Finite Group Databasebeta

← C31×#11012 #21467771

Subgroups — C31×#11012 #21467771

Order 7936.

1422 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×AGL(1,ℤ/8)C211yesmaximal, characteristic
2C2×C31×#421C211yesmaximal, characteristic, complemented
3C2×C31×#418C211yesmaximal, characteristic, complemented
4C2×C31×#410C211yesmaximal, characteristic, complemented
5C31×#2309C211yesmaximal, characteristic, complemented
6C2×C31×#344C211yesmaximal, characteristic, complemented
7C2×C31×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
8C22×#41×C31C2211yescharacteristic
9C23×D4×C31C2211yescharacteristic
10C2×C31×AGL(1,ℤ/8)—22no—
11C2×C31×AGL(1,ℤ/8)—22no—
12C2×C31×AGL(1,ℤ/8)—22no—
13C2×C31×AGL(1,ℤ/8)—22no—
14C2×C31×AGL(1,ℤ/8)—22no—
15C2×C31×AGL(1,ℤ/8)—22no—
16C22×SD16×C31C412yescomplemented
17C22×D8×C31C412yescomplemented
18C22×M16×C31C2211yescharacteristic
19C22×M16×C31C2211yescharacteristic
20C2×C31×#117C2211yescharacteristic
21C2×C31×#117C2211yescharacteristic
22C2×C31×#117C2211yescharacteristic
23C31×#421—22no—
24C31×#421—22no—
25C2×C31×#104—22no—
26C31×#418—22no—
27C31×#418—22no—
28C2×C31×#102—22no—
29C31×#410—22no—
30C31×#410—22no—
31C2×C31×#99—22no—
32C31×#390—22no—
33C31×#390—22no—
34C31×#379—22no—
35C31×#344—22no—
36C31×H(3,ℤ/4)—22no—
37C25×C31—21no—
38C2×#41×C31—21no—
39C2×#41×C31—21no—
40C2×#41×C31—21no—
41C2×#41×C31—21no—
42C2×#41×C31—21no—
43C2×#41×C31—21no—
44C2×#41×C31—21no—
45C2×#41×C31—21no—
46C2×#41×C31—21no—
47C2×#41×C31—21no—
48C2×#41×C31D412yes—
49C2×#41×C31D412yes—
50C22×Q8×C31C2×C411yescharacteristic
51C22×D4×C31—21no—
52C22×D4×C31—21no—
53C22×D4×C31—21no—
54C22×D4×C31—21no—
55C22×D4×C31—21no—
56C22×D4×C31—21no—
57C22×D4×C31—21no—
58C22×D4×C31—21no—
59C22×D4×C31—21no—
60C22×D4×C31—21no—
61C22×D4×C31—21no—
62C22×D4×C31—21no—
63C22×D4×C31C2×C412yes—
64C22×D4×C31C2×C411yescharacteristic
65C22×D4×C31D412yes—
66C22×D4×C31D412yes—
67C23×C4×C31—21no—
68C23×C4×C31C2311yescharacteristic
69C31×AGL(1,ℤ/8)—28no—
70C31×AGL(1,ℤ/8)—28no—
71C31×AGL(1,ℤ/8)—28no—
72C31×AGL(1,ℤ/8)—28no—
73C2×SD16×C31—24no—
74C2×SD16×C31—24no—
75C2×SD16×C31—24no—
76C2×D8×C31—24no—
77C2×D8×C31—24no—
78C2×D8×C31—24no—
79C2×M16×C31—21no—
80C2×M16×C31—21no—
81C2×M16×C31—21no—
82C2×M16×C31—21no—
83C2×M16×C31—21no—
84C2×M16×C31—21no—
85C2×M16×C31—21no—
86C2×M16×C31—21no—
87C2×M16×C31—21no—
88C2×M16×C31D412yes—
89C2×M16×C31D412yes—
90C2×M16×C31D412yes—
91C22×C8×C31—21no—
92C22×C8×C31C2×C412yes—
93C31×#117—21no—
94C31×#117—21no—
95C31×#117—21no—
96C31×#117—21no—
97C31×#117—21no—
98C31×#117—21no—
99C31×#117—21no—
100C31×#117—21no—
101C31×#117—21no—
102C31×#117—21no—
103C31×#117—21no—
104C31×#117D412yes—
105C2×C4⋊C4×C31—21no—
106C2×C4⋊C4×C31—21no—
107C2×C4⋊C4×C31—21no—
108C2×C22⋊C4×C31—21no—
109C2×C22⋊C4×C31—21no—
110C2×C22⋊C4×C31—28no—
111C2×C22⋊C4×C31D412yes—
112C2×C42×C31—21no—
113C2×C42×C31—21no—
114C2×C42×C31D412yes—
115C31×#104—28no—
