Finite Group Databasebeta

← C137×#24260 #46873646

Subgroups — C137×#24260 #46873646

Order 35072.

1918 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3496×C137C211yesmaximal, characteristic, complemented
2C2×B(4,𝔽2)×C137C212yesmaximal, complemented
3#2847×C137C212yesmaximal, complemented
4C4×#120×C137C211yesmaximal, characteristic, complemented
5#2044×C137C212yesmaximal, complemented
6#2021×C137C212yesmaximal, complemented
7#1964×C137C212yesmaximal, complemented
8#1799×C137C211yesmaximal, characteristic, complemented
9#1790×C137C212yesmaximal, complemented
10C2×H(5,𝔽2)×C137C2212yes—
11C24×C4×C137C2211yescharacteristic, complemented
12#547×C137—22no—
13#546×C137—24no—
14D42×C137—22no—
15#537×C137—21no—
16#534×C137—21no—
17#534×C137C2212yes—
18#532×C137—21no—
19C2×#121×C137—21no—
20C2×#121×C137—22no—
21C2×#121×C137C2212yes—
22C2×#120×C137C2211yescharacteristic
23C2×#120×C137C2214yescomplemented
24C2×C4×D4×C137—21no—
25C2×C4×D4×C137C2211yescharacteristic
26B(4,𝔽2)×C137—28no—
27C2×#99×C137C2212yes—
28C2×#99×C137C2214yescomplemented
29C2×#99×C137C2214yescomplemented
30#386×C137—21no—
31#386×C137—24no—
32#386×C137C2211yescharacteristic
33#386×C137C2214yescomplemented
34#385×C137—21no—
35#385×C137C2211yescharacteristic, complemented
36#380×C137—22no—
37#380×C137C2212yescomplemented
38#379×C137C2211yescharacteristic, complemented
39C4×C22⋊C4×C137—21no—
40C4×C22⋊C4×C137C2211yescharacteristic, complemented
41#342×C137C2212yescomplemented
42C25×C137C2311yescharacteristic
43H(5,𝔽2)×C137—24no—
44H(5,𝔽2)×C137—24no—
45H(5,𝔽2)×C137—44no—
46C2×#41×C137—22no—
47C2×#41×C137—24no—
48C22×D4×C137—21no—
49C22×D4×C137—22no—
50C22×D4×C137—24no—
51C22×D4×C137—21no—
52C22×D4×C137—24no—
53C22×D4×C137D412yescomplemented
54C22×D4×C137C2314yes—
55C22×D4×C137C2311yescharacteristic
56C23×C4×C137—21no—
57C23×C4×C137—22no—
58C23×C4×C137—21no—
59C23×C4×C137—22no—
60C23×C4×C137—44no—
61C23×C4×C137D411yescharacteristic, complemented
62C23×C4×C137C2311yescharacteristic
63C23×C4×C137C2311yescharacteristic
64C4⋊Q8×C137—21no—
65#127×C137—21no—
66#124×C137—22no—
67#123×C137—24no—
68#123×C137—24no—
69C22⋊Q8×C137—24no—
70#121×C137—22no—
71#121×C137—22no—
72#121×C137—24no—
73#121×C137—22no—
74#121×C137—22no—
75#121×C137—22no—
76#121×C137—22no—
77#121×C137—22no—
78#121×C137—22no—
79#121×C137—48no—
80#120×C137—24no—
81#120×C137—24no—
82#120×C137—22no—
83#120×C137—28no—
84#120×C137—44no—
85#120×C137D414yescomplemented
86C4×D4×C137—22no—
87C4×D4×C137—22no—
88C4×D4×C137—22no—
89C4×D4×C137—22no—
90C4×D4×C137—44no—
91C2×C4⋊C4×C137—21no—
92C2×C4⋊C4×C137—22no—
93C2×C4⋊C4×C137—21no—
94C2×C4⋊C4×C137D412yescomplemented
95C2×C4⋊C4×C137D411yescharacteristic, complemented
96C2×C22⋊C4×C137—22no—
97C2×C22⋊C4×C137—21no—
98C2×C22⋊C4×C137—21no—
99C2×C22⋊C4×C137—24no—
100C2×C22⋊C4×C137—21no—
101C2×C22⋊C4×C137—21no—
102C2×C22⋊C4×C137—24no—
103C2×C22⋊C4×C137D411yescharacteristic, complemented
104C2×C22⋊C4×C137D414yescomplemented
105C2×C22⋊C4×C137C2311yescharacteristic
