Finite Group Databasebeta

← C2×#2049×C151 #50328449

Subgroups — C2×#2049×C151 #50328449

Order 38656.

1322 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#137×C151C211yesmaximal, characteristic
2C2×#430×C151C211yesmaximal, characteristic, complemented
3C2×#421×C151C211yesmaximal, characteristic
4C2×#419×C151C211yesmaximal, characteristic, complemented
5C2×#413×C151C211yesmaximal, characteristic
6C22×#101×C151C211yesmaximal, characteristic, complemented
7#2049×C151C218yesmaximal, direct product factor
8C2×#344×C151C211yesmaximal, characteristic, complemented
9C22×#41×C151C2211yescharacteristic
10C23×Q8×C151C2211yescharacteristic
11C2×#137×C151—22no—
12C2×#137×C151—22no—
13C2×#137×C151—22no—
14C2×#137×C151—22no—
15C2×#137×C151—22no—
16C2×#137×C151C2214yes—
17C22×Q16×C151—21no—
18C22×SD16×C151—21no—
19C22×M16×C151C2211yescharacteristic
20C22×M16×C151C2211yescharacteristic
21C22×M16×C151C2211yescharacteristic
22C22×M16×C151C2211yescharacteristic
23C2×#117×C151C2211yescharacteristic
24#430×C151—22no—
25#430×C151C2214yescomplemented
26C2×#108×C151—22no—
27#421×C151—22no—
28#421×C151C2214yes—
29C2×#104×C151—22no—
30#419×C151—22no—
31#419×C151C2214yescomplemented
32C2×#103×C151—22no—
33#413×C151—22no—
34#413×C151C2214yes—
35C2×#101×C151—21no—
36C2×#101×C151—22no—
37C2×#101×C151—22no—
38C2×#101×C151C2214yescomplemented
39C2×#100×C151—21no—
40#344×C151C2214yescomplemented
41C2×#41×C151—21no—
42C2×#41×C151—21no—
43C2×#41×C151—21no—
44C2×#41×C151—21no—
45C2×#41×C151—21no—
46C2×#41×C151—21no—
47C2×#41×C151—21no—
48C2×#41×C151—21no—
49C2×#41×C151—21no—
50C2×#41×C151—21no—
51C2×#41×C151D412yes—
52C2×#41×C151C2312yes—
53C22×Q8×C151—21no—
54C22×Q8×C151—21no—
55C22×Q8×C151—21no—
56C22×Q8×C151—21no—
57C22×Q8×C151—21no—
58C22×Q8×C151—21no—
59C22×Q8×C151—21no—
60C22×Q8×C151—21no—
61C22×Q8×C151—21no—
62C22×Q8×C151—21no—
63C22×Q8×C151—21no—
64C22×Q8×C151D411yescharacteristic
65C22×Q8×C151D412yes—
66C22×Q8×C151D412yes—
67C22×Q8×C151C2312yes—
68C22×D4×C151—21no—
69C22×D4×C151D411yescharacteristic
70C23×C4×C151—21no—
71C23×C4×C151—21no—
72C23×C4×C151C2311yescharacteristic
73#137×C151—28no—
74#137×C151—28no—
75#137×C151—28no—
76#137×C151—28no—
77C2×Q16×C151—24no—
78C2×Q16×C151—24no—
79C2×Q16×C151—24no—
80C2×SD16×C151—24no—
81C2×SD16×C151—24no—
82C2×SD16×C151—24no—
83C2×M16×C151—21no—
84C2×M16×C151—21no—
85C2×M16×C151—21no—
86C2×M16×C151—21no—
87C2×M16×C151—21no—
88C2×M16×C151—21no—
89C2×M16×C151—21no—
90C2×M16×C151—21no—
91C2×M16×C151—21no—
92C2×M16×C151—21no—
93C2×M16×C151—21no—
94C2×M16×C151—21no—
95C2×M16×C151—21no—
96C2×M16×C151—21no—
97C2×M16×C151—21no—
98C2×M16×C151—21no—
99C2×M16×C151D412yes—
100C2×M16×C151D412yes—
101C2×M16×C151D412yes—
102C2×M16×C151D412yes—
103C2×M16×C151C2312yes—
104C2×M16×C151C2312yes—
105C2×M16×C151C2312yes—
106C2×M16×C151C2312yes—
107C22×C8×C151—21no—
108C22×C8×C151—21no—
109C22×C8×C151—21no—
110C22×C8×C151—21no—
