Finite Group Databasebeta

← C31×#24901 #21481660

Subgroups — C31×#24901 #21481660

Order 7936.

1156 conjugacy classes of subgroups.

The subgroup lattice has 778 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
3C31×#2423C211yesmaximal, characteristic, complemented
4D4×C22⋊C4×C31C211yesmaximal, characteristic
5C31×#2094C211yesmaximal, characteristic, complemented
6C31×#2077C211yesmaximal, characteristic, complemented
7C31×#2055C211yesmaximal, characteristic, complemented
8C31×#2035C211yesmaximal, characteristic, complemented
9C31×#1934C211yesmaximal, characteristic, complemented
10C31×#1923C211yesmaximal, characteristic, complemented
11C31×#1880C211yesmaximal, characteristic, complemented
12C31×#1877C211yesmaximal, characteristic, complemented
13C31×#1864C211yesmaximal, characteristic, complemented
14C31×#1802C211yesmaximal, characteristic, complemented
15C31×#1786C211yesmaximal, characteristic
16C23×D4×C31C2211yescharacteristic
17C22×SD16×C31C2211yescharacteristic
18C22×SD16×C31C2211yescharacteristic
19C2×C31×C22⋊Q8C2211yescharacteristic
20C2×C4×Q8×C31C2211yescharacteristic, complemented
21C2×C4×D4×C31C2211yescharacteristic
22C2×C4×D4×C31C2211yescharacteristic
23C22×C22⋊C4×C31—21no—
24C31×#450—24no—
25C4×SD16×C31—24no—
26C2×C31×#106C2211yescharacteristic, complemented
27C2×C31×#106C2211yescharacteristic, complemented
28C2×C31×C4⋊C8C2211yescharacteristic, complemented
29C2×C31×#103C2211yescharacteristic, complemented
30C2×C31×#103C2211yescharacteristic, complemented
31C2×C31×#102C2211yescharacteristic
32C2×C31×#102C2211yescharacteristic
33C2×C31×#102C2211yescharacteristic
34C2×C31×#102C2211yescharacteristic
35C2×C31×#102C2211yescharacteristic
36C2×C31×#102C2211yescharacteristic
37C2×C31×C22⋊C8C2211yescharacteristic
38C2×C31×C22⋊C8C2211yescharacteristic
39C2×C4×C8×C31C2211yescharacteristic, complemented
40C31×#399—21no—
41C31×#398—21no—
42C31×#391C2211yescharacteristic, complemented
43C31×#390C2211yescharacteristic
44C31×#390C2211yescharacteristic
45C31×#389C2211yescharacteristic, complemented
46C31×#388—21no—
47C31×#387—21no—
48C31×#386—21no—
49C31×#386—21no—
50C31×#384C2211yescharacteristic, complemented
51C31×#380C2211yescharacteristic
52C31×#380C2211yescharacteristic
53C31×#379—21no—
54C4×C22⋊C4×C31C2211yescharacteristic
55C31×#340C2211yescharacteristic, complemented
56C31×#340C2211yescharacteristic, complemented
57C31×#340C2211yescharacteristic, complemented
58C31×#340C2211yescharacteristic, complemented
59C31×#336C2211yescharacteristic, complemented
60C31×#336C2211yescharacteristic, complemented
61C25×C31—21no—
62C22×Q8×C31C2311yescharacteristic
63C22×D4×C31—22no—
64C22×D4×C31—22no—
65C22×D4×C31—22no—
66C22×D4×C31—22no—
67C22×D4×C31—21no—
68C22×D4×C31—41no—
69C22×D4×C31—41no—
70C22×D4×C31C2311yescharacteristic
71C22×D4×C31C2311yescharacteristic
72C23×C4×C31—21no—
73C23×C4×C31—21no—
74C23×C4×C31C2311yescharacteristic
75C2×SD16×C31—22no—
76C2×SD16×C31—22no—
77C2×SD16×C31—22no—
78C2×SD16×C31—22no—
79C2×SD16×C31—41no—
80C2×SD16×C31D414yes—
