Finite Group Databasebeta

← C31×#17427 #21474186

Subgroups — C31×#17427 #21474186

Order 7936.

1022 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#553C211yesmaximal, characteristic
2C31×#2974C212yesmaximal, complemented
3C31×#1473C212yesmaximal, complemented
4C31×#1471C212yesmaximal, complemented
5C31×#1468C212yesmaximal, complemented
6C31×#1465C211yesmaximal, characteristic, complemented
7C31×#1464C211yesmaximal, characteristic, complemented
8C31×#1463C211yesmaximal, characteristic, complemented
9C31×#1459C211yesmaximal, characteristic, complemented
10C31×#1458C211yesmaximal, characteristic, complemented
11C2×C31×#324C211yesmaximal, characteristic, complemented
12C31×#553—22no—
13C31×#553—22no—
14C31×#553—22no—
15C31×#553—22no—
16C2×C31×#126C411yescharacteristic
17C2×C31×#126C2211yescharacteristic
18C2×C31×#125C411yescharacteristic
19C2×C31×#123C411yescharacteristic
20C2×C31×#123C2211yescharacteristic
21C2×C31×#121C411yescharacteristic
22C2×C31×#121C411yescharacteristic
23C2×C31×#121C411yescharacteristic
24C2×C31×#121C2211yescharacteristic
25C2×C4×D4×C31C411yescharacteristic
26C2×C4×D4×C31C411yescharacteristic
27C2×C4×D4×C31C2211yescharacteristic
28C2×C4×D4×C31C2211yescharacteristic
29C2×C31×#117C2211yescharacteristic
30C22×C4⋊C4×C31C2211yescharacteristic
31C31×#436—22no—
32C31×#435—22no—
33C31×#435—22no—
34C8×D4×C31—22no—
35C31×#432C2212yes—
36C31×#431C2212yes—
37C31×#407C2212yes—
38C31×#407C2212yes—
39C2×C31×C22⋊C8C2212yes—
40C2×C31×C22⋊C8C2212yes—
41C31×#324C2211yescharacteristic
42C31×#324C2211yescharacteristic
43C31×#324C2212yes—
44C31×#324C2211yescharacteristic
45C31×#324C2211yescharacteristic
46C31×#324C2212yes—
47C31×#323C2212yes—
48C31×#323C2212yes—
49C31×#323C2212yes—
50C31×#323C2212yes—
51C22×D4×C31C2×C411yescharacteristic
52C22×D4×C31C2×C411yescharacteristic
53C22×D4×C31C2×C411yescharacteristic
54C22×D4×C31C2×C411yescharacteristic
55C22×D4×C31C2×C411yescharacteristic
56C22×D4×C31C2×C411yescharacteristic
57C23×C4×C31C2×C411yescharacteristic
58C23×C4×C31C2×C411yescharacteristic
59C23×C4×C31C2×C411yescharacteristic
60C23×C4×C31C2×C411yescharacteristic
61C23×C4×C31C2311yescharacteristic
62C23×C4×C31C2311yescharacteristic
63C2×M16×C31—22no—
64C2×M16×C31—22no—
65C22×C8×C31—22no—
66C22×C8×C31—22no—
67C31×#126—22no—
68C31×#126—22no—
69C31×#126—22no—
70C31×#126—22no—
71C31×#125—22no—
72C31×#125—22no—
73C31×#123—22no—
74C31×#123—22no—
75C31×#123—22no—
76C31×#123—22no—
77C31×#121—22no—
78C31×#121—22no—
79C31×#121—22no—
80C31×#121—22no—
81C31×#121—22no—
82C31×#121—22no—
83C31×#121—22no—
84C31×#121—22no—
85C4×D4×C31—22no—
86C4×D4×C31—22no—
87C4×D4×C31—21no—
88C4×D4×C31—21no—
89C4×D4×C31—21no—
90C4×D4×C31—21no—
91C4×D4×C31—21no—
92C4×D4×C31—21no—
93C4×D4×C31—21no—
94C4×D4×C31—21no—
95C4×D4×C31D412yes—