111#117×C151—21no—
112#117×C151—21no—
113#117×C151—21no—
114#117×C151C2312yes—
115C2×C4⋊C4×C151—21no—
116C2×C22⋊C4×C151—21no—
117C2×C42×C151—21no—
118#108×C151—28no—
119#104×C151—28no—
120#103×C151—28no—
121#101×C151—28no—
122#101×C151—24no—
123#100×C151—24no—
124C24×C151—21no—
125C24×C151#4111yescharacteristic
126#41×C151—22no—
127#41×C151—22no—
128#41×C151—22no—
129#41×C151—22no—
130#41×C151—22no—
131#41×C151—22no—
132#41×C151—22no—
133#41×C151—22no—
134#41×C151—41no—
135#41×C151—41no—
136#41×C151—41no—
137#41×C151—41no—
138#41×C151—41no—
139#41×C151—41no—
140#41×C151—41no—
141#41×C151—41no—
142C2×Q8×C151—22no—
143C2×Q8×C151—22no—
144C2×Q8×C151—21no—
145C2×Q8×C151—22no—
146C2×Q8×C151—22no—
147C2×Q8×C151—22no—
148C2×Q8×C151—21no—
149C2×Q8×C151—21no—
150C2×Q8×C151—22no—
151C2×Q8×C151—22no—
152C2×Q8×C151—21no—
153C2×Q8×C151—21no—
154C2×Q8×C151—22no—
155C2×Q8×C151—22no—
156C2×Q8×C151—22no—
157C2×Q8×C151—22no—
158C2×Q8×C151—22no—
159C2×Q8×C151—22no—
160C2×Q8×C151—22no—
161C2×Q8×C151—22no—
162C2×Q8×C151—41no—
163C2×Q8×C151—41no—
164C2×Q8×C151—41no—
165C2×Q8×C151—41no—
166C2×Q8×C151—41no—
167C2×Q8×C151—41no—
168C2×Q8×C151—41no—
169C2×Q8×C151—41no—
170C2×Q8×C151—41no—
171C2×Q8×C151—41no—
172C2×Q8×C151—41no—
173C2×Q8×C151—41no—
174C2×Q8×C151C2×D412yes—
175C2×Q8×C151C2×D414yes—
176C2×D4×C151—22no—
177C2×D4×C151—22no—
178C2×D4×C151—21no—
179C2×D4×C151—21no—
180C2×D4×C151—21no—
181C2×D4×C151—21no—
182C2×D4×C151—21no—
183C2×D4×C151—41no—
184C2×D4×C151—41no—
185C2×D4×C151—41no—
186C2×D4×C151—41no—
187C2×D4×C151C2×D412yes—
188C22×C4×C151—22no—
189C22×C4×C151—22no—
190C22×C4×C151—21no—
191C22×C4×C151—22no—
192C22×C4×C151—22no—
193C22×C4×C151—22no—
194C22×C4×C151—41no—
195C22×C4×C151—41no—
196C22×C4×C151—41no—
197C22×C4×C151—41no—
198C22×C4×C151—41no—
199C22×C4×C151—41no—
200C22×C4×C151—41no—
201C22×C4×C151—41no—
202C22×C4×C151—41no—
203C22×C4×C151C2×D411yescharacteristic
204C22×C4×C151C2×D411yescharacteristic
205C22×C4×C151C2×D411yescharacteristic
206C22×C4×C151C2×D411yescharacteristic
207C22×C4×C151C2×D411yescharacteristic
208C22×C4×C151C2×D411yescharacteristic
209C22×C4×C151C2×D411yescharacteristic
210C22×C4×C151C2×D411yescharacteristic
211C22×C4×C151#4111yescharacteristic
212C22×C4×C151#4111yescharacteristic
213C22×C4×C151#4111yescharacteristic
214C22×C4×C151#4111yescharacteristic
215C22×C4×C151#4111yescharacteristic
216C22×C4×C151C2411yescharacteristic
217Q16×C151—216no—
218SD16×C151—216no—
219M16×C151—22no—
220M16×C151—22no—
221M16×C151—22no—
222M16×C151—22no—
223M16×C151—22no—
224M16×C151—22no—
225M16×C151—22no—
226M16×C151—22no—
227M16×C151—22no—
228M16×C151—22no—
229M16×C151—41no—
230M16×C151—41no—
231M16×C151—41no—
232M16×C151—41no—
233M16×C151C2×D414yes—
234M16×C151C2×D414yes—
235C2×C8×C151—22no—
236C2×C8×C151—22no—
237C2×C8×C151—22no—
238C2×C8×C151—22no—
239C2×C8×C151—22no—
240C2×C8×C151—22no—
241C2×C8×C151—22no—
242C2×C8×C151—22no—
