Finite Group Databasebeta

← C31×#33006 #21489765

Subgroups — C31×#33006 #21489765

Order 7936.

1408 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#41×C31C211yesmaximal, characteristic, complemented
2C2×C31×#482C211yesmaximal, characteristic, complemented
3C2×C31×#449C211yesmaximal, characteristic
4C31×#2854C211yesmaximal, characteristic, complemented
5C31×#1880C211yesmaximal, characteristic, complemented
6C31×#1880C211yesmaximal, characteristic, complemented
7C31×#1879C211yesmaximal, characteristic, complemented
8C31×#1879C211yesmaximal, characteristic, complemented
9C31×#1865C211yesmaximal, characteristic, complemented
10C31×#1864C211yesmaximal, characteristic, complemented
11C31×#1863C211yesmaximal, characteristic, complemented
12C31×#1862C211yesmaximal, characteristic, complemented
13C31×#1825C211yesmaximal, characteristic, complemented
14C31×#1817C211yesmaximal, characteristic, complemented
15C31×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C22×SD16×C31C2211yescharacteristic
18C22×D8×C31C2211yescharacteristic
19C2×C31×#123—21no—
20C2×C31×#121C2211yescharacteristic
21C4×#41×C31—24no—
22C4×#41×C31—24no—
23C2×C4×Q8×C31C2211yescharacteristic
24C2×C4×Q8×C31C2211yescharacteristic
25C2×C4×D4×C31—21no—
26C2×C4×D4×C31—21no—
27C2×C4×D4×C31C2211yescharacteristic
28C2×C4×D4×C31C2211yescharacteristic
29C2×C31×#117—21no—
30C2×C31×#117C2211yescharacteristic
31C22×C42×C31—21no—
32C22×C42×C31C2211yescharacteristic
33C31×#482—24no—
34C31×#449—24no—
35C2×C31×#107C2211yescharacteristic
36C2×C31×#106C2211yescharacteristic
37C2×C31×#103C2211yescharacteristic
38C2×C31×#103C2211yescharacteristic
39C2×C31×#103C2211yescharacteristic
40C2×C31×#102C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×C22⋊C8C2211yescharacteristic
46C2×C31×C22⋊C8C2211yescharacteristic
47C31×#390C2211yescharacteristic
48C31×#390C2211yescharacteristic
49C31×#389C2211yescharacteristic
50C31×#389C2211yescharacteristic
51C31×#388—21no—
52C31×#388—21no—
53C31×#386—21no—
54C31×#380C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#336C2211yescharacteristic
60C31×#336C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C31×#336C2211yescharacteristic
63C2×#41×C31—22no—
64C2×#41×C31—22no—
65C2×#41×C31—22no—
66C2×#41×C31—22no—
67C2×#41×C31—22no—
68C2×#41×C31D414yes—
69C22×Q8×C31C2311yescharacteristic
70C22×D4×C31—21no—
71C22×D4×C31—21no—
72C22×D4×C31C2311yescharacteristic
73C22×D4×C31C2311yescharacteristic
74C23×C4×C31—21no—
75C23×C4×C31—21no—
76C23×C4×C31—21no—
77C23×C4×C31D411yescharacteristic
78C23×C4×C31D411yescharacteristic
79C23×C4×C31C2311yescharacteristic
80C2×SD16×C31—22no—
81C2×SD16×C31—22no—
82C2×SD16×C31—22no—
83C2×D8×C31—22no—
84C2×D8×C31—22no—
85C2×D8×C31—22no—
86C22×C8×C31C2311yescharacteristic
87C22×C8×C31C2311yescharacteristic
88C22×C8×C31C2311yescharacteristic
89C22×C8×C31C2311yescharacteristic
90C31×#123—44no—
91C31×#121—22no—
92C31×#121—22no—
93C4×Q8×C31—22no—
94C4×Q8×C31—22no—
95C4×Q8×C31—22no—
96C4×Q8×C31—22no—
