Finite Group Databasebeta

← C31×#24017 #21480776

Subgroups — C31×#24017 #21480776

Order 7936.

1340 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#537C211yesmaximal, characteristic
2C2×C31×#485C211yesmaximal, characteristic, complemented
3C2×C31×#482C211yesmaximal, characteristic, complemented
4C31×#2311C211yesmaximal, characteristic, complemented
5C31×#2036C211yesmaximal, characteristic, complemented
6C31×#2035C211yesmaximal, characteristic, complemented
7C31×#2034C211yesmaximal, characteristic, complemented
8C31×#2033C211yesmaximal, characteristic, complemented
9C31×#1874C211yesmaximal, characteristic, complemented
10C31×#1872C211yesmaximal, characteristic, complemented
11C31×#1853C211yesmaximal, characteristic, complemented
12C31×#1852C211yesmaximal, characteristic, complemented
13C31×#1788C211yesmaximal, characteristic, complemented
14C31×#1788C211yesmaximal, characteristic, complemented
15C31×#1780C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C22×#41×C31C2211yescharacteristic
18C31×#537—24no—
19C31×#537—24no—
20C2×C31×C22⋊Q8—21no—
21C2×C31×C22⋊Q8C2211yescharacteristic
22C2×C31×C22⋊Q8C2211yescharacteristic
23C2×C31×#121—21no—
24C2×C31×#121—21no—
25C2×C31×#121—21no—
26C2×C31×#121C2211yescharacteristic
27C2×C31×#121C2211yescharacteristic
28C2×C31×#117C2211yescharacteristic
29C22×C4⋊C4×C31C2211yescharacteristic
30C22×C4⋊C4×C31C2211yescharacteristic
31C31×#485—24no—
32C31×#482—24no—
33C2×C31×#107C2211yescharacteristic
34C2×C31×#107C2211yescharacteristic
35C2×C31×#106C2211yescharacteristic
36C2×C31×#106C2211yescharacteristic
37C2×C31×#103C2211yescharacteristic
38C2×C31×#103C2211yescharacteristic
39C2×C31×#103C2211yescharacteristic
40C2×C31×#103C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×C22⋊C8C2211yescharacteristic
46C2×C31×C22⋊C8C2211yescharacteristic
47C2×C31×C22⋊C8C2211yescharacteristic
48C2×C31×C22⋊C8C2211yescharacteristic
49C2×C31×C22⋊C8C2211yescharacteristic
50C2×C31×C22⋊C8C2211yescharacteristic
51C31×#391—21no—
52C31×#390—21no—
53C31×#386—21no—
54C31×#386—21no—
55C31×#380C2211yescharacteristic
56C31×#380C2211yescharacteristic
57C31×#380C2211yescharacteristic
58C31×#380C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#340C2211yescharacteristic
62C31×#340C2211yescharacteristic
63C2×#41×C31—22no—
64C2×#41×C31—22no—
65C2×#41×C31—22no—
66C2×#41×C31—22no—
67C2×#41×C31—22no—
68C2×#41×C31—22no—
69C2×#41×C31—22no—
70C2×#41×C31—22no—
71C2×#41×C31—41no—
72C2×#41×C31—41no—
73C2×#41×C31—41no—
74C2×#41×C31—41no—
75C22×Q8×C31D411yescharacteristic
76C22×Q8×C31C2311yescharacteristic
77C22×D4×C31—21no—
78C22×D4×C31—21no—
79C22×D4×C31—21no—
80C22×D4×C31D411yescharacteristic
81C22×D4×C31D411yescharacteristic
82C22×D4×C31D411yescharacteristic
83C22×D4×C31C2311yescharacteristic
84C23×C4×C31—21no—
85C23×C4×C31—21no—
86C23×C4×C31—21no—
87C23×C4×C31C2311yescharacteristic
88C23×C4×C31C2311yescharacteristic
89C23×C4×C31C2311yescharacteristic
90C22×C8×C31C2311yescharacteristic
91C22×C8×C31C2311yescharacteristic
92C22×C8×C31C2311yescharacteristic
93C22×C8×C31C2311yescharacteristic