243C2×C8×C151—41no—
244C2×C8×C151—41no—
245C2×C8×C151—41no—
246C2×C8×C151—41no—
247C4⋊C4×C151—22no—
248C4⋊C4×C151—41no—
249C22⋊C4×C151—22no—
250C22⋊C4×C151—41no—
251C42×C151—22no—
252C42×C151—41no—
253C23×C151—22no—
254C23×C151—42no—
255C23×C151—41no—
256C23×C151—41no—
257C23×C151—82no—
258C23×C151#12111yescharacteristic
259C23×C151#12111yescharacteristic
260C23×C151#12311yescharacteristic
261C23×C151#12311yescharacteristic
262C23×C151#12411yescharacteristic
263C23×C151#12411yescharacteristic
264C23×C151C2×#4111yescharacteristic
265Q8×C151—24no—
266Q8×C151—22no—
267Q8×C151—22no—
268Q8×C151—24no—
269Q8×C151—42no—
270Q8×C151—42no—
271Q8×C151—42no—
272Q8×C151—42no—
273Q8×C151—42no—
274Q8×C151—42no—
275Q8×C151—41no—
276Q8×C151—41no—
277D4×C151—22no—
278D4×C151—22no—
279D4×C151—42no—
280D4×C151—42no—
281D4×C151—42no—
282D4×C151—42no—
283D4×C151—41no—
284D4×C151—41no—
285C2×C4×C151—24no—
286C2×C4×C151—22no—
287C2×C4×C151—42no—
288C2×C4×C151—42no—
289C2×C4×C151—42no—
290C2×C4×C151—42no—
291C2×C4×C151—42no—
292C2×C4×C151—41no—
293C2×C4×C151—42no—
294C2×C4×C151—41no—
295C2×C4×C151—42no—
296C2×C4×C151—42no—
297C2×C4×C151—42no—
298C2×C4×C151—42no—
299C2×C4×C151—42no—
300C2×C4×C151—82no—
301C2×C4×C151#12011yescharacteristic
302C2×C4×C151#12011yescharacteristic
303C2×C4×C151#12011yescharacteristic
304C2×C4×C151#12011yescharacteristic
305C2×C4×C151#12111yescharacteristic
306C2×C4×C151#12111yescharacteristic
307C2×C4×C151#12111yescharacteristic
308C2×C4×C151#12111yescharacteristic
309C2×C4×C151#12111yescharacteristic
310C2×C4×C151#12111yescharacteristic
311C2×C4×C151#12111yescharacteristic
312C2×C4×C151#12111yescharacteristic
313C2×C4×C151#12111yescharacteristic
314C2×C4×C151#12111yescharacteristic
315C2×C4×C151#12311yescharacteristic
316C2×C4×C151#12311yescharacteristic
317C2×C4×C151#12311yescharacteristic
318C2×C4×C151#12311yescharacteristic
319C2×C4×C151#12311yescharacteristic
320C2×C4×C151#12311yescharacteristic
321C2×C4×C151#12411yescharacteristic
322C2×C4×C151#12411yescharacteristic
323C2×C4×C151C22×D411yescharacteristic
324C2×C4×C151C22×D411yescharacteristic
325C2×C4×C151C22×D411yescharacteristic
326C2×C4×C151C22×D411yescharacteristic
327C2×C4×C151C2×#4111yescharacteristic
328C2×C4×C151C2×#4111yescharacteristic
329C8×C151—24no—
330C8×C151—24no—
331C8×C151—42no—
332C8×C151—42no—
333C22×C151—22no—
334C22×C151—22no—
335C22×C151—22no—
336C22×C151—41no—
337C22×C151—41no—
338C22×C151—41no—
339C22×C151—41no—
340C22×C151—42no—
341C22×C151—82no—
342C22×C151—82no—
343C22×C151—82no—
344C22×C151#39411yescharacteristic
345C22×C151#39411yescharacteristic
346C22×C151#39411yescharacteristic
347C22×C151#39411yescharacteristic
348C22×C151C2×#12111yescharacteristic
349C22×C151C2×#12311yescharacteristic
350C22×C151C2×#12411yescharacteristic
351C4×C151—42no—
352C4×C151—44no—
353C4×C151—82no—
354C4×C151#39411yescharacteristic
355C4×C151#39411yescharacteristic
