Finite Group Databasebeta

← #34079108

Subgroups — #34079108

Order 19328.

492 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#23752759C211yesmaximal, characteristic, complemented
2C4×D4×D151C211yesmaximal, characteristic, complemented
3#23752527C211yesmaximal, characteristic, complemented
4#23752524C211yesmaximal, characteristic, complemented
5#23752491C211yesmaximal, characteristic, complemented
6#23752490C211yesmaximal, characteristic, complemented
7#23752406C211yesmaximal, characteristic, complemented
8#23752405C211yesmaximal, characteristic, complemented
9#23752347C211yesmaximal, characteristic, complemented
10#23752344C211yesmaximal, characteristic, complemented
11C4×D1208C211yesmaximal, characteristic, complemented
12C4×#14558989C211yesmaximal, characteristic, complemented
13C4×#14558989C211yesmaximal, characteristic, complemented
14#23752263C211yesmaximal, characteristic, complemented
15C4×D8×C151C211yesmaximal, characteristic, complemented
16C2×#14559004—21no—
17C2×D4×D151C2211yescharacteristic
18C22×C4×D151—21no—
19C2×D1208C2211yescharacteristic
20C2×#14558989C2211yescharacteristic
21C2×#14558989C2211yescharacteristic
22#18012738C2211yescharacteristic, complemented
23#18012735C2211yescharacteristic, complemented
24#18012725—21no—
25#18012714C2211yescharacteristic
26#18012712—21no—
27#18012710C2211yescharacteristic
28C4×D604C2211yescharacteristic
29C4×D604C2211yescharacteristic, complemented
30D4×Dic151C2211yescharacteristic
31#18012701C2211yescharacteristic
32C4×C22⋊D151—21no—
33C4×C22⋊D151—21no—
34(C22⋊D151)⋊C4—21no—
35C4⋊C4×D151C2211yescharacteristic
36C22⋊C4×D151—21no—
37C42×D151C2211yescharacteristic
38#18012673C2211yescharacteristic, complemented
39#18012672C2211yescharacteristic, complemented
40#18012672C2211yescharacteristic, complemented
41Dic151⋊C8C2211yescharacteristic, complemented
42Dic151⋊C8C2211yescharacteristic, complemented
43#18012661C2211yescharacteristic
44#18012661C2211yescharacteristic, complemented
45#18012660C2211yescharacteristic
46#18012660C2211yescharacteristic, complemented
47#18012659C2211yescharacteristic
48#18012659C2211yescharacteristic, complemented
49(C2×D151)⋊C8C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51C4×C151⋊C8C2211yescharacteristic, complemented
52C2×D8×C151C2211yescharacteristic
53C4×D4×C151C2211yescharacteristic
54C4×D4×C151C2211yescharacteristic, complemented
55#107×C151C2211yescharacteristic, complemented
56#102×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic, complemented
58C4×C8×C151C2211yescharacteristic, complemented
59C23×D151—21no—
60#14559004—44no—
61C2×Dic302—21no—
62C2×D604—21no—
63C2×D604C2311yescharacteristic
64C2×D604C2311yescharacteristic
65C2×C22⋊D151—21no—
66C2×C22⋊D151—21no—
67C2×C22⋊D151—21no—
68C2×C22⋊D151—21no—
69D4×D151—22no—
70D4×D151—22no—
71C22×Dic151—21no—
72C2×C4×D151—21no—
73C2×C4×D151—21no—
74C2×C4×D151—21no—
75C2×C4×D151—21no—
76C2×C4×D151—44no—
77C2×C4×D151D411yescharacteristic
78C2×C4×D151D411yescharacteristic
79C2×C4×D151C2311yescharacteristic
80D1208—22no—
81#14558989—22no—
82#14558989—22no—
83C2×C151⋊C8C2311yescharacteristic
84C2×C151⋊C8C2311yescharacteristic
85C4⋊Dic151C2311yescharacteristic
86C4⋊Dic151C2311yescharacteristic
87Dic151⋊C4—21no—
88Dic151⋊C4—21no—
89C22⋊Dic151—21no—
90C22⋊Dic151—21no—
91(C2×D151)⋊C4—21no—
92(C2×D151)⋊C4—21no—
93(C2×D151)⋊C4—21no—
94(C2×D151)⋊C4—21no—
95C4×Dic151D411yescharacteristic
96C4×Dic151D411yescharacteristic
97C4×Dic151C2311yescharacteristic
98C2×D4×C151C2311yescharacteristic
99C2×D4×C151C2311yescharacteristic
