Finite Group Databasebeta

← C151×#11113 #50316038

Subgroups — C151×#11113 #50316038

Order 38656.

1006 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#428×C151C211yesmaximal, characteristic, complemented
2C22×#104×C151C211yesmaximal, characteristic
3C2×#417×C151C211yesmaximal, characteristic
4#2311×C151C211yesmaximal, characteristic
5C2×#343×C151C211yesmaximal, characteristic, complemented
6C2×#339×C151C211yesmaximal, characteristic, complemented
7C4⋊#95×C151C211yesmaximal, characteristic, complemented
8C22×#41×C151C2211yescharacteristic
9C22×M16×C151C2211yescharacteristic
10C22×M16×C151C2211yescharacteristic
11C2×#117×C151C2211yescharacteristic
12C22×C4⋊C4×C151C2211yescharacteristic
13C22×C4⋊C4×C151C2211yescharacteristic
14C22×C42×C151C2211yescharacteristic
15#428×C151—22no—
16#428×C151—22no—
17C2×#107×C151—21no—
18C2×#106×C151—21no—
19C2×#104×C151—22no—
20C2×#104×C151—22no—
21C2×#104×C151C414yescomplemented
22#417×C151—22no—
23#417×C151—22no—
24C2×#103×C151—21no—
25C2×#102×C151—21no—
26#391×C151—21no—
27#390×C151—21no—
28#386×C151—22no—
29#380×C151—21no—
30#380×C151—21no—
31C2×#95×C151—22no—
32#343×C151—22no—
33#339×C151—22no—
34C2×#41×C151—21no—
35C2×#41×C151—21no—
36C2×#41×C151—21no—
37C2×#41×C151—21no—
38C2×#41×C151—21no—
39C2×#41×C151—21no—
40C2×#41×C151—21no—
41C2×#41×C151—21no—
42C2×#41×C151—21no—
43C2×#41×C151—21no—
44C2×#41×C151C2×C412yes—
45C2×#41×C151Q812yes—
46C22×Q8×C151D411yescharacteristic
47C22×D4×C151—21no—
48C22×D4×C151D411yescharacteristic
49C23×C4×C151—21no—
50C23×C4×C151—21no—
51C23×C4×C151—21no—
52C23×C4×C151D412yes—
53C23×C4×C151C2311yescharacteristic
54C2×M16×C151—21no—
55C2×M16×C151—21no—
56C2×M16×C151—21no—
57C2×M16×C151—21no—
58C2×M16×C151—21no—
59C2×M16×C151—21no—
60C2×M16×C151—21no—
61C2×M16×C151—21no—
62C2×M16×C151C2×C412yes—
63C2×M16×C151D412yes—
64C2×M16×C151D412yes—
65C2×M16×C151D412yes—
66C22×C8×C151—21no—
67C22×C8×C151—21no—
68#117×C151—21no—
69#117×C151—21no—
70#117×C151—21no—
71#117×C151—21no—
72C2×C4⋊C4×C151—21no—
73C2×C4⋊C4×C151—21no—
74C2×C4⋊C4×C151—21no—
75C2×C4⋊C4×C151—21no—
76C2×C4⋊C4×C151—21no—
77C2×C4⋊C4×C151—21no—
78C2×C4⋊C4×C151—21no—
79C2×C4⋊C4×C151—21no—
80C2×C4⋊C4×C151—21no—
81C2×C4⋊C4×C151—21no—
82C2×C4⋊C4×C151—21no—
83C2×C4⋊C4×C151D411yescharacteristic
84C2×C4⋊C4×C151D411yescharacteristic
85C2×C4⋊C4×C151D412yes—
86C2×C22⋊C4×C151—22no—
87C2×C22⋊C4×C151—22no—
88C2×C22⋊C4×C151—21no—
89C2×C42×C151—21no—
90C2×C42×C151—21no—
91C2×C42×C151—21no—
92C2×C42×C151—21no—
93C2×C42×C151—21no—
94C2×C42×C151—21no—
95C2×C42×C151C2×C412yes—
96#107×C151—24no—
97#106×C151—24no—
98#104×C151—28no—
99#103×C151—24no—
100#102×C151—24no—
101#95×C151—22no—
102#95×C151—22no—
103#95×C151—44no—
104C24×C151—21no—
105C24×C151C2×D411yescharacteristic
106#41×C151—22no—
