Finite Group Databasebeta

← C31×#13995 #21470754

Subgroups — C31×#13995 #21470754

Order 7936.

4210 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#120C211yesmaximal, characteristic
2C23×C22⋊C4×C31C211yesmaximal, characteristic, complemented
3C2×C31×#390C212yesmaximal, complemented
4C2×C31×#386C211yesmaximal, characteristic, complemented
5C2×C31×#386C211yesmaximal, characteristic, complemented
6C2×C31×#385C211yesmaximal, characteristic, complemented
7C2×C31×#379C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊C4×C31C211yesmaximal, characteristic, complemented
9C31×#1439C212yesmaximal, complemented
10C31×#1438C212yesmaximal, complemented
11C31×#1437C212yesmaximal, complemented
12C26×C31C2211yescharacteristic
13C23×D4×C31C2211yescharacteristic
14C23×D4×C31C2212yes—
15C24×C4×C31C2211yescharacteristic
16C24×C4×C31C2211yescharacteristic
17C2×C31×#120—24no—
18C2×C31×#120—24no—
19C2×C31×#120C418yescomplemented
20C22×C4⋊C4×C31C2212yescomplemented
21C22×C22⋊C4×C31—24no—
22C22×C22⋊C4×C31—28no—
23C22×C22⋊C4×C31C2212yes—
24C22×C22⋊C4×C31C2211yescharacteristic
25C22×C22⋊C4×C31C2212yes—
26C22×C22⋊C4×C31C2212yes—
27C22×C22⋊C4×C31C2212yes—
28C22×C22⋊C4×C31C2212yes—
29C22×C22⋊C4×C31C2211yescharacteristic
30C22×C22⋊C4×C31C2211yescharacteristic
31C22×C22⋊C4×C31C2211yescharacteristic, complemented
32C22×C22⋊C4×C31C2212yescomplemented
33C22×C22⋊C4×C31C2211yescharacteristic, complemented
34C22×C42×C31C2212yescomplemented
35C31×#390—28no—
36C31×#386—24no—
37C31×#386—24no—
38C31×#385—24no—
39C31×#379—24no—
40C4×C22⋊C4×C31—24no—
41C2×C31×#95C2211yescharacteristic, complemented
42C2×C31×#95C2212yescomplemented
43C2×C31×#95C2212yescomplemented
44C2×C31×#95C2212yescomplemented
45C2×C31×#95C2211yescharacteristic, complemented
46C25×C31—24no—
47C25×C31—22no—
48C25×C31—24no—
49C25×C31—22no—
50C25×C31—22no—
51C25×C31—22no—
52C25×C31—22no—
53C25×C31—22no—
54C25×C31—42no—
55C25×C31—42no—
56C25×C31C2×C414yes—
57C25×C31C2311yescharacteristic
58C25×C31C2312yes—
59C25×C31C2311yescharacteristic
60C22×D4×C31—22no—
61C22×D4×C31—22no—
62C22×D4×C31—22no—
63C22×D4×C31—22no—
64C22×D4×C31—24no—
65C22×D4×C31—24no—
66C22×D4×C31—22no—
67C22×D4×C31—22no—
68C22×D4×C31—24no—
69C22×D4×C31—24no—
70C22×D4×C31—42no—
71C22×D4×C31—42no—
72C22×D4×C31C2×C414yes—
73C22×D4×C31C2×C418yescomplemented
74C23×C4×C31—22no—
75C23×C4×C31—22no—
76C23×C4×C31—22no—
77C23×C4×C31—24no—
78C23×C4×C31—24no—
79C23×C4×C31—22no—
80C23×C4×C31—22no—
81C23×C4×C31—42no—
82C23×C4×C31—42no—
83C23×C4×C31D414yescomplemented
84C23×C4×C31C2311yescharacteristic
85C23×C4×C31C2311yescharacteristic
86C23×C4×C31C2311yescharacteristic
87C23×C4×C31C2312yes—
88C23×C4×C31C2312yes—
89C23×C4×C31C2311yescharacteristic
90C23×C4×C31C2312yes—
91C23×C4×C31C2311yescharacteristic
92C31×#120—232no—
93C2×C4⋊C4×C31—24no—
94C2×C4⋊C4×C31—24no—
95C2×C4⋊C4×C31—42no—
96C2×C22⋊C4×C31—232no—
97C2×C22⋊C4×C31—24no—
