Finite Group Databasebeta

← C151×#23953 #50328878

Subgroups — C151×#23953 #50328878

Order 38656.

1166 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3493×C151C211yesmaximal, characteristic
2#3004×C151C212yesmaximal, complemented
3#2310×C151C211yesmaximal, characteristic, complemented
4#2028×C151C212yesmaximal, complemented
5#2007×C151C212yesmaximal, complemented
6#1897×C151C212yesmaximal, complemented
7#1882×C151C214yesmaximal, complemented
8#1822×C151C211yesmaximal, characteristic, complemented
9C23×Q8×C151C2211yescharacteristic
10C2×#137×C151C2214yes—
11#556×C151—22no—
12#555×C151—22no—
13#553×C151—22no—
14#552×C151—22no—
15#544×C151C2211yescharacteristic
16#538×C151—22no—
17#537×C151C2211yescharacteristic
18#529×C151—22no—
19#525×C151C2212yes—
20#520×C151C2212yes—
21C2×#117×C151C2211yescharacteristic
22C2×#117×C151C2211yescharacteristic
23#451×C151—22no—
24#451×C151—22no—
25#448×C151—22no—
26#448×C151—22no—
27C2×#104×C151C2214yes—
28#419×C151C2214yes—
29#407×C151C2212yes—
30#391×C151—22no—
31#391×C151C2212yes—
32#391×C151C2212yes—
33#381×C151—22no—
34#343×C151C2212yes—
35#343×C151C2212yes—
36#339×C151C2214yes—
37C2×#41×C151C2312yes—
38C22×Q8×C151—21no—
39C22×Q8×C151—24no—
40C22×Q8×C151—22no—
41C22×Q8×C151—22no—
42C22×Q8×C151—42no—
43C22×Q8×C151C2312yes—
44C23×C4×C151—21no—
45C23×C4×C151C2311yescharacteristic
46#137×C151—28no—
47#137×C151—44no—
48C2×Q16×C151—24no—
49C2×SD16×C151—24no—
50C2×M16×C151C2314yes—
51C4⋊Q8×C151—22no—
52#126×C151—24no—
53#126×C151—24no—
54#125×C151—22no—
55#125×C151—22no—
56#124×C151—22no—
57#124×C151—24no—
58#123×C151—24no—
59#123×C151—22no—
60C22⋊Q8×C151—22no—
61C22⋊Q8×C151—22no—
62C22⋊Q8×C151D412yes—
63C22⋊Q8×C151D412yes—
64#121×C151—24no—
65#121×C151—22no—
66#121×C151—22no—
67#121×C151D412yes—
68#121×C151D412yes—
69#120×C151—22no—
70C4×Q8×C151—22no—
71C4×Q8×C151—22no—
72C4×D4×C151—22no—
73C4×D4×C151—22no—
74C4×D4×C151—24no—
75C4×D4×C151—22no—
76C4×D4×C151—22no—
77#117×C151—24no—
78#117×C151—22no—
79#117×C151—22no—
80#117×C151—22no—
81#117×C151—42no—
82#117×C151C2312yes—
83C2×C4⋊C4×C151—22no—
84C2×C4⋊C4×C151—21no—
85C2×C4⋊C4×C151C2311yescharacteristic
86C2×C4⋊C4×C151C2311yescharacteristic
87C2×C22⋊C4×C151—21no—
88C2×C22⋊C4×C151D412yes—
89C2×C42×C151D412yes—
90C2×C42×C151C2312yes—
91#104×C151—44no—
92#103×C151—24no—
93#103×C151—24no—
94C22⋊C8×C151—22no—
95C22⋊C8×C151—22no—
96#95×C151—24no—
97#95×C151—24no—
98C24×C151C2×D411yescharacteristic
99#41×C151—24no—
100#41×C151—24no—
101C2×Q8×C151—24no—
102C2×Q8×C151—22no—
103C2×Q8×C151—22no—
104C2×Q8×C151—24no—
105C2×Q8×C151—24no—
106C2×Q8×C151—48no—
107C2×Q8×C151—48no—
108C2×Q8×C151—42no—
