Finite Group Databasebeta

← C137×#14735 #46864121

Subgroups — C137×#14735 #46864121

Order 35072.

2110 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#397×C137C211yesmaximal, characteristic, complemented
2C2×#386×C137C212yesmaximal
3C2×#386×C137C211yesmaximal, characteristic
4C2×#380×C137C211yesmaximal, characteristic, complemented
5C22×#95×C137C211yesmaximal, characteristic, complemented
6#1445×C137C211yesmaximal, characteristic, complemented
7#1443×C137C212yesmaximal, complemented
8#1442×C137C211yesmaximal, characteristic, complemented
9#1440×C137C212yesmaximal, complemented
10#1439×C137C211yesmaximal, characteristic, complemented
11C22⋊#95×C137C212yesmaximal, complemented
12C23×D4×C137C2211yescharacteristic
13C24×C4×C137C2212yes—
14C24×C4×C137C2211yescharacteristic
15C22×C4⋊C4×C137C2211yescharacteristic
16C22×C4⋊C4×C137C2211yescharacteristic
17C22×C22⋊C4×C137C2212yes—
18C22×C22⋊C4×C137C2211yescharacteristic
19C22×C22⋊C4×C137C2211yescharacteristic
20C22×C22⋊C4×C137C2212yes—
21C22×C22⋊C4×C137C2212yes—
22C22×C22⋊C4×C137C2211yescharacteristic
23#397×C137—24no—
24#386×C137—28no—
25#386×C137—24no—
26#380×C137—24no—
27C2×#95×C137—24no—
28C2×#95×C137C2212yes—
29C2×#95×C137C2212yes—
30C2×#95×C137C2211yescharacteristic
31C2×#95×C137C2211yescharacteristic
32C2×#95×C137C2212yes—
33C2×#95×C137C2212yes—
34C2×#95×C137C2212yes—
35C2×#95×C137C2211yescharacteristic
36C2×#95×C137C2212yes—
37C2×#95×C137C2212yes—
38C2×#95×C137C2212yes—
39C2×#95×C137C2211yescharacteristic
40C25×C137C2311yescharacteristic
41C25×C137C2311yescharacteristic
42C22×D4×C137—22no—
43C22×D4×C137—22no—
44C22×D4×C137—24no—
45C22×D4×C137—24no—
46C22×D4×C137D414yes—
47C23×C4×C137—24no—
48C23×C4×C137—24no—
49C23×C4×C137—24no—
50C23×C4×C137—22no—
51C23×C4×C137—24no—
52C23×C4×C137—22no—
53C23×C4×C137—24no—
54C23×C4×C137—24no—
55C23×C4×C137—42no—
56C23×C4×C137—42no—
57C23×C4×C137—42no—
58C23×C4×C137D414yes—
59C23×C4×C137C2311yescharacteristic
60C23×C4×C137C2311yescharacteristic
61C23×C4×C137C2312yes—
62C23×C4×C137C2312yes—
63C23×C4×C137C2311yescharacteristic
64C23×C4×C137C2311yescharacteristic
65C23×C4×C137C2312yes—
66C23×C4×C137C2312yes—
67C23×C4×C137C2311yescharacteristic
68C2×C4⋊C4×C137—22no—
69C2×C4⋊C4×C137—22no—
70C2×C4⋊C4×C137—22no—
71C2×C4⋊C4×C137—22no—
72C2×C4⋊C4×C137—42no—
73C2×C22⋊C4×C137—24no—
74C2×C22⋊C4×C137—24no—
75C2×C22⋊C4×C137—24no—
76C2×C22⋊C4×C137—24no—
77C2×C22⋊C4×C137—22no—
78C2×C22⋊C4×C137—24no—
79C2×C22⋊C4×C137—24no—
80C2×C22⋊C4×C137—22no—
81C2×C22⋊C4×C137—22no—
82C2×C22⋊C4×C137—24no—
83C2×C22⋊C4×C137—22no—
84C2×C22⋊C4×C137—24no—
85C2×C22⋊C4×C137—22no—
86C2×C22⋊C4×C137—42no—
87C2×C22⋊C4×C137—42no—
88C2×C22⋊C4×C137—42no—
89#95×C137—24no—
90#95×C137—22no—
91#95×C137—24no—
92#95×C137—22no—
