Finite Group Databasebeta

← C137×#11016 #46860402

Subgroups — C137×#11016 #46860402

Order 35072.

1574 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)×C137C211yesmaximal, characteristic
2C22×#104×C137C211yesmaximal, characteristic, complemented
3C2×#418×C137C211yesmaximal, characteristic, complemented
4#2311×C137C211yesmaximal, characteristic, complemented
5C2×#390×C137C211yesmaximal, characteristic, complemented
6C2×#343×C137C211yesmaximal, characteristic, complemented
7C2×#339×C137C211yesmaximal, characteristic, complemented
8C22×#41×C137C2211yescharacteristic
9C23×D4×C137C2211yescharacteristic
10C2×AGL(1,ℤ/8)×C137—22no—
11C2×AGL(1,ℤ/8)×C137—22no—
12C2×AGL(1,ℤ/8)×C137—22no—
13C2×AGL(1,ℤ/8)×C137—22no—
14C2×AGL(1,ℤ/8)×C137—22no—
15C2×AGL(1,ℤ/8)×C137C414yescomplemented
16C22×SD16×C137—21no—
17C22×D8×C137—21no—
18C22×M16×C137C2211yescharacteristic
19C22×M16×C137C2211yescharacteristic
20C2×#117×C137C2211yescharacteristic
21C22×C4⋊C4×C137C2211yescharacteristic
22C22×C22⋊C4×C137—22no—
23C22×C42×C137C2211yescharacteristic
24C2×#104×C137—22no—
25C2×#104×C137—22no—
26C2×#104×C137—22no—
27#418×C137—22no—
28#418×C137—22no—
29C2×#102×C137—22no—
30#391×C137—21no—
31#390×C137—22no—
32#390×C137—21no—
33#390×C137—22no—
34#386×C137—22no—
35#380×C137—22no—
36#343×C137—22no—
37#339×C137—22no—
38C25×C137—21no—
39C2×#41×C137—21no—
40C2×#41×C137—21no—
41C2×#41×C137—21no—
42C2×#41×C137—21no—
43C2×#41×C137—21no—
44C2×#41×C137—21no—
45C2×#41×C137—21no—
46C2×#41×C137—21no—
47C2×#41×C137—21no—
48C2×#41×C137—21no—
49C2×#41×C137C2×C412yes—
50C2×#41×C137D412yes—
51C22×Q8×C137D411yescharacteristic
52C22×D4×C137—21no—
53C22×D4×C137—21no—
54C22×D4×C137—21no—
55C22×D4×C137—21no—
56C22×D4×C137—21no—
57C22×D4×C137—21no—
58C22×D4×C137—21no—
59C22×D4×C137—21no—
60C22×D4×C137—21no—
61C22×D4×C137—21no—
62C22×D4×C137—21no—
63C22×D4×C137—21no—
64C22×D4×C137C2×C412yes—
65C22×D4×C137D411yescharacteristic
66C22×D4×C137D412yes—
67C22×D4×C137D412yes—
68C23×C4×C137—21no—
69C23×C4×C137—21no—
70C23×C4×C137D412yes—
71C23×C4×C137C2311yescharacteristic
72AGL(1,ℤ/8)×C137—28no—
73AGL(1,ℤ/8)×C137—28no—
74AGL(1,ℤ/8)×C137—28no—
75AGL(1,ℤ/8)×C137—28no—
76C2×SD16×C137—24no—
77C2×SD16×C137—24no—
78C2×SD16×C137—24no—
79C2×D8×C137—24no—
80C2×D8×C137—24no—
81C2×D8×C137—24no—
82C2×M16×C137—21no—
83C2×M16×C137—21no—
84C2×M16×C137—21no—
85C2×M16×C137—21no—
86C2×M16×C137—21no—
87C2×M16×C137—21no—
88C2×M16×C137—21no—
89C2×M16×C137—21no—
90C2×M16×C137C2×C412yes—
91C2×M16×C137D412yes—
92C2×M16×C137D412yes—
93C2×M16×C137D412yes—
94C22×C8×C137—21no—
95C22×C8×C137—21no—
96#117×C137—21no—
97#117×C137—21no—
98#117×C137—21no—
99#117×C137—21no—
100C2×C4⋊C4×C137—21no—
101C2×C4⋊C4×C137—21no—
102C2×C4⋊C4×C137—21no—
