Finite Group Databasebeta

← C31×#24138 #21480897

Subgroups — C31×#24138 #21480897

Order 7936.

1154 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#553C211yesmaximal, characteristic
2C2×C31×#479C211yesmaximal, characteristic, complemented
3C2×C31×#440C211yesmaximal, characteristic, complemented
4C31×#2538C211yesmaximal, characteristic, complemented
5C31×#2034C211yesmaximal, characteristic, complemented
6C31×#2033C211yesmaximal, characteristic, complemented
7C31×#2000C211yesmaximal, characteristic, complemented
8C31×#2000C211yesmaximal, characteristic, complemented
9C31×#1992C211yesmaximal, characteristic, complemented
10C31×#1955C211yesmaximal, characteristic, complemented
11C31×#1873C211yesmaximal, characteristic, complemented
12C31×#1872C211yesmaximal, characteristic, complemented
13C31×#1854C211yesmaximal, characteristic, complemented
14C31×#1852C211yesmaximal, characteristic, complemented
15C31×#1802C211yesmaximal, characteristic, complemented
16C22×SD16×C31C2211yescharacteristic
17C31×#553—24no—
18C31×#553—24no—
19C2×C31×#126—21no—
20C2×C31×#125C2211yescharacteristic
21C2×C31×#123—21no—
22C2×C31×C22⋊Q8C2211yescharacteristic
23C2×C31×C22⋊Q8C2211yescharacteristic
24C2×C31×#121—21no—
25C2×C31×#121C2211yescharacteristic
26C2×C31×#121C2211yescharacteristic
27C2×C4×Q8×C31C2211yescharacteristic
28C2×C4×D4×C31—21no—
29C2×C4×D4×C31C2211yescharacteristic
30C2×C4×D4×C31C2211yescharacteristic
31C2×C31×#117C2211yescharacteristic
32C22×C4⋊C4×C31C2211yescharacteristic
33C31×#479—24no—
34C31×#440—24no—
35C2×C31×#107C2211yescharacteristic
36C2×C31×#107C2211yescharacteristic
37C2×C31×#106C2211yescharacteristic
38C2×C31×C4⋊C8C2211yescharacteristic
39C2×C31×#103C2211yescharacteristic
40C2×C31×#103C2211yescharacteristic
41C2×C31×#103C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×C22⋊C8C2211yescharacteristic
46C2×C31×C22⋊C8C2211yescharacteristic
47C2×C31×C22⋊C8C2211yescharacteristic
48C2×C31×C22⋊C8C2211yescharacteristic
49C2×C31×#97C2211yescharacteristic
50C31×#396—21no—
51C31×#396—21no—
52C31×#390—21no—
53C31×#389—21no—
54C31×#384C2211yescharacteristic
55C31×#380C2211yescharacteristic
56C31×#380C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#340C2211yescharacteristic
62C31×#340C2211yescharacteristic
63C22×Q8×C31C2311yescharacteristic
64C22×D4×C31—21no—
65C22×D4×C31—21no—
66C22×D4×C31D411yescharacteristic
67C22×D4×C31C2311yescharacteristic
68C23×C4×C31—21no—
69C23×C4×C31—21no—
70C23×C4×C31C2311yescharacteristic
71C23×C4×C31C2311yescharacteristic
72C2×SD16×C31—22no—
73C2×SD16×C31—22no—
74C2×SD16×C31—22no—
75C22×C8×C31C2311yescharacteristic
76C22×C8×C31C2311yescharacteristic
77C22×C8×C31C2311yescharacteristic
78C22×C8×C31C2311yescharacteristic
79C31×#126—28no—
80C31×#125—22no—
81C31×#125D414yes—
82C31×#123—28no—
83C31×C22⋊Q8—22no—
84C31×C22⋊Q8—22no—
