Finite Group Databasebeta

← C31×#18434 #21475193

Subgroups — C31×#18434 #21475193

Order 7936.

982 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3560C211yesmaximal, characteristic, complemented
2C31×#3213C211yesmaximal, characteristic, complemented
3C31×#3211C211yesmaximal, characteristic, complemented
4C31×#2662C211yesmaximal, characteristic, complemented
5C31×#1606C211yesmaximal, characteristic, complemented
6C31×#1604C211yesmaximal, characteristic, complemented
7C31×#1603C211yesmaximal, characteristic, complemented
8C31×#1601C211yesmaximal, characteristic, complemented
9C31×#1600C211yesmaximal, characteristic, complemented
10C31×#1598C211yesmaximal, characteristic, complemented
11C31×#1597C211yesmaximal, characteristic, complemented
12C31×#1595C211yesmaximal, characteristic, complemented
13C31×#1509C211yesmaximal, characteristic, complemented
14C31×#1502C211yesmaximal, 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×C31×#124C2211yescharacteristic, complemented
36C31×#496—21no—
37C31×#495—21no—
38C31×#489—21no—
39C31×#488—21no—
40C31×#464—21no—
41C31×#463—21no—
42C31×#463—21no—
43C31×#463—21no—
44C31×#451C2211yescharacteristic, complemented
45C31×#450C2211yescharacteristic, complemented
46C31×#448C2211yescharacteristic
47C31×#448C2211yescharacteristic
48C31×#448C2211yescharacteristic, complemented
49C31×#447C2211yescharacteristic
50C31×#447C2211yescharacteristic
51C31×#447C2211yescharacteristic, complemented
52C31×#432C2211yescharacteristic, complemented
53C31×#431C2211yescharacteristic, complemented
54C31×#396—21no—
55C31×#395C2211yescharacteristic, complemented
56C31×#394—21no—
57C31×#394C2211yescharacteristic, complemented
58C31×#393C2211yescharacteristic
59C31×#392C2211yescharacteristic
60C31×#390—21no—
61C31×#388—21no—
62C4×C4⋊C4×C31C2211yescharacteristic, 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×Q8×C31C2311yescharacteristic
78C22×D4×C31—21no—
79C22×D4×C31—21no—
80C22×D4×C31C2311yescharacteristic
81C2×Q16×C31—21no—
82C2×SD16×C31—21no—
83C2×SD16×C31—21no—
84C2×SD16×C31—21no—
85C2×SD16×C31—21no—
86C2×D8×C31—21no—
87C2×D8×C31—21no—
88C2×D8×C31—21no—
89C31×C4⋊Q8—21no—
90C31×C4⋊Q8D411yescharacteristic, complemented
91C31×#127D411yescharacteristic, complemented
92C31×#126—21no—
93C31×#126—21no—
94C31×#126—21no—
95C31×#126—21no—
96C31×#126—21no—
97C31×#126—21no—
98C31×#126—21no—
99C31×#126—21no—
100C31×#126—21no—
101C31×#125—21no—
102C31×#125—21no—
103C31×#125D411yescharacteristic, complemented
104C31×#124—21no—
105C31×#124—21no—
106C31×#124—21no—
107C31×#124—21no—
108C31×#124—21no—
109C31×#124—21no—
110C31×#124—21no—
111C31×#124—21no—
112C31×#124D411yescharacteristic, complemented
113C31×#123—21no—
114C31×#123—21no—
115C31×#123—21no—
116C31×#123—21no—
117C31×#123—21no—
118C31×#123—21no—
119C31×#123—21no—
120C31×#123—21no—
121C31×#123—21no—
122C31×#123—21no—
123C31×#123—21no—
124C31×#123—21no—
125C31×C22⋊Q8—21no—
126C31×C22⋊Q8—21no—
127C31×C22⋊Q8—21no—
128C31×C22⋊Q8—21no—
129C31×C22⋊Q8—21no—
130C31×C22⋊Q8—21no—
131C31×C22⋊Q8—21no—
132C31×C22⋊Q8C2311yescharacteristic
