Finite Group Databasebeta

← #34080790

Subgroups — #34080790

Order 19328.

526 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012760C211yesmaximal, characteristic, complemented
2C2×D8×D151C211yesmaximal, characteristic, complemented
3#23752857C211yesmaximal, characteristic, complemented
4#23752855C211yesmaximal, characteristic, complemented
5#23752594C211yesmaximal, characteristic, complemented
6#23752452C211yesmaximal, characteristic, complemented
7#23752447C211yesmaximal, characteristic, complemented
8#23752428C211yesmaximal, characteristic, complemented
9#23752364C211yesmaximal, characteristic, complemented
10#23752361C211yesmaximal, characteristic, complemented
11#23752360C211yesmaximal, characteristic, complemented
12#23752354C211yesmaximal, characteristic, complemented
13C4×#14558989C211yesmaximal, characteristic, complemented
14#23752277C211yesmaximal, characteristic, complemented
15#463×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic, complemented
17C2×#14559003C2211yescharacteristic, complemented
18C2×D4×D151C2211yescharacteristic
19C2×D4×D151C2211yescharacteristic
20#18012760—24no—
21C2×#14558994C2211yescharacteristic, complemented
22C2×#14558993C2211yescharacteristic, complemented
23C2×#14558992C2211yescharacteristic, complemented
24C2×#14558991C2211yescharacteristic, complemented
25C2×D1208C2211yescharacteristic
26C2×#14558989C2211yescharacteristic
27C2×#14558989C2211yescharacteristic
28D8×D151—24no—
29C2×C8×D151C2211yescharacteristic
30C2×C8×D151C2211yescharacteristic, complemented
31#18012727C2211yescharacteristic, complemented
32#18012723—21no—
33#18012721—21no—
34#18012719C2211yescharacteristic
35#18012715C2211yescharacteristic
36#18012714C2211yescharacteristic, complemented
37#18012713—21no—
38#18012712—21no—
39#18012710C2211yescharacteristic, complemented
40#18012709—21no—
41#18012709—21no—
42C4×D604C2211yescharacteristic
43C4×D604C2211yescharacteristic, complemented
44C2×(C2×D151)⋊C4—21no—
45C22⋊C4×D151—21no—
46#18012672C2211yescharacteristic, complemented
47#18012664C2211yescharacteristic, complemented
48#18012661C2211yescharacteristic, complemented
49#18012660C2211yescharacteristic, complemented
50#18012659C2211yescharacteristic, complemented
51(C2×D151)⋊C8C2211yescharacteristic
52(C2×D151)⋊C8C2211yescharacteristic, complemented
53C4×C151⋊C8C2211yescharacteristic, complemented
54C2×SD16×C151C2211yescharacteristic, complemented
55C2×D8×C151C2211yescharacteristic
56#124×C151C2211yescharacteristic, complemented
57C4×D4×C151C2211yescharacteristic, complemented
58C4⋊C8×C151C2211yescharacteristic, complemented
59#103×C151C2211yescharacteristic, complemented
60#102×C151C2211yescharacteristic, complemented
61C23×D151—21no—
62C23×D151—21no—
63#14559005—22no—
64#14559005—41no—
65#14559003—22no—
66#14559003—41no—
67C2×Dic302C2311yescharacteristic
68C2×D604—21no—
69C2×D604—21no—
