Finite Group Databasebeta

← C31×#22874 #21479633

Subgroups — C31×#22874 #21479633

Order 7936.

1314 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#450C211yesmaximal, characteristic
2C2×C4×SD16×C31C211yesmaximal, characteristic, complemented
3C22×C31×#102C211yesmaximal, characteristic
4C31×#2360C211yesmaximal, characteristic, complemented
5D4×C22⋊C4×C31C211yesmaximal, characteristic
6C31×#1968C211yesmaximal, characteristic, complemented
7C31×#1934C211yesmaximal, characteristic, complemented
8C31×#1926C211yesmaximal, characteristic, complemented
9C31×#1892C211yesmaximal, characteristic, complemented
10C31×#1880C211yesmaximal, characteristic, complemented
11C31×#1877C211yesmaximal, characteristic, complemented
12C31×#1864C211yesmaximal, characteristic, complemented
13C31×#1853C211yesmaximal, characteristic, complemented
14C4×C31×#102C211yesmaximal, characteristic, complemented
15C8×C22⋊C4×C31C211yesmaximal, characteristic, complemented
16C23×D4×C31C2211yescharacteristic
17C22×SD16×C31C2211yescharacteristic
18C22×SD16×C31C2211yescharacteristic
19C23×C8×C31C2211yescharacteristic
20C2×C31×C22⋊Q8C2211yescharacteristic
21C2×C4×Q8×C31C2211yescharacteristic, complemented
22C2×C4×D4×C31C2211yescharacteristic
23C2×C4×D4×C31C2211yescharacteristic
24C22×C4⋊C4×C31C2211yescharacteristic
25C22×C22⋊C4×C31—21no—
26C31×#450C418yescomplemented
27C4×SD16×C31—24no—
28C2×C31×#106C2211yescharacteristic, complemented
29C2×C31×#106C2211yescharacteristic, complemented
30C2×C31×#103C2211yescharacteristic, complemented
31C2×C31×#103C2211yescharacteristic, complemented
32C2×C31×#102—24no—
33C2×C31×#102C2211yescharacteristic
34C2×C31×#102C2211yescharacteristic
35C2×C31×#102C2211yescharacteristic
36C2×C31×#102C2211yescharacteristic
37C2×C31×#102C2211yescharacteristic
38C2×C31×#102C2211yescharacteristic
39C2×C31×C22⋊C8C2211yescharacteristic
40C2×C4×C8×C31C2211yescharacteristic, complemented
41C2×C4×C8×C31C2211yescharacteristic, complemented
42C31×#391C2211yescharacteristic, complemented
43C31×#390C2211yescharacteristic
44C31×#390C2211yescharacteristic
45C31×#389—21no—
46C31×#389C2211yescharacteristic, complemented
47C31×#387—21no—
48C31×#386—21no—
49C31×#386—21no—
50C31×#385—21no—
51C31×#380C2211yescharacteristic
52C31×#379—21no—
53C4×C4⋊C4×C31C2211yescharacteristic, complemented
54C4×C22⋊C4×C31—21no—
55C4×C22⋊C4×C31C2211yescharacteristic
56C31×#340C2211yescharacteristic, complemented
57C31×#340C2211yescharacteristic, complemented
58C31×#340C2211yescharacteristic, complemented
59C31×#340C2211yescharacteristic, complemented
60C31×#336C2211yescharacteristic, complemented
61C31×#336C2211yescharacteristic, complemented
62C25×C31—21no—
63C22×Q8×C31C2311yescharacteristic
64C22×D4×C31—22no—
65C22×D4×C31—22no—
66C22×D4×C31—21no—
67C22×D4×C31—22no—
68C22×D4×C31—41no—
69C22×D4×C31—41no—
70C22×D4×C31C2×C414yes—
