Finite Group Databasebeta

← C137×#24473 #46873859

Subgroups — C137×#24473 #46873859

Order 35072.

1314 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3586×C137C211yesmaximal, characteristic, complemented
2#3068×C137C211yesmaximal, characteristic, complemented
3#3040×C137C211yesmaximal, characteristic, complemented
4#3021×C137C211yesmaximal, characteristic, complemented
5C2×#454×C137C211yesmaximal, characteristic, complemented
6#2901×C137C211yesmaximal, characteristic, complemented
7#2050×C137C211yesmaximal, characteristic, complemented
8#2049×C137C211yesmaximal, characteristic, complemented
9#2008×C137C211yesmaximal, characteristic, complemented
10#2004×C137C211yesmaximal, characteristic, complemented
11#1906×C137C211yesmaximal, characteristic, complemented
12#1903×C137C211yesmaximal, characteristic, complemented
13#1902×C137C211yesmaximal, characteristic, complemented
14#1861×C137C211yesmaximal, characteristic, complemented
15#1796×C137C211yesmaximal, characteristic, complemented
16#585×C137C2211yescharacteristic
17C2×2−1+4×C137C2211yescharacteristic
18#578×C137—22no—
19#578×C137—22no—
20#577×C137—22no—
21#577×C137—22no—
22#575×C137—22no—
23#575×C137C2211yescharacteristic
24#575×C137C2211yescharacteristic
25C2×#137×C137—22no—
26C2×#137×C137C2211yescharacteristic
27C2×#137×C137C2211yescharacteristic
28C2×AGL(1,ℤ/8)×C137C2211yescharacteristic
29C2×AGL(1,ℤ/8)×C137C2211yescharacteristic
30C2×AGL(1,ℤ/8)×C137C2211yescharacteristic, complemented
31#568×C137C2211yescharacteristic
32#568×C137C2211yescharacteristic
33#535×C137C2211yescharacteristic
34C2×#124×C137C2211yescharacteristic, complemented
35C4×#41×C137C2211yescharacteristic
36#472×C137—22no—
37#471×C137—22no—
38#464×C137—22no—
39#463×C137—22no—
40#454×C137—22no—
41#454×C137—22no—
42#454×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
50#421×C137C2211yescharacteristic
51C2×#104×C137—22no—
52C2×#104×C137C2211yescharacteristic
53C2×#104×C137C2211yescharacteristic
54C2×#104×C137C2211yescharacteristic, complemented
55#419×C137C2211yescharacteristic, complemented
56#419×C137C2211yescharacteristic, complemented
57#418×C137C2211yescharacteristic, complemented
58#413×C137C2211yescharacteristic
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—22no—
682−1+4×C137—22no—
692−1+4×C137—21no—
702−1+4×C137—21no—
712−1+4×C137—22no—
722−1+4×C137—41no—
732−1+4×C137D412yes—
74H(5,𝔽2)×C137—21no—
75H(5,𝔽2)×C137—21no—
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×C137—41no—
84C2×#41×C137C2311yescharacteristic
85C2×#41×C137C2311yescharacteristic
86C2×#41×C137C2311yescharacteristic
87C2×#41×C137C2311yescharacteristic
88C22×Q8×C137—21no—
89C22×Q8×C137—21no—
90C22×Q8×C137C2311yescharacteristic
91C22×D4×C137C2311yescharacteristic
92#137×C137—24no—
93#137×C137—24no—
94#137×C137—24no—
95#137×C137—22no—
96#137×C137—22no—
97#137×C137—21no—
98#137×C137—22no—
99#137×C137—21no—
100#137×C137—21no—
101#137×C137—22no—
102#137×C137D412yescomplemented
103AGL(1,ℤ/8)×C137—24no—
104AGL(1,ℤ/8)×C137—21no—
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—41no—
113AGL(1,ℤ/8)×C137D412yescomplemented
114#135×C137—24no—
115#135×C137—24no—
