Finite Group Databasebeta

← C31×#18280 #21475039

Subgroups — C31×#18280 #21475039

Order 7936.

1002 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3560C211yesmaximal, characteristic, complemented
2C31×#3114C211yesmaximal, characteristic, complemented
3C31×#3100C211yesmaximal, characteristic, complemented
4C31×#2603C211yesmaximal, characteristic, complemented
5C31×#1612C211yesmaximal, characteristic, complemented
6C31×#1610C211yesmaximal, characteristic, complemented
7C31×#1609C211yesmaximal, characteristic, complemented
8C31×#1607C211yesmaximal, characteristic, complemented
9C31×#1600C211yesmaximal, characteristic, complemented
10C31×#1598C211yesmaximal, characteristic, complemented
11C31×#1597C211yesmaximal, characteristic, complemented
12C31×#1595C211yesmaximal, characteristic, complemented
13C31×#1505C211yesmaximal, characteristic, complemented
14C31×#1500C211yesmaximal, characteristic, complemented
15C31×#1473C211yesmaximal, characteristic, complemented
16C31×#563—21no—
17C31×#560—21no—
18C31×#553—21no—
19C31×#553—21no—
20C31×#551—21no—
21C31×#547—21no—
22C31×#546—21no—
23C31×#546—21no—
24C31×#542—21no—
25C31×#539—21no—
26C31×#539C2211yescharacteristic
27C31×#538—21no—
28C31×#538—21no—
29C31×#538C2211yescharacteristic
30C31×#537C2211yescharacteristic
31C31×#534C2211yescharacteristic
32C31×#532C2211yescharacteristic
33C31×#529C2211yescharacteristic
34C2×C31×#126C2211yescharacteristic
35C2×C4×D4×C31C2211yescharacteristic, complemented
36C31×#483C2211yescharacteristic, complemented
37C31×#480C2211yescharacteristic
38C31×#480C2211yescharacteristic
39C31×#480C2211yescharacteristic, complemented
40C31×#478—21no—
41C31×#474—21no—
42C31×#463—21no—
43C31×#459—21no—
44C31×#450C2211yescharacteristic, complemented
45C31×#447C2211yescharacteristic
46C31×#447C2211yescharacteristic
47C31×#447C2211yescharacteristic, complemented
48C31×#442—21no—
49C31×#440—21no—
50C4×D8×C31—21no—
51C4×D8×C31—21no—
52C31×#432C2211yescharacteristic, complemented
53C31×#431C2211yescharacteristic, complemented
54C31×#398C2211yescharacteristic, complemented
55C31×#397C2211yescharacteristic
56C31×#394C2211yescharacteristic, complemented
57C31×#392C2211yescharacteristic
58C31×#390—21no—
59C31×#388—21no—
60C31×#386—21no—
61C31×#385—21no—
62C31×#376C2211yescharacteristic, complemented
63C31×#328C2211yescharacteristic, complemented
64C31×#328C2211yescharacteristic, complemented
65C31×#327C2211yescharacteristic
66C31×#327C2211yescharacteristic
67C31×#327C2211yescharacteristic
68C31×#327C2211yescharacteristic
69C31×#327C2211yescharacteristic, complemented
70C31×#327C2211yescharacteristic, complemented
71C31×#324C2211yescharacteristic, complemented
72C31×#324C2211yescharacteristic, complemented
73C31×#323C2211yescharacteristic
74C31×#323C2211yescharacteristic
75C2×#41×C31—21no—
76C2×#41×C31—21no—
77C22×D4×C31—21no—
78C22×D4×C31—21no—
79C22×D4×C31C2311yescharacteristic
80C23×C4×C31—21no—
81C2×SD16×C31—21no—
82C2×D8×C31—21no—
83C2×D8×C31—21no—
84C2×D8×C31—21no—
85C31×C4⋊Q8—21no—
86C31×C4⋊Q8D411yescharacteristic, complemented
87C31×#127D411yescharacteristic, complemented
88C31×#126—21no—
89C31×#126—21no—
90C31×#126—21no—
91C31×#126—21no—
92C31×#126—21no—
93C31×#126—21no—
94C31×#126—21no—
95C31×#126—21no—
