Finite Group Databasebeta

← C137×#24472 #46873858

Subgroups — C137×#24472 #46873858

Order 35072.

1372 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3585×C137C211yesmaximal, characteristic, complemented
2#3068×C137C211yesmaximal, characteristic, complemented
3#3038×C137C211yesmaximal, characteristic, complemented
4#3021×C137C211yesmaximal, characteristic, complemented
5C2×#453×C137C211yesmaximal, characteristic, complemented
6#2901×C137C211yesmaximal, characteristic, complemented
7#2050×C137C211yesmaximal, characteristic, complemented
8#2048×C137C211yesmaximal, characteristic, complemented
9#2008×C137C211yesmaximal, characteristic, complemented
10#2002×C137C211yesmaximal, characteristic, complemented
11#1906×C137C211yesmaximal, characteristic, complemented
12#1903×C137C211yesmaximal, characteristic, complemented
13#1903×C137C211yesmaximal, characteristic, complemented
14#1861×C137C211yesmaximal, characteristic, complemented
15#1795×C137C211yesmaximal, characteristic, complemented
16#585×C137C2211yescharacteristic
17C2×H(5,𝔽2)×C137C2211yescharacteristic
18#577×C137—22no—
19#577×C137—22no—
20#576×C137—22no—
21#576×C137—22no—
22#575×C137—22no—
23#575×C137C2211yescharacteristic
24#575×C137C2211yescharacteristic
25C2×AGL(1,ℤ/8)×C137—22no—
26C2×AGL(1,ℤ/8)×C137C2211yescharacteristic
27C2×AGL(1,ℤ/8)×C137C2211yescharacteristic
28C2×AGL(1,ℤ/8)×C137C2211yescharacteristic
29C2×AGL(1,ℤ/8)×C137C2211yescharacteristic, complemented
30C2×AGL(1,ℤ/8)×C137C2211yescharacteristic, complemented
31#568×C137C2211yescharacteristic
32#568×C137C2211yescharacteristic, complemented
33#535×C137C2211yescharacteristic, complemented
34C2×#127×C137C2211yescharacteristic, complemented
35C4×#41×C137C2211yescharacteristic, complemented
36#472×C137—22no—
37#471×C137—22no—
38#460×C137—22no—
39#459×C137—22no—
40#454×C137—22no—
41#453×C137—22no—
42#453×C137—22no—
43#453×C137—22no—
44#430×C137C2211yescharacteristic, complemented
45#423×C137C2211yescharacteristic, complemented
46#421×C137—22no—
47#421×C137C2211yescharacteristic
48#421×C137C2211yescharacteristic
49#421×C137C2211yescharacteristic, complemented
50#421×C137C2211yescharacteristic, complemented
51C2×#104×C137—22no—
52C2×#104×C137C2211yescharacteristic
53C2×#104×C137C2211yescharacteristic, complemented
54C2×#104×C137C2211yescharacteristic, complemented
55#418×C137C2211yescharacteristic, complemented
56#418×C137C2211yescharacteristic, complemented
57#418×C137C2211yescharacteristic, complemented
58#413×C137C2211yescharacteristic, complemented
59#413×C137C2211yescharacteristic, complemented
60C2×#100×C137C2211yescharacteristic, complemented
61C2×#100×C137C2211yescharacteristic, complemented
62#410×C137C2211yescharacteristic, complemented
63#344×C137C2211yescharacteristic, complemented
64#344×C137C2211yescharacteristic, complemented
65#339×C137C2211yescharacteristic, complemented
66#338×C137C2211yescharacteristic, complemented
672−1+4×C137—21no—
