Finite Group Databasebeta

← C31×#13873 #21470632

Subgroups — C31×#13873 #21470632

Order 7936.

3526 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊C4×C31C211yesmaximal, characteristic
2C2×C31×#388C212yesmaximal, complemented
3C2×C31×#380C211yesmaximal, characteristic, complemented
4C2×C31×#379C211yesmaximal, characteristic
5C2×C31×#379C211yesmaximal, characteristic
6C2×C4×C22⋊C4×C31C211yesmaximal, characteristic, complemented
7C31×#1440C212yesmaximal, complemented
8C31×#1439C212yesmaximal, complemented
9C31×#1437C212yesmaximal, complemented
10C31×C22⋊#95C211yesmaximal, characteristic, complemented
11C31×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C31C2211yescharacteristic
13C24×C4×C31C2211yescharacteristic
14C24×C4×C31C2211yescharacteristic
15C22×C4⋊C4×C31C2212yescomplemented
16C22×C22⋊C4×C31—28no—
17C22×C22⋊C4×C31C418yescomplemented
18C22×C22⋊C4×C31C2211yescharacteristic
19C22×C22⋊C4×C31C2211yescharacteristic
20C22×C22⋊C4×C31C2212yes—
21C22×C22⋊C4×C31C2212yes—
22C22×C22⋊C4×C31C2212yes—
23C22×C22⋊C4×C31C2212yes—
24C22×C22⋊C4×C31C2211yescharacteristic
25C22×C22⋊C4×C31C2211yescharacteristic
26C22×C22⋊C4×C31C2211yescharacteristic
27C22×C22⋊C4×C31C2211yescharacteristic
28C22×C22⋊C4×C31C2211yescharacteristic
29C22×C22⋊C4×C31C2211yescharacteristic
30C22×C42×C31C2212yescomplemented
31C31×#388—28no—
32C31×#380—24no—
33C31×#379—24no—
34C31×#379—24no—
35C4×C22⋊C4×C31—24no—
36C2×C31×#95C2212yescomplemented
37C2×C31×#95C2212yescomplemented
38C2×C31×#95C2212yescomplemented
39C2×C31×#95C2212yescomplemented
40C2×C31×#95C2212yescomplemented
41C2×C31×#95C2212yescomplemented
42C25×C31—24no—
43C25×C31—24no—
44C25×C31—22no—
45C25×C31—22no—
46C25×C31—22no—
47C25×C31—22no—
48C25×C31—22no—
49C25×C31—22no—
50C25×C31—42no—
51C25×C31—42no—
52C25×C31C2×C414yes—
53C25×C31C2311yescharacteristic
54C25×C31C2311yescharacteristic
55C25×C31C2311yescharacteristic
56C23×C4×C31—22no—
57C23×C4×C31—22no—
58C23×C4×C31—22no—
59C23×C4×C31—22no—
60C23×C4×C31—24no—
61C23×C4×C31—24no—
62C23×C4×C31—42no—
63C23×C4×C31—42no—
64C23×C4×C31C2×C414yes—
65C23×C4×C31C2×C414yes—
66C23×C4×C31C2312yes—
67C23×C4×C31C2312yes—
68C23×C4×C31C2311yescharacteristic
69C23×C4×C31C2311yescharacteristic
70C23×C4×C31C2312yes—
71C23×C4×C31C2312yes—
72C23×C4×C31C2311yescharacteristic
73C23×C4×C31C2311yescharacteristic
74C2×C4⋊C4×C31—24no—
75C2×C4⋊C4×C31—24no—
76C2×C4⋊C4×C31—42no—
77C2×C22⋊C4×C31—24no—
78C2×C22⋊C4×C31—22no—
79C2×C22⋊C4×C31—22no—
80C2×C22⋊C4×C31—22no—
81C2×C22⋊C4×C31—22no—
82C2×C22⋊C4×C31—24no—
83C2×C22⋊C4×C31—24no—
84C2×C22⋊C4×C31—232no—
85C2×C22⋊C4×C31—22no—
86C2×C22⋊C4×C31—22no—
87C2×C22⋊C4×C31—22no—
88C2×C22⋊C4×C31—24no—
89C2×C22⋊C4×C31—24no—
90C2×C22⋊C4×C31—24no—
91C2×C22⋊C4×C31—24no—
92C2×C22⋊C4×C31—22no—
93C2×C22⋊C4×C31—22no—
94C2×C22⋊C4×C31—22no—