94C31×C22⋊Q8—28no—
95C31×C22⋊Q8—22no—
96C31×C22⋊Q8—22no—
97C31×C22⋊Q8—22no—
98C31×C22⋊Q8D414yes—
99C31×#121—28no—
100C31×#121—28no—
101C31×#121—28no—
102C31×#121—22no—
103C31×#121—22no—
104C31×#121—22no—
105C31×#121D414yes—
106C31×#117—22no—
107C31×#117—22no—
108C2×C4⋊C4×C31—21no—
109C2×C4⋊C4×C31—21no—
110C2×C4⋊C4×C31—21no—
111C2×C4⋊C4×C31—22no—
112C2×C4⋊C4×C31—22no—
113C2×C4⋊C4×C31—21no—
114C2×C4⋊C4×C31—41no—
115C2×C4⋊C4×C31—41no—
116C2×C4⋊C4×C31C2311yescharacteristic
117C2×C4⋊C4×C31C2311yescharacteristic
118C2×C4⋊C4×C31C2311yescharacteristic
119C2×C4⋊C4×C31C2311yescharacteristic
120C2×C4⋊C4×C31C2311yescharacteristic
121C2×C4⋊C4×C31C2311yescharacteristic
122C2×C22⋊C4×C31—21no—
123C2×C22⋊C4×C31—21no—
124C2×C22⋊C4×C31—21no—
125C2×C22⋊C4×C31—21no—
126C2×C22⋊C4×C31—21no—
127C2×C22⋊C4×C31—21no—
128C2×C22⋊C4×C31—21no—
129C2×C22⋊C4×C31—21no—
130C2×C22⋊C4×C31—21no—
131C2×C42×C31—21no—
132C31×#107—22no—
133C31×#107—22no—
134C31×#106—22no—
135C31×#106—22no—
136C31×#103—22no—
137C31×#103—22no—
138C31×#103—41no—
139C31×#103—41no—
140C31×#102—22no—
141C31×#102—22no—
142C31×#102—41no—
143C31×#102—41no—
144C31×C22⋊C8—22no—
145C31×C22⋊C8—22no—
146C31×C22⋊C8—22no—
147C31×C22⋊C8—22no—
148C31×C22⋊C8—41no—
149C31×C22⋊C8—41no—
150C31×#95—21no—
151C31×#95—21no—
152C31×#95—21no—
153C31×#95—21no—
154C24×C31—21no—
155C24×C31C2×D411yescharacteristic
156C24×C31C2×D411yescharacteristic
157C24×C31C2×D411yescharacteristic
158#41×C31—44no—
159#41×C31—44no—
160#41×C31—44no—
161#41×C31—44no—
162#41×C31—44no—
163#41×C31—44no—
164#41×C31—44no—
165#41×C31—44no—
166C2×Q8×C31—22no—
167C2×Q8×C31—22no—
168C2×Q8×C31—21no—
169C2×Q8×C31—21no—
170C2×Q8×C31—21no—
171C2×Q8×C31—21no—
172C2×Q8×C31—21no—
173C2×Q8×C31—41no—
174C2×Q8×C31C2×D412yes—
175C2×D4×C31—24no—
176C2×D4×C31—22no—
177C2×D4×C31—22no—
178C2×D4×C31—22no—
179C2×D4×C31—22no—
180C2×D4×C31—24no—
181C2×D4×C31—24no—
182C2×D4×C31—22no—
183C2×D4×C31—22no—
184C2×D4×C31—21no—
185C2×D4×C31—21no—
186C2×D4×C31—21no—
187C2×D4×C31—21no—
188C2×D4×C31—21no—
189C2×D4×C31—41no—
190C2×D4×C31—41no—
191C2×D4×C31—41no—
192C2×D4×C31—42no—
193C2×D4×C31—42no—
194C2×D4×C31—81no—
195C2×D4×C31—81no—
196C2×D4×C31—81no—
197C2×D4×C31—81no—
198C2×D4×C31C2×D412yes—
199C22×C4×C31—21no—
200C22×C4×C31—21no—
201C22×C4×C31—21no—
202C22×C4×C31—21no—
203C22×C4×C31—21no—
204C22×C4×C31—21no—
205C22×C4×C31—21no—
206C22×C4×C31—21no—
207C22×C4×C31—24no—
208C22×C4×C31—21no—
209C22×C4×C31—21no—
210C22×C4×C31—21no—
211C22×C4×C31—24no—
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—21no—
222C22×C4×C31—42no—
223C22×C4×C31—42no—
224C22×C4×C31—42no—
225C22×C4×C31—81no—
226C22×C4×C31—81no—
227C22×C4×C31—81no—
228C22×C4×C31—81no—
229C22×C4×C31C2×D411yescharacteristic
230C22×C4×C31C2×D411yescharacteristic
231C22×C4×C31C2×D412yes—
232C22×C4×C31C2×D412yes—
233C22×C4×C31C2×D411yescharacteristic
234C22×C4×C31#4112yes—
235C22×C4×C31#4112yes—
236C22×C4×C31C2411yescharacteristic
237C2×C8×C31—21no—
238C2×C8×C31—21no—
239C2×C8×C31—21no—
240C2×C8×C31—21no—
241C2×C8×C31—21no—
242C2×C8×C31—21no—
243C2×C8×C31—21no—
244C2×C8×C31—21no—
