Finite Group Databasebeta

← C31×#18415 #21475174

Subgroups — C31×#18415 #21475174

Order 7936.

992 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3534C211yesmaximal, characteristic
2C31×#3196C211yesmaximal, characteristic, complemented
3C31×#3187C211yesmaximal, characteristic, complemented
4C31×#2663C211yesmaximal, characteristic, complemented
5C31×#1618C211yesmaximal, characteristic, complemented
6C31×#1616C211yesmaximal, characteristic, complemented
7C31×#1615C211yesmaximal, characteristic, complemented
8C31×#1613C211yesmaximal, characteristic, complemented
9C31×#1606C211yesmaximal, characteristic, complemented
10C31×#1604C211yesmaximal, characteristic, complemented
11C31×#1603C211yesmaximal, characteristic, complemented
12C31×#1601C211yesmaximal, characteristic, complemented
13C31×#1507C211yesmaximal, characteristic, complemented
14C31×#1501C211yesmaximal, 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×C22⋊Q8C2211yescharacteristic, complemented
35C2×C31×#121C2211yescharacteristic
36C31×#485—21no—
37C31×#484C2211yescharacteristic, complemented
38C31×#483—21no—
39C31×#481C2211yescharacteristic
40C31×#481C2211yescharacteristic, complemented
41C31×#481C2211yescharacteristic, complemented
42C31×#470—21no—
43C31×#468—21no—
44C31×#465—21no—
45C31×#465—21no—
46C31×#452—21no—
47C31×#451C2211yescharacteristic, complemented
48C31×#450—21no—
49C31×#448C2211yescharacteristic
50C31×#448C2211yescharacteristic, complemented
51C31×#448C2211yescharacteristic, complemented
52C31×#407C2211yescharacteristic, complemented
53C2×C31×C22⋊C8C2211yescharacteristic, complemented
54C31×#400C2211yescharacteristic, complemented
55C31×#399C2211yescharacteristic, complemented
56C31×#397—21no—
57C31×#395C2211yescharacteristic, complemented
58C31×#394—21no—
59C31×#393C2211yescharacteristic, complemented
60C31×#389—21no—
61C31×#388—21no—
62C4×C22⋊C4×C31C2211yescharacteristic, 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×Q8×C31C2311yescharacteristic
78C22×D4×C31—21no—
79C22×D4×C31—21no—
80C22×D4×C31—21no—
81C22×D4×C31D411yescharacteristic
82C22×D4×C31D411yescharacteristic
83C23×C4×C31C2311yescharacteristic
84C2×Q16×C31—21no—
85C2×SD16×C31—21no—
86C2×SD16×C31—21no—
87C2×SD16×C31—21no—
88C2×M16×C31—21no—
89C22×C8×C31—21no—
90C31×#127—21no—
91C31×#126—21no—
92C31×#126—21no—
93C31×#126—21no—
94C31×#126—21no—
95C31×#125—21no—
96C31×#125—21no—
97C31×#124—21no—
98C31×#124—21no—
99C31×#124—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×#123—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⋊Q8D411yescharacteristic
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×#121—21no—
138C31×#121—21no—
139C31×#121—21no—
140C31×#121D411yescharacteristic
141C31×#121D411yescharacteristic
142C31×#121D411yescharacteristic
143C31×#121C2311yescharacteristic
144C31×#121C2311yescharacteristic
145C31×#121C2311yescharacteristic
146C31×#120—21no—
147C31×#120—21no—
148C31×#120—21no—
149C31×#120—21no—
150C31×#120—21no—
151C31×#120—21no—
152C31×#120—21no—
153C31×#120—21no—
154C4×D4×C31—21no—
155C4×D4×C31—21no—
156C4×D4×C31—21no—
157C4×D4×C31—21no—
158C4×D4×C31—21no—