95C2×C22⋊C4×C31—24no—
96C2×C22⋊C4×C31—24no—
97C2×C22⋊C4×C31—24no—
98C2×C22⋊C4×C31—24no—
99C2×C22⋊C4×C31—42no—
100C2×C22⋊C4×C31—42no—
101C2×C22⋊C4×C31—42no—
102C2×C22⋊C4×C31—42no—
103C2×C22⋊C4×C31C2×C414yes—
104C2×C22⋊C4×C31C2×C414yes—
105C2×C22⋊C4×C31C2×C414yes—
106C2×C22⋊C4×C31C2×C414yes—
107C2×C22⋊C4×C31D414yes—
108C2×C22⋊C4×C31D414yes—
109C2×C22⋊C4×C31D418yes—
110C2×C42×C31—24no—
111C2×C42×C31—24no—
112C2×C42×C31—42no—
113C31×#95—24no—
114C31×#95—24no—
115C31×#95—24no—
116C31×#95—24no—
117C31×#95—42no—
118C31×#95—42no—
119C24×C31—22no—
120C24×C31—22no—
121C24×C31—22no—
122C24×C31—22no—
123C24×C31—216no—
124C24×C31—216no—
125C24×C31—28no—
126C24×C31—28no—
127C24×C31—28no—
128C24×C31—22no—
129C24×C31—21no—
130C24×C31—21no—
131C24×C31—21no—
132C24×C31—21no—
133C24×C31—21no—
134C24×C31—21no—
135C24×C31—22no—
136C24×C31—21no—
137C24×C31—21no—
138C24×C31—21no—
139C24×C31—21no—
140C24×C31—21no—
141C24×C31—21no—
142C24×C31—22no—
143C24×C31—22no—
144C24×C31—22no—
145C24×C31—22no—
146C24×C31—28no—
147C24×C31—28no—
148C24×C31—44no—
149C24×C31—44no—
150C24×C31—48no—
151C24×C31—48no—
152C24×C31—48no—
153C24×C31—48no—
154C24×C31—48no—
155C24×C31—48no—
156C24×C31—48no—
157C24×C31—48no—
158C24×C31—48no—
159C24×C31—48no—
160C24×C31—44no—
161C24×C31—44no—
162C24×C31—44no—
163C24×C31—44no—
164C24×C31C22×C412yes—
165C24×C31C22×C412yes—
166C24×C31C22×C412yes—
167C24×C31C2×D414yes—
168C24×C31C2×D412yes—
169C24×C31C2×D412yes—
170C24×C31#4114yes—
171C24×C31#4112yes—
172C24×C31#4112yes—
173C24×C31#4112yes—
174C24×C31#4112yes—
175C24×C31C2411yescharacteristic
176C22×C4×C31—21no—
177C22×C4×C31—21no—
178C22×C4×C31—21no—
179C22×C4×C31—21no—
180C22×C4×C31—22no—
181C22×C4×C31—22no—
182C22×C4×C31—28no—
183C22×C4×C31—28no—
184C22×C4×C31—21no—
185C22×C4×C31—21no—
186C22×C4×C31—22no—
187C22×C4×C31—22no—
188C22×C4×C31—22no—
189C22×C4×C31—22no—
190C22×C4×C31—22no—
191C22×C4×C31—22no—
192C22×C4×C31—22no—
193C22×C4×C31—22no—
194C22×C4×C31—22no—
195C22×C4×C31—22no—
196C22×C4×C31—21no—
197C22×C4×C31—21no—
198C22×C4×C31—22no—
199C22×C4×C31—22no—
200C22×C4×C31—22no—
201C22×C4×C31—22no—
202C22×C4×C31—22no—
203C22×C4×C31—22no—
204C22×C4×C31—28no—
205C22×C4×C31—28no—
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—22no—
217C22×C4×C31—22no—
218C22×C4×C31—22no—
219C22×C4×C31—22no—
220C22×C4×C31—44no—
221C22×C4×C31—44no—
222C22×C4×C31—48no—
223C22×C4×C31—48no—
224C22×C4×C31—48no—
225C22×C4×C31—48no—
226C22×C4×C31C22×C412yes—
227C22×C4×C31C22×C412yes—
228C22×C4×C31C22×C412yes—
229C22×C4×C31C22×C412yes—
230C22×C4×C31C2×D414yes—
231C22×C4×C31C2×D414yes—
232C22×C4×C31C2×D414yes—
233C22×C4×C31C2×D414yes—
234C4⋊C4×C31—48no—
235C22⋊C4×C31—28no—
236C22⋊C4×C31—28no—
237C22⋊C4×C31—28no—
238C22⋊C4×C31—28no—
239C22⋊C4×C31—28no—
240C22⋊C4×C31—48no—
