Finite Group Databasebeta

← C151×#24114 #50329039

Subgroups — C151×#24114 #50329039

Order 38656.

1254 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#3490×C151C211yesmaximal, characteristic
2#2622×C151C212yesmaximal, complemented
3#2315×C151C211yesmaximal, characteristic, complemented
4#2062×C151C212yesmaximal, complemented
5#2044×C151C212yesmaximal, complemented
6#1898×C151C212yesmaximal, complemented
7#1867×C151C214yesmaximal, complemented
8#1819×C151C211yesmaximal, characteristic, complemented
9#551×C151—24no—
10#546×C151—24no—
11#543×C151C2211yescharacteristic
12#538×C151—22no—
13#534×C151C2211yescharacteristic
14#525×C151—22no—
15C2×#120×C151C2212yes—
16#518×C151C2212yes—
17C22×C22⋊C4×C151C2211yescharacteristic
18C22×C22⋊C4×C151C2211yescharacteristic
19C22×C22⋊C4×C151C2211yescharacteristic
20C2×#99×C151C2214yes—
21#397×C151—24no—
22#394×C151—24no—
23#386×C151C2214yes—
24#385×C151—22no—
25#385×C151C2214yes—
26#385×C151C2212yes—
27#385×C151C2212yes—
28#380×C151—22no—
29#379×C151C2212yes—
30#342×C151C2212yes—
31#342×C151C2214yes—
32#342×C151C2212yes—
33C25×C151C2311yescharacteristic
34C2×#41×C151—22no—
35C22×D4×C151D414yes—
36C22×D4×C151C2312yes—
37C23×C4×C151—21no—
38C23×C4×C151D412yes—
39C23×C4×C151C2312yes—
40#126×C151—24no—
41#124×C151—24no—
42#123×C151—24no—
43#123×C151—24no—
44#123×C151—22no—
45C22⋊Q8×C151—22no—
46C22⋊Q8×C151—22no—
47C22⋊Q8×C151—24no—
48#121×C151—22no—
49#121×C151—24no—
50#121×C151—22no—
51#120×C151—22no—
52#120×C151—22no—
53#120×C151—24no—
54#120×C151—22no—
55C4×D4×C151—24no—
56C4×D4×C151—24no—
57C4×D4×C151—24no—
58#117×C151—22no—
59#117×C151—22no—
60C2×C4⋊C4×C151—22no—
61C2×C4⋊C4×C151—22no—
62C2×C4⋊C4×C151—24no—
63C2×C22⋊C4×C151—24no—
64C2×C22⋊C4×C151—21no—
65C2×C22⋊C4×C151—24no—
66C2×C22⋊C4×C151—22no—
67C2×C22⋊C4×C151—21no—
68C2×C22⋊C4×C151—21no—
69C2×C22⋊C4×C151—24no—
70C2×C22⋊C4×C151—24no—
71C2×C22⋊C4×C151—24no—
72C2×C22⋊C4×C151D412yes—
73C2×C22⋊C4×C151D414yes—
74C2×C22⋊C4×C151C2314yes—
75C2×C22⋊C4×C151C2311yescharacteristic
76C2×C22⋊C4×C151C2311yescharacteristic
77C2×C22⋊C4×C151C2312yes—
78C2×C22⋊C4×C151C2312yes—
79#99×C151—28no—
80#95×C151—22no—
81#95×C151—22no—
82#95×C151—24no—
83#95×C151—24no—
84C24×C151—22no—
85C24×C151—22no—
86C24×C151—82no—
87C24×C151C2×D412yes—
88C24×C151C2×D414yes—
89C24×C151C2×D411yescharacteristic
90C24×C151C2×D411yescharacteristic
91C24×C151C2411yescharacteristic
92#41×C151—84no—
93C2×Q8×C151—22no—
94C2×D4×C151—24no—
95C2×D4×C151—22no—
96C2×D4×C151—22no—
97C2×D4×C151—24no—
98C2×D4×C151—24no—
99C2×D4×C151—22no—
100C2×D4×C151—24no—
101C2×D4×C151—84no—
102C22×C4×C151—22no—
103C22×C4×C151—22no—
