Finite Group Databasebeta

← C31×#24194 #21480953

Subgroups — C31×#24194 #21480953

Order 7936.

1138 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#559C211yesmaximal, characteristic
2C2×C31×#464C211yesmaximal, characteristic, complemented
3C2×C4×SD16×C31C211yesmaximal, characteristic, complemented
4C31×#2581C211yesmaximal, characteristic, complemented
5C31×#2042C211yesmaximal, characteristic, complemented
6C31×#2041C211yesmaximal, characteristic
7C31×#2015C211yesmaximal, characteristic, complemented
8C31×#2014C211yesmaximal, characteristic
9C31×#1984C211yesmaximal, characteristic, complemented
10C31×#1958C211yesmaximal, characteristic, complemented
11C31×#1878C211yesmaximal, characteristic, complemented
12C31×#1877C211yesmaximal, characteristic, complemented
13C31×#1865C211yesmaximal, characteristic, complemented
14C31×#1864C211yesmaximal, characteristic, complemented
15C31×#1804C211yesmaximal, characteristic, complemented
16C22×Q16×C31C2211yescharacteristic
17C22×SD16×C31C2211yescharacteristic
18C22×SD16×C31C2211yescharacteristic
19C31×#559—24no—
20C31×#559—24no—
21C2×C31×#127C2211yescharacteristic
22C2×C31×#124—21no—
23C2×C31×#124C2211yescharacteristic
24C2×C31×#124C2211yescharacteristic
25C2×C31×#123—21no—
26C2×C31×#123—21no—
27C2×C4×Q8×C31C2211yescharacteristic
28C2×C4×Q8×C31C2211yescharacteristic
29C2×C4×Q8×C31C2211yescharacteristic
30C2×C4×D4×C31—21no—
31C2×C4×D4×C31C2211yescharacteristic
32C2×C4×D4×C31C2211yescharacteristic
33C31×#464—24no—
34C4×SD16×C31—24no—
35C2×C31×#106C2211yescharacteristic
36C2×C31×C4⋊C8C2211yescharacteristic
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×#102C2211yescharacteristic
46C2×C31×#102C2211yescharacteristic
47C2×C4×C8×C31C2211yescharacteristic
48C31×#400—21no—
49C31×#395—21no—
50C31×#391C2211yescharacteristic
51C31×#391C2211yescharacteristic
52C31×#389C2211yescharacteristic
53C31×#389C2211yescharacteristic
54C31×#387—21no—
55C31×#387—21no—
56C31×#382C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#336C2211yescharacteristic
60C31×#336C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C31×#336C2211yescharacteristic
63C22×Q8×C31D411yescharacteristic
64C22×Q8×C31C2311yescharacteristic
65C22×Q8×C31C2311yescharacteristic
66C22×D4×C31—21no—
67C22×D4×C31—21no—
68C22×D4×C31C2311yescharacteristic
69C22×D4×C31C2311yescharacteristic
70C23×C4×C31—21no—
71C23×C4×C31—21no—
72C2×Q16×C31—22no—
73C2×Q16×C31—22no—
74C2×Q16×C31—41no—
75C2×SD16×C31—22no—
76C2×SD16×C31—22no—
77C2×SD16×C31—22no—
78C2×SD16×C31—22no—
79C2×SD16×C31—22no—
80C2×SD16×C31—41no—
81C22×C8×C31C2311yescharacteristic
82C22×C8×C31C2311yescharacteristic
83C22×C8×C31C2311yescharacteristic
84C22×C8×C31C2311yescharacteristic
85C31×#127—22no—
86C31×#127—22no—
87C31×#124—28no—
88C31×#124—22no—
89C31×#124—22no—
90C31×#124—22no—
91C31×#124D414yes—
92C31×#123—28no—
93C31×#123—28no—
94C4×Q8×C31—22no—
95C4×Q8×C31—22no—
96C4×Q8×C31—22no—
97C4×Q8×C31—22no—
98C4×Q8×C31—22no—
99C4×Q8×C31—22no—
100C4×D4×C31—28no—
101C4×D4×C31—22no—
102C4×D4×C31—22no—
103C4×D4×C31—22no—
104C4×D4×C31D414yes—
105C2×C4⋊C4×C31—21no—
106C2×C4⋊C4×C31—21no—
107C2×C4⋊C4×C31—21no—
108C2×C4⋊C4×C31—21no—
109C2×C4⋊C4×C31D411yescharacteristic