98C2×C22⋊C4×C31—22no—
99C2×C22⋊C4×C31—22no—
100C2×C22⋊C4×C31—24no—
101C2×C22⋊C4×C31—24no—
102C2×C22⋊C4×C31—24no—
103C2×C22⋊C4×C31—24no—
104C2×C22⋊C4×C31—24no—
105C2×C22⋊C4×C31—24no—
106C2×C22⋊C4×C31—22no—
107C2×C22⋊C4×C31—22no—
108C2×C22⋊C4×C31—22no—
109C2×C22⋊C4×C31—24no—
110C2×C22⋊C4×C31—24no—
111C2×C22⋊C4×C31—24no—
112C2×C22⋊C4×C31—24no—
113C2×C22⋊C4×C31—24no—
114C2×C22⋊C4×C31—22no—
115C2×C22⋊C4×C31—22no—
116C2×C22⋊C4×C31—24no—
117C2×C22⋊C4×C31—24no—
118C2×C22⋊C4×C31—42no—
119C2×C22⋊C4×C31—42no—
120C2×C22⋊C4×C31—42no—
121C2×C22⋊C4×C31—42no—
122C2×C22⋊C4×C31C2×C414yes—
123C2×C22⋊C4×C31C2×C418yescomplemented
124C2×C22⋊C4×C31D414yes—
125C2×C22⋊C4×C31D414yes—
126C2×C22⋊C4×C31D418yescomplemented
127C2×C22⋊C4×C31D414yescomplemented
128C2×C42×C31—24no—
129C2×C42×C31—24no—
130C2×C42×C31—42no—
131C31×#95—24no—
132C31×#95—24no—
133C31×#95—24no—
134C31×#95—22no—
135C31×#95—22no—
136C24×C31—22no—
137C24×C31—22no—
138C24×C31—22no—
139C24×C31—22no—
140C24×C31—28no—
141C24×C31—28no—
142C24×C31—216no—
143C24×C31—216no—
144C24×C31—28no—
145C24×C31—22no—
146C24×C31—22no—
147C24×C31—22no—
148C24×C31—22no—
149C24×C31—22no—
150C24×C31—22no—
151C24×C31—22no—
152C24×C31—22no—
153C24×C31—22no—
154C24×C31—22no—
155C24×C31—22no—
156C24×C31—22no—
157C24×C31—28no—
158C24×C31—28no—
159C24×C31—21no—
160C24×C31—22no—
161C24×C31—21no—
162C24×C31—21no—
163C24×C31—21no—
164C24×C31—21no—
165C24×C31—21no—
166C24×C31—22no—
167C24×C31—22no—
168C24×C31—22no—
169C24×C31—48no—
170C24×C31—48no—
171C24×C31—48no—
172C24×C31—48no—
173C24×C31—48no—
174C24×C31—48no—
175C24×C31—48no—
176C24×C31—48no—
177C24×C31—48no—
178C24×C31—44no—
179C24×C31—44no—
180C24×C31—48no—
181C24×C31—44no—
182C24×C31—44no—
183C24×C31—44no—
184C24×C31—44no—
185C24×C31C22×C412yes—
186C24×C31C22×C414yes—
187C24×C31C22×C412yes—
188C24×C31C2×D414yes—
189C24×C31C2×D412yes—
190C24×C31C2×D412yes—
191C24×C31C2×D412yes—
192C24×C31C2×D412yes—
193C24×C31#4114yes—
194C24×C31#4112yes—
195C24×C31#4112yes—
196C24×C31C2411yescharacteristic
197C2×D4×C31—28no—
198C2×D4×C31—28no—
199C2×D4×C31—28no—
200C2×D4×C31—216no—
201C2×D4×C31—216no—
202C2×D4×C31—48no—
203C2×D4×C31—48no—
204C2×D4×C31—48no—
205C2×D4×C31—48no—
206C2×D4×C31—48no—
207C2×D4×C31—44no—
208C2×D4×C31—44no—
209C2×D4×C31—44no—
210C2×D4×C31—44no—
211C22×C4×C31—21no—
212C22×C4×C31—22no—
213C22×C4×C31—21no—
214C22×C4×C31—22no—
215C22×C4×C31—22no—
216C22×C4×C31—22no—
217C22×C4×C31—22no—
218C22×C4×C31—28no—
219C22×C4×C31—28no—
220C22×C4×C31—21no—
221C22×C4×C31—21no—
222C22×C4×C31—21no—
223C22×C4×C31—22no—
224C22×C4×C31—22no—
225C22×C4×C31—22no—
226C22×C4×C31—22no—
227C22×C4×C31—22no—
228C22×C4×C31—22no—
229C22×C4×C31—22no—
230C22×C4×C31—21no—
231C22×C4×C31—21no—
232C22×C4×C31—22no—
233C22×C4×C31—22no—
234C22×C4×C31—21no—
235C22×C4×C31—21no—
236C22×C4×C31—21no—
237C22×C4×C31—22no—
238C22×C4×C31—22no—
239C22×C4×C31—22no—
240C22×C4×C31—22no—
