Finite Group Databasebeta

← C31×#25889 #21482648

Subgroups — C31×#25889 #21482648

Order 7936.

1292 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#548C211yesmaximal, characteristic
2C2×C31×#488C211yesmaximal, characteristic, complemented
3C2×C31×#479C211yesmaximal, characteristic, complemented
4C31×#2562C211yesmaximal, characteristic, complemented
5C31×#2036C211yesmaximal, characteristic, complemented
6C31×#2035C211yesmaximal, characteristic, complemented
7C31×#2034C211yesmaximal, characteristic, complemented
8C31×#2033C211yesmaximal, characteristic, complemented
9C31×#1983C211yesmaximal, characteristic, complemented
10C31×#1954C211yesmaximal, characteristic, complemented
11C31×#1788C211yesmaximal, characteristic, complemented
12C31×#1788C211yesmaximal, characteristic, complemented
13C31×#1787C211yesmaximal, characteristic, complemented
14C31×#1787C211yesmaximal, characteristic, complemented
15C4×C31×#103C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C23×Q8×C31C2211yescharacteristic
18C31×#548—24no—
19C31×#548—24no—
20C2×C31×#125C2211yescharacteristic
21C2×C31×#124—21no—
22C2×C31×#124C2211yescharacteristic
23C2×C31×C22⋊Q8—21no—
24C2×C31×C22⋊Q8C2211yescharacteristic
25C2×C31×#121—21no—
26C2×C31×#121C2211yescharacteristic
27C2×C4×Q8×C31C2211yescharacteristic
28C2×C4×D4×C31—21no—
29C2×C4×D4×C31C2211yescharacteristic
30C31×#488—24no—
31C31×#479—24no—
32C2×C31×#107C2211yescharacteristic
33C2×C31×#106C2211yescharacteristic
34C2×C31×C4⋊C8C2211yescharacteristic
35C2×C31×#103C2211yescharacteristic
36C2×C31×#103C2211yescharacteristic
37C2×C31×#103C2211yescharacteristic
38C2×C31×#103C2211yescharacteristic
39C2×C31×#103C2211yescharacteristic
40C2×C31×#103C2211yescharacteristic
41C2×C31×#103C2211yescharacteristic
42C2×C31×#103C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×#102C2211yescharacteristic
46C2×C31×#102C2211yescharacteristic
47C2×C31×C22⋊C8C2211yescharacteristic
48C2×C31×C22⋊C8C2211yescharacteristic
49C2×C31×C22⋊C8C2211yescharacteristic
50C2×C31×C22⋊C8C2211yescharacteristic
51C2×C4×C8×C31C2211yescharacteristic
52C31×#400—21no—
53C31×#394—21no—
54C31×#388—21no—
55C31×#388—21no—
56C31×#380C2211yescharacteristic
57C31×#380C2211yescharacteristic
58C31×#380C2211yescharacteristic
59C31×#380C2211yescharacteristic
60C4×C4⋊C4×C31C2211yescharacteristic
61C31×#340C2211yescharacteristic
62C31×#340C2211yescharacteristic
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×C31—22no—
70C22×Q8×C31—22no—
71C22×Q8×C31—21no—
72C22×Q8×C31—22no—
73C22×Q8×C31—22no—
74C22×Q8×C31—41no—
75C22×Q8×C31—41no—
76C22×Q8×C31C2311yescharacteristic
77C22×Q8×C31C2311yescharacteristic
78C22×D4×C31—21no—
79C22×D4×C31—21no—
80C22×D4×C31D411yescharacteristic
81C22×D4×C31C2311yescharacteristic
82C23×C4×C31—21no—
83C23×C4×C31—21no—
84C23×C4×C31C2311yescharacteristic
85C23×C4×C31C2311yescharacteristic
