Finite Group Databasebeta

← C31×#15126 #21471885

Subgroups — C31×#15126 #21471885

Order 7936.

2506 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#121C211yesmaximal, characteristic
2C2×C31×#394C212yesmaximal, complemented
3C2×C31×#390C211yesmaximal, characteristic, complemented
4C2×C31×#390C211yesmaximal, characteristic, complemented
5C2×C31×#389C211yesmaximal, characteristic, complemented
6C2×C31×#380C211yesmaximal, characteristic, complemented
7C2×C4×C22⋊C4×C31C211yesmaximal, characteristic, complemented
8C31×#1440C212yesmaximal, complemented
9C31×#1439C212yesmaximal, complemented
10C31×#1438C212yesmaximal, complemented
11C31×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×D4×C31C2211yescharacteristic
13C23×D4×C31C2212yes—
14C24×C4×C31C2211yescharacteristic
15C2×C31×#121—24no—
16C2×C31×#121—24no—
17C2×C31×#121—24no—
18C22×C4⋊C4×C31C2211yescharacteristic
19C22×C4⋊C4×C31C2212yes—
20C22×C4⋊C4×C31C2211yescharacteristic
21C22×C4⋊C4×C31C2211yescharacteristic
22C22×C22⋊C4×C31C2212yes—
23C22×C22⋊C4×C31C2211yescharacteristic
24C22×C22⋊C4×C31C2212yes—
25C22×C22⋊C4×C31C2212yes—
26C22×C22⋊C4×C31C2212yes—
27C22×C22⋊C4×C31C2212yes—
28C22×C22⋊C4×C31C2212yes—
29C22×C22⋊C4×C31C2211yescharacteristic
30C22×C42×C31C2211yescharacteristic
31C22×C42×C31C2211yescharacteristic
32C31×#394—28no—
33C31×#390—24no—
34C31×#390—24no—
35C31×#389—24no—
36C31×#380—24no—
37C4×C22⋊C4×C31—24no—
38C2×C31×#95C2212yes—
39C2×C31×#95C2212yes—
40C2×C31×#95C2211yescharacteristic
41C2×C31×#95C2212yes—
42C2×C31×#95C2211yescharacteristic
43C2×C31×#95C2212yes—
44C25×C31C2312yes—
45C25×C31C2311yescharacteristic
46C22×D4×C31—24no—
47C22×D4×C31—24no—
48C22×D4×C31—24no—
49C22×D4×C31—24no—
50C22×D4×C31—24no—
51C22×D4×C31—22no—
52C22×D4×C31—22no—
53C22×D4×C31—22no—
54C22×D4×C31—22no—
55C22×D4×C31—22no—
56C22×D4×C31—22no—
57C22×D4×C31—42no—
58C22×D4×C31—42no—
59C22×D4×C31D414yes—
60C23×C4×C31—22no—
61C23×C4×C31—22no—
62C23×C4×C31—22no—
63C23×C4×C31—22no—
64C23×C4×C31—22no—
65C23×C4×C31—22no—
66C23×C4×C31D414yes—
67C23×C4×C31C2312yes—
68C23×C4×C31C2311yescharacteristic
69C23×C4×C31C2311yescharacteristic
70C23×C4×C31C2312yes—
71C23×C4×C31C2311yescharacteristic
72C23×C4×C31C2312yes—
73C23×C4×C31C2311yescharacteristic
74C23×C4×C31C2311yescharacteristic
75C23×C4×C31C2311yescharacteristic
76C31×#121—232no—
77C2×C4⋊C4×C31—22no—
78C2×C4⋊C4×C31—22no—
79C2×C4⋊C4×C31—22no—
80C2×C4⋊C4×C31—22no—
81C2×C4⋊C4×C31—22no—
82C2×C4⋊C4×C31—24no—
83C2×C4⋊C4×C31—22no—
84C2×C4⋊C4×C31—24no—
85C2×C4⋊C4×C31—22no—
86C2×C4⋊C4×C31—42no—
87C2×C4⋊C4×C31D414yes—
88C2×C4⋊C4×C31D414yescomplemented
89C2×C22⋊C4×C31—24no—
90C2×C22⋊C4×C31—22no—
91C2×C22⋊C4×C31—22no—
92C2×C22⋊C4×C31—22no—
93C2×C22⋊C4×C31—24no—
94C2×C22⋊C4×C31—24no—
95C2×C22⋊C4×C31—22no—
96C2×C22⋊C4×C31—22no—
97C2×C22⋊C4×C31—24no—
98C2×C22⋊C4×C31—24no—
99C2×C22⋊C4×C31—24no—
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—24no—
107C2×C22⋊C4×C31—42no—
108C2×C22⋊C4×C31—42no—
109C2×C22⋊C4×C31—42no—
