Finite Group Databasebeta

← #34079974

Subgroups — #34079974

Order 19328.

442 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752781C211yesmaximal, characteristic, complemented
2#23752778C211yesmaximal, characteristic, complemented
3#23752539C211yesmaximal, characteristic, complemented
4#23752538C211yesmaximal, characteristic, complemented
5#23752536C211yesmaximal, characteristic, complemented
6#23752466C211yesmaximal, characteristic, complemented
7#23752464C211yesmaximal, characteristic, complemented
8#23752449C211yesmaximal, characteristic, complemented
9#23752447C211yesmaximal, characteristic, complemented
10#23752348C211yesmaximal, characteristic, complemented
11#23752347C211yesmaximal, characteristic, complemented
12#23752347C211yesmaximal, characteristic, complemented
13#23752345C211yesmaximal, characteristic, complemented
14#23752177C211yesmaximal, characteristic, complemented
15#482×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C22×D604C2211yescharacteristic, complemented
18C2×D4×D151C2211yescharacteristic, complemented
19C2×D1208C2211yescharacteristic
20C2×D1208C2211yescharacteristic
21C2×#14558989C2211yescharacteristic
22C2×#14558989C2211yescharacteristic
23C2×#14558987C2211yescharacteristic, complemented
24C2×C8×D151C2211yescharacteristic, complemented
25#18012736—21no—
26#18012735—21no—
27#18012727—21no—
28#18012725—21no—
29#18012714C2211yescharacteristic
30#18012714C2211yescharacteristic
31#18012714C2211yescharacteristic, complemented
32#18012714C2211yescharacteristic, complemented
33#18012714C2211yescharacteristic, complemented
34#18012713C2211yescharacteristic
35#18012710C2211yescharacteristic, complemented
36#18012709—21no—
37#18012709—21no—
38#18012709—21no—
39#18012707—21no—
40#18012697C2211yescharacteristic, complemented
41#18012672C2211yescharacteristic, complemented
42#18012670C2211yescharacteristic, complemented
43#18012661C2211yescharacteristic, complemented
44#18012661C2211yescharacteristic, complemented
45#18012659C2211yescharacteristic, complemented
46#18012659C2211yescharacteristic, complemented
47#18012659C2211yescharacteristic, complemented
48#18012659C2211yescharacteristic, complemented
49C22⋊(C151⋊C8)C2211yescharacteristic, complemented
50(C2×D151)⋊C8C2211yescharacteristic, complemented
51(C2×D151)⋊C8C2211yescharacteristic, complemented
52#121×C151C2211yescharacteristic
53#117×C151C2211yescharacteristic, complemented
54#107×C151C2211yescharacteristic, complemented
55#106×C151C2211yescharacteristic, complemented
56#102×C151C2211yescharacteristic, complemented
57#102×C151C2211yescharacteristic, complemented
58C22⋊C8×C151C2211yescharacteristic, complemented
59C23×D151—21no—
60C23×D151—21no—
61#14559004—41no—
62#14559004—41no—
63C2×Dic302D411yescharacteristic
64C2×D604—21no—
65C2×D604—21no—
66C2×D604—21no—
67C2×D604—21no—
68C2×D604—21no—
69C2×D604—21no—
70C2×D604—41no—
71C2×D604—41no—
72C2×D604D411yescharacteristic
73C2×D604C2311yescharacteristic
74C2×D604C2311yescharacteristic
75C2×D604C2311yescharacteristic
76C2×C22⋊D151—21no—
77C2×C22⋊D151—21no—
78C2×C22⋊D151—21no—
79C2×C22⋊D151D411yescharacteristic
80C2×C22⋊D151D411yescharacteristic
81D4×D151—41no—
82D4×D151—41no—
83C2×C4×D151C2311yescharacteristic
84C2×C4×D151C2311yescharacteristic
85D1208—41no—
86D1208—41no—
87#14558989—41no—
88#14558989—41no—
89#14558987—41no—
90C2×C151⋊C8C2311yescharacteristic
91C2×C151⋊C8C2311yescharacteristic
92C8×D151—41no—
93C4⋊Dic151C2311yescharacteristic
94C22⋊Dic151—21no—
95(C2×D151)⋊C4—21no—
96(C2×D151)⋊C4—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—
102C4×Dic151—21no—
103C2×D4×C151—21no—
104C2×D4×C151C2311yescharacteristic
105C22×C4×C151C2311yescharacteristic
106C2×C8×C151C2311yescharacteristic
107C2×C8×C151C2311yescharacteristic
