Finite Group Databasebeta

← C151×#11002 #50315927

Subgroups — C151×#11002 #50315927

Order 38656.

1430 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#537×C151C211yesmaximal, characteristic
2C22×#104×C151C212yesmaximal, complemented
3C2×#417×C151C212yesmaximal, complemented
4C2×#343×C151C211yesmaximal, characteristic, complemented
5C4⋊#95×C151C211yesmaximal, characteristic, complemented
6C22×#41×C151C2212yes—
7C22×M16×C151C2212yes—
8#537×C151—24no—
9#537×C151—22no—
10#537×C151C414yescomplemented
11C2×C22⋊Q8×C151—22no—
12C2×#121×C151—22no—
13C2×#121×C151—22no—
14C22×C4⋊C4×C151C2211yescharacteristic
15C22×C4⋊C4×C151C2211yescharacteristic
16C22×C42×C151C2211yescharacteristic
17C2×#104×C151—24no—
18C2×#104×C151—24no—
19C2×#104×C151—24no—
20#417×C151—24no—
21#417×C151—24no—
22C2×#103×C151—22no—
23C2×#102×C151—22no—
24C2×#95×C151—22no—
25#343×C151—22no—
26C2×#41×C151—22no—
27C2×#41×C151—22no—
28C2×#41×C151—22no—
29C2×#41×C151—22no—
30C2×#41×C151—22no—
31C2×#41×C151—22no—
32C2×#41×C151—22no—
33C2×#41×C151—22no—
34C2×#41×C151—22no—
35C2×#41×C151—22no—
36C2×#41×C151C2×C414yes—
37C2×#41×C151D414yes—
38C22×Q8×C151D412yes—
39C22×D4×C151—22no—
40C22×D4×C151—22no—
41C22×D4×C151D412yes—
42C23×C4×C151—22no—
43C23×C4×C151—21no—
44C23×C4×C151—21no—
45C23×C4×C151D412yes—
46C23×C4×C151C2311yescharacteristic
47C2×M16×C151—22no—
48C2×M16×C151—22no—
49C2×M16×C151—22no—
50C2×M16×C151—22no—
51C2×M16×C151—22no—
52C2×M16×C151D414yescomplemented
53C22×C8×C151—22no—
54C22⋊Q8×C151—28no—
55C22⋊Q8×C151—28no—
56#121×C151—28no—
57#121×C151—28no—
58#121×C151—28no—
59#121×C151—28no—
60C2×C4⋊C4×C151—22no—
61C2×C4⋊C4×C151—22no—
62C2×C4⋊C4×C151—22no—
63C2×C4⋊C4×C151—22no—
64C2×C4⋊C4×C151—22no—
65C2×C4⋊C4×C151—21no—
66C2×C4⋊C4×C151C2×C412yes—
67C2×C4⋊C4×C151D412yes—
68C2×C4⋊C4×C151D412yescomplemented
69C2×C22⋊C4×C151—24no—
70C2×C42×C151—22no—
71C2×C42×C151—22no—
72C2×C42×C151—21no—
73C2×C42×C151D412yescomplemented
74#104×C151—216no—
75#103×C151—28no—
76#102×C151—28no—
77#95×C151—44no—
78C24×C151—22no—
79C24×C151C2×D411yescharacteristic
80#41×C151—24no—
81#41×C151—24no—
82#41×C151—24no—
83#41×C151—24no—
84#41×C151—24no—
85#41×C151—24no—
86#41×C151—24no—
87#41×C151—24no—
88#41×C151—42no—
89#41×C151—42no—
90#41×C151—42no—
91#41×C151—42no—
92#41×C151—42no—
93#41×C151—42no—
94#41×C151—42no—
95#41×C151—42no—
96C2×Q8×C151—22no—
97C2×Q8×C151—22no—
98C2×Q8×C151—22no—
99C2×Q8×C151—22no—
100C2×Q8×C151—22no—
101C2×Q8×C151C22⋊C414yes—
102C2×D4×C151—24no—
103C2×D4×C151—24no—
104C2×D4×C151—28no—
105C2×D4×C151—22no—
106C2×D4×C151—22no—
107C2×D4×C151—22no—
108C2×D4×C151—22no—
109C2×D4×C151—22no—
110C2×D4×C151—42no—
111C2×D4×C151—42no—
112C2×D4×C151—42no—
113C2×D4×C151—42no—
114C2×D4×C151—82no—
115C2×D4×C151—82no—
116C2×D4×C151C22⋊C414yes—
117C22×C4×C151—22no—
118C22×C4×C151—22no—
119C22×C4×C151—22no—
120C22×C4×C151—22no—
121C22×C4×C151—22no—
122C22×C4×C151—22no—
123C22×C4×C151—24no—
124C22×C4×C151—24no—
125C22×C4×C151—22no—
126C22×C4×C151—41no—
127C22×C4×C151—41no—
128C22×C4×C151—41no—
129C22×C4×C151—41no—
130C22×C4×C151—42no—
131C22×C4×C151—42no—
132C22×C4×C151—42no—
133C22×C4×C151—42no—
134C22×C4×C151—42no—
135C22×C4×C151—42no—
136C22×C4×C151—42no—
137C22×C4×C151—42no—
138C22×C4×C151—41no—