241C22×C4×C31—22no—
242C22×C4×C31—28no—
243C22×C4×C31—21no—
244C22×C4×C31—21no—
245C22×C4×C31—21no—
246C22×C4×C31—21no—
247C22×C4×C31—21no—
248C22×C4×C31—22no—
249C22×C4×C31—21no—
250C22×C4×C31—22no—
251C22×C4×C31—22no—
252C22×C4×C31—22no—
253C22×C4×C31—44no—
254C22×C4×C31—48no—
255C22×C4×C31—48no—
256C22×C4×C31—48no—
257C22×C4×C31—48no—
258C22×C4×C31—44no—
259C22×C4×C31—44no—
260C22×C4×C31C22×C412yes—
261C22×C4×C31C22×C414yes—
262C22×C4×C31C2×D414yes—
263C22×C4×C31C2×D412yes—
264C22×C4×C31C2×D414yes—
265C22×C4×C31C2×D414yes—
266C22×C4×C31C2×D414yes—
267C22×C4×C31C2×D412yes—
268C22×C4×C31C2×D414yes—
269C4⋊C4×C31—48no—
270C22⋊C4×C31—216no—
271C22⋊C4×C31—28no—
272C22⋊C4×C31—216no—
273C22⋊C4×C31—216no—
274C22⋊C4×C31—48no—
275C22⋊C4×C31—48no—
276C22⋊C4×C31—48no—
277C22⋊C4×C31—44no—
278C22⋊C4×C31—44no—
279C22⋊C4×C31—44no—
280C22⋊C4×C31C22⋊C4116yescomplemented
281C42×C31—48no—
282#13995C3111yesmaximal, characteristic, direct product factor, Sylow
283C23×C31—24no—
284C23×C31—24no—
285C23×C31—22no—
286C23×C31—22no—
287C23×C31—24no—
288C23×C31—22no—
289C23×C31—22no—
290C23×C31—24no—
291C23×C31—24no—
292C23×C31—24no—
293C23×C31—24no—
294C23×C31—24no—
295C23×C31—24no—
296C23×C31—24no—
297C23×C31—24no—
298C23×C31—24no—
299C23×C31—232no—
300C23×C31—24no—
301C23×C31—24no—
302C23×C31—24no—
303C23×C31—24no—
304C23×C31—24no—
305C23×C31—24no—
306C23×C31—24no—
307C23×C31—24no—
308C23×C31—24no—
309C23×C31—24no—
310C23×C31—24no—
311C23×C31—24no—
312C23×C31—24no—
313C23×C31—24no—
314C23×C31—24no—
315C23×C31—24no—
316C23×C31—24no—
317C23×C31—24no—
318C23×C31—22no—
319C23×C31—22no—
320C23×C31—24no—
321C23×C31—22no—
322C23×C31—24no—
323C23×C31—432no—
324C23×C31—432no—
325C23×C31—416no—
326C23×C31—416no—
327C23×C31—416no—
328C23×C31—432no—
329C23×C31—416no—
330C23×C31—432no—
331C23×C31—416no—
332C23×C31—42no—
333C23×C31—42no—
334C23×C31—42no—
335C23×C31—42no—
336C23×C31—42no—
337C23×C31—42no—
338C23×C31—42no—
339C23×C31—42no—
340C23×C31—42no—
341C23×C31—42no—
342C23×C31—42no—
343C23×C31—42no—
344C23×C31—42no—
345C23×C31—42no—
346C23×C31—42no—
347C23×C31—42no—
348C23×C31—416no—
349C23×C31—41no—
350C23×C31—41no—
351C23×C31—41no—
352C23×C31—41no—
353C23×C31—42no—
354C23×C31—41no—
355C23×C31—41no—
356C23×C31—41no—
357C23×C31—41no—
358C23×C31—42no—
359C23×C31—42no—
360C23×C31—42no—
361C23×C31—42no—
362C23×C31—42no—
363C23×C31—42no—
364C23×C31—42no—
365C23×C31—42no—
366C23×C31—42no—
367C23×C31C2×C22⋊C414yes—
368C23×C31C4×D418yes—
369C23×C31C4×D414yes—
370C23×C31C4×D414yes—
371C23×C31#12114yes—
372C23×C31#12114yes—
373C23×C31#12414yes—
374C23×C31#12714yes—
375C23×C31C23×C411yescharacteristic
376C23×C31C22×D411yescharacteristic
377C23×C31C22×D411yescharacteristic
378C23×C31C22×D411yescharacteristic
379C23×C31C22×D412yes—
380C23×C31C22×D411yescharacteristic
381C23×C31C2×#4111yescharacteristic
382C23×C31C2×#4111yescharacteristic