70C2×D604D411yescharacteristic
71C2×D604C2311yescharacteristic
72C2×D604C2311yescharacteristic
73C2×C22⋊D151—21no—
74C2×C22⋊D151—21no—
75C2×C22⋊D151—21no—
76C2×C22⋊D151—21no—
77D4×D151—22no—
78D4×D151—22no—
79D4×D151—41no—
80D4×D151—41no—
81C22×Dic151—21no—
82C2×C4×D151—21no—
83C2×C4×D151—21no—
84C2×C4×D151C2311yescharacteristic
85C2×C4×D151C2311yescharacteristic
86#14558994—22no—
87#14558993—22no—
88#14558992—41no—
89#14558991—41no—
90D1208—22no—
91#14558989—22no—
92#14558989D414yescomplemented
93C2×C151⋊C8C2311yescharacteristic
94C2×C151⋊C8C2311yescharacteristic
95C8×D151—22no—
96C8×D151—22no—
97C4⋊Dic151—21no—
98C4⋊Dic151D411yescharacteristic
99C4⋊Dic151C2311yescharacteristic
100Dic151⋊C4—21no—
101C22⋊Dic151—21no—
102(C2×D151)⋊C4—21no—
103(C2×D151)⋊C4—21no—
104(C2×D151)⋊C4—21no—
105(C2×D151)⋊C4—21no—
106(C2×D151)⋊C4—21no—
107(C2×D151)⋊C4—21no—
108(C2×D151)⋊C4D411yescharacteristic
109(C2×D151)⋊C4D411yescharacteristic
110C2×Q8×C151C2311yescharacteristic
111C2×D4×C151C2311yescharacteristic
112C2×D4×C151C2311yescharacteristic
113C22×C4×C151—21no—
114SD16×C151—22no—
115D8×C151—22no—
116C2×C8×C151C2311yescharacteristic
117C2×C8×C151C2311yescharacteristic
118C4⋊C4×C151C2311yescharacteristic
119C22⋊C4×C151—21no—
120C22⋊C4×C151—21no—
121C22⋊C4×C151—21no—
122C42×C151C2311yescharacteristic
123C22×D151—21no—
124C22×D151—21no—
125C22×D151—42no—
126C22×D151—42no—
127C22×D151—42no—
128C22×D151—42no—
129C22×D151—81no—
130C22×D151—81no—
131C22×D151C2×D411yescharacteristic
132C22×D151C2×D411yescharacteristic
133Dic302—21no—
134Dic302—21no—
135D604—22no—
136D604—21no—
137D604—21no—
138D604—21no—
139D604—42no—
140D604—81no—
141D604C2×D412yes—
142C22⋊D151—42no—
143C22⋊D151—42no—
144C22⋊D151—42no—
145C22⋊D151—81no—
146C2×Dic151—21no—
147C2×Dic151—21no—
148C2×Dic151—42no—
149C2×Dic151C2×D411yescharacteristic
150C2×Dic151C2×D411yescharacteristic
151C4×D151—21no—
152C4×D151—21no—
153C4×D151—21no—
154C4×D151—21no—
155C4×D151—42no—
156C4×D151—81no—
157C151⋊C8—21no—
158C151⋊C8C2×D412yes—
159C23×C151—21no—
160C23×C151—21no—
161Q8×C151—21no—
162Q8×C151—21no—
163D4×C151—21no—
164D4×C151—21no—
165D4×C151—21no—
166D4×C151C2×D412yes—
167C2×C4×C151—21no—
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×C151C22×D411yescharacteristic
182C2×D151—21no—
183C2×D151—21no—
184C2×D151—21no—
185C2×D151—22no—
186C2×D151—21no—
187C2×D151—21no—
188C2×D151—41no—
189C2×D151—41no—
190C2×D151—41no—
191C2×D151—41no—
192C2×D151—41no—
193C2×D151—84no—
194C2×D151—84no—
195C2×D151#13512yescomplemented
196C4×C151—21no—
197C4×C151—21no—
198C4×C151—41no—
199C4×C151—41no—
200C4×C151C22×D411yescharacteristic
201C4×C151H(5,𝔽2)11yescharacteristic
202Dic151—21no—
203Dic151—21no—
204Dic151—41no—
205Dic151—41no—
206C2×C151—42no—
207C2×C151—81no—
208C2×C151D4211yescharacteristic
209C2×C151C2×#13511yescharacteristic
210C2×C151#57611yescharacteristic
211D151—22no—
212D151—41no—
213D151—42no—