106C2×C22⋊C4×C137C2314yes—
107C2×C22⋊C4×C137C2311yescharacteristic
108C2×C22⋊C4×C137C2311yescharacteristic
109C2×C42×C137—21no—
110C2×C42×C137D411yescharacteristic, complemented
111#99×C137—24no—
112#99×C137—28no—
113#99×C137—44no—
114#95×C137—21no—
115#95×C137—21no—
116#95×C137—21no—
117#95×C137—24no—
118#95×C137—22no—
119C24×C137—21no—
120C24×C137—22no—
121C24×C137—22no—
122C24×C137—21no—
123C24×C137—22no—
124C24×C137—42no—
125C24×C137—42no—
126C24×C137C2×D414yes—
127C24×C137C2×D411yescharacteristic
128C24×C137C2×D412yescomplemented
129C24×C137C2411yescharacteristic
130#41×C137—48no—
131#41×C137—48no—
132#41×C137—44no—
133#41×C137—44no—
134C2×Q8×C137—22no—
135C2×D4×C137—22no—
136C2×D4×C137—22no—
137C2×D4×C137—24no—
138C2×D4×C137—22no—
139C2×D4×C137—24no—
140C2×D4×C137—24no—
141C2×D4×C137—24no—
142C2×D4×C137—24no—
143C2×D4×C137—24no—
144C2×D4×C137—24no—
145C2×D4×C137—24no—
146C2×D4×C137—22no—
147C2×D4×C137—22no—
148C2×D4×C137—22no—
149C2×D4×C137—22no—
150C2×D4×C137—44no—
151C2×D4×C137—48no—
152C2×D4×C137—48no—
153C2×D4×C137—42no—
154C2×D4×C137—42no—
155C2×D4×C137—44no—
156C2×D4×C137—44no—
157C2×D4×C137—48no—
158C2×D4×C137—48no—
159C2×D4×C137—48no—
160C2×D4×C137—82no—
161C2×D4×C137C2×D412yes—
162C2×D4×C137#4112yes—
163C22×C4×C137—22no—
164C22×C4×C137—24no—
165C22×C4×C137—24no—
166C22×C4×C137—28no—
167C22×C4×C137—21no—
168C22×C4×C137—22no—
169C22×C4×C137—21no—
170C22×C4×C137—21no—
171C22×C4×C137—21no—
172C22×C4×C137—21no—
173C22×C4×C137—24no—
174C22×C4×C137—42no—
175C22×C4×C137—42no—
176C22×C4×C137—42no—
177C22×C4×C137—44no—
178C22×C4×C137—44no—
179C22×C4×C137—42no—
180C22×C4×C137—42no—
181C22×C4×C137—42no—
182C22×C4×C137—44no—
183C22×C4×C137—41no—
184C22×C4×C137—42no—
185C22×C4×C137—41no—
186C22×C4×C137C2×D414yes—
187C22×C4×C137C2×D411yescharacteristic
188C22×C4×C137C2×D412yes—
189C22×C4×C137C2×D411yescharacteristic
190C22×C4×C137C2×D411yescharacteristic
191C22×C4×C137C2×D411yescharacteristic
192C22×C4×C137C2×D412yes—
193C22×C4×C137C2×D411yescharacteristic
194C4⋊C4×C137—22no—
195C4⋊C4×C137—22no—
196C4⋊C4×C137—22no—
197C4⋊C4×C137—22no—
198C4⋊C4×C137—22no—
199C4⋊C4×C137—42no—
200C4⋊C4×C137—44no—
201C22⋊C4×C137—24no—
202C22⋊C4×C137—24no—
203C22⋊C4×C137—22no—
204C22⋊C4×C137—21no—
205C22⋊C4×C137—24no—
206C22⋊C4×C137—22no—
207C22⋊C4×C137—24no—
208C22⋊C4×C137—24no—
209C22⋊C4×C137—24no—
210C22⋊C4×C137—22no—
211C22⋊C4×C137—24no—
212C22⋊C4×C137—48no—
213C22⋊C4×C137—42no—
214C22⋊C4×C137—48no—
215C22⋊C4×C137—42no—
216C22⋊C4×C137—42no—
217C22⋊C4×C137C2×D412yescomplemented
218C42×C137—21no—
219C42×C137—21no—
220C42×C137—42no—
221C23×C137—22no—
222C23×C137—22no—
223C23×C137—24no—
224C23×C137—24no—
225C23×C137—21no—
226C23×C137—22no—
227C23×C137—24no—
228C23×C137—21no—
229C23×C137—24no—
230C23×C137—24no—
231C23×C137—24no—
232C23×C137—41no—
233C23×C137—44no—
234C23×C137—41no—
235C23×C137—41no—
236C23×C137—42no—
237C23×C137—41no—
238C23×C137—42no—
239C23×C137—44no—
240C23×C137—48no—
241C23×C137—41no—
