Finite Group Databasebeta

← C31×#24735 #21481494

Subgroups — C31×#24735 #21481494

Order 7936.

1064 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#463C211yesmaximal, characteristic, complemented
2C2×C31×#463C211yesmaximal, characteristic, complemented
3C2×C31×#459C211yesmaximal, characteristic
4C2×C4×D8×C31C211yesmaximal, characteristic, complemented
5C31×#2544C211yesmaximal, characteristic, complemented
6C31×#2349C211yesmaximal, characteristic, complemented
7C31×#2068C211yesmaximal, characteristic, complemented
8C31×#2067C211yesmaximal, characteristic, complemented
9C31×#2042C211yesmaximal, characteristic, complemented
10C31×#2041C211yesmaximal, characteristic, complemented
11C31×#1958C211yesmaximal, characteristic, complemented
12C31×#1939C211yesmaximal, characteristic, complemented
13C31×#1879C211yesmaximal, characteristic, complemented
14C31×#1877C211yesmaximal, characteristic, complemented
15C31×#1804C211yesmaximal, characteristic, complemented
16C22×SD16×C31C2211yescharacteristic
17C22×D8×C31C2211yescharacteristic
18C22×D8×C31C2211yescharacteristic
19C2×C31×#127C2211yescharacteristic
20C2×C31×#124C2211yescharacteristic
21C2×C31×#124C2211yescharacteristic
22C2×C4×D4×C31C2211yescharacteristic
23C2×C4×D4×C31C2211yescharacteristic
24C2×C4×D4×C31C2211yescharacteristic
25C2×C4×D4×C31C2211yescharacteristic
26C31×#463—24no—
27C31×#463—24no—
28C31×#459—24no—
29C4×D8×C31—24no—
30C2×C31×#107C2211yescharacteristic
31C2×C31×C4⋊C8C2211yescharacteristic
32C2×C31×C4⋊C8C2211yescharacteristic
33C2×C31×C4⋊C8C2211yescharacteristic
34C2×C31×#103C2211yescharacteristic
35C2×C31×#103C2211yescharacteristic
36C2×C31×#103C2211yescharacteristic
37C2×C31×#102C2211yescharacteristic
38C2×C31×#102C2211yescharacteristic
39C2×C31×#102C2211yescharacteristic
40C2×C31×#102C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C4×C8×C31C2211yescharacteristic
45C31×#394—21no—
46C31×#394—21no—
47C31×#391C2211yescharacteristic
48C31×#390C2211yescharacteristic
49C31×#389C2211yescharacteristic
50C31×#389C2211yescharacteristic
51C31×#386—21no—
52C31×#386—21no—
53C31×#385—21no—
54C31×#385—21no—
55C31×#382C2211yescharacteristic
56C31×#380—21no—
57C4×C4⋊C4×C31C2211yescharacteristic
58C2×C31×#95—21no—
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C31×#336C2211yescharacteristic
63C22×Q8×C31C2311yescharacteristic
64C22×D4×C31—21no—
65C22×D4×C31—21no—
66C22×D4×C31C2311yescharacteristic
67C22×D4×C31C2311yescharacteristic
68C22×D4×C31C2311yescharacteristic
69C23×C4×C31—21no—
70C23×C4×C31—21no—
71C23×C4×C31—21no—
72C23×C4×C31—21no—
73C2×SD16×C31—22no—
74C2×SD16×C31—22no—
75C2×SD16×C31—22no—
76C2×D8×C31—22no—
77C2×D8×C31—22no—
78C2×D8×C31—22no—
79C2×D8×C31—22no—
80C2×D8×C31—22no—
81C2×D8×C31D414yes—
82C22×C8×C31C2311yescharacteristic
83C22×C8×C31C2311yescharacteristic
84C22×C8×C31C2311yescharacteristic
85C22×C8×C31C2311yescharacteristic
86C31×#127—22no—
87C31×#127—41no—
88C31×#124—22no—
89C31×#124—22no—
90C31×#124—22no—
91C31×#124—41no—
92C4×D4×C31—22no—
93C4×D4×C31—22no—
94C4×D4×C31—22no—
95C4×D4×C31—22no—
96C4×D4×C31—22no—
97C4×D4×C31—41no—
98C4×D4×C31—41no—
99C4×D4×C31D414yescomplemented
100C2×C4⋊C4×C31—21no—
101C2×C4⋊C4×C31—21no—
102C2×C4⋊C4×C31D411yescharacteristic