682−1+4×C137—21no—
692−1+4×C137D412yescomplemented
70H(5,𝔽2)×C137—22no—
71H(5,𝔽2)×C137—21no—
72H(5,𝔽2)×C137—22no—
73H(5,𝔽2)×C137—21no—
74H(5,𝔽2)×C137—22no—
75H(5,𝔽2)×C137—41no—
76H(5,𝔽2)×C137—41no—
77H(5,𝔽2)×C137D412yescomplemented
78C2×#41×C137—22no—
79C2×#41×C137—22no—
80C2×#41×C137—21no—
81C2×#41×C137—21no—
82C2×#41×C137—41no—
83C2×#41×C137C2311yescharacteristic
84C2×#41×C137C2311yescharacteristic
85C2×#41×C137C2311yescharacteristic
86C2×#41×C137C2311yescharacteristic
87C22×D4×C137—21no—
88C22×D4×C137—21no—
89C22×D4×C137—41no—
90C22×D4×C137—41no—
91C22×D4×C137C2311yescharacteristic
92C22×D4×C137C2311yescharacteristic
93#137×C137—24no—
94#137×C137—21no—
95#137×C137—21no—
96#137×C137—21no—
97#137×C137D412yescomplemented
98AGL(1,ℤ/8)×C137—24no—
99AGL(1,ℤ/8)×C137—24no—
100AGL(1,ℤ/8)×C137—24no—
101AGL(1,ℤ/8)×C137—22no—
102AGL(1,ℤ/8)×C137—22no—
103AGL(1,ℤ/8)×C137—21no—
104AGL(1,ℤ/8)×C137—22no—
105AGL(1,ℤ/8)×C137—21no—
106AGL(1,ℤ/8)×C137—21no—
107AGL(1,ℤ/8)×C137—22no—
108AGL(1,ℤ/8)×C137—22no—
109AGL(1,ℤ/8)×C137—22no—
110AGL(1,ℤ/8)×C137—22no—
111AGL(1,ℤ/8)×C137—22no—
112AGL(1,ℤ/8)×C137—22no—
113AGL(1,ℤ/8)×C137—41no—
114AGL(1,ℤ/8)×C137D412yescomplemented
115#135×C137—24no—
116#135×C137—24no—
117#135×C137—22no—
118#135×C137—22no—
119C2×SD16×C137—24no—
120C2×SD16×C137—21no—
121C2×SD16×C137—21no—
122C2×SD16×C137—21no—
123C2×SD16×C137—21no—
124C2×SD16×C137D412yescomplemented
125C2×D8×C137—24no—
126C2×D8×C137—21no—
127C2×D8×C137—21no—
128C2×D8×C137—21no—
129C2×D8×C137—21no—
130C2×D8×C137D412yescomplemented
131#131×C137—22no—
132#131×C137—22no—
133#131×C137—22no—
134#131×C137—41no—
135C2×M16×C137—22no—
136C2×M16×C137—22no—
137C2×M16×C137C2311yescharacteristic
138C2×M16×C137C2311yescharacteristic
139C2×M16×C137C2311yescharacteristic
140C2×M16×C137C2311yescharacteristic
141C2×M16×C137C2311yescharacteristic
142C2×M16×C137C2311yescharacteristic
143#127×C137—21no—
144#127×C137—22no—
145#127×C137—21no—
146#127×C137—21no—
147#124×C137—21no—
148#121×C137—41no—
149#120×C137—41no—
150C4×Q8×C137—21no—
151C4×D4×C137—21no—
152C4×D4×C137—41no—
153#117×C137—21no—
154#117×C137C2311yescharacteristic
155#117×C137C2311yescharacteristic
156C2×C42×C137—21no—
157C2×C42×C137C2311yescharacteristic
158#108×C137—22no—
159C4⋊C8×C137—22no—
160#104×C137—22no—
161#104×C137—22no—
162#104×C137—22no—
163#104×C137—22no—
164#104×C137—21no—
165#104×C137—21no—
166#104×C137—21no—
167#104×C137—21no—
168#104×C137D412yescomplemented
169#104×C137D412yescomplemented
170#102×C137—22no—
171#102×C137—22no—
172#102×C137—41no—
173#101×C137—21no—
174#101×C137—21no—
175#100×C137—21no—
176#100×C137—21no—
177#100×C137—22no—
178#100×C137—22no—
179#99×C137—41no—
180C24×C137—21no—
181C24×C137—21no—
182C24×C137—41no—
183#41×C137—21no—
184#41×C137—21no—
185#41×C137—21no—
186#41×C137—21no—
187#41×C137—24no—
188#41×C137—22no—
189#41×C137—22no—
190#41×C137—22no—
191#41×C137—22no—
192#41×C137—21no—
193#41×C137—21no—
194#41×C137—21no—
195#41×C137—21no—
