Finite Group Databasebeta

← C151×#24183 #50329108

Subgroups — C151×#24183 #50329108

Order 38656.

1002 conjugacy classes of subgroups.

The subgroup lattice has 606 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
4#2327×C151C211yesmaximal, characteristic, complemented
5#2038×C151C212yesmaximal, complemented
6#2005×C151C212yesmaximal, complemented
7#1995×C151C211yesmaximal, characteristic, complemented
8#1963×C151C211yesmaximal, characteristic
9#1882×C151C212yesmaximal, complemented
10#1860×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#387×C151—22no—
45#387×C151—22no—
46#382×C151C2211yescharacteristic
47#376×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—21no—
107C2×C4⋊C4×C151D412yes—
108C2×C4⋊C4×C151C2311yescharacteristic
109C2×C4⋊C4×C151C2311yescharacteristic
110C2×C42×C151—21no—
111C2×C42×C151D412yes—
112C2×C42×C151C2311yescharacteristic
113C2×C42×C151C2311yescharacteristic
114C2×C42×C151C2311yescharacteristic
115#107×C151—22no—
116#106×C151—22no—
117C4⋊C8×C151—21no—
118C4⋊C8×C151—21no—
119C4⋊C8×C151—21no—
120C4⋊C8×C151—21no—
121#104×C151—24no—
122#104×C151—42no—
123#103×C151—22no—
124#103×C151—22no—
125#103×C151—22no—
126#102×C151—22no—
127#101×C151—42no—
128#95×C151—21no—
129#95×C151—21no—
130#95×C151—22no—
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—24no—
159C22×C4×C151—22no—
160C22×C4×C151—21no—
161C22×C4×C151—21no—
162C22×C4×C151C2×D412yes—
163C22×C4×C151C2×D412yes—
164C22×C4×C151C2×D411yescharacteristic
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—41no—
192C4⋊C4×C151—41no—
193C4⋊C4×C151C2×D412yes—
194C4⋊C4×C151C2×D412yes—
195C22⋊C4×C151—24no—
196C22⋊C4×C151—24no—
197C22⋊C4×C151—24no—
198C22⋊C4×C151—22no—
199C22⋊C4×C151—22no—
200C22⋊C4×C151—22no—
201C42×C151—24no—
202C42×C151—22no—
203C42×C151—22no—
204C42×C151—22no—
205C42×C151—21no—
206C42×C151—21no—
207C42×C151—21no—
208C42×C151—41no—
209C42×C151—41no—
210C42×C151C2×D411yescharacteristic
211C42×C151C2×D411yescharacteristic
212C42×C151C2×D411yescharacteristic
213C42×C151C2×D411yescharacteristic
214C42×C151#4112yes—
215C23×C151—22no—
216C23×C151C22×D411yescharacteristic
217Q8×C151—22no—
218Q8×C151—22no—
219Q8×C151—22no—
220Q8×C151—22no—
221Q8×C151—42no—
222Q8×C151—41no—
223Q8×C151—41no—
224Q8×C151—41no—
225Q8×C151—41no—
226Q8×C151—41no—
227Q8×C151—41no—
228Q8×C151—81no—
229D4×C151—22no—
230D4×C151—22no—
231D4×C151—42no—
232D4×C151—42no—
233D4×C151—42no—
234D4×C151—81no—
235C2×C4×C151—22no—
236C2×C4×C151—22no—
237C2×C4×C151—22no—
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—41no—
245C2×C4×C151—41no—
246C2×C4×C151—41no—
247C2×C4×C151—41no—
248C2×C4×C151—41no—
249C2×C4×C151—41no—
250C2×C4×C151—42no—
251C2×C4×C151—42no—
252C2×C4×C151—42no—
253C2×C4×C151—41no—
254C2×C4×C151—41no—
255C2×C4×C151—42no—
256C2×C4×C151—41no—
257C2×C4×C151—41no—
258C2×C4×C151—84no—
259C2×C4×C151#12011yescharacteristic
260C2×C4×C151#12011yescharacteristic
261C2×C4×C151#12011yescharacteristic
262C2×C4×C151#12011yescharacteristic
263C2×C4×C151C22×D411yescharacteristic
264C2×C4×C151C22×D411yescharacteristic
265C2×C4×C151C2×#4111yescharacteristic
266C2×C4×C151C2×#4111yescharacteristic
267C2×C4×C151H(5,𝔽2)11yescharacteristic
268C2×C4×C1512−1+411yescharacteristic
269C8×C151—42no—
270C8×C151—42no—
271C22×C151—21no—
272C22×C151—21no—
273C22×C151—42no—
274C22×C151—42no—
275C22×C151—42no—
276C22×C151C2×#12011yescharacteristic
277C22×C151#52511yescharacteristic