383C23×C31C2×#4112yes—
384C23×C31H(5,𝔽2)12yes—
385C23×C31H(5,𝔽2)12yes—
386D4×C31—432no—
387D4×C31—416no—
388C2×C4×C31—24no—
389C2×C4×C31—24no—
390C2×C4×C31—22no—
391C2×C4×C31—22no—
392C2×C4×C31—24no—
393C2×C4×C31—24no—
394C2×C4×C31—24no—
395C2×C4×C31—24no—
396C2×C4×C31—24no—
397C2×C4×C31—24no—
398C2×C4×C31—22no—
399C2×C4×C31—22no—
400C2×C4×C31—22no—
401C2×C4×C31—22no—
402C2×C4×C31—24no—
403C2×C4×C31—24no—
404C2×C4×C31—22no—
405C2×C4×C31—22no—
406C2×C4×C31—24no—
407C2×C4×C31—24no—
408C2×C4×C31—24no—
409C2×C4×C31—24no—
410C2×C4×C31—416no—
411C2×C4×C31—416no—
412C2×C4×C31—41no—
413C2×C4×C31—41no—
414C2×C4×C31—42no—
415C2×C4×C31—41no—
416C2×C4×C31—42no—
417C2×C4×C31—41no—
418C2×C4×C31—42no—
419C2×C4×C31—42no—
420C2×C4×C31—42no—
421C2×C4×C31—42no—
422C2×C4×C31—42no—
423C2×C4×C31—42no—
424C2×C4×C31—42no—
425C2×C4×C31—42no—
426C2×C4×C31—41no—
427C2×C4×C31—41no—
428C2×C4×C31—41no—
429C2×C4×C31—41no—
430C2×C4×C31—41no—
431C2×C4×C31—41no—
432C2×C4×C31—42no—
433C2×C4×C31—42no—
434C2×C4×C31—42no—
435C2×C4×C31—42no—
436C2×C4×C31C2×C22⋊C418yescomplemented
437C2×C4×C31#12014yescomplemented
438C22×#120C2×C3111yescharacteristic
439C23×C22⋊C4C2×C3111yescharacteristic, complemented
440C2×#390C2×C3112yescomplemented
441C2×#386C2×C3111yescharacteristic, complemented
442C2×#386C2×C3111yescharacteristic, complemented
443C2×#385C2×C3111yescharacteristic, complemented
444C2×#379C2×C3111yescharacteristic, complemented
445C2×C4×C22⋊C4C2×C3111yescharacteristic, complemented
446#1439C2×C3112yescomplemented
447#1438C2×C3112yescomplemented
448#1437C2×C3112yescomplemented
449C22×C31—24no—
450C22×C31—28no—
451C22×C31—28no—
452C22×C31—24no—
453C22×C31—24no—
454C22×C31—28no—
455C22×C31—24no—
456C22×C31—28no—
457C22×C31—24no—
458C22×C31—24no—
459C22×C31—28no—
460C22×C31—28no—
461C22×C31—28no—
462C22×C31—464no—
463C22×C31—44no—
464C22×C31—44no—
465C22×C31—44no—
466C22×C31—44no—
467C22×C31—44no—
468C22×C31—44no—
469C22×C31—44no—
470C22×C31—44no—
471C22×C31—44no—
472C22×C31—44no—
473C22×C31—44no—
474C22×C31—44no—
475C22×C31—42no—
476C22×C31—44no—
477C22×C31—44no—
478C22×C31—42no—
479C22×C31—42no—
480C22×C31—81no—
481C22×C31—81no—
482C22×C31—82no—
483C22×C31—81no—
484C22×C31—82no—
485C22×C31—81no—
486C22×C31#39018yescomplemented
487C22×C31C22×C22⋊C411yescharacteristic
488C22×C31C2×C4×D411yescharacteristic
489C22×C31C2×C4×D412yes—
490C22×C31C2×C4×D411yescharacteristic
491C22×C31#51812yes—
492C22×C31C2×#12011yescharacteristic
493C22×C31C2×#12111yescharacteristic
494C22×C31C2×#12111yescharacteristic
495C22×C31#52511yescharacteristic
496C22×C31#52512yes—
497C22×C31C2×#12411yescharacteristic
498C22×C31C2×#12711yescharacteristic
499C22×C31#53411yescharacteristic
500C22×C31#53511yescharacteristic
501C22×C31#53812yes—
502C22×C31D4212yes—
503C22×C31D4212yes—
504C22×C31D4212yes—
505C22×C31#54612yes—
506C22×C31#54612yes—
507C22×C31#54612yes—
508C22×C31#54612yes—