109C2×Q8×C151—41no—
110C2×Q8×C151—41no—
111C2×Q8×C151C2×D412yes—
112C2×Q8×C151#4114yes—
113C2×D4×C151—22no—
114C2×D4×C151—22no—
115C2×D4×C151—22no—
116C2×D4×C151—22no—
117C2×D4×C151C2×D412yes—
118C22×C4×C151—22no—
119C22×C4×C151—22no—
120C22×C4×C151—24no—
121C22×C4×C151—22no—
122C22×C4×C151—24no—
123C22×C4×C151—22no—
124C22×C4×C151—22no—
125C22×C4×C151—42no—
126C22×C4×C151—42no—
127C22×C4×C151C2×D411yescharacteristic
128C22×C4×C151C2×D412yes—
129C22×C4×C151C2×D412yes—
130C22×C4×C151C2×D412yes—
131C22×C4×C151C2×D412yes—
132C22×C4×C151C2411yescharacteristic
133Q16×C151—48no—
134SD16×C151—48no—
135M16×C151—24no—
136M16×C151—24no—
137C2×C8×C151—24no—
138C4⋊C4×C151—24no—
139C4⋊C4×C151—24no—
140C4⋊C4×C151—22no—
141C4⋊C4×C151—22no—
142C4⋊C4×C151—22no—
143C4⋊C4×C151—22no—
144C4⋊C4×C151—22no—
145C4⋊C4×C151—22no—
146C4⋊C4×C151—42no—
147C4⋊C4×C151C2×D412yes—
148C4⋊C4×C151C2×D412yes—
149C22⋊C4×C151—24no—
150C22⋊C4×C151—24no—
151C22⋊C4×C151—24no—
152C22⋊C4×C151—22no—
153C22⋊C4×C151—22no—
154C22⋊C4×C151—22no—
155C22⋊C4×C151—22no—
156C22⋊C4×C151—22no—
157C22⋊C4×C151—42no—
158C42×C151—24no—
159C42×C151—22no—
160C42×C151—22no—
161C42×C151—22no—
162C42×C151—24no—
163C23×C151—21no—
164C23×C151—21no—
165C23×C151—22no—
166C23×C151—41no—
167C23×C151—41no—
168C23×C151#12012yes—
169C23×C151C22×D411yescharacteristic
170Q8×C151—28no—
171Q8×C151—24no—
172Q8×C151—44no—
173Q8×C151—44no—
174Q8×C151—44no—
175Q8×C151—82no—
176D4×C151—24no—
177D4×C151—42no—
178D4×C151—42no—
179D4×C151—82no—
180D4×C151—82no—
181D4×C151—82no—
182C2×C4×C151—21no—
183C2×C4×C151—21no—
184C2×C4×C151—24no—
185C2×C4×C151—24no—
186C2×C4×C151—22no—
187C2×C4×C151—22no—
188C2×C4×C151—22no—
189C2×C4×C151—22no—
190C2×C4×C151—22no—
191C2×C4×C151—24no—
192C2×C4×C151—48no—
193C2×C4×C151—42no—
194C2×C4×C151—42no—
195C2×C4×C151—44no—
196C2×C4×C151—42no—
197C2×C4×C151—42no—
198C2×C4×C151—42no—
199C2×C4×C151—42no—
200C2×C4×C151—42no—
201C2×C4×C151—84no—
202C2×C4×C151#12011yescharacteristic
203C2×C4×C151#12011yescharacteristic
204C2×C4×C151C22×D412yes—
205C2×C4×C151C2×#4112yes—
206C2×C4×C151H(5,𝔽2)12yes—
207C8×C151—44no—
208C22×C151—21no—
209C22×C151—21no—
210C22×C151—22no—
211C22×C151—22no—
212C22×C151—22no—
213C22×C151—42no—
214C22×C151—42no—
215C22×C151—42no—
216C22×C151—42no—
217C22×C151—42no—
218C22×C151C2×#12011yescharacteristic
219C22×C151#52511yescharacteristic
220C22×C151#53511yescharacteristic
221C4×C151—21no—
222C4×C151—21no—
223C4×C151—44no—
224C4×C151—42no—
225C4×C151—42no—
226C4×C151—42no—
227C4×C151—42no—
228C4×C151—42no—
229C4×C151—82no—
230C4×C151#54614yes—
231C2×C151—21no—
232C2×C151—21no—
233C2×C151—42no—
234C2×C151—82no—