242C23×C137—41no—
243C23×C137—44no—
244C23×C137—44no—
245C23×C137—44no—
246C23×C137—41no—
247C23×C137—41no—
248C23×C137—42no—
249C23×C137—82no—
250C23×C137—82no—
251C23×C137#12112yescomplemented
252C23×C137C22×D411yescharacteristic
253C23×C137C22×D412yes—
254C23×C137C22×D411yescharacteristic
255C23×C137C2×#4111yescharacteristic
256C23×C137H(5,𝔽2)12yes—
257Q8×C137—44no—
258D4×C137—24no—
259D4×C137—24no—
260D4×C137—44no—
261D4×C137—48no—
262D4×C137—48no—
263D4×C137—44no—
264D4×C137—44no—
265D4×C137—44no—
266D4×C137—44no—
267D4×C137—44no—
268D4×C137—82no—
269D4×C137—82no—
270D4×C137—82no—
271D4×C137—816no—
272C2×C4×C137—21no—
273C2×C4×C137—21no—
274C2×C4×C137—22no—
275C2×C4×C137—24no—
276C2×C4×C137—24no—
277C2×C4×C137—22no—
278C2×C4×C137—21no—
279C2×C4×C137—21no—
280C2×C4×C137—24no—
281C2×C4×C137—22no—
282C2×C4×C137—24no—
283C2×C4×C137—24no—
284C2×C4×C137—42no—
285C2×C4×C137—41no—
286C2×C4×C137—44no—
287C2×C4×C137—48no—
288C2×C4×C137—48no—
289C2×C4×C137—41no—
290C2×C4×C137—41no—
291C2×C4×C137—42no—
292C2×C4×C137—41no—
293C2×C4×C137—44no—
294C2×C4×C137—41no—
295C2×C4×C137—44no—
296C2×C4×C137—42no—
297C2×C4×C137—41no—
298C2×C4×C137—41no—
299C2×C4×C137—41no—
300C2×C4×C137—44no—
301C2×C4×C137—41no—
302C2×C4×C137—44no—
303C2×C4×C137—41no—
304C2×C4×C137—44no—
305C2×C4×C137—81no—
306C2×C4×C137#12011yescharacteristic
307C2×C4×C137#12012yes—
308C2×C4×C137#12011yescharacteristic
309C2×C4×C137#12112yescomplemented
310C22×C137—21no—
311C22×C137—22no—
312C22×C137—21no—
313C22×C137—22no—
314C22×C137—24no—
315C22×C137—28no—
316C22×C137—22no—
317C22×C137—41no—
318C22×C137—41no—
319C22×C137—42no—
320C22×C137—42no—
321C22×C137—42no—
322C22×C137—44no—
323C22×C137—42no—
324C22×C137—42no—
325C22×C137—44no—
326C22×C137—44no—
327C22×C137—42no—
328C22×C137—42no—
329C22×C137—41no—
330C22×C137—42no—
331C22×C137—41no—
332C22×C137—44no—
333C22×C137—44no—
334C22×C137—44no—
335C22×C137—81no—
336C22×C137—84no—
337C22×C137—84no—
338C22×C137—164no—
339C22×C137C2×#12011yescharacteristic
340C22×C137C2×#12111yescharacteristic
341C22×C137#53511yescharacteristic
342C22×C137D4212yes—
343C22×C137#54612yes—
344C4×C137—22no—
345C4×C137—21no—
346C4×C137—22no—
347C4×C137—42no—
348C4×C137—44no—
349C4×C137—42no—
350C4×C137—41no—
351C4×C137—41no—
352C4×C137—81no—
353C4×C137—84no—
354C4×C137B(4,𝔽2)12yescomplemented
355C2×C137—21no—
356C2×C137—22no—
357C2×C137—21no—
358C2×C137—22no—
359C2×C137—44no—
360C2×C137—42no—
361C2×C137—84no—
362C2×C137#240811yescharacteristic
363C2×C137C2×B(4,𝔽2)11yescharacteristic
364C2×C137#302511yescharacteristic
365#24260C13711yesmaximal, characteristic, direct product factor, Sylow
366C137#2426011yescharacteristic, direct product factor, Sylow
367#3496C2×C13711yescharacteristic, complemented
368C2×B(4,𝔽2)C2×C13712yescomplemented
369#2847C2×C13712yescomplemented
370C4×#120C2×C13711yescharacteristic, complemented
371#2044C2×C13712yescomplemented
372#2021C2×C13712yescomplemented
373#1964C2×C13712yescomplemented
