Finite Group Databasebeta

← C151×#24175 #50329100

Subgroups — C151×#24175 #50329100

Order 38656.

1030 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3512×C151C211yesmaximal, characteristic
2#3037×C151C211yesmaximal, characteristic, complemented
3C4×#137×C151C211yesmaximal, characteristic, complemented
4#2565×C151C211yesmaximal, characteristic, complemented
5#2040×C151C211yesmaximal, characteristic, complemented
6#2039×C151C211yesmaximal, characteristic, complemented
7#2007×C151C211yesmaximal, characteristic, complemented
8#2007×C151C211yesmaximal, characteristic, complemented
9#1998×C151C211yesmaximal, characteristic, complemented
10#1980×C151C211yesmaximal, characteristic, complemented
11#1882×C151C211yesmaximal, characteristic, complemented
12#1882×C151C211yesmaximal, characteristic, complemented
13#1860×C151C211yesmaximal, characteristic, complemented
14#1859×C151C211yesmaximal, characteristic, complemented
15#1806×C151C211yesmaximal, characteristic, complemented
16C2×#137×C151C2211yescharacteristic
17C2×#137×C151C2211yescharacteristic
18C2×#137×C151C2211yescharacteristic
19#553×C151—21no—
20#553×C151—21no—
21#553×C151—22no—
22#553×C151—22no—
23#552×C151—21no—
24#552×C151—21no—
25#541×C151—21no—
26#540×C151—21no—
27#537×C151C2211yescharacteristic
28#537×C151C2211yescharacteristic
29#532×C151C2211yescharacteristic
30#529×C151—21no—
31#529×C151—21no—
32C2×#125×C151C2211yescharacteristic
33#520×C151C2211yescharacteristic
34#520×C151C2211yescharacteristic
35C4×#41×C151C2211yescharacteristic
36C2×C4×Q8×C151C2211yescharacteristic
37#464×C151—21no—
38#464×C151—21no—
39#462×C151—21no—
40#460×C151—21no—
41#441×C151—21no—
42#440×C151—21no—
43C4×Q16×C151—21no—
44C4×SD16×C151—21no—
45#428×C151C2211yescharacteristic
46#423×C151C2211yescharacteristic
47C2×#104×C151C2211yescharacteristic
48C2×#104×C151C2211yescharacteristic
49C2×#104×C151C2211yescharacteristic
50C2×#104×C151C2211yescharacteristic
51C2×#104×C151C2211yescharacteristic
52C2×#104×C151C2211yescharacteristic
53#419×C151C2211yescharacteristic
54#417×C151C2211yescharacteristic
55#417×C151C2211yescharacteristic
56#417×C151C2211yescharacteristic
57C4×M16×C151C2211yescharacteristic
58#398×C151—22no—
59#391×C151C2211yescharacteristic
60#391×C151C2211yescharacteristic
61#387×C151—22no—
62#384×C151C2211yescharacteristic
63#382×C151C2211yescharacteristic
64C4×C4⋊C4×C151C2211yescharacteristic
65#343×C151C2211yescharacteristic
66#343×C151C2211yescharacteristic
67#343×C151C2211yescharacteristic
68#343×C151C2211yescharacteristic
69#339×C151C2211yescharacteristic
70#339×C151C2211yescharacteristic
71C2×#41×C151C2311yescharacteristic
72C2×#41×C151C2311yescharacteristic
73C2×#41×C151C2311yescharacteristic
74C22×Q8×C151C2311yescharacteristic
75#137×C151—22no—
76#137×C151—22no—
77#137×C151—22no—
