Finite Group Databasebeta

← C31×#18416 #21475175

Subgroups — C31×#18416 #21475175

Order 7936.

978 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3535C211yesmaximal, characteristic, complemented
2C31×#3194C211yesmaximal, characteristic, complemented
3C31×#3187C211yesmaximal, characteristic, complemented
4C31×#2661C211yesmaximal, characteristic, complemented
5C31×#1612C211yesmaximal, characteristic, complemented
6C31×#1611C211yesmaximal, characteristic, complemented
7C31×#1609C211yesmaximal, characteristic, complemented
8C31×#1608C211yesmaximal, characteristic, complemented
9C31×#1600C211yesmaximal, characteristic, complemented
10C31×#1599C211yesmaximal, characteristic, complemented
11C31×#1597C211yesmaximal, characteristic, complemented
12C31×#1596C211yesmaximal, characteristic, complemented
13C31×#1508C211yesmaximal, characteristic, complemented
14C31×#1501C211yesmaximal, characteristic, complemented
15C31×#1468C211yesmaximal, characteristic, complemented
16C31×#563—21no—
17C31×#562—21no—
18C31×#554—21no—
19C31×#552—21no—
20C31×#551—21no—
21C31×#551—21no—
22C31×#547—21no—
23C31×#546—21no—
24C31×#544C2211yescharacteristic
25C31×#543C2211yescharacteristic
26C31×#542—21no—
27C31×#539—21no—
28C31×#539—21no—
29C31×#539C2211yescharacteristic
30C31×#538C2211yescharacteristic
31C31×#536—21no—
32C31×#525C2211yescharacteristic
33C2×C31×#123C2211yescharacteristic
34C2×C31×C22⋊Q8C2211yescharacteristic
35C2×C31×#121C2211yescharacteristic
36C31×#483C2211yescharacteristic
37C31×#483C2211yescharacteristic
38C31×#483C2211yescharacteristic
39C31×#482—21no—
40C31×#481—21no—
41C31×#480C2211yescharacteristic
42C31×#469—21no—
43C31×#468—21no—
44C31×#465—21no—
45C31×#465—21no—
46C31×#450C2211yescharacteristic
47C31×#450C2211yescharacteristic
48C31×#450C2211yescharacteristic
49C31×#449—21no—
50C31×#448—21no—
51C31×#447C2211yescharacteristic
52C31×#407C2211yescharacteristic
53C2×C31×C22⋊C8C2211yescharacteristic
54C31×#398C2211yescharacteristic
55C31×#397C2211yescharacteristic
56C31×#394—21no—
57C31×#394C2211yescharacteristic
58C31×#392—21no—
59C31×#392C2211yescharacteristic
60C31×#390—21no—
61C31×#388—21no—
62C4×C22⋊C4×C31C2211yescharacteristic
63C31×#328C2211yescharacteristic
64C31×#328C2211yescharacteristic
65C31×#328C2211yescharacteristic
66C31×#328C2211yescharacteristic
67C31×#328C2211yescharacteristic
68C31×#328C2211yescharacteristic
69C31×#327C2211yescharacteristic
70C31×#327C2211yescharacteristic
71C31×#324C2211yescharacteristic
72C31×#324C2211yescharacteristic
73C31×#323C2211yescharacteristic
74C31×#323C2211yescharacteristic
75C2×#41×C31—21no—
76C2×#41×C31D411yescharacteristic, complemented
77C22×Q8×C31D411yescharacteristic, complemented
78C22×D4×C31—21no—
79C22×D4×C31—21no—
80C22×D4×C31D411yescharacteristic
81C22×D4×C31C2311yescharacteristic
82C23×C4×C31C2311yescharacteristic
83C2×SD16×C31—21no—
84C2×SD16×C31—21no—
85C2×SD16×C31—21no—
86C2×D8×C31—21no—
87C2×M16×C31—21no—
88C22×C8×C31—21no—
89C31×C4⋊Q8—21no—