116C31×#102—28no—
117C31×#99—28no—
118C24×C31—22no—
119C24×C31—21no—
120C24×C31—22no—
121C24×C31—22no—
122C24×C31—41no—
123C24×C31—41no—
124C24×C31—41no—
125C24×C31—41no—
126C24×C31—84no—
127C24×C31C2×D411yescharacteristic
128#41×C31—22no—
129#41×C31—22no—
130#41×C31—22no—
131#41×C31—22no—
132#41×C31—22no—
133#41×C31—22no—
134#41×C31—22no—
135#41×C31—22no—
136#41×C31—41no—
137#41×C31—41no—
138#41×C31—41no—
139#41×C31—41no—
140#41×C31—41no—
141#41×C31—41no—
142#41×C31—41no—
143#41×C31—41no—
144C2×Q8×C31—21no—
145C2×Q8×C31—21no—
146C2×Q8×C31—21no—
147C2×Q8×C31—21no—
148C2×Q8×C31—21no—
149C2×Q8×C31C22⋊C412yescomplemented
150C2×D4×C31—22no—
151C2×D4×C31—22no—
152C2×D4×C31—21no—
153C2×D4×C31—21no—
154C2×D4×C31—22no—
155C2×D4×C31—22no—
156C2×D4×C31—22no—
157C2×D4×C31—22no—
158C2×D4×C31—21no—
159C2×D4×C31—21no—
160C2×D4×C31—22no—
161C2×D4×C31—21no—
162C2×D4×C31—22no—
163C2×D4×C31—22no—
164C2×D4×C31—22no—
165C2×D4×C31—22no—
166C2×D4×C31—22no—
167C2×D4×C31—22no—
168C2×D4×C31—22no—
169C2×D4×C31—22no—
170C2×D4×C31—22no—
171C2×D4×C31—22no—
172C2×D4×C31—41no—
173C2×D4×C31—41no—
174C2×D4×C31—41no—
175C2×D4×C31—41no—
176C2×D4×C31—41no—
177C2×D4×C31—41no—
178C2×D4×C31—41no—
179C2×D4×C31—41no—
180C2×D4×C31—41no—
181C2×D4×C31—41no—
182C2×D4×C31—41no—
183C2×D4×C31—41no—
184C2×D4×C31—41no—
185C2×D4×C31—41no—
186C2×D4×C31—41no—
187C2×D4×C31—41no—
188C2×D4×C31C22⋊C414yes—
189C2×D4×C31C22⋊C412yescomplemented
190C22×C4×C31—21no—
191C22×C4×C31—22no—
192C22×C4×C31—22no—
193C22×C4×C31—22no—
194C22×C4×C31—22no—
195C22×C4×C31—41no—
196C22×C4×C31—41no—
197C22×C4×C31—41no—
198C22×C4×C31—41no—
199C22×C4×C31—41no—
200C22×C4×C31C22×C411yescharacteristic
201C22×C4×C31C2×D411yescharacteristic
202C22×C4×C31C2×D411yescharacteristic
203C22×C4×C31C2×D411yescharacteristic
204C22×C4×C31C2×D411yescharacteristic
205C22×C4×C31C2×D411yescharacteristic
206C22×C4×C31C2×D411yescharacteristic
207C22×C4×C31C2×D411yescharacteristic
208C22×C4×C31C2×D411yescharacteristic
209C22×C4×C31C2×D411yescharacteristic
210C22×C4×C31#4111yescharacteristic
211C22×C4×C31#4111yescharacteristic
212C22×C4×C31#4111yescharacteristic
213C22×C4×C31#4111yescharacteristic
214SD16×C31—216no—
215D8×C31—216no—
216M16×C31—22no—
217M16×C31—22no—
218M16×C31—22no—
219M16×C31—22no—
220M16×C31—22no—
221M16×C31—22no—
222M16×C31—41no—
223M16×C31—41no—
224C2×C8×C31—22no—
225C2×C8×C31—22no—
226C2×C8×C31—22no—
227C2×C8×C31—41no—
228C2×C8×C31—41no—
229C2×C8×C31C22⋊C414yescomplemented
230C4⋊C4×C31—22no—
231C4⋊C4×C31—41no—
232C4⋊C4×C31—41no—
233C4⋊C4×C31—41no—
234C4⋊C4×C31—41no—
235C4⋊C4×C31—41no—
236C22⋊C4×C31—22no—
237C22⋊C4×C31—22no—
238C22⋊C4×C31—22no—
239C22⋊C4×C31—41no—
240C22⋊C4×C31—41no—
241C22⋊C4×C31—41no—
242C22⋊C4×C31—88no—
243C42×C31—22no—
244C42×C31—22no—
245C42×C31—22no—
246C42×C31—41no—
247C42×C31—41no—
248C42×C31—41no—
249#11012C3111yesmaximal, characteristic, direct product factor, Sylow
250C23×C31—24no—
