Finite Group Databasebeta

← C31×#17622 #21474381

Subgroups — C31×#17622 #21474381

Order 7936.

1074 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3505C211yesmaximal, characteristic
2C31×#2973C211yesmaximal, characteristic, complemented
3C31×#2349C211yesmaximal, characteristic, complemented
4C31×#1520C211yesmaximal, characteristic, complemented
5C31×#1519C211yesmaximal, characteristic, complemented
6C31×#1513C212yesmaximal, complemented
7C31×#1512C212yesmaximal, complemented
8C31×#1509C212yesmaximal, complemented
9C31×#1504C212yesmaximal, complemented
10C2×C31×#328C211yesmaximal, characteristic, complemented
11C2×C31×#327C211yesmaximal, characteristic, complemented
12C31×#553—22no—
13C31×#553C412yescomplemented
14C31×#552C412yescomplemented
15C31×#551—22no—
16C31×#548C412yescomplemented
17C31×#546C412yescomplemented
18C31×#539—21no—
19C31×#538—21no—
20C31×#534—21no—
21C31×#529C2212yes—
22C31×#525C2212yes—
23C2×C31×C22⋊Q8C2211yescharacteristic
24C2×C31×#121C2211yescharacteristic
25C31×#518—21no—
26C2×C4×D4×C31—21no—
27C2×C4×D4×C31C2211yescharacteristic
28C31×#435—22no—
29C31×#435—22no—
30C31×#432C2212yescomplemented
31C31×#407C2212yescomplemented
32C2×C31×C22⋊C8C2211yescharacteristic
33C2×C31×C22⋊C8C2211yescharacteristic
34C31×#389—21no—
35C31×#385—21no—
36C31×#385—21no—
37C31×#382C2211yescharacteristic, complemented
38C31×#380C2211yescharacteristic
39C31×#380C2211yescharacteristic, complemented
40C4×C4⋊C4×C31C2211yescharacteristic, complemented
41C2×C31×#95C2211yescharacteristic
42C2×C31×#95C2211yescharacteristic, complemented
43C31×#328C2212yescomplemented
44C31×#328C2212yescomplemented
45C31×#328C2212yescomplemented
46C31×#328C2212yescomplemented
47C31×#327C2212yes—
48C31×#327C2212yes—
49C31×#327C2212yes—
50C31×#327C2212yes—
51C2×#41×C31C2×C412yescomplemented
52C22×Q8×C31C2×C411yescharacteristic, complemented
53C22×D4×C31—21no—
54C22×D4×C31C2×C411yescharacteristic, complemented
55C22×D4×C31D411yescharacteristic
56C23×C4×C31—21no—
57C23×C4×C31—21no—
58C23×C4×C31C2311yescharacteristic
59C23×C4×C31C2311yescharacteristic
60C2×M16×C31—22no—
61C22×C8×C31—21no—
62C22×C8×C31—21no—
63C31×#126—22no—
64C31×#126—22no—
65C31×#126—22no—
66C31×#125—22no—
67C31×#125C2×C412yescomplemented
68C31×#124—22no—
69C31×#124C2×C412yescomplemented
70C31×#123—22no—
71C31×#123—22no—
72C31×#123—22no—
73C31×#123—22no—
74C31×#123—22no—
75C31×C22⋊Q8—21no—
76C31×C22⋊Q8—21no—
77C31×C22⋊Q8—22no—
78C31×C22⋊Q8C2×C412yescomplemented
79C31×C22⋊Q8C2×C412yescomplemented
80C31×C22⋊Q8C2312yes—
81C31×#121—22no—
82C31×#121—22no—
83C31×#121—21no—
84C31×#121—21no—
85C31×#121—22no—
86C31×#121C2×C412yescomplemented
87C31×#121C2×C412yescomplemented
88C31×#121C2312yes—
89C31×#120—22no—
90C31×#120—22no—
91C4×Q8×C31C2×C412yescomplemented
92C4×D4×C31—22no—
93C4×D4×C31—22no—
94C4×D4×C31—22no—
95C4×D4×C31—22no—
96C4×D4×C31—22no—
97C4×D4×C31—44no—
98C4×D4×C31C2×C412yes—
99C4×D4×C31C2×C412yes—