116#135×C137—22no—
117#135×C137—22no—
118C2×Q16×C137—24no—
119C2×Q16×C137—21no—
120C2×Q16×C137D412yescomplemented
121C2×SD16×C137—24no—
122C2×SD16×C137—21no—
123C2×SD16×C137—21no—
124C2×SD16×C137—21no—
125C2×SD16×C137—21no—
126C2×SD16×C137D412yescomplemented
127C2×D8×C137—21no—
128C2×D8×C137—21no—
129C2×D8×C137—21no—
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
142#127×C137—21no—
143#124×C137—21no—
144#124×C137—22no—
145#124×C137—21no—
146#124×C137—21no—
147#121×C137—41no—
148#120×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×C137D412yescomplemented
169#104×C137D412yescomplemented
170#103×C137—22no—
171#103×C137—41no—
172#102×C137—22no—
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—
181#41×C137—21no—
182#41×C137—21no—
183#41×C137—21no—
184#41×C137—21no—
185#41×C137—24no—
186#41×C137—22no—
187#41×C137—22no—
188#41×C137—22no—
189#41×C137—22no—
190#41×C137—21no—
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—42no—
199#41×C137—42no—
200#41×C137—42no—
201#41×C137—42no—
202#41×C137—42no—
203#41×C137—44no—
204#41×C137—42no—
205#41×C137—41no—
206#41×C137—41no—
207#41×C137—44no—
208#41×C137—42no—
209#41×C137C2×D412yes—
210#41×C137C2×D412yes—
211#41×C137C2×D412yes—
212#41×C137C2×D412yes—
213C2×Q8×C137—21no—
214C2×Q8×C137—24no—
215C2×Q8×C137—22no—
216C2×Q8×C137—22no—
217C2×Q8×C137—21no—
218C2×Q8×C137—21no—
219C2×Q8×C137—21no—
220C2×Q8×C137—21no—
221C2×Q8×C137—41no—
222C2×Q8×C137—42no—
223C2×Q8×C137—42no—
224C2×Q8×C137—41no—
225C2×Q8×C137—42no—
226C2×Q8×C137C2×D411yescharacteristic
227C2×Q8×C137C2×D411yescharacteristic
228C2×Q8×C137C2×D412yes—
229C2×Q8×C137C2×D411yescharacteristic
230C2×Q8×C137#4111yescharacteristic
231C2×D4×C137—21no—
232C2×D4×C137—21no—
233C2×D4×C137—22no—
234C2×D4×C137—22no—
235C2×D4×C137—21no—
236C2×D4×C137—21no—
237C2×D4×C137—21no—
238C2×D4×C137—21no—
239C2×D4×C137—21no—
240C2×D4×C137—21no—
241C2×D4×C137—21no—
242C2×D4×C137—21no—
243C2×D4×C137—42no—
244C2×D4×C137—41no—
245C2×D4×C137—42no—
246C2×D4×C137—42no—
247C2×D4×C137—41no—
248C2×D4×C137—42no—
249C2×D4×C137C2×D411yescharacteristic
250C2×D4×C137C2×D411yescharacteristic
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—42no—
260C22×C4×C137—41no—
261C22×C4×C137—41no—
262C22×C4×C137—41no—
263C22×C4×C137C2411yescharacteristic
264Q16×C137—24no—
265Q16×C137—22no—
266Q16×C137—22no—
267Q16×C137—24no—
268SD16×C137—24no—
269SD16×C137—22no—
270SD16×C137—22no—
271SD16×C137—22no—
272SD16×C137—22no—
273SD16×C137—24no—
274SD16×C137—42no—
275SD16×C137—42no—
276SD16×C137—42no—
277D8×C137—22no—
278D8×C137—22no—
279D8×C137—42no—
280D8×C137—42no—
281D8×C137—42no—
282M16×C137—24no—
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—21no—
293M16×C137—42no—
294M16×C137C2×D412yes—
295M16×C137C2×D412yes—
296C2×C8×C137—24no—
297C2×C8×C137—21no—
298C2×C8×C137—21no—
299C2×C8×C137—21no—
300C2×C8×C137—21no—
301C2×C8×C137—21no—
302C2×C8×C137—42no—
303C2×C8×C137C2×D412yes—
304C4⋊C4×C137—21no—
305C4⋊C4×C137—21no—
306C4⋊C4×C137—41no—
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—21no—
323C23×C137—42no—
324C23×C137—41no—
325C23×C137—41no—
326C23×C137—41no—
327C23×C137—82no—
328C23×C137H(5,𝔽2)11yescharacteristic