90C31×C4⋊Q8—21no—
91C31×C4⋊Q8—21no—
92C31×#126—21no—
93C31×#126—21no—
94C31×#126—21no—
95C31×#126—21no—
96C31×#126—21no—
97C31×#126—21no—
98C31×#125—21no—
99C31×#125—21no—
100C31×#125—21no—
101C31×#125—21no—
102C31×#125—21no—
103C31×#124—21no—
104C31×#124—21no—
105C31×#124—21no—
106C31×#124—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×#123—21no—
118C31×#123—21no—
119C31×#123—21no—
120C31×#123—21no—
121C31×C22⋊Q8—21no—
122C31×C22⋊Q8—21no—
123C31×C22⋊Q8—21no—
124C31×C22⋊Q8—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⋊Q8—21no—
133C31×C22⋊Q8—21no—
134C31×C22⋊Q8—21no—
135C31×C22⋊Q8D411yescharacteristic, complemented
136C31×C22⋊Q8D411yescharacteristic, complemented
137C31×C22⋊Q8D411yescharacteristic, complemented
138C31×C22⋊Q8C2311yescharacteristic
139C31×C22⋊Q8C2311yescharacteristic
140C31×C22⋊Q8C2311yescharacteristic
141C31×#121—21no—
142C31×#121—21no—
143C31×#121—21no—
144C31×#121—21no—
145C31×#121—21no—
146C31×#121—21no—
147C31×#121—21no—
148C31×#121—21no—
149C31×#121D411yescharacteristic, complemented
150C31×#121C2311yescharacteristic
151C31×#120—21no—
152C31×#120—21no—
153C4×Q8×C31—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—
161C31×#117—21no—
162C31×#117—21no—
163C31×#117—21no—
164C31×#117D411yescharacteristic, complemented
165C2×C4⋊C4×C31—21no—
166C2×C4⋊C4×C31—21no—
167C2×C4⋊C4×C31—21no—
168C2×C4⋊C4×C31D411yescharacteristic
169C2×C4⋊C4×C31D411yescharacteristic, complemented
170C2×C4⋊C4×C31C2311yescharacteristic
171C2×C4⋊C4×C31C2311yescharacteristic
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×C31—21no—
179C2×C22⋊C4×C31—21no—
180C2×C22⋊C4×C31D411yescharacteristic
181C2×C22⋊C4×C31D411yescharacteristic
182C2×C22⋊C4×C31C2311yescharacteristic
183C2×C42×C31—21no—
184C31×#107—21no—
185C31×#106—21no—
186C31×#106—21no—
187C31×#106—21no—
188C31×#103—21no—
189C31×#103—21no—
190C31×#103—21no—
191C31×#102—21no—
192C31×#102—21no—
193C31×#102—21no—
194C31×#102—21no—
195C31×#102—21no—
196C31×C22⋊C8—21no—
197C31×C22⋊C8—21no—
198C31×C22⋊C8C2311yescharacteristic
199C31×C22⋊C8C2311yescharacteristic
200C31×C22⋊C8C2311yescharacteristic
201C31×C22⋊C8C2311yescharacteristic
202C31×#95—21no—
203C31×#95—21no—
204C31×#95C2311yescharacteristic
205C31×#95C2311yescharacteristic
206C24×C31—21no—
207C24×C31C2×D411yescharacteristic
208C24×C31C2×D411yescharacteristic
209#41×C31—82no—
210#41×C31—81no—
211C2×Q8×C31—21no—
212C2×Q8×C31—21no—
213C2×Q8×C31—21no—
214C2×Q8×C31—81no—
215C2×Q8×C31C2×D411yescharacteristic
216C2×Q8×C31C2×D411yescharacteristic
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—42no—
228C2×D4×C31—41no—
229C2×D4×C31—41no—
230C2×D4×C31—81no—
231C2×D4×C31—81no—
232C2×D4×C31—81no—
233C2×D4×C31—81no—
234C2×D4×C31—81no—
235C2×D4×C31—81no—
236C2×D4×C31C2×D411yescharacteristic
237C22×C4×C31—21no—
238C22×C4×C31—21no—
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—81no—
248C22×C4×C31C2×D411yescharacteristic
249C22×C4×C31C2×D411yescharacteristic
250C22×C4×C31C2×D411yescharacteristic