97C4×D4×C31—28no—
98C4×D4×C31—28no—
99C4×D4×C31—22no—
100C4×D4×C31—22no—
101C4×D4×C31—22no—
102C4×D4×C31—22no—
103C31×#117—28no—
104C31×#117—22no—
105C31×#117D414yes—
106C2×C4⋊C4×C31—21no—
107C2×C4⋊C4×C31—21no—
108C2×C4⋊C4×C31—21no—
109C2×C4⋊C4×C31—21no—
110C2×C4⋊C4×C31C2311yescharacteristic
111C2×C4⋊C4×C31C2311yescharacteristic
112C2×C4⋊C4×C31C2311yescharacteristic
113C2×C4⋊C4×C31C2311yescharacteristic
114C2×C4⋊C4×C31C2311yescharacteristic
115C2×C22⋊C4×C31—21no—
116C2×C22⋊C4×C31—21no—
117C2×C22⋊C4×C31—21no—
118C2×C22⋊C4×C31—21no—
119C2×C22⋊C4×C31—21no—
120C2×C22⋊C4×C31—21no—
121C2×C22⋊C4×C31—21no—
122C2×C22⋊C4×C31—21no—
123C2×C22⋊C4×C31—21no—
124C2×C42×C31—28no—
125C2×C42×C31—21no—
126C2×C42×C31—21no—
127C2×C42×C31—21no—
128C2×C42×C31—22no—
129C2×C42×C31—22no—
130C2×C42×C31D411yescharacteristic
131C2×C42×C31D411yescharacteristic
132C2×C42×C31C2311yescharacteristic
133C2×C42×C31C2311yescharacteristic
134C31×#107—22no—
135C31×#106—22no—
136C31×#103—22no—
137C31×#103—22no—
138C31×#103—22no—
139C31×#102—22no—
140C31×#102—22no—
141C31×#102—22no—
142C31×#102—22no—
143C31×#102—22no—
144C31×C22⋊C8—22no—
145C31×C22⋊C8—22no—
146C31×#95—21no—
147C31×#95—21no—
148C31×#95—21no—
149C24×C31—21no—
150C24×C31—21no—
151C24×C31C2×D411yescharacteristic
152#41×C31—28no—
153#41×C31—28no—
154#41×C31—28no—
155#41×C31—28no—
156C2×Q8×C31—21no—
157C2×Q8×C31—21no—
158C2×Q8×C31—21no—
159C2×Q8×C31C2×D412yes—
160C2×Q8×C31#4112yes—
161C2×Q8×C31#4112yes—
162C2×D4×C31—24no—
163C2×D4×C31—24no—
164C2×D4×C31—24no—
165C2×D4×C31—21no—
166C2×D4×C31—21no—
167C2×D4×C31—21no—
168C2×D4×C31—21no—
169C2×D4×C31—21no—
170C2×D4×C31—21no—
171C2×D4×C31—21no—
172C2×D4×C31—21no—
173C2×D4×C31—21no—
174C2×D4×C31—42no—
175C2×D4×C31—42no—
176C2×D4×C31—42no—
177C2×D4×C31C2×D412yes—
178C2×D4×C31#4112yes—
179C2×D4×C31#4112yes—
180C22×C4×C31—24no—
181C22×C4×C31—24no—
182C22×C4×C31—21no—
183C22×C4×C31—24no—
184C22×C4×C31—21no—
185C22×C4×C31—21no—
186C22×C4×C31—21no—
187C22×C4×C31—21no—
188C22×C4×C31—24no—
189C22×C4×C31—24no—
190C22×C4×C31—22no—
191C22×C4×C31—22no—
192C22×C4×C31—21no—
193C22×C4×C31—21no—
194C22×C4×C31—22no—
195C22×C4×C31—22no—
196C22×C4×C31—21no—
197C22×C4×C31—21no—
198C22×C4×C31—21no—
199C22×C4×C31—41no—
200C22×C4×C31—41no—
201C22×C4×C31—42no—
202C22×C4×C31—42no—
203C22×C4×C31—42no—
204C22×C4×C31—42no—
205C22×C4×C31C2×D411yescharacteristic
206C22×C4×C31C2×D411yescharacteristic
207C22×C4×C31C2×D411yescharacteristic
208C22×C4×C31C2×D412yes—
209C22×C4×C31C2×D412yes—
210C22×C4×C31C2×D411yescharacteristic
211C22×C4×C31C2×D411yescharacteristic
212C22×C4×C31C2411yescharacteristic
213SD16×C31—44no—
214D8×C31—44no—
215C2×C8×C31—21no—
216C2×C8×C31—21no—
217C2×C8×C31—21no—
218C2×C8×C31—21no—
219C2×C8×C31—21no—
220C2×C8×C31—21no—
221C2×C8×C31—21no—
222C2×C8×C31—21no—
223C2×C8×C31—21no—
224C2×C8×C31—21no—
225C2×C8×C31—21no—
226C2×C8×C31—21no—
227C4⋊C4×C31—24no—
228C4⋊C4×C31—24no—
229C4⋊C4×C31—21no—
230C4⋊C4×C31—21no—
231C4⋊C4×C31—21no—
