Finite Group Databasebeta

← C31×#15275 #21472034

Subgroups — C31×#15275 #21472034

Order 7936.

2098 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×C31×#394C211yesmaximal, characteristic
3C2×C31×#393C211yesmaximal, characteristic, complemented
4C2×C31×#391C211yesmaximal, characteristic, complemented
5C2×C31×#388C211yesmaximal, characteristic, complemented
6C2×C31×#386C211yesmaximal, characteristic
7C31×#1442C211yesmaximal, characteristic, complemented
8C31×#1442C211yesmaximal, characteristic, complemented
9C31×#1441C211yesmaximal, characteristic, complemented
10C31×#1440C211yesmaximal, characteristic, complemented
11C31×#1439C211yesmaximal, characteristic, complemented
12C31×#1439C211yesmaximal, characteristic, complemented
13C31×#1438C211yesmaximal, characteristic
14C31×#1437C211yesmaximal, characteristic, complemented
15C31×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×Q8×C31C2211yescharacteristic
17C23×D4×C31C2211yescharacteristic
18C24×C4×C31C2211yescharacteristic
19C2×C31×C22⋊Q8—24no—
20C2×C31×C22⋊Q8—24no—
21C2×C31×C22⋊Q8—24no—
22C22×C4⋊C4×C31C2211yescharacteristic
23C22×C4⋊C4×C31C2211yescharacteristic
24C22×C4⋊C4×C31C2211yescharacteristic
25C22×C4⋊C4×C31C2211yescharacteristic
26C22×C22⋊C4×C31C2211yescharacteristic
27C22×C22⋊C4×C31C2211yescharacteristic
28C22×C22⋊C4×C31C2211yescharacteristic
29C22×C22⋊C4×C31C2211yescharacteristic
30C22×C22⋊C4×C31C2211yescharacteristic
31C22×C22⋊C4×C31C2211yescharacteristic
32C22×C22⋊C4×C31C2211yescharacteristic
33C22×C22⋊C4×C31C2211yescharacteristic
34C22×C22⋊C4×C31C2211yescharacteristic
35C22×C22⋊C4×C31C2211yescharacteristic
36C22×C22⋊C4×C31C2211yescharacteristic
37C22×C42×C31C2211yescharacteristic
38C31×#394—24no—
39C31×#393—24no—
40C31×#391—24no—
41C31×#388—24no—
42C31×#386—24no—
43C2×C31×#95C2211yescharacteristic
44C2×C31×#95C2211yescharacteristic
45C2×C31×#95C2211yescharacteristic
46C2×C31×#95C2211yescharacteristic
47C2×C31×#95C2211yescharacteristic
48C2×C31×#95C2211yescharacteristic
49C2×C31×#95C2211yescharacteristic
50C2×C31×#95C2211yescharacteristic
51C2×C31×#95C2211yescharacteristic
52C2×C31×#95C2211yescharacteristic
53C2×C31×#95C2211yescharacteristic
54C2×C31×#95C2211yescharacteristic
55C2×C31×#95C2211yescharacteristic
56C2×C31×#95C2211yescharacteristic
57C2×C31×#95C2211yescharacteristic
58C2×C31×#95C2211yescharacteristic
59C25×C31C2311yescharacteristic
60C25×C31C2311yescharacteristic
61C22×Q8×C31—22no—
62C22×Q8×C31—22no—
63C22×Q8×C31—22no—
64C22×Q8×C31—22no—
65C22×Q8×C31—41no—
66C22×Q8×C31—41no—
67C22×Q8×C31D414yescomplemented
68C22×D4×C31—22no—
69C22×D4×C31—22no—
70C22×D4×C31—22no—
71C22×D4×C31—22no—
72C22×D4×C31—22no—
73C22×D4×C31—41no—
74C22×D4×C31—41no—
75C23×C4×C31—22no—
76C23×C4×C31—22no—
77C23×C4×C31—22no—
78C23×C4×C31—22no—
79C23×C4×C31—22no—
80C23×C4×C31—41no—
81C23×C4×C31—41no—
82C23×C4×C31C2311yescharacteristic
