Finite Group Databasebeta

← C31×#25232 #21481991

Subgroups — C31×#25232 #21481991

Order 7936.

988 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#480C211yesmaximal, characteristic, complemented
2C2×C8×D4×C31C211yesmaximal, characteristic, complemented
3C31×#2486C211yesmaximal, characteristic, complemented
4C31×#2416C211yesmaximal, characteristic
5C31×#2086C211yesmaximal, characteristic, complemented
6C31×#2075C211yesmaximal, characteristic, complemented
7C31×#2067C211yesmaximal, characteristic, complemented
8C31×#2033C211yesmaximal, characteristic, complemented
9C31×#1942C211yesmaximal, characteristic, complemented
10C31×#1934C211yesmaximal, characteristic, complemented
11C31×#1893C211yesmaximal, characteristic, complemented
12C31×#1893C211yesmaximal, characteristic, complemented
13C31×#1852C211yesmaximal, characteristic, complemented
14C31×#1808C211yesmaximal, characteristic, complemented
15C2×C31×#340C211yesmaximal, characteristic, complemented
16C23×C8×C31C2211yescharacteristic
17C23×C8×C31C2211yescharacteristic
18C2×C31×#123—21no—
19C2×C31×#121—21no—
20C2×C31×#121C2211yescharacteristic
21C2×C31×#121C2211yescharacteristic
22C2×C4×D4×C31C2211yescharacteristic
23C22×C4⋊C4×C31C2211yescharacteristic
24C22×C4⋊C4×C31C2211yescharacteristic
25C31×#480—24no—
26C8×D4×C31—24no—
27C2×C31×#107C2211yescharacteristic
28C2×C31×#107C2211yescharacteristic
29C2×C31×#107C2211yescharacteristic
30C2×C31×#107C2211yescharacteristic
31C2×C31×C4⋊C8C2211yescharacteristic
32C2×C31×#102C2211yescharacteristic
33C2×C31×#102C2211yescharacteristic
34C2×C31×#102C2211yescharacteristic
35C2×C31×#102C2211yescharacteristic
36C2×C31×C22⋊C8C2211yescharacteristic
37C2×C31×C22⋊C8C2211yescharacteristic
38C2×C4×C8×C31C2211yescharacteristic
39C31×#398—21no—
40C31×#397—21no—
41C31×#396—21no—
42C31×#394—21no—
43C31×#390C2211yescharacteristic
44C31×#389C2211yescharacteristic
45C31×#389C2211yescharacteristic
46C31×#389C2211yescharacteristic
47C31×#386—21no—
48C31×#381—21no—
49C31×#380C2211yescharacteristic
50C31×#380C2211yescharacteristic
51C31×#380C2211yescharacteristic
52C31×#380C2211yescharacteristic
53C31×#340C2211yescharacteristic
54C31×#340C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C22×D4×C31—21no—
62C22×D4×C31—21no—
63C22×D4×C31D411yescharacteristic
64C22×D4×C31C2311yescharacteristic
65C23×C4×C31—21no—
66C23×C4×C31—21no—
67C23×C4×C31C2311yescharacteristic
68C23×C4×C31C2311yescharacteristic
69C22×C8×C31—22no—
70C22×C8×C31—22no—
71C22×C8×C31—22no—
72C22×C8×C31—22no—
73C22×C8×C31—41no—
74C22×C8×C31—41no—
75C22×C8×C31C2311yescharacteristic
76C22×C8×C31C2311yescharacteristic
77C22×C8×C31C2311yescharacteristic
78C22×C8×C31C2311yescharacteristic
79C31×#123—44no—
80C31×#121—22no—
81C31×#121—22no—
82C31×#121—22no—
83C31×#121—41no—
84C31×#121—44no—
85C4×D4×C31—22no—
86C4×D4×C31—22no—
87C2×C4⋊C4×C31—22no—
88C2×C4⋊C4×C31—22no—
89C2×C4⋊C4×C31—22no—
90C2×C4⋊C4×C31—21no—
91C2×C4⋊C4×C31—21no—
92C2×C4⋊C4×C31—21no—
93C2×C4⋊C4×C31—21no—
94C2×C4⋊C4×C31—21no—
95C2×C4⋊C4×C31—41no—
96C2×C4⋊C4×C31D411yescharacteristic
97C2×C4⋊C4×C31C2311yescharacteristic
98C2×C4⋊C4×C31C2311yescharacteristic
99C2×C4⋊C4×C31C2311yescharacteristic
100C2×C4⋊C4×C31C2311yescharacteristic