110C2×C22⋊C4×C31—42no—
111C2×C22⋊C4×C31—42no—
112C2×C22⋊C4×C31D414yescomplemented
113C2×C42×C31—22no—
114C2×C42×C31—22no—
115C2×C42×C31—22no—
116C2×C42×C31—22no—
117C2×C42×C31—22no—
118C2×C42×C31—22no—
119C31×#95—22no—
120C31×#95—22no—
121C31×#95—24no—
122C31×#95—24no—
123C31×#95—24no—
124C31×#95—42no—
125C24×C31—21no—
126C24×C31—21no—
127C24×C31—21no—
128C24×C31—21no—
129C24×C31—21no—
130C24×C31—21no—
131C24×C31—21no—
132C24×C31—21no—
133C24×C31—21no—
134C24×C31—21no—
135C24×C31—21no—
136C24×C31—21no—
137C24×C31—22no—
138C24×C31—22no—
139C24×C31—22no—
140C24×C31—22no—
141C24×C31—22no—
142C24×C31—22no—
143C24×C31—22no—
144C24×C31—22no—
145C24×C31—22no—
146C24×C31—22no—
147C24×C31—22no—
148C24×C31—22no—
149C24×C31—22no—
150C24×C31—22no—
151C24×C31C2×D414yes—
152C24×C31C2×D412yes—
153C24×C31C2×D412yes—
154C24×C31#4112yes—
155C24×C31C2411yescharacteristic
156C2×D4×C31—216no—
157C2×D4×C31—28no—
158C2×D4×C31—28no—
159C2×D4×C31—28no—
160C2×D4×C31—48no—
161C2×D4×C31—48no—
162C2×D4×C31—48no—
163C2×D4×C31—48no—
164C2×D4×C31—48no—
165C2×D4×C31—48no—
166C2×D4×C31—44no—
167C2×D4×C31—44no—
168C2×D4×C31—44no—
169C2×D4×C31—44no—
170C22×C4×C31—21no—
171C22×C4×C31—21no—
172C22×C4×C31—21no—
173C22×C4×C31—21no—
174C22×C4×C31—21no—
175C22×C4×C31—21no—
176C22×C4×C31—22no—
177C22×C4×C31—22no—
178C22×C4×C31—21no—
179C22×C4×C31—21no—
180C22×C4×C31—21no—
181C22×C4×C31—21no—
182C22×C4×C31—21no—
183C22×C4×C31—22no—
184C22×C4×C31—21no—
185C22×C4×C31—21no—
186C22×C4×C31—22no—
187C22×C4×C31—22no—
188C22×C4×C31—21no—
189C22×C4×C31—21no—
190C22×C4×C31—21no—
191C22×C4×C31—21no—
192C22×C4×C31—21no—
193C22×C4×C31—21no—
194C22×C4×C31—22no—
195C22×C4×C31—22no—
196C22×C4×C31—21no—
197C22×C4×C31—21no—
198C22×C4×C31—21no—
199C22×C4×C31—22no—
200C22×C4×C31—21no—
201C22×C4×C31—22no—
202C22×C4×C31—21no—
203C22×C4×C31—21no—
204C22×C4×C31—22no—
205C22×C4×C31—21no—
206C22×C4×C31—21no—
207C22×C4×C31—22no—
208C22×C4×C31—21no—
209C22×C4×C31—22no—
210C22×C4×C31—21no—
211C22×C4×C31—21no—
212C22×C4×C31—28no—
213C22×C4×C31—28no—
214C22×C4×C31—28no—
215C22×C4×C31—22no—
216C22×C4×C31—22no—
217C22×C4×C31—22no—
218C22×C4×C31—22no—
219C22×C4×C31—22no—
220C22×C4×C31—22no—
221C22×C4×C31—22no—
222C22×C4×C31—44no—
223C22×C4×C31—44no—
224C22×C4×C31—44no—
225C22×C4×C31—44no—
226C22×C4×C31C2×D412yes—
227C22×C4×C31C2×D412yes—
228C22×C4×C31C2×D414yes—
229C22×C4×C31C2×D414yes—
230C22×C4×C31C2×D412yes—
231C22×C4×C31C2×D412yes—
232C22×C4×C31C2×D412yes—
233C22×C4×C31C2×D412yes—
234C22×C4×C31C2×D412yes—
235C22×C4×C31#4112yes—
236C22×C4×C31#4112yes—
237C22×C4×C31#4112yes—
238C22×C4×C31#4112yes—
239C22×C4×C31#4112yes—
240C4⋊C4×C31—28no—
241C4⋊C4×C31—28no—
242C4⋊C4×C31—48no—
243C4⋊C4×C31—44no—
244C22⋊C4×C31—28no—
245C22⋊C4×C31—216no—
246C22⋊C4×C31—28no—
247C22⋊C4×C31—48no—
248C22⋊C4×C31—48no—
249C22⋊C4×C31—48no—
250C22⋊C4×C31—48no—
251C22⋊C4×C31—48no—
252C42×C31—44no—
253C42×C31—44no—
254#15126C3111yesmaximal, characteristic, direct product factor, Sylow
