Finite Group Databasebeta

← C31×#24368 #21481127

Subgroups — C31×#24368 #21481127

Order 7936.

1446 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#137C211yesmaximal, characteristic, complemented
2C2×C31×#464C211yesmaximal, characteristic, complemented
3C2×C31×#460C211yesmaximal, characteristic, complemented
4C2×C31×#448C211yesmaximal, characteristic, complemented
5C31×#2431C211yesmaximal, characteristic
6Q8×C22⋊C4×C31C211yesmaximal, characteristic, complemented
7C31×#2056C211yesmaximal, characteristic, complemented
8C31×#2055C211yesmaximal, characteristic, complemented
9C31×#2015C211yesmaximal, characteristic, complemented
10C31×#2014C211yesmaximal, characteristic, complemented
11C31×#1895C211yesmaximal, characteristic, complemented
12C31×#1880C211yesmaximal, characteristic, complemented
13C31×#1878C211yesmaximal, characteristic, complemented
14C31×#1851C211yesmaximal, characteristic, complemented
15C31×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C23×Q8×C31C2211yescharacteristic
18C2×C31×#137—24no—
19C2×C31×#137—24no—
20C2×C31×#137—24no—
21C22×Q16×C31C2211yescharacteristic
22C22×Q16×C31C2211yescharacteristic
23C22×SD16×C31C2211yescharacteristic
24C22×SD16×C31C2211yescharacteristic
25C22×SD16×C31C2211yescharacteristic
26C22×SD16×C31C2211yescharacteristic
27C22×M16×C31C2211yescharacteristic
28C2×C31×#127C2211yescharacteristic
29C2×C31×#124C2211yescharacteristic
30C2×C31×#121C2211yescharacteristic
31C2×C4×Q8×C31C2211yescharacteristic
32C2×C4×Q8×C31C2211yescharacteristic
33C31×#464—24no—
34C31×#460—24no—
35C31×#448—24no—
36C2×C31×C4⋊C8C2211yescharacteristic
37C2×C31×C4⋊C8C2211yescharacteristic
38C2×C31×#103C2211yescharacteristic
39C2×C31×#103C2211yescharacteristic
40C2×C31×#103C2211yescharacteristic
41C2×C31×#103C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×#102C2211yescharacteristic
46C2×C31×C22⋊C8C2211yescharacteristic
47C31×#392—21no—
48C31×#392—21no—
49C31×#391—21no—
50C31×#391—21no—
51C31×#391C2211yescharacteristic
52C31×#391C2211yescharacteristic
53C31×#391C2211yescharacteristic
54C31×#390C2211yescharacteristic
55C31×#386—21no—
56C31×#386—21no—
57C31×#380—21no—
58C31×#380C2211yescharacteristic
59C4×C22⋊C4×C31—21no—
60C4×C22⋊C4×C31C2211yescharacteristic
61C31×#340C2211yescharacteristic
62C31×#340C2211yescharacteristic
63C31×#336C2211yescharacteristic
64C31×#336C2211yescharacteristic
65C2×#41×C31—22no—
66C2×#41×C31—22no—
67C2×#41×C31—22no—
68C2×#41×C31—22no—
69C2×#41×C31—41no—
70C2×#41×C31—41no—
71C22×Q8×C31—21no—
72C22×Q8×C31—22no—
73C22×Q8×C31—22no—
74C22×Q8×C31—22no—
75C22×Q8×C31—41no—
76C22×Q8×C31—41no—
77C22×Q8×C31D414yescomplemented
78C22×Q8×C31C2311yescharacteristic
79C22×Q8×C31C2311yescharacteristic
80C22×Q8×C31C2311yescharacteristic