214D151—81no—
215C151#328011yescharacteristic, complemented, Sylow
216#3280—1511nomaximal, Sylow
217C2×#135—1511no—
218C22×D8—1511no—
219#546—1511no—
220#546—1511no—
221#495—1511no—
222#467—1511no—
223#466—1511no—
224#463—1511no—
225#463D15111yescharacteristic, complemented
226#450—1511no—
227#450—1511no—
228#449—1511no—
229#449—1511no—
230C4×D8—1511no—
231C8×D4—1511no—
232C2×#41—1511no—
233C2×#41—1511no—
234C22×D4—1511no—
235C22×D4—1511no—
236#135—3024no—
237C2×Q16—1511no—
238C2×SD16—1511no—
239C2×SD16—1511no—
240C2×SD16—1511no—
241C2×SD16C2×D15111yescharacteristic, complemented
242C2×D8—3024no—
243C2×D8—1511no—
244C2×D8—1511no—
245C2×D8—1511no—
246C2×D8C2×D15111yescharacteristic
247C22×C8—1511no—
248C22×C8—1511no—
249#124—1511no—
250#124C2×D15111yescharacteristic, complemented
251#123—3021no—
252#123—3021no—
253C22⋊Q8—1511no—
254C22⋊Q8—1511no—
255#121—3021no—
256#121—3021no—
257#121—1511no—
258#121—1511no—
259#120—3021no—
260#120—3021no—
261C4×D4—1511no—
262C4×D4—1511no—
263C4×D4C2×D15111yescharacteristic, complemented
264C2×C22⋊C4—3021no—
265C2×C22⋊C4—3021no—
266#107—1511no—
267C4⋊C8C2×D15111yescharacteristic, complemented
268#103—1511no—
269#103C2×D15111yescharacteristic, complemented
270#102—1511no—
271#102—1511no—
272#102—1511no—
273#102C2×D15111yescharacteristic, complemented
274C22⋊C8—1511no—
275C22⋊C8—1511no—
276C4×C8—1511no—
277C24—3021no—
278C24—3021no—
279#41—3022no—
280#41—3022no—
281#41—6041no—
282#41—6041no—
283C2×Q8—1511no—
284C2×Q8C22×D15111yescharacteristic
285C2×D4—3021no—
286C2×D4—3021no—
287C2×D4—3022no—
288C2×D4—3022no—
289C2×D4—3021no—
290C2×D4—3021no—
291C2×D4—3021no—
292C2×D4—3021no—
293C2×D4—6041no—
294C2×D4—6041no—
295C2×D4—1511no—
296C2×D4—1511no—
297C2×D4—1511no—
298C2×D4C22×D15111yescharacteristic
299C2×D4C22×D15111yescharacteristic
300C22×C4—21no—
301C22×C4—3021no—
302C22×C4—3021no—
303C22×C4—3021no—
304C22×C4—1511no—
305C22×C4—1511no—
306Q16—3022no—
307SD16—22no—
308SD16—3022no—
309SD16—6041no—
310SD16—6041no—
311D8—22no—
312D8—3022no—
313D8—3022no—
314D8—1514no—
315C2×C8—3022no—
316C2×C8—3022no—
317C2×C8—1511no—
318C2×C8—1511no—
319C2×C8C22×D15111yescharacteristic
320C2×C8C22×D15111yescharacteristic
321C4⋊C4—3021no—
322C4⋊C4—3021no—
323C4⋊C4—1511no—
324C4⋊C4—1511no—
325C4⋊C4C22×D15111yescharacteristic
326C22⋊C4—21no—
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—3021no—
330C22⋊C4—3021no—
331C22⋊C4—3021no—
332C22⋊C4—3021no—
333C22⋊C4—3021no—
334C22⋊C4—3021no—
335C22⋊C4—3021no—
336C22⋊C4—1511no—
337C22⋊C4—1511no—
338C42C22×D15111yescharacteristic
339C23—21no—
340C23—21no—
341C23—3021no—
342C23—3021no—
343C23—6042no—
344C23—6042no—
345C23—6042no—
346C23—6042no—
347C23—1511no—
348C23—1511no—
349C23—12081no—
350C23—12081no—
351Q8—21no—
352Q8—21no—
353Q8—3021no—
354Q8—3021no—
355D4—21no—
356D4—21no—
357D4—21no—
358D4—3022no—
359D4—3021no—
360D4—3021no—
361D4—3021no—
362D4—6042no—