81C22×C8×C31C2311yescharacteristic
82C22×C8×C31C2311yescharacteristic
83C22×C8×C31C2311yescharacteristic
84C22×C8×C31C2311yescharacteristic
85C31×C22⋊Q8—22no—
86C31×C22⋊Q8—41no—
87C4×Q8×C31—22no—
88C4×Q8×C31—41no—
89C4×D4×C31—22no—
90C4×D4×C31—22no—
91C4×D4×C31—41no—
92C4×D4×C31—41no—
93C2×C4⋊C4×C31—21no—
94C2×C4⋊C4×C31—21no—
95C2×C4⋊C4×C31—21no—
96C2×C4⋊C4×C31—21no—
97C2×C4⋊C4×C31—21no—
98C2×C4⋊C4×C31C2311yescharacteristic
99C2×C4⋊C4×C31C2311yescharacteristic
100C2×C4⋊C4×C31C2311yescharacteristic
101C2×C4⋊C4×C31C2311yescharacteristic
102C2×C4⋊C4×C31C2311yescharacteristic
103C2×C22⋊C4×C31—21no—
104C2×C22⋊C4×C31—21no—
105C2×C22⋊C4×C31—21no—
106C2×C22⋊C4×C31—21no—
107C2×C22⋊C4×C31—21no—
108C2×C22⋊C4×C31—21no—
109C2×C22⋊C4×C31—21no—
110C2×C22⋊C4×C31—21no—
111C2×C22⋊C4×C31—21no—
112C2×C22⋊C4×C31—44no—
113C2×C22⋊C4×C31D411yescharacteristic
114C2×C22⋊C4×C31D411yescharacteristic
115C2×C42×C31—21no—
116C2×C42×C31C2311yescharacteristic
117C2×C42×C31C2311yescharacteristic
118C31×#106—22no—
119C31×#106—41no—
120C31×C4⋊C8—41no—
121C31×#103—22no—
122C31×#103—41no—
123C31×#102—22no—
124C31×#102—22no—
125C31×#102—22no—
126C31×#102—22no—
127C31×#102—22no—
128C31×#102—41no—
129C31×C22⋊C8—22no—
130C31×C22⋊C8—41no—
131C4×C8×C31—22no—
132C31×#95—21no—
133C31×#95—21no—
134C31×#95—21no—
135C31×#95—21no—
136C31×#95—21no—
137C31×#95D411yescharacteristic
138C31×#95D411yescharacteristic
139C24×C31—21no—
140C24×C31—24no—
141C24×C31—21no—
142C24×C31—42no—
143C24×C31—42no—
144C24×C31—42no—
145C24×C31—42no—
146C24×C31—81no—
147C24×C31—81no—
148C24×C31C2×D411yescharacteristic
149C2×Q8×C31—21no—
150C2×Q8×C31—21no—
151C2×Q8×C31—21no—
152C2×Q8×C31—21no—
153C2×Q8×C31—21no—
154C2×Q8×C31C2×D412yes—
155C2×D4×C31—24no—
156C2×D4×C31—21no—
157C2×D4×C31—21no—
158C2×D4×C31—21no—
159C2×D4×C31—21no—
160C2×D4×C31—21no—
161C2×D4×C31—21no—
162C2×D4×C31—21no—
163C2×D4×C31—21no—
164C2×D4×C31—42no—
165C2×D4×C31—42no—
166C2×D4×C31—44no—
167C2×D4×C31—44no—
168C2×D4×C31—44no—
169C2×D4×C31—44no—
170C2×D4×C31C2×D412yes—
171C2×D4×C31#4112yes—
172C2×D4×C31#4112yes—
173C2×D4×C31#4112yes—
174C22×C4×C31—21no—
175C22×C4×C31—21no—
176C22×C4×C31—21no—
177C22×C4×C31—21no—
178C22×C4×C31—21no—
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—42no—
187C22×C4×C31—42no—
188C22×C4×C31—42no—
189C22×C4×C31—42no—
190C22×C4×C31—81no—
191C22×C4×C31—81no—
192C22×C4×C31C2×D411yescharacteristic
193C22×C4×C31C2×D411yescharacteristic
194C22×C4×C31C2×D411yescharacteristic
195C22×C4×C31C2×D411yescharacteristic
196C22×C4×C31C2×D411yescharacteristic
197C22×C4×C31C2411yescharacteristic
198SD16×C31—28no—
199SD16×C31—44no—
200C2×C8×C31—21no—
201C2×C8×C31—21no—
202C2×C8×C31—21no—
203C2×C8×C31—21no—
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×C31C2×D412yes—
212C4⋊C4×C31—21no—
213C4⋊C4×C31—21no—
214C4⋊C4×C31—21no—
215C4⋊C4×C31—21no—
216C4⋊C4×C31—21no—
217C4⋊C4×C31—21no—
218C4⋊C4×C31—21no—
219C4⋊C4×C31—21no—
220C4⋊C4×C31—21no—
221C4⋊C4×C31—21no—
222C4⋊C4×C31—42no—
223C4⋊C4×C31—42no—
224C4⋊C4×C31—42no—
