Finite Group Databasebeta

← C31×#18226 #21474985

Subgroups — C31×#18226 #21474985

Order 7936.

1306 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3535C211yesmaximal, characteristic, complemented
2C31×#3003C211yesmaximal, characteristic, complemented
3C2×C31×#450C211yesmaximal, characteristic, complemented
4C31×#2613C211yesmaximal, characteristic, complemented
5C31×#1600C212yesmaximal, complemented
6C31×#1599C212yesmaximal, complemented
7C31×#1597C212yesmaximal, complemented
8C31×#1596C212yesmaximal, complemented
9C31×#1516C211yesmaximal, characteristic, complemented
10C31×#1511C211yesmaximal, characteristic, complemented
11C31×#1468C211yesmaximal, characteristic, complemented
12C23×D4×C31C2211yescharacteristic
13C2×C31×AGL(1,ℤ/8)—21no—
14C22×SD16×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, complemented
24C31×#543C2211yescharacteristic, complemented
25C31×#542—21no—
26C31×#539—21no—
27C31×#539—21no—
28C31×#539C2211yescharacteristic, complemented
29C31×#538C2211yescharacteristic, complemented
30C31×#536—21no—
31C31×#525C2211yescharacteristic
32C2×C31×#123C2211yescharacteristic
33C2×C31×C22⋊Q8C2211yescharacteristic
34C2×C31×#120—21no—
35C31×#450—21no—
36C31×#450—21no—
37C31×#450—21no—
38C31×#450C2212yes—
39C31×#450C2212yes—
40C31×#450C2212yes—
41C31×#447—21no—
42C31×#447C2212yes—
43C31×#418—21no—
44C2×C31×#102—21no—
45C31×#407C2211yescharacteristic
46C2×C31×C22⋊C8C2211yescharacteristic
47C31×#394—21no—
48C31×#394C2212yes—
49C31×#392—21no—
50C31×#392C2212yes—
51C31×#381C2211yescharacteristic
52C31×#379—21no—
53C31×#328C2212yescomplemented
54C31×#328C2212yescomplemented
55C31×#328C2212yescomplemented
56C31×#327C2212yescomplemented
57C31×#324C2212yescomplemented
58C31×#323C2212yescomplemented
59C25×C31—21no—
60C2×#41×C31—21no—
61C2×#41×C31D411yescharacteristic, complemented
62C22×Q8×C31D411yescharacteristic, complemented
63C22×D4×C31—22no—
64C22×D4×C31—21no—
65C22×D4×C31—21no—
66C22×D4×C31—21no—
67C22×D4×C31—21no—
68C22×D4×C31—21no—
69C22×D4×C31—44no—
70C22×D4×C31D411yescharacteristic
71C22×D4×C31C2312yes—
72C23×C4×C31C2311yescharacteristic
73C31×AGL(1,ℤ/8)—44no—
74C2×SD16×C31—22no—
75C2×SD16×C31—22no—
76C2×SD16×C31—22no—
77C2×SD16×C31—44no—
78C2×D8×C31—22no—
79C2×M16×C31—21no—
80C22×C8×C31—21no—
81C31×C4⋊Q8—21no—
82C31×C4⋊Q8—21no—
83C31×C4⋊Q8—21no—
84C31×#126—21no—
85C31×#126—21no—
86C31×#126—21no—
87C31×#126—21no—
88C31×#126—21no—
89C31×#126—21no—
90C31×#125—21no—
91C31×#125—21no—
92C31×#125—21no—
93C31×#125—21no—
94C31×#125—21no—
95C31×#124—21no—
96C31×#124—21no—
97C31×#124—21no—
98C31×#124—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—21no—
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, complemented
128C31×C22⋊Q8D411yescharacteristic, complemented
129C31×C22⋊Q8D411yescharacteristic, complemented
130C31×C22⋊Q8C2311yescharacteristic
131C31×C22⋊Q8C2311yescharacteristic
132C31×C22⋊Q8C2311yescharacteristic
133C31×#121—21no—
134C31×#121—21no—
135C31×#121—21no—
136C31×#121—21no—
137C31×#121D411yescharacteristic, complemented
