Finite Group Databasebeta

← C151×#20679 #50325604

Subgroups — C151×#20679 #50325604

Order 38656.

1330 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#568×C151C211yesmaximal, characteristic
2C2×#430×C151C211yesmaximal, characteristic, complemented
3C2×#428×C151C211yesmaximal, characteristic, complemented
4#2896×C151C211yesmaximal, characteristic
5C2×#417×C151C211yesmaximal, characteristic
6#1816×C151C214yesmaximal, complemented
7#1815×C151C214yesmaximal, complemented
8#1742×C151C211yesmaximal, characteristic, complemented
9C2×#343×C151C211yesmaximal, characteristic, complemented
10C22×#41×C151C2211yescharacteristic
11#568×C151—24no—
12#568×C151C418yescomplemented
13C2×#131×C151—22no—
14C2×#131×C151C2214yes—
15C22×M16×C151—22no—
16C22×M16×C151C2211yescharacteristic
17C22×M16×C151C2211yescharacteristic
18C22×M16×C151C2211yescharacteristic
19C22×M16×C151C2211yescharacteristic
20C2×#117×C151C2211yescharacteristic
21C22×C4⋊C4×C151C2211yescharacteristic
22#430×C151—24no—
23C2×#108×C151C2214yescomplemented
24#428×C151—22no—
25#428×C151—22no—
26C2×#107×C151C2212yescomplemented
27C2×#106×C151C2212yescomplemented
28#419×C151—21no—
29#418×C151—21no—
30#417×C151—22no—
31#417×C151C2214yes—
32#417×C151C2212yes—
33#417×C151C2212yes—
34#416×C151—22no—
35C2×#103×C151—21no—
36C2×#102×C151—21no—
37#343×C151C2214yescomplemented
38#343×C151C2212yescomplemented
39#343×C151C2212yescomplemented
40C2×#41×C151—21no—
41C2×#41×C151—22no—
42C2×#41×C151—21no—
43C2×#41×C151—22no—
44C2×#41×C151C2×C414yes—
45C2×#41×C151D412yes—
46C2×#41×C151Q814yes—
47C2×#41×C151C2312yes—
48C22×Q8×C151D411yescharacteristic
49C22×D4×C151—21no—
50C22×D4×C151D411yescharacteristic
51C23×C4×C151—21no—
52C23×C4×C151—21no—
53C23×C4×C151C2311yescharacteristic
54#131×C151—216no—
55#131×C151—28no—
56#131×C151C2×C4116yescomplemented
57C2×M16×C151—21no—
58C2×M16×C151—22no—
59C2×M16×C151—216no—
60C2×M16×C151—21no—
61C2×M16×C151—21no—
62C2×M16×C151—24no—
63C2×M16×C151—22no—
64C2×M16×C151—22no—
65C2×M16×C151—22no—
66C2×M16×C151—22no—
67C2×M16×C151C2×C414yes—
68C2×M16×C151C2×C414yes—
69C2×M16×C151D412yes—
70C2×M16×C151D412yes—
71C2×M16×C151D414yes—
72C2×M16×C151C2312yes—
73C2×M16×C151C2312yes—
74C2×M16×C151C2312yes—
75C22×C8×C151—21no—
76C22×C8×C151—24no—
77C22×C8×C151—21no—
78C22×C8×C151—21no—
79C22×C8×C151C2312yes—
80#117×C151—21no—
81#117×C151—21no—
82#117×C151—21no—
83#117×C151—21no—
84C2×C4⋊C4×C151—21no—
85C2×C4⋊C4×C151—21no—
86C2×C4⋊C4×C151—21no—
87C2×C4⋊C4×C151—21no—
88C2×C4⋊C4×C151—21no—
89C2×C4⋊C4×C151C2311yescharacteristic
90C2×C4⋊C4×C151C2312yes—
91C2×C4⋊C4×C151C2311yescharacteristic
92C2×C22⋊C4×C151—21no—
93C2×C42×C151—21no—
94#108×C151—28no—
95#107×C151—24no—
96#106×C151—24no—
97#103×C151—24no—
98#103×C151—22no—
99#103×C151—22no—
100#102×C151—24no—
