Finite Group Databasebeta

← #34080601

Subgroups — #34080601

Order 19328.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012765C211yesmaximal, characteristic, complemented
2C22×#14558992C211yesmaximal, characteristic, complemented
3#23752871C211yesmaximal, characteristic, complemented
4#23752599C211yesmaximal, characteristic, complemented
5#23752456C211yesmaximal, characteristic, complemented
6#23752446C211yesmaximal, characteristic, complemented
7#23752427C211yesmaximal, characteristic, complemented
8#23752409C211yesmaximal, characteristic, complemented
9#23752363C211yesmaximal, characteristic, complemented
10#23752355C211yesmaximal, characteristic, complemented
11#23752350C211yesmaximal, characteristic, complemented
12#23752346C211yesmaximal, characteristic, complemented
13#23752312C211yesmaximal, characteristic, complemented
14#23752284C211yesmaximal, characteristic, complemented
15D42×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic, complemented
17C22×Dic302C2211yescharacteristic, complemented
18#18012765—24no—
19C2×#14558992—24no—
20C2×#14558992C2211yescharacteristic
21C2×#14558992C2211yescharacteristic
22C2×#14558992C2211yescharacteristic, complemented
23C2×#14558992C2211yescharacteristic, complemented
24C2×#14558992C2211yescharacteristic, complemented
25C2×#14558992C2211yescharacteristic, complemented
26C2×#14558989C2211yescharacteristic
27C2×#14558989C2211yescharacteristic, complemented
28C2×#14558989C2211yescharacteristic, complemented
29C2×#14558988C2211yescharacteristic, complemented
30C22×C151⋊C8C2211yescharacteristic, complemented
31#18012727C2211yescharacteristic, complemented
32#18012725—21no—
33#18012718C2211yescharacteristic, complemented
34#18012717—21no—
35#18012713C2211yescharacteristic, complemented
36#18012711—21no—
37C4×Dic302C2211yescharacteristic, complemented
38(C22⋊D151)⋊C4—21no—
39#18012672C2211yescharacteristic, complemented
40C4⋊(C151⋊C8)C2211yescharacteristic, complemented
41#18012662C2211yescharacteristic, complemented
42#18012662C2211yescharacteristic, complemented
43#18012660C2211yescharacteristic
44#18012660C2211yescharacteristic, complemented
45#18012660C2211yescharacteristic, complemented
46#18012659C2211yescharacteristic, complemented
47C22⋊(C151⋊C8)C2211yescharacteristic, complemented
48C22⋊(C151⋊C8)C2211yescharacteristic, complemented
49#18012650C2211yescharacteristic, complemented
50C22×D4×C151—21no—
51C22×D4×C151C2211yescharacteristic
52C22×D4×C151C2211yescharacteristic
53#127×C151C2211yescharacteristic
54#121×C151—21no—
55#121×C151C2211yescharacteristic
56#121×C151C2211yescharacteristic
57#120×C151—21no—
58#120×C151—21no—
59C4×D4×C151C2211yescharacteristic
60C4×D4×C151C2211yescharacteristic
61#14559004—22no—
62#14559004—41no—
63C2×Dic302—22no—
64C2×Dic302—21no—
65C2×Dic302—41no—
66C2×Dic302C2311yescharacteristic
67C2×Dic302C2311yescharacteristic
68C2×D604C2311yescharacteristic
69C2×C22⋊D151—21no—
70C2×C22⋊D151—21no—
71C22×Dic151—21no—