138C31×#121C2311yescharacteristic
139C31×#120—21no—
140C31×#120—21no—
141C31×#120—44no—
142C4×Q8×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—
149C4×D4×C31—21no—
150C31×#117—21no—
151C31×#117—21no—
152C31×#117—21no—
153C31×#117D411yescharacteristic, complemented
154C2×C4⋊C4×C31—21no—
155C2×C4⋊C4×C31—21no—
156C2×C4⋊C4×C31D411yescharacteristic
157C2×C4⋊C4×C31D411yescharacteristic, complemented
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×C31—22no—
164C2×C22⋊C4×C31—22no—
165C2×C22⋊C4×C31D411yescharacteristic
166C2×C22⋊C4×C31D411yescharacteristic
167C2×C22⋊C4×C31C2311yescharacteristic
168C31×#102—22no—
169C31×#102—22no—
170C31×#102—22no—
171C31×#102—22no—
172C31×C22⋊C8—21no—
173C31×C22⋊C8—21no—
174C31×C22⋊C8C2312yes—
175C31×C22⋊C8C2312yes—
176C31×#95—21no—
177C31×#95C2312yes—
178C24×C31—24no—
179C24×C31—22no—
180C24×C31—42no—
181C24×C31—41no—
182C24×C31—41no—
183C24×C31—82no—
184C24×C31—82no—
185C24×C31C2×D411yescharacteristic
186C24×C31C2×D411yescharacteristic
187#41×C31—42no—
188#41×C31—82no—
189C2×Q8×C31—21no—
190C2×Q8×C31—21no—
191C2×Q8×C31—21no—
192C2×Q8×C31—42no—
193C2×Q8×C31C2×D411yescharacteristic
194C2×Q8×C31C2×D411yescharacteristic
195C2×Q8×C31C2×D411yescharacteristic
196C2×D4×C31—24no—
197C2×D4×C31—24no—
198C2×D4×C31—21no—
199C2×D4×C31—21no—
200C2×D4×C31—21no—
201C2×D4×C31—21no—
202C2×D4×C31—21no—
203C2×D4×C31—21no—
204C2×D4×C31—21no—
205C2×D4×C31—22no—
206C2×D4×C31—22no—
207C2×D4×C31—42no—
208C2×D4×C31—42no—
209C2×D4×C31—44no—
210C2×D4×C31—44no—
211C2×D4×C31—44no—
212C2×D4×C31—44no—
213C2×D4×C31—42no—
214C2×D4×C31—44no—
215C2×D4×C31—41no—
216C2×D4×C31—41no—
217C2×D4×C31—82no—
218C2×D4×C31—82no—
219C2×D4×C31C2×D411yescharacteristic
220C22×C4×C31—21no—
221C22×C4×C31—21no—
222C22×C4×C31—21no—
223C22×C4×C31—21no—
224C22×C4×C31—21no—
225C22×C4×C31—21no—
226C22×C4×C31—21no—
227C22×C4×C31—22no—
228C22×C4×C31—42no—
229C22×C4×C31C2×D411yescharacteristic
230C22×C4×C31C2×D411yescharacteristic
231C22×C4×C31C2×D411yescharacteristic
232C22×C4×C31C2×D411yescharacteristic
233C22×C4×C31C2×D411yescharacteristic
234C22×C4×C31C2×D411yescharacteristic
235C22×C4×C31C2×D411yescharacteristic
236C22×C4×C31C2×D411yescharacteristic
237C22×C4×C31C2411yescharacteristic
238SD16×C31—44no—
239SD16×C31—44no—
240SD16×C31—44no—
241D8×C31—44no—
242M16×C31—42no—
243C2×C8×C31—22no—
244C2×C8×C31—22no—
245C2×C8×C31—42no—
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—21no—
265C4⋊C4×C31—21no—
266C4⋊C4×C31—21no—
267C4⋊C4×C31—21no—
268C4⋊C4×C31—21no—
269C4⋊C4×C31C2×D411yescharacteristic
270C4⋊C4×C31C2×D411yescharacteristic
271C4⋊C4×C31C2×D411yescharacteristic
272C4⋊C4×C31C2×D411yescharacteristic
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—21no—
293C22⋊C4×C31—21no—
294C22⋊C4×C31—21no—
295C22⋊C4×C31—21no—
296C22⋊C4×C31—44no—
297C22⋊C4×C31—42no—
298C22⋊C4×C31—82no—
299C22⋊C4×C31—82no—
300C42×C31—21no—
301C42×C31—21no—
302C42×C31—21no—
303C42×C31—21no—
304C42×C31—21no—
305#18226C3111yesmaximal, characteristic, direct product factor, Sylow
