Finite Group Databasebeta

← C31×#14733 #21471492

Subgroups — C31×#14733 #21471492

Order 7936.

2298 conjugacy classes of subgroups.

The subgroup lattice has 1200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C31C211yesmaximal, characteristic
2C2×C31×#398C211yesmaximal, characteristic, complemented
3C2×C31×#396C211yesmaximal, characteristic, complemented
4C2×C31×#385C211yesmaximal, characteristic, complemented
5C2×C31×#385C211yesmaximal, characteristic, complemented
6C2×C31×#380C211yesmaximal, characteristic, complemented
7C31×#1441C211yesmaximal, characteristic, complemented
8C31×#1439C211yesmaximal, characteristic, complemented
9C31×#1439C211yesmaximal, characteristic, complemented
10C31×#1439C211yesmaximal, characteristic, complemented
11C31×#1438C211yesmaximal, characteristic
12C31×#1438C211yesmaximal, characteristic
13C31×#1436C211yesmaximal, characteristic, complemented
14C31×#1436C211yesmaximal, characteristic, complemented
15C31×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C31C2211yescharacteristic
17C24×C4×C31C2211yescharacteristic
18C24×C4×C31C2211yescharacteristic
19C2×C4×D4×C31—24no—
20C2×C4×D4×C31—24no—
21C2×C4×D4×C31—24no—
22C22×C4⋊C4×C31C2211yescharacteristic
23C22×C4⋊C4×C31C2211yescharacteristic
24C22×C4⋊C4×C31C2211yescharacteristic
25C22×C4⋊C4×C31C2211yescharacteristic
26C22×C4⋊C4×C31C2211yescharacteristic
27C22×C4⋊C4×C31C2211yescharacteristic
28C22×C4⋊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×C22⋊C4×C31C2211yescharacteristic
38C22×C22⋊C4×C31C2211yescharacteristic
39C22×C42×C31C2211yescharacteristic
40C31×#398—24no—
41C31×#396—24no—
42C31×#385—24no—
43C31×#385—24no—
44C31×#380—24no—
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×D4×C31—22no—
62C22×D4×C31—22no—
63C22×D4×C31—22no—
64C22×D4×C31—22no—
65C22×D4×C31—22no—
66C22×D4×C31—22no—
67C22×D4×C31Q814yes—
68C23×C4×C31—22no—
69C23×C4×C31—22no—
70C23×C4×C31—22no—
71C23×C4×C31—22no—
72C23×C4×C31—22no—
73C23×C4×C31—22no—
74C23×C4×C31—22no—
75C23×C4×C31—22no—
76C23×C4×C31—22no—
77C23×C4×C31—41no—
78C23×C4×C31—41no—
79C23×C4×C31—41no—
80C23×C4×C31—41no—
81C23×C4×C31D414yes—
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
95C4×D4×C31—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—22no—
107C2×C4⋊C4×C31—22no—
108C2×C4⋊C4×C31—22no—
109C2×C4⋊C4×C31—22no—
110C2×C4⋊C4×C31—22no—
111C2×C4⋊C4×C31—22no—
112C2×C4⋊C4×C31—41no—
113C2×C4⋊C4×C31—41no—
114C2×C4⋊C4×C31—41no—
115C2×C4⋊C4×C31—41no—
116C2×C4⋊C4×C31D414yes—
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—22no—
135C2×C22⋊C4×C31—22no—
136C2×C22⋊C4×C31—22no—
137C2×C22⋊C4×C31—22no—
138C2×C22⋊C4×C31—41no—
139C2×C22⋊C4×C31—41no—
140C2×C22⋊C4×C31—41no—
141C2×C22⋊C4×C31—41no—
142C2×C22⋊C4×C31—41no—
143C2×C22⋊C4×C31—41no—
144C2×C22⋊C4×C31—41no—
145C2×C22⋊C4×C31—41no—
146C2×C22⋊C4×C31D414yes—
147C2×C42×C31—22no—
148C2×C42×C31—22no—
149C2×C42×C31—22no—
150C31×#95—22no—
151C31×#95—22no—
152C31×#95—22no—
153C31×#95—22no—
154C31×#95—22no—
155C31×#95—22no—
156C31×#95—22no—
