Finite Group Databasebeta

← C137×#24475 #46873861

Subgroups — C137×#24475 #46873861

Order 35072.

1324 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3585×C137C211yesmaximal, characteristic
2#3069×C137C211yesmaximal, characteristic, complemented
3#3040×C137C211yesmaximal, characteristic, complemented
4#3022×C137C211yesmaximal, characteristic, complemented
5C2×#455×C137C211yesmaximal, characteristic, complemented
6#2901×C137C211yesmaximal, characteristic, complemented
7#2050×C137C211yesmaximal, characteristic, complemented
8#2048×C137C211yesmaximal, characteristic, complemented
9#2009×C137C211yesmaximal, characteristic, complemented
10#2003×C137C211yesmaximal, characteristic, complemented
11#1906×C137C211yesmaximal, characteristic, complemented
12#1903×C137C211yesmaximal, characteristic, complemented
13#1902×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×#137×C137C2211yescharacteristic
26C2×#137×C137C2211yescharacteristic, complemented
27C2×#137×C137C2211yescharacteristic, complemented
28C2×AGL(1,ℤ/8)×C137—22no—
29C2×AGL(1,ℤ/8)×C137C2211yescharacteristic
30C2×AGL(1,ℤ/8)×C137C2211yescharacteristic
31#568×C137C2211yescharacteristic
32#568×C137C2211yescharacteristic, complemented
33#536×C137C2211yescharacteristic, complemented
34C2×#124×C137C2211yescharacteristic, complemented
35C4×#41×C137C2211yescharacteristic, complemented
36#473×C137—22no—
37#471×C137—22no—
38#464×C137—22no—
39#463×C137—22no—
40#456×C137—22no—
41#455×C137—22no—
42#455×C137—22no—
43#455×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#419×C137C2211yescharacteristic, complemented
56#418×C137C2211yescharacteristic, complemented
57#418×C137C2211yescharacteristic, complemented
58#413×C137C2211yescharacteristic, complemented
59#413×C137C2211yescharacteristic, complemented
60C2×#101×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×C137D412yes—
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)×C137D412yes—
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×Q8×C137C2311yescharacteristic
88C22×D4×C137—21no—
89C22×D4×C137—21no—
90C22×D4×C137—41no—
91C22×D4×C137C2311yescharacteristic
92#137×C137—24no—
93#137×C137—21no—
94#137×C137—21no—
95#137×C137—21no—
96#137×C137—22no—
97#137×C137—22no—
98#137×C137—22no—
99#137×C137—22no—
100#137×C137—22no—
101#137×C137—41no—
102#137×C137D412yes—
103AGL(1,ℤ/8)×C137—24no—
104AGL(1,ℤ/8)×C137—24no—
105AGL(1,ℤ/8)×C137—24no—
106AGL(1,ℤ/8)×C137—22no—
107AGL(1,ℤ/8)×C137—22no—
108AGL(1,ℤ/8)×C137—21no—
109AGL(1,ℤ/8)×C137—22no—
110AGL(1,ℤ/8)×C137—21no—
111AGL(1,ℤ/8)×C137—21no—
112AGL(1,ℤ/8)×C137—22no—
113AGL(1,ℤ/8)×C137D412yes—
114#135×C137—24no—
115#135×C137—24no—
116#135×C137—22no—
117#135×C137—22no—
118C2×Q16×C137—21no—
119C2×Q16×C137—21no—
120C2×Q16×C137—21no—
121C2×SD16×C137—24no—
122C2×SD16×C137—21no—
123C2×SD16×C137—21no—
124C2×SD16×C137—21no—
125C2×SD16×C137—21no—
126C2×SD16×C137D412yes—
127C2×D8×C137—24no—
128C2×D8×C137—21no—
129C2×D8×C137D412yes—