103C2×C4⋊C4×C31D411yescharacteristic
104C2×C4⋊C4×C31C2311yescharacteristic
105C2×C4⋊C4×C31C2311yescharacteristic
106C2×C4⋊C4×C31C2311yescharacteristic
107C2×C4⋊C4×C31C2311yescharacteristic
108C2×C22⋊C4×C31—21no—
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—21no—
118C2×C42×C31C2311yescharacteristic
119C2×C42×C31C2311yescharacteristic
120C2×C42×C31C2311yescharacteristic
121C31×#107—22no—
122C31×C4⋊C8—22no—
123C31×C4⋊C8—22no—
124C31×C4⋊C8—22no—
125C31×#103—22no—
126C31×#103—22no—
127C31×#103—41no—
128C31×#102—22no—
129C31×#102—22no—
130C31×#102—22no—
131C31×#102—22no—
132C31×#102—22no—
133C31×#102—22no—
134C31×#102—41no—
135C4×C8×C31—22no—
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×C31—21no—
146C24×C31—21no—
147C2×Q8×C31—21no—
148C2×Q8×C31—21no—
149C2×Q8×C31—21no—
150C2×Q8×C31—21no—
151C2×Q8×C31—21no—
152C2×Q8×C31—21no—
153C2×D4×C31—21no—
154C2×D4×C31—21no—
155C2×D4×C31—21no—
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—21no—
165C2×D4×C31—21no—
166C2×D4×C31—21no—
167C2×D4×C31—42no—
168C2×D4×C31—42no—
169C2×D4×C31—42no—
170C2×D4×C31—42no—
171C2×D4×C31—81no—
172C2×D4×C31—81no—
173C2×D4×C31C2×D412yes—
174C2×D4×C31C2×D412yes—
175C2×D4×C31C2×D412yes—
176C2×D4×C31#4112yes—
177C22×C4×C31—21no—
178C22×C4×C31—24no—
179C22×C4×C31—21no—
180C22×C4×C31—21no—
181C22×C4×C31—21no—
182C22×C4×C31—21no—
183C22×C4×C31—42no—
184C22×C4×C31—42no—
185C22×C4×C31—42no—
186C22×C4×C31—42no—
187C22×C4×C31—42no—
188C22×C4×C31—81no—
189C22×C4×C31—81no—
190C22×C4×C31—81no—
191C22×C4×C31—81no—
192C22×C4×C31—81no—
193C22×C4×C31—81no—
194C22×C4×C31C2×D411yescharacteristic
195C22×C4×C31C2×D411yescharacteristic
196C22×C4×C31C2×D411yescharacteristic
197C22×C4×C31C2×D411yescharacteristic
198C22×C4×C31C2×D411yescharacteristic
199C22×C4×C31C2×D411yescharacteristic
200C22×C4×C31C2411yescharacteristic
201SD16×C31—44no—
202D8×C31—28no—
203D8×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—21no—
214C2×C8×C31—21no—
215C2×C8×C31C2×D412yes—
216C4⋊C4×C31—22no—
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—41no—
225C4⋊C4×C31—81no—
226C4⋊C4×C31—81no—
227C4⋊C4×C31C2×D412yes—
228C22⋊C4×C31—24no—
229C22⋊C4×C31—42no—
230C22⋊C4×C31—42no—
231C22⋊C4×C31—42no—
232C22⋊C4×C31—42no—
233C22⋊C4×C31—42no—
234C22⋊C4×C31—42no—
235C22⋊C4×C31—42no—
236C22⋊C4×C31—81no—
237C22⋊C4×C31—81no—
238C42×C31—21no—
239C42×C31—21no—
240C42×C31—21no—
241C42×C31—21no—
242C42×C31C2×D412yes—
243C42×C31#4112yes—
244#24735C3111yesmaximal, characteristic, direct product factor, Sylow
245C23×C31—22no—
246C23×C31—22no—
247C23×C31—22no—
248C23×C31—22no—
249C23×C31—41no—
250C23×C31—41no—
251C23×C31—41no—
252C23×C31—41no—
253C23×C31—41no—
254C23×C31—41no—
255C23×C31—41no—
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×C31C22×D411yescharacteristic
267Q8×C31—41no—
268Q8×C31—41no—
269Q8×C31—41no—
270Q8×C31—41no—
271D4×C31—22no—
272D4×C31—22no—
273D4×C31—22no—
274D4×C31—22no—
275D4×C31—22no—
276D4×C31—41no—
277D4×C31—41no—
278D4×C31—41no—
279D4×C31—41no—
280D4×C31—41no—
281D4×C31—41no—
282D4×C31—84no—
283D4×C31—84no—
284D4×C31#12114yes—
285C2×C4×C31—21no—
286C2×C4×C31—21no—
287C2×C4×C31—21no—
288C2×C4×C31—21no—
289C2×C4×C31—21no—
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—21no—
