Finite Group Databasebeta

← C31×#23854 #21480613

Subgroups — C31×#23854 #21480613

Order 7936.

1794 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#135C211yesmaximal, characteristic, complemented
2C2×C31×#548C211yesmaximal, characteristic, complemented
3C2×C31×#452C211yesmaximal, characteristic, complemented
4C2×C31×#451C211yesmaximal, characteristic, complemented
5C2×C31×#448C211yesmaximal, characteristic, complemented
6C31×#2407C211yesmaximal, characteristic, complemented
7C31×#2015C211yesmaximal, characteristic, complemented
8C31×#2012C211yesmaximal, characteristic, complemented
9C31×#2000C211yesmaximal, characteristic, complemented
10C31×#1999C211yesmaximal, characteristic, complemented
11C31×#1892C211yesmaximal, characteristic, complemented
12C31×#1880C211yesmaximal, characteristic, complemented
13C31×#1878C211yesmaximal, characteristic, complemented
14C31×#1869C211yesmaximal, characteristic, complemented
15C31×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C22×#41×C31C2211yescharacteristic
18C23×Q8×C31C2211yescharacteristic
19C2×C31×#135—24no—
20C2×C31×#135—24no—
21C2×C31×#135—24no—
22C22×Q16×C31C2211yescharacteristic
23C22×Q16×C31C2211yescharacteristic
24C22×SD16×C31C2211yescharacteristic
25C22×SD16×C31C2211yescharacteristic
26C22×SD16×C31C2211yescharacteristic
27C22×D8×C31C2211yescharacteristic
28C23×C8×C31C2211yescharacteristic
29C31×#548—24no—
30C31×#548—24no—
31C2×C31×#124—21no—
32C2×C31×#124C2211yescharacteristic
33C2×C31×C22⋊Q8—21no—
34C2×C31×C22⋊Q8C2211yescharacteristic
35C2×C31×C22⋊Q8C2211yescharacteristic
36C2×C31×#121—21no—
37C2×C31×#121C2211yescharacteristic
38C2×C31×#121C2211yescharacteristic
39C2×C4×Q8×C31C2211yescharacteristic
40C2×C4×D4×C31—21no—
41C2×C4×D4×C31C2211yescharacteristic
42C31×#452—24no—
43C31×#451—24no—
44C31×#448—24no—
45C2×C31×#103C2211yescharacteristic
46C2×C31×#103C2211yescharacteristic
47C2×C31×#103C2211yescharacteristic
48C2×C31×#103C2211yescharacteristic
49C2×C31×#103C2211yescharacteristic
50C2×C31×#102C2211yescharacteristic
51C2×C31×#102C2211yescharacteristic
52C2×C31×#102C2211yescharacteristic
53C2×C31×C22⋊C8C2211yescharacteristic
54C2×C31×C22⋊C8C2211yescharacteristic
55C2×C31×C22⋊C8C2211yescharacteristic
56C31×#394—21no—
57C31×#392—21no—
58C31×#391C2211yescharacteristic
59C31×#390C2211yescharacteristic
60C31×#386—21no—
61C31×#385—21no—
62C31×#380C2211yescharacteristic
63C31×#340C2211yescharacteristic
64C31×#340C2211yescharacteristic
65C31×#336C2211yescharacteristic
66C31×#336C2211yescharacteristic
67C2×#41×C31—22no—
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—41no—
75C2×#41×C31—41no—
76C2×#41×C31—41no—
77C2×#41×C31—41no—
78C2×#41×C31D414yescomplemented
79C22×Q8×C31—22no—
80C22×Q8×C31—22no—
81C22×Q8×C31—21no—
82C22×Q8×C31—22no—
83C22×Q8×C31—22no—
84C22×Q8×C31—41no—
85C22×Q8×C31—41no—
86C22×Q8×C31C2311yescharacteristic
87C22×Q8×C31C2311yescharacteristic
88C22×Q8×C31C2311yescharacteristic
89C22×D4×C31—21no—
