Finite Group Databasebeta

← C151×#24312 #50329237

Subgroups — C151×#24312 #50329237

Order 38656.

1170 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3501×C151C211yesmaximal, characteristic, complemented
2#3077×C151C212yesmaximal, complemented
3C4×#127×C151C211yesmaximal, characteristic
4#2060×C151C212yesmaximal, complemented
5#2027×C151C212yesmaximal, complemented
6#1994×C151C212yesmaximal, complemented
7#1887×C151C212yesmaximal
8#1856×C151C212yesmaximal, complemented
9#1800×C151C211yesmaximal, characteristic, complemented
10#554×C151—22no—
11#554×C151—24no—
12D4×Q8×C151—22no—
13#544×C151C2212yes—
14#543×C151—22no—
15#533×C151C2212yes—
16C2×#127×C151C2211yescharacteristic
17C2×C22⋊Q8×C151—22no—
18#518×C151C2212yes—
19C2×C4×D4×C151—22no—
20C2×C4×D4×C151C2211yescharacteristic
21C2×C4×D4×C151C2211yescharacteristic
22#478×C151—24no—
23#476×C151—22no—
24#474×C151—22no—
25#428×C151C2214yes—
26#423×C151C2212yes—
27#418×C151C2214yes—
28C2×#100×C151C2212yes—
29#390×C151—22no—
30#390×C151C2211yescharacteristic
31#390×C151C2211yescharacteristic
32#384×C151C2211yescharacteristic
33C43×C151C2211yescharacteristic
34#343×C151C2212yes—
35#339×C151C2214yes—
36#339×C151C2214yes—
37C22×Q8×C151—22no—
38C22×D4×C151—22no—
39C22×D4×C151C2311yescharacteristic
40C22×D4×C151C2311yescharacteristic
41C23×C4×C151—21no—
42C23×C4×C151D412yes—
43C2×M16×C151C2314yes—
44C4⋊Q8×C151—24no—
45C4⋊Q8×C151D412yescomplemented
46C4⋊Q8×C151D412yescomplemented
47#127×C151—22no—
48#127×C151Q814yescomplemented
49#125×C151—24no—
50#125×C151D414yescomplemented
51C22⋊Q8×C151—24no—
52C22⋊Q8×C151—24no—
53C22⋊Q8×C151—28no—
54C22⋊Q8×C151—28no—
55C22⋊Q8×C151—22no—
56C22⋊Q8×C151—24no—
57C22⋊Q8×C151—22no—
58C4×Q8×C151—22no—
59C4×Q8×C151—22no—
60C4×D4×C151—24no—
61C4×D4×C151—24no—
62C4×D4×C151—22no—
63C4×D4×C151—22no—
64C4×D4×C151—22no—
65C4×D4×C151—22no—
66C4×D4×C151—48no—
67#117×C151C2314yes—
68C2×C4⋊C4×C151—22no—
69C2×C4⋊C4×C151—24no—
70C2×C4⋊C4×C151—22no—
71C2×C4⋊C4×C151C2311yescharacteristic
72C2×C4⋊C4×C151C2311yescharacteristic
73C2×C22⋊C4×C151—21no—
74C2×C22⋊C4×C151—22no—
75C2×C22⋊C4×C151—24no—
76C2×C22⋊C4×C151—22no—
77C2×C22⋊C4×C151D412yes—
78C2×C42×C151—21no—
79C2×C42×C151—21no—
80C2×C42×C151C2311yescharacteristic
81C2×C42×C151C2311yescharacteristic
82C2×C42×C151C2311yescharacteristic
83#107×C151—24no—
84#106×C151—24no—
85C4⋊C8×C151—22no—
86C4⋊C8×C151—22no—
87#102×C151—24no—
88#102×C151—24no—
89#100×C151—24no—
90C24×C151—21no—
91C24×C151C2×D412yes—
92C2×Q8×C151—24no—
93C2×Q8×C151—22no—
94C2×Q8×C151—22no—
95C2×Q8×C151—84no—
96C2×D4×C151—28no—
97C2×D4×C151—22no—
98C2×D4×C151—22no—
99C2×D4×C151—21no—
100C2×D4×C151—22no—
101C2×D4×C151—22no—
102C2×D4×C151—44no—
103C2×D4×C151—44no—
104C2×D4×C151C2×Q812yes—
105C2×D4×C151C2×Q812yescomplemented
106C2×D4×C151#4112yes—
107C22×C4×C151—21no—
