Finite Group Databasebeta

← C31×#14021 #21470780

Subgroups — C31×#14021 #21470780

Order 7936.

1506 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#391C211yesmaximal, characteristic
2C2×C31×#391C211yesmaximal, characteristic
3C2×C31×#391C211yesmaximal, characteristic
4C2×C4×C4⋊C4×C31C211yesmaximal, characteristic
5C2×C4×C4⋊C4×C31C211yesmaximal, characteristic
6C31×#1443C212yesmaximal
7C31×#1442C212yesmaximal
8C31×#1436C212yesmaximal
9C31×C4⋊#95C211yesmaximal, characteristic
10C31×C4⋊#95C211yesmaximal, characteristic
11C31×#1434C212yesmaximal
12C23×Q8×C31C2211yescharacteristic
13C22×C4⋊C4×C31C2211yescharacteristic
14C22×C4⋊C4×C31C2211yescharacteristic
15C22×C4⋊C4×C31C2211yescharacteristic
16C22×C4⋊C4×C31C2211yescharacteristic
17C22×C4⋊C4×C31C2211yescharacteristic
18C22×C42×C31C2211yescharacteristic
19C22×C42×C31C2212yes—
20C22×C42×C31C2211yescharacteristic
21C22×C42×C31C2211yescharacteristic
22C31×#391—24no—
23C31×#391—24no—
24C31×#391C418yescomplemented
25C4×C4⋊C4×C31—24no—
26C4×C4⋊C4×C31—24no—
27C2×C31×#95C2211yescharacteristic
28C2×C31×#95C2212yes—
29C2×C31×#95C2212yes—
30C2×C31×#95C2212yes—
31C2×C31×#95C2212yes—
32C2×C31×#95C2212yes—
33C2×C31×#95C2212yes—
34C2×C31×#95C2212yes—
35C2×C31×#95C2211yescharacteristic
36C2×C31×#95C2212yes—
37C2×C31×#95C2212yes—
38C2×C31×#95C2212yes—
39C2×C31×#95C2212yes—
40C22×Q8×C31—22no—
41C22×Q8×C31—22no—
42C22×Q8×C31—22no—
43C22×Q8×C31—22no—
44C22×Q8×C31—22no—
45C22×Q8×C31—22no—
46C22×Q8×C31C2×C414yes—
47C23×C4×C31C2312yes—
48C23×C4×C31C2312yes—
49C23×C4×C31C2311yescharacteristic
50C23×C4×C31C2312yes—
51C23×C4×C31C2311yescharacteristic
52C23×C4×C31C2312yes—
53C23×C4×C31C2311yescharacteristic
54C23×C4×C31C2311yescharacteristic
55C23×C4×C31C2311yescharacteristic
56C23×C4×C31C2311yescharacteristic
57C23×C4×C31C2311yescharacteristic
58C2×C4⋊C4×C31—22no—
59C2×C4⋊C4×C31—22no—
60C2×C4⋊C4×C31—22no—
61C2×C4⋊C4×C31—22no—
62C2×C4⋊C4×C31—22no—
63C2×C4⋊C4×C31—22no—
64C2×C4⋊C4×C31—22no—
65C2×C4⋊C4×C31—22no—
66C2×C4⋊C4×C31—22no—
67C2×C4⋊C4×C31—22no—
68C2×C4⋊C4×C31—22no—
69C2×C4⋊C4×C31—22no—
70C2×C4⋊C4×C31C2×C414yes—
71C2×C4⋊C4×C31D414yes—
72C2×C4⋊C4×C31Q814yescomplemented
73C2×C42×C31—22no—
74C2×C42×C31—22no—
75C2×C42×C31—22no—
76C2×C42×C31—22no—
77C2×C42×C31—24no—
78C2×C42×C31—22no—
79C2×C42×C31—22no—
80C2×C42×C31—24no—
81C2×C42×C31—22no—
82C2×C42×C31—42no—
83C2×C42×C31C2×C414yes—
84C2×C42×C31D414yes—
85C31×#95—24no—
86C31×#95—22no—
87C31×#95—22no—
88C31×#95—24no—
89C31×#95—24no—
90C31×#95—24no—
91C31×#95—24no—
92C31×#95—24no—
93C31×#95—24no—
94C31×#95—42no—
95C31×#95—42no—
96C31×#95C2×C418yes—
97C31×#95C2×C418yes—
98C24×C31C2411yescharacteristic
99C2×Q8×C31—28no—
100C2×Q8×C31—28no—
101C2×Q8×C31—28no—
102C2×Q8×C31—44no—
103C2×Q8×C31—44no—
104C2×Q8×C31—44no—
105C2×Q8×C31—44no—
106C22×C4×C31—21no—
107C22×C4×C31—21no—
108C22×C4×C31—21no—
109C22×C4×C31—21no—
110C22×C4×C31—21no—
111C22×C4×C31—21no—
112C22×C4×C31—21no—
113C22×C4×C31—21no—
114C22×C4×C31—21no—
115C22×C4×C31—21no—
116C22×C4×C31—21no—
117C22×C4×C31—21no—