509C22×C31#55112yes—
510C4×C31—28no—
511C4×C31—24no—
512C4×C31—42no—
513C4×C31—44no—
514C4×C31—44no—
515C4×C31—42no—
516C4×C31—81no—
517C4×C31—81no—
518C26C22×C3111yescharacteristic
519C23×D4C22×C3111yescharacteristic
520C23×D4C22×C3112yes—
521C24×C4C22×C3111yescharacteristic
522C24×C4C22×C3111yescharacteristic
523C2×#120—24no—
524C2×#120—24no—
525C2×#120C4×C3118yescomplemented
526C22×C4⋊C4C22×C3112yescomplemented
527C22×C22⋊C4—24no—
528C22×C22⋊C4—28no—
529C22×C22⋊C4C22×C3112yes—
530C22×C22⋊C4C22×C3111yescharacteristic
531C22×C22⋊C4C22×C3112yes—
532C22×C22⋊C4C22×C3112yes—
533C22×C22⋊C4C22×C3112yes—
534C22×C22⋊C4C22×C3112yes—
535C22×C22⋊C4C22×C3111yescharacteristic
536C22×C22⋊C4C22×C3111yescharacteristic
537C22×C22⋊C4C22×C3111yescharacteristic, complemented
538C22×C22⋊C4C22×C3112yescomplemented
539C22×C22⋊C4C22×C3111yescharacteristic, complemented
540C22×C42C22×C3112yescomplemented
541#390—28no—
542#386—24no—
543#386—24no—
544#385—24no—
545#379—24no—
546C4×C22⋊C4—24no—
547C2×#95C22×C3111yescharacteristic, complemented
548C2×#95C22×C3112yescomplemented
549C2×#95C22×C3112yescomplemented
550C2×#95C22×C3112yescomplemented
551C2×#95C22×C3111yescharacteristic, complemented
552C2×C31—28no—
553C2×C31—48no—
554C2×C31—82no—
555C2×C31C2×#39011yescharacteristic
556C2×C31C4×#12011yescharacteristic
557C2×C31#232111yescharacteristic
558C2×C31D4×C22⋊C412yes—
559C2×C31#235812yes—
560C2×C31#241011yescharacteristic
561C2×C31#241111yescharacteristic
562C2×C31#242412yes—
563C2×C31#243311yescharacteristic
564C2×C31#247212yes—
565C2×C31#253911yescharacteristic
566C25—24no—
567C25—22no—
568C25—24no—
569C25—22no—
570C25—22no—
571C25—22no—
572C25—22no—
573C25—22no—
574C25—42no—
575C25—42no—
576C25C2×C4×C3114yes—
577C25C23×C3111yescharacteristic
578C25C23×C3112yes—
579C25C23×C3111yescharacteristic
580C22×D4—22no—
581C22×D4—22no—
582C22×D4—22no—
583C22×D4—22no—
584C22×D4—24no—
585C22×D4—24no—
586C22×D4—22no—
587C22×D4—22no—
588C22×D4—24no—
589C22×D4—24no—
590C22×D4—42no—
591C22×D4—42no—
592C22×D4C2×C4×C3114yes—
593C22×D4C2×C4×C3118yescomplemented
594C23×C4—22no—
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—24no—
598C23×C4—24no—
599C23×C4—22no—
600C23×C4—22no—
601C23×C4—42no—
602C23×C4—42no—
603C23×C4D4×C3114yescomplemented
604C23×C4C23×C3111yescharacteristic
605C23×C4C23×C3111yescharacteristic
606C23×C4C23×C3111yescharacteristic
607C23×C4C23×C3112yes—
608C23×C4C23×C3112yes—
609C23×C4C23×C3111yescharacteristic
610C23×C4C23×C3112yes—
611C23×C4C23×C3111yescharacteristic
612#120—232no—
613C2×C4⋊C4—24no—
614C2×C4⋊C4—24no—
615C2×C4⋊C4—42no—
616C2×C22⋊C4—232no—
617C2×C22⋊C4—24no—
618C2×C22⋊C4—22no—
619C2×C22⋊C4—22no—
620C2×C22⋊C4—24no—
621C2×C22⋊C4—24no—
622C2×C22⋊C4—24no—
623C2×C22⋊C4—24no—
624C2×C22⋊C4—24no—
625C2×C22⋊C4—24no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—24no—
630C2×C22⋊C4—24no—
631C2×C22⋊C4—24no—
