Finite Group Databasebeta

← C151×#23061 #50327986

Subgroups — C151×#23061 #50327986

Order 38656.

826 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#476×C151C211yesmaximal, characteristic
2#2369×C151C211yesmaximal, characteristic, complemented
3#2354×C151C211yesmaximal, characteristic
4#1990×C151C211yesmaximal, characteristic, complemented
5#1948×C151C211yesmaximal, characteristic, complemented
6#1934×C151C212yesmaximal
7#1926×C151C212yesmaximal
8#1920×C151C212yesmaximal, complemented
9C4×#106×C151C212yesmaximal, complemented
10C8×C4⋊C4×C151C211yesmaximal, characteristic, complemented
11C4×#102×C151C211yesmaximal, characteristic
12C2×C4⋊Q8×C151C2211yescharacteristic
13C2×C4×D4×C151C2211yescharacteristic
14C2×#117×C151—21no—
15#476×C151C418yescomplemented
16C2×#106×C151C2212yes—
17C2×#106×C151C2212yes—
18C2×C4⋊C8×C151C2211yescharacteristic
19C2×#102×C151C2211yescharacteristic
20C2×#102×C151C2211yescharacteristic
21C2×#102×C151C2212yes—
22C2×C4×C8×C151C2212yes—
23C2×C4×C8×C151C2211yescharacteristic
24#391×C151—22no—
25#390×C151C2212yes—
26#389×C151—21no—
27#389×C151C2212yes—
28#388×C151—22no—
29#384×C151C2211yescharacteristic
30#380×C151—21no—
31C4×C4⋊C4×C151—21no—
32C4×C4⋊C4×C151C2212yes—
33C4×C4⋊C4×C151C2212yes—
34C4×C4⋊C4×C151C2211yescharacteristic
35C4×C4⋊C4×C151C2211yescharacteristic
36#340×C151C2211yescharacteristic
37#340×C151C2212yes—
38#340×C151C2212yes—
39#340×C151C2212yes—
40#340×C151C2211yescharacteristic
41#336×C151C2212yes—
42C22×Q8×C151—21no—
43C22×D4×C151C2311yescharacteristic
44C23×C4×C151—21no—
45C22×C8×C151C2311yescharacteristic
46C22×C8×C151C2312yes—
47C22×C8×C151C2311yescharacteristic
48C4⋊Q8×C151—22no—
49C4⋊Q8×C151C2×C414yes—
50C4×D4×C151—22no—
51C4×D4×C151C2×C414yes—
52#117×C151—44no—
53C2×C4⋊C4×C151—21no—
54C2×C4⋊C4×C151—21no—
55C2×C4⋊C4×C151—21no—
56C2×C4⋊C4×C151—22no—
57C2×C4⋊C4×C151D411yescharacteristic
58C2×C4⋊C4×C151D411yescharacteristic
59C2×C4⋊C4×C151C2312yes—
60C2×C4⋊C4×C151C2311yescharacteristic
61C2×C4⋊C4×C151C2311yescharacteristic
62C2×C4⋊C4×C151C2312yes—
63C2×C4⋊C4×C151C2311yescharacteristic
64C2×C22⋊C4×C151—21no—
65C2×C22⋊C4×C151—22no—
66C2×C22⋊C4×C151—22no—
67C2×C42×C151—21no—
68C2×C42×C151—22no—
69C2×C42×C151—22no—
70C2×C42×C151C2312yes—
71C2×C42×C151C2311yescharacteristic
72#106×C151—24no—
73#106×C151C2×C418yes—
74C4⋊C8×C151C2×C414yes—
75#102×C151—22no—
76#102×C151—22no—
77#102×C151C2×C418yes—
78C4×C8×C151—24no—
79C4×C8×C151—22no—
80#95×C151—22no—
81#95×C151—22no—
82#95×C151—22no—
83#95×C151—21no—
84#95×C151D412yes—
85C24×C151—21no—
86C2×Q8×C151—24no—
87C2×Q8×C151—81no—
88C2×Q8×C151—81no—
89C2×D4×C151—21no—
90C2×D4×C151—21no—
91C2×D4×C151—21no—
92C2×D4×C151—21no—
93C2×D4×C151—21no—
94C2×D4×C151C22×C412yes—
95C22×C4×C151—21no—
96C22×C4×C151—21no—
97C22×C4×C151—22no—
98C22×C4×C151—24no—
99C22×C4×C151—21no—
100C22×C4×C151—22no—
101C22×C4×C151—42no—
102C22×C4×C151—42no—
103C22×C4×C151C2×D412yes—
104C22×C4×C151C2×D411yescharacteristic
