Finite Group Databasebeta

← C31×#23850 #21480609

Subgroups — C31×#23850 #21480609

Order 7936.

1934 conjugacy classes of subgroups.

The subgroup lattice has 1020 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#135C211yesmaximal, characteristic, complemented
2C2×C31×#546C211yesmaximal, characteristic, complemented
3C2×C31×#449C211yesmaximal, characteristic, complemented
4C2×C31×#450C211yesmaximal, characteristic, complemented
5C2×C31×#447C211yesmaximal, characteristic, complemented
6C31×#2407C211yesmaximal, characteristic, complemented
7C31×#2015C211yesmaximal, characteristic, complemented
8C31×#2012C211yesmaximal, characteristic, complemented
9C31×#2001C211yesmaximal, characteristic, complemented
10C31×#2000C211yesmaximal, characteristic, complemented
11C31×#1893C211yesmaximal, characteristic, complemented
12C31×#1879C211yesmaximal, characteristic, complemented
13C31×#1877C211yesmaximal, characteristic, complemented
14C31×#1869C211yesmaximal, characteristic, complemented
15C31×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C22×#41×C31C2211yescharacteristic, complemented
18C23×D4×C31C2211yescharacteristic
19C2×C31×#135—24no—
20C2×C31×#135—24no—
21C2×C31×#135—24no—
22C22×Q16×C31C2211yescharacteristic, complemented
23C22×SD16×C31C2211yescharacteristic
24C22×SD16×C31C2211yescharacteristic
25C22×SD16×C31C2211yescharacteristic, complemented
26C22×D8×C31C2211yescharacteristic
27C22×D8×C31C2211yescharacteristic
28C23×C8×C31C2211yescharacteristic, complemented
29C31×#546—24no—
30C31×#546—24no—
31C2×C31×#124C2211yescharacteristic
32C2×C31×#123—21no—
33C2×C31×C22⋊Q8C2211yescharacteristic
34C2×C31×C22⋊Q8C2211yescharacteristic
35C2×C31×#121—21no—
36C2×C31×#121C2211yescharacteristic
37C2×C31×#121C2211yescharacteristic
38C2×C31×#120—21no—
39C2×C4×D4×C31C2211yescharacteristic
40C2×C4×D4×C31C2211yescharacteristic
41C22×C22⋊C4×C31—21no—
42C31×#450—24no—
43C31×#449—24no—
44C31×#447—24no—
45C2×C31×#103C2211yescharacteristic, complemented
46C2×C31×#103C2211yescharacteristic, complemented
47C2×C31×#103C2211yescharacteristic, complemented
48C2×C31×#102C2211yescharacteristic
49C2×C31×#102C2211yescharacteristic
50C2×C31×#102C2211yescharacteristic
51C2×C31×#102C2211yescharacteristic
52C2×C31×#102C2211yescharacteristic, complemented
53C2×C31×C22⋊C8C2211yescharacteristic
54C2×C31×C22⋊C8C2211yescharacteristic
55C2×C31×C22⋊C8C2211yescharacteristic, complemented
56C31×#394—21no—
57C31×#392—21no—
58C31×#391C2211yescharacteristic, complemented
59C31×#390C2211yescharacteristic, complemented
60C31×#386—21no—
61C31×#385—21no—
62C31×#380C2211yescharacteristic, complemented
63C31×#340C2211yescharacteristic, complemented
64C31×#340C2211yescharacteristic, complemented
65C31×#336C2211yescharacteristic, complemented
66C31×#336C2211yescharacteristic, complemented
67C25×C31—21no—
68C2×#41×C31—22no—
69C2×#41×C31—22no—
70C2×#41×C31—22no—
71C2×#41×C31—22no—