101C2×C4⋊C4×C31C2311yescharacteristic
102C2×C4⋊C4×C31C2311yescharacteristic
103C2×C4⋊C4×C31C2311yescharacteristic
104C2×C22⋊C4×C31—21no—
105C2×C22⋊C4×C31—21no—
106C2×C22⋊C4×C31—21no—
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×C31D411yescharacteristic
113C2×C22⋊C4×C31D411yescharacteristic
114C2×C42×C31C2311yescharacteristic
115C31×#107—22no—
116C31×#107—22no—
117C31×#107—22no—
118C31×#107—41no—
119C31×C4⋊C8—22no—
120C31×#102—22no—
121C31×#102—22no—
122C31×#102—22no—
123C31×#102—41no—
124C31×C22⋊C8—22no—
125C31×C22⋊C8D414yescomplemented
126C4×C8×C31—22no—
127C31×#95—21no—
128C31×#95—21no—
129C31×#95—21no—
130C31×#95—21no—
131C31×#95—21no—
132C31×#95—21no—
133C31×#95—21no—
134C24×C31—21no—
135C24×C31C2×D411yescharacteristic
136C24×C31C2×D411yescharacteristic
137C2×D4×C31—22no—
138C2×D4×C31—22no—
139C2×D4×C31—21no—
140C2×D4×C31—21no—
141C2×D4×C31—21no—
142C2×D4×C31—21no—
143C2×D4×C31—21no—
144C2×D4×C31—21no—
145C2×D4×C31—42no—
146C2×D4×C31—42no—
147C2×D4×C31—42no—
148C2×D4×C31—42no—
149C2×D4×C31—42no—
150C2×D4×C31—81no—
151C2×D4×C31D814yes—
152C22×C4×C31—21no—
153C22×C4×C31—21no—
154C22×C4×C31—21no—
155C22×C4×C31—21no—
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—21no—
165C22×C4×C31—21no—
166C22×C4×C31—21no—
167C22×C4×C31—21no—
168C22×C4×C31—21no—
169C22×C4×C31—42no—
170C22×C4×C31—42no—
171C22×C4×C31—42no—
172C22×C4×C31—42no—
173C22×C4×C31—42no—
174C22×C4×C31—81no—
175C22×C4×C31C2×D411yescharacteristic
176C22×C4×C31C2×D411yescharacteristic
177C22×C4×C31C2×D411yescharacteristic
178C22×C4×C31C2×D412yes—
179C22×C4×C31C2×D411yescharacteristic
180C22×C4×C31#4112yes—
181C22×C4×C31C2411yescharacteristic
182C2×C8×C31—21no—
183C2×C8×C31—21no—
184C2×C8×C31—21no—
185C2×C8×C31—21no—
186C2×C8×C31—21no—
187C2×C8×C31—21no—
188C2×C8×C31—21no—
189C2×C8×C31—21no—
190C2×C8×C31—21no—
191C2×C8×C31—44no—
192C2×C8×C31—44no—
193C2×C8×C31C2×D412yes—
194C2×C8×C31C2×D412yes—
195C2×C8×C31#4112yes—
196C4⋊C4×C31—22no—
197C4⋊C4×C31—21no—
198C4⋊C4×C31—21no—
199C4⋊C4×C31—21no—
200C4⋊C4×C31—21no—
201C4⋊C4×C31—21no—
202C4⋊C4×C31—21no—
203C4⋊C4×C31—21no—
204C4⋊C4×C31—21no—
205C4⋊C4×C31—21no—
206C4⋊C4×C31—21no—
207C4⋊C4×C31—21no—
208C4⋊C4×C31—21no—
209C4⋊C4×C31—21no—
210C4⋊C4×C31—42no—
211C4⋊C4×C31—42no—
212C4⋊C4×C31—42no—
213C4⋊C4×C31—42no—
214C4⋊C4×C31—42no—
215C4⋊C4×C31#4112yes—
216C22⋊C4×C31—22no—
217C22⋊C4×C31—22no—
218C22⋊C4×C31—42no—
219C22⋊C4×C31—42no—
220C22⋊C4×C31—42no—
221C22⋊C4×C31—42no—
222C22⋊C4×C31—42no—
223C22⋊C4×C31—42no—
224C22⋊C4×C31—42no—
225C22⋊C4×C31—81no—
226C42×C31—21no—
227C42×C31—21no—
228#25232C3111yesmaximal, characteristic, direct product factor, Sylow
229C23×C31—21no—
230C23×C31—21no—
231C23×C31—21no—
232C23×C31—21no—
233C23×C31—21no—
234C23×C31—21no—
235C23×C31—21no—
236C23×C31—21no—
237C23×C31—21no—
238C23×C31—21no—
239C23×C31—41no—
240C23×C31—41no—
241C23×C31—41no—
242C23×C31—41no—
243C23×C31—41no—
244C23×C31—41no—
245C23×C31—41no—
246C23×C31#12112yes—
247C23×C31C2×D812yes—
248C23×C31C2×D812yes—
249C23×C31#13512yes—
250C23×C31C22×D411yescharacteristic
251D4×C31—28no—
252D4×C31—41no—
253D4×C31—41no—
254D4×C31—41no—
255D4×C31—41no—
256D4×C31—84no—
257D4×C31—84no—
258C2×C4×C31—21no—
259C2×C4×C31—21no—
