Finite Group Databasebeta

← C31×#22875 #21479634

Subgroups — C31×#22875 #21479634

Order 7936.

1182 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#448C211yesmaximal, characteristic
2C2×C4×SD16×C31C211yesmaximal, characteristic, complemented
3C22×C31×#103C211yesmaximal, characteristic, complemented
4C31×#2361C211yesmaximal, characteristic
5Q8×C22⋊C4×C31C211yesmaximal, characteristic, complemented
6C31×#1968C211yesmaximal, characteristic, complemented
7C31×#1933C211yesmaximal, characteristic, complemented
8C31×#1927C211yesmaximal, characteristic, complemented
9C31×#1893C211yesmaximal, characteristic
10C31×#1880C211yesmaximal, characteristic, complemented
11C31×#1877C211yesmaximal, characteristic, complemented
12C31×#1865C211yesmaximal, characteristic, complemented
13C31×#1853C211yesmaximal, characteristic, complemented
14C4×C31×#103C211yesmaximal, characteristic, complemented
15C8×C22⋊C4×C31C211yesmaximal, characteristic, complemented
16C23×Q8×C31C2211yescharacteristic
17C22×SD16×C31C2211yescharacteristic
18C22×SD16×C31C2211yescharacteristic
19C23×C8×C31C2211yescharacteristic
20C2×C31×#121C2211yescharacteristic
21C2×C4×Q8×C31C2211yescharacteristic
22C2×C4×Q8×C31C2211yescharacteristic
23C2×C4×D4×C31—21no—
24C2×C4×D4×C31C2211yescharacteristic
25C22×C4⋊C4×C31C2211yescharacteristic
26C31×#448C418yescomplemented
27C4×SD16×C31—24no—
28C2×C31×#106C2211yescharacteristic
29C2×C31×#106C2211yescharacteristic
30C2×C31×#103—24no—
31C2×C31×#103C2211yescharacteristic
32C2×C31×#103C2211yescharacteristic
33C2×C31×#103C2211yescharacteristic
34C2×C31×#103C2211yescharacteristic
35C2×C31×#103C2211yescharacteristic
36C2×C31×#103C2211yescharacteristic
37C2×C31×#102C2211yescharacteristic
38C2×C31×#102C2211yescharacteristic
39C2×C31×C22⋊C8C2211yescharacteristic
40C2×C4×C8×C31C2211yescharacteristic
41C2×C4×C8×C31C2211yescharacteristic
42C31×#391—21no—
43C31×#391—21no—
44C31×#391C2211yescharacteristic
45C31×#391C2211yescharacteristic
46C31×#390C2211yescharacteristic
47C31×#389C2211yescharacteristic
48C31×#388—21no—
49C31×#386—21no—
50C31×#385—21no—
51C31×#380—21no—
52C31×#380C2211yescharacteristic
53C4×C4⋊C4×C31C2211yescharacteristic
54C4×C22⋊C4×C31—21no—
55C4×C22⋊C4×C31C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#336C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C22×Q8×C31—21no—
63C22×Q8×C31—22no—
64C22×Q8×C31—22no—
65C22×Q8×C31—22no—
66C22×Q8×C31—41no—
67C22×Q8×C31—41no—
68C22×Q8×C31C2×C414yescomplemented
69C22×Q8×C31C2311yescharacteristic
70C22×Q8×C31C2311yescharacteristic
71C22×D4×C31—21no—
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×#121—22no—
91C31×#121C2×C414yes—
92C4×Q8×C31—22no—
93C4×Q8×C31—22no—
94C4×Q8×C31—41no—
95C4×Q8×C31—41no—
96C4×D4×C31—22no—
97C4×D4×C31—41no—
98C4×D4×C31—44no—
99C2×C4⋊C4×C31—22no—
100C2×C4⋊C4×C31—21no—
101C2×C4⋊C4×C31—21no—
102C2×C4⋊C4×C31—21no—
103C2×C4⋊C4×C31—21no—
104C2×C4⋊C4×C31—41no—
105C2×C4⋊C4×C31C2311yescharacteristic
