Finite Group Databasebeta

← C31×#13967 #21470726

Subgroups — C31×#13967 #21470726

Order 7936.

4478 conjugacy classes of subgroups.

The subgroup lattice has 1062 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#120C211yesmaximal, characteristic
2C22×C4×D4×C31C211yesmaximal, characteristic, complemented
3C23×C22⋊C4×C31C211yesmaximal, characteristic, complemented
4C2×C31×#386C212yesmaximal, complemented
5C2×C31×#386C211yesmaximal, characteristic, complemented
6C2×C31×#379C211yesmaximal, characteristic, complemented
7C31×#1439C212yesmaximal, complemented
8C31×#1438C212yesmaximal, complemented
9C31×#1437C212yesmaximal, complemented
10C31×C22⋊#95C211yesmaximal, characteristic, complemented
11C31×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C31C2211yescharacteristic
13C23×D4×C31C2212yes—
14C23×D4×C31C2211yescharacteristic
15C24×C4×C31C2211yescharacteristic
16C24×C4×C31C2211yescharacteristic
17C24×C4×C31C2211yescharacteristic, complemented
18C2×C31×#120—24no—
19C2×C31×#120—24no—
20C2×C31×#120C418yescomplemented
21C2×C4×D4×C31—24no—
22C2×C4×D4×C31—24no—
23C2×C4×D4×C31—24no—
24C22×C4⋊C4×C31C2211yescharacteristic, complemented
25C22×C22⋊C4×C31—24no—
26C22×C22⋊C4×C31—28no—
27C22×C22⋊C4×C31C2212yes—
28C22×C22⋊C4×C31C2211yescharacteristic
29C22×C22⋊C4×C31C2212yes—
30C22×C22⋊C4×C31C2212yes—
31C22×C22⋊C4×C31C2211yescharacteristic
32C22×C22⋊C4×C31C2212yes—
33C22×C22⋊C4×C31C2212yes—
34C22×C22⋊C4×C31C2211yescharacteristic
35C22×C22⋊C4×C31C2211yescharacteristic, complemented
36C22×C22⋊C4×C31C2212yescomplemented
37C22×C42×C31C2211yescharacteristic, complemented
38C31×#386—24no—
39C31×#386—28no—
40C31×#379—24no—
41C2×C31×#95C2212yescomplemented
42C2×C31×#95C2212yescomplemented
43C2×C31×#95C2212yescomplemented
44C2×C31×#95C2212yescomplemented
45C2×C31×#95C2212yescomplemented
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×C414yescomplemented
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—24no—
67C22×D4×C31—24no—
68C22×D4×C31—42no—
69C22×D4×C31—42no—
70C22×D4×C31C2×C414yes—
71C22×D4×C31C2×C418yescomplemented
72C22×D4×C31D414yes—
73C22×D4×C31D414yes—
74C23×C4×C31—22no—
75C23×C4×C31—22no—
76C23×C4×C31—22no—
77C23×C4×C31—22no—
78C23×C4×C31—24no—
79C23×C4×C31—24no—
80C23×C4×C31—22no—
81C23×C4×C31—22no—
82C23×C4×C31—22no—
83C23×C4×C31—22no—
84C23×C4×C31—24no—
85C23×C4×C31—42no—
86C23×C4×C31—42no—
87C23×C4×C31—42no—
88C23×C4×C31D414yescomplemented
89C23×C4×C31C2312yes—
90C23×C4×C31C2312yes—
91C23×C4×C31C2311yescharacteristic
92C23×C4×C31C2311yescharacteristic
93C23×C4×C31C2311yescharacteristic
94C23×C4×C31C2312yes—
95C23×C4×C31C2311yescharacteristic
96C23×C4×C31C2311yescharacteristic
97C31×#120—232no—
98C4×D4×C31—232no—
99C2×C4⋊C4×C31—22no—
100C2×C4⋊C4×C31—22no—
101C2×C4⋊C4×C31—22no—
102C2×C22⋊C4×C31—232no—
103C2×C22⋊C4×C31—24no—
104C2×C22⋊C4×C31—22no—
105C2×C22⋊C4×C31—22no—
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—24no—
