Finite Group Databasebeta

← C31×#24109 #21480868

Subgroups — C31×#24109 #21480868

Order 7936.

1084 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#554C211yesmaximal, characteristic
2C2×C31×#485C211yesmaximal, characteristic, complemented
3C2×C31×#428C211yesmaximal, characteristic, complemented
4C31×#2485C211yesmaximal, characteristic
5C31×#2058C211yesmaximal, characteristic, complemented
6C31×#2057C211yesmaximal, characteristic, complemented
7C31×#2036C211yesmaximal, characteristic, complemented
8C31×#2035C211yesmaximal, characteristic, complemented
9C31×#1894C211yesmaximal, characteristic, complemented
10C31×#1870C211yesmaximal, characteristic
11C31×#1865C211yesmaximal, characteristic, complemented
12C31×#1863C211yesmaximal, characteristic, complemented
13C31×#1853C211yesmaximal, characteristic, complemented
14C31×#1852C211yesmaximal, characteristic, complemented
15C31×#1823C211yesmaximal, characteristic, complemented
16C22×M16×C31C2211yescharacteristic
17C31×#554—24no—
18C31×#554—24no—
19C2×C31×C4⋊Q8C2211yescharacteristic
20C2×C31×#125—21no—
21C2×C31×C22⋊Q8—21no—
22C2×C31×C22⋊Q8—21no—
23C2×C31×C22⋊Q8C2211yescharacteristic
24C2×C31×C22⋊Q8C2211yescharacteristic
25C2×C4×Q8×C31C2211yescharacteristic
26C2×C4×D4×C31—21no—
27C2×C4×D4×C31C2211yescharacteristic
28C2×C31×#117C2211yescharacteristic
29C22×C4⋊C4×C31C2211yescharacteristic
30C22×C4⋊C4×C31C2211yescharacteristic
31C31×#485—24no—
32C31×#428—24no—
33C2×C31×#107C2211yescharacteristic
34C2×C31×#107C2211yescharacteristic
35C2×C31×#107C2211yescharacteristic
36C2×C31×#106C2211yescharacteristic
37C2×C31×#106C2211yescharacteristic
38C2×C31×#106C2211yescharacteristic
39C2×C31×#103C2211yescharacteristic
40C2×C31×#103C2211yescharacteristic
41C2×C31×#103C2211yescharacteristic
42C2×C31×#103C2211yescharacteristic
43C2×C31×C22⋊C8C2211yescharacteristic
44C2×C31×C22⋊C8C2211yescharacteristic
45C2×C31×C22⋊C8C2211yescharacteristic
46C31×#397—21no—
47C31×#394—21no—
48C31×#389C2211yescharacteristic
49C31×#389C2211yescharacteristic
50C31×#388—21no—
51C31×#387—21no—
52C31×#380C2211yescharacteristic
53C31×#380C2211yescharacteristic
54C31×#380C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C31×#336C2211yescharacteristic
63C22×Q8×C31—21no—
64C22×Q8×C31C2311yescharacteristic
65C22×D4×C31D411yescharacteristic
66C23×C4×C31—21no—
67C23×C4×C31—21no—
68C23×C4×C31C2311yescharacteristic
69C23×C4×C31C2311yescharacteristic
70C2×M16×C31—22no—
71C2×M16×C31—22no—
72C2×M16×C31—22no—
73C22×C8×C31C2311yescharacteristic
74C22×C8×C31C2311yescharacteristic
75C22×C8×C31C2311yescharacteristic
76C22×C8×C31C2311yescharacteristic
77C31×C4⋊Q8—22no—
78C31×C4⋊Q8—22no—
79C31×#125—28no—
80C31×C22⋊Q8—28no—
81C31×C22⋊Q8—28no—
82C31×C22⋊Q8—22no—
83C31×C22⋊Q8—22no—
84C31×C22⋊Q8—22no—
85C31×C22⋊Q8D414yes—
86C4×Q8×C31—22no—
87C4×Q8×C31—22no—
88C4×D4×C31—28no—
89C4×D4×C31—22no—
90C4×D4×C31—22no—
91C31×#117—22no—
92C31×#117—22no—
93C2×C4⋊C4×C31—21no—
94C2×C4⋊C4×C31—21no—
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×C31—22no—
101C2×C4⋊C4×C31—22no—
102C2×C4⋊C4×C31—21no—
103C2×C4⋊C4×C31—21no—
104C2×C4⋊C4×C31D411yescharacteristic