86C22×C8×C31C2311yescharacteristic
87C22×C8×C31C2311yescharacteristic
88C22×C8×C31C2311yescharacteristic
89C22×C8×C31C2311yescharacteristic
90C31×#125—22no—
91C31×#125—22no—
92C31×#124—28no—
93C31×#124—22no—
94C31×#124D414yes—
95C31×C22⋊Q8—28no—
96C31×C22⋊Q8—22no—
97C31×C22⋊Q8—22no—
98C31×#121—28no—
99C31×#121—22no—
100C31×#121—22no—
101C4×Q8×C31—22no—
102C4×Q8×C31D414yes—
103C4×D4×C31—28no—
104C4×D4×C31—22no—
105C4×D4×C31—22no—
106C2×C4⋊C4×C31—21no—
107C2×C4⋊C4×C31—21no—
108C2×C4⋊C4×C31—21no—
109C2×C4⋊C4×C31—21no—
110C2×C4⋊C4×C31D411yescharacteristic
111C2×C4⋊C4×C31C2311yescharacteristic
112C2×C4⋊C4×C31C2311yescharacteristic
113C2×C4⋊C4×C31C2311yescharacteristic
114C2×C4⋊C4×C31C2311yescharacteristic
115C2×C4⋊C4×C31C2311yescharacteristic
116C2×C22⋊C4×C31—21no—
117C2×C22⋊C4×C31—21no—
118C2×C22⋊C4×C31—21no—
119C2×C22⋊C4×C31—21no—
120C2×C22⋊C4×C31—21no—
121C2×C22⋊C4×C31—21no—
122C2×C22⋊C4×C31—21no—
123C2×C22⋊C4×C31—21no—
124C2×C22⋊C4×C31D411yescharacteristic
125C2×C22⋊C4×C31D411yescharacteristic
126C2×C42×C31—21no—
127C2×C42×C31—21no—
128C2×C42×C31C2311yescharacteristic
129C31×#107—22no—
130C31×#106—22no—
131C31×C4⋊C8—22no—
132C31×#103—22no—
133C31×#103—22no—
134C31×#103—22no—
135C31×#103—22no—
136C31×#103—22no—
137C31×#103—22no—
138C31×#103—41no—
139C31×#103—41no—
140C31×#102—22no—
141C31×#102—22no—
142C31×#102—41no—
143C31×#102—41no—
144C31×C22⋊C8—41no—
145C31×C22⋊C8—41no—
146C31×C22⋊C8—41no—
147C31×C22⋊C8—41no—
148C4×C8×C31—22no—
149C31×#95—21no—
150C31×#95—21no—
151C31×#95—21no—
152C31×#95—21no—
153C31×#95—21no—
154C24×C31—21no—
155C24×C31C2×D411yescharacteristic
156C24×C31C2×D411yescharacteristic
157#41×C31—44no—
158#41×C31—44no—
159#41×C31—44no—
160#41×C31—44no—
161C2×Q8×C31—24no—
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—42no—
171C2×Q8×C31—42no—
172C2×Q8×C31—44no—
173C2×Q8×C31—44no—
174C2×Q8×C31—44no—
175C2×Q8×C31—44no—
176C2×Q8×C31C2×D412yes—
177C2×Q8×C31C2×D412yes—
178C2×Q8×C31#4112yes—
179C2×Q8×C31#4112yes—
180C2×D4×C31—24no—
181C2×D4×C31—24no—
182C2×D4×C31—22no—
183C2×D4×C31—22no—
184C2×D4×C31—21no—
185C2×D4×C31—21no—
186C2×D4×C31—21no—
187C2×D4×C31—21no—
188C2×D4×C31—21no—
189C2×D4×C31—41no—
190C2×D4×C31—42no—
191C2×D4×C31—42no—
192C2×D4×C31—42no—
193C2×D4×C31—42no—
194C2×D4×C31C2×D412yes—
195C22×C4×C31—21no—
196C22×C4×C31—24no—
197C22×C4×C31—24no—
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—21no—
207C22×C4×C31—21no—
208C22×C4×C31—21no—
209C22×C4×C31—21no—
210C22×C4×C31—21no—
211C22×C4×C31—21no—
212C22×C4×C31—21no—
213C22×C4×C31—21no—
214C22×C4×C31—21no—
215C22×C4×C31—21no—
216C22×C4×C31—42no—
217C22×C4×C31—42no—
218C22×C4×C31—42no—
219C22×C4×C31—42no—
220C22×C4×C31C2×D411yescharacteristic
221C22×C4×C31C2×D411yescharacteristic
222C22×C4×C31C2×D411yescharacteristic
223C22×C4×C31C2×D411yescharacteristic
224C22×C4×C31C2411yescharacteristic