159C4×D4×C31—21no—
160C4×D4×C31—21no—
161C4×D4×C31—21no—
162C31×#117—21no—
163C31×#117D411yescharacteristic
164C2×C4⋊C4×C31—21no—
165C2×C4⋊C4×C31—21no—
166C2×C4⋊C4×C31—21no—
167C2×C4⋊C4×C31D411yescharacteristic
168C2×C4⋊C4×C31D411yescharacteristic
169C2×C4⋊C4×C31C2311yescharacteristic
170C2×C4⋊C4×C31C2311yescharacteristic
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×C31—21no—
177C2×C22⋊C4×C31—21no—
178C2×C22⋊C4×C31D411yescharacteristic
179C2×C22⋊C4×C31D411yescharacteristic
180C2×C22⋊C4×C31C2311yescharacteristic
181C2×C42×C31—21no—
182C31×#107—21no—
183C31×#106—21no—
184C31×#106—21no—
185C31×#106—21no—
186C31×#103—21no—
187C31×#103—21no—
188C31×#103—21no—
189C31×#103—21no—
190C31×#103—21no—
191C31×#102—21no—
192C31×#102—21no—
193C31×#102—21no—
194C31×C22⋊C8—21no—
195C31×C22⋊C8—21no—
196C31×C22⋊C8C2311yescharacteristic
197C31×C22⋊C8C2311yescharacteristic
198C31×C22⋊C8C2311yescharacteristic
199C31×C22⋊C8C2311yescharacteristic
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—81no—
211#41×C31—81no—
212#41×C31—81no—
213C2×Q8×C31—21no—
214C2×Q8×C31—21no—
215C2×Q8×C31—21no—
216C2×Q8×C31—81no—
217C2×Q8×C31C2×D411yescharacteristic
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—21no—
233C2×D4×C31—21no—
234C2×D4×C31—21no—
235C2×D4×C31—81no—
236C2×D4×C31—81no—
237C2×D4×C31—81no—
238C2×D4×C31—81no—
239C2×D4×C31—81no—
240C2×D4×C31—81no—
241C2×D4×C31—82no—
242C2×D4×C31C2×D411yescharacteristic
243C2×D4×C31C2×D411yescharacteristic
244C2×D4×C31C2×D411yescharacteristic
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—21no—
254C22×C4×C31—21no—
255C22×C4×C31—21no—
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
266Q16×C31—81no—
267SD16×C31—81no—
268SD16×C31—81no—
269SD16×C31—81no—
270M16×C31—81no—
271C2×C8×C31—21no—
272C2×C8×C31—21no—
273C2×C8×C31—21no—
274C2×C8×C31—21no—
275C2×C8×C31—81no—
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—21no—
290C4⋊C4×C31—21no—
291C4⋊C4×C31—42no—
292C4⋊C4×C31—41no—
293C4⋊C4×C31—41no—
294C4⋊C4×C31—81no—
295C4⋊C4×C31C2×D411yescharacteristic
296C4⋊C4×C31C2×D411yescharacteristic
297C4⋊C4×C31C2×D411yescharacteristic
298C4⋊C4×C31C2×D411yescharacteristic
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—21no—
321C22⋊C4×C31—21no—
322C22⋊C4×C31—21no—
323C22⋊C4×C31—21no—
324C22⋊C4×C31—42no—
325C22⋊C4×C31—42no—
326C22⋊C4×C31—41no—
327C22⋊C4×C31—41no—
328C22⋊C4×C31—81no—
329C42×C31—21no—
330C42×C31—21no—
331C42×C31—21no—
332C42×C31—81no—
333#18415C3111yesmaximal, characteristic, direct product factor, Sylow
334C23×C31—21no—
335C23×C31—21no—
336C23×C31—21no—
337C23×C31—21no—
338C23×C31—21no—
339C23×C31—21no—
340C23×C31—21no—
341C23×C31—21no—
342C23×C31—41no—
343C23×C31—41no—
344C23×C31—42no—
345C23×C31—41no—
346C23×C31—41no—
347C23×C31—81no—
348C23×C31—81no—
349C23×C31—81no—
350C23×C31—81no—
351C23×C31—81no—
352C23×C31#12011yescharacteristic
353C23×C31#12011yescharacteristic
354C23×C31C22×D411yescharacteristic
355Q8×C31—41no—
356Q8×C31—41no—
357Q8×C31—41no—
358Q8×C31—41no—
359Q8×C31—41no—
360Q8×C31—81no—
361D4×C31—41no—
362D4×C31—41no—
363D4×C31—41no—
364D4×C31—42no—
365D4×C31—42no—