71C22×D4×C31C2311yescharacteristic
72C22×D4×C31C2311yescharacteristic
73C23×C4×C31—21no—
74C23×C4×C31—21no—
75C23×C4×C31—21no—
76C23×C4×C31C2311yescharacteristic
77C2×SD16×C31—22no—
78C2×SD16×C31—22no—
79C2×SD16×C31—41no—
80C2×SD16×C31—41no—
81C2×SD16×C31C2×C414yescomplemented
82C2×SD16×C31C2×C414yescomplemented
83C22×C8×C31—22no—
84C22×C8×C31—22no—
85C22×C8×C31—41no—
86C22×C8×C31C2311yescharacteristic
87C22×C8×C31C2311yescharacteristic
88C22×C8×C31C2311yescharacteristic
89C22×C8×C31C2311yescharacteristic
90C31×C22⋊Q8—22no—
91C31×C22⋊Q8C2×C414yescomplemented
92C4×Q8×C31—22no—
93C4×Q8×C31—41no—
94C4×D4×C31—22no—
95C4×D4×C31—22no—
96C4×D4×C31—41no—
97C4×D4×C31—41no—
98C2×C4⋊C4×C31—21no—
99C2×C4⋊C4×C31—22no—
100C2×C4⋊C4×C31—21no—
101C2×C4⋊C4×C31—21no—
102C2×C4⋊C4×C31—21no—
103C2×C4⋊C4×C31—41no—
104C2×C4⋊C4×C31C2311yescharacteristic
105C2×C4⋊C4×C31C2311yescharacteristic
106C2×C4⋊C4×C31C2311yescharacteristic
107C2×C4⋊C4×C31C2311yescharacteristic
108C2×C4⋊C4×C31C2311yescharacteristic
109C2×C22⋊C4×C31—21no—
110C2×C22⋊C4×C31—21no—
111C2×C22⋊C4×C31—21no—
112C2×C22⋊C4×C31—21no—
113C2×C22⋊C4×C31—21no—
114C2×C22⋊C4×C31—21no—
115C2×C22⋊C4×C31—21no—
116C2×C22⋊C4×C31—21no—
117C2×C22⋊C4×C31—44no—
118C2×C22⋊C4×C31D411yescharacteristic
119C2×C22⋊C4×C31D411yescharacteristic
120C2×C42×C31—21no—
121C2×C42×C31—21no—
122C2×C42×C31C2311yescharacteristic
123C2×C42×C31C2311yescharacteristic
124C31×#106—22no—
125C31×#106—41no—
126C31×#103—22no—
127C31×#103—41no—
128C31×#102—22no—
129C31×#102—22no—
130C31×#102—22no—
131C31×#102C2×C414yescomplemented
132C31×#102C2×C414yescomplemented
133C31×#102D414yes—
134C31×C22⋊C8C2×C414yescomplemented
135C4×C8×C31—22no—
136C4×C8×C31—41no—
137C31×#95—21no—
138C31×#95—21no—
139C31×#95—21no—
140C31×#95—21no—
141C31×#95—21no—
142C31×#95D411yescharacteristic
143C31×#95D411yescharacteristic
144C24×C31—21no—
145C24×C31—21no—
146C24×C31—24no—
147C24×C31—42no—
148C24×C31—42no—
149C24×C31—42no—
150C24×C31—42no—
151C24×C31—81no—
152C24×C31—81no—
153C24×C31C2×D411yescharacteristic
154C2×Q8×C31—21no—
155C2×Q8×C31—21no—
156C2×Q8×C31—21no—
157C2×Q8×C31—21no—
158C2×Q8×C31—21no—
159C2×Q8×C31C22×C412yes—
160C2×D4×C31—28no—
161C2×D4×C31—24no—
162C2×D4×C31—21no—
163C2×D4×C31—21no—
164C2×D4×C31—21no—
165C2×D4×C31—21no—
166C2×D4×C31—21no—
167C2×D4×C31—21no—
168C2×D4×C31—21no—
169C2×D4×C31—21no—
170C2×D4×C31—44no—
171C2×D4×C31—44no—
172C2×D4×C31—44no—
173C2×D4×C31—42no—
174C2×D4×C31—42no—
175C2×D4×C31C22×C412yes—
176C2×D4×C31C22×C412yes—
177C2×D4×C31C2×D412yes—
178C2×D4×C31#4112yes—
179C22×C4×C31—21no—
180C22×C4×C31—21no—
181C22×C4×C31—21no—
182C22×C4×C31—21no—
183C22×C4×C31—21no—
184C22×C4×C31—21no—
185C22×C4×C31—21no—
186C22×C4×C31—21no—
187C22×C4×C31—21no—
188C22×C4×C31—21no—
189C22×C4×C31—42no—
190C22×C4×C31—42no—
191C22×C4×C31—42no—
192C22×C4×C31—42no—
193C22×C4×C31—42no—
194C22×C4×C31—42no—
195C22×C4×C31—81no—
