Finite Group Databasebeta

← C31×#23971 #21480730

Subgroups — C31×#23971 #21480730

Order 7936.

1274 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#552C211yesmaximal, characteristic, complemented
2C2×C31×#452C211yesmaximal, characteristic, complemented
3C2×C31×#416C211yesmaximal, characteristic, complemented
4C31×#2407C211yesmaximal, characteristic
5C31×#2026C211yesmaximal, characteristic, complemented
6C31×#2025C211yesmaximal, characteristic, complemented
7C31×#2001C211yesmaximal, characteristic, complemented
8C31×#2000C211yesmaximal, characteristic, complemented
9C31×#1892C211yesmaximal, characteristic, complemented
10C31×#1880C211yesmaximal, characteristic, complemented
11C31×#1878C211yesmaximal, characteristic, complemented
12C31×#1874C211yesmaximal, characteristic, complemented
13C31×#1872C211yesmaximal, characteristic, complemented
14C31×#1869C211yesmaximal, characteristic, complemented
15C31×#1825C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C22×Q16×C31C2211yescharacteristic
18C22×SD16×C31C2211yescharacteristic
19C23×C8×C31C2211yescharacteristic
20C31×#552—24no—
21C31×#552—24no—
22C2×C31×#126—21no—
23C2×C31×#125—21no—
24C2×C31×#125C2211yescharacteristic
25C2×C31×#123—21no—
26C2×C31×C22⋊Q8C2211yescharacteristic
27C2×C31×C22⋊Q8C2211yescharacteristic
28C2×C31×C22⋊Q8C2211yescharacteristic
29C2×C31×#121C2211yescharacteristic
30C2×C4×Q8×C31C2211yescharacteristic
31C2×C4×D4×C31C2211yescharacteristic
32C2×C31×#117—21no—
33C2×C31×#117C2211yescharacteristic
34C22×C4⋊C4×C31C2211yescharacteristic
35C31×#452—24no—
36C31×#416—24no—
37C2×C31×#103C2211yescharacteristic
38C2×C31×#103C2211yescharacteristic
39C2×C31×#103C2211yescharacteristic
40C2×C31×#103C2211yescharacteristic
41C2×C31×#103C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×C22⋊C8C2211yescharacteristic
46C2×C31×C22⋊C8C2211yescharacteristic
47C2×C31×C22⋊C8C2211yescharacteristic
48C31×#394—21no—
49C31×#392—21no—
50C31×#391C2211yescharacteristic
51C31×#390C2211yescharacteristic
52C31×#386—21no—
53C31×#385—21no—
54C31×#380C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C31×#336C2211yescharacteristic
63C2×#41×C31—22no—
64C2×#41×C31—22no—
65C2×#41×C31—22no—
66C2×#41×C31—22no—
67C2×#41×C31—41no—
68C2×#41×C31—41no—
69C22×Q8×C31C2311yescharacteristic
70C22×Q8×C31C2311yescharacteristic
71C22×D4×C31—21no—
72C22×D4×C31—21no—
73C22×D4×C31D411yescharacteristic
74C22×D4×C31C2311yescharacteristic
75C23×C4×C31—21no—
76C23×C4×C31—21no—
77C23×C4×C31C2311yescharacteristic
78C23×C4×C31C2311yescharacteristic
79C2×Q16×C31—22no—
80C2×Q16×C31—22no—
81C2×Q16×C31—41no—
82C2×SD16×C31—22no—
83C2×SD16×C31—22no—
84C2×SD16×C31—41no—
85C22×C8×C31—22no—
86C22×C8×C31—41no—
87C22×C8×C31—41no—
88C22×C8×C31C2311yescharacteristic
89C22×C8×C31C2311yescharacteristic
90C22×C8×C31C2311yescharacteristic
91C22×C8×C31C2311yescharacteristic
92C31×#126—28no—
93C31×#125—28no—
94C31×#125—22no—
95C31×#125—22no—
96C31×#123—28no—
97C31×C22⋊Q8—22no—
98C31×C22⋊Q8—22no—