96C31×#126—21no—
97C31×#125—21no—
98C31×#125—21no—
99C31×#125D411yescharacteristic, complemented
100C31×#124—21no—
101C31×#124—21no—
102C31×#124—21no—
103C31×#124—21no—
104C31×#124D411yescharacteristic, complemented
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×#123—21no—
114C31×#123—21no—
115C31×#123—21no—
116C31×#123—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⋊Q8C2311yescharacteristic
125C31×#121—21no—
126C31×#121—21no—
127C31×#121—21no—
128C31×#121—21no—
129C31×#121—21no—
130C31×#121—21no—
131C31×#121—21no—
132C31×#121—21no—
133C31×#121—21no—
134C31×#121—21no—
135C31×#121—21no—
136C31×#121—21no—
137C31×#121C2311yescharacteristic
138C31×#121C2311yescharacteristic
139C31×#121C2311yescharacteristic
140C31×#120—21no—
141C31×#120—21no—
142C31×#120—21no—
143C31×#120—21no—
144C31×#120—21no—
145C4×Q8×C31D411yescharacteristic, complemented
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—
154C4×D4×C31—21no—
155C4×D4×C31—21no—
156C4×D4×C31—21no—
157C4×D4×C31—21no—
158C4×D4×C31D411yescharacteristic, complemented
159C4×D4×C31D411yescharacteristic, complemented
160C4×D4×C31D411yescharacteristic, complemented
161C31×#117—21no—
162C31×#117—21no—
163C2×C4⋊C4×C31—21no—
164C2×C4⋊C4×C31—21no—
165C2×C4⋊C4×C31D411yescharacteristic
166C2×C4⋊C4×C31D411yescharacteristic
167C2×C4⋊C4×C31C2311yescharacteristic
168C2×C4⋊C4×C31C2311yescharacteristic
169C2×C22⋊C4×C31—21no—
170C2×C22⋊C4×C31—21no—
171C2×C22⋊C4×C31—21no—
172C2×C22⋊C4×C31—21no—
173C2×C22⋊C4×C31—21no—
174C2×C22⋊C4×C31—21no—
175C2×C22⋊C4×C31—21no—
176C2×C22⋊C4×C31D411yescharacteristic
177C2×C22⋊C4×C31D411yescharacteristic
178C2×C22⋊C4×C31C2311yescharacteristic
179C2×C42×C31—21no—
180C2×C42×C31C2311yescharacteristic
181C31×#107—21no—
182C31×#107—21no—
183C31×#107—21no—
184C31×#106—21no—
185C31×C4⋊C8—21no—
186C31×C4⋊C8—21no—
187C31×#103—21no—
188C31×#102—21no—
189C31×#102—21no—
190C31×#102—21no—
191C31×#102—21no—
192C31×#102—21no—
193C31×#102—21no—
194C31×#102—21no—
195C31×C22⋊C8C2311yescharacteristic
196C31×C22⋊C8C2311yescharacteristic
197C31×C22⋊C8C2311yescharacteristic
198C31×C22⋊C8C2311yescharacteristic
199C31×#97—21no—
200C4×C8×C31—21no—
201C31×#95—21no—
202C31×#95—21no—
203C31×#95—21no—
204C31×#95C2311yescharacteristic
205C31×#95C2311yescharacteristic
206C24×C31—21no—
207C24×C31—21no—
208C24×C31C2×D411yescharacteristic
209#41×C31—81no—
210#41×C31—81no—
211#41×C31—81no—
212#41×C31—81no—
213C2×Q8×C31—21no—
214C2×Q8×C31—21no—
215C2×Q8×C31C2×D411yescharacteristic
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—42no—
231C2×D4×C31—42no—
232C2×D4×C31—42no—
233C2×D4×C31—81no—
234C2×D4×C31—81no—
235C2×D4×C31—81no—
236C2×D4×C31C2×D411yescharacteristic
237C2×D4×C31C2×D411yescharacteristic
238C2×D4×C31C2×D411yescharacteristic
239C22×C4×C31—21no—
240C22×C4×C31—21no—
241C22×C4×C31—21no—
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—41no—
251C22×C4×C31—41no—
252C22×C4×C31—81no—
253C22×C4×C31—81no—
254C22×C4×C31C2×D411yescharacteristic
255C22×C4×C31C2×D411yescharacteristic
256C22×C4×C31C2×D411yescharacteristic
257C22×C4×C31C2×D411yescharacteristic
258C22×C4×C31C2×D411yescharacteristic
259C22×C4×C31C2411yescharacteristic
260SD16×C31—42no—
261D8×C31—42no—
262D8×C31—42no—
263D8×C31—42no—
264C2×C8×C31—21no—
265C2×C8×C31—21no—