81C22×D4×C31—21no—
82C22×D4×C31—21no—
83C22×D4×C31—21no—
84C22×D4×C31—21no—
85C22×D4×C31C2311yescharacteristic
86C22×D4×C31C2311yescharacteristic
87C23×C4×C31—21no—
88C23×C4×C31—21no—
89C23×C4×C31C2311yescharacteristic
90C31×#137—232no—
91C2×Q16×C31—22no—
92C2×Q16×C31—22no—
93C2×Q16×C31—22no—
94C2×Q16×C31—22no—
95C2×Q16×C31—22no—
96C2×Q16×C31D414yescomplemented
97C2×SD16×C31—22no—
98C2×SD16×C31—22no—
99C2×SD16×C31—22no—
100C2×SD16×C31—22no—
101C2×SD16×C31—22no—
102C2×SD16×C31—22no—
103C2×SD16×C31—22no—
104C2×SD16×C31—22no—
105C2×SD16×C31—22no—
106C2×SD16×C31—41no—
107C2×SD16×C31—41no—
108C2×SD16×C31D414yescomplemented
109C2×M16×C31—22no—
110C2×M16×C31—22no—
111C2×M16×C31—22no—
112C22×C8×C31C2311yescharacteristic
113C22×C8×C31C2311yescharacteristic
114C22×C8×C31C2311yescharacteristic
115C22×C8×C31C2311yescharacteristic
116C31×#127—22no—
117C31×#127—41no—
118C31×#124—22no—
119C31×#124—41no—
120C31×#121—22no—
121C31×#121—22no—
122C4×Q8×C31—22no—
123C4×Q8×C31—22no—
124C4×Q8×C31—41no—
125C4×Q8×C31—41no—
126C2×C4⋊C4×C31—21no—
127C2×C4⋊C4×C31—21no—
128C2×C4⋊C4×C31C2311yescharacteristic
129C2×C4⋊C4×C31C2311yescharacteristic
130C2×C4⋊C4×C31C2311yescharacteristic
131C2×C22⋊C4×C31—21no—
132C2×C22⋊C4×C31—21no—
133C2×C22⋊C4×C31—21no—
134C2×C22⋊C4×C31—21no—
135C2×C22⋊C4×C31—21no—
136C2×C22⋊C4×C31—21no—
137C2×C22⋊C4×C31D411yescharacteristic
138C2×C22⋊C4×C31D411yescharacteristic
139C2×C42×C31—21no—
140C2×C42×C31—21no—
141C2×C42×C31C2311yescharacteristic
142C2×C42×C31C2311yescharacteristic
143C31×C4⋊C8—22no—
144C31×C4⋊C8—22no—
145C31×#103—22no—
146C31×#103—22no—
147C31×#103—22no—
148C31×#103—41no—
149C31×#102—22no—
150C31×#102—22no—
151C31×#102—22no—
152C31×#102—41no—
153C31×C22⋊C8—22no—
154C31×#95—21no—
155C31×#95—21no—
156C31×#95—21no—
157C31×#95—21no—
158C31×#95—21no—
159C31×#95—21no—
160C31×#95—21no—
161C31×#95D411yescharacteristic
162C31×#95D411yescharacteristic
163C24×C31—21no—
164C24×C31—21no—
165C24×C31C2×D411yescharacteristic
166#41×C31—28no—
167#41×C31—44no—
168#41×C31—44no—
169#41×C31—44no—
170C2×Q8×C31—24no—
171C2×Q8×C31—21no—
172C2×Q8×C31—21no—
173C2×Q8×C31—21no—
174C2×Q8×C31—21no—
175C2×Q8×C31—21no—
176C2×Q8×C31—28no—
177C2×Q8×C31—21no—
178C2×Q8×C31—21no—
179C2×Q8×C31—21no—
180C2×Q8×C31—21no—
181C2×Q8×C31—21no—
182C2×Q8×C31—21no—
183C2×Q8×C31—21no—
184C2×Q8×C31—21no—
185C2×Q8×C31—42no—
186C2×Q8×C31—42no—
187C2×Q8×C31—44no—
188C2×Q8×C31—44no—
189C2×Q8×C31—44no—
190C2×Q8×C31C2×D412yes—
191C2×Q8×C31C2×D412yes—
192C2×Q8×C31C2×D412yes—
193C2×Q8×C31C2×D412yes—
194C2×Q8×C31C2×D412yes—
195C2×D4×C31—21no—
196C2×D4×C31—21no—
197C2×D4×C31—21no—
198C2×D4×C31—21no—
199C2×D4×C31—21no—
200C2×D4×C31—21no—
201C2×D4×C31—21no—
202C2×D4×C31—21no—
203C2×D4×C31—21no—
204C2×D4×C31—21no—
205C2×D4×C31—21no—