260C2×C4×C31—21no—
261C2×C4×C31—21no—
262C2×C4×C31—22no—
263C2×C4×C31—22no—
264C2×C4×C31—22no—
265C2×C4×C31—22no—
266C2×C4×C31—21no—
267C2×C4×C31—21no—
268C2×C4×C31—21no—
269C2×C4×C31—22no—
270C2×C4×C31—21no—
271C2×C4×C31—21no—
272C2×C4×C31—21no—
273C2×C4×C31—41no—
274C2×C4×C31—41no—
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—84no—
298C2×C4×C31—84no—
299C2×C4×C31#12112yes—
300C2×C4×C31C2×D812yes—
301C2×C4×C31C22×D411yescharacteristic
302C2×C4×C31C2×#4111yescharacteristic
303C2×C4×C31C2×#4111yescharacteristic
304C2×C4×C31C2×#4111yescharacteristic
305C2×C4×C31H(5,𝔽2)11yescharacteristic
306C2×C4×C312−1+411yescharacteristic
307C8×C31—22no—
308C8×C31—22no—
309C8×C31—22no—
310C8×C31—41no—
311C2×#480C2×C3111yescharacteristic, complemented
312C2×C8×D4C2×C3111yescharacteristic, complemented
313#2486C2×C3111yescharacteristic, complemented
314#2416C2×C3111yescharacteristic
315#2086C2×C3111yescharacteristic, complemented
316#2075C2×C3111yescharacteristic, complemented
317#2067C2×C3111yescharacteristic, complemented
318#2033C2×C3111yescharacteristic, complemented
319#1942C2×C3111yescharacteristic, complemented
320#1934C2×C3111yescharacteristic, complemented
321#1893C2×C3111yescharacteristic, complemented
322#1893C2×C3111yescharacteristic, complemented
323#1852C2×C3111yescharacteristic, complemented
324#1808C2×C3111yescharacteristic, complemented
325C2×#340C2×C3111yescharacteristic, complemented
326C22×C31—22no—
327C22×C31—22no—
328C22×C31—22no—
329C22×C31—22no—
330C22×C31—22no—
331C22×C31—22no—
332C22×C31—22no—
333C22×C31—22no—
334C22×C31—22no—
335C22×C31—41no—
336C22×C31—41no—
337C22×C31—41no—
338C22×C31—41no—
339C22×C31—81no—
340C22×C31—81no—
341C22×C31—81no—
342C22×C31—81no—
343C22×C31—81no—
344C22×C31—81no—
345C22×C31—81no—
346C22×C31#46614yes—
347C22×C31C2×#12111yescharacteristic
348C22×C31#54611yescharacteristic
349C22×C31#54711yescharacteristic
350C22×C31C22×D811yescharacteristic
351C22×C31C2×#13511yescharacteristic
352C22×C31#57711yescharacteristic
353C22×C31#57811yescharacteristic
354C4×C31—22no—
355C4×C31—22no—
356C4×C31—41no—
357C4×C31—42no—
358C4×C31—41no—
359C4×C31—81no—
360C4×C31—81no—
361C4×C31—81no—
362C4×C31—81no—
363C4×C31—81no—
364C4×C31—81no—
365C4×C31#52911yescharacteristic
366C4×C31#53911yescharacteristic
367C4×C31#54611yescharacteristic
368C4×C31#54711yescharacteristic
369C23×C8C22×C3111yescharacteristic
370C23×C8C22×C3111yescharacteristic
371C2×#123—21no—
372C2×#121—21no—
373C2×#121C22×C3111yescharacteristic
374C2×#121C22×C3111yescharacteristic
375C2×C4×D4C22×C3111yescharacteristic
376C22×C4⋊C4C22×C3111yescharacteristic
377C22×C4⋊C4C22×C3111yescharacteristic
378#480—24no—
379C8×D4—24no—
380C2×#107C22×C3111yescharacteristic
381C2×#107C22×C3111yescharacteristic
382C2×#107C22×C3111yescharacteristic
383C2×#107C22×C3111yescharacteristic
384C2×C4⋊C8C22×C3111yescharacteristic
385C2×#102C22×C3111yescharacteristic
386C2×#102C22×C3111yescharacteristic
387C2×#102C22×C3111yescharacteristic
388C2×#102C22×C3111yescharacteristic
389C2×C22⋊C8C22×C3111yescharacteristic
390C2×C22⋊C8C22×C3111yescharacteristic
391C2×C4×C8C22×C3111yescharacteristic
392#398—21no—
393#397—21no—
394#396—21no—
395#394—21no—
396#390C22×C3111yescharacteristic