72C2×#41×C31—22no—
73C2×#41×C31—22no—
74C2×#41×C31—22no—
75C2×#41×C31—41no—
76C2×#41×C31—41no—
77C2×#41×C31—41no—
78C2×#41×C31—41no—
79C2×#41×C31D414yescomplemented
80C22×Q8×C31C2311yescharacteristic
81C22×Q8×C31C2311yescharacteristic
82C22×D4×C31—21no—
83C22×D4×C31—21no—
84C22×D4×C31—22no—
85C22×D4×C31—22no—
86C22×D4×C31—22no—
87C22×D4×C31—22no—
88C22×D4×C31—21no—
89C22×D4×C31—21no—
90C22×D4×C31—21no—
91C22×D4×C31—41no—
92C22×D4×C31—41no—
93C22×D4×C31D411yescharacteristic
94C22×D4×C31C2311yescharacteristic
95C22×D4×C31C2311yescharacteristic
96C22×D4×C31C2311yescharacteristic
97C23×C4×C31—21no—
98C23×C4×C31—21no—
99C23×C4×C31—21no—
100C23×C4×C31C2311yescharacteristic
101C23×C4×C31C2311yescharacteristic
102C31×#135—232no—
103C2×Q16×C31—22no—
104C2×Q16×C31—22no—
105C2×Q16×C31—22no—
106C2×SD16×C31—22no—
107C2×SD16×C31—22no—
108C2×SD16×C31—22no—
109C2×SD16×C31—22no—
110C2×SD16×C31—22no—
111C2×SD16×C31—22no—
112C2×SD16×C31—22no—
113C2×SD16×C31—41no—
114C2×SD16×C31D414yescomplemented
115C2×D8×C31—22no—
116C2×D8×C31—22no—
117C2×D8×C31—22no—
118C2×D8×C31—22no—
119C2×D8×C31—41no—
120C2×D8×C31D414yescomplemented
121C22×C8×C31—22no—
122C22×C8×C31—22no—
123C22×C8×C31—22no—
124C22×C8×C31C2311yescharacteristic
125C22×C8×C31C2311yescharacteristic
126C22×C8×C31C2311yescharacteristic
127C22×C8×C31C2311yescharacteristic
128C31×#124—22no—
129C31×#124—22no—
130C31×#123—28no—
131C31×C22⋊Q8—22no—
132C31×C22⋊Q8—22no—
133C31×C22⋊Q8—22no—
134C31×C22⋊Q8—41no—
135C31×#121—28no—
136C31×#121—22no—
137C31×#121—22no—
138C31×#121—41no—
139C31×#121D414yescomplemented
140C31×#120—28no—
141C4×D4×C31—22no—
142C4×D4×C31—22no—
143C4×D4×C31—22no—
144C4×D4×C31—22no—
145C2×C4⋊C4×C31—21no—
146C2×C4⋊C4×C31—21no—
147C2×C4⋊C4×C31D411yescharacteristic
148C2×C4⋊C4×C31C2311yescharacteristic
149C2×C4⋊C4×C31C2311yescharacteristic
150C2×C4⋊C4×C31C2311yescharacteristic
151C2×C22⋊C4×C31—28no—
152C2×C22⋊C4×C31—21no—
153C2×C22⋊C4×C31—21no—
154C2×C22⋊C4×C31—21no—
155C2×C22⋊C4×C31—21no—
156C2×C22⋊C4×C31—21no—
157C2×C22⋊C4×C31—21no—
158C2×C22⋊C4×C31—21no—
159C2×C22⋊C4×C31—21no—
160C2×C22⋊C4×C31—21no—
161C2×C22⋊C4×C31—21no—
162C2×C22⋊C4×C31D411yescharacteristic
163C2×C22⋊C4×C31D411yescharacteristic
164C2×C42×C31C2311yescharacteristic
165C31×#103—22no—
166C31×#103—41no—
167C31×#103—41no—
168C31×#102—22no—
169C31×#102—22no—
170C31×#102—22no—
171C31×#102—22no—
172C31×#102—22no—
173C31×C22⋊C8—22no—
174C31×C22⋊C8—22no—
175C31×C22⋊C8—22no—
176C31×#95—21no—
177C31×#95—21no—
178C31×#95—21no—
179C24×C31—21no—
180C24×C31—24no—
181C24×C31—21no—
182C24×C31—21no—
183C24×C31—42no—
184C24×C31—42no—
185C24×C31—42no—
186C24×C31—42no—
187C24×C31—81no—
188C24×C31—81no—
189C24×C31C2×D411yescharacteristic
190C24×C31C2×D411yescharacteristic
191#41×C31—28no—
192#41×C31—28no—
193#41×C31—44no—
194#41×C31—44no—
195#41×C31—44no—
196#41×C31—44no—
197#41×C31—44no—
198#41×C31—44no—
199C2×Q8×C31—21no—
200C2×Q8×C31—21no—