251C23×C31—22no—
252C23×C31—42no—
253C23×C31—48no—
254C23×C31—42no—
255C23×C31—41no—
256C23×C31—41no—
257C23×C31—42no—
258C23×C31—42no—
259C23×C31—42no—
260C23×C31—42no—
261C23×C31—42no—
262C23×C31—84no—
263C23×C31—84no—
264C23×C31—82no—
265C23×C31—84no—
266C23×C31—84no—
267C23×C31—84no—
268C23×C31—84no—
269C23×C31C4×D411yescharacteristic
270C23×C31#12011yescharacteristic
271C23×C31#12011yescharacteristic
272C23×C31#12111yescharacteristic
273C23×C31#12111yescharacteristic
274C23×C31#12111yescharacteristic
275C23×C31#12711yescharacteristic
276Q8×C31—22no—
277Q8×C31—22no—
278Q8×C31—41no—
279Q8×C31—41no—
280D4×C31—22no—
281D4×C31—24no—
282D4×C31—24no—
283D4×C31—22no—
284D4×C31—42no—
285D4×C31—42no—
286D4×C31—42no—
287D4×C31—42no—
288D4×C31—42no—
289D4×C31—41no—
290D4×C31—42no—
291D4×C31—41no—
292D4×C31—42no—
293D4×C31—42no—
294D4×C31—42no—
295D4×C31—42no—
296C2×C4×C31—22no—
297C2×C4×C31—41no—
298C2×C4×C31—41no—
299C2×C4×C31—42no—
300C2×C4×C31—42no—
301C2×C4×C31—42no—
302C2×C4×C31—42no—
303C2×C4×C31—44no—
304C2×C4×C31—44no—
305C2×C4×C31—42no—
306C2×C4×C31—42no—
307C2×C4×C31—42no—
308C2×C4×C31—82no—
309C2×C4×C31C2×C22⋊C411yescharacteristic
310C2×C4×C31C2×C22⋊C411yescharacteristic
311C2×C4×C31C2×C22⋊C411yescharacteristic
312C2×C4×C31C4×D411yescharacteristic
313C2×C4×C31C4×D411yescharacteristic
314C2×C4×C31C4×D411yescharacteristic
315C2×C4×C31#12011yescharacteristic
316C2×C4×C31#12011yescharacteristic
317C2×C4×C31#12011yescharacteristic
318C2×C4×C31#12011yescharacteristic
319C2×C4×C31#12011yescharacteristic
320C2×C4×C31#12011yescharacteristic
321C2×C4×C31#12111yescharacteristic
322C2×C4×C31#12111yescharacteristic
323C2×C4×C31#12111yescharacteristic
324C2×C4×C31#12111yescharacteristic
325C2×C4×C31#12111yescharacteristic
326C2×C4×C31#12111yescharacteristic
327C2×C4×C31#12111yescharacteristic
328C2×C4×C31#12111yescharacteristic
329C2×C4×C31#12111yescharacteristic
330C2×C4×C31#12311yescharacteristic
331C2×C4×C31#12311yescharacteristic
332C2×C4×C31#12311yescharacteristic
333C2×C4×C31#12311yescharacteristic
334C2×C4×C31#12411yescharacteristic
335C2×C4×C31#12411yescharacteristic
336C2×C4×C31#12711yescharacteristic
337C8×C31—24no—
338C8×C31—42no—
339C22×AGL(1,ℤ/8)C2×C3111yescharacteristic
340C2×#421C2×C3111yescharacteristic, complemented
341C2×#418C2×C3111yescharacteristic, complemented
342C2×#410C2×C3111yescharacteristic, complemented
343#2309C2×C3111yescharacteristic, complemented
344C2×#344C2×C3111yescharacteristic, complemented
345C2×H(3,ℤ/4)C2×C3111yescharacteristic, complemented
346C22×C31—22no—
347C22×C31—22no—
348C22×C31—22no—
349C22×C31—41no—
350C22×C31—41no—
351C22×C31—41no—
352C22×C31—41no—
353C22×C31—48no—
354C22×C31—42no—
355C22×C31—44no—
356C22×C31—82no—
357C22×C31—84no—
358C22×C31—84no—
359C22×C31—82no—
360C22×C31—84no—
361C22×C31—84no—
362C22×C31—84no—
363C22×C31—84no—
364C22×C31—82no—
365C22×C31#38611yescharacteristic