255C23×C31—22no—
256C23×C31—22no—
257C23×C31—22no—
258C23×C31—22no—
259C23×C31—22no—
260C23×C31—22no—
261C23×C31—22no—
262C23×C31—22no—
263C23×C31—22no—
264C23×C31—22no—
265C23×C31—22no—
266C23×C31—22no—
267C23×C31—22no—
268C23×C31—22no—
269C23×C31—22no—
270C23×C31—22no—
271C23×C31—22no—
272C23×C31—22no—
273C23×C31—24no—
274C23×C31—24no—
275C23×C31—24no—
276C23×C31—24no—
277C23×C31—24no—
278C23×C31—24no—
279C23×C31—24no—
280C23×C31—41no—
281C23×C31—41no—
282C23×C31—41no—
283C23×C31—41no—
284C23×C31—41no—
285C23×C31—41no—
286C23×C31—41no—
287C23×C31—41no—
288C23×C31—41no—
289C23×C31—41no—
290C23×C31—41no—
291C23×C31—41no—
292C23×C31—41no—
293C23×C31—41no—
294C23×C31—41no—
295C23×C31—41no—
296C23×C31—42no—
297C23×C31—42no—
298C23×C31—42no—
299C23×C31—42no—
300C23×C31—42no—
301C23×C31—42no—
302C23×C31—42no—
303C23×C31—42no—
304C23×C31—42no—
305C23×C31—42no—
306C23×C31—42no—
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—42no—
320C23×C31—42no—
321C23×C31—42no—
322C23×C31—42no—
323C23×C31—42no—
324C23×C31#12114yes—
325C23×C31C22×D411yescharacteristic
326C23×C31C22×D411yescharacteristic
327C23×C31C22×D411yescharacteristic
328C23×C31C22×D411yescharacteristic
329C23×C31C22×D411yescharacteristic
330C23×C31C2×#4111yescharacteristic
331C23×C31C2×#4111yescharacteristic
332C23×C31C2×#4111yescharacteristic
333C23×C31C2×#4111yescharacteristic
334C23×C31C2×#4111yescharacteristic
335C23×C31C2×#4111yescharacteristic
336C23×C31H(5,𝔽2)11yescharacteristic
337C23×C31H(5,𝔽2)11yescharacteristic
338C23×C31H(5,𝔽2)11yescharacteristic
339C23×C312−1+411yescharacteristic
340D4×C31—432no—
341D4×C31—416no—
342C2×C4×C31—22no—
343C2×C4×C31—24no—
344C2×C4×C31—22no—
345C2×C4×C31—22no—
346C2×C4×C31—24no—
347C2×C4×C31—22no—
348C2×C4×C31—22no—
349C2×C4×C31—22no—
350C2×C4×C31—22no—
351C2×C4×C31—22no—
352C2×C4×C31—22no—
353C2×C4×C31—24no—
354C2×C4×C31—22no—
355C2×C4×C31—24no—
356C2×C4×C31—22no—
357C2×C4×C31—22no—
358C2×C4×C31—24no—
359C2×C4×C31—24no—
360C2×C4×C31—22no—
361C2×C4×C31—22no—
362C2×C4×C31—22no—
363C2×C4×C31—41no—
364C2×C4×C31—41no—
365C2×C4×C31—41no—
366C2×C4×C31—41no—
367C2×C4×C31—41no—
368C2×C4×C31—41no—
369C2×C4×C31—42no—
370C2×C4×C31—41no—
371C2×C4×C31—41no—
372C2×C4×C31—42no—
373C2×C4×C31—41no—
374C2×C4×C31—41no—
375C2×C4×C31—42no—
376C2×C4×C31—41no—
377C2×C4×C31—41no—
378C2×C4×C31—42no—
379C2×C4×C31—42no—
380C2×C4×C31—42no—
381C2×C4×C31—41no—
382C2×C4×C31—41no—
383C2×C4×C31—42no—
384C2×C4×C31—41no—
385C2×C4×C31—41no—
386C2×C4×C31—41no—
387C2×C4×C31—41no—
388C2×C4×C31—42no—
389C2×C4×C31—41no—
390C2×C4×C31—41no—
391C2×C4×C31—416no—
392C2×C4×C31—42no—
393C2×C4×C31—42no—
394C2×C4×C31—42no—
395C2×C4×C31—42no—
396C2×C4×C31—42no—
397C2×C4×C31—42no—
398C2×C4×C31—42no—
399C2×C4×C31#12014yes—
400C2×C4×C31#12114yes—
401C2×C4×C31#12114yes—
402C2×C4×C31#12114yes—
403C2×C4×C31#12314yes—
404C2×C4×C31#12314yes—
405C2×C4×C31#12414yes—
406C22×#121C2×C3111yescharacteristic
407C2×#394C2×C3112yescomplemented