206C2×D4×C31—42no—
207C2×D4×C31—42no—
208C2×D4×C31—42no—
209C2×D4×C31—42no—
210C2×D4×C31—42no—
211C2×D4×C31—42no—
212C2×D4×C31—42no—
213C2×D4×C31—42no—
214C2×D4×C31—81no—
215C2×D4×C31—81no—
216C2×D4×C31—81no—
217C2×D4×C31—81no—
218C2×D4×C31C2×D412yes—
219C22×C4×C31—21no—
220C22×C4×C31—21no—
221C22×C4×C31—21no—
222C22×C4×C31—21no—
223C22×C4×C31—21no—
224C22×C4×C31—24no—
225C22×C4×C31—21no—
226C22×C4×C31—21no—
227C22×C4×C31—21no—
228C22×C4×C31—21no—
229C22×C4×C31—21no—
230C22×C4×C31—42no—
231C22×C4×C31—42no—
232C22×C4×C31—42no—
233C22×C4×C31—42no—
234C22×C4×C31—42no—
235C22×C4×C31C2×D411yescharacteristic
236C22×C4×C31C2×D411yescharacteristic
237C22×C4×C31C2×D411yescharacteristic
238C22×C4×C31C2×D411yescharacteristic
239C22×C4×C31C2×D412yes—
240C22×C4×C31C2×D411yescharacteristic
241C22×C4×C31#4112yes—
242C22×C4×C31C2411yescharacteristic
243Q16×C31—28no—
244Q16×C31—28no—
245SD16×C31—28no—
246SD16×C31—28no—
247SD16×C31—44no—
248SD16×C31—44no—
249M16×C31—28no—
250C2×C8×C31—21no—
251C2×C8×C31—21no—
252C2×C8×C31—21no—
253C2×C8×C31—21no—
254C2×C8×C31—21no—
255C2×C8×C31—21no—
256C2×C8×C31—21no—
257C2×C8×C31—21no—
258C2×C8×C31—21no—
259C2×C8×C31—21no—
260C2×C8×C31C2×D412yes—
261C2×C8×C31C2×D412yes—
262C4⋊C4×C31—21no—
263C4⋊C4×C31—21no—
264C4⋊C4×C31—21no—
265C4⋊C4×C31—21no—
266C4⋊C4×C31—21no—
267C4⋊C4×C31—21no—
268C4⋊C4×C31—42no—
269C4⋊C4×C31—42no—
270C22⋊C4×C31—22no—
271C22⋊C4×C31—41no—
272C22⋊C4×C31—42no—
273C22⋊C4×C31—42no—
274C22⋊C4×C31—42no—
275C22⋊C4×C31—42no—
276C22⋊C4×C31—81no—
277C22⋊C4×C31—81no—
278C42×C31—21no—
279C42×C31—21no—
280C42×C31—21no—
281C42×C31—21no—
282C42×C31—42no—
283C42×C31—42no—
284#24368C3111yesmaximal, characteristic, direct product factor, Sylow
285C23×C31—21no—
286C23×C31—21no—
287C23×C31—21no—
288C23×C31—21no—
289C23×C31—21no—
290C23×C31—21no—
291C23×C31—22no—
292C23×C31—41no—
293C23×C31—41no—
294C23×C31—41no—
295C23×C31—41no—
296C23×C31—41no—
297C23×C31—41no—
298C23×C31—41no—
299C23×C31—41no—
300C23×C31—41no—
301C23×C31—41no—
302C23×C31—41no—
303C23×C31—41no—
304C23×C31—41no—
305C23×C31#12112yes—
306C23×C31C22×D411yescharacteristic
307Q8×C31—22no—
308Q8×C31—22no—
309Q8×C31—22no—
310Q8×C31—22no—
311Q8×C31—22no—
312Q8×C31—22no—
313Q8×C31—22no—
314Q8×C31—48no—
315Q8×C31—41no—
316Q8×C31—41no—
317Q8×C31—41no—
318Q8×C31—41no—
319Q8×C31#12014yes—
320D4×C31—22no—
321D4×C31—22no—
322D4×C31—48no—
323D4×C31—41no—
324D4×C31—41no—
325D4×C31—41no—
326D4×C31—41no—
327D4×C31—41no—
328D4×C31—41no—
329D4×C31—84no—
330D4×C31—84no—
331D4×C31—84no—
332C2×C4×C31—22no—
333C2×C4×C31—21no—
334C2×C4×C31—22no—
335C2×C4×C31—22no—
336C2×C4×C31—21no—
337C2×C4×C31—21no—
338C2×C4×C31—21no—
339C2×C4×C31—22no—
340C2×C4×C31—22no—
341C2×C4×C31—22no—
342C2×C4×C31—22no—
343C2×C4×C31—22no—
