Finite Group Databasebeta

← C137×#23877 #46873263

Subgroups — C137×#23877 #46873263

Order 35072.

1764 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#137×C137C211yesmaximal, characteristic, complemented
2#3488×C137C211yesmaximal, characteristic
3C2×#455×C137C212yesmaximal, complemented
4#3004×C137C211yesmaximal, characteristic, complemented
5#2436×C137C211yesmaximal, characteristic, complemented
6#2007×C137C212yesmaximal, complemented
7#2004×C137C212yesmaximal, complemented
8#1900×C137C211yesmaximal, characteristic, complemented
9#1882×C137C212yesmaximal, complemented
10#1871×C137C211yesmaximal, characteristic, complemented
11#1789×C137C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C137C2211yescharacteristic
13C22×#41×C137C2211yescharacteristic
14C23×Q8×C137C2211yescharacteristic, complemented
15C2×#137×C137—21no—
16C2×#137×C137—21no—
17C2×#137×C137—28no—
18C2×#137×C137C2212yes—
19C2×#137×C137C2212yescomplemented
20C2×#137×C137C2212yescomplemented
21C22×Q16×C137—21no—
22C22×SD16×C137—21no—
23C22×M16×C137C2211yescharacteristic, complemented
24#550×C137—21no—
25#548×C137—21no—
26#546×C137—21no—
27#546×C137—22no—
28D42×C137—22no—
29D42×C137—21no—
30#537×C137—21no—
31#537×C137C2211yescharacteristic
32#535×C137—21no—
33#535×C137C2211yescharacteristic
34C2×#124×C137C2212yescomplemented
35#525×C137—21no—
36#525×C137C2211yescharacteristic
37C2×#121×C137—21no—
38C2×#121×C137C2211yescharacteristic
39#520×C137C2211yescharacteristic
40#455×C137—28no—
41#451×C137—21no—
42#451×C137—21no—
43#448×C137—21no—
44#448×C137—21no—
45C2×#104×C137C2212yes—
46C2×#104×C137C2212yescomplemented
47C2×#104×C137C2212yescomplemented
48#419×C137C2212yescomplemented
49C2×#100×C137C2212yescomplemented
50#407×C137C2211yescharacteristic, complemented
51#393×C137—22no—
52#391×C137C2212yescomplemented
53#386×C137—22no—
54C4×C22⋊C4×C137C2211yescharacteristic, complemented
55#343×C137C2212yescomplemented
56#339×C137C2212yescomplemented
57H(5,𝔽2)×C137—24no—
58H(5,𝔽2)×C137—42no—
59C2×#41×C137—21no—
60C2×#41×C137—21no—
61C2×#41×C137—21no—
62C2×#41×C137—21no—
63C2×#41×C137—24no—
64C2×#41×C137—42no—
65C2×#41×C137D411yescharacteristic
66C2×#41×C137D411yescharacteristic
67C2×#41×C137C2311yescharacteristic
68C2×#41×C137C2311yescharacteristic
69C2×#41×C137C2311yescharacteristic
70C22×Q8×C137—21no—
71C22×Q8×C137—24no—
72C22×Q8×C137—21no—
73C22×Q8×C137—21no—
74C22×Q8×C137—21no—
75C22×Q8×C137—21no—
76C22×Q8×C137—42no—
77C22×Q8×C137D411yescharacteristic
78C22×Q8×C137C2312yes—
79C22×D4×C137—21no—
80C22×D4×C137—22no—
81C22×D4×C137—22no—
82C22×D4×C137—21no—
83C22×D4×C137—21no—
84C22×D4×C137D411yescharacteristic
85C22×D4×C137D412yes—
86C22×D4×C137C2311yescharacteristic
87C23×C4×C137—21no—
88C23×C4×C137—21no—
89C23×C4×C137C2311yescharacteristic
90#137×C137—28no—
91#137×C137—28no—
92#137×C137—24no—
93#137×C137—24no—
94#137×C137—24no—
95#137×C137—24no—
96#137×C137—42no—
97#137×C137D418yescomplemented
98C2×Q16×C137—28no—
99C2×Q16×C137—22no—
100C2×Q16×C137—22no—