85C31×C22⋊Q8—41no—
86C31×C22⋊Q8—41no—
87C31×#121—28no—
88C31×#121—22no—
89C31×#121—22no—
90C31×#121—22no—
91C31×#121—22no—
92C4×Q8×C31—22no—
93C4×Q8×C31—22no—
94C4×D4×C31—28no—
95C4×D4×C31—22no—
96C4×D4×C31—22no—
97C4×D4×C31—22no—
98C4×D4×C31D414yes—
99C31×#117—22no—
100C31×#117—22no—
101C2×C4⋊C4×C31—21no—
102C2×C4⋊C4×C31—21no—
103C2×C4⋊C4×C31—21no—
104C2×C4⋊C4×C31—22no—
105C2×C4⋊C4×C31—22no—
106C2×C4⋊C4×C31—21no—
107C2×C4⋊C4×C31—21no—
108C2×C4⋊C4×C31—21no—
109C2×C4⋊C4×C31—21no—
110C2×C4⋊C4×C31—21no—
111C2×C4⋊C4×C31D411yescharacteristic
112C2×C4⋊C4×C31C2311yescharacteristic
113C2×C4⋊C4×C31C2311yescharacteristic
114C2×C4⋊C4×C31C2311yescharacteristic
115C2×C4⋊C4×C31C2311yescharacteristic
116C2×C4⋊C4×C31C2311yescharacteristic
117C2×C4⋊C4×C31C2311yescharacteristic
118C2×C22⋊C4×C31—21no—
119C2×C22⋊C4×C31—21no—
120C2×C22⋊C4×C31—21no—
121C2×C22⋊C4×C31—21no—
122C2×C22⋊C4×C31—21no—
123C2×C22⋊C4×C31—21no—
124C2×C22⋊C4×C31—21no—
125C2×C22⋊C4×C31—21no—
126C2×C22⋊C4×C31D411yescharacteristic
127C2×C22⋊C4×C31D411yescharacteristic
128C2×C42×C31—21no—
129C2×C42×C31—21no—
130C2×C42×C31C2311yescharacteristic
131C31×#107—22no—
132C31×#107—22no—
133C31×#106—22no—
134C31×C4⋊C8—22no—
135C31×#103—22no—
136C31×#103—22no—
137C31×#103—22no—
138C31×#102—22no—
139C31×#102—41no—
140C31×#102—41no—
141C31×C22⋊C8—22no—
142C31×C22⋊C8—22no—
143C31×C22⋊C8—41no—
144C31×C22⋊C8—41no—
145C31×#97—22no—
146C31×#95—21no—
147C31×#95—21no—
148C24×C31—21no—
149C24×C31C2×D411yescharacteristic
150C24×C31C2×D411yescharacteristic
151C2×Q8×C31—21no—
152C2×Q8×C31—21no—
153C2×Q8×C31—21no—
154C2×Q8×C31—21no—
155C2×Q8×C31—21no—
156C2×Q8×C31#4112yes—
157C2×D4×C31—24no—
158C2×D4×C31—22no—
159C2×D4×C31—24no—
160C2×D4×C31—22no—
161C2×D4×C31—21no—
162C2×D4×C31—21no—
163C2×D4×C31—21no—
164C2×D4×C31—21no—
165C2×D4×C31—21no—
166C2×D4×C31—41no—
167C2×D4×C31—42no—
168C2×D4×C31—42no—
169C2×D4×C31—81no—
170C2×D4×C31—81no—
171C2×D4×C31C2×D412yes—
172C22×C4×C31—21no—
173C22×C4×C31—21no—
174C22×C4×C31—21no—
175C22×C4×C31—21no—
176C22×C4×C31—24no—
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—21no—
187C22×C4×C31—21no—
188C22×C4×C31—21no—
189C22×C4×C31—24no—
190C22×C4×C31—21no—
191C22×C4×C31—21no—
192C22×C4×C31—21no—
193C22×C4×C31—81no—
194C22×C4×C31—81no—
195C22×C4×C31—81no—
196C22×C4×C31—81no—
197C22×C4×C31C2×D411yescharacteristic
198C22×C4×C31C2×D411yescharacteristic
199C22×C4×C31C2×D411yescharacteristic
200C22×C4×C31C2×D411yescharacteristic
201C22×C4×C31C2411yescharacteristic
202SD16×C31—28no—
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×C31—21no—
212C2×C8×C31—21no—
213C2×C8×C31—21no—
214C2×C8×C31#4112yes—
215C4⋊C4×C31—24no—
216C4⋊C4×C31—24no—
217C4⋊C4×C31—24no—
218C4⋊C4×C31—22no—
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—21no—
226C4⋊C4×C31—21no—
227C4⋊C4×C31—21no—
228C4⋊C4×C31—42no—