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—21no—
233C2×C8×C31—21no—
234C2×C8×C31—21no—
235C2×C8×C31—21no—
236C2×C8×C31—21no—
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—21no—
248C4⋊C4×C31—21no—
249C4⋊C4×C31—42no—
250C4⋊C4×C31—42no—
251C4⋊C4×C31C2×D412yes—
252C22⋊C4×C31—24no—
253C22⋊C4×C31—24no—
254C22⋊C4×C31—24no—
255C22⋊C4×C31—24no—
256C22⋊C4×C31—22no—
257C22⋊C4×C31—22no—
258C22⋊C4×C31—42no—
259C22⋊C4×C31—42no—
260C22⋊C4×C31—81no—
261C22⋊C4×C31—81no—
262C42×C31—24no—
263C42×C31—81no—
264C42×C31C2×D412yes—
265C42×C31C2×D412yes—
266#25889C3111yesmaximal, characteristic, direct product factor, Sylow
267C23×C31—21no—
268C23×C31—21no—
269C23×C31—21no—
270C23×C31—21no—
271C23×C31—21no—
272C23×C31—21no—
273C23×C31—21no—
274C23×C31—22no—
275C23×C31—21no—
276C23×C31—21no—
277C23×C31—21no—
278C23×C31—21no—
279C23×C31—21no—
280C23×C31—21no—
281C23×C31—41no—
282C23×C31—41no—
283C23×C31—41no—
284C23×C31—41no—
285C23×C31—41no—
286C23×C31—41no—
287C23×C31#13512yes—
288C23×C31C22×D411yescharacteristic
289Q8×C31—22no—
290Q8×C31—22no—
291Q8×C31—22no—
292Q8×C31—22no—
293Q8×C31—22no—
294Q8×C31—48no—
295Q8×C31—41no—
296Q8×C31—41no—
297Q8×C31#12414yes—
298D4×C31—22no—
299D4×C31—22no—
300D4×C31—44no—
301D4×C31—48no—
302D4×C31—48no—
303D4×C31—41no—
304D4×C31—41no—
305C2×C4×C31—22no—
306C2×C4×C31—22no—
307C2×C4×C31—22no—
308C2×C4×C31—21no—
309C2×C4×C31—21no—
310C2×C4×C31—21no—
311C2×C4×C31—21no—
312C2×C4×C31—22no—
313C2×C4×C31—22no—
314C2×C4×C31—21no—
315C2×C4×C31—21no—
316C2×C4×C31—21no—
317C2×C4×C31—21no—
318C2×C4×C31—21no—
319C2×C4×C31—21no—
320C2×C4×C31—48no—
321C2×C4×C31—48no—
322C2×C4×C31—41no—
323C2×C4×C31—41no—
324C2×C4×C31—41no—
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—41no—
346C2×C4×C31#12012yes—
347C2×C4×C31#12012yes—
348C2×C4×C31C22×D411yescharacteristic
349C2×C4×C31C22×D411yescharacteristic
350C2×C4×C31C2×#4111yescharacteristic
351C2×C4×C31C2×#4111yescharacteristic
352C2×C4×C31H(5,𝔽2)11yescharacteristic
353C2×C4×C31H(5,𝔽2)11yescharacteristic
354C8×C31—41no—
355C8×C31—41no—
356C8×C31—41no—
357C8×C31—41no—
358C2×#548C2×C3111yescharacteristic
359C2×#488C2×C3111yescharacteristic, complemented
360C2×#479C2×C3111yescharacteristic, complemented
361#2562C2×C3111yescharacteristic, complemented
362#2036C2×C3111yescharacteristic, complemented
363#2035C2×C3111yescharacteristic, complemented
364#2034C2×C3111yescharacteristic, complemented
365#2033C2×C3111yescharacteristic, complemented
366#1983C2×C3111yescharacteristic, complemented
367#1954C2×C3111yescharacteristic, complemented
368#1788C2×C3111yescharacteristic, complemented
369#1788C2×C3111yescharacteristic, complemented
370#1787C2×C3111yescharacteristic, complemented
371#1787C2×C3111yescharacteristic, complemented
372C4×#103C2×C3111yescharacteristic, complemented
373C22×C31—22no—
374C22×C31—22no—
375C22×C31—22no—
