Finite Group Databasebeta

← C31×#18262 #21475021

Subgroups — C31×#18262 #21475021

Order 7936.

1012 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3534C211yesmaximal, characteristic
2C31×#3094C211yesmaximal, characteristic, complemented
3C31×#3091C211yesmaximal, characteristic, complemented
4C31×#2498C211yesmaximal, characteristic, complemented
5C31×#1618C211yesmaximal, characteristic, complemented
6C31×#1616C211yesmaximal, characteristic, complemented
7C31×#1615C211yesmaximal, characteristic, complemented
8C31×#1613C211yesmaximal, characteristic, complemented
9C31×#1612C211yesmaximal, characteristic, complemented
10C31×#1610C211yesmaximal, characteristic, complemented
11C31×#1609C211yesmaximal, characteristic, complemented
12C31×#1607C211yesmaximal, characteristic, complemented
13C31×#1504C211yesmaximal, characteristic, complemented
14C2×C31×#327C211yesmaximal, characteristic, complemented
15C31×#1468C211yesmaximal, characteristic, complemented
16C31×#562—21no—
17C31×#560—21no—
18C31×#553—21no—
19C31×#551—21no—
20C31×#546—21no—
21C31×#546—21no—
22C31×#546—21no—
23D42×C31—21no—
24C31×#540—21no—
25C31×#539—21no—
26C31×#539C2211yescharacteristic
27C31×#538—21no—
28C31×#538C2211yescharacteristic
29C31×#537C2211yescharacteristic
30C31×#534—21no—
31C31×#534C2211yescharacteristic
32C31×#525C2211yescharacteristic
33C2×C31×#123C2211yescharacteristic
34C2×C31×#121C2211yescharacteristic
35C2×C31×#117C2211yescharacteristic, complemented
36C31×#485—21no—
37C31×#484C2211yescharacteristic, complemented
38C31×#483C2211yescharacteristic, complemented
39C31×#482—21no—
40C31×#482—21no—
41C31×#482—21no—
42C31×#481C2211yescharacteristic
43C31×#481C2211yescharacteristic, complemented
44C31×#481C2211yescharacteristic, complemented
45C31×#480C2211yescharacteristic
46C31×#480C2211yescharacteristic, complemented
47C31×#480C2211yescharacteristic, complemented
48C31×#428—21no—
49C31×#427—21no—
50C31×#418—21no—
51C31×#416—21no—
52C31×#407C2211yescharacteristic, complemented
53C2×C31×C22⋊C8C2211yescharacteristic, complemented
54C31×#400C2211yescharacteristic, complemented
55C31×#399C2211yescharacteristic, complemented
56C31×#398C2211yescharacteristic, complemented
57C31×#397C2211yescharacteristic, complemented
58C31×#388—21no—
59C31×#387—21no—
60C31×#386—21no—
61C31×#380—21no—
62C2×C31×#95C2211yescharacteristic, complemented
63C31×#328C2211yescharacteristic, complemented
64C31×#328C2211yescharacteristic, complemented
65C31×#327C2211yescharacteristic
66C31×#327C2211yescharacteristic
67C31×#327C2211yescharacteristic, complemented
68C31×#327C2211yescharacteristic, complemented
69C31×#327C2211yescharacteristic, complemented
70C31×#327C2211yescharacteristic, complemented
71C31×#324C2211yescharacteristic, complemented
72C31×#324C2211yescharacteristic, complemented
73C31×#323C2211yescharacteristic, complemented
74C31×#323C2211yescharacteristic, complemented
75C2×#41×C31—21no—
76C2×#41×C31D411yescharacteristic
77C22×D4×C31—21no—
78C22×D4×C31—21no—
79C22×D4×C31—21no—
80C22×D4×C31D411yescharacteristic