251C22×C4×C31C2×D411yescharacteristic
252C22×C4×C31C2×D411yescharacteristic
253C22×C4×C31C2×D411yescharacteristic
254C22×C4×C31C2×D411yescharacteristic
255C22×C4×C31C2×D411yescharacteristic
256C22×C4×C31C2411yescharacteristic
257SD16×C31—81no—
258SD16×C31—81no—
259SD16×C31—81no—
260D8×C31—81no—
261M16×C31—81no—
262C2×C8×C31—21no—
263C2×C8×C31—21no—
264C2×C8×C31—21no—
265C2×C8×C31—21no—
266C2×C8×C31—81no—
267C4⋊C4×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—21no—
288C4⋊C4×C31—21no—
289C4⋊C4×C31—21no—
290C4⋊C4×C31—21no—
291C4⋊C4×C31—21no—
292C4⋊C4×C31—81no—
293C4⋊C4×C31C2×D411yescharacteristic
294C4⋊C4×C31C2×D411yescharacteristic
295C4⋊C4×C31C2×D411yescharacteristic
296C4⋊C4×C31C2×D411yescharacteristic
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—42no—
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—21no—
331C42×C31—21no—
332C42×C31—81no—
333#18416C3111yesmaximal, 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—41no—
341C23×C31—41no—
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#12011yescharacteristic
352C23×C31#12011yescharacteristic
353C23×C31C22×D411yescharacteristic
354Q8×C31—41no—
355Q8×C31—41no—
356Q8×C31—41no—
357Q8×C31—81no—
358Q8×C31—81no—
359Q8×C31—81no—
360D4×C31—41no—
361D4×C31—41no—
362D4×C31—41no—
363D4×C31—41no—
364D4×C31—41no—
365D4×C31—42no—
366D4×C31—42no—
367D4×C31—41no—
368D4×C31—41no—
369D4×C31—81no—
370D4×C31—81no—
371D4×C31—81no—
372D4×C31—81no—
373D4×C31—84no—
374D4×C31—82no—
375D4×C31—82no—
376C2×C4×C31—22no—
377C2×C4×C31—21no—
378C2×C4×C31—21no—
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—42no—
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#12011yescharacteristic
413C2×C4×C31#12011yescharacteristic
414C2×C4×C31C22×D411yescharacteristic
415C2×C4×C31C22×D411yescharacteristic
416C8×C31—41no—
417C8×C31—41no—
418C8×C31—41no—
419C8×C31—41no—
420#3535C2×C3111yescharacteristic, complemented
421#3194C2×C3111yescharacteristic, complemented
422#3187C2×C3111yescharacteristic, complemented
423#2661C2×C3111yescharacteristic, complemented
424#1612C2×C3111yescharacteristic, complemented
425#1611C2×C3111yescharacteristic, complemented
426#1609C2×C3111yescharacteristic, complemented
427#1608C2×C3111yescharacteristic, complemented
428#1600C2×C3111yescharacteristic, complemented
429#1599C2×C3111yescharacteristic, complemented
430#1597C2×C3111yescharacteristic, complemented
431#1596C2×C3111yescharacteristic, complemented
432#1508C2×C3111yescharacteristic, complemented
433#1501C2×C3111yescharacteristic, complemented
434#1468C2×C3111yescharacteristic, complemented
435C22×C31—21no—
436C22×C31—21no—
437C22×C31—21no—
438C22×C31—21no—
439C22×C31—21no—
440C22×C31—21no—
441C22×C31—21no—
442C22×C31—21no—
443C22×C31—41no—
444C22×C31—41no—
445C22×C31—41no—
446C22×C31—41no—
447C22×C31—41no—
448C22×C31—41no—
449C22×C31—81no—
450C22×C31—81no—
451C22×C31—81no—
452C22×C31—81no—
453C22×C31—81no—
454C22×C31—81no—
455C22×C31—81no—
456C22×C31—81no—
