Finite Group Databasebeta

← C31×#14036 #21470795

Subgroups — C31×#14036 #21470795

Order 7936.

2062 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#390C211yesmaximal, characteristic
2C2×C31×#388C211yesmaximal, characteristic, complemented
3C2×C31×#388C211yesmaximal, characteristic, complemented
4C2×C31×#386C211yesmaximal, characteristic
5C2×C31×#385C211yesmaximal, characteristic, complemented
6C2×C4×C4⋊C4×C31C211yesmaximal, characteristic, complemented
7C2×C4×C22⋊C4×C31C211yesmaximal, characteristic, complemented
8C31×#1441C211yesmaximal, characteristic, complemented
9C31×#1439C211yesmaximal, characteristic, complemented
10C31×#1439C211yesmaximal, characteristic, complemented
11C31×#1438C211yesmaximal, characteristic
12C31×#1437C211yesmaximal, characteristic, complemented
13C31×#1437C211yesmaximal, characteristic, complemented
14C31×#1436C211yesmaximal, characteristic, complemented
15C31×#1434C211yesmaximal, characteristic, complemented
16C23×D4×C31C2211yescharacteristic
17C24×C4×C31C2211yescharacteristic
18C22×C4⋊C4×C31C2211yescharacteristic
19C22×C4⋊C4×C31C2211yescharacteristic
20C22×C4⋊C4×C31C2211yescharacteristic
21C22×C4⋊C4×C31C2211yescharacteristic
22C22×C22⋊C4×C31C2211yescharacteristic
23C22×C22⋊C4×C31C2211yescharacteristic
24C22×C22⋊C4×C31C2211yescharacteristic
25C22×C22⋊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×C42×C31C2211yescharacteristic
34C22×C42×C31C2211yescharacteristic
35C22×C42×C31C2211yescharacteristic
36C22×C42×C31C2211yescharacteristic
37C31×#390C418yescomplemented
38C31×#388—24no—
39C31×#388—24no—
40C31×#386—24no—
41C31×#385—24no—
42C4×C4⋊C4×C31—24no—
43C4×C22⋊C4×C31—24no—
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
58C25×C31C2311yescharacteristic
59C25×C31C2311yescharacteristic
60C22×D4×C31—22no—
61C22×D4×C31—22no—
62C22×D4×C31—22no—
63C22×D4×C31—22no—
64C22×D4×C31—41no—
65C22×D4×C31—41no—
66C22×D4×C31C2×C414yes—
67C23×C4×C31—22no—
68C23×C4×C31—22no—
69C23×C4×C31—22no—
70C23×C4×C31—22no—
71C23×C4×C31—22no—
72C23×C4×C31—41no—
73C23×C4×C31—41no—
74C23×C4×C31C2311yescharacteristic
75C23×C4×C31C2311yescharacteristic
76C23×C4×C31C2311yescharacteristic
77C23×C4×C31C2311yescharacteristic
78C23×C4×C31C2311yescharacteristic
79C23×C4×C31C2311yescharacteristic
80C23×C4×C31C2311yescharacteristic
81C23×C4×C31C2311yescharacteristic
82C23×C4×C31C2311yescharacteristic
83C23×C4×C31C2311yescharacteristic
84C23×C4×C31C2311yescharacteristic
85C23×C4×C31C2311yescharacteristic
86C23×C4×C31C2311yescharacteristic
87C2×C4⋊C4×C31—22no—
88C2×C4⋊C4×C31—22no—
89C2×C4⋊C4×C31—22no—
90C2×C4⋊C4×C31—22no—
91C2×C4⋊C4×C31—22no—
92C2×C4⋊C4×C31—22no—
93C2×C4⋊C4×C31—22no—
94C2×C4⋊C4×C31—41no—
95C2×C4⋊C4×C31—41no—
96C2×C4⋊C4×C31—41no—
97C2×C4⋊C4×C31C2×C414yescomplemented
98C2×C4⋊C4×C31D414yescomplemented
99C2×C22⋊C4×C31—22no—
100C2×C22⋊C4×C31—22no—
101C2×C22⋊C4×C31—22no—
102C2×C22⋊C4×C31—22no—
103C2×C22⋊C4×C31—22no—
104C2×C22⋊C4×C31—22no—
105C2×C22⋊C4×C31—22no—
106C2×C22⋊C4×C31—22no—
107C2×C22⋊C4×C31—22no—
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—41no—
123C2×C22⋊C4×C31—41no—
124C2×C22⋊C4×C31—41no—
125C2×C22⋊C4×C31—41no—