107#41×C151—22no—
108#41×C151—22no—
109#41×C151—22no—
110#41×C151—22no—
111#41×C151—22no—
112#41×C151—22no—
113#41×C151—22no—
114#41×C151—41no—
115#41×C151—41no—
116#41×C151—41no—
117#41×C151—41no—
118#41×C151—41no—
119#41×C151—41no—
120#41×C151—41no—
121#41×C151—41no—
122C2×Q8×C151—21no—
123C2×Q8×C151—21no—
124C2×Q8×C151—21no—
125C2×Q8×C151—21no—
126C2×Q8×C151—21no—
127C2×Q8×C151C4⋊C412yes—
128C2×D4×C151—22no—
129C2×D4×C151—22no—
130C2×D4×C151—21no—
131C2×D4×C151—21no—
132C2×D4×C151—21no—
133C2×D4×C151—21no—
134C2×D4×C151—21no—
135C2×D4×C151—41no—
136C2×D4×C151—41no—
137C2×D4×C151—41no—
138C2×D4×C151—41no—
139C2×D4×C151C4⋊C412yes—
140C22×C4×C151—22no—
141C22×C4×C151—22no—
142C22×C4×C151—22no—
143C22×C4×C151—21no—
144C22×C4×C151—22no—
145C22×C4×C151—22no—
146C22×C4×C151—21no—
147C22×C4×C151—21no—
148C22×C4×C151—22no—
149C22×C4×C151—22no—
150C22×C4×C151—22no—
151C22×C4×C151—22no—
152C22×C4×C151—41no—
153C22×C4×C151—41no—
154C22×C4×C151—41no—
155C22×C4×C151—41no—
156C22×C4×C151—41no—
157C22×C4×C151—41no—
158C22×C4×C151—41no—
159C22×C4×C151—41no—
160C22×C4×C151—42no—
161C22×C4×C151—42no—
162C22×C4×C151—42no—
163C22×C4×C151—42no—
164C22×C4×C151—41no—
165C22×C4×C151—41no—
166C22×C4×C151C22×C411yescharacteristic
167C22×C4×C151C2×D411yescharacteristic
168C22×C4×C151C2×D411yescharacteristic
169C22×C4×C151C2×D411yescharacteristic
170C22×C4×C151C2×D411yescharacteristic
171C22×C4×C151C2×D411yescharacteristic
172C22×C4×C151C2×D411yescharacteristic
173C22×C4×C151C2×Q811yescharacteristic
174C22×C4×C151#4111yescharacteristic
175C22×C4×C151#4111yescharacteristic
176C22×C4×C151#4111yescharacteristic
177C22×C4×C151#4111yescharacteristic
178C22×C4×C151#4111yescharacteristic
179C22×C4×C151#4111yescharacteristic
180M16×C151—22no—
181M16×C151—22no—
182M16×C151—22no—
183M16×C151—22no—
184M16×C151—22no—
185M16×C151—41no—
186M16×C151—41no—
187M16×C151C22⋊C414yescomplemented
188C2×C8×C151—22no—
189C2×C8×C151—22no—
190C2×C8×C151—22no—
191C2×C8×C151—22no—
192C2×C8×C151—41no—
193C2×C8×C151—41no—
194C4⋊C4×C151—22no—
195C4⋊C4×C151—21no—
196C4⋊C4×C151—22no—
197C4⋊C4×C151—21no—
198C4⋊C4×C151—21no—
199C4⋊C4×C151—21no—
200C4⋊C4×C151—41no—
201C4⋊C4×C151—41no—
202C4⋊C4×C151—41no—
203C4⋊C4×C151—41no—
204C4⋊C4×C151—41no—
205C4⋊C4×C151—41no—
206C22⋊C4×C151—41no—
207C22⋊C4×C151—41no—
208C22⋊C4×C151—82no—
209C22⋊C4×C151—82no—
210C42×C151—22no—
211C42×C151—22no—
212C42×C151—41no—
213C42×C151—41no—
214C42×C151—41no—
215C42×C151—41no—
216C23×C151—21no—
217C23×C151—21no—
218C23×C151—21no—
219C23×C151—21no—
220C23×C151—22no—
221C23×C151—41no—
222C23×C151—41no—
223C23×C151—41no—
224C23×C151—41no—
225C23×C151—41no—
226C23×C151—41no—
227C23×C151C4×D411yescharacteristic
228C23×C151#12011yescharacteristic
229C23×C151#12111yescharacteristic
230C23×C151#12111yescharacteristic