100C4×D4×C31C2×C412yescomplemented
101C4×D4×C31D412yes—
102C4×D4×C31D412yes—
103C31×#117—22no—
104C31×#117—22no—
105C31×#117C2×C412yescomplemented
106C2×C4⋊C4×C31—21no—
107C2×C4⋊C4×C31—21no—
108C2×C4⋊C4×C31—21no—
109C2×C4⋊C4×C31—21no—
110C2×C4⋊C4×C31—21no—
111C2×C4⋊C4×C31C2×C411yescharacteristic, complemented
112C2×C4⋊C4×C31C2×C411yescharacteristic, complemented
113C2×C4⋊C4×C31D411yescharacteristic
114C2×C22⋊C4×C31—21no—
115C2×C22⋊C4×C31—21no—
116C2×C22⋊C4×C31—22no—
117C2×C22⋊C4×C31—21no—
118C2×C22⋊C4×C31—21no—
119C2×C22⋊C4×C31D411yescharacteristic
120C2×C22⋊C4×C31D411yescharacteristic
121C2×C42×C31—21no—
122C2×C42×C31C2311yescharacteristic
123C31×C4⋊C8—22no—
124C31×C22⋊C8—21no—
125C31×C22⋊C8—21no—
126C31×C22⋊C8—22no—
127C31×C22⋊C8C2312yes—
128C31×C22⋊C8C2312yes—
129C31×#97—22no—
130C31×#95—21no—
131C31×#95—21no—
132C31×#95—21no—
133C31×#95C2311yescharacteristic
134C31×#95C2311yescharacteristic
135C31×#95C2311yescharacteristic
136C31×#95C2311yescharacteristic
137C24×C31—21no—
138C24×C31C2×D411yescharacteristic
139C24×C31C2×D411yescharacteristic
140#41×C31—82no—
141C2×Q8×C31—21no—
142C2×Q8×C31—81no—
143C2×Q8×C31C22×C412yes—
144C2×D4×C31—22no—
145C2×D4×C31—22no—
146C2×D4×C31—22no—
147C2×D4×C31—22no—
148C2×D4×C31—22no—
149C2×D4×C31—22no—
150C2×D4×C31—21no—
151C2×D4×C31—42no—
152C2×D4×C31—42no—
153C2×D4×C31—81no—
154C2×D4×C31C22⋊C412yes—
155C2×D4×C31C22⋊C412yes—
156C2×D4×C31C22×C412yes—
157C22×C4×C31—21no—
158C22×C4×C31—21no—
159C22×C4×C31—21no—
160C22×C4×C31—21no—
161C22×C4×C31—22no—
162C22×C4×C31—22no—
163C22×C4×C31—21no—
164C22×C4×C31—21no—
165C22×C4×C31—21no—
166C22×C4×C31—42no—
167C22×C4×C31—42no—
168C22×C4×C31—42no—
169C22×C4×C31—42no—
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×C412yes—
177C22×C4×C31C2×D411yescharacteristic
178C22×C4×C31C2×D411yescharacteristic
179C22×C4×C31C2×D411yescharacteristic
180C22×C4×C31C2×D411yescharacteristic
181C22×C4×C31C2×D411yescharacteristic
182C22×C4×C31C2×D411yescharacteristic
183C22×C4×C31C2×D412yes—
184C22×C4×C31C2411yescharacteristic
185M16×C31—82no—
186C2×C8×C31—22no—
187C2×C8×C31—22no—
188C2×C8×C31—81no—
189C2×C8×C31—81no—
190C4⋊C4×C31—22no—
191C4⋊C4×C31—21no—
192C4⋊C4×C31—21no—
193C4⋊C4×C31—22no—
194C4⋊C4×C31—22no—
195C4⋊C4×C31—22no—
196C4⋊C4×C31—22no—
197C4⋊C4×C31—22no—
198C4⋊C4×C31—42no—
199C4⋊C4×C31—42no—
200C4⋊C4×C31—81no—
201C4⋊C4×C31—81no—
202C4⋊C4×C31C22⋊C412yes—
203C4⋊C4×C31C22⋊C412yes—
204C4⋊C4×C31C22×C412yes—
205C4⋊C4×C31C22×C412yes—
206C22⋊C4×C31—22no—
207C22⋊C4×C31—22no—
208C22⋊C4×C31—22no—
209C22⋊C4×C31—22no—
210C22⋊C4×C31—22no—
211C22⋊C4×C31—22no—
212C22⋊C4×C31—22no—
213C22⋊C4×C31—22no—
214C22⋊C4×C31—22no—
215C22⋊C4×C31—22no—
216C22⋊C4×C31—42no—
217C22⋊C4×C31—42no—
218C22⋊C4×C31C22⋊C412yes—
219C22⋊C4×C31C22⋊C412yes—
220C22⋊C4×C31C22⋊C412yes—
221C22⋊C4×C31C22⋊C412yes—
222C42×C31—22no—
223C42×C31—22no—
224C42×C31—42no—
225C42×C31C22×C412yes—
226C42×C31C2×D412yes—