78#137×C151—22no—
79#137×C151—41no—
80#137×C151—41no—
81C2×Q16×C151—21no—
82C2×Q16×C151—21no—
83C2×Q16×C151—21no—
84C2×SD16×C151—21no—
85C2×SD16×C151—21no—
86C2×SD16×C151—21no—
87C2×M16×C151C2311yescharacteristic
88C2×M16×C151C2311yescharacteristic
89C2×M16×C151C2311yescharacteristic
90C2×M16×C151C2311yescharacteristic
91C4⋊Q8×C151D411yescharacteristic
92#127×C151D411yescharacteristic
93#126×C151—22no—
94#126×C151—22no—
95#126×C151—22no—
96#126×C151—22no—
97#125×C151—22no—
98#125×C151—22no—
99#125×C151—21no—
100#125×C151—21no—
101#125×C151—21no—
102#125×C151—21no—
103#124×C151D411yescharacteristic
104#124×C151D411yescharacteristic
105#123×C151—22no—
106#123×C151—22no—
107#123×C151—22no—
108#123×C151—22no—
109C22⋊Q8×C151—21no—
110C22⋊Q8×C151—21no—
111C22⋊Q8×C151—21no—
112C22⋊Q8×C151—21no—
113#121×C151—22no—
114#121×C151—22no—
115#121×C151—21no—
116#121×C151—21no—
117#121×C151—21no—
118#121×C151—21no—
119#121×C151—21no—
120#121×C151—21no—
121#121×C151—22no—
122#121×C151—22no—
123C4×Q8×C151—21no—
124C4×Q8×C151—21no—
125C4×Q8×C151—21no—
126C4×Q8×C151—21no—
127C4×Q8×C151—21no—
128C4×Q8×C151—21no—
129C4×Q8×C151D411yescharacteristic
130C4×Q8×C151D411yescharacteristic
131C4×D4×C151—22no—
132C4×D4×C151—22no—
133C4×D4×C151—21no—
134C4×D4×C151—21no—
135C4×D4×C151—21no—
136C4×D4×C151—21no—
137C4×D4×C151—22no—
138C4×D4×C151—22no—
139C4×D4×C151—21no—
140C4×D4×C151—21no—
141C4×D4×C151D411yescharacteristic
142C4×D4×C151D411yescharacteristic
143#117×C151—22no—
144#117×C151—22no—
145#117×C151—21no—
146#117×C151—21no—
147#117×C151—21no—
148#117×C151C2311yescharacteristic
149C2×C4⋊C4×C151—21no—
150C2×C4⋊C4×C151—21no—
151C2×C4⋊C4×C151—21no—
152C2×C4⋊C4×C151—22no—
153C2×C4⋊C4×C151—21no—
154C2×C4⋊C4×C151D412yes—
155C2×C4⋊C4×C151D412yes—
156C2×C4⋊C4×C151C2311yescharacteristic
157C2×C4⋊C4×C151C2311yescharacteristic
158C2×C4⋊C4×C151C2311yescharacteristic
159C2×C42×C151—21no—
160C2×C42×C151—21no—
161C2×C42×C151C2311yescharacteristic
162C2×C42×C151C2311yescharacteristic
163C2×C42×C151C2311yescharacteristic
164#107×C151—21no—
165#106×C151—21no—
166C4⋊C8×C151—21no—
167C4⋊C8×C151—21no—
168#104×C151—22no—
169#104×C151—22no—
170#104×C151—41no—
171#104×C151—41no—
172#104×C151—41no—
173#104×C151—41no—
174#103×C151—21no—
175#103×C151—21no—
176#103×C151—21no—
177#103×C151—21no—
178#103×C151—21no—
179#102×C151—21no—
180#102×C151—21no—
181#102×C151—21no—
182#97×C151—21no—
183C4×C8×C151—21no—
184#95×C151—21no—
185#95×C151—22no—
186#95×C151—22no—
187#95×C151—22no—
188#41×C151—21no—
189#41×C151—21no—
190#41×C151—21no—
191#41×C151—21no—
192#41×C151—21no—
193#41×C151—21no—
194#41×C151—21no—
195#41×C151—21no—
196#41×C151—21no—
197#41×C151—21no—
198#41×C151—21no—
199#41×C151—21no—
200C2×Q8×C151—21no—
201C2×Q8×C151—21no—
202C2×Q8×C151—21no—
203C2×Q8×C151—21no—
204C2×Q8×C151—21no—
