Finite Group Databasebeta

← #34080788

Subgroups — #34080788

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
2C22×#14558989C211yesmaximal, characteristic, complemented
3#23752856C211yesmaximal, characteristic, complemented
4#23752853C211yesmaximal, characteristic, complemented
5#23752593C211yesmaximal, characteristic, complemented
6#23752451C211yesmaximal, characteristic, complemented
7#23752447C211yesmaximal, characteristic, complemented
8#23752429C211yesmaximal, characteristic, complemented
9#23752426C211yesmaximal, characteristic, complemented
10#23752365C211yesmaximal, characteristic, complemented
11#23752358C211yesmaximal, characteristic, complemented
12#23752356C211yesmaximal, characteristic, complemented
13#23752292C211yesmaximal, characteristic, complemented
14(C22⋊D151)⋊C8C211yesmaximal, characteristic, complemented
15#450×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic, complemented
17C2×#14559003C2211yescharacteristic, complemented
18C22×D604C2211yescharacteristic
19#18012760—24no—
20C2×#14558994C2211yescharacteristic, complemented
21C2×#14558993C2211yescharacteristic, complemented
22C2×#14558993C2211yescharacteristic, complemented
23C2×#14558989—24no—
24C2×#14558989C2211yescharacteristic
25C2×#14558989C2211yescharacteristic
26C2×#14558989C2211yescharacteristic
27C2×#14558989C2211yescharacteristic
28C22×C151⋊C8C2211yescharacteristic
29C2×C8×D151C2211yescharacteristic, complemented
30#18012728C2211yescharacteristic, complemented
31#18012726C2211yescharacteristic, complemented
32#18012724—21no—
33#18012720—21no—
34#18012718C2211yescharacteristic
35#18012714—21no—
36#18012714C2211yescharacteristic, complemented
37#18012711—21no—
38#18012710C2211yescharacteristic, complemented
39#18012709—21no—
40#18012708—21no—
41D4×Dic151C2211yescharacteristic, complemented
42#18012701C2211yescharacteristic, complemented
43C4×C22⋊D151C2211yescharacteristic
44C2×C22⋊Dic151—21no—
45C22⋊C4×D151—21no—
46#18012672C2211yescharacteristic, complemented
47Dic151⋊C8C2211yescharacteristic, complemented
48#18012663C2211yescharacteristic, complemented
49#18012662C2211yescharacteristic, complemented
50#18012661C2211yescharacteristic, complemented
51#18012661C2211yescharacteristic, complemented
52(C2×D151)⋊C8C2211yescharacteristic, complemented
53C8×Dic151C2211yescharacteristic, complemented
54C22×D4×C151C2211yescharacteristic
55C2×SD16×C151C2211yescharacteristic, complemented
56C2×SD16×C151C2211yescharacteristic, complemented
57C22⋊Q8×C151C2211yescharacteristic
58#102×C151C2211yescharacteristic, complemented
59#102×C151C2211yescharacteristic, complemented
60C22⋊C8×C151C2211yescharacteristic
61C23×D151—21no—
62#14559005—22no—
63#14559005—41no—
64#14559003—22no—
65#14559003—41no—
66C2×Dic302C2311yescharacteristic
67C2×D604—22no—
68C2×D604—21no—
69C2×D604—21no—
70C2×D604—21no—
71C2×D604—41no—
72C2×D604C2311yescharacteristic
73C2×D604C2311yescharacteristic
74C2×C22⋊D151—21no—
75C2×C22⋊D151—21no—
76C2×C22⋊D151D411yescharacteristic
77C22×Dic151—21no—
78C22×Dic151—21no—
79C2×C4×D151—21no—
80C2×C4×D151—21no—
81C2×C4×D151C2311yescharacteristic
82#14558994—22no—
83#14558993—22no—
84#14558993—41no—
85#14558989—22no—
86#14558989—22no—
87#14558989—22no—
88#14558989D414yescomplemented
89C2×C151⋊C8—22no—
90C2×C151⋊C8C2311yescharacteristic
91C2×C151⋊C8C2311yescharacteristic
92C8×D151—22no—
93C4⋊Dic151C2311yescharacteristic
94Dic151⋊C4—21no—
95Dic151⋊C4D411yescharacteristic
96C22⋊Dic151—21no—
97C22⋊Dic151—21no—
98C22⋊Dic151—21no—
99C22⋊Dic151—21no—
100C22⋊Dic151—21no—
101C22⋊Dic151D411yescharacteristic
102(C2×D151)⋊C4—21no—
103(C2×D151)⋊C4—21no—
104(C2×D151)⋊C4—21no—
105(C2×D151)⋊C4—21no—
106(C2×D151)⋊C4D411yescharacteristic
107C4×Dic151C2311yescharacteristic