196C22×C4×C31—81no—
197C22×C4×C31—81no—
198C22×C4×C31C22×C412yes—
199C22×C4×C31C2×D411yescharacteristic
200C22×C4×C31C2×D411yescharacteristic
201C22×C4×C31C2×D411yescharacteristic
202C22×C4×C31C2×D411yescharacteristic
203C22×C4×C31C2×D411yescharacteristic
204C22×C4×C31#4112yes—
205C22×C4×C31C2411yescharacteristic
206SD16×C31—28no—
207SD16×C31—44no—
208C2×C8×C31—21no—
209C2×C8×C31—21no—
210C2×C8×C31—21no—
211C2×C8×C31—21no—
212C2×C8×C31—21no—
213C2×C8×C31—21no—
214C2×C8×C31—21no—
215C2×C8×C31—21no—
216C2×C8×C31—21no—
217C2×C8×C31—44no—
218C2×C8×C31C22×C412yes—
219C2×C8×C31C22×C412yes—
220C2×C8×C31C2×D412yes—
221C4⋊C4×C31—24no—
222C4⋊C4×C31—21no—
223C4⋊C4×C31—21no—
224C4⋊C4×C31—21no—
225C4⋊C4×C31—21no—
226C4⋊C4×C31—21no—
227C4⋊C4×C31—21no—
228C4⋊C4×C31—21no—
229C4⋊C4×C31—21no—
230C4⋊C4×C31—42no—
231C4⋊C4×C31—42no—
232C4⋊C4×C31—81no—
233C4⋊C4×C31C22×C412yes—
234C4⋊C4×C31C2×D412yes—
235C22⋊C4×C31—24no—
236C22⋊C4×C31—22no—
237C22⋊C4×C31—42no—
238C22⋊C4×C31—42no—
239C22⋊C4×C31—42no—
240C22⋊C4×C31—42no—
241C22⋊C4×C31—42no—
242C22⋊C4×C31—81no—
243C22⋊C4×C31—81no—
244C22⋊C4×C31SD1614yescomplemented
245C42×C31—21no—
246C42×C31—21no—
247C42×C31—21no—
248C42×C31—21no—
249C42×C31—42no—
250C42×C31—81no—
251#22874C3111yesmaximal, characteristic, direct product factor, Sylow
252C23×C31—21no—
253C23×C31—21no—
254C23×C31—21no—
255C23×C31—21no—
256C23×C31—22no—
257C23×C31—22no—
258C23×C31—22no—
259C23×C31—22no—
260C23×C31—48no—
261C23×C31—41no—
262C23×C31—41no—
263C23×C31—41no—
264C23×C31—41no—
265C23×C31—41no—
266C23×C31—41no—
267C23×C31—41no—
268C23×C31—41no—
269C23×C31—41no—
270C23×C31—41no—
271C23×C31—48no—
272C23×C31—84no—
273C23×C31—84no—
274C23×C31—84no—
275C23×C31—84no—
276C23×C31—84no—
277C23×C31C4×D412yes—
278C23×C31C2×SD1612yes—
279C23×C31#13512yes—
280C23×C31C22×D411yescharacteristic
281Q8×C31—22no—
282Q8×C31—22no—
283Q8×C31—41no—
284Q8×C31—41no—
285D4×C31—22no—
286D4×C31—22no—
287D4×C31—22no—
288D4×C31—22no—
289D4×C31—22no—
290D4×C31—48no—
291D4×C31—41no—
292D4×C31—41no—
293D4×C31C4×D414yes—
294C2×C4×C31—21no—
295C2×C4×C31—21no—
296C2×C4×C31—21no—
297C2×C4×C31—21no—
298C2×C4×C31—21no—
299C2×C4×C31—21no—
300C2×C4×C31—22no—
301C2×C4×C31—22no—
302C2×C4×C31—22no—
303C2×C4×C31—22no—
304C2×C4×C31—22no—
305C2×C4×C31—22no—
306C2×C4×C31—21no—
307C2×C4×C31—22no—
308C2×C4×C31—21no—
309C2×C4×C31—21no—
310C2×C4×C31—21no—
311C2×C4×C31—21no—
312C2×C4×C31—21no—
313C2×C4×C31—41no—
314C2×C4×C31—41no—
315C2×C4×C31—41no—
316C2×C4×C31—41no—
317C2×C4×C31—41no—
318C2×C4×C31—41no—
319C2×C4×C31—41no—
320C2×C4×C31—41no—
321C2×C4×C31—41no—
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—84no—
329C2×C4×C31—84no—
330C2×C4×C31—84no—
331C2×C4×C31C4×D412yes—
332C2×C4×C31C2×SD1612yes—
333C2×C4×C31C2×SD1612yes—
334C2×C4×C31C23×C411yescharacteristic
335C2×C4×C31C22×D411yescharacteristic
336C2×C4×C31C2×#4111yescharacteristic
