Finite Group Databasebeta

← C31×#24335 #21481094

Subgroups — C31×#24335 #21481094

Order 7936.

1118 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#554C211yesmaximal, characteristic, complemented
2C2×C31×#478C211yesmaximal, characteristic, complemented
3C2×C4×D8×C31C211yesmaximal, characteristic
4C31×#2580C211yesmaximal, characteristic, complemented
5C31×#2059C211yesmaximal, characteristic, complemented
6C31×#2057C211yesmaximal, characteristic, complemented
7C31×#2025C211yesmaximal, characteristic, complemented
8C31×#2023C211yesmaximal, characteristic, complemented
9C31×#1991C211yesmaximal, characteristic, complemented
10C31×#1984C211yesmaximal, characteristic, complemented
11C31×#1879C211yesmaximal, characteristic
12C31×#1879C211yesmaximal, characteristic
13C31×#1864C211yesmaximal, characteristic, complemented
14C31×#1862C211yesmaximal, characteristic, complemented
15C31×#1804C211yesmaximal, characteristic, complemented
16C22×D8×C31C2211yescharacteristic
17C31×#554—24no—
18C31×#554—24no—
19C2×C31×C4⋊Q8C2211yescharacteristic
20C2×C31×#125C2211yescharacteristic
21C2×C31×#125C2211yescharacteristic
22C2×C31×C22⋊Q8—21no—
23C2×C31×C22⋊Q8—21no—
24C2×C31×C22⋊Q8—21no—
25C2×C4×Q8×C31C2211yescharacteristic
26C2×C4×D4×C31C2211yescharacteristic
27C2×C4×D4×C31C2211yescharacteristic
28C2×C4×D4×C31C2211yescharacteristic
29C2×C4×D4×C31C2211yescharacteristic
30C22×C4⋊C4×C31—21no—
31C31×#478—24no—
32C4×D8×C31—24no—
33C2×C31×#107C2211yescharacteristic
34C2×C31×#107C2211yescharacteristic
35C2×C31×#106C2211yescharacteristic
36C2×C31×C4⋊C8C2211yescharacteristic
37C2×C31×#102C2211yescharacteristic
38C2×C31×#102C2211yescharacteristic
39C2×C31×#102C2211yescharacteristic
40C2×C31×#102C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C4×C8×C31C2211yescharacteristic
44C31×#399—21no—
45C31×#393—21no—
46C31×#390C2211yescharacteristic
47C31×#390C2211yescharacteristic
48C31×#389C2211yescharacteristic
49C31×#389C2211yescharacteristic
50C31×#385—21no—
51C31×#385—21no—
52C31×#382C2211yescharacteristic
53C31×#340C2211yescharacteristic
54C31×#340C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#336C2211yescharacteristic
60C31×#336C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C31×#336C2211yescharacteristic
63C22×Q8×C31—21no—
64C22×Q8×C31D411yescharacteristic
65C22×D4×C31C2311yescharacteristic
66C22×D4×C31C2311yescharacteristic
67C23×C4×C31—21no—
68C23×C4×C31—21no—
69C23×C4×C31—21no—
70C23×C4×C31—21no—
71C2×D8×C31—22no—
72C2×D8×C31—22no—
73C2×D8×C31Q814yescomplemented
74C22×C8×C31C2311yescharacteristic
75C22×C8×C31C2311yescharacteristic
76C22×C8×C31C2311yescharacteristic
77C22×C8×C31C2311yescharacteristic
78C31×C4⋊Q8—22no—
79C31×C4⋊Q8—22no—
80C31×#125—22no—
81C31×#125—22no—
82C31×#125—22no—
83C31×#125D414yes—
84C31×C22⋊Q8—28no—
85C31×C22⋊Q8—28no—
86C31×C22⋊Q8—28no—
87C4×Q8×C31—22no—
88C4×Q8×C31—22no—
89C4×D4×C31—22no—
90C4×D4×C31—22no—
91C4×D4×C31—22no—
92C4×D4×C31—22no—
93C4×D4×C31—22no—
94C4×D4×C31—22no—
95C4×D4×C31—22no—
96C4×D4×C31D414yes—
97C2×C4⋊C4×C31—28no—
98C2×C4⋊C4×C31—21no—
99C2×C4⋊C4×C31—21no—
100C2×C4⋊C4×C31—21no—
101C2×C4⋊C4×C31—21no—
102C2×C4⋊C4×C31—21no—
103C2×C4⋊C4×C31—21no—