96C4×D4×C31D412yes—
97C4×D4×C31D412yes—
98C4×D4×C31D412yes—
99C31×#117—22no—
100C31×#117—22no—
101C2×C4⋊C4×C31—22no—
102C2×C4⋊C4×C31—22no—
103C2×C4⋊C4×C31C2×C411yescharacteristic
104C2×C4⋊C4×C31C2×C411yescharacteristic
105C2×C4⋊C4×C31C2×C411yescharacteristic
106C2×C4⋊C4×C31C2×C411yescharacteristic
107C2×C4⋊C4×C31C2×C411yescharacteristic
108C2×C4⋊C4×C31C2×C411yescharacteristic
109C2×C4⋊C4×C31C2×C411yescharacteristic
110C2×C4⋊C4×C31C2×C411yescharacteristic
111C2×C4⋊C4×C31C2311yescharacteristic
112C2×C4⋊C4×C31C2311yescharacteristic
113C2×C22⋊C4×C31C2×C411yescharacteristic
114C2×C22⋊C4×C31C2×C411yescharacteristic
115C2×C22⋊C4×C31C2×C411yescharacteristic
116C2×C22⋊C4×C31C2×C411yescharacteristic
117C2×C22⋊C4×C31C2×C411yescharacteristic
118C2×C22⋊C4×C31C2×C411yescharacteristic
119C2×C22⋊C4×C31C2×C411yescharacteristic
120C2×C22⋊C4×C31C2×C411yescharacteristic
121C2×C22⋊C4×C31C2311yescharacteristic
122C2×C22⋊C4×C31C2311yescharacteristic
123C2×C42×C31C2×C411yescharacteristic
124C2×C42×C31C2×C411yescharacteristic
125C2×C42×C31C2311yescharacteristic
126C31×C4⋊C8—22no—
127C31×C4⋊C8—22no—
128C31×C22⋊C8—22no—
129C31×C22⋊C8—22no—
130C31×C22⋊C8—22no—
131C31×C22⋊C8—22no—
132C31×C22⋊C8C2312yes—
133C31×C22⋊C8C2312yes—
134C31×C22⋊C8C2312yes—
135C31×C22⋊C8C2312yes—
136C31×#97—22no—
137C4×C8×C31—22no—
138C24×C31C22×C411yescharacteristic
139C24×C31C22×C411yescharacteristic
140C24×C31C22×C411yescharacteristic
141C24×C31C22×C411yescharacteristic
142C2×D4×C31—22no—
143C2×D4×C31—21no—
144C2×D4×C31—21no—
145C2×D4×C31—21no—
146C2×D4×C31—21no—
147C2×D4×C31—22no—
148C2×D4×C31—22no—
149C2×D4×C31—22no—
150C2×D4×C31—41no—
151C2×D4×C31—42no—
152C2×D4×C31—42no—
153C2×D4×C31—42no—
154C2×D4×C31—81no—
155C2×D4×C31—81no—
156C2×D4×C31C22⋊C412yes—
157C2×D4×C31C22⋊C412yes—
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—22no—
165C22×C4×C31—22no—
166C22×C4×C31—21no—
167C22×C4×C31—21no—
168C22×C4×C31—41no—
169C22×C4×C31—41no—
170C22×C4×C31—81no—
171C22×C4×C31—81no—
172C22×C4×C31—81no—
173C22×C4×C31—81no—
174C22×C4×C31C22×C411yescharacteristic
175C22×C4×C31C22×C411yescharacteristic
176C22×C4×C31C22×C411yescharacteristic
177C22×C4×C31C22×C411yescharacteristic
178C22×C4×C31C22×C411yescharacteristic
179C22×C4×C31C22×C411yescharacteristic
180C22×C4×C31C22×C411yescharacteristic
181C22×C4×C31C22×C411yescharacteristic
182C22×C4×C31C22×C411yescharacteristic
183C22×C4×C31C22×C411yescharacteristic
184C22×C4×C31C2×D412yes—
185C22×C4×C31C2×D412yes—
186C22×C4×C31C2×D412yes—
187C22×C4×C31C2×D412yes—
188C22×C4×C31C2411yescharacteristic
189M16×C31—82no—
190M16×C31—82no—
191C2×C8×C31—22no—
192C2×C8×C31—22no—
193C2×C8×C31—22no—
194C2×C8×C31—22no—
195C2×C8×C31—82no—
196C2×C8×C31—82no—
197C4⋊C4×C31—22no—
198C4⋊C4×C31—22no—
199C4⋊C4×C31—22no—
200C4⋊C4×C31—21no—
201C4⋊C4×C31—21no—