133C31×#121—21no—
134C31×#121—21no—
135C31×#121—21no—
136C31×#121—21no—
137C31×#121—21no—
138C31×#121—21no—
139C31×#121—21no—
140C31×#121—21no—
141C31×#121—21no—
142C31×#121—21no—
143C31×#121—21no—
144C31×#121—21no—
145C31×#121C2311yescharacteristic
146C31×#121C2311yescharacteristic
147C31×#121C2311yescharacteristic
148C31×#120—21no—
149C31×#120—21no—
150C31×#120—21no—
151C31×#120—21no—
152C31×#120—21no—
153C4×Q8×C31D411yescharacteristic, complemented
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—
162C4×D4×C31D411yescharacteristic, complemented
163C4×D4×C31D411yescharacteristic, complemented
164C4×D4×C31D411yescharacteristic, complemented
165C31×#117—21no—
166C31×#117—21no—
167C2×C4⋊C4×C31—21no—
168C2×C4⋊C4×C31—21no—
169C2×C4⋊C4×C31—21no—
170C2×C4⋊C4×C31D411yescharacteristic
171C2×C4⋊C4×C31D411yescharacteristic
172C2×C4⋊C4×C31C2311yescharacteristic
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×C31—21no—
179C2×C22⋊C4×C31—21no—
180C2×C22⋊C4×C31—21no—
181C2×C22⋊C4×C31D411yescharacteristic
182C2×C22⋊C4×C31D411yescharacteristic
183C2×C22⋊C4×C31C2311yescharacteristic
184C2×C42×C31—21no—
185C2×C42×C31C2311yescharacteristic
186C31×C4⋊C8—21no—
187C31×C4⋊C8—21no—
188C31×#103—21no—
189C31×#103—21no—
190C31×#103—21no—
191C31×#103—21no—
192C31×#102—21no—
193C31×#102—21no—
194C31×#102—21no—
195C31×#102—21no—
196C31×C22⋊C8C2311yescharacteristic
197C31×C22⋊C8C2311yescharacteristic
198C31×C22⋊C8C2311yescharacteristic
199C31×C22⋊C8C2311yescharacteristic
200C31×#97—21no—
201C4×C8×C31—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×C31—21no—
216C2×Q8×C31—21no—
217C2×Q8×C31—81no—
218C2×Q8×C31C2×D411yescharacteristic
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—42no—
234C2×D4×C31—81no—
235C2×D4×C31—81no—
236C2×D4×C31—81no—
237C2×D4×C31—81no—
238C2×D4×C31—81no—
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×C31C2×D411yescharacteristic
254C22×C4×C31C2×D411yescharacteristic
255C22×C4×C31C2×D411yescharacteristic
256C22×C4×C31C2×D411yescharacteristic
257C22×C4×C31C2×D411yescharacteristic
258C22×C4×C31C2411yescharacteristic
259Q16×C31—81no—
260SD16×C31—81no—
261SD16×C31—81no—
262SD16×C31—81no—
263SD16×C31—81no—
264D8×C31—81no—
265D8×C31—81no—
266D8×C31—81no—
267C2×C8×C31—21no—
268C2×C8×C31—21no—
269C2×C8×C31—21no—
270C2×C8×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—21no—
288C4⋊C4×C31—42no—
289C4⋊C4×C31—81no—
290C4⋊C4×C31C2×D411yescharacteristic
291C4⋊C4×C31C2×D411yescharacteristic
292C4⋊C4×C31C2×D411yescharacteristic
293C4⋊C4×C31C2×D411yescharacteristic
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—21no—
318C22⋊C4×C31—21no—
319C22⋊C4×C31—42no—
320C22⋊C4×C31—41no—
321C22⋊C4×C31—41no—
322C22⋊C4×C31—41no—
323C22⋊C4×C31—41no—
324C22⋊C4×C31—81no—
325C22⋊C4×C31—81no—
326C22⋊C4×C31—81no—
327C42×C31—21no—
328C42×C31—21no—
329C42×C31—21no—
330C42×C31—81no—
331C42×C31C2×D411yescharacteristic
332C42×C31C2×D411yescharacteristic
333C42×C31C2×D411yescharacteristic
334C42×C31C2×D411yescharacteristic
335#18434C3111yesmaximal, characteristic, direct product factor, Sylow