229C4⋊C4×C31—42no—
230C4⋊C4×C31—42no—
231C4⋊C4×C31—42no—
232C4⋊C4×C31—81no—
233C4⋊C4×C31C2×D412yes—
234C4⋊C4×C31C2×D412yes—
235C4⋊C4×C31C2×D412yes—
236C22⋊C4×C31—24no—
237C22⋊C4×C31—24no—
238C22⋊C4×C31—24no—
239C22⋊C4×C31—24no—
240C22⋊C4×C31—22no—
241C22⋊C4×C31—22no—
242C22⋊C4×C31—42no—
243C22⋊C4×C31—42no—
244C22⋊C4×C31—81no—
245C22⋊C4×C31—81no—
246C42×C31—24no—
247C42×C31—42no—
248C42×C31C2×D412yes—
249C42×C31C2×D412yes—
250#24138C3111yesmaximal, characteristic, direct product factor, Sylow
251C23×C31—21no—
252C23×C31—21no—
253C23×C31—21no—
254C23×C31—21no—
255C23×C31—21no—
256C23×C31—21no—
257C23×C31—21no—
258C23×C31—22no—
259C23×C31—21no—
260C23×C31—21no—
261C23×C31—21no—
262C23×C31—21no—
263C23×C31—21no—
264C23×C31—21no—
265C23×C31—41no—
266C23×C31—41no—
267C23×C31—41no—
268C23×C31—41no—
269C23×C31—41no—
270C23×C31—41no—
271C23×C31#13712yes—
272C23×C31C22×D411yescharacteristic
273Q8×C31—22no—
274Q8×C31—22no—
275Q8×C31—41no—
276Q8×C31—41no—
277D4×C31—22no—
278D4×C31—22no—
279D4×C31—44no—
280D4×C31—48no—
281D4×C31—41no—
282D4×C31—41no—
283D4×C31—84no—
284C2×C4×C31—21no—
285C2×C4×C31—21no—
286C2×C4×C31—21no—
287C2×C4×C31—21no—
288C2×C4×C31—21no—
289C2×C4×C31—22no—
290C2×C4×C31—22no—
291C2×C4×C31—21no—
292C2×C4×C31—22no—
293C2×C4×C31—22no—
294C2×C4×C31—21no—
295C2×C4×C31—21no—
296C2×C4×C31—21no—
297C2×C4×C31—21no—
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—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—41no—
322C2×C4×C31—41no—
323C2×C4×C31—84no—
324C2×C4×C31—84no—
325C2×C4×C31#12012yes—
326C2×C4×C31#12012yes—
327C2×C4×C31C22×D411yescharacteristic
328C2×C4×C31C22×D411yescharacteristic
329C2×C4×C31C2×#4111yescharacteristic
330C2×C4×C31C2×#4111yescharacteristic
331C2×C4×C31H(5,𝔽2)11yescharacteristic
332C2×C4×C312−1+411yescharacteristic
333C8×C31—22no—
334C8×C31—41no—
335C8×C31—41no—
336C8×C31—41no—
337C2×#553C2×C3111yescharacteristic
338C2×#479C2×C3111yescharacteristic, complemented
339C2×#440C2×C3111yescharacteristic, complemented
340#2538C2×C3111yescharacteristic, complemented
341#2034C2×C3111yescharacteristic, complemented
342#2033C2×C3111yescharacteristic, complemented
343#2000C2×C3111yescharacteristic, complemented
344#2000C2×C3111yescharacteristic, complemented
345#1992C2×C3111yescharacteristic, complemented
346#1955C2×C3111yescharacteristic, complemented
347#1873C2×C3111yescharacteristic, complemented
348#1872C2×C3111yescharacteristic, complemented
349#1854C2×C3111yescharacteristic, complemented
350#1852C2×C3111yescharacteristic, complemented
351#1802C2×C3111yescharacteristic, complemented
352C22×C31—22no—
353C22×C31—22no—
354C22×C31—22no—
355C22×C31—41no—
356C22×C31—41no—
357C22×C31—41no—
358C22×C31—41no—
359C22×C31—41no—
360C22×C31—41no—
361C22×C31—41no—
362C22×C31—42no—
363C22×C31—41no—
364C22×C31—42no—
365C22×C31—42no—