104C2×C4⋊C4×C31—21no—
105C2×C4⋊C4×C31D411yescharacteristic
106C2×C4⋊C4×C31D411yescharacteristic
107C2×C4⋊C4×C31D411yescharacteristic
108C2×C4⋊C4×C31C2311yescharacteristic
109C2×C4⋊C4×C31C2311yescharacteristic
110C2×C4⋊C4×C31C2311yescharacteristic
111C2×C4⋊C4×C31C2311yescharacteristic
112C2×C4⋊C4×C31C2311yescharacteristic
113C2×C4⋊C4×C31C2311yescharacteristic
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×C31—21no—
120C2×C22⋊C4×C31—21no—
121C2×C22⋊C4×C31—21no—
122C2×C42×C31C2311yescharacteristic
123C2×C42×C31C2311yescharacteristic
124C2×C42×C31C2311yescharacteristic
125C31×#107—22no—
126C31×#107—22no—
127C31×#106—22no—
128C31×C4⋊C8—22no—
129C31×#102—22no—
130C31×#102—22no—
131C31×#102—22no—
132C31×#102—22no—
133C31×#102—22no—
134C31×#102—22no—
135C4×C8×C31—22no—
136C31×#95—21no—
137C31×#95—21no—
138C31×#95—21no—
139C31×#95—21no—
140C24×C31—21no—
141C24×C31—21no—
142C2×Q8×C31—24no—
143C2×Q8×C31—22no—
144C2×Q8×C31—22no—
145C2×Q8×C31—41no—
146C2×Q8×C31—81no—
147C2×Q8×C31—81no—
148C2×D4×C31—21no—
149C2×D4×C31—21no—
150C2×D4×C31—21no—
151C2×D4×C31—21no—
152C2×D4×C31—21no—
153C2×D4×C31—21no—
154C2×D4×C31—21no—
155C2×D4×C31—21no—
156C2×D4×C31C2×D412yes—
157C2×D4×C31C2×Q812yes—
158C2×D4×C31C2×Q812yes—
159C2×D4×C31#4112yes—
160C22×C4×C31—24no—
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—42no—
170C22×C4×C31—42no—
171C22×C4×C31—42no—
172C22×C4×C31—81no—
173C22×C4×C31—81no—
174C22×C4×C31—81no—
175C22×C4×C31—81no—
176C22×C4×C31—81no—
177C22×C4×C31—81no—
178C22×C4×C31C2×D411yescharacteristic
179C22×C4×C31C2×D411yescharacteristic
180C22×C4×C31C2×D411yescharacteristic
181C22×C4×C31C2×D411yescharacteristic
182C22×C4×C31C2×D411yescharacteristic
183C22×C4×C31C2×D411yescharacteristic
184C22×C4×C31C2411yescharacteristic
185D8×C31—28no—
186C2×C8×C31—21no—
187C2×C8×C31—21no—
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×C31C2×Q812yes—
198C4⋊C4×C31—24no—
199C4⋊C4×C31—24no—
200C4⋊C4×C31—24no—
201C4⋊C4×C31—22no—
202C4⋊C4×C31—24no—
203C4⋊C4×C31—24no—
204C4⋊C4×C31—22no—
205C4⋊C4×C31—22no—
206C4⋊C4×C31—21no—
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—81no—
216C4⋊C4×C31—81no—
217C4⋊C4×C31C2×D412yes—
218C4⋊C4×C31C2×D412yes—
219C4⋊C4×C31C2×D412yes—
220C22⋊C4×C31—24no—
221C22⋊C4×C31—24no—
222C22⋊C4×C31—24no—
223C22⋊C4×C31—42no—
224C22⋊C4×C31—42no—
225C22⋊C4×C31—42no—
226C22⋊C4×C31—81no—
227C22⋊C4×C31—81no—
228C42×C31—21no—
229C42×C31—21no—
230C42×C31—21no—
231C42×C31—21no—
232C42×C31C2×D412yes—
233C42×C31C2×D412yes—
234#24335C3111yesmaximal, characteristic, direct product factor, Sylow
235C23×C31—22no—
236C23×C31—22no—
237C23×C31—22no—
238C23×C31—22no—
239C23×C31—41no—
240C23×C31—41no—
241C23×C31—41no—
242C23×C31—41no—
243C23×C31—41no—
244C23×C31—41no—
245C23×C31—41no—
246C23×C31—41no—
247C23×C31—41no—
248C23×C31—41no—
249C23×C31C22×D411yescharacteristic
250Q8×C31—44no—
251Q8×C31—84no—
252D4×C31—22no—
253D4×C31—22no—
254D4×C31—22no—
255D4×C31—22no—
256D4×C31—22no—
257D4×C31—41no—
258D4×C31—41no—
259D4×C31C22⋊Q814yes—
260C2×C4×C31—21no—
261C2×C4×C31—21no—
262C2×C4×C31—21no—
263C2×C4×C31—21no—
264C2×C4×C31—21no—
265C2×C4×C31—21no—
266C2×C4×C31—21no—
267C2×C4×C31—21no—
268C2×C4×C31—21no—
