Finite Group Databasebeta

← C151×#24179 #50329104

Subgroups — C151×#24179 #50329104

Order 38656.

1038 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3507×C151C211yesmaximal, characteristic
2#3078×C151C211yesmaximal, characteristic, complemented
3#3037×C151C211yesmaximal, characteristic
4C4×C4⋊Q8×C151C211yesmaximal, characteristic, complemented
5#2038×C151C212yesmaximal, complemented
6#2005×C151C212yesmaximal, complemented
7#1994×C151C211yesmaximal, characteristic, complemented
8#1962×C151C211yesmaximal, characteristic
9#1882×C151C212yesmaximal, complemented
10#1859×C151C212yesmaximal, complemented
11#1801×C151C211yesmaximal, characteristic, complemented
12C2×#137×C151C2212yes—
13#559×C151—21no—
14#557×C151—21no—
15#556×C151—21no—
16#556×C151—22no—
17#554×C151—21no—
18#552×C151—22no—
19#539×C151—22no—
20#536×C151C2212yes—
21#533×C151C2211yescharacteristic
22#532×C151C2211yescharacteristic
23C2×C4⋊Q8×C151C2211yescharacteristic
24#529×C151—22no—
25#520×C151C2212yes—
26C2×C4×Q8×C151C2211yescharacteristic
27C2×C4×Q8×C151C2211yescharacteristic
28#479×C151—22no—
29#477×C151—21no—
30#475×C151—21no—
31#464×C151—22no—
32#462×C151—21no—
33#460×C151—21no—
34#428×C151C2212yes—
35#423×C151C2211yescharacteristic
36#423×C151C2211yescharacteristic
37C2×#104×C151C2212yes—
38C2×#104×C151C2212yes—
39#419×C151C2212yes—
40#417×C151C2212yes—
41C2×#101×C151C2212yes—
42#391×C151C2211yescharacteristic
43#391×C151C2211yescharacteristic
44#389×C151—22no—
45#384×C151C2211yescharacteristic
46C4×C4⋊C4×C151—22no—
47C43×C151C2211yescharacteristic
48#343×C151C2212yes—
49#339×C151C2212yes—
50#339×C151C2212yes—
51C2×#41×C151C2312yes—
52C22×Q8×C151C2311yescharacteristic
53C22×Q8×C151C2311yescharacteristic
54#137×C151—24no—
55#137×C151—42no—
56C2×Q16×C151—22no—
57C2×SD16×C151—22no—
58C2×M16×C151C2312yes—
59C2×M16×C151C2312yes—
60C4⋊Q8×C151—22no—
61C4⋊Q8×C151—22no—
62C4⋊Q8×C151—22no—
63C4⋊Q8×C151D411yescharacteristic
64C4⋊Q8×C151D411yescharacteristic
65C4⋊Q8×C151D411yescharacteristic
66#127×C151D411yescharacteristic
67#126×C151—24no—
68#126×C151—24no—
69#125×C151—22no—
70#125×C151—24no—
71#125×C151D412yes—
72#124×C151—22no—
73#124×C151—22no—
74#124×C151D412yes—
75#123×C151—24no—
76#123×C151—24no—
77C22⋊Q8×C151—24no—
78C22⋊Q8×C151—21no—
79C22⋊Q8×C151—21no—
80C22⋊Q8×C151—22no—
81C22⋊Q8×C151—22no—
82#121×C151—21no—
83#121×C151—21no—
84C4×Q8×C151—22no—
85C4×Q8×C151—21no—
86C4×Q8×C151—21no—
87C4×Q8×C151—21no—
88C4×Q8×C151—21no—
89C4×Q8×C151—21no—
90C4×Q8×C151—21no—
91C4×Q8×C151—21no—
92C4×Q8×C151—21no—
93C4×Q8×C151—21no—
94C4×Q8×C151—21no—
95C4×Q8×C151—22no—
96C4×D4×C151—22no—
97C4×D4×C151—22no—
98C4×D4×C151—24no—
99C4×D4×C151—21no—
100C4×D4×C151—21no—
101#117×C151—24no—
102#117×C151—22no—
103#117×C151C2312yes—