337C2×C4×C31C2×#4111yescharacteristic
338C2×C4×C31H(5,𝔽2)11yescharacteristic
339C2×C4×C31H(5,𝔽2)11yescharacteristic
340C8×C31—22no—
341C8×C31—22no—
342C8×C31—22no—
343C8×C31—41no—
344C2×#450C2×C3111yescharacteristic
345C2×C4×SD16C2×C3111yescharacteristic, complemented
346C22×#102C2×C3111yescharacteristic
347#2360C2×C3111yescharacteristic, complemented
348D4×C22⋊C4C2×C3111yescharacteristic
349#1968C2×C3111yescharacteristic, complemented
350#1934C2×C3111yescharacteristic, complemented
351#1926C2×C3111yescharacteristic, complemented
352#1892C2×C3111yescharacteristic, complemented
353#1880C2×C3111yescharacteristic, complemented
354#1877C2×C3111yescharacteristic, complemented
355#1864C2×C3111yescharacteristic, complemented
356#1853C2×C3111yescharacteristic, complemented
357C4×#102C2×C3111yescharacteristic, complemented
358C8×C22⋊C4C2×C3111yescharacteristic, complemented
359C22×C31—22no—
360C22×C31—22no—
361C22×C31—22no—
362C22×C31—22no—
363C22×C31—22no—
364C22×C31—22no—
365C22×C31—24no—
366C22×C31—42no—
367C22×C31—42no—
368C22×C31—42no—
369C22×C31—42no—
370C22×C31—42no—
371C22×C31—42no—
372C22×C31—42no—
373C22×C31—42no—
374C22×C31—42no—
375C22×C31—816no—
376C22×C31—81no—
377C22×C31—81no—
378C22×C31—81no—
379C22×C31—81no—
380C22×C31C4×SD1614yescomplemented
381C22×C31C2×C4×D411yescharacteristic
382C22×C31D4211yescharacteristic
383C22×C31#54611yescharacteristic
384C22×C31C22×SD1611yescharacteristic
385C22×C31C2×#13511yescharacteristic
386C22×C31#57611yescharacteristic
387C22×C31#57711yescharacteristic
388C4×C31—22no—
389C4×C31—22no—
390C4×C31—22no—
391C4×C31—42no—
392C4×C31—42no—
393C4×C31—41no—
394C4×C31—42no—
395C4×C31—41no—
396C4×C31—81no—
397C4×C31—81no—
398C4×C31—81no—
399C4×C31C2×C4×D411yescharacteristic
400C4×C31#51811yescharacteristic
401C4×C31#54611yescharacteristic
402C4×C31#55111yescharacteristic
403C23×D4C22×C3111yescharacteristic
404C22×SD16C22×C3111yescharacteristic
405C22×SD16C22×C3111yescharacteristic
406C23×C8C22×C3111yescharacteristic
407C2×C22⋊Q8C22×C3111yescharacteristic
408C2×C4×Q8C22×C3111yescharacteristic, complemented
409C2×C4×D4C22×C3111yescharacteristic
410C2×C4×D4C22×C3111yescharacteristic
411C22×C4⋊C4C22×C3111yescharacteristic
412C22×C22⋊C4—21no—
413#450C4×C3118yescomplemented
414C4×SD16—24no—
415C2×#106C22×C3111yescharacteristic, complemented
416C2×#106C22×C3111yescharacteristic, complemented
417C2×#103C22×C3111yescharacteristic, complemented
418C2×#103C22×C3111yescharacteristic, complemented
419C2×#102—24no—
420C2×#102C22×C3111yescharacteristic
421C2×#102C22×C3111yescharacteristic
422C2×#102C22×C3111yescharacteristic
423C2×#102C22×C3111yescharacteristic
424C2×#102C22×C3111yescharacteristic
425C2×#102C22×C3111yescharacteristic
426C2×C22⋊C8C22×C3111yescharacteristic
427C2×C4×C8C22×C3111yescharacteristic, complemented
428C2×C4×C8C22×C3111yescharacteristic, complemented