329Q8×C137—21no—
330Q8×C137—21no—
331Q8×C137—21no—
332Q8×C137—22no—
333Q8×C137—21no—
334Q8×C137—21no—
335Q8×C137—21no—
336Q8×C137—22no—
337Q8×C137—42no—
338Q8×C137—44no—
339Q8×C137—41no—
340Q8×C137—41no—
341Q8×C137#12012yes—
342Q8×C137#12112yes—
343D4×C137—22no—
344D4×C137—22no—
345D4×C137—22no—
346D4×C137—22no—
347D4×C137—21no—
348D4×C137—21no—
349D4×C137—21no—
350D4×C137—21no—
351D4×C137—21no—
352D4×C137—21no—
353D4×C137—42no—
354D4×C137—42no—
355D4×C137—42no—
356D4×C137—44no—
357D4×C137—41no—
358D4×C137—41no—
359D4×C137—41no—
360D4×C137—41no—
361D4×C137—41no—
362D4×C137—41no—
363D4×C137—41no—
364D4×C137—41no—
365D4×C137—162no—
366D4×C137#12012yes—
367D4×C137#12112yes—
368C2×C4×C137—21no—
369C2×C4×C137—21no—
370C2×C4×C137—22no—
371C2×C4×C137—22no—
372C2×C4×C137—22no—
373C2×C4×C137—22no—
374C2×C4×C137—21no—
375C2×C4×C137—21no—
376C2×C4×C137—21no—
377C2×C4×C137—22no—
378C2×C4×C137—21no—
379C2×C4×C137—42no—
380C2×C4×C137—42no—
381C2×C4×C137—42no—
382C2×C4×C137—44no—
383C2×C4×C137—44no—
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—41no—
411C22×C137—81no—
412C22×C137—81no—
413C22×C137—81no—
414C22×C137—81no—
415C22×C137—82no—
416C22×C137—82no—
417C22×C137—81no—
418C22×C137—161no—
419C22×C137—162no—
420C22×C137#53411yescharacteristic
421C22×C137D4211yescharacteristic
422C22×C137#54611yescharacteristic
423C4×C137—22no—
424C4×C137—22no—
425C4×C137—41no—
426C4×C137—41no—
427C4×C137—41no—
428C4×C137—42no—
429C4×C137—41no—
430C4×C137—81no—
431C4×C137—81no—
432C4×C137C2×#12011yescharacteristic
433C4×C137C2×#12111yescharacteristic
434C4×C137D4211yescharacteristic
435C4×C137#54611yescharacteristic
436C2×C137—21no—
437C2×C137—21no—
438C2×C137—21no—
439C2×C137—42no—
440C2×C137—42no—
441C2×C137—81no—
442C2×C137—81no—
443C2×C137—161no—
444C2×C137#241011yescharacteristic
445#24473C13711yesmaximal, characteristic, direct product factor, Sylow
446C137#2447311yescharacteristic, direct product factor, Sylow
447#3586C2×C13711yescharacteristic, complemented
448#3068C2×C13711yescharacteristic, complemented
449#3040C2×C13711yescharacteristic, complemented
450#3021C2×C13711yescharacteristic, complemented
451C2×#454C2×C13711yescharacteristic, complemented
452#2901C2×C13711yescharacteristic, complemented
453#2050C2×C13711yescharacteristic, complemented
454#2049C2×C13711yescharacteristic, complemented
455#2008C2×C13711yescharacteristic, complemented
456#2004C2×C13711yescharacteristic, complemented
457#1906C2×C13711yescharacteristic, complemented
458#1903C2×C13711yescharacteristic, complemented
459#1902C2×C13711yescharacteristic, complemented
460#1861C2×C13711yescharacteristic, complemented
461#1796C2×C13711yescharacteristic, complemented
462#585C22×C13711yescharacteristic
463C2×2−1+4C22×C13711yescharacteristic
464#578—22no—
465#578—22no—
466#577—22no—
467#577—22no—
468#575—22no—
469#575C22×C13711yescharacteristic
470#575C22×C13711yescharacteristic
471C2×#137—22no—
472C2×#137C22×C13711yescharacteristic
473C2×#137C22×C13711yescharacteristic
474C2×AGL(1,ℤ/8)C22×C13711yescharacteristic
475C2×AGL(1,ℤ/8)C22×C13711yescharacteristic
476C2×AGL(1,ℤ/8)C22×C13711yescharacteristic, complemented