157C31×#95—22no—
158C31×#95—22no—
159C31×#95—22no—
160C31×#95—22no—
161C31×#95—41no—
162C31×#95—41no—
163C31×#95D414yescomplemented
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×C31—21no—
187C24×C31—21no—
188C24×C31C2×D412yes—
189C24×C31C2×D412yes—
190C24×C31C2×Q812yes—
191C24×C31C2×Q812yes—
192C24×C31#4112yes—
193C24×C31#4112yes—
194C24×C31C2411yescharacteristic
195C2×D4×C31—28no—
196C2×D4×C31—28no—
197C2×D4×C31—28no—
198C2×D4×C31—28no—
199C2×D4×C31—28no—
200C2×D4×C31—28no—
201C2×D4×C31—28no—
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—28no—
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—28no—
252C22×C4×C31—28no—
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—44no—
282C22×C4×C31—44no—
283C22×C4×C31—44no—
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×C31—44no—
291C22×C4×C31—44no—
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×C31C2×D412yes—
302C22×C4×C31C2×Q812yes—
303C22×C4×C31#4112yes—
304C22×C4×C31#4112yes—
305C22×C4×C31#4112yes—
306C22×C4×C31#4112yes—
307C4⋊C4×C31—28no—
308C4⋊C4×C31—44no—
309C4⋊C4×C31—44no—
310C4⋊C4×C31—44no—
311C4⋊C4×C31—44no—
312C4⋊C4×C31—44no—
313C4⋊C4×C31—44no—
314C22⋊C4×C31—28no—
315C22⋊C4×C31—28no—
316C22⋊C4×C31—28no—
317C22⋊C4×C31—28no—
318C22⋊C4×C31—44no—
319C22⋊C4×C31—44no—
320C22⋊C4×C31—44no—
321C22⋊C4×C31—44no—
322C22⋊C4×C31—44no—
323C22⋊C4×C31—44no—
324C42×C31—28no—
325#14733C3111yesmaximal, characteristic, direct product factor, Sylow
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—22no—
346C23×C31—22no—
347C23×C31—22no—
348C23×C31—22no—
349C23×C31—22no—
350C23×C31—22no—
351C23×C31—22no—
352C23×C31—22no—
353C23×C31—22no—
354C23×C31—22no—
355C23×C31—22no—
356C23×C31—22no—
357C23×C31—22no—
358C23×C31—22no—
359C23×C31—22no—
360C23×C31—22no—
361C23×C31—22no—
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—41no—
390C23×C31—41no—
391C23×C31—41no—
392C23×C31—41no—
393C23×C31—41no—
394C23×C31C22⋊Q814yes—
395C23×C31C22⋊Q814yes—
396C23×C31C22×D411yescharacteristic
397C23×C31C22×D411yescharacteristic
398C23×C31C22×D411yescharacteristic
399C23×C31C22×D411yescharacteristic
400C23×C31C22×Q811yescharacteristic
401C23×C31C2×#4111yescharacteristic
402C23×C31C2×#4111yescharacteristic
403C23×C31C2×#4111yescharacteristic
404C23×C31C2×#4111yescharacteristic
405C23×C31C2×#4111yescharacteristic
406C23×C31C2×#4111yescharacteristic
407C23×C31H(5,𝔽2)11yescharacteristic
408C23×C31H(5,𝔽2)11yescharacteristic
409C23×C31H(5,𝔽2)11yescharacteristic
410C23×C312−1+411yescharacteristic
411D4×C31—232no—
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—22no—
446C2×C4×C31—22no—
447C2×C4×C31—22no—
448C2×C4×C31—416no—
449C2×C4×C31—416no—
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—41no—
498C2×C4×C31—41no—
499C2×C4×C31—41no—
500C2×C4×C31—41no—
501C2×C4×C31—41no—
502C2×C4×C31#12014yes—
503C2×C4×C31#12114yes—
504C2×C4×C31C22⋊Q814yes—
505C22×C4×D4C2×C3111yescharacteristic
506C2×#398C2×C3111yescharacteristic, complemented
507C2×#396C2×C3111yescharacteristic, complemented