108C22×C4×C151—21no—
109C22×C4×C151—24no—
110C22×C4×C151—24no—
111C22×C4×C151—22no—
112C22×C4×C151—22no—
113C22×C4×C151—21no—
114C22×C4×C151—44no—
115C22×C4×C151—44no—
116C22×C4×C151—41no—
117C22×C4×C151—41no—
118C22×C4×C151C2×D411yescharacteristic
119C22×C4×C151C2×D412yes—
120C22×C4×C151C2×D411yescharacteristic
121C22×C4×C151C2411yescharacteristic
122M16×C151—24no—
123M16×C151—24no—
124C2×C8×C151—24no—
125C4⋊C4×C151—24no—
126C4⋊C4×C151—28no—
127C4⋊C4×C151—24no—
128C4⋊C4×C151—22no—
129C4⋊C4×C151—24no—
130C4⋊C4×C151—22no—
131C4⋊C4×C151—22no—
132C4⋊C4×C151—22no—
133C4⋊C4×C151—44no—
134C4⋊C4×C151C2×D414yes—
135C4⋊C4×C151C2×D414yes—
136C22⋊C4×C151—28no—
137C22⋊C4×C151—24no—
138C22⋊C4×C151—24no—
139C22⋊C4×C151—44no—
140C22⋊C4×C151—44no—
141C22⋊C4×C151—42no—
142C42×C151—24no—
143C42×C151—24no—
144C42×C151—21no—
145C42×C151—22no—
146C42×C151—42no—
147C42×C151C2×D412yes—
148C42×C151C2×D412yes—
149C42×C151C2×Q812yescomplemented
150C23×C151—22no—
151C23×C151—22no—
152C23×C151—22no—
153C23×C151—42no—
154C23×C151—42no—
155C23×C151—42no—
156C23×C151—42no—
157C23×C151—41no—
158C23×C151—41no—
159C23×C151C22⋊Q814yes—
160C23×C151C22×D411yescharacteristic
161Q8×C151—44no—
162Q8×C151—82no—
163Q8×C151—84no—
164D4×C151—24no—
165D4×C151—24no—
166D4×C151—24no—
167D4×C151—416no—
168D4×C151—42no—
169C2×C4×C151—22no—
170C2×C4×C151—22no—
171C2×C4×C151—22no—
172C2×C4×C151—22no—
173C2×C4×C151—22no—
174C2×C4×C151—24no—
175C2×C4×C151—22no—
176C2×C4×C151—24no—
177C2×C4×C151—41no—
178C2×C4×C151—41no—
179C2×C4×C151—41no—
180C2×C4×C151—44no—
181C2×C4×C151—42no—
182C2×C4×C151—42no—
183C2×C4×C151—41no—
184C2×C4×C151—82no—
185C2×C4×C151—82no—
186C2×C4×C151—84no—
187C2×C4×C151—84no—
188C2×C4×C151—82no—
189C2×C4×C151#12012yes—
190C2×C4×C151#12011yescharacteristic
191C2×C4×C151#12011yescharacteristic
192C2×C4×C151C22×D412yes—
193C2×C4×C151C22×Q811yescharacteristic
194C2×C4×C151C2×#4111yescharacteristic
195C2×C4×C1512−1+412yes—
196C8×C151—44no—
197C22×C151—21no—
198C22×C151—21no—
199C22×C151—24no—
200C22×C151—44no—
201C22×C151—44no—
202C22×C151—42no—
203C22×C151—42no—
204C22×C151—42no—
205C22×C151—82no—
206C22×C151—82no—
207C22×C151—81no—
208C22×C151—81no—
209C22×C151C2×#12011yescharacteristic
210C22×C151C2×C22⋊Q811yescharacteristic
211C22×C151#53611yescharacteristic
212C4×C151—24no—
213C4×C151—21no—
214C4×C151—22no—
215C4×C151—42no—
216C4×C151—42no—
217C4×C151—44no—
218C4×C151—44no—
219C4×C151—81no—
220C4×C151#45312yes—
221C4×C151#54812yes—
222C4×C151D4×Q812yes—
223C2×C151—21no—
224C2×C151—21no—
225C2×C151—44no—
226C2×C151—82no—
227C2×C151#240911yescharacteristic
228C2×C151C2×#45311yescharacteristic
229C2×C151#301811yescharacteristic
230#24312C15111yesmaximal, characteristic, direct product factor, Sylow
231C151#2431211yescharacteristic, direct product factor, Sylow