103C2×C4⋊C4×C137—21no—
104C2×C4⋊C4×C137—21no—
105C2×C4⋊C4×C137—21no—
106C2×C4⋊C4×C137D412yes—
107C2×C22⋊C4×C137—28no—
108C2×C22⋊C4×C137—21no—
109C2×C22⋊C4×C137—24no—
110C2×C22⋊C4×C137—48no—
111C2×C42×C137—21no—
112C2×C42×C137—21no—
113C2×C42×C137—21no—
114C2×C42×C137—21no—
115C2×C42×C137—21no—
116C2×C42×C137—21no—
117C2×C42×C137D412yes—
118#104×C137—28no—
119#102×C137—28no—
120#95×C137—24no—
121C24×C137—22no—
122C24×C137—22no—
123C24×C137—21no—
124C24×C137—22no—
125C24×C137—44no—
126C24×C137—44no—
127C24×C137—41no—
128C24×C137—41no—
129C24×C137—41no—
130C24×C137—41no—
131C24×C137C2×D411yescharacteristic
132#41×C137—22no—
133#41×C137—22no—
134#41×C137—22no—
135#41×C137—22no—
136#41×C137—22no—
137#41×C137—22no—
138#41×C137—22no—
139#41×C137—22no—
140#41×C137—41no—
141#41×C137—41no—
142#41×C137—41no—
143#41×C137—41no—
144#41×C137—41no—
145#41×C137—41no—
146#41×C137—41no—
147#41×C137—41no—
148C2×Q8×C137—21no—
149C2×Q8×C137—21no—
150C2×Q8×C137—21no—
151C2×Q8×C137—21no—
152C2×Q8×C137—21no—
153C2×Q8×C137C22⋊C412yescomplemented
154C2×D4×C137—22no—
155C2×D4×C137—22no—
156C2×D4×C137—22no—
157C2×D4×C137—22no—
158C2×D4×C137—22no—
159C2×D4×C137—22no—
160C2×D4×C137—22no—
161C2×D4×C137—22no—
162C2×D4×C137—21no—
163C2×D4×C137—21no—
164C2×D4×C137—22no—
165C2×D4×C137—22no—
166C2×D4×C137—22no—
167C2×D4×C137—22no—
168C2×D4×C137—22no—
169C2×D4×C137—22no—
170C2×D4×C137—21no—
171C2×D4×C137—21no—
172C2×D4×C137—22no—
173C2×D4×C137—22no—
174C2×D4×C137—22no—
175C2×D4×C137—21no—
176C2×D4×C137—41no—
177C2×D4×C137—41no—
178C2×D4×C137—41no—
179C2×D4×C137—41no—
180C2×D4×C137—41no—
181C2×D4×C137—41no—
182C2×D4×C137—41no—
183C2×D4×C137—41no—
184C2×D4×C137—41no—
185C2×D4×C137—41no—
186C2×D4×C137—41no—
187C2×D4×C137—41no—
188C2×D4×C137—41no—
189C2×D4×C137—41no—
190C2×D4×C137—41no—
191C2×D4×C137—41no—
192C2×D4×C137C22⋊C412yescomplemented
193C2×D4×C137C22⋊C414yescomplemented
194C22×C4×C137—24no—
195C22×C4×C137—22no—
196C22×C4×C137—21no—
197C22×C4×C137—22no—
198C22×C4×C137—22no—
199C22×C4×C137—22no—
200C22×C4×C137—22no—
201C22×C4×C137—22no—
202C22×C4×C137—22no—
203C22×C4×C137—42no—
204C22×C4×C137—41no—
205C22×C4×C137—41no—
206C22×C4×C137—41no—
207C22×C4×C137—41no—
208C22×C4×C137—41no—
209C22×C4×C137—41no—
210C22×C4×C137—44no—
211C22×C4×C137C22×C411yescharacteristic
212C22×C4×C137C2×D411yescharacteristic
213C22×C4×C137C2×D411yescharacteristic
214C22×C4×C137C2×D411yescharacteristic
215C22×C4×C137C2×D411yescharacteristic
216C22×C4×C137C2×D411yescharacteristic
217C22×C4×C137C2×D411yescharacteristic
218C22×C4×C137C2×D411yescharacteristic
219C22×C4×C137C2×D411yescharacteristic
220C22×C4×C137C2×D411yescharacteristic
221C22×C4×C137#4111yescharacteristic
222C22×C4×C137#4111yescharacteristic