81C22×D4×C31D411yescharacteristic
82C23×C4×C31—21no—
83C23×C4×C31C2311yescharacteristic
84C2×M16×C31—21no—
85C22×C8×C31—21no—
86C31×#127—21no—
87C31×#126—21no—
88C31×#126—21no—
89C31×#126—21no—
90C31×#126—21no—
91C31×#125—21no—
92C31×#125—21no—
93C31×#124—21no—
94C31×#124—21no—
95C31×#124—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—21no—
108C31×#123—21no—
109C31×#123—21no—
110C31×C22⋊Q8—21no—
111C31×C22⋊Q8—21no—
112C31×C22⋊Q8—21no—
113C31×C22⋊Q8—21no—
114C31×C22⋊Q8—21no—
115C31×C22⋊Q8D411yescharacteristic
116C31×C22⋊Q8C2311yescharacteristic
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×#121—21no—
131C31×#121—21no—
132C31×#121D411yescharacteristic
133C31×#121D411yescharacteristic
134C31×#121D411yescharacteristic
135C31×#121C2311yescharacteristic
136C31×#121C2311yescharacteristic
137C31×#121C2311yescharacteristic
138C31×#120—21no—
139C31×#120—21no—
140C31×#120—21no—
141C31×#120—21no—
142C31×#120—21no—
143C31×#120—21no—
144C31×#120—21no—
145C31×#120—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—
152C4×D4×C31—21no—
153C4×D4×C31—21no—
154C31×#117—21no—
155C31×#117—21no—
156C31×#117—21no—
157C31×#117—21no—
158C31×#117—21no—
159C31×#117D411yescharacteristic
160C2×C4⋊C4×C31—21no—
161C2×C4⋊C4×C31—21no—
162C2×C4⋊C4×C31D411yescharacteristic
163C2×C4⋊C4×C31D411yescharacteristic
164C2×C4⋊C4×C31C2311yescharacteristic
165C2×C4⋊C4×C31C2311yescharacteristic
166C2×C4⋊C4×C31C2311yescharacteristic
167C2×C22⋊C4×C31—21no—
168C2×C22⋊C4×C31—21no—
169C2×C22⋊C4×C31—21no—
170C2×C22⋊C4×C31—21no—
171C2×C22⋊C4×C31—21no—
172C2×C22⋊C4×C31—21no—
173C2×C22⋊C4×C31D411yescharacteristic
174C2×C22⋊C4×C31D411yescharacteristic
175C2×C22⋊C4×C31C2311yescharacteristic
176C2×C42×C31—21no—
177C31×#107—21no—
178C31×#107—21no—
179C31×#107—21no—
180C31×#107—21no—
181C31×#106—21no—
182C31×#106—21no—
183C31×#106—21no—
184C31×#106—21no—
185C31×#103—21no—
186C31×#103—21no—
187C31×#102—21no—
188C31×#102—21no—
189C31×#102—21no—
190C31×#102—21no—
191C31×#102—21no—
192C31×#102—21no—
193C31×C22⋊C8—21no—
194C31×C22⋊C8—21no—
195C31×C22⋊C8C2311yescharacteristic
196C31×C22⋊C8C2311yescharacteristic
197C31×C22⋊C8C2311yescharacteristic
198C31×C22⋊C8C2311yescharacteristic
199C31×#95—21no—
200C31×#95—21no—
201C31×#95—21no—
202C31×#95—21no—
203C31×#95—21no—
204C31×#95C2311yescharacteristic
205C31×#95C2311yescharacteristic
206C24×C31—21no—
207C24×C31—21no—
208C24×C31C2×D411yescharacteristic
209C24×C31C2×D411yescharacteristic
210#41×C31—42no—
211#41×C31—81no—
212#41×C31—81no—
213C2×Q8×C31—21no—
214C2×Q8×C31C2×D411yescharacteristic
215C2×D4×C31—21no—
216C2×D4×C31—21no—
217C2×D4×C31—21no—
218C2×D4×C31—21no—
219C2×D4×C31—21no—
220C2×D4×C31—21no—
221C2×D4×C31—21no—
222C2×D4×C31—21no—
223C2×D4×C31—21no—
224C2×D4×C31—21no—
225C2×D4×C31—21no—
226C2×D4×C31—21no—
227C2×D4×C31—21no—
228C2×D4×C31—21no—
229C2×D4×C31—21no—
230C2×D4×C31—21no—
231C2×D4×C31—21no—
232C2×D4×C31—42no—
233C2×D4×C31—42no—
234C2×D4×C31—81no—
235C2×D4×C31—81no—
236C2×D4×C31—81no—
237C2×D4×C31—81no—
238C2×D4×C31—82no—
239C2×D4×C31C2×D411yescharacteristic
