Finite Group Databasebeta

← #2472×C151 #34065804

Subgroups — #2472×C151 #34065804

Order 19328.

786 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#124×C151C211yesmaximal, characteristic, complemented
2C2×C22⋊Q8×C151C211yesmaximal, characteristic, complemented
3C2×#120×C151C211yesmaximal, characteristic
4C22×C22⋊C4×C151C211yesmaximal, characteristic, complemented
5#397×C151C211yesmaximal, characteristic, complemented
6#394×C151C211yesmaximal, characteristic, complemented
7#394×C151C211yesmaximal, characteristic, complemented
8#393×C151C211yesmaximal, characteristic, complemented
9#390×C151C211yesmaximal, characteristic, complemented
10#388×C151C211yesmaximal, characteristic, complemented
11#388×C151C211yesmaximal, characteristic, complemented
12#386×C151C211yesmaximal, characteristic, complemented
13#386×C151C211yesmaximal, characteristic, complemented
14#379×C151C211yesmaximal, characteristic, complemented
15C4×C22⋊C4×C151C211yesmaximal, characteristic, complemented
16C25×C151C2211yescharacteristic
17C22×Q8×C151C2211yescharacteristic, complemented
18C22×D4×C151C2211yescharacteristic
19C22×D4×C151C2211yescharacteristic
20C22×D4×C151C2211yescharacteristic
21C23×C4×C151C2211yescharacteristic
22C23×C4×C151C2211yescharacteristic
23#124×C151—24no—
24C22⋊Q8×C151—24no—
25#120×C151—24no—
26C2×C4⋊C4×C151C2211yescharacteristic, complemented
27C2×C4⋊C4×C151C2211yescharacteristic, complemented
28C2×C4⋊C4×C151C2211yescharacteristic, complemented
29C2×C22⋊C4×C151—24no—
30C2×C22⋊C4×C151C2211yescharacteristic
31C2×C22⋊C4×C151C2211yescharacteristic
32C2×C22⋊C4×C151C2211yescharacteristic
33C2×C22⋊C4×C151C2211yescharacteristic
34C2×C22⋊C4×C151C2211yescharacteristic
35C2×C22⋊C4×C151C2211yescharacteristic
36C2×C22⋊C4×C151C2211yescharacteristic
37C2×C22⋊C4×C151C2211yescharacteristic
38C2×C22⋊C4×C151C2211yescharacteristic
39C2×C22⋊C4×C151C2211yescharacteristic
40C2×C22⋊C4×C151C2211yescharacteristic
41C2×C22⋊C4×C151C2211yescharacteristic
42C2×C22⋊C4×C151C2211yescharacteristic
43C2×C22⋊C4×C151C2211yescharacteristic, complemented
44C2×C22⋊C4×C151C2211yescharacteristic, complemented
45C2×C22⋊C4×C151C2211yescharacteristic, complemented
46C2×C22⋊C4×C151C2211yescharacteristic, complemented
47C2×C42×C151C2211yescharacteristic, complemented
48C2×C42×C151C2211yescharacteristic, complemented
49#95×C151C2211yescharacteristic, complemented
50#95×C151C2211yescharacteristic, complemented
51#95×C151C2211yescharacteristic, complemented
52#95×C151C2211yescharacteristic, complemented
53#95×C151C2211yescharacteristic, complemented
54#95×C151C2211yescharacteristic, complemented
55C24×C151—22no—
56C24×C151—22no—
57C24×C151—22no—
58C24×C151—22no—
59C24×C151—22no—
60C24×C151—41no—
61C24×C151—41no—
62C24×C151C2311yescharacteristic
63C24×C151C2311yescharacteristic
64C24×C151C2311yescharacteristic
65C24×C151C2311yescharacteristic
