Finite Group Databasebeta

← C151×#19068 #50323993

Subgroups — C151×#19068 #50323993

Order 38656.

920 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3545×C151C211yesmaximal, characteristic, complemented
2#3219×C151C211yesmaximal, characteristic, complemented
3#3213×C151C211yesmaximal, characteristic, complemented
4#3171×C151C211yesmaximal, characteristic, complemented
5#1664×C151C211yesmaximal, characteristic, complemented
6#1662×C151C211yesmaximal, characteristic, complemented
7#1661×C151C211yesmaximal, characteristic, complemented
8#1659×C151C211yesmaximal, characteristic, complemented
9#1657×C151C211yesmaximal, characteristic, complemented
10#1656×C151C211yesmaximal, characteristic, complemented
11#1656×C151C211yesmaximal, characteristic, complemented
12#1655×C151C211yesmaximal, characteristic, complemented
13#1535×C151C211yesmaximal, characteristic, complemented
14#1529×C151C211yesmaximal, characteristic, complemented
15#1527×C151C211yesmaximal, characteristic, complemented
16#563×C151C2211yescharacteristic
17#562×C151C2211yescharacteristic
18#562×C151C2211yescharacteristic
19H(3,𝔽4)×C151C2211yescharacteristic
20#555×C151—21no—
21#551×C151—21no—
22#551×C151—21no—
23#551×C151—21no—
24#546×C151—21no—
25#546×C151—21no—
26#542×C151—21no—
27#542×C151—21no—
28#538×C151—21no—
29#538×C151—21no—
30#536×C151—21no—
31#534×C151—21no—
32#532×C151C2211yescharacteristic, complemented
33#529×C151C2211yescharacteristic
34#529×C151C2211yescharacteristic
35C2×#124×C151C2211yescharacteristic
36#501×C151C2211yescharacteristic, complemented
37#497×C151C2211yescharacteristic, complemented
38#496×C151C2211yescharacteristic
39#496×C151C2211yescharacteristic, complemented
40#496×C151C2211yescharacteristic, complemented
41#496×C151C2211yescharacteristic, complemented
42#491×C151C2211yescharacteristic, complemented
43#490×C151C2211yescharacteristic, complemented
44#490×C151C2211yescharacteristic, complemented
45#489×C151C2211yescharacteristic
46#489×C151C2211yescharacteristic, complemented
47#489×C151C2211yescharacteristic, complemented
48#469×C151—21no—
49#468×C151—21no—
50#464×C151—21no—
51#463×C151—21no—
52#463×C151—21no—
53#463×C151—21no—
54#452×C151—21no—
55#449×C151—21no—
56#448×C151—21no—
57#447×C151—21no—
58C4×SD16×C151—21no—
59C4×D8×C151—21no—
60#432×C151C2211yescharacteristic, complemented
61#432×C151C2211yescharacteristic, complemented
62C4×M16×C151C2211yescharacteristic, complemented
63#330×C151C2211yescharacteristic, complemented
64#330×C151C2211yescharacteristic, complemented
65#330×C151C2211yescharacteristic, complemented
66#330×C151C2211yescharacteristic, complemented
67#329×C151C2211yescharacteristic
68#329×C151C2211yescharacteristic
69#329×C151C2211yescharacteristic, complemented
70#329×C151C2211yescharacteristic, complemented
71#329×C151C2211yescharacteristic, complemented
72#329×C151C2211yescharacteristic, complemented
73#329×C151C2211yescharacteristic, complemented
74#329×C151C2211yescharacteristic, complemented
75C2×#41×C151—21no—
76C2×#41×C151—21no—
77C22×Q8×C151D411yescharacteristic
78C22×D4×C151—21no—