118C22×C4×C31—22no—
119C22×C4×C31—22no—
120C22×C4×C31—22no—
121C22×C4×C31—21no—
122C22×C4×C31—21no—
123C22×C4×C31—22no—
124C22×C4×C31—22no—
125C22×C4×C31—21no—
126C22×C4×C31—22no—
127C22×C4×C31—21no—
128C22×C4×C31—22no—
129C22×C4×C31—21no—
130C22×C4×C31—21no—
131C22×C4×C31—22no—
132C22×C4×C31—21no—
133C22×C4×C31—22no—
134C22×C4×C31—22no—
135C22×C4×C31—21no—
136C22×C4×C31—21no—
137C22×C4×C31—21no—
138C22×C4×C31—22no—
139C22×C4×C31—22no—
140C22×C4×C31—22no—
141C22×C4×C31—22no—
142C22×C4×C31—21no—
143C22×C4×C31—21no—
144C22×C4×C31—22no—
145C22×C4×C31—22no—
146C22×C4×C31—21no—
147C22×C4×C31—21no—
148C22×C4×C31—21no—
149C22×C4×C31—22no—
150C22×C4×C31—21no—
151C22×C4×C31—21no—
152C22×C4×C31—22no—
153C22×C4×C31—21no—
154C22×C4×C31—21no—
155C22×C4×C31—21no—
156C22×C4×C31—22no—
157C22×C4×C31—22no—
158C22×C4×C31—22no—
159C22×C4×C31—22no—
160C22×C4×C31—22no—
161C22×C4×C31—22no—
162C22×C4×C31—22no—
163C22×C4×C31C22×C412yes—
164C22×C4×C31C22×C414yes—
165C22×C4×C31C22×C414yes—
166C22×C4×C31C22×C412yes—
167C22×C4×C31C22×C412yes—
168C22×C4×C31C2×D414yes—
169C22×C4×C31C2×D412yes—
170C22×C4×C31C2×D412yes—
171C22×C4×C31C2×D412yes—
172C22×C4×C31C2×D412yes—
173C22×C4×C31C2×Q812yes—
174C22×C4×C31C2×Q812yes—
175C22×C4×C31C2×Q812yes—
176C22×C4×C31#4112yes—
177C22×C4×C31#4112yes—
178C22×C4×C31#4112yes—
179C22×C4×C31#4112yes—
180C22×C4×C31#4112yes—
181C22×C4×C31#4112yes—
182C22×C4×C31#4112yes—
183C4⋊C4×C31—28no—
184C4⋊C4×C31—28no—
185C4⋊C4×C31—28no—
186C4⋊C4×C31—28no—
187C4⋊C4×C31—44no—
188C42×C31—28no—
189C42×C31—28no—
190C42×C31—48no—
191C42×C31—44no—
192#14021C3111yesmaximal, characteristic, direct product factor, Sylow
193C23×C31C23×C411yescharacteristic
194C23×C31C22×D411yescharacteristic
195C23×C31C22×D411yescharacteristic
196C23×C31C22×Q811yescharacteristic
197C23×C31C2×#4111yescharacteristic
198C23×C31C2×#4111yescharacteristic
199C23×C31C2×#4111yescharacteristic
200C23×C31C2×#4111yescharacteristic
201C23×C31C2×#4111yescharacteristic
202C23×C31C2×#4111yescharacteristic
203C23×C31C2×#4111yescharacteristic
204C23×C31H(5,𝔽2)11yescharacteristic
205C23×C312−1+411yescharacteristic
206C23×C312−1+411yescharacteristic
207C23×C312−1+411yescharacteristic
208Q8×C31—416no—
209C2×C4×C31—22no—
210C2×C4×C31—22no—
211C2×C4×C31—22no—
212C2×C4×C31—22no—
213C2×C4×C31—22no—
214C2×C4×C31—22no—
215C2×C4×C31—22no—
216C2×C4×C31—22no—
217C2×C4×C31—22no—
218C2×C4×C31—22no—
219C2×C4×C31—22no—
220C2×C4×C31—22no—
221C2×C4×C31—24no—
222C2×C4×C31—22no—
223C2×C4×C31—24no—
224C2×C4×C31—24no—
225C2×C4×C31—24no—
226C2×C4×C31—24no—
227C2×C4×C31—22no—
228C2×C4×C31—22no—
229C2×C4×C31—24no—
230C2×C4×C31—22no—
231C2×C4×C31—22no—
232C2×C4×C31—24no—
233C2×C4×C31—22no—
234C2×C4×C31—22no—
235C2×C4×C31—22no—
236C2×C4×C31—24no—
237C2×C4×C31—24no—
238C2×C4×C31—22no—
239C2×C4×C31—22no—
240C2×C4×C31—22no—
241C2×C4×C31—22no—
242C2×C4×C31—41no—
243C2×C4×C31—41no—
244C2×C4×C31—42no—
245C2×C4×C31—42no—
246C2×C4×C31—42no—
247C2×C4×C31—42no—
248C2×C4×C31—42no—
249C2×C4×C31—41no—
250C2×C4×C31—41no—
251C2×C4×C31—41no—