366C22×C31#38611yescharacteristic
367C22×C31#39011yescharacteristic
368C22×C31#39211yescharacteristic
369C22×C31#39211yescharacteristic
370C22×C31#39211yescharacteristic
371C22×C31#39411yescharacteristic
372C4×C31—42no—
373C4×C31—82no—
374C4×C31—82no—
375C4×C31—82no—
376C4×C31#37911yescharacteristic
377C4×C31#38611yescharacteristic
378C4×C31#38611yescharacteristic
379C4×C31#39011yescharacteristic
380C4×C31#39211yescharacteristic
381C4×C31#39411yescharacteristic
382C4×C31#39411yescharacteristic
383C4×C31#39411yescharacteristic
384C22×#41C22×C3111yescharacteristic
385C23×D4C22×C3111yescharacteristic
386C2×AGL(1,ℤ/8)—22no—
387C2×AGL(1,ℤ/8)—22no—
388C2×AGL(1,ℤ/8)—22no—
389C2×AGL(1,ℤ/8)—22no—
390C2×AGL(1,ℤ/8)—22no—
391C2×AGL(1,ℤ/8)—22no—
392C22×SD16C4×C3112yescomplemented
393C22×D8C4×C3112yescomplemented
394C22×M16C22×C3111yescharacteristic
395C22×M16C22×C3111yescharacteristic
396C2×#117C22×C3111yescharacteristic
397C2×#117C22×C3111yescharacteristic
398C2×#117C22×C3111yescharacteristic
399#421—22no—
400#421—22no—
401C2×#104—22no—
402#418—22no—
403#418—22no—
404C2×#102—22no—
405#410—22no—
406#410—22no—
407C2×#99—22no—
408#390—22no—
409#390—22no—
410#379—22no—
411#344—22no—
412H(3,ℤ/4)—22no—
413C2×C31—21no—
414C2×C31—21no—
415C2×C31—21no—
416C2×C31—21no—
417C2×C31—21no—
418C2×C31—21no—
419C2×C31—84no—
420C2×C31—82no—
421C2×C31#143811yescharacteristic
422C2×C31#190412yes—
423C25—21no—
424C2×#41—21no—
425C2×#41—21no—
426C2×#41—21no—
427C2×#41—21no—
428C2×#41—21no—
429C2×#41—21no—
430C2×#41—21no—
431C2×#41—21no—
432C2×#41—21no—
433C2×#41—21no—
434C2×#41D4×C3112yes—
435C2×#41D4×C3112yes—
436C22×Q8C2×C4×C3111yescharacteristic
437C22×D4—21no—
438C22×D4—21no—
439C22×D4—21no—
440C22×D4—21no—
441C22×D4—21no—
442C22×D4—21no—
443C22×D4—21no—
444C22×D4—21no—
445C22×D4—21no—
446C22×D4—21no—
447C22×D4—21no—
448C22×D4—21no—
449C22×D4C2×C4×C3112yes—
450C22×D4C2×C4×C3111yescharacteristic
451C22×D4D4×C3112yes—
452C22×D4D4×C3112yes—
453C23×C4—21no—
454C23×C4C23×C3111yescharacteristic
455AGL(1,ℤ/8)—28no—
456AGL(1,ℤ/8)—28no—
457AGL(1,ℤ/8)—28no—
458AGL(1,ℤ/8)—28no—
459C2×SD16—24no—
460C2×SD16—24no—
461C2×SD16—24no—
462C2×D8—24no—
463C2×D8—24no—
464C2×D8—24no—
465C2×M16—21no—
466C2×M16—21no—
467C2×M16—21no—
468C2×M16—21no—
469C2×M16—21no—
470C2×M16—21no—
471C2×M16—21no—
472C2×M16—21no—
473C2×M16—21no—
474C2×M16D4×C3112yes—
475C2×M16D4×C3112yes—
476C2×M16D4×C3112yes—
477C22×C8—21no—
478C22×C8C2×C4×C3112yes—
479#117—21no—
480#117—21no—
481#117—21no—
482#117—21no—
483#117—21no—
484#117—21no—
485#117—21no—
486#117—21no—
487#117—21no—
488#117—21no—
489#117—21no—
490#117D4×C3112yes—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—28no—
497C2×C22⋊C4D4×C3112yes—
498C2×C42—21no—
499C2×C42—21no—
500C2×C42D4×C3112yes—
501#104—28no—
502#102—28no—
503#99—28no—
504C31#1101211yescharacteristic, direct product factor, Sylow
505C24—22no—
506C24—21no—