227#17622C3111yesmaximal, characteristic, direct product factor, Sylow
228C23×C31—21no—
229C23×C31—21no—
230C23×C31—22no—
231C23×C31—41no—
232C23×C31—41no—
233C23×C31—41no—
234C23×C31—41no—
235C23×C31—42no—
236C23×C31—81no—
237C23×C31—81no—
238C23×C31C2×C22⋊C412yes—
239C23×C31C2×C22⋊C411yescharacteristic
240C23×C31C2×C22⋊C411yescharacteristic
241C23×C31AGL(1,ℤ/8)12yes—
242C23×C31#13712yes—
243C23×C31C22×D411yescharacteristic
244Q8×C31—42no—
245Q8×C31—81no—
246D4×C31—24no—
247D4×C31—24no—
248D4×C31—42no—
249D4×C31—42no—
250D4×C31—42no—
251D4×C31—44no—
252D4×C31—81no—
253D4×C31—82no—
254D4×C31—82no—
255C2×C4×C31—21no—
256C2×C4×C31—21no—
257C2×C4×C31—22no—
258C2×C4×C31—22no—
259C2×C4×C31—22no—
260C2×C4×C31—22no—
261C2×C4×C31—41no—
262C2×C4×C31—41no—
263C2×C4×C31—41no—
264C2×C4×C31—41no—
265C2×C4×C31—41no—
266C2×C4×C31—42no—
267C2×C4×C31—41no—
268C2×C4×C31—41no—
269C2×C4×C31—41no—
270C2×C4×C31—42no—
271C2×C4×C31—41no—
272C2×C4×C31—41no—
273C2×C4×C31—42no—
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—82no—
284C2×C4×C31—82no—
285C2×C4×C31—81no—
286C2×C4×C31—81no—
287C2×C4×C31—84no—
288C2×C4×C31—84no—
289C2×C4×C31C2×C22⋊C412yes—
290C2×C4×C31C2×C22⋊C412yes—
291C2×C4×C31C2×C22⋊C412yes—
292C2×C4×C31C2×C22⋊C411yescharacteristic
293C2×C4×C31C2×C22⋊C411yescharacteristic
294C2×C4×C31C23×C411yescharacteristic
295C2×C4×C31C22×D411yescharacteristic
296C8×C31—42no—
297C8×C31—42no—
298#3505C2×C3111yescharacteristic
299#2973C2×C3111yescharacteristic, complemented
300#2349C2×C3111yescharacteristic, complemented
301#1520C2×C3111yescharacteristic, complemented
302#1519C2×C3111yescharacteristic, complemented
303#1513C2×C3112yescomplemented
304#1512C2×C3112yescomplemented
305#1509C2×C3112yescomplemented
306#1504C2×C3112yescomplemented
307C2×#328C2×C3111yescharacteristic, complemented
308C2×#327C2×C3111yescharacteristic, complemented
309C22×C31—21no—
310C22×C31—21no—
311C22×C31—21no—
312C22×C31—21no—
313C22×C31—21no—
314C22×C31—21no—
315C22×C31—22no—
316C22×C31—22no—
317C22×C31—22no—
318C22×C31—42no—
319C22×C31—42no—
320C22×C31—42no—
321C22×C31—42no—
322C22×C31—42no—
323C22×C31—42no—
324C22×C31—42no—
325C22×C31—162no—
326C22×C31#41712yes—
327C22×C31#41712yes—
328C22×C31C22×C22⋊C411yescharacteristic
329C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
330C22×C31C2×#13711yescharacteristic
331C4×C31—21no—
332C4×C31—21no—
333C4×C31—22no—
334C4×C31—21no—
335C4×C31—21no—
336C4×C31—22no—
337C4×C31—22no—
338C4×C31—42no—
339C4×C31—42no—
340C4×C31—42no—
341C4×C31—42no—
342C4×C31—81no—
343C4×C31—81no—
344C4×C31—81no—
345#553—22no—
346#553C4×C3112yescomplemented
347#552C4×C3112yescomplemented
348#551—22no—
349#548C4×C3112yescomplemented
350#546C4×C3112yescomplemented
351#539—21no—
352#538—21no—
353#534—21no—
354#529C22×C3112yes—
355#525C22×C3112yes—
356C2×C22⋊Q8C22×C3111yescharacteristic
357C2×#121C22×C3111yescharacteristic
358#518—21no—
359C2×C4×D4—21no—