99C31×C22⋊Q8—22no—
100C31×C22⋊Q8—22no—
101C31×C22⋊Q8—41no—
102C31×C22⋊Q8D414yescomplemented
103C31×#121—22no—
104C31×#121—41no—
105C4×Q8×C31—22no—
106C4×Q8×C31—22no—
107C4×D4×C31—22no—
108C4×D4×C31—22no—
109C31×#117—28no—
110C31×#117—22no—
111C31×#117D414yescomplemented
112C2×C4⋊C4×C31—21no—
113C2×C4⋊C4×C31—21no—
114C2×C4⋊C4×C31—21no—
115C2×C4⋊C4×C31—21no—
116C2×C4⋊C4×C31—21no—
117C2×C4⋊C4×C31—21no—
118C2×C4⋊C4×C31—22no—
119C2×C4⋊C4×C31—22no—
120C2×C4⋊C4×C31—21no—
121C2×C4⋊C4×C31D411yescharacteristic
122C2×C4⋊C4×C31C2311yescharacteristic
123C2×C4⋊C4×C31C2311yescharacteristic
124C2×C4⋊C4×C31C2311yescharacteristic
125C2×C4⋊C4×C31C2311yescharacteristic
126C2×C4⋊C4×C31C2311yescharacteristic
127C2×C22⋊C4×C31—21no—
128C2×C22⋊C4×C31—21no—
129C2×C22⋊C4×C31—21no—
130C2×C22⋊C4×C31—21no—
131C2×C22⋊C4×C31—21no—
132C2×C22⋊C4×C31—21no—
133C2×C22⋊C4×C31—21no—
134C2×C22⋊C4×C31—21no—
135C2×C22⋊C4×C31D411yescharacteristic
136C2×C22⋊C4×C31D411yescharacteristic
137C2×C42×C31—21no—
138C2×C42×C31—21no—
139C2×C42×C31C2311yescharacteristic
140C31×#103—22no—
141C31×#103—22no—
142C31×#103—22no—
143C31×#103—41no—
144C31×#103—41no—
145C31×#102—22no—
146C31×#102—22no—
147C31×#102—22no—
148C31×C22⋊C8—22no—
149C31×C22⋊C8—41no—
150C31×C22⋊C8—41no—
151C31×#95—21no—
152C31×#95—21no—
153C31×#95—21no—
154C24×C31—21no—
155C24×C31C2×D411yescharacteristic
156C24×C31C2×D411yescharacteristic
157#41×C31—28no—
158#41×C31—44no—
159#41×C31—44no—
160#41×C31—44no—
161C2×Q8×C31—21no—
162C2×Q8×C31—21no—
163C2×Q8×C31—21no—
164C2×Q8×C31—21no—
165C2×Q8×C31—21no—
166C2×Q8×C31—21no—
167C2×Q8×C31—21no—
168C2×Q8×C31—21no—
169C2×Q8×C31—21no—
170C2×Q8×C31—21no—
171C2×Q8×C31C2×D412yes—
172C2×Q8×C31#4112yes—
173C2×D4×C31—22no—
174C2×D4×C31—22no—
175C2×D4×C31—21no—
176C2×D4×C31—21no—
177C2×D4×C31—21no—
178C2×D4×C31—21no—
179C2×D4×C31—21no—
180C2×D4×C31—41no—
181C2×D4×C31—42no—
182C2×D4×C31—42no—
183C2×D4×C31—42no—
184C2×D4×C31—42no—
185C2×D4×C31—42no—
186C2×D4×C31—81no—
187C2×D4×C31#4112yes—
188C22×C4×C31—21no—
189C22×C4×C31—21no—
190C22×C4×C31—21no—
191C22×C4×C31—21no—
192C22×C4×C31—24no—
193C22×C4×C31—21no—
194C22×C4×C31—21no—
195C22×C4×C31—21no—
196C22×C4×C31—21no—
197C22×C4×C31—21no—
198C22×C4×C31—21no—
199C22×C4×C31—21no—
200C22×C4×C31—21no—
201C22×C4×C31—21no—
202C22×C4×C31—21no—
203C22×C4×C31—21no—
204C22×C4×C31—21no—
205C22×C4×C31—21no—
206C22×C4×C31—42no—
207C22×C4×C31—42no—
208C22×C4×C31—42no—
209C22×C4×C31—42no—
210C22×C4×C31—42no—
211C22×C4×C31C2×D411yescharacteristic
212C22×C4×C31C2×D411yescharacteristic
213C22×C4×C31C2×D411yescharacteristic
214C22×C4×C31C2×D411yescharacteristic
215C22×C4×C31C2×D412yes—
216C22×C4×C31C2×D412yes—
217C22×C4×C31C2411yescharacteristic
218Q16×C31—44no—
219SD16×C31—44no—
220C2×C8×C31—21no—
221C2×C8×C31—21no—
222C2×C8×C31—21no—
223C2×C8×C31—21no—
224C2×C8×C31—21no—
225C2×C8×C31—21no—
226C2×C8×C31—21no—
227C2×C8×C31—21no—
228C2×C8×C31—21no—
229C2×C8×C31—21no—
230C2×C8×C31—21no—
231C2×C8×C31—21no—
232C2×C8×C31—44no—
233C4⋊C4×C31—24no—