205C2×Q8×C151C2×D411yescharacteristic
206C2×Q8×C151C2×D411yescharacteristic
207C2×Q8×C151C2×D411yescharacteristic
208C2×Q8×C151#4112yes—
209C2×D4×C151—21no—
210C2×D4×C151—21no—
211C2×D4×C151—21no—
212C2×D4×C151—22no—
213C2×D4×C151—22no—
214C2×D4×C151—21no—
215C2×D4×C151—21no—
216C2×D4×C151C2×D411yescharacteristic
217C2×D4×C151C2×D411yescharacteristic
218C2×D4×C151C2×D411yescharacteristic
219C22×C4×C151—21no—
220C22×C4×C151—21no—
221C22×C4×C151—22no—
222C22×C4×C151—22no—
223C22×C4×C151—21no—
224C22×C4×C151—21no—
225C22×C4×C151—21no—
226C22×C4×C151—21no—
227C22×C4×C151—21no—
228C22×C4×C151—21no—
229C22×C4×C151—21no—
230C22×C4×C151C2×D412yes—
231C22×C4×C151C2×D412yes—
232C22×C4×C151C2×D411yescharacteristic
233C22×C4×C151C2×D411yescharacteristic
234C22×C4×C151C2411yescharacteristic
235Q16×C151—24no—
236Q16×C151—42no—
237Q16×C151—42no—
238SD16×C151—24no—
239SD16×C151—42no—
240SD16×C151—42no—
241M16×C151—21no—
242M16×C151—21no—
243M16×C151—21no—
244M16×C151—21no—
245M16×C151—21no—
246M16×C151—21no—
247M16×C151—21no—
248M16×C151#4112yes—
249C2×C8×C151—21no—
250C2×C8×C151—21no—
251C2×C8×C151—21no—
252C2×C8×C151—21no—
253C4⋊C4×C151—22no—
254C4⋊C4×C151—22no—
255C4⋊C4×C151—22no—
256C4⋊C4×C151—22no—
257C4⋊C4×C151—22no—
258C4⋊C4×C151—22no—
259C4⋊C4×C151—22no—
260C4⋊C4×C151—22no—
261C4⋊C4×C151—21no—
262C4⋊C4×C151—21no—
263C4⋊C4×C151—21no—
264C4⋊C4×C151—21no—
265C4⋊C4×C151—21no—
266C4⋊C4×C151—21no—
267C4⋊C4×C151—21no—
268C4⋊C4×C151—21no—
269C4⋊C4×C151—21no—
270C4⋊C4×C151—21no—
271C4⋊C4×C151—42no—
272C4⋊C4×C151—44no—
273C4⋊C4×C151—41no—
274C4⋊C4×C151—41no—
275C4⋊C4×C151C2×D411yescharacteristic
276C4⋊C4×C151C2×D411yescharacteristic
277C22⋊C4×C151—22no—
278C22⋊C4×C151—22no—
279C22⋊C4×C151—22no—
280C22⋊C4×C151—22no—
281C22⋊C4×C151—22no—
282C22⋊C4×C151—22no—
283C22⋊C4×C151—21no—
284C22⋊C4×C151—21no—
285C22⋊C4×C151—21no—
286C22⋊C4×C151—21no—
287C22⋊C4×C151—21no—
288C22⋊C4×C151—21no—
289C22⋊C4×C151—21no—
290C42×C151—22no—
291C42×C151—22no—
292C42×C151—21no—
293C42×C151—21no—
294C42×C151—21no—
295C42×C151—21no—
296C42×C151—21no—
297C42×C151—21no—
298C42×C151—21no—
299C42×C151—41no—
300C42×C151—41no—
301C42×C151C2×D411yescharacteristic
302C42×C151C2×D411yescharacteristic
303C42×C151C2×D411yescharacteristic
304C42×C151C2×D411yescharacteristic
305C23×C151—21no—
306C23×C151—21no—
307C23×C151—21no—
308C23×C151C22×D411yescharacteristic
309Q8×C151—22no—
310Q8×C151—21no—
311Q8×C151—21no—
312Q8×C151—22no—
313Q8×C151—21no—
314Q8×C151—21no—
315Q8×C151—21no—
316Q8×C151—21no—
317Q8×C151—41no—
318Q8×C151—41no—
319D4×C151—21no—
320D4×C151—21no—
321D4×C151—21no—
322D4×C151—21no—
323D4×C151—21no—
324D4×C151—21no—
325D4×C151—41no—
326D4×C151—41no—
327D4×C151—41no—
328D4×C151—41no—
329D4×C151—41no—
330D4×C151—41no—
331D4×C151—81no—
332D4×C151—81no—
333D4×C151—82no—
334D4×C151—82no—