115C2×C22⋊C4×C31—22no—
116C2×C22⋊C4×C31—22no—
117C2×C22⋊C4×C31—22no—
118C2×C22⋊C4×C31—24no—
119C2×C22⋊C4×C31—22no—
120C2×C22⋊C4×C31—24no—
121C2×C22⋊C4×C31—24no—
122C2×C22⋊C4×C31—22no—
123C2×C22⋊C4×C31—24no—
124C2×C22⋊C4×C31—24no—
125C2×C22⋊C4×C31—24no—
126C2×C22⋊C4×C31—42no—
127C2×C22⋊C4×C31—42no—
128C2×C22⋊C4×C31—42no—
129C2×C22⋊C4×C31C2×C414yescomplemented
130C2×C22⋊C4×C31C2×C418yescomplemented
131C2×C22⋊C4×C31D418yescomplemented
132C2×C22⋊C4×C31D414yescomplemented
133C2×C42×C31—22no—
134C2×C42×C31—22no—
135C2×C42×C31—22no—
136C31×#95—24no—
137C31×#95—24no—
138C31×#95—24no—
139C31×#95—42no—
140C31×#95—42no—
141C24×C31—22no—
142C24×C31—22no—
143C24×C31—22no—
144C24×C31—22no—
145C24×C31—28no—
146C24×C31—28no—
147C24×C31—216no—
148C24×C31—28no—
149C24×C31—216no—
150C24×C31—22no—
151C24×C31—22no—
152C24×C31—22no—
153C24×C31—21no—
154C24×C31—21no—
155C24×C31—22no—
156C24×C31—22no—
157C24×C31—22no—
158C24×C31—21no—
159C24×C31—21no—
160C24×C31—22no—
161C24×C31—22no—
162C24×C31—22no—
163C24×C31—22no—
164C24×C31—22no—
165C24×C31—22no—
166C24×C31—22no—
167C24×C31—22no—
168C24×C31—22no—
169C24×C31—22no—
170C24×C31—28no—
171C24×C31—28no—
172C24×C31—48no—
173C24×C31—48no—
174C24×C31—48no—
175C24×C31—48no—
176C24×C31—48no—
177C24×C31—48no—
178C24×C31—48no—
179C24×C31—48no—
180C24×C31—48no—
181C24×C31—44no—
182C24×C31—44no—
183C24×C31—48no—
184C24×C31—44no—
185C24×C31—44no—
186C24×C31—44no—
187C24×C31—44no—
188C24×C31C22×C412yes—
189C24×C31C22×C414yes—
190C24×C31C22×C412yes—
191C24×C31C2×D412yes—
192C24×C31C2×D412yes—
193C24×C31C2×D414yes—
194C24×C31C2×D412yes—
195C24×C31C2×D412yes—
196C24×C31C2×D412yes—
197C24×C31C2×D412yes—
198C24×C31#4114yes—
199C24×C31#4112yes—
200C24×C31#4112yes—
201C24×C31C2411yescharacteristic
202C2×D4×C31—28no—
203C2×D4×C31—28no—
204C2×D4×C31—28no—
205C2×D4×C31—28no—
206C2×D4×C31—28no—
207C2×D4×C31—28no—
208C2×D4×C31—216no—
209C2×D4×C31—216no—
210C2×D4×C31—48no—
211C2×D4×C31—48no—
212C2×D4×C31—48no—
213C2×D4×C31—48no—
214C2×D4×C31—48no—
215C2×D4×C31C22⋊C4116yescomplemented
216C22×C4×C31—21no—
217C22×C4×C31—21no—
218C22×C4×C31—21no—
219C22×C4×C31—21no—
220C22×C4×C31—21no—
221C22×C4×C31—21no—
222C22×C4×C31—22no—
223C22×C4×C31—28no—
224C22×C4×C31—28no—
225C22×C4×C31—28no—
226C22×C4×C31—22no—
227C22×C4×C31—22no—
228C22×C4×C31—22no—
229C22×C4×C31—21no—
230C22×C4×C31—21no—
231C22×C4×C31—22no—
232C22×C4×C31—22no—
233C22×C4×C31—22no—
234C22×C4×C31—22no—
235C22×C4×C31—22no—
236C22×C4×C31—21no—
237C22×C4×C31—21no—
238C22×C4×C31—21no—
239C22×C4×C31—21no—
240C22×C4×C31—22no—
241C22×C4×C31—22no—
242C22×C4×C31—22no—
243C22×C4×C31—22no—
244C22×C4×C31—22no—
245C22×C4×C31—22no—
246C22×C4×C31—22no—
247C22×C4×C31—22no—
248C22×C4×C31—22no—
249C22×C4×C31—22no—
250C22×C4×C31—28no—
251C22×C4×C31—22no—
252C22×C4×C31—22no—
253C22×C4×C31—22no—
254C22×C4×C31—22no—
255C22×C4×C31—22no—
256C22×C4×C31—22no—