83C23×C4×C31C2311yescharacteristic
84C23×C4×C31C2311yescharacteristic
85C23×C4×C31C2311yescharacteristic
86C23×C4×C31C2311yescharacteristic
87C23×C4×C31C2311yescharacteristic
88C23×C4×C31C2311yescharacteristic
89C23×C4×C31C2311yescharacteristic
90C23×C4×C31C2311yescharacteristic
91C23×C4×C31C2311yescharacteristic
92C23×C4×C31C2311yescharacteristic
93C23×C4×C31C2311yescharacteristic
94C23×C4×C31C2311yescharacteristic
95C31×C22⋊Q8—232no—
96C2×C4⋊C4×C31—22no—
97C2×C4⋊C4×C31—22no—
98C2×C4⋊C4×C31—22no—
99C2×C4⋊C4×C31—22no—
100C2×C4⋊C4×C31—22no—
101C2×C4⋊C4×C31—22no—
102C2×C4⋊C4×C31—22no—
103C2×C4⋊C4×C31—22no—
104C2×C4⋊C4×C31—22no—
105C2×C4⋊C4×C31—22no—
106C2×C4⋊C4×C31—41no—
107C2×C4⋊C4×C31D414yescomplemented
108C2×C22⋊C4×C31—22no—
109C2×C22⋊C4×C31—22no—
110C2×C22⋊C4×C31—22no—
111C2×C22⋊C4×C31—22no—
112C2×C22⋊C4×C31—22no—
113C2×C22⋊C4×C31—22no—
114C2×C22⋊C4×C31—22no—
115C2×C22⋊C4×C31—22no—
116C2×C22⋊C4×C31—22no—
117C2×C22⋊C4×C31—22no—
118C2×C22⋊C4×C31—22no—
119C2×C22⋊C4×C31—22no—
120C2×C22⋊C4×C31—22no—
121C2×C22⋊C4×C31—22no—
122C2×C22⋊C4×C31—22no—
123C2×C22⋊C4×C31—22no—
124C2×C22⋊C4×C31—22no—
125C2×C22⋊C4×C31—22no—
126C2×C22⋊C4×C31—22no—
127C2×C22⋊C4×C31—22no—
128C2×C22⋊C4×C31—22no—
129C2×C22⋊C4×C31—22no—
130C2×C22⋊C4×C31—22no—
131C2×C22⋊C4×C31—22no—
132C2×C22⋊C4×C31—22no—
133C2×C22⋊C4×C31—22no—
134C2×C22⋊C4×C31—41no—
135C2×C22⋊C4×C31—41no—
136C2×C22⋊C4×C31—41no—
137C2×C22⋊C4×C31—41no—
138C2×C22⋊C4×C31—41no—
139C2×C22⋊C4×C31—41no—
140C2×C22⋊C4×C31D414yes—
141C2×C42×C31—22no—
142C2×C42×C31—22no—
143C2×C42×C31—41no—
144C31×#95—22no—
145C31×#95—22no—
146C31×#95—22no—
147C31×#95—22no—
148C31×#95—22no—
149C31×#95—22no—
150C31×#95—22no—
151C31×#95—22no—
152C31×#95—22no—
153C31×#95—22no—
154C31×#95—22no—
155C31×#95—41no—
156C31×#95—41no—
157C31×#95—41no—
158C31×#95—41no—
159C31×#95D414yes—
160C24×C31—21no—
161C24×C31—21no—
162C24×C31—21no—
163C24×C31—21no—
164C24×C31—21no—
165C24×C31—21no—
166C24×C31—21no—
167C24×C31—21no—
168C24×C31—21no—
169C24×C31—21no—
170C24×C31—21no—
171C24×C31—21no—
172C24×C31—21no—
173C24×C31—21no—
174C24×C31—21no—
175C24×C31—21no—
176C24×C31—21no—
177C24×C31—21no—
178C24×C31—21no—
179C24×C31—21no—
180C24×C31—21no—
181C24×C31—21no—
182C24×C31—21no—
183C24×C31—21no—
184C24×C31—21no—
185C24×C31—21no—
186C24×C31C2×D412yes—
187C24×C31#4112yes—
188C24×C31#4112yes—
189C24×C31#4112yes—
190C24×C31C2411yescharacteristic
191C2×Q8×C31—28no—
192C2×Q8×C31—28no—
193C2×Q8×C31—44no—
194C2×Q8×C31—44no—
195C2×Q8×C31—44no—
196C2×Q8×C31—44no—
197C2×Q8×C31—44no—
198C2×D4×C31—28no—
199C2×D4×C31—44no—
200C2×D4×C31—44no—
201C2×D4×C31—44no—
202C2×D4×C31—44no—
203C2×D4×C31—44no—
204C2×D4×C31—44no—
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—28no—
214C22×C4×C31—21no—
215C22×C4×C31—21no—
216C22×C4×C31—21no—
217C22×C4×C31—21no—
218C22×C4×C31—21no—
219C22×C4×C31—21no—
220C22×C4×C31—21no—