335C2×C4×C151—22no—
336C2×C4×C151—21no—
337C2×C4×C151—21no—
338C2×C4×C151—21no—
339C2×C4×C151—21no—
340C2×C4×C151—21no—
341C2×C4×C151—22no—
342C2×C4×C151—22no—
343C2×C4×C151—22no—
344C2×C4×C151—41no—
345C2×C4×C151—41no—
346C2×C4×C151—41no—
347C2×C4×C151—41no—
348C2×C4×C151—41no—
349C2×C4×C151—41no—
350C2×C4×C151—41no—
351C2×C4×C151—41no—
352C2×C4×C151—41no—
353C2×C4×C151—41no—
354C2×C4×C151—41no—
355C2×C4×C151—41no—
356C2×C4×C151—42no—
357C2×C4×C151—42no—
358C2×C4×C151—41no—
359C2×C4×C151—42no—
360C2×C4×C151—41no—
361C2×C4×C151—41no—
362C2×C4×C151—41no—
363C2×C4×C151—81no—
364C2×C4×C151—81no—
365C2×C4×C151—82no—
366C2×C4×C151—82no—
367C2×C4×C151#12011yescharacteristic
368C2×C4×C151#12011yescharacteristic
369C2×C4×C151#12011yescharacteristic
370C2×C4×C151#12011yescharacteristic
371C2×C4×C151C22×D411yescharacteristic
372C2×C4×C151C22×D411yescharacteristic
373C2×C4×C151C2×#4111yescharacteristic
374C2×C4×C151C2×#4111yescharacteristic
375C2×C4×C151H(5,𝔽2)11yescharacteristic
376C2×C4×C1512−1+411yescharacteristic
377C8×C151—22no—
378C8×C151—41no—
379C8×C151—41no—
380C8×C151—41no—
381C22×C151—21no—
382C22×C151—21no—
383C22×C151—41no—
384C22×C151—41no—
385C22×C151—41no—
386C22×C151—41no—
387C22×C151—41no—
388C22×C151—41no—
389C22×C151—41no—
390C22×C151—41no—
391C22×C151—41no—
392C22×C151C2×#12011yescharacteristic
393C22×C151#54811yescharacteristic
394C22×C151#55011yescharacteristic
395C4×C151—21no—
396C4×C151—21no—
397C4×C151—21no—
398C4×C151—21no—
399C4×C151—42no—
400C4×C151—41no—
401C4×C151—41no—
402C4×C151—41no—
403C4×C151—42no—
404C4×C151—42no—
405C4×C151—41no—
406C4×C151—42no—
407C4×C151—41no—
408C4×C151—81no—
409C4×C151—81no—
410C4×C151#52511yescharacteristic
411C4×C151#53711yescharacteristic
412C4×C151#54611yescharacteristic
413C4×C151#54711yescharacteristic
414C2×C151—21no—
415C2×C151—21no—
416C2×C151—81no—
417C2×C151—81no—
418C2×C151—81no—
419C2×C151#240711yescharacteristic
420C2×C151#301811yescharacteristic
421C2×C151#302211yescharacteristic
422#24175C15111yesmaximal, characteristic, direct product factor, Sylow
423C151#2417511yescharacteristic, direct product factor, Sylow
424#3512C2×C15111yescharacteristic
425#3037C2×C15111yescharacteristic, complemented
426C4×#137C2×C15111yescharacteristic, complemented
427#2565C2×C15111yescharacteristic, complemented
428#2040C2×C15111yescharacteristic, complemented
429#2039C2×C15111yescharacteristic, complemented
430#2007C2×C15111yescharacteristic, complemented
431#2007C2×C15111yescharacteristic, complemented
432#1998C2×C15111yescharacteristic, complemented
433#1980C2×C15111yescharacteristic, complemented
434#1882C2×C15111yescharacteristic, complemented
435#1882C2×C15111yescharacteristic, complemented
436#1860C2×C15111yescharacteristic, complemented
437#1859C2×C15111yescharacteristic, complemented