477#568C22×C13711yescharacteristic
478#568C22×C13711yescharacteristic
479#535C22×C13711yescharacteristic
480C2×#124C22×C13711yescharacteristic, complemented
481C4×#41C22×C13711yescharacteristic
482#472—22no—
483#471—22no—
484#464—22no—
485#463—22no—
486#454—22no—
487#454—22no—
488#454—22no—
489#453—22no—
490#430C22×C13711yescharacteristic, complemented
491#423C22×C13711yescharacteristic, complemented
492#421—22no—
493#421C22×C13711yescharacteristic
494#421C22×C13711yescharacteristic
495#421C22×C13711yescharacteristic
496#421C22×C13711yescharacteristic
497C2×#104—22no—
498C2×#104C22×C13711yescharacteristic
499C2×#104C22×C13711yescharacteristic
500C2×#104C22×C13711yescharacteristic, complemented
501#419C22×C13711yescharacteristic, complemented
502#419C22×C13711yescharacteristic, complemented
503#418C22×C13711yescharacteristic, complemented
504#413C22×C13711yescharacteristic
505#413C22×C13711yescharacteristic, complemented
506C2×#101C22×C13711yescharacteristic, complemented
507C2×#100C22×C13711yescharacteristic, complemented
508#410C22×C13711yescharacteristic, complemented
509#344C22×C13711yescharacteristic, complemented
510#344C22×C13711yescharacteristic, complemented
511#339C22×C13711yescharacteristic, complemented
512#338C22×C13711yescharacteristic, complemented
5132−1+4—22no—
5142−1+4—22no—
5152−1+4—21no—
5162−1+4—21no—
5172−1+4—22no—
5182−1+4—41no—
5192−1+4D4×C13712yes—
520H(5,𝔽2)—21no—
521H(5,𝔽2)—21no—
522H(5,𝔽2)—41no—
523H(5,𝔽2)D4×C13712yes—
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—21no—
527C2×#41—21no—
528C2×#41—41no—
529C2×#41—41no—
530C2×#41C23×C13711yescharacteristic
531C2×#41C23×C13711yescharacteristic
532C2×#41C23×C13711yescharacteristic
533C2×#41C23×C13711yescharacteristic
534C22×Q8—21no—
535C22×Q8—21no—
536C22×Q8C23×C13711yescharacteristic
537C22×D4C23×C13711yescharacteristic
538#137—24no—
539#137—24no—
540#137—24no—
541#137—22no—
542#137—22no—
543#137—21no—
544#137—22no—
545#137—21no—
546#137—21no—
547#137—22no—
548#137D4×C13712yescomplemented
549AGL(1,ℤ/8)—24no—
550AGL(1,ℤ/8)—21no—
551AGL(1,ℤ/8)—21no—
552AGL(1,ℤ/8)—21no—
553AGL(1,ℤ/8)—22no—
554AGL(1,ℤ/8)—22no—
555AGL(1,ℤ/8)—22no—
556AGL(1,ℤ/8)—22no—
557AGL(1,ℤ/8)—22no—
558AGL(1,ℤ/8)—41no—
559AGL(1,ℤ/8)D4×C13712yescomplemented
560#135—24no—
561#135—24no—
562#135—22no—
563#135—22no—
564C2×Q16—24no—
565C2×Q16—21no—
566C2×Q16D4×C13712yescomplemented
567C2×SD16—24no—
568C2×SD16—21no—
569C2×SD16—21no—
570C2×SD16—21no—
571C2×SD16—21no—
572C2×SD16D4×C13712yescomplemented
573C2×D8—21no—
574C2×D8—21no—
575C2×D8—21no—
576#131—22no—
577#131—22no—
578#131—22no—
579#131—41no—
580C2×M16—22no—
581C2×M16—22no—
582C2×M16C23×C13711yescharacteristic
583C2×M16C23×C13711yescharacteristic
584C2×M16C23×C13711yescharacteristic
585C2×M16C23×C13711yescharacteristic
586C2×M16C23×C13711yescharacteristic
587C2×M16C23×C13711yescharacteristic
588#127—21no—
589#124—22no—
590#124—21no—
591#124—21no—
592#124—21no—
593#121—41no—
594#120—41no—
595C4×Q8—21no—
596C4×D4—21no—
597C4×D4—41no—
598#117—21no—
599#117C23×C13711yescharacteristic
600#117C23×C13711yescharacteristic
601C2×C22⋊C4—41no—
602C2×C42—21no—
603C2×C42C23×C13711yescharacteristic
604#108—22no—