366D4×C31—41no—
367D4×C31—41no—
368D4×C31—41no—
369D4×C31—41no—
370D4×C31—41no—
371D4×C31—41no—
372D4×C31—81no—
373D4×C31—81no—
374D4×C31—81no—
375D4×C31—81no—
376D4×C31—81no—
377D4×C31—81no—
378D4×C31—81no—
379D4×C31—81no—
380D4×C31—81no—
381D4×C31—81no—
382D4×C31—81no—
383D4×C31—81no—
384C2×C4×C31—22no—
385C2×C4×C31—21no—
386C2×C4×C31—21no—
387C2×C4×C31—21no—
388C2×C4×C31—21no—
389C2×C4×C31—21no—
390C2×C4×C31—21no—
391C2×C4×C31—21no—
392C2×C4×C31—21no—
393C2×C4×C31—21no—
394C2×C4×C31—21no—
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—41no—
407C2×C4×C31—41no—
408C2×C4×C31—41no—
409C2×C4×C31—41no—
410C2×C4×C31—41no—
411C2×C4×C31—41no—
412C2×C4×C31—41no—
413C2×C4×C31—41no—
414C2×C4×C31—81no—
415C2×C4×C31—81no—
416C2×C4×C31—81no—
417C2×C4×C31—81no—
418C2×C4×C31—81no—
419C2×C4×C31—81no—
420C2×C4×C31—81no—
421C2×C4×C31#12011yescharacteristic
422C2×C4×C31#12011yescharacteristic
423C2×C4×C31C22×D411yescharacteristic
424C2×C4×C31C22×D411yescharacteristic
425C8×C31—41no—
426C8×C31—41no—
427C8×C31—41no—
428C8×C31—41no—
429#3534C2×C3111yescharacteristic
430#3196C2×C3111yescharacteristic, complemented
431#3187C2×C3111yescharacteristic, complemented
432#2663C2×C3111yescharacteristic, complemented
433#1618C2×C3111yescharacteristic, complemented
434#1616C2×C3111yescharacteristic, complemented
435#1615C2×C3111yescharacteristic, complemented
436#1613C2×C3111yescharacteristic, complemented
437#1606C2×C3111yescharacteristic, complemented
438#1604C2×C3111yescharacteristic, complemented
439#1603C2×C3111yescharacteristic, complemented
440#1601C2×C3111yescharacteristic, complemented
441#1507C2×C3111yescharacteristic, complemented
442#1501C2×C3111yescharacteristic, complemented
443#1468C2×C3111yescharacteristic, complemented
444C22×C31—21no—
445C22×C31—21no—
446C22×C31—21no—
447C22×C31—21no—
448C22×C31—21no—
449C22×C31—21no—
450C22×C31—21no—
451C22×C31—21no—
452C22×C31—41no—
453C22×C31—41no—
454C22×C31—41no—
455C22×C31—41no—
456C22×C31—41no—
457C22×C31—41no—
458C22×C31—41no—
459C22×C31—41no—
460C22×C31—41no—
461C22×C31—41no—
462C22×C31—41no—
463C22×C31—41no—
464C22×C31—81no—
465C22×C31—81no—
466C22×C31—81no—
467C22×C31—81no—
468C22×C31—162no—
469C22×C31—162no—
470C22×C31C2×#12011yescharacteristic
471C22×C31#57711yescharacteristic
472C22×C31#57711yescharacteristic
473C4×C31—21no—
474C4×C31—21no—
475C4×C31—21no—
476C4×C31—21no—
477C4×C31—42no—
478C4×C31—41no—
479C4×C31—41no—
480C4×C31—41no—
481C4×C31—41no—
482C4×C31—41no—
483C4×C31—41no—
484C4×C31—41no—
485C4×C31—41no—
486C4×C31—81no—
487C4×C31—81no—
488C4×C31—81no—
489#562—21no—
490#560—21no—
491#553—21no—
492#551—21no—
493#546—21no—
494#546—21no—
495#546—21no—
496D42—21no—
497#540—21no—
498#539—21no—
499#539C22×C3111yescharacteristic
500#538—21no—
501#538C22×C3111yescharacteristic
502#537C22×C3111yescharacteristic
503#534—21no—
504#534C22×C3111yescharacteristic
505#525C22×C3111yescharacteristic
506C2×#123C22×C3111yescharacteristic
507C2×C22⋊Q8C22×C3111yescharacteristic, complemented
508C2×#121C22×C3111yescharacteristic
509#485—21no—
510#484C22×C3111yescharacteristic, complemented
511#483—21no—