438#1806C2×C15111yescharacteristic, complemented
439C2×#137C22×C15111yescharacteristic
440C2×#137C22×C15111yescharacteristic
441C2×#137C22×C15111yescharacteristic
442#553—21no—
443#553—21no—
444#553—22no—
445#553—22no—
446#552—21no—
447#552—21no—
448#541—21no—
449#540—21no—
450#537C22×C15111yescharacteristic
451#537C22×C15111yescharacteristic
452#532C22×C15111yescharacteristic
453#529—21no—
454#529—21no—
455C2×#125C22×C15111yescharacteristic
456#520C22×C15111yescharacteristic
457#520C22×C15111yescharacteristic
458C4×#41C22×C15111yescharacteristic
459C2×C4×Q8C22×C15111yescharacteristic
460#464—21no—
461#464—21no—
462#462—21no—
463#460—21no—
464#441—21no—
465#440—21no—
466C4×Q16—21no—
467C4×SD16—21no—
468#428C22×C15111yescharacteristic
469#423C22×C15111yescharacteristic
470C2×#104C22×C15111yescharacteristic
471C2×#104C22×C15111yescharacteristic
472C2×#104C22×C15111yescharacteristic
473C2×#104C22×C15111yescharacteristic
474C2×#104C22×C15111yescharacteristic
475C2×#104C22×C15111yescharacteristic
476#419C22×C15111yescharacteristic
477#417C22×C15111yescharacteristic
478#417C22×C15111yescharacteristic
479#417C22×C15111yescharacteristic
480C4×M16C22×C15111yescharacteristic
481#398—22no—
482#391C22×C15111yescharacteristic
483#391C22×C15111yescharacteristic
484#387—22no—
485#384C22×C15111yescharacteristic
486#382C22×C15111yescharacteristic
487C4×C4⋊C4C22×C15111yescharacteristic
488#343C22×C15111yescharacteristic
489#343C22×C15111yescharacteristic
490#343C22×C15111yescharacteristic
491#343C22×C15111yescharacteristic
492#339C22×C15111yescharacteristic
493#339C22×C15111yescharacteristic
494C2×#41C23×C15111yescharacteristic
495C2×#41C23×C15111yescharacteristic
496C2×#41C23×C15111yescharacteristic
497C22×Q8C23×C15111yescharacteristic
498#137—22no—
499#137—22no—
500#137—22no—
501#137—22no—
502#137—41no—
503#137—41no—
504C2×Q16—21no—
505C2×Q16—21no—
506C2×Q16—21no—
507C2×SD16—21no—
508C2×SD16—21no—
509C2×SD16—21no—
510C2×M16C23×C15111yescharacteristic
511C2×M16C23×C15111yescharacteristic
512C2×M16C23×C15111yescharacteristic
513C2×M16C23×C15111yescharacteristic
514C4⋊Q8D4×C15111yescharacteristic
515#127D4×C15111yescharacteristic
516#126—22no—
517#126—22no—
518#126—22no—
519#126—22no—
520#125—22no—
521#125—22no—
522#125—21no—
523#125—21no—
524#125—21no—
525#125—21no—
526#124D4×C15111yescharacteristic
527#124D4×C15111yescharacteristic
528#123—22no—
529#123—22no—
530#123—22no—
531#123—22no—
532C22⋊Q8—21no—
533C22⋊Q8—21no—
534C22⋊Q8—21no—
535C22⋊Q8—21no—
536#121—22no—
537#121—22no—
538#121—21no—
539#121—21no—
540#121—21no—
541#121—21no—
542#121—21no—
543#121—21no—
544#121—22no—
545#121—22no—
546C4×Q8—21no—
547C4×Q8—21no—
548C4×Q8—21no—
549C4×Q8—21no—
550C4×Q8—21no—
551C4×Q8—21no—
552C4×Q8D4×C15111yescharacteristic
553C4×Q8D4×C15111yescharacteristic