101#102×C151—22no—
102#102×C151—22no—
103C24×C151—21no—
104C24×C151#4111yescharacteristic
105#41×C151—24no—
106#41×C151—24no—
107#41×C151—24no—
108#41×C151—24no—
109#41×C151—24no—
110#41×C151—22no—
111#41×C151—22no—
112#41×C151C4⋊C418yes—
113#41×C151C22×C414yes—
114#41×C151C2×Q814yes—
115C2×Q8×C151—21no—
116C2×Q8×C151—22no—
117C2×Q8×C151C4⋊C414yes—
118C2×Q8×C151C2×D412yes—
119C2×D4×C151—24no—
120C2×D4×C151—22no—
121C2×D4×C151—24no—
122C2×D4×C151—22no—
123C2×D4×C151—22no—
124C2×D4×C151—21no—
125C2×D4×C151C4⋊C414yes—
126C2×D4×C151C2×D412yes—
127C22×C4×C151—21no—
128C22×C4×C151—24no—
129C22×C4×C151—22no—
130C22×C4×C151—24no—
131C22×C4×C151—22no—
132C22×C4×C151—21no—
133C22×C4×C151—21no—
134C22×C4×C151—22no—
135C22×C4×C151—41no—
136C22×C4×C151—41no—
137C22×C4×C151—82no—
138C22×C4×C151C22×C412yes—
139C22×C4×C151C2×D412yes—
140C22×C4×C151C2×D411yescharacteristic
141C22×C4×C151C2×D411yescharacteristic
142C22×C4×C151C2×D411yescharacteristic
143C22×C4×C151C2×D411yescharacteristic
144C22×C4×C151C2×Q812yes—
145C22×C4×C151#4111yescharacteristic
146C22×C4×C151#4112yes—
147C22×C4×C151C2411yescharacteristic
148M16×C151—24no—
149M16×C151—22no—
150M16×C151—216no—
151M16×C151—22no—
152M16×C151—22no—
153M16×C151—22no—
154M16×C151—22no—
155M16×C151—42no—
156M16×C151—42no—
157M16×C151C22⋊C418yes—
158M16×C151C22⋊C418yes—
159M16×C151C22×C414yes—
160C2×C8×C151—24no—
161C2×C8×C151—22no—
162C2×C8×C151—216no—
163C2×C8×C151—22no—
164C2×C8×C151—22no—
165C2×C8×C151—42no—
166C2×C8×C151—42no—
167C2×C8×C151C22×C414yes—
168C2×C8×C151C2×D414yes—
169C2×C8×C151C2×D414yes—
170C4⋊C4×C151—22no—
171C4⋊C4×C151—21no—
172C4⋊C4×C151—21no—
173C4⋊C4×C151—21no—
174C4⋊C4×C151—22no—
175C4⋊C4×C151—21no—
176C4⋊C4×C151—41no—
177C4⋊C4×C151—41no—
178C22⋊C4×C151—41no—
179C22⋊C4×C151—41no—
180C42×C151—41no—
181C42×C151—41no—
182C23×C151—22no—
183C23×C151—24no—
184C23×C151—41no—
185C23×C151—41no—
186C23×C151—81no—
187C23×C151—81no—
188C23×C151#11712yes—
189C23×C151#12111yescharacteristic
190C23×C151#12111yescharacteristic
191C23×C151C22⋊Q812yes—
192C23×C151C2×#4111yescharacteristic
193Q8×C151—22no—
194Q8×C151—24no—
195Q8×C151C2×C4⋊C414yes—
196D4×C151—24no—
197D4×C151—24no—
198D4×C151—28no—
199D4×C151—22no—
200D4×C151—24no—
201D4×C151C2×C4⋊C414yes—
202C2×C4×C151—22no—
203C2×C4×C151—24no—
204C2×C4×C151—24no—
205C2×C4×C151—24no—
206C2×C4×C151—28no—
207C2×C4×C151—41no—
208C2×C4×C151—41no—
209C2×C4×C151—42no—
210C2×C4×C151—82no—
211C2×C4×C151—82no—
212C2×C4×C151—81no—
213C2×C4×C151—81no—
214C2×C4×C151—82no—
215C2×C4×C151C2×C22⋊C412yes—
216C2×C4×C151C2×C22⋊C412yes—
217C2×C4×C151C2×C4⋊C412yes—
218C2×C4×C151C2×C4⋊C412yes—
219C2×C4×C151#11712yes—
220C2×C4×C151#12112yes—
221C2×C4×C151#12112yes—
222C2×C4×C151#12111yescharacteristic
223C2×C4×C151#12111yescharacteristic