105C22×C4×C151C2×D412yes—
106C22×C4×C151C2×D411yescharacteristic
107C22×C4×C151C2411yescharacteristic
108C2×C8×C151—22no—
109C2×C8×C151—21no—
110C2×C8×C151—22no—
111C2×C8×C151—21no—
112C2×C8×C151—21no—
113C2×C8×C151—21no—
114C2×C8×C151—21no—
115C2×C8×C151C22×C414yes—
116C2×C8×C151#4112yes—
117C4⋊C4×C151—24no—
118C4⋊C4×C151—22no—
119C4⋊C4×C151—21no—
120C4⋊C4×C151—22no—
121C4⋊C4×C151—21no—
122C4⋊C4×C151—21no—
123C4⋊C4×C151—22no—
124C4⋊C4×C151—21no—
125C4⋊C4×C151—22no—
126C4⋊C4×C151—42no—
127C4⋊C4×C151—81no—
128C4⋊C4×C151—82no—
129C4⋊C4×C151SD1614yes—
130C4⋊C4×C151C22×C414yes—
131C4⋊C4×C151C22×C412yes—
132C4⋊C4×C151#4112yes—
133C22⋊C4×C151—24no—
134C22⋊C4×C151—44no—
135C22⋊C4×C151—82no—
136C42×C151—22no—
137C42×C151—22no—
138C42×C151—44no—
139C42×C151—42no—
140C42×C151—82no—
141C42×C151C22×C412yes—
142C42×C151#4112yes—
143C23×C151—22no—
144C23×C151—41no—
145C23×C151—41no—
146C23×C151—41no—
147C23×C151—41no—
148C23×C151—41no—
149C23×C151—41no—
150C23×C151C22×D411yescharacteristic
151Q8×C151—84no—
152D4×C151—22no—
153D4×C151—22no—
154D4×C151—41no—
155D4×C151—41no—
156C2×C4×C151—22no—
157C2×C4×C151—21no—
158C2×C4×C151—21no—
159C2×C4×C151—22no—
160C2×C4×C151—24no—
161C2×C4×C151—22no—
162C2×C4×C151—22no—
163C2×C4×C151—22no—
164C2×C4×C151—22no—
165C2×C4×C151—22no—
166C2×C4×C151—41no—
167C2×C4×C151—41no—
168C2×C4×C151—41no—
169C2×C4×C151—42no—
170C2×C4×C151—42no—
171C2×C4×C151—41no—
172C2×C4×C151—48no—
173C2×C4×C151—41no—
174C2×C4×C151—42no—
175C2×C4×C151—42no—
176C2×C4×C151—41no—
177C2×C4×C151—42no—
178C2×C4×C151—41no—
179C2×C4×C151C4×D412yes—
180C2×C4×C151C4×D412yes—
181C2×C4×C151C2×SD1614yes—
182C2×C4×C151C2×SD1612yes—
183C2×C4×C151#13512yes—
184C2×C4×C151C23×C411yescharacteristic
185C2×C4×C151C2×#4111yescharacteristic
186C2×C4×C151C2×#4111yescharacteristic
187C2×C4×C151C2×#4111yescharacteristic
188C2×C4×C1512−1+411yescharacteristic
189C2×C4×C1512−1+411yescharacteristic
190C8×C151—24no—
191C8×C151—22no—
192C8×C151—41no—
193C22×C151—42no—
194C22×C151—42no—
195C22×C151—42no—
196C22×C151—81no—
197C22×C151—81no—
198C22×C151—81no—
199C22×C151—81no—
200C22×C151C2×C4×D411yescharacteristic
201C22×C151#54711yescharacteristic
202C22×C151#54811yescharacteristic
203C22×C151C22×SD1611yescharacteristic
204C22×C151C2×#13511yescharacteristic
205C22×C151#57611yescharacteristic
206C22×C151#57711yescharacteristic
207C4×C151—24no—
208C4×C151—22no—
209C4×C151—42no—
210C4×C151—42no—
211C4×C151—42no—
212C4×C151—44no—
213C4×C151—81no—
214C4×C151—82no—
215C4×C151C4×SD1614yes—
216C4×C151C4×#4111yescharacteristic
217C4×C151#51911yescharacteristic
218C4×C151#55211yescharacteristic
219C4×C151#55611yescharacteristic
220C2×C151—82no—
221C2×C151#236211yescharacteristic
222C2×C151C2×C4×SD1611yescharacteristic
223C2×C151#294611yescharacteristic
224C2×C151#333511yescharacteristic
225C2×C151#334111yescharacteristic
226C2×C151#336011yescharacteristic
227C2×C151#336211yescharacteristic