457C22×C31—81no—
458C22×C31—81no—
459C22×C31—81no—
460C22×C31C2×#12011yescharacteristic
461C22×C31#57711yescharacteristic
462C22×C31#57711yescharacteristic
463C4×C31—21no—
464C4×C31—21no—
465C4×C31—21no—
466C4×C31—21no—
467C4×C31—42no—
468C4×C31—41no—
469C4×C31—41no—
470C4×C31—41no—
471C4×C31—41no—
472C4×C31—41no—
473C4×C31—41no—
474C4×C31—41no—
475C4×C31—41no—
476C4×C31—41no—
477C4×C31—41no—
478C4×C31—81no—
479C4×C31—81no—
480#563—21no—
481#562—21no—
482#554—21no—
483#552—21no—
484#551—21no—
485#551—21no—
486#547—21no—
487#546—21no—
488#544C22×C3111yescharacteristic
489#543C22×C3111yescharacteristic
490#542—21no—
491#539—21no—
492#539—21no—
493#539C22×C3111yescharacteristic
494#538C22×C3111yescharacteristic
495#536—21no—
496#525C22×C3111yescharacteristic
497C2×#123C22×C3111yescharacteristic
498C2×C22⋊Q8C22×C3111yescharacteristic
499C2×#121C22×C3111yescharacteristic
500#483C22×C3111yescharacteristic
501#483C22×C3111yescharacteristic
502#483C22×C3111yescharacteristic
503#482—21no—
504#481—21no—
505#480C22×C3111yescharacteristic
506#469—21no—
507#468—21no—
508#465—21no—
509#465—21no—
510#450C22×C3111yescharacteristic
511#450C22×C3111yescharacteristic
512#450C22×C3111yescharacteristic
513#449—21no—
514#448—21no—
515#447C22×C3111yescharacteristic
516#407C22×C3111yescharacteristic
517C2×C22⋊C8C22×C3111yescharacteristic
518#398C22×C3111yescharacteristic
519#397C22×C3111yescharacteristic
520#394—21no—
521#394C22×C3111yescharacteristic
522#392—21no—
523#392C22×C3111yescharacteristic
524#390—21no—
525#388—21no—
526C4×C22⋊C4C22×C3111yescharacteristic
527#328C22×C3111yescharacteristic
528#328C22×C3111yescharacteristic
529#328C22×C3111yescharacteristic
530#328C22×C3111yescharacteristic
531#328C22×C3111yescharacteristic
532#328C22×C3111yescharacteristic
533#327C22×C3111yescharacteristic
534#327C22×C3111yescharacteristic
535#324C22×C3111yescharacteristic
536#324C22×C3111yescharacteristic
537#323C22×C3111yescharacteristic
538#323C22×C3111yescharacteristic
539C2×C31—21no—
540C2×C31—21no—
541C2×C31—41no—
542C2×C31—41no—
543C2×C31—81no—
544C2×C31—81no—
545C2×C31—161no—
546C2×C31#301011yescharacteristic
547C2×C31#301811yescharacteristic
548C2×C31#302611yescharacteristic
549C2×#41—21no—
550C2×#41D4×C3111yescharacteristic, complemented
551C22×Q8D4×C3111yescharacteristic, complemented
552C22×D4—21no—
553C22×D4—21no—
554C22×D4D4×C3111yescharacteristic
555C22×D4C23×C3111yescharacteristic
556C23×C4C23×C3111yescharacteristic
557C2×SD16—21no—
558C2×SD16—21no—
559C2×SD16—21no—
560C2×D8—21no—
561C2×M16—21no—
562C22×C8—21no—
563C4⋊Q8—21no—
564C4⋊Q8—21no—
565C4⋊Q8—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#125—21no—
575#125—21no—
576#125—21no—
577#124—21no—
578#124—21no—
579#124—21no—
580#124—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—
592#123—21no—
593#123—21no—
594#123—21no—
595C22⋊Q8—21no—
596C22⋊Q8—21no—
597C22⋊Q8—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⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8D4×C3111yescharacteristic, complemented