72C2×C4×D151—21no—
73#14558992—22no—
74#14558992—22no—
75#14558992—22no—
76#14558992—22no—
77#14558992—41no—
78#14558992D414yescomplemented
79#14558989—22no—
80#14558989—22no—
81#14558989—41no—
82#14558988—22no—
83C2×C151⋊C8—22no—
84C2×C151⋊C8C2311yescharacteristic
85C2×C151⋊C8C2311yescharacteristic
86C2×C151⋊C8C2311yescharacteristic
87C2×C151⋊C8C2311yescharacteristic
88C4⋊Dic151C2311yescharacteristic
89Dic151⋊C4—21no—
90Dic151⋊C4—21no—
91C22⋊Dic151—21no—
92(C2×D151)⋊C4—21no—
93(C2×D151)⋊C4—21no—
94(C2×D151)⋊C4—21no—
95C4×Dic151—21no—
96C24×C151—21no—
97C24×C151—21no—
98C2×D4×C151—22no—
99C2×D4×C151—22no—
100C2×D4×C151—21no—
101C2×D4×C151—21no—
102C2×D4×C151—21no—
103C2×D4×C151—21no—
104C2×D4×C151—21no—
105C2×D4×C151—21no—
106C2×D4×C151—41no—
107C2×D4×C151—41no—
108C2×D4×C151—44no—
109C2×D4×C151D411yescharacteristic
110C2×D4×C151C2311yescharacteristic
111C2×D4×C151C2311yescharacteristic
112C2×D4×C151C2311yescharacteristic
113C22×C4×C151—21no—
114C22×C4×C151C2311yescharacteristic
115C22×C4×C151C2311yescharacteristic
116C4⋊C4×C151D411yescharacteristic
117C4⋊C4×C151C2311yescharacteristic
118C22⋊C4×C151—21no—
119C22⋊C4×C151—21no—
120C22⋊C4×C151—21no—
121C22⋊C4×C151D411yescharacteristic
122C22⋊C4×C151D411yescharacteristic
123C42×C151C2311yescharacteristic
124C22×D151—21no—
125Dic302—21no—
126Dic302—21no—
127Dic302—21no—
128Dic302—42no—
129Dic302C2×D412yescomplemented
130D604—21no—
131D604—21no—
132C22⋊D151—42no—
133C22⋊D151—42no—
134C2×Dic151—21no—
135C2×Dic151—21no—
136C2×Dic151—21no—
137C2×Dic151—42no—
138C4×D151—42no—
139C151⋊C8—21no—
140C151⋊C8—21no—
141C151⋊C8—21no—
142C151⋊C8C2×D412yescomplemented
143C23×C151—21no—
144C23×C151—21no—
145C23×C151—21no—
146C23×C151—42no—
147C23×C151—42no—
148C23×C151—42no—
149C23×C151—42no—
150C23×C151—81no—
151C23×C151—81no—
152C23×C151C2×D411yescharacteristic
153C23×C151C2×D411yescharacteristic
154D4×C151—22no—
155D4×C151—21no—
156D4×C151—21no—
157D4×C151—21no—
158D4×C151—21no—
159D4×C151—21no—
160D4×C151—42no—
161D4×C151—42no—
162D4×C151—42no—
163D4×C151—42no—
164D4×C151—42no—
165D4×C151—81no—
166D4×C151C2×D412yes—
167C2×C4×C151—21no—
168C2×C4×C151—21no—
169C2×C4×C151—21no—
170C2×C4×C151—21no—
171C2×C4×C151—21no—
172C2×C4×C151—42no—
173C2×C4×C151C2×D411yescharacteristic
174C2×C4×C151C2×D411yescharacteristic
175C2×C4×C151C2×D411yescharacteristic
176C2×C4×C151C2×D411yescharacteristic
177C2×C4×C151C2411yescharacteristic
178C22×C151—21no—
179C22×C151—21no—
180C22×C151—21no—
181C22×C151—22no—
182C22×C151—21no—
183C22×C151—21no—
184C22×C151—41no—
185C22×C151—41no—
186C22×C151—41no—
187C22×C151—41no—
188C22×C151—41no—
189C22×C151—41no—
190C22×C151—41no—
191C22×C151—41no—
192C22×C151—84no—
193C22×C151—84no—
194C22×C151AGL(1,ℤ/8)12yescomplemented
195C22×C151C22×D411yescharacteristic
196C2×D151—41no—
197C2×D151—41no—
198C2×D151—41no—
199C4×C151—21no—
200C4×C151—21no—
201C4×C151—21no—
202C4×C151—21no—
203C4×C151—41no—
204C4×C151C22×D411yescharacteristic