93#95×C137—22no—
94#95×C137—24no—
95#95×C137—24no—
96#95×C137—24no—
97#95×C137—24no—
98#95×C137—42no—
99#95×C137—42no—
100#95×C137D414yescomplemented
101C24×C137—21no—
102C24×C137—21no—
103C24×C137—22no—
104C24×C137—22no—
105C24×C137—21no—
106C24×C137—21no—
107C24×C137—21no—
108C24×C137—21no—
109C24×C137—22no—
110C24×C137—21no—
111C24×C137—21no—
112C24×C137—22no—
113C24×C137—22no—
114C24×C137—21no—
115C24×C137—22no—
116C24×C137—21no—
117C24×C137C2×D412yes—
118C24×C137C2×D412yes—
119C24×C137C2×D412yes—
120C24×C137#4112yes—
121C24×C137#4114yes—
122C24×C137#4114yes—
123C24×C137C2411yescharacteristic
124C2×D4×C137—28no—
125C2×D4×C137—216no—
126C2×D4×C137—44no—
127C2×D4×C137—44no—
128C2×D4×C137—48no—
129C22×C4×C137—22no—
130C22×C4×C137—22no—
131C22×C4×C137—216no—
132C22×C4×C137—28no—
133C22×C4×C137—21no—
134C22×C4×C137—22no—
135C22×C4×C137—21no—
136C22×C4×C137—22no—
137C22×C4×C137—22no—
138C22×C4×C137—21no—
139C22×C4×C137—22no—
140C22×C4×C137—22no—
141C22×C4×C137—22no—
142C22×C4×C137—22no—
143C22×C4×C137—22no—
144C22×C4×C137—22no—
145C22×C4×C137—21no—
146C22×C4×C137—22no—
147C22×C4×C137—22no—
148C22×C4×C137—22no—
149C22×C4×C137—22no—
150C22×C4×C137—22no—
151C22×C4×C137—22no—
152C22×C4×C137—22no—
153C22×C4×C137—28no—
154C22×C4×C137—21no—
155C22×C4×C137—21no—
156C22×C4×C137—22no—
157C22×C4×C137—22no—
158C22×C4×C137—21no—
159C22×C4×C137—22no—
160C22×C4×C137—22no—
161C22×C4×C137—22no—
162C22×C4×C137—22no—
163C22×C4×C137—22no—
164C22×C4×C137—21no—
165C22×C4×C137—22no—
166C22×C4×C137—22no—
167C22×C4×C137—22no—
168C22×C4×C137—22no—
169C22×C4×C137—22no—
170C22×C4×C137—22no—
171C22×C4×C137—21no—
172C22×C4×C137—22no—
173C22×C4×C137—22no—
174C22×C4×C137—22no—
175C22×C4×C137—22no—
176C22×C4×C137—21no—
177C22×C4×C137—22no—
178C22×C4×C137—44no—
179C22×C4×C137—48no—
180C22×C4×C137—48no—
181C22×C4×C137—48no—
182C22×C4×C137—48no—
183C22×C4×C137—48no—
184C22×C4×C137—48no—
185C22×C4×C137—48no—
186C22×C4×C137—48no—
187C22×C4×C137C2×D412yes—
188C22×C4×C137C2×D412yes—
189C22×C4×C137C2×D414yes—
190C22×C4×C137C2×D412yes—
191C22×C4×C137C2×D412yes—
192C22×C4×C137#4114yes—
193C22×C4×C137#4112yes—
194C4⋊C4×C137—44no—
195C4⋊C4×C137—44no—
196C22⋊C4×C137—48no—
197C22⋊C4×C137—48no—
198C22⋊C4×C137—44no—
199C22⋊C4×C137—48no—
200C22⋊C4×C137—44no—
201C22⋊C4×C137—44no—
202C23×C137—22no—
203C23×C137—24no—
204C23×C137—24no—
205C23×C137—22no—
206C23×C137—22no—
207C23×C137—22no—
208C23×C137—24no—
209C23×C137—24no—
210C23×C137—22no—
211C23×C137—24no—
212C23×C137—24no—
213C23×C137—22no—
214C23×C137—22no—
215C23×C137—24no—
216C23×C137—24no—
217C23×C137—24no—
218C23×C137—22no—
219C23×C137—24no—
220C23×C137—22no—
221C23×C137—24no—
222C23×C137—22no—
223C23×C137—24no—
224C23×C137—22no—
225C23×C137—41no—
226C23×C137—41no—
227C23×C137—42no—