104C2×C4⋊C4×C151—22no—
105C2×C4⋊C4×C151—22no—
106C2×C4⋊C4×C151—22no—
107C2×C4⋊C4×C151—21no—
108C2×C4⋊C4×C151D412yes—
109C2×C4⋊C4×C151C2311yescharacteristic
110C2×C4⋊C4×C151C2311yescharacteristic
111C2×C42×C151—21no—
112C2×C42×C151—21no—
113C2×C42×C151—21no—
114C2×C42×C151D412yes—
115C2×C42×C151C2311yescharacteristic
116C2×C42×C151C2311yescharacteristic
117C2×C42×C151C2311yescharacteristic
118#107×C151—22no—
119#106×C151—22no—
120C4⋊C8×C151—21no—
121C4⋊C8×C151—21no—
122C4⋊C8×C151—21no—
123C4⋊C8×C151—21no—
124#104×C151—24no—
125#104×C151—42no—
126#103×C151—22no—
127#103×C151—22no—
128#103×C151—22no—
129#102×C151—22no—
130#101×C151—42no—
131#95×C151—22no—
132#95×C151—22no—
133#41×C151—22no—
134#41×C151—22no—
135#41×C151—22no—
136#41×C151—22no—
137C2×Q8×C151—21no—
138C2×Q8×C151—21no—
139C2×Q8×C151—21no—
140C2×Q8×C151—21no—
141C2×Q8×C151—21no—
142C2×Q8×C151—21no—
143C2×Q8×C151—21no—
144C2×Q8×C151—21no—
145C2×Q8×C151—21no—
146C2×Q8×C151—21no—
147C2×Q8×C151—21no—
148C2×Q8×C151—21no—
149C2×Q8×C151—21no—
150C2×Q8×C151C2×D412yes—
151C2×Q8×C151#4112yes—
152C2×D4×C151—22no—
153C2×D4×C151—21no—
154C2×D4×C151—21no—
155C2×D4×C151C2×D412yes—
156C22×C4×C151—21no—
157C22×C4×C151—21no—
158C22×C4×C151—21no—
159C22×C4×C151—24no—
160C22×C4×C151—22no—
161C22×C4×C151—21no—
162C22×C4×C151C2×D412yes—
163C22×C4×C151C2×D411yescharacteristic
164C22×C4×C151C2×D412yes—
165C22×C4×C151C2×D411yescharacteristic
166C22×C4×C151C2411yescharacteristic
167Q16×C151—44no—
168SD16×C151—44no—
169M16×C151—22no—
170M16×C151—22no—
171M16×C151—22no—
172M16×C151—22no—
173C2×C8×C151—22no—
174C2×C8×C151—22no—
175C4⋊C4×C151—24no—
176C4⋊C4×C151—28no—
177C4⋊C4×C151—24no—
178C4⋊C4×C151—24no—
179C4⋊C4×C151—22no—
180C4⋊C4×C151—22no—
181C4⋊C4×C151—22no—
182C4⋊C4×C151—21no—
183C4⋊C4×C151—21no—
184C4⋊C4×C151—21no—
185C4⋊C4×C151—22no—
186C4⋊C4×C151—21no—
187C4⋊C4×C151—21no—
188C4⋊C4×C151—21no—
189C4⋊C4×C151—21no—
190C4⋊C4×C151—21no—
191C4⋊C4×C151—44no—
192C4⋊C4×C151—41no—
193C4⋊C4×C151—41no—
194C4⋊C4×C151C2×D412yes—
195C4⋊C4×C151C2×D412yes—
196C22⋊C4×C151—24no—
197C22⋊C4×C151—24no—
198C22⋊C4×C151—24no—
199C22⋊C4×C151—22no—
200C22⋊C4×C151—22no—
201C22⋊C4×C151—22no—
202C42×C151—24no—
203C42×C151—24no—
204C42×C151—22no—
205C42×C151—22no—
206C42×C151—22no—
207C42×C151—21no—
208C42×C151—21no—
209C42×C151—21no—
210C42×C151—42no—
211C42×C151—41no—
212C42×C151—41no—
213C42×C151C2×D411yescharacteristic
214C42×C151C2×D411yescharacteristic
215C42×C151C2×D411yescharacteristic
216C42×C151C2×D411yescharacteristic
217C42×C151#4112yes—
218C23×C151—22no—
219C23×C151C22×D411yescharacteristic
220Q8×C151—22no—
221Q8×C151—22no—
222Q8×C151—22no—
223Q8×C151—22no—
224Q8×C151—41no—
225Q8×C151—41no—
226Q8×C151—41no—
227Q8×C151—41no—
228Q8×C151—41no—
