Finite Group Databasebeta

← C31×#15280 #21472039

Subgroups — C31×#15280 #21472039

Order 7936.

2142 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×C31×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×C31×#396C211yesmaximal, characteristic, complemented
3C2×C31×#393C211yesmaximal, characteristic, complemented
4C2×C31×#391C211yesmaximal, characteristic, complemented
5C2×C31×#390C211yesmaximal, characteristic
6C2×C31×#386C211yesmaximal, characteristic
7C31×#1444C211yesmaximal, characteristic, complemented
8C31×#1441C211yesmaximal, characteristic, complemented
9C31×#1439C211yesmaximal, characteristic, complemented
10C31×#1439C211yesmaximal, characteristic, complemented
11C31×#1439C211yesmaximal, characteristic, complemented
12C31×#1439C211yesmaximal, characteristic, complemented
13C31×#1438C211yesmaximal, characteristic
14C31×#1436C211yesmaximal, 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×C4⋊C4×C31C2211yescharacteristic
27C22×C4⋊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×C22⋊C4×C31C2211yescharacteristic
38C22×C22⋊C4×C31C2211yescharacteristic
39C22×C42×C31C2211yescharacteristic
40C31×#396—24no—
41C31×#393—24no—
42C31×#391—24no—
43C31×#390—24no—
44C31×#386—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×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—41no—
73C22×D4×C31—41no—
74C22×D4×C31Q814yescomplemented
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—22no—
107C2×C4⋊C4×C31—22no—
108C2×C4⋊C4×C31—22no—
109C2×C4⋊C4×C31—41no—
110C2×C4⋊C4×C31—41no—
111C2×C4⋊C4×C31—41no—
112C2×C4⋊C4×C31—41no—
113C2×C4⋊C4×C31D414yescomplemented
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—22no—
135C2×C22⋊C4×C31—22no—
136C2×C22⋊C4×C31—41no—
137C2×C22⋊C4×C31—41no—
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—41no—
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—41no—
161C31×#95—41no—
162C31×#95—41no—
163C31×#95D414yes—
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×C31—21no—
189C24×C31—21no—
190C24×C31C2×D412yes—
191C24×C31C2×Q812yes—
192C24×C31C2×Q812yes—
193C24×C31#4112yes—
194C24×C31C2411yescharacteristic
195C2×Q8×C31—28no—
196C2×Q8×C31—28no—
197C2×Q8×C31—44no—
198C2×Q8×C31—44no—
199C2×Q8×C31—44no—
200C2×Q8×C31—44no—
201C2×Q8×C31—44no—
202C2×D4×C31—28no—
203C2×D4×C31—28no—
204C2×D4×C31—44no—
205C2×D4×C31—44no—
206C2×D4×C31—44no—
207C2×D4×C31—44no—
208C2×D4×C31—44no—
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—21no—
217C22×C4×C31—21no—
218C22×C4×C31—21no—
219C22×C4×C31—21no—
220C22×C4×C31—21no—
221C22×C4×C31—28no—
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—21no—
285C22×C4×C31—21no—
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×D412yes—
303C22×C4×C31C2×Q812yes—
304C22×C4×C31#4112yes—
305C22×C4×C31#4112yes—
306C22×C4×C31#4112yes—
307C4⋊C4×C31—28no—
308C4⋊C4×C31—28no—
309C4⋊C4×C31—28no—
310C4⋊C4×C31—44no—
311C4⋊C4×C31—44no—
312C4⋊C4×C31—44no—
313C22⋊C4×C31—28no—
314C22⋊C4×C31—28no—
315C22⋊C4×C31—44no—
316C22⋊C4×C31—44no—
317C22⋊C4×C31—44no—
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—44no—
325#15280C3111yesmaximal, 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—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—41no—
390C23×C31—41no—