110C2×C4⋊C4×C31D411yescharacteristic
111C2×C4⋊C4×C31D411yescharacteristic
112C2×C4⋊C4×C31C2311yescharacteristic
113C2×C4⋊C4×C31C2311yescharacteristic
114C2×C4⋊C4×C31C2311yescharacteristic
115C2×C4⋊C4×C31C2311yescharacteristic
116C2×C22⋊C4×C31—21no—
117C2×C22⋊C4×C31—21no—
118C2×C22⋊C4×C31—21no—
119C2×C22⋊C4×C31—21no—
120C2×C22⋊C4×C31—21no—
121C2×C22⋊C4×C31—21no—
122C2×C42×C31—21no—
123C2×C42×C31—21no—
124C2×C42×C31C2311yescharacteristic
125C2×C42×C31C2311yescharacteristic
126C2×C42×C31C2311yescharacteristic
127C31×#106—22no—
128C31×C4⋊C8—22no—
129C31×#103—22no—
130C31×#103—22no—
131C31×#103—22no—
132C31×#103—41no—
133C31×#102—22no—
134C31×#102—22no—
135C31×#102—22no—
136C31×#102—41no—
137C31×#102—41no—
138C31×#102—41no—
139C4×C8×C31—22no—
140C31×#95—21no—
141C31×#95—21no—
142C31×#95—21no—
143C31×#95—21no—
144C31×#95—21no—
145C31×#95—21no—
146C31×#95—21no—
147C31×#95—21no—
148C24×C31—21no—
149C24×C31—21no—
150C2×Q8×C31—22no—
151C2×Q8×C31—22no—
152C2×Q8×C31—21no—
153C2×Q8×C31—21no—
154C2×Q8×C31—21no—
155C2×Q8×C31—21no—
156C2×Q8×C31—21no—
157C2×Q8×C31—21no—
158C2×Q8×C31—21no—
159C2×Q8×C31—21no—
160C2×Q8×C31—21no—
161C2×Q8×C31—21no—
162C2×Q8×C31—41no—
163C2×Q8×C31C2×D412yes—
164C2×Q8×C31#4112yes—
165C2×D4×C31—24no—
166C2×D4×C31—24no—
167C2×D4×C31—21no—
168C2×D4×C31—21no—
169C2×D4×C31—21no—
170C2×D4×C31—21no—
171C2×D4×C31—21no—
172C2×D4×C31—21no—
173C2×D4×C31—21no—
174C2×D4×C31—21no—
175C2×D4×C31—21no—
176C2×D4×C31—21no—
177C2×D4×C31—42no—
178C2×D4×C31—42no—
179C2×D4×C31—81no—
180C2×D4×C31—81no—
181C2×D4×C31C2×D412yes—
182C2×D4×C31C2×D412yes—
183C22×C4×C31—21no—
184C22×C4×C31—21no—
185C22×C4×C31—21no—
186C22×C4×C31—24no—
187C22×C4×C31—24no—
188C22×C4×C31—21no—
189C22×C4×C31—21no—
190C22×C4×C31—21no—
191C22×C4×C31—81no—
192C22×C4×C31—81no—
193C22×C4×C31—81no—
194C22×C4×C31—81no—
195C22×C4×C31C2×D411yescharacteristic
196C22×C4×C31C2×D411yescharacteristic
197C22×C4×C31C2×D411yescharacteristic
198C22×C4×C31C2×D411yescharacteristic
199C22×C4×C31C2×D411yescharacteristic
200C22×C4×C31C2×D411yescharacteristic
201C22×C4×C31C2411yescharacteristic
202Q16×C31—44no—
203SD16×C31—28no—
204SD16×C31—44no—
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×C31—21no—
216C2×C8×C31#4112yes—
217C4⋊C4×C31—24no—
218C4⋊C4×C31—22no—
219C4⋊C4×C31—22no—
220C4⋊C4×C31—22no—
221C4⋊C4×C31—21no—
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—42no—
229C4⋊C4×C31—42no—
230C4⋊C4×C31—42no—
231C4⋊C4×C31C2×D412yes—
232C22⋊C4×C31—24no—
233C22⋊C4×C31—24no—
234C22⋊C4×C31—24no—
235C22⋊C4×C31—24no—
236C22⋊C4×C31—24no—
237C22⋊C4×C31—24no—
238C42×C31—24no—
239C42×C31—21no—
240C42×C31—21no—
241C42×C31—21no—
242C42×C31—21no—
243C42×C31—42no—
244C42×C31C2×D412yes—
245C42×C31C2×D412yes—
246#24194C3111yesmaximal, characteristic, direct product factor, Sylow
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×C31C22×D411yescharacteristic
262Q8×C31—22no—
263Q8×C31—22no—
264Q8×C31—22no—
265Q8×C31—22no—
266Q8×C31—44no—
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—48no—
276D4×C31—41no—
277D4×C31—41no—
278D4×C31—41no—
279D4×C31—41no—
280D4×C31—84no—
281C2×C4×C31—21no—
282C2×C4×C31—21no—
283C2×C4×C31—21no—
284C2×C4×C31—21no—
285C2×C4×C31—21no—
286C2×C4×C31—21no—