225C4⋊C4×C31—81no—
226C4⋊C4×C31—81no—
227C22⋊C4×C31—41no—
228C22⋊C4×C31—42no—
229C22⋊C4×C31—42no—
230C22⋊C4×C31—42no—
231C22⋊C4×C31—42no—
232C22⋊C4×C31—42no—
233C22⋊C4×C31—42no—
234C22⋊C4×C31—81no—
235C22⋊C4×C31—81no—
236C22⋊C4×C31—81no—
237C22⋊C4×C31SD1614yescomplemented
238C42×C31—21no—
239C42×C31—21no—
240C42×C31—21no—
241C42×C31—21no—
242C42×C31—42no—
243#24901C3111yesmaximal, characteristic, direct product factor, Sylow
244C23×C31—21no—
245C23×C31—22no—
246C23×C31—21no—
247C23×C31—22no—
248C23×C31—22no—
249C23×C31—21no—
250C23×C31—21no—
251C23×C31—21no—
252C23×C31—21no—
253C23×C31—22no—
254C23×C31—48no—
255C23×C31—48no—
256C23×C31—41no—
257C23×C31—41no—
258C23×C31—41no—
259C23×C31—41no—
260C23×C31—41no—
261C23×C31—41no—
262C23×C31—41no—
263C23×C31—41no—
264C23×C31—41no—
265C23×C31—41no—
266C23×C31—84no—
267C23×C31—84no—
268C23×C31—84no—
269C23×C31—84no—
270C23×C31—84no—
271C23×C31C2×SD1612yes—
272C23×C31C22×D411yescharacteristic
273Q8×C31—22no—
274Q8×C31—22no—
275Q8×C31—41no—
276Q8×C31—41no—
277D4×C31—22no—
278D4×C31—22no—
279D4×C31—22no—
280D4×C31—22no—
281D4×C31—22no—
282D4×C31—48no—
283D4×C31—41no—
284D4×C31—41no—
285D4×C31#12314yes—
286C2×C4×C31—21no—
287C2×C4×C31—21no—
288C2×C4×C31—21no—
289C2×C4×C31—21no—
290C2×C4×C31—21no—
291C2×C4×C31—21no—
292C2×C4×C31—22no—
293C2×C4×C31—21no—
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—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—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—84no—
322C2×C4×C31—84no—
323C2×C4×C31C2×SD1612yes—
324C2×C4×C31C2×SD1612yes—
325C2×C4×C31C22×D411yescharacteristic
326C2×C4×C31C2×#4111yescharacteristic
327C2×C4×C31C2×#4111yescharacteristic
328C2×C4×C31C2×#4111yescharacteristic
329C2×C4×C31H(5,𝔽2)11yescharacteristic
330C2×C4×C31H(5,𝔽2)11yescharacteristic
331C8×C31—22no—
332C8×C31—41no—
333C8×C31—41no—
334C8×C31—41no—
335C2×#450C2×C3111yescharacteristic
336C2×C4×SD16C2×C3111yescharacteristic, complemented
337#2423C2×C3111yescharacteristic, complemented
338D4×C22⋊C4C2×C3111yescharacteristic
339#2094C2×C3111yescharacteristic, complemented
340#2077C2×C3111yescharacteristic, complemented
341#2055C2×C3111yescharacteristic, complemented
342#2035C2×C3111yescharacteristic, complemented
343#1934C2×C3111yescharacteristic, complemented
344#1923C2×C3111yescharacteristic, complemented
345#1880C2×C3111yescharacteristic, complemented
346#1877C2×C3111yescharacteristic, complemented
347#1864C2×C3111yescharacteristic, complemented
348#1802C2×C3111yescharacteristic, complemented
349#1786C2×C3111yescharacteristic
350C22×C31—22no—
351C22×C31—24no—
352C22×C31—22no—
353C22×C31—22no—
354C22×C31—42no—
355C22×C31—41no—
356C22×C31—42no—
357C22×C31—41no—
358C22×C31—41no—
359C22×C31—42no—
360C22×C31—42no—
361C22×C31—42no—
362C22×C31—41no—
363C22×C31—42no—
364C22×C31—42no—
365C22×C31—42no—
366C22×C31—42no—
367C22×C31—816no—
368C22×C31—81no—
369C22×C31—81no—
370C22×C31—81no—
371C22×C31—81no—
372C22×C31#52511yescharacteristic
373C22×C31D4211yescharacteristic
374C22×C31#54611yescharacteristic