245C2×C8×C31—21no—
246C2×C8×C31—21no—
247C2×C8×C31—21no—
248C2×C8×C31—21no—
249C4⋊C4×C31—24no—
250C4⋊C4×C31—24no—
251C4⋊C4×C31—24no—
252C4⋊C4×C31—21no—
253C4⋊C4×C31—21no—
254C4⋊C4×C31—21no—
255C4⋊C4×C31—21no—
256C4⋊C4×C31—21no—
257C4⋊C4×C31—21no—
258C4⋊C4×C31—21no—
259C4⋊C4×C31—21no—
260C4⋊C4×C31—21no—
261C4⋊C4×C31—21no—
262C4⋊C4×C31—42no—
263C4⋊C4×C31C2×D412yes—
264C4⋊C4×C31C2×D412yes—
265C22⋊C4×C31—24no—
266C22⋊C4×C31—24no—
267C22⋊C4×C31—24no—
268C22⋊C4×C31—24no—
269C22⋊C4×C31—42no—
270C22⋊C4×C31—81no—
271C22⋊C4×C31—81no—
272C22⋊C4×C31—81no—
273C22⋊C4×C31—81no—
274C42×C31—42no—
275#24017C3111yesmaximal, characteristic, direct product factor, Sylow
276C23×C31—21no—
277C23×C31—21no—
278C23×C31—21no—
279C23×C31—21no—
280C23×C31—21no—
281C23×C31—21no—
282C23×C31—21no—
283C23×C31—21no—
284C23×C31—21no—
285C23×C31—21no—
286C23×C31—21no—
287C23×C31—21no—
288C23×C31—21no—
289C23×C31—22no—
290C23×C31—21no—
291C23×C31—21no—
292C23×C31—21no—
293C23×C31—21no—
294C23×C31—21no—
295C23×C31—21no—
296C23×C31—41no—
297C23×C31—41no—
298C23×C31—41no—
299C23×C31—41no—
300C23×C31—41no—
301C23×C31—41no—
302C23×C31#12012yes—
303C23×C31#12312yes—
304C23×C31C22×D411yescharacteristic
305Q8×C31—22no—
306Q8×C31—22no—
307Q8×C31—44no—
308Q8×C31—41no—
309Q8×C31—41no—
310D4×C31—22no—
311D4×C31—22no—
312D4×C31—44no—
313D4×C31—44no—
314D4×C31—44no—
315D4×C31—48no—
316D4×C31—41no—
317D4×C31—41no—
318D4×C31—84no—
319D4×C31—84no—
320C2×C4×C31—21no—
321C2×C4×C31—21no—
322C2×C4×C31—21no—
323C2×C4×C31—21no—
324C2×C4×C31—22no—
325C2×C4×C31—22no—
326C2×C4×C31—22no—
327C2×C4×C31—22no—
328C2×C4×C31—22no—
329C2×C4×C31—22no—
330C2×C4×C31—22no—
331C2×C4×C31—22no—
332C2×C4×C31—22no—
333C2×C4×C31—22no—
334C2×C4×C31—22no—
335C2×C4×C31—21no—
336C2×C4×C31—21no—
337C2×C4×C31—21no—
338C2×C4×C31—48no—
339C2×C4×C31—41no—
340C2×C4×C31—41no—
341C2×C4×C31—41no—
342C2×C4×C31—41no—
343C2×C4×C31—41no—
344C2×C4×C31—41no—
345C2×C4×C31—41no—
346C2×C4×C31—41no—
347C2×C4×C31—41no—
348C2×C4×C31—41no—
349C2×C4×C31—41no—
350C2×C4×C31—41no—
351C2×C4×C31—41no—
352C2×C4×C31—41no—
353C2×C4×C31—41no—
354C2×C4×C31—41no—
355C2×C4×C31—41no—
356C2×C4×C31—41no—
357C2×C4×C31—41no—
358C2×C4×C31—41no—
359C2×C4×C31—41no—
360C2×C4×C31—41no—
361C2×C4×C31—84no—
362C2×C4×C31—84no—
363C2×C4×C31#12012yes—
364C2×C4×C31#12312yes—
365C2×C4×C31C22×D411yescharacteristic
366C2×C4×C31C22×D411yescharacteristic
367C2×C4×C31C2×#4111yescharacteristic
368C2×C4×C31C2×#4111yescharacteristic
369C2×C4×C31H(5,𝔽2)11yescharacteristic
370C2×C4×C31H(5,𝔽2)11yescharacteristic
371C8×C31—41no—
372C8×C31—41no—
373C8×C31—41no—
374C8×C31—41no—
375C2×#537C2×C3111yescharacteristic
376C2×#485C2×C3111yescharacteristic, complemented
377C2×#482C2×C3111yescharacteristic, complemented
378#2311C2×C3111yescharacteristic, complemented
379#2036C2×C3111yescharacteristic, complemented
380#2035C2×C3111yescharacteristic, complemented
381#2034C2×C3111yescharacteristic, complemented
382#2033C2×C3111yescharacteristic, complemented
383#1874C2×C3111yescharacteristic, complemented
384#1872C2×C3111yescharacteristic, complemented