101C2×Q16×C137—22no—
102C2×SD16×C137—28no—
103C2×SD16×C137—22no—
104C2×SD16×C137—22no—
105C2×SD16×C137—22no—
106C2×M16×C137—21no—
107C2×M16×C137—24no—
108C2×M16×C137C2312yes—
109C2×M16×C137C2312yes—
110C22×C8×C137—21no—
111#127×C137—22no—
112#127×C137—21no—
113#124×C137—22no—
114#124×C137—21no—
115#124×C137—24no—
116#124×C137—42no—
117#123×C137—22no—
118#123×C137—21no—
119C22⋊Q8×C137—22no—
120C22⋊Q8×C137—21no—
121C22⋊Q8×C137—21no—
122C22⋊Q8×C137D411yescharacteristic
123C22⋊Q8×C137D411yescharacteristic
124#121×C137—22no—
125#121×C137—22no—
126#121×C137—22no—
127#121×C137—22no—
128#121×C137—22no—
129#121×C137—21no—
130#121×C137—21no—
131#121×C137—21no—
132#121×C137—21no—
133#121×C137—21no—
134#121×C137—21no—
135#121×C137—22no—
136#121×C137—21no—
137#121×C137—21no—
138#121×C137D411yescharacteristic
139#121×C137D411yescharacteristic
140#120×C137—22no—
141#120×C137—22no—
142#120×C137—22no—
143#120×C137—21no—
144#120×C137—22no—
145C4×Q8×C137—21no—
146C4×D4×C137—22no—
147C4×D4×C137—22no—
148C4×D4×C137—21no—
149C4×D4×C137—22no—
150C4×D4×C137—21no—
151C4×D4×C137—21no—
152#117×C137—21no—
153#117×C137C2311yescharacteristic
154C2×C4⋊C4×C137—21no—
155C2×C4⋊C4×C137C2311yescharacteristic
156C2×C22⋊C4×C137—22no—
157C2×C22⋊C4×C137—21no—
158C2×C22⋊C4×C137—24no—
159C2×C22⋊C4×C137D412yes—
160C2×C42×C137C2312yes—
161#104×C137—24no—
162#104×C137—24no—
163#104×C137—42no—
164#103×C137—22no—
165#103×C137—22no—
166#100×C137—24no—
167C22⋊C8×C137—21no—
168C22⋊C8×C137—21no—
169#95×C137—21no—
170#95×C137—24no—
171C24×C137—22no—
172C24×C137—21no—
173C24×C137C2×D411yescharacteristic
174C24×C137C2×D412yes—
175#41×C137—22no—
176#41×C137—22no—
177#41×C137—22no—
178#41×C137—22no—
179#41×C137—22no—
180#41×C137—22no—
181#41×C137—22no—
182#41×C137—44no—
183#41×C137—41no—
184#41×C137—41no—
185#41×C137—44no—
186#41×C137—44no—
187#41×C137—42no—
188#41×C137—42no—
189#41×C137C2×D414yes—
190C2×Q8×C137—21no—
191C2×Q8×C137—22no—
192C2×Q8×C137—24no—
193C2×Q8×C137—24no—
194C2×Q8×C137—22no—
195C2×Q8×C137—22no—
196C2×Q8×C137—22no—
197C2×Q8×C137—22no—
198C2×Q8×C137—22no—
199C2×Q8×C137—44no—
200C2×Q8×C137—41no—
201C2×Q8×C137—44no—
202C2×Q8×C137—44no—
203C2×Q8×C137—42no—
204C2×Q8×C137—42no—
205C2×Q8×C137—41no—
206C2×Q8×C137—41no—
207C2×Q8×C137C2×D411yescharacteristic
208C2×Q8×C137C2×D411yescharacteristic
209C2×Q8×C137C2×D411yescharacteristic
210C2×Q8×C137C2×D414yescomplemented
211C2×D4×C137—21no—
212C2×D4×C137—22no—
213C2×D4×C137—22no—
214C2×D4×C137—22no—
215C2×D4×C137—22no—
216C2×D4×C137—21no—
217C2×D4×C137—21no—
218C2×D4×C137—21no—
219C2×D4×C137—21no—
220C2×D4×C137—21no—
221C2×D4×C137—22no—
222C2×D4×C137—22no—
223C2×D4×C137—22no—
224C2×D4×C137—21no—
225C2×D4×C137—22no—
226C2×D4×C137—21no—
227C2×D4×C137—22no—
228C2×D4×C137—21no—
229C2×D4×C137—21no—
230C2×D4×C137—22no—
231C2×D4×C137—41no—
232C2×D4×C137—44no—
233C2×D4×C137—44no—
234C2×D4×C137—48no—
235C2×D4×C137—42no—
236C2×D4×C137—42no—
237C2×D4×C137—44no—
238C2×D4×C137—84no—
239C2×D4×C137C2×D411yescharacteristic
