Finite Group Databasebeta

← #34079886

Subgroups — #34079886

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#23752722C211yesmaximal, characteristic
2C22⋊Q8×D151C211yesmaximal, characteristic, complemented
3#23752556C211yesmaximal, characteristic, complemented
4#23752552C211yesmaximal, characteristic, complemented
5#23752544C211yesmaximal, characteristic, complemented
6#23752524C211yesmaximal, characteristic, complemented
7#23752453C211yesmaximal, characteristic, complemented
8#23752451C211yesmaximal, characteristic, complemented
9#23752439C211yesmaximal, characteristic, complemented
10#23752375C211yesmaximal, characteristic, complemented
11#23752371C211yesmaximal, characteristic, complemented
12#23752369C211yesmaximal, characteristic, complemented
13#23752349C211yesmaximal, characteristic, complemented
14C2×(C2×D151)⋊C8C211yesmaximal, characteristic, complemented
15#465×C151C211yesmaximal, characteristic, complemented
16C2×#14559003C2211yescharacteristic
17C2×Q8×D151C2211yescharacteristic
18C22×C4×D151C2211yescharacteristic
19C2×Dic604C2211yescharacteristic, complemented
20C2×#14558994C2211yescharacteristic, complemented
21C2×#14558992C2211yescharacteristic, complemented
22C22×C151⋊C8C2211yescharacteristic
23#18012721—21no—
24#18012719C2211yescharacteristic
25#18012719C2211yescharacteristic
26#18012718C2211yescharacteristic
27#18012718C2211yescharacteristic
28#18012717—21no—
29#18012716—21no—
30#18012715C2211yescharacteristic
31#18012710C2211yescharacteristic
32#18012707—21no—
33D4×Dic151—21no—
34(C22⋊D151)⋊C4—21no—
35#18012697C2211yescharacteristic
36C4⋊C4×D151—21no—
37C4⋊C4×D151C2211yescharacteristic
38C22⋊C4×D151—21no—
39#18012673C2211yescharacteristic, complemented
40#18012672C2211yescharacteristic, complemented
41#18012670C2211yescharacteristic, complemented
42#18012664C2211yescharacteristic, complemented
43#18012664C2211yescharacteristic, complemented
44#18012663C2211yescharacteristic, complemented
45#18012662C2211yescharacteristic, complemented
46#18012662C2211yescharacteristic, complemented
47#18012660C2211yescharacteristic, complemented
48(C2×D151)⋊C8C2211yescharacteristic
49(C2×D151)⋊C8C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51(C2×D151)⋊C8C2211yescharacteristic
52C2×SD16×C151C2211yescharacteristic, complemented
53C22×C8×C151C2211yescharacteristic
54C22⋊Q8×C151C2211yescharacteristic
55#121×C151C2211yescharacteristic
56#106×C151C2211yescharacteristic, complemented
57#103×C151C2211yescharacteristic, complemented
58#102×C151C2211yescharacteristic, complemented
59C23×D151D411yescharacteristic
60#14559003—41no—
61#14559003—41no—
62C2×Dic302—21no—
63C2×Dic302C2311yescharacteristic
64C2×Dic302C2311yescharacteristic
65Q8×D151—41no—
66Q8×D151—41no—
67C2×C22⋊D151—21no—
68C2×C22⋊D151—21no—
69C22×Dic151—21no—
70C22×Dic151D411yescharacteristic
71C2×C4×D151—21no—
72C2×C4×D151—21no—
73C2×C4×D151—41no—
74C2×C4×D151—41no—
75C2×C4×D151D411yescharacteristic
76C2×C4×D151D411yescharacteristic
77C2×C4×D151C2311yescharacteristic
78C2×C4×D151C2311yescharacteristic