252C2×C4×C31—41no—
253C2×C4×C31—41no—
254C2×C4×C31—41no—
255C2×C4×C31—42no—
256C2×C4×C31—42no—
257C2×C4×C31—41no—
258C2×C4×C31—41no—
259C2×C4×C31—41no—
260C2×C4×C31—42no—
261C2×C4×C31—41no—
262C2×C4×C31—41no—
263C2×C4×C31—41no—
264C2×C4×C31—42no—
265C2×C4×C31—41no—
266C2×C4×C31—41no—
267C2×C4×C31—42no—
268C2×C4×C31—42no—
269C2×C4×C31—42no—
270C2×C4×C31—42no—
271C2×C4×C31—42no—
272C2×C4×C31—42no—
273C2×C4×C31—42no—
274C2×C4×C31—42no—
275C2×C4×C31—42no—
276C2×C4×C31—42no—
277C2×C4×C31#11714yes—
278C2×C4×C31C4×D414yes—
279C2×C4×C31C4×D414yes—
280C2×C4×C31C4×Q814yes—
281C2×C4×C31#12114yes—
282C2×C4×C31C22⋊Q814yes—
283C2×C4×C31#12314yes—
284C2×C4×C31#12414yes—
285C2×C4×C31#12614yes—
286C2×#391C2×C3111yescharacteristic
287C2×#391C2×C3111yescharacteristic
288C2×#391C2×C3111yescharacteristic
289C2×C4×C4⋊C4C2×C3111yescharacteristic
290C2×C4×C4⋊C4C2×C3111yescharacteristic
291#1443C2×C3112yes—
292#1442C2×C3112yes—
293#1436C2×C3112yes—
294C4⋊#95C2×C3111yescharacteristic
295C4⋊#95C2×C3111yescharacteristic
296#1434C2×C3112yes—
297C22×C31C2×#11711yescharacteristic
298C22×C31C2×C4×D411yescharacteristic
299C22×C31C2×C4×D411yescharacteristic
300C22×C31C2×C4×Q811yescharacteristic
301C22×C31C4×#4111yescharacteristic
302C22×C31#51911yescharacteristic
303C22×C31#52011yescharacteristic
304C22×C31C2×#12111yescharacteristic
305C22×C31C2×C22⋊Q811yescharacteristic
306C22×C31C2×#12311yescharacteristic
307C22×C31#52511yescharacteristic
308C22×C31C2×#12411yescharacteristic
309C22×C31C2×#12611yescharacteristic
310C22×C31#52911yescharacteristic
311C22×C31#53311yescharacteristic
312C22×C31#53611yescharacteristic
313C22×C31#53711yescharacteristic
314C22×C31#54111yescharacteristic
315C22×C31#54211yescharacteristic
316C22×C31#54611yescharacteristic
317C22×C31#54711yescharacteristic
318C22×C31#54811yescharacteristic
319C22×C31D4×Q811yescharacteristic
320C22×C31#55211yescharacteristic
321C22×C31#55211yescharacteristic
322C22×C31#55411yescharacteristic
323C22×C31#55611yescharacteristic
324C22×C31#55611yescharacteristic
325C22×C31#55611yescharacteristic
326C22×C31#55611yescharacteristic
327C22×C31#55611yescharacteristic
328C22×C31#55711yescharacteristic
329C22×C31#55711yescharacteristic
330C22×C31#55911yescharacteristic
331C22×C31#55911yescharacteristic
332C4×C31—24no—
333C4×C31—24no—
334C4×C31—42no—
335C4×C31—44no—
336C4×C31—42no—
337C4×C31—42no—
338C4×C31—42no—
339C4×C31—44no—
340C4×C31—44no—
341C4×C31—82no—
342C4×C31#38818yes—
343C23×Q8C22×C3111yescharacteristic
344C22×C4⋊C4C22×C3111yescharacteristic
345C22×C4⋊C4C22×C3111yescharacteristic
346C22×C4⋊C4C22×C3111yescharacteristic
347C22×C4⋊C4C22×C3111yescharacteristic
348C22×C4⋊C4C22×C3111yescharacteristic
349C22×C42C22×C3111yescharacteristic
350C22×C42C22×C3112yes—
351C22×C42C22×C3111yescharacteristic
352C22×C42C22×C3111yescharacteristic
353#391—24no—
354#391—24no—
355#391C4×C3118yescomplemented
356C4×C4⋊C4—24no—
357C4×C4⋊C4—24no—
358C2×#95C22×C3111yescharacteristic
359C2×#95C22×C3112yes—
360C2×#95C22×C3112yes—
