Finite Group Databasebeta

← C31×#18253 #21475012

Subgroups — C31×#18253 #21475012

Order 7936.

1196 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3535C211yesmaximal, characteristic, complemented
2C31×#3007C211yesmaximal, characteristic, complemented
3C31×#3002C211yesmaximal, characteristic, complemented
4C31×#2430C211yesmaximal, characteristic, complemented
5C31×#1606C211yesmaximal, characteristic, complemented
6C31×#1605C211yesmaximal, characteristic, complemented
7C31×#1603C211yesmaximal, characteristic, complemented
8C31×#1602C211yesmaximal, characteristic, complemented
9C31×#1600C211yesmaximal, characteristic, complemented
10C31×#1599C211yesmaximal, characteristic, complemented
11C31×#1597C211yesmaximal, characteristic, complemented
12C31×#1596C211yesmaximal, characteristic, complemented
13C31×#1504C211yesmaximal, characteristic, complemented
14C2×C31×#328C211yesmaximal, characteristic, complemented
15C31×#1468C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C2×C31×#137—21no—
18C2×C31×#135—21no—
19C31×#563—21no—
20C31×#562—21no—
21C31×#554—21no—
22C31×#552—21no—
23C31×#551—21no—
24C31×#551—21no—
25C31×#547—21no—
26C31×#546—21no—
27C31×#544C2211yescharacteristic
28C31×#543C2211yescharacteristic
29C31×#542—21no—
30C31×#539—21no—
31C31×#539—21no—
32C31×#539C2211yescharacteristic
33C31×#538C2211yescharacteristic
34C31×#536—21no—
35C31×#525C2211yescharacteristic
36C2×C31×#123C2211yescharacteristic
37C2×C31×C22⋊Q8C2211yescharacteristic
38C2×C31×#121—21no—
39C31×#452—21no—
40C31×#452—21no—
41C31×#452—21no—
42C31×#451C2211yescharacteristic
43C31×#451C2211yescharacteristic
44C31×#451C2211yescharacteristic
45C31×#450C2211yescharacteristic
46C31×#450C2211yescharacteristic
47C31×#450C2211yescharacteristic
48C31×#449—21no—
49C31×#448C2211yescharacteristic
50C31×#447C2211yescharacteristic
51C31×#417—21no—
52C31×#416—21no—
53C31×#407C2211yescharacteristic
54C2×C31×C22⋊C8C2211yescharacteristic
55C31×#395C2211yescharacteristic
56C31×#394C2211yescharacteristic
57C31×#393C2211yescharacteristic
58C31×#392C2211yescharacteristic
59C31×#386—21no—
60C31×#386—21no—
61C31×#385—21no—
62C2×C31×#95C2211yescharacteristic
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×C31—21no—
77C2×#41×C31—21no—
78C2×#41×C31—21no—
79C2×#41×C31—21no—
80C2×#41×C31—44no—
81C2×#41×C31D411yescharacteristic, complemented
82C22×Q8×C31D411yescharacteristic, complemented
83C22×Q8×C31C2311yescharacteristic
84C22×D4×C31—21no—
85C22×D4×C31—21no—
86C22×D4×C31D411yescharacteristic
87C22×D4×C31C2311yescharacteristic
88C23×C4×C31—21no—
89C23×C4×C31—21no—
90C23×C4×C31C2311yescharacteristic
91C31×#137—44no—
92C31×#135—44no—
93C2×Q16×C31—21no—
94C2×Q16×C31—21no—
95C2×Q16×C31—21no—
96C2×SD16×C31—21no—
97C2×SD16×C31—21no—
98C2×SD16×C31—21no—