79Dic604—41no—
80#14558994—41no—
81#14558992—41no—
82C2×C151⋊C8—41no—
83C2×C151⋊C8C2311yescharacteristic
84C2×C151⋊C8C2311yescharacteristic
85C4⋊Dic151—21no—
86C4⋊Dic151—21no—
87C4⋊Dic151C2311yescharacteristic
88C4⋊Dic151C2311yescharacteristic
89Dic151⋊C4—21no—
90Dic151⋊C4—21no—
91Dic151⋊C4—21no—
92Dic151⋊C4—21no—
93C22⋊Dic151—21no—
94C22⋊Dic151—21no—
95C22⋊Dic151—21no—
96(C2×D151)⋊C4—21no—
97(C2×D151)⋊C4—21no—
98(C2×D151)⋊C4—21no—
99(C2×D151)⋊C4—21no—
100C4×Dic151—21no—
101C2×Q8×C151C2311yescharacteristic
102C2×D4×C151—21no—
103C2×D4×C151C2311yescharacteristic
104C22×C4×C151C2311yescharacteristic
105SD16×C151—41no—
106C2×C8×C151—41no—
107C2×C8×C151C2311yescharacteristic
108C2×C8×C151C2311yescharacteristic
109C4⋊C4×C151—21no—
110C4⋊C4×C151C2311yescharacteristic
111C4⋊C4×C151C2311yescharacteristic
112C22⋊C4×C151—21no—
113C22⋊C4×C151—21no—
114C22×D151—22no—
115C22×D151—22no—
116C22×D151—41no—
117C22×D151C2×D411yescharacteristic
118C22×D151C2×D411yescharacteristic
119Dic302—21no—
120Dic302—21no—
121Dic302—21no—
122Dic302—21no—
123Dic302—42no—
124C22⋊D151—42no—
125C22⋊D151—42no—
126C2×Dic151—21no—
127C2×Dic151—21no—
128C2×Dic151—21no—
129C2×Dic151—21no—
130C2×Dic151—41no—
131C2×Dic151—42no—
132C2×Dic151C2×D411yescharacteristic
133C2×Dic151C2×D411yescharacteristic
134C4×D151—21no—
135C4×D151—21no—
136C4×D151—21no—
137C4×D151—21no—
138C4×D151—41no—
139C4×D151—41no—
140C4×D151—42no—
141C4×D151—42no—
142C151⋊C8—21no—
143C151⋊C8—21no—
144C23×C151—21no—
145C23×C151C2×D411yescharacteristic
146Q8×C151—21no—
147Q8×C151—21no—
148D4×C151—21no—
149D4×C151—21no—
150D4×C151—42no—
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—41no—
163C22×C151—41no—
164C22×C151—41no—
165C22×C151#13712yes—
166C22×C151C22×D411yescharacteristic
167C2×D151—21no—
168C2×D151—21no—
169C2×D151—21no—
170C2×D151—21no—
171C2×D151—21no—
172C2×D151—44no—
173C2×D151#13512yes—
174C4×C151—21no—
175C4×C151—41no—
176C4×C151—41no—
177C4×C151—41no—
178C4×C151H(5,𝔽2)11yescharacteristic
179C4×C151H(5,𝔽2)11yescharacteristic
180Dic151—21no—
181Dic151—21no—
182Dic151—41no—
183Dic151—41no—
184Dic151—41no—
185Dic151—41no—
186C2×C151—22no—
187C2×C151—81no—
188C2×C151#53411yescharacteristic
189C2×C151C2×#13511yescharacteristic
190C2×C151C2×#13711yescharacteristic
191D151—22no—
192D151—41no—
193C151#319011yescharacteristic, complemented, Sylow
194#3190—1511nomaximal, Sylow
195#525—1511no—
196C2×C22⋊Q8—1511no—
197#485—1511no—
198#485—1511no—
199#483—1511no—
200#480—1511no—
201#467—1511no—
202#467—1511no—
203#465—1511no—
204#465D15111yescharacteristic, complemented
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×SD16C2×D15111yescharacteristic, complemented
217C22×C8—1511no—
218C22×C8C2×D15111yescharacteristic
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#121C2×D15111yescharacteristic
230#120—3021no—
231C4×D4—3021no—
232C4×D4—3021no—
233#117—1511no—
234C2×C4⋊C4—3021no—
235C2×C4⋊C4—1511no—
236C2×C22⋊C4—3021no—
237#107—1511no—
238#107—1511no—
239#106—1511no—
240#106C2×D15111yescharacteristic, complemented
