Finite Group Databasebeta

← C31×#24564 #21481323

Subgroups — C31×#24564 #21481323

Order 7936.

982 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#484C211yesmaximal, characteristic, complemented
2C2×C31×#408C211yesmaximal, characteristic
3C31×#2616C211yesmaximal, characteristic
4C31×#2311C211yesmaximal, characteristic
5C31×#2076C211yesmaximal, characteristic, complemented
6C31×#2075C211yesmaximal, characteristic, complemented
7C31×#2036C211yesmaximal, characteristic, complemented
8C31×#2035C211yesmaximal, characteristic, complemented
9C31×#1894C211yesmaximal, characteristic, complemented
10C31×#1892C211yesmaximal, characteristic, complemented
11C31×#1873C211yesmaximal, characteristic, complemented
12C31×#1854C211yesmaximal, characteristic, complemented
13C31×#1823C211yesmaximal, characteristic, complemented
14C31×#1809C211yesmaximal, characteristic, complemented
15C31×#1808C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C22×M16×C31C2211yescharacteristic
18C23×C8×C31C2211yescharacteristic
19C2×C31×C22⋊Q8C2211yescharacteristic
20C2×C31×C22⋊Q8C2211yescharacteristic
21C2×C31×C22⋊Q8C2211yescharacteristic
22C2×C31×#117C2211yescharacteristic
23C22×C4⋊C4×C31C2211yescharacteristic
24C31×#484—24no—
25C2×C31×#107C2211yescharacteristic
26C2×C31×#107C2211yescharacteristic
27C2×C31×#107C2211yescharacteristic
28C2×C31×#106C2211yescharacteristic
29C2×C31×#103C2211yescharacteristic
30C2×C31×#103C2211yescharacteristic
31C2×C31×#103C2211yescharacteristic
32C2×C31×#103C2211yescharacteristic
33C31×#408—24no—
34C2×C31×C22⋊C8C2211yescharacteristic
35C2×C31×C22⋊C8C2211yescharacteristic
36C2×C31×C22⋊C8C2211yescharacteristic
37C2×C31×C22⋊C8C2211yescharacteristic
38C31×#395—21no—
39C31×#394—21no—
40C31×#394—21no—
41C31×#394—21no—
42C31×#391—21no—
43C31×#390—21no—
44C31×#386—21no—
45C31×#386—21no—
46C31×#380C2211yescharacteristic
47C31×#380C2211yescharacteristic
48C31×#380C2211yescharacteristic
49C31×#380C2211yescharacteristic
50C31×#380C2211yescharacteristic
51C31×#380C2211yescharacteristic
52C31×#380C2211yescharacteristic
53C31×#340C2211yescharacteristic
54C31×#340C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C2×#41×C31—22no—
62C2×#41×C31—22no—
63C2×#41×C31—22no—
64C2×#41×C31—22no—
65C2×#41×C31—41no—
66C2×#41×C31—41no—
67C22×Q8×C31D411yescharacteristic
68C22×Q8×C31C2311yescharacteristic
69C22×D4×C31D411yescharacteristic
70C22×D4×C31D411yescharacteristic
71C22×D4×C31D411yescharacteristic
72C23×C4×C31—21no—
73C23×C4×C31C2311yescharacteristic
74C23×C4×C31C2311yescharacteristic
75C23×C4×C31C2311yescharacteristic
76C2×M16×C31—22no—
77C2×M16×C31—22no—
78C2×M16×C31—41no—
79C22×C8×C31—22no—
80C22×C8×C31—22no—
81C22×C8×C31—41no—
82C22×C8×C31C2311yescharacteristic
83C22×C8×C31C2311yescharacteristic
84C22×C8×C31C2311yescharacteristic
85C22×C8×C31C2311yescharacteristic
86C31×C22⋊Q8—22no—
87C31×C22⋊Q8—22no—
88C31×C22⋊Q8—22no—
89C31×C22⋊Q8—22no—
90C31×C22⋊Q8—41no—
91C31×C22⋊Q8—41no—
92C31×#117—41no—
93C31×#117—41no—
94C2×C4⋊C4×C31—22no—
95C2×C4⋊C4×C31—22no—
96C2×C4⋊C4×C31—21no—
97C2×C4⋊C4×C31—21no—
98C2×C4⋊C4×C31—21no—
99C2×C4⋊C4×C31—21no—