240C2×D4×C31C2×D411yescharacteristic
241C2×D4×C31C2×D411yescharacteristic
242C22×C4×C31—21no—
243C22×C4×C31—21no—
244C22×C4×C31—21no—
245C22×C4×C31—21no—
246C22×C4×C31—21no—
247C22×C4×C31—21no—
248C22×C4×C31—21no—
249C22×C4×C31—21no—
250C22×C4×C31—21no—
251C22×C4×C31—21no—
252C22×C4×C31—21no—
253C22×C4×C31—42no—
254C22×C4×C31—42no—
255C22×C4×C31—42no—
256C22×C4×C31—81no—
257C22×C4×C31C2×D411yescharacteristic
258C22×C4×C31C2×D411yescharacteristic
259C22×C4×C31C2×D411yescharacteristic
260C22×C4×C31C2×D411yescharacteristic
261C22×C4×C31C2×D411yescharacteristic
262C22×C4×C31C2×D411yescharacteristic
263C22×C4×C31C2×D411yescharacteristic
264C22×C4×C31C2×D411yescharacteristic
265C22×C4×C31C2411yescharacteristic
266M16×C31—42no—
267C2×C8×C31—21no—
268C2×C8×C31—21no—
269C2×C8×C31—21no—
270C2×C8×C31—21no—
271C2×C8×C31—42no—
272C4⋊C4×C31—21no—
273C4⋊C4×C31—21no—
274C4⋊C4×C31—21no—
275C4⋊C4×C31—21no—
276C4⋊C4×C31—21no—
277C4⋊C4×C31—21no—
278C4⋊C4×C31—21no—
279C4⋊C4×C31—21no—
280C4⋊C4×C31—21no—
281C4⋊C4×C31—21no—
282C4⋊C4×C31—21no—
283C4⋊C4×C31—21no—
284C4⋊C4×C31—21no—
285C4⋊C4×C31—21no—
286C4⋊C4×C31—21no—
287C4⋊C4×C31—21no—
288C4⋊C4×C31—21no—
289C4⋊C4×C31—42no—
290C4⋊C4×C31—81no—
291C4⋊C4×C31C2×D411yescharacteristic
292C4⋊C4×C31C2×D411yescharacteristic
293C4⋊C4×C31C2×D411yescharacteristic
294C4⋊C4×C31C2×D411yescharacteristic
295C22⋊C4×C31—21no—
296C22⋊C4×C31—21no—
297C22⋊C4×C31—21no—
298C22⋊C4×C31—21no—
299C22⋊C4×C31—21no—
300C22⋊C4×C31—21no—
301C22⋊C4×C31—21no—
302C22⋊C4×C31—21no—
303C22⋊C4×C31—21no—
304C22⋊C4×C31—21no—
305C22⋊C4×C31—21no—
306C22⋊C4×C31—21no—
307C22⋊C4×C31—21no—
308C22⋊C4×C31—21no—
309C22⋊C4×C31—21no—
310C22⋊C4×C31—21no—
311C22⋊C4×C31—21no—
312C22⋊C4×C31—21no—
313C22⋊C4×C31—21no—
314C22⋊C4×C31—21no—
315C22⋊C4×C31—21no—
316C22⋊C4×C31—21no—
317C22⋊C4×C31—21no—
318C22⋊C4×C31—21no—
319C22⋊C4×C31—21no—
320C22⋊C4×C31—42no—
321C22⋊C4×C31—41no—
322C22⋊C4×C31—41no—
323C22⋊C4×C31—81no—
324C42×C31—21no—
325C42×C31—21no—
326C42×C31—21no—
327C42×C31—41no—
328C42×C31—41no—
329#18262C3111yesmaximal, characteristic, direct product factor, Sylow
330C23×C31—21no—
331C23×C31—21no—
332C23×C31—22no—
333C23×C31—21no—
334C23×C31—21no—
335C23×C31—21no—
336C23×C31—21no—
337C23×C31—21no—
338C23×C31—21no—
339C23×C31—41no—
340C23×C31—41no—
341C23×C31—41no—
342C23×C31—42no—
343C23×C31—81no—
344C23×C31—81no—
345C23×C31—81no—
346C23×C31—81no—
347C23×C31—81no—
348C23×C31#12011yescharacteristic
349C23×C31#12011yescharacteristic
350C23×C31C22×D411yescharacteristic
351Q8×C31—41no—
352Q8×C31—81no—
353D4×C31—41no—
354D4×C31—41no—
355D4×C31—41no—
356D4×C31—41no—
357D4×C31—41no—
358D4×C31—41no—
359D4×C31—41no—
360D4×C31—41no—
361D4×C31—41no—
362D4×C31—42no—
363D4×C31—42no—
364D4×C31—81no—
365D4×C31—81no—
366D4×C31—81no—
367D4×C31—81no—
368D4×C31—81no—
369D4×C31—81no—
370D4×C31—81no—
371D4×C31—81no—
372D4×C31—81no—
373D4×C31—81no—
374D4×C31—81no—
375D4×C31—81no—
376C2×C4×C31—22no—
377C2×C4×C31—22no—
378C2×C4×C31—22no—
379C2×C4×C31—21no—
380C2×C4×C31—21no—
381C2×C4×C31—21no—
382C2×C4×C31—21no—
383C2×C4×C31—21no—