374#1799C2×C13711yescharacteristic, complemented
375#1790C2×C13712yescomplemented
376C2×H(5,𝔽2)C22×C13712yes—
377C24×C4C22×C13711yescharacteristic, complemented
378#547—22no—
379#546—24no—
380D42—22no—
381#537—21no—
382#534—21no—
383#534C22×C13712yes—
384#532—21no—
385C2×#121—21no—
386C2×#121—22no—
387C2×#121C22×C13712yes—
388C2×#120C22×C13711yescharacteristic
389C2×#120C22×C13714yescomplemented
390C2×C4×D4—21no—
391C2×C4×D4C22×C13711yescharacteristic
392B(4,𝔽2)—28no—
393C2×#99C22×C13712yes—
394C2×#99C22×C13714yescomplemented
395C2×#99C22×C13714yescomplemented
396#386—24no—
397#386—21no—
398#386C22×C13711yescharacteristic
399#386C22×C13714yescomplemented
400#385—21no—
401#385C22×C13711yescharacteristic, complemented
402#380—22no—
403#380C22×C13712yescomplemented
404#379C22×C13711yescharacteristic, complemented
405C4×C22⋊C4—21no—
406C4×C22⋊C4C22×C13711yescharacteristic, complemented
407#342C22×C13712yescomplemented
408C25C23×C13711yescharacteristic
409H(5,𝔽2)—24no—
410H(5,𝔽2)—24no—
411H(5,𝔽2)—44no—
412C2×#41—22no—
413C2×#41—24no—
414C22×D4—21no—
415C22×D4—22no—
416C22×D4—24no—
417C22×D4—21no—
418C22×D4—24no—
419C22×D4D4×C13712yescomplemented
420C22×D4C23×C13714yes—
421C22×D4C23×C13711yescharacteristic
422C23×C4—21no—
423C23×C4—22no—
424C23×C4—21no—
425C23×C4—22no—
426C23×C4—44no—
427C23×C4D4×C13711yescharacteristic, complemented
428C23×C4C23×C13711yescharacteristic
429C23×C4C23×C13711yescharacteristic
430C4⋊Q8—21no—
431#127—21no—
432#124—22no—
433#123—24no—
434#123—24no—
435C22⋊Q8—24no—
436#121—22no—
437#121—22no—
438#121—24no—
439#121—22no—
440#121—22no—
441#121—22no—
442#121—22no—
443#121—22no—
444#121—22no—
445#121—48no—
446#120—24no—
447#120—24no—
448#120—22no—
449#120—28no—
450#120—44no—
451#120D4×C13714yescomplemented
452C4×D4—22no—
453C4×D4—22no—
454C4×D4—22no—
455C4×D4—22no—
456C4×D4—44no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4D4×C13711yescharacteristic, complemented
461C2×C4⋊C4D4×C13712yescomplemented
462C2×C22⋊C4—22no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4D4×C13711yescharacteristic, complemented
470C2×C22⋊C4D4×C13714yescomplemented
471C2×C22⋊C4C23×C13714yes—
472C2×C22⋊C4C23×C13711yescharacteristic
473C2×C22⋊C4C23×C13711yescharacteristic
474C2×C22⋊C4C23×C13711yescharacteristic
475C2×C42—21no—
476C2×C42D4×C13711yescharacteristic, complemented
477#99—24no—
478#99—28no—
479#99—44no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—24no—
484#95—22no—
485C24—21no—
486C24—22no—
487C24—22no—
488C24—21no—
489C24—22no—
490C24—42no—
491C24—42no—
492C24C2×D4×C13714yes—
493C24C2×D4×C13711yescharacteristic
494C24C2×D4×C13712yescomplemented
495C24C24×C13711yescharacteristic
496#41—48no—
497#41—48no—
498#41—44no—
499#41—44no—
500C2×Q8—22no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—24no—
504C2×D4—22no—
505C2×D4—24no—
506C2×D4—24no—
507C2×D4—24no—
508C2×D4—24no—
509C2×D4—24no—
510C2×D4—24no—
511C2×D4—24no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4—44no—
517C2×D4—48no—