130#131×C137—22no—
131#131×C137—22no—
132#131×C137—22no—
133#131×C137—41no—
134C2×M16×C137—22no—
135C2×M16×C137—22no—
136C2×M16×C137C2311yescharacteristic
137C2×M16×C137C2311yescharacteristic
138C2×M16×C137C2311yescharacteristic
139C2×M16×C137C2311yescharacteristic
140C2×M16×C137C2311yescharacteristic
141C2×M16×C137C2311yescharacteristic
142C4⋊Q8×C137—21no—
143#124×C137—21no—
144#124×C137—22no—
145#124×C137—21no—
146#124×C137—21no—
147#123×C137—41no—
148C22⋊Q8×C137—41no—
149C4×Q8×C137—21no—
150C4×D4×C137—21no—
151C4×D4×C137—41no—
152#117×C137—21no—
153#117×C137C2311yescharacteristic
154#117×C137C2311yescharacteristic
155C2×C22⋊C4×C137—41no—
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×C137D412yes—
169#104×C137D412yes—
170#103×C137—22no—
171#102×C137—22no—
172#102×C137—41no—
173#101×C137—21no—
174#101×C137—21no—
175#101×C137—22no—
176#100×C137—21no—
177#100×C137—21no—
178#100×C137—22no—
179#99×C137—41no—
180C24×C137—21no—
181C24×C137—41no—
182#41×C137—21no—
183#41×C137—21no—
184#41×C137—21no—
185#41×C137—21no—
186#41×C137—24no—
187#41×C137—22no—
188#41×C137—22no—
189#41×C137—22no—
190#41×C137—22no—
191#41×C137—21no—
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—42no—
200#41×C137—42no—
201#41×C137—42no—
202#41×C137—42no—
203#41×C137—42no—
204#41×C137—42no—
205#41×C137—41no—
206#41×C137—41no—
207#41×C137—42no—
208#41×C137C2×D412yes—
209#41×C137C2×D412yes—
210#41×C137C2×D412yes—
211#41×C137C2×D412yes—
212C2×Q8×C137—22no—
213C2×Q8×C137—22no—
214C2×Q8×C137—21no—
215C2×Q8×C137—21no—
216C2×Q8×C137—21no—
217C2×Q8×C137—21no—
218C2×Q8×C137—21no—
219C2×Q8×C137—21no—
220C2×Q8×C137—41no—
221C2×Q8×C137C2×D411yescharacteristic
222C2×Q8×C137C2×D411yescharacteristic
223C2×Q8×C137C2×D411yescharacteristic
224C2×Q8×C137#4111yescharacteristic
225C2×D4×C137—21no—
226C2×D4×C137—21no—
227C2×D4×C137—24no—
228C2×D4×C137—22no—
229C2×D4×C137—22no—
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—42no—
238C2×D4×C137—41no—
239C2×D4×C137—41no—
240C2×D4×C137—42no—
241C2×D4×C137—42no—
242C2×D4×C137—41no—
243C2×D4×C137—44no—
244C2×D4×C137—42no—
245C2×D4×C137—42no—
246C2×D4×C137—44no—
247C2×D4×C137—42no—
248C2×D4×C137C2×D411yescharacteristic
249C2×D4×C137C2×D411yescharacteristic
250C2×D4×C137C2×D412yes—
251C2×D4×C137C2×D411yescharacteristic
252C2×D4×C137#4111yescharacteristic
253C22×C4×C137—21no—
254C22×C4×C137—21no—
255C22×C4×C137—21no—
256C22×C4×C137—21no—
257C22×C4×C137—21no—
258C22×C4×C137—21no—
259C22×C4×C137—41no—
260C22×C4×C137—42no—
261C22×C4×C137—41no—
262C22×C4×C137C2411yescharacteristic
263Q16×C137—22no—
264Q16×C137—22no—
265Q16×C137—42no—
266Q16×C137—42no—
267Q16×C137—42no—
268SD16×C137—24no—
269SD16×C137—22no—
270SD16×C137—22no—
271SD16×C137—22no—
272SD16×C137—24no—
273SD16×C137—22no—
274SD16×C137—42no—
275SD16×C137—42no—
276SD16×C137—42no—
277D8×C137—24no—
278D8×C137—22no—
279D8×C137—22no—
280D8×C137—24no—
281M16×C137—24no—
282M16×C137—21no—
283M16×C137—21no—