99C2×SD16×C31—21no—
100C2×D8×C31—21no—
101C2×M16×C31—21no—
102C22×C8×C31—21no—
103C31×C4⋊Q8—21no—
104C31×C4⋊Q8—21no—
105C31×C4⋊Q8—21no—
106C31×#126—21no—
107C31×#126—21no—
108C31×#126—21no—
109C31×#126—21no—
110C31×#126—21no—
111C31×#126—21no—
112C31×#125—21no—
113C31×#125—21no—
114C31×#125—21no—
115C31×#125—21no—
116C31×#125—21no—
117C31×#124—21no—
118C31×#124—21no—
119C31×#124—21no—
120C31×#124—21no—
121C31×#123—21no—
122C31×#123—21no—
123C31×#123—21no—
124C31×#123—21no—
125C31×#123—21no—
126C31×#123—21no—
127C31×#123—21no—
128C31×#123—21no—
129C31×#123—21no—
130C31×#123—21no—
131C31×#123—21no—
132C31×#123—21no—
133C31×#123—21no—
134C31×#123—21no—
135C31×C22⋊Q8—21no—
136C31×C22⋊Q8—21no—
137C31×C22⋊Q8—21no—
138C31×C22⋊Q8—21no—
139C31×C22⋊Q8—21no—
140C31×C22⋊Q8—21no—
141C31×C22⋊Q8—21no—
142C31×C22⋊Q8—21no—
143C31×C22⋊Q8—21no—
144C31×C22⋊Q8—21no—
145C31×C22⋊Q8—21no—
146C31×C22⋊Q8—21no—
147C31×C22⋊Q8—21no—
148C31×C22⋊Q8—21no—
149C31×C22⋊Q8D411yescharacteristic, complemented
150C31×C22⋊Q8D411yescharacteristic, complemented
151C31×C22⋊Q8D411yescharacteristic, complemented
152C31×C22⋊Q8C2311yescharacteristic
153C31×C22⋊Q8C2311yescharacteristic
154C31×C22⋊Q8C2311yescharacteristic
155C31×#121—21no—
156C31×#121—21no—
157C31×#121—21no—
158C31×#121—21no—
159C31×#121—44no—
160C31×#121D411yescharacteristic, complemented
161C31×#121C2311yescharacteristic
162C31×#120—21no—
163C31×#120—21no—
164C4×Q8×C31—21no—
165C4×D4×C31—21no—
166C4×D4×C31—21no—
167C4×D4×C31—21no—
168C4×D4×C31—21no—
169C4×D4×C31—21no—
170C4×D4×C31—21no—
171C4×D4×C31—21no—
172C31×#117—21no—
173C31×#117—21no—
174C31×#117—21no—
175C31×#117D411yescharacteristic, complemented
176C2×C4⋊C4×C31—21no—
177C2×C4⋊C4×C31—21no—
178C2×C4⋊C4×C31—21no—
179C2×C4⋊C4×C31D411yescharacteristic
180C2×C4⋊C4×C31D411yescharacteristic, complemented
181C2×C4⋊C4×C31C2311yescharacteristic
182C2×C22⋊C4×C31—21no—
183C2×C22⋊C4×C31—21no—
184C2×C22⋊C4×C31—21no—
185C2×C22⋊C4×C31—21no—
186C2×C22⋊C4×C31—21no—
187C2×C22⋊C4×C31—21no—
188C2×C22⋊C4×C31D411yescharacteristic
189C2×C22⋊C4×C31D411yescharacteristic
190C2×C22⋊C4×C31C2311yescharacteristic
191C31×#103—21no—
192C31×#103—21no—
193C31×#103—21no—
194C31×#103—21no—
195C31×#102—21no—
196C31×#102—21no—
197C31×#102—21no—
198C31×#102—21no—
199C31×C22⋊C8—21no—
200C31×C22⋊C8—21no—
201C31×C22⋊C8C2311yescharacteristic
202C31×C22⋊C8C2311yescharacteristic
203C31×C22⋊C8C2311yescharacteristic
204C31×C22⋊C8C2311yescharacteristic
205C31×#95—21no—
206C31×#95—21no—
207C31×#95—21no—
208C31×#95C2311yescharacteristic
209C31×#95C2311yescharacteristic
210C24×C31—21no—
211C24×C31C2×D411yescharacteristic
212C24×C31C2×D411yescharacteristic
213#41×C31—24no—
214#41×C31—24no—
215#41×C31—42no—
216#41×C31—42no—
217#41×C31—42no—
218#41×C31—42no—
