Finite Group Databasebeta

← C31×#18227 #21474986

Subgroups — C31×#18227 #21474986

Order 7936.

1130 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3535C211yesmaximal, characteristic
2C31×#3004C211yesmaximal, characteristic, complemented
3C2×C31×#451C211yesmaximal, characteristic, complemented
4C31×#2614C211yesmaximal, characteristic, complemented
5C31×#1606C212yesmaximal, complemented
6C31×#1605C212yesmaximal, complemented
7C31×#1603C212yesmaximal, complemented
8C31×#1602C212yesmaximal, complemented
9C31×#1516C211yesmaximal, characteristic, complemented
10C31×#1511C211yesmaximal, characteristic, complemented
11C31×#1468C211yesmaximal, characteristic, complemented
12C23×Q8×C31C2211yescharacteristic
13C2×C31×#137—21no—
14C22×Q16×C31—21no—
15C31×#563—21no—
16C31×#562—21no—
17C31×#554—21no—
18C31×#552—21no—
19C31×#551—21no—
20C31×#551—21no—
21C31×#547—21no—
22C31×#546—21no—
23C31×#544C2211yescharacteristic
24C31×#543C2211yescharacteristic
25C31×#542—21no—
26C31×#539—21no—
27C31×#539—21no—
28C31×#539C2211yescharacteristic
29C31×#538C2211yescharacteristic
30C31×#536—21no—
31C31×#525C2211yescharacteristic
32C2×C31×#123—21no—
33C2×C31×#123C2211yescharacteristic
34C2×C31×C22⋊Q8C2211yescharacteristic
35C31×#451—21no—
36C31×#451—21no—
37C31×#451—21no—
38C31×#451C2212yes—
39C31×#451C2212yes—
40C31×#451C2212yes—
41C31×#448—21no—
42C31×#448C2212yes—
43C31×#419—21no—
44C2×C31×#103—21no—
45C31×#407C2211yescharacteristic
46C2×C31×C22⋊C8C2211yescharacteristic
47C31×#395—21no—
48C31×#395C2212yes—
49C31×#393—21no—
50C31×#393C2212yes—
51C31×#381—21no—
52C31×#381C2211yescharacteristic
53C31×#328C2212yes—
54C31×#328C2212yes—
55C31×#328C2212yes—
56C31×#327C2212yes—
57C31×#324C2212yes—
58C31×#323C2212yes—
59C2×#41×C31—21no—
60C2×#41×C31D411yescharacteristic
61C22×Q8×C31—21no—
62C22×Q8×C31—21no—
63C22×Q8×C31—21no—
64C22×Q8×C31—21no—
65C22×Q8×C31—21no—
66C22×Q8×C31—44no—
67C22×Q8×C31D411yescharacteristic
68C22×Q8×C31C2312yes—
69C22×D4×C31D411yescharacteristic
70C23×C4×C31—21no—
71C23×C4×C31C2311yescharacteristic
72C31×#137—44no—
73C2×Q16×C31—22no—
74C2×Q16×C31—22no—
75C2×Q16×C31—22no—
76C2×Q16×C31—44no—
77C2×SD16×C31—22no—
78C2×M16×C31—21no—
79C22×C8×C31—21no—
80C31×C4⋊Q8—21no—
81C31×C4⋊Q8—21no—
82C31×C4⋊Q8—21no—
83C31×#126—21no—
84C31×#126—21no—
85C31×#126—21no—
86C31×#126—21no—
87C31×#126—21no—
88C31×#126—21no—
89C31×#125—21no—
90C31×#125—21no—
91C31×#125—21no—
92C31×#125—21no—
93C31×#125—21no—
94C31×#124—21no—
95C31×#124—21no—
96C31×#124—21no—
97C31×#124—21no—
98C31×#123—21no—
99C31×#123—21no—
100C31×#123—21no—
101C31×#123—21no—
102C31×#123—21no—
103C31×#123—21no—
104C31×#123—21no—
105C31×#123—21no—
106C31×#123—21no—
107C31×#123—21no—
108C31×#123—21no—
109C31×#123—21no—
110C31×#123—21no—
111C31×#123—21no—
112C31×#123—44no—
113C31×C22⋊Q8—21no—
114C31×C22⋊Q8—21no—
115C31×C22⋊Q8—21no—
116C31×C22⋊Q8—21no—