105C2×C4⋊C4×C31D414yes—
106C2×C4⋊C4×C31C2311yescharacteristic
107C2×C4⋊C4×C31C2311yescharacteristic
108C2×C4⋊C4×C31C2311yescharacteristic
109C2×C4⋊C4×C31C2311yescharacteristic
110C2×C4⋊C4×C31C2311yescharacteristic
111C2×C4⋊C4×C31C2311yescharacteristic
112C2×C4⋊C4×C31C2311yescharacteristic
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×C22⋊C4×C31—21no—
119C2×C22⋊C4×C31D411yescharacteristic
120C2×C22⋊C4×C31D411yescharacteristic
121C2×C42×C31—21no—
122C2×C42×C31—21no—
123C2×C42×C31C2311yescharacteristic
124C31×#107—22no—
125C31×#107—22no—
126C31×#107—22no—
127C31×#106—22no—
128C31×#106—22no—
129C31×#106—22no—
130C31×#103—22no—
131C31×#103—22no—
132C31×#103—22no—
133C31×#103—22no—
134C31×C22⋊C8—22no—
135C31×C22⋊C8—22no—
136C31×C22⋊C8—22no—
137C31×#95—21no—
138C31×#95—21no—
139C31×#95—21no—
140C31×#95—21no—
141C31×#95—21no—
142C24×C31C2×D411yescharacteristic
143C24×C31C2×D411yescharacteristic
144C2×Q8×C31—24no—
145C2×Q8×C31—21no—
146C2×Q8×C31—21no—
147C2×Q8×C31—21no—
148C2×Q8×C31—21no—
149C2×Q8×C31—21no—
150C2×Q8×C31—81no—
151C2×Q8×C31—81no—
152C2×Q8×C31C2×D412yes—
153C2×D4×C31—22no—
154C2×D4×C31—22no—
155C2×D4×C31—22no—
156C22×C4×C31—21no—
157C22×C4×C31—21no—
158C22×C4×C31—21no—
159C22×C4×C31—21no—
160C22×C4×C31—21no—
161C22×C4×C31—21no—
162C22×C4×C31—21no—
163C22×C4×C31—21no—
164C22×C4×C31—24no—
165C22×C4×C31—24no—
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—81no—
177C22×C4×C31—81no—
178C22×C4×C31—81no—
179C22×C4×C31—81no—
180C22×C4×C31C2×D411yescharacteristic
181C22×C4×C31C2×D411yescharacteristic
182C22×C4×C31C2×D411yescharacteristic
183C22×C4×C31C2×D412yes—
184C22×C4×C31C2×D412yes—
185C22×C4×C31C2×D411yescharacteristic
186C22×C4×C31C2411yescharacteristic
187M16×C31—28no—
188C2×C8×C31—21no—
189C2×C8×C31—21no—
190C2×C8×C31—21no—
191C2×C8×C31—21no—
192C2×C8×C31—21no—
193C2×C8×C31—21no—
194C2×C8×C31—21no—
195C2×C8×C31—21no—
196C2×C8×C31—21no—
197C2×C8×C31—21no—
198C2×C8×C31#4112yes—
199C2×C8×C31#4112yes—
200C4⋊C4×C31—24no—
201C4⋊C4×C31—24no—
202C4⋊C4×C31—24no—
203C4⋊C4×C31—24no—
204C4⋊C4×C31—24no—
205C4⋊C4×C31—24no—
206C4⋊C4×C31—22no—
207C4⋊C4×C31—21no—
208C4⋊C4×C31—21no—
209C4⋊C4×C31—21no—
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—42no—
219C4⋊C4×C31—81no—
220C4⋊C4×C31C2×D412yes—
221C4⋊C4×C31C2×D412yes—
222C4⋊C4×C31C2×D412yes—
223C22⋊C4×C31—24no—
224C22⋊C4×C31—24no—
225C22⋊C4×C31—22no—
226C22⋊C4×C31—22no—
227C22⋊C4×C31—42no—
228C22⋊C4×C31—42no—
229C22⋊C4×C31—81no—
230C22⋊C4×C31—81no—
231C42×C31—24no—
232C42×C31—21no—
233C42×C31—21no—
234C42×C31—42no—
235#24109C3111yesmaximal, characteristic, direct product factor, Sylow
236C23×C31—21no—
237C23×C31—21no—
238C23×C31—21no—
239C23×C31—21no—
240C23×C31—21no—
241C23×C31—21no—
242C23×C31—21no—
243C23×C31—21no—
244C23×C31—21no—
245C23×C31—21no—
246C23×C31—21no—
247C23×C31—21no—
248C23×C31#12012yes—
249C23×C31#13712yes—
250C23×C31C22×D411yescharacteristic
251Q8×C31—22no—
252Q8×C31—22no—
253Q8×C31—41no—
254Q8×C31—41no—
255Q8×C31—84no—
256D4×C31—28no—
257C2×C4×C31—21no—
258C2×C4×C31—21no—
259C2×C4×C31—21no—
260C2×C4×C31—21no—
261C2×C4×C31—22no—
262C2×C4×C31—22no—
263C2×C4×C31—22no—