106C2×C4⋊C4×C31C2311yescharacteristic
107C2×C4⋊C4×C31C2311yescharacteristic
108C2×C4⋊C4×C31C2311yescharacteristic
109C2×C4⋊C4×C31C2311yescharacteristic
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×C31D411yescharacteristic
116C2×C22⋊C4×C31D411yescharacteristic
117C2×C42×C31—21no—
118C2×C42×C31—21no—
119C2×C42×C31—21no—
120C2×C42×C31C2311yescharacteristic
121C2×C42×C31C2311yescharacteristic
122C31×#106—22no—
123C31×#106—41no—
124C31×#103—22no—
125C31×#103—22no—
126C31×#103—22no—
127C31×#103C2×C414yescomplemented
128C31×#103C2×C414yescomplemented
129C31×#103D414yescomplemented
130C31×#102—22no—
131C31×#102—41no—
132C31×C22⋊C8C2×C414yescomplemented
133C4×C8×C31—22no—
134C4×C8×C31—41no—
135C31×#95—21no—
136C31×#95—21no—
137C31×#95—21no—
138C31×#95—21no—
139C31×#95—21no—
140C31×#95—21no—
141C31×#95—21no—
142C31×#95D411yescharacteristic
143C31×#95D411yescharacteristic
144C24×C31—21no—
145C24×C31C2×D411yescharacteristic
146C2×Q8×C31—24no—
147C2×Q8×C31—21no—
148C2×Q8×C31—21no—
149C2×Q8×C31—21no—
150C2×Q8×C31—21no—
151C2×Q8×C31—28no—
152C2×Q8×C31—21no—
153C2×Q8×C31—21no—
154C2×Q8×C31—21no—
155C2×Q8×C31—21no—
156C2×Q8×C31—42no—
157C2×Q8×C31—42no—
158C2×Q8×C31—44no—
159C2×Q8×C31—44no—
160C2×Q8×C31—44no—
161C2×Q8×C31C22×C412yes—
162C2×Q8×C31C22×C412yes—
163C2×Q8×C31C2×D412yes—
164C2×Q8×C31#4112yes—
165C2×D4×C31—24no—
166C2×D4×C31—21no—
167C2×D4×C31—21no—
168C2×D4×C31—21no—
169C2×D4×C31—21no—
170C2×D4×C31—21no—
171C2×D4×C31—42no—
172C2×D4×C31—42no—
173C2×D4×C31C22×C412yes—
174C22×C4×C31—21no—
175C22×C4×C31—21no—
176C22×C4×C31—21no—
177C22×C4×C31—21no—
178C22×C4×C31—21no—
179C22×C4×C31—24no—
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—42no—
187C22×C4×C31—42no—
188C22×C4×C31—42no—
189C22×C4×C31—42no—
190C22×C4×C31—42no—
191C22×C4×C31—42no—
192C22×C4×C31—81no—
193C22×C4×C31—81no—
194C22×C4×C31C22×C412yes—
195C22×C4×C31C2×D411yescharacteristic
196C22×C4×C31C2×D411yescharacteristic
197C22×C4×C31C2×D411yescharacteristic
198C22×C4×C31C2×D411yescharacteristic
199C22×C4×C31C2×D411yescharacteristic
200C22×C4×C31#4112yes—
201C22×C4×C31C2411yescharacteristic
202SD16×C31—28no—
203SD16×C31—44no—
204C2×C8×C31—21no—
205C2×C8×C31—21no—
206C2×C8×C31—21no—
207C2×C8×C31—21no—
208C2×C8×C31—21no—
209C2×C8×C31—21no—
210C2×C8×C31—21no—
211C2×C8×C31—21no—
212C2×C8×C31—21no—
213C2×C8×C31—44no—
214C2×C8×C31C22×C412yes—
215C2×C8×C31C22×C412yes—
216C2×C8×C31C2×D412yes—
217C4⋊C4×C31—21no—
218C4⋊C4×C31—21no—
219C4⋊C4×C31—21no—
220C4⋊C4×C31—21no—
221C4⋊C4×C31—21no—
222C4⋊C4×C31—21no—
223C4⋊C4×C31—21no—
224C4⋊C4×C31—21no—
225C4⋊C4×C31—42no—
226C4⋊C4×C31—42no—
227C4⋊C4×C31—42no—
228C4⋊C4×C31—42no—
229C4⋊C4×C31C22×C412yes—
230C4⋊C4×C31C2×D412yes—
231C22⋊C4×C31—22no—
232C22⋊C4×C31—24no—
233C22⋊C4×C31—42no—
234C22⋊C4×C31—42no—
235C22⋊C4×C31—42no—
236C22⋊C4×C31—81no—
237C22⋊C4×C31SD1614yescomplemented
238C42×C31—21no—
239C42×C31—21no—
240C42×C31—21no—
241C42×C31—21no—
242C42×C31—42no—
243C42×C31—42no—
244C42×C31—42no—