117C31×C22⋊Q8—21no—
118C31×C22⋊Q8—21no—
119C31×C22⋊Q8—21no—
120C31×C22⋊Q8—21no—
121C31×C22⋊Q8—21no—
122C31×C22⋊Q8—21no—
123C31×C22⋊Q8—21no—
124C31×C22⋊Q8—21no—
125C31×C22⋊Q8—21no—
126C31×C22⋊Q8—21no—
127C31×C22⋊Q8D411yescharacteristic
128C31×C22⋊Q8D411yescharacteristic
129C31×C22⋊Q8D411yescharacteristic
130C31×C22⋊Q8C2311yescharacteristic
131C31×C22⋊Q8C2311yescharacteristic
132C31×C22⋊Q8C2311yescharacteristic
133C31×#121—21no—
134C31×#121—21no—
135C31×#121—21no—
136C31×#121—21no—
137C31×#121D411yescharacteristic
138C31×#121C2311yescharacteristic
139C31×#120—21no—
140C31×#120—21no—
141C4×Q8×C31—21no—
142C4×D4×C31—21no—
143C4×D4×C31—21no—
144C4×D4×C31—21no—
145C4×D4×C31—21no—
146C4×D4×C31—21no—
147C4×D4×C31—21no—
148C4×D4×C31—21no—
149C31×#117—21no—
150C31×#117—21no—
151C31×#117—21no—
152C31×#117D411yescharacteristic
153C2×C4⋊C4×C31—21no—
154C2×C4⋊C4×C31—21no—
155C2×C4⋊C4×C31—22no—
156C2×C4⋊C4×C31D411yescharacteristic
157C2×C4⋊C4×C31D411yescharacteristic
158C2×C4⋊C4×C31C2311yescharacteristic
159C2×C22⋊C4×C31—21no—
160C2×C22⋊C4×C31—21no—
161C2×C22⋊C4×C31—21no—
162C2×C22⋊C4×C31—22no—
163C2×C22⋊C4×C31D411yescharacteristic
164C2×C22⋊C4×C31D411yescharacteristic
165C2×C22⋊C4×C31C2311yescharacteristic
166C31×#103—22no—
167C31×#103—22no—
168C31×#103—22no—
169C31×#103—22no—
170C31×C22⋊C8—21no—
171C31×C22⋊C8—21no—
172C31×C22⋊C8C2312yes—
173C31×C22⋊C8C2312yes—
174C31×#95—22no—
175C31×#95—21no—
176C31×#95—22no—
177C31×#95C2312yes—
178C24×C31C2×D411yescharacteristic
179C24×C31C2×D411yescharacteristic
180#41×C31—42no—
181#41×C31—82no—
182C2×Q8×C31—21no—
183C2×Q8×C31—21no—
184C2×Q8×C31—21no—
185C2×Q8×C31—24no—
186C2×Q8×C31—24no—
187C2×Q8×C31—22no—
188C2×Q8×C31—22no—
189C2×Q8×C31—44no—
190C2×Q8×C31—42no—
191C2×Q8×C31—42no—
192C2×Q8×C31—44no—
193C2×Q8×C31—42no—
194C2×Q8×C31—44no—
195C2×Q8×C31—44no—
196C2×Q8×C31—41no—
197C2×Q8×C31—41no—
198C2×Q8×C31C2×D411yescharacteristic
199C2×Q8×C31C2×D411yescharacteristic
200C2×Q8×C31C2×D411yescharacteristic
201C2×D4×C31—21no—
202C2×D4×C31—21no—
203C2×D4×C31—21no—
204C2×D4×C31—21no—
205C2×D4×C31—21no—
206C2×D4×C31—21no—
207C2×D4×C31—21no—
208C2×D4×C31—42no—
209C2×D4×C31C2×D411yescharacteristic
210C22×C4×C31—24no—
211C22×C4×C31—21no—
212C22×C4×C31—22no—
213C22×C4×C31—21no—
214C22×C4×C31—21no—
215C22×C4×C31—21no—
216C22×C4×C31—21no—
217C22×C4×C31—21no—
218C22×C4×C31—21no—
219C22×C4×C31—22no—
220C22×C4×C31—42no—
221C22×C4×C31—42no—
222C22×C4×C31—41no—
223C22×C4×C31—41no—
224C22×C4×C31C2×D411yescharacteristic
225C22×C4×C31C2×D411yescharacteristic
226C22×C4×C31C2×D411yescharacteristic
227C22×C4×C31C2×D411yescharacteristic
228C22×C4×C31C2×D411yescharacteristic
229C22×C4×C31C2×D411yescharacteristic
230C22×C4×C31C2×D411yescharacteristic
231C22×C4×C31C2×D411yescharacteristic
232C22×C4×C31C2411yescharacteristic
233Q16×C31—44no—
234Q16×C31—44no—
235Q16×C31—44no—
236SD16×C31—44no—