232#3501C2×C15111yescharacteristic, complemented
233#3077C2×C15112yescomplemented
234C4×#127C2×C15111yescharacteristic
235#2060C2×C15112yescomplemented
236#2027C2×C15112yescomplemented
237#1994C2×C15112yescomplemented
238#1887C2×C15112yes—
239#1856C2×C15112yescomplemented
240#1800C2×C15111yescharacteristic, complemented
241#554—22no—
242#554—24no—
243D4×Q8—22no—
244#544C22×C15112yes—
245#543—22no—
246#533C22×C15112yes—
247C2×#127C22×C15111yescharacteristic
248C2×C22⋊Q8—22no—
249#518C22×C15112yes—
250C2×C4×D4—22no—
251C2×C4×D4C22×C15111yescharacteristic
252C2×C4×D4C22×C15111yescharacteristic
253#478—24no—
254#476—22no—
255#474—22no—
256#428C22×C15114yes—
257#423C22×C15112yes—
258#418C22×C15114yes—
259C2×#100C22×C15112yes—
260#390—22no—
261#390C22×C15111yescharacteristic
262#390C22×C15111yescharacteristic
263#384C22×C15111yescharacteristic
264C43C22×C15111yescharacteristic
265#343C22×C15112yes—
266#339C22×C15114yes—
267#339C22×C15114yes—
268C22×Q8—22no—
269C22×D4—22no—
270C22×D4C23×C15111yescharacteristic
271C22×D4C23×C15111yescharacteristic
272C23×C4—21no—
273C23×C4D4×C15112yes—
274C2×M16C23×C15114yes—
275C4⋊Q8—24no—
276C4⋊Q8D4×C15112yescomplemented
277C4⋊Q8D4×C15112yescomplemented
278#127—22no—
279#127Q8×C15114yescomplemented
280#125—24no—
281#125D4×C15114yescomplemented
282C22⋊Q8—24no—
283C22⋊Q8—24no—
284C22⋊Q8—28no—
285C22⋊Q8—28no—
286C22⋊Q8—22no—
287C22⋊Q8—24no—
288C22⋊Q8—22no—
289C4×Q8—22no—
290C4×Q8—22no—
291C4×D4—24no—
292C4×D4—24no—
293C4×D4—22no—
294C4×D4—22no—
295C4×D4—22no—
296C4×D4—22no—
297C4×D4—48no—
298#117C23×C15114yes—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4C23×C15111yescharacteristic
303C2×C4⋊C4C23×C15111yescharacteristic
304C2×C22⋊C4—24no—
305C2×C22⋊C4—22no—
306C2×C22⋊C4—22no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4D4×C15112yes—
309C2×C42—21no—
310C2×C42—21no—
311C2×C42C23×C15111yescharacteristic
312C2×C42C23×C15111yescharacteristic
313C2×C42C23×C15111yescharacteristic
314#107—24no—
315#106—24no—
316C4⋊C8—22no—
317C4⋊C8—22no—
318#102—24no—
319#102—24no—
320#100—24no—
321C24—21no—
322C24C2×D4×C15112yes—
323C2×Q8—24no—
324C2×Q8—22no—
325C2×Q8—22no—
326C2×Q8—84no—
327C2×D4—28no—
328C2×D4—22no—
329C2×D4—22no—
330C2×D4—21no—
331C2×D4—22no—
332C2×D4—22no—
333C2×D4—44no—
334C2×D4—44no—
335C2×D4C2×Q8×C15112yes—
336C2×D4C2×Q8×C15112yescomplemented
337C2×D4#41×C15112yes—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—24no—
341C22×C4—24no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—21no—
345C22×C4—44no—
346C22×C4—44no—
347C22×C4—41no—
348C22×C4—41no—
349C22×C4C2×D4×C15111yescharacteristic
350C22×C4C2×D4×C15112yes—
351C22×C4C2×D4×C15111yescharacteristic
352C22×C4C24×C15111yescharacteristic
353M16—24no—
354M16—24no—
355C2×C8—24no—
356C4⋊C4—24no—
357C4⋊C4—28no—
358C4⋊C4—24no—
359C4⋊C4—22no—