356C4×C151#39411yescharacteristic
357C4×C151#39411yescharacteristic
358C4×C151C2×#12011yescharacteristic
359C4×C151C2×#12111yescharacteristic
360C4×C151C2×#12111yescharacteristic
361C4×C151C2×#12311yescharacteristic
362C2×C151—21no—
363C2×C151—21no—
364C2×C151—21no—
365C2×C151—21no—
366C2×C151—21no—
367C2×C151—21no—
368C2×C151—82no—
369C2×C151#204912yesdirect product factor
370C2×C151C2×#39411yescharacteristic
371C2×#2049C15111yesmaximal, characteristic, direct product factor, Sylow
372C151C2×#204911yescharacteristic, direct product factor, Sylow
373C22×#137C2×C15111yescharacteristic
374C2×#430C2×C15111yescharacteristic, complemented
375C2×#421C2×C15111yescharacteristic
376C2×#419C2×C15111yescharacteristic, complemented
377C2×#413C2×C15111yescharacteristic
378C22×#101C2×C15111yescharacteristic, complemented
379#2049C2×C15118yesdirect product factor
380C2×#344C2×C15111yescharacteristic, complemented
381C22×#41C22×C15111yescharacteristic
382C23×Q8C22×C15111yescharacteristic
383C2×#137—22no—
384C2×#137—22no—
385C2×#137—22no—
386C2×#137—22no—
387C2×#137—22no—
388C2×#137C22×C15114yes—
389C22×Q16—21no—
390C22×SD16—21no—
391C22×M16C22×C15111yescharacteristic
392C22×M16C22×C15111yescharacteristic
393C22×M16C22×C15111yescharacteristic
394C22×M16C22×C15111yescharacteristic
395C2×#117C22×C15111yescharacteristic
396#430—22no—
397#430C22×C15114yescomplemented
398C2×#108—22no—
399#421—22no—
400#421C22×C15114yes—
401C2×#104—22no—
402#419—22no—
403#419C22×C15114yescomplemented
404C2×#103—22no—
405#413—22no—
406#413C22×C15114yes—
407C2×#101—21no—
408C2×#101—22no—
409C2×#101—22no—
410C2×#101C22×C15114yescomplemented
411C2×#100—21no—
412#344C22×C15114yescomplemented
413C2×#41—21no—
414C2×#41—21no—
415C2×#41—21no—
416C2×#41—21no—
417C2×#41—21no—
418C2×#41—21no—
419C2×#41—21no—
420C2×#41—21no—
421C2×#41—21no—
422C2×#41—21no—
423C2×#41D4×C15112yes—
424C2×#41C23×C15112yes—
425C22×Q8—21no—
426C22×Q8—21no—
427C22×Q8—21no—
428C22×Q8—21no—
429C22×Q8—21no—
430C22×Q8—21no—
431C22×Q8—21no—
432C22×Q8—21no—
433C22×Q8—21no—
434C22×Q8—21no—
435C22×Q8—21no—
436C22×Q8D4×C15111yescharacteristic
437C22×Q8D4×C15112yes—
438C22×Q8D4×C15112yes—
439C22×Q8C23×C15112yes—
440C22×D4—21no—
441C22×D4D4×C15111yescharacteristic
442C23×C4—21no—
443C23×C4—21no—
444C23×C4C23×C15111yescharacteristic
445#137—28no—
446#137—28no—
447#137—28no—
448#137—28no—
449C2×Q16—24no—
450C2×Q16—24no—
451C2×Q16—24no—
452C2×SD16—24no—
453C2×SD16—24no—
454C2×SD16—24no—
455C2×M16—21no—
456C2×M16—21no—
457C2×M16—21no—
458C2×M16—21no—
459C2×M16—21no—
460C2×M16—21no—
461C2×M16—21no—
462C2×M16—21no—
463C2×M16—21no—
464C2×M16—21no—
465C2×M16—21no—
466C2×M16—21no—
467C2×M16—21no—
468C2×M16—21no—
469C2×M16—21no—
470C2×M16—21no—
471C2×M16D4×C15112yes—
472C2×M16D4×C15112yes—
473C2×M16D4×C15112yes—
474C2×M16D4×C15112yes—
475C2×M16C23×C15112yes—
476C2×M16C23×C15112yes—
477C2×M16C23×C15112yes—
478C2×M16C23×C15112yes—