237M16×C31—42no—
238C2×C8×C31—22no—
239C2×C8×C31—22no—
240C2×C8×C31—42no—
241C4⋊C4×C31—21no—
242C4⋊C4×C31—21no—
243C4⋊C4×C31—21no—
244C4⋊C4×C31—21no—
245C4⋊C4×C31—21no—
246C4⋊C4×C31—21no—
247C4⋊C4×C31—21no—
248C4⋊C4×C31—21no—
249C4⋊C4×C31—21no—
250C4⋊C4×C31—21no—
251C4⋊C4×C31—21no—
252C4⋊C4×C31—21no—
253C4⋊C4×C31—21no—
254C4⋊C4×C31—21no—
255C4⋊C4×C31—21no—
256C4⋊C4×C31—21no—
257C4⋊C4×C31—21no—
258C4⋊C4×C31—21no—
259C4⋊C4×C31—21no—
260C4⋊C4×C31—21no—
261C4⋊C4×C31—21no—
262C4⋊C4×C31—21no—
263C4⋊C4×C31—21no—
264C4⋊C4×C31—44no—
265C4⋊C4×C31C2×D411yescharacteristic
266C4⋊C4×C31C2×D411yescharacteristic
267C4⋊C4×C31C2×D411yescharacteristic
268C4⋊C4×C31C2×D411yescharacteristic
269C22⋊C4×C31—21no—
270C22⋊C4×C31—21no—
271C22⋊C4×C31—21no—
272C22⋊C4×C31—21no—
273C22⋊C4×C31—21no—
274C22⋊C4×C31—21no—
275C22⋊C4×C31—21no—
276C22⋊C4×C31—21no—
277C22⋊C4×C31—21no—
278C22⋊C4×C31—21no—
279C22⋊C4×C31—21no—
280C22⋊C4×C31—21no—
281C22⋊C4×C31—21no—
282C22⋊C4×C31—21no—
283C22⋊C4×C31—21no—
284C22⋊C4×C31—21no—
285C22⋊C4×C31—21no—
286C22⋊C4×C31—21no—
287C22⋊C4×C31—21no—
288C22⋊C4×C31—21no—
289C22⋊C4×C31—21no—
290C22⋊C4×C31—21no—
291C22⋊C4×C31—21no—
292C22⋊C4×C31—44no—
293C22⋊C4×C31—42no—
294C42×C31—21no—
295C42×C31—21no—
296C42×C31—21no—
297C42×C31—21no—
298C42×C31—21no—
299#18227C3111yesmaximal, characteristic, direct product factor, Sylow
300C23×C31—22no—
301C23×C31—22no—
302C23×C31—21no—
303C23×C31—21no—
304C23×C31—22no—
305C23×C31—41no—
306C23×C31—41no—
307C23×C31—41no—
308C23×C31#12011yescharacteristic
309C23×C31#12011yescharacteristic
310C23×C31C22×D411yescharacteristic
311Q8×C31—24no—
312Q8×C31—24no—
313Q8×C31—41no—
314Q8×C31—41no—
315Q8×C31—41no—
316Q8×C31—42no—
317Q8×C31—42no—
318Q8×C31—44no—
319Q8×C31—44no—
320Q8×C31—81no—
321Q8×C31—81no—
322Q8×C31—81no—
323D4×C31—41no—
324D4×C31—42no—
325D4×C31—42no—
326D4×C31—42no—
327D4×C31—81no—
328D4×C31—81no—
329D4×C31—81no—
330D4×C31—81no—
331C2×C4×C31—22no—
332C2×C4×C31—22no—
333C2×C4×C31—24no—
334C2×C4×C31—21no—
335C2×C4×C31—21no—
336C2×C4×C31—21no—
337C2×C4×C31—21no—
338C2×C4×C31—21no—
339C2×C4×C31—21no—
340C2×C4×C31—21no—
341C2×C4×C31—21no—
342C2×C4×C31—21no—
343C2×C4×C31—21no—
344C2×C4×C31—22no—
345C2×C4×C31—41no—
346C2×C4×C31—41no—
347C2×C4×C31—41no—
348C2×C4×C31—41no—
349C2×C4×C31—42no—
350C2×C4×C31—44no—
351C2×C4×C31—42no—
352C2×C4×C31—44no—
353C2×C4×C31—42no—
354C2×C4×C31—41no—
355C2×C4×C31—41no—
356C2×C4×C31—42no—
357C2×C4×C31—42no—
358C2×C4×C31—42no—
359C2×C4×C31—81no—
360C2×C4×C31—81no—
361C2×C4×C31—81no—
362C2×C4×C31—81no—
363C2×C4×C31—81no—
364C2×C4×C31—81no—
365C2×C4×C31#12011yescharacteristic
366C2×C4×C31#12011yescharacteristic
367C2×C4×C31C22×D411yescharacteristic
368C2×C4×C31C22×D411yescharacteristic
369C8×C31—42no—
370C8×C31—42no—
371#3535C2×C3111yescharacteristic
372#3004C2×C3111yescharacteristic, complemented
373C2×#451C2×C3111yescharacteristic, complemented