508C2×#385C2×C3111yescharacteristic, complemented
509C2×#385C2×C3111yescharacteristic, complemented
510C2×#380C2×C3111yescharacteristic, complemented
511#1441C2×C3111yescharacteristic, complemented
512#1439C2×C3111yescharacteristic, complemented
513#1439C2×C3111yescharacteristic, complemented
514#1439C2×C3111yescharacteristic, complemented
515#1438C2×C3111yescharacteristic
516#1438C2×C3111yescharacteristic
517#1436C2×C3111yescharacteristic, complemented
518#1436C2×C3111yescharacteristic, complemented
519C22⋊#95C2×C3111yescharacteristic, complemented
520C22×C31—24no—
521C22×C31—24no—
522C22×C31—24no—
523C22×C31—24no—
524C22×C31—24no—
525C22×C31—24no—
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—42no—
537C22×C31—42no—
538C22×C31—42no—
539C22×C31—42no—
540C22×C31—42no—
541C22×C31—42no—
542C22×C31—42no—
543C22×C31—42no—
544C22×C31—42no—
545C22×C31—42no—
546C22×C31—42no—
547C22×C31—42no—
548C22×C31—42no—
549C22×C31—42no—
550C22×C31C2×#12011yescharacteristic
551C22×C31C2×#12111yescharacteristic
552C22×C31C2×C22⋊Q811yescharacteristic
553C22×C31C2×C22⋊Q811yescharacteristic
554C22×C31C2×C22⋊Q811yescharacteristic
555C22×C31#52511yescharacteristic
556C22×C31#52511yescharacteristic
557C22×C31#52511yescharacteristic
558C22×C31#52511yescharacteristic
559C22×C31#52511yescharacteristic
560C22×C31#52911yescharacteristic
561C22×C31#52911yescharacteristic
562C22×C31#53211yescharacteristic
563C22×C31#53411yescharacteristic
564C22×C31#53711yescharacteristic
565C22×C31#53811yescharacteristic
566C22×C31#53911yescharacteristic
567C22×C31#54011yescharacteristic
568C22×C31#54211yescharacteristic
569C22×C31D4211yescharacteristic
570C22×C31D4211yescharacteristic
571C22×C31#54611yescharacteristic
572C22×C31#54611yescharacteristic
573C22×C31#54611yescharacteristic
574C22×C31#54611yescharacteristic
575C22×C31#54711yescharacteristic
576C22×C31#54811yescharacteristic
577C22×C31D4×Q811yescharacteristic
578C22×C31#55011yescharacteristic
579C22×C31#55211yescharacteristic
580C22×C31#55311yescharacteristic
581C22×C31#55311yescharacteristic
582C22×C31#55411yescharacteristic
583C22×C31#55411yescharacteristic
584C22×C31#55411yescharacteristic
585C4×C31—24no—
586C4×C31—24no—
587C4×C31—24no—
588C4×C31—42no—
589C4×C31—42no—
590C4×C31—42no—
591C4×C31—42no—
592C4×C31—42no—
593C4×C31—42no—
594C4×C31—81no—
595C4×C31—81no—
596C4×C31—81no—
597C4×C31—81no—
598C23×D4C22×C3111yescharacteristic
599C24×C4C22×C3111yescharacteristic
600C24×C4C22×C3111yescharacteristic
601C2×C4×D4—24no—
602C2×C4×D4—24no—
603C2×C4×D4—24no—
604C22×C4⋊C4C22×C3111yescharacteristic
605C22×C4⋊C4C22×C3111yescharacteristic
606C22×C4⋊C4C22×C3111yescharacteristic
607C22×C4⋊C4C22×C3111yescharacteristic
608C22×C4⋊C4C22×C3111yescharacteristic
609C22×C4⋊C4C22×C3111yescharacteristic
610C22×C4⋊C4C22×C3111yescharacteristic
611C22×C22⋊C4C22×C3111yescharacteristic
612C22×C22⋊C4C22×C3111yescharacteristic
613C22×C22⋊C4C22×C3111yescharacteristic
614C22×C22⋊C4C22×C3111yescharacteristic
