Finite Group Databasebeta

← C31×#23880 #21480639

Subgroups — C31×#23880 #21480639

Order 7936.

1696 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#137C211yesmaximal, characteristic, complemented
2C31×#3489C211yesmaximal, characteristic
3C2×C31×#456C212yesmaximal, complemented
4C31×#3004C211yesmaximal, characteristic, complemented
5C31×#2434C211yesmaximal, characteristic, complemented
6C31×#2007C212yesmaximal, complemented
7C31×#2005C212yesmaximal, complemented
8C31×#1901C211yesmaximal, characteristic, complemented
9C31×#1882C212yesmaximal, complemented
10C31×#1871C211yesmaximal, characteristic, complemented
11C31×#1789C211yesmaximal, characteristic, complemented
12C2×C31×2−1+4C2211yescharacteristic
13C22×#41×C31C2211yescharacteristic
14C23×Q8×C31C2211yescharacteristic
15C2×C31×#137—21no—
16C2×C31×#137—21no—
17C2×C31×#137—28no—
18C2×C31×#137C2212yes—
19C2×C31×#137C2212yes—
20C2×C31×#137C2212yescomplemented
21C22×Q16×C31—21no—
22C22×SD16×C31—21no—
23C22×M16×C31C2211yescharacteristic
24D4×Q8×C31—21no—
25C31×#548—21no—
26C31×#547—21no—
27C31×#547—22no—
28C31×#546—21no—
29C31×#546—22no—
30C31×#537—21no—
31C31×#537C2211yescharacteristic
32C31×#536—21no—
33C31×#536C2211yescharacteristic
34C2×C31×C4⋊Q8C2212yescomplemented
35C31×#525—21no—
36C31×#525C2211yescharacteristic
37C2×C31×C22⋊Q8—21no—
38C2×C31×C22⋊Q8C2211yescharacteristic
39C31×#520C2211yescharacteristic
40C31×#456—28no—
41C31×#451—21no—
42C31×#451—21no—
43C31×#448—21no—
44C31×#448—21no—
45C2×C31×#104C2212yes—
46C2×C31×#104C2212yes—
47C2×C31×#104C2212yescomplemented
48C31×#419C2212yescomplemented
49C2×C31×#101C2212yescomplemented
50C31×#407C2211yescharacteristic
51C31×#395—22no—
52C31×#391C2212yescomplemented
53C31×#385—22no—
54C4×C22⋊C4×C31C2211yescharacteristic
55C31×#343C2212yescomplemented
56C31×#339C2212yescomplemented
57C31×2−1+4—24no—
58C31×2−1+4—42no—
59C2×#41×C31—21no—
60C2×#41×C31—21no—
61C2×#41×C31—21no—
62C2×#41×C31—22no—
63C2×#41×C31—21no—
64C2×#41×C31—24no—
65C2×#41×C31—42no—
66C2×#41×C31D411yescharacteristic
67C2×#41×C31D411yescharacteristic
68C2×#41×C31C2311yescharacteristic
69C2×#41×C31C2311yescharacteristic
70C2×#41×C31C2311yescharacteristic
71C22×Q8×C31—21no—
72C22×Q8×C31—21no—
73C22×Q8×C31—21no—
74C22×Q8×C31—24no—
75C22×Q8×C31—21no—
76C22×Q8×C31—21no—
77C22×Q8×C31—21no—
78C22×Q8×C31—21no—
79C22×Q8×C31—42no—
80C22×Q8×C31D411yescharacteristic
81C22×Q8×C31C2312yes—
82C22×Q8×C31C2311yescharacteristic
83C22×D4×C31—21no—
84C22×D4×C31D411yescharacteristic
85C23×C4×C31—21no—
86C23×C4×C31—21no—
87C23×C4×C31C2311yescharacteristic
88C31×#137—28no—
89C31×#137—28no—
90C31×#137—24no—
91C31×#137—24no—
92C31×#137—24no—
93C31×#137—24no—
94C31×#137—42no—
