteristic, complemented
15#485×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C2×Q8×D151C2211yescharacteristic
18C22×C4×D151C2211yescharacteristic
19C2×Dic604C2211yescharacteristic, complemented
20C2×#14558994C2211yescharacteristic, complemented
21C2×#14558993C2211yescharacteristic, complemented
22C2×#14558991C2211yescharacteristic, complemented
23C2×C8×D151C2211yescharacteristic
24C2×C8×D151C2211yescharacteristic
25#18012723—21no—
26#18012719C2211yescharacteristic
27#18012719C2211yescharacteristic
28#18012719C2211yescharacteristic
29#18012718C2211yescharacteristic
30#18012717—21no—
31#18012716—21no—
32#18012715C2211yescharacteristic
33#18012714C2211yescharacteristic
34#18012714C2211yescharacteristic
35#18012709—21no—
36C4×D604—21no—
37C4×D604—21no—
38C4⋊C4×D151—21no—
39C4⋊C4×D151C2211yescharacteristic
40C22⋊C4×D151—21no—
41#18012672C2211yescharacteristic, complemented
42#18012670C2211yescharacteristic, complemented
43#18012664C2211yescharacteristic, complemented
44#18012662C2211yescharacteristic, complemented
45#18012662C2211yescharacteristic, complemented
46#18012662C2211yescharacteristic, complemented
47#18012661C2211yescharacteristic, complemented
48#18012659C2211yescharacteristic, complemented
49C22⋊(C151⋊C8)C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51(C2×D151)⋊C8C2211yescharacteristic
52C22⋊Q8×C151C2211yescharacteristic
53#117×C151C2211yescharacteristic
54#107×C151C2211yescharacteristic, complemented
55#106×C151C2211yescharacteristic, complemented
56#103×C151C2211yescharacteristic, complemented
57#103×C151C2211yescharacteristic, complemented
58C22⋊C8×C151C2211yescharacteristic
59C23×D151D411yescharacteristic
60#14559004—41no—
61#14559004—41no—
62C2×Dic302—21no—
63C2×Dic302C2311yescharacteristic
64C2×Dic302C2311yescharacteristic
65Q8×D151—41no—
66Q8×D151—41no—
67C2×D604—21no—
68C2×D604—21no—
69C2×D604C2311yescharacteristic
70C2×C22⋊D151—21no—
71C22×Dic151D411yescharacteristic
72C2×C4×D151—21no—
73C2×C4×D151—21no—
74C2×C4×D151—21no—
75C2×C4×D151—41no—
76C2×C4×D151—41no—
77C2×C4×D151D411yescharacteristic
78C2×C4×D151D411yescharacteristic
79C2×C4×D151C2311yescharacteristic
80C2×C4×D151C2311yescharacteristic
81Dic604—41no—
82#14558994—41no—
83#14558993—41no—
84#14558991—41no—
85C2×C151⋊C8C2311yescharacteristic
86C2×C151⋊C8C2311yescharacteristic
87C8×D151—41no—
88C8×D151—41no—
89C4⋊Dic151—21no—
90C4⋊Dic151—21no—
91C4⋊Dic151—21no—
92C4⋊Dic151C2311yescharacteristic
93Dic151⋊C4—21no—
94Dic151⋊C4—21no—
95Dic151⋊C4—21no—
96C22⋊Dic151—21no—
97(C2×D151)⋊C4—21no—
98(C2×D151)⋊C4—21no—
99(C2×D151)⋊C4—21no—
100(C2×D151)⋊C4—21no—
101(C2×D151)⋊C4—21no—
102(C2×D151)⋊C4—21no—
103C2×Q8×C151C2311yescharacteristic
104C22×C4×C151C2311yescharacteristic
105C2×C8×C151C2311yescharacteristic
106C2×C8×C151C2311yescharacteristic
107C4⋊C4×C151—21no—
108C4⋊C4×C151C2311yescharacteristic
109C4⋊C4×C151C2311yescharacteristic
110C4⋊C4×C151C2311yescharacteristic
111C22⋊C4×C151—21no—
112C22⋊C4×C151—21no—
113C42×C151—21no—
114C22×D151—22no—
115C22×D151—22no—
116C22×D151—21no—
117C22×D151—41no—
118C22×D151C2×D411yescharacteristic
119C22×D151C2×D411yescharacteristic
120Dic302—21no—
121Dic302—21no—
122Dic302—21no—
123Dic302—21no—
124Dic302—42no—
125D604—21no—