384C2×C4×C31—21no—
385C2×C4×C31—21no—
386C2×C4×C31—21no—
387C2×C4×C31—21no—
388C2×C4×C31—21no—
389C2×C4×C31—41no—
390C2×C4×C31—41no—
391C2×C4×C31—41no—
392C2×C4×C31—41no—
393C2×C4×C31—41no—
394C2×C4×C31—41no—
395C2×C4×C31—41no—
396C2×C4×C31—41no—
397C2×C4×C31—41no—
398C2×C4×C31—41no—
399C2×C4×C31—41no—
400C2×C4×C31—41no—
401C2×C4×C31—41no—
402C2×C4×C31—41no—
403C2×C4×C31—41no—
404C2×C4×C31—41no—
405C2×C4×C31—41no—
406C2×C4×C31—81no—
407C2×C4×C31—81no—
408C2×C4×C31—81no—
409C2×C4×C31—81no—
410C2×C4×C31—81no—
411C2×C4×C31—81no—
412C2×C4×C31—81no—
413C2×C4×C31—84no—
414C2×C4×C31#12011yescharacteristic
415C2×C4×C31#12011yescharacteristic
416C2×C4×C31C22×D411yescharacteristic
417C2×C4×C31C22×D411yescharacteristic
418C8×C31—41no—
419C8×C31—41no—
420C8×C31—41no—
421C8×C31—41no—
422#3534C2×C3111yescharacteristic
423#3094C2×C3111yescharacteristic, complemented
424#3091C2×C3111yescharacteristic, complemented
425#2498C2×C3111yescharacteristic, complemented
426#1618C2×C3111yescharacteristic, complemented
427#1616C2×C3111yescharacteristic, complemented
428#1615C2×C3111yescharacteristic, complemented
429#1613C2×C3111yescharacteristic, complemented
430#1612C2×C3111yescharacteristic, complemented
431#1610C2×C3111yescharacteristic, complemented
432#1609C2×C3111yescharacteristic, complemented
433#1607C2×C3111yescharacteristic, complemented
434#1504C2×C3111yescharacteristic, complemented
435C2×#327C2×C3111yescharacteristic, complemented
436#1468C2×C3111yescharacteristic, complemented
437C22×C31—21no—
438C22×C31—21no—
439C22×C31—21no—
440C22×C31—21no—
441C22×C31—21no—
442C22×C31—21no—
443C22×C31—21no—
444C22×C31—42no—
445C22×C31—42no—
446C22×C31—41no—
447C22×C31—41no—
448C22×C31—41no—
449C22×C31—41no—
450C22×C31—41no—
451C22×C31—41no—
452C22×C31—41no—
453C22×C31—41no—
454C22×C31—41no—
455C22×C31—41no—
456C22×C31—41no—
457C22×C31—41no—
458C22×C31—81no—
459C22×C31—81no—
460C22×C31—162no—
461C22×C31—162no—
462C22×C31#45812yes—
463C22×C31C2×#12011yescharacteristic
464C22×C31#57611yescharacteristic
465C22×C31#57711yescharacteristic
466C4×C31—21no—
467C4×C31—21no—
468C4×C31—21no—
469C4×C31—21no—
470C4×C31—42no—
471C4×C31—41no—
472C4×C31—41no—
473C4×C31—41no—
474C4×C31—41no—
475C4×C31—41no—
476C4×C31—41no—
477C4×C31—41no—
478C4×C31—41no—
479C4×C31—81no—
480C4×C31—81no—
481C4×C31—81no—
482#562—21no—
483#560—21no—
484#553—21no—
485#551—21no—
486#546—21no—
487#546—21no—
488#546—21no—
489D42—21no—
490#540—21no—
491#539—21no—
492#539C22×C3111yescharacteristic
493#538—21no—
494#538C22×C3111yescharacteristic
495#537C22×C3111yescharacteristic
496#534—21no—
497#534C22×C3111yescharacteristic
498#525C22×C3111yescharacteristic
499C2×#123C22×C3111yescharacteristic
500C2×#121C22×C3111yescharacteristic
501C2×#117C22×C3111yescharacteristic, complemented
502#485—21no—
503#484C22×C3111yescharacteristic, complemented
504#483C22×C3111yescharacteristic, complemented
505#482—21no—
506#482—21no—
507#482—21no—
508#481C22×C3111yescharacteristic
509#481C22×C3111yescharacteristic, complemented
510#481C22×C3111yescharacteristic, complemented