221C22×C4×C31—21no—
222C22×C4×C31—21no—
223C22×C4×C31—21no—
224C22×C4×C31—21no—
225C22×C4×C31—21no—
226C22×C4×C31—21no—
227C22×C4×C31—21no—
228C22×C4×C31—21no—
229C22×C4×C31—21no—
230C22×C4×C31—21no—
231C22×C4×C31—21no—
232C22×C4×C31—21no—
233C22×C4×C31—21no—
234C22×C4×C31—21no—
235C22×C4×C31—21no—
236C22×C4×C31—21no—
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—21no—
248C22×C4×C31—21no—
249C22×C4×C31—21no—
250C22×C4×C31—21no—
251C22×C4×C31—21no—
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—21no—
263C22×C4×C31—21no—
264C22×C4×C31—21no—
265C22×C4×C31—21no—
266C22×C4×C31—21no—
267C22×C4×C31—21no—
268C22×C4×C31—21no—
269C22×C4×C31—21no—
270C22×C4×C31—21no—
271C22×C4×C31—21no—
272C22×C4×C31—21no—
273C22×C4×C31—21no—
274C22×C4×C31—21no—
275C22×C4×C31—21no—
276C22×C4×C31—21no—
277C22×C4×C31—21no—
278C22×C4×C31—21no—
279C22×C4×C31—21no—
280C22×C4×C31—21no—
281C22×C4×C31—21no—
282C22×C4×C31—21no—
283C22×C4×C31—21no—
284C22×C4×C31—44no—
285C22×C4×C31—44no—
286C22×C4×C31—44no—
287C22×C4×C31—44no—
288C22×C4×C31—44no—
289C22×C4×C31—44no—
290C22×C4×C31C2×D412yes—
291C22×C4×C31C2×D412yes—
292C22×C4×C31C2×D412yes—
293C22×C4×C31C2×D412yes—
294C22×C4×C31C2×D412yes—
295C22×C4×C31C2×D412yes—
296C22×C4×C31C2×D412yes—
297C22×C4×C31C2×D412yes—
298C22×C4×C31C2×D412yes—
299C22×C4×C31C2×D412yes—
300C22×C4×C31C2×D412yes—
301C22×C4×C31#4112yes—
302C22×C4×C31#4112yes—
303C4⋊C4×C31—28no—
304C4⋊C4×C31—28no—
305C4⋊C4×C31—28no—
306C4⋊C4×C31—44no—
307C22⋊C4×C31—28no—
308C22⋊C4×C31—28no—
309C22⋊C4×C31—28no—
310C22⋊C4×C31—44no—
311C22⋊C4×C31—44no—
312C22⋊C4×C31—44no—
313C22⋊C4×C31—44no—
314C22⋊C4×C31—44no—
315C22⋊C4×C31—44no—
316C22⋊C4×C31—44no—
317C22⋊C4×C31—44no—
318C42×C31—44no—
319#15275C3111yesmaximal, characteristic, direct product factor, Sylow
320C23×C31—22no—
321C23×C31—22no—
322C23×C31—22no—
323C23×C31—22no—
324C23×C31—22no—
325C23×C31—22no—
326C23×C31—22no—
327C23×C31—22no—
328C23×C31—22no—
329C23×C31—22no—
330C23×C31—22no—
331C23×C31—22no—
332C23×C31—22no—
333C23×C31—22no—
334C23×C31—22no—
335C23×C31—22no—
336C23×C31—22no—
337C23×C31—22no—
338C23×C31—22no—
339C23×C31—22no—
340C23×C31—22no—
341C23×C31—22no—
342C23×C31—22no—
343C23×C31—22no—
344C23×C31—22no—
345C23×C31—41no—
346C23×C31—41no—
347C23×C31—41no—
348C23×C31—41no—
349C23×C31—41no—
350C23×C31—41no—
351C23×C31—41no—
352C23×C31—41no—
353C23×C31—41no—
354C23×C31—41no—
355C23×C31—41no—
356C23×C31—41no—
357C23×C31—41no—
358C23×C31—41no—
359C23×C31—41no—
360C23×C31—41no—
361C23×C31—41no—
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—41no—
372C23×C31—41no—
373C23×C31—41no—
374C23×C31—41no—
375C23×C31—41no—
376C23×C31—41no—
377C23×C31—41no—
378C23×C31—41no—
379C23×C31—41no—
380C23×C31—41no—
381C23×C31—41no—
382C23×C31—41no—
383C23×C31—41no—
384C23×C31—41no—
385C23×C31—41no—
386C23×C31—41no—
387C23×C31—41no—
388C23×C31—41no—
389C23×C31#12414yes—