240C2×D4×C137C2×D411yescharacteristic
241C2×D4×C137C2×D411yescharacteristic
242C22×C4×C137—21no—
243C22×C4×C137—22no—
244C22×C4×C137—22no—
245C22×C4×C137—22no—
246C22×C4×C137—21no—
247C22×C4×C137—22no—
248C22×C4×C137—22no—
249C22×C4×C137—21no—
250C22×C4×C137—21no—
251C22×C4×C137—21no—
252C22×C4×C137—21no—
253C22×C4×C137—22no—
254C22×C4×C137—44no—
255C22×C4×C137—44no—
256C22×C4×C137—41no—
257C22×C4×C137—41no—
258C22×C4×C137C2×D411yescharacteristic
259C22×C4×C137C2×D411yescharacteristic
260C22×C4×C137C2×D411yescharacteristic
261C22×C4×C137C2×D411yescharacteristic
262C22×C4×C137C2×D411yescharacteristic
263C22×C4×C137C2×D412yes—
264C22×C4×C137C2411yescharacteristic
265Q16×C137—28no—
266Q16×C137—28no—
267Q16×C137—44no—
268SD16×C137—28no—
269SD16×C137—28no—
270SD16×C137—44no—
271M16×C137—24no—
272M16×C137—22no—
273M16×C137—22no—
274M16×C137—22no—
275M16×C137C2×D414yescomplemented
276C2×C8×C137—24no—
277C2×C8×C137—22no—
278C2×C8×C137—22no—
279C4⋊C4×C137—22no—
280C4⋊C4×C137—22no—
281C4⋊C4×C137—21no—
282C4⋊C4×C137—21no—
283C4⋊C4×C137—21no—
284C4⋊C4×C137—21no—
285C4⋊C4×C137C2×D411yescharacteristic
286C4⋊C4×C137C2×D411yescharacteristic
287C22⋊C4×C137—22no—
288C22⋊C4×C137—22no—
289C22⋊C4×C137—22no—
290C22⋊C4×C137—22no—
291C22⋊C4×C137—22no—
292C22⋊C4×C137—21no—
293C22⋊C4×C137—21no—
294C22⋊C4×C137—21no—
295C22⋊C4×C137—21no—
296C22⋊C4×C137—22no—
297C22⋊C4×C137—22no—
298C22⋊C4×C137—21no—
299C22⋊C4×C137—48no—
300C22⋊C4×C137—42no—
301C42×C137—22no—
302C42×C137—21no—
303C42×C137—22no—
304C42×C137—22no—
305C23×C137—21no—
306C23×C137—22no—
307C23×C137—22no—
308C23×C137—22no—
309C23×C137—21no—
310C23×C137—21no—
311C23×C137—24no—
312C23×C137—41no—
313C23×C137—42no—
314C23×C137—44no—
315C23×C137—42no—
316C23×C137—42no—
317C23×C137—42no—
318C23×C137—81no—
319C23×C137—82no—
320C23×C137—82no—
321C23×C137#12011yescharacteristic
322C23×C137#12011yescharacteristic
323C23×C137C22×D411yescharacteristic
324Q8×C137—21no—
325Q8×C137—24no—
326Q8×C137—21no—
327Q8×C137—21no—
328Q8×C137—24no—
329Q8×C137—22no—
330Q8×C137—42no—
331Q8×C137—44no—
332Q8×C137—44no—
333Q8×C137—42no—
334Q8×C137—42no—
335Q8×C137#12012yes—
336D4×C137—24no—
337D4×C137—21no—
338D4×C137—21no—
339D4×C137—21no—
340D4×C137—22no—
341D4×C137—42no—
342D4×C137—42no—
343D4×C137—44no—
344D4×C137—42no—
345D4×C137—44no—
346D4×C137—42no—
347D4×C137—42no—
348D4×C137—44no—
349D4×C137—42no—
350D4×C137—41no—
351D4×C137—41no—
352D4×C137—42no—
353D4×C137—81no—
354D4×C137—82no—
355D4×C137—82no—
356D4×C137—82no—
357D4×C137—82no—
358D4×C137#12012yes—
359C2×C4×C137—21no—
360C2×C4×C137—22no—
361C2×C4×C137—21no—
362C2×C4×C137—21no—
363C2×C4×C137—21no—
364C2×C4×C137—21no—
365C2×C4×C137—22no—
366C2×C4×C137—22no—
367C2×C4×C137—24no—
368C2×C4×C137—21no—
369C2×C4×C137—22no—
370C2×C4×C137—21no—
371C2×C4×C137—21no—
372C2×C4×C137—21no—
373C2×C4×C137—24no—
374C2×C4×C137—42no—
375C2×C4×C137—42no—
376C2×C4×C137—42no—
377C2×C4×C137—44no—
378C2×C4×C137—44no—
379C2×C4×C137—44no—
380C2×C4×C137—42no—
381C2×C4×C137—42no—