257C22×C4×C31—22no—
258C22×C4×C31—44no—
259C22×C4×C31—48no—
260C22×C4×C31—48no—
261C22×C4×C31—48no—
262C22×C4×C31—48no—
263C22×C4×C31—48no—
264C22×C4×C31—48no—
265C22×C4×C31—44no—
266C22×C4×C31—44no—
267C22×C4×C31—44no—
268C22×C4×C31—44no—
269C22×C4×C31C22×C414yes—
270C22×C4×C31C22×C412yes—
271C22×C4×C31C2×D414yes—
272C22×C4×C31C2×D412yes—
273C22×C4×C31C2×D412yes—
274C22×C4×C31C2×D412yes—
275C22×C4×C31C2×D412yes—
276C22×C4×C31C2×D412yes—
277C22×C4×C31C2×D414yes—
278C22×C4×C31C2×D412yes—
279C4⋊C4×C31—28no—
280C22⋊C4×C31—216no—
281C22⋊C4×C31—28no—
282C22⋊C4×C31—28no—
283C22⋊C4×C31—28no—
284C22⋊C4×C31—216no—
285C22⋊C4×C31—216no—
286C22⋊C4×C31—48no—
287C22⋊C4×C31—48no—
288C22⋊C4×C31—48no—
289C22⋊C4×C31—44no—
290C42×C31—28no—
291#13967C3111yesmaximal, characteristic, direct product factor, Sylow
292C23×C31—24no—
293C23×C31—24no—
294C23×C31—22no—
295C23×C31—22no—
296C23×C31—24no—
297C23×C31—22no—
298C23×C31—22no—
299C23×C31—24no—
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—232no—
309C23×C31—24no—
310C23×C31—24no—
311C23×C31—22no—
312C23×C31—22no—
313C23×C31—24no—
314C23×C31—24no—
315C23×C31—24no—
316C23×C31—24no—
317C23×C31—24no—
318C23×C31—24no—
319C23×C31—24no—
320C23×C31—22no—
321C23×C31—22no—
322C23×C31—22no—
323C23×C31—22no—
324C23×C31—24no—
325C23×C31—24no—
326C23×C31—24no—
327C23×C31—24no—
328C23×C31—24no—
329C23×C31—24no—
330C23×C31—24no—
331C23×C31—24no—
332C23×C31—24no—
333C23×C31—24no—
334C23×C31—24no—
335C23×C31—24no—
336C23×C31—24no—
337C23×C31—24no—
338C23×C31—24no—
339C23×C31—432no—
340C23×C31—432no—
341C23×C31—416no—
342C23×C31—416no—
343C23×C31—416no—
344C23×C31—416no—
345C23×C31—432no—
346C23×C31—432no—
347C23×C31—416no—
348C23×C31—41no—
349C23×C31—42no—
350C23×C31—42no—
351C23×C31—42no—
352C23×C31—42no—
353C23×C31—41no—
354C23×C31—42no—
355C23×C31—41no—
356C23×C31—42no—
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×C31—42no—
368C23×C31—42no—
369C23×C31—42no—
370C23×C31—42no—
371C23×C31—42no—
372C23×C31—42no—
373C23×C31—42no—
374C23×C31—416no—
375C23×C31C2×C22⋊C414yes—
376C23×C31C2×C22⋊C414yescomplemented
377C23×C31C4×D414yes—
378C23×C31C4×D414yes—
379C23×C31C4×D418yescomplemented
380C23×C31#12014yes—
381C23×C31#12114yes—
382C23×C31#12114yes—
383C23×C31#12314yes—
384C23×C31C23×C411yescharacteristic
385C23×C31C22×D411yescharacteristic
386C23×C31C22×D411yescharacteristic
387C23×C31C22×D411yescharacteristic
388C23×C31C22×D411yescharacteristic
389C23×C31C22×D412yes—
390C23×C31C2×#4111yescharacteristic
391C23×C31C2×#4111yescharacteristic
392C23×C31C2×#4112yes—
393C23×C31H(5,𝔽2)12yes—
394C23×C31H(5,𝔽2)12yes—
395D4×C31—232no—
396D4×C31—432no—
397C2×C4×C31—22no—
398C2×C4×C31—22no—
399C2×C4×C31—22no—
400C2×C4×C31—22no—
401C2×C4×C31—22no—
402C2×C4×C31—22no—
403C2×C4×C31—22no—
404C2×C4×C31—22no—
405C2×C4×C31—24no—
406C2×C4×C31—24no—
407C2×C4×C31—24no—
408C2×C4×C31—24no—
409C2×C4×C31—24no—
410C2×C4×C31—22no—