479C22×C8—21no—
480C22×C8—21no—
481C22×C8—21no—
482C22×C8—21no—
483#117—21no—
484#117—21no—
485#117—21no—
486#117C23×C15112yes—
487C2×C4⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C42—21no—
490#108—28no—
491#104—28no—
492#103—28no—
493#101—24no—
494#101—28no—
495#100—24no—
496C24—21no—
497C24#41×C15111yescharacteristic
498#41—22no—
499#41—22no—
500#41—22no—
501#41—22no—
502#41—22no—
503#41—22no—
504#41—22no—
505#41—22no—
506#41—41no—
507#41—41no—
508#41—41no—
509#41—41no—
510#41—41no—
511#41—41no—
512#41—41no—
513#41—41no—
514C2×Q8—22no—
515C2×Q8—22no—
516C2×Q8—21no—
517C2×Q8—22no—
518C2×Q8—22no—
519C2×Q8—22no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—22no—
523C2×Q8—22no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—22no—
527C2×Q8—22no—
528C2×Q8—22no—
529C2×Q8—22no—
530C2×Q8—22no—
531C2×Q8—22no—
532C2×Q8—22no—
533C2×Q8—22no—
534C2×Q8—41no—
535C2×Q8—41no—
536C2×Q8—41no—
537C2×Q8—41no—
538C2×Q8—41no—
539C2×Q8—41no—
540C2×Q8—41no—
541C2×Q8—41no—
542C2×Q8—41no—
543C2×Q8—41no—
544C2×Q8—41no—
545C2×Q8—41no—
546C2×Q8C2×D4×C15112yes—
547C2×Q8C2×D4×C15114yes—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—41no—
556C2×D4—41no—
557C2×D4—41no—
558C2×D4—41no—
559C2×D4C2×D4×C15112yes—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4C2×D4×C15111yescharacteristic
576C22×C4C2×D4×C15111yescharacteristic
577C22×C4C2×D4×C15111yescharacteristic
578C22×C4C2×D4×C15111yescharacteristic
579C22×C4C2×D4×C15111yescharacteristic
580C22×C4C2×D4×C15111yescharacteristic
581C22×C4C2×D4×C15111yescharacteristic
582C22×C4C2×D4×C15111yescharacteristic
583C22×C4#41×C15111yescharacteristic
584C22×C4#41×C15111yescharacteristic
585C22×C4#41×C15111yescharacteristic
586C22×C4#41×C15111yescharacteristic
587C22×C4#41×C15111yescharacteristic
588C22×C4C24×C15111yescharacteristic
589Q16—216no—
590SD16—216no—
591M16—22no—
592M16—22no—
593M16—22no—
594M16—22no—
595M16—22no—
596M16—22no—
597M16—22no—
598M16—22no—
599M16—22no—
600M16—22no—
601M16—41no—
602M16—41no—
603M16—41no—
604M16—41no—
605M16C2×D4×C15114yes—
606M16C2×D4×C15114yes—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—41no—
616C2×C8—41no—
617C2×C8—41no—
618C2×C8—41no—
619C4⋊C4—22no—
620C4⋊C4—41no—
621C22⋊C4—22no—
622C22⋊C4—41no—
623C42—22no—
624C42—41no—
625C23—22no—
626C23—42no—
627C23—41no—
628C23—41no—
629C23—82no—
630C23#121×C15111yescharacteristic
631C23#121×C15111yescharacteristic
632C23#123×C15111yescharacteristic
633C23#123×C15111yescharacteristic
634C23#124×C15111yescharacteristic
635C23#124×C15111yescharacteristic
636C23C2×#41×C15111yescharacteristic
637Q8—24no—
638Q8—22no—
639Q8—22no—
640Q8—24no—
641Q8—42no—
642Q8—42no—
643Q8—42no—
644Q8—42no—
645Q8—41no—
646Q8—41no—
647Q8—42no—
648Q8—42no—
649D4—22no—
650D4—22no—
651D4—42no—
652D4—42no—
653D4—42no—
654D4—42no—
655D4—41no—
656D4—41no—
657C2×C4—24no—
658C2×C4—22no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—82no—