104C22×C4×C151—24no—
105C22×C4×C151—24no—
106C22×C4×C151—22no—
107C22×C4×C151—24no—
108C22×C4×C151—24no—
109C22×C4×C151—22no—
110C22×C4×C151—82no—
111C22×C4×C151—82no—
112C22×C4×C151—82no—
113C22×C4×C151C2×D412yes—
114C22×C4×C151C2×D412yes—
115C22×C4×C151C2×D414yes—
116C22×C4×C151C2×D412yes—
117C4⋊C4×C151—24no—
118C4⋊C4×C151—22no—
119C4⋊C4×C151—22no—
120C4⋊C4×C151—24no—
121C4⋊C4×C151—82no—
122C4⋊C4×C151—82no—
123C4⋊C4×C151—84no—
124C22⋊C4×C151—24no—
125C22⋊C4×C151—24no—
126C22⋊C4×C151—24no—
127C22⋊C4×C151—24no—
128C22⋊C4×C151—24no—
129C22⋊C4×C151—24no—
130C22⋊C4×C151—22no—
131C22⋊C4×C151—22no—
132C22⋊C4×C151—22no—
133C22⋊C4×C151—22no—
134C22⋊C4×C151—22no—
135C22⋊C4×C151—24no—
136C22⋊C4×C151—24no—
137C22⋊C4×C151—42no—
138C22⋊C4×C151—42no—
139C22⋊C4×C151—84no—
140C22⋊C4×C151—84no—
141C22⋊C4×C151#4114yescomplemented
142C42×C151—24no—
143C23×C151—21no—
144C23×C151—21no—
145C23×C151—21no—
146C23×C151—21no—
147C23×C151—28no—
148C23×C151—22no—
149C23×C151—24no—
150C23×C151—42no—
151C23×C151—42no—
152C23×C151—42no—
153C23×C151—44no—
154C23×C151—44no—
155C23×C151—44no—
156C23×C151—84no—
157C23×C151—84no—
158C23×C151#12012yes—
159C23×C151#12012yes—
160C23×C151C22×D411yescharacteristic
161C23×C151C22×D412yes—
162C23×C151C2×#4112yes—
163C23×C1512−1+412yes—
164Q8×C151—82no—
165D4×C151—48no—
166D4×C151—42no—
167D4×C151—42no—
168D4×C151—44no—
169D4×C151—84no—
170D4×C151—82no—
171C2×C4×C151—24no—
172C2×C4×C151—22no—
173C2×C4×C151—22no—
174C2×C4×C151—22no—
175C2×C4×C151—24no—
176C2×C4×C151—24no—
177C2×C4×C151—44no—
178C2×C4×C151—42no—
179C2×C4×C151—42no—
180C2×C4×C151—42no—
181C2×C4×C151—42no—
182C2×C4×C151—44no—
183C2×C4×C151—44no—
184C2×C4×C151—44no—
185C2×C4×C151—44no—
186C2×C4×C151—42no—
187C2×C4×C151—42no—
188C2×C4×C151—44no—
189C2×C4×C151—42no—
190C2×C4×C151—44no—
191C2×C4×C151—82no—
192C2×C4×C151—84no—
193C2×C4×C151—84no—
194C22×C151—22no—
195C22×C151—24no—
196C22×C151—22no—
197C22×C151—22no—
198C22×C151—22no—
199C22×C151—22no—
200C22×C151—24no—
201C22×C151—42no—
202C22×C151—42no—
203C22×C151—42no—
204C22×C151—42no—
205C22×C151—42no—
206C22×C151—42no—
207C22×C151—42no—
208C22×C151—44no—
209C22×C151—88no—
210C22×C151—84no—
211C22×C151C2×#12011yescharacteristic
212C22×C151#52511yescharacteristic
213C22×C151#53611yescharacteristic
214C22×C151#54714yes—
215C4×C151—44no—
216C4×C151—42no—
217C4×C151—42no—
218C4×C151—42no—
219C4×C151—44no—
220C4×C151—84no—
221C4×C151—82no—
222C2×C151—21no—
223C2×C151—24no—
224C2×C151—21no—
225C2×C151—42no—
226C2×C151—42no—
227C2×C151—82no—
228C2×C151#240611yescharacteristic
229C2×C151#302612yes—
230#24114C15111yesmaximal, characteristic, direct product factor, Sylow