397#389C22×C3111yescharacteristic
398#389C22×C3111yescharacteristic
399#389C22×C3111yescharacteristic
400#386—21no—
401#381—21no—
402#380C22×C3111yescharacteristic
403#380C22×C3111yescharacteristic
404#380C22×C3111yescharacteristic
405#380C22×C3111yescharacteristic
406#340C22×C3111yescharacteristic
407#340C22×C3111yescharacteristic
408#340C22×C3111yescharacteristic
409#340C22×C3111yescharacteristic
410#340C22×C3111yescharacteristic
411#340C22×C3111yescharacteristic
412#340C22×C3111yescharacteristic
413#340C22×C3111yescharacteristic
414C2×C31—24no—
415C2×C31—42no—
416C2×C31—161no—
417C2×C31#242511yescharacteristic
418C2×C31C2×#46611yescharacteristic
419C2×C31#306311yescharacteristic
420C2×C31#329411yescharacteristic
421C2×C31#330011yescharacteristic
422C2×C31#333411yescharacteristic
423C2×C31#333711yescharacteristic
424C22×D4—21no—
425C22×D4—21no—
426C22×D4D4×C3111yescharacteristic
427C22×D4C23×C3111yescharacteristic
428C23×C4—21no—
429C23×C4—21no—
430C23×C4C23×C3111yescharacteristic
431C23×C4C23×C3111yescharacteristic
432C22×C8—22no—
433C22×C8—22no—
434C22×C8—22no—
435C22×C8—22no—
436C22×C8—41no—
437C22×C8—41no—
438C22×C8C23×C3111yescharacteristic
439C22×C8C23×C3111yescharacteristic
440C22×C8C23×C3111yescharacteristic
441C22×C8C23×C3111yescharacteristic
442#123—44no—
443#121—22no—
444#121—22no—
445#121—22no—
446#121—41no—
447#121—44no—
448C4×D4—22no—
449C4×D4—22no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—41no—
459C2×C4⋊C4D4×C3111yescharacteristic
460C2×C4⋊C4C23×C3111yescharacteristic
461C2×C4⋊C4C23×C3111yescharacteristic
462C2×C4⋊C4C23×C3111yescharacteristic
463C2×C4⋊C4C23×C3111yescharacteristic
464C2×C4⋊C4C23×C3111yescharacteristic
465C2×C4⋊C4C23×C3111yescharacteristic
466C2×C4⋊C4C23×C3111yescharacteristic
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4D4×C3111yescharacteristic
476C2×C22⋊C4D4×C3111yescharacteristic
477C2×C42C23×C3111yescharacteristic
478#107—22no—
479#107—22no—
480#107—22no—
481#107—41no—
482C4⋊C8—22no—
483#102—22no—
484#102—22no—
485#102—22no—
486#102—41no—
487C22⋊C8—22no—
488C22⋊C8D4×C3114yescomplemented
489C4×C8—22no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95—21no—
497C31#2523211yescharacteristic, direct product factor, Sylow
498C24—21no—
499C24C2×D4×C3111yescharacteristic
500C24C2×D4×C3111yescharacteristic
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—42no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—42no—
513C2×D4—42no—
514C2×D4—81no—
515C2×D4D8×C3114yes—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
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—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—81no—
539C22×C4C2×D4×C3111yescharacteristic
540C22×C4C2×D4×C3111yescharacteristic
541C22×C4C2×D4×C3111yescharacteristic
542C22×C4C2×D4×C3112yes—
543C22×C4C2×D4×C3111yescharacteristic
544C22×C4#41×C3112yes—
545C22×C4C24×C3111yescharacteristic
546C2×C8—21no—
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—44no—
556C2×C8—44no—
557C2×C8C2×D4×C3112yes—
558C2×C8C2×D4×C3112yes—
559C2×C8#41×C3112yes—
560C4⋊C4—22no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
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—42no—
575C4⋊C4—42no—