382C2×C4×C137—41no—
383C2×C4×C137—41no—
384C2×C4×C137—42no—
385C2×C4×C137—42no—
386C2×C4×C137—42no—
387C2×C4×C137—42no—
388C2×C4×C137—42no—
389C2×C4×C137—82no—
390C2×C4×C137#12011yescharacteristic
391C2×C4×C137#12011yescharacteristic
392C2×C4×C137C22×D411yescharacteristic
393C2×C4×C137C22×D412yes—
394C2×C4×C137C22×D411yescharacteristic
395C2×C4×C137H(5,𝔽2)12yes—
396C8×C137—24no—
397C8×C137—42no—
398C22×C137—21no—
399C22×C137—21no—
400C22×C137—21no—
401C22×C137—21no—
402C22×C137—21no—
403C22×C137—22no—
404C22×C137—21no—
405C22×C137—21no—
406C22×C137—44no—
407C22×C137—41no—
408C22×C137—41no—
409C22×C137—41no—
410C22×C137—41no—
411C22×C137—42no—
412C22×C137—42no—
413C22×C137—41no—
414C22×C137—41no—
415C22×C137—41no—
416C22×C137—42no—
417C22×C137—41no—
418C22×C137—84no—
419C22×C137—84no—
420C22×C137—164no—
421C22×C137#45512yescomplemented
422C22×C137C2×#12011yescharacteristic
423C22×C137D4212yes—
424C4×C137—21no—
425C4×C137—21no—
426C4×C137—22no—
427C4×C137—41no—
428C4×C137—41no—
429C4×C137—44no—
430C4×C137—42no—
431C4×C137—41no—
432C4×C137—41no—
433C4×C137—82no—
434C4×C137C2×#12011yescharacteristic
435C4×C137#53411yescharacteristic
436C4×C137D4212yes—
437C2×C137—22no—
438C2×C137—22no—
439C2×C137—41no—
440C2×C137—42no—
441C2×C137—81no—
442C2×C137—82no—
443C2×C137—81no—
444C2×C137#240311yescharacteristic
445C2×C137C2×#45511yescharacteristic
446C2×C137#302211yescharacteristic
447#23877C13711yesmaximal, characteristic, direct product factor, Sylow
448C137#2387711yescharacteristic, direct product factor, Sylow
449C22×#137C2×C13711yescharacteristic, complemented
450#3488C2×C13711yescharacteristic
451C2×#455C2×C13712yescomplemented
452#3004C2×C13711yescharacteristic, complemented
453#2436C2×C13711yescharacteristic, complemented
454#2007C2×C13712yescomplemented
455#2004C2×C13712yescomplemented
456#1900C2×C13711yescharacteristic, complemented
457#1882C2×C13712yescomplemented
458#1871C2×C13711yescharacteristic, complemented
459#1789C2×C13711yescharacteristic, complemented
460C2×H(5,𝔽2)C22×C13711yescharacteristic
461C22×#41C22×C13711yescharacteristic
462C23×Q8C22×C13711yescharacteristic, complemented
463C2×#137—21no—
464C2×#137—21no—
465C2×#137—28no—
466C2×#137C22×C13712yes—
467C2×#137C22×C13712yescomplemented
468C2×#137C22×C13712yescomplemented
469C22×Q16—21no—
470C22×SD16—21no—
471C22×M16C22×C13711yescharacteristic, complemented
472#550—21no—
473#548—21no—
474#546—21no—
475#546—22no—
476D42—22no—
477D42—21no—
478#537—21no—
479#537C22×C13711yescharacteristic
480#535—21no—
481#535C22×C13711yescharacteristic
482C2×#124C22×C13712yescomplemented
483#525—21no—
484#525C22×C13711yescharacteristic
485C2×#121—21no—
486C2×#121C22×C13711yescharacteristic
487#520C22×C13711yescharacteristic
488#455—28no—
489#451—21no—
490#451—21no—
491#448—21no—
492#448—21no—
493C2×#104C22×C13712yes—
494C2×#104C22×C13712yescomplemented
495C2×#104C22×C13712yescomplemented
496#419C22×C13712yescomplemented
497C2×#100C22×C13712yescomplemented