511#480C22×C3111yescharacteristic
512#480C22×C3111yescharacteristic, complemented
513#480C22×C3111yescharacteristic, complemented
514#428—21no—
515#427—21no—
516#418—21no—
517#416—21no—
518#407C22×C3111yescharacteristic, complemented
519C2×C22⋊C8C22×C3111yescharacteristic, complemented
520#400C22×C3111yescharacteristic, complemented
521#399C22×C3111yescharacteristic, complemented
522#398C22×C3111yescharacteristic, complemented
523#397C22×C3111yescharacteristic, complemented
524#388—21no—
525#387—21no—
526#386—21no—
527#380—21no—
528C2×#95C22×C3111yescharacteristic, complemented
529#328C22×C3111yescharacteristic, complemented
530#328C22×C3111yescharacteristic, complemented
531#327C22×C3111yescharacteristic
532#327C22×C3111yescharacteristic
533#327C22×C3111yescharacteristic, complemented
534#327C22×C3111yescharacteristic, complemented
535#327C22×C3111yescharacteristic, complemented
536#327C22×C3111yescharacteristic, complemented
537#324C22×C3111yescharacteristic, complemented
538#324C22×C3111yescharacteristic, complemented
539#323C22×C3111yescharacteristic, complemented
540#323C22×C3111yescharacteristic, complemented
541C2×C31—21no—
542C2×C31—21no—
543C2×C31—22no—
544C2×C31—41no—
545C2×C31—81no—
546C2×C31—81no—
547C2×C31—81no—
548C2×C31—81no—
549C2×C31#301211yescharacteristic
550C2×C31#301811yescharacteristic
551C2×C31C2×#45811yescharacteristic
552C2×#41—21no—
553C2×#41D4×C3111yescharacteristic
554C22×D4—21no—
555C22×D4—21no—
556C22×D4—21no—
557C22×D4D4×C3111yescharacteristic
558C22×D4D4×C3111yescharacteristic
559C23×C4—21no—
560C23×C4C23×C3111yescharacteristic
561C2×M16—21no—
562C22×C8—21no—
563#127—21no—
564#126—21no—
565#126—21no—
566#126—21no—
567#126—21no—
568#125—21no—
569#125—21no—
570#124—21no—
571#124—21no—
572#124—21no—
573#123—21no—
574#123—21no—
575#123—21no—
576#123—21no—
577#123—21no—
578#123—21no—
579#123—21no—
580#123—21no—
581#123—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587C22⋊Q8—21no—
588C22⋊Q8—21no—
589C22⋊Q8—21no—
590C22⋊Q8—21no—
591C22⋊Q8—21no—
592C22⋊Q8D4×C3111yescharacteristic
593C22⋊Q8C23×C3111yescharacteristic
594#121—21no—
595#121—21no—
596#121—21no—
597#121—21no—
598#121—21no—
599#121—21no—
600#121—21no—
601#121—21no—
602#121—21no—
603#121—21no—
604#121—21no—
605#121—21no—
606#121—21no—
607#121—21no—
608#121—21no—
609#121D4×C3111yescharacteristic
610#121D4×C3111yescharacteristic
611#121D4×C3111yescharacteristic
612#121C23×C3111yescharacteristic
613#121C23×C3111yescharacteristic
614#121C23×C3111yescharacteristic
615#120—21no—
616#120—21no—
617#120—21no—
618#120—21no—
619#120—21no—
620#120—21no—
621#120—21no—
622#120—21no—
623C4×D4—21no—
624C4×D4—21no—
625C4×D4—21no—
626C4×D4—21no—
627C4×D4—21no—
628C4×D4—21no—
629C4×D4—21no—
630C4×D4—21no—
631#117—21no—
632#117—21no—
633#117—21no—
634#117—21no—
635#117—21no—
636#117D4×C3111yescharacteristic
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4D4×C3111yescharacteristic
640C2×C4⋊C4D4×C3111yescharacteristic
641C2×C4⋊C4C23×C3111yescharacteristic
642C2×C4⋊C4C23×C3111yescharacteristic