126C2×C22⋊C4×C31—41no—
127C2×C22⋊C4×C31—41no—
128C2×C22⋊C4×C31C2×C414yes—
129C2×C22⋊C4×C31C2×C414yes—
130C2×C22⋊C4×C31C2×C414yescomplemented
131C2×C22⋊C4×C31C2×C414yescomplemented
132C2×C42×C31—22no—
133C2×C42×C31—22no—
134C2×C42×C31—22no—
135C2×C42×C31—22no—
136C2×C42×C31—22no—
137C2×C42×C31—22no—
138C2×C42×C31—22no—
139C2×C42×C31—22no—
140C2×C42×C31—41no—
141C2×C42×C31—41no—
142C2×C42×C31—41no—
143C2×C42×C31C2×C414yescomplemented
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—41no—
155C31×#95—41no—
156C31×#95D414yes—
157C31×#95D414yescomplemented
158C24×C31—21no—
159C24×C31—21no—
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×C31C22×C412yes—
185C24×C31C22×C412yes—
186C24×C31#4112yes—
187C24×C31#4112yes—
188C24×C31C2411yescharacteristic
189C2×D4×C31—28no—
190C2×D4×C31—28no—
191C2×D4×C31—44no—
192C2×D4×C31—44no—
193C2×D4×C31—44no—
194C2×D4×C31—44no—
195C2×D4×C31—44no—
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—21no—
207C22×C4×C31—21no—
208C22×C4×C31—21no—
209C22×C4×C31—21no—
210C22×C4×C31—21no—
211C22×C4×C31—21no—
212C22×C4×C31—28no—
213C22×C4×C31—21no—
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—44no—
270C22×C4×C31—44no—
271C22×C4×C31—44no—
272C22×C4×C31—44no—
273C22×C4×C31—44no—
274C22×C4×C31—44no—
275C22×C4×C31C22×C412yes—
276C22×C4×C31C22×C412yes—
277C22×C4×C31C22×C412yes—
278C22×C4×C31C22×C412yes—
279C22×C4×C31C22×C412yes—
280C22×C4×C31C2×D412yes—
281C22×C4×C31C2×D412yes—
282C22×C4×C31C2×D412yes—
283C22×C4×C31C2×D412yes—
284C22×C4×C31C2×D412yes—
285C22×C4×C31C2×D412yes—
286C22×C4×C31C2×D412yes—
287C22×C4×C31C2×D412yes—
288C22×C4×C31C2×D412yes—
289C22×C4×C31#4112yes—
290C22×C4×C31#4112yes—
291C22×C4×C31#4112yes—
292C22×C4×C31#4112yes—
293C22×C4×C31#4112yes—
294C4⋊C4×C31—28no—
295C4⋊C4×C31—28no—
296C4⋊C4×C31—44no—
297C4⋊C4×C31—44no—
298C22⋊C4×C31—28no—
299C22⋊C4×C31—28no—
300C22⋊C4×C31—28no—
301C22⋊C4×C31—28no—
302C22⋊C4×C31—28no—
303C22⋊C4×C31—44no—
304C22⋊C4×C31—44no—
305C22⋊C4×C31—44no—
306C22⋊C4×C31—44no—
307C22⋊C4×C31—44no—
308C22⋊C4×C31—44no—
309C42×C31—28no—
310C42×C31—44no—
311C42×C31—44no—
312C42×C31—44no—
313#14036C3111yesmaximal, characteristic, direct product factor, Sylow
314C23×C31—22no—
315C23×C31—22no—
316C23×C31—22no—
317C23×C31—22no—
318C23×C31—22no—
319C23×C31—22no—
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—41no—
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—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#11714yes—
384C23×C31C23×C411yescharacteristic
385C23×C31C22×D411yescharacteristic
386C23×C31C22×D411yescharacteristic
387C23×C31C22×D411yescharacteristic
388C23×C31C2×#4111yescharacteristic
389C23×C31C2×#4111yescharacteristic
390C23×C31C2×#4111yescharacteristic
391C23×C31C2×#4111yescharacteristic
392C23×C31C2×#4111yescharacteristic
393C23×C31C2×#4111yescharacteristic
394C23×C31C2×#4111yescharacteristic
395C23×C31H(5,𝔽2)11yescharacteristic
396C23×C31H(5,𝔽2)11yescharacteristic
397C23×C31H(5,𝔽2)11yescharacteristic
398C23×C312−1+411yescharacteristic
399D4×C31—416no—
400C2×C4×C31—22no—
401C2×C4×C31—22no—
402C2×C4×C31—22no—
403C2×C4×C31—22no—
404C2×C4×C31—22no—
405C2×C4×C31—22no—