408C2×#390C2×C3111yescharacteristic, complemented
409C2×#390C2×C3111yescharacteristic, complemented
410C2×#389C2×C3111yescharacteristic, complemented
411C2×#380C2×C3111yescharacteristic, complemented
412C2×C4×C22⋊C4C2×C3111yescharacteristic, complemented
413#1440C2×C3112yescomplemented
414#1439C2×C3112yescomplemented
415#1438C2×C3112yescomplemented
416C4⋊#95C2×C3111yescharacteristic, complemented
417C22×C31—24no—
418C22×C31—24no—
419C22×C31—24no—
420C22×C31—42no—
421C22×C31—42no—
422C22×C31—42no—
423C22×C31—42no—
424C22×C31—42no—
425C22×C31—42no—
426C22×C31—42no—
427C22×C31—42no—
428C22×C31—42no—
429C22×C31—42no—
430C22×C31—42no—
431C22×C31—42no—
432C22×C31—44no—
433C22×C31—44no—
434C22×C31—44no—
435C22×C31—44no—
436C22×C31—44no—
437C22×C31—44no—
438C22×C31—44no—
439C22×C31—82no—
440C22×C31—82no—
441C22×C31—82no—
442C22×C31—82no—
443C22×C31—82no—
444C22×C31—82no—
445C22×C31—82no—
446C22×C31—82no—
447C22×C31C2×#12011yescharacteristic
448C22×C31C2×#12111yescharacteristic
449C22×C31C2×#12111yescharacteristic
450C22×C31C2×#12111yescharacteristic
451C22×C31C2×#12111yescharacteristic
452C22×C31C2×#12311yescharacteristic
453C22×C31C2×#12311yescharacteristic
454C22×C31#52511yescharacteristic
455C22×C31C2×#12411yescharacteristic
456C22×C31#52911yescharacteristic
457C22×C31#52911yescharacteristic
458C22×C31#53211yescharacteristic
459C22×C31#53211yescharacteristic
460C22×C31#53511yescharacteristic
461C22×C31#53711yescharacteristic
462C22×C31#54011yescharacteristic
463C22×C31#54011yescharacteristic
464C22×C31#54211yescharacteristic
465C22×C31#54211yescharacteristic
466C22×C31D4211yescharacteristic
467C22×C31D4211yescharacteristic
468C22×C31D4211yescharacteristic
469C22×C31#54611yescharacteristic
470C22×C31#54611yescharacteristic
471C22×C31#54611yescharacteristic
472C22×C31#54611yescharacteristic
473C22×C31#54711yescharacteristic
474C22×C31#54711yescharacteristic
475C22×C31#54811yescharacteristic
476C22×C31#54811yescharacteristic
477C22×C31#55011yescharacteristic
478C22×C31#55011yescharacteristic
479C22×C31#55311yescharacteristic
480C22×C31#55311yescharacteristic
481C22×C31#55511yescharacteristic
482C4×C31—42no—
483C4×C31—42no—
484C4×C31—42no—
485C4×C31—44no—
486C4×C31—42no—
487C4×C31—42no—
488C4×C31—44no—
489C4×C31—82no—
490C4×C31#39418yescomplemented
491C23×D4C22×C3111yescharacteristic
492C23×D4C22×C3112yes—
493C24×C4C22×C3111yescharacteristic
494C2×#121—24no—
495C2×#121—24no—
496C2×#121—24no—
497C22×C4⋊C4C22×C3111yescharacteristic
498C22×C4⋊C4C22×C3112yes—
499C22×C4⋊C4C22×C3111yescharacteristic
500C22×C4⋊C4C22×C3111yescharacteristic
501C22×C22⋊C4C22×C3112yes—
502C22×C22⋊C4C22×C3111yescharacteristic
503C22×C22⋊C4C22×C3112yes—
504C22×C22⋊C4C22×C3112yes—
505C22×C22⋊C4C22×C3112yes—
506C22×C22⋊C4C22×C3112yes—
507C22×C22⋊C4C22×C3112yes—
508C22×C22⋊C4C22×C3111yescharacteristic
509C22×C42C22×C3111yescharacteristic
510C22×C42C22×C3111yescharacteristic
511#394—28no—
512#390—24no—
513#390—24no—
514#389—24no—
515#380—24no—
516C4×C22⋊C4—24no—