196#41×C137—21no—
197#41×C137—21no—
198#41×C137—21no—
199#41×C137—21no—
200#41×C137—42no—
201#41×C137—42no—
202#41×C137—42no—
203#41×C137—42no—
204#41×C137—42no—
205#41×C137—42no—
206#41×C137—41no—
207#41×C137—41no—
208#41×C137—42no—
209#41×C137C2×D412yes—
210#41×C137C2×D412yes—
211#41×C137C2×D412yes—
212#41×C137C2×D412yes—
213C2×Q8×C137—22no—
214C2×Q8×C137—22no—
215C2×Q8×C137—41no—
216C2×Q8×C137C2×D411yescharacteristic
217C2×Q8×C137C2×D411yescharacteristic
218C2×Q8×C137C2×D411yescharacteristic
219C2×Q8×C137#4111yescharacteristic
220C2×D4×C137—21no—
221C2×D4×C137—21no—
222C2×D4×C137—24no—
223C2×D4×C137—22no—
224C2×D4×C137—22no—
225C2×D4×C137—21no—
226C2×D4×C137—21no—
227C2×D4×C137—21no—
228C2×D4×C137—21no—
229C2×D4×C137—21no—
230C2×D4×C137—21no—
231C2×D4×C137—21no—
232C2×D4×C137—21no—
233C2×D4×C137—21no—
234C2×D4×C137—21no—
235C2×D4×C137—21no—
236C2×D4×C137—21no—
237C2×D4×C137—21no—
238C2×D4×C137—42no—
239C2×D4×C137—41no—
240C2×D4×C137—41no—
241C2×D4×C137—42no—
242C2×D4×C137—42no—
243C2×D4×C137—42no—
244C2×D4×C137—42no—
245C2×D4×C137—41no—
246C2×D4×C137—44no—
247C2×D4×C137—42no—
248C2×D4×C137—42no—
249C2×D4×C137—44no—
250C2×D4×C137—42no—
251C2×D4×C137—42no—
252C2×D4×C137—84no—
253C2×D4×C137C2×D411yescharacteristic
254C2×D4×C137C2×D411yescharacteristic
255C2×D4×C137C2×D412yes—
256C2×D4×C137C2×D411yescharacteristic
257C2×D4×C137#4111yescharacteristic
258C22×C4×C137—21no—
259C22×C4×C137—21no—
260C22×C4×C137—21no—
261C22×C4×C137—21no—
262C22×C4×C137—21no—
263C22×C4×C137—41no—
264C22×C4×C137—42no—
265C22×C4×C137—41no—
266C22×C4×C137C2411yescharacteristic
267Q16×C137—22no—
268Q16×C137—22no—
269SD16×C137—24no—
270SD16×C137—22no—
271SD16×C137—22no—
272SD16×C137—22no—
273SD16×C137—24no—
274SD16×C137—22no—
275SD16×C137—42no—
276SD16×C137—42no—
277SD16×C137—42no—
278D8×C137—24no—
279D8×C137—22no—
280D8×C137—22no—
281D8×C137—24no—
282D8×C137—42no—
283D8×C137—42no—
284D8×C137—42no—
285M16×C137—24no—
286M16×C137—21no—
287M16×C137—21no—
288M16×C137—21no—
289M16×C137—21no—
290M16×C137—21no—
291M16×C137—21no—
292M16×C137—21no—
293M16×C137—21no—
294M16×C137—21no—
295M16×C137—21no—
296M16×C137—42no—
297M16×C137C2×D412yes—
298M16×C137C2×D412yes—
299C2×C8×C137—24no—
300C2×C8×C137—21no—
301C2×C8×C137—21no—
302C2×C8×C137—21no—
303C2×C8×C137—21no—
304C2×C8×C137—21no—
305C2×C8×C137—42no—
306C2×C8×C137C2×D412yes—
307C4⋊C4×C137—21no—
308C4⋊C4×C137—21no—
309C4⋊C4×C137—41no—
310C22⋊C4×C137—21no—
311C22⋊C4×C137—21no—
312C22⋊C4×C137—41no—
313C22⋊C4×C137—42no—
314C42×C137—21no—
315C42×C137—21no—
316C42×C137—21no—
317C42×C137—41no—
318C42×C137C2×D411yescharacteristic
319C42×C137C2×D411yescharacteristic
320C23×C137—21no—
321C23×C137—21no—
322C23×C137—21no—
323C23×C137—22no—
324C23×C137—21no—
325C23×C137—42no—
326C23×C137—44no—
327C23×C137—41no—
328C23×C137—41no—
329C23×C137—41no—
330C23×C137—41no—
331C23×C137—41no—
332C23×C137—82no—
333C23×C137—82no—
334C23×C137—162no—
335C23×C137H(5,𝔽2)11yescharacteristic