201C2×Q8×C31—21no—
202C2×Q8×C31—21no—
203C2×Q8×C31—21no—
204C2×Q8×C31—21no—
205C2×Q8×C31—21no—
206C2×Q8×C31—21no—
207C2×Q8×C31—21no—
208C2×Q8×C31—21no—
209C2×Q8×C31C2×D412yes—
210C2×Q8×C31C2×D412yes—
211C2×D4×C31—24no—
212C2×D4×C31—22no—
213C2×D4×C31—24no—
214C2×D4×C31—22no—
215C2×D4×C31—24no—
216C2×D4×C31—21no—
217C2×D4×C31—21no—
218C2×D4×C31—21no—
219C2×D4×C31—21no—
220C2×D4×C31—21no—
221C2×D4×C31—21no—
222C2×D4×C31—21no—
223C2×D4×C31—21no—
224C2×D4×C31—21no—
225C2×D4×C31—21no—
226C2×D4×C31—21no—
227C2×D4×C31—21no—
228C2×D4×C31—21no—
229C2×D4×C31—41no—
230C2×D4×C31—42no—
231C2×D4×C31—42no—
232C2×D4×C31—42no—
233C2×D4×C31—44no—
234C2×D4×C31—44no—
235C2×D4×C31—44no—
236C2×D4×C31—42no—
237C2×D4×C31—42no—
238C2×D4×C31—42no—
239C2×D4×C31—42no—
240C2×D4×C31—44no—
241C2×D4×C31—42no—
242C2×D4×C31—42no—
243C2×D4×C31—81no—
244C2×D4×C31—81no—
245C2×D4×C31—81no—
246C2×D4×C31C2×D412yes—
247C2×D4×C31C2×D412yes—
248C2×D4×C31C2×D412yes—
249C2×D4×C31C2×D412yes—
250C2×D4×C31C2×D412yes—
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—24no—
259C22×C4×C31—24no—
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—42no—
269C22×C4×C31—42no—
270C22×C4×C31—42no—
271C22×C4×C31—42no—
272C22×C4×C31—42no—
273C22×C4×C31—81no—
274C22×C4×C31—81no—
275C22×C4×C31C2×D411yescharacteristic
276C22×C4×C31C2×D411yescharacteristic
277C22×C4×C31C2×D411yescharacteristic
278C22×C4×C31C2×D411yescharacteristic
279C22×C4×C31C2×D412yes—
280C22×C4×C31C2×D412yes—
281C22×C4×C31C2411yescharacteristic
282Q16×C31—28no—
283SD16×C31—28no—
284SD16×C31—28no—
285SD16×C31—44no—
286D8×C31—28no—
287D8×C31—44no—
288C2×C8×C31—28no—
289C2×C8×C31—21no—
290C2×C8×C31—21no—
291C2×C8×C31—21no—
292C2×C8×C31—21no—
293C2×C8×C31—21no—
294C2×C8×C31—21no—
295C2×C8×C31—21no—
296C2×C8×C31—21no—
297C2×C8×C31—21no—
298C2×C8×C31—21no—
299C2×C8×C31C2×D412yes—
300C2×C8×C31C2×D412yes—
301C4⋊C4×C31—24no—
302C4⋊C4×C31—22no—
303C4⋊C4×C31—21no—
304C4⋊C4×C31—21no—
305C4⋊C4×C31—21no—
306C4⋊C4×C31—21no—
307C4⋊C4×C31—21no—
308C4⋊C4×C31—42no—
309C4⋊C4×C31C2×D412yes—
310C22⋊C4×C31—24no—
311C22⋊C4×C31—24no—
312C22⋊C4×C31—24no—
313C22⋊C4×C31—24no—
314C22⋊C4×C31—22no—
315C22⋊C4×C31—22no—
316C22⋊C4×C31—24no—
317C22⋊C4×C31—42no—
318C22⋊C4×C31—42no—
319C22⋊C4×C31—42no—
320C22⋊C4×C31—81no—
321C22⋊C4×C31—81no—
322C42×C31—21no—
323C42×C31—21no—
324#23850C3111yesmaximal, characteristic, direct product factor, Sylow
325C23×C31—21no—
326C23×C31—22no—
327C23×C31—21no—
328C23×C31—21no—
329C23×C31—21no—
330C23×C31—21no—
331C23×C31—22no—
332C23×C31—22no—
333C23×C31—21no—
334C23×C31—21no—
335C23×C31—21no—
336C23×C31—21no—
337C23×C31—21no—
338C23×C31—21no—
339C23×C31—21no—
340C23×C31—22no—
341C23×C31—22no—
342C23×C31—48no—
343C23×C31—48no—
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—84no—
361C23×C31—84no—
362C23×C31—84no—
363C23×C31—84no—
364C23×C31—84no—
365C23×C31#12012yes—
366C23×C31#13512yescomplemented
367C23×C31C22×D411yescharacteristic