517C2×#95C22×C3112yes—
518C2×#95C22×C3112yes—
519C2×#95C22×C3111yescharacteristic
520C2×#95C22×C3112yes—
521C2×#95C22×C3111yescharacteristic
522C2×#95C22×C3112yes—
523C2×C31—44no—
524C2×C31—84no—
525C2×C31C2×#39411yescharacteristic
526C2×C31#240711yescharacteristic
527C2×C31#240811yescharacteristic
528C2×C31#241411yescharacteristic
529C2×C31#241611yescharacteristic
530C2×C31#242011yescharacteristic
531C2×C31#242211yescharacteristic
532C2×C31#242611yescharacteristic
533C2×C31#242711yescharacteristic
534C2×C31#242811yescharacteristic
535C2×C31#242811yescharacteristic
536C2×C31#249011yescharacteristic
537C2×C31#249111yescharacteristic
538C2×C31#262411yescharacteristic
539C2×C31#285411yescharacteristic
540C25C23×C3112yes—
541C25C23×C3111yescharacteristic
542C22×D4—24no—
543C22×D4—24no—
544C22×D4—24no—
545C22×D4—24no—
546C22×D4—24no—
547C22×D4—22no—
548C22×D4—22no—
549C22×D4—22no—
550C22×D4—22no—
551C22×D4—22no—
552C22×D4—22no—
553C22×D4—42no—
554C22×D4—42no—
555C22×D4D4×C3114yes—
556C23×C4—22no—
557C23×C4—22no—
558C23×C4—22no—
559C23×C4—22no—
560C23×C4—22no—
561C23×C4—22no—
562C23×C4D4×C3114yes—
563C23×C4C23×C3112yes—
564C23×C4C23×C3112yes—
565C23×C4C23×C3111yescharacteristic
566C23×C4C23×C3111yescharacteristic
567C23×C4C23×C3111yescharacteristic
568C23×C4C23×C3112yes—
569C23×C4C23×C3111yescharacteristic
570C23×C4C23×C3111yescharacteristic
571C23×C4C23×C3111yescharacteristic
572#121—232no—
573C2×C4⋊C4—22no—
574C2×C4⋊C4—22no—
575C2×C4⋊C4—22no—
576C2×C4⋊C4—22no—
577C2×C4⋊C4—22no—
578C2×C4⋊C4—24no—
579C2×C4⋊C4—22no—
580C2×C4⋊C4—24no—
581C2×C4⋊C4—22no—
582C2×C4⋊C4—42no—
583C2×C4⋊C4D4×C3114yes—
584C2×C4⋊C4D4×C3114yescomplemented
585C2×C22⋊C4—24no—
586C2×C22⋊C4—22no—
587C2×C22⋊C4—22no—
588C2×C22⋊C4—22no—
589C2×C22⋊C4—24no—
590C2×C22⋊C4—24no—
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—24no—
594C2×C22⋊C4—24no—
595C2×C22⋊C4—24no—
596C2×C22⋊C4—24no—
597C2×C22⋊C4—24no—
598C2×C22⋊C4—24no—
599C2×C22⋊C4—24no—
600C2×C22⋊C4—24no—
601C2×C22⋊C4—24no—
602C2×C22⋊C4—24no—
603C2×C22⋊C4—42no—
604C2×C22⋊C4—42no—
605C2×C22⋊C4—42no—
606C2×C22⋊C4—42no—
607C2×C22⋊C4—42no—
608C2×C22⋊C4D4×C3114yescomplemented
609C2×C42—22no—
610C2×C42—22no—
611C2×C42—22no—
612C2×C42—22no—
613C2×C42—22no—
614C2×C42—22no—
615#95—22no—
616#95—22no—
617#95—24no—
618#95—24no—
619#95—24no—
620#95—42no—
621C31#1512611yescharacteristic, direct product factor, Sylow
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—22no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24C2×D4×C3114yes—
649C24C2×D4×C3112yes—
650C24C2×D4×C3112yes—
651C24#41×C3112yes—
652C24C24×C3111yescharacteristic
653C2×D4—216no—
654C2×D4—28no—
655C2×D4—28no—
656C2×D4—28no—
657C2×D4—48no—
658C2×D4—48no—
659C2×D4—48no—
660C2×D4—48no—
661C2×D4—48no—
662C2×D4—48no—
663C2×D4—44no—
664C2×D4—44no—
665C2×D4—44no—
666C2×D4—44no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—22no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—22no—
697C22×C4—21no—