344C2×C4×C31—21no—
345C2×C4×C31—21no—
346C2×C4×C31—21no—
347C2×C4×C31—22no—
348C2×C4×C31—21no—
349C2×C4×C31—21no—
350C2×C4×C31—21no—
351C2×C4×C31—21no—
352C2×C4×C31—21no—
353C2×C4×C31—21no—
354C2×C4×C31—48no—
355C2×C4×C31—48no—
356C2×C4×C31—41no—
357C2×C4×C31—41no—
358C2×C4×C31—41no—
359C2×C4×C31—41no—
360C2×C4×C31—41no—
361C2×C4×C31—41no—
362C2×C4×C31—41no—
363C2×C4×C31—41no—
364C2×C4×C31—41no—
365C2×C4×C31—41no—
366C2×C4×C31—41no—
367C2×C4×C31—41no—
368C2×C4×C31—41no—
369C2×C4×C31#12112yes—
370C2×C4×C31#13712yescomplemented
371C2×C4×C31C22×D411yescharacteristic
372C2×C4×C31C22×D411yescharacteristic
373C2×C4×C31C22×D411yescharacteristic
374C2×C4×C31C2×#4111yescharacteristic
375C2×C4×C31H(5,𝔽2)11yescharacteristic
376C2×C4×C31H(5,𝔽2)11yescharacteristic
377C8×C31—22no—
378C8×C31—22no—
379C8×C31—41no—
380C8×C31—41no—
381C22×#137C2×C3111yescharacteristic, complemented
382C2×#464C2×C3111yescharacteristic, complemented
383C2×#460C2×C3111yescharacteristic, complemented
384C2×#448C2×C3111yescharacteristic, complemented
385#2431C2×C3111yescharacteristic
386Q8×C22⋊C4C2×C3111yescharacteristic, complemented
387#2056C2×C3111yescharacteristic, complemented
388#2055C2×C3111yescharacteristic, complemented
389#2015C2×C3111yescharacteristic, complemented
390#2014C2×C3111yescharacteristic, complemented
391#1895C2×C3111yescharacteristic, complemented
392#1880C2×C3111yescharacteristic, complemented
393#1878C2×C3111yescharacteristic, complemented
394#1851C2×C3111yescharacteristic, complemented
395#1788C2×C3111yescharacteristic, complemented
396C22×C31—22no—
397C22×C31—22no—
398C22×C31—22no—
399C22×C31—41no—
400C22×C31—41no—
401C22×C31—41no—
402C22×C31—41no—
403C22×C31—42no—
404C22×C31—42no—
405C22×C31—42no—
406C22×C31—81no—
407C22×C31—81no—
408C22×C31—81no—
409C22×C31—81no—
410C22×C31—81no—
411C22×C31—81no—
412C22×C31—81no—
413C22×C31—81no—
414C22×C31—81no—
415C22×C31—81no—
416C22×C31—81no—
417C22×C31C2×#12111yescharacteristic
418C22×C31D4211yescharacteristic
419C22×C31D4211yescharacteristic
420C22×C31C2×#13711yescharacteristic
421C22×C31#57511yescharacteristic
422C22×C31#57711yescharacteristic
423C22×C31#57711yescharacteristic
424C4×C31—22no—
425C4×C31—24no—
426C4×C31—22no—
427C4×C31—42no—
428C4×C31—42no—
429C4×C31—41no—
430C4×C31—41no—
431C4×C31—41no—
432C4×C31—81no—
433C4×C31—81no—
434C4×C31—81no—
435C4×C31C2×#12011yescharacteristic
436C4×C31#53411yescharacteristic
437C4×C31#54611yescharacteristic
438C4×C31#54611yescharacteristic
439C22×#41C22×C3111yescharacteristic
440C23×Q8C22×C3111yescharacteristic
441C2×#137—24no—
442C2×#137—24no—
443C2×#137—24no—
444C22×Q16C22×C3111yescharacteristic
445C22×Q16C22×C3111yescharacteristic
446C22×SD16C22×C3111yescharacteristic
447C22×SD16C22×C3111yescharacteristic