229Q8×C151—41no—
230Q8×C151—42no—
231Q8×C151—81no—
232D4×C151—22no—
233D4×C151—22no—
234D4×C151—42no—
235D4×C151—42no—
236D4×C151—42no—
237D4×C151—81no—
238C2×C4×C151—22no—
239C2×C4×C151—22no—
240C2×C4×C151—22no—
241C2×C4×C151—22no—
242C2×C4×C151—22no—
243C2×C4×C151—22no—
244C2×C4×C151—22no—
245C2×C4×C151—22no—
246C2×C4×C151—22no—
247C2×C4×C151—22no—
248C2×C4×C151—22no—
249C2×C4×C151—22no—
250C2×C4×C151—22no—
251C2×C4×C151—41no—
252C2×C4×C151—41no—
253C2×C4×C151—41no—
254C2×C4×C151—41no—
255C2×C4×C151—41no—
256C2×C4×C151—42no—
257C2×C4×C151—42no—
258C2×C4×C151—42no—
259C2×C4×C151—42no—
260C2×C4×C151—41no—
261C2×C4×C151—84no—
262C2×C4×C151#12011yescharacteristic
263C2×C4×C151#12011yescharacteristic
264C2×C4×C151#12011yescharacteristic
265C2×C4×C151#12011yescharacteristic
266C2×C4×C151C22×D411yescharacteristic
267C2×C4×C151C22×D411yescharacteristic
268C2×C4×C151C2×#4111yescharacteristic
269C2×C4×C151C2×#4111yescharacteristic
270C2×C4×C151H(5,𝔽2)11yescharacteristic
271C2×C4×C1512−1+411yescharacteristic
272C8×C151—42no—
273C8×C151—42no—
274C22×C151—21no—
275C22×C151—21no—
276C22×C151—42no—
277C22×C151—42no—
278C22×C151—42no—
279C22×C151C2×#12011yescharacteristic
280C22×C151#52511yescharacteristic
281C22×C151#53711yescharacteristic
282C4×C151—24no—
283C4×C151—21no—
284C4×C151—21no—
285C4×C151—21no—
286C4×C151—42no—
287C4×C151—42no—
288C4×C151—42no—
289C4×C151—42no—
290C4×C151—42no—
291C4×C151—42no—
292C4×C151—42no—
293C4×C151—81no—
294C4×C151#45612yes—
295C4×C151#54611yescharacteristic
296C4×C151#54711yescharacteristic
297C4×C151#54811yescharacteristic
298C4×C151#55011yescharacteristic
299C2×C151—21no—
300C2×C151—21no—
301C2×C151—82no—
302C2×C151#240711yescharacteristic
303C2×C151C2×#45611yescharacteristic
304C2×C151#301811yescharacteristic
305#24179C15111yesmaximal, characteristic, direct product factor, Sylow
306C151#2417911yescharacteristic, direct product factor, Sylow
307#3507C2×C15111yescharacteristic
308#3078C2×C15111yescharacteristic, complemented
309#3037C2×C15111yescharacteristic
310C4×C4⋊Q8C2×C15111yescharacteristic, complemented
311#2038C2×C15112yescomplemented
312#2005C2×C15112yescomplemented
313#1994C2×C15111yescharacteristic, complemented
314#1962C2×C15111yescharacteristic
315#1882C2×C15112yescomplemented
316#1859C2×C15112yescomplemented
317#1801C2×C15111yescharacteristic, complemented
318C2×#137C22×C15112yes—
319#559—21no—
320#557—21no—
321#556—21no—
322#556—22no—
323#554—21no—
324#552—22no—
325#539—22no—
326#536C22×C15112yes—
327#533C22×C15111yescharacteristic
328#532C22×C15111yescharacteristic
329C2×C4⋊Q8C22×C15111yescharacteristic
330#529—22no—
331#520C22×C15112yes—
332C2×C4×Q8C22×C15111yescharacteristic
333C2×C4×Q8C22×C15111yescharacteristic