202C4⋊C4×C31—21no—
203C4⋊C4×C31—21no—
204C4⋊C4×C31—22no—
205C4⋊C4×C31—22no—
206C4⋊C4×C31—22no—
207C4⋊C4×C31—22no—
208C4⋊C4×C31C22⋊C412yes—
209C4⋊C4×C31C22⋊C412yes—
210C22⋊C4×C31—22no—
211C22⋊C4×C31—22no—
212C22⋊C4×C31—22no—
213C22⋊C4×C31—21no—
214C22⋊C4×C31—21no—
215C22⋊C4×C31—21no—
216C22⋊C4×C31—21no—
217C22⋊C4×C31—22no—
218C22⋊C4×C31—22no—
219C22⋊C4×C31—22no—
220C22⋊C4×C31C22⋊C411yescharacteristic
221C22⋊C4×C31C22⋊C411yescharacteristic
222C22⋊C4×C31C22⋊C411yescharacteristic
223C22⋊C4×C31C22⋊C411yescharacteristic
224C22⋊C4×C31C22⋊C412yes—
225C22⋊C4×C31C22⋊C412yes—
226C42×C31—21no—
227C42×C31—21no—
228C42×C31—21no—
229C42×C31—21no—
230C42×C31C2×D412yes—
231C42×C31C2×D412yes—
232#17427C3111yesmaximal, characteristic, direct product factor, Sylow
233C23×C31—21no—
234C23×C31—21no—
235C23×C31—22no—
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—41no—
245C23×C31—41no—
246C23×C31—41no—
247C23×C31—41no—
248C23×C31—41no—
249C23×C31—41no—
250C23×C31—41no—
251C23×C31C2×C22⋊C412yes—
252C23×C31C2×C22⋊C411yescharacteristic
253C23×C31C2×C22⋊C411yescharacteristic
254C23×C31C23×C411yescharacteristic
255D4×C31—24no—
256D4×C31—42no—
257D4×C31—44no—
258D4×C31—42no—
259D4×C31—42no—
260D4×C31—42no—
261D4×C31—42no—
262D4×C31—82no—
263D4×C31—82no—
264C2×C4×C31—21no—
265C2×C4×C31—21no—
266C2×C4×C31—21no—
267C2×C4×C31—21no—
268C2×C4×C31—21no—
269C2×C4×C31—21no—
270C2×C4×C31—21no—
271C2×C4×C31—21no—
272C2×C4×C31—21no—
273C2×C4×C31—21no—
274C2×C4×C31—21no—
275C2×C4×C31—42no—
276C2×C4×C31—42no—
277C2×C4×C31—42no—
278C2×C4×C31—42no—
279C2×C4×C31—41no—
280C2×C4×C31—41no—
281C2×C4×C31—41no—
282C2×C4×C31—41no—
283C2×C4×C31—42no—
284C2×C4×C31—42no—
285C2×C4×C31—42no—
286C2×C4×C31—42no—
287C2×C4×C31—41no—
288C2×C4×C31—41no—
289C2×C4×C31—41no—
290C2×C4×C31—41no—
291C2×C4×C31—81no—
292C2×C4×C31—81no—
293C2×C4×C31—81no—
294C2×C4×C31—81no—
295C2×C4×C31C2×C22⋊C411yescharacteristic
296C2×C4×C31C2×C22⋊C411yescharacteristic
297C2×C4×C31C2×C22⋊C411yescharacteristic
298C2×C4×C31C2×C22⋊C411yescharacteristic
299C2×C4×C31C2×C22⋊C412yes—
300C2×C4×C31C2×C22⋊C412yes—
301C2×C4×C31#13112yes—
302C2×C4×C31C22×D412yes—
303C8×C31—42no—
304C8×C31—42no—
305C8×C31—42no—
306C8×C31—42no—
307C2×#553C2×C3111yescharacteristic
308#2974C2×C3112yescomplemented
309#1473C2×C3112yescomplemented
310#1471C2×C3112yescomplemented
311#1468C2×C3112yescomplemented
312#1465C2×C3111yescharacteristic, complemented
313#1464C2×C3111yescharacteristic, complemented
314#1463C2×C3111yescharacteristic, complemented
315#1459C2×C3111yescharacteristic, complemented
316#1458C2×C3111yescharacteristic, complemented
317C2×#324C2×C3111yescharacteristic, complemented
318C22×C31—21no—
319C22×C31—21no—
320C22×C31—21no—
321C22×C31—21no—
322C22×C31—21no—
323C22×C31—22no—
324C22×C31—21no—