411C2×C4×C31—22no—
412C2×C4×C31—24no—
413C2×C4×C31—22no—
414C2×C4×C31—22no—
415C2×C4×C31—22no—
416C2×C4×C31—24no—
417C2×C4×C31—24no—
418C2×C4×C31—24no—
419C2×C4×C31—24no—
420C2×C4×C31—416no—
421C2×C4×C31—416no—
422C2×C4×C31—416no—
423C2×C4×C31—41no—
424C2×C4×C31—42no—
425C2×C4×C31—41no—
426C2×C4×C31—41no—
427C2×C4×C31—41no—
428C2×C4×C31—42no—
429C2×C4×C31—42no—
430C2×C4×C31—42no—
431C2×C4×C31—42no—
432C2×C4×C31—42no—
433C2×C4×C31—42no—
434C2×C4×C31—42no—
435C2×C4×C31—42no—
436C2×C4×C31—42no—
437C2×C4×C31—42no—
438C2×C4×C31—42no—
439C2×C4×C31—42no—
440C2×C4×C31—42no—
441C2×C4×C31—42no—
442C2×C4×C31—42no—
443C2×C4×C31—42no—
444C2×C4×C31—42no—
445C2×C4×C31—42no—
446C2×C4×C31C2×C22⋊C414yescomplemented
447C2×C4×C31#12014yescomplemented
448C22×#120C2×C3111yescharacteristic
449C22×C4×D4C2×C3111yescharacteristic, complemented
450C23×C22⋊C4C2×C3111yescharacteristic, complemented
451C2×#386C2×C3112yescomplemented
452C2×#386C2×C3111yescharacteristic, complemented
453C2×#379C2×C3111yescharacteristic, complemented
454#1439C2×C3112yescomplemented
455#1438C2×C3112yescomplemented
456#1437C2×C3112yescomplemented
457C22⋊#95C2×C3111yescharacteristic, complemented
458C22⋊#95C2×C3111yescharacteristic, complemented
459C22×C31—24no—
460C22×C31—28no—
461C22×C31—28no—
462C22×C31—24no—
463C22×C31—24no—
464C22×C31—24no—
465C22×C31—28no—
466C22×C31—28no—
467C22×C31—24no—
468C22×C31—24no—
469C22×C31—28no—
470C22×C31—28no—
471C22×C31—28no—
472C22×C31—24no—
473C22×C31—28no—
474C22×C31—464no—
475C22×C31—42no—
476C22×C31—44no—
477C22×C31—44no—
478C22×C31—44no—
479C22×C31—44no—
480C22×C31—42no—
481C22×C31—44no—
482C22×C31—42no—
483C22×C31—44no—
484C22×C31—42no—
485C22×C31—44no—
486C22×C31—44no—
487C22×C31—44no—
488C22×C31—44no—
489C22×C31—44no—
490C22×C31—44no—
491C22×C31—44no—
492C22×C31—42no—
493C22×C31—44no—
494C22×C31—44no—
495C22×C31—42no—
496C22×C31#38618yescomplemented
497C22×C31C22×C22⋊C411yescharacteristic
498C22×C31C2×C4×D411yescharacteristic
499C22×C31C2×C4×D412yes—
500C22×C31C2×C4×D411yescharacteristic
501C22×C31#51812yes—
502C22×C31C2×#12011yescharacteristic
503C22×C31C2×#12011yescharacteristic
504C22×C31C2×#12111yescharacteristic
505C22×C31C2×#12111yescharacteristic
506C22×C31C2×#12311yescharacteristic
507C22×C31#52511yescharacteristic
508C22×C31#52512yes—
509C22×C31#53411yescharacteristic
510C22×C31#53511yescharacteristic
511C22×C31#53812yes—
512C22×C31D4212yes—
513C22×C31D4212yes—
514C22×C31D4212yes—
515C22×C31#54612yes—
516C22×C31#54612yes—
517C22×C31#54612yes—
518C22×C31#54612yes—
519C22×C31#55112yes—
520C4×C31—24no—
521C4×C31—24no—
522C4×C31—44no—
523C4×C31—42no—
524C4×C31—42no—
525C4×C31—42no—
526C4×C31—44no—
527C4×C31—82no—
528C26C22×C3111yescharacteristic
529C23×D4C22×C3112yes—
530C23×D4C22×C3111yescharacteristic
531C24×C4C22×C3111yescharacteristic
532C24×C4C22×C3111yescharacteristic
533C24×C4C22×C3111yescharacteristic, complemented