366C22×C31—41no—
367C22×C31—41no—
368C22×C31—41no—
369C22×C31—81no—
370C22×C31—81no—
371C22×C31—81no—
372C22×C31—81no—
373C22×C31C2×#12011yescharacteristic
374C22×C31#54611yescharacteristic
375C22×C31#54711yescharacteristic
376C22×C31C2×#13711yescharacteristic
377C22×C31#57511yescharacteristic
378C22×C31#57611yescharacteristic
379C22×C31#57711yescharacteristic
380C4×C31—22no—
381C4×C31—22no—
382C4×C31—41no—
383C4×C31—41no—
384C4×C31—42no—
385C4×C31—42no—
386C4×C31—42no—
387C4×C31—42no—
388C4×C31—81no—
389C4×C31—81no—
390C4×C31—81no—
391C4×C31#52511yescharacteristic
392C4×C31#53711yescharacteristic
393C4×C31#54811yescharacteristic
394C4×C31#55011yescharacteristic
395C22×SD16C22×C3111yescharacteristic
396#553—24no—
397#553—24no—
398C2×#126—21no—
399C2×#125C22×C3111yescharacteristic
400C2×#123—21no—
401C2×C22⋊Q8C22×C3111yescharacteristic
402C2×C22⋊Q8C22×C3111yescharacteristic
403C2×#121—21no—
404C2×#121C22×C3111yescharacteristic
405C2×#121C22×C3111yescharacteristic
406C2×C4×Q8C22×C3111yescharacteristic
407C2×C4×D4—21no—
408C2×C4×D4C22×C3111yescharacteristic
409C2×C4×D4C22×C3111yescharacteristic
410C2×#117C22×C3111yescharacteristic
411C22×C4⋊C4C22×C3111yescharacteristic
412#479—24no—
413#440—24no—
414C2×#107C22×C3111yescharacteristic
415C2×#107C22×C3111yescharacteristic
416C2×#106C22×C3111yescharacteristic
417C2×C4⋊C8C22×C3111yescharacteristic
418C2×#103C22×C3111yescharacteristic
419C2×#103C22×C3111yescharacteristic
420C2×#103C22×C3111yescharacteristic
421C2×#102C22×C3111yescharacteristic
422C2×#102C22×C3111yescharacteristic
423C2×#102C22×C3111yescharacteristic
424C2×C22⋊C8C22×C3111yescharacteristic
425C2×C22⋊C8C22×C3111yescharacteristic
426C2×C22⋊C8C22×C3111yescharacteristic
427C2×C22⋊C8C22×C3111yescharacteristic
428C2×#97C22×C3111yescharacteristic
429#396—21no—
430#396—21no—
431#390—21no—
432#389—21no—
433#384C22×C3111yescharacteristic
434#380C22×C3111yescharacteristic
435#380C22×C3111yescharacteristic
436#340C22×C3111yescharacteristic
437#340C22×C3111yescharacteristic
438#340C22×C3111yescharacteristic
439#340C22×C3111yescharacteristic
440#340C22×C3111yescharacteristic
441#340C22×C3111yescharacteristic
442C2×C31—42no—
443C2×C31—81no—
444C2×C31—82no—
445C2×C31#240711yescharacteristic
446C2×C31#300711yescharacteristic
447C2×C31#301211yescharacteristic
448C2×C31#330911yescharacteristic
449C2×C31#332011yescharacteristic
450C2×C31#334611yescharacteristic
451C2×C31#335011yescharacteristic
452C22×Q8C23×C3111yescharacteristic
453C22×D4—21no—
454C22×D4—21no—
455C22×D4D4×C3111yescharacteristic
456C22×D4C23×C3111yescharacteristic
457C23×C4—21no—
458C23×C4—21no—
459C23×C4C23×C3111yescharacteristic
460C23×C4C23×C3111yescharacteristic
461C2×SD16—22no—
462C2×SD16—22no—
463C2×SD16—22no—
464C22×C8C23×C3111yescharacteristic
465C22×C8C23×C3111yescharacteristic