306C23×C31—22no—
307C23×C31—22no—
308C23×C31—24no—
309C23×C31—21no—
310C23×C31—21no—
311C23×C31—22no—
312C23×C31—41no—
313C23×C31—42no—
314C23×C31—42no—
315C23×C31—44no—
316C23×C31—42no—
317C23×C31—41no—
318C23×C31—41no—
319C23×C31—42no—
320C23×C31—42no—
321C23×C31—42no—
322C23×C31—44no—
323C23×C31—82no—
324C23×C31—82no—
325C23×C31—82no—
326C23×C31—82no—
327C23×C31—88no—
328C23×C31—88no—
329C23×C31#12011yescharacteristic
330C23×C31#12011yescharacteristic
331C23×C31C22×D411yescharacteristic
332Q8×C31—41no—
333Q8×C31—41no—
334Q8×C31—41no—
335Q8×C31—81no—
336Q8×C31—81no—
337Q8×C31—81no—
338D4×C31—24no—
339D4×C31—24no—
340D4×C31—41no—
341D4×C31—42no—
342D4×C31—42no—
343D4×C31—44no—
344D4×C31—44no—
345D4×C31—42no—
346D4×C31—42no—
347D4×C31—42no—
348D4×C31—81no—
349D4×C31—81no—
350D4×C31—81no—
351D4×C31—81no—
352D4×C31—88no—
353C2×C4×C31—22no—
354C2×C4×C31—22no—
355C2×C4×C31—21no—
356C2×C4×C31—21no—
357C2×C4×C31—21no—
358C2×C4×C31—21no—
359C2×C4×C31—21no—
360C2×C4×C31—21no—
361C2×C4×C31—21no—
362C2×C4×C31—21no—
363C2×C4×C31—21no—
364C2×C4×C31—21no—
365C2×C4×C31—22no—
366C2×C4×C31—41no—
367C2×C4×C31—41no—
368C2×C4×C31—41no—
369C2×C4×C31—41no—
370C2×C4×C31—42no—
371C2×C4×C31—41no—
372C2×C4×C31—41no—
373C2×C4×C31—42no—
374C2×C4×C31—42no—
375C2×C4×C31—42no—
376C2×C4×C31—81no—
377C2×C4×C31—81no—
378C2×C4×C31—81no—
379C2×C4×C31—81no—
380C2×C4×C31—81no—
381C2×C4×C31—81no—
382C2×C4×C31#12011yescharacteristic
383C2×C4×C31#12011yescharacteristic
384C2×C4×C31C22×D411yescharacteristic
385C2×C4×C31C22×D411yescharacteristic
386C8×C31—42no—
387C8×C31—42no—
388#3535C2×C3111yescharacteristic, complemented
389#3003C2×C3111yescharacteristic, complemented
390C2×#450C2×C3111yescharacteristic, complemented
391#2613C2×C3111yescharacteristic, complemented
392#1600C2×C3112yescomplemented
393#1599C2×C3112yescomplemented
394#1597C2×C3112yescomplemented
395#1596C2×C3112yescomplemented
396#1516C2×C3111yescharacteristic, complemented
397#1511C2×C3111yescharacteristic, complemented
398#1468C2×C3111yescharacteristic, complemented
399C22×C31—21no—
400C22×C31—21no—
401C22×C31—21no—
402C22×C31—21no—
403C22×C31—21no—
404C22×C31—21no—
405C22×C31—21no—
406C22×C31—44no—
407C22×C31—44no—
408C22×C31—44no—
409C22×C31—41no—
410C22×C31—41no—
411C22×C31—41no—
412C22×C31—41no—
413C22×C31—41no—
414C22×C31—41no—
415C22×C31—44no—
416C22×C31—82no—
417C22×C31—82no—
418C22×C31—82no—
419C22×C31—88no—
420C22×C31—88no—
421C22×C31—82no—
422C22×C31—82no—
423C22×C31B(4,𝔽2)12yes—
424C22×C31C2×#12011yescharacteristic
425C22×C31#57712yes—
426C4×C31—21no—
427C4×C31—21no—
428C4×C31—21no—
429C4×C31—21no—
430C4×C31—41no—
431C4×C31—41no—
432C4×C31—41no—
433C4×C31—41no—
434C4×C31—41no—
435C4×C31—41no—
436C4×C31—41no—
437C4×C31—41no—
438C4×C31—41no—
439C4×C31—41no—
440C4×C31—82no—
441C23×D4C22×C3111yescharacteristic
442C2×AGL(1,ℤ/8)—21no—
443C22×SD16—21no—
444#563—21no—
445#562—21no—
446#554—21no—
447#552—21no—
448#551—21no—
449#551—21no—
450#547—21no—
451#546—21no—