336Q8×C137—21no—
337Q8×C137—21no—
338Q8×C137—21no—
339Q8×C137—21no—
340Q8×C137—21no—
341Q8×C137—21no—
342Q8×C137—42no—
343Q8×C137#12012yes—
344Q8×C137#12112yes—
345D4×C137—22no—
346D4×C137—22no—
347D4×C137—22no—
348D4×C137—22no—
349D4×C137—21no—
350D4×C137—21no—
351D4×C137—22no—
352D4×C137—21no—
353D4×C137—21no—
354D4×C137—21no—
355D4×C137—21no—
356D4×C137—22no—
357D4×C137—42no—
358D4×C137—42no—
359D4×C137—44no—
360D4×C137—42no—
361D4×C137—44no—
362D4×C137—41no—
363D4×C137—41no—
364D4×C137—41no—
365D4×C137—41no—
366D4×C137—41no—
367D4×C137—41no—
368D4×C137—41no—
369D4×C137—41no—
370D4×C137—41no—
371D4×C137—41no—
372D4×C137—84no—
373D4×C137—84no—
374D4×C137—162no—
375D4×C137#12012yes—
376D4×C137#12112yes—
377C2×C4×C137—21no—
378C2×C4×C137—21no—
379C2×C4×C137—21no—
380C2×C4×C137—22no—
381C2×C4×C137—22no—
382C2×C4×C137—22no—
383C2×C4×C137—22no—
384C2×C4×C137—21no—
385C2×C4×C137—21no—
386C2×C4×C137—21no—
387C2×C4×C137—42no—
388C2×C4×C137—42no—
389C2×C4×C137—42no—
390C2×C4×C137—42no—
391C2×C4×C137—44no—
392C2×C4×C137—41no—
393C2×C4×C137—41no—
394C2×C4×C137—41no—
395C2×C4×C137—41no—
396C2×C4×C137—41no—
397C2×C4×C137—41no—
398C2×C4×C137—82no—
399C2×C4×C137C22×D411yescharacteristic
400C2×C4×C137C22×D411yescharacteristic
401C2×C4×C137C22×D411yescharacteristic
402C2×C4×C137C22×D411yescharacteristic
403C2×C4×C137C2×#4111yescharacteristic
404C2×C4×C137H(5,𝔽2)11yescharacteristic
405C8×C137—22no—
406C8×C137—22no—
407C8×C137—22no—
408C8×C137—41no—
409C8×C137—41no—
410C8×C137—41no—
411C22×C137—22no—
412C22×C137—22no—
413C22×C137—41no—
414C22×C137—41no—
415C22×C137—42no—
416C22×C137—41no—
417C22×C137—81no—
418C22×C137—81no—
419C22×C137—82no—
420C22×C137—81no—
421C22×C137—81no—
422C22×C137—82no—
423C22×C137—82no—
424C22×C137—82no—
425C22×C137—81no—
426C22×C137—161no—
427C22×C137—161no—
428C22×C137—162no—
429C22×C137—164no—
430C22×C137#53411yescharacteristic
431C22×C137D4211yescharacteristic
432C22×C137#54611yescharacteristic
433C4×C137—22no—
434C4×C137—22no—
435C4×C137—22no—
436C4×C137—41no—
437C4×C137—41no—
438C4×C137—41no—
439C4×C137—81no—
440C4×C137—81no—
441C4×C137C2×#12011yescharacteristic
442C4×C137C2×#12111yescharacteristic
443C4×C137D4211yescharacteristic
444C4×C137#54611yescharacteristic
445C2×C137—21no—
446C2×C137—21no—
447C2×C137—21no—
448C2×C137—42no—
449C2×C137—42no—
450C2×C137—82no—
451C2×C137—81no—
452C2×C137—81no—
453C2×C137—161no—
454C2×C137#241011yescharacteristic
455#24472C13711yesmaximal, characteristic, direct product factor, Sylow
456C137#2447211yescharacteristic, direct product factor, Sylow
457#3585C2×C13711yescharacteristic, complemented
458#3068C2×C13711yescharacteristic, complemented
459#3038C2×C13711yescharacteristic, complemented
460#3021C2×C13711yescharacteristic, complemented
461C2×#453C2×C13711yescharacteristic, complemented
462#2901C2×C13711yescharacteristic, complemented
463#2050C2×C13711yescharacteristic, complemented
464#2048C2×C13711yescharacteristic, complemented
