Finite Group Databasebeta

← C31×#18225 #21474984

Subgroups — C31×#18225 #21474984

Order 7936.

1194 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3534C211yesmaximal, characteristic
2C31×#3004C211yesmaximal, characteristic, complemented
3C2×C31×#448C211yesmaximal, characteristic, complemented
4C31×#2614C211yesmaximal, characteristic, complemented
5C31×#1606C212yesmaximal, complemented
6C31×#1604C212yesmaximal, complemented
7C31×#1603C212yesmaximal, complemented
8C31×#1601C212yesmaximal, complemented
9C31×#1516C211yesmaximal, characteristic, complemented
10C31×#1510C211yesmaximal, characteristic, complemented
11C31×#1468C211yesmaximal, characteristic, complemented
12C23×Q8×C31C2211yescharacteristic, complemented
13C2×C31×#137—21no—
14C22×SD16×C31—21no—
15C31×#562—21no—
16C31×#560—21no—
17C31×#553—21no—
18C31×#551—21no—
19C31×#546—21no—
20C31×#546—21no—
21C31×#546—21no—
22D42×C31—21no—
23C31×#540—21no—
24C31×#539—21no—
25C31×#539C2211yescharacteristic
26C31×#538—21no—
27C31×#538C2211yescharacteristic
28C31×#537C2211yescharacteristic
29C31×#534—21no—
30C31×#534C2211yescharacteristic
31C31×#525C2211yescharacteristic
32C2×C31×#123—21no—
33C2×C31×#123C2211yescharacteristic
34C2×C31×#121C2211yescharacteristic
35C31×#451—21no—
36C31×#451C2212yescomplemented
37C31×#448—21no—
38C31×#448—21no—
39C31×#448—21no—
40C31×#448C2212yes—
41C31×#448C2212yescomplemented
42C31×#448C2212yescomplemented
43C31×#419—21no—
44C2×C31×#103—21no—
45C31×#407C2211yescharacteristic, complemented
46C2×C31×C22⋊C8C2211yescharacteristic, complemented
47C31×#395—21no—
48C31×#395C2212yescomplemented
49C31×#393—21no—
50C31×#393C2212yescomplemented
51C31×#381—21no—
52C31×#381C2211yescharacteristic, complemented
53C31×#328C2212yescomplemented
54C31×#327C2212yes—
55C31×#327C2212yescomplemented
56C31×#327C2212yescomplemented
57C31×#324C2212yescomplemented
58C31×#323C2212yescomplemented
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×C31C2312yes—
68C22×D4×C31—21no—
69C22×D4×C31—21no—
70C22×D4×C31—21no—
71C22×D4×C31D411yescharacteristic
72C22×D4×C31D411yescharacteristic
73C23×C4×C31—21no—
74C23×C4×C31C2311yescharacteristic
75C31×#137—44no—
76C2×Q16×C31—22no—
77C2×SD16×C31—22no—
78C2×SD16×C31—22no—
79C2×SD16×C31—22no—
80C2×SD16×C31—44no—
81C2×M16×C31—21no—
82C22×C8×C31—21no—
83C31×#127—21no—
84C31×#126—21no—
85C31×#126—21no—
86C31×#126—21no—
87C31×#126—21no—
88C31×#125—21no—
89C31×#125—21no—
90C31×#124—21no—
91C31×#124—21no—
92C31×#124—21no—
93C31×#123—21no—
94C31×#123—21no—
95C31×#123—21no—
96C31×#123—21no—
97C31×#123—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—44no—
108C31×C22⋊Q8—21no—
109C31×C22⋊Q8—21no—
110C31×C22⋊Q8—21no—
111C31×C22⋊Q8—21no—
112C31×C22⋊Q8—21no—
113C31×C22⋊Q8D411yescharacteristic
114C31×C22⋊Q8C2311yescharacteristic
115C31×#121—21no—
116C31×#121—21no—
117C31×#121—21no—
118C31×#121—21no—
119C31×#121—21no—
120C31×#121—21no—
121C31×#121—21no—
122C31×#121—21no—
123C31×#121—21no—
124C31×#121—21no—
125C31×#121—21no—
126C31×#121—21no—
127C31×#121—21no—
128C31×#121—21no—
129C31×#121—21no—
130C31×#121D411yescharacteristic
131C31×#121D411yescharacteristic
132C31×#121D411yescharacteristic
133C31×#121C2311yescharacteristic
134C31×#121C2311yescharacteristic
135C31×#121C2311yescharacteristic
136C31×#120—21no—
137C31×#120—21no—
138C31×#120—21no—
139C31×#120—21no—