264C2×C4×C31—22no—
265C2×C4×C31—22no—
266C2×C4×C31—21no—
267C2×C4×C31—22no—
268C2×C4×C31—21no—
269C2×C4×C31—22no—
270C2×C4×C31—22no—
271C2×C4×C31—21no—
272C2×C4×C31—21no—
273C2×C4×C31—21no—
274C2×C4×C31—21no—
275C2×C4×C31—41no—
276C2×C4×C31—41no—
277C2×C4×C31—41no—
278C2×C4×C31—41no—
279C2×C4×C31—41no—
280C2×C4×C31—41no—
281C2×C4×C31—41no—
282C2×C4×C31—41no—
283C2×C4×C31—41no—
284C2×C4×C31—41no—
285C2×C4×C31—41no—
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—84no—
300C2×C4×C31—84no—
301C2×C4×C31#12012yes—
302C2×C4×C31#13712yes—
303C2×C4×C31C22×D411yescharacteristic
304C2×C4×C31C22×D411yescharacteristic
305C2×C4×C31C2×#4111yescharacteristic
306C2×C4×C31C2×#4111yescharacteristic
307C2×C4×C312−1+411yescharacteristic
308C2×C4×C312−1+411yescharacteristic
309C8×C31—22no—
310C8×C31—22no—
311C8×C31—41no—
312C8×C31—41no—
313C2×#554C2×C3111yescharacteristic
314C2×#485C2×C3111yescharacteristic, complemented
315C2×#428C2×C3111yescharacteristic, complemented
316#2485C2×C3111yescharacteristic
317#2058C2×C3111yescharacteristic, complemented
318#2057C2×C3111yescharacteristic, complemented
319#2036C2×C3111yescharacteristic, complemented
320#2035C2×C3111yescharacteristic, complemented
321#1894C2×C3111yescharacteristic, complemented
322#1870C2×C3111yescharacteristic
323#1865C2×C3111yescharacteristic, complemented
324#1863C2×C3111yescharacteristic, complemented
325#1853C2×C3111yescharacteristic, complemented
326#1852C2×C3111yescharacteristic, complemented
327#1823C2×C3111yescharacteristic, complemented
328C22×C31—22no—
329C22×C31—22no—
330C22×C31—22no—
331C22×C31—22no—
332C22×C31—22no—
333C22×C31—22no—
334C22×C31—41no—
335C22×C31—41no—
336C22×C31—41no—
337C22×C31—41no—
338C22×C31—41no—
339C22×C31—41no—
340C22×C31—41no—
341C22×C31—41no—
342C22×C31C2×#12011yescharacteristic
343C22×C31#54711yescharacteristic
344C22×C31#54711yescharacteristic
345C22×C31C2×#13711yescharacteristic
346C22×C31C2×#13711yescharacteristic
347C22×C31#57611yescharacteristic
348C22×C31#57711yescharacteristic
349C4×C31—22no—
350C4×C31—22no—
351C4×C31—41no—
352C4×C31—42no—
353C4×C31—41no—
354C4×C31—42no—
355C4×C31—42no—
356C4×C31—42no—
357C4×C31—81no—
358C4×C31—81no—
359C4×C31—81no—
360C4×C31—81no—
361C4×C31#52511yescharacteristic
362C4×C31#53611yescharacteristic
363C4×C31#54711yescharacteristic
364C4×C31#54711yescharacteristic
365C22×M16C22×C3111yescharacteristic
366#554—24no—
367#554—24no—
368C2×C4⋊Q8C22×C3111yescharacteristic
369C2×#125—21no—
370C2×C22⋊Q8—21no—
371C2×C22⋊Q8—21no—
372C2×C22⋊Q8C22×C3111yescharacteristic
373C2×C22⋊Q8C22×C3111yescharacteristic
374C2×C4×Q8C22×C3111yescharacteristic
375C2×C4×D4—21no—
376C2×C4×D4C22×C3111yescharacteristic
377C2×#117C22×C3111yescharacteristic
378C22×C4⋊C4C22×C3111yescharacteristic
379C22×C4⋊C4C22×C3111yescharacteristic
380#485—24no—
381#428—24no—
382C2×#107C22×C3111yescharacteristic
383C2×#107C22×C3111yescharacteristic
384C2×#107C22×C3111yescharacteristic
385C2×#106C22×C3111yescharacteristic
386C2×#106C22×C3111yescharacteristic
387C2×#106C22×C3111yescharacteristic
388C2×#103C22×C3111yescharacteristic
389C2×#103C22×C3111yescharacteristic