406C2×C4×C31—22no—
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—22no—
441C2×C4×C31—22no—
442C2×C4×C31—22no—
443C2×C4×C31—22no—
444C2×C4×C31—22no—
445C2×C4×C31—416no—
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×C31C4×D414yes—
489C2×C4×C31C4×D414yes—
490C2×C4×C31C4×D414yes—
491C2×C4×C31#12114yes—
492C2×#390C2×C3111yescharacteristic
493C2×#388C2×C3111yescharacteristic, complemented
494C2×#388C2×C3111yescharacteristic, complemented
495C2×#386C2×C3111yescharacteristic
496C2×#385C2×C3111yescharacteristic, complemented
497C2×C4×C4⋊C4C2×C3111yescharacteristic, complemented
498C2×C4×C22⋊C4C2×C3111yescharacteristic, complemented
499#1441C2×C3111yescharacteristic, complemented
500#1439C2×C3111yescharacteristic, complemented
501#1439C2×C3111yescharacteristic, complemented
502#1438C2×C3111yescharacteristic
503#1437C2×C3111yescharacteristic, complemented
504#1437C2×C3111yescharacteristic, complemented
505#1436C2×C3111yescharacteristic, complemented
506#1434C2×C3111yescharacteristic, complemented
507C22×C31—24no—
508C22×C31—24no—
509C22×C31—24no—
510C22×C31—42no—
511C22×C31—42no—
512C22×C31—42no—
513C22×C31—42no—
514C22×C31—42no—
515C22×C31—42no—
516C22×C31—42no—
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—81no—
530C22×C31—81no—
531C22×C31—81no—
532C22×C31—81no—
533C22×C31—81no—
534C22×C31—81no—
535C22×C31—81no—
536C22×C31—81no—
537C22×C31C2×#11711yescharacteristic
538C22×C31C2×C4×D411yescharacteristic
539C22×C31C2×C4×D411yescharacteristic
540C22×C31C2×C4×D411yescharacteristic
541C22×C31C4×#4111yescharacteristic
542C22×C31#51811yescharacteristic
543C22×C31#52011yescharacteristic
544C22×C31C2×#12111yescharacteristic
545C22×C31#52511yescharacteristic
546C22×C31#52511yescharacteristic
547C22×C31#52511yescharacteristic
548C22×C31#52911yescharacteristic
549C22×C31#52911yescharacteristic
550C22×C31#52911yescharacteristic
551C22×C31#53211yescharacteristic
552C22×C31#53811yescharacteristic
553C22×C31#53811yescharacteristic
554C22×C31#54211yescharacteristic
555C22×C31#54211yescharacteristic
556C22×C31D4211yescharacteristic
557C22×C31D4211yescharacteristic
558C22×C31#54611yescharacteristic
559C22×C31#54611yescharacteristic
560C22×C31#54611yescharacteristic
561C22×C31#54711yescharacteristic
562C22×C31#54811yescharacteristic
563C22×C31#54811yescharacteristic
564C22×C31#55011yescharacteristic
565C22×C31#55011yescharacteristic
566C22×C31#55111yescharacteristic
567C22×C31#55111yescharacteristic
568C22×C31#55211yescharacteristic
569C22×C31#55311yescharacteristic
570C22×C31#55311yescharacteristic
571C22×C31#55911yescharacteristic
572C4×C31—24no—
573C4×C31—24no—
574C4×C31—24no—
575C4×C31—24no—
576C4×C31—42no—
577C4×C31—42no—
578C4×C31—42no—
579C4×C31—42no—
580C4×C31—42no—
581C4×C31—42no—
582C4×C31—42no—
583C4×C31—81no—
584C4×C31—81no—
585C23×D4C22×C3111yescharacteristic
586C24×C4C22×C3111yescharacteristic
587C22×C4⋊C4C22×C3111yescharacteristic
588C22×C4⋊C4C22×C3111yescharacteristic
589C22×C4⋊C4C22×C3111yescharacteristic
590C22×C4⋊C4C22×C3111yescharacteristic
591C22×C22⋊C4C22×C3111yescharacteristic
592C22×C22⋊C4C22×C3111yescharacteristic
593C22×C22⋊C4C22×C3111yescharacteristic