363D4—6042no—
364D4—6042no—
365D4—6042no—
366D4—1512no—
367D4—12081no—
368D4—12081no—
369D4D4×D15112yes—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—81no—
373C2×C4—3021no—
374C2×C4—3021no—
375C2×C4—3021no—
376C2×C4—3021no—
377C2×C4—3021no—
378C2×C4—3021no—
379C2×C4—6042no—
380C2×C4—6042no—
381C2×C4—1511no—
382C2×C4—1511no—
383C2×C4—12081no—
384C2×C4D4×D15111yescharacteristic
385C2×C4D4×D15111yescharacteristic
386C2×C4C23×D15111yescharacteristic
387C8—21no—
388C8—21no—
389C8—3021no—
390C8—1512no—
391C22—22no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—3021no—
398C22—3021no—
399C22—3021no—
400C22—3021no—
401C22—3021no—
402C22—3022no—
403C22—6041no—
404C22—6041no—
405C22—6041no—
406C22—6041no—
407C22—6041no—
408C22—1512no—
409C22—12084no—
410C22—12084no—
411C22C2×D4×D15111yescharacteristic
412C4—21no—
413C4—21no—
414C4—41no—
415C4—41no—
416C4—3021no—
417C4—3021no—
418C4—6041no—
419C4—6041no—
420C4C2×D4×D15111yescharacteristic
421C4#1801278511yescharacteristic
422C2—42no—
423C2—81no—
424C2—3022no—
425C2—6041no—
426C2—6042no—
427C2—12081no—
428C2#2375284611yescharacteristic
429C2#135×D15111yescharacteristic
430C2#2375301611yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#463×C151C2
socleC22×C151C22×D4
hypercenter#463D151
hypocenterC151#3280
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#18012760C2semidirect
2. C2×D8×D151C2semidirect
3. #23752857C2semidirect
4. #23752855C2semidirect
5. #23752594C2semidirect
6. #23752452C2semidirect
7. #23752447C2semidirect
8. #23752428C2semidirect
9. #23752364C2semidirect
10. #23752361C2semidirect
11. #23752360C2semidirect
12. #23752354C2semidirect
13. C4×#14558989C2semidirect
14. #23752277C2semidirect
15. #463×C151C2semidirect
16. C2×#14559005C22semidirect
17. C2×#14559003C22semidirect
21. C2×#14558994C22semidirect
22. C2×#14558993C22semidirect
23. C2×#14558992C22semidirect
24. C2×#14558991C22semidirect
30. C2×C8×D151C22semidirect
31. #18012727C22semidirect
36. #18012714C22semidirect
39. #18012710C22semidirect
43. C4×D604C22semidirect
46. #18012672C22semidirect
47. #18012664C22semidirect
48. #18012661C22semidirect
49. #18012660C22semidirect
50. #18012659C22semidirect
52. (C2×D151)⋊C8C22semidirect
53. C4×C151⋊C8C22semidirect
54. C2×SD16×C151C22semidirect
56. #124×C151C22semidirect
57. C4×D4×C151C22semidirect
58. C4⋊C8×C151C22semidirect
59. #103×C151C22semidirect
60. #102×C151C22semidirect
92. #14558989D4semidirect
195. C2×D151#135semidirect
215. C151#3280semidirect
225. #463D151semidirect
241. C2×SD16C2×D151semidirect
250. #124C2×D151semidirect
263. C4×D4C2×D151semidirect
267. C4⋊C8C2×D151semidirect
269. #103C2×D151semidirect
273. #102C2×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127602
C2×D8×D1512
#237528572
#237528552
#237525942
#237524522
#237524472
#237524282
#237523642
#237523612
#237523602
#237523542
C4×#145589892
#237522772
#463×C1512
#3280151