245#22875C3111yesmaximal, characteristic, direct product factor, Sylow
246C23×C31—21no—
247C23×C31—21no—
248C23×C31—21no—
249C23×C31—21no—
250C23×C31—22no—
251C23×C31—41no—
252C23×C31—41no—
253C23×C31—41no—
254C23×C31—41no—
255C23×C31—41no—
256C23×C31—41no—
257C23×C31C4×D412yes—
258C23×C31C2×SD1612yes—
259C23×C31#13512yes—
260C23×C31C22×D411yescharacteristic
261Q8×C31—22no—
262Q8×C31—22no—
263Q8×C31—22no—
264Q8×C31—22no—
265Q8×C31—22no—
266Q8×C31—48no—
267Q8×C31—41no—
268Q8×C31—41no—
269Q8×C31C4×D414yescomplemented
270D4×C31—22no—
271D4×C31—22no—
272D4×C31—48no—
273D4×C31—41no—
274D4×C31—41no—
275C2×C4×C31—22no—
276C2×C4×C31—21no—
277C2×C4×C31—22no—
278C2×C4×C31—21no—
279C2×C4×C31—21no—
280C2×C4×C31—22no—
281C2×C4×C31—21no—
282C2×C4×C31—21no—
283C2×C4×C31—21no—
284C2×C4×C31—22no—
285C2×C4×C31—22no—
286C2×C4×C31—22no—
287C2×C4×C31—22no—
288C2×C4×C31—22no—
289C2×C4×C31—22no—
290C2×C4×C31—21no—
291C2×C4×C31—22no—
292C2×C4×C31—21no—
293C2×C4×C31—21no—
294C2×C4×C31—21no—
295C2×C4×C31—21no—
296C2×C4×C31—21no—
297C2×C4×C31—48no—
298C2×C4×C31—41no—
299C2×C4×C31—41no—
300C2×C4×C31—41no—
301C2×C4×C31—41no—
302C2×C4×C31—41no—
303C2×C4×C31—41no—
304C2×C4×C31—41no—
305C2×C4×C31—41no—
306C2×C4×C31—41no—
307C2×C4×C31—41no—
308C2×C4×C31—41no—
309C2×C4×C31—41no—
310C2×C4×C31—41no—
311C2×C4×C31—41no—
312C2×C4×C31—41no—
313C2×C4×C31—84no—
314C2×C4×C31—84no—
315C2×C4×C31C4×D412yes—
316C2×C4×C31C2×SD1612yes—
317C2×C4×C31C2×SD1612yes—
318C2×C4×C31C23×C411yescharacteristic
319C2×C4×C31C22×D411yescharacteristic
320C2×C4×C31C2×#4111yescharacteristic
321C2×C4×C31C2×#4111yescharacteristic
322C2×C4×C31H(5,𝔽2)11yescharacteristic
323C2×C4×C31H(5,𝔽2)11yescharacteristic
324C8×C31—22no—
325C8×C31—22no—
326C8×C31—22no—
327C8×C31—41no—
328C2×#448C2×C3111yescharacteristic
329C2×C4×SD16C2×C3111yescharacteristic, complemented
330C22×#103C2×C3111yescharacteristic, complemented
331#2361C2×C3111yescharacteristic
332Q8×C22⋊C4C2×C3111yescharacteristic, complemented
333#1968C2×C3111yescharacteristic, complemented
334#1933C2×C3111yescharacteristic, complemented
335#1927C2×C3111yescharacteristic, complemented
336#1893C2×C3111yescharacteristic
337#1880C2×C3111yescharacteristic, complemented
338#1877C2×C3111yescharacteristic, complemented
339#1865C2×C3111yescharacteristic, complemented
340#1853C2×C3111yescharacteristic, complemented
341C4×#103C2×C3111yescharacteristic, complemented
342C8×C22⋊C4C2×C3111yescharacteristic, complemented
343C22×C31—22no—
344C22×C31—22no—
345C22×C31—22no—
346C22×C31—22no—
347C22×C31—22no—
348C22×C31—22no—
349C22×C31—42no—
350C22×C31—42no—
351C22×C31—42no—
352C22×C31—81no—
353C22×C31—81no—
354C22×C31—81no—
355C22×C31—81no—
356C22×C31C4×SD1614yescomplemented
357C22×C31C2×C4×D411yescharacteristic
358C22×C31D4211yescharacteristic
359C22×C31#54611yescharacteristic
360C22×C31C22×SD1611yescharacteristic
361C22×C31C2×#13511yescharacteristic
362C22×C31#57711yescharacteristic
363C22×C31#57811yescharacteristic
364C4×C31—22no—