79C22×D4×C151D411yescharacteristic
80C2×Q16×C151—21no—
81C2×SD16×C151—21no—
82C2×SD16×C151—21no—
83C2×SD16×C151—21no—
84C2×SD16×C151—21no—
85C2×SD16×C151—21no—
86C2×D8×C151—21no—
87C2×D8×C151—21no—
88C2×D8×C151—21no—
89C2×D8×C151—21no—
90C2×M16×C151—21no—
91C4⋊Q8×C151—21no—
92C4⋊Q8×C151—21no—
93C4⋊Q8×C151C2311yescharacteristic
94#127×C151C2311yescharacteristic
95#126×C151—21no—
96#126×C151—21no—
97#126×C151—21no—
98#126×C151—21no—
99#126×C151—21no—
100#126×C151—21no—
101#125×C151C2311yescharacteristic
102#125×C151C2311yescharacteristic
103#124×C151—21no—
104#124×C151—21no—
105#124×C151—21no—
106#124×C151—21no—
107#124×C151—21no—
108#124×C151—21no—
109#124×C151—21no—
110#124×C151—21no—
111#124×C151—21no—
112#124×C151D411yescharacteristic
113#124×C151D411yescharacteristic
114#124×C151C2311yescharacteristic
115#124×C151C2311yescharacteristic
116#124×C151C2311yescharacteristic
117#124×C151C2311yescharacteristic
118#123×C151—21no—
119#123×C151—21no—
120#123×C151—21no—
121#123×C151—21no—
122#123×C151—21no—
123#123×C151—21no—
124#123×C151—21no—
125#123×C151—21no—
126#123×C151—21no—
127#123×C151—21no—
128#123×C151—21no—
129#123×C151—21no—
130C22⋊Q8×C151—21no—
131C22⋊Q8×C151—21no—
132C22⋊Q8×C151—21no—
133C22⋊Q8×C151—21no—
134C22⋊Q8×C151—21no—
135C22⋊Q8×C151—21no—
136C22⋊Q8×C151—21no—
137C22⋊Q8×C151—21no—
138C22⋊Q8×C151D411yescharacteristic
139C22⋊Q8×C151D411yescharacteristic
140#121×C151—21no—
141#121×C151—21no—
142#121×C151—21no—
143#121×C151—21no—
144#121×C151—21no—
145#121×C151—21no—
146#121×C151—21no—
147#121×C151—21no—
148#121×C151—21no—
149#121×C151—21no—
150#121×C151D411yescharacteristic
151#121×C151D411yescharacteristic
152#120×C151—21no—
153#120×C151—21no—
154#120×C151—21no—
155#120×C151—21no—
156#120×C151—21no—
157#120×C151—21no—
158C4×Q8×C151D411yescharacteristic
159C4×Q8×C151D411yescharacteristic
160C4×D4×C151—21no—
161C4×D4×C151—21no—
162C4×D4×C151—21no—
163C4×D4×C151—21no—
164C4×D4×C151—21no—
165C4×D4×C151—21no—
166C4×D4×C151—21no—
167C4×D4×C151—21no—
168C4×D4×C151D411yescharacteristic
169C4×D4×C151D411yescharacteristic
170#117×C151—21no—
171#117×C151—21no—
172#117×C151—21no—
173#117×C151—21no—
174#117×C151—21no—
175C2×C22⋊C4×C151—21no—
176C2×C22⋊C4×C151—21no—
177C2×C22⋊C4×C151—21no—
178C2×C22⋊C4×C151—21no—
179C2×C22⋊C4×C151—21no—
180C2×C42×C151C2311yescharacteristic
181#107×C151—21no—
182#106×C151—21no—
183C4⋊C8×C151—21no—
184C4⋊C8×C151—21no—
185#103×C151—21no—
186#103×C151—21no—
187#103×C151—21no—
188#103×C151—21no—
189#103×C151—21no—
190#102×C151—21no—
191#102×C151—21no—
192#102×C151—21no—
193#102×C151—21no—
194#102×C151—21no—
195#102×C151—21no—
196#102×C151—21no—
197C22⋊C8×C151—21no—
198C22⋊C8×C151—21no—
199#97×C151C2311yescharacteristic
200#97×C151C2311yescharacteristic
201#97×C151C2311yescharacteristic
202#97×C151C2311yescharacteristic
203#97×C151C2311yescharacteristic
204#97×C151C2311yescharacteristic
205C4×C8×C151—21no—
206C24×C151—21no—
207C24×C151—21no—
208#41×C151—82no—
209#41×C151—81no—
210#41×C151—81no—
211C2×Q8×C151—21no—
212C2×Q8×C151—21no—
213C2×Q8×C151—21no—
214C2×Q8×C151—81no—
215C2×Q8×C151C2×D411yescharacteristic