223C22×C4×C137#4111yescharacteristic
224C22×C4×C137#4111yescharacteristic
225SD16×C137—216no—
226D8×C137—216no—
227M16×C137—22no—
228M16×C137—22no—
229M16×C137—22no—
230M16×C137—22no—
231M16×C137—22no—
232M16×C137—41no—
233M16×C137—41no—
234M16×C137C22⋊C414yescomplemented
235C2×C8×C137—22no—
236C2×C8×C137—22no—
237C2×C8×C137—22no—
238C2×C8×C137—22no—
239C2×C8×C137—41no—
240C2×C8×C137—41no—
241C4⋊C4×C137—22no—
242C4⋊C4×C137—22no—
243C4⋊C4×C137—41no—
244C4⋊C4×C137—41no—
245C4⋊C4×C137—41no—
246C4⋊C4×C137—41no—
247C22⋊C4×C137—416no—
248C22⋊C4×C137—41no—
249C22⋊C4×C137—41no—
250C22⋊C4×C137—84no—
251C42×C137—22no—
252C42×C137—22no—
253C42×C137—41no—
254C42×C137—41no—
255C42×C137—41no—
256C42×C137—41no—
257C23×C137—22no—
258C23×C137—22no—
259C23×C137—22no—
260C23×C137—24no—
261C23×C137—44no—
262C23×C137—48no—
263C23×C137—44no—
264C23×C137—48no—
265C23×C137—42no—
266C23×C137—42no—
267C23×C137—41no—
268C23×C137—41no—
269C23×C137—42no—
270C23×C137—42no—
271C23×C137—42no—
272C23×C137—42no—
273C23×C137—42no—
274C23×C137—42no—
275C23×C137—84no—
276C23×C137—82no—
277C23×C137—82no—
278C23×C137—84no—
279C23×C137—82no—
280C23×C137—82no—
281C23×C137C4×D411yescharacteristic
282C23×C137#12011yescharacteristic
283C23×C137#12011yescharacteristic
284C23×C137#12111yescharacteristic
285C23×C137#12111yescharacteristic
286C23×C137#12111yescharacteristic
287C23×C137#12711yescharacteristic
288Q8×C137—22no—
289Q8×C137—22no—
290Q8×C137—41no—
291Q8×C137—41no—
292D4×C137—22no—
293D4×C137—24no—
294D4×C137—24no—
295D4×C137—22no—
296D4×C137—42no—
297D4×C137—42no—
298D4×C137—42no—
299D4×C137—42no—
300D4×C137—42no—
301D4×C137—42no—
302D4×C137—42no—
303D4×C137—42no—
304D4×C137—42no—
305D4×C137—42no—
306D4×C137—41no—
307D4×C137—41no—
308C2×C4×C137—24no—
309C2×C4×C137—22no—
310C2×C4×C137—44no—
311C2×C4×C137—42no—
312C2×C4×C137—44no—
313C2×C4×C137—42no—
314C2×C4×C137—41no—
315C2×C4×C137—41no—
316C2×C4×C137—42no—
317C2×C4×C137—42no—
318C2×C4×C137—42no—
319C2×C4×C137—42no—
320C2×C4×C137—44no—
321C2×C4×C137—42no—
322C2×C4×C137—42no—
323C2×C4×C137—42no—
324C2×C4×C137—44no—
325C2×C4×C137—42no—
326C2×C4×C137—82no—
327C2×C4×C137C2×C22⋊C411yescharacteristic
328C2×C4×C137C2×C22⋊C411yescharacteristic
329C2×C4×C137C2×C22⋊C411yescharacteristic
330C2×C4×C137C4×D411yescharacteristic
331C2×C4×C137C4×D411yescharacteristic
332C2×C4×C137C4×D411yescharacteristic
333C2×C4×C137#12011yescharacteristic
334C2×C4×C137#12011yescharacteristic
335C2×C4×C137#12011yescharacteristic
336C2×C4×C137#12011yescharacteristic
337C2×C4×C137#12011yescharacteristic
338C2×C4×C137#12011yescharacteristic
339C2×C4×C137#12111yescharacteristic
340C2×C4×C137#12111yescharacteristic
341C2×C4×C137#12111yescharacteristic
342C2×C4×C137#12111yescharacteristic