228#23061C15111yesmaximal, characteristic, direct product factor, Sylow
229C151#2306111yescharacteristic, direct product factor, Sylow
230C2×#476C2×C15111yescharacteristic
231#2369C2×C15111yescharacteristic, complemented
232#2354C2×C15111yescharacteristic
233#1990C2×C15111yescharacteristic, complemented
234#1948C2×C15111yescharacteristic, complemented
235#1934C2×C15112yes—
236#1926C2×C15112yes—
237#1920C2×C15112yescomplemented
238C4×#106C2×C15112yescomplemented
239C8×C4⋊C4C2×C15111yescharacteristic, complemented
240C4×#102C2×C15111yescharacteristic
241C2×C4⋊Q8C22×C15111yescharacteristic
242C2×C4×D4C22×C15111yescharacteristic
243C2×#117—21no—
244#476C4×C15118yescomplemented
245C2×#106C22×C15112yes—
246C2×#106C22×C15112yes—
247C2×C4⋊C8C22×C15111yescharacteristic
248C2×#102C22×C15111yescharacteristic
249C2×#102C22×C15111yescharacteristic
250C2×#102C22×C15112yes—
251C2×C4×C8C22×C15112yes—
252C2×C4×C8C22×C15111yescharacteristic
253#391—22no—
254#390C22×C15112yes—
255#389—21no—
256#389C22×C15112yes—
257#388—22no—
258#384C22×C15111yescharacteristic
259#380—21no—
260C4×C4⋊C4—21no—
261C4×C4⋊C4C22×C15112yes—
262C4×C4⋊C4C22×C15112yes—
263C4×C4⋊C4C22×C15111yescharacteristic
264C4×C4⋊C4C22×C15111yescharacteristic
265#340C22×C15111yescharacteristic
266#340C22×C15112yes—
267#340C22×C15112yes—
268#340C22×C15112yes—
269#340C22×C15111yescharacteristic
270#336C22×C15112yes—
271C22×Q8—21no—
272C22×D4C23×C15111yescharacteristic
273C23×C4—21no—
274C22×C8C23×C15111yescharacteristic
275C22×C8C23×C15111yescharacteristic
276C22×C8C23×C15112yes—
277C4⋊Q8—22no—
278C4⋊Q8C2×C4×C15114yes—
279C4×D4—22no—
280C4×D4C2×C4×C15114yes—
281#117—44no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4D4×C15111yescharacteristic
287C2×C4⋊C4D4×C15111yescharacteristic
288C2×C4⋊C4C23×C15112yes—
289C2×C4⋊C4C23×C15111yescharacteristic
290C2×C4⋊C4C23×C15111yescharacteristic
291C2×C4⋊C4C23×C15111yescharacteristic
292C2×C4⋊C4C23×C15112yes—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—22no—
295C2×C22⋊C4—22no—
296C2×C42—22no—
297C2×C42—21no—
298C2×C42—22no—
299C2×C42C23×C15112yes—
300C2×C42C23×C15111yescharacteristic
301#106—24no—
302#106C2×C4×C15118yes—
303C4⋊C8C2×C4×C15114yes—
304#102—22no—
305#102—22no—
306#102C2×C4×C15118yes—
307C4×C8—24no—
308C4×C8—22no—
309#95—22no—
310#95—22no—
311#95—22no—
312#95—21no—
313#95D4×C15112yes—
314C24—21no—
315C2×Q8—24no—
316C2×Q8—81no—
317C2×Q8—81no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—21no—
323C2×D4C22×C4×C15112yes—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—22no—
327C22×C4—24no—
328C22×C4—21no—
329C22×C4—22no—
330C22×C4—42no—
331C22×C4—42no—
332C22×C4C2×D4×C15112yes—
333C22×C4C2×D4×C15111yescharacteristic
334C22×C4C2×D4×C15112yes—
335C22×C4C2×D4×C15111yescharacteristic
336C22×C4C24×C15111yescharacteristic
337C2×C8—22no—
338C2×C8—21no—
339C2×C8—22no—
340C2×C8—21no—
341C2×C8—21no—
342C2×C8—21no—
343C2×C8—21no—
344C2×C8C22×C4×C15114yes—
345C2×C8#41×C15112yes—