216C2×Q8×C151C2×D411yescharacteristic
217C2×Q8×C151C2×D411yescharacteristic
218C2×Q8×C151C2×D411yescharacteristic
219C2×D4×C151—21no—
220C2×D4×C151—21no—
221C2×D4×C151—21no—
222C2×D4×C151—21no—
223C2×D4×C151—21no—
224C2×D4×C151—21no—
225C2×D4×C151—21no—
226C2×D4×C151—21no—
227C2×D4×C151—21no—
228C2×D4×C151—21no—
229C2×D4×C151—21no—
230C2×D4×C151—21no—
231C2×D4×C151—21no—
232C2×D4×C151—41no—
233C2×D4×C151—81no—
234C2×D4×C151—82no—
235C2×D4×C151C2×D411yescharacteristic
236C2×D4×C151C2×D411yescharacteristic
237C2×D4×C151C2×D411yescharacteristic
238C2×D4×C151C2×D411yescharacteristic
239C22×C4×C151—21no—
240C22×C4×C151—21no—
241C22×C4×C151—21no—
242C22×C4×C151—21no—
243C22×C4×C151—21no—
244C22×C4×C151—21no—
245C22×C4×C151—21no—
246C22×C4×C151—21no—
247C22×C4×C151—41no—
248C22×C4×C151C2×D411yescharacteristic
249C22×C4×C151C2×D411yescharacteristic
250C22×C4×C151C2×D411yescharacteristic
251Q16×C151—81no—
252SD16×C151—42no—
253SD16×C151—81no—
254SD16×C151—81no—
255SD16×C151—81no—
256SD16×C151—81no—
257D8×C151—42no—
258D8×C151—81no—
259D8×C151—81no—
260D8×C151—81no—
261M16×C151—42no—
262C2×C8×C151—21no—
263C2×C8×C151—21no—
264C2×C8×C151—21no—
265C2×C8×C151—21no—
266C2×C8×C151—21no—
267C2×C8×C151—21no—
268C4⋊C4×C151—21no—
269C4⋊C4×C151—21no—
270C4⋊C4×C151—21no—
271C4⋊C4×C151—21no—
272C4⋊C4×C151—21no—
273C4⋊C4×C151—21no—
274C4⋊C4×C151—21no—
275C4⋊C4×C151—21no—
276C4⋊C4×C151—21no—
277C4⋊C4×C151—21no—
278C4⋊C4×C151—21no—
279C4⋊C4×C151—21no—
280C4⋊C4×C151—21no—
281C4⋊C4×C151—21no—
282C4⋊C4×C151—21no—
283C4⋊C4×C151—21no—
284C4⋊C4×C151C2×D411yescharacteristic
285C4⋊C4×C151C2×D411yescharacteristic
286C4⋊C4×C151C2×D411yescharacteristic
287C4⋊C4×C151C2×D411yescharacteristic
288C22⋊C4×C151—21no—
289C22⋊C4×C151—21no—
290C22⋊C4×C151—21no—
291C22⋊C4×C151—21no—
292C22⋊C4×C151—21no—
293C22⋊C4×C151—21no—
294C22⋊C4×C151—21no—
295C22⋊C4×C151—21no—
296C22⋊C4×C151—21no—
297C22⋊C4×C151—21no—
298C22⋊C4×C151—21no—
299C22⋊C4×C151—21no—
300C22⋊C4×C151—21no—
301C22⋊C4×C151—21no—
302C22⋊C4×C151—21no—
303C22⋊C4×C151—21no—
304C22⋊C4×C151—21no—
305C22⋊C4×C151—21no—
306C22⋊C4×C151—21no—
307C22⋊C4×C151—21no—
308C22⋊C4×C151—21no—
309C22⋊C4×C151—21no—
310C22⋊C4×C151—21no—
311C22⋊C4×C151—21no—
312C22⋊C4×C151—21no—
313C22⋊C4×C151—21no—
314C22⋊C4×C151—21no—
315C22⋊C4×C151—21no—
316C22⋊C4×C151—41no—
317C22⋊C4×C151—41no—
318C42×C151—21no—
319C42×C151—21no—
320C42×C151—21no—
321C42×C151—21no—
322C42×C151C2×D411yescharacteristic
323C42×C151C2×D411yescharacteristic
324C42×C151C2×D411yescharacteristic
325C42×C151C2411yescharacteristic
326C23×C151—21no—
327C23×C151—21no—
328C23×C151—21no—
329C23×C151—21no—
330C23×C151—42no—
331C23×C151—41no—
332C23×C151—81no—
333C23×C151—81no—
334C23×C151—81no—
335C23×C151—81no—
336C23×C151—81no—
337C23×C151#12011yescharacteristic
338Q8×C151—41no—
339Q8×C151—41no—
340Q8×C151—41no—
341Q8×C151—41no—
342Q8×C151—41no—
343Q8×C151—41no—
344Q8×C151—81no—
345Q8×C151—81no—
346D4×C151—41no—
347D4×C151—41no—
348D4×C151—41no—
349D4×C151—41no—
350D4×C151—41no—
351D4×C151—41no—
352D4×C151—41no—
353D4×C151—41no—
354D4×C151—41no—
355D4×C151—41no—
356D4×C151—42no—