615C22×C22⋊C4C22×C3111yescharacteristic
616C22×C22⋊C4C22×C3111yescharacteristic
617C22×C22⋊C4C22×C3111yescharacteristic
618C22×C22⋊C4C22×C3111yescharacteristic
619C22×C22⋊C4C22×C3111yescharacteristic
620C22×C22⋊C4C22×C3111yescharacteristic
621C22×C42C22×C3111yescharacteristic
622#398—24no—
623#396—24no—
624#385—24no—
625#385—24no—
626#380—24no—
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×#95C22×C3111yescharacteristic
636C2×#95C22×C3111yescharacteristic
637C2×#95C22×C3111yescharacteristic
638C2×#95C22×C3111yescharacteristic
639C2×#95C22×C3111yescharacteristic
640C2×#95C22×C3111yescharacteristic
641C2×C31—44no—
642C2×C31—44no—
643C2×C31#239211yescharacteristic
644C2×C31#240711yescharacteristic
645C2×C31#241011yescharacteristic
646C2×C31#241711yescharacteristic
647C2×C31#244911yescharacteristic
648C2×C31#245011yescharacteristic
649C2×C31#245211yescharacteristic
650C2×C31#245411yescharacteristic
651C2×C31#245611yescharacteristic
652C2×C31#246011yescharacteristic
653C2×C31#246411yescharacteristic
654C2×C31#246811yescharacteristic
655C2×C31#257911yescharacteristic
656C2×C31#263011yescharacteristic
657C2×C31#284811yescharacteristic
658C25C23×C3111yescharacteristic
659C25C23×C3111yescharacteristic
660C22×D4—22no—
661C22×D4—22no—
662C22×D4—22no—
663C22×D4—22no—
664C22×D4—22no—
665C22×D4—22no—
666C22×D4Q8×C3114yes—
667C23×C4—22no—
668C23×C4—22no—
669C23×C4—22no—
670C23×C4—22no—
671C23×C4—22no—
672C23×C4—22no—
673C23×C4—22no—
674C23×C4—22no—
675C23×C4—22no—
676C23×C4—41no—
677C23×C4—41no—
678C23×C4—41no—
679C23×C4—41no—
680C23×C4D4×C3114yes—
681C23×C4C23×C3111yescharacteristic
682C23×C4C23×C3111yescharacteristic
683C23×C4C23×C3111yescharacteristic
684C23×C4C23×C3111yescharacteristic
685C23×C4C23×C3111yescharacteristic
686C23×C4C23×C3111yescharacteristic
687C23×C4C23×C3111yescharacteristic
688C23×C4C23×C3111yescharacteristic
689C23×C4C23×C3111yescharacteristic
690C23×C4C23×C3111yescharacteristic
691C23×C4C23×C3111yescharacteristic
692C23×C4C23×C3111yescharacteristic
693C23×C4C23×C3111yescharacteristic
694C4×D4—232no—
695C2×C4⋊C4—22no—
696C2×C4⋊C4—22no—
697C2×C4⋊C4—22no—
698C2×C4⋊C4—22no—
699C2×C4⋊C4—22no—
700C2×C4⋊C4—22no—
701C2×C4⋊C4—22no—
702C2×C4⋊C4—22no—
703C2×C4⋊C4—22no—
704C2×C4⋊C4—22no—
705C2×C4⋊C4—22no—
706C2×C4⋊C4—22no—
707C2×C4⋊C4—22no—
708C2×C4⋊C4—22no—
709C2×C4⋊C4—22no—
710C2×C4⋊C4—22no—
711C2×C4⋊C4—41no—
712C2×C4⋊C4—41no—
713C2×C4⋊C4—41no—
714C2×C4⋊C4—41no—
715C2×C4⋊C4D4×C3114yes—
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—22no—
728C2×C22⋊C4—22no—
729C2×C22⋊C4—22no—
730C2×C22⋊C4—22no—
731C2×C22⋊C4—22no—
732C2×C22⋊C4—22no—
733C2×C22⋊C4—22no—
734C2×C22⋊C4—22no—
735C2×C22⋊C4—22no—
736C2×C22⋊C4—22no—
737C2×C22⋊C4—41no—
738C2×C22⋊C4—41no—
739C2×C22⋊C4—41no—
740C2×C22⋊C4—41no—
741C2×C22⋊C4—41no—
742C2×C22⋊C4—41no—
743C2×C22⋊C4—41no—
744C2×C22⋊C4—41no—
745C2×C22⋊C4D4×C3114yes—
746C2×C42—22no—
747C2×C42—22no—
748C2×C42—22no—
749#95—22no—
750#95—22no—
751#95—22no—
752#95—22no—
753#95—22no—
754#95—22no—
755#95—22no—
756#95—22no—