224C2×C4×C151C22⋊Q812yes—
225C2×C4×C151C22⋊Q812yes—
226C2×C4×C151C22⋊Q812yes—
227C2×C4×C151C23×C411yescharacteristic
228C2×C4×C151C22×D411yescharacteristic
229C2×C4×C151C22×D411yescharacteristic
230C2×C4×C151C22×D411yescharacteristic
231C2×C4×C151C22×Q811yescharacteristic
232C2×C4×C151C2×#4111yescharacteristic
233C8×C151—24no—
234C8×C151—42no—
235C8×C151—42no—
236C8×C151C2×C22⋊C418yes—
237C22×C151—21no—
238C22×C151—21no—
239C22×C151—21no—
240C22×C151—21no—
241C22×C151—21no—
242C22×C151—21no—
243C22×C151—24no—
244C22×C151—42no—
245C22×C151—42no—
246C22×C151—42no—
247C22×C151—42no—
248C22×C151—84no—
249C22×C151#38012yes—
250C22×C151#38012yes—
251C22×C151C2×#11711yescharacteristic
252C22×C151C2×#12111yescharacteristic
253C22×C151C2×C22⋊Q811yescharacteristic
254C4×C151—24no—
255C4×C151—81no—
256C4×C151—82no—
257C4×C151—81no—
258C4×C151#38012yes—
259C4×C151#38012yes—
260C4×C151C22×C22⋊C411yescharacteristic
261C4×C151C22×C4⋊C411yescharacteristic
262C4×C151C2×#12111yescharacteristic
263C4×C151C2×C22⋊Q811yescharacteristic
264C2×C151—22no—
265C2×C151—21no—
266C2×C151—21no—
267C2×C151—22no—
268C2×C151—44no—
269C2×C151C2×#38011yescharacteristic
270C2×C151#306811yescharacteristic
271C2×C151#306911yescharacteristic
272#20679C15111yesmaximal, characteristic, direct product factor, Sylow
273C151#2067911yescharacteristic, direct product factor, Sylow
274C2×#568C2×C15111yescharacteristic
275C2×#430C2×C15111yescharacteristic, complemented
276C2×#428C2×C15111yescharacteristic, complemented
277#2896C2×C15111yescharacteristic
278C2×#417C2×C15111yescharacteristic
279#1816C2×C15114yescomplemented
280#1815C2×C15114yescomplemented
281#1742C2×C15111yescharacteristic, complemented
282C2×#343C2×C15111yescharacteristic, complemented
283C22×#41C22×C15111yescharacteristic
284#568—24no—
285#568C4×C15118yescomplemented
286C2×#131—22no—
287C2×#131C22×C15114yes—
288C22×M16—22no—
289C22×M16C22×C15111yescharacteristic
290C22×M16C22×C15111yescharacteristic
291C22×M16C22×C15111yescharacteristic
292C22×M16C22×C15111yescharacteristic
293C2×#117C22×C15111yescharacteristic
294C22×C4⋊C4C22×C15111yescharacteristic
295#430—24no—
296C2×#108C22×C15114yescomplemented
297#428—22no—
298#428—22no—
299C2×#107C22×C15112yescomplemented
300C2×#106C22×C15112yescomplemented
301#419—21no—
302#418—21no—
303#417—22no—
304#417C22×C15112yes—
305#417C22×C15114yes—
306#417C22×C15112yes—
307#416—22no—
308C2×#103—21no—
309C2×#102—21no—
310#343C22×C15112yescomplemented
311#343C22×C15114yescomplemented
312#343C22×C15112yescomplemented
313C2×#41—21no—
314C2×#41—22no—
315C2×#41—21no—
316C2×#41—22no—
317C2×#41C2×C4×C15114yes—
318C2×#41D4×C15112yes—
319C2×#41Q8×C15114yes—
320C2×#41C23×C15112yes—
321C22×Q8D4×C15111yescharacteristic
322C22×D4—21no—