498#407C22×C13711yescharacteristic, complemented
499#393—22no—
500#391C22×C13712yescomplemented
501#386—22no—
502C4×C22⋊C4C22×C13711yescharacteristic, complemented
503#343C22×C13712yescomplemented
504#339C22×C13712yescomplemented
505H(5,𝔽2)—24no—
506H(5,𝔽2)—42no—
507C2×#41—21no—
508C2×#41—21no—
509C2×#41—21no—
510C2×#41—21no—
511C2×#41—24no—
512C2×#41—42no—
513C2×#41D4×C13711yescharacteristic
514C2×#41D4×C13711yescharacteristic
515C2×#41C23×C13711yescharacteristic
516C2×#41C23×C13711yescharacteristic
517C2×#41C23×C13711yescharacteristic
518C22×Q8—21no—
519C22×Q8—24no—
520C22×Q8—21no—
521C22×Q8—21no—
522C22×Q8—21no—
523C22×Q8—21no—
524C22×Q8—42no—
525C22×Q8D4×C13711yescharacteristic
526C22×Q8C23×C13712yes—
527C22×D4—21no—
528C22×D4—22no—
529C22×D4—22no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4D4×C13711yescharacteristic
533C22×D4D4×C13712yes—
534C22×D4C23×C13711yescharacteristic
535C23×C4—21no—
536C23×C4—21no—
537C23×C4C23×C13711yescharacteristic
538#137—28no—
539#137—28no—
540#137—24no—
541#137—24no—
542#137—24no—
543#137—24no—
544#137—42no—
545#137D4×C13718yescomplemented
546C2×Q16—28no—
547C2×Q16—22no—
548C2×Q16—22no—
549C2×Q16—22no—
550C2×SD16—28no—
551C2×SD16—22no—
552C2×SD16—22no—
553C2×SD16—22no—
554C2×M16—21no—
555C2×M16—24no—
556C2×M16C23×C13712yes—
557C2×M16C23×C13712yes—
558C22×C8—21no—
559#127—22no—
560#127—21no—
561#124—22no—
562#124—21no—
563#124—24no—
564#124—42no—
565#123—22no—
566#123—21no—
567C22⋊Q8—22no—
568C22⋊Q8—21no—
569C22⋊Q8—21no—
570C22⋊Q8D4×C13711yescharacteristic
571C22⋊Q8D4×C13711yescharacteristic
572#121—22no—
573#121—22no—
574#121—22no—
575#121—22no—
576#121—22no—
577#121—21no—
578#121—21no—
579#121—21no—
580#121—21no—
581#121—21no—
582#121—21no—
583#121—22no—
584#121—21no—
585#121—21no—
586#121D4×C13711yescharacteristic
587#121D4×C13711yescharacteristic
588#120—22no—
589#120—22no—
590#120—22no—
591#120—21no—
592#120—22no—
593C4×Q8—21no—
594C4×D4—22no—
595C4×D4—22no—
596C4×D4—21no—
597C4×D4—22no—
598C4×D4—21no—
599C4×D4—21no—
600#117—21no—
601#117C23×C13711yescharacteristic
602C2×C4⋊C4—21no—
603C2×C4⋊C4C23×C13711yescharacteristic
604C2×C22⋊C4—22no—
605C2×C22⋊C4—24no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4D4×C13712yes—
608C2×C42C23×C13712yes—
609#104—24no—
610#104—24no—
611#104—42no—
612#103—22no—
613#103—22no—
614#100—24no—
615C22⋊C8—21no—
616C22⋊C8—21no—
617#95—21no—
618#95—24no—
619C24—22no—
620C24—21no—
621C24C2×D4×C13711yescharacteristic
622C24C2×D4×C13712yes—
623#41—22no—
624#41—22no—
625#41—22no—
626#41—22no—
627#41—22no—
628#41—22no—
629#41—22no—
630#41—44no—
631#41—41no—
632#41—41no—
633#41—44no—
634#41—44no—
635#41—42no—
636#41—42no—
637#41C2×D4×C13714yes—
638C2×Q8—21no—
639C2×Q8—22no—
640C2×Q8—24no—
641C2×Q8—24no—
642C2×Q8—22no—
643C2×Q8—22no—
644C2×Q8—22no—
645C2×Q8—22no—
646C2×Q8—22no—
647C2×Q8—44no—
648C2×Q8—41no—
649C2×Q8—44no—
650C2×Q8—44no—
651C2×Q8—42no—
652C2×Q8—42no—
653C2×Q8—41no—
654C2×Q8—41no—
655C2×Q8C2×D4×C13711yescharacteristic