610C22⋊Q8D4×C3111yescharacteristic, complemented
611C22⋊Q8D4×C3111yescharacteristic, complemented
612C22⋊Q8C23×C3111yescharacteristic
613C22⋊Q8C23×C3111yescharacteristic
614C22⋊Q8C23×C3111yescharacteristic
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#121D4×C3111yescharacteristic, complemented
624#121C23×C3111yescharacteristic
625#120—21no—
626#120—21no—
627C4×Q8—21no—
628C4×D4—21no—
629C4×D4—21no—
630C4×D4—21no—
631C4×D4—21no—
632C4×D4—21no—
633C4×D4—21no—
634C4×D4—21no—
635#117—21no—
636#117—21no—
637#117—21no—
638#117D4×C3111yescharacteristic, complemented
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4D4×C3111yescharacteristic
643C2×C4⋊C4D4×C3111yescharacteristic, complemented
644C2×C4⋊C4C23×C3111yescharacteristic
645C2×C4⋊C4C23×C3111yescharacteristic
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4D4×C3111yescharacteristic
655C2×C22⋊C4D4×C3111yescharacteristic
656C2×C22⋊C4C23×C3111yescharacteristic
657C2×C42—21no—
658#107—21no—
659#106—21no—
660#106—21no—
661#106—21no—
662#103—21no—
663#103—21no—
664#103—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#95C23×C3111yescharacteristic
679#95C23×C3111yescharacteristic
680C31#1841611yescharacteristic, direct product factor, Sylow
681C24—21no—
682C24C2×D4×C3111yescharacteristic
683C24C2×D4×C3111yescharacteristic
684#41—82no—
685#41—81no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—81no—
690C2×Q8C2×D4×C3111yescharacteristic
691C2×Q8C2×D4×C3111yescharacteristic
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—42no—
703C2×D4—41no—
704C2×D4—41no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4—81no—
710C2×D4—81no—
711C2×D4C2×D4×C3111yescharacteristic
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—81no—
723C22×C4C2×D4×C3111yescharacteristic
724C22×C4C2×D4×C3111yescharacteristic
725C22×C4C2×D4×C3111yescharacteristic
726C22×C4C2×D4×C3111yescharacteristic
727C22×C4C2×D4×C3111yescharacteristic
728C22×C4C2×D4×C3111yescharacteristic
729C22×C4C2×D4×C3111yescharacteristic
730C22×C4C2×D4×C3111yescharacteristic
731C22×C4C24×C3111yescharacteristic
732SD16—81no—
733SD16—81no—
734SD16—81no—
735D8—81no—
736M16—81no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—81no—
742C4⋊C4—21no—
743C4⋊C4—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—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—81no—
768C4⋊C4C2×D4×C3111yescharacteristic
769C4⋊C4C2×D4×C3111yescharacteristic
770C4⋊C4C2×D4×C3111yescharacteristic
771C4⋊C4C2×D4×C3111yescharacteristic
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—21no—
794C22⋊C4—21no—
795C22⋊C4—42no—
796C22⋊C4—42no—
797C22⋊C4—41no—
798C22⋊C4—41no—
799C22⋊C4—81no—
800C22⋊C4—81no—
801C22⋊C4—81no—
802C42—21no—
803C42—21no—
804C42—21no—
805C42—21no—
806C42—21no—
807C42—81no—
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—41no—
823C23—41no—
824C23—41no—
825C23C31×#12011yescharacteristic
826C23C31×#12011yescharacteristic