287C2×C4×C31—22no—
288C2×C4×C31—21no—
289C2×C4×C31—21no—
290C2×C4×C31—22no—
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—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—41no—
314C2×C4×C31—84no—
315C2×C4×C31—84no—
316C2×C4×C31#12012yes—
317C2×C4×C31#12012yes—
318C2×C4×C31#13512yes—
319C2×C4×C31C22×D411yescharacteristic
320C2×C4×C31C22×D411yescharacteristic
321C2×C4×C31C2×#4111yescharacteristic
322C2×C4×C31C2×#4111yescharacteristic
323C2×C4×C31H(5,𝔽2)11yescharacteristic
324C2×C4×C312−1+411yescharacteristic
325C8×C31—22no—
326C8×C31—41no—
327C8×C31—41no—
328C8×C31—41no—
329C2×#559C2×C3111yescharacteristic
330C2×#464C2×C3111yescharacteristic, complemented
331C2×C4×SD16C2×C3111yescharacteristic, complemented
332#2581C2×C3111yescharacteristic, complemented
333#2042C2×C3111yescharacteristic, complemented
334#2041C2×C3111yescharacteristic
335#2015C2×C3111yescharacteristic, complemented
336#2014C2×C3111yescharacteristic
337#1984C2×C3111yescharacteristic, complemented
338#1958C2×C3111yescharacteristic, complemented
339#1878C2×C3111yescharacteristic, complemented
340#1877C2×C3111yescharacteristic, complemented
341#1865C2×C3111yescharacteristic, complemented
342#1864C2×C3111yescharacteristic, complemented
343#1804C2×C3111yescharacteristic, complemented
344C22×C31—42no—
345C22×C31—42no—
346C22×C31—42no—
347C22×C31—42no—
348C22×C31—42no—
349C22×C31—42no—
350C22×C31—81no—
351C22×C31—81no—
352C22×C31—81no—
353C22×C31—81no—
354C22×C31—81no—
355C22×C31—81no—
356C22×C31—81no—
357C22×C31—81no—
358C22×C31C2×#12011yescharacteristic
359C22×C31#54811yescharacteristic
360C22×C31#55011yescharacteristic
361C22×C31C2×#13511yescharacteristic
362C22×C31#57511yescharacteristic
363C22×C31#57711yescharacteristic
364C22×C31#57711yescharacteristic
365C4×C31—22no—
366C4×C31—22no—
367C4×C31—22no—
368C4×C31—42no—
369C4×C31—42no—
370C4×C31—41no—
371C4×C31—41no—
372C4×C31—41no—
373C4×C31—42no—
374C4×C31—81no—
375C4×C31—81no—
376C4×C31—81no—
377C4×C31#52511yescharacteristic
378C4×C31#53711yescharacteristic
379C4×C31#54611yescharacteristic
380C4×C31#54711yescharacteristic
381C22×Q16C22×C3111yescharacteristic
382C22×SD16C22×C3111yescharacteristic
383C22×SD16C22×C3111yescharacteristic
384#559—24no—
385#559—24no—
386C2×#127C22×C3111yescharacteristic
387C2×#124—21no—
388C2×#124C22×C3111yescharacteristic
389C2×#124C22×C3111yescharacteristic
390C2×#123—21no—
391C2×#123—21no—
392C2×C4×Q8C22×C3111yescharacteristic
393C2×C4×Q8C22×C3111yescharacteristic
394C2×C4×Q8C22×C3111yescharacteristic
395C2×C4×D4—21no—
396C2×C4×D4C22×C3111yescharacteristic
397C2×C4×D4C22×C3111yescharacteristic
398#464—24no—
399C4×SD16—24no—
400C2×#106C22×C3111yescharacteristic
401C2×C4⋊C8C22×C3111yescharacteristic
402C2×#103C22×C3111yescharacteristic
403C2×#103C22×C3111yescharacteristic
404C2×#103C22×C3111yescharacteristic
405C2×#103C22×C3111yescharacteristic
406C2×#102C22×C3111yescharacteristic
407C2×#102C22×C3111yescharacteristic
408C2×#102C22×C3111yescharacteristic
409C2×#102C22×C3111yescharacteristic
410C2×#102C22×C3111yescharacteristic
411C2×#102C22×C3111yescharacteristic
412C2×C4×C8C22×C3111yescharacteristic
413#400—21no—
414#395—21no—
415#391C22×C3111yescharacteristic
