Finite Group Databasebeta

← #34080656

Subgroups — #34080656

Order 19328.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012763C211yesmaximal, characteristic, complemented
2C2×#18012758C211yesmaximal, characteristic, complemented
3#23752882C211yesmaximal, characteristic, complemented
4#23752857C211yesmaximal, characteristic, complemented
5#23752599C211yesmaximal, characteristic, complemented
6#23752457C211yesmaximal, characteristic, complemented
7#23752447C211yesmaximal, characteristic, complemented
8#23752435C211yesmaximal, characteristic, complemented
9#23752375C211yesmaximal, characteristic, complemented
10#23752358C211yesmaximal, characteristic, complemented
11#23752354C211yesmaximal, characteristic, complemented
12#23752344C211yesmaximal, characteristic, complemented
13#23752312C211yesmaximal, characteristic, complemented
14#23752282C211yesmaximal, characteristic, complemented
15#459×C151C211yesmaximal, characteristic, complemented
16C2×#14559003C2211yescharacteristic
17C2×#14559003C2211yescharacteristic
18C2×#14559003C2211yescharacteristic, complemented
19C2×D4×D151C2211yescharacteristic
20#18012763—24no—
21#18012758—24no—
22C2×Dic604C2211yescharacteristic, complemented
23C2×#14558993C2211yescharacteristic
24C2×#14558992C2211yescharacteristic
25C2×#14558992C2211yescharacteristic, complemented
26C2×#14558992C2211yescharacteristic, complemented
27C2×#14558989C2211yescharacteristic
28C2×#14558989C2211yescharacteristic
29C2×#14558987C2211yescharacteristic
30C2×C8×D151C2211yescharacteristic, complemented
31#18012735—21no—
32#18012727C2211yescharacteristic
33#18012723—21no—
34#18012719C2211yescharacteristic
35#18012714C2211yescharacteristic
36#18012713—21no—
37#18012711—21no—
38#18012711—21no—
39#18012710C2211yescharacteristic
40#18012710C2211yescharacteristic, complemented
41#18012709—21no—
42C4×Dic302C2211yescharacteristic, complemented
43C4×D604C2211yescharacteristic
44D4×Dic151—21no—
45C2×(C2×D151)⋊C4—21no—
46#18012672C2211yescharacteristic, complemented
47#18012664C2211yescharacteristic, complemented
48#18012662C2211yescharacteristic, complemented
49#18012661C2211yescharacteristic
50#18012660C2211yescharacteristic
51(C2×D151)⋊C8C2211yescharacteristic
52(C2×D151)⋊C8C2211yescharacteristic, complemented
53#18012650C2211yescharacteristic, complemented
54C2×D8×C151C2211yescharacteristic
55C2×D8×C151C2211yescharacteristic
56#127×C151C2211yescharacteristic, complemented
57C4×D4×C151C2211yescharacteristic
58C4⋊C8×C151C2211yescharacteristic, complemented
59#102×C151C2211yescharacteristic, complemented
60#102×C151C2211yescharacteristic, complemented
61C23×D151—21no—
62#14559003—22no—
63#14559003—22no—
64#14559003—22no—
65#14559003—41no—
66#14559003—41no—
67#14559003—41no—
68C2×Dic302C2311yescharacteristic
69C2×Dic302C2311yescharacteristic