234C4⋊C4×C31—24no—
235C4⋊C4×C31—24no—
236C4⋊C4×C31—24no—
237C4⋊C4×C31—24no—
238C4⋊C4×C31—24no—
239C4⋊C4×C31—22no—
240C4⋊C4×C31—21no—
241C4⋊C4×C31—21no—
242C4⋊C4×C31—21no—
243C4⋊C4×C31—21no—
244C4⋊C4×C31—21no—
245C4⋊C4×C31—21no—
246C4⋊C4×C31—21no—
247C4⋊C4×C31—42no—
248C4⋊C4×C31C2×D412yes—
249C4⋊C4×C31C2×D412yes—
250C4⋊C4×C31C2×D412yes—
251C22⋊C4×C31—24no—
252C22⋊C4×C31—24no—
253C22⋊C4×C31—24no—
254C22⋊C4×C31—22no—
255C22⋊C4×C31—22no—
256C22⋊C4×C31—42no—
257C22⋊C4×C31—42no—
258C22⋊C4×C31—42no—
259C22⋊C4×C31—81no—
260C22⋊C4×C31—81no—
261C42×C31—24no—
262C42×C31—24no—
263C42×C31—21no—
264C42×C31—21no—
265#23971C3111yesmaximal, characteristic, direct product factor, Sylow
266C23×C31—21no—
267C23×C31—21no—
268C23×C31—21no—
269C23×C31—21no—
270C23×C31—21no—
271C23×C31—21no—
272C23×C31—21no—
273C23×C31—21no—
274C23×C31—21no—
275C23×C31—21no—
276C23×C31—21no—
277C23×C31—21no—
278C23×C31—22no—
279C23×C31—41no—
280C23×C31—41no—
281C23×C31—41no—
282C23×C31—41no—
283C23×C31—41no—
284C23×C31—41no—
285C23×C31#12012yes—
286C23×C31#13512yes—
287C23×C31C22×D411yescharacteristic
288Q8×C31—22no—
289Q8×C31—22no—
290Q8×C31—22no—
291Q8×C31—22no—
292Q8×C31—41no—
293Q8×C31—41no—
294Q8×C31—41no—
295Q8×C31—41no—
296D4×C31—22no—
297D4×C31—22no—
298D4×C31—44no—
299D4×C31—48no—
300D4×C31—41no—
301D4×C31—41no—
302D4×C31—84no—
303C2×C4×C31—21no—
304C2×C4×C31—21no—
305C2×C4×C31—22no—
306C2×C4×C31—22no—
307C2×C4×C31—22no—
308C2×C4×C31—22no—
309C2×C4×C31—21no—
310C2×C4×C31—22no—
311C2×C4×C31—22no—
312C2×C4×C31—22no—
313C2×C4×C31—21no—
314C2×C4×C31—21no—
315C2×C4×C31—22no—
316C2×C4×C31—21no—
317C2×C4×C31—22no—
318C2×C4×C31—21no—
319C2×C4×C31—21no—
320C2×C4×C31—21no—
321C2×C4×C31—21no—
322C2×C4×C31—21no—
323C2×C4×C31—48no—
324C2×C4×C31—48no—
325C2×C4×C31—41no—
326C2×C4×C31—41no—
327C2×C4×C31—41no—
328C2×C4×C31—41no—
329C2×C4×C31—41no—
330C2×C4×C31—41no—
331C2×C4×C31—41no—
332C2×C4×C31—41no—
333C2×C4×C31—41no—
334C2×C4×C31—41no—
335C2×C4×C31—41no—
336C2×C4×C31—41no—
337C2×C4×C31—41no—
338C2×C4×C31—41no—
339C2×C4×C31—41no—
340C2×C4×C31—41no—
341C2×C4×C31—41no—
342C2×C4×C31—41no—
343C2×C4×C31—41no—
344C2×C4×C31—41no—
345C2×C4×C31#12012yes—
346C2×C4×C31C22×D411yescharacteristic
347C2×C4×C31C22×D411yescharacteristic
348C2×C4×C31C2×#4111yescharacteristic
349C2×C4×C31C2×#4111yescharacteristic
350C2×C4×C31H(5,𝔽2)11yescharacteristic
351C2×C4×C31H(5,𝔽2)11yescharacteristic
352C8×C31—41no—
353C8×C31—41no—
354C8×C31—41no—
355C8×C31—41no—
356C2×#552C2×C3111yescharacteristic, complemented
357C2×#452C2×C3111yescharacteristic, complemented
358C2×#416C2×C3111yescharacteristic, complemented
359#2407C2×C3111yescharacteristic
360#2026C2×C3111yescharacteristic, complemented
361#2025C2×C3111yescharacteristic, complemented
362#2001C2×C3111yescharacteristic, complemented
363#2000C2×C3111yescharacteristic, complemented
364#1892C2×C3111yescharacteristic, complemented
365#1880C2×C3111yescharacteristic, complemented
366#1878C2×C3111yescharacteristic, complemented