390C2×#103C22×C3111yescharacteristic
391C2×#103C22×C3111yescharacteristic
392C2×C22⋊C8C22×C3111yescharacteristic
393C2×C22⋊C8C22×C3111yescharacteristic
394C2×C22⋊C8C22×C3111yescharacteristic
395#397—21no—
396#394—21no—
397#389C22×C3111yescharacteristic
398#389C22×C3111yescharacteristic
399#388—21no—
400#387—21no—
401#380C22×C3111yescharacteristic
402#380C22×C3111yescharacteristic
403#380C22×C3111yescharacteristic
404#340C22×C3111yescharacteristic
405#340C22×C3111yescharacteristic
406#340C22×C3111yescharacteristic
407#340C22×C3111yescharacteristic
408#340C22×C3111yescharacteristic
409#340C22×C3111yescharacteristic
410#336C22×C3111yescharacteristic
411#336C22×C3111yescharacteristic
412C2×C31—42no—
413C2×C31—42no—
414C2×C31#240611yescharacteristic
415C2×C31#300411yescharacteristic
416C2×C31#301211yescharacteristic
417C2×C31#334411yescharacteristic
418C2×C31#334611yescharacteristic
419C2×C31#335611yescharacteristic
420C2×C31#335711yescharacteristic
421C22×Q8—21no—
422C22×Q8C23×C3111yescharacteristic
423C22×D4D4×C3111yescharacteristic
424C23×C4—21no—
425C23×C4—21no—
426C23×C4C23×C3111yescharacteristic
427C23×C4C23×C3111yescharacteristic
428C2×M16—22no—
429C2×M16—22no—
430C2×M16—22no—
431C22×C8C23×C3111yescharacteristic
432C22×C8C23×C3111yescharacteristic
433C22×C8C23×C3111yescharacteristic
434C22×C8C23×C3111yescharacteristic
435C4⋊Q8—22no—
436C4⋊Q8—22no—
437#125—28no—
438C22⋊Q8—28no—
439C22⋊Q8—28no—
440C22⋊Q8—22no—
441C22⋊Q8—22no—
442C22⋊Q8—22no—
443C22⋊Q8D4×C3114yes—
444C4×Q8—22no—
445C4×Q8—22no—
446C4×D4—28no—
447C4×D4—22no—
448C4×D4—22no—
449#117—22no—
450#117—22no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4D4×C3111yescharacteristic
463C2×C4⋊C4D4×C3114yes—
464C2×C4⋊C4C23×C3111yescharacteristic
465C2×C4⋊C4C23×C3111yescharacteristic
466C2×C4⋊C4C23×C3111yescharacteristic
467C2×C4⋊C4C23×C3111yescharacteristic
468C2×C4⋊C4C23×C3111yescharacteristic
469C2×C4⋊C4C23×C3111yescharacteristic
470C2×C4⋊C4C23×C3111yescharacteristic
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4D4×C3111yescharacteristic
478C2×C22⋊C4D4×C3111yescharacteristic
479C2×C42—21no—
480C2×C42—21no—
481C2×C42C23×C3111yescharacteristic
482#107—22no—
483#107—22no—
484#107—22no—
485#106—22no—
486#106—22no—
487#106—22no—
488#103—22no—
489#103—22no—
490#103—22no—
491#103—22no—
492C22⋊C8—22no—
493C22⋊C8—22no—
494C22⋊C8—22no—
495#95—21no—
496#95—21no—
497#95—21no—
498#95—21no—
499#95—21no—
500C31#2410911yescharacteristic, direct product factor, Sylow
501C24C2×D4×C3111yescharacteristic
502C24C2×D4×C3111yescharacteristic
503C2×Q8—24no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—81no—
510C2×Q8—81no—
511C2×Q8C2×D4×C3112yes—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—22no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—81no—
536C22×C4—81no—
537C22×C4—81no—
538C22×C4—81no—
539C22×C4C2×D4×C3111yescharacteristic
540C22×C4C2×D4×C3111yescharacteristic
541C22×C4C2×D4×C3111yescharacteristic
542C22×C4C2×D4×C3112yes—
543C22×C4C2×D4×C3112yes—
544C22×C4C2×D4×C3111yescharacteristic
545C22×C4C24×C3111yescharacteristic
546M16—28no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8#41×C3112yes—