139C22×C4×C151—41no—
140C22×C4×C151C22⋊C414yes—
141C22×C4×C151C22×C411yescharacteristic
142C22×C4×C151C2×D412yes—
143C22×C4×C151C2×D412yes—
144C22×C4×C151C2×D412yes—
145C22×C4×C151C2×D411yescharacteristic
146C22×C4×C151C2×D411yescharacteristic
147C22×C4×C151C2×D411yescharacteristic
148C22×C4×C151#4112yes—
149C22×C4×C151#4111yescharacteristic
150C22×C4×C151#4111yescharacteristic
151M16×C151—24no—
152M16×C151—24no—
153M16×C151—42no—
154M16×C151—42no—
155C2×C8×C151—24no—
156C2×C8×C151—42no—
157C2×C8×C151—42no—
158C4⋊C4×C151—28no—
159C4⋊C4×C151—24no—
160C4⋊C4×C151—24no—
161C4⋊C4×C151—24no—
162C4⋊C4×C151—42no—
163C22⋊C4×C151—216no—
164C42×C151—24no—
165C42×C151—42no—
166C23×C151—21no—
167C23×C151—21no—
168C23×C151—21no—
169C23×C151—21no—
170C23×C151—24no—
171C23×C151—42no—
172C23×C151—42no—
173C23×C151—42no—
174C23×C151—42no—
175C23×C151—42no—
176C23×C151—42no—
177C23×C151C2×C22⋊C411yescharacteristic
178C23×C151#12011yescharacteristic
179C23×C151#12011yescharacteristic
180C23×C151#12111yescharacteristic
181C23×C151#12111yescharacteristic
182C23×C151#12411yescharacteristic
183C23×C151#12711yescharacteristic
184Q8×C151—24no—
185Q8×C151—24no—
186Q8×C151—42no—
187Q8×C151—42no—
188D4×C151—24no—
189D4×C151—24no—
190D4×C151—44no—
191D4×C151—44no—
192D4×C151—44no—
193D4×C151—44no—
194D4×C151—42no—
195D4×C151—42no—
196D4×C151—88no—
197C2×C4×C151—24no—
198C2×C4×C151—24no—
199C2×C4×C151—24no—
200C2×C4×C151—42no—
201C2×C4×C151—42no—
202C2×C4×C151—42no—
203C2×C4×C151—42no—
204C2×C4×C151—42no—
205C2×C4×C151—42no—
206C2×C4×C151—42no—
207C2×C4×C151—42no—
208C2×C4×C151—42no—
209C2×C4×C151—42no—
210C2×C4×C151—44no—
211C2×C4×C151—44no—
212C2×C4×C151—44no—
213C2×C4×C151—44no—
214C2×C4×C151—44no—
215C2×C4×C151—44no—
216C2×C4×C151—42no—
217C2×C4×C151—82no—
218C2×C4×C151—82no—
219C2×C4×C151—81no—
220C2×C4×C151—81no—
221C2×C4×C151C2×C22⋊C412yes—
222C2×C4×C151C4×D412yes—
223C2×C4×C151C4×D411yescharacteristic
224C2×C4×C151C4×D411yescharacteristic
225C2×C4×C151#12012yes—
226C2×C4×C151#12012yes—
227C2×C4×C151#12012yes—
228C2×C4×C151#12112yes—
229C2×C4×C151#12112yes—
230C2×C4×C151#12112yes—
231C2×C4×C151#12112yes—
232C2×C4×C151#12112yes—
233C2×C4×C151#12312yes—
234C2×C4×C151#12312yes—
235C2×C4×C151#12411yescharacteristic
236C2×C4×C151#12711yescharacteristic
237C8×C151—44no—
238C22×C151—21no—
239C22×C151—21no—
240C22×C151—21no—
241C22×C151—21no—
242C22×C151—21no—
243C22×C151—21no—
244C22×C151—21no—
245C22×C151—21no—
246C22×C151—21no—
247C22×C151—21no—
248C22×C151—21no—
249C22×C151—21no—
250C22×C151—44no—
251C22×C151—44no—
252C22×C151—44no—
253C22×C151—82no—
254C22×C151—82no—
255C22×C151—82no—
256C22×C151—82no—
257C22×C151#37911yescharacteristic
258C22×C151#39011yescharacteristic
259C22×C151#39011yescharacteristic
260C22×C151#39211yescharacteristic
261C22×C151#39211yescharacteristic
262C22×C151#39411yescharacteristic
263C22×C151#39411yescharacteristic
264C22×C151#45311yescharacteristic
265C22×C151#45411yescharacteristic
266C22×C151#45511yescharacteristic
267C22×C151#45611yescharacteristic
268C4×C151—44no—
269C4×C151—44no—
270C4×C151—44no—
271C4×C151—82no—
272C4×C151#38612yes—
273C4×C151#38612yes—
274C4×C151#39212yes—
275C4×C151#39412yes—
276C2×C151—21no—
277C2×C151—21no—
278C2×C151—21no—