95C31×#137D418yescomplemented
96C2×Q16×C31—28no—
97C2×Q16×C31—22no—
98C2×Q16×C31—22no—
99C2×Q16×C31—22no—
100C2×SD16×C31—28no—
101C2×SD16×C31—22no—
102C2×SD16×C31—22no—
103C2×SD16×C31—22no—
104C2×M16×C31—21no—
105C2×M16×C31—24no—
106C2×M16×C31C2312yes—
107C2×M16×C31C2312yes—
108C22×C8×C31—21no—
109C31×C4⋊Q8—22no—
110C31×C4⋊Q8—21no—
111C31×C4⋊Q8—24no—
112C31×C4⋊Q8—42no—
113C31×#124—22no—
114C31×#124—21no—
115C31×#123—22no—
116C31×#123—22no—
117C31×#123—22no—
118C31×#123—21no—
119C31×#123—22no—
120C31×C22⋊Q8—22no—
121C31×C22⋊Q8—22no—
122C31×C22⋊Q8—22no—
123C31×C22⋊Q8—21no—
124C31×C22⋊Q8—21no—
125C31×C22⋊Q8—21no—
126C31×C22⋊Q8—21no—
127C31×C22⋊Q8—21no—
128C31×C22⋊Q8—21no—
129C31×C22⋊Q8—21no—
130C31×C22⋊Q8—21no—
131C31×C22⋊Q8D411yescharacteristic
132C31×C22⋊Q8D411yescharacteristic
133C31×#121—22no—
134C31×#121—22no—
135C31×#121—22no—
136C31×#121—21no—
137C31×#121—21no—
138C31×#121—22no—
139C31×#121D411yescharacteristic
140C31×#121D411yescharacteristic
141C31×#120—22no—
142C31×#120—21no—
143C4×Q8×C31—21no—
144C4×D4×C31—22no—
145C4×D4×C31—22no—
146C4×D4×C31—21no—
147C4×D4×C31—22no—
148C4×D4×C31—21no—
149C4×D4×C31—21no—
150C31×#117—21no—
151C31×#117C2311yescharacteristic
152C2×C4⋊C4×C31—22no—
153C2×C4⋊C4×C31—21no—
154C2×C4⋊C4×C31—24no—
155C2×C4⋊C4×C31D412yes—
156C2×C4⋊C4×C31C2311yescharacteristic
157C2×C22⋊C4×C31—22no—
158C2×C22⋊C4×C31—21no—
159C2×C22⋊C4×C31D412yes—
160C2×C42×C31C2312yes—
161C31×#104—24no—
162C31×#104—24no—
163C31×#104—42no—
164C31×#103—22no—
165C31×#103—22no—
166C31×#101—24no—
167C31×C22⋊C8—21no—
168C31×C22⋊C8—21no—
169C31×#95—21no—
170C31×#95—24no—
171C24×C31—21no—
172C24×C31C2×D411yescharacteristic
173#41×C31—22no—
174#41×C31—22no—
175#41×C31—22no—
176#41×C31—22no—
177#41×C31—22no—
178#41×C31—22no—
179#41×C31—22no—
180#41×C31—44no—
181#41×C31—41no—
182#41×C31—41no—
183#41×C31—44no—
184#41×C31—44no—
185#41×C31—48no—
186#41×C31—42no—
187#41×C31—42no—
188#41×C31C2×D414yes—
189C2×Q8×C31—22no—
190C2×Q8×C31—21no—
191C2×Q8×C31—22no—
192C2×Q8×C31—21no—
193C2×Q8×C31—21no—
194C2×Q8×C31—22no—
195C2×Q8×C31—22no—
196C2×Q8×C31—24no—
197C2×Q8×C31—24no—
198C2×Q8×C31—22no—
199C2×Q8×C31—22no—
200C2×Q8×C31—22no—
201C2×Q8×C31—22no—
202C2×Q8×C31—22no—
203C2×Q8×C31—44no—
204C2×Q8×C31—41no—
205C2×Q8×C31—44no—
206C2×Q8×C31—44no—
207C2×Q8×C31—44no—
208C2×Q8×C31—42no—
209C2×Q8×C31—42no—
210C2×Q8×C31—42no—
211C2×Q8×C31—42no—
212C2×Q8×C31—41no—
213C2×Q8×C31—41no—
214C2×Q8×C31C2×D411yescharacteristic
215C2×Q8×C31C2×D411yescharacteristic
216C2×Q8×C31C2×D414yes—
217C2×Q8×C31C2×D411yescharacteristic
218C2×D4×C31—21no—
219C2×D4×C31—22no—
220C2×D4×C31—22no—
221C2×D4×C31—21no—
222C2×D4×C31—21no—
223C2×D4×C31—21no—
224C2×D4×C31—21no—
225C2×D4×C31—21no—