452#544C22×C3111yescharacteristic, complemented
453#543C22×C3111yescharacteristic, complemented
454#542—21no—
455#539—21no—
456#539—21no—
457#539C22×C3111yescharacteristic, complemented
458#538C22×C3111yescharacteristic, complemented
459#536—21no—
460#525C22×C3111yescharacteristic
461C2×#123C22×C3111yescharacteristic
462C2×C22⋊Q8C22×C3111yescharacteristic
463C2×#120—21no—
464#450—21no—
465#450—21no—
466#450—21no—
467#450C22×C3112yes—
468#450C22×C3112yes—
469#450C22×C3112yes—
470#447—21no—
471#447C22×C3112yes—
472#418—21no—
473C2×#102—21no—
474#407C22×C3111yescharacteristic
475C2×C22⋊C8C22×C3111yescharacteristic
476#394—21no—
477#394C22×C3112yes—
478#392—21no—
479#392C22×C3112yes—
480#381C22×C3111yescharacteristic
481#379—21no—
482#328C22×C3112yescomplemented
483#328C22×C3112yescomplemented
484#328C22×C3112yescomplemented
485#327C22×C3112yescomplemented
486#324C22×C3112yescomplemented
487#323C22×C3112yescomplemented
488C2×C31—22no—
489C2×C31—22no—
490C2×C31—41no—
491C2×C31—81no—
492C2×C31—81no—
493C2×C31—84no—
494C2×C31#301011yescharacteristic
495C2×C31#302111yescharacteristic
496C2×C31C2×B(4,𝔽2)11yescharacteristic
497C25—21no—
498C2×#41—21no—
499C2×#41D4×C3111yescharacteristic, complemented
500C22×Q8D4×C3111yescharacteristic, complemented
501C22×D4—22no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—44no—
508C22×D4D4×C3111yescharacteristic
509C22×D4C23×C3112yes—
510C23×C4C23×C3111yescharacteristic
511AGL(1,ℤ/8)—44no—
512C2×SD16—22no—
513C2×SD16—22no—
514C2×SD16—22no—
515C2×SD16—44no—
516C2×D8—22no—
517C2×M16—21no—
518C22×C8—21no—
519C4⋊Q8—21no—
520C4⋊Q8—21no—
521C4⋊Q8—21no—
522#126—21no—
523#126—21no—
524#126—21no—
525#126—21no—
526#126—21no—
527#126—21no—
528#125—21no—
529#125—21no—
530#125—21no—
531#125—21no—
532#125—21no—
533#124—21no—
534#124—21no—
535#124—21no—
536#124—21no—
537#123—21no—
538#123—21no—
539#123—21no—
540#123—21no—
541#123—21no—
542#123—21no—
543#123—21no—
544#123—21no—
545#123—21no—
546#123—21no—
547#123—21no—
548#123—21no—
549#123—21no—
550#123—21no—
551C22⋊Q8—21no—
552C22⋊Q8—21no—
553C22⋊Q8—21no—
554C22⋊Q8—21no—
555C22⋊Q8—21no—
556C22⋊Q8—21no—
557C22⋊Q8—21no—
558C22⋊Q8—21no—
559C22⋊Q8—21no—
560C22⋊Q8—21no—
561C22⋊Q8—21no—
562C22⋊Q8—21no—
563C22⋊Q8—21no—
564C22⋊Q8—21no—
565C22⋊Q8D4×C3111yescharacteristic, complemented
566C22⋊Q8D4×C3111yescharacteristic, complemented
567C22⋊Q8D4×C3111yescharacteristic, complemented
568C22⋊Q8C23×C3111yescharacteristic
569C22⋊Q8C23×C3111yescharacteristic
570C22⋊Q8C23×C3111yescharacteristic
571#121—21no—
572#121—21no—
573#121—21no—
574#121—21no—
575#121D4×C3111yescharacteristic, complemented
576#121C23×C3111yescharacteristic
577#120—21no—
578#120—21no—
579#120—44no—
580C4×Q8—21no—
581C4×D4—21no—
582C4×D4—21no—
583C4×D4—21no—
584C4×D4—21no—
585C4×D4—21no—
586C4×D4—21no—
587C4×D4—21no—
588#117—21no—
589#117—21no—
590#117—21no—
591#117D4×C3111yescharacteristic, complemented
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4D4×C3111yescharacteristic
595C2×C4⋊C4D4×C3111yescharacteristic, complemented