376C22×C31—41no—
377C22×C31—41no—
378C22×C31—41no—
379C22×C31—41no—
380C22×C31—42no—
381C22×C31—41no—
382C22×C31—41no—
383C22×C31—42no—
384C22×C31—41no—
385C22×C31—42no—
386C22×C31—41no—
387C22×C31—41no—
388C22×C31—41no—
389C22×C31—41no—
390C22×C31—81no—
391C22×C31—81no—
392C22×C31—81no—
393C22×C31—81no—
394C22×C31C2×#12011yescharacteristic
395C22×C31#54611yescharacteristic
396C22×C31#54611yescharacteristic
397C22×C31C2×#13511yescharacteristic
398C22×C31#57511yescharacteristic
399C22×C31#57711yescharacteristic
400C22×C31#57811yescharacteristic
401C4×C31—24no—
402C4×C31—22no—
403C4×C31—22no—
404C4×C31—41no—
405C4×C31—41no—
406C4×C31—42no—
407C4×C31—42no—
408C4×C31—81no—
409C4×C31—81no—
410C4×C31—81no—
411C4×C31—81no—
412C4×C31C2×#12411yescharacteristic
413C4×C31#53511yescharacteristic
414C4×C31#54611yescharacteristic
415C4×C31#54611yescharacteristic
416C22×#41C22×C3111yescharacteristic
417C23×Q8C22×C3111yescharacteristic
418#548—24no—
419#548—24no—
420C2×#125C22×C3111yescharacteristic
421C2×#124—21no—
422C2×#124C22×C3111yescharacteristic
423C2×C22⋊Q8—21no—
424C2×C22⋊Q8C22×C3111yescharacteristic
425C2×#121—21no—
426C2×#121C22×C3111yescharacteristic
427C2×C4×Q8C22×C3111yescharacteristic
428C2×C4×D4—21no—
429C2×C4×D4C22×C3111yescharacteristic
430#488—24no—
431#479—24no—
432C2×#107C22×C3111yescharacteristic
433C2×#106C22×C3111yescharacteristic
434C2×C4⋊C8C22×C3111yescharacteristic
435C2×#103C22×C3111yescharacteristic
436C2×#103C22×C3111yescharacteristic
437C2×#103C22×C3111yescharacteristic
438C2×#103C22×C3111yescharacteristic
439C2×#103C22×C3111yescharacteristic
440C2×#103C22×C3111yescharacteristic
441C2×#103C22×C3111yescharacteristic
442C2×#103C22×C3111yescharacteristic
443C2×#102C22×C3111yescharacteristic
444C2×#102C22×C3111yescharacteristic
445C2×#102C22×C3111yescharacteristic
446C2×#102C22×C3111yescharacteristic
447C2×C22⋊C8C22×C3111yescharacteristic
448C2×C22⋊C8C22×C3111yescharacteristic
449C2×C22⋊C8C22×C3111yescharacteristic
450C2×C22⋊C8C22×C3111yescharacteristic
451C2×C4×C8C22×C3111yescharacteristic
452#400—21no—
453#394—21no—
454#388—21no—
455#388—21no—
456#380C22×C3111yescharacteristic
457#380C22×C3111yescharacteristic
458#380C22×C3111yescharacteristic
459#380C22×C3111yescharacteristic
460C4×C4⋊C4C22×C3111yescharacteristic
461#340C22×C3111yescharacteristic
462#340C22×C3111yescharacteristic
463C2×C31—42no—
464C2×C31—81no—
465C2×C31—82no—
466C2×C31#243511yescharacteristic
467C2×C31#300211yescharacteristic
468C2×C31#301311yescharacteristic
469C2×C31#330011yescharacteristic
470C2×C31#330111yescharacteristic
471C2×C31#332611yescharacteristic
472C2×C31#332711yescharacteristic
473C2×#41—22no—
474C2×#41—22no—
475C2×#41—22no—
476C2×#41—22no—
477C2×#41—41no—
478C2×#41—41no—
479C22×Q8—22no—
480C22×Q8—22no—
481C22×Q8—21no—
482C22×Q8—22no—
483C22×Q8—22no—
484C22×Q8—41no—
485C22×Q8—41no—