429#391C22×C3111yescharacteristic, complemented
430#390C22×C3111yescharacteristic
431#390C22×C3111yescharacteristic
432#389—21no—
433#389C22×C3111yescharacteristic, complemented
434#387—21no—
435#386—21no—
436#386—21no—
437#385—21no—
438#380C22×C3111yescharacteristic
439#379—21no—
440C4×C4⋊C4C22×C3111yescharacteristic, complemented
441C4×C22⋊C4—21no—
442C4×C22⋊C4C22×C3111yescharacteristic
443#340C22×C3111yescharacteristic, complemented
444#340C22×C3111yescharacteristic, complemented
445#340C22×C3111yescharacteristic, complemented
446#340C22×C3111yescharacteristic, complemented
447#336C22×C3111yescharacteristic, complemented
448#336C22×C3111yescharacteristic, complemented
449C2×C31—24no—
450C2×C31—44no—
451C2×C31—82no—
452C2×C31#235811yescharacteristic
453C2×C31C2×C4×SD1611yescharacteristic
454C2×C31#294611yescharacteristic
455C2×C31#328011yescharacteristic
456C2×C31D4×SD1611yescharacteristic
457C2×C31#329511yescharacteristic
458C2×C31#329611yescharacteristic
459C25—21no—
460C22×Q8C23×C3111yescharacteristic
461C22×D4—22no—
462C22×D4—22no—
463C22×D4—21no—
464C22×D4—22no—
465C22×D4—41no—
466C22×D4—41no—
467C22×D4C2×C4×C3114yes—
468C22×D4C23×C3111yescharacteristic
469C22×D4C23×C3111yescharacteristic
470C23×C4—21no—
471C23×C4—21no—
472C23×C4—21no—
473C23×C4C23×C3111yescharacteristic
474C2×SD16—22no—
475C2×SD16—22no—
476C2×SD16—41no—
477C2×SD16—41no—
478C2×SD16C2×C4×C3114yescomplemented
479C2×SD16C2×C4×C3114yescomplemented
480C22×C8—22no—
481C22×C8—22no—
482C22×C8—41no—
483C22×C8C23×C3111yescharacteristic
484C22×C8C23×C3111yescharacteristic
485C22×C8C23×C3111yescharacteristic
486C22×C8C23×C3111yescharacteristic
487C22⋊Q8—22no—
488C22⋊Q8C2×C4×C3114yescomplemented
489C4×Q8—22no—
490C4×Q8—41no—
491C4×D4—22no—
492C4×D4—22no—
493C4×D4—41no—
494C4×D4—41no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—41no—
501C2×C4⋊C4C23×C3111yescharacteristic
502C2×C4⋊C4C23×C3111yescharacteristic
503C2×C4⋊C4C23×C3111yescharacteristic
504C2×C4⋊C4C23×C3111yescharacteristic
505C2×C4⋊C4C23×C3111yescharacteristic
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—44no—
515C2×C22⋊C4D4×C3111yescharacteristic
516C2×C22⋊C4D4×C3111yescharacteristic
517C2×C42—21no—
518C2×C42—21no—
519C2×C42C23×C3111yescharacteristic
520C2×C42C23×C3111yescharacteristic
521#106—22no—
522#106—41no—
523#103—22no—
524#103—41no—
525#102—22no—
526#102—22no—
527#102—22no—
528#102C2×C4×C3114yescomplemented
529#102C2×C4×C3114yescomplemented
530#102D4×C3114yes—
531C22⋊C8C2×C4×C3114yescomplemented
532C4×C8—22no—
533C4×C8—41no—
534#95—21no—
535#95—21no—
536#95—21no—
537#95—21no—
538#95—21no—
539#95D4×C3111yescharacteristic
540#95D4×C3111yescharacteristic
541C31#2287411yescharacteristic, direct product factor, Sylow
542C24—21no—
543C24—21no—
544C24—24no—
545C24—42no—
546C24—42no—
547C24—42no—
548C24—42no—
549C24—81no—
550C24—81no—
551C24C2×D4×C3111yescharacteristic