231C23×C151C22⋊Q811yescharacteristic
232C23×C151#12311yescharacteristic
233C23×C151#12711yescharacteristic
234Q8×C151—22no—
235Q8×C151—22no—
236Q8×C151—41no—
237Q8×C151—41no—
238D4×C151—22no—
239D4×C151—22no—
240D4×C151—42no—
241D4×C151—42no—
242D4×C151—42no—
243D4×C151—42no—
244D4×C151—41no—
245D4×C151—41no—
246C2×C4×C151—24no—
247C2×C4×C151—22no—
248C2×C4×C151—42no—
249C2×C4×C151—42no—
250C2×C4×C151—42no—
251C2×C4×C151—42no—
252C2×C4×C151—42no—
253C2×C4×C151—42no—
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—44no—
261C2×C4×C151—44no—
262C2×C4×C151—41no—
263C2×C4×C151—41no—
264C2×C4×C151—42no—
265C2×C4×C151—42no—
266C2×C4×C151—41no—
267C2×C4×C151—42no—
268C2×C4×C151—41no—
269C2×C4×C151—41no—
270C2×C4×C151—42no—
271C2×C4×C151—41no—
272C2×C4×C151—82no—
273C2×C4×C151—81no—
274C2×C4×C151—81no—
275C2×C4×C151—82no—
276C2×C4×C151C2×C22⋊C411yescharacteristic
277C2×C4×C151C2×C4⋊C411yescharacteristic
278C2×C4×C151#11711yescharacteristic
279C2×C4×C151C4×D411yescharacteristic
280C2×C4×C151C4×D411yescharacteristic
281C2×C4×C151C4×D411yescharacteristic
282C2×C4×C151#12011yescharacteristic
283C2×C4×C151#12011yescharacteristic
284C2×C4×C151#12111yescharacteristic
285C2×C4×C151#12111yescharacteristic
286C2×C4×C151#12111yescharacteristic
287C2×C4×C151#12111yescharacteristic
288C2×C4×C151#12111yescharacteristic
289C2×C4×C151#12111yescharacteristic
290C2×C4×C151C22⋊Q811yescharacteristic
291C2×C4×C151C22⋊Q811yescharacteristic
292C2×C4×C151C22⋊Q811yescharacteristic
293C2×C4×C151C22⋊Q811yescharacteristic
294C2×C4×C151C22⋊Q811yescharacteristic
295C2×C4×C151#12311yescharacteristic
296C2×C4×C151#12311yescharacteristic
297C2×C4×C151#12311yescharacteristic
298C2×C4×C151#12311yescharacteristic
299C2×C4×C151#12411yescharacteristic
300C2×C4×C151#12411yescharacteristic
301C2×C4×C151#12411yescharacteristic
302C2×C4×C151#12611yescharacteristic
303C2×C4×C151#12611yescharacteristic
304C8×C151—24no—
305C8×C151—42no—
306C22×C151—21no—
307C22×C151—21no—
308C22×C151—21no—
309C22×C151—21no—
310C22×C151—21no—
311C22×C151—21no—
312C22×C151—21no—
313C22×C151—21no—
314C22×C151—21no—
315C22×C151—21no—
316C22×C151—21no—
317C22×C151—21no—
318C22×C151—42no—
319C22×C151—42no—
320C22×C151—42no—
321C22×C151—81no—
322C22×C151—81no—
323C22×C151—81no—
324C22×C151—81no—
325C22×C151#38511yescharacteristic
326C22×C151#38811yescharacteristic
327C22×C151#39011yescharacteristic
328C22×C151#39211yescharacteristic
329C22×C151#39411yescharacteristic
330C22×C151#39611yescharacteristic
331C22×C151#39911yescharacteristic
332C22×C151#45311yescharacteristic
333C22×C151#45411yescharacteristic
334C22×C151#45511yescharacteristic
335C22×C151#45611yescharacteristic
336C4×C151—44no—
337C4×C151—42no—
338C4×C151—81no—
339C4×C151—82no—
340C4×C151—81no—