298C2×C4×C31—21no—
299C2×C4×C31—21no—
300C2×C4×C31—21no—
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—84no—
316C2×C4×C31—84no—
317C2×C4×C31—84no—
318C2×C4×C31—84no—
319C2×C4×C31#12112yes—
320C2×C4×C31#12112yes—
321C2×C4×C31#13512yes—
322C2×C4×C31C22×D411yescharacteristic
323C2×C4×C31C22×D411yescharacteristic
324C2×C4×C31C2×#4111yescharacteristic
325C2×C4×C31C2×#4111yescharacteristic
326C2×C4×C31H(5,𝔽2)11yescharacteristic
327C2×C4×C312−1+411yescharacteristic
328C8×C31—22no—
329C8×C31—41no—
330C8×C31—41no—
331C8×C31—41no—
332C2×#463C2×C3111yescharacteristic, complemented
333C2×#463C2×C3111yescharacteristic, complemented
334C2×#459C2×C3111yescharacteristic
335C2×C4×D8C2×C3111yescharacteristic, complemented
336#2544C2×C3111yescharacteristic, complemented
337#2349C2×C3111yescharacteristic, complemented
338#2068C2×C3111yescharacteristic, complemented
339#2067C2×C3111yescharacteristic, complemented
340#2042C2×C3111yescharacteristic, complemented
341#2041C2×C3111yescharacteristic, complemented
342#1958C2×C3111yescharacteristic, complemented
343#1939C2×C3111yescharacteristic, complemented
344#1879C2×C3111yescharacteristic, complemented
345#1877C2×C3111yescharacteristic, complemented
346#1804C2×C3111yescharacteristic, complemented
347C22×C31—24no—
348C22×C31—42no—
349C22×C31—42no—
350C22×C31—42no—
351C22×C31—42no—
352C22×C31—42no—
353C22×C31—42no—
354C22×C31—42no—
355C22×C31—42no—
356C22×C31—42no—
357C22×C31—81no—
358C22×C31—81no—
359C22×C31—81no—
360C22×C31—81no—
361C22×C31—81no—
362C22×C31—81no—
363C22×C31—81no—
364C22×C31—81no—
365C22×C31—81no—
366C22×C31—81no—
367C22×C31—81no—
368C22×C31C2×#12111yescharacteristic
369C22×C31D4211yescharacteristic
370C22×C31#54811yescharacteristic
371C22×C31C2×#13511yescharacteristic
372C22×C31#57511yescharacteristic
373C22×C31#57611yescharacteristic
374C22×C31#57611yescharacteristic
375C4×C31—22no—
376C4×C31—22no—
377C4×C31—22no—
378C4×C31—41no—
379C4×C31—41no—
380C4×C31—41no—
381C4×C31—42no—
382C4×C31—81no—
383C4×C31—81no—
384C4×C31—81no—
385C4×C31—81no—
386C4×C31C2×#12111yescharacteristic
387C4×C31#53711yescharacteristic
388C4×C31#54711yescharacteristic
389C4×C31#55311yescharacteristic
390C22×SD16C22×C3111yescharacteristic
391C22×D8C22×C3111yescharacteristic
392C22×D8C22×C3111yescharacteristic
393C2×#127C22×C3111yescharacteristic
394C2×#124C22×C3111yescharacteristic
395C2×#124C22×C3111yescharacteristic
396C2×C4×D4C22×C3111yescharacteristic
397C2×C4×D4C22×C3111yescharacteristic
398C2×C4×D4C22×C3111yescharacteristic
399C2×C4×D4C22×C3111yescharacteristic
400#463—24no—
401#463—24no—
402#459—24no—
403C4×D8—24no—
404C2×#107C22×C3111yescharacteristic
405C2×C4⋊C8C22×C3111yescharacteristic
406C2×C4⋊C8C22×C3111yescharacteristic
407C2×C4⋊C8C22×C3111yescharacteristic
408C2×#103C22×C3111yescharacteristic
409C2×#103C22×C3111yescharacteristic
410C2×#103C22×C3111yescharacteristic
411C2×#102C22×C3111yescharacteristic
412C2×#102C22×C3111yescharacteristic
413C2×#102C22×C3111yescharacteristic
414C2×#102C22×C3111yescharacteristic
415C2×#102C22×C3111yescharacteristic
416C2×#102C22×C3111yescharacteristic
417C2×#102C22×C3111yescharacteristic
418C2×C4×C8C22×C3111yescharacteristic
419#394—21no—
420#394—21no—
