Finite Group Databasebeta

← C151×#18941 #50323866

Subgroups — C151×#18941 #50323866

Order 38656.

914 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3548×C151C211yesmaximal, characteristic
2#3249×C151C211yesmaximal, characteristic, complemented
3#3235×C151C211yesmaximal, characteristic, complemented
4#3210×C151C211yesmaximal, characteristic, complemented
5#1644×C151C212yesmaximal, complemented
6#1641×C151C212yesmaximal, complemented
7#1632×C151C212yesmaximal, complemented
8#1631×C151C212yesmaximal, complemented
9#1551×C151C211yesmaximal, characteristic, complemented
10#1497×C151C211yesmaximal, characteristic, complemented
11#1480×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#490×C151—21no—
30#487×C151C2211yescharacteristic
31#486×C151C2211yescharacteristic
32#482×C151—22no—
33#477×C151—21no—
34#477×C151C2212yes—
35#476×C151C2212yes—
36#474×C151C2212yes—
37#467×C151—22no—
38#464×C151—22no—
39#462×C151—21no—
40#462×C151C2212yes—
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×Q16×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#107×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#102×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—81no—
127#41×C151—81no—
128#41×C151—82no—
129#41×C151—82no—
130#41×C151—82no—
131#41×C151—84no—
132C2×Q8×C151—21no—
133C2×Q8×C151—21no—
134C2×Q8×C151—21no—
135C2×Q8×C151—21no—
136C2×Q8×C151C2×D412yes—
137C2×Q8×C151C2×D412yes—
138C2×D4×C151—24no—
139C2×D4×C151—24no—
140C2×D4×C151—22no—
141C2×D4×C151—22no—
142C2×D4×C151—21no—
143C2×D4×C151—21no—
144C2×D4×C151—21no—
145C2×D4×C151—21no—
146C2×D4×C151C2×D412yes—
147C2×D4×C151C2×D412yes—
148C22×C4×C151—24no—
149C22×C4×C151—24no—
150C22×C4×C151—22no—
151C22×C4×C151—22no—
152C22×C4×C151C2×D411yescharacteristic
153C22×C4×C151C2×D411yescharacteristic
154C22×C4×C151C2×D411yescharacteristic
155Q16×C151—82no—
156Q16×C151—82no—
157SD16×C151—82no—
158C2×C8×C151—21no—
159C2×C8×C151—21no—
160C2×C8×C151—22no—
161C2×C8×C151—22no—
162C2×C8×C151—81no—
163C4⋊C4×C151—24no—
164C4⋊C4×C151—24no—
165C4⋊C4×C151—21no—
166C4⋊C4×C151—21no—
167C4⋊C4×C151—21no—
168C4⋊C4×C151—21no—
169C4⋊C4×C151—22no—
170C4⋊C4×C151—21no—
171C4⋊C4×C151—21no—
172C4⋊C4×C151—22no—
173C4⋊C4×C151—21no—
174C4⋊C4×C151—21no—
175C4⋊C4×C151—21no—
176C4⋊C4×C151—21no—
177C4⋊C4×C151—41no—
178C4⋊C4×C151—41no—
179C4⋊C4×C151C2×D412yes—
180C4⋊C4×C151C2×D412yes—
181C22⋊C4×C151—24no—
182C22⋊C4×C151—24no—
183C22⋊C4×C151—22no—
184C22⋊C4×C151—22no—
185C22⋊C4×C151—22no—
186C22⋊C4×C151—22no—
187C22⋊C4×C151—22no—
188C22⋊C4×C151—41no—
189C42×C151—22no—
190C42×C151—41no—
191C42×C151C2×D411yescharacteristic
192C42×C151C2×D411yescharacteristic
193C42×C151C2×D411yescharacteristic
194C42×C151C2411yescharacteristic
195C23×C151—22no—
196C23×C151—22no—
197C23×C151#12011yescharacteristic
198Q8×C151—22no—
199Q8×C151—22no—
200Q8×C151—42no—
201Q8×C151—42no—
202Q8×C151—42no—
203Q8×C151—41no—
204Q8×C151—41no—
205Q8×C151—81no—
206D4×C151—24no—
207D4×C151—42no—
208D4×C151—42no—
209D4×C151—41no—
210D4×C151—41no—
211D4×C151—42no—
212D4×C151—81no—
213D4×C151—82no—
214D4×C151—82no—
215D4×C151—84no—
216D4×C151—84no—
217C2×C4×C151—21no—
218C2×C4×C151—21no—
219C2×C4×C151—22no—
220C2×C4×C151—22no—
221C2×C4×C151—22no—
222C2×C4×C151—22no—
223C2×C4×C151—22no—
224C2×C4×C151—41no—
225C2×C4×C151—44no—
226C2×C4×C151—42no—
227C2×C4×C151—42no—
228C2×C4×C151—41no—
229C2×C4×C151—41no—
230C2×C4×C151—84no—
231C2×C4×C151—84no—
232C2×C4×C151#12011yescharacteristic
233C2×C4×C151#12011yescharacteristic
234C2×C4×C151#12011yescharacteristic