284M16×C137—21no—
285M16×C137—21no—
286M16×C137—21no—
287M16×C137—21no—
288M16×C137—21no—
289M16×C137—21no—
290M16×C137—21no—
291M16×C137—21no—
292M16×C137—42no—
293M16×C137C2×D412yes—
294M16×C137C2×D412yes—
295C2×C8×C137—24no—
296C2×C8×C137—21no—
297C2×C8×C137—21no—
298C2×C8×C137—21no—
299C2×C8×C137—21no—
300C2×C8×C137—21no—
301C2×C8×C137—42no—
302C2×C8×C137C2×D412yes—
303C4⋊C4×C137—21no—
304C4⋊C4×C137—21no—
305C4⋊C4×C137—41no—
306C4⋊C4×C137—42no—
307C22⋊C4×C137—21no—
308C22⋊C4×C137—21no—
309C22⋊C4×C137—42no—
310C22⋊C4×C137—42no—
311C22⋊C4×C137—41no—
312C22⋊C4×C137—42no—
313C42×C137—21no—
314C42×C137—21no—
315C42×C137—21no—
316C42×C137—41no—
317C42×C137C2×D411yescharacteristic
318C42×C137C2×D411yescharacteristic
319C23×C137—21no—
320C23×C137—21no—
321C23×C137—21no—
322C23×C137—22no—
323C23×C137—21no—
324C23×C137—42no—
325C23×C137—44no—
326C23×C137—41no—
327C23×C137—41no—
328C23×C137—82no—
329C23×C137—162no—
330C23×C137H(5,𝔽2)11yescharacteristic
331Q8×C137—21no—
332Q8×C137—21no—
333Q8×C137—21no—
334Q8×C137—21no—
335Q8×C137—21no—
336Q8×C137—21no—
337Q8×C137—42no—
338Q8×C137—41no—
339Q8×C137—41no—
340Q8×C137—41no—
341Q8×C137—41no—
342Q8×C137#12012yes—
343Q8×C137#12112yes—
344D4×C137—22no—
345D4×C137—22no—
346D4×C137—22no—
347D4×C137—22no—
348D4×C137—21no—
349D4×C137—21no—
350D4×C137—22no—
351D4×C137—21no—
352D4×C137—21no—
353D4×C137—21no—
354D4×C137—21no—
355D4×C137—22no—
356D4×C137—42no—
357D4×C137—42no—
358D4×C137—44no—
359D4×C137—42no—
360D4×C137—44no—
361D4×C137—41no—
362D4×C137—41no—
363D4×C137—41no—
364D4×C137—41no—
365D4×C137—41no—
366D4×C137—41no—
367D4×C137#12012yes—
368D4×C137#12112yes—
369C2×C4×C137—21no—
370C2×C4×C137—21no—
371C2×C4×C137—22no—
372C2×C4×C137—22no—
373C2×C4×C137—22no—
374C2×C4×C137—22no—
375C2×C4×C137—21no—
376C2×C4×C137—21no—
377C2×C4×C137—21no—
378C2×C4×C137—21no—
379C2×C4×C137—42no—
380C2×C4×C137—42no—
381C2×C4×C137—42no—
382C2×C4×C137—44no—
383C2×C4×C137—41no—
384C2×C4×C137—41no—
385C2×C4×C137—41no—
386C2×C4×C137—41no—
387C2×C4×C137—41no—
388C2×C4×C137—41no—
389C2×C4×C137—41no—
390C2×C4×C137—41no—
391C2×C4×C137—41no—
392C2×C4×C137—81no—
393C2×C4×C137—82no—
394C2×C4×C137C22×D411yescharacteristic
395C2×C4×C137C22×D411yescharacteristic
396C2×C4×C137C22×D411yescharacteristic
397C2×C4×C137C22×D411yescharacteristic
398C2×C4×C137C2×#4111yescharacteristic
399C2×C4×C137H(5,𝔽2)11yescharacteristic
400C8×C137—22no—
401C8×C137—22no—
402C8×C137—22no—
403C8×C137—41no—
404C8×C137—41no—
405C8×C137—41no—
406C22×C137—22no—
407C22×C137—22no—
408C22×C137—41no—
409C22×C137—41no—
410C22×C137—42no—
411C22×C137—41no—
412C22×C137—81no—
413C22×C137—81no—
414C22×C137—81no—
415C22×C137—82no—
416C22×C137—81no—
417C22×C137—82no—
418C22×C137—161no—
419C22×C137—162no—
420C22×C137—164no—
421C22×C137#53411yescharacteristic
422C22×C137D4211yescharacteristic
423C22×C137#54611yescharacteristic
424C4×C137—22no—
425C4×C137—22no—
426C4×C137—41no—
427C4×C137—41no—
428C4×C137—41no—