100C2×C4⋊C4×C31C2311yescharacteristic
101C2×C4⋊C4×C31C2311yescharacteristic
102C2×C4⋊C4×C31C2311yescharacteristic
103C2×C4⋊C4×C31C2311yescharacteristic
104C2×C4⋊C4×C31C2311yescharacteristic
105C2×C4⋊C4×C31C2311yescharacteristic
106C2×C4⋊C4×C31C2311yescharacteristic
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—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×C31—21no—
119C31×#107—22no—
120C31×#107—22no—
121C31×#107—41no—
122C31×#106—41no—
123C31×#103—22no—
124C31×#103—22no—
125C31×#103—41no—
126C31×#103—41no—
127C31×C22⋊C8—22no—
128C31×C22⋊C8—22no—
129C31×C22⋊C8—22no—
130C31×C22⋊C8D414yes—
131C31×#95—21no—
132C31×#95—21no—
133C31×#95—21no—
134C31×#95—21no—
135C31×#95—21no—
136C31×#95—21no—
137C31×#95—21no—
138C24×C31C2×D411yescharacteristic
139C24×C31C2×D411yescharacteristic
140C24×C31C2×D411yescharacteristic
141#41×C31—44no—
142#41×C31—44no—
143#41×C31—44no—
144#41×C31—44no—
145C2×Q8×C31—22no—
146C2×Q8×C31—22no—
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×Q8×C31—41no—
154C2×D4×C31—22no—
155C2×D4×C31—22no—
156C2×D4×C31—22no—
157C2×D4×C31—22no—
158C2×D4×C31—22no—
159C2×D4×C31—22no—
160C2×D4×C31—41no—
161C2×D4×C31—41no—
162C2×D4×C31—41no—
163C22×C4×C31—21no—
164C22×C4×C31—21no—
165C22×C4×C31—21no—
166C22×C4×C31—21no—
167C22×C4×C31—21no—
168C22×C4×C31—21no—
169C22×C4×C31—21no—
170C22×C4×C31—21no—
171C22×C4×C31—21no—
172C22×C4×C31—21no—
173C22×C4×C31—21no—
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—42no—
186C22×C4×C31—81no—
187C22×C4×C31—81no—
188C22×C4×C31C2×D411yescharacteristic
189C22×C4×C31C2×D411yescharacteristic
190C22×C4×C31C2×D412yes—
191C22×C4×C31C2×D411yescharacteristic
192C22×C4×C31#4112yes—
193C22×C4×C31#4112yes—
194C22×C4×C31#4112yes—
195C22×C4×C31C2411yescharacteristic
196M16×C31—44no—
197C2×C8×C31—21no—
198C2×C8×C31—21no—
199C2×C8×C31—21no—
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—44no—
208C2×C8×C31C2×D412yes—
209C2×C8×C31C2×D412yes—
210C4⋊C4×C31—21no—
211C4⋊C4×C31—21no—
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—21no—
223C4⋊C4×C31—21no—
224C4⋊C4×C31—42no—
225C4⋊C4×C31—42no—
226C4⋊C4×C31—42no—
227C4⋊C4×C31—42no—
228C22⋊C4×C31—42no—
229C22⋊C4×C31—42no—
230C22⋊C4×C31—42no—
231C22⋊C4×C31—42no—
232C22⋊C4×C31—81no—
233C22⋊C4×C31—81no—
234C22⋊C4×C31—81no—
235C22⋊C4×C31—81no—
236C22⋊C4×C31—81no—
237C22⋊C4×C31—81no—
238C22⋊C4×C31—81no—
239C42×C31—42no—
240#24564C3111yesmaximal, characteristic, direct product factor, Sylow
241C23×C31—21no—
242C23×C31—21no—
243C23×C31—21no—
244C23×C31—21no—
245C23×C31—21no—
246C23×C31—21no—
247C23×C31—21no—
248C23×C31—21no—
249C23×C31—21no—
250C23×C31—21no—
251C23×C31—21no—
252C23×C31—21no—
253C23×C31—21no—
254C23×C31—21no—
255C23×C31—21no—
256C23×C31—21no—
257C23×C31—21no—
258C23×C31—21no—
259C23×C31—21no—
260C23×C31#12112yes—
261C23×C31#12312yes—
262C23×C31C22×D411yescharacteristic
263Q8×C31—44no—
264Q8×C31—41no—
265Q8×C31—41no—
266Q8×C31—41no—
267Q8×C31—41no—
268D4×C31—44no—
269D4×C31—44no—
270D4×C31—44no—
271C2×C4×C31—21no—
272C2×C4×C31—21no—
273C2×C4×C31—21no—
274C2×C4×C31—21no—
275C2×C4×C31—22no—
276C2×C4×C31—22no—
277C2×C4×C31—22no—
278C2×C4×C31—22no—