205C4×C151H(5,𝔽2)11yescharacteristic
206Dic151—22no—
207Dic151—41no—
208Dic151—41no—
209C2×C151—22no—
210C2×C151—41no—
211C2×C151—42no—
212C2×C151—81no—
213C2×C151—81no—
214C2×C151D4211yescharacteristic
215C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
216C2×C151#57711yescharacteristic
217D151—81no—
218C151#326511yescharacteristic, complemented, Sylow
219#3265—1511nomaximal, Sylow
220C2×AGL(1,ℤ/8)—1511no—
221C22×SD16—1511no—
222#548—1511no—
223D42D15111yescharacteristic, complemented
224#496—1511no—
225#468—1511no—
226#466—1511no—
227#463—1511no—
228#460—1511no—
229#450—1511no—
230#449—1511no—
231#448—1511no—
232#447—1511no—
233#440—1511no—
234#435—1511no—
235C2×#41—1511no—
236C22×Q8—1511no—
237C22×D4—21no—
238C22×D4C2×D15111yescharacteristic
239C22×D4C2×D15111yescharacteristic
240AGL(1,ℤ/8)—3024no—
241C2×SD16—3024no—
242C2×SD16—1511no—
243C2×SD16—1511no—
244C2×SD16—1511no—
245C2×SD16—1511no—
246C2×SD16—1511no—
247C2×SD16—1511no—
248C2×D8—1511no—
249C2×D8—1511no—
250C2×D8—1511no—
251C2×M16—1511no—
252C22×C8—1511no—
253#127C2×D15111yescharacteristic
254#124—3021no—
255#124—1511no—
256C22⋊Q8—3021no—
257C22⋊Q8—1511no—
258#121—21no—
259#121—3021no—
260#121—1511no—
261#121C2×D15111yescharacteristic
262#121C2×D15111yescharacteristic
263#120—21no—
264#120—21no—
265C4×Q8—1511no—
266C4×D4—3021no—
267C4×D4C2×D15111yescharacteristic
268C4×D4C2×D15111yescharacteristic
269#107—1511no—
270C4⋊C8—1511no—
271#103—1511no—
272#103—1511no—
273#102—1511no—
274#102—1511no—
275#102—1511no—
276#102—1511no—
277C22⋊C8—1511no—
278C22⋊C8—1511no—
279#97—1511no—
280C24—21no—
281C24—21no—
282#41—3022no—
283#41—6041no—
284C2×Q8—3022no—
285C2×Q8—3021no—
286C2×Q8—6041no—
287C2×Q8—1511no—
288C2×Q8—1511no—
289C2×D4—22no—
290C2×D4—22no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—44no—
300C2×D4—3021no—
301C2×D4—3021no—
302C2×D4—1511no—
303C2×D4C22⋊D15111yescharacteristic
304C2×D4C22×D15111yescharacteristic
305C2×D4C22×D15111yescharacteristic
306C2×D4C22×D15111yescharacteristic
307C22×C4—21no—
308C22×C4—3021no—
309C22×C4—3021no—
310C22×C4C22×D15111yescharacteristic
311C22×C4C22×D15111yescharacteristic
312SD16—3022no—
313SD16—3022no—
314SD16—3022no—
315SD16—3022no—
316SD16—6041no—
317SD16—1514no—
318D8—3022no—
319D8—3022no—
320D8—6041no—
321M16—3022no—
322C2×C8—3022no—
323C2×C8—1511no—
324C2×C8—1511no—
325C2×C8—1511no—
326C2×C8—1511no—
327C4⋊C4—3021no—
328C4⋊C4—3021no—
329C4⋊C4—1511no—
330C4⋊C4C22⋊D15111yescharacteristic
331C4⋊C4C22×D15111yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—21no—
335C22⋊C4—3021no—
336C22⋊C4—3021no—
337C22⋊C4—3021no—
338C22⋊C4—3021no—
339C22⋊C4C22⋊D15111yescharacteristic
340C22⋊C4C22⋊D15111yescharacteristic
341C42—3021no—
342C42C22×D15111yescharacteristic
343C23—21no—
344C23—21no—
345C23—21no—
346C23—42no—
347C23—42no—
348C23—42no—
349C23—42no—
350C23—81no—
351C23—81no—
352C23—3021no—
353C23C2×C22⋊D15111yescharacteristic
354C23C2×C22⋊D15111yescharacteristic
355Q8—3021no—
356Q8—3021no—
