Finite Group Databasebeta

← C137×#23900 #46873286

Subgroups — C137×#23900 #46873286

Order 35072.

3520 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3484×C137C211yesmaximal, characteristic, complemented
2C22×#120×C137C211yesmaximal, characteristic, complemented
3C2×B(4,𝔽2)×C137C212yesmaximal, complemented
4#2846×C137C212yesmaximal, complemented
5#2021×C137C214yesmaximal, complemented
6#1898×C137C212yesmaximal, complemented
7#1889×C137C212yesmaximal, complemented
8#1781×C137C211yesmaximal, characteristic, complemented
9C26×C137C2211yescharacteristic, complemented
10C2×H(5,𝔽2)×C137C2211yescharacteristic, complemented
11C23×D4×C137—21no—
12C23×D4×C137C2211yescharacteristic
13#546×C137—24no—
14D42×C137—24no—
15#535×C137—21no—
16#534×C137—21no—
17#534×C137C2212yescomplemented
18#525×C137—21no—
19C2×#120×C137—21no—
20C2×#120×C137—21no—
21C2×#120×C137—21no—
22C2×#120×C137—28no—
23C2×#120×C137—24no—
24C2×#120×C137C2212yes—
25C2×#120×C137C2212yes—
26C2×#120×C137C2212yescomplemented
27C2×#120×C137C2214yescomplemented
28#518×C137C2211yescharacteristic, complemented
29C22×C22⋊C4×C137—21no—
30C22×C22⋊C4×C137C2211yescharacteristic, complemented
31B(4,𝔽2)×C137—28no—
32C2×#99×C137C2214yescomplemented
33C2×#99×C137C2212yescomplemented
34C2×#99×C137C2212yescomplemented
35#379×C137—24no—
36#379×C137C2214yescomplemented
37#379×C137C2212yescomplemented
38#342×C137C2214yescomplemented
39C25×C137—21no—
40C25×C137—24no—
41C25×C137—21no—
42C25×C137—24no—
43C25×C137—48no—
44C25×C137—42no—
45C25×C137D411yescharacteristic, complemented
46C25×C137C2312yes—
47C25×C137C2311yescharacteristic
48H(5,𝔽2)×C137—24no—
49H(5,𝔽2)×C137—42no—
50C2×#41×C137—21no—
51C2×#41×C137—22no—
52C22×D4×C137—28no—
53C22×D4×C137—22no—
54C22×D4×C137—22no—
55C22×D4×C137—21no—
56C22×D4×C137—24no—
57C22×D4×C137—22no—
58C22×D4×C137—22no—
59C22×D4×C137—24no—
60C22×D4×C137—24no—
61C22×D4×C137—42no—
62C22×D4×C137—48no—
63C22×D4×C137D411yescharacteristic, complemented
64C22×D4×C137D411yescharacteristic, complemented
65C22×D4×C137D414yescomplemented
66C22×D4×C137C2311yescharacteristic
67C22×D4×C137C2311yescharacteristic
68C22×D4×C137C2312yes—
69C23×C4×C137—21no—
70C23×C4×C137D411yescharacteristic, complemented
71#127×C137—22no—
72#124×C137—22no—
73#123×C137—22no—
74#123×C137—22no—
75#123×C137—22no—
76C22⋊Q8×C137—22no—
77#121×C137—22no—
78#121×C137—24no—
79#121×C137—24no—
80#121×C137—24no—
81#120×C137—28no—
82#120×C137—28no—
83#120×C137—24no—
84#120×C137—22no—
85#120×C137—22no—
86#120×C137—22no—
87#120×C137—22no—
88#120×C137—24no—
89#120×C137—24no—
90#120×C137—22no—
91#120×C137—24no—
92#120×C137—24no—
93#120×C137—28no—
94#120×C137—44no—
95#120×C137—416no—
96#120×C137D418yescomplemented
97C4×D4×C137—24no—
98C4×D4×C137—24no—
99#117×C137—21no—
100C2×C22⋊C4×C137—28no—
101C2×C22⋊C4×C137—22no—
102C2×C22⋊C4×C137—21no—
103C2×C22⋊C4×C137—21no—
104C2×C22⋊C4×C137—22no—
105C2×C22⋊C4×C137—22no—
106C2×C22⋊C4×C137—24no—
107C2×C22⋊C4×C137—24no—
108C2×C22⋊C4×C137—24no—
109C2×C22⋊C4×C137—28no—