486C22×Q8C23×C3111yescharacteristic
487C22×Q8C23×C3111yescharacteristic
488C22×D4—21no—
489C22×D4—21no—
490C22×D4D4×C3111yescharacteristic
491C22×D4C23×C3111yescharacteristic
492C23×C4—21no—
493C23×C4—21no—
494C23×C4C23×C3111yescharacteristic
495C23×C4C23×C3111yescharacteristic
496C22×C8C23×C3111yescharacteristic
497C22×C8C23×C3111yescharacteristic
498C22×C8C23×C3111yescharacteristic
499C22×C8C23×C3111yescharacteristic
500#125—22no—
501#125—22no—
502#124—28no—
503#124—22no—
504#124D4×C3114yes—
505C22⋊Q8—28no—
506C22⋊Q8—22no—
507C22⋊Q8—22no—
508#121—28no—
509#121—22no—
510#121—22no—
511C4×Q8—22no—
512C4×Q8D4×C3114yes—
513C4×D4—28no—
514C4×D4—22no—
515C4×D4—22no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4D4×C3111yescharacteristic
521C2×C4⋊C4C23×C3111yescharacteristic
522C2×C4⋊C4C23×C3111yescharacteristic
523C2×C4⋊C4C23×C3111yescharacteristic
524C2×C4⋊C4C23×C3111yescharacteristic
525C2×C4⋊C4C23×C3111yescharacteristic
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4D4×C3111yescharacteristic
535C2×C22⋊C4D4×C3111yescharacteristic
536C2×C42—21no—
537C2×C42—21no—
538C2×C42C23×C3111yescharacteristic
539#107—22no—
540#106—22no—
541C4⋊C8—22no—
542#103—22no—
543#103—22no—
544#103—22no—
545#103—22no—
546#103—22no—
547#103—22no—
548#103—41no—
549#103—41no—
550#102—22no—
551#102—22no—
552#102—41no—
553#102—41no—
554C22⋊C8—41no—
555C22⋊C8—41no—
556C22⋊C8—41no—
557C22⋊C8—41no—
558C4×C8—22no—
559#95—21no—
560#95—21no—
561#95—21no—
562#95—21no—
563#95—21no—
564C31#2588911yescharacteristic, direct product factor, Sylow
565C24—21no—
566C24C2×D4×C3111yescharacteristic
567C24C2×D4×C3111yescharacteristic
568#41—44no—
569#41—44no—
570#41—44no—
571#41—44no—
572C2×Q8—24no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—42no—
582C2×Q8—42no—
583C2×Q8—44no—
584C2×Q8—44no—
585C2×Q8—44no—
586C2×Q8—44no—
587C2×Q8C2×D4×C3112yes—
588C2×Q8C2×D4×C3112yes—
589C2×Q8#41×C3112yes—
590C2×Q8#41×C3112yes—
591C2×D4—24no—
592C2×D4—24no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—41no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4C2×D4×C3112yes—
606C22×C4—21no—
607C22×C4—24no—
608C22×C4—24no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—42no—
631C22×C4C2×D4×C3111yescharacteristic
632C22×C4C2×D4×C3111yescharacteristic
633C22×C4C2×D4×C3111yescharacteristic
634C22×C4C2×D4×C3111yescharacteristic
635C22×C4C24×C3111yescharacteristic
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C4⋊C4—24no—
649C4⋊C4—24no—
650C4⋊C4—22no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—42no—
661C4⋊C4—42no—
662C4⋊C4C2×D4×C3112yes—
663C22⋊C4—24no—
664C22⋊C4—24no—
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—81no—
672C22⋊C4—81no—
673C42—24no—
674C42—81no—
675C42C2×D4×C3112yes—
676C42C2×D4×C3112yes—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—22no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23C31×#13512yes—