632C2×C22⋊C4—24no—
633C2×C22⋊C4—24no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—24no—
637C2×C22⋊C4—24no—
638C2×C22⋊C4—42no—
639C2×C22⋊C4—42no—
640C2×C22⋊C4—42no—
641C2×C22⋊C4—42no—
642C2×C22⋊C4C2×C4×C3114yes—
643C2×C22⋊C4C2×C4×C3118yescomplemented
644C2×C22⋊C4D4×C3114yes—
645C2×C22⋊C4D4×C3114yes—
646C2×C22⋊C4D4×C3118yescomplemented
647C2×C22⋊C4D4×C3114yescomplemented
648C2×C42—24no—
649C2×C42—24no—
650C2×C42—42no—
651#95—24no—
652#95—24no—
653#95—24no—
654#95—22no—
655#95—22no—
656C31#1399511yescharacteristic, direct product factor, Sylow
657C24—22no—
658C24—22no—
659C24—22no—
660C24—22no—
661C24—28no—
662C24—28no—
663C24—216no—
664C24—216no—
665C24—28no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—28no—
679C24—28no—
680C24—21no—
681C24—22no—
682C24—21no—
683C24—21no—
684C24—21no—
685C24—21no—
686C24—21no—
687C24—22no—
688C24—22no—
689C24—22no—
690C24—48no—
691C24—48no—
692C24—48no—
693C24—48no—
694C24—48no—
695C24—48no—
696C24—48no—
697C24—48no—
698C24—48no—
699C24—44no—
700C24—44no—
701C24—48no—
702C24—44no—
703C24—44no—
704C24—44no—
705C24—44no—
706C24C22×C4×C3112yes—
707C24C22×C4×C3114yes—
708C24C22×C4×C3112yes—
709C24C2×D4×C3114yes—
710C24C2×D4×C3112yes—
711C24C2×D4×C3112yes—
712C24C2×D4×C3112yes—
713C24C2×D4×C3112yes—
714C24#41×C3114yes—
715C24#41×C3112yes—
716C24#41×C3112yes—
717C24C24×C3111yescharacteristic
718C2×D4—28no—
719C2×D4—28no—
720C2×D4—28no—
721C2×D4—216no—
722C2×D4—216no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4—48no—
726C2×D4—48no—
727C2×D4—48no—
728C2×D4—44no—
729C2×D4—44no—
730C2×D4—44no—
731C2×D4—44no—
732C22×C4—21no—
733C22×C4—22no—
734C22×C4—21no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—28no—
740C22×C4—28no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—28no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—22no—
770C22×C4—21no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—44no—
775C22×C4—48no—
776C22×C4—48no—
777C22×C4—48no—
778C22×C4—48no—
779C22×C4—44no—
780C22×C4—44no—
781C22×C4C22×C4×C3112yes—
782C22×C4C22×C4×C3114yes—
783C22×C4C2×D4×C3114yes—
784C22×C4C2×D4×C3112yes—
785C22×C4C2×D4×C3114yes—
786C22×C4C2×D4×C3114yes—
787C22×C4C2×D4×C3114yes—
788C22×C4C2×D4×C3112yes—
789C22×C4C2×D4×C3114yes—
790C4⋊C4—48no—
791C22⋊C4—216no—
792C22⋊C4—28no—
793C22⋊C4—216no—
794C22⋊C4—216no—
795C22⋊C4—48no—
796C22⋊C4—48no—
797C22⋊C4—48no—
798C22⋊C4—44no—
799C22⋊C4—44no—
800C22⋊C4—44no—
801C22⋊C4C22⋊C4×C31116yescomplemented
802C42—48no—
803C23—24no—
804C23—24no—
805C23—22no—
806C23—22no—
807C23—24no—
808C23—22no—
809C23—22no—
810C23—24no—
811C23—24no—
812C23—24no—
813C23—24no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—24no—
818C23—24no—
819C23—232no—
820C23—24no—
821C23—24no—
822C23—24no—
823C23—24no—
824C23—24no—
825C23—24no—
826C23—24no—
827C23—24no—
828C23—24no—
829C23—24no—
830C23—24no—
831C23—24no—
832C23—24no—
833C23—24no—
834C23—24no—