231C151#2411411yescharacteristic, direct product factor, Sylow
232#3490C2×C15111yescharacteristic
233#2622C2×C15112yescomplemented
234#2315C2×C15111yescharacteristic, complemented
235#2062C2×C15112yescomplemented
236#2044C2×C15112yescomplemented
237#1898C2×C15112yescomplemented
238#1867C2×C15114yescomplemented
239#1819C2×C15111yescharacteristic, complemented
240#551—24no—
241#546—24no—
242#543C22×C15111yescharacteristic
243#538—22no—
244#534C22×C15111yescharacteristic
245#525—22no—
246C2×#120C22×C15112yes—
247#518C22×C15112yes—
248C22×C22⋊C4C22×C15111yescharacteristic
249C22×C22⋊C4C22×C15111yescharacteristic
250C22×C22⋊C4C22×C15111yescharacteristic
251C2×#99C22×C15114yes—
252#397—24no—
253#394—24no—
254#386C22×C15114yes—
255#385—22no—
256#385C22×C15112yes—
257#385C22×C15112yes—
258#385C22×C15114yes—
259#380—22no—
260#379C22×C15112yes—
261#342C22×C15112yes—
262#342C22×C15114yes—
263#342C22×C15112yes—
264C25C23×C15111yescharacteristic
265C2×#41—22no—
266C22×D4D4×C15114yes—
267C22×D4C23×C15112yes—
268C23×C4—21no—
269C23×C4D4×C15112yes—
270C23×C4C23×C15112yes—
271#126—24no—
272#124—24no—
273#123—24no—
274#123—24no—
275#123—22no—
276C22⋊Q8—22no—
277C22⋊Q8—22no—
278C22⋊Q8—24no—
279#121—22no—
280#121—24no—
281#121—22no—
282#120—22no—
283#120—22no—
284#120—24no—
285#120—22no—
286C4×D4—24no—
287C4×D4—24no—
288C4×D4—24no—
289#117—22no—
290#117—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—24no—
294C2×C22⋊C4—24no—
295C2×C22⋊C4—21no—
296C2×C22⋊C4—22no—
297C2×C22⋊C4—24no—
298C2×C22⋊C4—21no—
299C2×C22⋊C4—21no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4D4×C15112yes—
304C2×C22⋊C4D4×C15114yes—
305C2×C22⋊C4C23×C15114yes—
306C2×C22⋊C4C23×C15111yescharacteristic
307C2×C22⋊C4C23×C15111yescharacteristic
308C2×C22⋊C4C23×C15112yes—
309C2×C22⋊C4C23×C15112yes—
310#99—28no—
311#95—22no—
312#95—22no—
313#95—24no—
314#95—24no—
315C24—22no—
316C24—22no—
317C24—82no—
318C24C2×D4×C15112yes—
319C24C2×D4×C15114yes—
320C24C2×D4×C15111yescharacteristic
321C24C2×D4×C15111yescharacteristic
322C24C24×C15111yescharacteristic
323#41—84no—
324C2×Q8—22no—
325C2×D4—24no—
326C2×D4—22no—
327C2×D4—22no—
328C2×D4—24no—
329C2×D4—24no—
330C2×D4—22no—
331C2×D4—24no—
332C2×D4—84no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—24no—
336C22×C4—24no—
337C22×C4—22no—
338C22×C4—24no—
339C22×C4—24no—
340C22×C4—22no—
341C22×C4—82no—
342C22×C4—82no—
343C22×C4—82no—
344C22×C4C2×D4×C15112yes—
345C22×C4C2×D4×C15112yes—
346C22×C4C2×D4×C15114yes—
347C22×C4C2×D4×C15112yes—
348C4⋊C4—24no—
349C4⋊C4—22no—
350C4⋊C4—22no—
351C4⋊C4—24no—
352C4⋊C4—82no—
353C4⋊C4—82no—