596C2×C4⋊C4C23×C3111yescharacteristic
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—22no—
602C2×C22⋊C4—22no—
603C2×C22⋊C4D4×C3111yescharacteristic
604C2×C22⋊C4D4×C3111yescharacteristic
605C2×C22⋊C4C23×C3111yescharacteristic
606#102—22no—
607#102—22no—
608#102—22no—
609#102—22no—
610C22⋊C8—21no—
611C22⋊C8—21no—
612C22⋊C8C23×C3112yes—
613C22⋊C8C23×C3112yes—
614#95—21no—
615#95C23×C3112yes—
616C31#1822611yescharacteristic, direct product factor, Sylow
617C24—24no—
618C24—22no—
619C24—42no—
620C24—41no—
621C24—41no—
622C24—82no—
623C24—82no—
624C24C2×D4×C3111yescharacteristic
625C24C2×D4×C3111yescharacteristic
626#41—42no—
627#41—82no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—42no—
632C2×Q8C2×D4×C3111yescharacteristic
633C2×Q8C2×D4×C3111yescharacteristic
634C2×Q8C2×D4×C3111yescharacteristic
635C2×D4—24no—
636C2×D4—24no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—22no—
645C2×D4—22no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4—44no—
649C2×D4—44no—
650C2×D4—44no—
651C2×D4—44no—
652C2×D4—42no—
653C2×D4—44no—
654C2×D4—41no—
655C2×D4—41no—
656C2×D4—82no—
657C2×D4—82no—
658C2×D4C2×D4×C3111yescharacteristic
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—22no—
667C22×C4—42no—
668C22×C4C2×D4×C3111yescharacteristic
669C22×C4C2×D4×C3111yescharacteristic
670C22×C4C2×D4×C3111yescharacteristic
671C22×C4C2×D4×C3111yescharacteristic
672C22×C4C2×D4×C3111yescharacteristic
673C22×C4C2×D4×C3111yescharacteristic
674C22×C4C2×D4×C3111yescharacteristic
675C22×C4C2×D4×C3111yescharacteristic
676C22×C4C24×C3111yescharacteristic
677SD16—44no—
678SD16—44no—
679SD16—44no—
680D8—44no—
681M16—42no—
682C2×C8—22no—
683C2×C8—22no—
684C2×C8—42no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4C2×D4×C3111yescharacteristic
709C4⋊C4C2×D4×C3111yescharacteristic
710C4⋊C4C2×D4×C3111yescharacteristic
711C4⋊C4C2×D4×C3111yescharacteristic
712C22⋊C4—21no—
713C22⋊C4—21no—
714C22⋊C4—21no—
715C22⋊C4—21no—
716C22⋊C4—21no—
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—21no—
723C22⋊C4—21no—
724C22⋊C4—21no—
725C22⋊C4—21no—
726C22⋊C4—21no—
727C22⋊C4—21no—
728C22⋊C4—21no—
729C22⋊C4—21no—
730C22⋊C4—21no—
731C22⋊C4—21no—
732C22⋊C4—21no—
733C22⋊C4—21no—
734C22⋊C4—21no—
735C22⋊C4—44no—
736C22⋊C4—42no—
737C22⋊C4—82no—
738C22⋊C4—82no—
739C42—21no—
740C42—21no—
741C42—21no—
742C42—21no—
743C42—21no—
744C23—22no—
745C23—22no—
746C23—24no—
747C23—21no—
748C23—21no—
749C23—22no—
750C23—41no—
751C23—42no—
752C23—42no—
753C23—44no—
754C23—42no—
755C23—41no—
756C23—41no—
757C23—44no—
758C23—42no—
759C23—42no—
760C23—42no—
761C23—82no—
762C23—82no—
763C23—82no—
764C23—82no—
765C23—88no—
766C23—88no—
767C23C31×#12011yescharacteristic
768C23C31×#12011yescharacteristic
769C23C22×D4×C3111yescharacteristic
770Q8—41no—
771Q8—41no—
772Q8—41no—
773Q8—81no—
774Q8—81no—
775Q8—81no—
776D4—24no—
777D4—24no—
778D4—41no—
779D4—42no—
780D4—42no—
781D4—44no—
782D4—44no—
783D4—42no—
784D4—42no—
785D4—42no—
786D4—81no—
787D4—81no—
788D4—81no—
789D4—81no—