835C23—24no—
836C23—24no—
837C23—24no—
838C23—22no—
839C23—22no—
840C23—24no—
841C23—22no—
842C23—24no—
843C23—432no—
844C23—432no—
845C23—416no—
846C23—416no—
847C23—416no—
848C23—432no—
849C23—416no—
850C23—432no—
851C23—416no—
852C23—42no—
853C23—42no—
854C23—42no—
855C23—42no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—42no—
861C23—42no—
862C23—42no—
863C23—42no—
864C23—42no—
865C23—42no—
866C23—42no—
867C23—42no—
868C23—416no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—41no—
873C23—42no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—42no—
879C23—42no—
880C23—42no—
881C23—42no—
882C23—42no—
883C23—42no—
884C23—42no—
885C23—42no—
886C23—42no—
887C23C2×C22⋊C4×C3114yes—
888C23C4×D4×C3118yes—
889C23C4×D4×C3114yes—
890C23C4×D4×C3114yes—
891C23C31×#12114yes—
892C23C31×#12114yes—
893C23C31×#12414yes—
894C23C31×#12714yes—
895C23C23×C4×C3111yescharacteristic
896C23C22×D4×C3111yescharacteristic
897C23C22×D4×C3111yescharacteristic
898C23C22×D4×C3111yescharacteristic
899C23C22×D4×C3112yes—
900C23C22×D4×C3111yescharacteristic
901C23C2×#41×C3111yescharacteristic
902C23C2×#41×C3111yescharacteristic
903C23C2×#41×C3112yes—
904C23C31×H(5,𝔽2)12yes—
905C23C31×H(5,𝔽2)12yes—
906D4—432no—
907D4—416no—
908C2×C4—24no—
909C2×C4—24no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—24no—
917C2×C4—24no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—24no—
923C2×C4—24no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—24no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—24no—
930C2×C4—416no—
931C2×C4—416no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—42no—
935C2×C4—41no—
936C2×C4—42no—
937C2×C4—41no—
938C2×C4—42no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—42no—
942C2×C4—42no—
943C2×C4—42no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—42no—
953C2×C4—42no—
954C2×C4—42no—
955C2×C4—42no—
956C2×C4C2×C22⋊C4×C3118yescomplemented
957C2×C4C31×#12014yescomplemented
958C22—24no—
959C22—28no—
960C22—28no—
961C22—24no—
962C22—24no—
963C22—28no—
964C22—24no—
965C22—28no—
966C22—24no—
967C22—24no—
968C22—28no—
969C22—28no—
970C22—28no—
971C22—464no—
972C22—44no—
973C22—44no—
974C22—44no—
975C22—44no—
976C22—44no—
977C22—44no—
978C22—44no—
979C22—44no—
980C22—44no—
981C22—44no—
982C22—44no—
983C22—44no—
984C22—42no—
985C22—44no—
986C22—44no—
987C22—42no—
988C22—42no—
989C22—81no—
990C22—81no—
991C22—82no—
992C22—81no—
993C22—82no—
994C22—81no—
995C22C31×#39018yescomplemented
996C22C22×C22⋊C4×C3111yescharacteristic
997C22C2×C4×D4×C3111yescharacteristic
998C22C2×C4×D4×C3112yes—
999C22C2×C4×D4×C3111yescharacteristic
1000C22C31×#51812yes—
1001C22C2×C31×#12011yescharacteristic
1002C22C2×C31×#12111yescharacteristic
1003C22C2×C31×#12111yescharacteristic
1004C22C31×#52511yescharacteristic
1005C22C31×#52512yes—
1006C22C2×C31×#12411yescharacteristic
1007C22C2×C31×#12711yescharacteristic