368Q8×C31—22no—
369Q8×C31—22no—
370Q8×C31—22no—
371Q8×C31—22no—
372Q8×C31—41no—
373Q8×C31—41no—
374Q8×C31—41no—
375Q8×C31—41no—
376D4×C31—22no—
377D4×C31—22no—
378D4×C31—22no—
379D4×C31—22no—
380D4×C31—22no—
381D4×C31—22no—
382D4×C31—22no—
383D4×C31—44no—
384D4×C31—48no—
385D4×C31—48no—
386D4×C31—48no—
387D4×C31—41no—
388D4×C31—41no—
389D4×C31—41no—
390D4×C31—41no—
391D4×C31—84no—
392D4×C31—84no—
393D4×C31#12014yes—
394C2×C4×C31—21no—
395C2×C4×C31—21no—
396C2×C4×C31—22no—
397C2×C4×C31—22no—
398C2×C4×C31—22no—
399C2×C4×C31—22no—
400C2×C4×C31—21no—
401C2×C4×C31—21no—
402C2×C4×C31—22no—
403C2×C4×C31—22no—
404C2×C4×C31—21no—
405C2×C4×C31—21no—
406C2×C4×C31—22no—
407C2×C4×C31—21no—
408C2×C4×C31—21no—
409C2×C4×C31—21no—
410C2×C4×C31—21no—
411C2×C4×C31—21no—
412C2×C4×C31—48no—
413C2×C4×C31—48no—
414C2×C4×C31—41no—
415C2×C4×C31—41no—
416C2×C4×C31—41no—
417C2×C4×C31—41no—
418C2×C4×C31—41no—
419C2×C4×C31—41no—
420C2×C4×C31—41no—
421C2×C4×C31—41no—
422C2×C4×C31—41no—
423C2×C4×C31—41no—
424C2×C4×C31—41no—
425C2×C4×C31—41no—
426C2×C4×C31—41no—
427C2×C4×C31—41no—
428C2×C4×C31—41no—
429C2×C4×C31—41no—
430C2×C4×C31—84no—
431C2×C4×C31#12012yes—
432C2×C4×C31C22×D411yescharacteristic
433C2×C4×C31C22×D411yescharacteristic
434C2×C4×C31C22×D411yescharacteristic
435C2×C4×C31C22×D411yescharacteristic
436C2×C4×C31H(5,𝔽2)11yescharacteristic
437C2×C4×C31H(5,𝔽2)11yescharacteristic
438C8×C31—22no—
439C8×C31—22no—
440C8×C31—41no—
441C8×C31—41no—
442C22×#135C2×C3111yescharacteristic, complemented
443C2×#546C2×C3111yescharacteristic, complemented
444C2×#449C2×C3111yescharacteristic, complemented
445C2×#450C2×C3111yescharacteristic, complemented
446C2×#447C2×C3111yescharacteristic, complemented
447#2407C2×C3111yescharacteristic, complemented
448#2015C2×C3111yescharacteristic, complemented
449#2012C2×C3111yescharacteristic, complemented
450#2001C2×C3111yescharacteristic, complemented
451#2000C2×C3111yescharacteristic, complemented
452#1893C2×C3111yescharacteristic, complemented
453#1879C2×C3111yescharacteristic, complemented
454#1877C2×C3111yescharacteristic, complemented
455#1869C2×C3111yescharacteristic, complemented
456#1788C2×C3111yescharacteristic, complemented
457C22×C31—22no—
458C22×C31—24no—
459C22×C31—22no—
460C22×C31—22no—
461C22×C31—22no—
462C22×C31—22no—
463C22×C31—22no—
464C22×C31—41no—
465C22×C31—42no—
466C22×C31—41no—
467C22×C31—41no—
468C22×C31—42no—
469C22×C31—42no—
470C22×C31—41no—
471C22×C31—41no—
472C22×C31—41no—
473C22×C31—42no—
474C22×C31—41no—
475C22×C31—42no—
476C22×C31—41no—
477C22×C31—42no—
478C22×C31—42no—
479C22×C31—42no—
480C22×C31—42no—
481C22×C31—42no—
482C22×C31—42no—
483C22×C31—42no—
484C22×C31—816no—
485C22×C31—81no—
486C22×C31—81no—
487C22×C31—81no—
488C22×C31—81no—
489C22×C31—81no—
490C22×C31—81no—
491C22×C31—81no—
492C22×C31—81no—
493C22×C31C2×#12011yescharacteristic
494C22×C31D4211yescharacteristic