385#1853C2×C3111yescharacteristic, complemented
386#1852C2×C3111yescharacteristic, complemented
387#1788C2×C3111yescharacteristic, complemented
388#1788C2×C3111yescharacteristic, complemented
389#1780C2×C3111yescharacteristic, complemented
390C22×C31—22no—
391C22×C31—22no—
392C22×C31—22no—
393C22×C31—22no—
394C22×C31—22no—
395C22×C31—22no—
396C22×C31—41no—
397C22×C31—41no—
398C22×C31—41no—
399C22×C31—41no—
400C22×C31—41no—
401C22×C31—41no—
402C22×C31—41no—
403C22×C31—41no—
404C22×C31—41no—
405C22×C31—41no—
406C22×C31—42no—
407C22×C31—41no—
408C22×C31—41no—
409C22×C31—41no—
410C22×C31—41no—
411C22×C31—42no—
412C22×C31—41no—
413C22×C31—42no—
414C22×C31—81no—
415C22×C31—81no—
416C22×C31—81no—
417C22×C31—81no—
418C22×C31C2×#12011yescharacteristic
419C22×C31C2×#12311yescharacteristic
420C22×C31#53411yescharacteristic
421C22×C31#57611yescharacteristic
422C22×C31#57711yescharacteristic
423C22×C31#57711yescharacteristic
424C22×C31#57811yescharacteristic
425C4×C31—22no—
426C4×C31—22no—
427C4×C31—41no—
428C4×C31—42no—
429C4×C31—42no—
430C4×C31—42no—
431C4×C31—81no—
432C4×C31—81no—
433C4×C31—81no—
434C4×C31—81no—
435C4×C31#54611yescharacteristic
436C4×C31#54611yescharacteristic
437C4×C31#54611yescharacteristic
438C4×C31#54611yescharacteristic
439C22×#41C22×C3111yescharacteristic
440C22×#41C22×C3111yescharacteristic
441#537—24no—
442#537—24no—
443C2×C22⋊Q8—21no—
444C2×C22⋊Q8C22×C3111yescharacteristic
445C2×C22⋊Q8C22×C3111yescharacteristic
446C2×#121—21no—
447C2×#121—21no—
448C2×#121—21no—
449C2×#121C22×C3111yescharacteristic
450C2×#121C22×C3111yescharacteristic
451C2×#117C22×C3111yescharacteristic
452C22×C4⋊C4C22×C3111yescharacteristic
453C22×C4⋊C4C22×C3111yescharacteristic
454#485—24no—
455#482—24no—
456C2×#107C22×C3111yescharacteristic
457C2×#107C22×C3111yescharacteristic
458C2×#106C22×C3111yescharacteristic
459C2×#106C22×C3111yescharacteristic
460C2×#103C22×C3111yescharacteristic
461C2×#103C22×C3111yescharacteristic
462C2×#103C22×C3111yescharacteristic
463C2×#103C22×C3111yescharacteristic
464C2×#102C22×C3111yescharacteristic
465C2×#102C22×C3111yescharacteristic
466C2×#102C22×C3111yescharacteristic
467C2×#102C22×C3111yescharacteristic
468C2×C22⋊C8C22×C3111yescharacteristic
469C2×C22⋊C8C22×C3111yescharacteristic
470C2×C22⋊C8C22×C3111yescharacteristic
471C2×C22⋊C8C22×C3111yescharacteristic
472C2×C22⋊C8C22×C3111yescharacteristic
473C2×C22⋊C8C22×C3111yescharacteristic
474#391—21no—
475#390—21no—
476#386—21no—
477#386—21no—
478#380C22×C3111yescharacteristic
479#380C22×C3111yescharacteristic
480#380C22×C3111yescharacteristic
481#380C22×C3111yescharacteristic
482#340C22×C3111yescharacteristic
483#340C22×C3111yescharacteristic
484#340C22×C3111yescharacteristic
485#340C22×C3111yescharacteristic
486C2×C31—42no—
487C2×C31—42no—
488C2×C31—81no—
489C2×C31—82no—
490C2×C31#240511yescharacteristic
491C2×C31#301211yescharacteristic
492C2×C31#301311yescharacteristic
493C2×C31#309811yescharacteristic
494C2×C31#309911yescharacteristic
495C2×C31#319811yescharacteristic
496C2×C31#320111yescharacteristic