374#2614C2×C3111yescharacteristic, complemented
375#1606C2×C3112yescomplemented
376#1605C2×C3112yescomplemented
377#1603C2×C3112yescomplemented
378#1602C2×C3112yescomplemented
379#1516C2×C3111yescharacteristic, complemented
380#1511C2×C3111yescharacteristic, complemented
381#1468C2×C3111yescharacteristic, complemented
382C22×C31—21no—
383C22×C31—21no—
384C22×C31—21no—
385C22×C31—21no—
386C22×C31—21no—
387C22×C31—21no—
388C22×C31—21no—
389C22×C31—44no—
390C22×C31—41no—
391C22×C31—41no—
392C22×C31—41no—
393C22×C31—41no—
394C22×C31—41no—
395C22×C31—41no—
396C22×C31—82no—
397C22×C31B(4,𝔽2)12yes—
398C22×C31C2×#12011yescharacteristic
399C22×C31#57812yes—
400C4×C31—21no—
401C4×C31—21no—
402C4×C31—21no—
403C4×C31—21no—
404C4×C31—41no—
405C4×C31—41no—
406C4×C31—41no—
407C4×C31—41no—
408C4×C31—41no—
409C4×C31—41no—
410C4×C31—44no—
411C4×C31—41no—
412C4×C31—41no—
413C4×C31—41no—
414C4×C31—41no—
415C4×C31—82no—
416C23×Q8C22×C3111yescharacteristic
417C2×#137—21no—
418C22×Q16—21no—
419#563—21no—
420#562—21no—
421#554—21no—
422#552—21no—
423#551—21no—
424#551—21no—
425#547—21no—
426#546—21no—
427#544C22×C3111yescharacteristic
428#543C22×C3111yescharacteristic
429#542—21no—
430#539—21no—
431#539—21no—
432#539C22×C3111yescharacteristic
433#538C22×C3111yescharacteristic
434#536—21no—
435#525C22×C3111yescharacteristic
436C2×#123—21no—
437C2×#123C22×C3111yescharacteristic
438C2×C22⋊Q8C22×C3111yescharacteristic
439#451—21no—
440#451—21no—
441#451—21no—
442#451C22×C3112yes—
443#451C22×C3112yes—
444#451C22×C3112yes—
445#448—21no—
446#448C22×C3112yes—
447#419—21no—
448C2×#103—21no—
449#407C22×C3111yescharacteristic
450C2×C22⋊C8C22×C3111yescharacteristic
451#395—21no—
452#395C22×C3112yes—
453#393—21no—
454#393C22×C3112yes—
455#381—21no—
456#381C22×C3111yescharacteristic
457#328C22×C3112yes—
458#328C22×C3112yes—
459#328C22×C3112yes—
460#327C22×C3112yes—
461#324C22×C3112yes—
462#323C22×C3112yes—
463C2×C31—22no—
464C2×C31—22no—
465C2×C31—41no—
466C2×C31—81no—
467C2×C31—81no—
468C2×C31#301111yescharacteristic
469C2×C31#302211yescharacteristic
470C2×C31C2×B(4,𝔽2)11yescharacteristic
471C2×#41—21no—
472C2×#41D4×C3111yescharacteristic
473C22×Q8—21no—
474C22×Q8—21no—
475C22×Q8—21no—
476C22×Q8—21no—
477C22×Q8—21no—
478C22×Q8—44no—
479C22×Q8D4×C3111yescharacteristic
480C22×Q8C23×C3112yes—
481C22×D4D4×C3111yescharacteristic
482C23×C4—21no—
483C23×C4C23×C3111yescharacteristic
484#137—44no—
485C2×Q16—22no—
486C2×Q16—22no—
487C2×Q16—22no—
488C2×Q16—44no—
489C2×SD16—22no—
490C2×M16—21no—
491C22×C8—21no—
492C4⋊Q8—21no—
493C4⋊Q8—21no—
494C4⋊Q8—21no—
495#126—21no—
496#126—21no—
497#126—21no—
498#126—21no—
499#126—21no—
500#126—21no—
501#125—21no—
502#125—21no—
503#125—21no—
504#125—21no—
505#125—21no—
506#124—21no—
507#124—21no—
508#124—21no—
509#124—21no—
510#123—21no—
511#123—21no—
512#123—21no—
513#123—21no—
514#123—21no—
515#123—21no—