232C4⋊C4×C31—21no—
233C4⋊C4×C31—21no—
234C4⋊C4×C31—21no—
235C4⋊C4×C31—21no—
236C4⋊C4×C31—21no—
237C4⋊C4×C31—42no—
238C4⋊C4×C31—42no—
239C4⋊C4×C31C2×D412yes—
240C4⋊C4×C31C2×D412yes—
241C22⋊C4×C31—24no—
242C22⋊C4×C31—24no—
243C22⋊C4×C31—24no—
244C22⋊C4×C31—42no—
245C22⋊C4×C31—42no—
246C22⋊C4×C31—42no—
247C22⋊C4×C31—42no—
248C22⋊C4×C31—42no—
249C22⋊C4×C31—42no—
250C42×C31—24no—
251C42×C31—24no—
252C42×C31—22no—
253C42×C31—24no—
254C42×C31—22no—
255C42×C31—21no—
256C42×C31—21no—
257C42×C31—21no—
258C42×C31—21no—
259#33006C3111yesmaximal, characteristic, direct product factor, Sylow
260C23×C31—22no—
261C23×C31—21no—
262C23×C31—21no—
263C23×C31—22no—
264C23×C31—22no—
265C23×C31—21no—
266C23×C31—21no—
267C23×C31—21no—
268C23×C31—21no—
269C23×C31—41no—
270C23×C31—41no—
271C23×C31—41no—
272C23×C31—41no—
273C23×C31—41no—
274C23×C31—41no—
275C23×C31—41no—
276C23×C31—41no—
277C23×C31—41no—
278C23×C31—41no—
279C23×C31—41no—
280C23×C31#12012yes—
281C23×C31C22×D411yescharacteristic
282Q8×C31—22no—
283Q8×C31—22no—
284Q8×C31—22no—
285Q8×C31#12314yescomplemented
286D4×C31—216no—
287D4×C31—22no—
288D4×C31—22no—
289D4×C31—22no—
290D4×C31—41no—
291D4×C31—41no—
292D4×C31—41no—
293D4×C31—41no—
294D4×C31—84no—
295D4×C31#12314yescomplemented
296C2×C4×C31—216no—
297C2×C4×C31—21no—
298C2×C4×C31—21no—
299C2×C4×C31—22no—
300C2×C4×C31—21no—
301C2×C4×C31—21no—
302C2×C4×C31—22no—
303C2×C4×C31—22no—
304C2×C4×C31—21no—
305C2×C4×C31—21no—
306C2×C4×C31—22no—
307C2×C4×C31—22no—
308C2×C4×C31—22no—
309C2×C4×C31—22no—
310C2×C4×C31—21no—
311C2×C4×C31—21no—
312C2×C4×C31—22no—
313C2×C4×C31—22no—
314C2×C4×C31—21no—
315C2×C4×C31—21no—
316C2×C4×C31—21no—
317C2×C4×C31—21no—
318C2×C4×C31—44no—
319C2×C4×C31—44no—
320C2×C4×C31—48no—
321C2×C4×C31—48no—
322C2×C4×C31—41no—
323C2×C4×C31—41no—
324C2×C4×C31—41no—
325C2×C4×C31—41no—
326C2×C4×C31—41no—
327C2×C4×C31—41no—
328C2×C4×C31—41no—
329C2×C4×C31—41no—
330C2×C4×C31—41no—
331C2×C4×C31—41no—
332C2×C4×C31—41no—
333C2×C4×C31—41no—
334C2×C4×C31—41no—
335C2×C4×C31#12012yes—
336C2×C4×C31#13512yes—
337C2×C4×C31AGL(1,ℤ/8)12yes—
338C2×C4×C31C22×D411yescharacteristic
339C2×C4×C31C22×D411yescharacteristic
340C2×C4×C31C2×#4111yescharacteristic
341C2×C4×C31C2×#4111yescharacteristic
342C2×C4×C31C2×#4111yescharacteristic
343C2×C4×C31C2×#4111yescharacteristic
344C8×C31—41no—
345C8×C31—41no—
346C8×C31—41no—
347C8×C31—41no—
348C2×C4×#41C2×C3111yescharacteristic, complemented
349C2×#482C2×C3111yescharacteristic, complemented
350C2×#449C2×C3111yescharacteristic
351#2854C2×C3111yescharacteristic, complemented
352#1880C2×C3111yescharacteristic, complemented
353#1880C2×C3111yescharacteristic, complemented
354#1879C2×C3111yescharacteristic, complemented
355#1879C2×C3111yescharacteristic, complemented
356#1865C2×C3111yescharacteristic, complemented
357#1864C2×C3111yescharacteristic, complemented
358#1863C2×C3111yescharacteristic, complemented
359#1862C2×C3111yescharacteristic, complemented
360#1825C2×C3111yescharacteristic, complemented