346C4⋊C4—24no—
347C4⋊C4—22no—
348C4⋊C4—21no—
349C4⋊C4—22no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—22no—
353C4⋊C4—21no—
354C4⋊C4—22no—
355C4⋊C4—42no—
356C4⋊C4—81no—
357C4⋊C4—82no—
358C4⋊C4SD16×C15114yes—
359C4⋊C4C22×C4×C15114yes—
360C4⋊C4C22×C4×C15112yes—
361C4⋊C4#41×C15112yes—
362C22⋊C4—24no—
363C22⋊C4—44no—
364C22⋊C4—82no—
365C42—22no—
366C42—22no—
367C42—44no—
368C42—42no—
369C42—82no—
370C42C22×C4×C15112yes—
371C42#41×C15112yes—
372C23—22no—
373C23—41no—
374C23—41no—
375C23—41no—
376C23—41no—
377C23—41no—
378C23—41no—
379C23C22×D4×C15111yescharacteristic
380Q8—84no—
381D4—22no—
382D4—22no—
383D4—41no—
384D4—41no—
385C2×C4—22no—
386C2×C4—21no—
387C2×C4—22no—
388C2×C4—21no—
389C2×C4—22no—
390C2×C4—24no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—42no—
399C2×C4—41no—
400C2×C4—42no—
401C2×C4—48no—
402C2×C4—41no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—41no—
406C2×C4—42no—
407C2×C4—41no—
408C2×C4C4×D4×C15112yes—
409C2×C4C4×D4×C15112yes—
410C2×C4C2×SD16×C15114yes—
411C2×C4C2×SD16×C15112yes—
412C2×C4#135×C15112yes—
413C2×C4C23×C4×C15111yescharacteristic
414C2×C4C2×#41×C15111yescharacteristic
415C2×C4C2×#41×C15111yescharacteristic
416C2×C4C2×#41×C15111yescharacteristic
417C2×C42−1+4×C15111yescharacteristic
418C2×C42−1+4×C15111yescharacteristic
419C8—24no—
420C8—22no—
421C8—41no—
422C22—42no—
423C22—42no—
424C22—42no—
425C22—81no—
426C22—81no—
427C22—81no—
428C22—81no—
429C22C2×C4×D4×C15111yescharacteristic
430C22#547×C15111yescharacteristic
431C22#548×C15111yescharacteristic
432C22C22×SD16×C15111yescharacteristic
433C22C2×#135×C15111yescharacteristic
434C22#576×C15111yescharacteristic
435C22#577×C15111yescharacteristic
436C4—22no—
437C4—24no—
438C4—42no—
439C4—42no—
440C4—44no—
441C4—42no—
442C4—82no—
443C4—81no—
444C4C4×SD16×C15114yes—
445C4C4×#41×C15111yescharacteristic
446C4#519×C15111yescharacteristic
447C4#552×C15111yescharacteristic
448C4#556×C15111yescharacteristic
449C2—82no—
450C2#2362×C15111yescharacteristic
451C2C2×C4×SD16×C15111yescharacteristic
452C2#2946×C15111yescharacteristic
453C2#3335×C15111yescharacteristic
454C2#3341×C15111yescharacteristic
455C2#3360×C15111yescharacteristic
456C2#3362×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C4×C4⋊C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2369×C151C2semidirect
4. #1990×C151C2semidirect
5. #1948×C151C2semidirect
8. #1920×C151C2semidirect
9. C4×#106×C151C2semidirect
10. C8×C4⋊C4×C151C2semidirect
15. #476×C151C4semidirect
228. #23061C151direct (N × H)
229. C151#23061direct (N × H)
231. #2369C2×C151semidirect
233. #1990C2×C151semidirect
234. #1948C2×C151semidirect
237. #1920C2×C151semidirect
238. C4×#106C2×C151semidirect
239. C8×C4⋊C4C2×C151semidirect
244. #476C4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#476×C1512
#2369×C1512
#2354×C1512
#1990×C1512
#1948×C1512
#1934×C1512
#1926×C1512
#1920×C1512
C4×#106×C1512
C8×C4⋊C4×C1512
C4×#102×C1512
#23061151