325C22×C31—22no—
326C22×C31—22no—
327C22×C31—21no—
328C22×C31—42no—
329C22×C31—42no—
330C22×C31—41no—
331C22×C31—41no—
332C22×C31—41no—
333C22×C31—41no—
334C22×C31—41no—
335C22×C31—41no—
336C22×C31—81no—
337C22×C31—81no—
338C22×C31—81no—
339C22×C31—81no—
340C22×C31—81no—
341C22×C31—81no—
342C22×C31#41312yes—
343C22×C31C22×C22⋊C411yescharacteristic
344C22×C31C2×#13111yescharacteristic
345C22×C31#56811yescharacteristic
346C4×C31—22no—
347C4×C31—21no—
348C4×C31—21no—
349C4×C31—22no—
350C4×C31—21no—
351C4×C31—21no—
352C4×C31—22no—
353C4×C31—22no—
354C4×C31—41no—
355C4×C31—41no—
356C4×C31—41no—
357C4×C31—41no—
358C4×C31—41no—
359#553—22no—
360#553—22no—
361#553—22no—
362#553—22no—
363C2×#126C4×C3111yescharacteristic
364C2×#126C22×C3111yescharacteristic
365C2×#125C4×C3111yescharacteristic
366C2×#123C4×C3111yescharacteristic
367C2×#123C22×C3111yescharacteristic
368C2×#121C4×C3111yescharacteristic
369C2×#121C4×C3111yescharacteristic
370C2×#121C4×C3111yescharacteristic
371C2×#121C22×C3111yescharacteristic
372C2×C4×D4C4×C3111yescharacteristic
373C2×C4×D4C4×C3111yescharacteristic
374C2×C4×D4C22×C3111yescharacteristic
375C2×C4×D4C22×C3111yescharacteristic
376C2×#117C22×C3111yescharacteristic
377C22×C4⋊C4C22×C3111yescharacteristic
378#436—22no—
379#435—22no—
380#435—22no—
381C8×D4—22no—
382#432C22×C3112yes—
383#431C22×C3112yes—
384#407C22×C3112yes—
385#407C22×C3112yes—
386C2×C22⋊C8C22×C3112yes—
387C2×C22⋊C8C22×C3112yes—
388#324C22×C3111yescharacteristic
389#324C22×C3111yescharacteristic
390#324C22×C3112yes—
391#324C22×C3111yescharacteristic
392#324C22×C3111yescharacteristic
393#324C22×C3112yes—
394#323C22×C3112yes—
395#323C22×C3112yes—
396#323C22×C3112yes—
397#323C22×C3112yes—
398C2×C31—21no—
399C2×C31—21no—
400C2×C31—22no—
401C2×C31—41no—
402C2×C31—42no—
403C2×C31—81no—
404C2×C31—81no—
405C2×C31#288011yescharacteristic
406C2×C31#288311yescharacteristic
407C2×C31C2×#41311yescharacteristic
408C22×D4C2×C4×C3111yescharacteristic
409C22×D4C2×C4×C3111yescharacteristic
410C22×D4C2×C4×C3111yescharacteristic
411C22×D4C2×C4×C3111yescharacteristic
412C22×D4C2×C4×C3111yescharacteristic
413C22×D4C2×C4×C3111yescharacteristic
414C23×C4C2×C4×C3111yescharacteristic
415C23×C4C2×C4×C3111yescharacteristic
416C23×C4C2×C4×C3111yescharacteristic
417C23×C4C2×C4×C3111yescharacteristic
418C23×C4C23×C3111yescharacteristic
419C23×C4C23×C3111yescharacteristic
420C2×M16—22no—
421C2×M16—22no—
422C22×C8—22no—
423C22×C8—22no—
424#126—22no—
425#126—22no—
426#126—22no—
427#126—22no—
428#125—22no—
429#125—22no—
430#123—22no—
431#123—22no—
432#123—22no—
433#123—22no—
434#121—22no—
435#121—22no—
436#121—22no—
437#121—22no—
438#121—22no—
439#121—22no—
440#121—22no—
441#121—22no—
442C4×D4—22no—
443C4×D4—22no—
444C4×D4—21no—
445C4×D4—21no—
446C4×D4—21no—
447C4×D4—21no—