757#95—22no—
758#95—22no—
759#95—22no—
760#95—41no—
761#95—41no—
762#95D4×C3114yescomplemented
763C31#1473311yescharacteristic, direct product factor, Sylow
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—
780C24—21no—
781C24—21no—
782C24—21no—
783C24—21no—
784C24—21no—
785C24—21no—
786C24—21no—
787C24—21no—
788C24C2×D4×C3112yes—
789C24C2×D4×C3112yes—
790C24C2×Q8×C3112yes—
791C24C2×Q8×C3112yes—
792C24#41×C3112yes—
793C24#41×C3112yes—
794C24C24×C3111yescharacteristic
795C2×D4—28no—
796C2×D4—28no—
797C2×D4—28no—
798C2×D4—28no—
799C2×D4—28no—
800C2×D4—28no—
801C2×D4—28no—
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—28no—
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—28no—
852C22×C4—28no—
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—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—44no—
882C22×C4—44no—
883C22×C4—44no—
884C22×C4—44no—
885C22×C4—44no—
886C22×C4—44no—
887C22×C4—44no—
888C22×C4—44no—
889C22×C4—44no—
890C22×C4—44no—
891C22×C4—44no—
892C22×C4C2×D4×C3112yes—
893C22×C4C2×D4×C3112yes—
894C22×C4C2×D4×C3112yes—
895C22×C4C2×D4×C3112yes—
896C22×C4C2×D4×C3112yes—
897C22×C4C2×D4×C3112yes—
898C22×C4C2×D4×C3112yes—
899C22×C4C2×D4×C3112yes—
900C22×C4C2×D4×C3112yes—
901C22×C4C2×D4×C3112yes—
902C22×C4C2×Q8×C3112yes—
903C22×C4#41×C3112yes—
904C22×C4#41×C3112yes—
905C22×C4#41×C3112yes—
906C22×C4#41×C3112yes—
907C4⋊C4—28no—
908C4⋊C4—44no—
909C4⋊C4—44no—
910C4⋊C4—44no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C4⋊C4—44no—
914C22⋊C4—28no—
915C22⋊C4—28no—
916C22⋊C4—28no—
917C22⋊C4—28no—
918C22⋊C4—44no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C22⋊C4—44no—
922C22⋊C4—44no—
923C22⋊C4—44no—
924C42—28no—
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—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
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—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23C31×C22⋊Q814yes—
994C23C31×C22⋊Q814yes—
995C23C22×D4×C3111yescharacteristic
996C23C22×D4×C3111yescharacteristic
997C23C22×D4×C3111yescharacteristic
998C23C22×D4×C3111yescharacteristic
999C23C22×Q8×C3111yescharacteristic
1000C23C2×#41×C3111yescharacteristic
1001C23C2×#41×C3111yescharacteristic
1002C23C2×#41×C3111yescharacteristic
1003C23C2×#41×C3111yescharacteristic
1004C23C2×#41×C3111yescharacteristic
1005C23C2×#41×C3111yescharacteristic
1006C23C31×H(5,𝔽2)11yescharacteristic
1007C23C31×H(5,𝔽2)11yescharacteristic
1008C23C31×H(5,𝔽2)11yescharacteristic
1009C23C31×2−1+411yescharacteristic
1010D4—232no—
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—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—416no—
1048C2×C4—416no—
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×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4C31×#12014yes—
1102C2×C4C31×#12114yes—
1103C2×C4C31×C22⋊Q814yes—
1104C22—24no—
1105C22—24no—
1106C22—24no—
1107C22—24no—
1108C22—24no—
1109C22—24no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22—42no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—42no—