421#391C22×C3111yescharacteristic
422#390C22×C3111yescharacteristic
423#389C22×C3111yescharacteristic
424#389C22×C3111yescharacteristic
425#386—21no—
426#386—21no—
427#385—21no—
428#385—21no—
429#382C22×C3111yescharacteristic
430#380—21no—
431C4×C4⋊C4C22×C3111yescharacteristic
432C2×#95—21no—
433#340C22×C3111yescharacteristic
434#340C22×C3111yescharacteristic
435#336C22×C3111yescharacteristic
436#336C22×C3111yescharacteristic
437C2×C31—44no—
438C2×C31—82no—
439C2×C31—161no—
440C2×C31#241611yescharacteristic
441C2×C31#303511yescharacteristic
442C2×C31#304111yescharacteristic
443C2×C31#327311yescharacteristic
444C2×C31#328011yescharacteristic
445C2×C31#336111yescharacteristic
446C2×C31#337011yescharacteristic
447C22×Q8C23×C3111yescharacteristic
448C22×D4—21no—
449C22×D4—21no—
450C22×D4C23×C3111yescharacteristic
451C22×D4C23×C3111yescharacteristic
452C22×D4C23×C3111yescharacteristic
453C23×C4—21no—
454C23×C4—21no—
455C23×C4—21no—
456C23×C4—21no—
457C2×SD16—22no—
458C2×SD16—22no—
459C2×SD16—22no—
460C2×D8—22no—
461C2×D8—22no—
462C2×D8—22no—
463C2×D8—22no—
464C2×D8—22no—
465C2×D8D4×C3114yes—
466C22×C8C23×C3111yescharacteristic
467C22×C8C23×C3111yescharacteristic
468C22×C8C23×C3111yescharacteristic
469C22×C8C23×C3111yescharacteristic
470#127—22no—
471#127—41no—
472#124—22no—
473#124—22no—
474#124—22no—
475#124—41no—
476C4×D4—22no—
477C4×D4—22no—
478C4×D4—22no—
479C4×D4—22no—
480C4×D4—22no—
481C4×D4—41no—
482C4×D4—41no—
483C4×D4D4×C3114yescomplemented
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4D4×C3111yescharacteristic
487C2×C4⋊C4D4×C3111yescharacteristic
488C2×C4⋊C4C23×C3111yescharacteristic
489C2×C4⋊C4C23×C3111yescharacteristic
490C2×C4⋊C4C23×C3111yescharacteristic
491C2×C4⋊C4C23×C3111yescharacteristic
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—21no—
501C2×C22⋊C4—21no—
502C2×C42C23×C3111yescharacteristic
503C2×C42C23×C3111yescharacteristic
504C2×C42C23×C3111yescharacteristic
505#107—22no—
506C4⋊C8—22no—
507C4⋊C8—22no—
508C4⋊C8—22no—
509#103—22no—
510#103—22no—
511#103—41no—
512#102—22no—
513#102—22no—
514#102—22no—
515#102—22no—
516#102—22no—
517#102—22no—
518#102—41no—
519C4×C8—22no—
520#95—21no—
521#95—21no—
522#95—21no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95D4×C3111yescharacteristic
527#95D4×C3111yescharacteristic
528C31#2473511yescharacteristic, direct product factor, Sylow
529C24—21no—
530C24—21no—
531C24—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—42no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—81no—
557C2×D4—81no—
558C2×D4C2×D4×C3112yes—
559C2×D4C2×D4×C3112yes—
560C2×D4C2×D4×C3112yes—
561C2×D4#41×C3112yes—
562C22×C4—21no—
563C22×C4—24no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—81no—
574C22×C4—81no—
575C22×C4—81no—
576C22×C4—81no—
577C22×C4—81no—
578C22×C4—81no—
579C22×C4C2×D4×C3111yescharacteristic
580C22×C4C2×D4×C3111yescharacteristic
581C22×C4C2×D4×C3111yescharacteristic
582C22×C4C2×D4×C3111yescharacteristic
583C22×C4C2×D4×C3111yescharacteristic
584C22×C4C2×D4×C3111yescharacteristic
585C22×C4C24×C3111yescharacteristic
586SD16—44no—
587D8—28no—
588D8—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—22no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—41no—
610C4⋊C4—81no—