226C2×D4×C31—22no—
227C2×D4×C31—21no—
228C2×D4×C31—21no—
229C2×D4×C31—41no—
230C2×D4×C31—44no—
231C2×D4×C31C2×D411yescharacteristic
232C2×D4×C31C2×D411yescharacteristic
233C2×D4×C31C2×D411yescharacteristic
234C22×C4×C31—21no—
235C22×C4×C31—22no—
236C22×C4×C31—22no—
237C22×C4×C31—22no—
238C22×C4×C31—22no—
239C22×C4×C31—21no—
240C22×C4×C31—22no—
241C22×C4×C31—22no—
242C22×C4×C31—22no—
243C22×C4×C31—21no—
244C22×C4×C31—21no—
245C22×C4×C31—21no—
246C22×C4×C31—21no—
247C22×C4×C31—44no—
248C22×C4×C31—44no—
249C22×C4×C31—41no—
250C22×C4×C31—41no—
251C22×C4×C31C2×D412yes—
252C22×C4×C31C2×D411yescharacteristic
253C22×C4×C31C2×D411yescharacteristic
254C22×C4×C31C2×D411yescharacteristic
255C22×C4×C31C2×D411yescharacteristic
256C22×C4×C31C2×D411yescharacteristic
257C22×C4×C31C2×D412yes—
258C22×C4×C31C2411yescharacteristic
259Q16×C31—28no—
260Q16×C31—28no—
261Q16×C31—44no—
262SD16×C31—28no—
263SD16×C31—28no—
264SD16×C31—44no—
265M16×C31—24no—
266M16×C31—22no—
267M16×C31—22no—
268M16×C31—22no—
269M16×C31C2×D414yes—
270C2×C8×C31—24no—
271C2×C8×C31—22no—
272C2×C8×C31—22no—
273C4⋊C4×C31—22no—
274C4⋊C4×C31—22no—
275C4⋊C4×C31—22no—
276C4⋊C4×C31—22no—
277C4⋊C4×C31—21no—
278C4⋊C4×C31—22no—
279C4⋊C4×C31—22no—
280C4⋊C4×C31—21no—
281C4⋊C4×C31—21no—
282C4⋊C4×C31—21no—
283C4⋊C4×C31—48no—
284C4⋊C4×C31C2×D411yescharacteristic
285C4⋊C4×C31C2×D411yescharacteristic
286C22⋊C4×C31—24no—
287C22⋊C4×C31—22no—
288C22⋊C4×C31—22no—
289C22⋊C4×C31—22no—
290C22⋊C4×C31—22no—
291C22⋊C4×C31—22no—
292C22⋊C4×C31—21no—
293C22⋊C4×C31—22no—
294C22⋊C4×C31—22no—
295C22⋊C4×C31—21no—
296C22⋊C4×C31—21no—
297C22⋊C4×C31—21no—
298C22⋊C4×C31—21no—
299C42×C31—22no—
300C42×C31—21no—
301C42×C31—22no—
302C42×C31—22no—
303#23880C3111yesmaximal, characteristic, direct product factor, Sylow
304C23×C31—21no—
305C23×C31—22no—
306C23×C31—22no—
307C23×C31—21no—
308C23×C31—21no—
309C23×C31—41no—
310C23×C31—42no—
311C23×C31—42no—
312C23×C31—81no—
313C23×C31#12011yescharacteristic
314C23×C31#12011yescharacteristic
315C23×C31C22×D411yescharacteristic
316Q8×C31—21no—
317Q8×C31—24no—
318Q8×C31—21no—
319Q8×C31—21no—
320Q8×C31—24no—
321Q8×C31—22no—
322Q8×C31—42no—
323Q8×C31—44no—
324Q8×C31—44no—
325Q8×C31—44no—
326Q8×C31—41no—
327Q8×C31—42no—
328Q8×C31—41no—
329Q8×C31—42no—
330Q8×C31—42no—
331Q8×C31#12012yes—
332D4×C31—24no—
333D4×C31—21no—
334D4×C31—21no—
335D4×C31—21no—
336D4×C31—22no—
337D4×C31—42no—
338D4×C31—42no—
339D4×C31—42no—
340D4×C31—44no—
341D4×C31—42no—
342D4×C31—42no—
343D4×C31—42no—
344D4×C31—81no—
345D4×C31—82no—
346D4×C31#12012yes—
347C2×C4×C31—21no—
348C2×C4×C31—22no—
349C2×C4×C31—21no—
350C2×C4×C31—21no—
351C2×C4×C31—21no—
352C2×C4×C31—21no—
353C2×C4×C31—22no—
354C2×C4×C31—22no—