465#2008C2×C13711yescharacteristic, complemented
466#2002C2×C13711yescharacteristic, complemented
467#1906C2×C13711yescharacteristic, complemented
468#1903C2×C13711yescharacteristic, complemented
469#1903C2×C13711yescharacteristic, complemented
470#1861C2×C13711yescharacteristic, complemented
471#1795C2×C13711yescharacteristic, complemented
472#585C22×C13711yescharacteristic
473C2×H(5,𝔽2)C22×C13711yescharacteristic
474#577—22no—
475#577—22no—
476#576—22no—
477#576—22no—
478#575—22no—
479#575C22×C13711yescharacteristic
480#575C22×C13711yescharacteristic
481C2×AGL(1,ℤ/8)—22no—
482C2×AGL(1,ℤ/8)C22×C13711yescharacteristic
483C2×AGL(1,ℤ/8)C22×C13711yescharacteristic
484C2×AGL(1,ℤ/8)C22×C13711yescharacteristic
485C2×AGL(1,ℤ/8)C22×C13711yescharacteristic, complemented
486C2×AGL(1,ℤ/8)C22×C13711yescharacteristic, complemented
487#568C22×C13711yescharacteristic
488#568C22×C13711yescharacteristic, complemented
489#535C22×C13711yescharacteristic, complemented
490C2×#127C22×C13711yescharacteristic, complemented
491C4×#41C22×C13711yescharacteristic, complemented
492#472—22no—
493#471—22no—
494#460—22no—
495#459—22no—
496#454—22no—
497#453—22no—
498#453—22no—
499#453—22no—
500#430C22×C13711yescharacteristic, complemented
501#423C22×C13711yescharacteristic, complemented
502#421—22no—
503#421C22×C13711yescharacteristic
504#421C22×C13711yescharacteristic
505#421C22×C13711yescharacteristic, complemented
506#421C22×C13711yescharacteristic, complemented
507C2×#104—22no—
508C2×#104C22×C13711yescharacteristic
509C2×#104C22×C13711yescharacteristic, complemented
510C2×#104C22×C13711yescharacteristic, complemented
511#418C22×C13711yescharacteristic, complemented
512#418C22×C13711yescharacteristic, complemented
513#418C22×C13711yescharacteristic, complemented
514#413C22×C13711yescharacteristic, complemented
515#413C22×C13711yescharacteristic, complemented
516C2×#100C22×C13711yescharacteristic, complemented
517C2×#100C22×C13711yescharacteristic, complemented
518#410C22×C13711yescharacteristic, complemented
519#344C22×C13711yescharacteristic, complemented
520#344C22×C13711yescharacteristic, complemented
521#339C22×C13711yescharacteristic, complemented
522#338C22×C13711yescharacteristic, complemented
5232−1+4—21no—
5242−1+4—21no—
5252−1+4D4×C13712yescomplemented
526H(5,𝔽2)—22no—
527H(5,𝔽2)—21no—
528H(5,𝔽2)—22no—
529H(5,𝔽2)—21no—
530H(5,𝔽2)—22no—
531H(5,𝔽2)—41no—
532H(5,𝔽2)—41no—
533H(5,𝔽2)D4×C13712yescomplemented
534C2×#41—22no—
535C2×#41—22no—
536C2×#41—21no—
537C2×#41—21no—
538C2×#41—41no—
539C2×#41C23×C13711yescharacteristic
540C2×#41C23×C13711yescharacteristic
541C2×#41C23×C13711yescharacteristic
542C2×#41C23×C13711yescharacteristic
543C22×D4—21no—
544C22×D4—21no—
545C22×D4—41no—
546C22×D4—41no—
547C22×D4C23×C13711yescharacteristic
548C22×D4C23×C13711yescharacteristic
549#137—24no—
550#137—21no—
551#137—21no—
552#137—21no—
553#137D4×C13712yescomplemented
554AGL(1,ℤ/8)—24no—