516#123—21no—
517#123—21no—
518#123—21no—
519#123—21no—
520#123—21no—
521#123—21no—
522#123—21no—
523#123—21no—
524#123—44no—
525C22⋊Q8—21no—
526C22⋊Q8—21no—
527C22⋊Q8—21no—
528C22⋊Q8—21no—
529C22⋊Q8—21no—
530C22⋊Q8—21no—
531C22⋊Q8—21no—
532C22⋊Q8—21no—
533C22⋊Q8—21no—
534C22⋊Q8—21no—
535C22⋊Q8—21no—
536C22⋊Q8—21no—
537C22⋊Q8—21no—
538C22⋊Q8—21no—
539C22⋊Q8D4×C3111yescharacteristic
540C22⋊Q8D4×C3111yescharacteristic
541C22⋊Q8D4×C3111yescharacteristic
542C22⋊Q8C23×C3111yescharacteristic
543C22⋊Q8C23×C3111yescharacteristic
544C22⋊Q8C23×C3111yescharacteristic
545#121—21no—
546#121—21no—
547#121—21no—
548#121—21no—
549#121D4×C3111yescharacteristic
550#121C23×C3111yescharacteristic
551#120—21no—
552#120—21no—
553C4×Q8—21no—
554C4×D4—21no—
555C4×D4—21no—
556C4×D4—21no—
557C4×D4—21no—
558C4×D4—21no—
559C4×D4—21no—
560C4×D4—21no—
561#117—21no—
562#117—21no—
563#117—21no—
564#117D4×C3111yescharacteristic
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—22no—
568C2×C4⋊C4D4×C3111yescharacteristic
569C2×C4⋊C4D4×C3111yescharacteristic
570C2×C4⋊C4C23×C3111yescharacteristic
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—22no—
575C2×C22⋊C4D4×C3111yescharacteristic
576C2×C22⋊C4D4×C3111yescharacteristic
577C2×C22⋊C4C23×C3111yescharacteristic
578#103—22no—
579#103—22no—
580#103—22no—
581#103—22no—
582C22⋊C8—21no—
583C22⋊C8—21no—
584C22⋊C8C23×C3112yes—
585C22⋊C8C23×C3112yes—
586#95—22no—
587#95—22no—
588#95—21no—
589#95C23×C3112yes—
590C31#1822711yescharacteristic, direct product factor, Sylow
591C24C2×D4×C3111yescharacteristic
592C24C2×D4×C3111yescharacteristic
593#41—42no—
594#41—82no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—24no—
599C2×Q8—24no—
600C2×Q8—22no—
601C2×Q8—22no—
602C2×Q8—44no—
603C2×Q8—42no—
604C2×Q8—42no—
605C2×Q8—44no—
606C2×Q8—42no—
607C2×Q8—44no—
608C2×Q8—44no—
609C2×Q8—41no—
610C2×Q8—41no—
611C2×Q8C2×D4×C3111yescharacteristic
612C2×Q8C2×D4×C3111yescharacteristic
613C2×Q8C2×D4×C3111yescharacteristic
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—42no—
622C2×D4C2×D4×C3111yescharacteristic
623C22×C4—24no—
624C22×C4—21no—
625C22×C4—22no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—22no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—41no—
636C22×C4—41no—
637C22×C4C2×D4×C3111yescharacteristic
638C22×C4C2×D4×C3111yescharacteristic
639C22×C4C2×D4×C3111yescharacteristic
640C22×C4C2×D4×C3111yescharacteristic
641C22×C4C2×D4×C3111yescharacteristic
642C22×C4C2×D4×C3111yescharacteristic
643C22×C4C2×D4×C3111yescharacteristic
644C22×C4C2×D4×C3111yescharacteristic
645C22×C4C24×C3111yescharacteristic
646Q16—44no—
647Q16—44no—
648Q16—44no—
649SD16—44no—
650M16—42no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—42no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—44no—
678C4⋊C4C2×D4×C3111yescharacteristic
679C4⋊C4C2×D4×C3111yescharacteristic