341C4×C151—82no—
342C4×C151#38011yescharacteristic
343C4×C151#38511yescharacteristic
344C4×C151#38611yescharacteristic
345C4×C151#38811yescharacteristic
346C4×C151#39311yescharacteristic
347C4×C151#39411yescharacteristic
348C4×C151#39611yescharacteristic
349C4×C151#39711yescharacteristic
350C2×C151—21no—
351C2×C151—21no—
352C2×C151—21no—
353C2×C151—21no—
354C2×C151—82no—
355C2×C151#143911yescharacteristic
356C2×C151#185911yescharacteristic
357C2×C151#186011yescharacteristic
358C2×C151#200611yescharacteristic
359C2×C151#200711yescharacteristic
360C2×C151#203711yescharacteristic
361C2×C151#203811yescharacteristic
362#11113C15111yesmaximal, characteristic, direct product factor, Sylow
363C151#1111311yescharacteristic, direct product factor, Sylow
364C2×#428C2×C15111yescharacteristic, complemented
365C22×#104C2×C15111yescharacteristic
366C2×#417C2×C15111yescharacteristic
367#2311C2×C15111yescharacteristic
368C2×#343C2×C15111yescharacteristic, complemented
369C2×#339C2×C15111yescharacteristic, complemented
370C4⋊#95C2×C15111yescharacteristic, complemented
371C22×#41C22×C15111yescharacteristic
372C22×M16C22×C15111yescharacteristic
373C22×M16C22×C15111yescharacteristic
374C2×#117C22×C15111yescharacteristic
375C22×C4⋊C4C22×C15111yescharacteristic
376C22×C4⋊C4C22×C15111yescharacteristic
377C22×C42C22×C15111yescharacteristic
378#428—22no—
379#428—22no—
380C2×#107—21no—
381C2×#106—21no—
382C2×#104—22no—
383C2×#104—22no—
384C2×#104C4×C15114yescomplemented
385#417—22no—
386#417—22no—
387C2×#103—21no—
388C2×#102—21no—
389#391—21no—
390#390—21no—
391#386—22no—
392#380—21no—
393#380—21no—
394C2×#95—22no—
395#343—22no—
396#339—22no—
397C2×#41—21no—
398C2×#41—21no—
399C2×#41—21no—
400C2×#41—21no—
401C2×#41—21no—
402C2×#41—21no—
403C2×#41—21no—
404C2×#41—21no—
405C2×#41—21no—
406C2×#41—21no—
407C2×#41C2×C4×C15112yes—
408C2×#41Q8×C15112yes—
409C22×Q8D4×C15111yescharacteristic
410C22×D4—21no—
411C22×D4D4×C15111yescharacteristic
412C23×C4—21no—
413C23×C4—21no—
414C23×C4—21no—
415C23×C4D4×C15112yes—
416C23×C4C23×C15111yescharacteristic
417C2×M16—21no—
418C2×M16—21no—
419C2×M16—21no—
420C2×M16—21no—
421C2×M16—21no—
422C2×M16—21no—
423C2×M16—21no—
424C2×M16—21no—
425C2×M16C2×C4×C15112yes—
426C2×M16D4×C15112yes—
427C2×M16D4×C15112yes—
428C2×M16D4×C15112yes—
429C22×C8—21no—
430C22×C8—21no—
431#117—21no—
432#117—21no—
433#117—21no—
434#117—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4D4×C15112yes—
447C2×C4⋊C4D4×C15111yescharacteristic
448C2×C4⋊C4D4×C15111yescharacteristic
449C2×C22⋊C4—21no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—22no—
452C2×C42—21no—
453C2×C42—21no—
454C2×C42—21no—
455C2×C42—21no—
456C2×C42—21no—
457C2×C42—21no—
458C2×C42C2×C4×C15112yes—
459#107—24no—
460#106—24no—
461#104—28no—
462#103—24no—
463#102—24no—