279C2×C151—21no—
280C2×C151—84no—
281C2×C151#143811yescharacteristic
282C2×C151#179211yescharacteristic
283C2×C151#179311yescharacteristic
284C2×C151#200611yescharacteristic
285C2×C151#200711yescharacteristic
286C2×C151#203911yescharacteristic
287C2×C151#204011yescharacteristic
288#11002C15111yesmaximal, characteristic, direct product factor, Sylow
289C151#1100211yescharacteristic, direct product factor, Sylow
290C2×#537C2×C15111yescharacteristic
291C22×#104C2×C15112yescomplemented
292C2×#417C2×C15112yescomplemented
293C2×#343C2×C15111yescharacteristic, complemented
294C4⋊#95C2×C15111yescharacteristic, complemented
295C22×#41C22×C15112yes—
296C22×M16C22×C15112yes—
297#537—24no—
298#537—22no—
299#537C4×C15114yescomplemented
300C2×C22⋊Q8—22no—
301C2×#121—22no—
302C2×#121—22no—
303C22×C4⋊C4C22×C15111yescharacteristic
304C22×C4⋊C4C22×C15111yescharacteristic
305C22×C42C22×C15111yescharacteristic
306C2×#104—24no—
307C2×#104—24no—
308C2×#104—24no—
309#417—24no—
310#417—24no—
311C2×#103—22no—
312C2×#102—22no—
313C2×#95—22no—
314#343—22no—
315C2×#41—22no—
316C2×#41—22no—
317C2×#41—22no—
318C2×#41—22no—
319C2×#41—22no—
320C2×#41—22no—
321C2×#41—22no—
322C2×#41—22no—
323C2×#41—22no—
324C2×#41—22no—
325C2×#41C2×C4×C15114yes—
326C2×#41D4×C15114yes—
327C22×Q8D4×C15112yes—
328C22×D4—22no—
329C22×D4—22no—
330C22×D4D4×C15112yes—
331C23×C4—21no—
332C23×C4—22no—
333C23×C4—21no—
334C23×C4D4×C15112yes—
335C23×C4C23×C15111yescharacteristic
336C2×M16—22no—
337C2×M16—22no—
338C2×M16—22no—
339C2×M16—22no—
340C2×M16—22no—
341C2×M16D4×C15114yescomplemented
342C22×C8—22no—
343C22⋊Q8—28no—
344C22⋊Q8—28no—
345#121—28no—
346#121—28no—
347#121—28no—
348#121—28no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4C2×C4×C15112yes—
356C2×C4⋊C4D4×C15112yes—
357C2×C4⋊C4D4×C15112yescomplemented
358C2×C22⋊C4—24no—
359C2×C42—22no—
360C2×C42—22no—
361C2×C42—21no—
362C2×C42D4×C15112yescomplemented
363#104—216no—
364#103—28no—
365#102—28no—
366#95—44no—
367C24—22no—
368C24C2×D4×C15111yescharacteristic
369#41—24no—
370#41—24no—
371#41—24no—
372#41—24no—
373#41—24no—
374#41—24no—
375#41—24no—
376#41—24no—
377#41—42no—
378#41—42no—
379#41—42no—
380#41—42no—
381#41—42no—
382#41—42no—
383#41—42no—
384#41—42no—
385C2×Q8—22no—
386C2×Q8—22no—
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8C22⋊C4×C15114yes—
391C2×D4—24no—
392C2×D4—24no—
393C2×D4—28no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—42no—
400C2×D4—42no—
401C2×D4—42no—
402C2×D4—42no—
403C2×D4—82no—
404C2×D4—82no—
405C2×D4C22⋊C4×C15114yes—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—24no—
413C22×C4—24no—
414C22×C4—22no—
415C22×C4—41no—
416C22×C4—41no—
417C22×C4—41no—
418C22×C4—41no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—42no—
425C22×C4—42no—
426C22×C4—42no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4C22⋊C4×C15114yes—
430C22×C4C22×C4×C15111yescharacteristic
431C22×C4C2×D4×C15112yes—
432C22×C4C2×D4×C15112yes—
433C22×C4C2×D4×C15112yes—
434C22×C4C2×D4×C15111yescharacteristic
435C22×C4C2×D4×C15111yescharacteristic
436C22×C4C2×D4×C15111yescharacteristic
437C22×C4#41×C15112yes—
438C22×C4#41×C15111yescharacteristic
439C22×C4#41×C15111yescharacteristic
440M16—24no—
441M16—24no—
442M16—42no—
443M16—42no—