228C23×C137—41no—
229C23×C137—42no—
230C23×C137—42no—
231C23×C137—41no—
232C23×C137—41no—
233C23×C137—41no—
234C23×C137—42no—
235C23×C137—42no—
236C23×C137—42no—
237C23×C137—41no—
238C23×C137—42no—
239C23×C137—42no—
240C23×C137—42no—
241C23×C137—41no—
242C23×C137—42no—
243C23×C137#12114yes—
244C23×C137#12314yes—
245C23×C137#12318yes—
246C23×C137#12414yes—
247C23×C137#12618yes—
248C23×C137C22×D411yescharacteristic
249C23×C137C22×D411yescharacteristic
250C23×C137C22×D411yescharacteristic
251C23×C137C2×#4111yescharacteristic
252C23×C137C2×#4111yescharacteristic
253C23×C137C2×#4112yes—
254C23×C137C2×#4112yes—
255C23×C137C2×#4112yes—
256C23×C137H(5,𝔽2)12yes—
257C23×C137H(5,𝔽2)11yescharacteristic
258C23×C1372−1+411yescharacteristic
259D4×C137—416no—
260C2×C4×C137—22no—
261C2×C4×C137—22no—
262C2×C4×C137—24no—
263C2×C4×C137—24no—
264C2×C4×C137—22no—
265C2×C4×C137—22no—
266C2×C4×C137—22no—
267C2×C4×C137—24no—
268C2×C4×C137—24no—
269C2×C4×C137—24no—
270C2×C4×C137—22no—
271C2×C4×C137—24no—
272C2×C4×C137—24no—
273C2×C4×C137—24no—
274C2×C4×C137—24no—
275C2×C4×C137—416no—
276C2×C4×C137—432no—
277C2×C4×C137—42no—
278C2×C4×C137—42no—
279C2×C4×C137—41no—
280C2×C4×C137—41no—
281C2×C4×C137—42no—
282C2×C4×C137—42no—
283C2×C4×C137—42no—
284C2×C4×C137—42no—
285C2×C4×C137—42no—
286C2×C4×C137—42no—
287C2×C4×C137—42no—
288C2×C4×C137—42no—
289C2×C4×C137—42no—
290C2×C4×C137—41no—
291C2×C4×C137—42no—
292C2×C4×C137—42no—
293C2×C4×C137—42no—
294C2×C4×C137—42no—
295C2×C4×C137—41no—
296C2×C4×C137—41no—
297C2×C4×C137—42no—
298C2×C4×C137—41no—
299C2×C4×C137—42no—
300C2×C4×C137—41no—
301C2×C4×C137—42no—
302C2×C4×C137—41no—
303C2×C4×C137—42no—
304C2×C4×C137—42no—
305C2×C4×C137—42no—
306C2×C4×C137—42no—
307C2×C4×C137—42no—
308C2×C4×C137—42no—
309C2×C4×C137—42no—
310C2×C4×C137—42no—
311C2×C4×C137—42no—
312C2×C4×C137—42no—
313C2×C4×C137—42no—
314C2×C4×C137#12114yes—
315C22×C137—24no—
316C22×C137—24no—
317C22×C137—24no—
318C22×C137—24no—
319C22×C137—28no—
320C22×C137—28no—
321C22×C137—28no—
322C22×C137—24no—
323C22×C137—28no—
324C22×C137—24no—
325C22×C137—42no—
326C22×C137—42no—
327C22×C137—44no—
328C22×C137—44no—
329C22×C137—42no—
330C22×C137—81no—
331C22×C137—81no—
332C22×C137—81no—
333C22×C137—82no—
334C22×C137—81no—
335C22×C137—82no—
336C22×C137#39718yescomplemented
337C22×C137C2×#12111yescharacteristic
338C22×C137C2×#12111yescharacteristic
339C22×C137C2×#12311yescharacteristic
340C22×C137C2×#12312yes—
341C22×C137#52512yes—
342C22×C137C2×#12411yescharacteristic
343C22×C137C2×#12612yes—
344C22×C137#52912yes—
345C22×C137#53211yescharacteristic
346C22×C137#53411yescharacteristic
347C22×C137#53711yescharacteristic
348C22×C137#53812yes—
349C22×C137#53912yes—
350C22×C137D4211yescharacteristic
351C22×C137#54612yes—