375C22×C31C22×SD1611yescharacteristic
376C22×C31#57511yescharacteristic
377C22×C31#57611yescharacteristic
378C22×C31#57711yescharacteristic
379C4×C31—22no—
380C4×C31—22no—
381C4×C31—41no—
382C4×C31—42no—
383C4×C31—41no—
384C4×C31—41no—
385C4×C31—81no—
386C4×C31—81no—
387C4×C31—81no—
388C4×C31—81no—
389C4×C31—81no—
390C4×C31C2×#12311yescharacteristic
391C4×C31#53811yescharacteristic
392C4×C31#54611yescharacteristic
393C4×C31#55111yescharacteristic
394C23×D4C22×C3111yescharacteristic
395C22×SD16C22×C3111yescharacteristic
396C22×SD16C22×C3111yescharacteristic
397C2×C22⋊Q8C22×C3111yescharacteristic
398C2×C4×Q8C22×C3111yescharacteristic, complemented
399C2×C4×D4C22×C3111yescharacteristic
400C2×C4×D4C22×C3111yescharacteristic
401C22×C22⋊C4—21no—
402#450—24no—
403C4×SD16—24no—
404C2×#106C22×C3111yescharacteristic, complemented
405C2×#106C22×C3111yescharacteristic, complemented
406C2×C4⋊C8C22×C3111yescharacteristic, complemented
407C2×#103C22×C3111yescharacteristic, complemented
408C2×#103C22×C3111yescharacteristic, complemented
409C2×#102C22×C3111yescharacteristic
410C2×#102C22×C3111yescharacteristic
411C2×#102C22×C3111yescharacteristic
412C2×#102C22×C3111yescharacteristic
413C2×#102C22×C3111yescharacteristic
414C2×#102C22×C3111yescharacteristic
415C2×C22⋊C8C22×C3111yescharacteristic
416C2×C22⋊C8C22×C3111yescharacteristic
417C2×C4×C8C22×C3111yescharacteristic, complemented
418#399—21no—
419#398—21no—
420#391C22×C3111yescharacteristic, complemented
421#390C22×C3111yescharacteristic
422#390C22×C3111yescharacteristic
423#389C22×C3111yescharacteristic, complemented
424#388—21no—
425#387—21no—
426#386—21no—
427#386—21no—
428#384C22×C3111yescharacteristic, complemented
429#380C22×C3111yescharacteristic
430#380C22×C3111yescharacteristic
431#379—21no—
432C4×C22⋊C4C22×C3111yescharacteristic
433#340C22×C3111yescharacteristic, complemented
434#340C22×C3111yescharacteristic, complemented
435#340C22×C3111yescharacteristic, complemented
436#340C22×C3111yescharacteristic, complemented
437#336C22×C3111yescharacteristic, complemented
438#336C22×C3111yescharacteristic, complemented
439C2×C31—42no—
440C2×C31—44no—
441C2×C31—82no—
442C2×C31#241811yescharacteristic
443C2×C31#310111yescharacteristic
444C2×C31#311811yescharacteristic
445C2×C31#326811yescharacteristic
446C2×C31D4×SD1611yescharacteristic
447C2×C31#329511yescharacteristic
448C2×C31#332311yescharacteristic
449C25—21no—
450C22×Q8C23×C3111yescharacteristic
451C22×D4—22no—
452C22×D4—22no—
453C22×D4—22no—
454C22×D4—22no—
455C22×D4—21no—
456C22×D4—41no—
457C22×D4—41no—
458C22×D4C23×C3111yescharacteristic
459C22×D4C23×C3111yescharacteristic
460C23×C4—21no—
461C23×C4—21no—
462C23×C4C23×C3111yescharacteristic
463C2×SD16—22no—
464C2×SD16—22no—
465C2×SD16—22no—
466C2×SD16—22no—
467C2×SD16—41no—
468C2×SD16D4×C3114yes—
469C22×C8C23×C3111yescharacteristic
470C22×C8C23×C3111yescharacteristic
471C22×C8C23×C3111yescharacteristic
472C22×C8C23×C3111yescharacteristic
473C22⋊Q8—22no—
474C22⋊Q8—41no—
475C4×Q8—22no—