219#41×C31—42no—
220#41×C31—42no—
221#41×C31—42no—
222#41×C31—82no—
223C2×Q8×C31—21no—
224C2×Q8×C31—21no—
225C2×Q8×C31—21no—
226C2×Q8×C31—21no—
227C2×Q8×C31—21no—
228C2×Q8×C31—42no—
229C2×Q8×C31—42no—
230C2×Q8×C31C2×D411yescharacteristic
231C2×Q8×C31C2×D411yescharacteristic
232C2×Q8×C31C2×D411yescharacteristic
233C2×D4×C31—24no—
234C2×D4×C31—21no—
235C2×D4×C31—21no—
236C2×D4×C31—21no—
237C2×D4×C31—21no—
238C2×D4×C31—21no—
239C2×D4×C31—21no—
240C2×D4×C31—21no—
241C2×D4×C31—21no—
242C2×D4×C31—21no—
243C2×D4×C31—42no—
244C2×D4×C31—42no—
245C2×D4×C31—42no—
246C2×D4×C31—41no—
247C2×D4×C31—41no—
248C2×D4×C31—42no—
249C2×D4×C31—42no—
250C2×D4×C31—81no—
251C2×D4×C31C2×D411yescharacteristic
252C22×C4×C31—21no—
253C22×C4×C31—21no—
254C22×C4×C31—21no—
255C22×C4×C31—21no—
256C22×C4×C31—21no—
257C22×C4×C31—21no—
258C22×C4×C31—21no—
259C22×C4×C31—21no—
260C22×C4×C31—21no—
261C22×C4×C31—21no—
262C22×C4×C31—42no—
263C22×C4×C31—42no—
264C22×C4×C31—42no—
265C22×C4×C31—42no—
266C22×C4×C31—41no—
267C22×C4×C31—41no—
268C22×C4×C31—42no—
269C22×C4×C31—81no—
270C22×C4×C31C2×D411yescharacteristic
271C22×C4×C31C2×D411yescharacteristic
272C22×C4×C31C2×D411yescharacteristic
273C22×C4×C31C2×D411yescharacteristic
274C22×C4×C31C2×D411yescharacteristic
275C22×C4×C31C2×D411yescharacteristic
276C22×C4×C31C2×D411yescharacteristic
277C22×C4×C31C2×D411yescharacteristic
278C22×C4×C31C2411yescharacteristic
279Q16×C31—42no—
280Q16×C31—42no—
281Q16×C31—42no—
282SD16×C31—42no—
283SD16×C31—42no—
284SD16×C31—42no—
285SD16×C31—42no—
286D8×C31—42no—
287M16×C31—42no—
288C2×C8×C31—21no—
289C2×C8×C31—21no—
290C2×C8×C31—21no—
291C2×C8×C31—21no—
292C2×C8×C31—42no—
293C4⋊C4×C31—21no—
294C4⋊C4×C31—21no—
295C4⋊C4×C31—21no—
296C4⋊C4×C31—21no—
297C4⋊C4×C31—21no—
298C4⋊C4×C31—21no—
299C4⋊C4×C31—21no—
300C4⋊C4×C31—21no—
301C4⋊C4×C31—21no—
302C4⋊C4×C31—21no—
303C4⋊C4×C31—21no—
304C4⋊C4×C31—21no—
305C4⋊C4×C31—21no—
306C4⋊C4×C31—21no—
307C4⋊C4×C31—21no—
308C4⋊C4×C31—21no—
309C4⋊C4×C31—21no—
310C4⋊C4×C31—21no—
311C4⋊C4×C31—21no—
312C4⋊C4×C31—21no—
313C4⋊C4×C31—21no—
314C4⋊C4×C31—21no—
315C4⋊C4×C31—21no—
316C4⋊C4×C31—42no—
317C4⋊C4×C31C2×D411yescharacteristic
318C4⋊C4×C31C2×D411yescharacteristic
319C4⋊C4×C31C2×D411yescharacteristic
320C4⋊C4×C31C2×D411yescharacteristic
321C22⋊C4×C31—21no—
322C22⋊C4×C31—21no—
323C22⋊C4×C31—21no—
324C22⋊C4×C31—21no—
325C22⋊C4×C31—21no—
326C22⋊C4×C31—21no—
327C22⋊C4×C31—21no—
328C22⋊C4×C31—21no—
329C22⋊C4×C31—21no—
330C22⋊C4×C31—21no—
331C22⋊C4×C31—21no—
332C22⋊C4×C31—21no—
333C22⋊C4×C31—21no—
334C22⋊C4×C31—21no—
335C22⋊C4×C31—21no—
336C22⋊C4×C31—21no—
337C22⋊C4×C31—21no—
338C22⋊C4×C31—21no—
339C22⋊C4×C31—21no—
340C22⋊C4×C31—21no—
341C22⋊C4×C31—21no—
342C22⋊C4×C31—21no—
343C22⋊C4×C31—21no—
344C22⋊C4×C31—42no—
345C22⋊C4×C31—42no—