235C2×C4×C151C22×D411yescharacteristic
236C2×C4×C151C22×D411yescharacteristic
237C2×C4×C151C22×D411yescharacteristic
238C8×C151—41no—
239C8×C151—41no—
240C8×C151—42no—
241C8×C151—42no—
242C22×C151—21no—
243C22×C151—21no—
244C22×C151—21no—
245C22×C151—42no—
246C22×C151—42no—
247C22×C151—42no—
248C22×C151—42no—
249C22×C151—42no—
250C22×C151—42no—
251C22×C151C2×#12011yescharacteristic
252C4×C151—21no—
253C4×C151—21no—
254C4×C151—21no—
255C4×C151—21no—
256C4×C151—42no—
257C4×C151—42no—
258C4×C151—42no—
259C4×C151—42no—
260C4×C151—81no—
261C4×C151—81no—
262C4×C151#57611yescharacteristic
263C4×C151#57711yescharacteristic
264C4×C151#57812yes—
265C2×C151—41no—
266C2×C151—82no—
267C2×C151—82no—
268C2×C151#301111yescharacteristic
269C2×C151#301211yescharacteristic
270C2×C151#301911yescharacteristic
271#18941C15111yesmaximal, characteristic, direct product factor, Sylow
272C151#1894111yescharacteristic, direct product factor, Sylow
273#3548C2×C15111yescharacteristic
274#3249C2×C15111yescharacteristic, complemented
275#3235C2×C15111yescharacteristic, complemented
276#3210C2×C15111yescharacteristic, complemented
277#1644C2×C15112yescomplemented
278#1641C2×C15112yescomplemented
279#1632C2×C15112yescomplemented
280#1631C2×C15112yescomplemented
281#1551C2×C15111yescharacteristic, complemented
282#1497C2×C15111yescharacteristic, complemented
283#1480C2×C15111yescharacteristic, complemented
284#562—22no—
285#554—21no—
286#554C22×C15112yes—
287#550—21no—
288#550C22×C15112yes—
289#547—21no—
290#547—21no—
291#540—22no—
292#537—22no—
293#537—22no—
294#533C22×C15111yescharacteristic
295#533C22×C15111yescharacteristic
296#532C22×C15111yescharacteristic
297#532C22×C15111yescharacteristic
298#501—21no—
299#494C22×C15111yescharacteristic
300#492C22×C15111yescharacteristic
301#490—21no—
302#487C22×C15111yescharacteristic
303#486C22×C15111yescharacteristic
304#482—22no—
305#477—21no—
306#477C22×C15112yes—
307#476C22×C15112yes—
308#474C22×C15112yes—
309#467—22no—
310#464—22no—
311#462—21no—
312#462C22×C15112yes—
313#452—22no—
314#432C22×C15111yescharacteristic
315#431C22×C15111yescharacteristic
316C2×C4⋊C8C22×C15111yescharacteristic
317#333C22×C15112yes—
318#331C22×C15112yes—
319Q8⋊C8C22×C15112yes—
320Q8⋊C8C22×C15112yes—
321D4⋊C8C22×C15112yes—
322D4⋊C8C22×C15112yes—
323C2×#41—22no—
324C2×#41—22no—
325C2×#41—21no—
326C2×#41D4×C15112yes—
327C2×Q16—22no—
328C2×Q16—22no—
329C2×SD16—22no—
330C22×C8—21no—
331C4⋊Q8D4×C15111yescharacteristic
332C4⋊Q8D4×C15111yescharacteristic
333C4⋊Q8D4×C15111yescharacteristic
334C4⋊Q8C23×C15111yescharacteristic
335C4⋊Q8C23×C15111yescharacteristic
336C4⋊Q8C23×C15111yescharacteristic
337#127—22no—
338#127D4×C15111yescharacteristic
339#127C23×C15111yescharacteristic
340#125—22no—
341#125—21no—
342#125—21no—
343#124—21no—
344#124D4×C15112yes—
345#123—24no—
346#123—24no—
347C22⋊Q8—22no—
348C22⋊Q8—24no—
349C22⋊Q8—22no—
350C22⋊Q8—24no—
351C22⋊Q8—21no—
352C22⋊Q8—21no—
353C22⋊Q8—21no—
354C22⋊Q8D4×C15112yes—
355#121—24no—
356#121—24no—
357#121—22no—
358#121—24no—
359#121—24no—
360#121—21no—
361#121—21no—
362#121—21no—
363#121—22no—
364#121D4×C15112yes—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8—21no—
368C4×Q8C23×C15112yes—
369C4×D4—22no—
370C4×D4—22no—
371C4×D4—21no—
372C4×D4—21no—
373C4×D4—21no—
374C4×D4C23×C15112yes—
375#117—21no—
376#117—21no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C42C23×C15111yescharacteristic
380#107—22no—
381#107—22no—
382#106—22no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8C23×C15112yes—