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—41no—
509C22×Q8D4×C3111yescharacteristic
510C22×Q8C23×C3111yescharacteristic
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4D4×C3111yescharacteristic
515C22×D4D4×C3111yescharacteristic
516C22×D4D4×C3111yescharacteristic
517C22×D4C23×C3111yescharacteristic
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4C23×C3111yescharacteristic
522C23×C4C23×C3111yescharacteristic
523C23×C4C23×C3111yescharacteristic
524C22×C8C23×C3111yescharacteristic
525C22×C8C23×C3111yescharacteristic
526C22×C8C23×C3111yescharacteristic
527C22×C8C23×C3111yescharacteristic
528C22⋊Q8—28no—
529C22⋊Q8—22no—
530C22⋊Q8—22no—
531C22⋊Q8—22no—
532C22⋊Q8D4×C3114yes—
533#121—28no—
534#121—28no—
535#121—28no—
536#121—22no—
537#121—22no—
538#121—22no—
539#121D4×C3114yes—
540#117—22no—
541#117—22no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—22no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—41no—
549C2×C4⋊C4—41no—
550C2×C4⋊C4C23×C3111yescharacteristic
551C2×C4⋊C4C23×C3111yescharacteristic
552C2×C4⋊C4C23×C3111yescharacteristic
553C2×C4⋊C4C23×C3111yescharacteristic
554C2×C4⋊C4C23×C3111yescharacteristic
555C2×C4⋊C4C23×C3111yescharacteristic
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C42—21no—
566#107—22no—
567#107—22no—
568#106—22no—
569#106—22no—
570#103—22no—
571#103—22no—
572#103—41no—
573#103—41no—
574#102—22no—
575#102—22no—
576#102—41no—
577#102—41no—
578C22⋊C8—22no—
579C22⋊C8—22no—
580C22⋊C8—22no—
581C22⋊C8—22no—
582C22⋊C8—41no—
583C22⋊C8—41no—
584#95—21no—
585#95—21no—
586#95—21no—
587#95—21no—
588C31#2401711yescharacteristic, direct product factor, Sylow
589C24—21no—
590C24C2×D4×C3111yescharacteristic
591C24C2×D4×C3111yescharacteristic
592C24C2×D4×C3111yescharacteristic
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—44no—
598#41—44no—
599#41—44no—
600#41—44no—
601C2×Q8—22no—
602C2×Q8—22no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—41no—
609C2×Q8C2×D4×C3112yes—
610C2×D4—24no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—24no—
616C2×D4—24no—
617C2×D4—22no—
618C2×D4—22no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—41no—
625C2×D4—41no—
626C2×D4—41no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—81no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—81no—
633C2×D4C2×D4×C3112yes—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—24no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—24no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—81no—
661C22×C4—81no—
662C22×C4—81no—
663C22×C4—81no—
664C22×C4C2×D4×C3111yescharacteristic
665C22×C4C2×D4×C3111yescharacteristic
666C22×C4C2×D4×C3112yes—
667C22×C4C2×D4×C3112yes—
668C22×C4C2×D4×C3111yescharacteristic
669C22×C4#41×C3112yes—
670C22×C4#41×C3112yes—
671C22×C4C24×C3111yescharacteristic
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C4⋊C4—24no—
685C4⋊C4—24no—
686C4⋊C4—24no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—42no—
698C4⋊C4C2×D4×C3112yes—
699C4⋊C4C2×D4×C3112yes—
700C22⋊C4—24no—
701C22⋊C4—24no—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—42no—