266C2×C8×C31—21no—
267C2×C8×C31—21no—
268C4⋊C4×C31—21no—
269C4⋊C4×C31—21no—
270C4⋊C4×C31—21no—
271C4⋊C4×C31—21no—
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—81no—
288C4⋊C4×C31C2×D411yescharacteristic
289C4⋊C4×C31C2×D411yescharacteristic
290C4⋊C4×C31C2×D411yescharacteristic
291C4⋊C4×C31C2×D411yescharacteristic
292C22⋊C4×C31—21no—
293C22⋊C4×C31—21no—
294C22⋊C4×C31—21no—
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—42no—
318C22⋊C4×C31—42no—
319C22⋊C4×C31—41no—
320C22⋊C4×C31—41no—
321C22⋊C4×C31—81no—
322C22⋊C4×C31—81no—
323C42×C31—21no—
324C42×C31—21no—
325C42×C31—21no—
326C42×C31—42no—
327C42×C31C2×D411yescharacteristic
328C42×C31C2×D411yescharacteristic
329C42×C31C2×D411yescharacteristic
330C42×C31C2×D411yescharacteristic
331#18280C3111yesmaximal, characteristic, direct product factor, Sylow
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—41no—
343C23×C31—41no—
344C23×C31—41no—
345C23×C31—41no—
346C23×C31—41no—
347C23×C31—81no—
348C23×C31—81no—
349C23×C31—81no—
350C23×C31C22×D411yescharacteristic
351Q8×C31—41no—
352Q8×C31—81no—
353Q8×C31—81no—
354D4×C31—22no—
355D4×C31—22no—
356D4×C31—41no—
357D4×C31—41no—
358D4×C31—41no—
359D4×C31—41no—
360D4×C31—41no—
361D4×C31—41no—
362D4×C31—41no—
363D4×C31—41no—
364D4×C31—41no—
365D4×C31—41no—
366D4×C31—41no—
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—
376D4×C31—84no—
377C2×C4×C31—21no—
378C2×C4×C31—21no—
379C2×C4×C31—22no—
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—21no—
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—81no—
403C2×C4×C31—81no—
404C2×C4×C31—81no—
405C2×C4×C31—82no—
406C2×C4×C31—82no—
407C2×C4×C31—81no—
408C2×C4×C31—81no—
409C2×C4×C31—81no—
410C2×C4×C31—81no—
411C2×C4×C31—81no—
412C2×C4×C31#12011yescharacteristic
413C2×C4×C31#12011yescharacteristic
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#3560C2×C3111yescharacteristic, complemented
423#3114C2×C3111yescharacteristic, complemented
424#3100C2×C3111yescharacteristic, complemented
425#2603C2×C3111yescharacteristic, complemented
426#1612C2×C3111yescharacteristic, complemented
427#1610C2×C3111yescharacteristic, complemented
428#1609C2×C3111yescharacteristic, complemented
429#1607C2×C3111yescharacteristic, complemented
430#1600C2×C3111yescharacteristic, complemented
431#1598C2×C3111yescharacteristic, complemented
432#1597C2×C3111yescharacteristic, complemented
433#1595C2×C3111yescharacteristic, complemented
434#1505C2×C3111yescharacteristic, complemented
435#1500C2×C3111yescharacteristic, complemented
436#1473C2×C3111yescharacteristic, complemented
437C22×C31—21no—
438C22×C31—21no—
439C22×C31—42no—
440C22×C31—42no—
441C22×C31—41no—
442C22×C31—41no—
443C22×C31—41no—
444C22×C31—41no—
445C22×C31—41no—
446C22×C31—41no—
447C22×C31—41no—
448C22×C31—41no—
449C22×C31—41no—
450C22×C31—42no—
451C22×C31—41no—
452C22×C31—41no—
453C22×C31—41no—
454C22×C31—81no—
455C22×C31—81no—
456C22×C31—81no—
457C22×C31—81no—
458C22×C31—81no—
459C22×C31—81no—
460C22×C31—162no—
461C22×C31C2×#12011yescharacteristic
462C22×C31#57611yescharacteristic
463C22×C31#57611yescharacteristic
464C4×C31—21no—
465C4×C31—21no—
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—
481#563—21no—
482#560—21no—
483#553—21no—
484#553—21no—
485#551—21no—
486#547—21no—