643C2×C4⋊C4C23×C3111yescharacteristic
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4D4×C3111yescharacteristic
651C2×C22⋊C4D4×C3111yescharacteristic
652C2×C22⋊C4C23×C3111yescharacteristic
653C2×C42—21no—
654#107—21no—
655#107—21no—
656#107—21no—
657#107—21no—
658#106—21no—
659#106—21no—
660#106—21no—
661#106—21no—
662#103—21no—
663#103—21no—
664#102—21no—
665#102—21no—
666#102—21no—
667#102—21no—
668#102—21no—
669#102—21no—
670C22⋊C8—21no—
671C22⋊C8—21no—
672C22⋊C8C23×C3111yescharacteristic
673C22⋊C8C23×C3111yescharacteristic
674C22⋊C8C23×C3111yescharacteristic
675C22⋊C8C23×C3111yescharacteristic
676#95—21no—
677#95—21no—
678#95—21no—
679#95—21no—
680#95—21no—
681#95C23×C3111yescharacteristic
682#95C23×C3111yescharacteristic
683C31#1826211yescharacteristic, direct product factor, Sylow
684C24—21no—
685C24—21no—
686C24C2×D4×C3111yescharacteristic
687C24C2×D4×C3111yescharacteristic
688#41—42no—
689#41—81no—
690#41—81no—
691C2×Q8—21no—
692C2×Q8C2×D4×C3111yescharacteristic
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—42no—
711C2×D4—42no—
712C2×D4—81no—
713C2×D4—81no—
714C2×D4—81no—
715C2×D4—81no—
716C2×D4—82no—
717C2×D4C2×D4×C3111yescharacteristic
718C2×D4C2×D4×C3111yescharacteristic
719C2×D4C2×D4×C3111yescharacteristic
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—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—81no—
735C22×C4C2×D4×C3111yescharacteristic
736C22×C4C2×D4×C3111yescharacteristic
737C22×C4C2×D4×C3111yescharacteristic
738C22×C4C2×D4×C3111yescharacteristic
739C22×C4C2×D4×C3111yescharacteristic
740C22×C4C2×D4×C3111yescharacteristic
741C22×C4C2×D4×C3111yescharacteristic
742C22×C4C2×D4×C3111yescharacteristic
743C22×C4C24×C3111yescharacteristic
744M16—42no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—42no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—42no—
768C4⋊C4—81no—
769C4⋊C4C2×D4×C3111yescharacteristic
770C4⋊C4C2×D4×C3111yescharacteristic
771C4⋊C4C2×D4×C3111yescharacteristic
772C4⋊C4C2×D4×C3111yescharacteristic
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—42no—
799C22⋊C4—41no—
800C22⋊C4—41no—
801C22⋊C4—81no—
802C42—21no—
803C42—21no—
804C42—21no—
805C42—41no—
806C42—41no—
807C23—22no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—42no—
820C23—81no—
821C23—81no—
822C23—81no—
823C23—81no—
824C23—81no—
825C23C31×#12011yescharacteristic
826C23C31×#12011yescharacteristic
827C23C22×D4×C3111yescharacteristic
828Q8—41no—
829Q8—81no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4—42no—
834D4—42no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—41no—
840D4—41no—
841D4—81no—
842D4—81no—
843D4—81no—
844D4—81no—
845D4—81no—
846D4—81no—
847D4—81no—
848D4—81no—
849D4—81no—
850D4—81no—
851D4—81no—
852D4—81no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4—81no—
887C2×C4—81no—
888C2×C4—81no—
889C2×C4—81no—
890C2×C4—84no—
891C2×C4C31×#12011yescharacteristic
892C2×C4C31×#12011yescharacteristic
893C2×C4C22×D4×C3111yescharacteristic
894C2×C4C22×D4×C3111yescharacteristic
895C8—41no—
896C8—41no—
897C8—41no—