346C22⋊C4×C31—42no—
347C22⋊C4×C31—81no—
348C42×C31—21no—
349C42×C31—21no—
350C42×C31—21no—
351C42×C31—21no—
352C42×C31—21no—
353#18253C3111yesmaximal, characteristic, direct product factor, Sylow
354C23×C31—21no—
355C23×C31—21no—
356C23×C31—22no—
357C23×C31—22no—
358C23×C31—21no—
359C23×C31—21no—
360C23×C31—21no—
361C23×C31—21no—
362C23×C31—41no—
363C23×C31—41no—
364C23×C31—41no—
365C23×C31—41no—
366C23×C31—41no—
367C23×C31—41no—
368C23×C31—41no—
369C23×C31—41no—
370C23×C31—41no—
371C23×C31#12011yescharacteristic
372C23×C31#12011yescharacteristic
373C23×C31C22×D411yescharacteristic
374Q8×C31—22no—
375Q8×C31—22no—
376Q8×C31—41no—
377Q8×C31—41no—
378Q8×C31—41no—
379Q8×C31—41no—
380Q8×C31—41no—
381Q8×C31—81no—
382Q8×C31—81no—
383Q8×C31—81no—
384D4×C31—22no—
385D4×C31—22no—
386D4×C31—41no—
387D4×C31—41no—
388D4×C31—41no—
389D4×C31—44no—
390D4×C31—41no—
391D4×C31—41no—
392D4×C31—44no—
393D4×C31—42no—
394D4×C31—42no—
395D4×C31—81no—
396D4×C31—81no—
397D4×C31—81no—
398D4×C31—81no—
399D4×C31—84no—
400C2×C4×C31—22no—
401C2×C4×C31—22no—
402C2×C4×C31—22no—
403C2×C4×C31—22no—
404C2×C4×C31—21no—
405C2×C4×C31—21no—
406C2×C4×C31—21no—
407C2×C4×C31—21no—
408C2×C4×C31—21no—
409C2×C4×C31—21no—
410C2×C4×C31—21no—
411C2×C4×C31—21no—
412C2×C4×C31—21no—
413C2×C4×C31—21no—
414C2×C4×C31—21no—
415C2×C4×C31—21no—
416C2×C4×C31—41no—
417C2×C4×C31—41no—
418C2×C4×C31—41no—
419C2×C4×C31—41no—
420C2×C4×C31—44no—
421C2×C4×C31—44no—
422C2×C4×C31—41no—
423C2×C4×C31—41no—
424C2×C4×C31—41no—
425C2×C4×C31—41no—
426C2×C4×C31—42no—
427C2×C4×C31—41no—
428C2×C4×C31—41no—
429C2×C4×C31—41no—
430C2×C4×C31—41no—
431C2×C4×C31—41no—
432C2×C4×C31—81no—
433C2×C4×C31—81no—
434C2×C4×C31—81no—
435C2×C4×C31—81no—
436C2×C4×C31—81no—
437C2×C4×C31—81no—
438C2×C4×C31—84no—
439C2×C4×C31#12011yescharacteristic
440C2×C4×C31#12011yescharacteristic
441C2×C4×C31C22×D411yescharacteristic
442C2×C4×C31C22×D411yescharacteristic
443C8×C31—41no—
444C8×C31—41no—
445C8×C31—41no—
446C8×C31—41no—
447#3535C2×C3111yescharacteristic, complemented
448#3007C2×C3111yescharacteristic, complemented
449#3002C2×C3111yescharacteristic, complemented
450#2430C2×C3111yescharacteristic, complemented
451#1606C2×C3111yescharacteristic, complemented
452#1605C2×C3111yescharacteristic, complemented
453#1603C2×C3111yescharacteristic, complemented
454#1602C2×C3111yescharacteristic, complemented
455#1600C2×C3111yescharacteristic, complemented
456#1599C2×C3111yescharacteristic, complemented
457#1597C2×C3111yescharacteristic, complemented
458#1596C2×C3111yescharacteristic, complemented
459#1504C2×C3111yescharacteristic, complemented
460C2×#328C2×C3111yescharacteristic, complemented
461#1468C2×C3111yescharacteristic, complemented
462C22×C31—21no—
463C22×C31—21no—
464C22×C31—21no—
465C22×C31—21no—