269C2×C4×C31—22no—
270C2×C4×C31—22no—
271C2×C4×C31—22no—
272C2×C4×C31—21no—
273C2×C4×C31—21no—
274C2×C4×C31—21no—
275C2×C4×C31—21no—
276C2×C4×C31—21no—
277C2×C4×C31—21no—
278C2×C4×C31—48no—
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—84no—
295C2×C4×C31—84no—
296C2×C4×C31—84no—
297C2×C4×C31#12012yes—
298C2×C4×C31#12012yes—
299C2×C4×C31#13512yes—
300C2×C4×C31C22×D411yescharacteristic
301C2×C4×C31C22×D411yescharacteristic
302C2×C4×C31C22×Q811yescharacteristic
303C2×C4×C31C2×#4111yescharacteristic
304C2×C4×C312−1+411yescharacteristic
305C2×C4×C312−1+411yescharacteristic
306C8×C31—22no—
307C8×C31—41no—
308C8×C31—41no—
309C8×C31—41no—
310C2×#554C2×C3111yescharacteristic, complemented
311C2×#478C2×C3111yescharacteristic, complemented
312C2×C4×D8C2×C3111yescharacteristic
313#2580C2×C3111yescharacteristic, complemented
314#2059C2×C3111yescharacteristic, complemented
315#2057C2×C3111yescharacteristic, complemented
316#2025C2×C3111yescharacteristic, complemented
317#2023C2×C3111yescharacteristic, complemented
318#1991C2×C3111yescharacteristic, complemented
319#1984C2×C3111yescharacteristic, complemented
320#1879C2×C3111yescharacteristic
321#1879C2×C3111yescharacteristic
322#1864C2×C3111yescharacteristic, complemented
323#1862C2×C3111yescharacteristic, complemented
324#1804C2×C3111yescharacteristic, complemented
325C22×C31—24no—
326C22×C31—42no—
327C22×C31—42no—
328C22×C31—42no—
329C22×C31—42no—
330C22×C31—42no—
331C22×C31—42no—
332C22×C31—42no—
333C22×C31—42no—
334C22×C31—42no—
335C22×C31—81no—
336C22×C31—81no—
337C22×C31—81no—
338C22×C31—81no—
339C22×C31C2×#12011yescharacteristic
340C22×C31#54811yescharacteristic
341C22×C31D4×Q811yescharacteristic
342C22×C31C2×#13511yescharacteristic
343C22×C31#57511yescharacteristic
344C22×C31#57611yescharacteristic
345C22×C31#57611yescharacteristic
346C4×C31—22no—
347C4×C31—22no—
348C4×C31—22no—
349C4×C31—41no—
350C4×C31—42no—
351C4×C31—41no—
352C4×C31—41no—
353C4×C31—42no—
354C4×C31—42no—
355C4×C31—81no—
356C4×C31—81no—
357C4×C31—81no—
358C4×C31C2×C22⋊Q811yescharacteristic
359C4×C31#53611yescharacteristic
360C4×C31#54811yescharacteristic
361C4×C31D4×Q811yescharacteristic
362C22×D8C22×C3111yescharacteristic
363#554—24no—
364#554—24no—
365C2×C4⋊Q8C22×C3111yescharacteristic
366C2×#125C22×C3111yescharacteristic
367C2×#125C22×C3111yescharacteristic
368C2×C22⋊Q8—21no—
369C2×C22⋊Q8—21no—
370C2×C22⋊Q8—21no—
371C2×C4×Q8C22×C3111yescharacteristic
372C2×C4×D4C22×C3111yescharacteristic
373C2×C4×D4C22×C3111yescharacteristic
374C2×C4×D4C22×C3111yescharacteristic
375C2×C4×D4C22×C3111yescharacteristic
376C22×C4⋊C4—21no—
377#478—24no—
378C4×D8—24no—
379C2×#107C22×C3111yescharacteristic
380C2×#107C22×C3111yescharacteristic
381C2×#106C22×C3111yescharacteristic
382C2×C4⋊C8C22×C3111yescharacteristic
383C2×#102C22×C3111yescharacteristic
384C2×#102C22×C3111yescharacteristic
385C2×#102C22×C3111yescharacteristic
386C2×#102C22×C3111yescharacteristic
387C2×#102C22×C3111yescharacteristic
388C2×#102C22×C3111yescharacteristic
389C2×C4×C8C22×C3111yescharacteristic
390#399—21no—
391#393—21no—
392#390C22×C3111yescharacteristic
393#390C22×C3111yescharacteristic
394#389C22×C3111yescharacteristic