365C4×C31—24no—
366C4×C31—22no—
367C4×C31—22no—
368C4×C31—42no—
369C4×C31—42no—
370C4×C31—42no—
371C4×C31—41no—
372C4×C31—41no—
373C4×C31—81no—
374C4×C31—81no—
375C4×C31—81no—
376C4×C31C2×C4×D411yescharacteristic
377C4×C31#51811yescharacteristic
378C4×C31#54611yescharacteristic
379C4×C31#55111yescharacteristic
380C23×Q8C22×C3111yescharacteristic
381C22×SD16C22×C3111yescharacteristic
382C22×SD16C22×C3111yescharacteristic
383C23×C8C22×C3111yescharacteristic
384C2×#121C22×C3111yescharacteristic
385C2×C4×Q8C22×C3111yescharacteristic
386C2×C4×Q8C22×C3111yescharacteristic
387C2×C4×D4—21no—
388C2×C4×D4C22×C3111yescharacteristic
389C22×C4⋊C4C22×C3111yescharacteristic
390#448C4×C3118yescomplemented
391C4×SD16—24no—
392C2×#106C22×C3111yescharacteristic
393C2×#106C22×C3111yescharacteristic
394C2×#103—24no—
395C2×#103C22×C3111yescharacteristic
396C2×#103C22×C3111yescharacteristic
397C2×#103C22×C3111yescharacteristic
398C2×#103C22×C3111yescharacteristic
399C2×#103C22×C3111yescharacteristic
400C2×#103C22×C3111yescharacteristic
401C2×#102C22×C3111yescharacteristic
402C2×#102C22×C3111yescharacteristic
403C2×C22⋊C8C22×C3111yescharacteristic
404C2×C4×C8C22×C3111yescharacteristic
405C2×C4×C8C22×C3111yescharacteristic
406#391—21no—
407#391—21no—
408#391C22×C3111yescharacteristic
409#391C22×C3111yescharacteristic
410#390C22×C3111yescharacteristic
411#389C22×C3111yescharacteristic
412#388—21no—
413#386—21no—
414#385—21no—
415#380—21no—
416#380C22×C3111yescharacteristic
417C4×C4⋊C4C22×C3111yescharacteristic
418C4×C22⋊C4—21no—
419C4×C22⋊C4C22×C3111yescharacteristic
420#340C22×C3111yescharacteristic
421#340C22×C3111yescharacteristic
422#340C22×C3111yescharacteristic
423#340C22×C3111yescharacteristic
424#336C22×C3111yescharacteristic
425#336C22×C3111yescharacteristic
426C2×C31—24no—
427C2×C31—82no—
428C2×C31#235811yescharacteristic
429C2×C31C2×C4×SD1611yescharacteristic
430C2×C31#294711yescharacteristic
431C2×C31D4×SD1611yescharacteristic
432C2×C31#328511yescharacteristic
433C2×C31#329811yescharacteristic
434C2×C31#330111yescharacteristic
435C22×Q8—21no—
436C22×Q8—22no—
437C22×Q8—22no—
438C22×Q8—22no—
439C22×Q8—41no—
440C22×Q8—41no—
441C22×Q8C2×C4×C3114yescomplemented
442C22×Q8C23×C3111yescharacteristic
443C22×Q8C23×C3111yescharacteristic
444C22×D4—21no—
445C22×D4C23×C3111yescharacteristic
446C23×C4—21no—
447C23×C4—21no—
448C23×C4—21no—
449C23×C4C23×C3111yescharacteristic
450C2×SD16—22no—
451C2×SD16—22no—
452C2×SD16—41no—
453C2×SD16—41no—
454C2×SD16C2×C4×C3114yescomplemented
455C2×SD16C2×C4×C3114yescomplemented
456C22×C8—22no—
457C22×C8—22no—
458C22×C8—41no—
459C22×C8C23×C3111yescharacteristic
460C22×C8C23×C3111yescharacteristic
461C22×C8C23×C3111yescharacteristic
462C22×C8C23×C3111yescharacteristic
463#121—22no—
464#121C2×C4×C3114yes—
465C4×Q8—22no—
466C4×Q8—22no—
467C4×Q8—41no—
468C4×Q8—41no—
469C4×D4—22no—
470C4×D4—41no—
471C4×D4—44no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—41no—