108C4⋊C4×C151C2311yescharacteristic
109C4⋊C4×C151C2311yescharacteristic
110C4⋊C4×C151C2311yescharacteristic
111C22⋊C4×C151—21no—
112C22⋊C4×C151—21no—
113C42×C151—21no—
114C22×D151—21no—
115C22×D151—21no—
116C22×D151—21no—
117C22×D151—42no—
118C22×D151—42no—
119C22×D151—81no—
120C22×D151—81no—
121C22×D151—81no—
122C22×D151—81no—
123C22×D151C2×D411yescharacteristic
124C22×D151C2×D411yescharacteristic
125Dic302—41no—
126D604—21no—
127D604—21no—
128D604—21no—
129D604—21no—
130D604—21no—
131D604—21no—
132D604—41no—
133D604—42no—
134D604—81no—
135D604—81no—
136D604—81no—
137D604—81no—
138D604—81no—
139C22⋊D151—41no—
140C22⋊D151—41no—
141C22⋊D151—42no—
142C22⋊D151—81no—
143C22⋊D151—81no—
144C2×Dic151—21no—
145C2×Dic151C2×D411yescharacteristic
146C2×Dic151C2×D411yescharacteristic
147C4×D151—21no—
148C4×D151—21no—
149C4×D151—21no—
150C4×D151—21no—
151C151⋊C8—21no—
152C151⋊C8—21no—
153C23×C151—21no—
154C23×C151C2×D411yescharacteristic
155D4×C151—21no—
156D4×C151—21no—
157D4×C151—81no—
158C2×C4×C151—21no—
159C2×C4×C151—21no—
160C2×C4×C151—21no—
161C2×C4×C151—21no—
162C2×C4×C151—21no—
163C2×C4×C151C2×D411yescharacteristic
164C2×C4×C151C2411yescharacteristic
165C8×C151—21no—
166C8×C151—21no—
167C22×C151—21no—
168C22×C151—21no—
169C22×C151—21no—
170C22×C151—41no—
171C22×C151—41no—
172C22×C151—41no—
173C22×C151C22×D411yescharacteristic
174C2×D151—21no—
175C2×D151—21no—
176C2×D151—21no—
177C2×D151—21no—
178C2×D151—21no—
179C2×D151—21no—
180C2×D151—41no—
181C2×D151—41no—
182C2×D151—41no—
183C2×D151—41no—
184C2×D151—41no—
185C2×D151—41no—
186C2×D151—41no—
187C2×D151—41no—
188C2×D151—41no—
189C2×D151—84no—
190C2×D151—84no—
191C4×C151—21no—
192C4×C151—41no—
193C4×C151—41no—
194C4×C151—41no—
195C4×C151H(5,𝔽2)11yescharacteristic
196C4×C151H(5,𝔽2)11yescharacteristic
197Dic151—21no—
198Dic151—21no—
199Dic151—41no—
200C2×C151—41no—
201C2×C151—81no—
202C2×C151#53411yescharacteristic
203C2×C151#57611yescharacteristic
204C2×C151#57611yescharacteristic
205D151—41no—
206D151—41no—
207D151—81no—
208D151—81no—
209D151—81no—
210C151#319911yescharacteristic, complemented, Sylow
211#3199—1511nomaximal, Sylow
212#535—1511no—
213#535—1511no—
214#482—1511no—
215#482—1511no—
216#482—1511no—
217#482D15111yescharacteristic, complemented
218#469—1511no—
219#469—1511no—
220#466—1511no—
221#466—1511no—
222#447—1511no—
223#447—1511no—
224#447—1511no—
225#447—1511no—
226#408—1511no—
227C2×#41—1511no—
228C22×D4—1511no—
229C22×D4—1511no—
230C2×D8—1511no—
231C2×D8—1511no—
232C2×D8—1511no—
233C2×D8—1511no—
234C2×M16—1511no—
235C22×C8—1511no—
236#127—3021no—
237#127—3021no—
238#124—3021no—
239#124—3021no—
240#121—1511no—
241#121—1511no—
242#121—1511no—
243#121—1511no—
244#121—1511no—
245#121—1511no—
246#121—1511no—
247#121C2×D15111yescharacteristic
248#120—3021no—
249#120—3021no—
250#120—3021no—
251#120—3021no—
252#117—1511no—
253#117C2×D15111yescharacteristic, complemented
254#107—1511no—
255#107C2×D15111yescharacteristic, complemented
256#106—1511no—
257#106C2×D15111yescharacteristic, complemented
258#102—1511no—
259#102—1511no—
260#102—1511no—
261#102—1511no—
262#102—1511no—
263#102—1511no—
264#102C2×D15111yescharacteristic, complemented
265#102C2×D15111yescharacteristic, complemented
266C22⋊C8—1511no—
267C22⋊C8—1511no—
268C22⋊C8—1511no—
269C22⋊C8C2×D15111yescharacteristic, complemented
270C24—3021no—
271C24—3021no—
272#41—6041no—
273#41—6041no—
274C2×Q8—1511no—
275C2×D4—21no—
276C2×D4—3021no—
277C2×D4—3021no—
278C2×D4—3021no—
279C2×D4—3021no—
280C2×D4—3021no—
281C2×D4—3021no—
282C2×D4—3021no—
283C2×D4—3021no—
284C2×D4—3021no—
285C2×D4—6041no—
286C2×D4—6041no—
287C2×D4—6041no—
288C2×D4—6041no—
289C2×D4—1511no—
290C2×D4—1511no—
291C2×D4—1511no—
292C2×D4—1511no—
293C2×D4—1511no—
294C2×D4—1511no—
295C2×D4C22×D15111yescharacteristic
296C22×C4—1511no—