605C4⋊C8—22no—
606#104—22no—
607#104—22no—
608#104—22no—
609#104—22no—
610#104—21no—
611#104—21no—
612#104—21no—
613#104—21no—
614#104D4×C13712yescomplemented
615#104D4×C13712yescomplemented
616#103—22no—
617#103—41no—
618#102—22no—
619#101—21no—
620#101—21no—
621#101—22no—
622#100—21no—
623#100—21no—
624#100—22no—
625#99—41no—
626C24—21no—
627#41—21no—
628#41—21no—
629#41—21no—
630#41—21no—
631#41—24no—
632#41—22no—
633#41—22no—
634#41—22no—
635#41—22no—
636#41—21no—
637#41—21no—
638#41—21no—
639#41—21no—
640#41—21no—
641#41—21no—
642#41—21no—
643#41—21no—
644#41—42no—
645#41—42no—
646#41—42no—
647#41—42no—
648#41—42no—
649#41—44no—
650#41—42no—
651#41—41no—
652#41—41no—
653#41—44no—
654#41—42no—
655#41C2×D4×C13712yes—
656#41C2×D4×C13712yes—
657#41C2×D4×C13712yes—
658#41C2×D4×C13712yes—
659C2×Q8—21no—
660C2×Q8—24no—
661C2×Q8—22no—
662C2×Q8—22no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8—41no—
668C2×Q8—42no—
669C2×Q8—42no—
670C2×Q8—41no—
671C2×Q8—42no—
672C2×Q8C2×D4×C13711yescharacteristic
673C2×Q8C2×D4×C13711yescharacteristic
674C2×Q8C2×D4×C13712yes—
675C2×Q8C2×D4×C13711yescharacteristic
676C2×Q8#41×C13711yescharacteristic
677C2×D4—21no—
678C2×D4—21no—
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—42no—
690C2×D4—41no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—41no—
694C2×D4—42no—
695C2×D4C2×D4×C13711yescharacteristic
696C2×D4C2×D4×C13711yescharacteristic
697C2×D4C2×D4×C13711yescharacteristic
698C2×D4#41×C13711yescharacteristic
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—42no—
706C22×C4—41no—
707C22×C4—41no—
708C22×C4—41no—
709C22×C4C24×C13711yescharacteristic
710Q16—24no—
711Q16—22no—
712Q16—22no—
713Q16—24no—
714SD16—24no—
715SD16—22no—
716SD16—22no—
717SD16—22no—
718SD16—22no—
719SD16—24no—
720SD16—42no—
721SD16—42no—
722SD16—42no—
723D8—22no—
724D8—22no—
725D8—42no—
726D8—42no—
727D8—42no—
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—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—42no—
756C22⋊C4—42no—
757C22⋊C4—41no—
758C22⋊C4—42no—
759C42—21no—
760C42—21no—
761C42—21no—
762C42—41no—
763C42C2×D4×C13711yescharacteristic
764C42C2×D4×C13711yescharacteristic
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—42no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—82no—
774C23H(5,𝔽2)×C13711yescharacteristic
775Q8—21no—
776Q8—21no—
777Q8—21no—
778Q8—22no—
779Q8—21no—
780Q8—21no—
781Q8—21no—
782Q8—22no—
783Q8—42no—
784Q8—44no—
785Q8—41no—
786Q8—41no—
787Q8#120×C13712yes—
788Q8#121×C13712yes—
789D4—22no—
790D4—22no—
791D4—22no—
792D4—22no—
793D4—21no—
794D4—21no—
795D4—21no—
796D4—21no—
797D4—21no—
798D4—21no—
799D4—42no—
800D4—42no—
801D4—42no—
802D4—44no—
803D4—41no—
804D4—41no—
805D4—41no—
806D4—41no—
807D4—41no—
808D4—41no—
809D4—41no—
810D4—41no—
811D4—162no—
812D4#120×C13712yes—
813D4#121×C13712yes—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—22no—
824C2×C4—21no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—44no—
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—81no—
839C2×C4—82no—
840C2×C4C22×D4×C13711yescharacteristic
841C2×C4C22×D4×C13711yescharacteristic
842C2×C4C22×D4×C13711yescharacteristic