390C23×C31C22×D411yescharacteristic
391C23×C31C22×D411yescharacteristic
392C23×C31C22×D411yescharacteristic
393C23×C31C22×D411yescharacteristic
394C23×C31C2×#4111yescharacteristic
395C23×C31C2×#4111yescharacteristic
396C23×C31C2×#4111yescharacteristic
397C23×C31C2×#4111yescharacteristic
398C23×C31C2×#4111yescharacteristic
399C23×C31H(5,𝔽2)11yescharacteristic
400C23×C31H(5,𝔽2)11yescharacteristic
401C23×C31H(5,𝔽2)11yescharacteristic
402C23×C312−1+411yescharacteristic
403C23×C312−1+411yescharacteristic
404C23×C312−1+411yescharacteristic
405Q8×C31—416no—
406D4×C31—416no—
407C2×C4×C31—22no—
408C2×C4×C31—22no—
409C2×C4×C31—22no—
410C2×C4×C31—22no—
411C2×C4×C31—22no—
412C2×C4×C31—22no—
413C2×C4×C31—22no—
414C2×C4×C31—22no—
415C2×C4×C31—22no—
416C2×C4×C31—22no—
417C2×C4×C31—22no—
418C2×C4×C31—22no—
419C2×C4×C31—22no—
420C2×C4×C31—22no—
421C2×C4×C31—22no—
422C2×C4×C31—22no—
423C2×C4×C31—22no—
424C2×C4×C31—22no—
425C2×C4×C31—22no—
426C2×C4×C31—22no—
427C2×C4×C31—22no—
428C2×C4×C31—22no—
429C2×C4×C31—22no—
430C2×C4×C31—22no—
431C2×C4×C31—22no—
432C2×C4×C31—22no—
433C2×C4×C31—22no—
434C2×C4×C31—22no—
435C2×C4×C31—22no—
436C2×C4×C31—22no—
437C2×C4×C31—22no—
438C2×C4×C31—22no—
439C2×C4×C31—22no—
440C2×C4×C31—416no—
441C2×C4×C31—41no—
442C2×C4×C31—41no—
443C2×C4×C31—41no—
444C2×C4×C31—41no—
445C2×C4×C31—41no—
446C2×C4×C31—41no—
447C2×C4×C31—41no—
448C2×C4×C31—41no—
449C2×C4×C31—41no—
450C2×C4×C31—41no—
451C2×C4×C31—41no—
452C2×C4×C31—41no—
453C2×C4×C31—41no—
454C2×C4×C31—41no—
455C2×C4×C31—41no—
456C2×C4×C31—41no—
457C2×C4×C31—41no—
458C2×C4×C31—41no—
459C2×C4×C31—41no—
460C2×C4×C31—41no—
461C2×C4×C31—41no—
462C2×C4×C31—41no—
463C2×C4×C31—41no—
464C2×C4×C31—41no—
465C2×C4×C31—41no—
466C2×C4×C31—41no—
467C2×C4×C31—41no—
468C2×C4×C31—41no—
469C2×C4×C31—41no—
470C2×C4×C31—41no—
471C2×C4×C31—41no—
472C2×C4×C31—41no—
473C2×C4×C31—41no—
474C2×C4×C31—41no—
475C2×C4×C31—41no—
476C2×C4×C31—41no—
477C2×C4×C31—41no—
478C2×C4×C31—41no—
479C2×C4×C31—41no—
480C2×C4×C31—41no—
481C2×C4×C31—41no—
482C2×C4×C31—41no—
483C2×C4×C31—41no—
484C2×C4×C31—41no—
485C2×C4×C31—41no—
486C2×C4×C31—41no—
487C2×C4×C31—41no—
488C2×C4×C31—41no—
489C2×C4×C31—41no—
490C2×C4×C31—41no—
491C2×C4×C31—41no—
492C2×C4×C31—41no—
493C2×C4×C31—41no—
494C2×C4×C31—41no—
495C2×C4×C31—41no—
496C2×C4×C31—41no—
497C2×C4×C31#12014yes—
498C2×C4×C31#12114yes—
499C22×C22⋊Q8C2×C3111yescharacteristic, complemented
500C2×#394C2×C3111yescharacteristic
501C2×#393C2×C3111yescharacteristic, complemented
502C2×#391C2×C3111yescharacteristic, complemented
503C2×#388C2×C3111yescharacteristic, complemented
504C2×#386C2×C3111yescharacteristic
505#1442C2×C3111yescharacteristic, complemented
506#1442C2×C3111yescharacteristic, complemented
507#1441C2×C3111yescharacteristic, complemented
508#1440C2×C3111yescharacteristic, complemented
509#1439C2×C3111yescharacteristic, complemented