444C2×C8—24no—
445C2×C8—42no—
446C2×C8—42no—
447C4⋊C4—28no—
448C4⋊C4—24no—
449C4⋊C4—24no—
450C4⋊C4—24no—
451C4⋊C4—42no—
452C22⋊C4—216no—
453C42—24no—
454C42—42no—
455C23—21no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—24no—
460C23—42no—
461C23—42no—
462C23—42no—
463C23—42no—
464C23—42no—
465C23—42no—
466C23C2×C22⋊C4×C15111yescharacteristic
467C23#120×C15111yescharacteristic
468C23#120×C15111yescharacteristic
469C23#121×C15111yescharacteristic
470C23#121×C15111yescharacteristic
471C23#124×C15111yescharacteristic
472C23#127×C15111yescharacteristic
473Q8—24no—
474Q8—24no—
475Q8—42no—
476Q8—42no—
477D4—24no—
478D4—24no—
479D4—44no—
480D4—44no—
481D4—44no—
482D4—44no—
483D4—42no—
484D4—42no—
485D4—88no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—44no—
500C2×C4—44no—
501C2×C4—44no—
502C2×C4—44no—
503C2×C4—44no—
504C2×C4—44no—
505C2×C4—42no—
506C2×C4—82no—
507C2×C4—82no—
508C2×C4—81no—
509C2×C4—81no—
510C2×C4C2×C22⋊C4×C15112yes—
511C2×C4C4×D4×C15112yes—
512C2×C4C4×D4×C15111yescharacteristic
513C2×C4C4×D4×C15111yescharacteristic
514C2×C4#120×C15112yes—
515C2×C4#120×C15112yes—
516C2×C4#120×C15112yes—
517C2×C4#121×C15112yes—
518C2×C4#121×C15112yes—
519C2×C4#121×C15112yes—
520C2×C4#121×C15112yes—
521C2×C4#121×C15112yes—
522C2×C4#123×C15112yes—
523C2×C4#123×C15112yes—
524C2×C4#124×C15111yescharacteristic
525C2×C4#127×C15111yescharacteristic
526C8—44no—
527C22—21no—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—21no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—44no—
540C22—44no—
541C22—44no—
542C22—82no—
543C22—82no—
544C22—82no—
545C22—82no—
546C22#379×C15111yescharacteristic
547C22#390×C15111yescharacteristic
548C22#390×C15111yescharacteristic
549C22#392×C15111yescharacteristic
550C22#392×C15111yescharacteristic
551C22#394×C15111yescharacteristic
552C22#394×C15111yescharacteristic
553C22#453×C15111yescharacteristic
554C22#454×C15111yescharacteristic
555C22#455×C15111yescharacteristic
556C22#456×C15111yescharacteristic
557C4—44no—
558C4—44no—
559C4—44no—
560C4—82no—
561C4#386×C15112yes—
562C4#386×C15112yes—
563C4#392×C15112yes—
564C4#394×C15112yes—
565C2—21no—
566C2—21no—
567C2—21no—
568C2—21no—
569C2—84no—
570C2#1438×C15111yescharacteristic
571C2#1792×C15111yescharacteristic
572C2#1793×C15111yescharacteristic
573C2#2006×C15111yescharacteristic
574C2#2007×C15111yescharacteristic
575C2#2039×C15111yescharacteristic
576C2#2040×C15111yescharacteristic
subgroupG/H
center, socleC23×C151#120
commutatorC22×C4C22×C4×C151
Frattini, cosocleC23×C4C23×C151
prime radicalC2×#537×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×#104×C151C2semidirect
3. C2×#417×C151C2semidirect
4. C2×#343×C151C2semidirect
5. C4⋊#95×C151C2semidirect
10. #537×C151C4semidirect
52. C2×M16×C151D4semidirect
68. C2×C4⋊C4×C151D4semidirect
73. C2×C42×C151D4semidirect
288. #11002C151direct (N × H)
289. C151#11002direct (N × H)
291. C22×#104C2×C151semidirect
292. C2×#417C2×C151semidirect
293. C2×#343C2×C151semidirect
294. C4⋊#95C2×C151semidirect
299. #537C4×C151semidirect
341. C2×M16D4×C151semidirect
357. C2×C4⋊C4D4×C151semidirect
362. C2×C42D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#537×C1512
C22×#104×C1512
C2×#417×C1512
C2×#343×C1512
C4⋊#95×C1512
#11002151