391C23×C31—41no—
392C23×C31—41no—
393C23×C31—41no—
394C23×C31—41no—
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×C31H(5,𝔽2)11yescharacteristic
406C23×C31H(5,𝔽2)11yescharacteristic
407C23×C31H(5,𝔽2)11yescharacteristic
408C23×C31H(5,𝔽2)11yescharacteristic
409C23×C312−1+411yescharacteristic
410C23×C312−1+411yescharacteristic
411Q8×C31—416no—
412D4×C31—416no—
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—22no—
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⋊Q814yescomplemented
505C22×C22⋊Q8C2×C3111yescharacteristic, complemented
506C2×#396C2×C3111yescharacteristic, complemented
507C2×#393C2×C3111yescharacteristic, complemented
508C2×#391C2×C3111yescharacteristic, complemented
509C2×#390C2×C3111yescharacteristic
510C2×#386C2×C3111yescharacteristic
511#1444C2×C3111yescharacteristic, complemented
512#1441C2×C3111yescharacteristic, complemented
513#1439C2×C3111yescharacteristic, complemented
514#1439C2×C3111yescharacteristic, complemented
515#1439C2×C3111yescharacteristic, complemented
516#1439C2×C3111yescharacteristic, complemented
517#1438C2×C3111yescharacteristic
518#1436C2×C3111yescharacteristic, complemented
519C22⋊#95C2×C3111yescharacteristic, complemented
520C22×C31—24no—
521C22×C31—24no—
522C22×C31—24no—
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—42no—
537C22×C31—42no—
538C22×C31—42no—
539C22×C31—42no—
540C22×C31—42no—
541C22×C31—42no—
542C22×C31—81no—
543C22×C31—81no—
544C22×C31—81no—
545C22×C31—81no—
546C22×C31—81no—
547C22×C31—81no—
548C22×C31—81no—
549C22×C31—81no—
550C22×C31C2×#12011yescharacteristic
551C22×C31C2×#12111yescharacteristic
552C22×C31C2×C22⋊Q811yescharacteristic
553C22×C31C2×C22⋊Q811yescharacteristic
554C22×C31#52911yescharacteristic
555C22×C31#53211yescharacteristic
556C22×C31#53411yescharacteristic
557C22×C31#53511yescharacteristic
558C22×C31#53611yescharacteristic
559C22×C31#53711yescharacteristic
560C22×C31#53811yescharacteristic
561C22×C31#53911yescharacteristic
562C22×C31#54211yescharacteristic
563C22×C31#54211yescharacteristic
564C22×C31#54311yescharacteristic
565C22×C31D4211yescharacteristic
566C22×C31D4211yescharacteristic
567C22×C31#54611yescharacteristic
568C22×C31#54611yescharacteristic
569C22×C31#54611yescharacteristic
570C22×C31#54611yescharacteristic
571C22×C31#54611yescharacteristic
572C22×C31#54811yescharacteristic
573C22×C31#54811yescharacteristic
574C22×C31#54811yescharacteristic
575C22×C31D4×Q811yescharacteristic
576C22×C31D4×Q811yescharacteristic
577C22×C31#55011yescharacteristic
578C22×C31#55011yescharacteristic
579C22×C31#55111yescharacteristic
580C22×C31#55411yescharacteristic
581C22×C31#55411yescharacteristic
582C22×C31#55611yescharacteristic
583C22×C31#56211yescharacteristic
584C22×C31#56211yescharacteristic
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×Q8C22×C3111yescharacteristic
599C23×D4C22×C3111yescharacteristic
600C24×C4C22×C3111yescharacteristic
601C2×C22⋊Q8—24no—
602C2×C22⋊Q8—24no—
603C2×C22⋊Q8—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×C22⋊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#396—24no—
623#393—24no—
624#391—24no—
625#390—24no—
626#386—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—82no—