510#1439C2×C3111yescharacteristic, complemented
511#1438C2×C3111yescharacteristic
512#1437C2×C3111yescharacteristic, complemented
513C22⋊#95C2×C3111yescharacteristic, complemented
514C22×C31—24no—
515C22×C31—24no—
516C22×C31—24no—
517C22×C31—42no—
518C22×C31—42no—
519C22×C31—42no—
520C22×C31—42no—
521C22×C31—42no—
522C22×C31—42no—
523C22×C31—42no—
524C22×C31—42no—
525C22×C31—42no—
526C22×C31—42no—
527C22×C31—42no—
528C22×C31—42no—
529C22×C31—42no—
530C22×C31—42no—
531C22×C31—42no—
532C22×C31—42no—
533C22×C31—42no—
534C22×C31—42no—
535C22×C31—42no—
536C22×C31—81no—
537C22×C31—81no—
538C22×C31—81no—
539C22×C31—81no—
540C22×C31—81no—
541C22×C31—81no—
542C22×C31—81no—
543C22×C31—81no—
544C22×C31C2×#12011yescharacteristic
545C22×C31C2×#12111yescharacteristic
546C22×C31#52511yescharacteristic
547C22×C31#52511yescharacteristic
548C22×C31C2×#12411yescharacteristic
549C22×C31#52911yescharacteristic
550C22×C31#53411yescharacteristic
551C22×C31#53611yescharacteristic
552C22×C31#53611yescharacteristic
553C22×C31#53711yescharacteristic
554C22×C31#53811yescharacteristic
555C22×C31#53911yescharacteristic
556C22×C31#53911yescharacteristic
557C22×C31#54211yescharacteristic
558C22×C31#54211yescharacteristic
559C22×C31D4211yescharacteristic
560C22×C31D4211yescharacteristic
561C22×C31#54611yescharacteristic
562C22×C31#54611yescharacteristic
563C22×C31#54611yescharacteristic
564C22×C31#54611yescharacteristic
565C22×C31#54711yescharacteristic
566C22×C31#54811yescharacteristic
567C22×C31#54811yescharacteristic
568C22×C31#54811yescharacteristic
569C22×C31#54811yescharacteristic
570C22×C31#54811yescharacteristic
571C22×C31#54811yescharacteristic
572C22×C31#55011yescharacteristic
573C22×C31#55111yescharacteristic
574C22×C31#55111yescharacteristic
575C22×C31#55211yescharacteristic
576C22×C31#55211yescharacteristic
577C22×C31#56211yescharacteristic
578C22×C31#56311yescharacteristic
579C4×C31—24no—
580C4×C31—24no—
581C4×C31—42no—
582C4×C31—42no—
583C4×C31—42no—
584C4×C31—42no—
585C4×C31—42no—
586C4×C31—42no—
587C4×C31—42no—
588C4×C31—81no—
589C4×C31—81no—
590C4×C31—81no—
591C4×C31—81no—
592C23×Q8C22×C3111yescharacteristic
593C23×D4C22×C3111yescharacteristic
594C24×C4C22×C3111yescharacteristic
595C2×C22⋊Q8—24no—
596C2×C22⋊Q8—24no—
597C2×C22⋊Q8—24no—
598C22×C4⋊C4C22×C3111yescharacteristic
599C22×C4⋊C4C22×C3111yescharacteristic
600C22×C4⋊C4C22×C3111yescharacteristic
601C22×C4⋊C4C22×C3111yescharacteristic
602C22×C22⋊C4C22×C3111yescharacteristic
603C22×C22⋊C4C22×C3111yescharacteristic
604C22×C22⋊C4C22×C3111yescharacteristic
605C22×C22⋊C4C22×C3111yescharacteristic
606C22×C22⋊C4C22×C3111yescharacteristic
607C22×C22⋊C4C22×C3111yescharacteristic
608C22×C22⋊C4C22×C3111yescharacteristic
609C22×C22⋊C4C22×C3111yescharacteristic
610C22×C22⋊C4C22×C3111yescharacteristic
611C22×C22⋊C4C22×C3111yescharacteristic