140C31×#120—21no—
141C31×#120—21no—
142C31×#120—21no—
143C31×#120—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—
150C4×D4×C31—21no—
151C4×D4×C31—21no—
152C31×#117—21no—
153C31×#117D411yescharacteristic
154C2×C4⋊C4×C31—22no—
155C2×C4⋊C4×C31D411yescharacteristic
156C2×C4⋊C4×C31D411yescharacteristic
157C2×C4⋊C4×C31C2311yescharacteristic
158C2×C22⋊C4×C31—21no—
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×C31—21no—
179C24×C31—21no—
180C24×C31C2×D411yescharacteristic
181C24×C31C2×D411yescharacteristic
182#41×C31—42no—
183#41×C31—82no—
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—44no—
194C2×Q8×C31—44no—
195C2×Q8×C31—41no—
196C2×Q8×C31—41no—
197C2×Q8×C31C2×D411yescharacteristic
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—21no—
206C2×D4×C31—21no—
207C2×D4×C31—21no—
208C2×D4×C31—21no—
209C2×D4×C31—21no—
210C2×D4×C31—21no—
211C2×D4×C31—21no—
212C2×D4×C31—21no—
213C2×D4×C31—21no—
214C2×D4×C31—21no—
215C2×D4×C31—42no—
216C2×D4×C31—42no—
217C2×D4×C31—82no—
218C2×D4×C31—82no—
219C2×D4×C31—82no—
220C2×D4×C31C2×D411yescharacteristic
221C2×D4×C31C2×D411yescharacteristic
222C2×D4×C31C2×D411yescharacteristic
223C22×C4×C31—24no—
224C22×C4×C31—22no—
225C22×C4×C31—21no—
226C22×C4×C31—21no—
227C22×C4×C31—21no—
228C22×C4×C31—21no—
229C22×C4×C31—21no—
230C22×C4×C31—21no—
231C22×C4×C31—21no—
232C22×C4×C31—22no—
233C22×C4×C31—42no—
234C22×C4×C31—42no—
235C22×C4×C31—41no—
236C22×C4×C31—41no—
237C22×C4×C31C2×D411yescharacteristic
238C22×C4×C31C2×D411yescharacteristic
239C22×C4×C31C2×D411yescharacteristic
240C22×C4×C31C2×D411yescharacteristic
241C22×C4×C31C2×D411yescharacteristic
242C22×C4×C31C2×D411yescharacteristic
243C22×C4×C31C2×D411yescharacteristic
244C22×C4×C31C2×D411yescharacteristic
245C22×C4×C31C2411yescharacteristic
246Q16×C31—44no—
247SD16×C31—44no—
248SD16×C31—44no—
249SD16×C31—44no—
250M16×C31—42no—
251C2×C8×C31—22no—
252C2×C8×C31—22no—
253C2×C8×C31—42no—
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—44no—
268C4⋊C4×C31C2×D411yescharacteristic
269C4⋊C4×C31C2×D411yescharacteristic
270C4⋊C4×C31C2×D411yescharacteristic
271C4⋊C4×C31C2×D411yescharacteristic
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—21no—
293C22⋊C4×C31—21no—
294C22⋊C4×C31—21no—
295C22⋊C4×C31—21no—
296C22⋊C4×C31—21no—
297C22⋊C4×C31—44no—
298C22⋊C4×C31—42no—
299C42×C31—21no—
300C42×C31—21no—
301C42×C31—21no—
302#18225C3111yesmaximal, characteristic, direct product factor, Sylow
303C23×C31—22no—
304C23×C31—22no—
305C23×C31—21no—
306C23×C31—21no—
307C23×C31—21no—
308C23×C31—21no—
309C23×C31—22no—
310C23×C31—41no—
311C23×C31—41no—
312C23×C31—41no—
313C23×C31—42no—
314C23×C31—81no—
315C23×C31—81no—
316C23×C31—81no—
317C23×C31—81no—
318C23×C31—81no—
319C23×C31#12011yescharacteristic
320C23×C31#12011yescharacteristic
321C23×C31C22×D411yescharacteristic
322Q8×C31—24no—
323Q8×C31—24no—
324Q8×C31—41no—
325Q8×C31—42no—
326Q8×C31—42no—
327Q8×C31—44no—
328Q8×C31—44no—
329Q8×C31—81no—
330D4×C31—41no—
331D4×C31—41no—
332D4×C31—41no—
333D4×C31—42no—
334D4×C31—42no—
335D4×C31—42no—
336D4×C31—42no—
337D4×C31—42no—
338D4×C31—81no—
339D4×C31—81no—
340D4×C31—81no—
341D4×C31—81no—
342D4×C31—81no—
343D4×C31—81no—
344D4×C31—81no—
345D4×C31—81no—
346D4×C31—81no—
347D4×C31—81no—
348D4×C31—81no—
349D4×C31—81no—
350C2×C4×C31—22no—
351C2×C4×C31—22no—
352C2×C4×C31—24no—