643C2×C31#240911yescharacteristic
644C2×C31#241011yescharacteristic
645C2×C31#242611yescharacteristic
646C2×C31#243111yescharacteristic
647C2×C31#243711yescharacteristic
648C2×C31#245011yescharacteristic
649C2×C31#245211yescharacteristic
650C2×C31#253811yescharacteristic
651C2×C31#256011yescharacteristic
652C2×C31#267611yescharacteristic
653C2×C31#268111yescharacteristic
654C2×C31#269211yescharacteristic
655C2×C31#270011yescharacteristic
656C2×C31#273011yescharacteristic
657C2×C31#273211yescharacteristic
658C25C23×C3111yescharacteristic
659C25C23×C3111yescharacteristic
660C22×Q8—22no—
661C22×Q8—22no—
662C22×Q8—22no—
663C22×Q8—22no—
664C22×Q8—41no—
665C22×Q8—41no—
666C22×Q8D4×C3114yescomplemented
667C22×D4—22no—
668C22×D4—22no—
669C22×D4—22no—
670C22×D4—22no—
671C22×D4—41no—
672C22×D4—41no—
673C22×D4Q8×C3114yescomplemented
674C23×C4—22no—
675C23×C4—22no—
676C23×C4—22no—
677C23×C4—22no—
678C23×C4—22no—
679C23×C4—41no—
680C23×C4—41no—
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
694C22⋊Q8—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—41no—
709C2×C4⋊C4—41no—
710C2×C4⋊C4—41no—
711C2×C4⋊C4—41no—
712C2×C4⋊C4D4×C3114yescomplemented
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—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—41no—
736C2×C22⋊C4—41no—
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—41no—
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—41no—
760#95—41no—
761#95—41no—
762#95D4×C3114yes—
763C31#1528011yescharacteristic, 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—
788C24—21no—
789C24—21no—
790C24C2×D4×C3112yes—
791C24C2×Q8×C3112yes—
792C24C2×Q8×C3112yes—
793C24#41×C3112yes—
794C24C24×C3111yescharacteristic
795C2×Q8—28no—
796C2×Q8—28no—
797C2×Q8—44no—
798C2×Q8—44no—
799C2×Q8—44no—
800C2×Q8—44no—
801C2×Q8—44no—
802C2×D4—28no—
803C2×D4—28no—
804C2×D4—44no—
805C2×D4—44no—
806C2×D4—44no—
807C2×D4—44no—
808C2×D4—44no—
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—28no—
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—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
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×D4×C3112yes—
903C22×C4C2×Q8×C3112yes—
904C22×C4#41×C3112yes—
905C22×C4#41×C3112yes—
906C22×C4#41×C3112yes—
907C4⋊C4—28no—
908C4⋊C4—28no—
909C4⋊C4—28no—
910C4⋊C4—44no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C22⋊C4—28no—
914C22⋊C4—28no—
915C22⋊C4—44no—
916C22⋊C4—44no—
917C22⋊C4—44no—
918C22⋊C4—44no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C22⋊C4—44no—
922C22⋊C4—44no—
923C22⋊C4—44no—
924C42—44no—
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—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—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
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
1004C23C31×H(5,𝔽2)11yescharacteristic
1005C23C31×H(5,𝔽2)11yescharacteristic
1006C23C31×H(5,𝔽2)11yescharacteristic
1007C23C31×H(5,𝔽2)11yescharacteristic
1008C23C31×2−1+411yescharacteristic
1009C23C31×2−1+411yescharacteristic
1010Q8—416no—
1011D4—416no—
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—22no—
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⋊Q814yescomplemented
1104C22—24no—
1105C22—24no—