395#389C22×C3111yescharacteristic
396#385—21no—
397#385—21no—
398#382C22×C3111yescharacteristic
399#340C22×C3111yescharacteristic
400#340C22×C3111yescharacteristic
401#340C22×C3111yescharacteristic
402#340C22×C3111yescharacteristic
403#340C22×C3111yescharacteristic
404#340C22×C3111yescharacteristic
405#336C22×C3111yescharacteristic
406#336C22×C3111yescharacteristic
407#336C22×C3111yescharacteristic
408#336C22×C3111yescharacteristic
409C2×C31—44no—
410C2×C31—82no—
411C2×C31#240911yescharacteristic
412C2×C31#300211yescharacteristic
413C2×C31#300811yescharacteristic
414C2×C31#336111yescharacteristic
415C2×C31#337011yescharacteristic
416C2×C31#338011yescharacteristic
417C2×C31#338911yescharacteristic
418C22×Q8—21no—
419C22×Q8D4×C3111yescharacteristic
420C22×D4C23×C3111yescharacteristic
421C22×D4C23×C3111yescharacteristic
422C23×C4—21no—
423C23×C4—21no—
424C23×C4—21no—
425C23×C4—21no—
426C2×D8—22no—
427C2×D8—22no—
428C2×D8Q8×C3114yescomplemented
429C22×C8C23×C3111yescharacteristic
430C22×C8C23×C3111yescharacteristic
431C22×C8C23×C3111yescharacteristic
432C22×C8C23×C3111yescharacteristic
433C4⋊Q8—22no—
434C4⋊Q8—22no—
435#125—22no—
436#125—22no—
437#125—22no—
438#125D4×C3114yes—
439C22⋊Q8—28no—
440C22⋊Q8—28no—
441C22⋊Q8—28no—
442C4×Q8—22no—
443C4×Q8—22no—
444C4×D4—22no—
445C4×D4—22no—
446C4×D4—22no—
447C4×D4—22no—
448C4×D4—22no—
449C4×D4—22no—
450C4×D4—22no—
451C4×D4D4×C3114yes—
452C2×C4⋊C4—28no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4D4×C3111yescharacteristic
461C2×C4⋊C4D4×C3111yescharacteristic
462C2×C4⋊C4D4×C3111yescharacteristic
463C2×C4⋊C4C23×C3111yescharacteristic
464C2×C4⋊C4C23×C3111yescharacteristic
465C2×C4⋊C4C23×C3111yescharacteristic
466C2×C4⋊C4C23×C3111yescharacteristic
467C2×C4⋊C4C23×C3111yescharacteristic
468C2×C4⋊C4C23×C3111yescharacteristic
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⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C42C23×C3111yescharacteristic
478C2×C42C23×C3111yescharacteristic
479C2×C42C23×C3111yescharacteristic
480#107—22no—
481#107—22no—
482#106—22no—
483C4⋊C8—22no—
484#102—22no—
485#102—22no—
486#102—22no—
487#102—22no—
488#102—22no—
489#102—22no—
490C4×C8—22no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495C31#2433511yescharacteristic, direct product factor, Sylow
496C24—21no—
497C24—21no—
498C2×Q8—24no—
499C2×Q8—22no—
500C2×Q8—22no—
501C2×Q8—41no—
502C2×Q8—81no—
503C2×Q8—81no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4C2×D4×C3112yes—
513C2×D4C2×Q8×C3112yes—
514C2×D4C2×Q8×C3112yes—
515C2×D4#41×C3112yes—
516C22×C4—24no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—81no—
529C22×C4—81no—
530C22×C4—81no—
531C22×C4—81no—
532C22×C4—81no—
533C22×C4—81no—
534C22×C4C2×D4×C3111yescharacteristic
535C22×C4C2×D4×C3111yescharacteristic
536C22×C4C2×D4×C3111yescharacteristic
537C22×C4C2×D4×C3111yescharacteristic
538C22×C4C2×D4×C3111yescharacteristic
539C22×C4C2×D4×C3111yescharacteristic
540C22×C4C24×C3111yescharacteristic
541D8—28no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8C2×Q8×C3112yes—
554C4⋊C4—24no—
555C4⋊C4—24no—
556C4⋊C4—24no—
557C4⋊C4—22no—
558C4⋊C4—24no—
559C4⋊C4—24no—
560C4⋊C4—22no—