466C22×C31—21no—
467C22×C31—21no—
468C22×C31—21no—
469C22×C31—42no—
470C22×C31—42no—
471C22×C31—42no—
472C22×C31—42no—
473C22×C31—41no—
474C22×C31—41no—
475C22×C31—41no—
476C22×C31—41no—
477C22×C31—42no—
478C22×C31—41no—
479C22×C31—41no—
480C22×C31—81no—
481C22×C31—81no—
482C22×C31—81no—
483C22×C31—81no—
484C22×C31—81no—
485C22×C31—81no—
486C22×C31B(4,𝔽2)12yes—
487C22×C31C2×#12011yescharacteristic
488C22×C31#57711yescharacteristic
489C22×C31#57811yescharacteristic
490C4×C31—21no—
491C4×C31—21no—
492C4×C31—21no—
493C4×C31—21no—
494C4×C31—42no—
495C4×C31—41no—
496C4×C31—41no—
497C4×C31—41no—
498C4×C31—41no—
499C4×C31—41no—
500C4×C31—41no—
501C4×C31—42no—
502C4×C31—41no—
503C4×C31—41no—
504C4×C31—41no—
505C4×C31—41no—
506C4×C31—81no—
507C22×#41C22×C3111yescharacteristic
508C2×#137—21no—
509C2×#135—21no—
510#563—21no—
511#562—21no—
512#554—21no—
513#552—21no—
514#551—21no—
515#551—21no—
516#547—21no—
517#546—21no—
518#544C22×C3111yescharacteristic
519#543C22×C3111yescharacteristic
520#542—21no—
521#539—21no—
522#539—21no—
523#539C22×C3111yescharacteristic
524#538C22×C3111yescharacteristic
525#536—21no—
526#525C22×C3111yescharacteristic
527C2×#123C22×C3111yescharacteristic
528C2×C22⋊Q8C22×C3111yescharacteristic
529C2×#121—21no—
530#452—21no—
531#452—21no—
532#452—21no—
533#451C22×C3111yescharacteristic
534#451C22×C3111yescharacteristic
535#451C22×C3111yescharacteristic
536#450C22×C3111yescharacteristic
537#450C22×C3111yescharacteristic
538#450C22×C3111yescharacteristic
539#449—21no—
540#448C22×C3111yescharacteristic
541#447C22×C3111yescharacteristic
542#417—21no—
543#416—21no—
544#407C22×C3111yescharacteristic
545C2×C22⋊C8C22×C3111yescharacteristic
546#395C22×C3111yescharacteristic
547#394C22×C3111yescharacteristic
548#393C22×C3111yescharacteristic
549#392C22×C3111yescharacteristic
550#386—21no—
551#386—21no—
552#385—21no—
553C2×#95C22×C3111yescharacteristic
554#328C22×C3111yescharacteristic
555#328C22×C3111yescharacteristic
556#328C22×C3111yescharacteristic
557#328C22×C3111yescharacteristic
558#328C22×C3111yescharacteristic
559#328C22×C3111yescharacteristic
560#327C22×C3111yescharacteristic
561#327C22×C3111yescharacteristic
562#324C22×C3111yescharacteristic
563#324C22×C3111yescharacteristic
564#323C22×C3111yescharacteristic
565#323C22×C3111yescharacteristic
566C2×C31—21no—
567C2×C31—21no—
568C2×C31—22no—
569C2×C31—41no—
570C2×C31—81no—
571C2×C31—81no—
572C2×C31—82no—
573C2×C31#301311yescharacteristic
574C2×C31#301811yescharacteristic
575C2×C31C2×B(4,𝔽2)11yescharacteristic
576C2×#41—21no—
577C2×#41—21no—
578C2×#41—21no—
579C2×#41—21no—
580C2×#41—21no—
581C2×#41—44no—
582C2×#41D4×C3111yescharacteristic, complemented
583C22×Q8D4×C3111yescharacteristic, complemented
584C22×Q8C23×C3111yescharacteristic