429C4×C137—41no—
430C4×C137—81no—
431C4×C137—81no—
432C4×C137—81no—
433C4×C137C2×#12011yescharacteristic
434C4×C137C2×#12111yescharacteristic
435C4×C137D4211yescharacteristic
436C4×C137#54611yescharacteristic
437C2×C137—21no—
438C2×C137—21no—
439C2×C137—21no—
440C2×C137—42no—
441C2×C137—42no—
442C2×C137—82no—
443C2×C137—81no—
444C2×C137—81no—
445C2×C137#241011yescharacteristic
446#24475C13711yesmaximal, characteristic, direct product factor, Sylow
447C137#2447511yescharacteristic, direct product factor, Sylow
448#3585C2×C13711yescharacteristic
449#3069C2×C13711yescharacteristic, complemented
450#3040C2×C13711yescharacteristic, complemented
451#3022C2×C13711yescharacteristic, complemented
452C2×#455C2×C13711yescharacteristic, complemented
453#2901C2×C13711yescharacteristic, complemented
454#2050C2×C13711yescharacteristic, complemented
455#2048C2×C13711yescharacteristic, complemented
456#2009C2×C13711yescharacteristic, complemented
457#2003C2×C13711yescharacteristic, complemented
458#1906C2×C13711yescharacteristic, complemented
459#1903C2×C13711yescharacteristic, complemented
460#1902C2×C13711yescharacteristic, complemented
461#1861C2×C13711yescharacteristic, complemented
462#1795C2×C13711yescharacteristic, complemented
463#585C22×C13711yescharacteristic
464C2×H(5,𝔽2)C22×C13711yescharacteristic
465#577—22no—
466#577—22no—
467#576—22no—
468#576—22no—
469#575—22no—
470#575C22×C13711yescharacteristic
471#575C22×C13711yescharacteristic
472C2×#137C22×C13711yescharacteristic
473C2×#137C22×C13711yescharacteristic, complemented
474C2×#137C22×C13711yescharacteristic, complemented
475C2×AGL(1,ℤ/8)—22no—
476C2×AGL(1,ℤ/8)C22×C13711yescharacteristic
477C2×AGL(1,ℤ/8)C22×C13711yescharacteristic
478#568C22×C13711yescharacteristic
479#568C22×C13711yescharacteristic, complemented
480#536C22×C13711yescharacteristic, complemented
481C2×#124C22×C13711yescharacteristic, complemented
482C4×#41C22×C13711yescharacteristic, complemented
483#473—22no—
484#471—22no—
485#464—22no—
486#463—22no—
487#456—22no—
488#455—22no—
489#455—22no—
490#455—22no—
491#430C22×C13711yescharacteristic, complemented
492#423C22×C13711yescharacteristic, complemented
493#421—22no—
494#421C22×C13711yescharacteristic
495#421C22×C13711yescharacteristic
496#421C22×C13711yescharacteristic, complemented
497#421C22×C13711yescharacteristic, complemented
498C2×#104—22no—
499C2×#104C22×C13711yescharacteristic
500C2×#104C22×C13711yescharacteristic, complemented
501C2×#104C22×C13711yescharacteristic, complemented
502#419C22×C13711yescharacteristic, complemented
503#418C22×C13711yescharacteristic, complemented
504#418C22×C13711yescharacteristic, complemented
505#413C22×C13711yescharacteristic, complemented
506#413C22×C13711yescharacteristic, complemented
507C2×#101C22×C13711yescharacteristic, complemented
508C2×#100C22×C13711yescharacteristic, complemented
509#410C22×C13711yescharacteristic, complemented