352C22×C137#54612yes—
353C22×C137#54711yescharacteristic
354C22×C137#54811yescharacteristic
355C22×C137#55112yes—
356C22×C137#55112yes—
357C22×C137#55212yes—
358C22×C137#55311yescharacteristic
359C22×C137#55312yes—
360C4×C137—24no—
361C4×C137—42no—
362C4×C137—42no—
363C4×C137—44no—
364C4×C137—44no—
365C4×C137—81no—
366C4×C137—81no—
367C4×C137—82no—
368C4×C137—82no—
369C2×C137—28no—
370C2×C137—82no—
371C2×C137C2×#39711yescharacteristic
372C2×C137#241211yescharacteristic
373C2×C137#241611yescharacteristic
374C2×C137#241812yes—
375C2×C137#241912yes—
376C2×C137#248112yes—
377C2×C137#249811yescharacteristic
378C2×C137#251012yes—
379C2×C137#254311yescharacteristic
380C2×C137#263911yescharacteristic
381C2×C137#285011yescharacteristic
382#14735C13711yesmaximal, characteristic, direct product factor, Sylow
383C137#1473511yescharacteristic, direct product factor, Sylow
384C2×#397C2×C13711yescharacteristic, complemented
385C2×#386C2×C13711yescharacteristic
386C2×#386C2×C13712yes—
387C2×#380C2×C13711yescharacteristic, complemented
388C22×#95C2×C13711yescharacteristic, complemented
389#1445C2×C13711yescharacteristic, complemented
390#1443C2×C13712yescomplemented
391#1442C2×C13711yescharacteristic, complemented
392#1440C2×C13712yescomplemented
393#1439C2×C13711yescharacteristic, complemented
394C22⋊#95C2×C13712yescomplemented
395C23×D4C22×C13711yescharacteristic
396C24×C4C22×C13712yes—
397C24×C4C22×C13711yescharacteristic
398C22×C4⋊C4C22×C13711yescharacteristic
399C22×C4⋊C4C22×C13711yescharacteristic
400C22×C22⋊C4C22×C13711yescharacteristic
401C22×C22⋊C4C22×C13711yescharacteristic
402C22×C22⋊C4C22×C13712yes—
403C22×C22⋊C4C22×C13712yes—
404C22×C22⋊C4C22×C13712yes—
405C22×C22⋊C4C22×C13711yescharacteristic
406#397—24no—
407#386—28no—
408#386—24no—
409#380—24no—
410C2×#95—24no—
411C2×#95C22×C13712yes—
412C2×#95C22×C13712yes—
413C2×#95C22×C13711yescharacteristic
414C2×#95C22×C13712yes—
415C2×#95C22×C13712yes—
416C2×#95C22×C13712yes—
417C2×#95C22×C13711yescharacteristic
418C2×#95C22×C13711yescharacteristic
419C2×#95C22×C13712yes—
420C2×#95C22×C13712yes—
421C2×#95C22×C13712yes—
422C2×#95C22×C13711yescharacteristic
423C25C23×C13711yescharacteristic
424C25C23×C13711yescharacteristic
425C22×D4—22no—
426C22×D4—22no—
427C22×D4—24no—
428C22×D4—24no—
429C22×D4D4×C13714yes—
430C23×C4—24no—
431C23×C4—24no—
432C23×C4—24no—
433C23×C4—22no—
434C23×C4—24no—
435C23×C4—22no—
436C23×C4—24no—
437C23×C4—24no—
438C23×C4—42no—
439C23×C4—42no—
440C23×C4—42no—
441C23×C4D4×C13714yes—
442C23×C4C23×C13712yes—
443C23×C4C23×C13712yes—
444C23×C4C23×C13711yescharacteristic
445C23×C4C23×C13711yescharacteristic
446C23×C4C23×C13711yescharacteristic
447C23×C4C23×C13712yes—
448C23×C4C23×C13711yescharacteristic
449C23×C4C23×C13712yes—