518C2×D4—48no—
519C2×D4—42no—
520C2×D4—42no—
521C2×D4—44no—
522C2×D4—44no—
523C2×D4—48no—
524C2×D4—48no—
525C2×D4—48no—
526C2×D4—82no—
527C2×D4C2×D4×C13712yes—
528C2×D4#41×C13712yes—
529C22×C4—22no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—28no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—24no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—44no—
544C22×C4—44no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—44no—
549C22×C4—41no—
550C22×C4—42no—
551C22×C4—41no—
552C22×C4C2×D4×C13714yes—
553C22×C4C2×D4×C13711yescharacteristic
554C22×C4C2×D4×C13712yes—
555C22×C4C2×D4×C13711yescharacteristic
556C22×C4C2×D4×C13711yescharacteristic
557C22×C4C2×D4×C13711yescharacteristic
558C22×C4C2×D4×C13712yes—
559C22×C4C2×D4×C13711yescharacteristic
560C4⋊C4—22no—
561C4⋊C4—22no—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—42no—
566C4⋊C4—44no—
567C22⋊C4—24no—
568C22⋊C4—24no—
569C22⋊C4—22no—
570C22⋊C4—21no—
571C22⋊C4—24no—
572C22⋊C4—22no—
573C22⋊C4—24no—
574C22⋊C4—24no—
575C22⋊C4—24no—
576C22⋊C4—22no—
577C22⋊C4—24no—
578C22⋊C4—48no—
579C22⋊C4—42no—
580C22⋊C4—48no—
581C22⋊C4—42no—
582C22⋊C4—42no—
583C22⋊C4C2×D4×C13712yescomplemented
584C42—21no—
585C42—21no—
586C42—42no—
587C23—22no—
588C23—22no—
589C23—24no—
590C23—24no—
591C23—21no—
592C23—22no—
593C23—24no—
594C23—21no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—41no—
599C23—44no—
600C23—41no—
601C23—41no—
602C23—42no—
603C23—41no—
604C23—42no—
605C23—44no—
606C23—48no—
607C23—41no—
608C23—41no—
609C23—44no—
610C23—44no—
611C23—44no—
612C23—41no—
613C23—41no—
614C23—42no—
615C23—82no—
616C23—82no—
617C23#121×C13712yescomplemented
618C23C22×D4×C13711yescharacteristic
619C23C22×D4×C13712yes—
620C23C22×D4×C13711yescharacteristic
621C23C2×#41×C13711yescharacteristic
622C23H(5,𝔽2)×C13712yes—
623Q8—44no—
624D4—24no—
625D4—24no—
626D4—44no—
627D4—48no—
628D4—48no—
629D4—44no—
630D4—44no—
631D4—44no—
632D4—44no—
633D4—44no—
634D4—82no—
635D4—82no—
636D4—82no—
637D4—816no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—22no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—22no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—24no—
647C2×C4—22no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—42no—
651C2×C4—41no—
652C2×C4—44no—
653C2×C4—48no—
654C2×C4—48no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—42no—
658C2×C4—44no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—44no—
662C2×C4—42no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—44no—
667C2×C4—41no—
668C2×C4—44no—
669C2×C4—41no—
670C2×C4—44no—
671C2×C4—81no—
672C2×C4#120×C13711yescharacteristic
673C2×C4#120×C13712yes—
674C2×C4#120×C13711yescharacteristic
675C2×C4#121×C13712yescomplemented
676C22—21no—
677C22—22no—
678C22—21no—
679C22—22no—
680C22—24no—
681C22—28no—
682C22—22no—
683C22—41no—
684C22—41no—
685C22—42no—
686C22—42no—
687C22—42no—
688C22—44no—
689C22—42no—
690C22—42no—
691C22—44no—
692C22—44no—
693C22—42no—
694C22—42no—
695C22—41no—
