Finite Group Databasebeta

← C31×#25560 #21482319

Subgroups — C31×#25560 #21482319

Order 7936.

1178 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#552C211yesmaximal, characteristic, complemented
2C2×C31×#482C211yesmaximal, characteristic, complemented
3C2×C31×#468C211yesmaximal, characteristic, complemented
4C31×#2416C211yesmaximal, characteristic
5C31×#2059C211yesmaximal, characteristic, complemented
6C31×#2035C211yesmaximal, characteristic, complemented
7C31×#2025C211yesmaximal, characteristic, complemented
8C31×#2000C211yesmaximal, characteristic, complemented
9C31×#1880C211yesmaximal, characteristic, complemented
10C31×#1874C211yesmaximal, characteristic, complemented
11C31×#1872C211yesmaximal, characteristic, complemented
12C31×#1870C211yesmaximal, characteristic, complemented
13C31×#1863C211yesmaximal, characteristic, complemented
14C31×#1852C211yesmaximal, characteristic, complemented
15C31×#1736C211yesmaximal, characteristic, complemented
16C22×SD16×C31C2211yescharacteristic
17C22×M16×C31C2211yescharacteristic
18C31×#552—24no—
19C31×#552—24no—
20C2×C31×#126—21no—
21C2×C31×#125—21no—
22C2×C31×#125C2211yescharacteristic
23C2×C31×#123—21no—
24C2×C31×C22⋊Q8C2211yescharacteristic
25C2×C31×C22⋊Q8C2211yescharacteristic
26C2×C31×#121—21no—
27C2×C31×#121C2211yescharacteristic
28C2×C31×#121C2211yescharacteristic
29C2×C4×Q8×C31C2211yescharacteristic
30C2×C4×D4×C31C2211yescharacteristic
31C2×C31×#117—21no—
32C2×C31×#117C2211yescharacteristic
33C22×C4⋊C4×C31C2211yescharacteristic
34C22×C4⋊C4×C31C2211yescharacteristic
35C31×#482—24no—
36C31×#468—24no—
37C2×C31×#107C2211yescharacteristic
38C2×C31×#107C2211yescharacteristic
39C2×C31×#106C2211yescharacteristic
40C2×C31×#103C2211yescharacteristic
41C2×C31×#103C2211yescharacteristic
42C2×C31×#103C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×#102C2211yescharacteristic
46C2×C31×C22⋊C8C2211yescharacteristic
47C2×C31×C22⋊C8C2211yescharacteristic
48C2×C31×C22⋊C8C2211yescharacteristic
49C31×#396—21no—
50C31×#394—21no—
51C31×#390C2211yescharacteristic
52C31×#389C2211yescharacteristic
53C31×#386—21no—
54C31×#380C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C31×#336C2211yescharacteristic
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—41no—
75C2×M16×C31—22no—
76C2×M16×C31—22no—
77C2×M16×C31—41no—
78C22×C8×C31C2311yescharacteristic
79C22×C8×C31C2311yescharacteristic
80C22×C8×C31C2311yescharacteristic
81C22×C8×C31C2311yescharacteristic
82C31×#126—28no—
83C31×#125—28no—
84C31×#125—22no—
85C31×#125—22no—
86C31×#123—28no—
87C31×C22⋊Q8—22no—
88C31×C22⋊Q8—22no—
89C31×C22⋊Q8—22no—
90C31×C22⋊Q8D414yescomplemented
91C31×#121—22no—
92C31×#121—22no—
93C31×#121—22no—
94C31×#121—41no—
95C31×#121—44no—
96C4×Q8×C31—22no—
97C4×Q8×C31—22no—
98C4×D4×C31—22no—
99C4×D4×C31—22no—
100C31×#117—28no—
101C31×#117—22no—
102C31×#117D414yescomplemented
103C2×C4⋊C4×C31—21no—
104C2×C4⋊C4×C31—21no—
105C2×C4⋊C4×C31—21no—
106C2×C4⋊C4×C31—21no—
107C2×C4⋊C4×C31—21no—
108C2×C4⋊C4×C31—21no—
109C2×C4⋊C4×C31—22no—
110C2×C4⋊C4×C31—22no—
111C2×C4⋊C4×C31—22no—
112C2×C4⋊C4×C31—21no—
113C2×C4⋊C4×C31—21no—
114C2×C4⋊C4×C31—41no—
115C2×C4⋊C4×C31D411yescharacteristic
116C2×C4⋊C4×C31C2311yescharacteristic
117C2×C4⋊C4×C31C2311yescharacteristic