680C4⋊C4C2×D4×C3111yescharacteristic
681C4⋊C4C2×D4×C3111yescharacteristic
682C22⋊C4—21no—
683C22⋊C4—21no—
684C22⋊C4—21no—
685C22⋊C4—21no—
686C22⋊C4—21no—
687C22⋊C4—21no—
688C22⋊C4—21no—
689C22⋊C4—21no—
690C22⋊C4—21no—
691C22⋊C4—21no—
692C22⋊C4—21no—
693C22⋊C4—21no—
694C22⋊C4—21no—
695C22⋊C4—21no—
696C22⋊C4—21no—
697C22⋊C4—21no—
698C22⋊C4—21no—
699C22⋊C4—21no—
700C22⋊C4—21no—
701C22⋊C4—21no—
702C22⋊C4—21no—
703C22⋊C4—21no—
704C22⋊C4—21no—
705C22⋊C4—44no—
706C22⋊C4—42no—
707C42—21no—
708C42—21no—
709C42—21no—
710C42—21no—
711C42—21no—
712C23—22no—
713C23—22no—
714C23—21no—
715C23—21no—
716C23—22no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23C31×#12011yescharacteristic
721C23C31×#12011yescharacteristic
722C23C22×D4×C3111yescharacteristic
723Q8—24no—
724Q8—24no—
725Q8—41no—
726Q8—41no—
727Q8—41no—
728Q8—42no—
729Q8—42no—
730Q8—44no—
731Q8—44no—
732Q8—81no—
733Q8—81no—
734Q8—81no—
735D4—41no—
736D4—42no—
737D4—42no—
738D4—42no—
739D4—81no—
740D4—81no—
741D4—81no—
742D4—81no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—22no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—42no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—81no—
772C2×C4—81no—
773C2×C4—81no—
774C2×C4—81no—
775C2×C4—81no—
776C2×C4—81no—
777C2×C4C31×#12011yescharacteristic
778C2×C4C31×#12011yescharacteristic
779C2×C4C22×D4×C3111yescharacteristic
780C2×C4C22×D4×C3111yescharacteristic
781C8—42no—
782C8—42no—
783C22—21no—
784C22—21no—
785C22—21no—
786C22—21no—
787C22—21no—
788C22—21no—
789C22—21no—
790C22—44no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—82no—
798C22C31×B(4,𝔽2)12yes—
799C22C2×C31×#12011yescharacteristic
800C22C31×#57812yes—
801C4—21no—
802C4—21no—
803C4—21no—
804C4—21no—
805C4—41no—
806C4—41no—
807C4—41no—
808C4—41no—
809C4—41no—
810C4—41no—
811C4—44no—
812C4—41no—
813C4—41no—
814C4—41no—
815C4—41no—
816C4—82no—
817C2—22no—
818C2—22no—
819C2—41no—
820C2—81no—
821C2—81no—
822C2C31×#301111yescharacteristic
823C2C31×#302211yescharacteristic
824C2C2×C31×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#3535C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#3004C2semidirect
3. C2×C31×#451C2semidirect
4. C31×#2614C2semidirect
5. C31×#1606C2semidirect
6. C31×#1605C2semidirect
7. C31×#1603C2semidirect
8. C31×#1602C2semidirect
9. C31×#1516C2semidirect
10. C31×#1511C2semidirect
11. C31×#1468C2semidirect
299. #18227C31direct (N × H)
372. #3004C2×C31semidirect
373. C2×#451C2×C31semidirect
374. #2614C2×C31semidirect
375. #1606C2×C31semidirect
376. #1605C2×C31semidirect
377. #1603C2×C31semidirect
378. #1602C2×C31semidirect
379. #1516C2×C31semidirect
380. #1511C2×C31semidirect
381. #1468C2×C31semidirect
590. C31#18227direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35352
C31×#30042
C2×C31×#4512
C31×#26142
C31×#16062
C31×#16052
C31×#16032
C31×#16022
C31×#15162
C31×#15112
C31×#14682
#1822731