343C2×C4×C137#12111yescharacteristic
344C2×C4×C137#12111yescharacteristic
345C2×C4×C137#12111yescharacteristic
346C2×C4×C137#12111yescharacteristic
347C2×C4×C137#12111yescharacteristic
348C2×C4×C137#12311yescharacteristic
349C2×C4×C137#12311yescharacteristic
350C2×C4×C137#12311yescharacteristic
351C2×C4×C137#12311yescharacteristic
352C2×C4×C137#12411yescharacteristic
353C2×C4×C137#12411yescharacteristic
354C2×C4×C137#12711yescharacteristic
355C8×C137—24no—
356C8×C137—42no—
357C22×C137—22no—
358C22×C137—22no—
359C22×C137—21no—
360C22×C137—21no—
361C22×C137—21no—
362C22×C137—21no—
363C22×C137—22no—
364C22×C137—22no—
365C22×C137—48no—
366C22×C137—44no—
367C22×C137—42no—
368C22×C137—44no—
369C22×C137—84no—
370C22×C137—84no—
371C22×C137—84no—
372C22×C137—84no—
373C22×C137—81no—
374C22×C137—82no—
375C22×C137—81no—
376C22×C137—82no—
377C22×C137—82no—
378C22×C137—84no—
379C22×C137#38611yescharacteristic
380C22×C137#38611yescharacteristic
381C22×C137#39011yescharacteristic
382C22×C137#39211yescharacteristic
383C22×C137#39211yescharacteristic
384C22×C137#39211yescharacteristic
385C22×C137#39411yescharacteristic
386C22×C137#45312yes—
387C22×C137#45412yes—
388C4×C137—44no—
389C4×C137—42no—
390C4×C137—82no—
391C4×C137—82no—
392C4×C137#37911yescharacteristic
393C4×C137#38611yescharacteristic
394C4×C137#38611yescharacteristic
395C4×C137#39011yescharacteristic
396C4×C137#39211yescharacteristic
397C4×C137#39411yescharacteristic
398C4×C137#39411yescharacteristic
399C4×C137#39411yescharacteristic
400C2×C137—21no—
401C2×C137—21no—
402C2×C137—21no—
403C2×C137—21no—
404C2×C137—82no—
405C2×C137—84no—
406C2×C137#143811yescharacteristic
407C2×C137#188312yes—
408C2×C137#200211yescharacteristic
409C2×C137#200311yescharacteristic
410C2×C137#200612yes—
411#11016C13711yesmaximal, characteristic, direct product factor, Sylow
412C137#1101611yescharacteristic, direct product factor, Sylow
413C22×AGL(1,ℤ/8)C2×C13711yescharacteristic
414C22×#104C2×C13711yescharacteristic, complemented
415C2×#418C2×C13711yescharacteristic, complemented
416#2311C2×C13711yescharacteristic, complemented
417C2×#390C2×C13711yescharacteristic, complemented
418C2×#343C2×C13711yescharacteristic, complemented
419C2×#339C2×C13711yescharacteristic, complemented
420C22×#41C22×C13711yescharacteristic
421C23×D4C22×C13711yescharacteristic
422C2×AGL(1,ℤ/8)—22no—
423C2×AGL(1,ℤ/8)—22no—
424C2×AGL(1,ℤ/8)—22no—
425C2×AGL(1,ℤ/8)—22no—
426C2×AGL(1,ℤ/8)—22no—
427C2×AGL(1,ℤ/8)C4×C13714yescomplemented
428C22×SD16—21no—
429C22×D8—21no—
430C22×M16C22×C13711yescharacteristic
431C22×M16C22×C13711yescharacteristic
432C2×#117C22×C13711yescharacteristic
433C22×C4⋊C4C22×C13711yescharacteristic
434C22×C22⋊C4—22no—
