Finite Group Databasebeta

← C151×#18937 #50323862

Subgroups — C151×#18937 #50323862

Order 38656.

914 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3548×C151C211yesmaximal, characteristic
2#3246×C151C211yesmaximal, characteristic, complemented
3#3237×C151C211yesmaximal, characteristic, complemented
4#3210×C151C211yesmaximal, characteristic, complemented
5#1643×C151C212yesmaximal, complemented
6#1642×C151C212yesmaximal, complemented
7#1632×C151C212yesmaximal, complemented
8#1631×C151C212yesmaximal, complemented
9#1551×C151C211yesmaximal, characteristic, complemented
10#1496×C151C211yesmaximal, characteristic, complemented
11#1481×C151C211yesmaximal, characteristic, complemented
12#562×C151—22no—
13#554×C151—21no—
14#554×C151C2212yes—
15#550×C151—21no—
16#550×C151C2212yes—
17#547×C151—21no—
18#547×C151—21no—
19#540×C151—22no—
20#537×C151—22no—
21#537×C151—22no—
22#533×C151C2211yescharacteristic
23#533×C151C2211yescharacteristic
24#532×C151C2211yescharacteristic
25#532×C151C2211yescharacteristic
26#501×C151—21no—
27#494×C151C2211yescharacteristic
28#492×C151C2211yescharacteristic
29#491×C151—21no—
30#487×C151C2211yescharacteristic
31#486×C151C2211yescharacteristic
32#485×C151—22no—
33#477×C151C2212yes—
34#476×C151C2212yes—
35#475×C151—21no—
36#475×C151C2212yes—
37#465×C151—22no—
38#464×C151—22no—
39#461×C151C2212yes—
40#460×C151—21no—
41#452×C151—22no—
42#432×C151C2211yescharacteristic
43#431×C151C2211yescharacteristic
44C2×C4⋊C8×C151C2211yescharacteristic
45#333×C151C2212yes—
46#331×C151C2212yes—
47Q8⋊C8×C151C2212yes—
48Q8⋊C8×C151C2212yes—
49D4⋊C8×C151C2212yes—
50D4⋊C8×C151C2212yes—
51C2×#41×C151—22no—
52C2×#41×C151—21no—
53C2×#41×C151—22no—
54C2×#41×C151D412yes—
55C2×Q16×C151—22no—
56C2×SD16×C151—22no—
57C2×SD16×C151—22no—
58C22×C8×C151—21no—
59C4⋊Q8×C151D411yescharacteristic
60C4⋊Q8×C151D411yescharacteristic
61C4⋊Q8×C151D411yescharacteristic
62C4⋊Q8×C151C2311yescharacteristic
63C4⋊Q8×C151C2311yescharacteristic
64C4⋊Q8×C151C2311yescharacteristic
65#127×C151—22no—
66#127×C151D411yescharacteristic
67#127×C151C2311yescharacteristic
68#125×C151—22no—
69#125×C151—21no—
70#125×C151—21no—
71#124×C151—21no—
72#124×C151D412yes—
73#123×C151—24no—
74#123×C151—24no—
75C22⋊Q8×C151—22no—
76C22⋊Q8×C151—24no—
77C22⋊Q8×C151—21no—
78C22⋊Q8×C151—21no—
79C22⋊Q8×C151—21no—
80C22⋊Q8×C151—22no—
81C22⋊Q8×C151—24no—
82C22⋊Q8×C151D412yes—
83#121×C151—24no—
84#121×C151—24no—
85#121×C151—22no—
86#121×C151—24no—
87#121×C151—24no—
88#121×C151—21no—
89#121×C151—21no—
90#121×C151—21no—
91#121×C151—22no—
92#121×C151D412yes—
93C4×Q8×C151—21no—
94C4×Q8×C151—21no—
95C4×Q8×C151—21no—
96C4×Q8×C151C2312yes—
97C4×D4×C151—22no—
98C4×D4×C151—22no—
99C4×D4×C151—21no—
100C4×D4×C151—21no—
101C4×D4×C151—21no—
102C4×D4×C151C2312yes—
103#117×C151—21no—
104#117×C151—21no—
105C2×C4⋊C4×C151—22no—
106C2×C4⋊C4×C151—22no—
107C2×C42×C151C2311yescharacteristic
108#107×C151—22no—
109#106×C151—22no—
110#106×C151—22no—
111C4⋊C8×C151—21no—
112C4⋊C8×C151—21no—
113C4⋊C8×C151C2312yes—
114C4⋊C8×C151C2312yes—
115#103×C151—22no—
116#103×C151—22no—
117#103×C151—22no—
118#103×C151—22no—
119#102×C151—22no—
120#102×C151—22no—
121C22⋊C8×C151—21no—