241C22⋊C4×C31—48no—
242C22⋊C4×C31—48no—
243C22⋊C4×C31—48no—
244C22⋊C4×C31—44no—
245C22⋊C4×C31—44no—
246C22⋊C4×C31C22⋊C4116yescomplemented
247C42×C31—48no—
248#13873C3111yesmaximal, characteristic, direct product factor, Sylow
249C23×C31—22no—
250C23×C31—22no—
251C23×C31—22no—
252C23×C31—22no—
253C23×C31—24no—
254C23×C31—24no—
255C23×C31—24no—
256C23×C31—24no—
257C23×C31—24no—
258C23×C31—24no—
259C23×C31—24no—
260C23×C31—24no—
261C23×C31—24no—
262C23×C31—24no—
263C23×C31—24no—
264C23×C31—24no—
265C23×C31—232no—
266C23×C31—22no—
267C23×C31—22no—
268C23×C31—22no—
269C23×C31—22no—
270C23×C31—22no—
271C23×C31—22no—
272C23×C31—22no—
273C23×C31—22no—
274C23×C31—22no—
275C23×C31—22no—
276C23×C31—22no—
277C23×C31—22no—
278C23×C31—24no—
279C23×C31—24no—
280C23×C31—24no—
281C23×C31—24no—
282C23×C31—24no—
283C23×C31—24no—
284C23×C31—24no—
285C23×C31—24no—
286C23×C31—24no—
287C23×C31—24no—
288C23×C31—24no—
289C23×C31—24no—
290C23×C31—416no—
291C23×C31—416no—
292C23×C31—416no—
293C23×C31—416no—
294C23×C31—416no—
295C23×C31—432no—
296C23×C31—432no—
297C23×C31—432no—
298C23×C31—432no—
299C23×C31—41no—
300C23×C31—41no—
301C23×C31—41no—
302C23×C31—41no—
303C23×C31—41no—
304C23×C31—41no—
305C23×C31—41no—
306C23×C31—41no—
307C23×C31—42no—
308C23×C31—42no—
309C23×C31—42no—
310C23×C31—42no—
311C23×C31—42no—
312C23×C31—42no—
313C23×C31—42no—
314C23×C31—42no—
315C23×C31—42no—
316C23×C31—42no—
317C23×C31—42no—
318C23×C31—42no—
319C23×C31—416no—
320C23×C31C2×C22⋊C414yes—
321C23×C31#11714yes—
322C23×C31#11714yes—
323C23×C31C4×D414yes—
324C23×C31C4×D414yes—
325C23×C31#12114yes—
326C23×C31#12314yes—
327C23×C31#12414yes—
328C23×C31#12614yes—
329C23×C31C23×C411yescharacteristic
330C23×C31C22×D412yes—
331C23×C31C22×D411yescharacteristic
332C23×C31C22×D411yescharacteristic
333C23×C31C2×#4111yescharacteristic
334C23×C31C2×#4111yescharacteristic
335C23×C31C2×#4112yes—
336C23×C31C2×#4111yescharacteristic
337C23×C31C2×#4111yescharacteristic
338C23×C31H(5,𝔽2)12yes—
339C23×C31H(5,𝔽2)12yes—
340C2×C4×C31—22no—
341C2×C4×C31—22no—
342C2×C4×C31—22no—
343C2×C4×C31—22no—
344C2×C4×C31—24no—
345C2×C4×C31—24no—
346C2×C4×C31—24no—
347C2×C4×C31—24no—
348C2×C4×C31—22no—
349C2×C4×C31—22no—
350C2×C4×C31—22no—
351C2×C4×C31—22no—
352C2×C4×C31—22no—
353C2×C4×C31—22no—
354C2×C4×C31—24no—
355C2×C4×C31—24no—
356C2×C4×C31—24no—
357C2×C4×C31—24no—
358C2×C4×C31—24no—
359C2×C4×C31—24no—
360C2×C4×C31—416no—
361C2×C4×C31—416no—
362C2×C4×C31—42no—
363C2×C4×C31—42no—
364C2×C4×C31—42no—
365C2×C4×C31—42no—
366C2×C4×C31—42no—
367C2×C4×C31—42no—
368C2×C4×C31—42no—
369C2×C4×C31—42no—
370C2×C4×C31—42no—
371C2×C4×C31—42no—
372C2×C4×C31—42no—
373C2×C4×C31—42no—
374C2×C4×C31—42no—
375C2×C4×C31—42no—
376C2×C4×C31—42no—
377C2×C4×C31—42no—
378C2×C4×C31—42no—
379C2×C4×C31—42no—
380C2×C4×C31—42no—