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—41no—
345C23×C31—41no—
346C23×C31—41no—
347C23×C31—41no—
348C23×C31—41no—
349C23×C31—41no—
350C23×C31—41no—
351C23×C31—81no—
352C23×C31—81no—
353C23×C31—81no—
354C23×C31C22×D411yescharacteristic
355Q8×C31—41no—
356Q8×C31—41no—
357Q8×C31—41no—
358Q8×C31—41no—
359Q8×C31—41no—
360Q8×C31—81no—
361Q8×C31—81no—
362D4×C31—41no—
363D4×C31—41no—
364D4×C31—41no—
365D4×C31—41no—
366D4×C31—41no—
367D4×C31—41no—
368D4×C31—41no—
369D4×C31—41no—
370D4×C31—41no—
371D4×C31—41no—
372D4×C31—41no—
373D4×C31—41no—
374D4×C31—41no—
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—
384D4×C31—84no—
385C2×C4×C31—21no—
386C2×C4×C31—21no—
387C2×C4×C31—22no—
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—21no—
396C2×C4×C31—21no—
397C2×C4×C31—21no—
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—81no—
411C2×C4×C31—81no—
412C2×C4×C31—81no—
413C2×C4×C31—81no—
414C2×C4×C31—81no—
415C2×C4×C31—81no—
416C2×C4×C31—81no—
417C2×C4×C31—81no—
418C2×C4×C31#12011yescharacteristic
419C2×C4×C31#12011yescharacteristic
420C2×C4×C31#12011yescharacteristic
421C2×C4×C31#12011yescharacteristic
422C2×C4×C31C22×D411yescharacteristic
423C2×C4×C31C22×D411yescharacteristic
424C8×C31—41no—
425C8×C31—41no—
426C8×C31—41no—
427C8×C31—41no—
428#3560C2×C3111yescharacteristic, complemented
429#3213C2×C3111yescharacteristic, complemented
430#3211C2×C3111yescharacteristic, complemented
431#2662C2×C3111yescharacteristic, complemented
432#1606C2×C3111yescharacteristic, complemented
433#1604C2×C3111yescharacteristic, complemented
434#1603C2×C3111yescharacteristic, complemented
435#1601C2×C3111yescharacteristic, complemented
436#1600C2×C3111yescharacteristic, complemented
437#1598C2×C3111yescharacteristic, complemented
438#1597C2×C3111yescharacteristic, complemented
439#1595C2×C3111yescharacteristic, complemented
440#1509C2×C3111yescharacteristic, complemented
441#1502C2×C3111yescharacteristic, complemented
442#1473C2×C3111yescharacteristic, complemented
443C22×C31—21no—
444C22×C31—21no—
445C22×C31—41no—
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—81no—
458C22×C31—81no—
459C22×C31—81no—
460C22×C31—81no—
461C22×C31—81no—
462C22×C31—81no—
463C22×C31—81no—
464C22×C31—81no—
465C22×C31—81no—
466C22×C31—162no—
467C22×C31C2×#12011yescharacteristic
468C22×C31#57611yescharacteristic
469C22×C31#57711yescharacteristic
470C4×C31—21no—
471C4×C31—21no—
472C4×C31—21no—
473C4×C31—21no—
474C4×C31—21no—
475C4×C31—21no—
476C4×C31—42no—
477C4×C31—41no—
478C4×C31—41no—
479C4×C31—41no—
480C4×C31—41no—
481C4×C31—41no—
482C4×C31—41no—
483C4×C31—41no—
484C4×C31—41no—
485C4×C31—81no—
486C4×C31—81no—
487#563—21no—
488#560—21no—
489#553—21no—
490#553—21no—
491#551—21no—
492#547—21no—
493#546—21no—
494#546—21no—
495#542—21no—
496#539—21no—
497#539C22×C3111yescharacteristic
498#538—21no—
499#538—21no—
500#538C22×C3111yescharacteristic
501#537C22×C3111yescharacteristic
502#534C22×C3111yescharacteristic
503#532C22×C3111yescharacteristic
504#529C22×C3111yescharacteristic
505C2×#126C22×C3111yescharacteristic