612C22×C22⋊C4C22×C3111yescharacteristic
613C22×C42C22×C3111yescharacteristic
614#394—24no—
615#393—24no—
616#391—24no—
617#388—24no—
618#386—24no—
619C2×#95C22×C3111yescharacteristic
620C2×#95C22×C3111yescharacteristic
621C2×#95C22×C3111yescharacteristic
622C2×#95C22×C3111yescharacteristic
623C2×#95C22×C3111yescharacteristic
624C2×#95C22×C3111yescharacteristic
625C2×#95C22×C3111yescharacteristic
626C2×#95C22×C3111yescharacteristic
627C2×#95C22×C3111yescharacteristic
628C2×#95C22×C3111yescharacteristic
629C2×#95C22×C3111yescharacteristic
630C2×#95C22×C3111yescharacteristic
631C2×#95C22×C3111yescharacteristic
632C2×#95C22×C3111yescharacteristic
633C2×#95C22×C3111yescharacteristic
634C2×#95C22×C3111yescharacteristic
635C2×C31—44no—
636C2×C31—82no—
637C2×C31#240711yescharacteristic
638C2×C31#241011yescharacteristic
639C2×C31#242611yescharacteristic
640C2×C31#243611yescharacteristic
641C2×C31#246311yescharacteristic
642C2×C31#247211yescharacteristic
643C2×C31#247711yescharacteristic
644C2×C31#248811yescharacteristic
645C2×C31#253611yescharacteristic
646C2×C31#267411yescharacteristic
647C2×C31#268111yescharacteristic
648C2×C31#268711yescharacteristic
649C2×C31#270211yescharacteristic
650C2×C31#272811yescharacteristic
651C2×C31#273011yescharacteristic
652C25C23×C3111yescharacteristic
653C25C23×C3111yescharacteristic
654C22×Q8—22no—
655C22×Q8—22no—
656C22×Q8—22no—
657C22×Q8—22no—
658C22×Q8—41no—
659C22×Q8—41no—
660C22×Q8D4×C3114yescomplemented
661C22×D4—22no—
662C22×D4—22no—
663C22×D4—22no—
664C22×D4—22no—
665C22×D4—22no—
666C22×D4—41no—
667C22×D4—41no—
668C23×C4—22no—
669C23×C4—22no—
670C23×C4—22no—
671C23×C4—22no—
672C23×C4—22no—
673C23×C4—41no—
674C23×C4—41no—
675C23×C4C23×C3111yescharacteristic
676C23×C4C23×C3111yescharacteristic
677C23×C4C23×C3111yescharacteristic
678C23×C4C23×C3111yescharacteristic
679C23×C4C23×C3111yescharacteristic
680C23×C4C23×C3111yescharacteristic
681C23×C4C23×C3111yescharacteristic
682C23×C4C23×C3111yescharacteristic
683C23×C4C23×C3111yescharacteristic
684C23×C4C23×C3111yescharacteristic
685C23×C4C23×C3111yescharacteristic
686C23×C4C23×C3111yescharacteristic
687C23×C4C23×C3111yescharacteristic
688C22⋊Q8—232no—
689C2×C4⋊C4—22no—
690C2×C4⋊C4—22no—
691C2×C4⋊C4—22no—
692C2×C4⋊C4—22no—
693C2×C4⋊C4—22no—
694C2×C4⋊C4—22no—
695C2×C4⋊C4—22no—
696C2×C4⋊C4—22no—
697C2×C4⋊C4—22no—
698C2×C4⋊C4—22no—
699C2×C4⋊C4—41no—
700C2×C4⋊C4D4×C3114yescomplemented
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4—22no—
715C2×C22⋊C4—22no—
716C2×C22⋊C4—22no—
717C2×C22⋊C4—22no—
718C2×C22⋊C4—22no—
719C2×C22⋊C4—22no—
720C2×C22⋊C4—22no—
721C2×C22⋊C4—22no—
722C2×C22⋊C4—22no—
723C2×C22⋊C4—22no—
724C2×C22⋊C4—22no—
725C2×C22⋊C4—22no—
726C2×C22⋊C4—22no—
727C2×C22⋊C4—41no—
728C2×C22⋊C4—41no—
729C2×C22⋊C4—41no—
730C2×C22⋊C4—41no—
731C2×C22⋊C4—41no—
732C2×C22⋊C4—41no—
733C2×C22⋊C4D4×C3114yes—
734C2×C42—22no—