512#481C22×C3111yescharacteristic
513#481C22×C3111yescharacteristic, complemented
514#481C22×C3111yescharacteristic, complemented
515#470—21no—
516#468—21no—
517#465—21no—
518#465—21no—
519#452—21no—
520#451C22×C3111yescharacteristic, complemented
521#450—21no—
522#448C22×C3111yescharacteristic
523#448C22×C3111yescharacteristic, complemented
524#448C22×C3111yescharacteristic, complemented
525#407C22×C3111yescharacteristic, complemented
526C2×C22⋊C8C22×C3111yescharacteristic, complemented
527#400C22×C3111yescharacteristic, complemented
528#399C22×C3111yescharacteristic, complemented
529#397—21no—
530#395C22×C3111yescharacteristic, complemented
531#394—21no—
532#393C22×C3111yescharacteristic, complemented
533#389—21no—
534#388—21no—
535C4×C22⋊C4C22×C3111yescharacteristic, complemented
536#328C22×C3111yescharacteristic, complemented
537#328C22×C3111yescharacteristic, complemented
538#327C22×C3111yescharacteristic
539#327C22×C3111yescharacteristic
540#327C22×C3111yescharacteristic, complemented
541#327C22×C3111yescharacteristic, complemented
542#327C22×C3111yescharacteristic, complemented
543#327C22×C3111yescharacteristic, complemented
544#324C22×C3111yescharacteristic, complemented
545#324C22×C3111yescharacteristic, complemented
546#323C22×C3111yescharacteristic, complemented
547#323C22×C3111yescharacteristic, complemented
548C2×C31—21no—
549C2×C31—21no—
550C2×C31—41no—
551C2×C31—41no—
552C2×C31—81no—
553C2×C31—81no—
554C2×C31—81no—
555C2×C31—81no—
556C2×C31#300911yescharacteristic
557C2×C31#301811yescharacteristic
558C2×C31#302611yescharacteristic
559C2×#41—21no—
560C2×#41D4×C3111yescharacteristic
561C22×Q8C23×C3111yescharacteristic
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—21no—
565C22×D4D4×C3111yescharacteristic
566C22×D4D4×C3111yescharacteristic
567C23×C4C23×C3111yescharacteristic
568C2×Q16—21no—
569C2×SD16—21no—
570C2×SD16—21no—
571C2×SD16—21no—
572C2×M16—21no—
573C22×C8—21no—
574#127—21no—
575#126—21no—
576#126—21no—
577#126—21no—
578#126—21no—
579#125—21no—
580#125—21no—
581#124—21no—
582#124—21no—
583#124—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—
592#123—21no—
593#123—21no—
594#123—21no—
595#123—21no—
596#123—21no—
597#123—21no—
598C22⋊Q8—21no—
599C22⋊Q8—21no—
600C22⋊Q8—21no—
601C22⋊Q8—21no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8D4×C3111yescharacteristic
608C22⋊Q8C23×C3111yescharacteristic
609#121—21no—
610#121—21no—
611#121—21no—
612#121—21no—
613#121—21no—
614#121—21no—
615#121—21no—
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121D4×C3111yescharacteristic
625#121D4×C3111yescharacteristic
626#121D4×C3111yescharacteristic
627#121C23×C3111yescharacteristic
628#121C23×C3111yescharacteristic
629#121C23×C3111yescharacteristic
630#120—21no—
631#120—21no—
632#120—21no—
633#120—21no—
634#120—21no—
635#120—21no—
636#120—21no—
637#120—21no—
638C4×D4—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643C4×D4—21no—
644C4×D4—21no—
645C4×D4—21no—
646#117—21no—
647#117D4×C3111yescharacteristic
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4D4×C3111yescharacteristic
652C2×C4⋊C4D4×C3111yescharacteristic