594C22×C22⋊C4C22×C3111yescharacteristic
595C22×C22⋊C4C22×C3111yescharacteristic
596C22×C22⋊C4C22×C3111yescharacteristic
597C22×C22⋊C4C22×C3111yescharacteristic
598C22×C22⋊C4C22×C3111yescharacteristic
599C22×C22⋊C4C22×C3111yescharacteristic
600C22×C22⋊C4C22×C3111yescharacteristic
601C22×C22⋊C4C22×C3111yescharacteristic
602C22×C42C22×C3111yescharacteristic
603C22×C42C22×C3111yescharacteristic
604C22×C42C22×C3111yescharacteristic
605C22×C42C22×C3111yescharacteristic
606#390C4×C3118yescomplemented
607#388—24no—
608#388—24no—
609#386—24no—
610#385—24no—
611C4×C4⋊C4—24no—
612C4×C22⋊C4—24no—
613C2×#95C22×C3111yescharacteristic
614C2×#95C22×C3111yescharacteristic
615C2×#95C22×C3111yescharacteristic
616C2×#95C22×C3111yescharacteristic
617C2×#95C22×C3111yescharacteristic
618C2×#95C22×C3111yescharacteristic
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×C31—44no—
628C2×C31—82no—
629C2×C31#229011yescharacteristic
630C2×C31C4×#12111yescharacteristic
631C2×C31#233711yescharacteristic
632C2×C31#234211yescharacteristic
633C2×C31#235211yescharacteristic
634C2×C31#236111yescharacteristic
635C2×C31#236611yescharacteristic
636C2×C31#242411yescharacteristic
637C2×C31#242611yescharacteristic
638C2×C31#245611yescharacteristic
639C2×C31#245811yescharacteristic
640C2×C31#246111yescharacteristic
641C2×C31#247911yescharacteristic
642C2×C31#255411yescharacteristic
643C2×C31#259711yescharacteristic
644C25C23×C3111yescharacteristic
645C25C23×C3111yescharacteristic
646C22×D4—22no—
647C22×D4—22no—
648C22×D4—22no—
649C22×D4—22no—
650C22×D4—41no—
651C22×D4—41no—
652C22×D4C2×C4×C3114yes—
653C23×C4—22no—
654C23×C4—22no—
655C23×C4—22no—
656C23×C4—22no—
657C23×C4—22no—
658C23×C4—41no—
659C23×C4—41no—
660C23×C4C23×C3111yescharacteristic
661C23×C4C23×C3111yescharacteristic
662C23×C4C23×C3111yescharacteristic
663C23×C4C23×C3111yescharacteristic
664C23×C4C23×C3111yescharacteristic
665C23×C4C23×C3111yescharacteristic
666C23×C4C23×C3111yescharacteristic
667C23×C4C23×C3111yescharacteristic
668C23×C4C23×C3111yescharacteristic
669C23×C4C23×C3111yescharacteristic
670C23×C4C23×C3111yescharacteristic
671C23×C4C23×C3111yescharacteristic
672C23×C4C23×C3111yescharacteristic
673C2×C4⋊C4—22no—
674C2×C4⋊C4—22no—
675C2×C4⋊C4—22no—
676C2×C4⋊C4—22no—
677C2×C4⋊C4—22no—
678C2×C4⋊C4—22no—
679C2×C4⋊C4—22no—
680C2×C4⋊C4—41no—
681C2×C4⋊C4—41no—
682C2×C4⋊C4—41no—
683C2×C4⋊C4C2×C4×C3114yescomplemented
684C2×C4⋊C4D4×C3114yescomplemented
685C2×C22⋊C4—22no—
686C2×C22⋊C4—22no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
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—41no—
709C2×C22⋊C4—41no—
710C2×C22⋊C4—41no—
711C2×C22⋊C4—41no—
712C2×C22⋊C4—41no—
713C2×C22⋊C4—41no—
714C2×C22⋊C4C2×C4×C3114yes—
715C2×C22⋊C4C2×C4×C3114yes—
716C2×C22⋊C4C2×C4×C3114yescomplemented
717C2×C22⋊C4C2×C4×C3114yescomplemented
718C2×C42—22no—
719C2×C42—22no—
720C2×C42—22no—
721C2×C42—22no—
722C2×C42—22no—
723C2×C42—22no—
724C2×C42—22no—
725C2×C42—22no—
726C2×C42—41no—
727C2×C42—41no—
728C2×C42—41no—
729C2×C42C2×C4×C3114yescomplemented
730#95—22no—
731#95—22no—
732#95—22no—
733#95—22no—
734#95—22no—
735#95—22no—