507C24—22no—
508C24—22no—
509C24—41no—
510C24—41no—
511C24—41no—
512C24—41no—
513C24—84no—
514C24C2×D4×C3111yescharacteristic
515#41—22no—
516#41—22no—
517#41—22no—
518#41—22no—
519#41—22no—
520#41—22no—
521#41—22no—
522#41—22no—
523#41—41no—
524#41—41no—
525#41—41no—
526#41—41no—
527#41—41no—
528#41—41no—
529#41—41no—
530#41—41no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8C22⋊C4×C3112yescomplemented
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—22no—
548C2×D4—21no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—41no—
560C2×D4—41no—
561C2×D4—41no—
562C2×D4—41no—
563C2×D4—41no—
564C2×D4—41no—
565C2×D4—41no—
566C2×D4—41no—
567C2×D4—41no—
568C2×D4—41no—
569C2×D4—41no—
570C2×D4—41no—
571C2×D4—41no—
572C2×D4—41no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4C22⋊C4×C3114yes—
576C2×D4C22⋊C4×C3112yescomplemented
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4C22×C4×C3111yescharacteristic
588C22×C4C2×D4×C3111yescharacteristic
589C22×C4C2×D4×C3111yescharacteristic
590C22×C4C2×D4×C3111yescharacteristic
591C22×C4C2×D4×C3111yescharacteristic
592C22×C4C2×D4×C3111yescharacteristic
593C22×C4C2×D4×C3111yescharacteristic
594C22×C4C2×D4×C3111yescharacteristic
595C22×C4C2×D4×C3111yescharacteristic
596C22×C4C2×D4×C3111yescharacteristic
597C22×C4#41×C3111yescharacteristic
598C22×C4#41×C3111yescharacteristic
599C22×C4#41×C3111yescharacteristic
600C22×C4#41×C3111yescharacteristic
601SD16—216no—
602D8—216no—
603M16—22no—
604M16—22no—
605M16—22no—
606M16—22no—
607M16—22no—
608M16—22no—
609M16—41no—
610M16—41no—
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—22no—
614C2×C8—41no—
615C2×C8—41no—
616C2×C8C22⋊C4×C3114yescomplemented
617C4⋊C4—22no—
618C4⋊C4—41no—
619C4⋊C4—41no—
620C4⋊C4—41no—
621C4⋊C4—41no—
622C4⋊C4—41no—
623C22⋊C4—22no—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—41no—
627C22⋊C4—41no—
628C22⋊C4—41no—
629C22⋊C4—88no—
630C42—22no—
631C42—22no—
632C42—22no—
633C42—41no—
634C42—41no—
635C42—41no—
636C23—24no—
637C23—22no—
638C23—42no—
639C23—48no—
640C23—41no—
641C23—42no—
642C23—41no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—84no—
649C23—84no—
650C23—82no—
651C23—84no—
652C23—84no—
653C23—84no—
654C23—84no—
655C23C4×D4×C3111yescharacteristic
656C23C31×#12011yescharacteristic
657C23C31×#12011yescharacteristic
658C23C31×#12111yescharacteristic
659C23C31×#12111yescharacteristic
660C23C31×#12111yescharacteristic
661C23C31×#12711yescharacteristic
662Q8—22no—
663Q8—22no—
664Q8—41no—
665Q8—41no—
666D4—22no—
667D4—24no—
668D4—24no—
669D4—22no—
670D4—42no—
671D4—42no—
672D4—42no—
673D4—42no—
674D4—42no—
675D4—41no—
676D4—42no—
677D4—41no—
678D4—42no—
679D4—42no—
680D4—42no—
681D4—42no—
682C2×C4—22no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—82no—
695C2×C4C2×C22⋊C4×C3111yescharacteristic
696C2×C4C2×C22⋊C4×C3111yescharacteristic
697C2×C4C2×C22⋊C4×C3111yescharacteristic