108C24×C151—21no—
109C2×Q8×C151C2311yescharacteristic
110C2×D4×C151—22no—
111C2×D4×C151—21no—
112C2×D4×C151—41no—
113C2×D4×C151C2311yescharacteristic
114C2×D4×C151C2311yescharacteristic
115C22×C4×C151C2311yescharacteristic
116SD16×C151—22no—
117SD16×C151—41no—
118C2×C8×C151C2311yescharacteristic
119C2×C8×C151C2311yescharacteristic
120C4⋊C4×C151—21no—
121C4⋊C4×C151C2311yescharacteristic
122C22⋊C4×C151—21no—
123C22×D151—21no—
124C22×D151—21no—
125C22×D151—42no—
126C22×D151—42no—
127C22×D151—81no—
128C22×D151C2×D411yescharacteristic
129Dic302—21no—
130Dic302—21no—
131D604—21no—
132D604—21no—
133D604—21no—
134D604—42no—
135D604—42no—
136D604—81no—
137D604C2×D412yes—
138C22⋊D151—22no—
139C22⋊D151—42no—
140C22⋊D151—81no—
141C2×Dic151—21no—
142C2×Dic151—21no—
143C2×Dic151—42no—
144C2×Dic151—81no—
145C2×Dic151C2×D411yescharacteristic
146C2×Dic151C2×D411yescharacteristic
147C2×Dic151C2×D411yescharacteristic
148C4×D151—21no—
149C4×D151—21no—
150C4×D151—42no—
151C4×D151—81no—
152C151⋊C8—21no—
153C151⋊C8C2×D412yes—
154C23×C151—21no—
155C23×C151—21no—
156C23×C151—42no—
157C23×C151—42no—
158C23×C151—81no—
159C23×C151C2×D411yescharacteristic
160Q8×C151—21no—
161Q8×C151—21no—
162D4×C151—21no—
163D4×C151—21no—
164D4×C151—21no—
165D4×C151—42no—
166D4×C151C2×D412yes—
167C2×C4×C151—21no—
168C2×C4×C151—21no—
169C2×C4×C151—21no—
170C2×C4×C151—21no—
171C2×C4×C151C2×D411yescharacteristic
172C2×C4×C151C2411yescharacteristic
173C8×C151—21no—
174C8×C151—21no—
175C22×C151—21no—
176C22×C151—21no—
177C22×C151—22no—
178C22×C151—41no—
179C22×C151—41no—
180C22×C151—41no—
181C22×C151—41no—
182C22×C151—41no—
183C22×C151—84no—
184C22×C151#13512yescomplemented
185C22×C151C22×D411yescharacteristic
186C2×D151—21no—
187C2×D151—22no—
188C2×D151—21no—
189C2×D151—21no—
190C2×D151—41no—
191C2×D151—41no—
192C2×D151—41no—
193C2×D151—41no—
194C2×D151—41no—
195C2×D151—84no—
196C4×C151—21no—
197C4×C151—41no—
198C4×C151—41no—
199C4×C151C22×D411yescharacteristic
200C4×C151H(5,𝔽2)11yescharacteristic
201Dic151—21no—
202Dic151—21no—
203Dic151—21no—
204Dic151—41no—
205Dic151—41no—
206C2×C151—22no—
207C2×C151—42no—
208C2×C151—81no—
209C2×C151D4211yescharacteristic
210C2×C151C2×#13511yescharacteristic
211C2×C151#57611yescharacteristic
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#463—1511no—
226#450—1511no—
227#450D15111yescharacteristic, complemented
228#449—1511no—
229#449—1511no—
230C4×D8—1511no—
231C8×D4—1511no—
232C2×#41—1511no—
233C2×#41—1511no—
234C22×D4—1511no—
235C22×D4C2×D15111yescharacteristic
236#135—3024no—
237C2×Q16—1511no—
238C2×SD16—1511no—
239C2×SD16—1511no—
240C2×SD16C2×D15111yescharacteristic, complemented
241C2×SD16C2×D15111yescharacteristic, complemented
242C2×D8—3024no—
243C2×D8—1511no—
244C2×D8—1511no—
245C2×D8—1511no—
246C2×D8—1511no—
247C22×C8—1511no—
248C22×C8—1511no—
249#124—1511no—
250#124—1511no—
251#123—3021no—
252#123—3021no—
253C22⋊Q8—1511no—
254C22⋊Q8C2×D15111yescharacteristic
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×D4—1511no—
264C2×C22⋊C4—3021no—
265C2×C22⋊C4—3021no—
266#107—1511no—
267C4⋊C8—1511no—
268#103—1511no—
269#103—1511no—
270#102—1511no—
271#102—1511no—
272#102C2×D15111yescharacteristic, complemented
273#102C2×D15111yescharacteristic, complemented
274C22⋊C8—1511no—
275C22⋊C8C2×D15111yescharacteristic
276C4×C8—1511no—
277C24—21no—
278C24—3021no—
279#41—3022no—
280#41—3022no—
281#41—6041no—
282#41—6041no—
283C2×Q8—1511no—
284C2×Q8C22×D15111yescharacteristic
285C2×D4—22no—
286C2×D4—21no—
287C2×D4—41no—
288C2×D4—3022no—
289C2×D4—3021no—
290C2×D4—3021no—
291C2×D4—3021no—
292C2×D4—3021no—
293C2×D4—3021no—
294C2×D4—6041no—
295C2×D4—1511no—
296C2×D4—1511no—
297C2×D4—1511no—
298C2×D4C22×D15111yescharacteristic
299C2×D4C22×D15111yescharacteristic