118C2×C4⋊C4×C31C2311yescharacteristic
119C2×C4⋊C4×C31C2311yescharacteristic
120C2×C4⋊C4×C31C2311yescharacteristic
121C2×C4⋊C4×C31C2311yescharacteristic
122C2×C22⋊C4×C31—21no—
123C2×C22⋊C4×C31—21no—
124C2×C22⋊C4×C31—21no—
125C2×C22⋊C4×C31—21no—
126C2×C22⋊C4×C31—21no—
127C2×C22⋊C4×C31—21no—
128C2×C22⋊C4×C31—21no—
129C2×C22⋊C4×C31—21no—
130C2×C22⋊C4×C31D411yescharacteristic
131C2×C22⋊C4×C31D411yescharacteristic
132C2×C42×C31—21no—
133C2×C42×C31—21no—
134C2×C42×C31C2311yescharacteristic
135C31×#107—22no—
136C31×#107—22no—
137C31×#106—22no—
138C31×#103—22no—
139C31×#103—22no—
140C31×#103—41no—
141C31×#102—22no—
142C31×#102—22no—
143C31×#102—22no—
144C31×C22⋊C8—22no—
145C31×C22⋊C8—22no—
146C31×C22⋊C8—41no—
147C31×#95—21no—
148C31×#95—21no—
149C24×C31—21no—
150C24×C31C2×D411yescharacteristic
151C24×C31C2×D411yescharacteristic
152C2×Q8×C31—21no—
153C2×Q8×C31—21no—
154C2×Q8×C31—21no—
155C2×Q8×C31—21no—
156C2×Q8×C31—21no—
157C2×Q8×C31C2×D412yes—
158C2×D4×C31—22no—
159C2×D4×C31—22no—
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—41no—
167C2×D4×C31—42no—
168C2×D4×C31—42no—
169C2×D4×C31—42no—
170C2×D4×C31—42no—
171C2×D4×C31—42no—
172C2×D4×C31—81no—
173C22×C4×C31—21no—
174C22×C4×C31—21no—
175C22×C4×C31—21no—
176C22×C4×C31—21no—
177C22×C4×C31—24no—
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—21no—
190C22×C4×C31—21no—
191C22×C4×C31—42no—
192C22×C4×C31—42no—
193C22×C4×C31—42no—
194C22×C4×C31—42no—
195C22×C4×C31—81no—
196C22×C4×C31C2×D411yescharacteristic
197C22×C4×C31C2×D411yescharacteristic
198C22×C4×C31C2×D411yescharacteristic
199C22×C4×C31C2×D411yescharacteristic
200C22×C4×C31C2×D412yes—
201C22×C4×C31C2×D412yes—
202C22×C4×C31C2411yescharacteristic
203SD16×C31—44no—
204M16×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—24no—
219C4⋊C4×C31—24no—
220C4⋊C4×C31—24no—
221C4⋊C4×C31—24no—
222C4⋊C4×C31—24no—
223C4⋊C4×C31—22no—
224C4⋊C4×C31—21no—
225C4⋊C4×C31—21no—
226C4⋊C4×C31—21no—
227C4⋊C4×C31—21no—
228C4⋊C4×C31—21no—
229C4⋊C4×C31—21no—
230C4⋊C4×C31—21no—
231C4⋊C4×C31—21no—
232C4⋊C4×C31—42no—
233C4⋊C4×C31—42no—
234C4⋊C4×C31C2×D412yes—
235C4⋊C4×C31C2×D412yes—
236C4⋊C4×C31C2×D412yes—
237C4⋊C4×C31#4112yes—
238C22⋊C4×C31—24no—
239C22⋊C4×C31—24no—
240C22⋊C4×C31—24no—
241C22⋊C4×C31—22no—
242C22⋊C4×C31—22no—
243C22⋊C4×C31—42no—
244C22⋊C4×C31—42no—
245C22⋊C4×C31—42no—
246C22⋊C4×C31—42no—
247C22⋊C4×C31—81no—
248C42×C31—24no—
249C42×C31—24no—
250C42×C31—21no—
251C42×C31—21no—
252#25560C3111yesmaximal, characteristic, direct product factor, Sylow
253C23×C31—21no—
254C23×C31—21no—
255C23×C31—21no—
256C23×C31—21no—
257C23×C31—21no—
258C23×C31—21no—
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—41no—
272C23×C31#12012yes—
273C23×C31AGL(1,ℤ/8)12yes—
274C23×C31C22×D411yescharacteristic
275Q8×C31—22no—
276Q8×C31—22no—
277Q8×C31—41no—
278Q8×C31—41no—
279D4×C31—44no—
280D4×C31—41no—
281D4×C31—41no—
282D4×C31—41no—
283D4×C31—41no—
284D4×C31—84no—
285D4×C31—84no—
286C2×C4×C31—21no—
287C2×C4×C31—21no—
288C2×C4×C31—22no—
289C2×C4×C31—22no—
290C2×C4×C31—22no—
291C2×C4×C31—22no—
292C2×C4×C31—21no—
293C2×C4×C31—22no—
294C2×C4×C31—22no—
295C2×C4×C31—22no—
296C2×C4×C31—21no—
297C2×C4×C31—21no—
298C2×C4×C31—22no—
299C2×C4×C31—21no—
300C2×C4×C31—22no—