416#391C22×C3111yescharacteristic
417#389C22×C3111yescharacteristic
418#389C22×C3111yescharacteristic
419#387—21no—
420#387—21no—
421#382C22×C3111yescharacteristic
422#340C22×C3111yescharacteristic
423#340C22×C3111yescharacteristic
424#336C22×C3111yescharacteristic
425#336C22×C3111yescharacteristic
426#336C22×C3111yescharacteristic
427#336C22×C3111yescharacteristic
428C2×C31—82no—
429C2×C31—82no—
430C2×C31#240711yescharacteristic
431C2×C31#300211yescharacteristic
432C2×C31#300911yescharacteristic
433C2×C31#336511yescharacteristic
434C2×C31#337111yescharacteristic
435C2×C31#339411yescharacteristic
436C2×C31#340111yescharacteristic
437C22×Q8D4×C3111yescharacteristic
438C22×Q8C23×C3111yescharacteristic
439C22×Q8C23×C3111yescharacteristic
440C22×D4—21no—
441C22×D4—21no—
442C22×D4C23×C3111yescharacteristic
443C22×D4C23×C3111yescharacteristic
444C23×C4—21no—
445C23×C4—21no—
446C2×Q16—22no—
447C2×Q16—22no—
448C2×Q16—41no—
449C2×SD16—22no—
450C2×SD16—22no—
451C2×SD16—22no—
452C2×SD16—22no—
453C2×SD16—22no—
454C2×SD16—41no—
455C22×C8C23×C3111yescharacteristic
456C22×C8C23×C3111yescharacteristic
457C22×C8C23×C3111yescharacteristic
458C22×C8C23×C3111yescharacteristic
459#127—22no—
460#127—22no—
461#124—28no—
462#124—22no—
463#124—22no—
464#124—22no—
465#124D4×C3114yes—
466#123—28no—
467#123—28no—
468C4×Q8—22no—
469C4×Q8—22no—
470C4×Q8—22no—
471C4×Q8—22no—
472C4×Q8—22no—
473C4×Q8—22no—
474C4×D4—28no—
475C4×D4—22no—
476C4×D4—22no—
477C4×D4—22no—
478C4×D4D4×C3114yes—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4D4×C3111yescharacteristic
484C2×C4⋊C4D4×C3111yescharacteristic
485C2×C4⋊C4D4×C3111yescharacteristic
486C2×C4⋊C4C23×C3111yescharacteristic
487C2×C4⋊C4C23×C3111yescharacteristic
488C2×C4⋊C4C23×C3111yescharacteristic
489C2×C4⋊C4C23×C3111yescharacteristic
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C42—21no—
497C2×C42—21no—
498C2×C42C23×C3111yescharacteristic
499C2×C42C23×C3111yescharacteristic
500C2×C42C23×C3111yescharacteristic
501#106—22no—
502C4⋊C8—22no—
503#103—22no—
504#103—22no—
505#103—22no—
506#103—41no—
507#102—22no—
508#102—22no—
509#102—22no—
510#102—41no—
511#102—41no—
512#102—41no—
513C4×C8—22no—
514#95—21no—
515#95—21no—
516#95—21no—
517#95—21no—
518#95—21no—
519#95—21no—
520#95—21no—
521#95—21no—
522C31#2419411yescharacteristic, direct product factor, Sylow
523C24—21no—
524C24—21no—
525C2×Q8—22no—
526C2×Q8—22no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—41no—
538C2×Q8C2×D4×C3112yes—
539C2×Q8#41×C3112yes—
540C2×D4—24no—
541C2×D4—24no—
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—81no—
555C2×D4—81no—
556C2×D4C2×D4×C3112yes—
557C2×D4C2×D4×C3112yes—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—81no—
567C22×C4—81no—
568C22×C4—81no—
569C22×C4—81no—
570C22×C4C2×D4×C3111yescharacteristic
571C22×C4C2×D4×C3111yescharacteristic
572C22×C4C2×D4×C3111yescharacteristic
573C22×C4C2×D4×C3111yescharacteristic
574C22×C4C2×D4×C3111yescharacteristic
575C22×C4C2×D4×C3111yescharacteristic
576C22×C4C24×C3111yescharacteristic
577Q16—44no—
578SD16—28no—
579SD16—44no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8#41×C3112yes—
592C4⋊C4—24no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—42no—