381C2×C4×C31—42no—
382C2×C4×C31—42no—
383C2×C4×C31—42no—
384C2×C4×C31—42no—
385C2×C4×C31—42no—
386C2×C4×C31—42no—
387C2×C4×C31—42no—
388C2×C4×C31C2×C22⋊C414yes—
389C2×C4×C31C2×C22⋊C414yes—
390C23×C22⋊C4C2×C3111yescharacteristic
391C2×#388C2×C3112yescomplemented
392C2×#380C2×C3111yescharacteristic, complemented
393C2×#379C2×C3111yescharacteristic
394C2×#379C2×C3111yescharacteristic
395C2×C4×C22⋊C4C2×C3111yescharacteristic, complemented
396#1440C2×C3112yescomplemented
397#1439C2×C3112yescomplemented
398#1437C2×C3112yescomplemented
399C22⋊#95C2×C3111yescharacteristic, complemented
400C22⋊#95C2×C3111yescharacteristic, complemented
401C22×C31—24no—
402C22×C31—24no—
403C22×C31—24no—
404C22×C31—24no—
405C22×C31—24no—
406C22×C31—28no—
407C22×C31—28no—
408C22×C31—28no—
409C22×C31—28no—
410C22×C31—24no—
411C22×C31—24no—
412C22×C31—24no—
413C22×C31—24no—
414C22×C31—24no—
415C22×C31—24no—
416C22×C31—24no—
417C22×C31—464no—
418C22×C31—42no—
419C22×C31—42no—
420C22×C31—42no—
421C22×C31—42no—
422C22×C31—42no—
423C22×C31—42no—
424C22×C31—44no—
425C22×C31—44no—
426C22×C31—44no—
427C22×C31—44no—
428C22×C31—44no—
429C22×C31—44no—
430C22×C31—44no—
431C22×C31—44no—
432C22×C31—42no—
433C22×C31—42no—
434C22×C31#38818yescomplemented
435C22×C31C22×C22⋊C411yescharacteristic
436C22×C31C2×#11711yescharacteristic
437C22×C31C2×#11711yescharacteristic
438C22×C31C2×C4×D411yescharacteristic
439C22×C31C2×C4×D411yescharacteristic
440C22×C31#51811yescharacteristic
441C22×C31#51811yescharacteristic
442C22×C31C2×#12111yescharacteristic
443C22×C31C2×#12311yescharacteristic
444C22×C31#52512yes—
445C22×C31#52512yes—
446C22×C31C2×#12411yescharacteristic
447C22×C31C2×#12611yescharacteristic
448C22×C31#53812yes—
449C22×C31#53812yes—
450C22×C31D4212yes—
451C22×C31D4212yes—
452C22×C31#54612yes—
453C22×C31#54612yes—
454C22×C31#54612yes—
455C22×C31#54612yes—
456C22×C31#55112yes—
457C22×C31#55112yes—
458C4×C31—24no—
459C4×C31—24no—
460C4×C31—42no—
461C4×C31—42no—
462C4×C31—44no—
463C4×C31—44no—
464C4×C31—82no—
465C4×C31—82no—
466C26C22×C3111yescharacteristic
467C24×C4C22×C3111yescharacteristic
468C24×C4C22×C3111yescharacteristic
469C22×C4⋊C4C22×C3112yescomplemented
470C22×C22⋊C4—28no—
471C22×C22⋊C4C4×C3118yescomplemented
472C22×C22⋊C4C22×C3111yescharacteristic
473C22×C22⋊C4C22×C3111yescharacteristic
474C22×C22⋊C4C22×C3112yes—
475C22×C22⋊C4C22×C3112yes—
476C22×C22⋊C4C22×C3112yes—
477C22×C22⋊C4C22×C3112yes—
478C22×C22⋊C4C22×C3111yescharacteristic
479C22×C22⋊C4C22×C3111yescharacteristic
480C22×C22⋊C4C22×C3111yescharacteristic
481C22×C22⋊C4C22×C3111yescharacteristic
482C22×C22⋊C4C22×C3111yescharacteristic
483C22×C22⋊C4C22×C3111yescharacteristic
484C22×C42C22×C3112yescomplemented
485#388—28no—
486#380—24no—
487#379—24no—
488#379—24no—
489C4×C22⋊C4—24no—