66C2×Q8×C151—22no—
67C2×Q8×C151—22no—
68C2×Q8×C151—41no—
69C2×D4×C151—22no—
70C2×D4×C151—22no—
71C2×D4×C151—22no—
72C2×D4×C151—22no—
73C2×D4×C151—22no—
74C2×D4×C151—22no—
75C2×D4×C151—22no—
76C2×D4×C151—41no—
77C2×D4×C151—41no—
78C22×C4×C151—22no—
79C22×C4×C151—22no—
80C22×C4×C151—22no—
81C22×C4×C151—22no—
82C22×C4×C151—41no—
83C22×C4×C151—41no—
84C22×C4×C151C2311yescharacteristic
85C22×C4×C151C2311yescharacteristic
86C22×C4×C151C2311yescharacteristic
87C22×C4×C151C2311yescharacteristic
88C22×C4×C151C2311yescharacteristic
89C22×C4×C151C2311yescharacteristic
90C22×C4×C151C2311yescharacteristic
91C22×C4×C151C2311yescharacteristic
92C22×C4×C151C2311yescharacteristic
93C22×C4×C151C2311yescharacteristic
94C22×C4×C151C2311yescharacteristic
95C4⋊C4×C151—22no—
96C4⋊C4×C151—22no—
97C4⋊C4×C151—22no—
98C22⋊C4×C151—22no—
99C22⋊C4×C151—22no—
100C22⋊C4×C151—22no—
101C22⋊C4×C151—22no—
102C22⋊C4×C151—22no—
103C22⋊C4×C151—22no—
104C22⋊C4×C151—22no—
105C22⋊C4×C151—22no—
106C22⋊C4×C151—22no—
107C22⋊C4×C151—22no—
108C22⋊C4×C151—22no—
109C22⋊C4×C151—41no—
110C22⋊C4×C151—41no—
111C22⋊C4×C151—41no—
112C22⋊C4×C151—41no—
113C22⋊C4×C151D414yes—
114C22⋊C4×C151D414yescomplemented
115C42×C151—22no—
116C42×C151—41no—
117C23×C151—21no—
118C23×C151—21no—
119C23×C151—21no—
120C23×C151—21no—
121C23×C151—28no—
122C23×C151—21no—
123C23×C151—21no—
124C23×C151—21no—
125C23×C151—21no—
126C23×C151—21no—
127C23×C151—21no—
128C23×C151—21no—
129C23×C151—21no—
130C23×C151—21no—
131C23×C151—21no—
132C23×C151—21no—
133C23×C151—21no—
134C23×C151—21no—
135C23×C151—21no—
136C23×C151—21no—
137C23×C151—21no—
138C23×C151—21no—
139C23×C151—21no—
140C23×C151—21no—
141C23×C151—44no—
142C23×C151—44no—
143C23×C151—44no—
144C23×C151—44no—
145C23×C151—44no—
146C23×C151—44no—
147C23×C151C2×D412yes—
148C23×C151C2×D412yes—
149C23×C151#4112yes—
150C23×C151#4112yes—
151C23×C151#4112yes—
152C23×C151C2411yescharacteristic
153Q8×C151—44no—
154D4×C151—44no—
155D4×C151—44no—
156D4×C151—44no—
157C2×C4×C151—21no—
158C2×C4×C151—21no—
159C2×C4×C151—21no—
160C2×C4×C151—21no—
161C2×C4×C151—21no—
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—21no—
169C2×C4×C151—21no—
170C2×C4×C151—21no—
171C2×C4×C151—21no—
172C2×C4×C151—21no—
173C2×C4×C151—21no—
174C2×C4×C151—21no—
175C2×C4×C151—21no—
176C2×C4×C151—21no—
177C2×C4×C151—21no—
178C2×C4×C151—21no—
179C2×C4×C151—21no—
180C2×C4×C151—21no—
181C2×C4×C151—21no—
182C2×C4×C151—21no—
183C2×C4×C151—21no—
184C2×C4×C151—21no—
185C2×C4×C151—21no—
186C2×C4×C151—44no—
187C2×C4×C151—44no—
188C2×C4×C151C2×D412yes—
189C2×C4×C151C2×D412yes—
190C2×C4×C151C2×D412yes—
191C2×C4×C151C2×D412yes—
192C22×C151—22no—
193C22×C151—22no—
194C22×C151—22no—
195C22×C151—22no—
196C22×C151—22no—
197C22×C151—22no—
198C22×C151—22no—
199C22×C151—22no—
200C22×C151—22no—
201C22×C151—22no—
202C22×C151—22no—
203C22×C151—22no—
204C22×C151—416no—