235C2×C151#240411yescharacteristic
236C2×C151#302211yescharacteristic
237C2×C151#302211yescharacteristic
238#23953C15111yesmaximal, characteristic, direct product factor, Sylow
239C151#2395311yescharacteristic, direct product factor, Sylow
240#3493C2×C15111yescharacteristic
241#3004C2×C15112yescomplemented
242#2310C2×C15111yescharacteristic, complemented
243#2028C2×C15112yescomplemented
244#2007C2×C15112yescomplemented
245#1897C2×C15112yescomplemented
246#1882C2×C15114yescomplemented
247#1822C2×C15111yescharacteristic, complemented
248C23×Q8C22×C15111yescharacteristic
249C2×#137C22×C15114yes—
250#556—22no—
251#555—22no—
252#553—22no—
253#552—22no—
254#544C22×C15111yescharacteristic
255#538—22no—
256#537C22×C15111yescharacteristic
257#529—22no—
258#525C22×C15112yes—
259#520C22×C15112yes—
260C2×#117C22×C15111yescharacteristic
261C2×#117C22×C15111yescharacteristic
262#451—22no—
263#451—22no—
264#448—22no—
265#448—22no—
266C2×#104C22×C15114yes—
267#419C22×C15114yes—
268#407C22×C15112yes—
269#391—22no—
270#391C22×C15112yes—
271#391C22×C15112yes—
272#381—22no—
273#343C22×C15112yes—
274#343C22×C15112yes—
275#339C22×C15114yes—
276C2×#41C23×C15112yes—
277C22×Q8—24no—
278C22×Q8—21no—
279C22×Q8—22no—
280C22×Q8—22no—
281C22×Q8—42no—
282C22×Q8C23×C15112yes—
283C23×C4—21no—
284C23×C4C23×C15111yescharacteristic
285#137—28no—
286#137—44no—
287C2×Q16—24no—
288C2×SD16—24no—
289C2×M16C23×C15114yes—
290C4⋊Q8—22no—
291#126—24no—
292#126—24no—
293#125—22no—
294#125—22no—
295#124—22no—
296#124—24no—
297#123—24no—
298#123—22no—
299C22⋊Q8—22no—
300C22⋊Q8—22no—
301C22⋊Q8D4×C15112yes—
302C22⋊Q8D4×C15112yes—
303#121—24no—
304#121—22no—
305#121—22no—
306#121D4×C15112yes—
307#121D4×C15112yes—
308#120—22no—
309C4×Q8—22no—
310C4×Q8—22no—
311C4×D4—22no—
312C4×D4—22no—
313C4×D4—24no—
314C4×D4—22no—
315C4×D4—22no—
316#117—24no—
317#117—22no—
318#117—22no—
319#117—22no—
320#117—42no—
321#117C23×C15112yes—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4C23×C15111yescharacteristic
325C2×C4⋊C4C23×C15111yescharacteristic
326C2×C22⋊C4—21no—
327C2×C22⋊C4D4×C15112yes—
328C2×C42D4×C15112yes—
329C2×C42C23×C15112yes—
330#104—44no—
331#103—24no—
332#103—24no—
333C22⋊C8—22no—
334C22⋊C8—22no—
335#95—24no—
336#95—24no—
337C24C2×D4×C15111yescharacteristic
338#41—24no—
339#41—24no—
340C2×Q8—24no—
341C2×Q8—22no—
342C2×Q8—22no—
343C2×Q8—24no—
344C2×Q8—24no—
345C2×Q8—48no—
346C2×Q8—48no—
347C2×Q8—42no—
348C2×Q8—41no—
349C2×Q8—41no—
350C2×Q8C2×D4×C15112yes—
351C2×Q8#41×C15114yes—
352C2×D4—22no—
353C2×D4—22no—
354C2×D4—22no—
355C2×D4—22no—
356C2×D4C2×D4×C15112yes—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—24no—
360C22×C4—22no—