70C2×D604—21no—
71C2×D604D411yescharacteristic
72C2×D604C2311yescharacteristic
73C2×C22⋊D151—21no—
74C2×C22⋊D151—21no—
75C2×C22⋊D151—21no—
76C2×C22⋊D151—21no—
77C2×C22⋊D151—21no—
78C2×C22⋊D151—21no—
79D4×D151—22no—
80D4×D151—41no—
81C22×Dic151—21no—
82C22×Dic151—21no—
83C22×Dic151—21no—
84C2×C4×D151C2311yescharacteristic
85C2×C4×D151C2311yescharacteristic
86Dic604—22no—
87#14558993—22no—
88#14558992—22no—
89#14558992—41no—
90#14558992D414yescomplemented
91#14558989—22no—
92#14558989—41no—
93#14558987—22no—
94C2×C151⋊C8C2311yescharacteristic
95C2×C151⋊C8C2311yescharacteristic
96C8×D151—22no—
97C4⋊Dic151—21no—
98C4⋊Dic151D411yescharacteristic
99C4⋊Dic151C2311yescharacteristic
100Dic151⋊C4—21no—
101C22⋊Dic151—21no—
102C22⋊Dic151—21no—
103(C2×D151)⋊C4—21no—
104(C2×D151)⋊C4—21no—
105(C2×D151)⋊C4—21no—
106(C2×D151)⋊C4—21no—
107(C2×D151)⋊C4D411yescharacteristic
108(C2×D151)⋊C4D411yescharacteristic
109C4×Dic151—21no—
110C2×D4×C151—21no—
111C2×D4×C151—21no—
112C2×D4×C151C2311yescharacteristic
113C2×D4×C151C2311yescharacteristic
114C2×D4×C151C2311yescharacteristic
115C22×C4×C151—21no—
116D8×C151—22no—
117D8×C151—22no—
118C2×C8×C151C2311yescharacteristic
119C2×C8×C151C2311yescharacteristic
120C4⋊C4×C151C2311yescharacteristic
121C22⋊C4×C151—21no—
122C42×C151C2311yescharacteristic
123C22×D151—21no—
124C22×D151—42no—
125C22×D151—42no—
126C22×D151—81no—
127C22×D151C2×D411yescharacteristic
128C22×D151C2×D411yescharacteristic
129Dic302—21no—
130Dic302—21no—
131Dic302—21no—
132Dic302C2×D412yes—
133D604—21no—
134D604—21no—
135D604—41no—
136D604—81no—
137C22⋊D151—42no—
138C22⋊D151—42no—
139C22⋊D151—42no—
140C22⋊D151—42no—
141C22⋊D151—81no—
142C22⋊D151—81no—
143C2×Dic151—21no—
144C2×Dic151—21no—
145C2×Dic151—21no—
146C2×Dic151—42no—
147C2×Dic151—42no—
148C2×Dic151—42no—
149C2×Dic151C2×D411yescharacteristic
150C2×Dic151C2×D411yescharacteristic
151C4×D151—21no—
152C4×D151—21no—
153C4×D151—21no—
154C4×D151—21no—
155C151⋊C8—21no—
156C151⋊C8C2×D412yes—
157C23×C151—21no—
158C23×C151—21no—
159C23×C151—21no—
160D4×C151—21no—
161D4×C151—21no—
162D4×C151—21no—
163D4×C151—21no—
164D4×C151—21no—
165D4×C151—42no—
166D4×C151—81no—
167D4×C151C2×D412yes—
168C2×C4×C151—21no—
169C2×C4×C151—81no—
170C2×C4×C151C2×D411yescharacteristic
171C2×C4×C151C2×D411yescharacteristic
172C2×C4×C151C2411yescharacteristic
173C8×C151—21no—
174C8×C151—21no—
175C22×C151—22no—
176C22×C151—41no—
177C22×C151—41no—
178C22×C151—41no—
179C22×C151—41no—
180C22×C151—41no—
181C22×C151—41no—
182C22×C151—41no—
183C22×C151—41no—
184C22×C151C22×D411yescharacteristic
185C2×D151—21no—
186C2×D151—21no—
187C2×D151—21no—
188C2×D151—21no—
189C2×D151—21no—
190C2×D151—21no—
191C2×D151—41no—
192C2×D151—41no—
193C2×D151—41no—
194C2×D151—84no—
195C4×C151—21no—
196C4×C151—21no—
197C4×C151—41no—