361C2×#95C22×C3112yes—
362C2×#95C22×C3112yes—
363C2×#95C22×C3112yes—
364C2×#95C22×C3112yes—
365C2×#95C22×C3112yes—
366C2×#95C22×C3111yescharacteristic
367C2×#95C22×C3112yes—
368C2×#95C22×C3112yes—
369C2×#95C22×C3112yes—
370C2×#95C22×C3112yes—
371C2×C31C2×#38811yescharacteristic
372C2×C31C4×C22⋊Q811yescharacteristic
373C2×C31#232311yescharacteristic
374C2×C31#235511yescharacteristic
375C2×C31#235611yescharacteristic
376C2×C31#236511yescharacteristic
377C2×C31#236711yescharacteristic
378C2×C31#241511yescharacteristic
379C2×C31#241711yescharacteristic
380C2×C31#244611yescharacteristic
381C2×C31#244711yescharacteristic
382C2×C31#251111yescharacteristic
383C2×C31#251411yescharacteristic
384C2×C31#256811yescharacteristic
385C2×C31#259211yescharacteristic
386C22×Q8—22no—
387C22×Q8—22no—
388C22×Q8—22no—
389C22×Q8—22no—
390C22×Q8—22no—
391C22×Q8—22no—
392C22×Q8C2×C4×C3114yes—
393C23×C4C23×C3112yes—
394C23×C4C23×C3112yes—
395C23×C4C23×C3112yes—
396C23×C4C23×C3111yescharacteristic
397C23×C4C23×C3111yescharacteristic
398C23×C4C23×C3112yes—
399C23×C4C23×C3111yescharacteristic
400C23×C4C23×C3111yescharacteristic
401C23×C4C23×C3111yescharacteristic
402C23×C4C23×C3111yescharacteristic
403C23×C4C23×C3111yescharacteristic
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4C2×C4×C3114yes—
417C2×C4⋊C4D4×C3114yes—
418C2×C4⋊C4Q8×C3114yescomplemented
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—24no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—24no—
427C2×C42—22no—
428C2×C42—42no—
429C2×C42C2×C4×C3114yes—
430C2×C42D4×C3114yes—
431#95—24no—
432#95—22no—
433#95—22no—
434#95—24no—
435#95—24no—
436#95—24no—
437#95—24no—
438#95—24no—
439#95—24no—
440#95—42no—
441#95—42no—
442#95C2×C4×C3118yes—
443#95C2×C4×C3118yes—
444C31#1402111yescharacteristic, direct product factor, Sylow
445C24C24×C3111yescharacteristic
446C2×Q8—28no—
447C2×Q8—28no—
448C2×Q8—28no—
449C2×Q8—44no—
450C2×Q8—44no—
451C2×Q8—44no—
452C2×Q8—44no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4C22×C4×C3112yes—
511C22×C4C22×C4×C3114yes—
512C22×C4C22×C4×C3114yes—
513C22×C4C22×C4×C3112yes—
514C22×C4C22×C4×C3112yes—
515C22×C4C2×D4×C3114yes—
516C22×C4C2×D4×C3112yes—
517C22×C4C2×D4×C3112yes—
518C22×C4C2×D4×C3112yes—
519C22×C4C2×D4×C3112yes—
520C22×C4C2×Q8×C3112yes—
521C22×C4C2×Q8×C3112yes—
522C22×C4C2×Q8×C3112yes—
523C22×C4#41×C3112yes—
524C22×C4#41×C3112yes—
525C22×C4#41×C3112yes—
526C22×C4#41×C3112yes—
527C22×C4#41×C3112yes—
528C22×C4#41×C3112yes—
529C22×C4#41×C3112yes—
530C4⋊C4—28no—
531C4⋊C4—28no—
532C4⋊C4—28no—
533C4⋊C4—28no—
534C4⋊C4—44no—
535C42—28no—
536C42—28no—
537C42—48no—
538C42—44no—
539C23C23×C4×C3111yescharacteristic
540C23C22×D4×C3111yescharacteristic
541C23C22×D4×C3111yescharacteristic
542C23C22×Q8×C3111yescharacteristic
543C23C2×#41×C3111yescharacteristic
544C23C2×#41×C3111yescharacteristic
545C23C2×#41×C3111yescharacteristic
546C23C2×#41×C3111yescharacteristic
547C23C2×#41×C3111yescharacteristic
548C23C2×#41×C3111yescharacteristic
549C23C2×#41×C3111yescharacteristic