100C22×C4×C151—21no—
101C22×C4×C151—21no—
102D8×C151—22no—
103C2×C8×C151C2311yescharacteristic
104C2×C8×C151C2311yescharacteristic
105C4⋊C4×C151C2311yescharacteristic
106C4⋊C4×C151C2311yescharacteristic
107C22⋊C4×C151—21no—
108C22⋊C4×C151—21no—
109C42×C151C2311yescharacteristic
110C22×D151—24no—
111C22×D151—21no—
112C22×D151—21no—
113C22×D151—42no—
114C22×D151—42no—
115C22×D151C2×D411yescharacteristic
116Dic302—42no—
117D604—21no—
118D604—21no—
119D604—21no—
120D604—42no—
121D604#4112yescomplemented
122C22⋊D151—24no—
123C22⋊D151—42no—
124C22⋊D151—42no—
125C22⋊D151—42no—
126C2×Dic151—21no—
127C2×Dic151—21no—
128C2×Dic151—42no—
129C2×Dic151C2×D411yescharacteristic
130C2×Dic151C2×D411yescharacteristic
131C2×Dic151C2×D411yescharacteristic
132C4×D151—21no—
133C4×D151—21no—
134C4×D151—41no—
135C4×D151—42no—
136C4×D151—42no—
137C4×D151—42no—
138C4×D151—42no—
139C4×D151D814yescomplemented
140C151⋊C8—21no—
141C151⋊C8—21no—
142C23×C151—21no—
143C23×C151—21no—
144D4×C151—21no—
145D4×C151—21no—
146D4×C151—21no—
147D4×C151#4112yescomplemented
148C2×C4×C151—21no—
149C2×C4×C151—21no—
150C2×C4×C151—42no—
151C2×C4×C151—42no—
152C2×C4×C151C2×D411yescharacteristic
153C2×C4×C151C2×D411yescharacteristic
154C2×C4×C151C2411yescharacteristic
155C8×C151—21no—
156C8×C151—21no—
157C22×C151—22no—
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—22no—
167C2×D151—48no—
168C2×D151—41no—
169C2×D151—41no—
170C2×D151—41no—
171C2×D151—41no—
172C2×D151—41no—
173C2×D151C2×D812yes—
174C4×C151—21no—
175C4×C151—41no—
176C4×C151—41no—
177C4×C151C2×D812yes—
178C4×C151C2×#4111yescharacteristic
179C4×C151C2×#4111yescharacteristic
180Dic151—21no—
181Dic151—21no—
182Dic151—41no—
183Dic151—41no—
184Dic151C2×D812yes—
185C2×C151—42no—
186C2×C151—81no—
187C2×C151#52511yescharacteristic
188C2×C151C22×D811yescharacteristic
189C2×C151#57511yescharacteristic
190D151—22no—
191D151—42no—
192D151—81no—
193C151#310011yescharacteristic, complemented, Sylow
194#3100—1511nomaximal, Sylow
195#532—1511no—
196C2×C4×D4—1511no—
197#480—1511no—
198#480—1511no—
199#474—1511no—
200#474—1511no—
201#459—1511no—
202#459—1511no—
203#447—1511no—
204#447—1511no—
205C4×D8—1511no—
206C4×D8—1511no—
207C4×D8—1511no—
208C4×D8D15111yescharacteristic, complemented
209#431—1511no—
210C2×#41—3021no—
211C22×D4—1511no—
212C23×C4—3021no—
213C2×D8—1511no—
214C2×D8—1511no—
215C2×D8—1511no—
216C2×D8C2×D15111yescharacteristic
217C4⋊Q8—1511no—
218#127—1511no—
219#124—3021no—
220#121—3021no—
221#121—1511no—
222#121—1511no—
223C4×D4—3021no—
224C4×D4—3021no—
225C4×D4—3021no—
226C4×D4—1511no—
227C4×D4—1511no—
228C4×D4—1511no—
229C4×D4—1511no—
230C4×D4C2×D15111yescharacteristic
231C4×D4C2×D15111yescharacteristic, complemented
232C2×C4⋊C4—1511no—
233C2×C22⋊C4—3021no—
234C2×C42—1511no—
235#107—1511no—
236#107—1511no—
237#107—1511no—
238#107C2×D15111yescharacteristic, complemented
239C4⋊C8—1511no—
240C4⋊C8—1511no—
241#102—1511no—
242#102—1511no—
243#102—1511no—
244#102—1511no—
245#102—1511no—
246#102—1511no—
247#102C2×D15111yescharacteristic
248#102C2×D15111yescharacteristic, complemented
249C22⋊C8—1511no—
250C22⋊C8—1511no—
251C4×C8—1511no—
252C4×C8C2×D15111yescharacteristic, complemented
253C24—3021no—
254#41—6044no—
255C2×Q8—3021no—
256C2×D4—3021no—
257C2×D4—3022no—
258C2×D4—3022no—
259C2×D4—3021no—
260C2×D4—3021no—
261C2×D4—3021no—
262C2×D4—3021no—
263C2×D4—1511no—
264C2×D4—1511no—
265C2×D4C22×D15111yescharacteristic
266C2×D4C22×D15111yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—3021no—
270C22×C4—3021no—
271C22×C4—3021no—
272C22×C4—3021no—