450C23×C4C23×C13711yescharacteristic
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—42no—
456C2×C22⋊C4—24no—
457C2×C22⋊C4—24no—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—42no—
470C2×C22⋊C4—42no—
471C2×C22⋊C4—42no—
472#95—24no—
473#95—22no—
474#95—24no—
475#95—22no—
476#95—22no—
477#95—24no—
478#95—24no—
479#95—24no—
480#95—24no—
481#95—42no—
482#95—42no—
483#95D4×C13714yescomplemented
484C24—21no—
485C24—21no—
486C24—22no—
487C24—22no—
488C24—21no—
489C24—21no—
490C24—21no—
491C24—21no—
492C24—22no—
493C24—21no—
494C24—21no—
495C24—22no—
496C24—22no—
497C24—21no—
498C24—22no—
499C24—21no—
500C24C2×D4×C13712yes—
501C24C2×D4×C13712yes—
502C24C2×D4×C13712yes—
503C24#41×C13712yes—
504C24#41×C13714yes—
505C24#41×C13714yes—
506C24C24×C13711yescharacteristic
507C2×D4—28no—
508C2×D4—216no—
509C2×D4—44no—
510C2×D4—44no—
511C2×D4—48no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—216no—
515C22×C4—28no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—28no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—22no—
561C22×C4—44no—
562C22×C4—48no—
563C22×C4—48no—
564C22×C4—48no—
565C22×C4—48no—
566C22×C4—48no—
567C22×C4—48no—
568C22×C4—48no—
569C22×C4—48no—
570C22×C4C2×D4×C13712yes—
571C22×C4C2×D4×C13712yes—
572C22×C4C2×D4×C13714yes—
573C22×C4C2×D4×C13712yes—
574C22×C4C2×D4×C13712yes—
575C22×C4#41×C13714yes—
576C22×C4#41×C13712yes—
577C4⋊C4—44no—
578C4⋊C4—44no—
579C22⋊C4—48no—
580C22⋊C4—48no—
581C22⋊C4—44no—
582C22⋊C4—48no—
583C22⋊C4—44no—
584C22⋊C4—44no—
585C23—22no—
586C23—24no—
587C23—24no—
588C23—22no—
589C23—22no—
590C23—22no—
591C23—24no—
592C23—24no—
593C23—22no—
594C23—24no—
595C23—24no—
596C23—22no—
597C23—22no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—22no—
603C23—22no—
604C23—24no—
605C23—22no—
606C23—24no—
607C23—22no—
608C23—41no—
609C23—41no—
610C23—42no—
611C23—41no—
612C23—42no—
613C23—42no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—41no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—41no—
626C23#121×C13714yes—
627C23#123×C13714yes—
628C23#123×C13718yes—
629C23#124×C13714yes—
630C23#126×C13718yes—
631C23C22×D4×C13711yescharacteristic
632C23C22×D4×C13711yescharacteristic
633C23C22×D4×C13711yescharacteristic
634C23C2×#41×C13711yescharacteristic
635C23C2×#41×C13711yescharacteristic
636C23C2×#41×C13712yes—
637C23C2×#41×C13712yes—
638C23C2×#41×C13712yes—
639C23H(5,𝔽2)×C13712yes—
640C23H(5,𝔽2)×C13711yescharacteristic
641C232−1+4×C13711yescharacteristic
642D4—416no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—22no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—416no—
659C2×C4—432no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—41no—
663C2×C4—41no—
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—42no—