360C2×C4×D4C22×C3111yescharacteristic
361#435—22no—
362#435—22no—
363#432C22×C3112yescomplemented
364#407C22×C3112yescomplemented
365C2×C22⋊C8C22×C3111yescharacteristic
366C2×C22⋊C8C22×C3111yescharacteristic
367#389—21no—
368#385—21no—
369#385—21no—
370#382C22×C3111yescharacteristic, complemented
371#380C22×C3111yescharacteristic
372#380C22×C3111yescharacteristic, complemented
373C4×C4⋊C4C22×C3111yescharacteristic, complemented
374C2×#95C22×C3111yescharacteristic
375C2×#95C22×C3111yescharacteristic, complemented
376#328C22×C3112yescomplemented
377#328C22×C3112yescomplemented
378#328C22×C3112yescomplemented
379#328C22×C3112yescomplemented
380#327C22×C3112yes—
381#327C22×C3112yes—
382#327C22×C3112yes—
383#327C22×C3112yes—
384C2×C31—21no—
385C2×C31—21no—
386C2×C31—22no—
387C2×C31—22no—
388C2×C31—42no—
389C2×C31—82no—
390C2×C31#288311yescharacteristic
391C2×C31C2×#41711yescharacteristic
392C2×C31#290111yescharacteristic
393C2×#41C2×C4×C3112yescomplemented
394C22×Q8C2×C4×C3111yescharacteristic, complemented
395C22×D4—21no—
396C22×D4C2×C4×C3111yescharacteristic, complemented
397C22×D4D4×C3111yescharacteristic
398C23×C4—21no—
399C23×C4—21no—
400C23×C4C23×C3111yescharacteristic
401C23×C4C23×C3111yescharacteristic
402C2×M16—22no—
403C22×C8—21no—
404C22×C8—21no—
405#126—22no—
406#126—22no—
407#126—22no—
408#125—22no—
409#125C2×C4×C3112yescomplemented
410#124—22no—
411#124C2×C4×C3112yescomplemented
412#123—22no—
413#123—22no—
414#123—22no—
415#123—22no—
416#123—22no—
417C22⋊Q8—21no—
418C22⋊Q8—21no—
419C22⋊Q8—22no—
420C22⋊Q8C2×C4×C3112yescomplemented
421C22⋊Q8C2×C4×C3112yescomplemented
422C22⋊Q8C23×C3112yes—
423#121—22no—
424#121—22no—
425#121—21no—
426#121—21no—
427#121—22no—
428#121C2×C4×C3112yescomplemented
429#121C2×C4×C3112yescomplemented
430#121C23×C3112yes—
431#120—22no—
432#120—22no—
433C4×Q8C2×C4×C3112yescomplemented
434C4×D4—22no—
435C4×D4—22no—
436C4×D4—22no—
437C4×D4—22no—
438C4×D4—22no—
439C4×D4—44no—
440C4×D4C2×C4×C3112yes—
441C4×D4C2×C4×C3112yes—
442C4×D4C2×C4×C3112yescomplemented
443C4×D4D4×C3112yes—
444C4×D4D4×C3112yes—
445#117—22no—
446#117—22no—
447#117C2×C4×C3112yescomplemented
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4C2×C4×C3111yescharacteristic, complemented
454C2×C4⋊C4C2×C4×C3111yescharacteristic, complemented
455C2×C4⋊C4D4×C3111yescharacteristic
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4D4×C3111yescharacteristic
462C2×C22⋊C4D4×C3111yescharacteristic
463C2×C42—21no—
464C2×C42C23×C3111yescharacteristic
465C4⋊C8—22no—
466C22⋊C8—21no—
467C22⋊C8—21no—
468C22⋊C8—22no—
469C22⋊C8C23×C3112yes—
470C22⋊C8C23×C3112yes—
471#97—22no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95C23×C3111yescharacteristic
476#95C23×C3111yescharacteristic
477#95C23×C3111yescharacteristic
478#95C23×C3111yescharacteristic
479C31#1762211yescharacteristic, direct product factor, Sylow
480C24—21no—
481C24C2×D4×C3111yescharacteristic