698C23C22×D4×C3111yescharacteristic
699Q8—22no—
700Q8—22no—
701Q8—22no—
702Q8—22no—
703Q8—22no—
704Q8—48no—
705Q8—41no—
706Q8—41no—
707Q8C31×#12414yes—
708D4—22no—
709D4—22no—
710D4—44no—
711D4—48no—
712D4—48no—
713D4—41no—
714D4—41no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—48no—
731C2×C4—48no—
732C2×C4—41no—
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×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4C31×#12012yes—
757C2×C4C31×#12012yes—
758C2×C4C22×D4×C3111yescharacteristic
759C2×C4C22×D4×C3111yescharacteristic
760C2×C4C2×#41×C3111yescharacteristic
761C2×C4C2×#41×C3111yescharacteristic
762C2×C4C31×H(5,𝔽2)11yescharacteristic
763C2×C4C31×H(5,𝔽2)11yescharacteristic
764C8—41no—
765C8—41no—
766C8—41no—
767C8—41no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—42no—
776C22—41no—
777C22—41no—
778C22—42no—
779C22—41no—
780C22—42no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22C2×C31×#12011yescharacteristic
790C22C31×#54611yescharacteristic
791C22C31×#54611yescharacteristic
792C22C2×C31×#13511yescharacteristic
793C22C31×#57511yescharacteristic
794C22C31×#57711yescharacteristic
795C22C31×#57811yescharacteristic
796C4—24no—
797C4—22no—
798C4—22no—
799C4—41no—
800C4—41no—
801C4—42no—
802C4—42no—
803C4—81no—
804C4—81no—
805C4—81no—
806C4—81no—
807C4C2×C31×#12411yescharacteristic
808C4C31×#53511yescharacteristic
809C4C31×#54611yescharacteristic
810C4C31×#54611yescharacteristic
811C2—42no—
812C2—81no—
813C2—82no—
814C2C31×#243511yescharacteristic
815C2C31×#300211yescharacteristic
816C2C31×#301311yescharacteristic
817C2C31×#330011yescharacteristic
818C2C31×#330111yescharacteristic
819C2C31×#332611yescharacteristic
820C2C31×#332711yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#548C2
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
2. C2×C31×#488C2semidirect
3. C2×C31×#479C2semidirect
4. C31×#2562C2semidirect
5. C31×#2036C2semidirect
6. C31×#2035C2semidirect
7. C31×#2034C2semidirect
8. C31×#2033C2semidirect
9. C31×#1983C2semidirect
10. C31×#1954C2semidirect
11. C31×#1788C2semidirect
12. C31×#1788C2semidirect
13. C31×#1787C2semidirect
14. C31×#1787C2semidirect
15. C4×C31×#103C2semidirect
266. #25889C31direct (N × H)
359. C2×#488C2×C31semidirect
360. C2×#479C2×C31semidirect
361. #2562C2×C31semidirect
362. #2036C2×C31semidirect
363. #2035C2×C31semidirect
364. #2034C2×C31semidirect
365. #2033C2×C31semidirect
366. #1983C2×C31semidirect
367. #1954C2×C31semidirect
368. #1788C2×C31semidirect
369. #1788C2×C31semidirect
370. #1787C2×C31semidirect
371. #1787C2×C31semidirect
372. C4×#103C2×C31semidirect
564. C31#25889direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5482
C2×C31×#4882
C2×C31×#4792
C31×#25622
C31×#20362
C31×#20352
C31×#20342
C31×#20332
C31×#19832
C31×#19542
C31×#17882
C31×#17872
C4×C31×#1032
#2588931