110C2×C22⋊C4×C137D414yescomplemented
111C2×C22⋊C4×C137C2314yes—
112C2×C22⋊C4×C137C2312yes—
113C2×C22⋊C4×C137C2312yes—
114#99×C137—24no—
115#99×C137—28no—
116#99×C137—42no—
117C24×C137—24no—
118C24×C137—28no—
119C24×C137—24no—
120C24×C137—22no—
121C24×C137—22no—
122C24×C137—22no—
123C24×C137—24no—
124C24×C137—216no—
125C24×C137—21no—
126C24×C137—22no—
127C24×C137—22no—
128C24×C137—24no—
129C24×C137—22no—
130C24×C137—48no—
131C24×C137—44no—
132C24×C137—41no—
133C24×C137—416no—
134C24×C137—42no—
135C24×C137—44no—
136C24×C137—416no—
137C24×C137—48no—
138C24×C137—432no—
139C24×C137—42no—
140C24×C137—48no—
141C24×C137—44no—
142C24×C137—432no—
143C24×C137—42no—
144C24×C137—42no—
145C24×C137C2×D411yescharacteristic
146C24×C137C2×D414yes—
147C24×C137C2×D411yescharacteristic
148C24×C137C2×D411yescharacteristic
149C24×C137C2×D411yescharacteristic
150C24×C137C2×D414yescomplemented
151C24×C137C2×D412yescomplemented
152C24×C137C2411yescharacteristic
153#41×C137—48no—
154#41×C137—42no—
155#41×C137—42no—
156C2×Q8×C137—21no—
157C2×D4×C137—22no—
158C2×D4×C137—22no—
159C2×D4×C137—28no—
160C2×D4×C137—22no—
161C2×D4×C137—21no—
162C2×D4×C137—24no—
163C2×D4×C137—22no—
164C2×D4×C137—22no—
165C2×D4×C137—22no—
166C2×D4×C137—28no—
167C2×D4×C137—24no—
168C2×D4×C137—22no—
169C2×D4×C137—22no—
170C2×D4×C137—22no—
171C2×D4×C137—22no—
172C2×D4×C137—22no—
173C2×D4×C137—24no—
174C2×D4×C137—24no—
175C2×D4×C137—24no—
176C2×D4×C137—22no—
177C2×D4×C137—41no—
178C2×D4×C137—41no—
179C2×D4×C137—416no—
180C2×D4×C137—48no—
181C2×D4×C137—48no—
182C2×D4×C137—48no—
183C2×D4×C137—432no—
184C2×D4×C137—42no—
185C2×D4×C137—42no—
186C2×D4×C137—48no—
187C2×D4×C137—48no—
188C2×D4×C137—416no—
189C2×D4×C137—84no—
190C2×D4×C137C2×D414yes—
191C22×C4×C137—24no—
192C22×C4×C137—21no—
193C22×C4×C137—22no—
194C22×C4×C137—22no—
195C22×C4×C137—22no—
196C22×C4×C137—22no—
197C22×C4×C137—22no—
198C22×C4×C137—24no—
199C22×C4×C137—41no—
200C22×C4×C137—44no—
201C22×C4×C137C2×D411yescharacteristic
202C22×C4×C137C2×D411yescharacteristic
203C22×C4×C137C2×D412yescomplemented
204C22×C4×C137C2×D414yescomplemented
205C4⋊C4×C137—22no—
206C4⋊C4×C137—24no—
207C22⋊C4×C137—28no—
208C22⋊C4×C137—24no—
209C22⋊C4×C137—22no—
210C22⋊C4×C137—24no—
211C22⋊C4×C137—24no—
212C22⋊C4×C137—24no—
213C22⋊C4×C137—24no—
214C22⋊C4×C137—22no—
215C22⋊C4×C137—22no—
216C22⋊C4×C137—22no—
217C22⋊C4×C137—28no—
218C22⋊C4×C137—24no—
219C22⋊C4×C137—24no—
220C22⋊C4×C137—48no—
221C22⋊C4×C137—416no—
222C22⋊C4×C137—48no—
223C22⋊C4×C137C2×D414yescomplemented
224C42×C137—22no—
225C23×C137—21no—
226C23×C137—21no—
227C23×C137—24no—
228C23×C137—216no—
229C23×C137—216no—
230C23×C137—28no—
231C23×C137—21no—
232C23×C137—24no—
233C23×C137—21no—
234C23×C137—21no—
235C23×C137—28no—
236C23×C137—28no—
237C23×C137—28no—
238C23×C137—21no—
239C23×C137—21no—
240C23×C137—21no—
241C23×C137—22no—
242C23×C137—21no—
243C23×C137—24no—
244C23×C137—44no—
245C23×C137—42no—
246C23×C137—48no—
247C23×C137—42no—
248C23×C137—44no—
249C23×C137—48no—