555AGL(1,ℤ/8)—24no—
556AGL(1,ℤ/8)—24no—
557AGL(1,ℤ/8)—22no—
558AGL(1,ℤ/8)—22no—
559AGL(1,ℤ/8)—21no—
560AGL(1,ℤ/8)—22no—
561AGL(1,ℤ/8)—21no—
562AGL(1,ℤ/8)—21no—
563AGL(1,ℤ/8)—22no—
564AGL(1,ℤ/8)—22no—
565AGL(1,ℤ/8)—22no—
566AGL(1,ℤ/8)—22no—
567AGL(1,ℤ/8)—22no—
568AGL(1,ℤ/8)—22no—
569AGL(1,ℤ/8)—41no—
570AGL(1,ℤ/8)D4×C13712yescomplemented
571#135—24no—
572#135—24no—
573#135—22no—
574#135—22no—
575C2×SD16—24no—
576C2×SD16—21no—
577C2×SD16—21no—
578C2×SD16—21no—
579C2×SD16—21no—
580C2×SD16D4×C13712yescomplemented
581C2×D8—24no—
582C2×D8—21no—
583C2×D8—21no—
584C2×D8—21no—
585C2×D8—21no—
586C2×D8D4×C13712yescomplemented
587#131—22no—
588#131—22no—
589#131—22no—
590#131—41no—
591C2×M16—22no—
592C2×M16—22no—
593C2×M16C23×C13711yescharacteristic
594C2×M16C23×C13711yescharacteristic
595C2×M16C23×C13711yescharacteristic
596C2×M16C23×C13711yescharacteristic
597C2×M16C23×C13711yescharacteristic
598C2×M16C23×C13711yescharacteristic
599#127—22no—
600#127—21no—
601#127—21no—
602#127—21no—
603#124—21no—
604#121—41no—
605#120—41no—
606C4×Q8—21no—
607C4×D4—21no—
608C4×D4—41no—
609#117—21no—
610#117C23×C13711yescharacteristic
611#117C23×C13711yescharacteristic
612C2×C42—21no—
613C2×C42C23×C13711yescharacteristic
614#108—22no—
615C4⋊C8—22no—
616#104—22no—
617#104—22no—
618#104—22no—
619#104—22no—
620#104—21no—
621#104—21no—
622#104—21no—
623#104—21no—
624#104D4×C13712yescomplemented
625#104D4×C13712yescomplemented
626#102—22no—
627#102—22no—
628#102—41no—
629#101—21no—
630#101—21no—
631#100—21no—
632#100—21no—
633#100—22no—
634#100—22no—
635#99—41no—
636C24—21no—
637C24—21no—
638C24—41no—
639#41—21no—
640#41—21no—
641#41—21no—
642#41—21no—
643#41—24no—
644#41—22no—
645#41—22no—
646#41—22no—
647#41—22no—
648#41—21no—
649#41—21no—
650#41—21no—
651#41—21no—
652#41—21no—
653#41—21no—
654#41—21no—
655#41—21no—
656#41—42no—
657#41—42no—
658#41—42no—
659#41—42no—
660#41—42no—
661#41—42no—
662#41—41no—
663#41—41no—
664#41—42no—
665#41C2×D4×C13712yes—
666#41C2×D4×C13712yes—
667#41C2×D4×C13712yes—
668#41C2×D4×C13712yes—
669C2×Q8—22no—
670C2×Q8—22no—
671C2×Q8—41no—
672C2×Q8C2×D4×C13711yescharacteristic
673C2×Q8C2×D4×C13711yescharacteristic
674C2×Q8C2×D4×C13711yescharacteristic
675C2×Q8#41×C13711yescharacteristic
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—24no—
679C2×D4—22no—
680C2×D4—22no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—42no—
695C2×D4—41no—
696C2×D4—41no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—41no—
702C2×D4—44no—
703C2×D4—42no—
704C2×D4—42no—
705C2×D4—44no—
706C2×D4—42no—
707C2×D4—42no—
708C2×D4—84no—
709C2×D4C2×D4×C13711yescharacteristic
710C2×D4C2×D4×C13711yescharacteristic
711C2×D4C2×D4×C13712yes—
712C2×D4C2×D4×C13711yescharacteristic
713C2×D4#41×C13711yescharacteristic
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—41no—
720C22×C4—42no—
721C22×C4—41no—
722C22×C4C24×C13711yescharacteristic
723Q16—22no—
724Q16—22no—
725SD16—24no—
726SD16—22no—