90C22×D4×C31—21no—
91C22×D4×C31—21no—
92C22×D4×C31—21no—
93C22×D4×C31D411yescharacteristic
94C22×D4×C31C2311yescharacteristic
95C22×D4×C31C2311yescharacteristic
96C23×C4×C31—21no—
97C23×C4×C31—21no—
98C23×C4×C31—21no—
99C23×C4×C31C2311yescharacteristic
100C23×C4×C31C2311yescharacteristic
101C31×#135—232no—
102C2×Q16×C31—22no—
103C2×Q16×C31—22no—
104C2×Q16×C31—22no—
105C2×Q16×C31—22no—
106C2×Q16×C31—41no—
107C2×Q16×C31D414yescomplemented
108C2×SD16×C31—22no—
109C2×SD16×C31—22no—
110C2×SD16×C31—22no—
111C2×SD16×C31—22no—
112C2×SD16×C31—22no—
113C2×SD16×C31—22no—
114C2×SD16×C31—22no—
115C2×SD16×C31—41no—
116C2×SD16×C31D414yescomplemented
117C2×D8×C31—22no—
118C2×D8×C31—22no—
119C2×D8×C31—22no—
120C22×C8×C31—22no—
121C22×C8×C31—22no—
122C22×C8×C31—22no—
123C22×C8×C31C2311yescharacteristic
124C22×C8×C31C2311yescharacteristic
125C22×C8×C31C2311yescharacteristic
126C22×C8×C31C2311yescharacteristic
127C31×#124—28no—
128C31×#124—22no—
129C31×#124—22no—
130C31×C22⋊Q8—28no—
131C31×C22⋊Q8—22no—
132C31×C22⋊Q8—22no—
133C31×C22⋊Q8—41no—
134C31×C22⋊Q8D414yescomplemented
135C31×#121—28no—
136C31×#121—22no—
137C31×#121—22no—
138C31×#121—22no—
139C31×#121—41no—
140C4×Q8×C31—22no—
141C4×Q8×C31—22no—
142C4×D4×C31—28no—
143C4×D4×C31—22no—
144C4×D4×C31—22no—
145C2×C4⋊C4×C31—21no—
146C2×C4⋊C4×C31—21no—
147C2×C4⋊C4×C31—21no—
148C2×C4⋊C4×C31D411yescharacteristic
149C2×C4⋊C4×C31C2311yescharacteristic
150C2×C4⋊C4×C31C2311yescharacteristic
151C2×C4⋊C4×C31C2311yescharacteristic
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×C31D411yescharacteristic
162C2×C22⋊C4×C31D411yescharacteristic
163C2×C42×C31—21no—
164C2×C42×C31C2311yescharacteristic
165C31×#103—22no—
166C31×#103—22no—
167C31×#103—22no—
168C31×#103—22no—
169C31×#103—22no—
170C31×#102—22no—
171C31×#102—41no—
172C31×#102—41no—
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—21no—
181C24×C31C2×D411yescharacteristic
182C24×C31C2×D411yescharacteristic
183#41×C31—28no—
184#41×C31—28no—
185#41×C31—44no—
186#41×C31—44no—
187#41×C31—44no—
188#41×C31—44no—
189#41×C31—44no—
190#41×C31—44no—
191C2×Q8×C31—24no—
192C2×Q8×C31—21no—
193C2×Q8×C31—21no—
194C2×Q8×C31—21no—
195C2×Q8×C31—21no—
196C2×Q8×C31—21no—
197C2×Q8×C31—21no—
198C2×Q8×C31—21no—
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—42no—
206C2×Q8×C31—42no—
207C2×Q8×C31—44no—
208C2×Q8×C31—44no—
209C2×Q8×C31—44no—
210C2×Q8×C31—44no—
211C2×Q8×C31C2×D412yes—
212C2×Q8×C31C2×D412yes—
213C2×Q8×C31C2×D412yes—
214C2×Q8×C31C2×D412yes—
215C2×Q8×C31C2×D412yes—
216C2×D4×C31—24no—
217C2×D4×C31—22no—
218C2×D4×C31—24no—
219C2×D4×C31—22no—
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—21no—
230C2×D4×C31—41no—
231C2×D4×C31—42no—
232C2×D4×C31—42no—
233C2×D4×C31—42no—
234C2×D4×C31—42no—
235C2×D4×C31—42no—
236C2×D4×C31—42no—
237C2×D4×C31—42no—
238C2×D4×C31—42no—
239C2×D4×C31—42no—
240C2×D4×C31—81no—
241C2×D4×C31C2×D412yes—
242C2×D4×C31C2×D412yes—
243C22×C4×C31—21no—
244C22×C4×C31—21no—