361#1817C2×C3111yescharacteristic, complemented
362#1788C2×C3111yescharacteristic, complemented
363C22×C31—22no—
364C22×C31—24no—
365C22×C31—22no—
366C22×C31—22no—
367C22×C31—41no—
368C22×C31—42no—
369C22×C31—41no—
370C22×C31—42no—
371C22×C31—41no—
372C22×C31—42no—
373C22×C31—41no—
374C22×C31—42no—
375C22×C31—42no—
376C22×C31—42no—
377C22×C31—81no—
378C22×C31—81no—
379C22×C31—81no—
380C22×C31—81no—
381C22×C31—81no—
382C22×C31—81no—
383C22×C31—81no—
384C22×C31C2×#12011yescharacteristic
385C22×C31#52511yescharacteristic
386C22×C31#52511yescharacteristic
387C22×C31C2×#13511yescharacteristic
388C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
389C22×C31#57511yescharacteristic
390C22×C31#57511yescharacteristic
391C4×C31—22no—
392C4×C31—24no—
393C4×C31—22no—
394C4×C31—22no—
395C4×C31—41no—
396C4×C31—42no—
397C4×C31—41no—
398C4×C31—42no—
399C4×C31—81no—
400C4×C31—81no—
401C4×C31—81no—
402C4×C31C2×#12311yescharacteristic
403C4×C31C2×#12311yescharacteristic
404C4×C31#52511yescharacteristic
405C4×C31#52511yescharacteristic
406C22×#41C22×C3111yescharacteristic
407C22×SD16C22×C3111yescharacteristic
408C22×D8C22×C3111yescharacteristic
409C2×#123—21no—
410C2×#121C22×C3111yescharacteristic
411C4×#41—24no—
412C4×#41—24no—
413C2×C4×Q8C22×C3111yescharacteristic
414C2×C4×Q8C22×C3111yescharacteristic
415C2×C4×D4—21no—
416C2×C4×D4—21no—
417C2×C4×D4C22×C3111yescharacteristic
418C2×C4×D4C22×C3111yescharacteristic
419C2×#117—21no—
420C2×#117C22×C3111yescharacteristic
421C22×C42—21no—
422C22×C42C22×C3111yescharacteristic
423#482—24no—
424#449—24no—
425C2×#107C22×C3111yescharacteristic
426C2×#106C22×C3111yescharacteristic
427C2×#103C22×C3111yescharacteristic
428C2×#103C22×C3111yescharacteristic
429C2×#103C22×C3111yescharacteristic
430C2×#102C22×C3111yescharacteristic
431C2×#102C22×C3111yescharacteristic
432C2×#102C22×C3111yescharacteristic
433C2×#102C22×C3111yescharacteristic
434C2×#102C22×C3111yescharacteristic
435C2×C22⋊C8C22×C3111yescharacteristic
436C2×C22⋊C8C22×C3111yescharacteristic
437#390C22×C3111yescharacteristic
438#390C22×C3111yescharacteristic
439#389C22×C3111yescharacteristic
440#389C22×C3111yescharacteristic
441#388—21no—
442#388—21no—
443#386—21no—
444#380C22×C3111yescharacteristic
445#340C22×C3111yescharacteristic
446#340C22×C3111yescharacteristic
447#340C22×C3111yescharacteristic
448#340C22×C3111yescharacteristic
449#336C22×C3111yescharacteristic
450#336C22×C3111yescharacteristic
451#336C22×C3111yescharacteristic
452#336C22×C3111yescharacteristic
453C2×C31—42no—
454C2×C31—44no—
455C2×C31—161no—
456C2×C31#284911yescharacteristic
457C2×C31#300211yescharacteristic
458C2×C31#300611yescharacteristic
459C2×C31#310211yescharacteristic
460C2×C31#310611yescharacteristic
461C2×C31#311111yescharacteristic
462C2×C31#311511yescharacteristic
463C2×#41—22no—
464C2×#41—22no—
465C2×#41—22no—
466C2×#41—22no—
467C2×#41—22no—
468C2×#41D4×C3114yes—
469C22×Q8C23×C3111yescharacteristic
470C22×D4—21no—
471C22×D4—21no—