653C2×C4⋊C4C23×C3111yescharacteristic
654C2×C4⋊C4C23×C3111yescharacteristic
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4D4×C3111yescharacteristic
663C2×C22⋊C4D4×C3111yescharacteristic
664C2×C22⋊C4C23×C3111yescharacteristic
665C2×C42—21no—
666#107—21no—
667#106—21no—
668#106—21no—
669#106—21no—
670#103—21no—
671#103—21no—
672#103—21no—
673#103—21no—
674#103—21no—
675#102—21no—
676#102—21no—
677#102—21no—
678C22⋊C8—21no—
679C22⋊C8—21no—
680C22⋊C8C23×C3111yescharacteristic
681C22⋊C8C23×C3111yescharacteristic
682C22⋊C8C23×C3111yescharacteristic
683C22⋊C8C23×C3111yescharacteristic
684#95—21no—
685#95—21no—
686#95—21no—
687#95—21no—
688#95C23×C3111yescharacteristic
689#95C23×C3111yescharacteristic
690C31#1841511yescharacteristic, direct product factor, Sylow
691C24—21no—
692C24—21no—
693C24C2×D4×C3111yescharacteristic
694C24C2×D4×C3111yescharacteristic
695#41—81no—
696#41—81no—
697#41—81no—
698C2×Q8—21no—
699C2×Q8—21no—
700C2×Q8—21no—
701C2×Q8—81no—
702C2×Q8C2×D4×C3111yescharacteristic
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—81no—
721C2×D4—81no—
722C2×D4—81no—
723C2×D4—81no—
724C2×D4—81no—
725C2×D4—81no—
726C2×D4—82no—
727C2×D4C2×D4×C3111yescharacteristic
728C2×D4C2×D4×C3111yescharacteristic
729C2×D4C2×D4×C3111yescharacteristic
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—81no—
742C22×C4C2×D4×C3111yescharacteristic
743C22×C4C2×D4×C3111yescharacteristic
744C22×C4C2×D4×C3111yescharacteristic
745C22×C4C2×D4×C3111yescharacteristic
746C22×C4C2×D4×C3111yescharacteristic
747C22×C4C2×D4×C3111yescharacteristic
748C22×C4C2×D4×C3111yescharacteristic
749C22×C4C2×D4×C3111yescharacteristic
750C22×C4C24×C3111yescharacteristic
751Q16—81no—
752SD16—81no—
753SD16—81no—
754SD16—81no—
755M16—81no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—81no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—21no—
774C4⋊C4—21no—
775C4⋊C4—21no—
776C4⋊C4—42no—
777C4⋊C4—41no—
778C4⋊C4—41no—
779C4⋊C4—81no—
780C4⋊C4C2×D4×C3111yescharacteristic
781C4⋊C4C2×D4×C3111yescharacteristic
782C4⋊C4C2×D4×C3111yescharacteristic
783C4⋊C4C2×D4×C3111yescharacteristic
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—21no—
799C22⋊C4—21no—
800C22⋊C4—21no—
801C22⋊C4—21no—
802C22⋊C4—21no—
803C22⋊C4—21no—
804C22⋊C4—21no—
805C22⋊C4—21no—
806C22⋊C4—21no—
807C22⋊C4—21no—
808C22⋊C4—21no—
809C22⋊C4—42no—
810C22⋊C4—42no—
811C22⋊C4—41no—
812C22⋊C4—41no—
813C22⋊C4—81no—
814C42—21no—
815C42—21no—
816C42—21no—
817C42—81no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—41no—
827C23—41no—
828C23—42no—
829C23—41no—
830C23—41no—
831C23—81no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23—81no—
836C23C31×#12011yescharacteristic
837C23C31×#12011yescharacteristic
838C23C22×D4×C3111yescharacteristic
839Q8—41no—
840Q8—41no—
841Q8—41no—
842Q8—41no—
843Q8—41no—
844Q8—81no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—42no—
849D4—42no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—81no—
857D4—81no—
858D4—81no—
859D4—81no—
860D4—81no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—81no—
866D4—81no—
867D4—81no—