297C22×C4—1511no—
298C22×C4C22×D15111yescharacteristic
299D8—6041no—
300D8—6041no—
301D8—6041no—
302D8—6041no—
303M16—6041no—
304C2×C8—6041no—
305C2×C8—1511no—
306C2×C8—1511no—
307C2×C8C22×D15111yescharacteristic
308C2×C8C22×D15111yescharacteristic
309C4⋊C4—1511no—
310C4⋊C4C22×D15111yescharacteristic
311C4⋊C4C22×D15111yescharacteristic
312C4⋊C4C22×D15111yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—3021no—
316C22⋊C4—3021no—
317C22⋊C4—3021no—
318C22⋊C4—3021no—
319C22⋊C4—3021no—
320C22⋊C4—3021no—
321C22⋊C4—3021no—
322C22⋊C4—3021no—
323C42—21no—
324C42—3021no—
325C23—21no—
326C23—3021no—
327C23—3021no—
328C23—3021no—
329C23—6042no—
330C23—6042no—
331C23—1511no—
332C23—1511no—
333C23—12081no—
334C23—12081no—
335C23—12081no—
336C23—12081no—
337C23D4×D15111yescharacteristic
338Q8—6041no—
339D4—21no—
340D4—21no—
341D4—81no—
342D4—3021no—
343D4—3021no—
344D4—3021no—
345D4—3021no—
346D4—3021no—
347D4—3021no—
348D4—6041no—
349D4—6042no—
350D4—6041no—
351D4—6041no—
352D4—6042no—
353D4—12081no—
354D4—12081no—
355D4—12081no—
356D4—12081no—
357D4—12081no—
358D4—12081no—
359D4—12081no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—3021no—
366C2×C4—3021no—
367C2×C4—3021no—
368C2×C4—3021no—
369C2×C4—3021no—
370C2×C4—1511no—
371C2×C4—1511no—
372C2×C4D4×D15111yescharacteristic
373C2×C4C23×D15111yescharacteristic
374C8—21no—
375C8—21no—
376C8—3021no—
377C8—3021no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—3021no—
385C22—3021no—
386C22—3021no—
387C22—3021no—
388C22—3021no—
389C22—3021no—
390C22—6041no—
391C22—6041no—
392C22—6041no—
393C22—6041no—
394C22—6041no—
395C22—6041no—
396C22—6041no—
397C22—6041no—
398C22—6041no—
399C22—12084no—
400C22—12084no—
401C22C2×D4×D15111yescharacteristic
402C4—21no—
403C4—41no—
404C4—41no—
405C4—41no—
406C4—3021no—
407C4—3021no—
408C4—6041no—
409C4#1801278511yescharacteristic
410C4#1801278511yescharacteristic
411C2—41no—
412C2—81no—
413C2—6041no—
414C2—6041no—
415C2—12081no—
416C2—12081no—
417C2—12081no—
418C2#2375277311yescharacteristic
419C2#2375301411yescharacteristic
420C2#2375301611yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#482×C151C2
socleC22×C151C22×D4
hypercenter#482D151
hypocenterC151#3199
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #23752781C2semidirect
2. #23752778C2semidirect
3. #23752539C2semidirect
4. #23752538C2semidirect
5. #23752536C2semidirect
6. #23752466C2semidirect
7. #23752464C2semidirect
8. #23752449C2semidirect
9. #23752447C2semidirect
10. #23752348C2semidirect
11. #23752347C2semidirect
12. #23752347C2semidirect
13. #23752345C2semidirect
14. #23752177C2semidirect
15. #482×C151C2semidirect
17. C22×D604C22semidirect
18. C2×D4×D151C22semidirect
23. C2×#14558987C22semidirect
24. C2×C8×D151C22semidirect
31. #18012714C22semidirect
32. #18012714C22semidirect
33. #18012714C22semidirect
35. #18012710C22semidirect
40. #18012697C22semidirect
41. #18012672C22semidirect
42. #18012670C22semidirect
43. #18012661C22semidirect
44. #18012661C22semidirect
45. #18012659C22semidirect
46. #18012659C22semidirect
47. #18012659C22semidirect
48. #18012659C22semidirect
49. C22⋊(C151⋊C8)C22semidirect
50. (C2×D151)⋊C8C22semidirect
51. (C2×D151)⋊C8C22semidirect
53. #117×C151C22semidirect
54. #107×C151C22semidirect
55. #106×C151C22semidirect
56. #102×C151C22semidirect
57. #102×C151C22semidirect
58. C22⋊C8×C151C22semidirect
210. C151#3199semidirect
217. #482D151semidirect
253. #117C2×D151semidirect
255. #107C2×D151semidirect
257. #106C2×D151semidirect
264. #102C2×D151semidirect
265. #102C2×D151semidirect
269. C22⋊C8C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527812
#237527782
#237525392
#237525382
#237525362
#237524662
#237524642
#237524492
#237524472
#237523482
#237523472
#237523452
#237521772
#482×C1512
#3199151