Finite Group Databasebeta

← C151×#18365 #50323290

Subgroups — C151×#18365 #50323290

Order 38656.

862 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3507×C151C211yesmaximal, characteristic
2#3236×C151C211yesmaximal, characteristic, complemented
3#3234×C151C211yesmaximal, characteristic
4#2634×C151C211yesmaximal, characteristic, complemented
5#1615×C151C214yesmaximal, complemented
6#1609×C151C214yesmaximal, complemented
7#1515×C151C211yesmaximal, characteristic, complemented
8#1514×C151C211yesmaximal, characteristic
9#1467×C151C211yesmaximal, characteristic, complemented
10#559×C151—21no—
11#557×C151—21no—
12#556×C151—21no—
13#556×C151—22no—
14#554×C151—21no—
15#552×C151—22no—
16#539×C151C2214yes—
17#536×C151—21no—
18#533×C151C2211yescharacteristic
19#532×C151C2211yescharacteristic
20#529×C151—22no—
21C2×#125×C151C2211yescharacteristic
22#520×C151—21no—
23C2×C4×Q8×C151C2211yescharacteristic
24#501×C151—21no—
25#501×C151—21no—
26#491×C151—21no—
27#490×C151—21no—
28#484×C151C2212yes—
29#483×C151C2212yes—
30#481×C151C2212yes—
31#480×C151C2212yes—
32#479×C151—22no—
33#478×C151—22no—
34#432×C151C2211yescharacteristic
35#432×C151C2211yescharacteristic
36#400×C151—21no—
37#400×C151C2212yes—
38#398×C151C2212yes—
39#395×C151—21no—
40#387×C151—22no—
41#383×C151C2211yescharacteristic
42#328×C151C2214yes—
43#327×C151C2214yes—
44#324×C151C2214yes—
45C2×#41×C151—21no—
46C22×Q8×C151D411yescharacteristic
47C4⋊Q8×C151—22no—
48C4⋊Q8×C151D411yescharacteristic
49C4⋊Q8×C151D411yescharacteristic
50C4⋊Q8×C151D411yescharacteristic
51#127×C151D411yescharacteristic
52#126×C151—24no—
53#126×C151—24no—
54#125×C151—22no—
55#125×C151—24no—
56#125×C151—21no—
57#125×C151—21no—
58#125×C151—21no—
59#125×C151—21no—
60#125×C151—21no—
61#124×C151—22no—
62#124×C151—22no—
63#124×C151—21no—
64#123×C151—24no—
65#123×C151—24no—
66C22⋊Q8×C151—22no—
67C22⋊Q8×C151—22no—
68C22⋊Q8×C151—21no—
69C22⋊Q8×C151—24no—
70C22⋊Q8×C151C2312yes—
71#121×C151—21no—
72#121×C151C2312yes—
73C4×Q8×C151—22no—
74C4×Q8×C151—22no—
75C4×Q8×C151—21no—
76C4×Q8×C151—21no—
77C4×Q8×C151—21no—
78C4×Q8×C151—21no—
79C4×Q8×C151—21no—
80C4×Q8×C151D412yes—
81C4×D4×C151—22no—
82C4×D4×C151—22no—
83C4×D4×C151—24no—
84C4×D4×C151—21no—
85C4×D4×C151D412yes—
86#117×C151—22no—
87#117×C151—24no—
88#117×C151—21no—
89C2×C4⋊C4×C151—22no—
90C2×C4⋊C4×C151—21no—
91C2×C4⋊C4×C151—22no—
92C2×C4⋊C4×C151—21no—
93C2×C4⋊C4×C151D411yescharacteristic
94C2×C4⋊C4×C151C2311yescharacteristic
95C2×C4⋊C4×C151C2311yescharacteristic
96C2×C4⋊C4×C151C2312yes—
97C2×C42×C151D412yes—
98C2×C42×C151C2311yescharacteristic
99#107×C151—22no—
100#107×C151—22no—
101#106×C151—22no—
102#106×C151—22no—
103C4⋊C8×C151—21no—
104C4⋊C8×C151—21no—
105#103×C151—22no—
106#103×C151—22no—