898C8—41no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—42no—
907C22—42no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—81no—
921C22—81no—
922C22—162no—
923C22—162no—
924C22C31×#45812yes—
925C22C2×C31×#12011yescharacteristic
926C22C31×#57611yescharacteristic
927C22C31×#57711yescharacteristic
928C4—21no—
929C4—21no—
930C4—21no—
931C4—21no—
932C4—42no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—41no—
938C4—41no—
939C4—41no—
940C4—41no—
941C4—81no—
942C4—81no—
943C4—81no—
944C2—21no—
945C2—21no—
946C2—22no—
947C2—41no—
948C2—81no—
949C2—81no—
950C2—81no—
951C2—81no—
952C2C31×#301211yescharacteristic
953C2C31×#301811yescharacteristic
954C2C2×C31×#45811yescharacteristic
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×#3094C2semidirect
3. C31×#3091C2semidirect
4. C31×#2498C2semidirect
5. C31×#1618C2semidirect
6. C31×#1616C2semidirect
7. C31×#1615C2semidirect
8. C31×#1613C2semidirect
9. C31×#1612C2semidirect
10. C31×#1610C2semidirect
11. C31×#1609C2semidirect
12. C31×#1607C2semidirect
13. C31×#1504C2semidirect
14. C2×C31×#327C2semidirect
15. C31×#1468C2semidirect
35. C2×C31×#117C22semidirect
37. C31×#484C22semidirect
38. C31×#483C22semidirect
43. C31×#481C22semidirect
44. C31×#481C22semidirect
46. C31×#480C22semidirect
47. C31×#480C22semidirect
52. C31×#407C22semidirect
53. C2×C31×C22⋊C8C22semidirect
54. C31×#400C22semidirect
55. C31×#399C22semidirect
56. C31×#398C22semidirect
57. C31×#397C22semidirect
62. C2×C31×#95C22semidirect
63. C31×#328C22semidirect
64. C31×#328C22semidirect
67. C31×#327C22semidirect
68. C31×#327C22semidirect
69. C31×#327C22semidirect
70. C31×#327C22semidirect
71. C31×#324C22semidirect
72. C31×#324C22semidirect
73. C31×#323C22semidirect
74. C31×#323C22semidirect
329. #18262C31direct (N × H)
423. #3094C2×C31semidirect
424. #3091C2×C31semidirect
425. #2498C2×C31semidirect
426. #1618C2×C31semidirect
427. #1616C2×C31semidirect
428. #1615C2×C31semidirect
429. #1613C2×C31semidirect
430. #1612C2×C31semidirect
431. #1610C2×C31semidirect
432. #1609C2×C31semidirect
433. #1607C2×C31semidirect
434. #1504C2×C31semidirect
435. C2×#327C2×C31semidirect
436. #1468C2×C31semidirect
501. C2×#117C22×C31semidirect
503. #484C22×C31semidirect
504. #483C22×C31semidirect
509. #481C22×C31semidirect
510. #481C22×C31semidirect
512. #480C22×C31semidirect
513. #480C22×C31semidirect
518. #407C22×C31semidirect
519. C2×C22⋊C8C22×C31semidirect
520. #400C22×C31semidirect
521. #399C22×C31semidirect
522. #398C22×C31semidirect
523. #397C22×C31semidirect
528. C2×#95C22×C31semidirect
529. #328C22×C31semidirect
530. #328C22×C31semidirect
533. #327C22×C31semidirect
534. #327C22×C31semidirect
535. #327C22×C31semidirect
536. #327C22×C31semidirect
537. #324C22×C31semidirect
538. #324C22×C31semidirect
539. #323C22×C31semidirect
540. #323C22×C31semidirect
683. C31#18262direct (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×#30942
C31×#30912
C31×#24982
C31×#16182
C31×#16162
C31×#16152
C31×#16132
C31×#16122
C31×#16102
C31×#16092
C31×#16072
C31×#15042
C2×C31×#3272
C31×#14682
#1826231