245C22×C4×C31—21no—
246C22×C4×C31—21no—
247C22×C4×C31—21no—
248C22×C4×C31—24no—
249C22×C4×C31—21no—
250C22×C4×C31—21no—
251C22×C4×C31—21no—
252C22×C4×C31—24no—
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—42no—
262C22×C4×C31—42no—
263C22×C4×C31—42no—
264C22×C4×C31—42no—
265C22×C4×C31—42no—
266C22×C4×C31—42no—
267C22×C4×C31—42no—
268C22×C4×C31C2×D411yescharacteristic
269C22×C4×C31C2×D411yescharacteristic
270C22×C4×C31C2×D411yescharacteristic
271C22×C4×C31C2×D411yescharacteristic
272C22×C4×C31C2×D412yes—
273C22×C4×C31C2×D412yes—
274C22×C4×C31C2411yescharacteristic
275Q16×C31—28no—
276Q16×C31—44no—
277SD16×C31—28no—
278SD16×C31—28no—
279SD16×C31—44no—
280D8×C31—28no—
281C2×C8×C31—28no—
282C2×C8×C31—21no—
283C2×C8×C31—21no—
284C2×C8×C31—21no—
285C2×C8×C31—21no—
286C2×C8×C31—21no—
287C2×C8×C31—21no—
288C2×C8×C31—21no—
289C2×C8×C31—21no—
290C2×C8×C31—21no—
291C2×C8×C31—21no—
292C2×C8×C31C2×D412yes—
293C2×C8×C31C2×D412yes—
294C4⋊C4×C31—24no—
295C4⋊C4×C31—24no—
296C4⋊C4×C31—22no—
297C4⋊C4×C31—21no—
298C4⋊C4×C31—21no—
299C4⋊C4×C31—21no—
300C4⋊C4×C31—21no—
301C4⋊C4×C31—21no—
302C4⋊C4×C31—42no—
303C4⋊C4×C31C2×D412yes—
304C22⋊C4×C31—24no—
305C22⋊C4×C31—24no—
306C22⋊C4×C31—24no—
307C22⋊C4×C31—24no—
308C22⋊C4×C31—22no—
309C22⋊C4×C31—22no—
310C22⋊C4×C31—42no—
311C22⋊C4×C31—42no—
312C22⋊C4×C31—42no—
313C22⋊C4×C31—81no—
314C22⋊C4×C31—81no—
315C42×C31—24no—
316C42×C31—21no—
317C42×C31—21no—
318#23854C3111yesmaximal, characteristic, direct product factor, Sylow
319C23×C31—21no—
320C23×C31—21no—
321C23×C31—21no—
322C23×C31—21no—
323C23×C31—21no—
324C23×C31—21no—
325C23×C31—21no—
326C23×C31—21no—
327C23×C31—21no—
328C23×C31—21no—
329C23×C31—21no—
330C23×C31—21no—
331C23×C31—22no—
332C23×C31—22no—
333C23×C31—41no—
334C23×C31—41no—
335C23×C31—41no—
336C23×C31—41no—
337C23×C31—41no—
338C23×C31—41no—
339C23×C31—41no—
340C23×C31—41no—
341C23×C31—41no—
342C23×C31—41no—
343C23×C31—41no—
344C23×C31—41no—
345C23×C31#12012yes—
346C23×C31#13512yescomplemented
347C23×C31C22×D411yescharacteristic
348Q8×C31—22no—
349Q8×C31—22no—
350Q8×C31—22no—
351Q8×C31—22no—
352Q8×C31—22no—
353Q8×C31—22no—
354Q8×C31—22no—
355Q8×C31—48no—
356Q8×C31—41no—
357Q8×C31—41no—
358Q8×C31—41no—
359Q8×C31—41no—
360Q8×C31#12014yes—
361D4×C31—22no—
362D4×C31—22no—
363D4×C31—22no—
364D4×C31—22no—
365D4×C31—48no—
366D4×C31—44no—
367D4×C31—48no—
368D4×C31—48no—
369D4×C31—41no—
370D4×C31—41no—
371D4×C31—41no—
372D4×C31—41no—
373D4×C31—84no—
374C2×C4×C31—22no—
375C2×C4×C31—21no—
376C2×C4×C31—21no—
377C2×C4×C31—22no—
378C2×C4×C31—22no—
379C2×C4×C31—22no—
380C2×C4×C31—22no—
381C2×C4×C31—22no—
382C2×C4×C31—22no—
383C2×C4×C31—21no—
384C2×C4×C31—21no—
385C2×C4×C31—22no—
386C2×C4×C31—22no—
387C2×C4×C31—21no—
388C2×C4×C31—21no—
389C2×C4×C31—22no—
390C2×C4×C31—21no—
391C2×C4×C31—21no—
392C2×C4×C31—21no—
393C2×C4×C31—21no—
394C2×C4×C31—21no—
395C2×C4×C31—48no—
396C2×C4×C31—48no—
397C2×C4×C31—48no—
398C2×C4×C31—41no—
399C2×C4×C31—41no—
400C2×C4×C31—41no—