534C2×#120—24no—
535C2×#120—24no—
536C2×#120C4×C3118yescomplemented
537C2×C4×D4—24no—
538C2×C4×D4—24no—
539C2×C4×D4—24no—
540C22×C4⋊C4C22×C3111yescharacteristic, complemented
541C22×C22⋊C4—24no—
542C22×C22⋊C4—28no—
543C22×C22⋊C4C22×C3112yes—
544C22×C22⋊C4C22×C3111yescharacteristic
545C22×C22⋊C4C22×C3112yes—
546C22×C22⋊C4C22×C3112yes—
547C22×C22⋊C4C22×C3111yescharacteristic
548C22×C22⋊C4C22×C3112yes—
549C22×C22⋊C4C22×C3112yes—
550C22×C22⋊C4C22×C3111yescharacteristic
551C22×C22⋊C4C22×C3111yescharacteristic, complemented
552C22×C22⋊C4C22×C3112yescomplemented
553C22×C42C22×C3111yescharacteristic, complemented
554#386—24no—
555#386—28no—
556#379—24no—
557C2×#95C22×C3112yescomplemented
558C2×#95C22×C3112yescomplemented
559C2×#95C22×C3112yescomplemented
560C2×#95C22×C3112yescomplemented
561C2×#95C22×C3112yescomplemented
562C2×C31—28no—
563C2×C31—44no—
564C2×C31—48no—
565C2×C31C2×#38611yescharacteristic
566C2×C31C4×#12011yescharacteristic
567C2×C31#232111yescharacteristic
568C2×C31D4×C22⋊C412yes—
569C2×C31#235812yes—
570C2×C31#240311yescharacteristic
571C2×C31#240411yescharacteristic
572C2×C31#240811yescharacteristic
573C2×C31#241812yes—
574C2×C31#242412yes—
575C2×C31#253411yescharacteristic
576C25—24no—
577C25—22no—
578C25—24no—
579C25—22no—
580C25—22no—
581C25—22no—
582C25—22no—
583C25—22no—
584C25—42no—
585C25—42no—
586C25C2×C4×C3114yescomplemented
587C25C23×C3111yescharacteristic
588C25C23×C3112yes—
589C25C23×C3111yescharacteristic
590C22×D4—22no—
591C22×D4—22no—
592C22×D4—22no—
593C22×D4—22no—
594C22×D4—24no—
595C22×D4—24no—
596C22×D4—24no—
597C22×D4—24no—
598C22×D4—42no—
599C22×D4—42no—
600C22×D4C2×C4×C3114yes—
601C22×D4C2×C4×C3118yescomplemented
602C22×D4D4×C3114yes—
603C22×D4D4×C3114yes—
604C23×C4—22no—
605C23×C4—22no—
606C23×C4—22no—
607C23×C4—22no—
608C23×C4—24no—
609C23×C4—24no—
610C23×C4—22no—
611C23×C4—22no—
612C23×C4—22no—
613C23×C4—22no—
614C23×C4—24no—
615C23×C4—42no—
616C23×C4—42no—
617C23×C4—42no—
618C23×C4D4×C3114yescomplemented
619C23×C4C23×C3112yes—
620C23×C4C23×C3112yes—
621C23×C4C23×C3111yescharacteristic
622C23×C4C23×C3111yescharacteristic
623C23×C4C23×C3111yescharacteristic
624C23×C4C23×C3112yes—
625C23×C4C23×C3111yescharacteristic
626C23×C4C23×C3111yescharacteristic
627#120—232no—
628C4×D4—232no—
629C2×C4⋊C4—22no—
630C2×C4⋊C4—22no—
631C2×C4⋊C4—22no—
632C2×C22⋊C4—232no—
633C2×C22⋊C4—24no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—22no—
637C2×C22⋊C4—22no—
638C2×C22⋊C4—22no—
639C2×C22⋊C4—24no—
640C2×C22⋊C4—24no—
641C2×C22⋊C4—24no—
642C2×C22⋊C4—24no—
643C2×C22⋊C4—24no—
644C2×C22⋊C4—24no—
645C2×C22⋊C4—22no—
646C2×C22⋊C4—22no—
647C2×C22⋊C4—22no—
648C2×C22⋊C4—24no—
649C2×C22⋊C4—22no—
650C2×C22⋊C4—24no—
651C2×C22⋊C4—24no—
652C2×C22⋊C4—22no—
653C2×C22⋊C4—24no—
654C2×C22⋊C4—24no—
655C2×C22⋊C4—24no—
656C2×C22⋊C4—42no—
657C2×C22⋊C4—42no—
658C2×C22⋊C4—42no—
659C2×C22⋊C4C2×C4×C3114yescomplemented