478C2×C4⋊C4C23×C3111yescharacteristic
479C2×C4⋊C4C23×C3111yescharacteristic
480C2×C4⋊C4C23×C3111yescharacteristic
481C2×C4⋊C4C23×C3111yescharacteristic
482C2×C4⋊C4C23×C3111yescharacteristic
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4D4×C3111yescharacteristic
489C2×C22⋊C4D4×C3111yescharacteristic
490C2×C42—21no—
491C2×C42—21no—
492C2×C42—21no—
493C2×C42C23×C3111yescharacteristic
494C2×C42C23×C3111yescharacteristic
495#106—22no—
496#106—41no—
497#103—22no—
498#103—22no—
499#103—22no—
500#103C2×C4×C3114yescomplemented
501#103C2×C4×C3114yescomplemented
502#103D4×C3114yescomplemented
503#102—22no—
504#102—41no—
505C22⋊C8C2×C4×C3114yescomplemented
506C4×C8—22no—
507C4×C8—41no—
508#95—21no—
509#95—21no—
510#95—21no—
511#95—21no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95D4×C3111yescharacteristic
516#95D4×C3111yescharacteristic
517C31#2287511yescharacteristic, direct product factor, Sylow
518C24—21no—
519C24C2×D4×C3111yescharacteristic
520C2×Q8—24no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—28no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—42no—
531C2×Q8—42no—
532C2×Q8—44no—
533C2×Q8—44no—
534C2×Q8—44no—
535C2×Q8C22×C4×C3112yes—
536C2×Q8C22×C4×C3112yes—
537C2×Q8C2×D4×C3112yes—
538C2×Q8#41×C3112yes—
539C2×D4—24no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4C22×C4×C3112yes—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—24no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—81no—
567C22×C4—81no—
568C22×C4C22×C4×C3112yes—
569C22×C4C2×D4×C3111yescharacteristic
570C22×C4C2×D4×C3111yescharacteristic
571C22×C4C2×D4×C3111yescharacteristic
572C22×C4C2×D4×C3111yescharacteristic
573C22×C4C2×D4×C3111yescharacteristic
574C22×C4#41×C3112yes—
575C22×C4C24×C3111yescharacteristic
576SD16—28no—
577SD16—44no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—44no—
588C2×C8C22×C4×C3112yes—
589C2×C8C22×C4×C3112yes—
590C2×C8C2×D4×C3112yes—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—42no—
602C4⋊C4—42no—
603C4⋊C4C22×C4×C3112yes—
604C4⋊C4C2×D4×C3112yes—
605C22⋊C4—22no—
606C22⋊C4—24no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—81no—
611C22⋊C4SD16×C3114yescomplemented
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—42no—
617C42—42no—
618C42—42no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—22no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23C4×D4×C3112yes—
631C23C2×SD16×C3112yes—
632C23C31×#13512yes—
633C23C22×D4×C3111yescharacteristic
634Q8—22no—
635Q8—22no—
636Q8—22no—
637Q8—22no—
638Q8—22no—
639Q8—48no—
640Q8—41no—
641Q8—41no—
642Q8C4×D4×C3114yescomplemented
643D4—22no—
644D4—22no—
645D4—48no—
646D4—41no—
647D4—41no—
648C2×C4—22no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—21no—
664C2×C4—22no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—48no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—84no—
687C2×C4—84no—
688C2×C4C4×D4×C3112yes—
689C2×C4C2×SD16×C3112yes—
690C2×C4C2×SD16×C3112yes—
691C2×C4C23×C4×C3111yescharacteristic