435C22×C42C22×C13711yescharacteristic
436C2×#104—22no—
437C2×#104—22no—
438C2×#104—22no—
439#418—22no—
440#418—22no—
441C2×#102—22no—
442#391—21no—
443#390—21no—
444#390—22no—
445#390—22no—
446#386—22no—
447#380—22no—
448#343—22no—
449#339—22no—
450C25—21no—
451C2×#41—21no—
452C2×#41—21no—
453C2×#41—21no—
454C2×#41—21no—
455C2×#41—21no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—21no—
459C2×#41—21no—
460C2×#41—21no—
461C2×#41C2×C4×C13712yes—
462C2×#41D4×C13712yes—
463C22×Q8D4×C13711yescharacteristic
464C22×D4—21no—
465C22×D4—21no—
466C22×D4—21no—
467C22×D4—21no—
468C22×D4—21no—
469C22×D4—21no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—21no—
473C22×D4—21no—
474C22×D4—21no—
475C22×D4—21no—
476C22×D4C2×C4×C13712yes—
477C22×D4D4×C13711yescharacteristic
478C22×D4D4×C13712yes—
479C22×D4D4×C13712yes—
480C23×C4—21no—
481C23×C4—21no—
482C23×C4D4×C13712yes—
483C23×C4C23×C13711yescharacteristic
484AGL(1,ℤ/8)—28no—
485AGL(1,ℤ/8)—28no—
486AGL(1,ℤ/8)—28no—
487AGL(1,ℤ/8)—28no—
488C2×SD16—24no—
489C2×SD16—24no—
490C2×SD16—24no—
491C2×D8—24no—
492C2×D8—24no—
493C2×D8—24no—
494C2×M16—21no—
495C2×M16—21no—
496C2×M16—21no—
497C2×M16—21no—
498C2×M16—21no—
499C2×M16—21no—
500C2×M16—21no—
501C2×M16—21no—
502C2×M16C2×C4×C13712yes—
503C2×M16D4×C13712yes—
504C2×M16D4×C13712yes—
505C2×M16D4×C13712yes—
506C22×C8—21no—
507C22×C8—21no—
508#117—21no—
509#117—21no—
510#117—21no—
511#117—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4D4×C13712yes—
519C2×C22⋊C4—28no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—48no—
523C2×C42—21no—
524C2×C42—21no—
525C2×C42—21no—
526C2×C42—21no—
527C2×C42—21no—
528C2×C42—21no—
529C2×C42D4×C13712yes—
530#104—28no—
531#102—28no—
532#95—24no—
533C24—22no—
534C24—21no—
535C24—22no—
536C24—22no—
537C24—44no—
538C24—44no—
539C24—41no—
540C24—41no—
541C24—41no—
542C24—41no—
543C24C2×D4×C13711yescharacteristic
544#41—22no—
545#41—22no—
546#41—22no—
547#41—22no—
548#41—22no—
549#41—22no—
550#41—22no—
551#41—22no—
552#41—41no—
553#41—41no—
554#41—41no—
555#41—41no—
556#41—41no—
557#41—41no—
558#41—41no—
559#41—41no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8C22⋊C4×C13712yescomplemented
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—21no—
588C2×D4—41no—
589C2×D4—41no—
590C2×D4—41no—
591C2×D4—41no—
592C2×D4—41no—
593C2×D4—41no—
594C2×D4—41no—
595C2×D4—41no—
596C2×D4—41no—
597C2×D4—41no—
598C2×D4—41no—
599C2×D4—41no—
600C2×D4—41no—
601C2×D4—41no—
602C2×D4—41no—
603C2×D4—41no—
604C2×D4C22⋊C4×C13712yescomplemented
605C2×D4C22⋊C4×C13714yescomplemented
606C22×C4—24no—
607C22×C4—21no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—42no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—41no—
621C22×C4—41no—
622C22×C4—44no—
