Finite Group Databasebeta

← #34078608

Subgroups — #34078608

Order 19328.

526 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012763C211yesmaximal, characteristic, complemented
2C2×D8×D151C211yesmaximal, characteristic, complemented
3#23752775C211yesmaximal, characteristic, complemented
4#23752684C211yesmaximal, characteristic, complemented
5#23752428C211yesmaximal, characteristic, complemented
6#23752427C211yesmaximal, characteristic, complemented
7#23752426C211yesmaximal, characteristic, complemented
8#23752425C211yesmaximal, characteristic, complemented
9#23752406C211yesmaximal, characteristic, complemented
10#23752405C211yesmaximal, characteristic, complemented
11#23752404C211yesmaximal, characteristic, complemented
12#23752237C211yesmaximal, characteristic, complemented
13#23752215C211yesmaximal, characteristic, complemented
14#23752205C211yesmaximal, characteristic, complemented
15#459×C151C211yesmaximal, characteristic, complemented
16C2×#14559003C2211yescharacteristic
17C2×D4×D151C2211yescharacteristic
18C2×D4×D151C2211yescharacteristic
19#18012763—24no—
20C2×#14558993C2211yescharacteristic, complemented
21C2×#14558992C2211yescharacteristic, complemented
22C2×D1208C2211yescharacteristic
23C2×#14558989C2211yescharacteristic
24C2×#14558989C2211yescharacteristic
25C2×#14558989C2211yescharacteristic, complemented
26D8×D151—24no—
27C2×#14558987C2211yescharacteristic
28C2×C8×D151C2211yescharacteristic
29#18012735C2211yescharacteristic, complemented
30#18012727C2211yescharacteristic, complemented
31#18012726C2211yescharacteristic, complemented
32#18012711—21no—
33#18012711—21no—
34#18012707—21no—
35#18012707—21no—
36C4×D604C2211yescharacteristic, complemented
37D4×Dic151C2211yescharacteristic, complemented
38#18012701C2211yescharacteristic, complemented
39C4×C22⋊D151—21no—
40(C22⋊D151)⋊C4—21no—
41#18012697C2211yescharacteristic
42#18012696C2211yescharacteristic
43C2×(C2×D151)⋊C4—21no—
44C22⋊C4×D151—21no—
45C4⋊(C151⋊C8)C2211yescharacteristic, complemented
46Dic151⋊C8C2211yescharacteristic, complemented
47Dic151⋊C8C2211yescharacteristic, complemented
48#18012664C2211yescharacteristic, complemented
49#18012662C2211yescharacteristic, complemented
50#18012661C2211yescharacteristic, complemented
51#18012660C2211yescharacteristic, complemented
52#18012660C2211yescharacteristic, complemented
53#18012659C2211yescharacteristic, complemented
54C2×D8×C151C2211yescharacteristic
55C2×D8×C151C2211yescharacteristic, complemented
56#127×C151C2211yescharacteristic, complemented
57C4×D4×C151C2211yescharacteristic, complemented
58C4⋊C8×C151C2211yescharacteristic, complemented
59#102×C151C2211yescharacteristic, complemented
60#102×C151C2211yescharacteristic, complemented
61C23×D151—21no—
62C23×D151—21no—
63#14559003—22no—
64#14559003—22no—
65C2×Dic302C2311yescharacteristic
66C2×D604C2311yescharacteristic
67C2×D604C2311yescharacteristic