357D4×C151—42no—
358D4×C151—81no—
359D4×C151—81no—
360D4×C151—81no—
361D4×C151—81no—
362D4×C151—81no—
363D4×C151—81no—
364D4×C151—81no—
365D4×C151—81no—
366D4×C151—82no—
367C2×C4×C151—21no—
368C2×C4×C151—21no—
369C2×C4×C151—21no—
370C2×C4×C151—21no—
371C2×C4×C151—21no—
372C2×C4×C151—21no—
373C2×C4×C151—21no—
374C2×C4×C151—21no—
375C2×C4×C151—41no—
376C2×C4×C151—41no—
377C2×C4×C151—41no—
378C2×C4×C151—42no—
379C2×C4×C151—41no—
380C2×C4×C151—81no—
381C2×C4×C151—81no—
382C2×C4×C151—82no—
383C2×C4×C151—81no—
384C2×C4×C151—81no—
385C2×C4×C151—81no—
386C2×C4×C151—81no—
387C2×C4×C151—81no—
388C2×C4×C151#12011yescharacteristic
389C2×C4×C151#12011yescharacteristic
390C2×C4×C151#12011yescharacteristic
391C2×C4×C151C22×D411yescharacteristic
392C2×C4×C151C22×D411yescharacteristic
393C2×C4×C151C22×D411yescharacteristic
394C8×C151—22no—
395C8×C151—41no—
396C8×C151—41no—
397C8×C151—41no—
398C8×C151—41no—
399C8×C151—41no—
400C22×C151—21no—
401C22×C151—21no—
402C22×C151—21no—
403C22×C151—41no—
404C22×C151—41no—
405C22×C151—41no—
406C22×C151—41no—
407C22×C151—41no—
408C22×C151—41no—
409C22×C151—41no—
410C22×C151—41no—
411C22×C151—41no—
412C22×C151—41no—
413C22×C151—41no—
414C22×C151—41no—
415C22×C151—81no—
416C22×C151—81no—
417C22×C151—81no—
418C22×C151—162no—
419C22×C151—162no—
420C22×C151C2×#12011yescharacteristic
421C4×C151—21no—
422C4×C151—21no—
423C4×C151—21no—
424C4×C151—21no—
425C4×C151—21no—
426C4×C151—21no—
427C4×C151—41no—
428C4×C151—41no—
429C4×C151—41no—
430C4×C151—41no—
431C4×C151—41no—
432C4×C151—41no—
433C4×C151—41no—
434C4×C151—41no—
435C4×C151—81no—
436C2×C151—41no—
437C2×C151—81no—
438C2×C151—81no—
439C2×C151—81no—
440C2×C151—81no—
441C2×C151—161no—
442C2×C151#301811yescharacteristic
443C2×C151#301911yescharacteristic
444C2×C151#302111yescharacteristic
445#19068C15111yesmaximal, characteristic, direct product factor, Sylow
446C151#1906811yescharacteristic, direct product factor, Sylow
447#3545C2×C15111yescharacteristic, complemented
448#3219C2×C15111yescharacteristic, complemented
449#3213C2×C15111yescharacteristic, complemented
450#3171C2×C15111yescharacteristic, complemented
451#1664C2×C15111yescharacteristic, complemented
452#1662C2×C15111yescharacteristic, complemented
453#1661C2×C15111yescharacteristic, complemented
454#1659C2×C15111yescharacteristic, complemented
455#1657C2×C15111yescharacteristic, complemented
456#1656C2×C15111yescharacteristic, complemented
457#1656C2×C15111yescharacteristic, complemented
458#1655C2×C15111yescharacteristic, complemented
459#1535C2×C15111yescharacteristic, complemented
460#1529C2×C15111yescharacteristic, complemented
461#1527C2×C15111yescharacteristic, complemented
462#563C22×C15111yescharacteristic
463#562C22×C15111yescharacteristic
464#562C22×C15111yescharacteristic
465H(3,𝔽4)C22×C15111yescharacteristic
466#555—21no—
467#551—21no—
468#551—21no—
469#551—21no—
470#546—21no—
471#546—21no—
472#542—21no—
473#542—21no—
474#538—21no—
475#538—21no—
476#536—21no—
477#534—21no—
478#532C22×C15111yescharacteristic, complemented
479#529C22×C15111yescharacteristic
480#529C22×C15111yescharacteristic