495C22×C31D4211yescharacteristic
496C22×C31C2×#13511yescharacteristic
497C22×C31#57511yescharacteristic
498C22×C31#57611yescharacteristic
499C22×C31#57711yescharacteristic
500C4×C31—22no—
501C4×C31—41no—
502C4×C31—42no—
503C4×C31—42no—
504C4×C31—41no—
505C4×C31—41no—
506C4×C31—42no—
507C4×C31—81no—
508C4×C31—81no—
509C4×C31C2×#12011yescharacteristic
510C4×C31#53411yescharacteristic
511C4×C31D4211yescharacteristic
512C4×C31D4211yescharacteristic
513C22×#41C22×C3111yescharacteristic
514C22×#41C22×C3111yescharacteristic, complemented
515C23×D4C22×C3111yescharacteristic
516C2×#135—24no—
517C2×#135—24no—
518C2×#135—24no—
519C22×Q16C22×C3111yescharacteristic, complemented
520C22×SD16C22×C3111yescharacteristic
521C22×SD16C22×C3111yescharacteristic
522C22×SD16C22×C3111yescharacteristic, complemented
523C22×D8C22×C3111yescharacteristic
524C22×D8C22×C3111yescharacteristic
525C23×C8C22×C3111yescharacteristic, complemented
526#546—24no—
527#546—24no—
528C2×#124C22×C3111yescharacteristic
529C2×#123—21no—
530C2×C22⋊Q8C22×C3111yescharacteristic
531C2×C22⋊Q8C22×C3111yescharacteristic
532C2×#121—21no—
533C2×#121C22×C3111yescharacteristic
534C2×#121C22×C3111yescharacteristic
535C2×#120—21no—
536C2×C4×D4C22×C3111yescharacteristic
537C2×C4×D4C22×C3111yescharacteristic
538C22×C22⋊C4—21no—
539#450—24no—
540#449—24no—
541#447—24no—
542C2×#103C22×C3111yescharacteristic, complemented
543C2×#103C22×C3111yescharacteristic, complemented
544C2×#103C22×C3111yescharacteristic, complemented
545C2×#102C22×C3111yescharacteristic
546C2×#102C22×C3111yescharacteristic
547C2×#102C22×C3111yescharacteristic
548C2×#102C22×C3111yescharacteristic
549C2×#102C22×C3111yescharacteristic, complemented
550C2×C22⋊C8C22×C3111yescharacteristic
551C2×C22⋊C8C22×C3111yescharacteristic
552C2×C22⋊C8C22×C3111yescharacteristic, complemented
553#394—21no—
554#392—21no—
555#391C22×C3111yescharacteristic, complemented
556#390C22×C3111yescharacteristic, complemented
557#386—21no—
558#385—21no—
559#380C22×C3111yescharacteristic, complemented
560#340C22×C3111yescharacteristic, complemented
561#340C22×C3111yescharacteristic, complemented
562#336C22×C3111yescharacteristic, complemented
563#336C22×C3111yescharacteristic, complemented
564C2×C31—42no—
565C2×C31—42no—
566C2×C31—44no—
567C2×C31—82no—
568C2×C31—82no—
569C2×C31#240311yescharacteristic
570C2×C31#300211yescharacteristic
571C2×C31#301211yescharacteristic
572C2×C31#326711yescharacteristic
573C2×C31#326811yescharacteristic
574C2×C31#328011yescharacteristic
575C2×C31#328211yescharacteristic
576C25—21no—
577C2×#41—22no—
578C2×#41—22no—
579C2×#41—22no—
580C2×#41—22no—
581C2×#41—22no—
582C2×#41—22no—
583C2×#41—22no—
584C2×#41—41no—
585C2×#41—41no—
586C2×#41—41no—
587C2×#41—41no—
588C2×#41D4×C3114yescomplemented
589C22×Q8C23×C3111yescharacteristic
590C22×Q8C23×C3111yescharacteristic
591C22×D4—21no—
592C22×D4—21no—
593C22×D4—22no—
594C22×D4—22no—
595C22×D4—22no—