355C2×C4×C31—24no—
356C2×C4×C31—24no—
357C2×C4×C31—21no—
358C2×C4×C31—22no—
359C2×C4×C31—21no—
360C2×C4×C31—21no—
361C2×C4×C31—22no—
362C2×C4×C31—21no—
363C2×C4×C31—24no—
364C2×C4×C31—24no—
365C2×C4×C31—42no—
366C2×C4×C31—42no—
367C2×C4×C31—42no—
368C2×C4×C31—44no—
369C2×C4×C31—42no—
370C2×C4×C31—44no—
371C2×C4×C31—44no—
372C2×C4×C31—44no—
373C2×C4×C31—42no—
374C2×C4×C31—42no—
375C2×C4×C31—42no—
376C2×C4×C31—41no—
377C2×C4×C31—41no—
378C2×C4×C31—42no—
379C2×C4×C31—42no—
380C2×C4×C31—82no—
381C2×C4×C31#12011yescharacteristic
382C2×C4×C31#12011yescharacteristic
383C2×C4×C31C22×D411yescharacteristic
384C2×C4×C31C22×D412yes—
385C2×C4×C31C22×D411yescharacteristic
386C2×C4×C31H(5,𝔽2)12yes—
387C8×C31—24no—
388C8×C31—42no—
389C22×#137C2×C3111yescharacteristic, complemented
390#3489C2×C3111yescharacteristic
391C2×#456C2×C3112yescomplemented
392#3004C2×C3111yescharacteristic, complemented
393#2434C2×C3111yescharacteristic, complemented
394#2007C2×C3112yescomplemented
395#2005C2×C3112yescomplemented
396#1901C2×C3111yescharacteristic, complemented
397#1882C2×C3112yescomplemented
398#1871C2×C3111yescharacteristic, complemented
399#1789C2×C3111yescharacteristic, complemented
400C22×C31—21no—
401C22×C31—21no—
402C22×C31—21no—
403C22×C31—21no—
404C22×C31—21no—
405C22×C31—22no—
406C22×C31—21no—
407C22×C31—21no—
408C22×C31—44no—
409C22×C31—41no—
410C22×C31—41no—
411C22×C31—41no—
412C22×C31—41no—
413C22×C31—41no—
414C22×C31—41no—
415C22×C31—41no—
416C22×C31—41no—
417C22×C31—84no—
418C22×C31#45612yescomplemented
419C22×C31C2×#12011yescharacteristic
420C22×C31D4212yes—
421C4×C31—21no—
422C4×C31—21no—
423C4×C31—22no—
424C4×C31—44no—
425C4×C31—42no—
426C4×C31—41no—
427C4×C31—41no—
428C4×C31—44no—
429C4×C31—41no—
430C4×C31—42no—
431C4×C31—41no—
432C4×C31C2×#12011yescharacteristic
433C4×C31#53411yescharacteristic
434C4×C31D4212yes—
435C2×2−1+4C22×C3111yescharacteristic
436C22×#41C22×C3111yescharacteristic
437C23×Q8C22×C3111yescharacteristic
438C2×#137—21no—
439C2×#137—21no—
440C2×#137—28no—
441C2×#137C22×C3112yes—
442C2×#137C22×C3112yes—
443C2×#137C22×C3112yescomplemented
444C22×Q16—21no—
445C22×SD16—21no—
446C22×M16C22×C3111yescharacteristic
447D4×Q8—21no—
448#548—21no—
449#547—21no—
450#547—22no—
451#546—21no—
452#546—22no—
453#537—21no—
454#537C22×C3111yescharacteristic
455#536—21no—
456#536C22×C3111yescharacteristic
457C2×C4⋊Q8C22×C3112yescomplemented
458#525—21no—
459#525C22×C3111yescharacteristic
460C2×C22⋊Q8—21no—
461C2×C22⋊Q8C22×C3111yescharacteristic
462#520C22×C3111yescharacteristic
463#456—28no—
464#451—21no—
465#451—21no—
466#448—21no—
467#448—21no—
468C2×#104C22×C3112yes—
469C2×#104C22×C3112yes—
470C2×#104C22×C3112yescomplemented