482C24C2×D4×C3111yescharacteristic
483#41—82no—
484C2×Q8—21no—
485C2×Q8—81no—
486C2×Q8C22×C4×C3112yes—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—21no—
494C2×D4—42no—
495C2×D4—42no—
496C2×D4—81no—
497C2×D4C22⋊C4×C3112yes—
498C2×D4C22⋊C4×C3112yes—
499C2×D4C22×C4×C3112yes—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—81no—
514C22×C4—81no—
515C22×C4—81no—
516C22×C4—81no—
517C22×C4C22×C4×C3111yescharacteristic
518C22×C4C22×C4×C3111yescharacteristic
519C22×C4C22×C4×C3112yes—
520C22×C4C2×D4×C3111yescharacteristic
521C22×C4C2×D4×C3111yescharacteristic
522C22×C4C2×D4×C3111yescharacteristic
523C22×C4C2×D4×C3111yescharacteristic
524C22×C4C2×D4×C3111yescharacteristic
525C22×C4C2×D4×C3111yescharacteristic
526C22×C4C2×D4×C3112yes—
527C22×C4C24×C3111yescharacteristic
528M16—82no—
529C2×C8—22no—
530C2×C8—22no—
531C2×C8—81no—
532C2×C8—81no—
533C4⋊C4—22no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—22no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—42no—
542C4⋊C4—42no—
543C4⋊C4—81no—
544C4⋊C4—81no—
545C4⋊C4C22⋊C4×C3112yes—
546C4⋊C4C22⋊C4×C3112yes—
547C4⋊C4C22×C4×C3112yes—
548C4⋊C4C22×C4×C3112yes—
549C22⋊C4—22no—
550C22⋊C4—22no—
551C22⋊C4—22no—
552C22⋊C4—22no—
553C22⋊C4—22no—
554C22⋊C4—22no—
555C22⋊C4—22no—
556C22⋊C4—22no—
557C22⋊C4—22no—
558C22⋊C4—22no—
559C22⋊C4—42no—
560C22⋊C4—42no—
561C22⋊C4C22⋊C4×C3112yes—
562C22⋊C4C22⋊C4×C3112yes—
563C22⋊C4C22⋊C4×C3112yes—
564C22⋊C4C22⋊C4×C3112yes—
565C42—22no—
566C42—22no—
567C42—42no—
568C42C22×C4×C3112yes—
569C42C2×D4×C3112yes—
570C23—21no—
571C23—21no—
572C23—22no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—42no—
578C23—81no—
579C23—81no—
580C23C2×C22⋊C4×C3112yes—
581C23C2×C22⋊C4×C3111yescharacteristic
582C23C2×C22⋊C4×C3111yescharacteristic
583C23C31×AGL(1,ℤ/8)12yes—
584C23C31×#13712yes—
585C23C22×D4×C3111yescharacteristic
586Q8—42no—
587Q8—81no—
588D4—24no—
589D4—24no—
590D4—42no—
591D4—44no—
592D4—42no—
593D4—42no—
594D4—81no—
595D4—82no—
596D4—82no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—42no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—42no—
613C2×C4—41no—
614C2×C4—42no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—82no—
626C2×C4—82no—
627C2×C4—81no—
628C2×C4—81no—
629C2×C4—84no—
630C2×C4—84no—
631C2×C4C2×C22⋊C4×C3112yes—
632C2×C4C2×C22⋊C4×C3112yes—
633C2×C4C2×C22⋊C4×C3112yes—
634C2×C4C2×C22⋊C4×C3111yescharacteristic
635C2×C4C2×C22⋊C4×C3111yescharacteristic
636C2×C4C23×C4×C3111yescharacteristic
637C2×C4C22×D4×C3111yescharacteristic
638C8—42no—
639C8—42no—
640C22—21no—
641C22—21no—
642C22—21no—
643C22—21no—
644C22—21no—
645C22—21no—
646C22—22no—
647C22—22no—
648C22—22no—
649C22—42no—
650C22—42no—
651C22—42no—
652C22—42no—
653C22—42no—
654C22—42no—
655C22—42no—
656C22—162no—
657C22C31×#41712yes—
658C22C31×#41712yes—
659C22C22×C22⋊C4×C3111yescharacteristic
660C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
661C22C2×C31×#13711yescharacteristic