705C22⋊C4—81no—
706C22⋊C4—81no—
707C22⋊C4—81no—
708C22⋊C4—81no—
709C42—42no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—22no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23C31×#12012yes—
737C23C31×#12312yes—
738C23C22×D4×C3111yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—44no—
742Q8—41no—
743Q8—41no—
744D4—22no—
745D4—22no—
746D4—44no—
747D4—44no—
748D4—44no—
749D4—48no—
750D4—41no—
751D4—41no—
752D4—84no—
753D4—84no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—48no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—84no—
796C2×C4—84no—
797C2×C4C31×#12012yes—
798C2×C4C31×#12312yes—
799C2×C4C22×D4×C3111yescharacteristic
800C2×C4C22×D4×C3111yescharacteristic
801C2×C4C2×#41×C3111yescharacteristic
802C2×C4C2×#41×C3111yescharacteristic
803C2×C4C31×H(5,𝔽2)11yescharacteristic
804C2×C4C31×H(5,𝔽2)11yescharacteristic
805C8—41no—
806C8—41no—
807C8—41no—
808C8—41no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—42no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—42no—
831C22—41no—
832C22—42no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—81no—
837C22C2×C31×#12011yescharacteristic
838C22C2×C31×#12311yescharacteristic
839C22C31×#53411yescharacteristic
840C22C31×#57611yescharacteristic
841C22C31×#57711yescharacteristic
842C22C31×#57711yescharacteristic
843C22C31×#57811yescharacteristic
844C4—22no—
845C4—22no—
846C4—41no—
847C4—42no—
848C4—42no—
849C4—42no—
850C4—81no—
851C4—81no—
852C4—81no—
853C4—81no—
854C4C31×#54611yescharacteristic
855C4C31×#54611yescharacteristic
856C4C31×#54611yescharacteristic
857C4C31×#54611yescharacteristic
858C2—42no—
859C2—42no—
860C2—81no—
861C2—82no—
862C2C31×#240511yescharacteristic
863C2C31×#301211yescharacteristic
864C2C31×#301311yescharacteristic
865C2C31×#309811yescharacteristic
866C2C31×#309911yescharacteristic
867C2C31×#319811yescharacteristic
868C2C31×#320111yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#537C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×#41×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#485C2semidirect
3. C2×C31×#482C2semidirect
4. C31×#2311C2semidirect
5. C31×#2036C2semidirect
6. C31×#2035C2semidirect
7. C31×#2034C2semidirect
8. C31×#2033C2semidirect
9. C31×#1874C2semidirect
10. C31×#1872C2semidirect
11. C31×#1853C2semidirect
12. C31×#1852C2semidirect
13. C31×#1788C2semidirect
14. C31×#1788C2semidirect
15. C31×#1780C2semidirect
275. #24017C31direct (N × H)
376. C2×#485C2×C31semidirect
377. C2×#482C2×C31semidirect
378. #2311C2×C31semidirect
379. #2036C2×C31semidirect
380. #2035C2×C31semidirect
381. #2034C2×C31semidirect
382. #2033C2×C31semidirect
383. #1874C2×C31semidirect
384. #1872C2×C31semidirect
385. #1853C2×C31semidirect
386. #1852C2×C31semidirect
387. #1788C2×C31semidirect
388. #1788C2×C31semidirect
389. #1780C2×C31semidirect
588. C31#24017direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5372
C2×C31×#4852
C2×C31×#4822
C31×#23112
C31×#20362
C31×#20352
C31×#20342
C31×#20332
C31×#18742
C31×#18722
C31×#18532
C31×#18522
C31×#17882
C31×#17802
#2401731