561C4⋊C4—22no—
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—81no—
572C4⋊C4—81no—
573C4⋊C4C2×D4×C3112yes—
574C4⋊C4C2×D4×C3112yes—
575C4⋊C4C2×D4×C3112yes—
576C22⋊C4—24no—
577C22⋊C4—24no—
578C22⋊C4—24no—
579C22⋊C4—42no—
580C22⋊C4—42no—
581C22⋊C4—42no—
582C22⋊C4—81no—
583C22⋊C4—81no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42C2×D4×C3112yes—
589C42C2×D4×C3112yes—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23C22×D4×C3111yescharacteristic
605Q8—44no—
606Q8—84no—
607D4—22no—
608D4—22no—
609D4—22no—
610D4—22no—
611D4—22no—
612D4—41no—
613D4—41no—
614D4C31×C22⋊Q814yes—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—48no—
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—84no—
650C2×C4—84no—
651C2×C4—84no—
652C2×C4C31×#12012yes—
653C2×C4C31×#12012yes—
654C2×C4C31×#13512yes—
655C2×C4C22×D4×C3111yescharacteristic
656C2×C4C22×D4×C3111yescharacteristic
657C2×C4C22×Q8×C3111yescharacteristic
658C2×C4C2×#41×C3111yescharacteristic
659C2×C4C31×2−1+411yescharacteristic
660C2×C4C31×2−1+411yescharacteristic
661C8—22no—
662C8—41no—
663C8—41no—
664C8—41no—
665C22—24no—
666C22—42no—
667C22—42no—
668C22—42no—
669C22—42no—
670C22—42no—
671C22—42no—
672C22—42no—
673C22—42no—
674C22—42no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22C2×C31×#12011yescharacteristic
680C22C31×#54811yescharacteristic
681C22D4×Q8×C3111yescharacteristic
682C22C2×C31×#13511yescharacteristic
683C22C31×#57511yescharacteristic
684C22C31×#57611yescharacteristic
685C22C31×#57611yescharacteristic
686C4—22no—
687C4—22no—
688C4—22no—
689C4—41no—
690C4—42no—
691C4—41no—
692C4—41no—
693C4—42no—
694C4—42no—
695C4—81no—
696C4—81no—
697C4—81no—
698C4C2×C31×C22⋊Q811yescharacteristic
699C4C31×#53611yescharacteristic
700C4C31×#54811yescharacteristic
701C4D4×Q8×C3111yescharacteristic
702C2—44no—
703C2—82no—
704C2C31×#240911yescharacteristic
705C2C31×#300211yescharacteristic
706C2C31×#300811yescharacteristic
707C2C31×#336111yescharacteristic
708C2C31×#337011yescharacteristic
709C2C31×#338011yescharacteristic
710C2C31×#338911yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC22×D8×C31C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C4×Q8×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#554C2semidirect
2. C2×C31×#478C2semidirect
4. C31×#2580C2semidirect
5. C31×#2059C2semidirect
6. C31×#2057C2semidirect
7. C31×#2025C2semidirect
8. C31×#2023C2semidirect
9. C31×#1991C2semidirect
10. C31×#1984C2semidirect
13. C31×#1864C2semidirect
14. C31×#1862C2semidirect
15. C31×#1804C2semidirect
73. C2×D8×C31Q8semidirect
234. #24335C31direct (N × H)
310. C2×#554C2×C31semidirect
311. C2×#478C2×C31semidirect
313. #2580C2×C31semidirect
314. #2059C2×C31semidirect
315. #2057C2×C31semidirect
316. #2025C2×C31semidirect
317. #2023C2×C31semidirect
318. #1991C2×C31semidirect
319. #1984C2×C31semidirect
322. #1864C2×C31semidirect
323. #1862C2×C31semidirect
324. #1804C2×C31semidirect
428. C2×D8Q8×C31semidirect
495. C31#24335direct (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×#4782
C2×C4×D8×C312
C31×#25802
C31×#20592
C31×#20572
C31×#20252
C31×#20232
C31×#19912
C31×#19842
C31×#18792
C31×#18642
C31×#18622
C31×#18042
#2433531