273C22×C4—3021no—
274C22×C4—6044no—
275C22×C4—1511no—
276C22×C4—1511no—
277C22×C4—1511no—
278D8—22no—
279D8—3022no—
280D8—3022no—
281D8—3022no—
282C2×C8—1511no—
283C2×C8—1511no—
284C2×C8C22×D15111yescharacteristic
285C2×C8C22×D15111yescharacteristic
286C4⋊C4—3021no—
287C4⋊C4—3021no—
288C4⋊C4—1511no—
289C4⋊C4—1511no—
290C4⋊C4C22×D15111yescharacteristic
291C4⋊C4C22×D15111yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—3021no—
295C22⋊C4—3021no—
296C22⋊C4—3021no—
297C22⋊C4—3021no—
298C22⋊C4—3021no—
299C22⋊C4—3021no—
300C42—1511no—
301C42—1511no—
302C42—1511no—
303C42C22×D15111yescharacteristic
304C23—21no—
305C23—21no—
306C23—3024no—
307C23—3021no—
308C23—3021no—
309C23—6042no—
310C23—6042no—
311C23—1511no—
312Q8—6042no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—3024no—
317D4—3021no—
318D4—3021no—
319D4—3021no—
320D4—6042no—
321D4—6042no—
322D4—6042no—
323D4—6042no—
324D4—1512no—
325D4#1455900412yescomplemented
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—3021no—
331C2×C4—3021no—
332C2×C4—3021no—
333C2×C4—3021no—
334C2×C4—6041no—
335C2×C4—6042no—
336C2×C4—6042no—
337C2×C4—6042no—
338C2×C4—6042no—
339C2×C4—6042no—
340C2×C4—1511no—
341C2×C4—1511no—
342C2×C4—1511no—
343C2×C4—1514no—
344C2×C4D4×D15111yescharacteristic
345C2×C4D4×D15111yescharacteristic
346C2×C4C23×D15111yescharacteristic
347C8—21no—
348C8—21no—
349C8—3021no—
350C8—3021no—
351C22—22no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—3021no—
358C22—3021no—
359C22—3022no—
360C22—6048no—
361C22—6041no—
362C22—6041no—
363C22—6041no—
364C22—6041no—
365C22—6041no—
366C22—1512no—
367C22C2×D4×D15111yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—3021no—
372C4—3021no—
373C4—6041no—
374C4—6041no—
375C4—1512no—
376C4D8×D15112yes—
377C4#41×D15111yescharacteristic
378C4C2×#1455900411yescharacteristic
379C2—42no—
380C2—81no—
381C2—3022no—
382C2—6042no—
383C2—12081no—
384C2#2375272111yescharacteristic
385C2C2×D8×D15111yescharacteristic
386C2#2375300911yescharacteristic
subgroupG/H
centerC2×C4D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC4×D8×C151C2
socleC22×C151C22×D4
hypercenterC4×D8D151
hypocenterC151#3100
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #23752759C2semidirect
2. C4×D4×D151C2semidirect
3. #23752527C2semidirect
4. #23752524C2semidirect
5. #23752491C2semidirect
6. #23752490C2semidirect
7. #23752406C2semidirect
8. #23752405C2semidirect
9. #23752347C2semidirect
10. #23752344C2semidirect
11. C4×D1208C2semidirect
12. C4×#14558989C2semidirect
13. C4×#14558989C2semidirect
14. #23752263C2semidirect
15. C4×D8×C151C2semidirect
22. #18012738C22semidirect
23. #18012735C22semidirect
29. C4×D604C22semidirect
38. #18012673C22semidirect
39. #18012672C22semidirect
40. #18012672C22semidirect
41. Dic151⋊C8C22semidirect
42. Dic151⋊C8C22semidirect
44. #18012661C22semidirect
46. #18012660C22semidirect
48. #18012659C22semidirect
51. C4×C151⋊C8C22semidirect
54. C4×D4×C151C22semidirect
55. #107×C151C22semidirect
57. #102×C151C22semidirect
58. C4×C8×C151C22semidirect
121. D604#41semidirect
139. C4×D151D8semidirect
147. D4×C151#41semidirect
193. C151#3100semidirect
208. C4×D8D151semidirect
231. C4×D4C2×D151semidirect
238. #107C2×D151semidirect
248. #102C2×D151semidirect
252. C4×C8C2×D151semidirect
325. D4#14559004semidirect

Maximal subgroups

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

subgroupindex
#237527592
C4×D4×D1512
#237525272
#237525242
#237524912
#237524902
#237524062
#237524052
#237523472
#237523442
C4×D12082
C4×#145589892
#237522632
C4×D8×C1512
#3100151