464#95—22no—
465#95—22no—
466#95—44no—
467C24—21no—
468C24C2×D4×C15111yescharacteristic
469#41—22no—
470#41—22no—
471#41—22no—
472#41—22no—
473#41—22no—
474#41—22no—
475#41—22no—
476#41—22no—
477#41—41no—
478#41—41no—
479#41—41no—
480#41—41no—
481#41—41no—
482#41—41no—
483#41—41no—
484#41—41no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8C4⋊C4×C15112yes—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—41no—
499C2×D4—41no—
500C2×D4—41no—
501C2×D4—41no—
502C2×D4C4⋊C4×C15112yes—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4C22×C4×C15111yescharacteristic
530C22×C4C2×D4×C15111yescharacteristic
531C22×C4C2×D4×C15111yescharacteristic
532C22×C4C2×D4×C15111yescharacteristic
533C22×C4C2×D4×C15111yescharacteristic
534C22×C4C2×D4×C15111yescharacteristic
535C22×C4C2×D4×C15111yescharacteristic
536C22×C4C2×Q8×C15111yescharacteristic
537C22×C4#41×C15111yescharacteristic
538C22×C4#41×C15111yescharacteristic
539C22×C4#41×C15111yescharacteristic
540C22×C4#41×C15111yescharacteristic
541C22×C4#41×C15111yescharacteristic
542C22×C4#41×C15111yescharacteristic
543M16—22no—
544M16—22no—
545M16—22no—
546M16—22no—
547M16—22no—
548M16—41no—
549M16—41no—
550M16C22⋊C4×C15114yescomplemented
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—22no—
555C2×C8—41no—
556C2×C8—41no—
557C4⋊C4—22no—
558C4⋊C4—21no—
559C4⋊C4—22no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—41no—
564C4⋊C4—41no—
565C4⋊C4—41no—
566C4⋊C4—41no—
567C4⋊C4—41no—
568C4⋊C4—41no—
569C22⋊C4—41no—
570C22⋊C4—41no—
571C22⋊C4—82no—
572C22⋊C4—82no—
573C42—22no—
574C42—22no—
575C42—41no—
576C42—41no—
577C42—41no—
578C42—41no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—22no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23C4×D4×C15111yescharacteristic
591C23#120×C15111yescharacteristic
592C23#121×C15111yescharacteristic
593C23#121×C15111yescharacteristic
594C23C22⋊Q8×C15111yescharacteristic
595C23#123×C15111yescharacteristic
596C23#127×C15111yescharacteristic
597Q8—22no—
598Q8—22no—
599Q8—41no—
600Q8—41no—
601D4—22no—
602D4—22no—
603D4—42no—
604D4—42no—
605D4—42no—
606D4—42no—
607D4—41no—
608D4—41no—
609C2×C4—24no—
610C2×C4—22no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—44no—
624C2×C4—44no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—41no—
630C2×C4—42no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—42no—
634C2×C4—41no—
635C2×C4—82no—
636C2×C4—81no—
637C2×C4—81no—
638C2×C4—82no—
639C2×C4C2×C22⋊C4×C15111yescharacteristic
640C2×C4C2×C4⋊C4×C15111yescharacteristic
641C2×C4#117×C15111yescharacteristic
642C2×C4C4×D4×C15111yescharacteristic
643C2×C4C4×D4×C15111yescharacteristic
644C2×C4C4×D4×C15111yescharacteristic
645C2×C4#120×C15111yescharacteristic
646C2×C4#120×C15111yescharacteristic
647C2×C4#121×C15111yescharacteristic