735C2×C42—22no—
736C2×C42—41no—
737#95—22no—
738#95—22no—
739#95—22no—
740#95—22no—
741#95—22no—
742#95—22no—
743#95—22no—
744#95—22no—
745#95—22no—
746#95—22no—
747#95—22no—
748#95—41no—
749#95—41no—
750#95—41no—
751#95—41no—
752#95D4×C3114yes—
753C31#1527511yescharacteristic, direct product factor, Sylow
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—21no—
778C24—21no—
779C24—21no—
780C24C2×D4×C3112yes—
781C24#41×C3112yes—
782C24#41×C3112yes—
783C24#41×C3112yes—
784C24C24×C3111yescharacteristic
785C2×Q8—28no—
786C2×Q8—28no—
787C2×Q8—44no—
788C2×Q8—44no—
789C2×Q8—44no—
790C2×Q8—44no—
791C2×Q8—44no—
792C2×D4—28no—
793C2×D4—44no—
794C2×D4—44no—
795C2×D4—44no—
796C2×D4—44no—
797C2×D4—44no—
798C2×D4—44no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—28no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
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—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—44no—
879C22×C4—44no—
880C22×C4—44no—
881C22×C4—44no—
882C22×C4—44no—
883C22×C4—44no—
884C22×C4C2×D4×C3112yes—
885C22×C4C2×D4×C3112yes—
886C22×C4C2×D4×C3112yes—
887C22×C4C2×D4×C3112yes—
888C22×C4C2×D4×C3112yes—
889C22×C4C2×D4×C3112yes—
890C22×C4C2×D4×C3112yes—
891C22×C4C2×D4×C3112yes—
892C22×C4C2×D4×C3112yes—
893C22×C4C2×D4×C3112yes—
894C22×C4C2×D4×C3112yes—
895C22×C4#41×C3112yes—
896C22×C4#41×C3112yes—
897C4⋊C4—28no—
898C4⋊C4—28no—
899C4⋊C4—28no—
900C4⋊C4—44no—
901C22⋊C4—28no—
902C22⋊C4—28no—
903C22⋊C4—28no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C22⋊C4—44no—
907C22⋊C4—44no—
908C22⋊C4—44no—
909C22⋊C4—44no—
910C22⋊C4—44no—
911C22⋊C4—44no—
912C42—44no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23C31×#12414yes—
983C23C22×D4×C3111yescharacteristic
984C23C22×D4×C3111yescharacteristic
985C23C22×D4×C3111yescharacteristic
986C23C22×D4×C3111yescharacteristic
987C23C2×#41×C3111yescharacteristic
988C23C2×#41×C3111yescharacteristic
989C23C2×#41×C3111yescharacteristic
990C23C2×#41×C3111yescharacteristic
991C23C2×#41×C3111yescharacteristic
992C23C31×H(5,𝔽2)11yescharacteristic
993C23C31×H(5,𝔽2)11yescharacteristic
994C23C31×H(5,𝔽2)11yescharacteristic
995C23C31×2−1+411yescharacteristic
996C23C31×2−1+411yescharacteristic
997C23C31×2−1+411yescharacteristic
998Q8—416no—
999D4—416no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—416no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4C31×#12014yes—
1091C2×C4C31×#12114yes—
1092C22—24no—
1093C22—24no—
1094C22—24no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—81no—
1115C22—81no—
1116C22—81no—
1117C22—81no—
1118C22—81no—
1119C22—81no—
1120C22—81no—
1121C22—81no—
1122C22C2×C31×#12011yescharacteristic
1123C22C2×C31×#12111yescharacteristic
1124C22C31×#52511yescharacteristic
1125C22C31×#52511yescharacteristic
1126C22C2×C31×#12411yescharacteristic
1127C22C31×#52911yescharacteristic
1128C22C31×#53411yescharacteristic