323C22×D4D4×C15111yescharacteristic
324C23×C4—21no—
325C23×C4—21no—
326C23×C4C23×C15111yescharacteristic
327#131—216no—
328#131—28no—
329#131C2×C4×C151116yescomplemented
330C2×M16—21no—
331C2×M16—22no—
332C2×M16—216no—
333C2×M16—21no—
334C2×M16—21no—
335C2×M16—24no—
336C2×M16—22no—
337C2×M16—22no—
338C2×M16—22no—
339C2×M16—22no—
340C2×M16C2×C4×C15114yes—
341C2×M16C2×C4×C15114yes—
342C2×M16D4×C15112yes—
343C2×M16D4×C15112yes—
344C2×M16D4×C15114yes—
345C2×M16C23×C15112yes—
346C2×M16C23×C15112yes—
347C2×M16C23×C15112yes—
348C22×C8—21no—
349C22×C8—24no—
350C22×C8—21no—
351C22×C8—21no—
352C22×C8C23×C15112yes—
353#117—21no—
354#117—21no—
355#117—21no—
356#117—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4C23×C15112yes—
363C2×C4⋊C4C23×C15111yescharacteristic
364C2×C4⋊C4C23×C15111yescharacteristic
365C2×C22⋊C4—21no—
366C2×C42—21no—
367#108—28no—
368#107—24no—
369#106—24no—
370#103—24no—
371#103—22no—
372#103—22no—
373#102—24no—
374#102—22no—
375#102—22no—
376C24—21no—
377C24#41×C15111yescharacteristic
378#41—24no—
379#41—24no—
380#41—24no—
381#41—24no—
382#41—24no—
383#41—22no—
384#41—22no—
385#41C4⋊C4×C15118yes—
386#41C22×C4×C15114yes—
387#41C2×Q8×C15114yes—
388C2×Q8—22no—
389C2×Q8—21no—
390C2×Q8C4⋊C4×C15114yes—
391C2×Q8C2×D4×C15112yes—
392C2×D4—24no—
393C2×D4—22no—
394C2×D4—24no—
395C2×D4—22no—
396C2×D4—21no—
397C2×D4—22no—
398C2×D4C4⋊C4×C15114yes—
399C2×D4C2×D4×C15112yes—
400C22×C4—21no—
401C22×C4—24no—
402C22×C4—22no—
403C22×C4—24no—
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—22no—
408C22×C4—41no—
409C22×C4—41no—
410C22×C4—82no—
411C22×C4C22×C4×C15112yes—
412C22×C4C2×D4×C15112yes—
413C22×C4C2×D4×C15111yescharacteristic
414C22×C4C2×D4×C15111yescharacteristic
415C22×C4C2×D4×C15111yescharacteristic
416C22×C4C2×D4×C15111yescharacteristic
417C22×C4C2×Q8×C15112yes—
418C22×C4#41×C15111yescharacteristic
419C22×C4#41×C15112yes—
420C22×C4C24×C15111yescharacteristic
421M16—24no—
422M16—22no—
423M16—216no—
424M16—22no—
425M16—22no—
426M16—22no—
427M16—22no—
428M16—42no—
429M16—42no—
430M16C22⋊C4×C15118yes—
431M16C22⋊C4×C15118yes—
432M16C22×C4×C15114yes—
433C2×C8—24no—
434C2×C8—22no—
435C2×C8—216no—
436C2×C8—22no—
437C2×C8—22no—
438C2×C8—42no—
439C2×C8—42no—
440C2×C8C22×C4×C15114yes—
441C2×C8C2×D4×C15114yes—
442C2×C8C2×D4×C15114yes—
443C4⋊C4—22no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—22no—
448C4⋊C4—21no—
449C4⋊C4—41no—
450C4⋊C4—41no—
451C22⋊C4—41no—
452C22⋊C4—41no—
453C42—41no—
454C42—41no—
455C23—22no—
456C23—24no—
457C23—41no—
458C23—41no—
459C23—81no—
460C23—81no—
461C23#117×C15112yes—
462C23#121×C15111yescharacteristic
463C23#121×C15111yescharacteristic
464C23C22⋊Q8×C15112yes—
465C23C2×#41×C15111yescharacteristic
466Q8—24no—
467Q8—22no—
468Q8C2×C4⋊C4×C15114yes—
469D4—28no—
470D4—24no—
471D4—24no—