126D604—21no—
127D604—42no—
128D604—42no—
129C22⋊D151—42no—
130C2×Dic151—21no—
131C2×Dic151—21no—
132C2×Dic151—21no—
133C2×Dic151—41no—
134C2×Dic151C2×D411yescharacteristic
135C2×Dic151C2×D411yescharacteristic
136C4×D151—21no—
137C4×D151—21no—
138C4×D151—21no—
139C4×D151—21no—
140C4×D151—41no—
141C4×D151—41no—
142C4×D151—42no—
143C4×D151—42no—
144C4×D151—42no—
145C151⋊C8—21no—
146C151⋊C8—21no—
147C23×C151C2×D411yescharacteristic
148Q8×C151—21no—
149Q8×C151—21no—
150C2×C4×C151—21no—
151C2×C4×C151—21no—
152C2×C4×C151—21no—
153C2×C4×C151—21no—
154C2×C4×C151—21no—
155C2×C4×C151—21no—
156C2×C4×C151C2×D411yescharacteristic
157C2×C4×C151C2411yescharacteristic
158C8×C151—21no—
159C8×C151—21no—
160C22×C151—21no—
161C22×C151—21no—
162C22×C151—21no—
163C22×C151C22×D411yescharacteristic
164C2×D151—21no—
165C2×D151—21no—
166C2×D151—21no—
167C2×D151—21no—
168C2×D151—44no—
169C2×D151—41no—
170C2×D151—41no—
171C2×D151—41no—
172C2×D151#13512yes—
173C2×D151#13712yes—
174C4×C151—21no—
175C4×C151—41no—
176C4×C151—41no—
177C4×C151—41no—
178C4×C151—41no—
179C4×C151H(5,𝔽2)11yescharacteristic
180C4×C151H(5,𝔽2)11yescharacteristic
181Dic151—21no—
182Dic151—21no—
183Dic151—41no—
184Dic151—41no—
185Dic151—41no—
186C2×C151—41no—
187C2×C151#53411yescharacteristic
188C2×C151C2×#13511yescharacteristic
189C2×C151C2×#13711yescharacteristic
190D151—22no—
191D151—22no—
192D151—81no—
193C151#319011yescharacteristic, complemented, Sylow
194#3190—1511nomaximal, Sylow
195#525—1511no—
196C2×C22⋊Q8—1511no—
197#485—1511no—
198#485D15111yescharacteristic, complemented
199#483—1511no—
200#480—1511no—
201#467—1511no—
202#467—1511no—
203#465—1511no—
204#465—1511no—
205#452—1511no—
206#452—1511no—
207#451—1511no—
208#448—1511no—
209C2×C22⋊C8—1511no—
210C2×#41—1511no—
211C22×Q8—1511no—
212C23×C4—1511no—
213C2×Q16—1511no—
214C2×Q16—1511no—
215C2×SD16—1511no—
216C2×SD16—1511no—
217C22×C8—1511no—
218C22×C8—1511no—
219#123—3021no—
220C22⋊Q8—3021no—
221C22⋊Q8—3021no—
222C22⋊Q8—1511no—
223C22⋊Q8—1511no—
224C22⋊Q8—1511no—
225C22⋊Q8—1511no—
226C22⋊Q8—1511no—
227C22⋊Q8C2×D15111yescharacteristic
228#121—1511no—
229#121—1511no—
230#120—3021no—
231C4×D4—3021no—
232C4×D4—3021no—
233#117C2×D15111yescharacteristic
234C2×C4⋊C4—3021no—
235C2×C4⋊C4—1511no—
236C2×C22⋊C4—3021no—
237#107—1511no—
238#107C2×D15111yescharacteristic, complemented
239#106—1511no—
240#106C2×D15111yescharacteristic, complemented
241#103—1511no—
242#103—1511no—
243#103—1511no—
244#103—1511no—
245#103C2×D15111yescharacteristic, complemented
246#103C2×D15111yescharacteristic, complemented
247#102—1511no—
248#102—1511no—
249C22⋊C8—1511no—
250C22⋊C8—1511no—
251C22⋊C8—1511no—
252C22⋊C8C2×D15111yescharacteristic
253C24—1511no—
254#41—6041no—
255#41—6041no—
256C2×Q8—3021no—
257C2×Q8—6041no—
258C2×Q8—6041no—
259C2×Q8—1511no—
260C2×Q8—1511no—
261C2×Q8C22×D15111yescharacteristic
262C2×D4—3021no—
263C2×D4—3021no—
264C2×D4—3021no—
265C2×D4—1511no—
266C22×C4—3021no—
267C22×C4—3021no—
268C22×C4—3021no—
269C22×C4—6041no—
270C22×C4—6041no—
271C22×C4—1511no—
272C22×C4—1511no—
273C22×C4—1511no—
274C22×C4—1511no—
275C22×C4—1511no—
276C22×C4C22×D15111yescharacteristic
277Q16—6041no—
278Q16—6041no—
279SD16—6041no—
280SD16—6041no—
281C2×C8—6041no—