367#1874C2×C3111yescharacteristic, complemented
368#1872C2×C3111yescharacteristic, complemented
369#1869C2×C3111yescharacteristic, complemented
370#1825C2×C3111yescharacteristic, complemented
371C22×C31—22no—
372C22×C31—22no—
373C22×C31—22no—
374C22×C31—22no—
375C22×C31—22no—
376C22×C31—22no—
377C22×C31—41no—
378C22×C31—41no—
379C22×C31—41no—
380C22×C31—41no—
381C22×C31—41no—
382C22×C31—41no—
383C22×C31—41no—
384C22×C31—41no—
385C22×C31—42no—
386C22×C31—42no—
387C22×C31—42no—
388C22×C31—81no—
389C22×C31—81no—
390C22×C31—81no—
391C22×C31—81no—
392C22×C31C2×#12011yescharacteristic
393C22×C31#54611yescharacteristic
394C22×C31#54611yescharacteristic
395C22×C31C2×#13511yescharacteristic
396C22×C31#57511yescharacteristic
397C22×C31#57711yescharacteristic
398C22×C31#57811yescharacteristic
399C4×C31—22no—
400C4×C31—41no—
401C4×C31—42no—
402C4×C31—42no—
403C4×C31—41no—
404C4×C31—42no—
405C4×C31—42no—
406C4×C31—41no—
407C4×C31—42no—
408C4×C31—81no—
409C4×C31—81no—
410C4×C31#52511yescharacteristic
411C4×C31#53511yescharacteristic
412C4×C31#54611yescharacteristic
413C4×C31#54611yescharacteristic
414C22×#41C22×C3111yescharacteristic
415C22×Q16C22×C3111yescharacteristic
416C22×SD16C22×C3111yescharacteristic
417C23×C8C22×C3111yescharacteristic
418#552—24no—
419#552—24no—
420C2×#126—21no—
421C2×#125—21no—
422C2×#125C22×C3111yescharacteristic
423C2×#123—21no—
424C2×C22⋊Q8C22×C3111yescharacteristic
425C2×C22⋊Q8C22×C3111yescharacteristic
426C2×C22⋊Q8C22×C3111yescharacteristic
427C2×#121C22×C3111yescharacteristic
428C2×C4×Q8C22×C3111yescharacteristic
429C2×C4×D4C22×C3111yescharacteristic
430C2×#117—21no—
431C2×#117C22×C3111yescharacteristic
432C22×C4⋊C4C22×C3111yescharacteristic
433#452—24no—
434#416—24no—
435C2×#103C22×C3111yescharacteristic
436C2×#103C22×C3111yescharacteristic
437C2×#103C22×C3111yescharacteristic
438C2×#103C22×C3111yescharacteristic
439C2×#103C22×C3111yescharacteristic
440C2×#102C22×C3111yescharacteristic
441C2×#102C22×C3111yescharacteristic
442C2×#102C22×C3111yescharacteristic
443C2×C22⋊C8C22×C3111yescharacteristic
444C2×C22⋊C8C22×C3111yescharacteristic
445C2×C22⋊C8C22×C3111yescharacteristic
446#394—21no—
447#392—21no—
448#391C22×C3111yescharacteristic
449#390C22×C3111yescharacteristic
450#386—21no—
451#385—21no—
452#380C22×C3111yescharacteristic
453#340C22×C3111yescharacteristic
454#340C22×C3111yescharacteristic
455#340C22×C3111yescharacteristic
456#340C22×C3111yescharacteristic
457#340C22×C3111yescharacteristic
458#340C22×C3111yescharacteristic
459#336C22×C3111yescharacteristic
460#336C22×C3111yescharacteristic
461C2×C31—42no—
462C2×C31—42no—
463C2×C31—82no—
464C2×C31#240411yescharacteristic
465C2×C31#300211yescharacteristic
466C2×C31#301311yescharacteristic
467C2×C31#329611yescharacteristic
468C2×C31#330011yescharacteristic
469C2×C31#331511yescharacteristic
470C2×C31#331711yescharacteristic
471C2×#41—22no—
472C2×#41—22no—
473C2×#41—22no—
474C2×#41—22no—
475C2×#41—41no—
476C2×#41—41no—