510#344C22×C13711yescharacteristic, complemented
511#344C22×C13711yescharacteristic, complemented
512#339C22×C13711yescharacteristic, complemented
513#338C22×C13711yescharacteristic, complemented
5142−1+4—21no—
5152−1+4—21no—
5162−1+4D4×C13712yes—
517H(5,𝔽2)—22no—
518H(5,𝔽2)—21no—
519H(5,𝔽2)—22no—
520H(5,𝔽2)—21no—
521H(5,𝔽2)—22no—
522H(5,𝔽2)—41no—
523H(5,𝔽2)—41no—
524H(5,𝔽2)D4×C13712yes—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—21no—
528C2×#41—21no—
529C2×#41—41no—
530C2×#41C23×C13711yescharacteristic
531C2×#41C23×C13711yescharacteristic
532C2×#41C23×C13711yescharacteristic
533C2×#41C23×C13711yescharacteristic
534C22×Q8C23×C13711yescharacteristic
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—41no—
538C22×D4C23×C13711yescharacteristic
539#137—24no—
540#137—21no—
541#137—21no—
542#137—21no—
543#137—22no—
544#137—22no—
545#137—22no—
546#137—22no—
547#137—22no—
548#137—41no—
549#137D4×C13712yes—
550AGL(1,ℤ/8)—24no—
551AGL(1,ℤ/8)—24no—
552AGL(1,ℤ/8)—24no—
553AGL(1,ℤ/8)—22no—
554AGL(1,ℤ/8)—22no—
555AGL(1,ℤ/8)—21no—
556AGL(1,ℤ/8)—22no—
557AGL(1,ℤ/8)—21no—
558AGL(1,ℤ/8)—21no—
559AGL(1,ℤ/8)—22no—
560AGL(1,ℤ/8)D4×C13712yes—
561#135—24no—
562#135—24no—
563#135—22no—
564#135—22no—
565C2×Q16—21no—
566C2×Q16—21no—
567C2×Q16—21no—
568C2×SD16—24no—
569C2×SD16—21no—
570C2×SD16—21no—
571C2×SD16—21no—
572C2×SD16—21no—
573C2×SD16D4×C13712yes—
574C2×D8—24no—
575C2×D8—21no—
576C2×D8D4×C13712yes—
577#131—22no—
578#131—22no—
579#131—22no—
580#131—41no—
581C2×M16—22no—
582C2×M16—22no—
583C2×M16C23×C13711yescharacteristic
584C2×M16C23×C13711yescharacteristic
585C2×M16C23×C13711yescharacteristic
586C2×M16C23×C13711yescharacteristic
587C2×M16C23×C13711yescharacteristic
588C2×M16C23×C13711yescharacteristic
589C4⋊Q8—21no—
590#124—22no—
591#124—21no—
592#124—21no—
593#124—21no—
594#123—41no—
595C22⋊Q8—41no—
596C4×Q8—21no—
597C4×D4—21no—
598C4×D4—41no—
599#117—21no—
600#117C23×C13711yescharacteristic
601#117C23×C13711yescharacteristic
602C2×C22⋊C4—41no—
603C2×C42—21no—
604C2×C42C23×C13711yescharacteristic
605#108—22no—
606C4⋊C8—22no—
607#104—22no—
608#104—22no—
609#104—22no—
610#104—22no—
611#104—21no—
612#104—21no—
613#104—21no—
614#104—21no—
615#104D4×C13712yes—
616#104D4×C13712yes—
617#103—22no—
618#102—22no—
619#102—41no—
620#101—21no—
621#101—21no—
622#101—22no—
623#100—21no—
624#100—21no—
625#100—22no—
626#99—41no—
627C24—21no—
628C24—41no—
629#41—21no—
630#41—21no—
631#41—21no—
632#41—21no—
633#41—24no—
634#41—22no—
635#41—22no—
636#41—22no—
637#41—22no—
638#41—21no—
639#41—21no—
640#41—21no—
641#41—21no—
642#41—21no—
643#41—21no—
644#41—21no—
645#41—21no—
646#41—42no—
647#41—42no—
648#41—42no—
649#41—42no—
650#41—42no—
651#41—42no—
652#41—41no—
653#41—41no—
654#41—42no—
655#41C2×D4×C13712yes—
656#41C2×D4×C13712yes—
657#41C2×D4×C13712yes—
658#41C2×D4×C13712yes—
659C2×Q8—22no—
660C2×Q8—22no—
661C2×Q8—21no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8—41no—
668C2×Q8C2×D4×C13711yescharacteristic