353C2×C4×C31—21no—
354C2×C4×C31—21no—
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—22no—
362C2×C4×C31—41no—
363C2×C4×C31—41no—
364C2×C4×C31—41no—
365C2×C4×C31—41no—
366C2×C4×C31—42no—
367C2×C4×C31—44no—
368C2×C4×C31—42no—
369C2×C4×C31—44no—
370C2×C4×C31—41no—
371C2×C4×C31—41no—
372C2×C4×C31—42no—
373C2×C4×C31—42no—
374C2×C4×C31—42no—
375C2×C4×C31—81no—
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#3534C2×C3111yescharacteristic
389#3004C2×C3111yescharacteristic, complemented
390C2×#448C2×C3111yescharacteristic, complemented
391#2614C2×C3111yescharacteristic, complemented
392#1606C2×C3112yescomplemented
393#1604C2×C3112yescomplemented
394#1603C2×C3112yescomplemented
395#1601C2×C3112yescomplemented
396#1516C2×C3111yescharacteristic, complemented
397#1510C2×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—41no—
408C22×C31—41no—
409C22×C31—41no—
410C22×C31—41no—
411C22×C31—41no—
412C22×C31—41no—
413C22×C31—41no—
414C22×C31—41no—
415C22×C31—41no—
416C22×C31—41no—
417C22×C31—41no—
418C22×C31—41no—
419C22×C31—82no—
420C22×C31—162no—
421C22×C31—162no—
422C22×C31B(4,𝔽2)12yes—
423C22×C31C2×#12011yescharacteristic
424C22×C31#57712yes—
425C4×C31—21no—
426C4×C31—21no—
427C4×C31—21no—
428C4×C31—21no—
429C4×C31—41no—
430C4×C31—41no—
431C4×C31—41no—
432C4×C31—41no—
433C4×C31—41no—
434C4×C31—41no—
435C4×C31—44no—
436C4×C31—41no—
437C4×C31—41no—
438C4×C31—82no—
439C23×Q8C22×C3111yescharacteristic, complemented
440C2×#137—21no—
441C22×SD16—21no—
442#562—21no—
443#560—21no—
444#553—21no—
445#551—21no—
446#546—21no—
447#546—21no—
448#546—21no—
449D42—21no—
450#540—21no—
451#539—21no—
452#539C22×C3111yescharacteristic
453#538—21no—
454#538C22×C3111yescharacteristic
455#537C22×C3111yescharacteristic
456#534—21no—
457#534C22×C3111yescharacteristic
458#525C22×C3111yescharacteristic
459C2×#123—21no—
460C2×#123C22×C3111yescharacteristic
461C2×#121C22×C3111yescharacteristic
462#451—21no—
463#451C22×C3112yescomplemented
464#448—21no—
465#448—21no—
466#448—21no—
467#448C22×C3112yes—
468#448C22×C3112yescomplemented
469#448C22×C3112yescomplemented
470#419—21no—
471C2×#103—21no—
472#407C22×C3111yescharacteristic, complemented
473C2×C22⋊C8C22×C3111yescharacteristic, complemented
474#395—21no—
475#395C22×C3112yescomplemented
476#393—21no—
477#393C22×C3112yescomplemented
478#381—21no—
479#381C22×C3111yescharacteristic, complemented
480#328C22×C3112yescomplemented
481#327C22×C3112yes—
482#327C22×C3112yescomplemented
483#327C22×C3112yescomplemented
484#324C22×C3112yescomplemented
485#323C22×C3112yescomplemented
486C2×C31—22no—
487C2×C31—22no—
488C2×C31—41no—
489C2×C31—81no—
490C2×C31—81no—
491C2×C31—81no—
492C2×C31—81no—
493C2×C31#300911yescharacteristic
494C2×C31#302211yescharacteristic
495C2×C31C2×B(4,𝔽2)11yescharacteristic
496C2×#41—21no—
497C2×#41D4×C3111yescharacteristic
498C22×Q8—21no—
499C22×Q8—21no—
500C22×Q8—21no—
501C22×Q8—21no—
502C22×Q8—21no—
503C22×Q8—44no—
504C22×Q8C23×C3112yes—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4D4×C3111yescharacteristic
509C22×D4D4×C3111yescharacteristic
510C23×C4—21no—
511C23×C4C23×C3111yescharacteristic
512#137—44no—
513C2×Q16—22no—
514C2×SD16—22no—
515C2×SD16—22no—
516C2×SD16—22no—
517C2×SD16—44no—
518C2×M16—21no—
519C22×C8—21no—
520#127—21no—
521#126—21no—
522#126—21no—
523#126—21no—
524#126—21no—