68C2×C22⋊D151—21no—
69C2×C22⋊D151—21no—
70C2×C22⋊D151—21no—
71C2×C22⋊D151—21no—
72C2×C22⋊D151—21no—
73D4×D151—22no—
74D4×D151—22no—
75D4×D151—22no—
76D4×D151D414yescomplemented
77C22×Dic151—21no—
78C22×Dic151—21no—
79C2×C4×D151—21no—
80C2×C4×D151—21no—
81C2×C4×D151C2311yescharacteristic
82#14558993—22no—
83#14558992—22no—
84D1208—22no—
85#14558989—22no—
86#14558989—22no—
87#14558989—22no—
88#14558987—22no—
89C2×C151⋊C8C2311yescharacteristic
90C2×C151⋊C8C2311yescharacteristic
91C8×D151—22no—
92C4⋊Dic151C2311yescharacteristic
93Dic151⋊C4D411yescharacteristic
94Dic151⋊C4D411yescharacteristic
95C22⋊Dic151—21no—
96C22⋊Dic151—21no—
97C22⋊Dic151—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—
103(C2×D151)⋊C4D411yescharacteristic
104(C2×D151)⋊C4D411yescharacteristic
105C4×Dic151—21no—
106C4×Dic151C2311yescharacteristic
107C2×D4×C151—21no—
108C2×D4×C151—21no—
109C2×D4×C151C2311yescharacteristic
110C2×D4×C151C2311yescharacteristic
111C2×D4×C151C2311yescharacteristic
112C22×C4×C151—21no—
113D8×C151—22no—
114D8×C151—22no—
115C2×C8×C151C2311yescharacteristic
116C2×C8×C151C2311yescharacteristic
117C4⋊C4×C151C2311yescharacteristic
118C22⋊C4×C151—21no—
119C42×C151C2311yescharacteristic
120C22×D151—21no—
121C22×D151—24no—
122C22×D151—21no—
123C22×D151—42no—
124C22×D151—81no—
125C22×D151—81no—
126C22×D151—81no—
127C22×D151—81no—
128C22×D151C2×D411yescharacteristic
129Dic302—21no—
130Dic302—21no—
131D604—21no—
132D604—21no—
133D604—21no—
134D604C2×D412yes—
135C22⋊D151—24no—
136C22⋊D151—42no—
137C22⋊D151—42no—
138C22⋊D151—81no—
139C22⋊D151—81no—
140C2×Dic151—21no—
141C2×Dic151—21no—
142C2×Dic151—42no—
143C2×Dic151—81no—
144C2×Dic151C2×D411yescharacteristic
145C2×Dic151C2×D411yescharacteristic
146C2×Dic151C2×D411yescharacteristic
147C4×D151—81no—
148C4×D151—81no—
149C4×D151C2×D412yes—
150C4×D151#4112yes—
151C151⋊C8—21no—
152C151⋊C8—21no—
153C23×C151—21no—
154C23×C151—21no—
155C23×C151—21no—
156D4×C151—21no—
157D4×C151—21no—
158D4×C151—21no—
159D4×C151—21no—
160D4×C151—21no—
161D4×C151—81no—
162D4×C151—81no—
163D4×C151C2×D412yes—
164C2×C4×C151—21no—
165C2×C4×C151—81no—
166C2×C4×C151C2×D411yescharacteristic
167C2×C4×C151C2×D411yescharacteristic
168C2×C4×C151C2411yescharacteristic
169C8×C151—21no—
170C8×C151—21no—
171C22×C151—22no—
172C22×C151—41no—
173C22×C151—41no—
174C22×C151—41no—
175C22×C151—41no—
176C22×C151—41no—
177C22×C151—41no—
178C22×C151—41no—
179C22×C151—41no—
180C22×C151C22×D411yescharacteristic
181C2×D151—21no—
182C2×D151—21no—
183C2×D151—22no—
184C2×D151—41no—
185C2×D151—41no—
186C2×D151—41no—
187C2×D151—41no—
188C2×D151—41no—
189C2×D151—84no—
190C2×D151—84no—
191C2×D151#12112yes—
192C4×C151—21no—
193C4×C151—21no—
194C4×C151—41no—
195C4×C151C22×D411yescharacteristic
196C4×C151C2×#4111yescharacteristic
197Dic151—21no—
198Dic151—21no—
199Dic151—41no—
200Dic151—41no—
201Dic151#12112yes—
202C2×C151—42no—