669C2×Q8C2×D4×C13711yescharacteristic
670C2×Q8C2×D4×C13711yescharacteristic
671C2×Q8#41×C13711yescharacteristic
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—24no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—42no—
685C2×D4—41no—
686C2×D4—41no—
687C2×D4—42no—
688C2×D4—42no—
689C2×D4—41no—
690C2×D4—44no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—44no—
694C2×D4—42no—
695C2×D4C2×D4×C13711yescharacteristic
696C2×D4C2×D4×C13711yescharacteristic
697C2×D4C2×D4×C13712yes—
698C2×D4C2×D4×C13711yescharacteristic
699C2×D4#41×C13711yescharacteristic
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—41no—
707C22×C4—42no—
708C22×C4—41no—
709C22×C4C24×C13711yescharacteristic
710Q16—22no—
711Q16—22no—
712Q16—42no—
713Q16—42no—
714Q16—42no—
715SD16—24no—
716SD16—22no—
717SD16—22no—
718SD16—22no—
719SD16—24no—
720SD16—22no—
721SD16—42no—
722SD16—42no—
723SD16—42no—
724D8—24no—
725D8—22no—
726D8—22no—
727D8—24no—
728M16—24no—
729M16—21no—
730M16—21no—
731M16—21no—
732M16—21no—
733M16—21no—
734M16—21no—
735M16—21no—
736M16—21no—
737M16—21no—
738M16—21no—
739M16—42no—
740M16C2×D4×C13712yes—
741M16C2×D4×C13712yes—
742C2×C8—24no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—42no—
749C2×C8C2×D4×C13712yes—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—41no—
753C4⋊C4—42no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—42no—
757C22⋊C4—42no—
758C22⋊C4—41no—
759C22⋊C4—42no—
760C42—21no—
761C42—21no—
762C42—21no—
763C42—41no—
764C42C2×D4×C13711yescharacteristic
765C42C2×D4×C13711yescharacteristic
766C23—21no—
767C23—21no—
768C23—21no—
769C23—22no—
770C23—21no—
771C23—42no—
772C23—44no—
773C23—41no—
774C23—41no—
775C23—82no—
776C23—162no—
777C23H(5,𝔽2)×C13711yescharacteristic
778Q8—21no—
779Q8—21no—
780Q8—21no—
781Q8—21no—
782Q8—21no—
783Q8—21no—
784Q8—42no—
785Q8—41no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789Q8#120×C13712yes—
790Q8#121×C13712yes—
791D4—22no—
792D4—22no—
793D4—22no—
794D4—22no—
795D4—21no—
796D4—21no—
797D4—22no—
798D4—21no—
799D4—21no—
800D4—21no—
801D4—21no—
802D4—22no—
803D4—42no—
804D4—42no—
805D4—44no—
806D4—42no—
807D4—44no—
808D4—41no—
809D4—41no—
810D4—41no—
811D4—41no—
812D4—41no—
813D4—41no—
814D4#120×C13712yes—
815D4#121×C13712yes—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—44no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—81no—
840C2×C4—82no—
841C2×C4C22×D4×C13711yescharacteristic
842C2×C4C22×D4×C13711yescharacteristic
843C2×C4C22×D4×C13711yescharacteristic
844C2×C4C22×D4×C13711yescharacteristic
845C2×C4C2×#41×C13711yescharacteristic
846C2×C4H(5,𝔽2)×C13711yescharacteristic
847C8—22no—
848C8—22no—
849C8—22no—
850C8—41no—
851C8—41no—
852C8—41no—
853C22—22no—
854C22—22no—
855C22—41no—
856C22—41no—
857C22—42no—
858C22—41no—
859C22—81no—
860C22—81no—
861C22—82no—
862C22—81no—
863C22—81no—
864C22—82no—
865C22—161no—
866C22—162no—
867C22—164no—
868C22#534×C13711yescharacteristic