660C2×C22⋊C4C2×C4×C3118yescomplemented
661C2×C22⋊C4D4×C3118yescomplemented
662C2×C22⋊C4D4×C3114yescomplemented
663C2×C42—22no—
664C2×C42—22no—
665C2×C42—22no—
666#95—24no—
667#95—24no—
668#95—24no—
669#95—42no—
670#95—42no—
671C31#1396711yescharacteristic, direct product factor, Sylow
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—28no—
677C24—28no—
678C24—216no—
679C24—28no—
680C24—216no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—21no—
685C24—21no—
686C24—22no—
687C24—22no—
688C24—22no—
689C24—21no—
690C24—21no—
691C24—22no—
692C24—22no—
693C24—22no—
694C24—22no—
695C24—22no—
696C24—22no—
697C24—22no—
698C24—22no—
699C24—22no—
700C24—22no—
701C24—28no—
702C24—28no—
703C24—48no—
704C24—48no—
705C24—48no—
706C24—48no—
707C24—48no—
708C24—48no—
709C24—48no—
710C24—48no—
711C24—48no—
712C24—44no—
713C24—44no—
714C24—48no—
715C24—44no—
716C24—44no—
717C24—44no—
718C24—44no—
719C24C22×C4×C3112yes—
720C24C22×C4×C3114yes—
721C24C22×C4×C3112yes—
722C24C2×D4×C3112yes—
723C24C2×D4×C3112yes—
724C24C2×D4×C3114yes—
725C24C2×D4×C3112yes—
726C24C2×D4×C3112yes—
727C24C2×D4×C3112yes—
728C24C2×D4×C3112yes—
729C24#41×C3114yes—
730C24#41×C3112yes—
731C24#41×C3112yes—
732C24C24×C3111yescharacteristic
733C2×D4—28no—
734C2×D4—28no—
735C2×D4—28no—
736C2×D4—28no—
737C2×D4—28no—
738C2×D4—28no—
739C2×D4—216no—
740C2×D4—216no—
741C2×D4—48no—
742C2×D4—48no—
743C2×D4—48no—
744C2×D4—48no—
745C2×D4—48no—
746C2×D4C22⋊C4×C31116yescomplemented
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—22no—
754C22×C4—28no—
755C22×C4—28no—
756C22×C4—28no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—28no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—44no—
790C22×C4—48no—
791C22×C4—48no—
792C22×C4—48no—
793C22×C4—48no—
794C22×C4—48no—
795C22×C4—48no—
796C22×C4—44no—
797C22×C4—44no—
798C22×C4—44no—
799C22×C4—44no—
800C22×C4C22×C4×C3114yes—
801C22×C4C22×C4×C3112yes—
802C22×C4C2×D4×C3114yes—
803C22×C4C2×D4×C3112yes—
804C22×C4C2×D4×C3112yes—
805C22×C4C2×D4×C3112yes—
806C22×C4C2×D4×C3112yes—
807C22×C4C2×D4×C3112yes—
808C22×C4C2×D4×C3114yes—
809C22×C4C2×D4×C3112yes—
810C4⋊C4—28no—
811C22⋊C4—216no—
812C22⋊C4—28no—
813C22⋊C4—28no—
814C22⋊C4—28no—
815C22⋊C4—216no—
816C22⋊C4—216no—
817C22⋊C4—48no—
818C22⋊C4—48no—
819C22⋊C4—48no—
820C22⋊C4—44no—
821C42—28no—
822C23—24no—
823C23—24no—
824C23—22no—
825C23—22no—
826C23—24no—
827C23—22no—
828C23—22no—
829C23—24no—
830C23—24no—
831C23—24no—
832C23—24no—
833C23—24no—
834C23—24no—
835C23—24no—
836C23—24no—
837C23—24no—
838C23—232no—
839C23—24no—
840C23—24no—
841C23—22no—
842C23—22no—
843C23—24no—
844C23—24no—
845C23—24no—
846C23—24no—
847C23—24no—
848C23—24no—
849C23—24no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—24no—
855C23—24no—
856C23—24no—
857C23—24no—
858C23—24no—
859C23—24no—
860C23—24no—
861C23—24no—
862C23—24no—
863C23—24no—
864C23—24no—
865C23—24no—
866C23—24no—
867C23—24no—