401C2×C4×C31—41no—
402C2×C4×C31—41no—
403C2×C4×C31—41no—
404C2×C4×C31—41no—
405C2×C4×C31—41no—
406C2×C4×C31—41no—
407C2×C4×C31—41no—
408C2×C4×C31—41no—
409C2×C4×C31—41no—
410C2×C4×C31—41no—
411C2×C4×C31—41no—
412C2×C4×C31—41no—
413C2×C4×C31—41no—
414C2×C4×C31#12012yes—
415C2×C4×C31C22×D411yescharacteristic
416C2×C4×C31C22×D411yescharacteristic
417C2×C4×C31C22×D411yescharacteristic
418C2×C4×C31C22×D411yescharacteristic
419C2×C4×C31H(5,𝔽2)11yescharacteristic
420C2×C4×C31H(5,𝔽2)11yescharacteristic
421C8×C31—22no—
422C8×C31—22no—
423C8×C31—41no—
424C8×C31—41no—
425C22×#135C2×C3111yescharacteristic, complemented
426C2×#548C2×C3111yescharacteristic, complemented
427C2×#452C2×C3111yescharacteristic, complemented
428C2×#451C2×C3111yescharacteristic, complemented
429C2×#448C2×C3111yescharacteristic, complemented
430#2407C2×C3111yescharacteristic, complemented
431#2015C2×C3111yescharacteristic, complemented
432#2012C2×C3111yescharacteristic, complemented
433#2000C2×C3111yescharacteristic, complemented
434#1999C2×C3111yescharacteristic, complemented
435#1892C2×C3111yescharacteristic, complemented
436#1880C2×C3111yescharacteristic, complemented
437#1878C2×C3111yescharacteristic, complemented
438#1869C2×C3111yescharacteristic, complemented
439#1788C2×C3111yescharacteristic, complemented
440C22×C31—22no—
441C22×C31—22no—
442C22×C31—22no—
443C22×C31—22no—
444C22×C31—22no—
445C22×C31—22no—
446C22×C31—41no—
447C22×C31—41no—
448C22×C31—41no—
449C22×C31—41no—
450C22×C31—41no—
451C22×C31—41no—
452C22×C31—41no—
453C22×C31—41no—
454C22×C31—42no—
455C22×C31—42no—
456C22×C31—42no—
457C22×C31—42no—
458C22×C31—42no—
459C22×C31—42no—
460C22×C31—81no—
461C22×C31—81no—
462C22×C31—81no—
463C22×C31—81no—
464C22×C31—81no—
465C22×C31—81no—
466C22×C31—81no—
467C22×C31—81no—
468C22×C31C2×#12011yescharacteristic
469C22×C31D4211yescharacteristic
470C22×C31D4211yescharacteristic
471C22×C31C2×#13511yescharacteristic
472C22×C31#57511yescharacteristic
473C22×C31#57711yescharacteristic
474C22×C31#57811yescharacteristic
475C4×C31—22no—
476C4×C31—24no—
477C4×C31—41no—
478C4×C31—42no—
479C4×C31—42no—
480C4×C31—41no—
481C4×C31—42no—
482C4×C31—41no—
483C4×C31—81no—
484C4×C31—81no—
485C4×C31C2×#12011yescharacteristic
486C4×C31#53411yescharacteristic
487C4×C31D4211yescharacteristic
488C4×C31D4211yescharacteristic
489C22×#41C22×C3111yescharacteristic
490C22×#41C22×C3111yescharacteristic
491C23×Q8C22×C3111yescharacteristic
492C2×#135—24no—
493C2×#135—24no—
494C2×#135—24no—
495C22×Q16C22×C3111yescharacteristic
496C22×Q16C22×C3111yescharacteristic
497C22×SD16C22×C3111yescharacteristic
498C22×SD16C22×C3111yescharacteristic
499C22×SD16C22×C3111yescharacteristic
500C22×D8C22×C3111yescharacteristic
501C23×C8C22×C3111yescharacteristic
502#548—24no—
503#548—24no—
504C2×#124—21no—
505C2×#124C22×C3111yescharacteristic
506C2×C22⋊Q8—21no—
507C2×C22⋊Q8C22×C3111yescharacteristic
508C2×C22⋊Q8C22×C3111yescharacteristic
509C2×#121—21no—