301C2×C4×C31—21no—
302C2×C4×C31—21no—
303C2×C4×C31—21no—
304C2×C4×C31—21no—
305C2×C4×C31—21no—
306C2×C4×C31—48no—
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—41no—
324C2×C4×C31—41no—
325C2×C4×C31—41no—
326C2×C4×C31—41no—
327C2×C4×C31—84no—
328C2×C4×C31#12012yes—
329C2×C4×C31C22×D411yescharacteristic
330C2×C4×C31C22×D411yescharacteristic
331C2×C4×C31C2×#4111yescharacteristic
332C2×C4×C31C2×#4111yescharacteristic
333C2×C4×C31H(5,𝔽2)11yescharacteristic
334C2×C4×C312−1+411yescharacteristic
335C8×C31—22no—
336C8×C31—41no—
337C8×C31—41no—
338C8×C31—41no—
339C2×#552C2×C3111yescharacteristic, complemented
340C2×#482C2×C3111yescharacteristic, complemented
341C2×#468C2×C3111yescharacteristic, complemented
342#2416C2×C3111yescharacteristic
343#2059C2×C3111yescharacteristic, complemented
344#2035C2×C3111yescharacteristic, complemented
345#2025C2×C3111yescharacteristic, complemented
346#2000C2×C3111yescharacteristic, complemented
347#1880C2×C3111yescharacteristic, complemented
348#1874C2×C3111yescharacteristic, complemented
349#1872C2×C3111yescharacteristic, complemented
350#1870C2×C3111yescharacteristic, complemented
351#1863C2×C3111yescharacteristic, complemented
352#1852C2×C3111yescharacteristic, complemented
353#1736C2×C3111yescharacteristic, complemented
354C22×C31—22no—
355C22×C31—22no—
356C22×C31—22no—
357C22×C31—22no—
358C22×C31—22no—
359C22×C31—22no—
360C22×C31—41no—
361C22×C31—41no—
362C22×C31—41no—
363C22×C31—41no—
364C22×C31—41no—
365C22×C31—41no—
366C22×C31—41no—
367C22×C31—41no—
368C22×C31—81no—
369C22×C31—81no—
370C22×C31—81no—
371C22×C31—81no—
372C22×C31—81no—
373C22×C31—81no—
374C22×C31—81no—
375C22×C31C2×#12011yescharacteristic
376C22×C31#54611yescharacteristic
377C22×C31#54711yescharacteristic
378C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
379C22×C31#57511yescharacteristic
380C22×C31#57711yescharacteristic
381C22×C31#57811yescharacteristic
382C4×C31—22no—
383C4×C31—41no—
384C4×C31—42no—
385C4×C31—41no—
386C4×C31—42no—
387C4×C31—42no—
388C4×C31—41no—
389C4×C31—42no—
390C4×C31—42no—
391C4×C31—81no—
392C4×C31—81no—
393C4×C31#53211yescharacteristic
394C4×C31#53711yescharacteristic
395C4×C31#54611yescharacteristic
396C4×C31#54711yescharacteristic
397C22×SD16C22×C3111yescharacteristic
398C22×M16C22×C3111yescharacteristic
399#552—24no—
400#552—24no—
401C2×#126—21no—
402C2×#125—21no—
403C2×#125C22×C3111yescharacteristic
404C2×#123—21no—
405C2×C22⋊Q8C22×C3111yescharacteristic
406C2×C22⋊Q8C22×C3111yescharacteristic
407C2×#121—21no—
408C2×#121C22×C3111yescharacteristic
409C2×#121C22×C3111yescharacteristic
410C2×C4×Q8C22×C3111yescharacteristic
411C2×C4×D4C22×C3111yescharacteristic
412C2×#117—21no—
413C2×#117C22×C3111yescharacteristic
414C22×C4⋊C4C22×C3111yescharacteristic
415C22×C4⋊C4C22×C3111yescharacteristic
416#482—24no—
417#468—24no—
418C2×#107C22×C3111yescharacteristic
419C2×#107C22×C3111yescharacteristic
420C2×#106C22×C3111yescharacteristic
421C2×#103C22×C3111yescharacteristic
422C2×#103C22×C3111yescharacteristic
423C2×#103C22×C3111yescharacteristic
424C2×#102C22×C3111yescharacteristic
425C2×#102C22×C3111yescharacteristic
426C2×#102C22×C3111yescharacteristic
427C2×C22⋊C8C22×C3111yescharacteristic
428C2×C22⋊C8C22×C3111yescharacteristic
