Finite Group Databasebeta

← #34080791

Subgroups — #34080791

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×#18012759C211yesmaximal, characteristic, complemented
2C22×#14558989C211yesmaximal, characteristic, complemented
3#23752858C211yesmaximal, characteristic, complemented
4#23752594C211yesmaximal, characteristic, complemented
5#23752451C211yesmaximal, characteristic, complemented
6#23752446C211yesmaximal, characteristic, complemented
7#23752427C211yesmaximal, characteristic, complemented
8#23752424C211yesmaximal, characteristic, complemented
9#23752363C211yesmaximal, characteristic, complemented
10#23752362C211yesmaximal, characteristic, complemented
11#23752357C211yesmaximal, characteristic, complemented
12#23752355C211yesmaximal, characteristic, complemented
13C4×#14558989C211yesmaximal, characteristic, complemented
14D4×C151⋊C8C211yesmaximal, characteristic, complemented
15#546×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic, complemented
17C22×D604C2211yescharacteristic
18#18012759—24no—
19C2×#14558994C2211yescharacteristic, complemented
20C2×#14558992C2211yescharacteristic, complemented
21C2×#14558992C2211yescharacteristic, complemented
22C2×#14558991C2211yescharacteristic, complemented
23C2×#14558991C2211yescharacteristic, complemented
24C2×#14558989—24no—
25C2×#14558989C2211yescharacteristic
26C2×#14558989C2211yescharacteristic
27C2×#14558989C2211yescharacteristic
28C2×#14558989C2211yescharacteristic
29C22×C151⋊C8C2211yescharacteristic
30C22×C151⋊C8C2211yescharacteristic, complemented
31#18012727C2211yescharacteristic, complemented
32#18012724—21no—
33#18012718C2211yescharacteristic
34#18012713C2211yescharacteristic, complemented
35#18012712—21no—
36#18012707—21no—
37C4×D604C2211yescharacteristic, complemented
38C22⋊C4×D151—21no—
39#18012672C2211yescharacteristic, complemented
40C4⋊(C151⋊C8)C2211yescharacteristic, complemented
41#18012663C2211yescharacteristic, complemented
42#18012662C2211yescharacteristic, complemented
43#18012660C2211yescharacteristic, complemented
44#18012660C2211yescharacteristic, complemented
45#18012659C2211yescharacteristic, complemented
46#18012659C2211yescharacteristic, complemented
47C22⋊(C151⋊C8)C2211yescharacteristic
48C22⋊(C151⋊C8)C2211yescharacteristic, complemented
49C4×C151⋊C8C2211yescharacteristic, complemented
50C2×#41×C151C2211yescharacteristic, complemented
51C22×D4×C151C2211yescharacteristic
52#124×C151C2211yescharacteristic, complemented
53#123×C151—21no—
54C22⋊Q8×C151C2211yescharacteristic
55#121×C151—21no—
56#121×C151C2211yescharacteristic, complemented
57#120×C151—21no—
58C4×D4×C151C2211yescharacteristic
59C4×D4×C151C2211yescharacteristic, complemented
60C2×C22⋊C4×C151—21no—
61C23×D151—21no—
62#14559004—22no—
63#14559004—41no—
64C2×Dic302C2311yescharacteristic
65C2×D604—22no—
66C2×D604—21no—
67C2×D604—41no—
68C2×D604C2311yescharacteristic
69C2×D604C2311yescharacteristic
70C2×C22⋊D151—21no—
71C2×C22⋊D151—21no—
72C2×C4×D151—21no—