357Q8—3021no—
358Q8—6042no—
359Q8—1512no—
360D4—22no—
361D4—21no—
362D4—21no—
363D4—21no—
364D4—21no—
365D4—21no—
366D4—42no—
367D4—42no—
368D4—42no—
369D4—42no—
370D4—42no—
371D4—81no—
372D4—3021no—
373D4—3021no—
374D4—6042no—
375D4—6042no—
376D4D4×D15112yes—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—42no—
383C2×C4—3021no—
384C2×C4—3021no—
385C2×C4—3021no—
386C2×C4—6042no—
387C2×C4—6042no—
388C2×C4C2×C22⋊D15111yescharacteristic
389C2×C4C2×C22⋊D15111yescharacteristic
390C2×C4C2×C22⋊D15111yescharacteristic
391C2×C4C2×C22⋊D15111yescharacteristic
392C2×C4C23×D15111yescharacteristic
393C8—3021no—
394C8—3021no—
395C8—3021no—
396C8—1512no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—22no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—84no—
412C22—84no—
413C22—6041no—
414C22—6041no—
415C22—6041no—
416C22#1801276512yescomplemented
417C22C22×C22⋊D15111yescharacteristic
418C4—21no—
419C4—21no—
420C4—21no—
421C4—21no—
422C4—41no—
423C4—3022no—
424C4—6041no—
425C4—6041no—
426C4C2×D4×D15111yescharacteristic
427C4#1801278411yescharacteristic
428C2—22no—
429C2—41no—
430C2—42no—
431C2—81no—
432C2—81no—
433C2—12081no—
434C2D4×C22⋊D15111yescharacteristic
435C2C2×#1801276511yescharacteristic
436C2#2375302311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingD42×C151C2
socleC22×C151C22×D4
hypercenterD42D151
hypocenterC151#3265
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. C2×#18012765C2semidirect
2. C22×#14558992C2semidirect
3. #23752871C2semidirect
4. #23752599C2semidirect
5. #23752456C2semidirect
6. #23752446C2semidirect
7. #23752427C2semidirect
8. #23752409C2semidirect
9. #23752363C2semidirect
10. #23752355C2semidirect
11. #23752350C2semidirect
12. #23752346C2semidirect
13. #23752312C2semidirect
14. #23752284C2semidirect
15. D42×C151C2semidirect
16. C2×#14559004C22semidirect
17. C22×Dic302C22semidirect
22. C2×#14558992C22semidirect
23. C2×#14558992C22semidirect
24. C2×#14558992C22semidirect
25. C2×#14558992C22semidirect
27. C2×#14558989C22semidirect
28. C2×#14558989C22semidirect
29. C2×#14558988C22semidirect
30. C22×C151⋊C8C22semidirect
31. #18012727C22semidirect
33. #18012718C22semidirect
35. #18012713C22semidirect
37. C4×Dic302C22semidirect
39. #18012672C22semidirect
40. C4⋊(C151⋊C8)C22semidirect
41. #18012662C22semidirect
42. #18012662C22semidirect
44. #18012660C22semidirect
45. #18012660C22semidirect
46. #18012659C22semidirect
47. C22⋊(C151⋊C8)C22semidirect
48. C22⋊(C151⋊C8)C22semidirect
49. #18012650C22semidirect
78. #14558992D4semidirect
129. Dic302C2×D4semidirect
142. C151⋊C8C2×D4semidirect
194. C22×C151AGL(1,ℤ/8)semidirect
218. C151#3265semidirect
223. D42D151semidirect
416. C22#18012765semidirect

Maximal subgroups

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

subgroupindex
C2×#180127652
C22×#145589922
#237528712
#237525992
#237524562
#237524462
#237524272
#237524092
#237523632
#237523552
#237523502
#237523462
#237523122
#237522842
D42×C1512
#3265151