662C4—21no—
663C4—21no—
664C4—22no—
665C4—21no—
666C4—21no—
667C4—22no—
668C4—22no—
669C4—42no—
670C4—42no—
671C4—42no—
672C4—42no—
673C4—81no—
674C4—81no—
675C4—81no—
676C2—21no—
677C2—21no—
678C2—22no—
679C2—22no—
680C2—42no—
681C2—82no—
682C2C31×#288311yescharacteristic
683C2C2×C31×#41711yescharacteristic
684C2C31×#290111yescharacteristic
subgroupG/H
center, socleC22×C31C22×C22⋊C4
commutatorC2×C4C23×C4×C31
Frattini, cosocleC22×C4C24×C31
prime radicalC31×#3505C2
LCSG ▷ C2×C4 ▷ C22 ▷ 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×#2973C2semidirect
3. C31×#2349C2semidirect
4. C31×#1520C2semidirect
5. C31×#1519C2semidirect
6. C31×#1513C2semidirect
7. C31×#1512C2semidirect
8. C31×#1509C2semidirect
9. C31×#1504C2semidirect
10. C2×C31×#328C2semidirect
11. C2×C31×#327C2semidirect
13. C31×#553C4semidirect
14. C31×#552C4semidirect
16. C31×#548C4semidirect
17. C31×#546C4semidirect
30. C31×#432C22semidirect
31. C31×#407C22semidirect
37. C31×#382C22semidirect
39. C31×#380C22semidirect
40. C4×C4⋊C4×C31C22semidirect
42. C2×C31×#95C22semidirect
43. C31×#328C22semidirect
44. C31×#328C22semidirect
45. C31×#328C22semidirect
46. C31×#328C22semidirect
51. C2×#41×C31C2×C4semidirect
52. C22×Q8×C31C2×C4semidirect
54. C22×D4×C31C2×C4semidirect
67. C31×#125C2×C4semidirect
69. C31×#124C2×C4semidirect
78. C31×C22⋊Q8C2×C4semidirect
79. C31×C22⋊Q8C2×C4semidirect
86. C31×#121C2×C4semidirect
87. C31×#121C2×C4semidirect
91. C4×Q8×C31C2×C4semidirect
100. C4×D4×C31C2×C4semidirect
105. C31×#117C2×C4semidirect
111. C2×C4⋊C4×C31C2×C4semidirect
112. C2×C4⋊C4×C31C2×C4semidirect
227. #17622C31direct (N × H)
299. #2973C2×C31semidirect
300. #2349C2×C31semidirect
301. #1520C2×C31semidirect
302. #1519C2×C31semidirect
303. #1513C2×C31semidirect
304. #1512C2×C31semidirect
305. #1509C2×C31semidirect
306. #1504C2×C31semidirect
307. C2×#328C2×C31semidirect
308. C2×#327C2×C31semidirect
346. #553C4×C31semidirect
347. #552C4×C31semidirect
349. #548C4×C31semidirect
350. #546C4×C31semidirect
363. #432C22×C31semidirect
364. #407C22×C31semidirect
370. #382C22×C31semidirect
372. #380C22×C31semidirect
373. C4×C4⋊C4C22×C31semidirect
375. C2×#95C22×C31semidirect
376. #328C22×C31semidirect
377. #328C22×C31semidirect
378. #328C22×C31semidirect
379. #328C22×C31semidirect
393. C2×#41C2×C4×C31semidirect
394. C22×Q8C2×C4×C31semidirect
396. C22×D4C2×C4×C31semidirect
409. #125C2×C4×C31semidirect
411. #124C2×C4×C31semidirect
420. C22⋊Q8C2×C4×C31semidirect
421. C22⋊Q8C2×C4×C31semidirect
428. #121C2×C4×C31semidirect
429. #121C2×C4×C31semidirect
433. C4×Q8C2×C4×C31semidirect
442. C4×D4C2×C4×C31semidirect
447. #117C2×C4×C31semidirect
453. C2×C4⋊C4C2×C4×C31semidirect
454. C2×C4⋊C4C2×C4×C31semidirect
479. C31#17622direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35052
C31×#29732
C31×#23492
C31×#15202
C31×#15192
C31×#15132
C31×#15122
C31×#15092
C31×#15042
C2×C31×#3282
C2×C31×#3272
#1762231