596C22×D4—22no—
597C22×D4—21no—
598C22×D4—21no—
599C22×D4—21no—
600C22×D4—41no—
601C22×D4—41no—
602C22×D4D4×C3111yescharacteristic
603C22×D4C23×C3111yescharacteristic
604C22×D4C23×C3111yescharacteristic
605C22×D4C23×C3111yescharacteristic
606C23×C4—21no—
607C23×C4—21no—
608C23×C4—21no—
609C23×C4C23×C3111yescharacteristic
610C23×C4C23×C3111yescharacteristic
611#135—232no—
612C2×Q16—22no—
613C2×Q16—22no—
614C2×Q16—22no—
615C2×SD16—22no—
616C2×SD16—22no—
617C2×SD16—22no—
618C2×SD16—22no—
619C2×SD16—22no—
620C2×SD16—22no—
621C2×SD16—22no—
622C2×SD16—41no—
623C2×SD16D4×C3114yescomplemented
624C2×D8—22no—
625C2×D8—22no—
626C2×D8—22no—
627C2×D8—22no—
628C2×D8—41no—
629C2×D8D4×C3114yescomplemented
630C22×C8—22no—
631C22×C8—22no—
632C22×C8—22no—
633C22×C8C23×C3111yescharacteristic
634C22×C8C23×C3111yescharacteristic
635C22×C8C23×C3111yescharacteristic
636C22×C8C23×C3111yescharacteristic
637#124—22no—
638#124—22no—
639#123—28no—
640C22⋊Q8—22no—
641C22⋊Q8—22no—
642C22⋊Q8—22no—
643C22⋊Q8—41no—
644#121—28no—
645#121—22no—
646#121—22no—
647#121—41no—
648#121D4×C3114yescomplemented
649#120—28no—
650C4×D4—22no—
651C4×D4—22no—
652C4×D4—22no—
653C4×D4—22no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4D4×C3111yescharacteristic
657C2×C4⋊C4C23×C3111yescharacteristic
658C2×C4⋊C4C23×C3111yescharacteristic
659C2×C4⋊C4C23×C3111yescharacteristic
660C2×C22⋊C4—28no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4D4×C3111yescharacteristic
672C2×C22⋊C4D4×C3111yescharacteristic
673C2×C42C23×C3111yescharacteristic
674#103—22no—
675#103—41no—
676#103—41no—
677#102—22no—
678#102—22no—
679#102—22no—
680#102—22no—
681#102—22no—
682C22⋊C8—22no—
683C22⋊C8—22no—
684C22⋊C8—22no—
685#95—21no—
686#95—21no—
687#95—21no—
688C31#2385011yescharacteristic, direct product factor, Sylow
689C24—21no—
690C24—24no—
691C24—21no—
692C24—21no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—42no—
697C24—81no—
698C24—81no—
699C24C2×D4×C3111yescharacteristic
700C24C2×D4×C3111yescharacteristic
701#41—28no—
702#41—28no—
703#41—44no—
704#41—44no—
705#41—44no—
706#41—44no—
707#41—44no—
708#41—44no—
709C2×Q8—21no—
710C2×Q8—21no—
711C2×Q8—21no—
712C2×Q8—21no—
713C2×Q8—21no—
714C2×Q8—21no—
715C2×Q8—21no—
716C2×Q8—21no—
717C2×Q8—21no—
718C2×Q8—21no—
719C2×Q8C2×D4×C3112yes—
720C2×Q8C2×D4×C3112yes—
721C2×D4—24no—
722C2×D4—22no—
723C2×D4—24no—
724C2×D4—22no—
725C2×D4—24no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—41no—
740C2×D4—42no—
741C2×D4—42no—
742C2×D4—42no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—42no—
747C2×D4—42no—
748C2×D4—42no—
749C2×D4—42no—
750C2×D4—44no—
751C2×D4—42no—
752C2×D4—42no—
753C2×D4—81no—
754C2×D4—81no—
755C2×D4—81no—
756C2×D4C2×D4×C3112yes—
757C2×D4C2×D4×C3112yes—
758C2×D4C2×D4×C3112yes—
759C2×D4C2×D4×C3112yes—
760C2×D4C2×D4×C3112yes—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—24no—
769C22×C4—24no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—42no—