692C2×C4C22×D4×C3111yescharacteristic
693C2×C4C2×#41×C3111yescharacteristic
694C2×C4C2×#41×C3111yescharacteristic
695C2×C4C31×H(5,𝔽2)11yescharacteristic
696C2×C4C31×H(5,𝔽2)11yescharacteristic
697C8—22no—
698C8—22no—
699C8—22no—
700C8—41no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—42no—
708C22—42no—
709C22—42no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22C4×SD16×C3114yescomplemented
715C22C2×C4×D4×C3111yescharacteristic
716C22D42×C3111yescharacteristic
717C22C31×#54611yescharacteristic
718C22C22×SD16×C3111yescharacteristic
719C22C2×C31×#13511yescharacteristic
720C22C31×#57711yescharacteristic
721C22C31×#57811yescharacteristic
722C4—22no—
723C4—24no—
724C4—22no—
725C4—22no—
726C4—42no—
727C4—42no—
728C4—42no—
729C4—41no—
730C4—41no—
731C4—81no—
732C4—81no—
733C4—81no—
734C4C2×C4×D4×C3111yescharacteristic
735C4C31×#51811yescharacteristic
736C4C31×#54611yescharacteristic
737C4C31×#55111yescharacteristic
738C2—24no—
739C2—82no—
740C2C31×#235811yescharacteristic
741C2C2×C4×SD16×C3111yescharacteristic
742C2C31×#294711yescharacteristic
743C2D4×SD16×C3111yescharacteristic
744C2C31×#328511yescharacteristic
745C2C31×#329811yescharacteristic
746C2C31×#330111yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutatorC2×C4C23×C4×C31
Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#121C22
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
3. C22×C31×#103C2semidirect
5. Q8×C22⋊C4×C31C2semidirect
6. C31×#1968C2semidirect
7. C31×#1933C2semidirect
8. C31×#1927C2semidirect
10. C31×#1880C2semidirect
11. C31×#1877C2semidirect
12. C31×#1865C2semidirect
13. C31×#1853C2semidirect
14. C4×C31×#103C2semidirect
15. C8×C22⋊C4×C31C2semidirect
26. C31×#448C4semidirect
68. C22×Q8×C31C2×C4semidirect
81. C2×SD16×C31C2×C4semidirect
82. C2×SD16×C31C2×C4semidirect
127. C31×#103C2×C4semidirect
128. C31×#103C2×C4semidirect
129. C31×#103D4semidirect
132. C31×C22⋊C8C2×C4semidirect
237. C22⋊C4×C31SD16semidirect
245. #22875C31direct (N × H)
269. Q8×C31C4×D4semidirect
329. C2×C4×SD16C2×C31semidirect
330. C22×#103C2×C31semidirect
332. Q8×C22⋊C4C2×C31semidirect
333. #1968C2×C31semidirect
334. #1933C2×C31semidirect
335. #1927C2×C31semidirect
337. #1880C2×C31semidirect
338. #1877C2×C31semidirect
339. #1865C2×C31semidirect
340. #1853C2×C31semidirect
341. C4×#103C2×C31semidirect
342. C8×C22⋊C4C2×C31semidirect
356. C22×C31C4×SD16semidirect
390. #448C4×C31semidirect
441. C22×Q8C2×C4×C31semidirect
454. C2×SD16C2×C4×C31semidirect
455. C2×SD16C2×C4×C31semidirect
500. #103C2×C4×C31semidirect
501. #103C2×C4×C31semidirect
502. #103D4×C31semidirect
505. C22⋊C8C2×C4×C31semidirect
517. C31#22875direct (N × H)
611. C22⋊C4SD16×C31semidirect
642. Q8C4×D4×C31semidirect
714. 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×#4482
C2×C4×SD16×C312
C22×C31×#1032
C31×#23612
Q8×C22⋊C4×C312
C31×#19682
C31×#19332
C31×#19272
C31×#18932
C31×#18802
C31×#18772
C31×#18652
C31×#18532
C4×C31×#1032
C8×C22⋊C4×C312
#2287531