334#479—22no—
335#477—21no—
336#475—21no—
337#464—22no—
338#462—21no—
339#460—21no—
340#428C22×C15112yes—
341#423C22×C15111yescharacteristic
342#423C22×C15111yescharacteristic
343C2×#104C22×C15112yes—
344C2×#104C22×C15112yes—
345#419C22×C15112yes—
346#417C22×C15112yes—
347C2×#101C22×C15112yes—
348#391C22×C15111yescharacteristic
349#391C22×C15111yescharacteristic
350#389—22no—
351#384C22×C15111yescharacteristic
352C4×C4⋊C4—22no—
353C43C22×C15111yescharacteristic
354#343C22×C15112yes—
355#339C22×C15112yes—
356#339C22×C15112yes—
357C2×#41C23×C15112yes—
358C22×Q8C23×C15111yescharacteristic
359C22×Q8C23×C15111yescharacteristic
360#137—24no—
361#137—42no—
362C2×Q16—22no—
363C2×SD16—22no—
364C2×M16C23×C15112yes—
365C2×M16C23×C15112yes—
366C4⋊Q8—22no—
367C4⋊Q8—22no—
368C4⋊Q8—22no—
369C4⋊Q8D4×C15111yescharacteristic
370C4⋊Q8D4×C15111yescharacteristic
371C4⋊Q8D4×C15111yescharacteristic
372#127D4×C15111yescharacteristic
373#126—24no—
374#126—24no—
375#125—22no—
376#125—24no—
377#125D4×C15112yes—
378#124—22no—
379#124—22no—
380#124D4×C15112yes—
381#123—24no—
382#123—24no—
383C22⋊Q8—24no—
384C22⋊Q8—21no—
385C22⋊Q8—21no—
386C22⋊Q8—22no—
387C22⋊Q8—22no—
388#121—21no—
389#121—21no—
390C4×Q8—22no—
391C4×Q8—22no—
392C4×Q8—21no—
393C4×Q8—21no—
394C4×Q8—21no—
395C4×Q8—21no—
396C4×Q8—21no—
397C4×Q8—21no—
398C4×Q8—21no—
399C4×Q8—21no—
400C4×Q8—21no—
401C4×Q8—21no—
402C4×D4—22no—
403C4×D4—22no—
404C4×D4—24no—
405C4×D4—21no—
406C4×D4—21no—
407#117—24no—
408#117—22no—
409#117C23×C15112yes—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4D4×C15112yes—
415C2×C4⋊C4C23×C15111yescharacteristic
416C2×C4⋊C4C23×C15111yescharacteristic
417C2×C42—21no—
418C2×C42—21no—
419C2×C42—21no—
420C2×C42D4×C15112yes—
421C2×C42C23×C15111yescharacteristic
422C2×C42C23×C15111yescharacteristic
423C2×C42C23×C15111yescharacteristic
424#107—22no—
425#106—22no—
426C4⋊C8—21no—
427C4⋊C8—21no—
428C4⋊C8—21no—
429C4⋊C8—21no—
430#104—24no—
431#104—42no—
432#103—22no—
433#103—22no—
434#103—22no—
435#102—22no—
436#101—42no—
437#95—22no—
438#95—22no—
439#41—22no—
440#41—22no—
441#41—22no—
442#41—22no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8C2×D4×C15112yes—
457C2×Q8#41×C15112yes—
458C2×D4—22no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4C2×D4×C15112yes—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—24no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4C2×D4×C15112yes—
469C22×C4C2×D4×C15111yescharacteristic
470C22×C4C2×D4×C15112yes—
471C22×C4C2×D4×C15111yescharacteristic
472C22×C4C24×C15111yescharacteristic
473Q16—44no—
474SD16—44no—
475M16—22no—
476M16—22no—
477M16—22no—
478M16—22no—
479C2×C8—22no—
480C2×C8—22no—
481C4⋊C4—24no—
482C4⋊C4—28no—
483C4⋊C4—24no—