673C2×C4#120×C15111yescharacteristic
674C2×C4#120×C15111yescharacteristic
675C2×C4#120×C15111yescharacteristic
676C2×C4#120×C15111yescharacteristic
677C2×C4#121×C15111yescharacteristic
678C2×C4#121×C15111yescharacteristic
679C2×C4#121×C15111yescharacteristic
680C2×C4#121×C15111yescharacteristic
681C2×C4#121×C15111yescharacteristic
682C2×C4#121×C15111yescharacteristic
683C2×C4#121×C15111yescharacteristic
684C2×C4#121×C15111yescharacteristic
685C2×C4#121×C15111yescharacteristic
686C2×C4#121×C15111yescharacteristic
687C2×C4#123×C15111yescharacteristic
688C2×C4#123×C15111yescharacteristic
689C2×C4#123×C15111yescharacteristic
690C2×C4#123×C15111yescharacteristic
691C2×C4#123×C15111yescharacteristic
692C2×C4#123×C15111yescharacteristic
693C2×C4#124×C15111yescharacteristic
694C2×C4#124×C15111yescharacteristic
695C2×C4C22×D4×C15111yescharacteristic
696C2×C4C22×D4×C15111yescharacteristic
697C2×C4C22×D4×C15111yescharacteristic
698C2×C4C22×D4×C15111yescharacteristic
699C2×C4C2×#41×C15111yescharacteristic
700C2×C4C2×#41×C15111yescharacteristic
701C8—24no—
702C8—24no—
703C8—42no—
704C8—42no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—42no—
713C22—82no—
714C22—82no—
715C22—82no—
716C22#394×C15111yescharacteristic
717C22#394×C15111yescharacteristic
718C22#394×C15111yescharacteristic
719C22#394×C15111yescharacteristic
720C22C2×#121×C15111yescharacteristic
721C22C2×#123×C15111yescharacteristic
722C22C2×#124×C15111yescharacteristic
723C4—42no—
724C4—44no—
725C4—82no—
726C4#394×C15111yescharacteristic
727C4#394×C15111yescharacteristic
728C4#394×C15111yescharacteristic
729C4#394×C15111yescharacteristic
730C4C2×#120×C15111yescharacteristic
731C4C2×#121×C15111yescharacteristic
732C4C2×#121×C15111yescharacteristic
733C4C2×#123×C15111yescharacteristic
734C2—21no—
735C2—21no—
736C2—21no—
737C2—21no—
738C2—21no—
739C2—21no—
740C2—82no—
741C2#2049×C15112yesdirect product factor
742C2C2×#394×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#394
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×#41×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#430×C151C2semidirect
4. C2×#419×C151C2semidirect
6. C22×#101×C151C2semidirect
7. #2049×C151C2direct (N × H)
8. C2×#344×C151C2semidirect
25. #430×C151C22semidirect
31. #419×C151C22semidirect
38. C2×#101×C151C22semidirect
40. #344×C151C22semidirect
369. C2×C151#2049direct (N × H)
371. C2×#2049C151direct (N × H)
372. C151C2×#2049direct (N × H)
374. C2×#430C2×C151semidirect
376. C2×#419C2×C151semidirect
378. C22×#101C2×C151semidirect
379. #2049C2×C151direct (N × H)
380. C2×#344C2×C151semidirect
397. #430C22×C151semidirect
403. #419C22×C151semidirect
410. C2×#101C22×C151semidirect
412. #344C22×C151semidirect
741. C2#2049×C151direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#137×C1512
C2×#430×C1512
C2×#421×C1512
C2×#419×C1512
C2×#413×C1512
C22×#101×C1512
#2049×C1512
C2×#344×C1512
C2×#2049151