656C2×Q8C2×D4×C13711yescharacteristic
657C2×Q8C2×D4×C13711yescharacteristic
658C2×Q8C2×D4×C13714yescomplemented
659C2×D4—21no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—22no—
663C2×D4—22no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—22no—
670C2×D4—22no—
671C2×D4—22no—
672C2×D4—21no—
673C2×D4—22no—
674C2×D4—21no—
675C2×D4—22no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—22no—
679C2×D4—41no—
680C2×D4—44no—
681C2×D4—44no—
682C2×D4—48no—
683C2×D4—42no—
684C2×D4—42no—
685C2×D4—44no—
686C2×D4—84no—
687C2×D4C2×D4×C13711yescharacteristic
688C2×D4C2×D4×C13711yescharacteristic
689C2×D4C2×D4×C13711yescharacteristic
690C22×C4—21no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—21no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—22no—
702C22×C4—44no—
703C22×C4—44no—
704C22×C4—41no—
705C22×C4—41no—
706C22×C4C2×D4×C13711yescharacteristic
707C22×C4C2×D4×C13711yescharacteristic
708C22×C4C2×D4×C13711yescharacteristic
709C22×C4C2×D4×C13711yescharacteristic
710C22×C4C2×D4×C13711yescharacteristic
711C22×C4C2×D4×C13712yes—
712C22×C4C24×C13711yescharacteristic
713Q16—28no—
714Q16—28no—
715Q16—44no—
716SD16—28no—
717SD16—28no—
718SD16—44no—
719M16—24no—
720M16—22no—
721M16—22no—
722M16—22no—
723M16C2×D4×C13714yescomplemented
724C2×C8—24no—
725C2×C8—22no—
726C2×C8—22no—
727C4⋊C4—22no—
728C4⋊C4—22no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4C2×D4×C13711yescharacteristic
734C4⋊C4C2×D4×C13711yescharacteristic
735C22⋊C4—22no—
736C22⋊C4—22no—
737C22⋊C4—22no—
738C22⋊C4—22no—
739C22⋊C4—22no—
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—22no—
745C22⋊C4—22no—
746C22⋊C4—21no—
747C22⋊C4—48no—
748C22⋊C4—42no—
749C42—22no—
750C42—21no—
751C42—22no—
752C42—22no—
753C23—22no—
754C23—21no—
755C23—22no—
756C23—22no—
757C23—21no—
758C23—21no—
759C23—24no—
760C23—41no—
761C23—42no—
762C23—44no—
763C23—42no—
764C23—42no—
765C23—42no—
766C23—81no—
767C23—82no—
768C23—82no—
769C23#120×C13711yescharacteristic
770C23#120×C13711yescharacteristic
771C23C22×D4×C13711yescharacteristic
772Q8—21no—
773Q8—24no—
774Q8—21no—
775Q8—21no—
776Q8—24no—
777Q8—22no—
778Q8—42no—
779Q8—44no—
780Q8—44no—
781Q8—42no—
782Q8—42no—
783Q8#120×C13712yes—
784D4—24no—
785D4—21no—
786D4—21no—
787D4—21no—
788D4—22no—
789D4—42no—
790D4—42no—
791D4—44no—
792D4—42no—
793D4—44no—
794D4—44no—
795D4—42no—
796D4—42no—
797D4—42no—
798D4—41no—
799D4—41no—
800D4—42no—
801D4—82no—
802D4—81no—
803D4—82no—
804D4—82no—
805D4—82no—
806D4#120×C13712yes—
807C2×C4—21no—
808C2×C4—22no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—24no—
816C2×C4—21no—
817C2×C4—22no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—24no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—44no—
826C2×C4—44no—
827C2×C4—44no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—82no—
838C2×C4#120×C13711yescharacteristic
839C2×C4#120×C13711yescharacteristic
840C2×C4C22×D4×C13711yescharacteristic
841C2×C4C22×D4×C13712yes—
842C2×C4C22×D4×C13711yescharacteristic
843C2×C4H(5,𝔽2)×C13712yes—