448C22×SD16C22×C3111yescharacteristic
449C22×SD16C22×C3111yescharacteristic
450C22×M16C22×C3111yescharacteristic
451C2×#127C22×C3111yescharacteristic
452C2×#124C22×C3111yescharacteristic
453C2×#121C22×C3111yescharacteristic
454C2×C4×Q8C22×C3111yescharacteristic
455C2×C4×Q8C22×C3111yescharacteristic
456#464—24no—
457#460—24no—
458#448—24no—
459C2×C4⋊C8C22×C3111yescharacteristic
460C2×C4⋊C8C22×C3111yescharacteristic
461C2×#103C22×C3111yescharacteristic
462C2×#103C22×C3111yescharacteristic
463C2×#103C22×C3111yescharacteristic
464C2×#103C22×C3111yescharacteristic
465C2×#102C22×C3111yescharacteristic
466C2×#102C22×C3111yescharacteristic
467C2×#102C22×C3111yescharacteristic
468C2×#102C22×C3111yescharacteristic
469C2×C22⋊C8C22×C3111yescharacteristic
470#392—21no—
471#392—21no—
472#391—21no—
473#391—21no—
474#391C22×C3111yescharacteristic
475#391C22×C3111yescharacteristic
476#391C22×C3111yescharacteristic
477#390C22×C3111yescharacteristic
478#386—21no—
479#386—21no—
480#380—21no—
481#380C22×C3111yescharacteristic
482C4×C22⋊C4—21no—
483C4×C22⋊C4C22×C3111yescharacteristic
484#340C22×C3111yescharacteristic
485#340C22×C3111yescharacteristic
486#336C22×C3111yescharacteristic
487#336C22×C3111yescharacteristic
488C2×C31—42no—
489C2×C31—82no—
490C2×C31—161no—
491C2×C31#241011yescharacteristic
492C2×C31#303711yescharacteristic
493C2×C31#304311yescharacteristic
494C2×C31#326611yescharacteristic
495C2×C31#327111yescharacteristic
496C2×C31#327511yescharacteristic
497C2×C31#327811yescharacteristic
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—41no—
503C2×#41—41no—
504C22×Q8—21no—
505C22×Q8—22no—
506C22×Q8—22no—
507C22×Q8—22no—
508C22×Q8—41no—
509C22×Q8—41no—
510C22×Q8D4×C3114yescomplemented
511C22×Q8C23×C3111yescharacteristic
512C22×Q8C23×C3111yescharacteristic
513C22×Q8C23×C3111yescharacteristic
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4C23×C3111yescharacteristic
519C22×D4C23×C3111yescharacteristic
520C23×C4—21no—
521C23×C4—21no—
522C23×C4C23×C3111yescharacteristic
523#137—232no—
524C2×Q16—22no—
525C2×Q16—22no—
526C2×Q16—22no—
527C2×Q16—22no—
528C2×Q16—22no—
529C2×Q16D4×C3114yescomplemented
530C2×SD16—22no—
531C2×SD16—22no—
532C2×SD16—22no—
533C2×SD16—22no—
534C2×SD16—22no—
535C2×SD16—22no—
536C2×SD16—22no—
537C2×SD16—22no—
538C2×SD16—22no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×SD16D4×C3114yescomplemented
542C2×M16—22no—
543C2×M16—22no—
544C2×M16—22no—
545C22×C8C23×C3111yescharacteristic
546C22×C8C23×C3111yescharacteristic
547C22×C8C23×C3111yescharacteristic
548C22×C8C23×C3111yescharacteristic
549#127—22no—
550#127—41no—
551#124—22no—
552#124—41no—
553#121—22no—
554#121—22no—
555C4×Q8—22no—
556C4×Q8—22no—
557C4×Q8—41no—