506C2×#124C22×C3111yescharacteristic, complemented
507#496—21no—
508#495—21no—
509#489—21no—
510#488—21no—
511#464—21no—
512#463—21no—
513#463—21no—
514#463—21no—
515#451C22×C3111yescharacteristic, complemented
516#450C22×C3111yescharacteristic, complemented
517#448C22×C3111yescharacteristic
518#448C22×C3111yescharacteristic
519#448C22×C3111yescharacteristic, complemented
520#447C22×C3111yescharacteristic
521#447C22×C3111yescharacteristic
522#447C22×C3111yescharacteristic, complemented
523#432C22×C3111yescharacteristic, complemented
524#431C22×C3111yescharacteristic, complemented
525#396—21no—
526#395C22×C3111yescharacteristic, complemented
527#394—21no—
528#394C22×C3111yescharacteristic, complemented
529#393C22×C3111yescharacteristic
530#392C22×C3111yescharacteristic
531#390—21no—
532#388—21no—
533C4×C4⋊C4C22×C3111yescharacteristic, complemented
534#328C22×C3111yescharacteristic, complemented
535#328C22×C3111yescharacteristic, complemented
536#327C22×C3111yescharacteristic
537#327C22×C3111yescharacteristic
538#327C22×C3111yescharacteristic
539#327C22×C3111yescharacteristic
540#327C22×C3111yescharacteristic, complemented
541#327C22×C3111yescharacteristic, complemented
542#324C22×C3111yescharacteristic, complemented
543#324C22×C3111yescharacteristic, complemented
544#323C22×C3111yescharacteristic
545#323C22×C3111yescharacteristic
546C2×C31—21no—
547C2×C31—21no—
548C2×C31—81no—
549C2×C31—81no—
550C2×C31—81no—
551C2×C31—81no—
552C2×C31—161no—
553C2×C31#301211yescharacteristic
554C2×C31#301811yescharacteristic
555C2×C31#302711yescharacteristic
556C2×#41—21no—
557C2×#41—21no—
558C22×Q8C23×C3111yescharacteristic
559C22×D4—21no—
560C22×D4—21no—
561C22×D4C23×C3111yescharacteristic
562C2×Q16—21no—
563C2×SD16—21no—
564C2×SD16—21no—
565C2×SD16—21no—
566C2×SD16—21no—
567C2×D8—21no—
568C2×D8—21no—
569C2×D8—21no—
570C4⋊Q8—21no—
571C4⋊Q8D4×C3111yescharacteristic, complemented
572#127D4×C3111yescharacteristic, complemented
573#126—21no—
574#126—21no—
575#126—21no—
576#126—21no—
577#126—21no—
578#126—21no—
579#126—21no—
580#126—21no—
581#126—21no—
582#125—21no—
583#125—21no—
584#125D4×C3111yescharacteristic, complemented
585#124—21no—
586#124—21no—
587#124—21no—
588#124—21no—
589#124—21no—
590#124—21no—
591#124—21no—
592#124—21no—
593#124D4×C3111yescharacteristic, complemented
594#123—21no—
595#123—21no—
596#123—21no—
597#123—21no—
598#123—21no—
599#123—21no—
600#123—21no—
601#123—21no—
602#123—21no—
603#123—21no—
604#123—21no—
605#123—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
611C22⋊Q8—21no—
612C22⋊Q8—21no—
613C22⋊Q8C23×C3111yescharacteristic
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#121—21no—
625#121—21no—
626#121C23×C3111yescharacteristic
627#121C23×C3111yescharacteristic
628#121C23×C3111yescharacteristic
629#120—21no—
630#120—21no—
631#120—21no—
632#120—21no—
633#120—21no—
634C4×Q8D4×C3111yescharacteristic, complemented
635C4×D4—21no—
636C4×D4—21no—
637C4×D4—21no—
638C4×D4—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643C4×D4D4×C3111yescharacteristic, complemented