73C2×C4×D151—21no—
74#14558994—22no—
75#14558992—22no—
76#14558992—41no—
77#14558991—22no—
78#14558991—41no—
79#14558989—22no—
80#14558989—22no—
81#14558989—22no—
82#14558989D414yescomplemented
83C2×C151⋊C8—22no—
84C2×C151⋊C8—22no—
85C2×C151⋊C8C2311yescharacteristic
86C2×C151⋊C8C2311yescharacteristic
87C2×C151⋊C8C2311yescharacteristic
88C2×C151⋊C8C2311yescharacteristic
89C4⋊Dic151C2311yescharacteristic
90Dic151⋊C4—21no—
91C22⋊Dic151—21no—
92(C2×D151)⋊C4—21no—
93(C2×D151)⋊C4—21no—
94(C2×D151)⋊C4—21no—
95(C2×D151)⋊C4—21no—
96C24×C151—21no—
97#41×C151—22no—
98#41×C151—41no—
99C2×Q8×C151C2311yescharacteristic
100C2×D4×C151—22no—
101C2×D4×C151—21no—
102C2×D4×C151—21no—
103C2×D4×C151—21no—
104C2×D4×C151—41no—
105C2×D4×C151D411yescharacteristic
106C2×D4×C151C2311yescharacteristic
107C2×D4×C151C2311yescharacteristic
108C22×C4×C151—21no—
109C22×C4×C151—21no—
110C22×C4×C151C2311yescharacteristic
111C22×C4×C151C2311yescharacteristic
112C4⋊C4×C151—21no—
113C4⋊C4×C151D411yescharacteristic
114C4⋊C4×C151C2311yescharacteristic
115C22⋊C4×C151—21no—
116C22⋊C4×C151—21no—
117C22⋊C4×C151—21no—
118C22⋊C4×C151—21no—
119C22⋊C4×C151—21no—
120C22⋊C4×C151D411yescharacteristic
121C22⋊C4×C151D411yescharacteristic
122C42×C151C2311yescharacteristic
123C22×D151—21no—
124C22×D151—21no—
125C22×D151—42no—
126C22×D151—42no—
127C22×D151—81no—
128Dic302—21no—
129Dic302—21no—
130D604—21no—
131D604—21no—
132D604—21no—
133D604—42no—
134D604C2×D412yes—
135C22⋊D151—42no—
136C22⋊D151—81no—
137C2×Dic151—21no—
138C2×Dic151—21no—
139C4×D151—42no—
140C4×D151—81no—
141C151⋊C8—21no—
142C151⋊C8—21no—
143C151⋊C8—21no—
144C151⋊C8C2×D412yes—
145C23×C151—21no—
146C23×C151—21no—
147C23×C151—42no—
148C23×C151—42no—
149C23×C151—81no—
150C23×C151C2×D411yescharacteristic
151C23×C151C2×D411yescharacteristic
152Q8×C151—21no—
153Q8×C151—21no—
154D4×C151—22no—
155D4×C151—21no—
156D4×C151—21no—
157D4×C151—21no—
158D4×C151—42no—
159D4×C151—42no—
160D4×C151—81no—
161D4×C151C2×D412yes—
162C2×C4×C151—21no—
163C2×C4×C151—21no—
164C2×C4×C151—21no—
165C2×C4×C151—21no—
166C2×C4×C151—21no—
167C2×C4×C151—21no—
168C2×C4×C151—42no—
169C2×C4×C151—81no—
170C2×C4×C151C2×D411yescharacteristic
171C2×C4×C151C2×D411yescharacteristic
172C2×C4×C151C2×D411yescharacteristic
173C2×C4×C151C2×D411yescharacteristic
174C2×C4×C151C2411yescharacteristic
175C22×C151—21no—
176C22×C151—21no—
177C22×C151—21no—
178C22×C151—22no—
179C22×C151—21no—
180C22×C151—21no—
181C22×C151—41no—
182C22×C151—41no—
183C22×C151—41no—
184C22×C151—41no—
185C22×C151—41no—
186C22×C151—84no—
187C22×C151#13512yescomplemented
188C22×C151C22×D411yescharacteristic
189C2×D151—22no—
190C2×D151—41no—
191C2×D151—41no—
192C2×D151—41no—
193C2×D151—41no—
194C2×D151—41no—
195C2×D151—84no—
196C4×C151—21no—
197C4×C151—21no—
198C4×C151—21no—
199C4×C151—21no—
200C4×C151—41no—
201C4×C151—41no—
202C4×C151C22×D411yescharacteristic
203C4×C151H(5,𝔽2)11yescharacteristic
204Dic151—41no—
205Dic151—41no—
206C2×C151—22no—