471#419C22×C3112yescomplemented
472C2×#101C22×C3112yescomplemented
473#407C22×C3111yescharacteristic
474#395—22no—
475#391C22×C3112yescomplemented
476#385—22no—
477C4×C22⋊C4C22×C3111yescharacteristic
478#343C22×C3112yescomplemented
479#339C22×C3112yescomplemented
480C2×C31—22no—
481C2×C31—22no—
482C2×C31—41no—
483C2×C31—42no—
484C2×C31—81no—
485C2×C31—81no—
486C2×C31#240311yescharacteristic
487C2×C31C2×#45611yescharacteristic
488C2×C31#302211yescharacteristic
4892−1+4—24no—
4902−1+4—42no—
491C2×#41—21no—
492C2×#41—21no—
493C2×#41—21no—
494C2×#41—22no—
495C2×#41—21no—
496C2×#41—24no—
497C2×#41—42no—
498C2×#41D4×C3111yescharacteristic
499C2×#41D4×C3111yescharacteristic
500C2×#41C23×C3111yescharacteristic
501C2×#41C23×C3111yescharacteristic
502C2×#41C23×C3111yescharacteristic
503C22×Q8—21no—
504C22×Q8—21no—
505C22×Q8—21no—
506C22×Q8—24no—
507C22×Q8—21no—
508C22×Q8—21no—
509C22×Q8—21no—
510C22×Q8—21no—
511C22×Q8—42no—
512C22×Q8D4×C3111yescharacteristic
513C22×Q8C23×C3112yes—
514C22×Q8C23×C3111yescharacteristic
515C22×D4—21no—
516C22×D4D4×C3111yescharacteristic
517C23×C4—21no—
518C23×C4—21no—
519C23×C4C23×C3111yescharacteristic
520#137—28no—
521#137—28no—
522#137—24no—
523#137—24no—
524#137—24no—
525#137—24no—
526#137—42no—
527#137D4×C3118yescomplemented
528C2×Q16—28no—
529C2×Q16—22no—
530C2×Q16—22no—
531C2×Q16—22no—
532C2×SD16—28no—
533C2×SD16—22no—
534C2×SD16—22no—
535C2×SD16—22no—
536C2×M16—21no—
537C2×M16—24no—
538C2×M16C23×C3112yes—
539C2×M16C23×C3112yes—
540C22×C8—21no—
541C4⋊Q8—22no—
542C4⋊Q8—21no—
543C4⋊Q8—24no—
544C4⋊Q8—42no—
545#124—22no—
546#124—21no—
547#123—22no—
548#123—22no—
549#123—22no—
550#123—21no—
551#123—22no—
552C22⋊Q8—22no—
553C22⋊Q8—22no—
554C22⋊Q8—22no—
555C22⋊Q8—21no—
556C22⋊Q8—21no—
557C22⋊Q8—21no—
558C22⋊Q8—21no—
559C22⋊Q8—21no—
560C22⋊Q8—21no—
561C22⋊Q8—21no—
562C22⋊Q8—21no—
563C22⋊Q8D4×C3111yescharacteristic
564C22⋊Q8D4×C3111yescharacteristic
565#121—22no—
566#121—22no—
567#121—22no—
568#121—21no—
569#121—21no—
570#121—22no—
571#121D4×C3111yescharacteristic
572#121D4×C3111yescharacteristic
573#120—22no—
574#120—21no—
575C4×Q8—21no—
576C4×D4—22no—
577C4×D4—22no—
578C4×D4—21no—
579C4×D4—22no—
580C4×D4—21no—
581C4×D4—21no—
582#117—21no—
583#117C23×C3111yescharacteristic
584C2×C4⋊C4—22no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—24no—
587C2×C4⋊C4D4×C3112yes—
588C2×C4⋊C4C23×C3111yescharacteristic
589C2×C22⋊C4—22no—
590C2×C22⋊C4—21no—
591C2×C22⋊C4D4×C3112yes—
592C2×C42C23×C3112yes—
593#104—24no—
594#104—24no—
595#104—42no—
596#103—22no—
597#103—22no—
598#101—24no—
599C22⋊C8—21no—
600C22⋊C8—21no—
601#95—21no—
602#95—24no—
603C31#2388011yescharacteristic, direct product factor, Sylow
604C24—21no—