466C22×C8C23×C3111yescharacteristic
467C22×C8C23×C3111yescharacteristic
468#126—28no—
469#125—22no—
470#125D4×C3114yes—
471#123—28no—
472C22⋊Q8—22no—
473C22⋊Q8—22no—
474C22⋊Q8—41no—
475C22⋊Q8—41no—
476#121—28no—
477#121—22no—
478#121—22no—
479#121—22no—
480#121—22no—
481C4×Q8—22no—
482C4×Q8—22no—
483C4×D4—28no—
484C4×D4—22no—
485C4×D4—22no—
486C4×D4—22no—
487C4×D4D4×C3114yes—
488#117—22no—
489#117—22no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—22no—
494C2×C4⋊C4—22no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4D4×C3111yescharacteristic
501C2×C4⋊C4C23×C3111yescharacteristic
502C2×C4⋊C4C23×C3111yescharacteristic
503C2×C4⋊C4C23×C3111yescharacteristic
504C2×C4⋊C4C23×C3111yescharacteristic
505C2×C4⋊C4C23×C3111yescharacteristic
506C2×C4⋊C4C23×C3111yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4D4×C3111yescharacteristic
516C2×C22⋊C4D4×C3111yescharacteristic
517C2×C42—21no—
518C2×C42—21no—
519C2×C42C23×C3111yescharacteristic
520#107—22no—
521#107—22no—
522#106—22no—
523C4⋊C8—22no—
524#103—22no—
525#103—22no—
526#103—22no—
527#102—22no—
528#102—41no—
529#102—41no—
530C22⋊C8—22no—
531C22⋊C8—22no—
532C22⋊C8—41no—
533C22⋊C8—41no—
534#97—22no—
535#95—21no—
536#95—21no—
537C31#2413811yescharacteristic, direct product factor, Sylow
538C24—21no—
539C24C2×D4×C3111yescharacteristic
540C24C2×D4×C3111yescharacteristic
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8#41×C3112yes—
547C2×D4—24no—
548C2×D4—22no—
549C2×D4—24no—
550C2×D4—22no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—41no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—81no—
560C2×D4—81no—
561C2×D4C2×D4×C3112yes—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—24no—
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—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—24no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—81no—
584C22×C4—81no—
585C22×C4—81no—
586C22×C4—81no—
587C22×C4C2×D4×C3111yescharacteristic
588C22×C4C2×D4×C3111yescharacteristic
589C22×C4C2×D4×C3111yescharacteristic
590C22×C4C2×D4×C3111yescharacteristic
591C22×C4C24×C3111yescharacteristic
592SD16—28no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8#41×C3112yes—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—22no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—42no—
619C4⋊C4—42no—
620C4⋊C4—42no—
621C4⋊C4—42no—
622C4⋊C4—81no—
623C4⋊C4C2×D4×C3112yes—
624C4⋊C4C2×D4×C3112yes—
625C4⋊C4C2×D4×C3112yes—
626C22⋊C4—24no—
627C22⋊C4—24no—
628C22⋊C4—24no—
629C22⋊C4—24no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—81no—
635C22⋊C4—81no—
636C42—24no—
637C42—42no—
638C42C2×D4×C3112yes—
639C42C2×D4×C3112yes—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—22no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23C31×#13712yes—
661C23C22×D4×C3111yescharacteristic