477C22×Q8C23×C3111yescharacteristic
478C22×Q8C23×C3111yescharacteristic
479C22×D4—21no—
480C22×D4—21no—
481C22×D4D4×C3111yescharacteristic
482C22×D4C23×C3111yescharacteristic
483C23×C4—21no—
484C23×C4—21no—
485C23×C4C23×C3111yescharacteristic
486C23×C4C23×C3111yescharacteristic
487C2×Q16—22no—
488C2×Q16—22no—
489C2×Q16—41no—
490C2×SD16—22no—
491C2×SD16—22no—
492C2×SD16—41no—
493C22×C8—22no—
494C22×C8—41no—
495C22×C8—41no—
496C22×C8C23×C3111yescharacteristic
497C22×C8C23×C3111yescharacteristic
498C22×C8C23×C3111yescharacteristic
499C22×C8C23×C3111yescharacteristic
500#126—28no—
501#125—28no—
502#125—22no—
503#125—22no—
504#123—28no—
505C22⋊Q8—22no—
506C22⋊Q8—22no—
507C22⋊Q8—22no—
508C22⋊Q8—22no—
509C22⋊Q8—41no—
510C22⋊Q8D4×C3114yescomplemented
511#121—22no—
512#121—41no—
513C4×Q8—22no—
514C4×Q8—22no—
515C4×D4—22no—
516C4×D4—22no—
517#117—28no—
518#117—22no—
519#117D4×C3114yescomplemented
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—22no—
527C2×C4⋊C4—22no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4D4×C3111yescharacteristic
530C2×C4⋊C4C23×C3111yescharacteristic
531C2×C4⋊C4C23×C3111yescharacteristic
532C2×C4⋊C4C23×C3111yescharacteristic
533C2×C4⋊C4C23×C3111yescharacteristic
534C2×C4⋊C4C23×C3111yescharacteristic
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4D4×C3111yescharacteristic
544C2×C22⋊C4D4×C3111yescharacteristic
545C2×C42—21no—
546C2×C42—21no—
547C2×C42C23×C3111yescharacteristic
548#103—22no—
549#103—22no—
550#103—22no—
551#103—41no—
552#103—41no—
553#102—22no—
554#102—22no—
555#102—22no—
556C22⋊C8—22no—
557C22⋊C8—41no—
558C22⋊C8—41no—
559#95—21no—
560#95—21no—
561#95—21no—
562C31#2397111yescharacteristic, direct product factor, Sylow
563C24—21no—
564C24C2×D4×C3111yescharacteristic
565C24C2×D4×C3111yescharacteristic
566#41—28no—
567#41—44no—
568#41—44no—
569#41—44no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8C2×D4×C3112yes—
581C2×Q8#41×C3112yes—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—41no—
590C2×D4—42no—
591C2×D4—42no—
592C2×D4—42no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—81no—
596C2×D4#41×C3112yes—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—24no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4C2×D4×C3111yescharacteristic
621C22×C4C2×D4×C3111yescharacteristic
622C22×C4C2×D4×C3111yescharacteristic
623C22×C4C2×D4×C3111yescharacteristic
624C22×C4C2×D4×C3112yes—
625C22×C4C2×D4×C3112yes—
626C22×C4C24×C3111yescharacteristic
627Q16—44no—
628SD16—44no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—44no—
642C4⋊C4—24no—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—24no—
646C4⋊C4—24no—
647C4⋊C4—24no—
648C4⋊C4—22no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—42no—
657C4⋊C4C2×D4×C3112yes—
658C4⋊C4C2×D4×C3112yes—
659C4⋊C4C2×D4×C3112yes—
660C22⋊C4—24no—
661C22⋊C4—24no—
662C22⋊C4—24no—
663C22⋊C4—22no—
664C22⋊C4—22no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—81no—
669C22⋊C4—81no—
670C42—24no—
671C42—24no—