827C23C22×D4×C3111yescharacteristic
828Q8—41no—
829Q8—41no—
830Q8—41no—
831Q8—81no—
832Q8—81no—
833Q8—81no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—42no—
840D4—42no—
841D4—41no—
842D4—41no—
843D4—81no—
844D4—81no—
845D4—81no—
846D4—81no—
847D4—84no—
848D4—82no—
849D4—82no—
850C2×C4—22no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
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—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—42no—
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—81no—
881C2×C4—81no—
882C2×C4—81no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4C31×#12011yescharacteristic
887C2×C4C31×#12011yescharacteristic
888C2×C4C22×D4×C3111yescharacteristic
889C2×C4C22×D4×C3111yescharacteristic
890C8—41no—
891C8—41no—
892C8—41no—
893C8—41no—
894C22—21no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22C2×C31×#12011yescharacteristic
920C22C31×#57711yescharacteristic
921C22C31×#57711yescharacteristic
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—42no—
927C4—41no—
928C4—41no—
929C4—41no—
930C4—41no—
931C4—41no—
932C4—41no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—81no—
938C4—81no—
939C2—21no—
940C2—21no—
941C2—41no—
942C2—41no—
943C2—81no—
944C2—81no—
945C2—161no—
946C2C31×#301011yescharacteristic
947C2C31×#301811yescharacteristic
948C2C31×#302611yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
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
1. C31×#3535C2semidirect
2. C31×#3194C2semidirect
3. C31×#3187C2semidirect
4. C31×#2661C2semidirect
5. C31×#1612C2semidirect
6. C31×#1611C2semidirect
7. C31×#1609C2semidirect
8. C31×#1608C2semidirect
9. C31×#1600C2semidirect
10. C31×#1599C2semidirect
11. C31×#1597C2semidirect
12. C31×#1596C2semidirect
13. C31×#1508C2semidirect
14. C31×#1501C2semidirect
15. C31×#1468C2semidirect
76. C2×#41×C31D4semidirect
77. C22×Q8×C31D4semidirect
135. C31×C22⋊Q8D4semidirect
136. C31×C22⋊Q8D4semidirect
137. C31×C22⋊Q8D4semidirect
149. C31×#121D4semidirect
164. C31×#117D4semidirect
169. C2×C4⋊C4×C31D4semidirect
333. #18416C31direct (N × H)
420. #3535C2×C31semidirect
421. #3194C2×C31semidirect
422. #3187C2×C31semidirect
423. #2661C2×C31semidirect
424. #1612C2×C31semidirect
425. #1611C2×C31semidirect
426. #1609C2×C31semidirect
427. #1608C2×C31semidirect
428. #1600C2×C31semidirect
429. #1599C2×C31semidirect
430. #1597C2×C31semidirect
431. #1596C2×C31semidirect
432. #1508C2×C31semidirect
433. #1501C2×C31semidirect
434. #1468C2×C31semidirect
550. C2×#41D4×C31semidirect
551. C22×Q8D4×C31semidirect
609. C22⋊Q8D4×C31semidirect
610. C22⋊Q8D4×C31semidirect
611. C22⋊Q8D4×C31semidirect
623. #121D4×C31semidirect
638. #117D4×C31semidirect
643. C2×C4⋊C4D4×C31semidirect
680. C31#18416direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35352
C31×#31942
C31×#31872
C31×#26612
C31×#16122
C31×#16112
C31×#16092
C31×#16082
C31×#16002
C31×#15992
C31×#15972
C31×#15962
C31×#15082
C31×#15012
C31×#14682
#1841631