250C23×C137—48no—
251C23×C137—48no—
252C23×C137—416no—
253C23×C137—48no—
254C23×C137—48no—
255C23×C137—44no—
256C23×C137—48no—
257C23×C137—48no—
258C23×C137—416no—
259C23×C137—416no—
260C23×C137—464no—
261C23×C137—48no—
262C23×C137—416no—
263C23×C137—42no—
264C23×C137—42no—
265C23×C137—48no—
266C23×C137—42no—
267C23×C137—44no—
268C23×C137—464no—
269C23×C137—416no—
270C23×C137—42no—
271C23×C137—42no—
272C23×C137—44no—
273C23×C137—48no—
274C23×C137—44no—
275C23×C137—82no—
276C23×C137—84no—
277C23×C137—82no—
278C23×C137#12012yes—
279C23×C137#12012yes—
280C23×C137#12012yescomplemented
281C23×C137C22×D411yescharacteristic
282C23×C137C22×D412yes—
283C23×C137C22×D412yes—
284C23×C137H(5,𝔽2)12yes—
285Q8×C137—42no—
286D4×C137—28no—
287D4×C137—44no—
288D4×C137—42no—
289D4×C137—44no—
290D4×C137—416no—
291D4×C137—416no—
292D4×C137—44no—
293D4×C137—42no—
294D4×C137—42no—
295D4×C137—44no—
296D4×C137—44no—
297D4×C137—48no—
298D4×C137—84no—
299D4×C137—84no—
300D4×C137—816no—
301C2×C4×C137—21no—
302C2×C4×C137—21no—
303C2×C4×C137—21no—
304C2×C4×C137—24no—
305C2×C4×C137—24no—
306C2×C4×C137—22no—
307C2×C4×C137—21no—
308C2×C4×C137—21no—
309C2×C4×C137—24no—
310C2×C4×C137—44no—
311C2×C4×C137—44no—
312C2×C4×C137—48no—
313C2×C4×C137—44no—
314C2×C4×C137—42no—
315C2×C4×C137—44no—
316C2×C4×C137—48no—
317C2×C4×C137—44no—
318C2×C4×C137—82no—
319C2×C4×C137#12012yescomplemented
320C22×C137—24no—
321C22×C137—24no—
322C22×C137—22no—
323C22×C137—24no—
324C22×C137—22no—
325C22×C137—22no—
326C22×C137—28no—
327C22×C137—216no—
328C22×C137—22no—
329C22×C137—22no—
330C22×C137—24no—
331C22×C137—42no—
332C22×C137—42no—
333C22×C137—416no—
334C22×C137—42no—
335C22×C137—42no—
336C22×C137—44no—
337C22×C137—416no—
338C22×C137—48no—
339C22×C137—48no—
340C22×C137—42no—
341C22×C137—432no—
342C22×C137—42no—
343C22×C137—432no—
344C22×C137—44no—
345C22×C137—42no—
346C22×C137—48no—
347C22×C137—42no—
348C22×C137—41no—
349C22×C137—44no—
350C22×C137—42no—
351C22×C137—81no—
352C22×C137—88no—
353C22×C137—84no—
354C22×C137—81no—
355C22×C137—162no—
356C22×C137B(4,𝔽2)14yescomplemented
357C22×C137C2×#12011yescharacteristic
358C22×C137C2×#12011yescharacteristic
359C22×C137#53411yescharacteristic
360C22×C137D4214yes—
361C4×C137—22no—
362C4×C137—44no—
363C4×C137—41no—
364C4×C137—42no—
365C4×C137—44no—
366C4×C137—84no—
367C2×C137—21no—
368C2×C137—24no—
369C2×C137—21no—
370C2×C137—24no—
371C2×C137—48no—
372C2×C137—42no—
373C2×C137—42no—
374C2×C137—81no—
375C2×C137—82no—
376C2×C137#240311yescharacteristic
377C2×C137C2×B(4,𝔽2)12yes—
378#23900C13711yesmaximal, characteristic, direct product factor, Sylow
379C137#2390011yescharacteristic, direct product factor, Sylow
380#3484C2×C13711yescharacteristic, complemented
381C22×#120C2×C13711yescharacteristic, complemented
382C2×B(4,𝔽2)C2×C13712yescomplemented
383#2846C2×C13712yescomplemented
384#2021C2×C13714yescomplemented
385#1898C2×C13712yescomplemented
386#1889C2×C13712yescomplemented
387#1781C2×C13711yescharacteristic, complemented