605C24C2×D4×C3111yescharacteristic
606#41—22no—
607#41—22no—
608#41—22no—
609#41—22no—
610#41—22no—
611#41—22no—
612#41—22no—
613#41—44no—
614#41—41no—
615#41—41no—
616#41—44no—
617#41—44no—
618#41—48no—
619#41—42no—
620#41—42no—
621#41C2×D4×C3114yes—
622C2×Q8—22no—
623C2×Q8—21no—
624C2×Q8—22no—
625C2×Q8—21no—
626C2×Q8—21no—
627C2×Q8—22no—
628C2×Q8—22no—
629C2×Q8—24no—
630C2×Q8—24no—
631C2×Q8—22no—
632C2×Q8—22no—
633C2×Q8—22no—
634C2×Q8—22no—
635C2×Q8—22no—
636C2×Q8—44no—
637C2×Q8—41no—
638C2×Q8—44no—
639C2×Q8—44no—
640C2×Q8—44no—
641C2×Q8—42no—
642C2×Q8—42no—
643C2×Q8—42no—
644C2×Q8—42no—
645C2×Q8—41no—
646C2×Q8—41no—
647C2×Q8C2×D4×C3111yescharacteristic
648C2×Q8C2×D4×C3111yescharacteristic
649C2×Q8C2×D4×C3114yes—
650C2×Q8C2×D4×C3111yescharacteristic
651C2×D4—21no—
652C2×D4—22no—
653C2×D4—22no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—22no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—41no—
663C2×D4—44no—
664C2×D4C2×D4×C3111yescharacteristic
665C2×D4C2×D4×C3111yescharacteristic
666C2×D4C2×D4×C3111yescharacteristic
667C22×C4—21no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—21no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—44no—
681C22×C4—44no—
682C22×C4—41no—
683C22×C4—41no—
684C22×C4C2×D4×C3112yes—
685C22×C4C2×D4×C3111yescharacteristic
686C22×C4C2×D4×C3111yescharacteristic
687C22×C4C2×D4×C3111yescharacteristic
688C22×C4C2×D4×C3111yescharacteristic
689C22×C4C2×D4×C3111yescharacteristic
690C22×C4C2×D4×C3112yes—
691C22×C4C24×C3111yescharacteristic
692Q16—28no—
693Q16—28no—
694Q16—44no—
695SD16—28no—
696SD16—28no—
697SD16—44no—
698M16—24no—
699M16—22no—
700M16—22no—
701M16—22no—
702M16C2×D4×C3114yes—
703C2×C8—24no—
704C2×C8—22no—
705C2×C8—22no—
706C4⋊C4—22no—
707C4⋊C4—22no—
708C4⋊C4—22no—
709C4⋊C4—22no—
710C4⋊C4—21no—
711C4⋊C4—22no—
712C4⋊C4—22no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—48no—
717C4⋊C4C2×D4×C3111yescharacteristic
718C4⋊C4C2×D4×C3111yescharacteristic
719C22⋊C4—24no—
720C22⋊C4—22no—
721C22⋊C4—22no—
722C22⋊C4—22no—
723C22⋊C4—22no—
724C22⋊C4—22no—
725C22⋊C4—21no—
726C22⋊C4—22no—
727C22⋊C4—22no—
728C22⋊C4—21no—
729C22⋊C4—21no—
730C22⋊C4—21no—
731C22⋊C4—21no—
732C42—22no—
733C42—21no—
734C42—22no—
735C42—22no—
736C23—22no—
737C23—21no—
738C23—22no—
739C23—21no—
740C23—21no—
741C23—41no—
742C23—42no—
743C23—42no—
744C23—81no—
745C23C31×#12011yescharacteristic
746C23C31×#12011yescharacteristic
747C23C22×D4×C3111yescharacteristic
748Q8—21no—
749Q8—24no—
750Q8—21no—
751Q8—21no—
752Q8—24no—
753Q8—22no—
754Q8—42no—
755Q8—44no—
756Q8—44no—
757Q8—44no—
758Q8—41no—
759Q8—42no—
760Q8—41no—
761Q8—42no—
762Q8—42no—
763Q8C31×#12012yes—
764D4—24no—
765D4—21no—
766D4—21no—
767D4—21no—
768D4—22no—