481C2×#124C22×C15111yescharacteristic
482#501C22×C15111yescharacteristic, complemented
483#497C22×C15111yescharacteristic, complemented
484#496C22×C15111yescharacteristic
485#496C22×C15111yescharacteristic, complemented
486#496C22×C15111yescharacteristic, complemented
487#496C22×C15111yescharacteristic, complemented
488#491C22×C15111yescharacteristic, complemented
489#490C22×C15111yescharacteristic, complemented
490#490C22×C15111yescharacteristic, complemented
491#489C22×C15111yescharacteristic
492#489C22×C15111yescharacteristic, complemented
493#489C22×C15111yescharacteristic, complemented
494#469—21no—
495#468—21no—
496#464—21no—
497#463—21no—
498#463—21no—
499#463—21no—
500#452—21no—
501#449—21no—
502#448—21no—
503#447—21no—
504C4×SD16—21no—
505C4×D8—21no—
506#432C22×C15111yescharacteristic, complemented
507#432C22×C15111yescharacteristic, complemented
508C4×M16C22×C15111yescharacteristic, complemented
509#330C22×C15111yescharacteristic, complemented
510#330C22×C15111yescharacteristic, complemented
511#330C22×C15111yescharacteristic, complemented
512#330C22×C15111yescharacteristic, complemented
513#329C22×C15111yescharacteristic
514#329C22×C15111yescharacteristic
515#329C22×C15111yescharacteristic, complemented
516#329C22×C15111yescharacteristic, complemented
517#329C22×C15111yescharacteristic, complemented
518#329C22×C15111yescharacteristic, complemented
519#329C22×C15111yescharacteristic, complemented
520#329C22×C15111yescharacteristic, complemented
521C2×#41—21no—
522C2×#41—21no—
523C22×Q8D4×C15111yescharacteristic
524C22×D4—21no—
525C22×D4D4×C15111yescharacteristic
526C2×Q16—21no—
527C2×SD16—21no—
528C2×SD16—21no—
529C2×SD16—21no—
530C2×SD16—21no—
531C2×SD16—21no—
532C2×D8—21no—
533C2×D8—21no—
534C2×D8—21no—
535C2×D8—21no—
536C2×M16—21no—
537C4⋊Q8—21no—
538C4⋊Q8—21no—
539C4⋊Q8C23×C15111yescharacteristic
540#127C23×C15111yescharacteristic
541#126—21no—
542#126—21no—
543#126—21no—
544#126—21no—
545#126—21no—
546#126—21no—
547#125C23×C15111yescharacteristic
548#125C23×C15111yescharacteristic
549#124—21no—
550#124—21no—
551#124—21no—
552#124—21no—
553#124—21no—
554#124—21no—
555#124—21no—
556#124—21no—
557#124—21no—
558#124D4×C15111yescharacteristic
559#124D4×C15111yescharacteristic
560#124C23×C15111yescharacteristic
561#124C23×C15111yescharacteristic
562#124C23×C15111yescharacteristic
563#124C23×C15111yescharacteristic
564#123—21no—
565#123—21no—
566#123—21no—
567#123—21no—
568#123—21no—
569#123—21no—
570#123—21no—
571#123—21no—
572#123—21no—
573#123—21no—
574#123—21no—
575#123—21no—
576C22⋊Q8—21no—
577C22⋊Q8—21no—
578C22⋊Q8—21no—
579C22⋊Q8—21no—
580C22⋊Q8—21no—
581C22⋊Q8—21no—
582C22⋊Q8—21no—
583C22⋊Q8—21no—
584C22⋊Q8D4×C15111yescharacteristic
585C22⋊Q8D4×C15111yescharacteristic
586#121—21no—
587#121—21no—
588#121—21no—
589#121—21no—
590#121—21no—
591#121—21no—
592#121—21no—
593#121—21no—
594#121—21no—
595#121—21no—
596#121D4×C15111yescharacteristic
597#121D4×C15111yescharacteristic
598#120—21no—
599#120—21no—
600#120—21no—
601#120—21no—
602#120—21no—
603#120—21no—
604C4×Q8D4×C15111yescharacteristic
605C4×Q8D4×C15111yescharacteristic