779C22×C4—42no—
780C22×C4—42no—
781C22×C4—42no—
782C22×C4—42no—
783C22×C4—81no—
784C22×C4—81no—
785C22×C4C2×D4×C3111yescharacteristic
786C22×C4C2×D4×C3111yescharacteristic
787C22×C4C2×D4×C3111yescharacteristic
788C22×C4C2×D4×C3111yescharacteristic
789C22×C4C2×D4×C3112yes—
790C22×C4C2×D4×C3112yes—
791C22×C4C24×C3111yescharacteristic
792Q16—28no—
793SD16—28no—
794SD16—28no—
795SD16—44no—
796D8—28no—
797D8—44no—
798C2×C8—28no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—21no—
809C2×C8C2×D4×C3112yes—
810C2×C8C2×D4×C3112yes—
811C4⋊C4—24no—
812C4⋊C4—22no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—21no—
818C4⋊C4—42no—
819C4⋊C4C2×D4×C3112yes—
820C22⋊C4—24no—
821C22⋊C4—24no—
822C22⋊C4—24no—
823C22⋊C4—24no—
824C22⋊C4—22no—
825C22⋊C4—22no—
826C22⋊C4—24no—
827C22⋊C4—42no—
828C22⋊C4—42no—
829C22⋊C4—42no—
830C22⋊C4—81no—
831C22⋊C4—81no—
832C42—21no—
833C42—21no—
834C23—21no—
835C23—22no—
836C23—21no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—22no—
841C23—22no—
842C23—21no—
843C23—21no—
844C23—21no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—22no—
850C23—22no—
851C23—48no—
852C23—48no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—84no—
870C23—84no—
871C23—84no—
872C23—84no—
873C23—84no—
874C23C31×#12012yes—
875C23C31×#13512yescomplemented
876C23C22×D4×C3111yescharacteristic
877Q8—22no—
878Q8—22no—
879Q8—22no—
880Q8—22no—
881Q8—41no—
882Q8—41no—
883Q8—41no—
884Q8—41no—
885D4—22no—
886D4—22no—
887D4—22no—
888D4—22no—
889D4—22no—
890D4—22no—
891D4—22no—
892D4—44no—
893D4—48no—
894D4—48no—
895D4—48no—
896D4—41no—
897D4—41no—
898D4—41no—
899D4—41no—
900D4—84no—
901D4—84no—
902D4C31×#12014yes—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—22no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—21no—
921C2×C4—48no—
922C2×C4—48no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—84no—
940C2×C4C31×#12012yes—
941C2×C4C22×D4×C3111yescharacteristic
942C2×C4C22×D4×C3111yescharacteristic
943C2×C4C22×D4×C3111yescharacteristic
944C2×C4C22×D4×C3111yescharacteristic
945C2×C4C31×H(5,𝔽2)11yescharacteristic
946C2×C4C31×H(5,𝔽2)11yescharacteristic
947C8—22no—
948C8—22no—
949C8—41no—
950C8—41no—
951C22—22no—
952C22—24no—
953C22—22no—
954C22—22no—
955C22—22no—
956C22—22no—
957C22—22no—
958C22—41no—
959C22—42no—
960C22—41no—
961C22—41no—
962C22—42no—
963C22—42no—
964C22—41no—
965C22—41no—
966C22—41no—
967C22—42no—
968C22—41no—
969C22—42no—
970C22—41no—
971C22—42no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—816no—
979C22—81no—
980C22—81no—
981C22—81no—
982C22—81no—
983C22—81no—
984C22—81no—
985C22—81no—
986C22—81no—
987C22C2×C31×#12011yescharacteristic
988C22D42×C3111yescharacteristic
989C22D42×C3111yescharacteristic
990C22C2×C31×#13511yescharacteristic
991C22C31×#57511yescharacteristic
992C22C31×#57611yescharacteristic
993C22C31×#57711yescharacteristic
994C4—22no—
995C4—41no—