107#102×C151—22no—
108#102×C151—22no—
109C22⋊C8×C151C2312yes—
110C22⋊C8×C151C2312yes—
111#97×C151—21no—
112#97×C151—21no—
113#95×C151—21no—
114#95×C151—21no—
115#95×C151—22no—
116#95×C151—22no—
117#95×C151—22no—
118#95×C151C2312yes—
119#41×C151—44no—
120C2×Q8×C151—21no—
121C2×Q8×C151—21no—
122C2×Q8×C151—21no—
123C2×Q8×C151—21no—
124C2×Q8×C151—42no—
125C2×Q8×C151C2×D412yes—
126C2×D4×C151—22no—
127C2×D4×C151—21no—
128C2×D4×C151—21no—
129C2×D4×C151C2×D412yes—
130C22×C4×C151—24no—
131C22×C4×C151—22no—
132C22×C4×C151—22no—
133C22×C4×C151—21no—
134C22×C4×C151—21no—
135C22×C4×C151C2×D412yes—
136C22×C4×C151C2×D411yescharacteristic
137C22×C4×C151C2×D412yes—
138C22×C4×C151C2×D411yescharacteristic
139C22×C4×C151C2411yescharacteristic
140C2×C8×C151—22no—
141C2×C8×C151—22no—
142C4⋊C4×C151—24no—
143C4⋊C4×C151—24no—
144C4⋊C4×C151—24no—
145C4⋊C4×C151—21no—
146C4⋊C4×C151—21no—
147C4⋊C4×C151—21no—
148C4⋊C4×C151—21no—
149C4⋊C4×C151—22no—
150C4⋊C4×C151—21no—
151C4⋊C4×C151—21no—
152C4⋊C4×C151—22no—
153C4⋊C4×C151—22no—
154C4⋊C4×C151—22no—
155C4⋊C4×C151—21no—
156C4⋊C4×C151—21no—
157C4⋊C4×C151—21no—
158C4⋊C4×C151—21no—
159C4⋊C4×C151—44no—
160C4⋊C4×C151—41no—
161C4⋊C4×C151—41no—
162C4⋊C4×C151—41no—
163C4⋊C4×C151—41no—
164C4⋊C4×C151C2×D412yes—
165C4⋊C4×C151C2×D412yes—
166C22⋊C4×C151—24no—
167C22⋊C4×C151—24no—
168C22⋊C4×C151—24no—
169C22⋊C4×C151—22no—
170C22⋊C4×C151—22no—
171C22⋊C4×C151—22no—
172C42×C151—24no—
173C42×C151—22no—
174C42×C151—22no—
175C42×C151—22no—
176C42×C151C2×D411yescharacteristic
177C42×C151C2×D411yescharacteristic
178C42×C151C2×D411yescharacteristic
179C42×C151C2×D411yescharacteristic
180C23×C151—22no—
181C23×C151C22×D411yescharacteristic
182Q8×C151—42no—
183Q8×C151—42no—
184Q8×C151—42no—
185Q8×C151—42no—
186Q8×C151—42no—
187D4×C151—42no—
188D4×C151—42no—
189D4×C151—42no—
190D4×C151—44no—
191C2×C4×C151—22no—
192C2×C4×C151—22no—
193C2×C4×C151—22no—
194C2×C4×C151—22no—
195C2×C4×C151—22no—
196C2×C4×C151—22no—
197C2×C4×C151—22no—
198C2×C4×C151—22no—
199C2×C4×C151—41no—
200C2×C4×C151—41no—
201C2×C4×C151—44no—
202C2×C4×C151—42no—
203C2×C4×C151—42no—
204C2×C4×C151—42no—
205C2×C4×C151—42no—
206C2×C4×C151—41no—
207C2×C4×C151—41no—
208C2×C4×C151—42no—
209C2×C4×C151—42no—
210C2×C4×C151—84no—
211C2×C4×C151#12011yescharacteristic
212C2×C4×C151#12011yescharacteristic
213C2×C4×C151#12011yescharacteristic
214C2×C4×C151#12011yescharacteristic
215C2×C4×C151C22×D411yescharacteristic
216C2×C4×C151C22×D411yescharacteristic
217C8×C151—42no—
218C8×C151—42no—
219C22×C151—21no—
220C22×C151—21no—
221C22×C151—42no—
222C22×C151—42no—
223C22×C151—42no—
224C22×C151C2×#12011yescharacteristic
225C22×C151#57512yes—
226C4×C151—21no—
227C4×C151—21no—
228C4×C151—21no—
229C4×C151—21no—
230C4×C151—21no—