576C4⋊C4—42no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4#41×C3112yes—
580C22⋊C4—22no—
581C22⋊C4—22no—
582C22⋊C4—42no—
583C22⋊C4—42no—
584C22⋊C4—42no—
585C22⋊C4—42no—
586C22⋊C4—42no—
587C22⋊C4—42no—
588C22⋊C4—42no—
589C22⋊C4—81no—
590C42—21no—
591C42—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23C31×#12112yes—
610C23C2×D8×C3112yes—
611C23C2×D8×C3112yes—
612C23C31×#13512yes—
613C23C22×D4×C3111yescharacteristic
614D4—28no—
615D4—41no—
616D4—41no—
617D4—41no—
618D4—41no—
619D4—84no—
620D4—84no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—22no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
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—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—84no—
661C2×C4—84no—
662C2×C4C31×#12112yes—
663C2×C4C2×D8×C3112yes—
664C2×C4C22×D4×C3111yescharacteristic
665C2×C4C2×#41×C3111yescharacteristic
666C2×C4C2×#41×C3111yescharacteristic
667C2×C4C2×#41×C3111yescharacteristic
668C2×C4C31×H(5,𝔽2)11yescharacteristic
669C2×C4C31×2−1+411yescharacteristic
670C8—22no—
671C8—22no—
672C8—22no—
673C8—41no—
674C22—22no—
675C22—22no—
676C22—22no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—41no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22—81no—
692C22—81no—
693C22—81no—
694C22C31×#46614yes—
695C22C2×C31×#12111yescharacteristic
696C22C31×#54611yescharacteristic
697C22C31×#54711yescharacteristic
698C22C22×D8×C3111yescharacteristic
699C22C2×C31×#13511yescharacteristic
700C22C31×#57711yescharacteristic
701C22C31×#57811yescharacteristic
702C4—22no—
703C4—22no—
704C4—41no—
705C4—42no—
706C4—41no—
707C4—81no—
708C4—81no—
709C4—81no—
710C4—81no—
711C4—81no—
712C4—81no—
713C4C31×#52911yescharacteristic
714C4C31×#53911yescharacteristic
715C4C31×#54611yescharacteristic
716C4C31×#54711yescharacteristic
717C2—24no—
718C2—42no—
719C2—161no—
720C2C31×#242511yescharacteristic
721C2C2×C31×#46611yescharacteristic
722C2C31×#306311yescharacteristic
723C2C31×#329411yescharacteristic
724C2C31×#330011yescharacteristic
725C2C31×#333411yescharacteristic
726C2C31×#333711yescharacteristic
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×#480C2semidirect
2. C2×C8×D4×C31C2semidirect
3. C31×#2486C2semidirect
5. C31×#2086C2semidirect
6. C31×#2075C2semidirect
7. C31×#2067C2semidirect
8. C31×#2033C2semidirect
9. C31×#1942C2semidirect
10. C31×#1934C2semidirect
11. C31×#1893C2semidirect
12. C31×#1893C2semidirect
13. C31×#1852C2semidirect
14. C31×#1808C2semidirect
15. C2×C31×#340C2semidirect
125. C31×C22⋊C8D4semidirect
228. #25232C31direct (N × H)
311. C2×#480C2×C31semidirect
312. C2×C8×D4C2×C31semidirect
313. #2486C2×C31semidirect
315. #2086C2×C31semidirect
316. #2075C2×C31semidirect
317. #2067C2×C31semidirect
318. #2033C2×C31semidirect
319. #1942C2×C31semidirect
320. #1934C2×C31semidirect
321. #1893C2×C31semidirect
322. #1893C2×C31semidirect
323. #1852C2×C31semidirect
324. #1808C2×C31semidirect
325. C2×#340C2×C31semidirect
488. C22⋊C8D4×C31semidirect
497. C31#25232direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4802
C2×C8×D4×C312
C31×#24862
C31×#24162
C31×#20862
C31×#20752
C31×#20672
C31×#20332
C31×#19422
C31×#19342
C31×#18932
C31×#18522
C31×#18082
C2×C31×#3402
#2523231