525#125—21no—
526#125—21no—
527#124—21no—
528#124—21no—
529#124—21no—
530#123—21no—
531#123—21no—
532#123—21no—
533#123—21no—
534#123—21no—
535#123—21no—
536#123—21no—
537#123—21no—
538#123—21no—
539#123—21no—
540#123—21no—
541#123—21no—
542#123—21no—
543#123—21no—
544#123—44no—
545C22⋊Q8—21no—
546C22⋊Q8—21no—
547C22⋊Q8—21no—
548C22⋊Q8—21no—
549C22⋊Q8—21no—
550C22⋊Q8D4×C3111yescharacteristic
551C22⋊Q8C23×C3111yescharacteristic
552#121—21no—
553#121—21no—
554#121—21no—
555#121—21no—
556#121—21no—
557#121—21no—
558#121—21no—
559#121—21no—
560#121—21no—
561#121—21no—
562#121—21no—
563#121—21no—
564#121—21no—
565#121—21no—
566#121—21no—
567#121D4×C3111yescharacteristic
568#121D4×C3111yescharacteristic
569#121D4×C3111yescharacteristic
570#121C23×C3111yescharacteristic
571#121C23×C3111yescharacteristic
572#121C23×C3111yescharacteristic
573#120—21no—
574#120—21no—
575#120—21no—
576#120—21no—
577#120—21no—
578#120—21no—
579#120—21no—
580#120—21no—
581C4×D4—21no—
582C4×D4—21no—
583C4×D4—21no—
584C4×D4—21no—
585C4×D4—21no—
586C4×D4—21no—
587C4×D4—21no—
588C4×D4—21no—
589#117—21no—
590#117D4×C3111yescharacteristic
591C2×C4⋊C4—22no—
592C2×C4⋊C4D4×C3111yescharacteristic
593C2×C4⋊C4D4×C3111yescharacteristic
594C2×C4⋊C4C23×C3111yescharacteristic
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4D4×C3111yescharacteristic
601C2×C22⋊C4D4×C3111yescharacteristic
602C2×C22⋊C4C23×C3111yescharacteristic
603#103—22no—
604#103—22no—
605#103—22no—
606#103—22no—
607C22⋊C8—21no—
608C22⋊C8—21no—
609C22⋊C8C23×C3112yes—
610C22⋊C8C23×C3112yes—
611#95—22no—
612#95—22no—
613#95—21no—
614#95C23×C3112yes—
615C31#1822511yescharacteristic, direct product factor, Sylow
616C24—21no—
617C24—21no—
618C24C2×D4×C3111yescharacteristic
619C24C2×D4×C3111yescharacteristic
620#41—42no—
621#41—82no—
622C2×Q8—21no—
623C2×Q8—24no—
624C2×Q8—24no—
625C2×Q8—22no—
626C2×Q8—22no—
627C2×Q8—44no—
628C2×Q8—42no—
629C2×Q8—42no—
630C2×Q8—44no—
631C2×Q8—44no—
632C2×Q8—44no—
633C2×Q8—41no—
634C2×Q8—41no—
635C2×Q8C2×D4×C3111yescharacteristic
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—42no—
654C2×D4—42no—
655C2×D4—82no—
656C2×D4—82no—
657C2×D4—82no—
658C2×D4C2×D4×C3111yescharacteristic
659C2×D4C2×D4×C3111yescharacteristic
660C2×D4C2×D4×C3111yescharacteristic
661C22×C4—24no—
662C22×C4—22no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—22no—
671C22×C4—42no—
672C22×C4—42no—
673C22×C4—41no—
674C22×C4—41no—
675C22×C4C2×D4×C3111yescharacteristic
676C22×C4C2×D4×C3111yescharacteristic
677C22×C4C2×D4×C3111yescharacteristic
678C22×C4C2×D4×C3111yescharacteristic
679C22×C4C2×D4×C3111yescharacteristic
680C22×C4C2×D4×C3111yescharacteristic
681C22×C4C2×D4×C3111yescharacteristic
682C22×C4C2×D4×C3111yescharacteristic
683C22×C4C24×C3111yescharacteristic
684Q16—44no—
685SD16—44no—
686SD16—44no—
687SD16—44no—
688M16—42no—
689C2×C8—22no—
690C2×C8—22no—
691C2×C8—42no—
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—44no—
706C4⋊C4C2×D4×C3111yescharacteristic
707C4⋊C4C2×D4×C3111yescharacteristic
708C4⋊C4C2×D4×C3111yescharacteristic
709C4⋊C4C2×D4×C3111yescharacteristic
710C22⋊C4—21no—
711C22⋊C4—21no—
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—
737C42—21no—
738C42—21no—
739C42—21no—
740C23—22no—
741C23—22no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—22no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—42no—