231C4×C151—21no—
232C4×C151—42no—
233C4×C151—42no—
234C4×C151—42no—
235C4×C151—42no—
236C4×C151—42no—
237C4×C151—82no—
238C4×C151—81no—
239C4×C151—81no—
240C2×C151—22no—
241C2×C151—82no—
242C2×C151#300511yescharacteristic
243C2×C151#302011yescharacteristic
244C2×C151#302811yescharacteristic
245#18365C15111yesmaximal, characteristic, direct product factor, Sylow
246C151#1836511yescharacteristic, direct product factor, Sylow
247#3507C2×C15111yescharacteristic
248#3236C2×C15111yescharacteristic, complemented
249#3234C2×C15111yescharacteristic
250#2634C2×C15111yescharacteristic, complemented
251#1615C2×C15114yescomplemented
252#1609C2×C15114yescomplemented
253#1515C2×C15111yescharacteristic, complemented
254#1514C2×C15111yescharacteristic
255#1467C2×C15111yescharacteristic, complemented
256#559—21no—
257#557—21no—
258#556—21no—
259#556—22no—
260#554—21no—
261#552—22no—
262#539C22×C15114yes—
263#536—21no—
264#533C22×C15111yescharacteristic
265#532C22×C15111yescharacteristic
266#529—22no—
267C2×#125C22×C15111yescharacteristic
268#520—21no—
269C2×C4×Q8C22×C15111yescharacteristic
270#501—21no—
271#501—21no—
272#491—21no—
273#490—21no—
274#484C22×C15112yes—
275#483C22×C15112yes—
276#481C22×C15112yes—
277#480C22×C15112yes—
278#479—22no—
279#478—22no—
280#432C22×C15111yescharacteristic
281#432C22×C15111yescharacteristic
282#400—21no—
283#400C22×C15112yes—
284#398C22×C15112yes—
285#395—21no—
286#387—22no—
287#383C22×C15111yescharacteristic
288#328C22×C15114yes—
289#327C22×C15114yes—
290#324C22×C15114yes—
291C2×#41—21no—
292C22×Q8D4×C15111yescharacteristic
293C4⋊Q8—22no—
294C4⋊Q8D4×C15111yescharacteristic
295C4⋊Q8D4×C15111yescharacteristic
296C4⋊Q8D4×C15111yescharacteristic
297#127D4×C15111yescharacteristic
298#126—24no—
299#126—24no—
300#125—22no—
301#125—24no—
302#125—21no—
303#125—21no—
304#125—21no—
305#125—21no—
306#125—21no—
307#124—22no—
308#124—22no—
309#124—21no—
310#123—24no—
311#123—24no—
312C22⋊Q8—22no—
313C22⋊Q8—22no—
314C22⋊Q8—24no—
315C22⋊Q8—21no—
316C22⋊Q8C23×C15112yes—
317#121—21no—
318#121C23×C15112yes—
319C4×Q8—22no—
320C4×Q8—22no—
321C4×Q8—21no—
322C4×Q8—21no—
323C4×Q8—21no—
324C4×Q8—21no—
325C4×Q8—21no—
326C4×Q8D4×C15112yes—
327C4×D4—22no—
328C4×D4—22no—
329C4×D4—24no—
330C4×D4—21no—
331C4×D4D4×C15112yes—
332#117—22no—
333#117—24no—
334#117—21no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4D4×C15111yescharacteristic
340C2×C4⋊C4C23×C15111yescharacteristic
341C2×C4⋊C4C23×C15111yescharacteristic
342C2×C4⋊C4C23×C15112yes—
343C2×C42D4×C15112yes—
344C2×C42C23×C15111yescharacteristic
345#107—22no—
346#107—22no—
347#106—22no—
348#106—22no—
349C4⋊C8—21no—
350C4⋊C8—21no—
351#103—22no—
352#103—22no—
353#102—22no—
354#102—22no—
355C22⋊C8C23×C15112yes—