207C2×C151—41no—
208C2×C151—42no—
209C2×C151—81no—
210C2×C151D4211yescharacteristic
211C2×C151C2×#13511yescharacteristic
212C2×C151#57611yescharacteristic
213D151—42no—
214D151—81no—
215C151#328011yescharacteristic, complemented, Sylow
216#3280—1511nomaximal, Sylow
217C2×#135—1511no—
218C22×D8—1511no—
219#546—1511no—
220#546D15111yescharacteristic, complemented
221#495—1511no—
222#467—1511no—
223#466—1511no—
224#463—1511no—
225#463—1511no—
226#450—1511no—
227#450—1511no—
228#449—1511no—
229#449—1511no—
230C4×D8—1511no—
231C8×D4—1511no—
232C2×#41—1511no—
233C2×#41C2×D15111yescharacteristic, complemented
234C22×D4—1511no—
235C22×D4C2×D15111yescharacteristic
236#135—3024no—
237C2×Q16—1511no—
238C2×SD16—1511no—
239C2×SD16—1511no—
240C2×SD16—1511no—
241C2×SD16—1511no—
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#124C2×D15111yescharacteristic, complemented
251#123—21no—
252#123—3021no—
253C22⋊Q8—1511no—
254C22⋊Q8C2×D15111yescharacteristic
255#121—21no—
256#121—3021no—
257#121—1511no—
258#121C2×D15111yescharacteristic, complemented
259#120—21no—
260#120—3021no—
261C4×D4—1511no—
262C4×D4C2×D15111yescharacteristic
263C4×D4C2×D15111yescharacteristic, complemented
264C2×C22⋊C4—21no—
265C2×C22⋊C4—3021no—
266#107—1511no—
267C4⋊C8—1511no—
268#103—1511no—
269#103—1511no—
270#102—1511no—
271#102—1511no—
272#102—1511no—
273#102—1511no—
274C22⋊C8—1511no—
275C22⋊C8—1511no—
276C4×C8—1511no—
277C24—21no—
278C24—3021no—
279#41—22no—
280#41—41no—
281#41—3022no—
282#41—6041no—
283C2×Q8—1511no—
284C2×Q8C22×D15111yescharacteristic
285C2×D4—22no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—41no—
290C2×D4—3022no—
291C2×D4—3021no—
292C2×D4—3021no—
293C2×D4—3021no—
294C2×D4—6041no—
295C2×D4—1511no—
296C2×D4—1511no—
297C2×D4C22⋊D15111yescharacteristic
298C2×D4C22×D15111yescharacteristic
299C2×D4C22×D15111yescharacteristic
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—3021no—
303C22×C4—3021no—
304C22×C4C22×D15111yescharacteristic
305C22×C4C22×D15111yescharacteristic
306Q16—3022no—
307SD16—3022no—
308SD16—3022no—
309SD16—6041no—
310SD16—6041no—
311D8—3022no—
312D8—3022no—
313D8—3022no—
314D8—1514no—
315C2×C8—3022no—
316C2×C8—3022no—
317C2×C8—1511no—
318C2×C8—1511no—
319C2×C8—1511no—
320C2×C8—1511no—
321C4⋊C4—21no—
322C4⋊C4—3021no—
323C4⋊C4—1511no—
324C4⋊C4C22⋊D15111yescharacteristic
325C4⋊C4C22×D15111yescharacteristic
326C22⋊C4—21no—
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—21no—
330C22⋊C4—21no—
331C22⋊C4—3021no—
332C22⋊C4—3021no—
333C22⋊C4—3021no—
334C22⋊C4—3021no—
335C22⋊C4—3021no—
336C22⋊C4C22⋊D15111yescharacteristic
337C22⋊C4C22⋊D15111yescharacteristic
338C42C22×D15111yescharacteristic
339C23—21no—
340C23—21no—
341C23—42no—
342C23—42no—
343C23—81no—
344C23—3021no—
345C23—3021no—
346C23—6042no—
347C23—6042no—
348C23—12081no—
349C23C2×C22⋊D15111yescharacteristic
350C23C2×C22⋊D15111yescharacteristic
351Q8—21no—
352Q8—21no—
353Q8—3021no—
354Q8—3021no—
355D4—22no—
356D4—21no—
357D4—21no—