448C4×D4—21no—
449C4×D4—21no—
450C4×D4—21no—
451C4×D4—21no—
452C4×D4D4×C3112yes—
453C4×D4D4×C3112yes—
454C4×D4D4×C3112yes—
455C4×D4D4×C3112yes—
456#117—22no—
457#117—22no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4C2×C4×C3111yescharacteristic
461C2×C4⋊C4C2×C4×C3111yescharacteristic
462C2×C4⋊C4C2×C4×C3111yescharacteristic
463C2×C4⋊C4C2×C4×C3111yescharacteristic
464C2×C4⋊C4C2×C4×C3111yescharacteristic
465C2×C4⋊C4C2×C4×C3111yescharacteristic
466C2×C4⋊C4C2×C4×C3111yescharacteristic
467C2×C4⋊C4C2×C4×C3111yescharacteristic
468C2×C4⋊C4C23×C3111yescharacteristic
469C2×C4⋊C4C23×C3111yescharacteristic
470C2×C22⋊C4C2×C4×C3111yescharacteristic
471C2×C22⋊C4C2×C4×C3111yescharacteristic
472C2×C22⋊C4C2×C4×C3111yescharacteristic
473C2×C22⋊C4C2×C4×C3111yescharacteristic
474C2×C22⋊C4C2×C4×C3111yescharacteristic
475C2×C22⋊C4C2×C4×C3111yescharacteristic
476C2×C22⋊C4C2×C4×C3111yescharacteristic
477C2×C22⋊C4C2×C4×C3111yescharacteristic
478C2×C22⋊C4C23×C3111yescharacteristic
479C2×C22⋊C4C23×C3111yescharacteristic
480C2×C42C2×C4×C3111yescharacteristic
481C2×C42C2×C4×C3111yescharacteristic
482C2×C42C23×C3111yescharacteristic
483C4⋊C8—22no—
484C4⋊C8—22no—
485C22⋊C8—22no—
486C22⋊C8—22no—
487C22⋊C8—22no—
488C22⋊C8—22no—
489C22⋊C8C23×C3112yes—
490C22⋊C8C23×C3112yes—
491C22⋊C8C23×C3112yes—
492C22⋊C8C23×C3112yes—
493#97—22no—
494C4×C8—22no—
495C31#1742711yescharacteristic, direct product factor, Sylow
496C24C22×C4×C3111yescharacteristic
497C24C22×C4×C3111yescharacteristic
498C24C22×C4×C3111yescharacteristic
499C24C22×C4×C3111yescharacteristic
500C2×D4—22no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—22no—
506C2×D4—22no—
507C2×D4—22no—
508C2×D4—41no—
509C2×D4—42no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—81no—
513C2×D4—81no—
514C2×D4C22⋊C4×C3112yes—
515C2×D4C22⋊C4×C3112yes—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—81no—
529C22×C4—81no—
530C22×C4—81no—
531C22×C4—81no—
532C22×C4C22×C4×C3111yescharacteristic
533C22×C4C22×C4×C3111yescharacteristic
534C22×C4C22×C4×C3111yescharacteristic
535C22×C4C22×C4×C3111yescharacteristic
536C22×C4C22×C4×C3111yescharacteristic
537C22×C4C22×C4×C3111yescharacteristic
538C22×C4C22×C4×C3111yescharacteristic
539C22×C4C22×C4×C3111yescharacteristic
540C22×C4C22×C4×C3111yescharacteristic
541C22×C4C22×C4×C3111yescharacteristic
542C22×C4C2×D4×C3112yes—
543C22×C4C2×D4×C3112yes—
544C22×C4C2×D4×C3112yes—
545C22×C4C2×D4×C3112yes—
546C22×C4C24×C3111yescharacteristic
547M16—82no—
548M16—82no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—82no—
554C2×C8—82no—
555C4⋊C4—22no—
556C4⋊C4—22no—
557C4⋊C4—22no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4C22⋊C4×C3112yes—
567C4⋊C4C22⋊C4×C3112yes—
568C22⋊C4—22no—
569C22⋊C4—22no—
570C22⋊C4—22no—
571C22⋊C4—21no—
572C22⋊C4—21no—