558C2×C8#41×C3112yes—
559C4⋊C4—24no—
560C4⋊C4—24no—
561C4⋊C4—24no—
562C4⋊C4—24no—
563C4⋊C4—24no—
564C4⋊C4—24no—
565C4⋊C4—22no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—42no—
578C4⋊C4—81no—
579C4⋊C4C2×D4×C3112yes—
580C4⋊C4C2×D4×C3112yes—
581C4⋊C4C2×D4×C3112yes—
582C22⋊C4—24no—
583C22⋊C4—24no—
584C22⋊C4—22no—
585C22⋊C4—22no—
586C22⋊C4—42no—
587C22⋊C4—42no—
588C22⋊C4—81no—
589C22⋊C4—81no—
590C42—24no—
591C42—21no—
592C42—21no—
593C42—42no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23C31×#12012yes—
607C23C31×#13712yes—
608C23C22×D4×C3111yescharacteristic
609Q8—22no—
610Q8—22no—
611Q8—41no—
612Q8—41no—
613Q8—84no—
614D4—28no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—21no—
625C2×C4—22no—
626C2×C4—21no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—84no—
658C2×C4—84no—
659C2×C4C31×#12012yes—
660C2×C4C31×#13712yes—
661C2×C4C22×D4×C3111yescharacteristic
662C2×C4C22×D4×C3111yescharacteristic
663C2×C4C2×#41×C3111yescharacteristic
664C2×C4C2×#41×C3111yescharacteristic
665C2×C4C31×2−1+411yescharacteristic
666C2×C4C31×2−1+411yescharacteristic
667C8—22no—
668C8—22no—
669C8—41no—
670C8—41no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22—22no—
675C22—22no—
676C22—22no—
677C22—41no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22C2×C31×#12011yescharacteristic
686C22C31×#54711yescharacteristic
687C22C31×#54711yescharacteristic
688C22C2×C31×#13711yescharacteristic
689C22C2×C31×#13711yescharacteristic
690C22C31×#57611yescharacteristic
691C22C31×#57711yescharacteristic
692C4—22no—
693C4—22no—
694C4—41no—
695C4—42no—
696C4—41no—
697C4—42no—
698C4—42no—
699C4—42no—
700C4—81no—
701C4—81no—
702C4—81no—
703C4—81no—
704C4C31×#52511yescharacteristic
705C4C31×#53611yescharacteristic
706C4C31×#54711yescharacteristic
707C4C31×#54711yescharacteristic
708C2—42no—
709C2—42no—
710C2C31×#240611yescharacteristic
711C2C31×#300411yescharacteristic
712C2C31×#301211yescharacteristic
713C2C31×#334411yescharacteristic
714C2C31×#334611yescharacteristic
715C2C31×#335611yescharacteristic
716C2C31×#335711yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC22×D4×C31D4
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×#485C2semidirect
3. C2×C31×#428C2semidirect
5. C31×#2058C2semidirect
6. C31×#2057C2semidirect
7. C31×#2036C2semidirect
8. C31×#2035C2semidirect
9. C31×#1894C2semidirect
11. C31×#1865C2semidirect
12. C31×#1863C2semidirect
13. C31×#1853C2semidirect
14. C31×#1852C2semidirect
15. C31×#1823C2semidirect
235. #24109C31direct (N × H)
314. C2×#485C2×C31semidirect
315. C2×#428C2×C31semidirect
317. #2058C2×C31semidirect
318. #2057C2×C31semidirect
319. #2036C2×C31semidirect
320. #2035C2×C31semidirect
321. #1894C2×C31semidirect
323. #1865C2×C31semidirect
324. #1863C2×C31semidirect
325. #1853C2×C31semidirect
326. #1852C2×C31semidirect
327. #1823C2×C31semidirect
500. C31#24109direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5542
C2×C31×#4852
C2×C31×#4282
C31×#24852
C31×#20582
C31×#20572
C31×#20362
C31×#20352
C31×#18942
C31×#18702
C31×#18652
C31×#18632
C31×#18532
C31×#18522
C31×#18232
#2410931