490C2×#95C22×C3112yescomplemented
491C2×#95C22×C3112yescomplemented
492C2×#95C22×C3112yescomplemented
493C2×#95C22×C3112yescomplemented
494C2×#95C22×C3112yescomplemented
495C2×#95C22×C3112yescomplemented
496C2×C31—28no—
497C2×C31—44no—
498C2×C31—44no—
499C2×C31#228011yescharacteristic
500C2×C31C2×#38811yescharacteristic
501C2×C31#231211yescharacteristic
502C2×C31D4×C22⋊C411yescharacteristic
503C2×C31D4×C22⋊C411yescharacteristic
504C2×C31#234211yescharacteristic
505C2×C31#234211yescharacteristic
506C2×C31#241812yes—
507C2×C31#242412yes—
508C2×C31#247212yes—
509C2×C31#248012yes—
510C25—24no—
511C25—24no—
512C25—22no—
513C25—22no—
514C25—22no—
515C25—22no—
516C25—22no—
517C25—22no—
518C25—42no—
519C25—42no—
520C25C2×C4×C3114yes—
521C25C23×C3111yescharacteristic
522C25C23×C3111yescharacteristic
523C25C23×C3111yescharacteristic
524C23×C4—22no—
525C23×C4—22no—
526C23×C4—22no—
527C23×C4—22no—
528C23×C4—24no—
529C23×C4—24no—
530C23×C4—42no—
531C23×C4—42no—
532C23×C4C2×C4×C3114yes—
533C23×C4C2×C4×C3114yes—
534C23×C4C23×C3112yes—
535C23×C4C23×C3112yes—
536C23×C4C23×C3111yescharacteristic
537C23×C4C23×C3111yescharacteristic
538C23×C4C23×C3112yes—
539C23×C4C23×C3112yes—
540C23×C4C23×C3111yescharacteristic
541C23×C4C23×C3111yescharacteristic
542C2×C4⋊C4—24no—
543C2×C4⋊C4—24no—
544C2×C4⋊C4—42no—
545C2×C22⋊C4—24no—
546C2×C22⋊C4—22no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—24no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—232no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—22no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—24no—
557C2×C22⋊C4—24no—
558C2×C22⋊C4—24no—
559C2×C22⋊C4—24no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4—22no—
562C2×C22⋊C4—22no—
563C2×C22⋊C4—24no—
564C2×C22⋊C4—24no—
565C2×C22⋊C4—24no—
566C2×C22⋊C4—24no—
567C2×C22⋊C4—42no—
568C2×C22⋊C4—42no—
569C2×C22⋊C4—42no—
570C2×C22⋊C4—42no—
571C2×C22⋊C4C2×C4×C3114yes—
572C2×C22⋊C4C2×C4×C3114yes—
573C2×C22⋊C4C2×C4×C3114yes—
574C2×C22⋊C4C2×C4×C3114yes—
575C2×C22⋊C4D4×C3114yes—
576C2×C22⋊C4D4×C3114yes—
577C2×C22⋊C4D4×C3118yes—
578C2×C42—24no—
579C2×C42—24no—
580C2×C42—42no—
581#95—24no—
582#95—24no—
583#95—24no—
584#95—24no—
585#95—42no—
586#95—42no—
587C31#1387311yescharacteristic, direct product factor, Sylow
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—216no—
593C24—216no—
594C24—28no—
595C24—28no—
596C24—28no—
597C24—22no—
598C24—21no—
599C24—21no—
600C24—21no—
601C24—21no—
602C24—21no—
603C24—21no—
604C24—22no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—21no—
610C24—21no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—28no—
616C24—28no—
617C24—44no—
618C24—44no—
619C24—48no—
620C24—48no—
621C24—48no—
622C24—48no—
623C24—48no—
624C24—48no—
625C24—48no—
626C24—48no—
627C24—48no—
628C24—48no—
629C24—44no—
630C24—44no—