751C23—81no—
752C23—81no—
753C23—81no—
754C23—81no—
755C23—81no—
756C23C31×#12011yescharacteristic
757C23C31×#12011yescharacteristic
758C23C22×D4×C3111yescharacteristic
759Q8—24no—
760Q8—24no—
761Q8—41no—
762Q8—42no—
763Q8—42no—
764Q8—44no—
765Q8—44no—
766Q8—81no—
767D4—41no—
768D4—41no—
769D4—41no—
770D4—42no—
771D4—42no—
772D4—42no—
773D4—42no—
774D4—42no—
775D4—81no—
776D4—81no—
777D4—81no—
778D4—81no—
779D4—81no—
780D4—81no—
781D4—81no—
782D4—81no—
783D4—81no—
784D4—81no—
785D4—81no—
786D4—81no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—24no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—22no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—42no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—42no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—81no—
813C2×C4—81no—
814C2×C4—81no—
815C2×C4—81no—
816C2×C4—81no—
817C2×C4—81no—
818C2×C4—81no—
819C2×C4C31×#12011yescharacteristic
820C2×C4C31×#12011yescharacteristic
821C2×C4C22×D4×C3111yescharacteristic
822C2×C4C22×D4×C3111yescharacteristic
823C8—42no—
824C8—42no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—21no—
829C22—21no—
830C22—21no—
831C22—21no—
832C22—44no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—41no—
845C22—82no—
846C22—162no—
847C22—162no—
848C22C31×B(4,𝔽2)12yes—
849C22C2×C31×#12011yescharacteristic
850C22C31×#57712yes—
851C4—21no—
852C4—21no—
853C4—21no—
854C4—21no—
855C4—41no—
856C4—41no—
857C4—41no—
858C4—41no—
859C4—41no—
860C4—41no—
861C4—44no—
862C4—41no—
863C4—41no—
864C4—82no—
865C2—22no—
866C2—22no—
867C2—41no—
868C2—81no—
869C2—81no—
870C2—81no—
871C2—81no—
872C2C31×#300911yescharacteristic
873C2C31×#302211yescharacteristic
874C2C2×C31×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#3534C2
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×#448C2semidirect
4. C31×#2614C2semidirect
5. C31×#1606C2semidirect
6. C31×#1604C2semidirect
7. C31×#1603C2semidirect
8. C31×#1601C2semidirect
9. C31×#1516C2semidirect
10. C31×#1510C2semidirect
11. C31×#1468C2semidirect
12. C23×Q8×C31C22semidirect
36. C31×#451C22semidirect
41. C31×#448C22semidirect
42. C31×#448C22semidirect
45. C31×#407C22semidirect
46. C2×C31×C22⋊C8C22semidirect
48. C31×#395C22semidirect
50. C31×#393C22semidirect
52. C31×#381C22semidirect
53. C31×#328C22semidirect
55. C31×#327C22semidirect
56. C31×#327C22semidirect
57. C31×#324C22semidirect
58. C31×#323C22semidirect
302. #18225C31direct (N × H)
389. #3004C2×C31semidirect
390. C2×#448C2×C31semidirect
391. #2614C2×C31semidirect
392. #1606C2×C31semidirect
393. #1604C2×C31semidirect
394. #1603C2×C31semidirect
395. #1601C2×C31semidirect
396. #1516C2×C31semidirect
397. #1510C2×C31semidirect
398. #1468C2×C31semidirect
439. C23×Q8C22×C31semidirect
463. #451C22×C31semidirect
468. #448C22×C31semidirect
469. #448C22×C31semidirect
472. #407C22×C31semidirect
473. C2×C22⋊C8C22×C31semidirect
475. #395C22×C31semidirect
477. #393C22×C31semidirect
479. #381C22×C31semidirect
480. #328C22×C31semidirect
482. #327C22×C31semidirect
483. #327C22×C31semidirect
484. #324C22×C31semidirect
485. #323C22×C31semidirect
615. C31#18225direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35342
C31×#30042
C2×C31×#4482
C31×#26142
C31×#16062
C31×#16042
C31×#16032
C31×#16012
C31×#15162
C31×#15102
C31×#14682
#1822531