585C22×D4—21no—
586C22×D4—21no—
587C22×D4D4×C3111yescharacteristic
588C22×D4C23×C3111yescharacteristic
589C23×C4—21no—
590C23×C4—21no—
591C23×C4C23×C3111yescharacteristic
592#137—44no—
593#135—44no—
594C2×Q16—21no—
595C2×Q16—21no—
596C2×Q16—21no—
597C2×SD16—21no—
598C2×SD16—21no—
599C2×SD16—21no—
600C2×SD16—21no—
601C2×D8—21no—
602C2×M16—21no—
603C22×C8—21no—
604C4⋊Q8—21no—
605C4⋊Q8—21no—
606C4⋊Q8—21no—
607#126—21no—
608#126—21no—
609#126—21no—
610#126—21no—
611#126—21no—
612#126—21no—
613#125—21no—
614#125—21no—
615#125—21no—
616#125—21no—
617#125—21no—
618#124—21no—
619#124—21no—
620#124—21no—
621#124—21no—
622#123—21no—
623#123—21no—
624#123—21no—
625#123—21no—
626#123—21no—
627#123—21no—
628#123—21no—
629#123—21no—
630#123—21no—
631#123—21no—
632#123—21no—
633#123—21no—
634#123—21no—
635#123—21no—
636C22⋊Q8—21no—
637C22⋊Q8—21no—
638C22⋊Q8—21no—
639C22⋊Q8—21no—
640C22⋊Q8—21no—
641C22⋊Q8—21no—
642C22⋊Q8—21no—
643C22⋊Q8—21no—
644C22⋊Q8—21no—
645C22⋊Q8—21no—
646C22⋊Q8—21no—
647C22⋊Q8—21no—
648C22⋊Q8—21no—
649C22⋊Q8—21no—
650C22⋊Q8D4×C3111yescharacteristic, complemented
651C22⋊Q8D4×C3111yescharacteristic, complemented
652C22⋊Q8D4×C3111yescharacteristic, complemented
653C22⋊Q8C23×C3111yescharacteristic
654C22⋊Q8C23×C3111yescharacteristic
655C22⋊Q8C23×C3111yescharacteristic
656#121—21no—
657#121—21no—
658#121—21no—
659#121—21no—
660#121—44no—
661#121D4×C3111yescharacteristic, complemented
662#121C23×C3111yescharacteristic
663#120—21no—
664#120—21no—
665C4×Q8—21no—
666C4×D4—21no—
667C4×D4—21no—
668C4×D4—21no—
669C4×D4—21no—
670C4×D4—21no—
671C4×D4—21no—
672C4×D4—21no—
673#117—21no—
674#117—21no—
675#117—21no—
676#117D4×C3111yescharacteristic, complemented
677C2×C4⋊C4—21no—
678C2×C4⋊C4—21no—
679C2×C4⋊C4—21no—
680C2×C4⋊C4D4×C3111yescharacteristic
681C2×C4⋊C4D4×C3111yescharacteristic, complemented
682C2×C4⋊C4C23×C3111yescharacteristic
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4D4×C3111yescharacteristic
690C2×C22⋊C4D4×C3111yescharacteristic
691C2×C22⋊C4C23×C3111yescharacteristic
692#103—21no—
693#103—21no—
694#103—21no—
695#103—21no—
696#102—21no—
697#102—21no—
698#102—21no—
699#102—21no—
700C22⋊C8—21no—
701C22⋊C8—21no—
702C22⋊C8C23×C3111yescharacteristic
703C22⋊C8C23×C3111yescharacteristic
704C22⋊C8C23×C3111yescharacteristic
705C22⋊C8C23×C3111yescharacteristic
706#95—21no—
707#95—21no—
708#95—21no—
709#95C23×C3111yescharacteristic
710#95C23×C3111yescharacteristic
711C31#1825311yescharacteristic, direct product factor, Sylow
712C24—21no—
713C24C2×D4×C3111yescharacteristic
714C24C2×D4×C3111yescharacteristic
715#41—24no—
716#41—24no—
717#41—42no—
718#41—42no—
719#41—42no—
720#41—42no—
721#41—42no—
722#41—42no—
723#41—42no—
724#41—82no—
725C2×Q8—21no—
726C2×Q8—21no—
727C2×Q8—21no—
728C2×Q8—21no—