510C2×#121C22×C3111yescharacteristic
511C2×#121C22×C3111yescharacteristic
512C2×C4×Q8C22×C3111yescharacteristic
513C2×C4×D4—21no—
514C2×C4×D4C22×C3111yescharacteristic
515#452—24no—
516#451—24no—
517#448—24no—
518C2×#103C22×C3111yescharacteristic
519C2×#103C22×C3111yescharacteristic
520C2×#103C22×C3111yescharacteristic
521C2×#103C22×C3111yescharacteristic
522C2×#103C22×C3111yescharacteristic
523C2×#102C22×C3111yescharacteristic
524C2×#102C22×C3111yescharacteristic
525C2×#102C22×C3111yescharacteristic
526C2×C22⋊C8C22×C3111yescharacteristic
527C2×C22⋊C8C22×C3111yescharacteristic
528C2×C22⋊C8C22×C3111yescharacteristic
529#394—21no—
530#392—21no—
531#391C22×C3111yescharacteristic
532#390C22×C3111yescharacteristic
533#386—21no—
534#385—21no—
535#380C22×C3111yescharacteristic
536#340C22×C3111yescharacteristic
537#340C22×C3111yescharacteristic
538#336C22×C3111yescharacteristic
539#336C22×C3111yescharacteristic
540C2×C31—42no—
541C2×C31—42no—
542C2×C31—82no—
543C2×C31—82no—
544C2×C31#240311yescharacteristic
545C2×C31#300211yescharacteristic
546C2×C31#301311yescharacteristic
547C2×C31#326911yescharacteristic
548C2×C31#327111yescharacteristic
549C2×C31#328211yescharacteristic
550C2×C31#328511yescharacteristic
551C2×#41—22no—
552C2×#41—22no—
553C2×#41—22no—
554C2×#41—22no—
555C2×#41—22no—
556C2×#41—22no—
557C2×#41—22no—
558C2×#41—41no—
559C2×#41—41no—
560C2×#41—41no—
561C2×#41—41no—
562C2×#41D4×C3114yescomplemented
563C22×Q8—22no—
564C22×Q8—22no—
565C22×Q8—21no—
566C22×Q8—22no—
567C22×Q8—22no—
568C22×Q8—41no—
569C22×Q8—41no—
570C22×Q8C23×C3111yescharacteristic
571C22×Q8C23×C3111yescharacteristic
572C22×Q8C23×C3111yescharacteristic
573C22×D4—21no—
574C22×D4—21no—
575C22×D4—21no—
576C22×D4—21no—
577C22×D4D4×C3111yescharacteristic
578C22×D4C23×C3111yescharacteristic
579C22×D4C23×C3111yescharacteristic
580C23×C4—21no—
581C23×C4—21no—
582C23×C4—21no—
583C23×C4C23×C3111yescharacteristic
584C23×C4C23×C3111yescharacteristic
585#135—232no—
586C2×Q16—22no—
587C2×Q16—22no—
588C2×Q16—22no—
589C2×Q16—22no—
590C2×Q16—41no—
591C2×Q16D4×C3114yescomplemented
592C2×SD16—22no—
593C2×SD16—22no—
594C2×SD16—22no—
595C2×SD16—22no—
596C2×SD16—22no—
597C2×SD16—22no—
598C2×SD16—22no—
599C2×SD16—41no—
600C2×SD16D4×C3114yescomplemented
601C2×D8—22no—
602C2×D8—22no—
603C2×D8—22no—
604C22×C8—22no—
605C22×C8—22no—
606C22×C8—22no—
607C22×C8C23×C3111yescharacteristic
608C22×C8C23×C3111yescharacteristic
609C22×C8C23×C3111yescharacteristic
610C22×C8C23×C3111yescharacteristic
611#124—28no—
612#124—22no—
613#124—22no—
614C22⋊Q8—28no—
615C22⋊Q8—22no—
616C22⋊Q8—22no—
617C22⋊Q8—41no—
618C22⋊Q8D4×C3114yescomplemented
619#121—28no—
620#121—22no—
621#121—22no—
622#121—22no—
623#121—41no—
624C4×Q8—22no—
625C4×Q8—22no—
626C4×D4—28no—
627C4×D4—22no—
628C4×D4—22no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4D4×C3111yescharacteristic
633C2×C4⋊C4C23×C3111yescharacteristic
634C2×C4⋊C4C23×C3111yescharacteristic