386C4⋊C8C23×C15112yes—
387#103—22no—
388#103—22no—
389#103—22no—
390#102—22no—
391#102—22no—
392#102—22no—
393C22⋊C8—21no—
394C22⋊C8—21no—
395#97—21no—
396C4×C8C23×C15111yescharacteristic
397C4×C8C23×C15111yescharacteristic
398#41—81no—
399#41—81no—
400#41—82no—
401#41—82no—
402#41—82no—
403#41—84no—
404C2×Q8—21no—
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×Q8C2×D4×C15112yes—
409C2×Q8C2×D4×C15112yes—
410C2×D4—24no—
411C2×D4—24no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4C2×D4×C15112yes—
419C2×D4C2×D4×C15112yes—
420C22×C4—24no—
421C22×C4—24no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4C2×D4×C15111yescharacteristic
425C22×C4C2×D4×C15111yescharacteristic
426C22×C4C2×D4×C15111yescharacteristic
427Q16—82no—
428Q16—82no—
429SD16—82no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—22no—
433C2×C8—22no—
434C2×C8—81no—
435C4⋊C4—24no—
436C4⋊C4—24no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—22no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—22no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—41no—
450C4⋊C4—41no—
451C4⋊C4C2×D4×C15112yes—
452C4⋊C4C2×D4×C15112yes—
453C22⋊C4—24no—
454C22⋊C4—24no—
455C22⋊C4—22no—
456C22⋊C4—22no—
457C22⋊C4—22no—
458C22⋊C4—22no—
459C22⋊C4—22no—
460C22⋊C4—41no—
461C42—22no—
462C42—41no—
463C42C2×D4×C15111yescharacteristic
464C42C2×D4×C15111yescharacteristic
465C42C2×D4×C15111yescharacteristic
466C42C24×C15111yescharacteristic
467C23—22no—
468C23—22no—
469C23#120×C15111yescharacteristic
470Q8—22no—
471Q8—22no—
472Q8—42no—
473Q8—42no—
474Q8—42no—
475Q8—41no—
476Q8—41no—
477Q8—81no—
478D4—24no—
479D4—42no—
480D4—42no—
481D4—41no—
482D4—41no—
483D4—42no—
484D4—81no—
485D4—82no—
486D4—82no—
487D4—84no—
488D4—84no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—41no—
497C2×C4—44no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—84no—
503C2×C4—84no—
504C2×C4#120×C15111yescharacteristic
505C2×C4#120×C15111yescharacteristic
506C2×C4#120×C15111yescharacteristic
507C2×C4C22×D4×C15111yescharacteristic
508C2×C4C22×D4×C15111yescharacteristic
509C2×C4C22×D4×C15111yescharacteristic
510C8—41no—
511C8—41no—
512C8—42no—
513C8—42no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—42no—
518C22—42no—
519C22—42no—
520C22—42no—
521C22—42no—
522C22—42no—
523C22C2×#120×C15111yescharacteristic
524C4—21no—
525C4—21no—
526C4—21no—
527C4—21no—
528C4—42no—
529C4—42no—
530C4—42no—
531C4—42no—
532C4—81no—
533C4—81no—
534C4#576×C15111yescharacteristic
535C4#577×C15111yescharacteristic
536C4#578×C15112yes—
537C2—41no—
538C2—82no—
539C2—82no—
540C2#3011×C15111yescharacteristic
541C2#3012×C15111yescharacteristic
542C2#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. #3249×C151C2semidirect
3. #3235×C151C2semidirect
4. #3210×C151C2semidirect
5. #1644×C151C2semidirect
6. #1641×C151C2semidirect
7. #1632×C151C2semidirect
8. #1631×C151C2semidirect
9. #1551×C151C2semidirect
10. #1497×C151C2semidirect
11. #1480×C151C2semidirect
271. #18941C151direct (N × H)
272. C151#18941direct (N × H)
274. #3249C2×C151semidirect
275. #3235C2×C151semidirect
276. #3210C2×C151semidirect
277. #1644C2×C151semidirect
278. #1641C2×C151semidirect
279. #1632C2×C151semidirect
280. #1631C2×C151semidirect
281. #1551C2×C151semidirect
282. #1497C2×C151semidirect
283. #1480C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3548×C1512
#3249×C1512
#3235×C1512
#3210×C1512
#1644×C1512
#1641×C1512
#1632×C1512
#1631×C1512
#1551×C1512
#1497×C1512
#1480×C1512
#18941151