843C2×C4C22×D4×C13711yescharacteristic
844C2×C4C2×#41×C13711yescharacteristic
845C2×C4H(5,𝔽2)×C13711yescharacteristic
846C8—22no—
847C8—22no—
848C8—22no—
849C8—41no—
850C8—41no—
851C8—41no—
852C22—22no—
853C22—22no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—81no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—82no—
862C22—82no—
863C22—81no—
864C22—161no—
865C22—162no—
866C22#534×C13711yescharacteristic
867C22D42×C13711yescharacteristic
868C22#546×C13711yescharacteristic
869C4—22no—
870C4—22no—
871C4—41no—
872C4—41no—
873C4—41no—
874C4—42no—
875C4—41no—
876C4—81no—
877C4—81no—
878C4C2×#120×C13711yescharacteristic
879C4C2×#121×C13711yescharacteristic
880C4D42×C13711yescharacteristic
881C4#546×C13711yescharacteristic
882C2—21no—
883C2—21no—
884C2—21no—
885C2—42no—
886C2—42no—
887C2—81no—
888C2—81no—
889C2—161no—
890C2#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. #3586×C137C2semidirect
2. #3068×C137C2semidirect
3. #3040×C137C2semidirect
4. #3021×C137C2semidirect
5. C2×#454×C137C2semidirect
6. #2901×C137C2semidirect
7. #2050×C137C2semidirect
8. #2049×C137C2semidirect
9. #2008×C137C2semidirect
10. #2004×C137C2semidirect
11. #1906×C137C2semidirect
12. #1903×C137C2semidirect
13. #1902×C137C2semidirect
14. #1861×C137C2semidirect
15. #1796×C137C2semidirect
30. C2×AGL(1,ℤ/8)×C137C22semidirect
34. C2×#124×C137C22semidirect
44. #430×C137C22semidirect
45. #423×C137C22semidirect
54. C2×#104×C137C22semidirect
55. #419×C137C22semidirect
56. #419×C137C22semidirect
57. #418×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
102. #137×C137D4semidirect
113. AGL(1,ℤ/8)×C137D4semidirect
120. C2×Q16×C137D4semidirect
126. C2×SD16×C137D4semidirect
168. #104×C137D4semidirect
169. #104×C137D4semidirect
445. #24473C137direct (N × H)
446. C137#24473direct (N × H)
447. #3586C2×C137semidirect
448. #3068C2×C137semidirect
449. #3040C2×C137semidirect
450. #3021C2×C137semidirect
451. C2×#454C2×C137semidirect
452. #2901C2×C137semidirect
453. #2050C2×C137semidirect
454. #2049C2×C137semidirect
455. #2008C2×C137semidirect
456. #2004C2×C137semidirect
457. #1906C2×C137semidirect
458. #1903C2×C137semidirect
459. #1902C2×C137semidirect
460. #1861C2×C137semidirect
461. #1796C2×C137semidirect
476. C2×AGL(1,ℤ/8)C22×C137semidirect
480. C2×#124C22×C137semidirect
490. #430C22×C137semidirect
491. #423C22×C137semidirect
500. C2×#104C22×C137semidirect
501. #419C22×C137semidirect
502. #419C22×C137semidirect
503. #418C22×C137semidirect
505. #413C22×C137semidirect
506. C2×#101C22×C137semidirect
507. C2×#100C22×C137semidirect
508. #410C22×C137semidirect
509. #344C22×C137semidirect
510. #344C22×C137semidirect
511. #339C22×C137semidirect
512. #338C22×C137semidirect
548. #137D4×C137semidirect
559. AGL(1,ℤ/8)D4×C137semidirect
566. C2×Q16D4×C137semidirect
572. C2×SD16D4×C137semidirect
614. #104D4×C137semidirect
615. #104D4×C137semidirect

Maximal subgroups

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

subgroupindex
#3586×C1372
#3068×C1372
#3040×C1372
#3021×C1372
C2×#454×C1372
#2901×C1372
#2050×C1372
#2049×C1372
#2008×C1372
#2004×C1372
#1906×C1372
#1903×C1372
#1902×C1372
#1861×C1372
#1796×C1372
#24473137