644C4×D4D4×C3111yescharacteristic, complemented
645C4×D4D4×C3111yescharacteristic, complemented
646#117—21no—
647#117—21no—
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×C22⋊C4—21no—
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—
666C2×C42C23×C3111yescharacteristic
667C4⋊C8—21no—
668C4⋊C8—21no—
669#103—21no—
670#103—21no—
671#103—21no—
672#103—21no—
673#102—21no—
674#102—21no—
675#102—21no—
676#102—21no—
677C22⋊C8C23×C3111yescharacteristic
678C22⋊C8C23×C3111yescharacteristic
679C22⋊C8C23×C3111yescharacteristic
680C22⋊C8C23×C3111yescharacteristic
681#97—21no—
682C4×C8—21no—
683#95—21no—
684#95—21no—
685#95C23×C3111yescharacteristic
686#95C23×C3111yescharacteristic
687C31#1843411yescharacteristic, direct product factor, Sylow
688C24—21no—
689C24—21no—
690C24C2×D4×C3111yescharacteristic
691#41—81no—
692#41—81no—
693#41—81no—
694#41—81no—
695C2×Q8—21no—
696C2×Q8—21no—
697C2×Q8—21no—
698C2×Q8—21no—
699C2×Q8—81no—
700C2×Q8C2×D4×C3111yescharacteristic
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—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—42no—
716C2×D4—81no—
717C2×D4—81no—
718C2×D4—81no—
719C2×D4—81no—
720C2×D4—81no—
721C2×D4C2×D4×C3111yescharacteristic
722C2×D4C2×D4×C3111yescharacteristic
723C2×D4C2×D4×C3111yescharacteristic
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×C4C2×D4×C3111yescharacteristic
736C22×C4C2×D4×C3111yescharacteristic
737C22×C4C2×D4×C3111yescharacteristic
738C22×C4C2×D4×C3111yescharacteristic
739C22×C4C2×D4×C3111yescharacteristic
740C22×C4C24×C3111yescharacteristic
741Q16—81no—
742SD16—81no—
743SD16—81no—
744SD16—81no—
745SD16—81no—
746D8—81no—
747D8—81no—
748D8—81no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—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—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—42no—
771C4⋊C4—81no—
772C4⋊C4C2×D4×C3111yescharacteristic
773C4⋊C4C2×D4×C3111yescharacteristic
774C4⋊C4C2×D4×C3111yescharacteristic
775C4⋊C4C2×D4×C3111yescharacteristic
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—21no—
799C22⋊C4—21no—
800C22⋊C4—21no—
801C22⋊C4—42no—
802C22⋊C4—41no—
803C22⋊C4—41no—
804C22⋊C4—41no—
805C22⋊C4—41no—
806C22⋊C4—81no—
807C22⋊C4—81no—
808C22⋊C4—81no—
809C42—21no—
810C42—21no—
811C42—21no—
812C42—81no—
813C42C2×D4×C3111yescharacteristic
814C42C2×D4×C3111yescharacteristic
815C42C2×D4×C3111yescharacteristic
816C42C2×D4×C3111yescharacteristic
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23C22×D4×C3111yescharacteristic
836Q8—41no—
837Q8—41no—
838Q8—41no—
839Q8—41no—
840Q8—41no—
841Q8—81no—
842Q8—81no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—41no—
849D4—41no—
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—84no—
866C2×C4—21no—
867C2×C4—21no—
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—81no—
892C2×C4—81no—
893C2×C4—81no—
894C2×C4—81no—
895C2×C4—81no—
896C2×C4—81no—
897C2×C4—81no—
898C2×C4—81no—
899C2×C4C31×#12011yescharacteristic
900C2×C4C31×#12011yescharacteristic
901C2×C4C31×#12011yescharacteristic
902C2×C4C31×#12011yescharacteristic