279C2×C4×C31—22no—
280C2×C4×C31—22no—
281C2×C4×C31—22no—
282C2×C4×C31—22no—
283C2×C4×C31—21no—
284C2×C4×C31—21no—
285C2×C4×C31—21no—
286C2×C4×C31—41no—
287C2×C4×C31—41no—
288C2×C4×C31—41no—
289C2×C4×C31—41no—
290C2×C4×C31—41no—
291C2×C4×C31—41no—
292C2×C4×C31—41no—
293C2×C4×C31—41no—
294C2×C4×C31—41no—
295C2×C4×C31—41no—
296C2×C4×C31—41no—
297C2×C4×C31—41no—
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—41no—
314C2×C4×C31—84no—
315C2×C4×C31#12112yes—
316C2×C4×C31#12312yes—
317C2×C4×C31C22×D411yescharacteristic
318C2×C4×C31C2×#4111yescharacteristic
319C2×C4×C31C2×#4111yescharacteristic
320C2×C4×C31C2×#4111yescharacteristic
321C2×C4×C31H(5,𝔽2)11yescharacteristic
322C2×C4×C31H(5,𝔽2)11yescharacteristic
323C8×C31—22no—
324C8×C31—22no—
325C8×C31—41no—
326C8×C31—41no—
327C2×#484C2×C3111yescharacteristic, complemented
328C2×#408C2×C3111yescharacteristic
329#2616C2×C3111yescharacteristic
330#2311C2×C3111yescharacteristic
331#2076C2×C3111yescharacteristic, complemented
332#2075C2×C3111yescharacteristic, complemented
333#2036C2×C3111yescharacteristic, complemented
334#2035C2×C3111yescharacteristic, complemented
335#1894C2×C3111yescharacteristic, complemented
336#1892C2×C3111yescharacteristic, complemented
337#1873C2×C3111yescharacteristic, complemented
338#1854C2×C3111yescharacteristic, complemented
339#1823C2×C3111yescharacteristic, complemented
340#1809C2×C3111yescharacteristic, complemented
341#1808C2×C3111yescharacteristic, complemented
342C22×C31—22no—
343C22×C31—22no—
344C22×C31—22no—
345C22×C31—22no—
346C22×C31—22no—
347C22×C31—22no—
348C22×C31—41no—
349C22×C31—41no—
350C22×C31—41no—
351C22×C31—41no—
352C22×C31—41no—
353C22×C31—41no—
354C22×C31—41no—
355C22×C31—41no—
356C22×C31—41no—
357C22×C31—41no—
358C22×C31—41no—
359C22×C31—41no—
360C22×C31—41no—
361C22×C31—41no—
362C22×C31—41no—
363C22×C31C2×#12111yescharacteristic
364C22×C31C2×#12311yescharacteristic
365C22×C31#53411yescharacteristic
366C22×C31#57611yescharacteristic
367C22×C31#57711yescharacteristic
368C22×C31#57811yescharacteristic
369C22×C31#57811yescharacteristic
370C4×C31—22no—
371C4×C31—22no—
372C4×C31—41no—
373C4×C31—81no—
374C4×C31—81no—
375C4×C31—81no—
376C4×C31—81no—
377C4×C31—81no—
378C4×C31—81no—
379C4×C31—81no—
380C4×C31—81no—
381C4×C31#54611yescharacteristic
382C4×C31#54611yescharacteristic
383C4×C31#55111yescharacteristic
384C4×C31#55111yescharacteristic
385C22×#41C22×C3111yescharacteristic
386C22×M16C22×C3111yescharacteristic
387C23×C8C22×C3111yescharacteristic
388C2×C22⋊Q8C22×C3111yescharacteristic
389C2×C22⋊Q8C22×C3111yescharacteristic
390C2×C22⋊Q8C22×C3111yescharacteristic
391C2×#117C22×C3111yescharacteristic
392C22×C4⋊C4C22×C3111yescharacteristic
393#484—24no—
394C2×#107C22×C3111yescharacteristic
395C2×#107C22×C3111yescharacteristic
396C2×#107C22×C3111yescharacteristic
397C2×#106C22×C3111yescharacteristic
398C2×#103C22×C3111yescharacteristic
399C2×#103C22×C3111yescharacteristic
400C2×#103C22×C3111yescharacteristic
401C2×#103C22×C3111yescharacteristic
402#408—24no—
403C2×C22⋊C8C22×C3111yescharacteristic
404C2×C22⋊C8C22×C3111yescharacteristic