606C4⋊C4C2×D4×C3112yes—
607C22⋊C4—24no—
608C22⋊C4—24no—
609C22⋊C4—24no—
610C22⋊C4—24no—
611C22⋊C4—24no—
612C22⋊C4—24no—
613C42—24no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42—42no—
619C42C2×D4×C3112yes—
620C42C2×D4×C3112yes—
621C23—22no—
622C23—22no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23C22×D4×C3111yescharacteristic
636Q8—22no—
637Q8—22no—
638Q8—22no—
639Q8—22no—
640Q8—44no—
641Q8—41no—
642Q8—41no—
643Q8—41no—
644Q8—41no—
645D4—22no—
646D4—22no—
647D4—22no—
648D4—22no—
649D4—48no—
650D4—41no—
651D4—41no—
652D4—41no—
653D4—41no—
654D4—84no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—22no—
665C2×C4—21no—
666C2×C4—22no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
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—41no—
687C2×C4—41no—
688C2×C4—84no—
689C2×C4—84no—
690C2×C4C31×#12012yes—
691C2×C4C31×#12012yes—
692C2×C4C31×#13512yes—
693C2×C4C22×D4×C3111yescharacteristic
694C2×C4C22×D4×C3111yescharacteristic
695C2×C4C2×#41×C3111yescharacteristic
696C2×C4C2×#41×C3111yescharacteristic
697C2×C4C31×H(5,𝔽2)11yescharacteristic
698C2×C4C31×2−1+411yescharacteristic
699C8—22no—
700C8—41no—
701C8—41no—
702C8—41no—
703C22—42no—
704C22—42no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—81no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22C2×C31×#12011yescharacteristic
718C22C31×#54811yescharacteristic
719C22C31×#55011yescharacteristic
720C22C2×C31×#13511yescharacteristic
721C22C31×#57511yescharacteristic
722C22C31×#57711yescharacteristic
723C22C31×#57711yescharacteristic
724C4—22no—
725C4—22no—
726C4—22no—
727C4—42no—
728C4—42no—
729C4—41no—
730C4—41no—
731C4—41no—
732C4—42no—
733C4—81no—
734C4—81no—
735C4—81no—
736C4C31×#52511yescharacteristic
737C4C31×#53711yescharacteristic
738C4C31×#54611yescharacteristic
739C4C31×#54711yescharacteristic
740C2—82no—
741C2—82no—
742C2C31×#240711yescharacteristic
743C2C31×#300211yescharacteristic
744C2C31×#300911yescharacteristic
745C2C31×#336511yescharacteristic
746C2C31×#337111yescharacteristic
747C2C31×#339411yescharacteristic
748C2C31×#340111yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#127C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C4×Q8×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#464C2semidirect
3. C2×C4×SD16×C31C2semidirect
4. C31×#2581C2semidirect
5. C31×#2042C2semidirect
7. C31×#2015C2semidirect
9. C31×#1984C2semidirect
10. C31×#1958C2semidirect
11. C31×#1878C2semidirect
12. C31×#1877C2semidirect
13. C31×#1865C2semidirect
14. C31×#1864C2semidirect
15. C31×#1804C2semidirect
246. #24194C31direct (N × H)
330. C2×#464C2×C31semidirect
331. C2×C4×SD16C2×C31semidirect
332. #2581C2×C31semidirect
333. #2042C2×C31semidirect
335. #2015C2×C31semidirect
337. #1984C2×C31semidirect
338. #1958C2×C31semidirect
339. #1878C2×C31semidirect
340. #1877C2×C31semidirect
341. #1865C2×C31semidirect
342. #1864C2×C31semidirect
343. #1804C2×C31semidirect
522. C31#24194direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5592
C2×C31×#4642
C2×C4×SD16×C312
C31×#25812
C31×#20422
C31×#20412
C31×#20152
C31×#20142
C31×#19842
C31×#19582
C31×#18782
C31×#18772
C31×#18652
C31×#18642
C31×#18042
#2419431