662Q8—22no—
663Q8—22no—
664Q8—41no—
665Q8—41no—
666D4—22no—
667D4—22no—
668D4—44no—
669D4—48no—
670D4—41no—
671D4—41no—
672D4—84no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
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—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—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—84no—
713C2×C4—84no—
714C2×C4C31×#12012yes—
715C2×C4C31×#12012yes—
716C2×C4C22×D4×C3111yescharacteristic
717C2×C4C22×D4×C3111yescharacteristic
718C2×C4C2×#41×C3111yescharacteristic
719C2×C4C2×#41×C3111yescharacteristic
720C2×C4C31×H(5,𝔽2)11yescharacteristic
721C2×C4C31×2−1+411yescharacteristic
722C8—22no—
723C8—41no—
724C8—41no—
725C8—41no—
726C22—22no—
727C22—22no—
728C22—22no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—42no—
737C22—41no—
738C22—42no—
739C22—42no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22C2×C31×#12011yescharacteristic
748C22C31×#54611yescharacteristic
749C22C31×#54711yescharacteristic
750C22C2×C31×#13711yescharacteristic
751C22C31×#57511yescharacteristic
752C22C31×#57611yescharacteristic
753C22C31×#57711yescharacteristic
754C4—22no—
755C4—22no—
756C4—41no—
757C4—41no—
758C4—42no—
759C4—42no—
760C4—42no—
761C4—42no—
762C4—81no—
763C4—81no—
764C4—81no—
765C4C31×#52511yescharacteristic
766C4C31×#53711yescharacteristic
767C4C31×#54811yescharacteristic
768C4C31×#55011yescharacteristic
769C2—42no—
770C2—81no—
771C2—82no—
772C2C31×#240711yescharacteristic
773C2C31×#300711yescharacteristic
774C2C31×#301211yescharacteristic
775C2C31×#330911yescharacteristic
776C2C31×#332011yescharacteristic
777C2C31×#334611yescharacteristic
778C2C31×#335011yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#553C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C4×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#479C2semidirect
3. C2×C31×#440C2semidirect
4. C31×#2538C2semidirect
5. C31×#2034C2semidirect
6. C31×#2033C2semidirect
7. C31×#2000C2semidirect
8. C31×#2000C2semidirect
9. C31×#1992C2semidirect
10. C31×#1955C2semidirect
11. C31×#1873C2semidirect
12. C31×#1872C2semidirect
13. C31×#1854C2semidirect
14. C31×#1852C2semidirect
15. C31×#1802C2semidirect
250. #24138C31direct (N × H)
338. C2×#479C2×C31semidirect
339. C2×#440C2×C31semidirect
340. #2538C2×C31semidirect
341. #2034C2×C31semidirect
342. #2033C2×C31semidirect
343. #2000C2×C31semidirect
344. #2000C2×C31semidirect
345. #1992C2×C31semidirect
346. #1955C2×C31semidirect
347. #1873C2×C31semidirect
348. #1872C2×C31semidirect
349. #1854C2×C31semidirect
350. #1852C2×C31semidirect
351. #1802C2×C31semidirect
537. C31#24138direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5532
C2×C31×#4792
C2×C31×#4402
C31×#25382
C31×#20342
C31×#20332
C31×#20002
C31×#19922
C31×#19552
C31×#18732
C31×#18722
C31×#18542
C31×#18522
C31×#18022
#2413831