388C26C22×C13711yescharacteristic, complemented
389C2×H(5,𝔽2)C22×C13711yescharacteristic, complemented
390C23×D4—21no—
391C23×D4C22×C13711yescharacteristic
392#546—24no—
393D42—24no—
394#535—21no—
395#534—21no—
396#534C22×C13712yescomplemented
397#525—21no—
398C2×#120—21no—
399C2×#120—21no—
400C2×#120—21no—
401C2×#120—28no—
402C2×#120—24no—
403C2×#120C22×C13712yes—
404C2×#120C22×C13712yes—
405C2×#120C22×C13712yescomplemented
406C2×#120C22×C13714yescomplemented
407#518C22×C13711yescharacteristic, complemented
408C22×C22⋊C4—21no—
409C22×C22⋊C4C22×C13711yescharacteristic, complemented
410B(4,𝔽2)—28no—
411C2×#99C22×C13712yescomplemented
412C2×#99C22×C13714yescomplemented
413C2×#99C22×C13712yescomplemented
414#379—24no—
415#379C22×C13714yescomplemented
416#379C22×C13712yescomplemented
417#342C22×C13714yescomplemented
418C25—21no—
419C25—21no—
420C25—24no—
421C25—24no—
422C25—48no—
423C25—42no—
424C25D4×C13711yescharacteristic, complemented
425C25C23×C13712yes—
426C25C23×C13711yescharacteristic
427H(5,𝔽2)—24no—
428H(5,𝔽2)—42no—
429C2×#41—21no—
430C2×#41—22no—
431C22×D4—28no—
432C22×D4—22no—
433C22×D4—22no—
434C22×D4—21no—
435C22×D4—24no—
436C22×D4—22no—
437C22×D4—22no—
438C22×D4—24no—
439C22×D4—24no—
440C22×D4—42no—
441C22×D4—48no—
442C22×D4D4×C13711yescharacteristic, complemented
443C22×D4D4×C13711yescharacteristic, complemented
444C22×D4D4×C13714yescomplemented
445C22×D4C23×C13711yescharacteristic
446C22×D4C23×C13711yescharacteristic
447C22×D4C23×C13712yes—
448C23×C4—21no—
449C23×C4D4×C13711yescharacteristic, complemented
450#127—22no—
451#124—22no—
452#123—22no—
453#123—22no—
454#123—22no—
455C22⋊Q8—22no—
456#121—22no—
457#121—24no—
458#121—24no—
459#121—24no—
460#120—28no—
461#120—28no—
462#120—24no—
463#120—22no—
464#120—22no—
465#120—22no—
466#120—22no—
467#120—24no—
468#120—24no—
469#120—22no—
470#120—24no—
471#120—24no—
472#120—28no—
473#120—44no—
474#120—416no—
475#120D4×C13718yescomplemented
476C4×D4—24no—
477C4×D4—24no—
478#117—21no—
479C2×C22⋊C4—28no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—28no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4D4×C13714yescomplemented
490C2×C22⋊C4C23×C13714yes—
491C2×C22⋊C4C23×C13712yes—
492C2×C22⋊C4C23×C13712yes—
493#99—24no—
494#99—28no—
495#99—42no—
496C24—24no—
497C24—28no—
498C24—24no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24—24no—
503C24—216no—
504C24—21no—
505C24—22no—
506C24—22no—
507C24—24no—
508C24—22no—
509C24—44no—
510C24—48no—
511C24—41no—
512C24—416no—
513C24—44no—
514C24—42no—
515C24—416no—
516C24—48no—
517C24—432no—
518C24—48no—
519C24—42no—
520C24—44no—
521C24—432no—
522C24—42no—
523C24—42no—
524C24C2×D4×C13711yescharacteristic
525C24C2×D4×C13714yes—
526C24C2×D4×C13711yescharacteristic
527C24C2×D4×C13711yescharacteristic
528C24C2×D4×C13711yescharacteristic
529C24C2×D4×C13714yescomplemented
530C24C2×D4×C13712yescomplemented
531C24C24×C13711yescharacteristic
532#41—48no—
533#41—42no—
534#41—42no—
535C2×Q8—21no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—28no—