278C22×C151#53711yescharacteristic
279C4×C151—21no—
280C4×C151—21no—
281C4×C151—21no—
282C4×C151—21no—
283C4×C151—42no—
284C4×C151—42no—
285C4×C151—42no—
286C4×C151—42no—
287C4×C151—42no—
288C4×C151—42no—
289C4×C151—42no—
290C4×C151—81no—
291C4×C151—81no—
292C4×C151#54611yescharacteristic
293C4×C151#54711yescharacteristic
294C4×C151#54811yescharacteristic
295C4×C151#55011yescharacteristic
296C2×C151—21no—
297C2×C151—21no—
298C2×C151—82no—
299C2×C151#240711yescharacteristic
300C2×C151#302011yescharacteristic
301C2×C151#302211yescharacteristic
302#24183C15111yesmaximal, characteristic, direct product factor, Sylow
303C151#2418311yescharacteristic, direct product factor, Sylow
304#3507C2×C15111yescharacteristic
305#3078C2×C15111yescharacteristic, complemented
306#3037C2×C15111yescharacteristic
307#2327C2×C15111yescharacteristic, complemented
308#2038C2×C15112yescomplemented
309#2005C2×C15112yescomplemented
310#1995C2×C15111yescharacteristic, complemented
311#1963C2×C15111yescharacteristic
312#1882C2×C15112yescomplemented
313#1860C2×C15112yescomplemented
314#1801C2×C15111yescharacteristic, complemented
315C2×#137C22×C15112yes—
316#559—21no—
317#557—21no—
318#556—21no—
319#556—22no—
320#554—21no—
321#552—22no—
322#539—22no—
323#536C22×C15112yes—
324#533C22×C15111yescharacteristic
325#532C22×C15111yescharacteristic
326C2×C4⋊Q8C22×C15111yescharacteristic
327#529—22no—
328#520C22×C15112yes—
329C2×C4×Q8C22×C15111yescharacteristic
330C2×C4×Q8C22×C15111yescharacteristic
331#479—22no—
332#477—21no—
333#475—21no—
334#464—22no—
335#462—21no—
336#460—21no—
337#428C22×C15112yes—
338#423C22×C15111yescharacteristic
339#423C22×C15111yescharacteristic
340C2×#104C22×C15112yes—
341C2×#104C22×C15112yes—
342#419C22×C15112yes—
343#417C22×C15112yes—
344C2×#101C22×C15112yes—
345#391C22×C15111yescharacteristic
346#391C22×C15111yescharacteristic
347#387—22no—
348#387—22no—
349#382C22×C15111yescharacteristic
350#376C22×C15111yescharacteristic
351#343C22×C15112yes—
352#339C22×C15112yes—
353#339C22×C15112yes—
354C2×#41C23×C15112yes—
355C22×Q8C23×C15111yescharacteristic
356C22×Q8C23×C15111yescharacteristic
357#137—24no—
358#137—42no—
359C2×Q16—22no—
360C2×SD16—22no—
361C2×M16C23×C15112yes—
362C2×M16C23×C15112yes—
363C4⋊Q8—22no—
364C4⋊Q8—22no—
365C4⋊Q8—22no—
366C4⋊Q8D4×C15111yescharacteristic
367C4⋊Q8D4×C15111yescharacteristic
368C4⋊Q8D4×C15111yescharacteristic
369#127D4×C15111yescharacteristic
370#126—24no—
371#126—24no—
372#125—22no—
373#125—24no—
374#125D4×C15112yes—
375#124—22no—
376#124—22no—
377#124D4×C15112yes—
378#123—24no—
379#123—24no—
380C22⋊Q8—24no—
381C22⋊Q8—21no—
382C22⋊Q8—21no—
383C22⋊Q8—22no—
384C22⋊Q8—22no—
385#121—21no—
386#121—21no—
387C4×Q8—22no—
388C4×Q8—22no—
389C4×Q8—21no—
390C4×Q8—21no—
391C4×Q8—21no—
392C4×Q8—21no—
393C4×Q8—21no—
394C4×Q8—21no—
395C4×Q8—21no—
396C4×Q8—21no—
397C4×Q8—21no—
398C4×Q8—21no—
399C4×D4—22no—
400C4×D4—22no—
401C4×D4—24no—
402C4×D4—21no—
403C4×D4—21no—
404#117—24no—
405#117—22no—
406#117C23×C15112yes—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4D4×C15112yes—
411C2×C4⋊C4C23×C15111yescharacteristic
412C2×C4⋊C4C23×C15111yescharacteristic
413C2×C42—21no—
414C2×C42D4×C15112yes—
415C2×C42C23×C15111yescharacteristic
416C2×C42C23×C15111yescharacteristic
417C2×C42C23×C15111yescharacteristic
418#107—22no—
419#106—22no—
420C4⋊C8—21no—
421C4⋊C8—21no—
422C4⋊C8—21no—
423C4⋊C8—21no—
424#104—24no—
425#104—42no—
426#103—22no—
427#103—22no—
428#103—22no—