736#95—22no—
737#95—22no—
738#95—22no—
739#95—22no—
740#95—41no—
741#95—41no—
742#95D4×C3114yes—
743#95D4×C3114yescomplemented
744C31#1403611yescharacteristic, direct product factor, Sylow
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
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—
771C24C22×C4×C3112yes—
772C24C22×C4×C3112yes—
773C24#41×C3112yes—
774C24#41×C3112yes—
775C24C24×C3111yescharacteristic
776C2×D4—28no—
777C2×D4—28no—
778C2×D4—44no—
779C2×D4—44no—
780C2×D4—44no—
781C2×D4—44no—
782C2×D4—44no—
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—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—28no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
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—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4C22×C4×C3112yes—
863C22×C4C22×C4×C3112yes—
864C22×C4C22×C4×C3112yes—
865C22×C4C22×C4×C3112yes—
866C22×C4C22×C4×C3112yes—
867C22×C4C2×D4×C3112yes—
868C22×C4C2×D4×C3112yes—
869C22×C4C2×D4×C3112yes—
870C22×C4C2×D4×C3112yes—
871C22×C4C2×D4×C3112yes—
872C22×C4C2×D4×C3112yes—
873C22×C4C2×D4×C3112yes—
874C22×C4C2×D4×C3112yes—
875C22×C4C2×D4×C3112yes—
876C22×C4#41×C3112yes—
877C22×C4#41×C3112yes—
878C22×C4#41×C3112yes—
879C22×C4#41×C3112yes—
880C22×C4#41×C3112yes—
881C4⋊C4—28no—
882C4⋊C4—28no—
883C4⋊C4—44no—
884C4⋊C4—44no—
885C22⋊C4—28no—
886C22⋊C4—28no—
887C22⋊C4—28no—
888C22⋊C4—28no—
889C22⋊C4—28no—
890C22⋊C4—44no—
891C22⋊C4—44no—
892C22⋊C4—44no—
893C22⋊C4—44no—
894C22⋊C4—44no—
895C22⋊C4—44no—
896C42—28no—
897C42—44no—
898C42—44no—
899C42—44no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
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—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
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—
969C23C31×#11714yes—
970C23C23×C4×C3111yescharacteristic
971C23C22×D4×C3111yescharacteristic
972C23C22×D4×C3111yescharacteristic
973C23C22×D4×C3111yescharacteristic
974C23C2×#41×C3111yescharacteristic
975C23C2×#41×C3111yescharacteristic
976C23C2×#41×C3111yescharacteristic
977C23C2×#41×C3111yescharacteristic
978C23C2×#41×C3111yescharacteristic
979C23C2×#41×C3111yescharacteristic
980C23C2×#41×C3111yescharacteristic
981C23C31×H(5,𝔽2)11yescharacteristic
982C23C31×H(5,𝔽2)11yescharacteristic
983C23C31×H(5,𝔽2)11yescharacteristic
984C23C31×2−1+411yescharacteristic
985D4—416no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
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—416no—
1032C2×C4—41no—
1033C2×C4—41no—
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×C4C4×D4×C3114yes—
1075C2×C4C4×D4×C3114yes—
1076C2×C4C4×D4×C3114yes—
1077C2×C4C31×#12114yes—
1078C22—24no—
1079C22—24no—
1080C22—24no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—81no—
1101C22—81no—
1102C22—81no—
1103C22—81no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22C2×C31×#11711yescharacteristic
1109C22C2×C4×D4×C3111yescharacteristic
1110C22C2×C4×D4×C3111yescharacteristic
1111C22C2×C4×D4×C3111yescharacteristic
1112C22C4×#41×C3111yescharacteristic
1113C22C31×#51811yescharacteristic
1114C22C31×#52011yescharacteristic
1115C22C2×C31×#12111yescharacteristic