729C2×Q8—21no—
730C2×Q8—42no—
731C2×Q8—42no—
732C2×Q8C2×D4×C3111yescharacteristic
733C2×Q8C2×D4×C3111yescharacteristic
734C2×Q8C2×D4×C3111yescharacteristic
735C2×D4—24no—
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—21no—
741C2×D4—21no—
742C2×D4—21no—
743C2×D4—21no—
744C2×D4—21no—
745C2×D4—42no—
746C2×D4—42no—
747C2×D4—42no—
748C2×D4—41no—
749C2×D4—41no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—81no—
753C2×D4C2×D4×C3111yescharacteristic
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—42no—
765C22×C4—42no—
766C22×C4—42no—
767C22×C4—42no—
768C22×C4—41no—
769C22×C4—41no—
770C22×C4—42no—
771C22×C4—81no—
772C22×C4C2×D4×C3111yescharacteristic
773C22×C4C2×D4×C3111yescharacteristic
774C22×C4C2×D4×C3111yescharacteristic
775C22×C4C2×D4×C3111yescharacteristic
776C22×C4C2×D4×C3111yescharacteristic
777C22×C4C2×D4×C3111yescharacteristic
778C22×C4C2×D4×C3111yescharacteristic
779C22×C4C2×D4×C3111yescharacteristic
780C22×C4C24×C3111yescharacteristic
781Q16—42no—
782Q16—42no—
783Q16—42no—
784SD16—42no—
785SD16—42no—
786SD16—42no—
787SD16—42no—
788D8—42no—
789M16—42no—
790C2×C8—21no—
791C2×C8—21no—
792C2×C8—21no—
793C2×C8—21no—
794C2×C8—42no—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—21no—
798C4⋊C4—21no—
799C4⋊C4—21no—
800C4⋊C4—21no—
801C4⋊C4—21no—
802C4⋊C4—21no—
803C4⋊C4—21no—
804C4⋊C4—21no—
805C4⋊C4—21no—
806C4⋊C4—21no—
807C4⋊C4—21no—
808C4⋊C4—21no—
809C4⋊C4—21no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—21no—
818C4⋊C4—42no—
819C4⋊C4C2×D4×C3111yescharacteristic
820C4⋊C4C2×D4×C3111yescharacteristic
821C4⋊C4C2×D4×C3111yescharacteristic
822C4⋊C4C2×D4×C3111yescharacteristic
823C22⋊C4—21no—
824C22⋊C4—21no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—21no—
828C22⋊C4—21no—
829C22⋊C4—21no—
830C22⋊C4—21no—
831C22⋊C4—21no—
832C22⋊C4—21no—
833C22⋊C4—21no—
834C22⋊C4—21no—
835C22⋊C4—21no—
836C22⋊C4—21no—
837C22⋊C4—21no—
838C22⋊C4—21no—
839C22⋊C4—21no—
840C22⋊C4—21no—
841C22⋊C4—21no—
842C22⋊C4—21no—
843C22⋊C4—21no—
844C22⋊C4—21no—
845C22⋊C4—21no—
846C22⋊C4—42no—
847C22⋊C4—42no—
848C22⋊C4—42no—
849C22⋊C4—81no—
850C42—21no—
851C42—21no—
852C42—21no—
853C42—21no—
854C42—21no—
855C23—22no—
856C23—21no—
857C23—21no—
858C23—22no—
859C23—21no—
860C23—21no—
861C23—21no—
862C23—21no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23C31×#12011yescharacteristic
873C23C31×#12011yescharacteristic
874C23C22×D4×C3111yescharacteristic
875Q8—22no—
876Q8—22no—
877Q8—41no—
878Q8—41no—
879Q8—41no—
880Q8—41no—
881Q8—41no—
882Q8—81no—
883Q8—81no—
884Q8—81no—
885D4—22no—
886D4—22no—
887D4—41no—
888D4—41no—
889D4—41no—
890D4—44no—
891D4—44no—
892D4—42no—
893D4—42no—
894D4—41no—
895D4—41no—
896D4—81no—
897D4—81no—
898D4—81no—
899D4—81no—
900D4—84no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—21no—