241#103—1511no—
242#103—1511no—
243#103—1511no—
244#103—1511no—
245#103—1511no—
246#103C2×D15111yescharacteristic, complemented
247#102—1511no—
248#102C2×D15111yescharacteristic, complemented
249C22⋊C8—1511no—
250C22⋊C8—1511no—
251C22⋊C8—1511no—
252C22⋊C8—1511no—
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—21no—
263C2×D4—3021no—
264C2×D4—3021no—
265C2×D4C22×D15111yescharacteristic
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—41no—
280SD16—6041no—
281C2×C8—41no—
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⋊C4—1511no—
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—3021no—
308C23—21no—
309C23—3022no—
310C23—3022no—
311C23—6041no—
312C23—1511no—
313C23—1511no—
314C23D4×D15111yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—3021no—
318Q8—3021no—
319Q8—3021no—
320Q8—3021no—
321Q8—6042no—
322D4—21no—
323D4—21no—
324D4—42no—
325D4—6042no—
326D4—6042no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—3021no—
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—6041no—
345C2×C4—6042no—
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—41no—
357C22—41no—
358C22—41no—
359C22—3021no—
360C22—3021no—
361C22—3021no—
362C22—3021no—
363C22—3021no—
364C22—6044no—
365C22—1512no—
366C22#1801276812yes—
367C22C2×D4×D15111yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—3021no—
373C4—3021no—
374C4—6041no—
375C4—6041no—
376C4—6041no—
377C4—6041no—
378C4#1801278411yescharacteristic
379C4#1801278511yescharacteristic
380C2—22no—
381C2—81no—
382C2—3022no—
383C2—6041no—
384C2#2375277011yescharacteristic
385C2#135×D15111yescharacteristic
386C2C2×#1801276811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#465×C151C2
socleC22×C151C22×D4
prime radical#23752722C2
hypercenter#465D151
hypocenterC151#3190
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
2. C22⋊Q8×D151C2semidirect
3. #23752556C2semidirect
4. #23752552C2semidirect
5. #23752544C2semidirect
6. #23752524C2semidirect
7. #23752453C2semidirect
8. #23752451C2semidirect
9. #23752439C2semidirect
10. #23752375C2semidirect
11. #23752371C2semidirect
12. #23752369C2semidirect
13. #23752349C2semidirect
14. C2×(C2×D151)⋊C8C2semidirect
15. #465×C151C2semidirect
19. C2×Dic604C22semidirect
20. C2×#14558994C22semidirect
21. C2×#14558992C22semidirect
39. #18012673C22semidirect
40. #18012672C22semidirect
41. #18012670C22semidirect
42. #18012664C22semidirect
43. #18012664C22semidirect
44. #18012663C22semidirect
45. #18012662C22semidirect
46. #18012662C22semidirect
47. #18012660C22semidirect
52. C2×SD16×C151C22semidirect
56. #106×C151C22semidirect
57. #103×C151C22semidirect
58. #102×C151C22semidirect
193. C151#3190semidirect
204. #465D151semidirect
216. C2×SD16C2×D151semidirect
240. #106C2×D151semidirect
246. #103C2×D151semidirect
248. #102C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527222
C22⋊Q8×D1512
#237525562
#237525522
#237525442
#237525242
#237524532
#237524512
#237524392
#237523752
#237523712
#237523692
#237523492
C2×(C2×D151)⋊C82
#465×C1512
#3190151