429C2×C22⋊C8C22×C3111yescharacteristic
430#396—21no—
431#394—21no—
432#390C22×C3111yescharacteristic
433#389C22×C3111yescharacteristic
434#386—21no—
435#380C22×C3111yescharacteristic
436#340C22×C3111yescharacteristic
437#340C22×C3111yescharacteristic
438#340C22×C3111yescharacteristic
439#340C22×C3111yescharacteristic
440#340C22×C3111yescharacteristic
441#340C22×C3111yescharacteristic
442#336C22×C3111yescharacteristic
443#336C22×C3111yescharacteristic
444C2×C31—42no—
445C2×C31—42no—
446C2×C31—161no—
447C2×C31#243011yescharacteristic
448C2×C31#300611yescharacteristic
449C2×C31#301311yescharacteristic
450C2×C31#331011yescharacteristic
451C2×C31#332711yescharacteristic
452C2×C31#334311yescharacteristic
453C2×C31#335111yescharacteristic
454C22×Q8C23×C3111yescharacteristic
455C22×D4—21no—
456C22×D4—21no—
457C22×D4D4×C3111yescharacteristic
458C22×D4C23×C3111yescharacteristic
459C23×C4—21no—
460C23×C4—21no—
461C23×C4C23×C3111yescharacteristic
462C23×C4C23×C3111yescharacteristic
463C2×SD16—22no—
464C2×SD16—22no—
465C2×SD16—41no—
466C2×M16—22no—
467C2×M16—22no—
468C2×M16—41no—
469C22×C8C23×C3111yescharacteristic
470C22×C8C23×C3111yescharacteristic
471C22×C8C23×C3111yescharacteristic
472C22×C8C23×C3111yescharacteristic
473#126—28no—
474#125—28no—
475#125—22no—
476#125—22no—
477#123—28no—
478C22⋊Q8—22no—
479C22⋊Q8—22no—
480C22⋊Q8—22no—
481C22⋊Q8D4×C3114yescomplemented
482#121—22no—
483#121—22no—
484#121—22no—
485#121—41no—
486#121—44no—
487C4×Q8—22no—
488C4×Q8—22no—
489C4×D4—22no—
490C4×D4—22no—
491#117—28no—
492#117—22no—
493#117D4×C3114yescomplemented
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—41no—
506C2×C4⋊C4D4×C3111yescharacteristic
507C2×C4⋊C4C23×C3111yescharacteristic
508C2×C4⋊C4C23×C3111yescharacteristic
509C2×C4⋊C4C23×C3111yescharacteristic
510C2×C4⋊C4C23×C3111yescharacteristic
511C2×C4⋊C4C23×C3111yescharacteristic
512C2×C4⋊C4C23×C3111yescharacteristic
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4D4×C3111yescharacteristic
522C2×C22⋊C4D4×C3111yescharacteristic
523C2×C42—21no—
524C2×C42—21no—
525C2×C42C23×C3111yescharacteristic
526#107—22no—
527#107—22no—
528#106—22no—
529#103—22no—
530#103—22no—
531#103—41no—
532#102—22no—
533#102—22no—
534#102—22no—
535C22⋊C8—22no—
536C22⋊C8—22no—
537C22⋊C8—41no—
538#95—21no—
539#95—21no—
540C31#2556011yescharacteristic, direct product factor, Sylow
541C24—21no—
542C24C2×D4×C3111yescharacteristic
543C24C2×D4×C3111yescharacteristic
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8C2×D4×C3112yes—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—41no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—81no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—24no—
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—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—81no—
588C22×C4C2×D4×C3111yescharacteristic
589C22×C4C2×D4×C3111yescharacteristic
590C22×C4C2×D4×C3111yescharacteristic
591C22×C4C2×D4×C3111yescharacteristic
592C22×C4C2×D4×C3112yes—
593C22×C4C2×D4×C3112yes—
594C22×C4C24×C3111yescharacteristic
595SD16—44no—
596M16—44no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8#41×C3112yes—
609C4⋊C4—24no—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—24no—