868C2×C4—22no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—81no—
899C2×C4—81no—
900C2×C4—81no—
901C2×C4—81no—
902C2×C4—81no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4C31×#12011yescharacteristic
906C2×C4C31×#12011yescharacteristic
907C2×C4C22×D4×C3111yescharacteristic
908C2×C4C22×D4×C3111yescharacteristic
909C8—41no—
910C8—41no—
911C8—41no—
912C8—41no—
913C22—21no—
914C22—21no—
915C22—21no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22—162no—
938C22—162no—
939C22C2×C31×#12011yescharacteristic
940C22C31×#57711yescharacteristic
941C22C31×#57711yescharacteristic
942C4—21no—
943C4—21no—
944C4—21no—
945C4—21no—
946C4—42no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—41no—
952C4—41no—
953C4—41no—
954C4—41no—
955C4—81no—
956C4—81no—
957C4—81no—
958C2—21no—
959C2—21no—
960C2—41no—
961C2—41no—
962C2—81no—
963C2—81no—
964C2—81no—
965C2—81no—
966C2C31×#300911yescharacteristic
967C2C31×#301811yescharacteristic
968C2C31×#302611yescharacteristic
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×#3196C2semidirect
3. C31×#3187C2semidirect
4. C31×#2663C2semidirect
5. C31×#1618C2semidirect
6. C31×#1616C2semidirect
7. C31×#1615C2semidirect
8. C31×#1613C2semidirect
9. C31×#1606C2semidirect
10. C31×#1604C2semidirect
11. C31×#1603C2semidirect
12. C31×#1601C2semidirect
13. C31×#1507C2semidirect
14. C31×#1501C2semidirect
15. C31×#1468C2semidirect
34. C2×C31×C22⋊Q8C22semidirect
37. C31×#484C22semidirect
40. C31×#481C22semidirect
41. C31×#481C22semidirect
47. C31×#451C22semidirect
50. C31×#448C22semidirect
51. C31×#448C22semidirect
52. C31×#407C22semidirect
53. C2×C31×C22⋊C8C22semidirect
54. C31×#400C22semidirect
55. C31×#399C22semidirect
57. C31×#395C22semidirect
59. C31×#393C22semidirect
62. C4×C22⋊C4×C31C22semidirect
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
333. #18415C31direct (N × H)
430. #3196C2×C31semidirect
431. #3187C2×C31semidirect
432. #2663C2×C31semidirect
433. #1618C2×C31semidirect
434. #1616C2×C31semidirect
435. #1615C2×C31semidirect
436. #1613C2×C31semidirect
437. #1606C2×C31semidirect
438. #1604C2×C31semidirect
439. #1603C2×C31semidirect
440. #1601C2×C31semidirect
441. #1507C2×C31semidirect
442. #1501C2×C31semidirect
443. #1468C2×C31semidirect
507. C2×C22⋊Q8C22×C31semidirect
510. #484C22×C31semidirect
513. #481C22×C31semidirect
514. #481C22×C31semidirect
520. #451C22×C31semidirect
523. #448C22×C31semidirect
524. #448C22×C31semidirect
525. #407C22×C31semidirect
526. C2×C22⋊C8C22×C31semidirect
527. #400C22×C31semidirect
528. #399C22×C31semidirect
530. #395C22×C31semidirect
532. #393C22×C31semidirect
535. C4×C22⋊C4C22×C31semidirect
536. #328C22×C31semidirect
537. #328C22×C31semidirect
540. #327C22×C31semidirect
541. #327C22×C31semidirect
542. #327C22×C31semidirect
543. #327C22×C31semidirect
544. #324C22×C31semidirect
545. #324C22×C31semidirect
546. #323C22×C31semidirect
547. #323C22×C31semidirect
690. C31#18415direct (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×#31962
C31×#31872
C31×#26632
C31×#16182
C31×#16162
C31×#16152
C31×#16132
C31×#16062
C31×#16042
C31×#16032
C31×#16012
C31×#15072
C31×#15012
C31×#14682
#1841531