472C22×D4C23×C3111yescharacteristic
473C22×D4C23×C3111yescharacteristic
474C23×C4—21no—
475C23×C4—21no—
476C23×C4—21no—
477C23×C4D4×C3111yescharacteristic
478C23×C4D4×C3111yescharacteristic
479C23×C4C23×C3111yescharacteristic
480C2×SD16—22no—
481C2×SD16—22no—
482C2×SD16—22no—
483C2×D8—22no—
484C2×D8—22no—
485C2×D8—22no—
486C22×C8C23×C3111yescharacteristic
487C22×C8C23×C3111yescharacteristic
488C22×C8C23×C3111yescharacteristic
489C22×C8C23×C3111yescharacteristic
490#123—44no—
491#121—22no—
492#121—22no—
493C4×Q8—22no—
494C4×Q8—22no—
495C4×Q8—22no—
496C4×Q8—22no—
497C4×D4—28no—
498C4×D4—28no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—22no—
502C4×D4—22no—
503#117—28no—
504#117—22no—
505#117D4×C3114yes—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4C23×C3111yescharacteristic
511C2×C4⋊C4C23×C3111yescharacteristic
512C2×C4⋊C4C23×C3111yescharacteristic
513C2×C4⋊C4C23×C3111yescharacteristic
514C2×C4⋊C4C23×C3111yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C42—28no—
525C2×C42—21no—
526C2×C42—21no—
527C2×C42—21no—
528C2×C42—22no—
529C2×C42—22no—
530C2×C42D4×C3111yescharacteristic
531C2×C42D4×C3111yescharacteristic
532C2×C42C23×C3111yescharacteristic
533C2×C42C23×C3111yescharacteristic
534#107—22no—
535#106—22no—
536#103—22no—
537#103—22no—
538#103—22no—
539#102—22no—
540#102—22no—
541#102—22no—
542#102—22no—
543#102—22no—
544C22⋊C8—22no—
545C22⋊C8—22no—
546#95—21no—
547#95—21no—
548#95—21no—
549C31#3300611yescharacteristic, direct product factor, Sylow
550C24—21no—
551C24—21no—
552C24C2×D4×C3111yescharacteristic
553#41—28no—
554#41—28no—
555#41—28no—
556#41—28no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8C2×D4×C3112yes—
561C2×Q8#41×C3112yes—
562C2×Q8#41×C3112yes—
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—24no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4C2×D4×C3112yes—
579C2×D4#41×C3112yes—
580C2×D4#41×C3112yes—
581C22×C4—24no—
582C22×C4—24no—
583C22×C4—21no—
584C22×C4—24no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—24no—
590C22×C4—24no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4C2×D4×C3111yescharacteristic
607C22×C4C2×D4×C3111yescharacteristic
608C22×C4C2×D4×C3111yescharacteristic
609C22×C4C2×D4×C3112yes—
610C22×C4C2×D4×C3112yes—
611C22×C4C2×D4×C3111yescharacteristic
612C22×C4C2×D4×C3111yescharacteristic
613C22×C4C24×C3111yescharacteristic
614SD16—44no—
615D8—44no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C4⋊C4—24no—
629C4⋊C4—24no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—42no—
639C4⋊C4—42no—
640C4⋊C4C2×D4×C3112yes—
641C4⋊C4C2×D4×C3112yes—
642C22⋊C4—24no—
643C22⋊C4—24no—
644C22⋊C4—24no—
645C22⋊C4—42no—
646C22⋊C4—42no—
647C22⋊C4—42no—
648C22⋊C4—42no—
649C22⋊C4—42no—
650C22⋊C4—42no—
651C42—24no—
652C42—24no—
653C42—22no—
654C42—24no—
655C42—22no—
656C42—21no—
657C42—21no—
658C42—21no—
659C42—21no—
660C23—22no—
661C23—21no—
662C23—21no—
663C23—22no—
664C23—22no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23C31×#12012yes—