996C4—42no—
997C4—42no—
998C4—41no—
999C4—41no—
1000C4—42no—
1001C4—81no—
1002C4—81no—
1003C4C2×C31×#12011yescharacteristic
1004C4C31×#53411yescharacteristic
1005C4D42×C3111yescharacteristic
1006C4D42×C3111yescharacteristic
1007C2—42no—
1008C2—42no—
1009C2—44no—
1010C2—82no—
1011C2—82no—
1012C2C31×#240311yescharacteristic
1013C2C31×#300211yescharacteristic
1014C2C31×#301211yescharacteristic
1015C2C31×#326711yescharacteristic
1016C2C31×#326811yescharacteristic
1017C2C31×#328011yescharacteristic
1018C2C31×#328211yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C4×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C31×#135C2semidirect
2. C2×C31×#546C2semidirect
3. C2×C31×#449C2semidirect
4. C2×C31×#450C2semidirect
5. C2×C31×#447C2semidirect
6. C31×#2407C2semidirect
7. C31×#2015C2semidirect
8. C31×#2012C2semidirect
9. C31×#2001C2semidirect
10. C31×#2000C2semidirect
11. C31×#1893C2semidirect
12. C31×#1879C2semidirect
13. C31×#1877C2semidirect
14. C31×#1869C2semidirect
15. C31×#1788C2semidirect
17. C22×#41×C31C22semidirect
22. C22×Q16×C31C22semidirect
25. C22×SD16×C31C22semidirect
28. C23×C8×C31C22semidirect
45. C2×C31×#103C22semidirect
46. C2×C31×#103C22semidirect
47. C2×C31×#103C22semidirect
52. C2×C31×#102C22semidirect
55. C2×C31×C22⋊C8C22semidirect
58. C31×#391C22semidirect
59. C31×#390C22semidirect
62. C31×#380C22semidirect
63. C31×#340C22semidirect
64. C31×#340C22semidirect
65. C31×#336C22semidirect
66. C31×#336C22semidirect
79. C2×#41×C31D4semidirect
114. C2×SD16×C31D4semidirect
120. C2×D8×C31D4semidirect
139. C31×#121D4semidirect
324. #23850C31direct (N × H)
366. C23×C31#135semidirect
442. C22×#135C2×C31semidirect
443. C2×#546C2×C31semidirect
444. C2×#449C2×C31semidirect
445. C2×#450C2×C31semidirect
446. C2×#447C2×C31semidirect
447. #2407C2×C31semidirect
448. #2015C2×C31semidirect
449. #2012C2×C31semidirect
450. #2001C2×C31semidirect
451. #2000C2×C31semidirect
452. #1893C2×C31semidirect
453. #1879C2×C31semidirect
454. #1877C2×C31semidirect
455. #1869C2×C31semidirect
456. #1788C2×C31semidirect
514. C22×#41C22×C31semidirect
519. C22×Q16C22×C31semidirect
522. C22×SD16C22×C31semidirect
525. C23×C8C22×C31semidirect
542. C2×#103C22×C31semidirect
543. C2×#103C22×C31semidirect
544. C2×#103C22×C31semidirect
549. C2×#102C22×C31semidirect
552. C2×C22⋊C8C22×C31semidirect
555. #391C22×C31semidirect
556. #390C22×C31semidirect
559. #380C22×C31semidirect
560. #340C22×C31semidirect
561. #340C22×C31semidirect
562. #336C22×C31semidirect
563. #336C22×C31semidirect
588. C2×#41D4×C31semidirect
623. C2×SD16D4×C31semidirect
629. C2×D8D4×C31semidirect
648. #121D4×C31semidirect
688. C31#23850direct (N × H)
875. C23C31×#135semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1352
C2×C31×#5462
C2×C31×#4492
C2×C31×#4502
C2×C31×#4472
C31×#24072
C31×#20152
C31×#20122
C31×#20012
C31×#20002
C31×#18932
C31×#18792
C31×#18772
C31×#18692
C31×#17882
#2385031