198C4×C151C22×D411yescharacteristic
199C4×C151H(5,𝔽2)11yescharacteristic
200Dic151—21no—
201Dic151—21no—
202Dic151—22no—
203Dic151—41no—
204Dic151—41no—
205C2×C151—42no—
206C2×C151—81no—
207C2×C151—81no—
208C2×C151D4211yescharacteristic
209C2×C151#57511yescharacteristic
210C2×C151#57611yescharacteristic
211D151—41no—
212D151—41no—
213D151—81no—
214C151#326811yescharacteristic, complemented, Sylow
215#3268—1511nomaximal, Sylow
216C2×AGL(1,ℤ/8)—1511no—
217C2×#135—1511no—
218#550—1511no—
219#546—1511no—
220#496—1511no—
221#468—1511no—
222#466—1511no—
223#464—1511no—
224#459D15111yescharacteristic, complemented
225#452—1511no—
226#449—1511no—
227#449—1511no—
228#447—1511no—
229#440—1511no—
230#435—1511no—
231C2×#41—1511no—
232C2×#41—1511no—
233C2×#41—1511no—
234C22×D4—1511no—
235AGL(1,ℤ/8)—3024no—
236#135—3024no—
237C2×Q16—1511no—
238C2×SD16—1511no—
239C2×SD16—1511no—
240C2×SD16—1511no—
241C2×SD16—1511no—
242C2×D8—1511no—
243C2×D8—1511no—
244C2×D8C2×D15111yescharacteristic
245C2×D8C2×D15111yescharacteristic
246C2×M16—1511no—
247C22×C8—1511no—
248#127—3021no—
249#127C2×D15111yescharacteristic, complemented
250#124—1511no—
251#123—3021no—
252C22⋊Q8—1511no—
253#121—3021no—
254#121—3021no—
255#121—3021no—
256#121—1511no—
257#121—1511no—
258#121—1511no—
259#120—3021no—
260C4×Q8—1511no—
261C4×D4—3021no—
262C4×D4—1511no—
263C4×D4C2×D15111yescharacteristic
264C2×C22⋊C4—3021no—
265#107—1511no—
266C4⋊C8C2×D15111yescharacteristic, complemented
267#103—1511no—
268#103—1511no—
269#102—1511no—
270#102—1511no—
271#102C2×D15111yescharacteristic, complemented
272#102C2×D15111yescharacteristic, complemented
273C22⋊C8—1511no—
274C22⋊C8—1511no—
275#97—1511no—
276C24—3021no—
277#41—3022no—
278#41—3022no—
279#41—3022no—
280#41—6041no—
281#41—6041no—
282#41—6041no—
283C2×Q8—1511no—
284C2×Q8—1511no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—3021no—
288C2×D4—3022no—
289C2×D4—3021no—
290C2×D4—3021no—
291C2×D4—3021no—
292C2×D4—3021no—
293C2×D4—3021no—
294C2×D4—3021no—
295C2×D4—6041no—
296C2×D4—1511no—
297C2×D4—1511no—
298C2×D4C22×D15111yescharacteristic
299C2×D4C22×D15111yescharacteristic
300C2×D4C22×D15111yescharacteristic
301C22×C4—21no—
302C22×C4—3021no—
303C22×C4—3021no—
304C22×C4—3021no—
305C22×C4—1511no—
306C22×C4—1511no—
307Q16—3022no—
308SD16—3022no—
309SD16—3022no—
310SD16—6041no—
311SD16—1514no—
312D8—22no—
313D8—22no—
314D8—3022no—
315D8—6041no—
316M16—3022no—
317C2×C8—3022no—
318C2×C8—1511no—
319C2×C8—1511no—
320C2×C8C22×D15111yescharacteristic
321C2×C8C22×D15111yescharacteristic
322C4⋊C4—3021no—
323C4⋊C4—3021no—
324C4⋊C4—1511no—
325C4⋊C4—1511no—
326C4⋊C4C22×D15111yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—3021no—
329C22⋊C4—3021no—
330C22⋊C4—3021no—
331C22⋊C4—3021no—
332C22⋊C4—3021no—
333C22⋊C4—3021no—
334C22⋊C4—1511no—