1106C22—24no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
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—81no—
1127C22—81no—
1128C22—81no—
1129C22—81no—
1130C22—81no—
1131C22—81no—
1132C22—81no—
1133C22—81no—
1134C22C2×C31×#12011yescharacteristic
1135C22C2×C31×#12111yescharacteristic
1136C22C2×C31×C22⋊Q811yescharacteristic
1137C22C2×C31×C22⋊Q811yescharacteristic
1138C22C31×#52911yescharacteristic
1139C22C31×#53211yescharacteristic
1140C22C31×#53411yescharacteristic
1141C22C31×#53511yescharacteristic
1142C22C31×#53611yescharacteristic
1143C22C31×#53711yescharacteristic
1144C22C31×#53811yescharacteristic
1145C22C31×#53911yescharacteristic
1146C22C31×#54211yescharacteristic
1147C22C31×#54211yescharacteristic
1148C22C31×#54311yescharacteristic
1149C22D42×C3111yescharacteristic
1150C22D42×C3111yescharacteristic
1151C22C31×#54611yescharacteristic
1152C22C31×#54611yescharacteristic
1153C22C31×#54611yescharacteristic
1154C22C31×#54611yescharacteristic
1155C22C31×#54611yescharacteristic
1156C22C31×#54811yescharacteristic
1157C22C31×#54811yescharacteristic
1158C22C31×#54811yescharacteristic
1159C22D4×Q8×C3111yescharacteristic
1160C22D4×Q8×C3111yescharacteristic
1161C22C31×#55011yescharacteristic
1162C22C31×#55011yescharacteristic
1163C22C31×#55111yescharacteristic
1164C22C31×#55411yescharacteristic
1165C22C31×#55411yescharacteristic
1166C22C31×#55611yescharacteristic
1167C22C31×#56211yescharacteristic
1168C22C31×#56211yescharacteristic
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—82no—
1184C2C31×#240911yescharacteristic
1185C2C31×#241011yescharacteristic
1186C2C31×#242611yescharacteristic
1187C2C31×#243111yescharacteristic
1188C2C31×#243711yescharacteristic
1189C2C31×#245011yescharacteristic
1190C2C31×#245211yescharacteristic
1191C2C31×#253811yescharacteristic
1192C2C31×#256011yescharacteristic
1193C2C31×#267611yescharacteristic
1194C2C31×#268111yescharacteristic
1195C2C31×#269211yescharacteristic
1196C2C31×#270011yescharacteristic
1197C2C31×#273011yescharacteristic
1198C2C31×#273211yescharacteristic
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
2. C2×C31×#396C2semidirect
3. C2×C31×#393C2semidirect
4. C2×C31×#391C2semidirect
7. C31×#1444C2semidirect
8. C31×#1441C2semidirect
9. C31×#1439C2semidirect
10. C31×#1439C2semidirect
11. C31×#1439C2semidirect
12. C31×#1439C2semidirect
14. C31×#1436C2semidirect
15. C31×C22⋊#95C2semidirect
67. C22×Q8×C31D4semidirect
74. C22×D4×C31Q8semidirect
113. C2×C4⋊C4×C31D4semidirect
325. #15280C31direct (N × H)
504. C2×C4×C31C22⋊Q8semidirect
505. C22×C22⋊Q8C2×C31semidirect
506. C2×#396C2×C31semidirect
507. C2×#393C2×C31semidirect
508. C2×#391C2×C31semidirect
511. #1444C2×C31semidirect
512. #1441C2×C31semidirect
513. #1439C2×C31semidirect
514. #1439C2×C31semidirect
515. #1439C2×C31semidirect
516. #1439C2×C31semidirect
518. #1436C2×C31semidirect
519. C22⋊#95C2×C31semidirect
666. C22×Q8D4×C31semidirect
673. C22×D4Q8×C31semidirect
712. C2×C4⋊C4D4×C31semidirect
763. C31#15280direct (N × H)
1103. C2×C4C31×C22⋊Q8semidirect

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×#3962
C2×C31×#3932
C2×C31×#3912
C2×C31×#3902
C2×C31×#3862
C31×#14442
C31×#14412
C31×#14392
C31×#14382
C31×#14362
C31×C22⋊#952
#1528031