727SD16—22no—
728SD16—22no—
729SD16—24no—
730SD16—22no—
731SD16—42no—
732SD16—42no—
733SD16—42no—
734D8—24no—
735D8—22no—
736D8—22no—
737D8—24no—
738D8—42no—
739D8—42no—
740D8—42no—
741M16—24no—
742M16—21no—
743M16—21no—
744M16—21no—
745M16—21no—
746M16—21no—
747M16—21no—
748M16—21no—
749M16—21no—
750M16—21no—
751M16—21no—
752M16—42no—
753M16C2×D4×C13712yes—
754M16C2×D4×C13712yes—
755C2×C8—24no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—21no—
761C2×C8—42no—
762C2×C8C2×D4×C13712yes—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—41no—
766C22⋊C4—21no—
767C22⋊C4—21no—
768C22⋊C4—41no—
769C22⋊C4—42no—
770C42—21no—
771C42—21no—
772C42—21no—
773C42—41no—
774C42C2×D4×C13711yescharacteristic
775C42C2×D4×C13711yescharacteristic
776C23—21no—
777C23—21no—
778C23—21no—
779C23—22no—
780C23—21no—
781C23—42no—
782C23—44no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—82no—
789C23—82no—
790C23—162no—
791C23H(5,𝔽2)×C13711yescharacteristic
792Q8—21no—
793Q8—21no—
794Q8—21no—
795Q8—21no—
796Q8—21no—
797Q8—21no—
798Q8—42no—
799Q8#120×C13712yes—
800Q8#121×C13712yes—
801D4—22no—
802D4—22no—
803D4—22no—
804D4—22no—
805D4—21no—
806D4—21no—
807D4—22no—
808D4—21no—
809D4—21no—
810D4—21no—
811D4—21no—
812D4—22no—
813D4—42no—
814D4—42no—
815D4—44no—
816D4—42no—
817D4—44no—
818D4—41no—
819D4—41no—
820D4—41no—
821D4—41no—
822D4—41no—
823D4—41no—
824D4—41no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—84no—
829D4—84no—
830D4—162no—
831D4#120×C13712yes—
832D4#121×C13712yes—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—44no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—82no—
855C2×C4C22×D4×C13711yescharacteristic
856C2×C4C22×D4×C13711yescharacteristic
857C2×C4C22×D4×C13711yescharacteristic
858C2×C4C22×D4×C13711yescharacteristic
859C2×C4C2×#41×C13711yescharacteristic
860C2×C4H(5,𝔽2)×C13711yescharacteristic
861C8—22no—
862C8—22no—
863C8—22no—
864C8—41no—
865C8—41no—
866C8—41no—
867C22—22no—
868C22—22no—
869C22—41no—
870C22—41no—
871C22—42no—
872C22—41no—
873C22—81no—
874C22—81no—
875C22—82no—
876C22—81no—
877C22—81no—
878C22—82no—
879C22—82no—
880C22—82no—
881C22—81no—
882C22—161no—
883C22—161no—
884C22—162no—
885C22—164no—
886C22#534×C13711yescharacteristic
887C22D42×C13711yescharacteristic
888C22#546×C13711yescharacteristic
889C4—22no—
890C4—22no—
891C4—22no—
892C4—41no—
893C4—41no—
894C4—41no—
895C4—81no—
896C4—81no—
897C4C2×#120×C13711yescharacteristic
898C4C2×#121×C13711yescharacteristic
899C4D42×C13711yescharacteristic
900C4#546×C13711yescharacteristic
901C2—21no—
902C2—21no—
903C2—21no—
904C2—42no—
905C2—42no—
906C2—82no—
907C2—81no—
908C2—81no—
909C2—161no—
910C2#2410×C13711yescharacteristic
subgroupG/H
center, socleC2×C137#2410
commutator, Frattini, cosocleC22×C4C24×C137
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C137 ◁ C22×C4×C137 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3585×C137C2semidirect
2. #3068×C137C2semidirect
3. #3038×C137C2semidirect