769D4—42no—
770D4—42no—
771D4—42no—
772D4—44no—
773D4—42no—
774D4—42no—
775D4—42no—
776D4—81no—
777D4—82no—
778D4C31×#12012yes—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—21no—
790C2×C4—22no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—22no—
794C2×C4—21no—
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—44no—
801C2×C4—42no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—82no—
813C2×C4C31×#12011yescharacteristic
814C2×C4C31×#12011yescharacteristic
815C2×C4C22×D4×C3111yescharacteristic
816C2×C4C22×D4×C3112yes—
817C2×C4C22×D4×C3111yescharacteristic
818C2×C4C31×H(5,𝔽2)12yes—
819C8—24no—
820C8—42no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—22no—
827C22—21no—
828C22—21no—
829C22—44no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—84no—
839C22C31×#45612yescomplemented
840C22C2×C31×#12011yescharacteristic
841C22D42×C3112yes—
842C4—21no—
843C4—21no—
844C4—22no—
845C4—44no—
846C4—42no—
847C4—41no—
848C4—41no—
849C4—44no—
850C4—41no—
851C4—42no—
852C4—41no—
853C4C2×C31×#12011yescharacteristic
854C4C31×#53411yescharacteristic
855C4D42×C3112yes—
856C2—22no—
857C2—22no—
858C2—41no—
859C2—42no—
860C2—81no—
861C2—81no—
862C2C31×#240311yescharacteristic
863C2C2×C31×#45611yescharacteristic
864C2C31×#302211yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#3489C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C31×#137C2semidirect
3. C2×C31×#456C2semidirect
4. C31×#3004C2semidirect
5. C31×#2434C2semidirect
6. C31×#2007C2semidirect
7. C31×#2005C2semidirect
8. C31×#1901C2semidirect
9. C31×#1882C2semidirect
10. C31×#1871C2semidirect
11. C31×#1789C2semidirect
20. C2×C31×#137C22semidirect
34. C2×C31×C4⋊Q8C22semidirect
47. C2×C31×#104C22semidirect
48. C31×#419C22semidirect
49. C2×C31×#101C22semidirect
52. C31×#391C22semidirect
55. C31×#343C22semidirect
56. C31×#339C22semidirect
95. C31×#137D4semidirect
303. #23880C31direct (N × H)
389. C22×#137C2×C31semidirect
391. C2×#456C2×C31semidirect
392. #3004C2×C31semidirect
393. #2434C2×C31semidirect
394. #2007C2×C31semidirect
395. #2005C2×C31semidirect
396. #1901C2×C31semidirect
397. #1882C2×C31semidirect
398. #1871C2×C31semidirect
399. #1789C2×C31semidirect
418. C22×C31#456semidirect
443. C2×#137C22×C31semidirect
457. C2×C4⋊Q8C22×C31semidirect
470. C2×#104C22×C31semidirect
471. #419C22×C31semidirect
472. C2×#101C22×C31semidirect
475. #391C22×C31semidirect
478. #343C22×C31semidirect
479. #339C22×C31semidirect
527. #137D4×C31semidirect
603. C31#23880direct (N × H)
839. C22C31×#456semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1372
C31×#34892
C2×C31×#4562
C31×#30042
C31×#24342
C31×#20072
C31×#20052
C31×#19012
C31×#18822
C31×#18712
C31×#17892
#2388031