487#546—21no—
488#546—21no—
489#542—21no—
490#539—21no—
491#539C22×C3111yescharacteristic
492#538—21no—
493#538—21no—
494#538C22×C3111yescharacteristic
495#537C22×C3111yescharacteristic
496#534C22×C3111yescharacteristic
497#532C22×C3111yescharacteristic
498#529C22×C3111yescharacteristic
499C2×#126C22×C3111yescharacteristic
500C2×C4×D4C22×C3111yescharacteristic, complemented
501#483C22×C3111yescharacteristic, complemented
502#480C22×C3111yescharacteristic
503#480C22×C3111yescharacteristic
504#480C22×C3111yescharacteristic, complemented
505#478—21no—
506#474—21no—
507#463—21no—
508#459—21no—
509#450C22×C3111yescharacteristic, complemented
510#447C22×C3111yescharacteristic
511#447C22×C3111yescharacteristic
512#447C22×C3111yescharacteristic, complemented
513#442—21no—
514#440—21no—
515C4×D8—21no—
516C4×D8—21no—
517#432C22×C3111yescharacteristic, complemented
518#431C22×C3111yescharacteristic, complemented
519#398C22×C3111yescharacteristic, complemented
520#397C22×C3111yescharacteristic
521#394C22×C3111yescharacteristic, complemented
522#392C22×C3111yescharacteristic
523#390—21no—
524#388—21no—
525#386—21no—
526#385—21no—
527#376C22×C3111yescharacteristic, complemented
528#328C22×C3111yescharacteristic, complemented
529#328C22×C3111yescharacteristic, complemented
530#327C22×C3111yescharacteristic
531#327C22×C3111yescharacteristic
532#327C22×C3111yescharacteristic
533#327C22×C3111yescharacteristic
534#327C22×C3111yescharacteristic, complemented
535#327C22×C3111yescharacteristic, complemented
536#324C22×C3111yescharacteristic, complemented
537#324C22×C3111yescharacteristic, complemented
538#323C22×C3111yescharacteristic
539#323C22×C3111yescharacteristic
540C2×C31—21no—
541C2×C31—21no—
542C2×C31—81no—
543C2×C31—82no—
544C2×C31—81no—
545C2×C31—81no—
546C2×C31—81no—
547C2×C31#300811yescharacteristic
548C2×C31#301811yescharacteristic
549C2×C31#302511yescharacteristic
550C2×#41—21no—
551C2×#41—21no—
552C22×D4—21no—
553C22×D4—21no—
554C22×D4C23×C3111yescharacteristic
555C23×C4—21no—
556C2×SD16—21no—
557C2×D8—21no—
558C2×D8—21no—
559C2×D8—21no—
560C4⋊Q8—21no—
561C4⋊Q8D4×C3111yescharacteristic, complemented
562#127D4×C3111yescharacteristic, complemented
563#126—21no—
564#126—21no—
565#126—21no—
566#126—21no—
567#126—21no—
568#126—21no—
569#126—21no—
570#126—21no—
571#126—21no—
572#125—21no—
573#125—21no—
574#125D4×C3111yescharacteristic, complemented
575#124—21no—
576#124—21no—
577#124—21no—
578#124—21no—
579#124D4×C3111yescharacteristic, complemented
580#123—21no—
581#123—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592C22⋊Q8—21no—
593C22⋊Q8—21no—
594C22⋊Q8—21no—
595C22⋊Q8—21no—
596C22⋊Q8—21no—
597C22⋊Q8—21no—
598C22⋊Q8—21no—
599C22⋊Q8C23×C3111yescharacteristic
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#121—21no—
610#121—21no—
611#121—21no—
612#121C23×C3111yescharacteristic
613#121C23×C3111yescharacteristic
614#121C23×C3111yescharacteristic
615#120—21no—
616#120—21no—
617#120—21no—
618#120—21no—
619#120—21no—
620C4×Q8D4×C3111yescharacteristic, complemented
621C4×D4—21no—
622C4×D4—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—
631C4×D4—21no—
632C4×D4—21no—
633C4×D4D4×C3111yescharacteristic, complemented
634C4×D4D4×C3111yescharacteristic, complemented