631C24—44no—
632C24—44no—
633C24C22×C4×C3112yes—
634C24C22×C4×C3112yes—
635C24C22×C4×C3112yes—
636C24C2×D4×C3114yes—
637C24C2×D4×C3112yes—
638C24C2×D4×C3112yes—
639C24#41×C3114yes—
640C24#41×C3112yes—
641C24#41×C3112yes—
642C24#41×C3112yes—
643C24#41×C3112yes—
644C24C24×C3111yescharacteristic
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—28no—
652C22×C4—28no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—28no—
674C22×C4—28no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—44no—
690C22×C4—44no—
691C22×C4—48no—
692C22×C4—48no—
693C22×C4—48no—
694C22×C4—48no—
695C22×C4C22×C4×C3112yes—
696C22×C4C22×C4×C3112yes—
697C22×C4C22×C4×C3112yes—
698C22×C4C22×C4×C3112yes—
699C22×C4C2×D4×C3114yes—
700C22×C4C2×D4×C3114yes—
701C22×C4C2×D4×C3114yes—
702C22×C4C2×D4×C3114yes—
703C4⋊C4—48no—
704C22⋊C4—28no—
705C22⋊C4—28no—
706C22⋊C4—28no—
707C22⋊C4—28no—
708C22⋊C4—28no—
709C22⋊C4—48no—
710C22⋊C4—48no—
711C22⋊C4—48no—
712C22⋊C4—48no—
713C22⋊C4—44no—
714C22⋊C4—44no—
715C22⋊C4C22⋊C4×C31116yescomplemented
716C42—48no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—24no—
726C23—24no—
727C23—24no—
728C23—24no—
729C23—24no—
730C23—24no—
731C23—24no—
732C23—24no—
733C23—232no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—24no—
747C23—24no—
748C23—24no—
749C23—24no—
750C23—24no—
751C23—24no—
752C23—24no—
753C23—24no—
754C23—24no—
755C23—24no—
756C23—24no—
757C23—24no—
758C23—416no—
759C23—416no—
760C23—416no—
761C23—416no—
762C23—416no—
763C23—432no—
764C23—432no—
765C23—432no—
766C23—432no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—42no—
776C23—42no—
777C23—42no—
778C23—42no—
779C23—42no—
780C23—42no—
781C23—42no—
782C23—42no—
783C23—42no—
784C23—42no—
785C23—42no—
786C23—42no—
787C23—416no—
788C23C2×C22⋊C4×C3114yes—
789C23C31×#11714yes—
790C23C31×#11714yes—
791C23C4×D4×C3114yes—
792C23C4×D4×C3114yes—
793C23C31×#12114yes—
794C23C31×#12314yes—
795C23C31×#12414yes—
796C23C31×#12614yes—
797C23C23×C4×C3111yescharacteristic
798C23C22×D4×C3112yes—
799C23C22×D4×C3111yescharacteristic
800C23C22×D4×C3111yescharacteristic
801C23C2×#41×C3111yescharacteristic
802C23C2×#41×C3111yescharacteristic
803C23C2×#41×C3112yes—
804C23C2×#41×C3111yescharacteristic
805C23C2×#41×C3111yescharacteristic
806C23C31×H(5,𝔽2)12yes—
807C23C31×H(5,𝔽2)12yes—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—24no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—416no—
829C2×C4—416no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4C2×C22⋊C4×C3114yes—
857C2×C4C2×C22⋊C4×C3114yes—
858C22—24no—
859C22—24no—
860C22—24no—
861C22—24no—
862C22—24no—
863C22—28no—
864C22—28no—
865C22—28no—
866C22—28no—
867C22—24no—
868C22—24no—
869C22—24no—
870C22—24no—
871C22—24no—
872C22—24no—
873C22—24no—
874C22—464no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—42no—