476C4×Q8—41no—
477C4×D4—22no—
478C4×D4—22no—
479C4×D4—41no—
480C4×D4—41no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4C23×C3111yescharacteristic
487C2×C4⋊C4C23×C3111yescharacteristic
488C2×C4⋊C4C23×C3111yescharacteristic
489C2×C4⋊C4C23×C3111yescharacteristic
490C2×C4⋊C4C23×C3111yescharacteristic
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—44no—
501C2×C22⋊C4D4×C3111yescharacteristic
502C2×C22⋊C4D4×C3111yescharacteristic
503C2×C42—21no—
504C2×C42C23×C3111yescharacteristic
505C2×C42C23×C3111yescharacteristic
506#106—22no—
507#106—41no—
508C4⋊C8—41no—
509#103—22no—
510#103—41no—
511#102—22no—
512#102—22no—
513#102—22no—
514#102—22no—
515#102—22no—
516#102—41no—
517C22⋊C8—22no—
518C22⋊C8—41no—
519C4×C8—22no—
520#95—21no—
521#95—21no—
522#95—21no—
523#95—21no—
524#95—21no—
525#95D4×C3111yescharacteristic
526#95D4×C3111yescharacteristic
527C31#2490111yescharacteristic, direct product factor, Sylow
528C24—21no—
529C24—24no—
530C24—21no—
531C24—42no—
532C24—42no—
533C24—42no—
534C24—42no—
535C24—81no—
536C24—81no—
537C24C2×D4×C3111yescharacteristic
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8C2×D4×C3112yes—
544C2×D4—24no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—44no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4C2×D4×C3112yes—
560C2×D4#41×C3112yes—
561C2×D4#41×C3112yes—
562C2×D4#41×C3112yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—81no—
580C22×C4—81no—
581C22×C4C2×D4×C3111yescharacteristic
582C22×C4C2×D4×C3111yescharacteristic
583C22×C4C2×D4×C3111yescharacteristic
584C22×C4C2×D4×C3111yescharacteristic
585C22×C4C2×D4×C3111yescharacteristic
586C22×C4C24×C3111yescharacteristic
587SD16—28no—
588SD16—44no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8C2×D4×C3112yes—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—42no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊C4—81no—
615C4⋊C4—81no—
616C22⋊C4—41no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—81no—
624C22⋊C4—81no—
625C22⋊C4—81no—
626C22⋊C4SD16×C3114yescomplemented
627C42—21no—
628C42—21no—
629C42—21no—
630C42—21no—
631C42—42no—
632C23—21no—
633C23—22no—
634C23—21no—
635C23—22no—
636C23—22no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—22no—
642C23—48no—
643C23—48no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—84no—
655C23—84no—
656C23—84no—
657C23—84no—
658C23—84no—
659C23C2×SD16×C3112yes—
660C23C22×D4×C3111yescharacteristic
661Q8—22no—
662Q8—22no—
663Q8—41no—
664Q8—41no—
665D4—22no—
666D4—22no—
667D4—22no—
668D4—22no—
669D4—22no—
670D4—48no—
671D4—41no—
672D4—41no—
673D4C31×#12314yes—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—84no—
710C2×C4—84no—
711C2×C4C2×SD16×C3112yes—
712C2×C4C2×SD16×C3112yes—
713C2×C4C22×D4×C3111yescharacteristic
714C2×C4C2×#41×C3111yescharacteristic
715C2×C4C2×#41×C3111yescharacteristic
716C2×C4C2×#41×C3111yescharacteristic
717C2×C4C31×H(5,𝔽2)11yescharacteristic
718C2×C4C31×H(5,𝔽2)11yescharacteristic
719C8—22no—
720C8—41no—
721C8—41no—
722C8—41no—
723C22—22no—
724C22—24no—