635C2×C4⋊C4C23×C3111yescharacteristic
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4D4×C3111yescharacteristic
646C2×C22⋊C4D4×C3111yescharacteristic
647C2×C42—21no—
648C2×C42C23×C3111yescharacteristic
649#103—22no—
650#103—22no—
651#103—22no—
652#103—22no—
653#103—22no—
654#102—22no—
655#102—41no—
656#102—41no—
657C22⋊C8—22no—
658C22⋊C8—22no—
659C22⋊C8—22no—
660#95—21no—
661#95—21no—
662#95—21no—
663C31#2385411yescharacteristic, direct product factor, Sylow
664C24—21no—
665C24—21no—
666C24C2×D4×C3111yescharacteristic
667C24C2×D4×C3111yescharacteristic
668#41—28no—
669#41—28no—
670#41—44no—
671#41—44no—
672#41—44no—
673#41—44no—
674#41—44no—
675#41—44no—
676C2×Q8—24no—
677C2×Q8—21no—
678C2×Q8—21no—
679C2×Q8—21no—
680C2×Q8—21no—
681C2×Q8—21no—
682C2×Q8—21no—
683C2×Q8—21no—
684C2×Q8—21no—
685C2×Q8—21no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8—42no—
691C2×Q8—42no—
692C2×Q8—44no—
693C2×Q8—44no—
694C2×Q8—44no—
695C2×Q8—44no—
696C2×Q8C2×D4×C3112yes—
697C2×Q8C2×D4×C3112yes—
698C2×Q8C2×D4×C3112yes—
699C2×Q8C2×D4×C3112yes—
700C2×Q8C2×D4×C3112yes—
701C2×D4—24no—
702C2×D4—22no—
703C2×D4—24no—
704C2×D4—22no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—41no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4—42no—
719C2×D4—42no—
720C2×D4—42no—
721C2×D4—42no—
722C2×D4—42no—
723C2×D4—42no—
724C2×D4—42no—
725C2×D4—81no—
726C2×D4C2×D4×C3112yes—
727C2×D4C2×D4×C3112yes—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—24no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—24no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—42no—
747C22×C4—42no—
748C22×C4—42no—
749C22×C4—42no—
750C22×C4—42no—
751C22×C4—42no—
752C22×C4—42no—
753C22×C4C2×D4×C3111yescharacteristic
754C22×C4C2×D4×C3111yescharacteristic
755C22×C4C2×D4×C3111yescharacteristic
756C22×C4C2×D4×C3111yescharacteristic
757C22×C4C2×D4×C3112yes—
758C22×C4C2×D4×C3112yes—
759C22×C4C24×C3111yescharacteristic
760Q16—28no—
761Q16—44no—
762SD16—28no—
763SD16—28no—
764SD16—44no—
765D8—28no—
766C2×C8—28no—
767C2×C8—21no—
768C2×C8—21no—
769C2×C8—21no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8C2×D4×C3112yes—
778C2×C8C2×D4×C3112yes—
779C4⋊C4—24no—
780C4⋊C4—24no—
781C4⋊C4—22no—
782C4⋊C4—21no—
783C4⋊C4—21no—
784C4⋊C4—21no—
785C4⋊C4—21no—
786C4⋊C4—21no—
787C4⋊C4—42no—
788C4⋊C4C2×D4×C3112yes—
789C22⋊C4—24no—
790C22⋊C4—24no—
791C22⋊C4—24no—
792C22⋊C4—24no—
793C22⋊C4—22no—
794C22⋊C4—22no—
795C22⋊C4—42no—
796C22⋊C4—42no—
797C22⋊C4—42no—
798C22⋊C4—81no—
799C22⋊C4—81no—
800C42—24no—
801C42—21no—
802C42—21no—
803C23—21no—
804C23—21no—
805C23—21no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—22no—
816C23—22no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23C31×#12012yes—
830C23C31×#13512yescomplemented
831C23C22×D4×C3111yescharacteristic
832Q8—22no—
833Q8—22no—
834Q8—22no—
835Q8—22no—
836Q8—22no—
837Q8—22no—
838Q8—22no—
839Q8—48no—
840Q8—41no—
841Q8—41no—
842Q8—41no—
843Q8—41no—
844Q8C31×#12014yes—
845D4—22no—