358D4—21no—
359D4—42no—
360D4—42no—
361D4—81no—
362D4—3021no—
363D4—3021no—
364D4—3021no—
365D4—6042no—
366D4—6042no—
367D4—1512no—
368D4—12081no—
369D4D4×D15112yes—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—42no—
377C2×C4—81no—
378C2×C4—3021no—
379C2×C4—3021no—
380C2×C4—6042no—
381C2×C4—12081no—
382C2×C4C2×C22⋊D15111yescharacteristic
383C2×C4C2×C22⋊D15111yescharacteristic
384C2×C4C2×C22⋊D15111yescharacteristic
385C2×C4C2×C22⋊D15111yescharacteristic
386C2×C4C23×D15111yescharacteristic
387C8—3021no—
388C8—3021no—
389C8—3021no—
390C8—1512no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—22no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—84no—
403C22—3022no—
404C22—6041no—
405C22—6041no—
406C22—6041no—
407C22—6041no—
408C22—6041no—
409C22—12084no—
410C22#1801275912yescomplemented
411C22C22×C22⋊D15111yescharacteristic
412C4—21no—
413C4—21no—
414C4—21no—
415C4—21no—
416C4—41no—
417C4—41no—
418C4—6041no—
419C4—6041no—
420C4C2×D4×D15111yescharacteristic
421C4#1801278411yescharacteristic
422C2—22no—
423C2—41no—
424C2—42no—
425C2—81no—
426C2—6042no—
427C2—12081no—
428C2D4×C22⋊D15111yescharacteristic
429C2C2×#1801275911yescharacteristic
430C2#2375301511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#546×C151C2
socleC22×C151C22×D4
hypercenter#546D151
hypocenterC151#3280
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. C2×#18012759C2semidirect
2. C22×#14558989C2semidirect
3. #23752858C2semidirect
4. #23752594C2semidirect
5. #23752451C2semidirect
6. #23752446C2semidirect
7. #23752427C2semidirect
8. #23752424C2semidirect
9. #23752363C2semidirect
10. #23752362C2semidirect
11. #23752357C2semidirect
12. #23752355C2semidirect
13. C4×#14558989C2semidirect
14. D4×C151⋊C8C2semidirect
15. #546×C151C2semidirect
16. C2×#14559004C22semidirect
19. C2×#14558994C22semidirect
20. C2×#14558992C22semidirect
21. C2×#14558992C22semidirect
22. C2×#14558991C22semidirect
23. C2×#14558991C22semidirect
30. C22×C151⋊C8C22semidirect
31. #18012727C22semidirect
34. #18012713C22semidirect
37. C4×D604C22semidirect
39. #18012672C22semidirect
40. C4⋊(C151⋊C8)C22semidirect
41. #18012663C22semidirect
42. #18012662C22semidirect
43. #18012660C22semidirect
44. #18012660C22semidirect
45. #18012659C22semidirect
46. #18012659C22semidirect
48. C22⋊(C151⋊C8)C22semidirect
49. C4×C151⋊C8C22semidirect
50. C2×#41×C151C22semidirect
52. #124×C151C22semidirect
56. #121×C151C22semidirect
59. C4×D4×C151C22semidirect
82. #14558989D4semidirect
187. C22×C151#135semidirect
215. C151#3280semidirect
220. #546D151semidirect
233. C2×#41C2×D151semidirect
250. #124C2×D151semidirect
258. #121C2×D151semidirect
263. C4×D4C2×D151semidirect
410. C22#18012759semidirect

Maximal subgroups

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

subgroupindex
C2×#180127592
C22×#145589892
#237528582
#237525942
#237524512
#237524462
#237524272
#237524242
#237523632
#237523622
#237523572
#237523552
C4×#145589892
D4×C151⋊C82
#546×C1512
#3280151