205C22×C151—41no—
206C22×C151—41no—
207C22×C151—41no—
208C22×C151—41no—
209C22×C151—41no—
210C22×C151—41no—
211C22×C151—41no—
212C22×C151—41no—
213C22×C151—41no—
214C22×C151—41no—
215C22×C151—41no—
216C22×C151—41no—
217C22×C151—41no—
218C22×C151—41no—
219C22×C151—41no—
220C22×C151#12414yescomplemented
221C22×C151C22×D411yescharacteristic
222C22×C151C22×D411yescharacteristic
223C22×C151C2×#4111yescharacteristic
224C22×C151C2×#4111yescharacteristic
225C22×C151C2×#4111yescharacteristic
226C22×C151H(5,𝔽2)11yescharacteristic
227C22×C151H(5,𝔽2)11yescharacteristic
228C4×C151—22no—
229C4×C151—22no—
230C4×C151—22no—
231C4×C151—22no—
232C4×C151—41no—
233C4×C151—41no—
234C4×C151—41no—
235C4×C151—41no—
236C4×C151—41no—
237C4×C151—41no—
238C4×C151—41no—
239C2×C151—24no—
240C2×C151—42no—
241C2×C151—42no—
242C2×C151—81no—
243C2×C151#52511yescharacteristic
244C2×C151C2×#12411yescharacteristic
245C2×C151#53811yescharacteristic
246C2×C151D4211yescharacteristic
247C2×C151#54611yescharacteristic
248C2×C151#54611yescharacteristic
249C2×C151#55111yescharacteristic
250C151#247211yescharacteristic, direct product factor, Sylow
251#2472C15111yesmaximal, characteristic, direct product factor, Sylow
252C2×#124C2×C15111yescharacteristic, complemented
253C2×C22⋊Q8C2×C15111yescharacteristic, complemented
254C2×#120C2×C15111yescharacteristic
255C22×C22⋊C4C2×C15111yescharacteristic, complemented
256#397C2×C15111yescharacteristic, complemented
257#394C2×C15111yescharacteristic, complemented
258#394C2×C15111yescharacteristic, complemented
259#393C2×C15111yescharacteristic, complemented
260#390C2×C15111yescharacteristic, complemented
261#388C2×C15111yescharacteristic, complemented
262#388C2×C15111yescharacteristic, complemented
263#386C2×C15111yescharacteristic, complemented
264#386C2×C15111yescharacteristic, complemented
265#379C2×C15111yescharacteristic, complemented
266C4×C22⋊C4C2×C15111yescharacteristic, complemented
267C25C22×C15111yescharacteristic
268C22×Q8C22×C15111yescharacteristic, complemented
269C22×D4C22×C15111yescharacteristic
270C22×D4C22×C15111yescharacteristic
271C22×D4C22×C15111yescharacteristic
272C23×C4C22×C15111yescharacteristic
273C23×C4C22×C15111yescharacteristic
274#124—24no—
275C22⋊Q8—24no—
276#120—24no—
277C2×C4⋊C4C22×C15111yescharacteristic, complemented
278C2×C4⋊C4C22×C15111yescharacteristic, complemented
279C2×C4⋊C4C22×C15111yescharacteristic, complemented
280C2×C22⋊C4—24no—
281C2×C22⋊C4C22×C15111yescharacteristic
282C2×C22⋊C4C22×C15111yescharacteristic
283C2×C22⋊C4C22×C15111yescharacteristic
284C2×C22⋊C4C22×C15111yescharacteristic
285C2×C22⋊C4C22×C15111yescharacteristic
286C2×C22⋊C4C22×C15111yescharacteristic
287C2×C22⋊C4C22×C15111yescharacteristic
288C2×C22⋊C4C22×C15111yescharacteristic
289C2×C22⋊C4C22×C15111yescharacteristic
290C2×C22⋊C4C22×C15111yescharacteristic