558C4×Q8—41no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4C23×C3111yescharacteristic
562C2×C4⋊C4C23×C3111yescharacteristic
563C2×C4⋊C4C23×C3111yescharacteristic
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4D4×C3111yescharacteristic
571C2×C22⋊C4D4×C3111yescharacteristic
572C2×C42—21no—
573C2×C42—21no—
574C2×C42C23×C3111yescharacteristic
575C2×C42C23×C3111yescharacteristic
576C4⋊C8—22no—
577C4⋊C8—22no—
578#103—22no—
579#103—22no—
580#103—22no—
581#103—41no—
582#102—22no—
583#102—22no—
584#102—22no—
585#102—41no—
586C22⋊C8—22no—
587#95—21no—
588#95—21no—
589#95—21no—
590#95—21no—
591#95—21no—
592#95—21no—
593#95—21no—
594#95D4×C3111yescharacteristic
595#95D4×C3111yescharacteristic
596C31#2436811yescharacteristic, direct product factor, Sylow
597C24—21no—
598C24—21no—
599C24C2×D4×C3111yescharacteristic
600#41—28no—
601#41—44no—
602#41—44no—
603#41—44no—
604C2×Q8—24no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—28no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—42no—
620C2×Q8—42no—
621C2×Q8—44no—
622C2×Q8—44no—
623C2×Q8—44no—
624C2×Q8C2×D4×C3112yes—
625C2×Q8C2×D4×C3112yes—
626C2×Q8C2×D4×C3112yes—
627C2×Q8C2×D4×C3112yes—
628C2×Q8C2×D4×C3112yes—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—42no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4—81no—
649C2×D4—81no—
650C2×D4—81no—
651C2×D4—81no—
652C2×D4C2×D4×C3112yes—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—24no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4—42no—
669C22×C4C2×D4×C3111yescharacteristic
670C22×C4C2×D4×C3111yescharacteristic
671C22×C4C2×D4×C3111yescharacteristic
672C22×C4C2×D4×C3111yescharacteristic
673C22×C4C2×D4×C3112yes—
674C22×C4C2×D4×C3111yescharacteristic
675C22×C4#41×C3112yes—
676C22×C4C24×C3111yescharacteristic
677Q16—28no—
678Q16—28no—
679SD16—28no—
680SD16—28no—
681SD16—44no—
682SD16—44no—
683M16—28no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8C2×D4×C3112yes—
695C2×C8C2×D4×C3112yes—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—42no—
703C4⋊C4—42no—
704C22⋊C4—22no—
705C22⋊C4—41no—
706C22⋊C4—42no—
707C22⋊C4—42no—
708C22⋊C4—42no—
709C22⋊C4—42no—
710C22⋊C4—81no—
711C22⋊C4—81no—
712C42—21no—
713C42—21no—
714C42—21no—
715C42—21no—
716C42—42no—
717C42—42no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—22no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23C31×#12112yes—
739C23C22×D4×C3111yescharacteristic
740Q8—22no—
741Q8—22no—
742Q8—22no—
743Q8—22no—
744Q8—22no—
745Q8—22no—
746Q8—22no—
747Q8—48no—
748Q8—41no—
749Q8—41no—
750Q8—41no—
751Q8—41no—
752Q8C31×#12014yes—
753D4—22no—
754D4—22no—
755D4—48no—
756D4—41no—
757D4—41no—
758D4—41no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—84no—
763D4—84no—
764D4—84no—