696C22—42no—
697C22—41no—
698C22—44no—
699C22—44no—
700C22—44no—
701C22—81no—
702C22—84no—
703C22—84no—
704C22—164no—
705C22C2×#120×C13711yescharacteristic
706C22C2×#121×C13711yescharacteristic
707C22#535×C13711yescharacteristic
708C22D42×C13712yes—
709C22#546×C13712yes—
710C4—22no—
711C4—21no—
712C4—22no—
713C4—42no—
714C4—44no—
715C4—42no—
716C4—41no—
717C4—41no—
718C4—84no—
719C4—81no—
720C4B(4,𝔽2)×C13712yescomplemented
721C2—21no—
722C2—22no—
723C2—21no—
724C2—22no—
725C2—44no—
726C2—42no—
727C2—84no—
728C2#2408×C13711yescharacteristic
729C2C2×B(4,𝔽2)×C13711yescharacteristic
730C2#3025×C13711yescharacteristic
subgroupG/H
center, socleC22×C137C2×#120
commutator, Frattini, cosocleC24C24×C137
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C137 ◁ C23×C4×C137 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3496×C137C2semidirect
2. C2×B(4,𝔽2)×C137C2semidirect
3. #2847×C137C2semidirect
4. C4×#120×C137C2semidirect
5. #2044×C137C2semidirect
6. #2021×C137C2semidirect
7. #1964×C137C2semidirect
8. #1799×C137C2semidirect
9. #1790×C137C2semidirect
11. C24×C4×C137C22semidirect
23. C2×#120×C137C22semidirect
28. C2×#99×C137C22semidirect
29. C2×#99×C137C22semidirect
33. #386×C137C22semidirect
35. #385×C137C22semidirect
37. #380×C137C22semidirect
38. #379×C137C22semidirect
40. C4×C22⋊C4×C137C22semidirect
41. #342×C137C22semidirect
53. C22×D4×C137D4semidirect
61. C23×C4×C137D4semidirect
85. #120×C137D4semidirect
94. C2×C4⋊C4×C137D4semidirect
95. C2×C4⋊C4×C137D4semidirect
103. C2×C22⋊C4×C137D4semidirect
104. C2×C22⋊C4×C137D4semidirect
110. C2×C42×C137D4semidirect
128. C24×C137C2×D4semidirect
217. C22⋊C4×C137C2×D4semidirect
251. C23×C137#121semidirect
309. C2×C4×C137#121semidirect
354. C4×C137B(4,𝔽2)semidirect
365. #24260C137direct (N × H)
366. C137#24260direct (N × H)
367. #3496C2×C137semidirect
368. C2×B(4,𝔽2)C2×C137semidirect
369. #2847C2×C137semidirect
370. C4×#120C2×C137semidirect
371. #2044C2×C137semidirect
372. #2021C2×C137semidirect
373. #1964C2×C137semidirect
374. #1799C2×C137semidirect
375. #1790C2×C137semidirect
377. C24×C4C22×C137semidirect
389. C2×#120C22×C137semidirect
394. C2×#99C22×C137semidirect
395. C2×#99C22×C137semidirect
399. #386C22×C137semidirect
401. #385C22×C137semidirect
403. #380C22×C137semidirect
404. #379C22×C137semidirect
406. C4×C22⋊C4C22×C137semidirect
407. #342C22×C137semidirect
419. C22×D4D4×C137semidirect
427. C23×C4D4×C137semidirect
451. #120D4×C137semidirect
460. C2×C4⋊C4D4×C137semidirect
461. C2×C4⋊C4D4×C137semidirect
469. C2×C22⋊C4D4×C137semidirect
470. C2×C22⋊C4D4×C137semidirect
476. C2×C42D4×C137semidirect
494. C24C2×D4×C137semidirect
583. C22⋊C4C2×D4×C137semidirect
617. C23#121×C137semidirect
675. C2×C4#121×C137semidirect
720. C4B(4,𝔽2)×C137semidirect

Maximal subgroups

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

subgroupindex
#3496×C1372
C2×B(4,𝔽2)×C1372
#2847×C1372
C4×#120×C1372
#2044×C1372
#2021×C1372
#1964×C1372
#1799×C1372
#1790×C1372
#24260137