868C23—24no—
869C23—432no—
870C23—432no—
871C23—416no—
872C23—416no—
873C23—416no—
874C23—416no—
875C23—432no—
876C23—432no—
877C23—416no—
878C23—41no—
879C23—42no—
880C23—42no—
881C23—42no—
882C23—42no—
883C23—41no—
884C23—42no—
885C23—41no—
886C23—42no—
887C23—41no—
888C23—42no—
889C23—42no—
890C23—42no—
891C23—42no—
892C23—42no—
893C23—42no—
894C23—42no—
895C23—42no—
896C23—42no—
897C23—42no—
898C23—42no—
899C23—42no—
900C23—42no—
901C23—42no—
902C23—42no—
903C23—42no—
904C23—416no—
905C23C2×C22⋊C4×C3114yes—
906C23C2×C22⋊C4×C3114yescomplemented
907C23C4×D4×C3114yes—
908C23C4×D4×C3114yes—
909C23C4×D4×C3118yescomplemented
910C23C31×#12014yes—
911C23C31×#12114yes—
912C23C31×#12114yes—
913C23C31×#12314yes—
914C23C23×C4×C3111yescharacteristic
915C23C22×D4×C3111yescharacteristic
916C23C22×D4×C3111yescharacteristic
917C23C22×D4×C3111yescharacteristic
918C23C22×D4×C3111yescharacteristic
919C23C22×D4×C3112yes—
920C23C2×#41×C3111yescharacteristic
921C23C2×#41×C3111yescharacteristic
922C23C2×#41×C3112yes—
923C23C31×H(5,𝔽2)12yes—
924C23C31×H(5,𝔽2)12yes—
925D4—232no—
926D4—432no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—24no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—24no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—24no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—416no—
951C2×C4—416no—
952C2×C4—416no—
953C2×C4—41no—
954C2×C4—42no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—42no—
959C2×C4—42no—
960C2×C4—42no—
961C2×C4—42no—
962C2×C4—42no—
963C2×C4—42no—
964C2×C4—42no—
965C2×C4—42no—
966C2×C4—42no—
967C2×C4—42no—
968C2×C4—42no—
969C2×C4—42no—
970C2×C4—42no—
971C2×C4—42no—
972C2×C4—42no—
973C2×C4—42no—
974C2×C4—42no—
975C2×C4—42no—
976C2×C4C2×C22⋊C4×C3114yescomplemented
977C2×C4C31×#12014yescomplemented
978C22—24no—
979C22—28no—
980C22—28no—
981C22—24no—
982C22—24no—
983C22—24no—
984C22—28no—
985C22—28no—
986C22—24no—
987C22—24no—
988C22—28no—
989C22—28no—
990C22—28no—
991C22—24no—
992C22—28no—
993C22—464no—
994C22—44no—
995C22—42no—
996C22—44no—
997C22—44no—
998C22—44no—
999C22—42no—
1000C22—44no—
1001C22—44no—
1002C22—42no—
1003C22—44no—
1004C22—42no—
1005C22—44no—
1006C22—44no—
1007C22—44no—
1008C22—44no—
1009C22—44no—
1010C22—44no—
1011C22—44no—
1012C22—42no—
1013C22—44no—
1014C22—42no—
1015C22C31×#38618yescomplemented
1016C22C22×C22⋊C4×C3111yescharacteristic
1017C22C2×C4×D4×C3111yescharacteristic
1018C22C2×C4×D4×C3112yes—
1019C22C2×C4×D4×C3111yescharacteristic
1020C22C31×#51812yes—
1021C22C2×C31×#12011yescharacteristic
1022C22C2×C31×#12011yescharacteristic
1023C22C2×C31×#12111yescharacteristic
1024C22C2×C31×#12111yescharacteristic
1025C22C2×C31×#12311yescharacteristic
1026C22C31×#52511yescharacteristic
1027C22C31×#52512yes—
1028C22C31×#53411yescharacteristic
1029C22C31×#53511yescharacteristic
1030C22C31×#53812yes—
1031C22D42×C3112yes—
1032C22D42×C3112yes—
1033C22D42×C3112yes—