300C22×C4—3021no—
301C22×C4—3021no—
302C22×C4—3021no—
303C22×C4—3021no—
304C22×C4—1511no—
305C22×C4C22×D15111yescharacteristic
306Q16—3022no—
307SD16—22no—
308SD16—41no—
309SD16—3022no—
310SD16—6041no—
311D8—3022no—
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—21no—
322C4⋊C4—3021no—
323C4⋊C4—1511no—
324C4⋊C4—1511no—
325C4⋊C4C22×D15111yescharacteristic
326C22⋊C4—21no—
327C22⋊C4—3021no—
328C22⋊C4—3021no—
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—
338C42—1511no—
339C23—21no—
340C23—21no—
341C23—42no—
342C23—42no—
343C23—81no—
344C23—3021no—
345C23—3021no—
346C23—6042no—
347C23—6042no—
348C23—1511no—
349C23—12081no—
350C23D4×D15111yescharacteristic
351Q8—21no—
352Q8—21no—
353Q8—3021no—
354Q8—3021no—
355D4—21no—
356D4—21no—
357D4—21no—
358D4—42no—
359D4—3022no—
360D4—3021no—
361D4—3021no—
362D4—3021no—
363D4—6042no—
364D4—6042no—
365D4—6042no—
366D4—1512no—
367D4—12081no—
368D4—12081no—
369D4D4×D15112yes—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—3021no—
375C2×C4—3021no—
376C2×C4—3021no—
377C2×C4—3021no—
378C2×C4—6042no—
379C2×C4—6042no—
380C2×C4—1511no—
381C2×C4—1511no—
382C2×C4—1511no—
383C2×C4—12081no—
384C2×C4—12081no—
385C2×C4D4×D15111yescharacteristic
386C2×C4C23×D15111yescharacteristic
387C8—21no—
388C8—21no—
389C8—3021no—
390C8—1512no—
391C22—21no—
392C22—21no—
393C22—22no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—84no—
400C22—3021no—
401C22—3021no—
402C22—3021no—
403C22—3022no—
404C22—6041no—
405C22—6041no—
406C22—6041no—
407C22—6041no—
408C22—6041no—
409C22—12084no—
410C22#1801276012yescomplemented
411C22C2×D4×D15111yescharacteristic
412C4—21no—
413C4—41no—
414C4—41no—
415C4—3021no—
416C4—3021no—
417C4—3021no—
418C4—6041no—
419C4—6041no—
420C4C2×D4×D15111yescharacteristic
421C4#1801278411yescharacteristic
422C2—22no—
423C2—42no—
424C2—81no—
425C2—6041no—
426C2—6042no—
427C2—12081no—
428C2#2375284411yescharacteristic
429C2C2×#1801276011yescharacteristic
430C2#2375301611yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#450×C151C2
socleC22×C151C22×D4
hypercenter#450D151
hypocenterC151#3280
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. C2×#18012760C2semidirect
2. C22×#14558989C2semidirect
3. #23752856C2semidirect
4. #23752853C2semidirect
5. #23752593C2semidirect
6. #23752451C2semidirect
7. #23752447C2semidirect
8. #23752429C2semidirect
9. #23752426C2semidirect
10. #23752365C2semidirect
11. #23752358C2semidirect
12. #23752356C2semidirect
13. #23752292C2semidirect
14. (C22⋊D151)⋊C8C2semidirect
15. #450×C151C2semidirect
16. C2×#14559005C22semidirect
17. C2×#14559003C22semidirect
20. C2×#14558994C22semidirect
21. C2×#14558993C22semidirect
22. C2×#14558993C22semidirect
29. C2×C8×D151C22semidirect
30. #18012728C22semidirect
31. #18012726C22semidirect
36. #18012714C22semidirect
38. #18012710C22semidirect
41. D4×Dic151C22semidirect
42. #18012701C22semidirect
46. #18012672C22semidirect
47. Dic151⋊C8C22semidirect
48. #18012663C22semidirect
49. #18012662C22semidirect
50. #18012661C22semidirect
51. #18012661C22semidirect
52. (C2×D151)⋊C8C22semidirect
53. C8×Dic151C22semidirect
55. C2×SD16×C151C22semidirect
56. C2×SD16×C151C22semidirect
58. #102×C151C22semidirect
59. #102×C151C22semidirect
88. #14558989D4semidirect
184. C22×C151#135semidirect
215. C151#3280semidirect
227. #450D151semidirect
240. C2×SD16C2×D151semidirect
241. C2×SD16C2×D151semidirect
272. #102C2×D151semidirect
273. #102C2×D151semidirect
410. C22#18012760semidirect

Maximal subgroups

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

subgroupindex
C2×#180127602
C22×#145589892
#237528562
#237528532
#237525932
#237524512
#237524472
#237524292
#237524262
#237523652
#237523582
#237523562
#237522922
(C22⋊D151)⋊C82
#450×C1512
#3280151