916C2×C4—21no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—44no—
922C2×C4—44no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—42no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—81no—
934C2×C4—81no—
935C2×C4—81no—
936C2×C4—81no—
937C2×C4—81no—
938C2×C4—81no—
939C2×C4—84no—
940C2×C4C31×#12011yescharacteristic
941C2×C4C31×#12011yescharacteristic
942C2×C4C22×D4×C3111yescharacteristic
943C2×C4C22×D4×C3111yescharacteristic
944C8—41no—
945C8—41no—
946C8—41no—
947C8—41no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—42no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—42no—
964C22—41no—
965C22—41no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22—81no—
972C22C31×B(4,𝔽2)12yes—
973C22C2×C31×#12011yescharacteristic
974C22C31×#57711yescharacteristic
975C22C31×#57811yescharacteristic
976C4—21no—
977C4—21no—
978C4—21no—
979C4—21no—
980C4—42no—
981C4—41no—
982C4—41no—
983C4—41no—
984C4—41no—
985C4—41no—
986C4—41no—
987C4—42no—
988C4—41no—
989C4—41no—
990C4—41no—
991C4—41no—
992C4—81no—
993C2—21no—
994C2—21no—
995C2—22no—
996C2—41no—
997C2—82no—
998C2—81no—
999C2—81no—
1000C2C31×#301311yescharacteristic
1001C2C31×#301811yescharacteristic
1002C2C2×C31×B(4,𝔽2)11yescharacteristic
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×#3007C2semidirect
3. C31×#3002C2semidirect
4. C31×#2430C2semidirect
5. C31×#1606C2semidirect
6. C31×#1605C2semidirect
7. C31×#1603C2semidirect
8. C31×#1602C2semidirect
9. C31×#1600C2semidirect
10. C31×#1599C2semidirect
11. C31×#1597C2semidirect
12. C31×#1596C2semidirect
13. C31×#1504C2semidirect
14. C2×C31×#328C2semidirect
15. C31×#1468C2semidirect
81. C2×#41×C31D4semidirect
82. C22×Q8×C31D4semidirect
149. C31×C22⋊Q8D4semidirect
150. C31×C22⋊Q8D4semidirect
151. C31×C22⋊Q8D4semidirect
160. C31×#121D4semidirect
175. C31×#117D4semidirect
180. C2×C4⋊C4×C31D4semidirect
353. #18253C31direct (N × H)
447. #3535C2×C31semidirect
448. #3007C2×C31semidirect
449. #3002C2×C31semidirect
450. #2430C2×C31semidirect
451. #1606C2×C31semidirect
452. #1605C2×C31semidirect
453. #1603C2×C31semidirect
454. #1602C2×C31semidirect
455. #1600C2×C31semidirect
456. #1599C2×C31semidirect
457. #1597C2×C31semidirect
458. #1596C2×C31semidirect
459. #1504C2×C31semidirect
460. C2×#328C2×C31semidirect
461. #1468C2×C31semidirect
582. C2×#41D4×C31semidirect
583. C22×Q8D4×C31semidirect
650. C22⋊Q8D4×C31semidirect
651. C22⋊Q8D4×C31semidirect
652. C22⋊Q8D4×C31semidirect
661. #121D4×C31semidirect
676. #117D4×C31semidirect
681. C2×C4⋊C4D4×C31semidirect
711. C31#18253direct (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×#30072
C31×#30022
C31×#24302
C31×#16062
C31×#16052
C31×#16032
C31×#16022
C31×#16002
C31×#15992
C31×#15972
C31×#15962
C31×#15042
C2×C31×#3282
C31×#14682
#1825331