698C2×C4C4×D4×C3111yescharacteristic
699C2×C4C4×D4×C3111yescharacteristic
700C2×C4C4×D4×C3111yescharacteristic
701C2×C4C31×#12011yescharacteristic
702C2×C4C31×#12011yescharacteristic
703C2×C4C31×#12011yescharacteristic
704C2×C4C31×#12011yescharacteristic
705C2×C4C31×#12011yescharacteristic
706C2×C4C31×#12011yescharacteristic
707C2×C4C31×#12111yescharacteristic
708C2×C4C31×#12111yescharacteristic
709C2×C4C31×#12111yescharacteristic
710C2×C4C31×#12111yescharacteristic
711C2×C4C31×#12111yescharacteristic
712C2×C4C31×#12111yescharacteristic
713C2×C4C31×#12111yescharacteristic
714C2×C4C31×#12111yescharacteristic
715C2×C4C31×#12111yescharacteristic
716C2×C4C31×#12311yescharacteristic
717C2×C4C31×#12311yescharacteristic
718C2×C4C31×#12311yescharacteristic
719C2×C4C31×#12311yescharacteristic
720C2×C4C31×#12411yescharacteristic
721C2×C4C31×#12411yescharacteristic
722C2×C4C31×#12711yescharacteristic
723C8—24no—
724C8—42no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—48no—
733C22—42no—
734C22—44no—
735C22—82no—
736C22—84no—
737C22—84no—
738C22—84no—
739C22—84no—
740C22—84no—
741C22—84no—
742C22—82no—
743C22—82no—
744C22C31×#38611yescharacteristic
745C22C31×#38611yescharacteristic
746C22C31×#39011yescharacteristic
747C22C31×#39211yescharacteristic
748C22C31×#39211yescharacteristic
749C22C31×#39211yescharacteristic
750C22C31×#39411yescharacteristic
751C4—42no—
752C4—82no—
753C4—82no—
754C4—82no—
755C4C31×#37911yescharacteristic
756C4C31×#38611yescharacteristic
757C4C31×#38611yescharacteristic
758C4C31×#39011yescharacteristic
759C4C31×#39211yescharacteristic
760C4C31×#39411yescharacteristic
761C4C31×#39411yescharacteristic
762C4C31×#39411yescharacteristic
763C2—21no—
764C2—21no—
765C2—21no—
766C2—21no—
767C2—21no—
768C2—21no—
769C2—84no—
770C2—82no—
771C2C31×#143811yescharacteristic
772C2C31×#190412yes—
subgroupG/H
center, socleC22×C31#386
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC22×C31×AGL(1,ℤ/8)C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#421C2semidirect
3. C2×C31×#418C2semidirect
4. C2×C31×#410C2semidirect
5. C31×#2309C2semidirect
6. C2×C31×#344C2semidirect
7. C2×C31×H(3,ℤ/4)C2semidirect
16. C22×SD16×C31C4semidirect
17. C22×D8×C31C4semidirect
149. C2×Q8×C31C22⋊C4semidirect
189. C2×D4×C31C22⋊C4semidirect
229. C2×C8×C31C22⋊C4semidirect
249. #11012C31direct (N × H)
340. C2×#421C2×C31semidirect
341. C2×#418C2×C31semidirect
342. C2×#410C2×C31semidirect
343. #2309C2×C31semidirect
344. C2×#344C2×C31semidirect
345. C2×H(3,ℤ/4)C2×C31semidirect
392. C22×SD16C4×C31semidirect
393. C22×D8C4×C31semidirect
504. C31#11012direct (N × H)
536. C2×Q8C22⋊C4×C31semidirect
576. C2×D4C22⋊C4×C31semidirect
616. C2×C8C22⋊C4×C31semidirect

Maximal subgroups

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

subgroupindex
C22×C31×AGL(1,ℤ/8)2
C2×C31×#4212
C2×C31×#4182
C2×C31×#4102
C31×#23092
C2×C31×#3442
C2×C31×H(3,ℤ/4)2
#1101231