903C2×C4C22×D4×C3111yescharacteristic
904C2×C4C22×D4×C3111yescharacteristic
905C8—41no—
906C8—41no—
907C8—41no—
908C8—41no—
909C22—21no—
910C22—21no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—162no—
933C22C2×C31×#12011yescharacteristic
934C22C31×#57611yescharacteristic
935C22C31×#57711yescharacteristic
936C4—21no—
937C4—21no—
938C4—21no—
939C4—21no—
940C4—21no—
941C4—21no—
942C4—42no—
943C4—41no—
944C4—41no—
945C4—41no—
946C4—41no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—81no—
952C4—81no—
953C2—21no—
954C2—21no—
955C2—81no—
956C2—81no—
957C2—81no—
958C2—81no—
959C2—161no—
960C2C31×#301211yescharacteristic
961C2C31×#301811yescharacteristic
962C2C31×#302711yescharacteristic
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×#3213C2semidirect
3. C31×#3211C2semidirect
4. C31×#2662C2semidirect
5. C31×#1606C2semidirect
6. C31×#1604C2semidirect
7. C31×#1603C2semidirect
8. C31×#1601C2semidirect
9. C31×#1600C2semidirect
10. C31×#1598C2semidirect
11. C31×#1597C2semidirect
12. C31×#1595C2semidirect
13. C31×#1509C2semidirect
14. C31×#1502C2semidirect
15. C31×#1473C2semidirect
35. C2×C31×#124C22semidirect
44. C31×#451C22semidirect
45. C31×#450C22semidirect
48. C31×#448C22semidirect
51. C31×#447C22semidirect
52. C31×#432C22semidirect
53. C31×#431C22semidirect
55. C31×#395C22semidirect
57. C31×#394C22semidirect
62. C4×C4⋊C4×C31C22semidirect
63. C31×#328C22semidirect
64. C31×#328C22semidirect
69. C31×#327C22semidirect
70. C31×#327C22semidirect
71. C31×#324C22semidirect
72. C31×#324C22semidirect
90. C31×C4⋊Q8D4semidirect
91. C31×#127D4semidirect
103. C31×#125D4semidirect
112. C31×#124D4semidirect
153. C4×Q8×C31D4semidirect
162. C4×D4×C31D4semidirect
163. C4×D4×C31D4semidirect
164. C4×D4×C31D4semidirect
335. #18434C31direct (N × H)
428. #3560C2×C31semidirect
429. #3213C2×C31semidirect
430. #3211C2×C31semidirect
431. #2662C2×C31semidirect
432. #1606C2×C31semidirect
433. #1604C2×C31semidirect
434. #1603C2×C31semidirect
435. #1601C2×C31semidirect
436. #1600C2×C31semidirect
437. #1598C2×C31semidirect
438. #1597C2×C31semidirect
439. #1595C2×C31semidirect
440. #1509C2×C31semidirect
441. #1502C2×C31semidirect
442. #1473C2×C31semidirect
506. C2×#124C22×C31semidirect
515. #451C22×C31semidirect
516. #450C22×C31semidirect
519. #448C22×C31semidirect
522. #447C22×C31semidirect
523. #432C22×C31semidirect
524. #431C22×C31semidirect
526. #395C22×C31semidirect
528. #394C22×C31semidirect
533. C4×C4⋊C4C22×C31semidirect
534. #328C22×C31semidirect
535. #328C22×C31semidirect
540. #327C22×C31semidirect
541. #327C22×C31semidirect
542. #324C22×C31semidirect
543. #324C22×C31semidirect
571. C4⋊Q8D4×C31semidirect
572. #127D4×C31semidirect
584. #125D4×C31semidirect
593. #124D4×C31semidirect
634. C4×Q8D4×C31semidirect
643. C4×D4D4×C31semidirect
644. C4×D4D4×C31semidirect
645. C4×D4D4×C31semidirect
687. C31#18434direct (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×#32132
C31×#32112
C31×#26622
C31×#16062
C31×#16042
C31×#16032
C31×#16012
C31×#16002
C31×#15982
C31×#15972
C31×#15952
C31×#15092
C31×#15022
C31×#14732
#1843431