1008C22C31×#53411yescharacteristic
1009C22C31×#53511yescharacteristic
1010C22C31×#53812yes—
1011C22D42×C3112yes—
1012C22D42×C3112yes—
1013C22D42×C3112yes—
1014C22C31×#54612yes—
1015C22C31×#54612yes—
1016C22C31×#54612yes—
1017C22C31×#54612yes—
1018C22C31×#55112yes—
1019C4—28no—
1020C4—24no—
1021C4—42no—
1022C4—44no—
1023C4—44no—
1024C4—42no—
1025C4—81no—
1026C4—81no—
1027C2—28no—
1028C2—48no—
1029C2—82no—
1030C2C2×C31×#39011yescharacteristic
1031C2C4×C31×#12011yescharacteristic
1032C2C31×#232111yescharacteristic
1033C2D4×C22⋊C4×C3112yes—
1034C2C31×#235812yes—
1035C2C31×#241011yescharacteristic
1036C2C31×#241111yescharacteristic
1037C2C31×#242412yes—
1038C2C31×#243311yescharacteristic
1039C2C31×#247212yes—
1040C2C31×#253911yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC22×C31×#120C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C22⋊C4×C31C2semidirect
3. C2×C31×#390C2semidirect
4. C2×C31×#386C2semidirect
5. C2×C31×#386C2semidirect
6. C2×C31×#385C2semidirect
7. C2×C31×#379C2semidirect
8. C2×C4×C22⋊C4×C31C2semidirect
9. C31×#1439C2semidirect
10. C31×#1438C2semidirect
11. C31×#1437C2semidirect
19. C2×C31×#120C4semidirect
20. C22×C4⋊C4×C31C22semidirect
31. C22×C22⋊C4×C31C22semidirect
32. C22×C22⋊C4×C31C22semidirect
33. C22×C22⋊C4×C31C22semidirect
34. C22×C42×C31C22semidirect
41. C2×C31×#95C22semidirect
42. C2×C31×#95C22semidirect
43. C2×C31×#95C22semidirect
44. C2×C31×#95C22semidirect
45. C2×C31×#95C22semidirect
73. C22×D4×C31C2×C4semidirect
83. C23×C4×C31D4semidirect
123. C2×C22⋊C4×C31C2×C4semidirect
126. C2×C22⋊C4×C31D4semidirect
127. C2×C22⋊C4×C31D4semidirect
280. C22⋊C4×C31C22⋊C4semidirect
282. #13995C31direct (N × H)
436. C2×C4×C31C2×C22⋊C4semidirect
437. C2×C4×C31#120semidirect
439. C23×C22⋊C4C2×C31semidirect
440. C2×#390C2×C31semidirect
441. C2×#386C2×C31semidirect
442. C2×#386C2×C31semidirect
443. C2×#385C2×C31semidirect
444. C2×#379C2×C31semidirect
445. C2×C4×C22⋊C4C2×C31semidirect
446. #1439C2×C31semidirect
447. #1438C2×C31semidirect
448. #1437C2×C31semidirect
486. C22×C31#390semidirect
525. C2×#120C4×C31semidirect
526. C22×C4⋊C4C22×C31semidirect
537. C22×C22⋊C4C22×C31semidirect
538. C22×C22⋊C4C22×C31semidirect
539. C22×C22⋊C4C22×C31semidirect
540. C22×C42C22×C31semidirect
547. C2×#95C22×C31semidirect
548. C2×#95C22×C31semidirect
549. C2×#95C22×C31semidirect
550. C2×#95C22×C31semidirect
551. C2×#95C22×C31semidirect
593. C22×D4C2×C4×C31semidirect
603. C23×C4D4×C31semidirect
643. C2×C22⋊C4C2×C4×C31semidirect
646. C2×C22⋊C4D4×C31semidirect
647. C2×C22⋊C4D4×C31semidirect
656. C31#13995direct (N × H)
801. C22⋊C4C22⋊C4×C31semidirect
956. C2×C4C2×C22⋊C4×C31semidirect
957. C2×C4C31×#120semidirect
995. C22C31×#390semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1202
C23×C22⋊C4×C312
C2×C31×#3902
C2×C31×#3862
C2×C31×#3852
C2×C31×#3792
C2×C4×C22⋊C4×C312
C31×#14392
C31×#14382
C31×#14372
#1399531