606C4×D4—21no—
607C4×D4—21no—
608C4×D4—21no—
609C4×D4—21no—
610C4×D4—21no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—21no—
614C4×D4D4×C15111yescharacteristic
615C4×D4D4×C15111yescharacteristic
616#117—21no—
617#117—21no—
618#117—21no—
619#117—21no—
620#117—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C42C23×C15111yescharacteristic
627#107—21no—
628#106—21no—
629C4⋊C8—21no—
630C4⋊C8—21no—
631#103—21no—
632#103—21no—
633#103—21no—
634#103—21no—
635#103—21no—
636#102—21no—
637#102—21no—
638#102—21no—
639#102—21no—
640#102—21no—
641#102—21no—
642#102—21no—
643C22⋊C8—21no—
644C22⋊C8—21no—
645#97C23×C15111yescharacteristic
646#97C23×C15111yescharacteristic
647#97C23×C15111yescharacteristic
648#97C23×C15111yescharacteristic
649#97C23×C15111yescharacteristic
650#97C23×C15111yescharacteristic
651C4×C8—21no—
652C24—21no—
653C24—21no—
654#41—82no—
655#41—81no—
656#41—81no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—81no—
661C2×Q8C2×D4×C15111yescharacteristic
662C2×Q8C2×D4×C15111yescharacteristic
663C2×Q8C2×D4×C15111yescharacteristic
664C2×Q8C2×D4×C15111yescharacteristic
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—41no—
679C2×D4—81no—
680C2×D4—82no—
681C2×D4C2×D4×C15111yescharacteristic
682C2×D4C2×D4×C15111yescharacteristic
683C2×D4C2×D4×C15111yescharacteristic
684C2×D4C2×D4×C15111yescharacteristic
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—41no—
694C22×C4C2×D4×C15111yescharacteristic
695C22×C4C2×D4×C15111yescharacteristic
696C22×C4C2×D4×C15111yescharacteristic
697Q16—81no—
698SD16—42no—
699SD16—81no—
700SD16—81no—
701SD16—81no—
702SD16—81no—
703D8—42no—
704D8—81no—
705D8—81no—
706D8—81no—
707M16—42no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4C2×D4×C15111yescharacteristic
731C4⋊C4C2×D4×C15111yescharacteristic
732C4⋊C4C2×D4×C15111yescharacteristic
733C4⋊C4C2×D4×C15111yescharacteristic
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—21no—
758C22⋊C4—21no—
759C22⋊C4—21no—
760C22⋊C4—21no—
761C22⋊C4—21no—
762C22⋊C4—41no—
763C22⋊C4—41no—
764C42—21no—
765C42—21no—
766C42—21no—
767C42—21no—
768C42C2×D4×C15111yescharacteristic
769C42C2×D4×C15111yescharacteristic
770C42C2×D4×C15111yescharacteristic
771C42C24×C15111yescharacteristic
772C23—21no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—42no—
777C23—41no—
778C23—81no—
779C23—81no—
780C23—81no—
781C23—81no—
782C23—81no—
783C23#120×C15111yescharacteristic
784Q8—41no—
785Q8—41no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789Q8—41no—
790Q8—81no—
791Q8—81no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—41no—
798D4—41no—
799D4—41no—
800D4—41no—
801D4—41no—
802D4—42no—
803D4—42no—
804D4—81no—
805D4—81no—
806D4—81no—
807D4—81no—
808D4—81no—
809D4—81no—
810D4—81no—
811D4—81no—
812D4—82no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—42no—
825C2×C4—41no—
826C2×C4—81no—
827C2×C4—81no—
828C2×C4—82no—
829C2×C4—81no—
830C2×C4—81no—
831C2×C4—81no—
832C2×C4—81no—
833C2×C4—81no—
834C2×C4#120×C15111yescharacteristic
835C2×C4#120×C15111yescharacteristic
836C2×C4#120×C15111yescharacteristic