472D4—24no—
473D4—22no—
474D4C2×C4⋊C4×C15114yes—
475C2×C4—24no—
476C2×C4—22no—
477C2×C4—28no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—42no—
483C2×C4—82no—
484C2×C4—82no—
485C2×C4—82no—
486C2×C4—81no—
487C2×C4—81no—
488C2×C4C2×C22⋊C4×C15112yes—
489C2×C4C2×C22⋊C4×C15112yes—
490C2×C4C2×C4⋊C4×C15112yes—
491C2×C4C2×C4⋊C4×C15112yes—
492C2×C4#117×C15112yes—
493C2×C4#121×C15111yescharacteristic
494C2×C4#121×C15111yescharacteristic
495C2×C4#121×C15112yes—
496C2×C4#121×C15112yes—
497C2×C4C22⋊Q8×C15112yes—
498C2×C4C22⋊Q8×C15112yes—
499C2×C4C22⋊Q8×C15112yes—
500C2×C4C23×C4×C15111yescharacteristic
501C2×C4C22×D4×C15111yescharacteristic
502C2×C4C22×D4×C15111yescharacteristic
503C2×C4C22×D4×C15111yescharacteristic
504C2×C4C22×Q8×C15111yescharacteristic
505C2×C4C2×#41×C15111yescharacteristic
506C8—24no—
507C8—42no—
508C8—42no—
509C8C2×C22⋊C4×C15118yes—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—24no—
517C22—42no—
518C22—42no—
519C22—42no—
520C22—42no—
521C22—84no—
522C22#380×C15112yes—
523C22#380×C15112yes—
524C22C2×#117×C15111yescharacteristic
525C22C2×#121×C15111yescharacteristic
526C22C2×C22⋊Q8×C15111yescharacteristic
527C4—24no—
528C4—82no—
529C4—81no—
530C4—81no—
531C4#380×C15112yes—
532C4#380×C15112yes—
533C4C22×C22⋊C4×C15111yescharacteristic
534C4C22×C4⋊C4×C15111yescharacteristic
535C4C2×#121×C15111yescharacteristic
536C4C2×C22⋊Q8×C15111yescharacteristic
537C2—22no—
538C2—22no—
539C2—21no—
540C2—21no—
541C2—44no—
542C2C2×#380×C15111yescharacteristic
543C2#3068×C15111yescharacteristic
544C2#3069×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutatorC2×C4C23×C4×C151
Frattini, cosocleC22×C4C24×C151
prime radicalC22×#41×C151C22
LCSG ▷ C2×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. C2×#430×C151C2semidirect
3. C2×#428×C151C2semidirect
6. #1816×C151C2semidirect
7. #1815×C151C2semidirect
8. #1742×C151C2semidirect
9. C2×#343×C151C2semidirect
12. #568×C151C4semidirect
23. C2×#108×C151C22semidirect
26. C2×#107×C151C22semidirect
27. C2×#106×C151C22semidirect
37. #343×C151C22semidirect
38. #343×C151C22semidirect
39. #343×C151C22semidirect
56. #131×C151C2×C4semidirect
272. #20679C151direct (N × H)
273. C151#20679direct (N × H)
275. C2×#430C2×C151semidirect
276. C2×#428C2×C151semidirect
279. #1816C2×C151semidirect
280. #1815C2×C151semidirect
281. #1742C2×C151semidirect
282. C2×#343C2×C151semidirect
285. #568C4×C151semidirect
296. C2×#108C22×C151semidirect
299. C2×#107C22×C151semidirect
300. C2×#106C22×C151semidirect
310. #343C22×C151semidirect
311. #343C22×C151semidirect
312. #343C22×C151semidirect
329. #131C2×C4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#568×C1512
C2×#430×C1512
C2×#428×C1512
#2896×C1512
C2×#417×C1512
#1816×C1512
#1815×C1512
#1742×C1512
C2×#343×C1512
#20679151