291C2×C22⋊C4C22×C15111yescharacteristic
292C2×C22⋊C4C22×C15111yescharacteristic
293C2×C22⋊C4C22×C15111yescharacteristic
294C2×C22⋊C4C22×C15111yescharacteristic, complemented
295C2×C22⋊C4C22×C15111yescharacteristic, complemented
296C2×C22⋊C4C22×C15111yescharacteristic, complemented
297C2×C22⋊C4C22×C15111yescharacteristic, complemented
298C2×C42C22×C15111yescharacteristic, complemented
299C2×C42C22×C15111yescharacteristic, complemented
300#95C22×C15111yescharacteristic, complemented
301#95C22×C15111yescharacteristic, complemented
302#95C22×C15111yescharacteristic, complemented
303#95C22×C15111yescharacteristic, complemented
304#95C22×C15111yescharacteristic, complemented
305#95C22×C15111yescharacteristic, complemented
306C24—22no—
307C24—22no—
308C24—22no—
309C24—22no—
310C24—22no—
311C24—41no—
312C24—41no—
313C24C23×C15111yescharacteristic
314C24C23×C15111yescharacteristic
315C24C23×C15111yescharacteristic
316C24C23×C15111yescharacteristic
317C2×Q8—22no—
318C2×Q8—22no—
319C2×Q8—41no—
320C2×D4—22no—
321C2×D4—22no—
322C2×D4—22no—
323C2×D4—22no—
324C2×D4—22no—
325C2×D4—22no—
326C2×D4—22no—
327C2×D4—41no—
328C2×D4—41no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—41no—
334C22×C4—41no—
335C22×C4C23×C15111yescharacteristic
336C22×C4C23×C15111yescharacteristic
337C22×C4C23×C15111yescharacteristic
338C22×C4C23×C15111yescharacteristic
339C22×C4C23×C15111yescharacteristic
340C22×C4C23×C15111yescharacteristic
341C22×C4C23×C15111yescharacteristic
342C22×C4C23×C15111yescharacteristic
343C22×C4C23×C15111yescharacteristic
344C22×C4C23×C15111yescharacteristic
345C22×C4C23×C15111yescharacteristic
346C4⋊C4—22no—
347C4⋊C4—22no—
348C4⋊C4—22no—
349C22⋊C4—22no—
350C22⋊C4—22no—
351C22⋊C4—22no—
352C22⋊C4—22no—
353C22⋊C4—22no—
354C22⋊C4—22no—
355C22⋊C4—22no—
356C22⋊C4—22no—
357C22⋊C4—22no—
358C22⋊C4—22no—
359C22⋊C4—22no—
360C22⋊C4—41no—
361C22⋊C4—41no—
362C22⋊C4—41no—
363C22⋊C4—41no—
364C22⋊C4D4×C15114yes—
365C22⋊C4D4×C15114yescomplemented
366C42—22no—
367C42—41no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—28no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—21no—
391C23—21no—
392C23—44no—
393C23—44no—
394C23—44no—
395C23—44no—
396C23—44no—
397C23—44no—
398C23C2×D4×C15112yes—
399C23C2×D4×C15112yes—
400C23#41×C15112yes—
401C23#41×C15112yes—
402C23#41×C15112yes—
403C23C24×C15111yescharacteristic
404Q8—44no—
405D4—44no—
406D4—44no—
407D4—44no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—44no—
438C2×C4—44no—
439C2×C4C2×D4×C15112yes—
440C2×C4C2×D4×C15112yes—
441C2×C4C2×D4×C15112yes—
442C2×C4C2×D4×C15112yes—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—22no—
452C22—22no—
453C22—22no—
454C22—22no—
455C22—416no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—41no—
470C22—41no—
471C22#124×C15114yescomplemented
472C22C22×D4×C15111yescharacteristic
473C22C22×D4×C15111yescharacteristic