648C2×C4#121×C15111yescharacteristic
649C2×C4#121×C15111yescharacteristic
650C2×C4#121×C15111yescharacteristic
651C2×C4#121×C15111yescharacteristic
652C2×C4#121×C15111yescharacteristic
653C2×C4C22⋊Q8×C15111yescharacteristic
654C2×C4C22⋊Q8×C15111yescharacteristic
655C2×C4C22⋊Q8×C15111yescharacteristic
656C2×C4C22⋊Q8×C15111yescharacteristic
657C2×C4C22⋊Q8×C15111yescharacteristic
658C2×C4#123×C15111yescharacteristic
659C2×C4#123×C15111yescharacteristic
660C2×C4#123×C15111yescharacteristic
661C2×C4#123×C15111yescharacteristic
662C2×C4#124×C15111yescharacteristic
663C2×C4#124×C15111yescharacteristic
664C2×C4#124×C15111yescharacteristic
665C2×C4#126×C15111yescharacteristic
666C2×C4#126×C15111yescharacteristic
667C8—24no—
668C8—42no—
669C22—21no—
670C22—21no—
671C22—21no—
672C22—21no—
673C22—21no—
674C22—21no—
675C22—21no—
676C22—21no—
677C22—21no—
678C22—21no—
679C22—21no—
680C22—21no—
681C22—42no—
682C22—42no—
683C22—42no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22#385×C15111yescharacteristic
689C22#388×C15111yescharacteristic
690C22#390×C15111yescharacteristic
691C22#392×C15111yescharacteristic
692C22#394×C15111yescharacteristic
693C22#396×C15111yescharacteristic
694C22#399×C15111yescharacteristic
695C22#453×C15111yescharacteristic
696C22#454×C15111yescharacteristic
697C22#455×C15111yescharacteristic
698C22#456×C15111yescharacteristic
699C4—44no—
700C4—42no—
701C4—82no—
702C4—81no—
703C4—81no—
704C4—82no—
705C4#380×C15111yescharacteristic
706C4#385×C15111yescharacteristic
707C4#386×C15111yescharacteristic
708C4#388×C15111yescharacteristic
709C4#393×C15111yescharacteristic
710C4#394×C15111yescharacteristic
711C4#396×C15111yescharacteristic
712C4#397×C15111yescharacteristic
713C2—21no—
714C2—21no—
715C2—21no—
716C2—21no—
717C2—82no—
718C2#1439×C15111yescharacteristic
719C2#1859×C15111yescharacteristic
720C2#1860×C15111yescharacteristic
721C2#2006×C15111yescharacteristic
722C2#2007×C15111yescharacteristic
723C2#2037×C15111yescharacteristic
724C2#2038×C15111yescharacteristic
subgroupG/H
center, socleC23×C151#120
commutatorC22×C4C22×C4×C151
Frattini, cosocleC23×C4C23×C151
prime radicalC22×#41×C151C22
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
1. C2×#428×C151C2semidirect
5. C2×#343×C151C2semidirect
6. C2×#339×C151C2semidirect
7. C4⋊#95×C151C2semidirect
21. C2×#104×C151C4semidirect
187. M16×C151C22⋊C4semidirect
362. #11113C151direct (N × H)
363. C151#11113direct (N × H)
364. C2×#428C2×C151semidirect
368. C2×#343C2×C151semidirect
369. C2×#339C2×C151semidirect
370. C4⋊#95C2×C151semidirect
384. C2×#104C4×C151semidirect
550. M16C22⋊C4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#428×C1512
C22×#104×C1512
C2×#417×C1512
#2311×C1512
C2×#343×C1512
C2×#339×C1512
C4⋊#95×C1512
#11113151