361C22×C4—24no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—42no—
365C22×C4—42no—
366C22×C4C2×D4×C15111yescharacteristic
367C22×C4C2×D4×C15112yes—
368C22×C4C2×D4×C15112yes—
369C22×C4C2×D4×C15112yes—
370C22×C4C2×D4×C15112yes—
371C22×C4C24×C15111yescharacteristic
372Q16—48no—
373SD16—48no—
374M16—24no—
375M16—24no—
376C2×C8—24no—
377C4⋊C4—24no—
378C4⋊C4—24no—
379C4⋊C4—22no—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4—22no—
383C4⋊C4—22no—
384C4⋊C4—22no—
385C4⋊C4—42no—
386C4⋊C4C2×D4×C15112yes—
387C4⋊C4C2×D4×C15112yes—
388C22⋊C4—24no—
389C22⋊C4—24no—
390C22⋊C4—24no—
391C22⋊C4—22no—
392C22⋊C4—22no—
393C22⋊C4—22no—
394C22⋊C4—22no—
395C22⋊C4—22no—
396C22⋊C4—42no—
397C42—24no—
398C42—22no—
399C42—22no—
400C42—22no—
401C42—24no—
402C23—21no—
403C23—21no—
404C23—22no—
405C23—41no—
406C23—41no—
407C23#120×C15112yes—
408C23C22×D4×C15111yescharacteristic
409Q8—28no—
410Q8—24no—
411Q8—44no—
412Q8—44no—
413Q8—44no—
414Q8—82no—
415D4—24no—
416D4—42no—
417D4—42no—
418D4—82no—
419D4—82no—
420D4—82no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—24no—
424C2×C4—24no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—24no—
431C2×C4—48no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—44no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—84no—
441C2×C4#120×C15111yescharacteristic
442C2×C4#120×C15111yescharacteristic
443C2×C4C22×D4×C15112yes—
444C2×C4C2×#41×C15112yes—
445C2×C4H(5,𝔽2)×C15112yes—
446C8—44no—
447C22—21no—
448C22—21no—
449C22—22no—
450C22—22no—
451C22—22no—
452C22—42no—
453C22—42no—
454C22—42no—
455C22—42no—
456C22—42no—
457C22C2×#120×C15111yescharacteristic
458C22#525×C15111yescharacteristic
459C22#535×C15111yescharacteristic
460C4—21no—
461C4—21no—
462C4—44no—
463C4—42no—
464C4—42no—
465C4—42no—
466C4—42no—
467C4—42no—
468C4—82no—
469C4#546×C15114yes—
470C2—21no—
471C2—21no—
472C2—42no—
473C2—82no—
474C2#2404×C15111yescharacteristic
475C2#3022×C15111yescharacteristic
476C2#3022×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#3493×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3004×C151C2semidirect
3. #2310×C151C2semidirect
4. #2028×C151C2semidirect
5. #2007×C151C2semidirect
6. #1897×C151C2semidirect
7. #1882×C151C2semidirect
8. #1822×C151C2semidirect
238. #23953C151direct (N × H)
239. C151#23953direct (N × H)
241. #3004C2×C151semidirect
242. #2310C2×C151semidirect
243. #2028C2×C151semidirect
244. #2007C2×C151semidirect
245. #1897C2×C151semidirect
246. #1882C2×C151semidirect
247. #1822C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3493×C1512
#3004×C1512
#2310×C1512
#2028×C1512
#2007×C1512
#1897×C1512
#1882×C1512
#1822×C1512
#23953151