673C2×C4—42no—
674C2×C4—41no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—42no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4#121×C13714yes—
698C22—24no—
699C22—24no—
700C22—24no—
701C22—24no—
702C22—24no—
703C22—28no—
704C22—28no—
705C22—28no—
706C22—24no—
707C22—28no—
708C22—42no—
709C22—42no—
710C22—42no—
711C22—44no—
712C22—44no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—82no—
717C22—81no—
718C22—82no—
719C22#397×C13718yescomplemented
720C22C2×#121×C13711yescharacteristic
721C22C2×#121×C13711yescharacteristic
722C22C2×#123×C13711yescharacteristic
723C22C2×#123×C13712yes—
724C22#525×C13712yes—
725C22C2×#124×C13711yescharacteristic
726C22C2×#126×C13712yes—
727C22#529×C13712yes—
728C22#532×C13711yescharacteristic
729C22#534×C13711yescharacteristic
730C22#537×C13711yescharacteristic
731C22#538×C13712yes—
732C22#539×C13712yes—
733C22D42×C13711yescharacteristic
734C22#546×C13712yes—
735C22#546×C13712yes—
736C22#547×C13711yescharacteristic
737C22#548×C13711yescharacteristic
738C22#551×C13712yes—
739C22#551×C13712yes—
740C22#552×C13712yes—
741C22#553×C13712yes—
742C22#553×C13711yescharacteristic
743C4—24no—
744C4—42no—
745C4—42no—
746C4—44no—
747C4—44no—
748C4—82no—
749C4—81no—
750C4—81no—
751C4—82no—
752C2—28no—
753C2—82no—
754C2C2×#397×C13711yescharacteristic
755C2#2412×C13711yescharacteristic
756C2#2416×C13711yescharacteristic
757C2#2418×C13712yes—
758C2#2419×C13712yes—
759C2#2481×C13712yes—
760C2#2498×C13711yescharacteristic
761C2#2510×C13712yes—
762C2#2543×C13711yescharacteristic
763C2#2639×C13711yescharacteristic
764C2#2850×C13711yescharacteristic
subgroupG/H
center, socleC24×C137C24
commutator, Frattini, cosocleC24C24×C137
prime radicalC23×D4×C137C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C137 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#397×C137C2semidirect
4. C2×#380×C137C2semidirect
5. C22×#95×C137C2semidirect
6. #1445×C137C2semidirect
7. #1443×C137C2semidirect
8. #1442×C137C2semidirect
9. #1440×C137C2semidirect
10. #1439×C137C2semidirect
11. C22⋊#95×C137C2semidirect
100. #95×C137D4semidirect
336. C22×C137#397semidirect
382. #14735C137direct (N × H)
383. C137#14735direct (N × H)
384. C2×#397C2×C137semidirect
387. C2×#380C2×C137semidirect
388. C22×#95C2×C137semidirect
389. #1445C2×C137semidirect
390. #1443C2×C137semidirect
391. #1442C2×C137semidirect
392. #1440C2×C137semidirect
393. #1439C2×C137semidirect
394. C22⋊#95C2×C137semidirect
483. #95D4×C137semidirect
719. C22#397×C137semidirect

Maximal subgroups

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

subgroupindex
C2×#397×C1372
C2×#386×C1372
C2×#380×C1372
C22×#95×C1372
#1445×C1372
#1443×C1372
#1442×C1372
#1440×C1372
#1439×C1372
C22⋊#95×C1372
#14735137