550C23C31×H(5,𝔽2)11yescharacteristic
551C23C31×2−1+411yescharacteristic
552C23C31×2−1+411yescharacteristic
553C23C31×2−1+411yescharacteristic
554Q8—416no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—24no—
568C2×C4—22no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—24no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—24no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—24no—
583C2×C4—24no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—42no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—42no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4C31×#11714yes—
624C2×C4C4×D4×C3114yes—
625C2×C4C4×D4×C3114yes—
626C2×C4C4×Q8×C3114yes—
627C2×C4C31×#12114yes—
628C2×C4C31×C22⋊Q814yes—
629C2×C4C31×#12314yes—
630C2×C4C31×#12414yes—
631C2×C4C31×#12614yes—
632C22C2×C31×#11711yescharacteristic
633C22C2×C4×D4×C3111yescharacteristic
634C22C2×C4×D4×C3111yescharacteristic
635C22C2×C4×Q8×C3111yescharacteristic
636C22C4×#41×C3111yescharacteristic
637C22C31×#51911yescharacteristic
638C22C31×#52011yescharacteristic
639C22C2×C31×#12111yescharacteristic
640C22C2×C31×C22⋊Q811yescharacteristic
641C22C2×C31×#12311yescharacteristic
642C22C31×#52511yescharacteristic
643C22C2×C31×#12411yescharacteristic
644C22C2×C31×#12611yescharacteristic
645C22C31×#52911yescharacteristic
646C22C31×#53311yescharacteristic
647C22C31×#53611yescharacteristic
648C22C31×#53711yescharacteristic
649C22C31×#54111yescharacteristic
650C22C31×#54211yescharacteristic
651C22C31×#54611yescharacteristic
652C22C31×#54711yescharacteristic
653C22C31×#54811yescharacteristic
654C22D4×Q8×C3111yescharacteristic
655C22C31×#55211yescharacteristic
656C22C31×#55211yescharacteristic
657C22C31×#55411yescharacteristic
658C22C31×#55611yescharacteristic
659C22C31×#55611yescharacteristic
660C22C31×#55611yescharacteristic
661C22C31×#55611yescharacteristic
662C22C31×#55611yescharacteristic
663C22C31×#55711yescharacteristic
664C22C31×#55711yescharacteristic
665C22C31×#55911yescharacteristic
666C22C31×#55911yescharacteristic
667C4—24no—
668C4—24no—
669C4—42no—
670C4—44no—
671C4—42no—
672C4—42no—
673C4—42no—
674C4—44no—
675C4—44no—
676C4—82no—
677C4C31×#38818yes—
678C2C2×C31×#38811yescharacteristic
679C2C4×C31×C22⋊Q811yescharacteristic
680C2C31×#232311yescharacteristic
681C2C31×#235511yescharacteristic
682C2C31×#235611yescharacteristic
683C2C31×#236511yescharacteristic
684C2C31×#236711yescharacteristic
685C2C31×#241511yescharacteristic
686C2C31×#241711yescharacteristic
687C2C31×#244611yescharacteristic
688C2C31×#244711yescharacteristic
689C2C31×#251111yescharacteristic
690C2C31×#251411yescharacteristic
691C2C31×#256811yescharacteristic
692C2C31×#259211yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
24. C31×#391C4semidirect
72. C2×C4⋊C4×C31Q8semidirect
192. #14021C31direct (N × H)
355. #391C4×C31semidirect
418. C2×C4⋊C4Q8×C31semidirect
444. C31#14021direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3912
C2×C4×C4⋊C4×C312
C31×#14432
C31×#14422
C31×#14362
C31×C4⋊#952
C31×#14342
#1402131