837C2×C4C22×D4×C15111yescharacteristic
838C2×C4C22×D4×C15111yescharacteristic
839C2×C4C22×D4×C15111yescharacteristic
840C8—22no—
841C8—41no—
842C8—41no—
843C8—41no—
844C8—41no—
845C8—41no—
846C22—21no—
847C22—21no—
848C22—21no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—162no—
865C22—162no—
866C22C2×#120×C15111yescharacteristic
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—41no—
880C4—41no—
881C4—81no—
882C2—41no—
883C2—81no—
884C2—81no—
885C2—81no—
886C2—81no—
887C2—161no—
888C2#3018×C15111yescharacteristic
889C2#3019×C15111yescharacteristic
890C2#3021×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
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
1. #3545×C151C2semidirect
2. #3219×C151C2semidirect
3. #3213×C151C2semidirect
4. #3171×C151C2semidirect
5. #1664×C151C2semidirect
6. #1662×C151C2semidirect
7. #1661×C151C2semidirect
8. #1659×C151C2semidirect
9. #1657×C151C2semidirect
10. #1656×C151C2semidirect
11. #1656×C151C2semidirect
12. #1655×C151C2semidirect
13. #1535×C151C2semidirect
14. #1529×C151C2semidirect
15. #1527×C151C2semidirect
32. #532×C151C22semidirect
36. #501×C151C22semidirect
37. #497×C151C22semidirect
39. #496×C151C22semidirect
40. #496×C151C22semidirect
41. #496×C151C22semidirect
42. #491×C151C22semidirect
43. #490×C151C22semidirect
44. #490×C151C22semidirect
46. #489×C151C22semidirect
47. #489×C151C22semidirect
60. #432×C151C22semidirect
61. #432×C151C22semidirect
62. C4×M16×C151C22semidirect
63. #330×C151C22semidirect
64. #330×C151C22semidirect
65. #330×C151C22semidirect
66. #330×C151C22semidirect
69. #329×C151C22semidirect
70. #329×C151C22semidirect
71. #329×C151C22semidirect
72. #329×C151C22semidirect
73. #329×C151C22semidirect
74. #329×C151C22semidirect
445. #19068C151direct (N × H)
446. C151#19068direct (N × H)
447. #3545C2×C151semidirect
448. #3219C2×C151semidirect
449. #3213C2×C151semidirect
450. #3171C2×C151semidirect
451. #1664C2×C151semidirect
452. #1662C2×C151semidirect
453. #1661C2×C151semidirect
454. #1659C2×C151semidirect
455. #1657C2×C151semidirect
456. #1656C2×C151semidirect
457. #1656C2×C151semidirect
458. #1655C2×C151semidirect
459. #1535C2×C151semidirect
460. #1529C2×C151semidirect
461. #1527C2×C151semidirect
478. #532C22×C151semidirect
482. #501C22×C151semidirect
483. #497C22×C151semidirect
485. #496C22×C151semidirect
486. #496C22×C151semidirect
487. #496C22×C151semidirect
488. #491C22×C151semidirect
489. #490C22×C151semidirect
490. #490C22×C151semidirect
492. #489C22×C151semidirect
493. #489C22×C151semidirect
506. #432C22×C151semidirect
507. #432C22×C151semidirect
508. C4×M16C22×C151semidirect
509. #330C22×C151semidirect
510. #330C22×C151semidirect
511. #330C22×C151semidirect
512. #330C22×C151semidirect
515. #329C22×C151semidirect
516. #329C22×C151semidirect
517. #329C22×C151semidirect
518. #329C22×C151semidirect
519. #329C22×C151semidirect
520. #329C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3545×C1512
#3219×C1512
#3213×C1512
#3171×C1512
#1664×C1512
#1662×C1512
#1661×C1512
#1659×C1512
#1657×C1512
#1656×C1512
#1655×C1512
#1535×C1512
#1529×C1512
#1527×C1512
#19068151