282C2×C8—6041no—
283C2×C8—1511no—
284C2×C8—1511no—
285C2×C8C22×D15111yescharacteristic
286C2×C8C22×D15111yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—3021no—
289C4⋊C4—3021no—
290C4⋊C4—3021no—
291C4⋊C4—3021no—
292C4⋊C4—3021no—
293C4⋊C4—3021no—
294C4⋊C4—1511no—
295C4⋊C4C22×D15111yescharacteristic
296C4⋊C4C22×D15111yescharacteristic
297C4⋊C4C22×D15111yescharacteristic
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—3021no—
301C22⋊C4—3021no—
302C22⋊C4—3021no—
303C22⋊C4—3021no—
304C22⋊C4—3021no—
305C22⋊C4—3021no—
306C22⋊C4—3021no—
307C42—21no—
308C23—3022no—
309C23—3022no—
310C23—3021no—
311C23—6041no—
312C23—1511no—
313C23—1511no—
314C23D4×D15111yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—3021no—
318Q8—3021no—
319Q8—3021no—
320Q8—3021no—
321Q8—6042no—
322D4—3021no—
323D4—3021no—
324D4—6042no—
325D4—6042no—
326D4—6042no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—3021no—
334C2×C4—3021no—
335C2×C4—3021no—
336C2×C4—3021no—
337C2×C4—3021no—
338C2×C4—3021no—
339C2×C4—3021no—
340C2×C4—6041no—
341C2×C4—6041no—
342C2×C4—6042no—
343C2×C4—6042no—
344C2×C4—6042no—
345C2×C4—6041no—
346C2×C4—1511no—
347C2×C4—1511no—
348C2×C4D4×D15111yescharacteristic
349C2×C4C23×D15111yescharacteristic
350C8—21no—
351C8—21no—
352C8—3021no—
353C8—3021no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—3021no—
358C22—3021no—
359C22—3021no—
360C22—3021no—
361C22—6044no—
362C22—6041no—
363C22—6041no—
364C22—6041no—
365C22—1512no—
366C22—1512no—
367C22C2×D4×D15111yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—41no—
373C4—3021no—
374C4—3021no—
375C4—6041no—
376C4—6041no—
377C4—6041no—
378C4#1801278511yescharacteristic
379C4#1801278511yescharacteristic
380C2—41no—
381C2—3022no—
382C2—3022no—
383C2—12081no—
384C2#2375277311yescharacteristic
385C2#135×D15111yescharacteristic
386C2#137×D15111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#485×C151C2
socleC22×C151C22×D4
prime radical#23752724C2
hypercenter#485D151
hypocenterC151#3190
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
2. C22⋊Q8×D151C2semidirect
3. #23752553C2semidirect
4. #23752544C2semidirect
5. #23752527C2semidirect
6. #23752454C2semidirect
7. #23752452C2semidirect
8. #23752444C2semidirect
9. #23752442C2semidirect
10. #23752376C2semidirect
11. #23752372C2semidirect
12. #23752369C2semidirect
13. #23752352C2semidirect
14. C22⋊C8×D151C2semidirect
15. #485×C151C2semidirect
19. C2×Dic604C22semidirect
20. C2×#14558994C22semidirect
21. C2×#14558993C22semidirect
22. C2×#14558991C22semidirect
41. #18012672C22semidirect
42. #18012670C22semidirect
43. #18012664C22semidirect
44. #18012662C22semidirect
45. #18012662C22semidirect
46. #18012662C22semidirect
47. #18012661C22semidirect
48. #18012659C22semidirect
54. #107×C151C22semidirect
55. #106×C151C22semidirect
56. #103×C151C22semidirect
57. #103×C151C22semidirect
193. C151#3190semidirect
198. #485D151semidirect
238. #107C2×D151semidirect
240. #106C2×D151semidirect
245. #103C2×D151semidirect
246. #103C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527242
C22⋊Q8×D1512
#237525532
#237525442
#237525272
#237524542
#237524522
#237524442
#237524422
#237523762
#237523722
#237523692
#237523522
C22⋊C8×D1512
#485×C1512
#3190151