203C2×C151—81no—
204C2×C151—81no—
205C2×C151C2×#12111yescharacteristic
206C2×C151#57611yescharacteristic
207C2×C151#57611yescharacteristic
208D151—22no—
209D151—42no—
210D151—81no—
211C151#304111yescharacteristic, complemented, Sylow
212#3041—1511nomaximal, Sylow
213C2×AGL(1,ℤ/8)—1511no—
214C22×D8—1511no—
215#535—1511no—
216#518—1511no—
217#463—1511no—
218#463—1511no—
219#463—1511no—
220#463—1511no—
221#459—1511no—
222#459—1511no—
223#459—1511no—
224#459D15111yescharacteristic, complemented
225#424—1511no—
226#418—1511no—
227#416—1511no—
228C2×#41—1511no—
229C22×D4—1511no—
230C22×D4—1511no—
231AGL(1,ℤ/8)—3024no—
232C2×SD16—1511no—
233C2×SD16—1511no—
234C2×D8—3024no—
235C2×D8—1511no—
236C2×D8—1511no—
237C2×D8—1511no—
238C2×D8—1511no—
239C2×D8C2×D15111yescharacteristic
240C2×D8C2×D15111yescharacteristic, complemented
241C2×M16—1511no—
242C22×C8—1511no—
243#127—1511no—
244#127C2×D15111yescharacteristic, complemented
245#124—1511no—
246#124—1511no—
247#121—3021no—
248#121—3021no—
249#120—3021no—
250#120—3021no—
251C4×D4—3021no—
252C4×D4—3021no—
253C4×D4—1511no—
254C4×D4—1511no—
255C4×D4—1511no—
256C4×D4C2×D15111yescharacteristic, complemented
257#117—1511no—
258#117—1511no—
259C2×C22⋊C4—3021no—
260C2×C22⋊C4—3021no—
261C4⋊C8—1511no—
262C4⋊C8—1511no—
263C4⋊C8—1511no—
264C4⋊C8C2×D15111yescharacteristic, complemented
265#103—1511no—
266#103—1511no—
267#102—1511no—
268#102—1511no—
269#102—1511no—
270#102—1511no—
271#102C2×D15111yescharacteristic, complemented
272#102C2×D15111yescharacteristic, complemented
273C24—3021no—
274C24—3021no—
275#41—3022no—
276#41—3022no—
277C2×Q8—1511no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4—3021no—
281C2×D4—3022no—
282C2×D4—3022no—
283C2×D4—3022no—
284C2×D4—3021no—
285C2×D4—3021no—
286C2×D4—3021no—
287C2×D4—3021no—
288C2×D4—1514no—
289C2×D4—1511no—
290C2×D4—1511no—
291C2×D4C22×D15111yescharacteristic
292C2×D4C22×D15111yescharacteristic
293C2×D4C22×D15111yescharacteristic
294C22×C4—21no—
295C22×C4—3021no—
296C22×C4—3021no—
297C22×C4—3021no—
298C22×C4—3021no—
299C22×C4—1511no—
300SD16—3022no—
301SD16—3022no—
302D8—22no—
303D8—22no—
304D8—3022no—
305D8—3022no—
306D8—3022no—
307D8—3022no—
308M16—3022no—
309C2×C8—3022no—
310C2×C8—1511no—
311C2×C8—1511no—
312C2×C8C22×D15111yescharacteristic
313C2×C8C22×D15111yescharacteristic
314C4⋊C4—1511no—
315C4⋊C4—1511no—
316C4⋊C4—1511no—
317C4⋊C4C22×D15111yescharacteristic
318C22⋊C4—21no—
319C22⋊C4—3021no—
320C22⋊C4—3021no—
321C22⋊C4—3021no—
322C22⋊C4—3021no—
323C22⋊C4—3021no—
324C22⋊C4—3021no—
325C22⋊C4—3021no—
326C22⋊C4—3021no—
327C22⋊C4—1511no—
328C22⋊C4—1511no—
329C42—3021no—
330C42—1511no—
331C42C22×D15111yescharacteristic
332C23—21no—
333C23—21no—
334C23—21no—
335C23—3024no—
336C23—3021no—
337C23—3021no—
338C23—6042no—
339C23—1511no—
340C23—12081no—
341C23—12081no—
342C23—12081no—
343C23—12081no—
344Q8—3021no—