354C4⋊C4—84no—
355C22⋊C4—24no—
356C22⋊C4—24no—
357C22⋊C4—24no—
358C22⋊C4—24no—
359C22⋊C4—24no—
360C22⋊C4—24no—
361C22⋊C4—22no—
362C22⋊C4—22no—
363C22⋊C4—22no—
364C22⋊C4—22no—
365C22⋊C4—22no—
366C22⋊C4—24no—
367C22⋊C4—24no—
368C22⋊C4—42no—
369C22⋊C4—42no—
370C22⋊C4—84no—
371C22⋊C4—84no—
372C22⋊C4#41×C15114yescomplemented
373C42—24no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—28no—
379C23—22no—
380C23—24no—
381C23—42no—
382C23—42no—
383C23—42no—
384C23—44no—
385C23—44no—
386C23—44no—
387C23—84no—
388C23—84no—
389C23#120×C15112yes—
390C23#120×C15112yes—
391C23C22×D4×C15111yescharacteristic
392C23C22×D4×C15112yes—
393C23C2×#41×C15112yes—
394C232−1+4×C15112yes—
395Q8—82no—
396D4—48no—
397D4—42no—
398D4—42no—
399D4—44no—
400D4—84no—
401D4—82no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—24no—
405C2×C4—22no—
406C2×C4—24no—
407C2×C4—24no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—44no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—44no—
414C2×C4—44no—
415C2×C4—44no—
416C2×C4—44no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—44no—
420C2×C4—42no—
421C2×C4—44no—
422C2×C4—82no—
423C2×C4—84no—
424C2×C4—84no—
425C22—22no—
426C22—24no—
427C22—22no—
428C22—22no—
429C22—22no—
430C22—22no—
431C22—24no—
432C22—42no—
433C22—42no—
434C22—42no—
435C22—42no—
436C22—42no—
437C22—42no—
438C22—42no—
439C22—44no—
440C22—88no—
441C22—84no—
442C22C2×#120×C15111yescharacteristic
443C22#525×C15111yescharacteristic
444C22#536×C15111yescharacteristic
445C22#547×C15114yes—
446C4—44no—
447C4—42no—
448C4—42no—
449C4—42no—
450C4—44no—
451C4—84no—
452C4—82no—
453C2—21no—
454C2—24no—
455C2—21no—
456C2—42no—
457C2—42no—
458C2—82no—
459C2#2406×C15111yescharacteristic
460C2#3026×C15112yes—
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC24C24×C151
prime radical#3490×C151C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C25×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2622×C151C2semidirect
3. #2315×C151C2semidirect
4. #2062×C151C2semidirect
5. #2044×C151C2semidirect
6. #1898×C151C2semidirect
7. #1867×C151C2semidirect
8. #1819×C151C2semidirect
141. C22⋊C4×C151#41semidirect
230. #24114C151direct (N × H)
231. C151#24114direct (N × H)
233. #2622C2×C151semidirect
234. #2315C2×C151semidirect
235. #2062C2×C151semidirect
236. #2044C2×C151semidirect
237. #1898C2×C151semidirect
238. #1867C2×C151semidirect
239. #1819C2×C151semidirect
372. C22⋊C4#41×C151semidirect

Maximal subgroups

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

subgroupindex
#3490×C1512
#2622×C1512
#2315×C1512
#2062×C1512
#2044×C1512
#1898×C1512
#1867×C1512
#1819×C1512
#24114151