554C4×D4—22no—
555C4×D4—22no—
556C4×D4—21no—
557C4×D4—21no—
558C4×D4—21no—
559C4×D4—21no—
560C4×D4—22no—
561C4×D4—22no—
562C4×D4—21no—
563C4×D4—21no—
564C4×D4D4×C15111yescharacteristic
565C4×D4D4×C15111yescharacteristic
566#117—22no—
567#117—22no—
568#117—21no—
569#117—21no—
570#117—21no—
571#117C23×C15111yescharacteristic
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—22no—
577C2×C4⋊C4D4×C15112yes—
578C2×C4⋊C4D4×C15112yes—
579C2×C4⋊C4C23×C15111yescharacteristic
580C2×C4⋊C4C23×C15111yescharacteristic
581C2×C4⋊C4C23×C15111yescharacteristic
582C2×C42—21no—
583C2×C42—21no—
584C2×C42C23×C15111yescharacteristic
585C2×C42C23×C15111yescharacteristic
586C2×C42C23×C15111yescharacteristic
587#107—21no—
588#106—21no—
589C4⋊C8—21no—
590C4⋊C8—21no—
591#104—22no—
592#104—22no—
593#104—41no—
594#104—41no—
595#104—41no—
596#104—41no—
597#103—21no—
598#103—21no—
599#103—21no—
600#103—21no—
601#103—21no—
602#102—21no—
603#102—21no—
604#102—21no—
605#97—21no—
606C4×C8—21no—
607#95—21no—
608#95—22no—
609#95—22no—
610#95—22no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—21no—
619#41—21no—
620#41—21no—
621#41—21no—
622#41—21no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8—21no—
626C2×Q8—21no—
627C2×Q8—21no—
628C2×Q8C2×D4×C15111yescharacteristic
629C2×Q8C2×D4×C15111yescharacteristic
630C2×Q8C2×D4×C15111yescharacteristic
631C2×Q8#41×C15112yes—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—22no—
636C2×D4—22no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4C2×D4×C15111yescharacteristic
640C2×D4C2×D4×C15111yescharacteristic
641C2×D4C2×D4×C15111yescharacteristic
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4C2×D4×C15112yes—
654C22×C4C2×D4×C15112yes—
655C22×C4C2×D4×C15111yescharacteristic
656C22×C4C2×D4×C15111yescharacteristic
657C22×C4C24×C15111yescharacteristic
658Q16—24no—
659Q16—42no—
660Q16—42no—
661SD16—24no—
662SD16—42no—
663SD16—42no—
664M16—21no—
665M16—21no—
666M16—21no—
667M16—21no—
668M16—21no—
669M16—21no—
670M16—21no—
671M16#41×C15112yes—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C4⋊C4—22no—
677C4⋊C4—22no—
678C4⋊C4—22no—
679C4⋊C4—22no—
680C4⋊C4—22no—
681C4⋊C4—22no—
682C4⋊C4—22no—
683C4⋊C4—22no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—42no—
695C4⋊C4—44no—
696C4⋊C4—41no—
697C4⋊C4—41no—
698C4⋊C4C2×D4×C15111yescharacteristic
699C4⋊C4C2×D4×C15111yescharacteristic
700C22⋊C4—22no—
701C22⋊C4—22no—
702C22⋊C4—22no—
703C22⋊C4—22no—
704C22⋊C4—22no—
705C22⋊C4—22no—
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—21no—
709C22⋊C4—21no—
710C22⋊C4—21no—
711C22⋊C4—21no—
712C22⋊C4—21no—
713C42—22no—
714C42—22no—
715C42—21no—
716C42—21no—
717C42—21no—
718C42—21no—
719C42—21no—
720C42—21no—
721C42—21no—
722C42—41no—
723C42—41no—
724C42C2×D4×C15111yescharacteristic
725C42C2×D4×C15111yescharacteristic