790D4—88no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—22no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—42no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—81no—
815C2×C4—81no—
816C2×C4—81no—
817C2×C4—81no—
818C2×C4—81no—
819C2×C4—81no—
820C2×C4C31×#12011yescharacteristic
821C2×C4C31×#12011yescharacteristic
822C2×C4C22×D4×C3111yescharacteristic
823C2×C4C22×D4×C3111yescharacteristic
824C8—42no—
825C8—42no—
826C22—21no—
827C22—21no—
828C22—21no—
829C22—21no—
830C22—21no—
831C22—21no—
832C22—21no—
833C22—44no—
834C22—44no—
835C22—44no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—44no—
843C22—82no—
844C22—82no—
845C22—82no—
846C22—88no—
847C22—88no—
848C22—82no—
849C22—82no—
850C22C31×B(4,𝔽2)12yes—
851C22C2×C31×#12011yescharacteristic
852C22C31×#57712yes—
853C4—21no—
854C4—21no—
855C4—21no—
856C4—21no—
857C4—41no—
858C4—41no—
859C4—41no—
860C4—41no—
861C4—41no—
862C4—41no—
863C4—41no—
864C4—41no—
865C4—41no—
866C4—41no—
867C4—82no—
868C2—22no—
869C2—22no—
870C2—41no—
871C2—84no—
872C2—81no—
873C2—81no—
874C2C31×#301011yescharacteristic
875C2C31×#302111yescharacteristic
876C2C2×C31×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
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
1. C31×#3535C2semidirect
2. C31×#3003C2semidirect
3. C2×C31×#450C2semidirect
4. C31×#2613C2semidirect
5. C31×#1600C2semidirect
6. C31×#1599C2semidirect
7. C31×#1597C2semidirect
8. C31×#1596C2semidirect
9. C31×#1516C2semidirect
10. C31×#1511C2semidirect
11. C31×#1468C2semidirect
23. C31×#544C22semidirect
24. C31×#543C22semidirect
28. C31×#539C22semidirect
29. C31×#538C22semidirect
53. C31×#328C22semidirect
54. C31×#328C22semidirect
55. C31×#328C22semidirect
56. C31×#327C22semidirect
57. C31×#324C22semidirect
58. C31×#323C22semidirect
61. C2×#41×C31D4semidirect
62. C22×Q8×C31D4semidirect
127. C31×C22⋊Q8D4semidirect
128. C31×C22⋊Q8D4semidirect
129. C31×C22⋊Q8D4semidirect
137. C31×#121D4semidirect
153. C31×#117D4semidirect
157. C2×C4⋊C4×C31D4semidirect
305. #18226C31direct (N × H)
388. #3535C2×C31semidirect
389. #3003C2×C31semidirect
390. C2×#450C2×C31semidirect
391. #2613C2×C31semidirect
392. #1600C2×C31semidirect
393. #1599C2×C31semidirect
394. #1597C2×C31semidirect
395. #1596C2×C31semidirect
396. #1516C2×C31semidirect
397. #1511C2×C31semidirect
398. #1468C2×C31semidirect
452. #544C22×C31semidirect
453. #543C22×C31semidirect
457. #539C22×C31semidirect
458. #538C22×C31semidirect
482. #328C22×C31semidirect
483. #328C22×C31semidirect
484. #328C22×C31semidirect
485. #327C22×C31semidirect
486. #324C22×C31semidirect
487. #323C22×C31semidirect
499. C2×#41D4×C31semidirect
500. C22×Q8D4×C31semidirect
565. C22⋊Q8D4×C31semidirect
566. C22⋊Q8D4×C31semidirect
567. C22⋊Q8D4×C31semidirect
575. #121D4×C31semidirect
591. #117D4×C31semidirect
595. C2×C4⋊C4D4×C31semidirect
616. C31#18226direct (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×#30032
C2×C31×#4502
C31×#26132
C31×#16002
C31×#15992
C31×#15972
C31×#15962
C31×#15162
C31×#15112
C31×#14682
#1822631