623C22×C4C22×C4×C13711yescharacteristic
624C22×C4C2×D4×C13711yescharacteristic
625C22×C4C2×D4×C13711yescharacteristic
626C22×C4C2×D4×C13711yescharacteristic
627C22×C4C2×D4×C13711yescharacteristic
628C22×C4C2×D4×C13711yescharacteristic
629C22×C4C2×D4×C13711yescharacteristic
630C22×C4C2×D4×C13711yescharacteristic
631C22×C4C2×D4×C13711yescharacteristic
632C22×C4C2×D4×C13711yescharacteristic
633C22×C4#41×C13711yescharacteristic
634C22×C4#41×C13711yescharacteristic
635C22×C4#41×C13711yescharacteristic
636C22×C4#41×C13711yescharacteristic
637SD16—216no—
638D8—216no—
639M16—22no—
640M16—22no—
641M16—22no—
642M16—22no—
643M16—22no—
644M16—41no—
645M16—41no—
646M16C22⋊C4×C13714yescomplemented
647C2×C8—22no—
648C2×C8—22no—
649C2×C8—22no—
650C2×C8—22no—
651C2×C8—41no—
652C2×C8—41no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—41no—
656C4⋊C4—41no—
657C4⋊C4—41no—
658C4⋊C4—41no—
659C22⋊C4—416no—
660C22⋊C4—41no—
661C22⋊C4—41no—
662C22⋊C4—84no—
663C42—22no—
664C42—22no—
665C42—41no—
666C42—41no—
667C42—41no—
668C42—41no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—24no—
673C23—44no—
674C23—48no—
675C23—44no—
676C23—48no—
677C23—42no—
678C23—42no—
679C23—41no—
680C23—41no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—84no—
688C23—82no—
689C23—82no—
690C23—84no—
691C23—82no—
692C23—82no—
693C23C4×D4×C13711yescharacteristic
694C23#120×C13711yescharacteristic
695C23#120×C13711yescharacteristic
696C23#121×C13711yescharacteristic
697C23#121×C13711yescharacteristic
698C23#121×C13711yescharacteristic
699C23#127×C13711yescharacteristic
700Q8—22no—
701Q8—22no—
702Q8—41no—
703Q8—41no—
704D4—22no—
705D4—24no—
706D4—24no—
707D4—22no—
708D4—42no—
709D4—42no—
710D4—42no—
711D4—42no—
712D4—42no—
713D4—42no—
714D4—42no—
715D4—42no—
716D4—42no—
717D4—42no—
718D4—41no—
719D4—41no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—44no—
723C2×C4—42no—
724C2×C4—44no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—44no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—44no—
737C2×C4—42no—
738C2×C4—82no—
739C2×C4C2×C22⋊C4×C13711yescharacteristic
740C2×C4C2×C22⋊C4×C13711yescharacteristic
741C2×C4C2×C22⋊C4×C13711yescharacteristic
742C2×C4C4×D4×C13711yescharacteristic
743C2×C4C4×D4×C13711yescharacteristic
744C2×C4C4×D4×C13711yescharacteristic
745C2×C4#120×C13711yescharacteristic
746C2×C4#120×C13711yescharacteristic
747C2×C4#120×C13711yescharacteristic
748C2×C4#120×C13711yescharacteristic
749C2×C4#120×C13711yescharacteristic
750C2×C4#120×C13711yescharacteristic
751C2×C4#121×C13711yescharacteristic
752C2×C4#121×C13711yescharacteristic
753C2×C4#121×C13711yescharacteristic
754C2×C4#121×C13711yescharacteristic
755C2×C4#121×C13711yescharacteristic
756C2×C4#121×C13711yescharacteristic