345Q8—3021no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—21no—
351D4—81no—
352D4—81no—
353D4—3024no—
354D4—3021no—
355D4—3021no—
356D4—3021no—
357D4—6042no—
358D4—6042no—
359D4—1512no—
360D4—12081no—
361D4—12081no—
362D4D4×D15112yes—
363C2×C4—21no—
364C2×C4—81no—
365C2×C4—3021no—
366C2×C4—3021no—
367C2×C4—6042no—
368C2×C4—1511no—
369C2×C4—1511no—
370C2×C4—1511no—
371C2×C4—1512no—
372C2×C4—1512no—
373C2×C4—12081no—
374C2×C4—12081no—
375C2×C4—12081no—
376C2×C4D4×D15111yescharacteristic
377C2×C4D4×D15111yescharacteristic
378C2×C4C23×D15111yescharacteristic
379C8—21no—
380C8—21no—
381C8—3021no—
382C8—3021no—
383C22—22no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—3021no—
393C22—3021no—
394C22—3022no—
395C22—6041no—
396C22—6041no—
397C22—6041no—
398C22—6041no—
399C22—6041no—
400C22—1512no—
401C22—12084no—
402C22—12084no—
403C22C2×D4×D15111yescharacteristic
404C4—21no—
405C4—21no—
406C4—41no—
407C4—3021no—
408C4—3021no—
409C4—6041no—
410C4—6041no—
411C4—1512no—
412C4C2×D4×D15111yescharacteristic
413C4#41×D15111yescharacteristic
414C2—42no—
415C2—81no—
416C2—81no—
417C2—3022no—
418C2—6042no—
419C2—12081no—
420C2#121×D15111yescharacteristic
421C2#2375301311yescharacteristic
422C2#2375301611yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#459×C151C2
socleC22×C151C22×D4
hypercenter#459D151
hypocenterC151#3041
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×#18012763C2semidirect
2. C2×D8×D151C2semidirect
3. #23752775C2semidirect
4. #23752684C2semidirect
5. #23752428C2semidirect
6. #23752427C2semidirect
7. #23752426C2semidirect
8. #23752425C2semidirect
9. #23752406C2semidirect
10. #23752405C2semidirect
11. #23752404C2semidirect
12. #23752237C2semidirect
13. #23752215C2semidirect
14. #23752205C2semidirect
15. #459×C151C2semidirect
20. C2×#14558993C22semidirect
21. C2×#14558992C22semidirect
25. C2×#14558989C22semidirect
29. #18012735C22semidirect
30. #18012727C22semidirect
31. #18012726C22semidirect
36. C4×D604C22semidirect
37. D4×Dic151C22semidirect
38. #18012701C22semidirect
45. C4⋊(C151⋊C8)C22semidirect
46. Dic151⋊C8C22semidirect
47. Dic151⋊C8C22semidirect
48. #18012664C22semidirect
49. #18012662C22semidirect
50. #18012661C22semidirect
51. #18012660C22semidirect
52. #18012660C22semidirect
53. #18012659C22semidirect
55. C2×D8×C151C22semidirect
56. #127×C151C22semidirect
57. C4×D4×C151C22semidirect
58. C4⋊C8×C151C22semidirect
59. #102×C151C22semidirect
60. #102×C151C22semidirect
76. D4×D151D4semidirect
211. C151#3041semidirect
224. #459D151semidirect
240. C2×D8C2×D151semidirect
244. #127C2×D151semidirect
256. C4×D4C2×D151semidirect
264. C4⋊C8C2×D151semidirect
271. #102C2×D151semidirect
272. #102C2×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127632
C2×D8×D1512
#237527752
#237526842
#237524282
#237524272
#237524262
#237524252
#237524062
#237524052
#237524042
#237522372
#237522152
#237522052
#459×C1512
#3041151