635C4×D4D4×C3111yescharacteristic, complemented
636#117—21no—
637#117—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4D4×C3111yescharacteristic
641C2×C4⋊C4D4×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⋊C4—21no—
651C2×C22⋊C4D4×C3111yescharacteristic
652C2×C22⋊C4D4×C3111yescharacteristic
653C2×C22⋊C4C23×C3111yescharacteristic
654C2×C42—21no—
655C2×C42C23×C3111yescharacteristic
656#107—21no—
657#107—21no—
658#107—21no—
659#106—21no—
660C4⋊C8—21no—
661C4⋊C8—21no—
662#103—21no—
663#102—21no—
664#102—21no—
665#102—21no—
666#102—21no—
667#102—21no—
668#102—21no—
669#102—21no—
670C22⋊C8C23×C3111yescharacteristic
671C22⋊C8C23×C3111yescharacteristic
672C22⋊C8C23×C3111yescharacteristic
673C22⋊C8C23×C3111yescharacteristic
674#97—21no—
675C4×C8—21no—
676#95—21no—
677#95—21no—
678#95—21no—
679#95C23×C3111yescharacteristic
680#95C23×C3111yescharacteristic
681C31#1828011yescharacteristic, direct product factor, Sylow
682C24—21no—
683C24—21no—
684C24C2×D4×C3111yescharacteristic
685#41—81no—
686#41—81no—
687#41—81no—
688#41—81no—
689C2×Q8—21no—
690C2×Q8—21no—
691C2×Q8C2×D4×C3111yescharacteristic
692C2×D4—21no—
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—42no—
707C2×D4—42no—
708C2×D4—42no—
709C2×D4—81no—
710C2×D4—81no—
711C2×D4—81no—
712C2×D4C2×D4×C3111yescharacteristic
713C2×D4C2×D4×C3111yescharacteristic
714C2×D4C2×D4×C3111yescharacteristic
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—41no—
727C22×C4—41no—
728C22×C4—81no—
729C22×C4—81no—
730C22×C4C2×D4×C3111yescharacteristic
731C22×C4C2×D4×C3111yescharacteristic
732C22×C4C2×D4×C3111yescharacteristic
733C22×C4C2×D4×C3111yescharacteristic
734C22×C4C2×D4×C3111yescharacteristic
735C22×C4C24×C3111yescharacteristic
736SD16—42no—
737D8—42no—
738D8—42no—
739D8—42no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
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—81no—
764C4⋊C4C2×D4×C3111yescharacteristic
765C4⋊C4C2×D4×C3111yescharacteristic
766C4⋊C4C2×D4×C3111yescharacteristic
767C4⋊C4C2×D4×C3111yescharacteristic
768C22⋊C4—21no—
769C22⋊C4—21no—
770C22⋊C4—21no—
771C22⋊C4—21no—
772C22⋊C4—21no—
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—42no—
794C22⋊C4—42no—
795C22⋊C4—41no—
796C22⋊C4—41no—
797C22⋊C4—81no—
798C22⋊C4—81no—
799C42—21no—
800C42—21no—
801C42—21no—
802C42—42no—
803C42C2×D4×C3111yescharacteristic
804C42C2×D4×C3111yescharacteristic
805C42C2×D4×C3111yescharacteristic
806C42C2×D4×C3111yescharacteristic
807C23—22no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—81no—
823C23—81no—
824C23—81no—
825C23C22×D4×C3111yescharacteristic
826Q8—41no—
827Q8—81no—
828Q8—81no—
829D4—22no—
830D4—22no—
831D4—41no—
832D4—41no—
833D4—41no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—41no—
840D4—41no—
841D4—41no—
842D4—81no—
843D4—81no—
844D4—81no—
845D4—81no—
846D4—81no—
847D4—81no—
848D4—81no—
849D4—81no—
850D4—81no—
851D4—84no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—22no—
855C2×C4—21no—
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—41no—
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—81no—
878C2×C4—81no—
879C2×C4—81no—
880C2×C4—82no—
881C2×C4—82no—
882C2×C4—81no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4—81no—
887C2×C4C31×#12011yescharacteristic
888C2×C4C31×#12011yescharacteristic