672C42—21no—
673C42—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—22no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23C31×#12012yes—
694C23C31×#13512yes—
695C23C22×D4×C3111yescharacteristic
696Q8—22no—
697Q8—22no—
698Q8—22no—
699Q8—22no—
700Q8—41no—
701Q8—41no—
702Q8—41no—
703Q8—41no—
704D4—22no—
705D4—22no—
706D4—44no—
707D4—48no—
708D4—41no—
709D4—41no—
710D4—84no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—21no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—48no—
732C2×C4—48no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4C31×#12012yes—
754C2×C4C22×D4×C3111yescharacteristic
755C2×C4C22×D4×C3111yescharacteristic
756C2×C4C2×#41×C3111yescharacteristic
757C2×C4C2×#41×C3111yescharacteristic
758C2×C4C31×H(5,𝔽2)11yescharacteristic
759C2×C4C31×H(5,𝔽2)11yescharacteristic
760C8—41no—
761C8—41no—
762C8—41no—
763C8—41no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22C2×C31×#12011yescharacteristic
786C22C31×#54611yescharacteristic
787C22C31×#54611yescharacteristic
788C22C2×C31×#13511yescharacteristic
789C22C31×#57511yescharacteristic
790C22C31×#57711yescharacteristic
791C22C31×#57811yescharacteristic
792C4—22no—
793C4—41no—
794C4—42no—
795C4—42no—
796C4—41no—
797C4—42no—
798C4—42no—
799C4—41no—
800C4—42no—
801C4—81no—
802C4—81no—
803C4C31×#52511yescharacteristic
804C4C31×#53511yescharacteristic
805C4C31×#54611yescharacteristic
806C4C31×#54611yescharacteristic
807C2—42no—
808C2—42no—
809C2—82no—
810C2C31×#240411yescharacteristic
811C2C31×#300211yescharacteristic
812C2C31×#301311yescharacteristic
813C2C31×#329611yescharacteristic
814C2C31×#330011yescharacteristic
815C2C31×#331511yescharacteristic
816C2C31×#331711yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#2407C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C4×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#552C2semidirect
2. C2×C31×#452C2semidirect
3. C2×C31×#416C2semidirect
5. C31×#2026C2semidirect
6. C31×#2025C2semidirect
7. C31×#2001C2semidirect
8. C31×#2000C2semidirect
9. C31×#1892C2semidirect
10. C31×#1880C2semidirect
11. C31×#1878C2semidirect
12. C31×#1874C2semidirect
13. C31×#1872C2semidirect
14. C31×#1869C2semidirect
15. C31×#1825C2semidirect
102. C31×C22⋊Q8D4semidirect
111. C31×#117D4semidirect
265. #23971C31direct (N × H)
356. C2×#552C2×C31semidirect
357. C2×#452C2×C31semidirect
358. C2×#416C2×C31semidirect
360. #2026C2×C31semidirect
361. #2025C2×C31semidirect
362. #2001C2×C31semidirect
363. #2000C2×C31semidirect
364. #1892C2×C31semidirect
365. #1880C2×C31semidirect
366. #1878C2×C31semidirect
367. #1874C2×C31semidirect
368. #1872C2×C31semidirect
369. #1869C2×C31semidirect
370. #1825C2×C31semidirect
510. C22⋊Q8D4×C31semidirect
519. #117D4×C31semidirect
562. C31#23971direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5522
C2×C31×#4522
C2×C31×#4162
C31×#24072
C31×#20262
C31×#20252
C31×#20012
C31×#20002
C31×#18922
C31×#18802
C31×#18782
C31×#18742
C31×#18722
C31×#18692
C31×#18252
#2397131