869C22D42×C13711yescharacteristic
870C22#546×C13711yescharacteristic
871C4—22no—
872C4—22no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—81no—
878C4—81no—
879C4—81no—
880C4C2×#120×C13711yescharacteristic
881C4C2×#121×C13711yescharacteristic
882C4D42×C13711yescharacteristic
883C4#546×C13711yescharacteristic
884C2—21no—
885C2—21no—
886C2—21no—
887C2—42no—
888C2—42no—
889C2—82no—
890C2—81no—
891C2—81no—
892C2#2410×C13711yescharacteristic
subgroupG/H
center, socleC2×C137#2410
commutator, Frattini, cosocleC22×C4C24×C137
prime radical#3585×C137C2
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
2. #3069×C137C2semidirect
3. #3040×C137C2semidirect
4. #3022×C137C2semidirect
5. C2×#455×C137C2semidirect
6. #2901×C137C2semidirect
7. #2050×C137C2semidirect
8. #2048×C137C2semidirect
9. #2009×C137C2semidirect
10. #2003×C137C2semidirect
11. #1906×C137C2semidirect
12. #1903×C137C2semidirect
13. #1902×C137C2semidirect
14. #1861×C137C2semidirect
15. #1795×C137C2semidirect
26. C2×#137×C137C22semidirect
27. C2×#137×C137C22semidirect
32. #568×C137C22semidirect
33. #536×C137C22semidirect
34. C2×#124×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. #419×C137C22semidirect
56. #418×C137C22semidirect
57. #418×C137C22semidirect
58. #413×C137C22semidirect
59. #413×C137C22semidirect
60. C2×#101×C137C22semidirect
61. C2×#100×C137C22semidirect
62. #410×C137C22semidirect
63. #344×C137C22semidirect
64. #344×C137C22semidirect
65. #339×C137C22semidirect
66. #338×C137C22semidirect
446. #24475C137direct (N × H)
447. C137#24475direct (N × H)
449. #3069C2×C137semidirect
450. #3040C2×C137semidirect
451. #3022C2×C137semidirect
452. C2×#455C2×C137semidirect
453. #2901C2×C137semidirect
454. #2050C2×C137semidirect
455. #2048C2×C137semidirect
456. #2009C2×C137semidirect
457. #2003C2×C137semidirect
458. #1906C2×C137semidirect
459. #1903C2×C137semidirect
460. #1902C2×C137semidirect
461. #1861C2×C137semidirect
462. #1795C2×C137semidirect
473. C2×#137C22×C137semidirect
474. C2×#137C22×C137semidirect
479. #568C22×C137semidirect
480. #536C22×C137semidirect
481. C2×#124C22×C137semidirect
482. C4×#41C22×C137semidirect
491. #430C22×C137semidirect
492. #423C22×C137semidirect
496. #421C22×C137semidirect
497. #421C22×C137semidirect
500. C2×#104C22×C137semidirect
501. C2×#104C22×C137semidirect
502. #419C22×C137semidirect
503. #418C22×C137semidirect
504. #418C22×C137semidirect
505. #413C22×C137semidirect
506. #413C22×C137semidirect
507. C2×#101C22×C137semidirect
508. C2×#100C22×C137semidirect
509. #410C22×C137semidirect
510. #344C22×C137semidirect
511. #344C22×C137semidirect
512. #339C22×C137semidirect
513. #338C22×C137semidirect

Maximal subgroups

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

subgroupindex
#3585×C1372
#3069×C1372
#3040×C1372
#3022×C1372
C2×#455×C1372
#2901×C1372
#2050×C1372
#2048×C1372
#2009×C1372
#2003×C1372
#1906×C1372
#1903×C1372
#1902×C1372
#1861×C1372
#1795×C1372
#24475137