615C4⋊C4—22no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—42no—
625C4⋊C4—42no—
626C4⋊C4C2×D4×C3112yes—
627C4⋊C4C2×D4×C3112yes—
628C4⋊C4C2×D4×C3112yes—
629C4⋊C4#41×C3112yes—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—22no—
634C22⋊C4—22no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—81no—
640C42—24no—
641C42—24no—
642C42—21no—
643C42—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23C31×#12012yes—
664C23C31×AGL(1,ℤ/8)12yes—
665C23C22×D4×C3111yescharacteristic
666Q8—22no—
667Q8—22no—
668Q8—41no—
669Q8—41no—
670D4—44no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—84no—
676D4—84no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—22no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—48no—
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—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—84no—
719C2×C4C31×#12012yes—
720C2×C4C22×D4×C3111yescharacteristic
721C2×C4C22×D4×C3111yescharacteristic
722C2×C4C2×#41×C3111yescharacteristic
723C2×C4C2×#41×C3111yescharacteristic
724C2×C4C31×H(5,𝔽2)11yescharacteristic
725C2×C4C31×2−1+411yescharacteristic
726C8—22no—
727C8—41no—
728C8—41no—
729C8—41no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22C2×C31×#12011yescharacteristic
752C22C31×#54611yescharacteristic
753C22C31×#54711yescharacteristic
754C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
755C22C31×#57511yescharacteristic
756C22C31×#57711yescharacteristic
757C22C31×#57811yescharacteristic
758C4—22no—
759C4—41no—
760C4—42no—
761C4—41no—
762C4—42no—
763C4—42no—
764C4—41no—
765C4—42no—
766C4—42no—
767C4—81no—
768C4—81no—
769C4C31×#53211yescharacteristic
770C4C31×#53711yescharacteristic
771C4C31×#54611yescharacteristic
772C4C31×#54711yescharacteristic
773C2—42no—
774C2—42no—
775C2—161no—
776C2C31×#243011yescharacteristic
777C2C31×#300611yescharacteristic
778C2C31×#301311yescharacteristic
779C2C31×#331011yescharacteristic
780C2C31×#332711yescharacteristic
781C2C31×#334311yescharacteristic
782C2C31×#335111yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#2416C2
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
1. C2×C31×#552C2semidirect
2. C2×C31×#482C2semidirect
3. C2×C31×#468C2semidirect
5. C31×#2059C2semidirect
6. C31×#2035C2semidirect
7. C31×#2025C2semidirect
8. C31×#2000C2semidirect
9. C31×#1880C2semidirect
10. C31×#1874C2semidirect
11. C31×#1872C2semidirect
12. C31×#1870C2semidirect
13. C31×#1863C2semidirect
14. C31×#1852C2semidirect
15. C31×#1736C2semidirect
90. C31×C22⋊Q8D4semidirect
102. C31×#117D4semidirect
252. #25560C31direct (N × H)
339. C2×#552C2×C31semidirect
340. C2×#482C2×C31semidirect
341. C2×#468C2×C31semidirect
343. #2059C2×C31semidirect
344. #2035C2×C31semidirect
345. #2025C2×C31semidirect
346. #2000C2×C31semidirect
347. #1880C2×C31semidirect
348. #1874C2×C31semidirect
349. #1872C2×C31semidirect
350. #1870C2×C31semidirect
351. #1863C2×C31semidirect
352. #1852C2×C31semidirect
353. #1736C2×C31semidirect
481. C22⋊Q8D4×C31semidirect
493. #117D4×C31semidirect
540. C31#25560direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5522
C2×C31×#4822
C2×C31×#4682
C31×#24162
C31×#20592
C31×#20352
C31×#20252
C31×#20002
C31×#18802
C31×#18742
C31×#18722
C31×#18702
C31×#18632
C31×#18522
C31×#17362
#2556031