360C4⋊C4—24no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—44no—
365C4⋊C4C2×D4×C15114yes—
366C4⋊C4C2×D4×C15114yes—
367C22⋊C4—28no—
368C22⋊C4—24no—
369C22⋊C4—24no—
370C22⋊C4—44no—
371C22⋊C4—44no—
372C22⋊C4—42no—
373C42—24no—
374C42—24no—
375C42—21no—
376C42—22no—
377C42—42no—
378C42C2×D4×C15112yes—
379C42C2×D4×C15112yes—
380C42C2×Q8×C15112yescomplemented
381C23—22no—
382C23—22no—
383C23—22no—
384C23—42no—
385C23—42no—
386C23—42no—
387C23—42no—
388C23—41no—
389C23—41no—
390C23C22⋊Q8×C15114yes—
391C23C22×D4×C15111yescharacteristic
392Q8—44no—
393Q8—82no—
394Q8—84no—
395D4—24no—
396D4—24no—
397D4—24no—
398D4—416no—
399D4—42no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—24no—
406C2×C4—24no—
407C2×C4—22no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—44no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—41no—
415C2×C4—82no—
416C2×C4—82no—
417C2×C4—84no—
418C2×C4—84no—
419C2×C4—82no—
420C2×C4#120×C15112yes—
421C2×C4#120×C15111yescharacteristic
422C2×C4#120×C15111yescharacteristic
423C2×C4C22×D4×C15112yes—
424C2×C4C22×Q8×C15111yescharacteristic
425C2×C4C2×#41×C15111yescharacteristic
426C2×C42−1+4×C15112yes—
427C8—44no—
428C22—21no—
429C22—21no—
430C22—24no—
431C22—44no—
432C22—44no—
433C22—42no—
434C22—42no—
435C22—42no—
436C22—82no—
437C22—82no—
438C22—81no—
439C22—81no—
440C22C2×#120×C15111yescharacteristic
441C22C2×C22⋊Q8×C15111yescharacteristic
442C22#536×C15111yescharacteristic
443C4—24no—
444C4—21no—
445C4—22no—
446C4—42no—
447C4—42no—
448C4—44no—
449C4—44no—
450C4—81no—
451C4#453×C15112yes—
452C4#548×C15112yes—
453C4D4×Q8×C15112yes—
454C2—21no—
455C2—21no—
456C2—44no—
457C2—82no—
458C2#2409×C15111yescharacteristic
459C2C2×#453×C15111yescharacteristic
460C2#3018×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#127×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3501×C151C2semidirect
2. #3077×C151C2semidirect
4. #2060×C151C2semidirect
5. #2027×C151C2semidirect
6. #1994×C151C2semidirect
8. #1856×C151C2semidirect
9. #1800×C151C2semidirect
45. C4⋊Q8×C151D4semidirect
46. C4⋊Q8×C151D4semidirect
48. #127×C151Q8semidirect
50. #125×C151D4semidirect
105. C2×D4×C151C2×Q8semidirect
149. C42×C151C2×Q8semidirect
230. #24312C151direct (N × H)
231. C151#24312direct (N × H)
232. #3501C2×C151semidirect
233. #3077C2×C151semidirect
235. #2060C2×C151semidirect
236. #2027C2×C151semidirect
237. #1994C2×C151semidirect
239. #1856C2×C151semidirect
240. #1800C2×C151semidirect
276. C4⋊Q8D4×C151semidirect
277. C4⋊Q8D4×C151semidirect
279. #127Q8×C151semidirect
281. #125D4×C151semidirect
336. C2×D4C2×Q8×C151semidirect
380. C42C2×Q8×C151semidirect

Maximal subgroups

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

subgroupindex
#3501×C1512
#3077×C1512
C4×#127×C1512
#2060×C1512
#2027×C1512
#1994×C1512
#1887×C1512
#1856×C1512
#1800×C1512
#24312151