122C22⋊C8×C151—21no—
123#97×C151—21no—
124C4×C8×C151C2311yescharacteristic
125C4×C8×C151C2311yescharacteristic
126#41×C151—82no—
127#41×C151—82no—
128#41×C151—84no—
129#41×C151—84no—
130C2×Q8×C151—21no—
131C2×Q8×C151—21no—
132C2×Q8×C151—21no—
133C2×Q8×C151—21no—
134C2×Q8×C151C2×D412yes—
135C2×Q8×C151C2×D412yes—
136C2×D4×C151—24no—
137C2×D4×C151—24no—
138C2×D4×C151—22no—
139C2×D4×C151—22no—
140C2×D4×C151—21no—
141C2×D4×C151—21no—
142C2×D4×C151—21no—
143C2×D4×C151—21no—
144C2×D4×C151C2×D412yes—
145C2×D4×C151C2×D412yes—
146C22×C4×C151—24no—
147C22×C4×C151—24no—
148C22×C4×C151—22no—
149C22×C4×C151—22no—
150C22×C4×C151C2×D411yescharacteristic
151C22×C4×C151C2×D411yescharacteristic
152C22×C4×C151C2×D411yescharacteristic
153Q16×C151—82no—
154SD16×C151—82no—
155SD16×C151—82no—
156C2×C8×C151—21no—
157C2×C8×C151—21no—
158C2×C8×C151—22no—
159C2×C8×C151—22no—
160C2×C8×C151—81no—
161C4⋊C4×C151—24no—
162C4⋊C4×C151—24no—
163C4⋊C4×C151—21no—
164C4⋊C4×C151—21no—
165C4⋊C4×C151—21no—
166C4⋊C4×C151—21no—
167C4⋊C4×C151—22no—
168C4⋊C4×C151—21no—
169C4⋊C4×C151—21no—
170C4⋊C4×C151—22no—
171C4⋊C4×C151—21no—
172C4⋊C4×C151—21no—
173C4⋊C4×C151—21no—
174C4⋊C4×C151—21no—
175C4⋊C4×C151—41no—
176C4⋊C4×C151—41no—
177C4⋊C4×C151C2×D412yes—
178C4⋊C4×C151C2×D412yes—
179C22⋊C4×C151—24no—
180C22⋊C4×C151—24no—
181C22⋊C4×C151—22no—
182C22⋊C4×C151—22no—
183C22⋊C4×C151—22no—
184C22⋊C4×C151—22no—
185C22⋊C4×C151—22no—
186C22⋊C4×C151—41no—
187C42×C151—22no—
188C42×C151—41no—
189C42×C151C2×D411yescharacteristic
190C42×C151C2×D411yescharacteristic
191C42×C151C2×D411yescharacteristic
192C42×C151C2411yescharacteristic
193C23×C151—22no—
194C23×C151—22no—
195C23×C151#12011yescharacteristic
196Q8×C151—24no—
197Q8×C151—42no—
198Q8×C151—42no—
199Q8×C151—42no—
200Q8×C151—41no—
201Q8×C151—41no—
202Q8×C151—81no—
203D4×C151—22no—
204D4×C151—22no—
205D4×C151—42no—
206D4×C151—42no—
207D4×C151—42no—
208D4×C151—41no—
209D4×C151—41no—
210D4×C151—81no—
211D4×C151—82no—
212D4×C151—82no—
213D4×C151—84no—
214D4×C151—84no—
215C2×C4×C151—22no—
216C2×C4×C151—21no—
217C2×C4×C151—21no—
218C2×C4×C151—22no—
219C2×C4×C151—22no—
220C2×C4×C151—22no—
221C2×C4×C151—22no—
222C2×C4×C151—41no—
223C2×C4×C151—44no—
224C2×C4×C151—44no—
225C2×C4×C151—41no—
226C2×C4×C151—41no—
227C2×C4×C151—84no—
228C2×C4×C151—84no—
229C2×C4×C151#12011yescharacteristic
230C2×C4×C151#12011yescharacteristic
231C2×C4×C151#12011yescharacteristic
232C2×C4×C151C22×D411yescharacteristic
233C2×C4×C151C22×D411yescharacteristic
234C2×C4×C151C22×D411yescharacteristic
235C8×C151—41no—
236C8×C151—41no—
237C8×C151—42no—
238C8×C151—42no—
239C22×C151—21no—
240C22×C151—21no—
241C22×C151—21no—
242C22×C151—42no—
243C22×C151—42no—
244C22×C151—42no—
245C22×C151—42no—
246C22×C151—42no—
247C22×C151—42no—
248C22×C151C2×#12011yescharacteristic
249C4×C151—21no—
250C4×C151—21no—
251C4×C151—21no—
252C4×C151—21no—
253C4×C151—42no—
254C4×C151—42no—
255C4×C151—42no—
256C4×C151—42no—
257C4×C151—81no—
258C4×C151—81no—
259C4×C151#57712yes—
260C4×C151#57711yescharacteristic
261C4×C151#57811yescharacteristic
262C2×C151—41no—
263C2×C151—82no—
264C2×C151—82no—
265C2×C151#300911yescharacteristic