757C2×C4#121×C13711yescharacteristic
758C2×C4#121×C13711yescharacteristic
759C2×C4#121×C13711yescharacteristic
760C2×C4#123×C13711yescharacteristic
761C2×C4#123×C13711yescharacteristic
762C2×C4#123×C13711yescharacteristic
763C2×C4#123×C13711yescharacteristic
764C2×C4#124×C13711yescharacteristic
765C2×C4#124×C13711yescharacteristic
766C2×C4#127×C13711yescharacteristic
767C8—24no—
768C8—42no—
769C22—22no—
770C22—22no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—22no—
776C22—22no—
777C22—48no—
778C22—44no—
779C22—42no—
780C22—44no—
781C22—84no—
782C22—84no—
783C22—84no—
784C22—84no—
785C22—82no—
786C22—81no—
787C22—82no—
788C22—81no—
789C22—84no—
790C22—82no—
791C22#386×C13711yescharacteristic
792C22#386×C13711yescharacteristic
793C22#390×C13711yescharacteristic
794C22#392×C13711yescharacteristic
795C22#392×C13711yescharacteristic
796C22#392×C13711yescharacteristic
797C22#394×C13711yescharacteristic
798C22#453×C13712yes—
799C22#454×C13712yes—
800C4—44no—
801C4—42no—
802C4—82no—
803C4—82no—
804C4#379×C13711yescharacteristic
805C4#386×C13711yescharacteristic
806C4#386×C13711yescharacteristic
807C4#390×C13711yescharacteristic
808C4#392×C13711yescharacteristic
809C4#394×C13711yescharacteristic
810C4#394×C13711yescharacteristic
811C4#394×C13711yescharacteristic
812C2—21no—
813C2—21no—
814C2—21no—
815C2—21no—
816C2—84no—
817C2—82no—
818C2#1438×C13711yescharacteristic
819C2#1883×C13712yes—
820C2#2002×C13711yescharacteristic
821C2#2003×C13711yescharacteristic
822C2#2006×C13712yes—
subgroupG/H
center, socleC23×C137#120
commutatorC22×C4C22×C4×C137
Frattini, cosocleC23×C4C23×C137
prime radicalC22×AGL(1,ℤ/8)×C137C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C137 ◁ C23×C4×C137 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×#104×C137C2semidirect
3. C2×#418×C137C2semidirect
4. #2311×C137C2semidirect
5. C2×#390×C137C2semidirect
6. C2×#343×C137C2semidirect
7. C2×#339×C137C2semidirect
15. C2×AGL(1,ℤ/8)×C137C4semidirect
153. C2×Q8×C137C22⋊C4semidirect
192. C2×D4×C137C22⋊C4semidirect
193. C2×D4×C137C22⋊C4semidirect
234. M16×C137C22⋊C4semidirect
411. #11016C137direct (N × H)
412. C137#11016direct (N × H)
414. C22×#104C2×C137semidirect
415. C2×#418C2×C137semidirect
416. #2311C2×C137semidirect
417. C2×#390C2×C137semidirect
418. C2×#343C2×C137semidirect
419. C2×#339C2×C137semidirect
427. C2×AGL(1,ℤ/8)C4×C137semidirect
565. C2×Q8C22⋊C4×C137semidirect
604. C2×D4C22⋊C4×C137semidirect
605. C2×D4C22⋊C4×C137semidirect
646. M16C22⋊C4×C137semidirect

Maximal subgroups

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

subgroupindex
C22×AGL(1,ℤ/8)×C1372
C22×#104×C1372
C2×#418×C1372
#2311×C1372
C2×#390×C1372
C2×#343×C1372
C2×#339×C1372
#11016137