405C2×C22⋊C8C22×C3111yescharacteristic
406C2×C22⋊C8C22×C3111yescharacteristic
407#395—21no—
408#394—21no—
409#394—21no—
410#394—21no—
411#391—21no—
412#390—21no—
413#386—21no—
414#386—21no—
415#380C22×C3111yescharacteristic
416#380C22×C3111yescharacteristic
417#380C22×C3111yescharacteristic
418#380C22×C3111yescharacteristic
419#380C22×C3111yescharacteristic
420#380C22×C3111yescharacteristic
421#380C22×C3111yescharacteristic
422#340C22×C3111yescharacteristic
423#340C22×C3111yescharacteristic
424#340C22×C3111yescharacteristic
425#340C22×C3111yescharacteristic
426#340C22×C3111yescharacteristic
427#340C22×C3111yescharacteristic
428#340C22×C3111yescharacteristic
429#340C22×C3111yescharacteristic
430C2×C31—42no—
431C2×C31—42no—
432C2×C31—81no—
433C2×C31#241211yescharacteristic
434C2×C31#305911yescharacteristic
435C2×C31#306211yescharacteristic
436C2×C31#309711yescharacteristic
437C2×C31#309811yescharacteristic
438C2×C31#320111yescharacteristic
439C2×C31#320311yescharacteristic
440C2×#41—22no—
441C2×#41—22no—
442C2×#41—22no—
443C2×#41—22no—
444C2×#41—41no—
445C2×#41—41no—
446C22×Q8D4×C3111yescharacteristic
447C22×Q8C23×C3111yescharacteristic
448C22×D4D4×C3111yescharacteristic
449C22×D4D4×C3111yescharacteristic
450C22×D4D4×C3111yescharacteristic
451C23×C4—21no—
452C23×C4C23×C3111yescharacteristic
453C23×C4C23×C3111yescharacteristic
454C23×C4C23×C3111yescharacteristic
455C2×M16—22no—
456C2×M16—22no—
457C2×M16—41no—
458C22×C8—22no—
459C22×C8—22no—
460C22×C8—41no—
461C22×C8C23×C3111yescharacteristic
462C22×C8C23×C3111yescharacteristic
463C22×C8C23×C3111yescharacteristic
464C22×C8C23×C3111yescharacteristic
465C22⋊Q8—22no—
466C22⋊Q8—22no—
467C22⋊Q8—22no—
468C22⋊Q8—22no—
469C22⋊Q8—41no—
470C22⋊Q8—41no—
471#117—41no—
472#117—41no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4C23×C3111yescharacteristic
480C2×C4⋊C4C23×C3111yescharacteristic
481C2×C4⋊C4C23×C3111yescharacteristic
482C2×C4⋊C4C23×C3111yescharacteristic
483C2×C4⋊C4C23×C3111yescharacteristic
484C2×C4⋊C4C23×C3111yescharacteristic
485C2×C4⋊C4C23×C3111yescharacteristic
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
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×C22⋊C4—21no—
497C2×C42—21no—
498#107—22no—
499#107—22no—
500#107—41no—
501#106—41no—
502#103—22no—
503#103—22no—
504#103—41no—
505#103—41no—
506C22⋊C8—22no—
507C22⋊C8—22no—
508C22⋊C8—22no—
509C22⋊C8D4×C3114yes—
510#95—21no—
511#95—21no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95—21no—
516#95—21no—
517C31#2456411yescharacteristic, direct product factor, Sylow
518C24C2×D4×C3111yescharacteristic
519C24C2×D4×C3111yescharacteristic
520C24C2×D4×C3111yescharacteristic
521#41—44no—
522#41—44no—
523#41—44no—
524#41—44no—
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—41no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—41no—
541C2×D4—41no—
542C2×D4—41no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—42no—
566C22×C4—81no—
567C22×C4—81no—
568C22×C4C2×D4×C3111yescharacteristic
569C22×C4C2×D4×C3111yescharacteristic
570C22×C4C2×D4×C3112yes—
571C22×C4C2×D4×C3111yescharacteristic
572C22×C4#41×C3112yes—
573C22×C4#41×C3112yes—