844C8—24no—
845C8—42no—
846C22—21no—
847C22—21no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—22no—
852C22—21no—
853C22—21no—
854C22—44no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—42no—
860C22—42no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—42no—
865C22—41no—
866C22—84no—
867C22—84no—
868C22—164no—
869C22#455×C13712yescomplemented
870C22C2×#120×C13711yescharacteristic
871C22D42×C13712yes—
872C4—21no—
873C4—21no—
874C4—22no—
875C4—41no—
876C4—41no—
877C4—44no—
878C4—42no—
879C4—41no—
880C4—41no—
881C4—82no—
882C4C2×#120×C13711yescharacteristic
883C4#534×C13711yescharacteristic
884C4D42×C13712yes—
885C2—22no—
886C2—22no—
887C2—41no—
888C2—42no—
889C2—81no—
890C2—82no—
891C2—81no—
892C2#2403×C13711yescharacteristic
893C2C2×#455×C13711yescharacteristic
894C2#3022×C13711yescharacteristic
subgroupG/H
center, socleC22×C137C2×#120
commutator, Frattini, cosocleC22×C4C24×C137
prime radical#3488×C137C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C137 ◁ C23×C4×C137 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#137×C137C2semidirect
3. C2×#455×C137C2semidirect
4. #3004×C137C2semidirect
5. #2436×C137C2semidirect
6. #2007×C137C2semidirect
7. #2004×C137C2semidirect
8. #1900×C137C2semidirect
9. #1882×C137C2semidirect
10. #1871×C137C2semidirect
11. #1789×C137C2semidirect
14. C23×Q8×C137C22semidirect
19. C2×#137×C137C22semidirect
20. C2×#137×C137C22semidirect
23. C22×M16×C137C22semidirect
34. C2×#124×C137C22semidirect
46. C2×#104×C137C22semidirect
47. C2×#104×C137C22semidirect
48. #419×C137C22semidirect
49. C2×#100×C137C22semidirect
50. #407×C137C22semidirect
52. #391×C137C22semidirect
54. C4×C22⋊C4×C137C22semidirect
55. #343×C137C22semidirect
56. #339×C137C22semidirect
97. #137×C137D4semidirect
210. C2×Q8×C137C2×D4semidirect
275. M16×C137C2×D4semidirect
421. C22×C137#455semidirect
447. #23877C137direct (N × H)
448. C137#23877direct (N × H)
449. C22×#137C2×C137semidirect
451. C2×#455C2×C137semidirect
452. #3004C2×C137semidirect
453. #2436C2×C137semidirect
454. #2007C2×C137semidirect
455. #2004C2×C137semidirect
456. #1900C2×C137semidirect
457. #1882C2×C137semidirect
458. #1871C2×C137semidirect
459. #1789C2×C137semidirect
462. C23×Q8C22×C137semidirect
467. C2×#137C22×C137semidirect
468. C2×#137C22×C137semidirect
471. C22×M16C22×C137semidirect
482. C2×#124C22×C137semidirect
494. C2×#104C22×C137semidirect
495. C2×#104C22×C137semidirect
496. #419C22×C137semidirect
497. C2×#100C22×C137semidirect
498. #407C22×C137semidirect
500. #391C22×C137semidirect
502. C4×C22⋊C4C22×C137semidirect
503. #343C22×C137semidirect
504. #339C22×C137semidirect
545. #137D4×C137semidirect
658. C2×Q8C2×D4×C137semidirect
723. M16C2×D4×C137semidirect
869. C22#455×C137semidirect

Maximal subgroups

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

subgroupindex
C22×#137×C1372
#3488×C1372
C2×#455×C1372
#3004×C1372
#2436×C1372
#2007×C1372
#2004×C1372
#1900×C1372
#1882×C1372
#1871×C1372
#1789×C1372
#23877137