765C2×C4—22no—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—48no—
788C2×C4—48no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4C31×#12112yes—
803C2×C4C31×#13712yescomplemented
804C2×C4C22×D4×C3111yescharacteristic
805C2×C4C22×D4×C3111yescharacteristic
806C2×C4C22×D4×C3111yescharacteristic
807C2×C4C2×#41×C3111yescharacteristic
808C2×C4C31×H(5,𝔽2)11yescharacteristic
809C2×C4C31×H(5,𝔽2)11yescharacteristic
810C8—22no—
811C8—22no—
812C8—41no—
813C8—41no—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22—81no—
833C22—81no—
834C22—81no—
835C22C2×C31×#12111yescharacteristic
836C22D42×C3111yescharacteristic
837C22D42×C3111yescharacteristic
838C22C2×C31×#13711yescharacteristic
839C22C31×#57511yescharacteristic
840C22C31×#57711yescharacteristic
841C22C31×#57711yescharacteristic
842C4—22no—
843C4—24no—
844C4—22no—
845C4—42no—
846C4—42no—
847C4—41no—
848C4—41no—
849C4—41no—
850C4—81no—
851C4—81no—
852C4—81no—
853C4C2×C31×#12011yescharacteristic
854C4C31×#53411yescharacteristic
855C4C31×#54611yescharacteristic
856C4C31×#54611yescharacteristic
857C2—42no—
858C2—82no—
859C2—161no—
860C2C31×#241011yescharacteristic
861C2C31×#303711yescharacteristic
862C2C31×#304311yescharacteristic
863C2C31×#326611yescharacteristic
864C2C31×#327111yescharacteristic
865C2C31×#327511yescharacteristic
866C2C31×#327811yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#2431C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C4×C22⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C31×#137C2semidirect
2. C2×C31×#464C2semidirect
3. C2×C31×#460C2semidirect
4. C2×C31×#448C2semidirect
6. Q8×C22⋊C4×C31C2semidirect
7. C31×#2056C2semidirect
8. C31×#2055C2semidirect
9. C31×#2015C2semidirect
10. C31×#2014C2semidirect
11. C31×#1895C2semidirect
12. C31×#1880C2semidirect
13. C31×#1878C2semidirect
14. C31×#1851C2semidirect
15. C31×#1788C2semidirect
77. C22×Q8×C31D4semidirect
96. C2×Q16×C31D4semidirect
108. C2×SD16×C31D4semidirect
284. #24368C31direct (N × H)
370. C2×C4×C31#137semidirect
381. C22×#137C2×C31semidirect
382. C2×#464C2×C31semidirect
383. C2×#460C2×C31semidirect
384. C2×#448C2×C31semidirect
386. Q8×C22⋊C4C2×C31semidirect
387. #2056C2×C31semidirect
388. #2055C2×C31semidirect
389. #2015C2×C31semidirect
390. #2014C2×C31semidirect
391. #1895C2×C31semidirect
392. #1880C2×C31semidirect
393. #1878C2×C31semidirect
394. #1851C2×C31semidirect
395. #1788C2×C31semidirect
510. C22×Q8D4×C31semidirect
529. C2×Q16D4×C31semidirect
541. C2×SD16D4×C31semidirect
596. C31#24368direct (N × H)
803. C2×C4C31×#137semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1372
C2×C31×#4642
C2×C31×#4602
C2×C31×#4482
C31×#24312
Q8×C22⋊C4×C312
C31×#20562
C31×#20552
C31×#20152
C31×#20142
C31×#18952
C31×#18802
C31×#18782
C31×#18512
C31×#17882
#2436831