881C22—44no—
882C22—44no—
883C22—44no—
884C22—44no—
885C22—44no—
886C22—44no—
887C22—44no—
888C22—44no—
889C22—42no—
890C22—42no—
891C22C31×#38818yescomplemented
892C22C22×C22⋊C4×C3111yescharacteristic
893C22C2×C31×#11711yescharacteristic
894C22C2×C31×#11711yescharacteristic
895C22C2×C4×D4×C3111yescharacteristic
896C22C2×C4×D4×C3111yescharacteristic
897C22C31×#51811yescharacteristic
898C22C31×#51811yescharacteristic
899C22C2×C31×#12111yescharacteristic
900C22C2×C31×#12311yescharacteristic
901C22C31×#52512yes—
902C22C31×#52512yes—
903C22C2×C31×#12411yescharacteristic
904C22C2×C31×#12611yescharacteristic
905C22C31×#53812yes—
906C22C31×#53812yes—
907C22D42×C3112yes—
908C22D42×C3112yes—
909C22C31×#54612yes—
910C22C31×#54612yes—
911C22C31×#54612yes—
912C22C31×#54612yes—
913C22C31×#55112yes—
914C22C31×#55112yes—
915C4—24no—
916C4—24no—
917C4—42no—
918C4—42no—
919C4—44no—
920C4—44no—
921C4—82no—
922C4—82no—
923C2—28no—
924C2—44no—
925C2—44no—
926C2C31×#228011yescharacteristic
927C2C2×C31×#38811yescharacteristic
928C2C31×#231211yescharacteristic
929C2D4×C22⋊C4×C3111yescharacteristic
930C2D4×C22⋊C4×C3111yescharacteristic
931C2C31×#234211yescharacteristic
932C2C31×#234211yescharacteristic
933C2C31×#241812yes—
934C2C31×#242412yes—
935C2C31×#247212yes—
936C2C31×#248012yes—
subgroupG/H
center, socleC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC26×C31C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#388C2semidirect
3. C2×C31×#380C2semidirect
6. C2×C4×C22⋊C4×C31C2semidirect
7. C31×#1440C2semidirect
8. C31×#1439C2semidirect
9. C31×#1437C2semidirect
10. C31×C22⋊#95C2semidirect
11. C31×C22⋊#95C2semidirect
15. C22×C4⋊C4×C31C22semidirect
17. C22×C22⋊C4×C31C4semidirect
30. C22×C42×C31C22semidirect
36. C2×C31×#95C22semidirect
37. C2×C31×#95C22semidirect
38. C2×C31×#95C22semidirect
39. C2×C31×#95C22semidirect
40. C2×C31×#95C22semidirect
41. C2×C31×#95C22semidirect
246. C22⋊C4×C31C22⋊C4semidirect
248. #13873C31direct (N × H)
391. C2×#388C2×C31semidirect
392. C2×#380C2×C31semidirect
395. C2×C4×C22⋊C4C2×C31semidirect
396. #1440C2×C31semidirect
397. #1439C2×C31semidirect
398. #1437C2×C31semidirect
399. C22⋊#95C2×C31semidirect
400. C22⋊#95C2×C31semidirect
434. C22×C31#388semidirect
469. C22×C4⋊C4C22×C31semidirect
471. C22×C22⋊C4C4×C31semidirect
484. C22×C42C22×C31semidirect
490. C2×#95C22×C31semidirect
491. C2×#95C22×C31semidirect
492. C2×#95C22×C31semidirect
493. C2×#95C22×C31semidirect
494. C2×#95C22×C31semidirect
495. C2×#95C22×C31semidirect
587. C31#13873direct (N × H)
715. C22⋊C4C22⋊C4×C31semidirect
891. C22C31×#388semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊C4×C312
C2×C31×#3882
C2×C31×#3802
C2×C31×#3792
C2×C4×C22⋊C4×C312
C31×#14402
C31×#14392
C31×#14372
C31×C22⋊#952
#1387331