611C4⋊C4—81no—
612C4⋊C4C2×D4×C3112yes—
613C22⋊C4—24no—
614C22⋊C4—42no—
615C22⋊C4—42no—
616C22⋊C4—42no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—81no—
622C22⋊C4—81no—
623C42—21no—
624C42—21no—
625C42—21no—
626C42—21no—
627C42C2×D4×C3112yes—
628C42#41×C3112yes—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23C22×D4×C3111yescharacteristic
651Q8—41no—
652Q8—41no—
653Q8—41no—
654Q8—41no—
655D4—22no—
656D4—22no—
657D4—22no—
658D4—22no—
659D4—22no—
660D4—41no—
661D4—41no—
662D4—41no—
663D4—41no—
664D4—41no—
665D4—41no—
666D4—84no—
667D4—84no—
668D4C31×#12114yes—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
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—84no—
700C2×C4—84no—
701C2×C4—84no—
702C2×C4—84no—
703C2×C4C31×#12112yes—
704C2×C4C31×#12112yes—
705C2×C4C31×#13512yes—
706C2×C4C22×D4×C3111yescharacteristic
707C2×C4C22×D4×C3111yescharacteristic
708C2×C4C2×#41×C3111yescharacteristic
709C2×C4C2×#41×C3111yescharacteristic
710C2×C4C31×H(5,𝔽2)11yescharacteristic
711C2×C4C31×2−1+411yescharacteristic
712C8—22no—
713C8—41no—
714C8—41no—
715C8—41no—
716C22—24no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22—81no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22C2×C31×#12111yescharacteristic
738C22D42×C3111yescharacteristic
739C22C31×#54811yescharacteristic
740C22C2×C31×#13511yescharacteristic
741C22C31×#57511yescharacteristic
742C22C31×#57611yescharacteristic
743C22C31×#57611yescharacteristic
744C4—22no—
745C4—22no—
746C4—22no—
747C4—41no—
748C4—41no—
749C4—41no—
750C4—42no—
751C4—81no—
752C4—81no—
753C4—81no—
754C4—81no—
755C4C2×C31×#12111yescharacteristic
756C4C31×#53711yescharacteristic
757C4C31×#54711yescharacteristic
758C4C31×#55311yescharacteristic
759C2—44no—
760C2—82no—
761C2—161no—
762C2C31×#241611yescharacteristic
763C2C31×#303511yescharacteristic
764C2C31×#304111yescharacteristic
765C2C31×#327311yescharacteristic
766C2C31×#328011yescharacteristic
767C2C31×#336111yescharacteristic
768C2C31×#337011yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#459C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C4×C4⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#463C2semidirect
2. C2×C31×#463C2semidirect
4. C2×C4×D8×C31C2semidirect
5. C31×#2544C2semidirect
6. C31×#2349C2semidirect
7. C31×#2068C2semidirect
8. C31×#2067C2semidirect
9. C31×#2042C2semidirect
10. C31×#2041C2semidirect
11. C31×#1958C2semidirect
12. C31×#1939C2semidirect
13. C31×#1879C2semidirect
14. C31×#1877C2semidirect
15. C31×#1804C2semidirect
99. C4×D4×C31D4semidirect
244. #24735C31direct (N × H)
332. C2×#463C2×C31semidirect
333. C2×#463C2×C31semidirect
335. C2×C4×D8C2×C31semidirect
336. #2544C2×C31semidirect
337. #2349C2×C31semidirect
338. #2068C2×C31semidirect
339. #2067C2×C31semidirect
340. #2042C2×C31semidirect
341. #2041C2×C31semidirect
342. #1958C2×C31semidirect
343. #1939C2×C31semidirect
344. #1879C2×C31semidirect
345. #1877C2×C31semidirect
346. #1804C2×C31semidirect
483. C4×D4D4×C31semidirect
528. C31#24735direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4632
C2×C31×#4592
C2×C4×D8×C312
C31×#25442
C31×#23492
C31×#20682
C31×#20672
C31×#20422
C31×#20412
C31×#19582
C31×#19392
C31×#18792
C31×#18772
C31×#18042
#2473531