573C22⋊C4—21no—
574C22⋊C4—21no—
575C22⋊C4—22no—
576C22⋊C4—22no—
577C22⋊C4—22no—
578C22⋊C4C22⋊C4×C3111yescharacteristic
579C22⋊C4C22⋊C4×C3111yescharacteristic
580C22⋊C4C22⋊C4×C3111yescharacteristic
581C22⋊C4C22⋊C4×C3111yescharacteristic
582C22⋊C4C22⋊C4×C3112yes—
583C22⋊C4C22⋊C4×C3112yes—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42C2×D4×C3112yes—
589C42C2×D4×C3112yes—
590C23—22no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23C2×C22⋊C4×C3112yes—
609C23C2×C22⋊C4×C3111yescharacteristic
610C23C2×C22⋊C4×C3111yescharacteristic
611C23C23×C4×C3111yescharacteristic
612D4—24no—
613D4—42no—
614D4—44no—
615D4—42no—
616D4—42no—
617D4—42no—
618D4—42no—
619D4—82no—
620D4—82no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—81no—
649C2×C4—81no—
650C2×C4—81no—
651C2×C4—81no—
652C2×C4C2×C22⋊C4×C3111yescharacteristic
653C2×C4C2×C22⋊C4×C3111yescharacteristic
654C2×C4C2×C22⋊C4×C3111yescharacteristic
655C2×C4C2×C22⋊C4×C3111yescharacteristic
656C2×C4C2×C22⋊C4×C3112yes—
657C2×C4C2×C22⋊C4×C3112yes—
658C2×C4C31×#13112yes—
659C2×C4C22×D4×C3112yes—
660C8—42no—
661C8—42no—
662C8—42no—
663C8—42no—
664C22—21no—
665C22—21no—
666C22—21no—
667C22—21no—
668C22—21no—
669C22—22no—
670C22—21no—
671C22—22no—
672C22—22no—
673C22—21no—
674C22—42no—
675C22—42no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22C31×#41312yes—
689C22C22×C22⋊C4×C3111yescharacteristic
690C22C2×C31×#13111yescharacteristic
691C22C31×#56811yescharacteristic
692C4—22no—
693C4—21no—
694C4—21no—
695C4—22no—
696C4—21no—
697C4—21no—
698C4—22no—
699C4—22no—
700C4—41no—
701C4—41no—
702C4—41no—
703C4—41no—
704C4—41no—
705C2—21no—
706C2—21no—
707C2—22no—
708C2—41no—
709C2—42no—
710C2—81no—
711C2—81no—
712C2C31×#288011yescharacteristic
713C2C31×#288311yescharacteristic
714C2C2×C31×#41311yescharacteristic
subgroupG/H
center, socleC22×C31C22×C22⋊C4
commutatorC23C23×C4×C31
Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#553C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C4×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2974C2semidirect
3. C31×#1473C2semidirect
4. C31×#1471C2semidirect
5. C31×#1468C2semidirect
6. C31×#1465C2semidirect
7. C31×#1464C2semidirect
8. C31×#1463C2semidirect
9. C31×#1459C2semidirect
10. C31×#1458C2semidirect
11. C2×C31×#324C2semidirect
232. #17427C31direct (N × H)
308. #2974C2×C31semidirect
309. #1473C2×C31semidirect
310. #1471C2×C31semidirect
311. #1468C2×C31semidirect
312. #1465C2×C31semidirect
313. #1464C2×C31semidirect
314. #1463C2×C31semidirect
315. #1459C2×C31semidirect
316. #1458C2×C31semidirect
317. C2×#324C2×C31semidirect
495. C31#17427direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5532
C31×#29742
C31×#14732
C31×#14712
C31×#14682
C31×#14652
C31×#14642
C31×#14632
C31×#14592
C31×#14582
C2×C31×#3242
#1742731