574C22×C4#41×C3112yes—
575C22×C4C24×C3111yescharacteristic
576M16—44no—
577C2×C8—21no—
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×C8C2×D4×C3112yes—
589C2×C8C2×D4×C3112yes—
590C4⋊C4—21no—
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—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—42no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—42no—
612C22⋊C4—81no—
613C22⋊C4—81no—
614C22⋊C4—81no—
615C22⋊C4—81no—
616C22⋊C4—81no—
617C22⋊C4—81no—
618C22⋊C4—81no—
619C42—42no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23C31×#12112yes—
640C23C31×#12312yes—
641C23C22×D4×C3111yescharacteristic
642Q8—44no—
643Q8—41no—
644Q8—41no—
645Q8—41no—
646Q8—41no—
647D4—44no—
648D4—44no—
649D4—44no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
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—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—84no—
694C2×C4C31×#12112yes—
695C2×C4C31×#12312yes—
696C2×C4C22×D4×C3111yescharacteristic
697C2×C4C2×#41×C3111yescharacteristic
698C2×C4C2×#41×C3111yescharacteristic
699C2×C4C2×#41×C3111yescharacteristic
700C2×C4C31×H(5,𝔽2)11yescharacteristic
701C2×C4C31×H(5,𝔽2)11yescharacteristic
702C8—22no—
703C8—22no—
704C8—41no—
705C8—41no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22C2×C31×#12111yescharacteristic
728C22C2×C31×#12311yescharacteristic
729C22C31×#53411yescharacteristic
730C22C31×#57611yescharacteristic
731C22C31×#57711yescharacteristic
732C22C31×#57811yescharacteristic
733C22C31×#57811yescharacteristic
734C4—22no—
735C4—22no—
736C4—41no—
737C4—81no—
738C4—81no—
739C4—81no—
740C4—81no—
741C4—81no—
742C4—81no—
743C4—81no—
744C4—81no—
745C4C31×#54611yescharacteristic
746C4C31×#54611yescharacteristic
747C4C31×#55111yescharacteristic
748C4C31×#55111yescharacteristic
749C2—42no—
750C2—42no—
751C2—81no—
752C2C31×#241211yescharacteristic
753C2C31×#305911yescharacteristic
754C2C31×#306211yescharacteristic
755C2C31×#309711yescharacteristic
756C2C31×#309811yescharacteristic
757C2C31×#320111yescharacteristic
758C2C31×#320311yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC22×#41×C31C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×#41×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#484C2semidirect
5. C31×#2076C2semidirect
6. C31×#2075C2semidirect
7. C31×#2036C2semidirect
8. C31×#2035C2semidirect
9. C31×#1894C2semidirect
10. C31×#1892C2semidirect
11. C31×#1873C2semidirect
12. C31×#1854C2semidirect
13. C31×#1823C2semidirect
14. C31×#1809C2semidirect
15. C31×#1808C2semidirect
240. #24564C31direct (N × H)
327. C2×#484C2×C31semidirect
331. #2076C2×C31semidirect
332. #2075C2×C31semidirect
333. #2036C2×C31semidirect
334. #2035C2×C31semidirect
335. #1894C2×C31semidirect
336. #1892C2×C31semidirect
337. #1873C2×C31semidirect
338. #1854C2×C31semidirect
339. #1823C2×C31semidirect
340. #1809C2×C31semidirect
341. #1808C2×C31semidirect
517. C31#24564direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4842
C2×C31×#4082
C31×#26162
C31×#23112
C31×#20762
C31×#20752
C31×#20362
C31×#20352
C31×#18942
C31×#18922
C31×#18732
C31×#18542
C31×#18232
C31×#18092
C31×#18082
#2456431