725C22—22no—
726C22—22no—
727C22—42no—
728C22—41no—
729C22—42no—
730C22—41no—
731C22—41no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—41no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—816no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22C31×#52511yescharacteristic
746C22D42×C3111yescharacteristic
747C22C31×#54611yescharacteristic
748C22C22×SD16×C3111yescharacteristic
749C22C31×#57511yescharacteristic
750C22C31×#57611yescharacteristic
751C22C31×#57711yescharacteristic
752C4—22no—
753C4—22no—
754C4—41no—
755C4—42no—
756C4—41no—
757C4—41no—
758C4—81no—
759C4—81no—
760C4—81no—
761C4—81no—
762C4—81no—
763C4C2×C31×#12311yescharacteristic
764C4C31×#53811yescharacteristic
765C4C31×#54611yescharacteristic
766C4C31×#55111yescharacteristic
767C2—42no—
768C2—44no—
769C2—82no—
770C2C31×#241811yescharacteristic
771C2C31×#310111yescharacteristic
772C2C31×#311811yescharacteristic
773C2C31×#326811yescharacteristic
774C2D4×SD16×C3111yescharacteristic
775C2C31×#329511yescharacteristic
776C2C31×#332311yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC23×D4×C31C22
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
2. C2×C4×SD16×C31C2semidirect
3. C31×#2423C2semidirect
5. C31×#2094C2semidirect
6. C31×#2077C2semidirect
7. C31×#2055C2semidirect
8. C31×#2035C2semidirect
9. C31×#1934C2semidirect
10. C31×#1923C2semidirect
11. C31×#1880C2semidirect
12. C31×#1877C2semidirect
13. C31×#1864C2semidirect
14. C31×#1802C2semidirect
20. C2×C4×Q8×C31C22semidirect
26. C2×C31×#106C22semidirect
27. C2×C31×#106C22semidirect
28. C2×C31×C4⋊C8C22semidirect
29. C2×C31×#103C22semidirect
30. C2×C31×#103C22semidirect
39. C2×C4×C8×C31C22semidirect
42. C31×#391C22semidirect
45. C31×#389C22semidirect
50. C31×#384C22semidirect
55. C31×#340C22semidirect
56. C31×#340C22semidirect
57. C31×#340C22semidirect
58. C31×#340C22semidirect
59. C31×#336C22semidirect
60. C31×#336C22semidirect
237. C22⋊C4×C31SD16semidirect
243. #24901C31direct (N × H)
336. C2×C4×SD16C2×C31semidirect
337. #2423C2×C31semidirect
339. #2094C2×C31semidirect
340. #2077C2×C31semidirect
341. #2055C2×C31semidirect
342. #2035C2×C31semidirect
343. #1934C2×C31semidirect
344. #1923C2×C31semidirect
345. #1880C2×C31semidirect
346. #1877C2×C31semidirect
347. #1864C2×C31semidirect
348. #1802C2×C31semidirect
398. C2×C4×Q8C22×C31semidirect
404. C2×#106C22×C31semidirect
405. C2×#106C22×C31semidirect
406. C2×C4⋊C8C22×C31semidirect
407. C2×#103C22×C31semidirect
408. C2×#103C22×C31semidirect
417. C2×C4×C8C22×C31semidirect
420. #391C22×C31semidirect
423. #389C22×C31semidirect
428. #384C22×C31semidirect
433. #340C22×C31semidirect
434. #340C22×C31semidirect
435. #340C22×C31semidirect
436. #340C22×C31semidirect
437. #336C22×C31semidirect
438. #336C22×C31semidirect
527. C31#24901direct (N × H)
626. C22⋊C4SD16×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
C31×#24232
D4×C22⋊C4×C312
C31×#20942
C31×#20772
C31×#20552
C31×#20352
C31×#19342
C31×#19232
C31×#18802
C31×#18772
C31×#18642
C31×#18022
C31×#17862
#2490131