266C2×C151#301311yescharacteristic
267C2×C151#301911yescharacteristic
268#18937C15111yesmaximal, characteristic, direct product factor, Sylow
269C151#1893711yescharacteristic, direct product factor, Sylow
270#3548C2×C15111yescharacteristic
271#3246C2×C15111yescharacteristic, complemented
272#3237C2×C15111yescharacteristic, complemented
273#3210C2×C15111yescharacteristic, complemented
274#1643C2×C15112yescomplemented
275#1642C2×C15112yescomplemented
276#1632C2×C15112yescomplemented
277#1631C2×C15112yescomplemented
278#1551C2×C15111yescharacteristic, complemented
279#1496C2×C15111yescharacteristic, complemented
280#1481C2×C15111yescharacteristic, complemented
281#562—22no—
282#554—21no—
283#554C22×C15112yes—
284#550—21no—
285#550C22×C15112yes—
286#547—21no—
287#547—21no—
288#540—22no—
289#537—22no—
290#537—22no—
291#533C22×C15111yescharacteristic
292#533C22×C15111yescharacteristic
293#532C22×C15111yescharacteristic
294#532C22×C15111yescharacteristic
295#501—21no—
296#494C22×C15111yescharacteristic
297#492C22×C15111yescharacteristic
298#491—21no—
299#487C22×C15111yescharacteristic
300#486C22×C15111yescharacteristic
301#485—22no—
302#477C22×C15112yes—
303#476C22×C15112yes—
304#475—21no—
305#475C22×C15112yes—
306#465—22no—
307#464—22no—
308#461C22×C15112yes—
309#460—21no—
310#452—22no—
311#432C22×C15111yescharacteristic
312#431C22×C15111yescharacteristic
313C2×C4⋊C8C22×C15111yescharacteristic
314#333C22×C15112yes—
315#331C22×C15112yes—
316Q8⋊C8C22×C15112yes—
317Q8⋊C8C22×C15112yes—
318D4⋊C8C22×C15112yes—
319D4⋊C8C22×C15112yes—
320C2×#41—22no—
321C2×#41—22no—
322C2×#41—21no—
323C2×#41D4×C15112yes—
324C2×Q16—22no—
325C2×SD16—22no—
326C2×SD16—22no—
327C22×C8—21no—
328C4⋊Q8D4×C15111yescharacteristic
329C4⋊Q8D4×C15111yescharacteristic
330C4⋊Q8D4×C15111yescharacteristic
331C4⋊Q8C23×C15111yescharacteristic
332C4⋊Q8C23×C15111yescharacteristic
333C4⋊Q8C23×C15111yescharacteristic
334#127—22no—
335#127D4×C15111yescharacteristic
336#127C23×C15111yescharacteristic
337#125—22no—
338#125—21no—
339#125—21no—
340#124—21no—
341#124D4×C15112yes—
342#123—24no—
343#123—24no—
344C22⋊Q8—22no—
345C22⋊Q8—24no—
346C22⋊Q8—22no—
347C22⋊Q8—24no—
348C22⋊Q8—21no—
349C22⋊Q8—21no—
350C22⋊Q8—21no—
351C22⋊Q8D4×C15112yes—
352#121—24no—
353#121—24no—
354#121—22no—
355#121—24no—
356#121—24no—
357#121—21no—
358#121—21no—
359#121—21no—
360#121—22no—
361#121D4×C15112yes—
362C4×Q8—21no—
363C4×Q8—21no—
364C4×Q8—21no—
365C4×Q8C23×C15112yes—
366C4×D4—22no—
367C4×D4—22no—
368C4×D4—21no—
369C4×D4—21no—
370C4×D4—21no—
371C4×D4C23×C15112yes—
372#117—21no—
373#117—21no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C42C23×C15111yescharacteristic
377#107—22no—
378#106—22no—
379#106—22no—
380C4⋊C8—21no—
381C4⋊C8—21no—
382C4⋊C8C23×C15112yes—
383C4⋊C8C23×C15112yes—
384#103—22no—
385#103—22no—
386#103—22no—
387#103—22no—
388#102—22no—
389#102—22no—
390C22⋊C8—21no—
391C22⋊C8—21no—
392#97—21no—
393C4×C8C23×C15111yescharacteristic
394C4×C8C23×C15111yescharacteristic
395#41—82no—
396#41—82no—
397#41—84no—
398#41—84no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—21no—
402C2×Q8—21no—
403C2×Q8C2×D4×C15112yes—
404C2×Q8C2×D4×C15112yes—
405C2×D4—24no—