335C22⋊C4—1511no—
336C42—3021no—
337C42C22×D15111yescharacteristic
338C23—21no—
339C23—21no—
340C23—21no—
341C23—3021no—
342C23—6042no—
343C23—6042no—
344C23—1511no—
345C23—1511no—
346C23—12081no—
347Q8—3021no—
348Q8—3021no—
349Q8—3021no—
350Q8—1512no—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—21no—
355D4—21no—
356D4—42no—
357D4—81no—
358D4—3021no—
359D4—3021no—
360D4—6041no—
361D4—6042no—
362D4—6042no—
363D4—6042no—
364D4—6042no—
365D4—12081no—
366D4—12081no—
367D4—12081no—
368D4D4×D15112yes—
369C2×C4—21no—
370C2×C4—81no—
371C2×C4—3021no—
372C2×C4—3021no—
373C2×C4—3021no—
374C2×C4—3021no—
375C2×C4—3021no—
376C2×C4—3021no—
377C2×C4—3021no—
378C2×C4—6042no—
379C2×C4—6042no—
380C2×C4—6042no—
381C2×C4—1511no—
382C2×C4—1511no—
383C2×C4D4×D15111yescharacteristic
384C2×C4D4×D15111yescharacteristic
385C2×C4C23×D15111yescharacteristic
386C8—21no—
387C8—21no—
388C8—3021no—
389C8—1512no—
390C22—22no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—3021no—
400C22—3021no—
401C22—3021no—
402C22—3021no—
403C22—3021no—
404C22—3021no—
405C22—6041no—
406C22—6041no—
407C22—6041no—
408C22—12084no—
409C22C2×D4×D15111yescharacteristic
410C4—21no—
411C4—21no—
412C4—41no—
413C4—3021no—
414C4—3021no—
415C4—3022no—
416C4—6041no—
417C4—6041no—
418C4C2×D4×D15111yescharacteristic
419C4#1801278511yescharacteristic
420C2—42no—
421C2—81no—
422C2—81no—
423C2—6041no—
424C2—6041no—
425C2—12081no—
426C2#2375284611yescharacteristic
427C2#2375300811yescharacteristic
428C2#2375301311yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#459×C151C2
socleC22×C151C22×D4
hypercenter#459D151
hypocenterC151#3268
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×#18012758C2semidirect
3. #23752882C2semidirect
4. #23752857C2semidirect
5. #23752599C2semidirect
6. #23752457C2semidirect
7. #23752447C2semidirect
8. #23752435C2semidirect
9. #23752375C2semidirect
10. #23752358C2semidirect
11. #23752354C2semidirect
12. #23752344C2semidirect
13. #23752312C2semidirect
14. #23752282C2semidirect
15. #459×C151C2semidirect
18. C2×#14559003C22semidirect
22. C2×Dic604C22semidirect
25. C2×#14558992C22semidirect
26. C2×#14558992C22semidirect
30. C2×C8×D151C22semidirect
40. #18012710C22semidirect
42. C4×Dic302C22semidirect
46. #18012672C22semidirect
47. #18012664C22semidirect
48. #18012662C22semidirect
52. (C2×D151)⋊C8C22semidirect
53. #18012650C22semidirect
56. #127×C151C22semidirect
58. C4⋊C8×C151C22semidirect
59. #102×C151C22semidirect
60. #102×C151C22semidirect
90. #14558992D4semidirect
214. C151#3268semidirect
224. #459D151semidirect
249. #127C2×D151semidirect
266. 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×#180127582
#237528822
#237528572
#237525992
#237524572
#237524472
#237524352
#237523752
#237523582
#237523542
#237523442
#237523122
#237522822
#459×C1512
#3268151