846D4—22no—
847D4—22no—
848D4—22no—
849D4—48no—
850D4—44no—
851D4—48no—
852D4—48no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—41no—
857D4—84no—
858C2×C4—22no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—22no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—48no—
880C2×C4—48no—
881C2×C4—48no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4C31×#12012yes—
899C2×C4C22×D4×C3111yescharacteristic
900C2×C4C22×D4×C3111yescharacteristic
901C2×C4C22×D4×C3111yescharacteristic
902C2×C4C22×D4×C3111yescharacteristic
903C2×C4C31×H(5,𝔽2)11yescharacteristic
904C2×C4C31×H(5,𝔽2)11yescharacteristic
905C8—22no—
906C8—22no—
907C8—41no—
908C8—41no—
909C22—22no—
910C22—22no—
911C22—22no—
912C22—22no—
913C22—22no—
914C22—22no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22C2×C31×#12011yescharacteristic
938C22D42×C3111yescharacteristic
939C22D42×C3111yescharacteristic
940C22C2×C31×#13511yescharacteristic
941C22C31×#57511yescharacteristic
942C22C31×#57711yescharacteristic
943C22C31×#57811yescharacteristic
944C4—22no—
945C4—24no—
946C4—41no—
947C4—42no—
948C4—42no—
949C4—41no—
950C4—42no—
951C4—41no—
952C4—81no—
953C4—81no—
954C4C2×C31×#12011yescharacteristic
955C4C31×#53411yescharacteristic
956C4D42×C3111yescharacteristic
957C4D42×C3111yescharacteristic
958C2—42no—
959C2—42no—
960C2—82no—
961C2—82no—
962C2C31×#240311yescharacteristic
963C2C31×#300211yescharacteristic
964C2C31×#301311yescharacteristic
965C2C31×#326911yescharacteristic
966C2C31×#327111yescharacteristic
967C2C31×#328211yescharacteristic
968C2C31×#328511yescharacteristic
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×#548C2semidirect
3. C2×C31×#452C2semidirect
4. C2×C31×#451C2semidirect
5. C2×C31×#448C2semidirect
6. C31×#2407C2semidirect
7. C31×#2015C2semidirect
8. C31×#2012C2semidirect
9. C31×#2000C2semidirect
10. C31×#1999C2semidirect
11. C31×#1892C2semidirect
12. C31×#1880C2semidirect
13. C31×#1878C2semidirect
14. C31×#1869C2semidirect
15. C31×#1788C2semidirect
78. C2×#41×C31D4semidirect
107. C2×Q16×C31D4semidirect
116. C2×SD16×C31D4semidirect
134. C31×C22⋊Q8D4semidirect
318. #23854C31direct (N × H)
346. C23×C31#135semidirect
425. C22×#135C2×C31semidirect
426. C2×#548C2×C31semidirect
427. C2×#452C2×C31semidirect
428. C2×#451C2×C31semidirect
429. C2×#448C2×C31semidirect
430. #2407C2×C31semidirect
431. #2015C2×C31semidirect
432. #2012C2×C31semidirect
433. #2000C2×C31semidirect
434. #1999C2×C31semidirect
435. #1892C2×C31semidirect
436. #1880C2×C31semidirect
437. #1878C2×C31semidirect
438. #1869C2×C31semidirect
439. #1788C2×C31semidirect
562. C2×#41D4×C31semidirect
591. C2×Q16D4×C31semidirect
600. C2×SD16D4×C31semidirect
618. C22⋊Q8D4×C31semidirect
663. C31#23854direct (N × H)
830. 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×#5482
C2×C31×#4522
C2×C31×#4512
C2×C31×#4482
C31×#24072
C31×#20152
C31×#20122
C31×#20002
C31×#19992
C31×#18922
C31×#18802
C31×#18782
C31×#18692
C31×#17882
#2385431