1134C22C2×C31×#12011yescharacteristic
1135C22C2×C31×#12111yescharacteristic
1136C22C2×C31×C22⋊Q811yescharacteristic
1137C22C2×C31×C22⋊Q811yescharacteristic
1138C22C2×C31×C22⋊Q811yescharacteristic
1139C22C31×#52511yescharacteristic
1140C22C31×#52511yescharacteristic
1141C22C31×#52511yescharacteristic
1142C22C31×#52511yescharacteristic
1143C22C31×#52511yescharacteristic
1144C22C31×#52911yescharacteristic
1145C22C31×#52911yescharacteristic
1146C22C31×#53211yescharacteristic
1147C22C31×#53411yescharacteristic
1148C22C31×#53711yescharacteristic
1149C22C31×#53811yescharacteristic
1150C22C31×#53911yescharacteristic
1151C22C31×#54011yescharacteristic
1152C22C31×#54211yescharacteristic
1153C22D42×C3111yescharacteristic
1154C22D42×C3111yescharacteristic
1155C22C31×#54611yescharacteristic
1156C22C31×#54611yescharacteristic
1157C22C31×#54611yescharacteristic
1158C22C31×#54611yescharacteristic
1159C22C31×#54711yescharacteristic
1160C22C31×#54811yescharacteristic
1161C22D4×Q8×C3111yescharacteristic
1162C22C31×#55011yescharacteristic
1163C22C31×#55211yescharacteristic
1164C22C31×#55311yescharacteristic
1165C22C31×#55311yescharacteristic
1166C22C31×#55411yescharacteristic
1167C22C31×#55411yescharacteristic
1168C22C31×#55411yescharacteristic
1169C4—24no—
1170C4—24no—
1171C4—24no—
1172C4—42no—
1173C4—42no—
1174C4—42no—
1175C4—42no—
1176C4—42no—
1177C4—42no—
1178C4—81no—
1179C4—81no—
1180C4—81no—
1181C4—81no—
1182C2—44no—
1183C2—44no—
1184C2C31×#239211yescharacteristic
1185C2C31×#240711yescharacteristic
1186C2C31×#241011yescharacteristic
1187C2C31×#241711yescharacteristic
1188C2C31×#244911yescharacteristic
1189C2C31×#245011yescharacteristic
1190C2C31×#245211yescharacteristic
1191C2C31×#245411yescharacteristic
1192C2C31×#245611yescharacteristic
1193C2C31×#246011yescharacteristic
1194C2C31×#246411yescharacteristic
1195C2C31×#246811yescharacteristic
1196C2C31×#257911yescharacteristic
1197C2C31×#263011yescharacteristic
1198C2C31×#284811yescharacteristic
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
2. C2×C31×#398C2semidirect
3. C2×C31×#396C2semidirect
4. C2×C31×#385C2semidirect
5. C2×C31×#385C2semidirect
6. C2×C31×#380C2semidirect
7. C31×#1441C2semidirect
8. C31×#1439C2semidirect
9. C31×#1439C2semidirect
10. C31×#1439C2semidirect
13. C31×#1436C2semidirect
14. C31×#1436C2semidirect
15. C31×C22⋊#95C2semidirect
163. C31×#95D4semidirect
325. #14733C31direct (N × H)
506. C2×#398C2×C31semidirect
507. C2×#396C2×C31semidirect
508. C2×#385C2×C31semidirect
509. C2×#385C2×C31semidirect
510. C2×#380C2×C31semidirect
511. #1441C2×C31semidirect
512. #1439C2×C31semidirect
513. #1439C2×C31semidirect
514. #1439C2×C31semidirect
517. #1436C2×C31semidirect
518. #1436C2×C31semidirect
519. C22⋊#95C2×C31semidirect
762. #95D4×C31semidirect
763. C31#14733direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×D4×C312
C2×C31×#3982
C2×C31×#3962
C2×C31×#3852
C2×C31×#3802
C31×#14412
C31×#14392
C31×#14382
C31×#14362
C31×C22⋊#952
#1473331