4. #3021×C137C2semidirect
5. C2×#453×C137C2semidirect
6. #2901×C137C2semidirect
7. #2050×C137C2semidirect
8. #2048×C137C2semidirect
9. #2008×C137C2semidirect
10. #2002×C137C2semidirect
11. #1906×C137C2semidirect
12. #1903×C137C2semidirect
13. #1903×C137C2semidirect
14. #1861×C137C2semidirect
15. #1795×C137C2semidirect
29. C2×AGL(1,ℤ/8)×C137C22semidirect
30. C2×AGL(1,ℤ/8)×C137C22semidirect
32. #568×C137C22semidirect
33. #535×C137C22semidirect
34. C2×#127×C137C22semidirect
35. C4×#41×C137C22semidirect
44. #430×C137C22semidirect
45. #423×C137C22semidirect
49. #421×C137C22semidirect
50. #421×C137C22semidirect
53. C2×#104×C137C22semidirect
54. C2×#104×C137C22semidirect
55. #418×C137C22semidirect
56. #418×C137C22semidirect
57. #418×C137C22semidirect
58. #413×C137C22semidirect
59. #413×C137C22semidirect
60. C2×#100×C137C22semidirect
61. C2×#100×C137C22semidirect
62. #410×C137C22semidirect
63. #344×C137C22semidirect
64. #344×C137C22semidirect
65. #339×C137C22semidirect
66. #338×C137C22semidirect
69. 2−1+4×C137D4semidirect
77. H(5,𝔽2)×C137D4semidirect
97. #137×C137D4semidirect
114. AGL(1,ℤ/8)×C137D4semidirect
124. C2×SD16×C137D4semidirect
130. C2×D8×C137D4semidirect
168. #104×C137D4semidirect
169. #104×C137D4semidirect
455. #24472C137direct (N × H)
456. C137#24472direct (N × H)
457. #3585C2×C137semidirect
458. #3068C2×C137semidirect
459. #3038C2×C137semidirect
460. #3021C2×C137semidirect
461. C2×#453C2×C137semidirect
462. #2901C2×C137semidirect
463. #2050C2×C137semidirect
464. #2048C2×C137semidirect
465. #2008C2×C137semidirect
466. #2002C2×C137semidirect
467. #1906C2×C137semidirect
468. #1903C2×C137semidirect
469. #1903C2×C137semidirect
470. #1861C2×C137semidirect
471. #1795C2×C137semidirect
485. C2×AGL(1,ℤ/8)C22×C137semidirect
486. C2×AGL(1,ℤ/8)C22×C137semidirect
488. #568C22×C137semidirect
489. #535C22×C137semidirect
490. C2×#127C22×C137semidirect
491. C4×#41C22×C137semidirect
500. #430C22×C137semidirect
501. #423C22×C137semidirect
505. #421C22×C137semidirect
506. #421C22×C137semidirect
509. C2×#104C22×C137semidirect
510. C2×#104C22×C137semidirect
511. #418C22×C137semidirect
512. #418C22×C137semidirect
513. #418C22×C137semidirect
514. #413C22×C137semidirect
515. #413C22×C137semidirect
516. C2×#100C22×C137semidirect
517. C2×#100C22×C137semidirect
518. #410C22×C137semidirect
519. #344C22×C137semidirect
520. #344C22×C137semidirect
521. #339C22×C137semidirect
522. #338C22×C137semidirect
525. 2−1+4D4×C137semidirect
533. H(5,𝔽2)D4×C137semidirect
553. #137D4×C137semidirect
570. AGL(1,ℤ/8)D4×C137semidirect
580. C2×SD16D4×C137semidirect
586. C2×D8D4×C137semidirect
624. #104D4×C137semidirect
625. #104D4×C137semidirect

Maximal subgroups

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

subgroupindex
#3585×C1372
#3068×C1372
#3038×C1372
#3021×C1372
C2×#453×C1372
#2901×C1372
#2050×C1372
#2048×C1372
#2008×C1372
#2002×C1372
#1906×C1372
#1903×C1372
#1861×C1372
#1795×C1372
#24472137