474C22C2×#41×C15111yescharacteristic
475C22C2×#41×C15111yescharacteristic
476C22C2×#41×C15111yescharacteristic
477C22H(5,𝔽2)×C15111yescharacteristic
478C22H(5,𝔽2)×C15111yescharacteristic
479C4—22no—
480C4—22no—
481C4—22no—
482C4—22no—
483C4—41no—
484C4—41no—
485C4—41no—
486C4—41no—
487C4—41no—
488C4—41no—
489C4—41no—
490C2—24no—
491C2—42no—
492C2—42no—
493C2—81no—
494C2#525×C15111yescharacteristic
495C2C2×#124×C15111yescharacteristic
496C2#538×C15111yescharacteristic
497C2D42×C15111yescharacteristic
498C2#546×C15111yescharacteristic
499C2#546×C15111yescharacteristic
500C2#551×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C24
commutator, Frattini, cosocleC23C24×C151
prime radicalC2×#120×C151C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#124×C151C2semidirect
2. C2×C22⋊Q8×C151C2semidirect
4. C22×C22⋊C4×C151C2semidirect
5. #397×C151C2semidirect
6. #394×C151C2semidirect
7. #394×C151C2semidirect
8. #393×C151C2semidirect
9. #390×C151C2semidirect
10. #388×C151C2semidirect
11. #388×C151C2semidirect
12. #386×C151C2semidirect
13. #386×C151C2semidirect
14. #379×C151C2semidirect
15. C4×C22⋊C4×C151C2semidirect
17. C22×Q8×C151C22semidirect
26. C2×C4⋊C4×C151C22semidirect
27. C2×C4⋊C4×C151C22semidirect
28. C2×C4⋊C4×C151C22semidirect
43. C2×C22⋊C4×C151C22semidirect
44. C2×C22⋊C4×C151C22semidirect
45. C2×C22⋊C4×C151C22semidirect
46. C2×C22⋊C4×C151C22semidirect
47. C2×C42×C151C22semidirect
48. C2×C42×C151C22semidirect
49. #95×C151C22semidirect
50. #95×C151C22semidirect
51. #95×C151C22semidirect
52. #95×C151C22semidirect
53. #95×C151C22semidirect
54. #95×C151C22semidirect
114. C22⋊C4×C151D4semidirect
220. C22×C151#124semidirect
250. C151#2472direct (N × H)
251. #2472C151direct (N × H)
252. C2×#124C2×C151semidirect
253. C2×C22⋊Q8C2×C151semidirect
255. C22×C22⋊C4C2×C151semidirect
256. #397C2×C151semidirect
257. #394C2×C151semidirect
258. #394C2×C151semidirect
259. #393C2×C151semidirect
260. #390C2×C151semidirect
261. #388C2×C151semidirect
262. #388C2×C151semidirect
263. #386C2×C151semidirect
264. #386C2×C151semidirect
265. #379C2×C151semidirect
266. C4×C22⋊C4C2×C151semidirect
268. C22×Q8C22×C151semidirect
277. C2×C4⋊C4C22×C151semidirect
278. C2×C4⋊C4C22×C151semidirect
279. C2×C4⋊C4C22×C151semidirect
294. C2×C22⋊C4C22×C151semidirect
295. C2×C22⋊C4C22×C151semidirect
296. C2×C22⋊C4C22×C151semidirect
297. C2×C22⋊C4C22×C151semidirect
298. C2×C42C22×C151semidirect
299. C2×C42C22×C151semidirect
300. #95C22×C151semidirect
301. #95C22×C151semidirect
302. #95C22×C151semidirect
303. #95C22×C151semidirect
304. #95C22×C151semidirect
305. #95C22×C151semidirect
365. C22⋊C4D4×C151semidirect
471. C22#124×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#124×C1512
C2×C22⋊Q8×C1512
C2×#120×C1512
C22×C22⋊C4×C1512
#397×C1512
#394×C1512
#393×C1512
#390×C1512
#388×C1512
#386×C1512
#379×C1512
C4×C22⋊C4×C1512
#2472151