484C4⋊C4—24no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—22no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—44no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4C2×D4×C15112yes—
501C4⋊C4C2×D4×C15112yes—
502C22⋊C4—24no—
503C22⋊C4—24no—
504C22⋊C4—24no—
505C22⋊C4—22no—
506C22⋊C4—22no—
507C22⋊C4—22no—
508C42—24no—
509C42—24no—
510C42—22no—
511C42—22no—
512C42—22no—
513C42—21no—
514C42—21no—
515C42—21no—
516C42—42no—
517C42—41no—
518C42—41no—
519C42C2×D4×C15111yescharacteristic
520C42C2×D4×C15111yescharacteristic
521C42C2×D4×C15111yescharacteristic
522C42C2×D4×C15111yescharacteristic
523C42#41×C15112yes—
524C23—22no—
525C23C22×D4×C15111yescharacteristic
526Q8—22no—
527Q8—22no—
528Q8—22no—
529Q8—22no—
530Q8—42no—
531Q8—41no—
532Q8—41no—
533Q8—41no—
534Q8—41no—
535Q8—41no—
536Q8—41no—
537Q8—81no—
538D4—22no—
539D4—22no—
540D4—42no—
541D4—42no—
542D4—42no—
543D4—81no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—41no—
567C2×C4—84no—
568C2×C4#120×C15111yescharacteristic
569C2×C4#120×C15111yescharacteristic
570C2×C4#120×C15111yescharacteristic
571C2×C4#120×C15111yescharacteristic
572C2×C4C22×D4×C15111yescharacteristic
573C2×C4C22×D4×C15111yescharacteristic
574C2×C4C2×#41×C15111yescharacteristic
575C2×C4C2×#41×C15111yescharacteristic
576C2×C4H(5,𝔽2)×C15111yescharacteristic
577C2×C42−1+4×C15111yescharacteristic
578C8—42no—
579C8—42no—
580C22—21no—
581C22—21no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22C2×#120×C15111yescharacteristic
586C22#525×C15111yescharacteristic
587C22#537×C15111yescharacteristic
588C4—24no—
589C4—21no—
590C4—21no—
591C4—21no—
592C4—42no—
593C4—42no—
594C4—42no—
595C4—42no—
596C4—42no—
597C4—42no—
598C4—42no—
599C4—81no—
600C4#456×C15112yes—
601C4#546×C15111yescharacteristic
602C4#547×C15111yescharacteristic
603C4#548×C15111yescharacteristic
604C4#550×C15111yescharacteristic
605C2—21no—
606C2—21no—
607C2—82no—
608C2#2407×C15111yescharacteristic
609C2C2×#456×C15111yescharacteristic
610C2#3018×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#532×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3078×C151C2semidirect
4. C4×C4⋊Q8×C151C2semidirect
5. #2038×C151C2semidirect
6. #2005×C151C2semidirect
7. #1994×C151C2semidirect
9. #1882×C151C2semidirect
10. #1859×C151C2semidirect
11. #1801×C151C2semidirect
305. #24179C151direct (N × H)
306. C151#24179direct (N × H)
308. #3078C2×C151semidirect
310. C4×C4⋊Q8C2×C151semidirect
311. #2038C2×C151semidirect
312. #2005C2×C151semidirect
313. #1994C2×C151semidirect
315. #1882C2×C151semidirect
316. #1859C2×C151semidirect
317. #1801C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3507×C1512
#3078×C1512
#3037×C1512
C4×C4⋊Q8×C1512
#2038×C1512
#2005×C1512
#1994×C1512
#1962×C1512
#1882×C1512
#1859×C1512
#1801×C1512
#24179151