539C2×D4—22no—
540C2×D4—21no—
541C2×D4—24no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—28no—
546C2×D4—24no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—24no—
553C2×D4—24no—
554C2×D4—24no—
555C2×D4—22no—
556C2×D4—41no—
557C2×D4—41no—
558C2×D4—416no—
559C2×D4—48no—
560C2×D4—48no—
561C2×D4—48no—
562C2×D4—432no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—48no—
566C2×D4—48no—
567C2×D4—416no—
568C2×D4—84no—
569C2×D4C2×D4×C13714yes—
570C22×C4—24no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—24no—
578C22×C4—41no—
579C22×C4—44no—
580C22×C4C2×D4×C13711yescharacteristic
581C22×C4C2×D4×C13711yescharacteristic
582C22×C4C2×D4×C13712yescomplemented
583C22×C4C2×D4×C13714yescomplemented
584C4⋊C4—22no—
585C4⋊C4—24no—
586C22⋊C4—28no—
587C22⋊C4—24no—
588C22⋊C4—22no—
589C22⋊C4—24no—
590C22⋊C4—24no—
591C22⋊C4—24no—
592C22⋊C4—24no—
593C22⋊C4—22no—
594C22⋊C4—22no—
595C22⋊C4—22no—
596C22⋊C4—28no—
597C22⋊C4—24no—
598C22⋊C4—24no—
599C22⋊C4—48no—
600C22⋊C4—416no—
601C22⋊C4—48no—
602C22⋊C4C2×D4×C13714yescomplemented
603C42—22no—
604C23—24no—
605C23—21no—
606C23—21no—
607C23—216no—
608C23—216no—
609C23—28no—
610C23—28no—
611C23—21no—
612C23—24no—
613C23—21no—
614C23—21no—
615C23—28no—
616C23—28no—
617C23—21no—
618C23—21no—
619C23—22no—
620C23—21no—
621C23—21no—
622C23—24no—
623C23—44no—
624C23—42no—
625C23—48no—
626C23—42no—
627C23—44no—
628C23—48no—
629C23—48no—
630C23—48no—
631C23—416no—
632C23—48no—
633C23—48no—
634C23—44no—
635C23—48no—
636C23—48no—
637C23—416no—
638C23—416no—
639C23—464no—
640C23—48no—
641C23—416no—
642C23—42no—
643C23—42no—
644C23—48no—
645C23—42no—
646C23—44no—
647C23—464no—
648C23—416no—
649C23—48no—
650C23—42no—
651C23—42no—
652C23—44no—
653C23—44no—
654C23—82no—
655C23—84no—
656C23—82no—
657C23#120×C13712yes—
658C23#120×C13712yes—
659C23#120×C13712yescomplemented
660C23C22×D4×C13711yescharacteristic
661C23C22×D4×C13712yes—
662C23C22×D4×C13712yes—
663C23H(5,𝔽2)×C13712yes—
664Q8—42no—
665D4—28no—
666D4—44no—
667D4—42no—
668D4—44no—
669D4—416no—
670D4—416no—
671D4—44no—
672D4—48no—
673D4—42no—
674D4—42no—
675D4—44no—
676D4—44no—
677D4—84no—
678D4—84no—
679D4—816no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—24no—
683C2×C4—21no—
684C2×C4—24no—
685C2×C4—22no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—24no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—48no—
692C2×C4—44no—
693C2×C4—42no—
694C2×C4—44no—
695C2×C4—48no—
696C2×C4—44no—
697C2×C4—82no—
698C2×C4#120×C13712yescomplemented
699C22—24no—
700C22—24no—
701C22—22no—
702C22—24no—
703C22—22no—
704C22—22no—
705C22—28no—
706C22—216no—
707C22—22no—
708C22—22no—
709C22—24no—
710C22—42no—
711C22—42no—
712C22—416no—
713C22—42no—
714C22—42no—
715C22—44no—
716C22—416no—
717C22—48no—
718C22—432no—
719C22—48no—
720C22—42no—
721C22—42no—
722C22—432no—
723C22—44no—
724C22—42no—
725C22—48no—
726C22—42no—
727C22—41no—
728C22—44no—
729C22—42no—
730C22—81no—
731C22—88no—
732C22—84no—
733C22—81no—
734C22—162no—