429#102—22no—
430#101—42no—
431#95—21no—
432#95—21no—
433#95—22no—
434#95—22no—
435#95—22no—
436#41—22no—
437#41—22no—
438#41—22no—
439#41—22no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
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×Q8C2×D4×C15112yes—
454C2×Q8#41×C15112yes—
455C2×D4—22no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4C2×D4×C15112yes—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—24no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4C2×D4×C15112yes—
466C22×C4C2×D4×C15112yes—
467C22×C4C2×D4×C15111yescharacteristic
468C22×C4C2×D4×C15111yescharacteristic
469C22×C4C24×C15111yescharacteristic
470Q16—44no—
471SD16—44no—
472M16—22no—
473M16—22no—
474M16—22no—
475M16—22no—
476C2×C8—22no—
477C2×C8—22no—
478C4⋊C4—24no—
479C4⋊C4—28no—
480C4⋊C4—24no—
481C4⋊C4—24no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—22no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—41no—
495C4⋊C4—41no—
496C4⋊C4C2×D4×C15112yes—
497C4⋊C4C2×D4×C15112yes—
498C22⋊C4—24no—
499C22⋊C4—24no—
500C22⋊C4—24no—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C42—24no—
505C42—22no—
506C42—22no—
507C42—22no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42—41no—
512C42—41no—
513C42C2×D4×C15111yescharacteristic
514C42C2×D4×C15111yescharacteristic
515C42C2×D4×C15111yescharacteristic
516C42C2×D4×C15111yescharacteristic
517C42#41×C15112yes—
518C23—22no—
519C23C22×D4×C15111yescharacteristic
520Q8—22no—
521Q8—22no—
522Q8—22no—
523Q8—22no—
524Q8—42no—
525Q8—41no—
526Q8—41no—
527Q8—41no—
528Q8—41no—
529Q8—41no—
530Q8—41no—
531Q8—81no—
532D4—22no—
533D4—22no—
534D4—42no—
535D4—42no—
536D4—42no—
537D4—81no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—42no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—84no—
562C2×C4#120×C15111yescharacteristic
563C2×C4#120×C15111yescharacteristic
564C2×C4#120×C15111yescharacteristic
565C2×C4#120×C15111yescharacteristic
566C2×C4C22×D4×C15111yescharacteristic
567C2×C4C22×D4×C15111yescharacteristic
568C2×C4C2×#41×C15111yescharacteristic
569C2×C4C2×#41×C15111yescharacteristic
570C2×C4H(5,𝔽2)×C15111yescharacteristic
571C2×C42−1+4×C15111yescharacteristic
572C8—42no—
573C8—42no—
574C22—21no—
575C22—21no—
576C22—42no—
577C22—42no—
578C22—42no—
579C22C2×#120×C15111yescharacteristic
580C22#525×C15111yescharacteristic
581C22#537×C15111yescharacteristic
582C4—21no—
583C4—21no—
584C4—21no—
585C4—21no—
586C4—42no—
587C4—42no—
588C4—42no—
589C4—42no—
590C4—42no—
591C4—42no—
592C4—42no—
593C4—81no—
594C4—81no—
595C4#546×C15111yescharacteristic
596C4#547×C15111yescharacteristic
597C4#548×C15111yescharacteristic
598C4#550×C15111yescharacteristic
599C2—21no—
600C2—21no—
601C2—82no—
602C2#2407×C15111yescharacteristic
603C2#3020×C15111yescharacteristic
604C2#3022×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. #2327×C151C2semidirect
5. #2038×C151C2semidirect
6. #2005×C151C2semidirect
7. #1995×C151C2semidirect
9. #1882×C151C2semidirect
10. #1860×C151C2semidirect
11. #1801×C151C2semidirect
302. #24183C151direct (N × H)
303. C151#24183direct (N × H)
305. #3078C2×C151semidirect
307. #2327C2×C151semidirect
308. #2038C2×C151semidirect
309. #2005C2×C151semidirect
310. #1995C2×C151semidirect
312. #1882C2×C151semidirect
313. #1860C2×C151semidirect
314. #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
#2327×C1512
#2038×C1512
#2005×C1512
#1995×C1512
#1963×C1512
#1882×C1512
#1860×C1512
#1801×C1512
#24183151