356C22⋊C8C23×C15112yes—
357#97—21no—
358#97—21no—
359#95—21no—
360#95—21no—
361#95—22no—
362#95—22no—
363#95—22no—
364#95C23×C15112yes—
365#41—44no—
366C2×Q8—21no—
367C2×Q8—21no—
368C2×Q8—21no—
369C2×Q8—21no—
370C2×Q8—42no—
371C2×Q8C2×D4×C15112yes—
372C2×D4—22no—
373C2×D4—21no—
374C2×D4—21no—
375C2×D4C2×D4×C15112yes—
376C22×C4—24no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4C2×D4×C15112yes—
382C22×C4C2×D4×C15111yescharacteristic
383C22×C4C2×D4×C15112yes—
384C22×C4C2×D4×C15111yescharacteristic
385C22×C4C24×C15111yescharacteristic
386C2×C8—22no—
387C2×C8—22no—
388C4⋊C4—24no—
389C4⋊C4—24no—
390C4⋊C4—24no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—22no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—44no—
406C4⋊C4—41no—
407C4⋊C4—41no—
408C4⋊C4—41no—
409C4⋊C4—41no—
410C4⋊C4C2×D4×C15112yes—
411C4⋊C4C2×D4×C15112yes—
412C22⋊C4—24no—
413C22⋊C4—24no—
414C22⋊C4—24no—
415C22⋊C4—22no—
416C22⋊C4—22no—
417C22⋊C4—22no—
418C42—24no—
419C42—22no—
420C42—22no—
421C42—22no—
422C42C2×D4×C15111yescharacteristic
423C42C2×D4×C15111yescharacteristic
424C42C2×D4×C15111yescharacteristic
425C42C2×D4×C15111yescharacteristic
426C23—22no—
427C23C22×D4×C15111yescharacteristic
428Q8—42no—
429Q8—42no—
430Q8—42no—
431Q8—42no—
432Q8—42no—
433D4—42no—
434D4—42no—
435D4—42no—
436D4—44no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—44no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—84no—
457C2×C4#120×C15111yescharacteristic
458C2×C4#120×C15111yescharacteristic
459C2×C4#120×C15111yescharacteristic
460C2×C4#120×C15111yescharacteristic
461C2×C4C22×D4×C15111yescharacteristic
462C2×C4C22×D4×C15111yescharacteristic
463C8—42no—
464C8—42no—
465C22—21no—
466C22—21no—
467C22—42no—
468C22—42no—
469C22—42no—
470C22C2×#120×C15111yescharacteristic
471C22#575×C15112yes—
472C4—21no—
473C4—21no—
474C4—21no—
475C4—21no—
476C4—21no—
477C4—21no—
478C4—42no—
479C4—42no—
480C4—42no—
481C4—42no—
482C4—42no—
483C4—82no—
484C4—81no—
485C4—81no—
486C2—22no—
487C2—82no—
488C2#3005×C15111yescharacteristic
489C2#3020×C15111yescharacteristic
490C2#3028×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#532×C151C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3236×C151C2semidirect
4. #2634×C151C2semidirect
5. #1615×C151C2semidirect
6. #1609×C151C2semidirect
7. #1515×C151C2semidirect
9. #1467×C151C2semidirect
245. #18365C151direct (N × H)
246. C151#18365direct (N × H)
248. #3236C2×C151semidirect
250. #2634C2×C151semidirect
251. #1615C2×C151semidirect
252. #1609C2×C151semidirect
253. #1515C2×C151semidirect
255. #1467C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3507×C1512
#3236×C1512
#3234×C1512
#2634×C1512
#1615×C1512
#1609×C1512
#1515×C1512
#1514×C1512
#1467×C1512
#18365151