889C2×C4C31×#12011yescharacteristic
890C2×C4C31×#12011yescharacteristic
891C2×C4C22×D4×C3111yescharacteristic
892C2×C4C22×D4×C3111yescharacteristic
893C8—41no—
894C8—41no—
895C8—41no—
896C8—41no—
897C22—21no—
898C22—21no—
899C22—42no—
900C22—42no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—42no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—162no—
921C22C2×C31×#12011yescharacteristic
922C22C31×#57611yescharacteristic
923C22C31×#57611yescharacteristic
924C4—21no—
925C4—21no—
926C4—21no—
927C4—21no—
928C4—21no—
929C4—21no—
930C4—42no—
931C4—41no—
932C4—41no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—41no—
938C4—41no—
939C4—81no—
940C4—81no—
941C2—21no—
942C2—21no—
943C2—82no—
944C2—81no—
945C2—81no—
946C2—81no—
947C2—81no—
948C2C31×#300811yescharacteristic
949C2C31×#301811yescharacteristic
950C2C31×#302511yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3560C2semidirect
2. C31×#3114C2semidirect
3. C31×#3100C2semidirect
4. C31×#2603C2semidirect
5. C31×#1612C2semidirect
6. C31×#1610C2semidirect
7. C31×#1609C2semidirect
8. C31×#1607C2semidirect
9. C31×#1600C2semidirect
10. C31×#1598C2semidirect
11. C31×#1597C2semidirect
12. C31×#1595C2semidirect
13. C31×#1505C2semidirect
14. C31×#1500C2semidirect
15. C31×#1473C2semidirect
35. C2×C4×D4×C31C22semidirect
36. C31×#483C22semidirect
39. C31×#480C22semidirect
44. C31×#450C22semidirect
47. C31×#447C22semidirect
52. C31×#432C22semidirect
53. C31×#431C22semidirect
54. C31×#398C22semidirect
56. C31×#394C22semidirect
62. C31×#376C22semidirect
63. C31×#328C22semidirect
64. C31×#328C22semidirect
69. C31×#327C22semidirect
70. C31×#327C22semidirect
71. C31×#324C22semidirect
72. C31×#324C22semidirect
86. C31×C4⋊Q8D4semidirect
87. C31×#127D4semidirect
99. C31×#125D4semidirect
104. C31×#124D4semidirect
145. C4×Q8×C31D4semidirect
158. C4×D4×C31D4semidirect
159. C4×D4×C31D4semidirect
160. C4×D4×C31D4semidirect
331. #18280C31direct (N × H)
422. #3560C2×C31semidirect
423. #3114C2×C31semidirect
424. #3100C2×C31semidirect
425. #2603C2×C31semidirect
426. #1612C2×C31semidirect
427. #1610C2×C31semidirect
428. #1609C2×C31semidirect
429. #1607C2×C31semidirect
430. #1600C2×C31semidirect
431. #1598C2×C31semidirect
432. #1597C2×C31semidirect
433. #1595C2×C31semidirect
434. #1505C2×C31semidirect
435. #1500C2×C31semidirect
436. #1473C2×C31semidirect
500. C2×C4×D4C22×C31semidirect
501. #483C22×C31semidirect
504. #480C22×C31semidirect
509. #450C22×C31semidirect
512. #447C22×C31semidirect
517. #432C22×C31semidirect
518. #431C22×C31semidirect
519. #398C22×C31semidirect
521. #394C22×C31semidirect
527. #376C22×C31semidirect
528. #328C22×C31semidirect
529. #328C22×C31semidirect
534. #327C22×C31semidirect
535. #327C22×C31semidirect
536. #324C22×C31semidirect
537. #324C22×C31semidirect
561. C4⋊Q8D4×C31semidirect
562. #127D4×C31semidirect
574. #125D4×C31semidirect
579. #124D4×C31semidirect
620. C4×Q8D4×C31semidirect
633. C4×D4D4×C31semidirect
634. C4×D4D4×C31semidirect
635. C4×D4D4×C31semidirect
681. C31#18280direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35602
C31×#31142
C31×#31002
C31×#26032
C31×#16122
C31×#16102
C31×#16092
C31×#16072
C31×#16002
C31×#15982
C31×#15972
C31×#15952
C31×#15052
C31×#15002
C31×#14732
#1828031