735C22B(4,𝔽2)×C13714yescomplemented
736C22C2×#120×C13711yescharacteristic
737C22C2×#120×C13711yescharacteristic
738C22#534×C13711yescharacteristic
739C22D42×C13714yes—
740C4—22no—
741C4—44no—
742C4—41no—
743C4—42no—
744C4—44no—
745C4—84no—
746C2—21no—
747C2—24no—
748C2—24no—
749C2—21no—
750C2—48no—
751C2—42no—
752C2—42no—
753C2—81no—
754C2—82no—
755C2#2403×C13711yescharacteristic
756C2C2×B(4,𝔽2)×C13712yes—
subgroupG/H
center, socleC22×C137C2×#120
commutator, Frattini, cosocleC24C24×C137
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C137 ◁ C25×C137 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3484×C137C2semidirect
2. C22×#120×C137C2semidirect
3. C2×B(4,𝔽2)×C137C2semidirect
4. #2846×C137C2semidirect
5. #2021×C137C2semidirect
6. #1898×C137C2semidirect
7. #1889×C137C2semidirect
8. #1781×C137C2semidirect
9. C26×C137C22semidirect
10. C2×H(5,𝔽2)×C137C22semidirect
17. #534×C137C22semidirect
26. C2×#120×C137C22semidirect
27. C2×#120×C137C22semidirect
28. #518×C137C22semidirect
30. C22×C22⋊C4×C137C22semidirect
32. C2×#99×C137C22semidirect
33. C2×#99×C137C22semidirect
34. C2×#99×C137C22semidirect
36. #379×C137C22semidirect
37. #379×C137C22semidirect
38. #342×C137C22semidirect
45. C25×C137D4semidirect
63. C22×D4×C137D4semidirect
64. C22×D4×C137D4semidirect
65. C22×D4×C137D4semidirect
70. C23×C4×C137D4semidirect
96. #120×C137D4semidirect
110. C2×C22⋊C4×C137D4semidirect
150. C24×C137C2×D4semidirect
151. C24×C137C2×D4semidirect
203. C22×C4×C137C2×D4semidirect
204. C22×C4×C137C2×D4semidirect
223. C22⋊C4×C137C2×D4semidirect
280. C23×C137#120semidirect
319. C2×C4×C137#120semidirect
356. C22×C137B(4,𝔽2)semidirect
378. #23900C137direct (N × H)
379. C137#23900direct (N × H)
380. #3484C2×C137semidirect
381. C22×#120C2×C137semidirect
382. C2×B(4,𝔽2)C2×C137semidirect
383. #2846C2×C137semidirect
384. #2021C2×C137semidirect
385. #1898C2×C137semidirect
386. #1889C2×C137semidirect
387. #1781C2×C137semidirect
388. C26C22×C137semidirect
389. C2×H(5,𝔽2)C22×C137semidirect
396. #534C22×C137semidirect
405. C2×#120C22×C137semidirect
406. C2×#120C22×C137semidirect
407. #518C22×C137semidirect
409. C22×C22⋊C4C22×C137semidirect
411. C2×#99C22×C137semidirect
412. C2×#99C22×C137semidirect
413. C2×#99C22×C137semidirect
415. #379C22×C137semidirect
416. #379C22×C137semidirect
417. #342C22×C137semidirect
424. C25D4×C137semidirect
442. C22×D4D4×C137semidirect
443. C22×D4D4×C137semidirect
444. C22×D4D4×C137semidirect
449. C23×C4D4×C137semidirect
475. #120D4×C137semidirect
489. C2×C22⋊C4D4×C137semidirect
529. C24C2×D4×C137semidirect
530. C24C2×D4×C137semidirect
582. C22×C4C2×D4×C137semidirect
583. C22×C4C2×D4×C137semidirect
602. C22⋊C4C2×D4×C137semidirect
659. C23#120×C137semidirect
698. C2×C4#120×C137semidirect
735. C22B(4,𝔽2)×C137semidirect

Maximal subgroups

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

subgroupindex
#3484×C1372
C22×#120×C1372
C2×B(4,𝔽2)×C1372
#2846×C1372
#2021×C1372
#1898×C1372
#1889×C1372
#1781×C1372
#23900137