1116C22C31×#52511yescharacteristic
1117C22C31×#52511yescharacteristic
1118C22C31×#52511yescharacteristic
1119C22C31×#52911yescharacteristic
1120C22C31×#52911yescharacteristic
1121C22C31×#52911yescharacteristic
1122C22C31×#53211yescharacteristic
1123C22C31×#53811yescharacteristic
1124C22C31×#53811yescharacteristic
1125C22C31×#54211yescharacteristic
1126C22C31×#54211yescharacteristic
1127C22D42×C3111yescharacteristic
1128C22D42×C3111yescharacteristic
1129C22C31×#54611yescharacteristic
1130C22C31×#54611yescharacteristic
1131C22C31×#54611yescharacteristic
1132C22C31×#54711yescharacteristic
1133C22C31×#54811yescharacteristic
1134C22C31×#54811yescharacteristic
1135C22C31×#55011yescharacteristic
1136C22C31×#55011yescharacteristic
1137C22C31×#55111yescharacteristic
1138C22C31×#55111yescharacteristic
1139C22C31×#55211yescharacteristic
1140C22C31×#55311yescharacteristic
1141C22C31×#55311yescharacteristic
1142C22C31×#55911yescharacteristic
1143C4—24no—
1144C4—24no—
1145C4—24no—
1146C4—24no—
1147C4—42no—
1148C4—42no—
1149C4—42no—
1150C4—42no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—81no—
1155C4—81no—
1156C2—44no—
1157C2—82no—
1158C2C31×#229011yescharacteristic
1159C2C4×C31×#12111yescharacteristic
1160C2C31×#233711yescharacteristic
1161C2C31×#234211yescharacteristic
1162C2C31×#235211yescharacteristic
1163C2C31×#236111yescharacteristic
1164C2C31×#236611yescharacteristic
1165C2C31×#242411yescharacteristic
1166C2C31×#242611yescharacteristic
1167C2C31×#245611yescharacteristic
1168C2C31×#245811yescharacteristic
1169C2C31×#246111yescharacteristic
1170C2C31×#247911yescharacteristic
1171C2C31×#255411yescharacteristic
1172C2C31×#259711yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC23×D4×C31C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#388C2semidirect
3. C2×C31×#388C2semidirect
5. C2×C31×#385C2semidirect
6. C2×C4×C4⋊C4×C31C2semidirect
7. C2×C4×C22⋊C4×C31C2semidirect
8. C31×#1441C2semidirect
9. C31×#1439C2semidirect
10. C31×#1439C2semidirect
12. C31×#1437C2semidirect
13. C31×#1437C2semidirect
14. C31×#1436C2semidirect
15. C31×#1434C2semidirect
37. C31×#390C4semidirect
97. C2×C4⋊C4×C31C2×C4semidirect
98. C2×C4⋊C4×C31D4semidirect
130. C2×C22⋊C4×C31C2×C4semidirect
131. C2×C22⋊C4×C31C2×C4semidirect
143. C2×C42×C31C2×C4semidirect
157. C31×#95D4semidirect
313. #14036C31direct (N × H)
493. C2×#388C2×C31semidirect
494. C2×#388C2×C31semidirect
496. C2×#385C2×C31semidirect
497. C2×C4×C4⋊C4C2×C31semidirect
498. C2×C4×C22⋊C4C2×C31semidirect
499. #1441C2×C31semidirect
500. #1439C2×C31semidirect
501. #1439C2×C31semidirect
503. #1437C2×C31semidirect
504. #1437C2×C31semidirect
505. #1436C2×C31semidirect
506. #1434C2×C31semidirect
606. #390C4×C31semidirect
683. C2×C4⋊C4C2×C4×C31semidirect
684. C2×C4⋊C4D4×C31semidirect
716. C2×C22⋊C4C2×C4×C31semidirect
717. C2×C22⋊C4C2×C4×C31semidirect
729. C2×C42C2×C4×C31semidirect
743. #95D4×C31semidirect
744. C31#14036direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3902
C2×C31×#3882
C2×C31×#3862
C2×C31×#3852
C2×C4×C4⋊C4×C312
C2×C4×C22⋊C4×C312
C31×#14412
C31×#14392
C31×#14382
C31×#14372
C31×#14362
C31×#14342
#1403631