1034C22C31×#54612yes—
1035C22C31×#54612yes—
1036C22C31×#54612yes—
1037C22C31×#54612yes—
1038C22C31×#55112yes—
1039C4—24no—
1040C4—24no—
1041C4—44no—
1042C4—42no—
1043C4—42no—
1044C4—42no—
1045C4—44no—
1046C4—82no—
1047C2—28no—
1048C2—48no—
1049C2—44no—
1050C2C2×C31×#38611yescharacteristic
1051C2C4×C31×#12011yescharacteristic
1052C2C31×#232111yescharacteristic
1053C2D4×C22⋊C4×C3112yes—
1054C2C31×#235812yes—
1055C2C31×#240311yescharacteristic
1056C2C31×#240411yescharacteristic
1057C2C31×#240811yescharacteristic
1058C2C31×#241812yes—
1059C2C31×#242412yes—
1060C2C31×#253411yescharacteristic
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. C22×C4×D4×C31C2semidirect
3. C23×C22⋊C4×C31C2semidirect
4. C2×C31×#386C2semidirect
5. C2×C31×#386C2semidirect
6. C2×C31×#379C2semidirect
7. C31×#1439C2semidirect
8. C31×#1438C2semidirect
9. C31×#1437C2semidirect
10. C31×C22⋊#95C2semidirect
11. C31×C22⋊#95C2semidirect
17. C24×C4×C31C22semidirect
20. C2×C31×#120C4semidirect
24. C22×C4⋊C4×C31C22semidirect
35. C22×C22⋊C4×C31C22semidirect
36. C22×C22⋊C4×C31C22semidirect
37. C22×C42×C31C22semidirect
41. C2×C31×#95C22semidirect
42. C2×C31×#95C22semidirect
43. C2×C31×#95C22semidirect
44. C2×C31×#95C22semidirect
45. C2×C31×#95C22semidirect
56. C25×C31C2×C4semidirect
71. C22×D4×C31C2×C4semidirect
88. C23×C4×C31D4semidirect
129. C2×C22⋊C4×C31C2×C4semidirect
130. C2×C22⋊C4×C31C2×C4semidirect
131. C2×C22⋊C4×C31D4semidirect
132. C2×C22⋊C4×C31D4semidirect
215. C2×D4×C31C22⋊C4semidirect
291. #13967C31direct (N × H)
376. C23×C31C2×C22⋊C4semidirect
379. C23×C31C4×D4semidirect
446. C2×C4×C31C2×C22⋊C4semidirect
447. C2×C4×C31#120semidirect
449. C22×C4×D4C2×C31semidirect
450. C23×C22⋊C4C2×C31semidirect
451. C2×#386C2×C31semidirect
452. C2×#386C2×C31semidirect
453. C2×#379C2×C31semidirect
454. #1439C2×C31semidirect
455. #1438C2×C31semidirect
456. #1437C2×C31semidirect
457. C22⋊#95C2×C31semidirect
458. C22⋊#95C2×C31semidirect
496. C22×C31#386semidirect
533. C24×C4C22×C31semidirect
536. C2×#120C4×C31semidirect
540. C22×C4⋊C4C22×C31semidirect
551. C22×C22⋊C4C22×C31semidirect
552. C22×C22⋊C4C22×C31semidirect
553. C22×C42C22×C31semidirect
557. C2×#95C22×C31semidirect
558. C2×#95C22×C31semidirect
559. C2×#95C22×C31semidirect
560. C2×#95C22×C31semidirect
561. C2×#95C22×C31semidirect
586. C25C2×C4×C31semidirect
601. C22×D4C2×C4×C31semidirect
618. C23×C4D4×C31semidirect
659. C2×C22⋊C4C2×C4×C31semidirect
660. C2×C22⋊C4C2×C4×C31semidirect
661. C2×C22⋊C4D4×C31semidirect
662. C2×C22⋊C4D4×C31semidirect
671. C31#13967direct (N × H)
746. C2×D4C22⋊C4×C31semidirect
906. C23C2×C22⋊C4×C31semidirect
909. C23C4×D4×C31semidirect
976. C2×C4C2×C22⋊C4×C31semidirect
977. C2×C4C31×#120semidirect
1015. C22C31×#386semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1202
C22×C4×D4×C312
C23×C22⋊C4×C312
C2×C31×#3862
C2×C31×#3792
C31×#14392
C31×#14382
C31×#14372
C31×C22⋊#952
#1396731