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8C22×C4×C3112yes—
558C2×D4—28no—
559C2×D4—24no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—44no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4C22×C4×C3112yes—
574C2×D4C22×C4×C3112yes—
575C2×D4C2×D4×C3112yes—
576C2×D4#41×C3112yes—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—81no—
594C22×C4—81no—
595C22×C4—81no—
596C22×C4C22×C4×C3112yes—
597C22×C4C2×D4×C3111yescharacteristic
598C22×C4C2×D4×C3111yescharacteristic
599C22×C4C2×D4×C3111yescharacteristic
600C22×C4C2×D4×C3111yescharacteristic
601C22×C4C2×D4×C3111yescharacteristic
602C22×C4#41×C3112yes—
603C22×C4C24×C3111yescharacteristic
604SD16—28no—
605SD16—44no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—44no—
616C2×C8C22×C4×C3112yes—
617C2×C8C22×C4×C3112yes—
618C2×C8C2×D4×C3112yes—
619C4⋊C4—24no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—42no—
629C4⋊C4—42no—
630C4⋊C4—81no—
631C4⋊C4C22×C4×C3112yes—
632C4⋊C4C2×D4×C3112yes—
633C22⋊C4—24no—
634C22⋊C4—22no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—81no—
641C22⋊C4—81no—
642C22⋊C4SD16×C3114yescomplemented
643C42—21no—
644C42—21no—
645C42—21no—
646C42—21no—
647C42—42no—
648C42—81no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—48no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—48no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—84no—
670C23—84no—
671C23—84no—
672C23—84no—
673C23—84no—
674C23C4×D4×C3112yes—
675C23C2×SD16×C3112yes—
676C23C31×#13512yes—
677C23C22×D4×C3111yescharacteristic
678Q8—22no—
679Q8—22no—
680Q8—41no—
681Q8—41no—
682D4—22no—
683D4—22no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—48no—
688D4—41no—
689D4—41no—
690D4C4×D4×C3114yes—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—84no—
726C2×C4—84no—
727C2×C4—84no—
728C2×C4C4×D4×C3112yes—
729C2×C4C2×SD16×C3112yes—
730C2×C4C2×SD16×C3112yes—
731C2×C4C23×C4×C3111yescharacteristic
732C2×C4C22×D4×C3111yescharacteristic
733C2×C4C2×#41×C3111yescharacteristic
734C2×C4C2×#41×C3111yescharacteristic
735C2×C4C31×H(5,𝔽2)11yescharacteristic
736C2×C4C31×H(5,𝔽2)11yescharacteristic
737C8—22no—
738C8—22no—
739C8—22no—
740C8—41no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—24no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—816no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22C4×SD16×C3114yescomplemented
763C22C2×C4×D4×C3111yescharacteristic
764C22D42×C3111yescharacteristic
765C22C31×#54611yescharacteristic
766C22C22×SD16×C3111yescharacteristic
767C22C2×C31×#13511yescharacteristic
768C22C31×#57611yescharacteristic
769C22C31×#57711yescharacteristic
770C4—22no—
771C4—22no—
772C4—22no—
773C4—42no—
774C4—42no—
775C4—41no—
776C4—42no—
777C4—41no—
778C4—81no—
779C4—81no—
780C4—81no—
781C4C2×C4×D4×C3111yescharacteristic
782C4C31×#51811yescharacteristic
783C4C31×#54611yescharacteristic
784C4C31×#55111yescharacteristic