1129C22C31×#53611yescharacteristic
1130C22C31×#53611yescharacteristic
1131C22C31×#53711yescharacteristic
1132C22C31×#53811yescharacteristic
1133C22C31×#53911yescharacteristic
1134C22C31×#53911yescharacteristic
1135C22C31×#54211yescharacteristic
1136C22C31×#54211yescharacteristic
1137C22D42×C3111yescharacteristic
1138C22D42×C3111yescharacteristic
1139C22C31×#54611yescharacteristic
1140C22C31×#54611yescharacteristic
1141C22C31×#54611yescharacteristic
1142C22C31×#54611yescharacteristic
1143C22C31×#54711yescharacteristic
1144C22C31×#54811yescharacteristic
1145C22C31×#54811yescharacteristic
1146C22C31×#54811yescharacteristic
1147C22C31×#54811yescharacteristic
1148C22C31×#54811yescharacteristic
1149C22C31×#54811yescharacteristic
1150C22C31×#55011yescharacteristic
1151C22C31×#55111yescharacteristic
1152C22C31×#55111yescharacteristic
1153C22C31×#55211yescharacteristic
1154C22C31×#55211yescharacteristic
1155C22C31×#56211yescharacteristic
1156C22C31×#56311yescharacteristic
1157C4—24no—
1158C4—24no—
1159C4—42no—
1160C4—42no—
1161C4—42no—
1162C4—42no—
1163C4—42no—
1164C4—42no—
1165C4—42no—
1166C4—81no—
1167C4—81no—
1168C4—81no—
1169C4—81no—
1170C2—44no—
1171C2—82no—
1172C2C31×#240711yescharacteristic
1173C2C31×#241011yescharacteristic
1174C2C31×#242611yescharacteristic
1175C2C31×#243611yescharacteristic
1176C2C31×#246311yescharacteristic
1177C2C31×#247211yescharacteristic
1178C2C31×#247711yescharacteristic
1179C2C31×#248811yescharacteristic
1180C2C31×#253611yescharacteristic
1181C2C31×#267411yescharacteristic
1182C2C31×#268111yescharacteristic
1183C2C31×#268711yescharacteristic
1184C2C31×#270211yescharacteristic
1185C2C31×#272811yescharacteristic
1186C2C31×#273011yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
prime radicalC23×D4×C31C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C31×C22⋊Q8C2semidirect
3. C2×C31×#393C2semidirect
4. C2×C31×#391C2semidirect
5. C2×C31×#388C2semidirect
7. C31×#1442C2semidirect
8. C31×#1442C2semidirect
9. C31×#1441C2semidirect
10. C31×#1440C2semidirect
11. C31×#1439C2semidirect
12. C31×#1439C2semidirect
14. C31×#1437C2semidirect
15. C31×C22⋊#95C2semidirect
67. C22×Q8×C31D4semidirect
107. C2×C4⋊C4×C31D4semidirect
319. #15275C31direct (N × H)
499. C22×C22⋊Q8C2×C31semidirect
501. C2×#393C2×C31semidirect
502. C2×#391C2×C31semidirect
503. C2×#388C2×C31semidirect
505. #1442C2×C31semidirect
506. #1442C2×C31semidirect
507. #1441C2×C31semidirect
508. #1440C2×C31semidirect
509. #1439C2×C31semidirect
510. #1439C2×C31semidirect
512. #1437C2×C31semidirect
513. C22⋊#95C2×C31semidirect
660. C22×Q8D4×C31semidirect
700. C2×C4⋊C4D4×C31semidirect
753. C31#15275direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×C22⋊Q82
C2×C31×#3942
C2×C31×#3932
C2×C31×#3912
C2×C31×#3882
C2×C31×#3862
C31×#14422
C31×#14412
C31×#14402
C31×#14392
C31×#14382
C31×#14372
C31×C22⋊#952
#1527531