406C2×D4—24no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4C2×D4×C15112yes—
414C2×D4C2×D4×C15112yes—
415C22×C4—24no—
416C22×C4—24no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4C2×D4×C15111yescharacteristic
420C22×C4C2×D4×C15111yescharacteristic
421C22×C4C2×D4×C15111yescharacteristic
422Q16—82no—
423SD16—82no—
424SD16—82no—
425C2×C8—21no—
426C2×C8—21no—
427C2×C8—22no—
428C2×C8—22no—
429C2×C8—81no—
430C4⋊C4—24no—
431C4⋊C4—24no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—22no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—22no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—41no—
445C4⋊C4—41no—
446C4⋊C4C2×D4×C15112yes—
447C4⋊C4C2×D4×C15112yes—
448C22⋊C4—24no—
449C22⋊C4—24no—
450C22⋊C4—22no—
451C22⋊C4—22no—
452C22⋊C4—22no—
453C22⋊C4—22no—
454C22⋊C4—22no—
455C22⋊C4—41no—
456C42—22no—
457C42—41no—
458C42C2×D4×C15111yescharacteristic
459C42C2×D4×C15111yescharacteristic
460C42C2×D4×C15111yescharacteristic
461C42C24×C15111yescharacteristic
462C23—22no—
463C23—22no—
464C23#120×C15111yescharacteristic
465Q8—24no—
466Q8—42no—
467Q8—42no—
468Q8—42no—
469Q8—41no—
470Q8—41no—
471Q8—81no—
472D4—22no—
473D4—22no—
474D4—42no—
475D4—42no—
476D4—42no—
477D4—41no—
478D4—41no—
479D4—81no—
480D4—82no—
481D4—82no—
482D4—84no—
483D4—84no—
484C2×C4—21no—
485C2×C4—22no—
486C2×C4—21no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—41no—
492C2×C4—44no—
493C2×C4—44no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—84no—
497C2×C4—84no—
498C2×C4#120×C15111yescharacteristic
499C2×C4#120×C15111yescharacteristic
500C2×C4#120×C15111yescharacteristic
501C2×C4C22×D4×C15111yescharacteristic
502C2×C4C22×D4×C15111yescharacteristic
503C2×C4C22×D4×C15111yescharacteristic
504C8—41no—
505C8—41no—
506C8—42no—
507C8—42no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—42no—
512C22—42no—
513C22—42no—
514C22—42no—
515C22—42no—
516C22—42no—
517C22C2×#120×C15111yescharacteristic
518C4—21no—
519C4—21no—
520C4—21no—
521C4—21no—
522C4—42no—
523C4—42no—
524C4—42no—
525C4—42no—
526C4—81no—
527C4—81no—
528C4#577×C15112yes—
529C4#577×C15111yescharacteristic
530C4#578×C15111yescharacteristic
531C2—41no—
532C2—82no—
533C2—82no—
534C2#3009×C15111yescharacteristic
535C2#3013×C15111yescharacteristic
536C2#3019×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3548×C151C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3246×C151C2semidirect
3. #3237×C151C2semidirect
4. #3210×C151C2semidirect
5. #1643×C151C2semidirect
6. #1642×C151C2semidirect
7. #1632×C151C2semidirect
8. #1631×C151C2semidirect
9. #1551×C151C2semidirect
10. #1496×C151C2semidirect
11. #1481×C151C2semidirect
268. #18937C151direct (N × H)
269. C151#18937direct (N × H)
271. #3246C2×C151semidirect
272. #3237C2×C151semidirect
273. #3210C2×C151semidirect
274. #1643C2×C151semidirect
275. #1642C2×C151semidirect
276. #1632C2×C151semidirect
277. #1631C2×C151semidirect
278. #1551C2×C151semidirect
279. #1496C2×C151semidirect
280. #1481C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3548×C1512
#3246×C1512
#3237×C1512
#3210×C1512
#1643×C1512
#1642×C1512
#1632×C1512
#1631×C1512
#1551×C1512
#1496×C1512
#1481×C1512
#18937151