785C2—24no—
786C2—44no—
787C2—82no—
788C2C31×#235811yescharacteristic
789C2C2×C4×SD16×C3111yescharacteristic
790C2C31×#294611yescharacteristic
791C2C31×#328011yescharacteristic
792C2D4×SD16×C3111yescharacteristic
793C2C31×#329511yescharacteristic
794C2C31×#329611yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutatorC2×C4C23×C4×C31
Frattini, cosocleC22×C4C24×C31
prime radicalC23×D4×C31C22
LCSG ▷ C2×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
2. C2×C4×SD16×C31C2semidirect
4. C31×#2360C2semidirect
6. C31×#1968C2semidirect
7. C31×#1934C2semidirect
8. C31×#1926C2semidirect
9. C31×#1892C2semidirect
10. C31×#1880C2semidirect
11. C31×#1877C2semidirect
12. C31×#1864C2semidirect
13. C31×#1853C2semidirect
14. C4×C31×#102C2semidirect
15. C8×C22⋊C4×C31C2semidirect
21. C2×C4×Q8×C31C22semidirect
26. C31×#450C4semidirect
28. C2×C31×#106C22semidirect
29. C2×C31×#106C22semidirect
30. C2×C31×#103C22semidirect
31. C2×C31×#103C22semidirect
40. C2×C4×C8×C31C22semidirect
41. C2×C4×C8×C31C22semidirect
42. C31×#391C22semidirect
46. C31×#389C22semidirect
53. C4×C4⋊C4×C31C22semidirect
56. C31×#340C22semidirect
57. C31×#340C22semidirect
58. C31×#340C22semidirect
59. C31×#340C22semidirect
60. C31×#336C22semidirect
61. C31×#336C22semidirect
81. C2×SD16×C31C2×C4semidirect
82. C2×SD16×C31C2×C4semidirect
91. C31×C22⋊Q8C2×C4semidirect
131. C31×#102C2×C4semidirect
132. C31×#102C2×C4semidirect
134. C31×C22⋊C8C2×C4semidirect
244. C22⋊C4×C31SD16semidirect
251. #22874C31direct (N × H)
345. C2×C4×SD16C2×C31semidirect
347. #2360C2×C31semidirect
349. #1968C2×C31semidirect
350. #1934C2×C31semidirect
351. #1926C2×C31semidirect
352. #1892C2×C31semidirect
353. #1880C2×C31semidirect
354. #1877C2×C31semidirect
355. #1864C2×C31semidirect
356. #1853C2×C31semidirect
357. C4×#102C2×C31semidirect
358. C8×C22⋊C4C2×C31semidirect
380. C22×C31C4×SD16semidirect
408. C2×C4×Q8C22×C31semidirect
413. #450C4×C31semidirect
415. C2×#106C22×C31semidirect
416. C2×#106C22×C31semidirect
417. C2×#103C22×C31semidirect
418. C2×#103C22×C31semidirect
427. C2×C4×C8C22×C31semidirect
428. C2×C4×C8C22×C31semidirect
429. #391C22×C31semidirect
433. #389C22×C31semidirect
440. C4×C4⋊C4C22×C31semidirect
443. #340C22×C31semidirect
444. #340C22×C31semidirect
445. #340C22×C31semidirect
446. #340C22×C31semidirect
447. #336C22×C31semidirect
448. #336C22×C31semidirect
478. C2×SD16C2×C4×C31semidirect
479. C2×SD16C2×C4×C31semidirect
488. C22⋊Q8C2×C4×C31semidirect
528. #102C2×C4×C31semidirect
529. #102C2×C4×C31semidirect
531. C22⋊C8C2×C4×C31semidirect
541. C31#22874direct (N × H)
642. C22⋊C4SD16×C31semidirect
762. C22C4×SD16×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4502
C2×C4×SD16×C312
C22×C31×#1022
C31×#23602
D4×C22⋊C4×C312
C31×#19682
C31×#19342
C31×#19262
C31×#18922
C31×#18802
C31×#18772
C31×#18642
C31×#18532
C4×C31×#1022
C8×C22⋊C4×C312
#2287431