681C23C22×D4×C3111yescharacteristic
682Q8—22no—
683Q8—22no—
684Q8—22no—
685Q8C31×#12314yescomplemented
686D4—216no—
687D4—22no—
688D4—22no—
689D4—22no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—41no—
694D4—84no—
695D4C31×#12314yescomplemented
696C2×C4—216no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—48no—
721C2×C4—48no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4C31×#12012yes—
736C2×C4C31×#13512yes—
737C2×C4C31×AGL(1,ℤ/8)12yes—
738C2×C4C22×D4×C3111yescharacteristic
739C2×C4C22×D4×C3111yescharacteristic
740C2×C4C2×#41×C3111yescharacteristic
741C2×C4C2×#41×C3111yescharacteristic
742C2×C4C2×#41×C3111yescharacteristic
743C2×C4C2×#41×C3111yescharacteristic
744C8—41no—
745C8—41no—
746C8—41no—
747C8—41no—
748C22—22no—
749C22—24no—
750C22—22no—
751C22—22no—
752C22—41no—
753C22—42no—
754C22—41no—
755C22—42no—
756C22—41no—
757C22—42no—
758C22—41no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22C2×C31×#12011yescharacteristic
770C22C31×#52511yescharacteristic
771C22C31×#52511yescharacteristic
772C22C2×C31×#13511yescharacteristic
773C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
774C22C31×#57511yescharacteristic
775C22C31×#57511yescharacteristic
776C4—22no—
777C4—24no—
778C4—22no—
779C4—22no—
780C4—41no—
781C4—42no—
782C4—41no—
783C4—42no—
784C4—81no—
785C4—81no—
786C4—81no—
787C4C2×C31×#12311yescharacteristic
788C4C2×C31×#12311yescharacteristic
789C4C31×#52511yescharacteristic
790C4C31×#52511yescharacteristic
791C2—42no—
792C2—44no—
793C2—161no—
794C2C31×#284911yescharacteristic
795C2C31×#300211yescharacteristic
796C2C31×#300611yescharacteristic
797C2C31×#310211yescharacteristic
798C2C31×#310611yescharacteristic
799C2C31×#311111yescharacteristic
800C2C31×#311511yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#449C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C4×#41×C31C2semidirect
2. C2×C31×#482C2semidirect
4. C31×#2854C2semidirect
5. C31×#1880C2semidirect
6. C31×#1880C2semidirect
7. C31×#1879C2semidirect
8. C31×#1879C2semidirect
9. C31×#1865C2semidirect
10. C31×#1864C2semidirect
11. C31×#1863C2semidirect
12. C31×#1862C2semidirect
13. C31×#1825C2semidirect
14. C31×#1817C2semidirect
15. C31×#1788C2semidirect
259. #33006C31direct (N × H)
285. Q8×C31#123semidirect
295. D4×C31#123semidirect
348. C2×C4×#41C2×C31semidirect
349. C2×#482C2×C31semidirect
351. #2854C2×C31semidirect
352. #1880C2×C31semidirect
353. #1880C2×C31semidirect
354. #1879C2×C31semidirect
355. #1879C2×C31semidirect
356. #1865C2×C31semidirect
357. #1864C2×C31semidirect
358. #1863C2×C31semidirect
359. #1862C2×C31semidirect
360. #1825C2×C31semidirect
361. #1817C2×C31semidirect
362. #1788C2×C31semidirect
549. C31#33006direct (N × H)
685. Q8C31×#123semidirect
695. D4C31×#123semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#41×C312
C2×C31×#4822
C2×C31×#4492
C31×#28542
C31×#18802
C31×#18792
C31×#18652
C31×#18642
C31×#18632
C31×#18622
C31×#18252
C31×#18172
C31×#17882
#3300631