726C42C2×D4×C15111yescharacteristic
727C42C2×D4×C15111yescharacteristic
728C23—21no—
729C23—21no—
730C23—21no—
731C23C22×D4×C15111yescharacteristic
732Q8—22no—
733Q8—21no—
734Q8—21no—
735Q8—22no—
736Q8—21no—
737Q8—21no—
738Q8—21no—
739Q8—21no—
740Q8—41no—
741Q8—41no—
742D4—21no—
743D4—21no—
744D4—21no—
745D4—21no—
746D4—21no—
747D4—21no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—41no—
754D4—81no—
755D4—81no—
756D4—82no—
757D4—82no—
758C2×C4—22no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—81no—
787C2×C4—81no—
788C2×C4—82no—
789C2×C4—82no—
790C2×C4#120×C15111yescharacteristic
791C2×C4#120×C15111yescharacteristic
792C2×C4#120×C15111yescharacteristic
793C2×C4#120×C15111yescharacteristic
794C2×C4C22×D4×C15111yescharacteristic
795C2×C4C22×D4×C15111yescharacteristic
796C2×C4C2×#41×C15111yescharacteristic
797C2×C4C2×#41×C15111yescharacteristic
798C2×C4H(5,𝔽2)×C15111yescharacteristic
799C2×C42−1+4×C15111yescharacteristic
800C8—22no—
801C8—41no—
802C8—41no—
803C8—41no—
804C22—21no—
805C22—21no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22C2×#120×C15111yescharacteristic
816C22#548×C15111yescharacteristic
817C22#550×C15111yescharacteristic
818C4—21no—
819C4—21no—
820C4—21no—
821C4—21no—
822C4—42no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4—42no—
827C4—42no—
828C4—41no—
829C4—42no—
830C4—41no—
831C4—81no—
832C4—81no—
833C4#525×C15111yescharacteristic
834C4#537×C15111yescharacteristic
835C4#546×C15111yescharacteristic
836C4#547×C15111yescharacteristic
837C2—21no—
838C2—21no—
839C2—81no—
840C2—81no—
841C2—81no—
842C2#2407×C15111yescharacteristic
843C2#3018×C15111yescharacteristic
844C2#3022×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#3512×C151C2
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. #3037×C151C2semidirect
3. C4×#137×C151C2semidirect
4. #2565×C151C2semidirect
5. #2040×C151C2semidirect
6. #2039×C151C2semidirect
7. #2007×C151C2semidirect
8. #2007×C151C2semidirect
9. #1998×C151C2semidirect
10. #1980×C151C2semidirect
11. #1882×C151C2semidirect
12. #1882×C151C2semidirect
13. #1860×C151C2semidirect
14. #1859×C151C2semidirect
15. #1806×C151C2semidirect
422. #24175C151direct (N × H)
423. C151#24175direct (N × H)
425. #3037C2×C151semidirect
426. C4×#137C2×C151semidirect
427. #2565C2×C151semidirect
428. #2040C2×C151semidirect
429. #2039C2×C151semidirect
430. #2007C2×C151semidirect
431. #2007C2×C151semidirect
432. #1998C2×C151semidirect
433. #1980C2×C151semidirect
434. #1882C2×C151semidirect
435. #1882C2×C151semidirect
436. #1860C2×C151semidirect
437. #1859C2×C151semidirect
438. #1806C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3512×C1512
#3037×C1512
C4×#137×C1512
#2565×C1512
#2040×C1512
#2039×C1512
#2007×C1512
#1998×C1512
#1980×C1512
#1882×C1512
#1860×C1512
#1859×C1512
#1806×C1512
#24175151