698C22×C4—22no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—22no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—22no—
705C22×C4—21no—
706C22×C4—22no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—28no—
710C22×C4—28no—
711C22×C4—28no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—44no—
720C22×C4—44no—
721C22×C4—44no—
722C22×C4—44no—
723C22×C4C2×D4×C3112yes—
724C22×C4C2×D4×C3112yes—
725C22×C4C2×D4×C3114yes—
726C22×C4C2×D4×C3114yes—
727C22×C4C2×D4×C3112yes—
728C22×C4C2×D4×C3112yes—
729C22×C4C2×D4×C3112yes—
730C22×C4C2×D4×C3112yes—
731C22×C4C2×D4×C3112yes—
732C22×C4#41×C3112yes—
733C22×C4#41×C3112yes—
734C22×C4#41×C3112yes—
735C22×C4#41×C3112yes—
736C22×C4#41×C3112yes—
737C4⋊C4—28no—
738C4⋊C4—28no—
739C4⋊C4—48no—
740C4⋊C4—44no—
741C22⋊C4—28no—
742C22⋊C4—216no—
743C22⋊C4—28no—
744C22⋊C4—48no—
745C22⋊C4—48no—
746C22⋊C4—48no—
747C22⋊C4—48no—
748C22⋊C4—48no—
749C42—44no—
750C42—44no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—24no—
770C23—24no—
771C23—24no—
772C23—24no—
773C23—24no—
774C23—24no—
775C23—24no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—42no—
801C23—42no—
802C23—42no—
803C23—42no—
804C23—42no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—42no—
816C23—42no—
817C23—42no—
818C23—42no—
819C23—42no—
820C23C31×#12114yes—
821C23C22×D4×C3111yescharacteristic
822C23C22×D4×C3111yescharacteristic
823C23C22×D4×C3111yescharacteristic
824C23C22×D4×C3111yescharacteristic
825C23C22×D4×C3111yescharacteristic
826C23C2×#41×C3111yescharacteristic
827C23C2×#41×C3111yescharacteristic
828C23C2×#41×C3111yescharacteristic
829C23C2×#41×C3111yescharacteristic
830C23C2×#41×C3111yescharacteristic
831C23C2×#41×C3111yescharacteristic
832C23C31×H(5,𝔽2)11yescharacteristic
833C23C31×H(5,𝔽2)11yescharacteristic
834C23C31×H(5,𝔽2)11yescharacteristic
835C23C31×2−1+411yescharacteristic
836D4—432no—
837D4—416no—
838C2×C4—22no—
839C2×C4—24no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—24no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—24no—
850C2×C4—22no—
851C2×C4—24no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—24no—
855C2×C4—24no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—42no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—42no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—42no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—42no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—42no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—416no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4C31×#12014yes—
896C2×C4C31×#12114yes—
897C2×C4C31×#12114yes—
898C2×C4C31×#12114yes—
899C2×C4C31×#12314yes—
900C2×C4C31×#12314yes—
901C2×C4C31×#12414yes—
902C22—24no—
903C22—24no—
904C22—24no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—44no—
918C22—44no—
919C22—44no—
920C22—44no—
921C22—44no—
922C22—44no—
923C22—44no—
924C22—82no—
925C22—82no—
926C22—82no—
927C22—82no—
928C22—82no—
929C22—82no—
930C22—82no—
931C22—82no—
932C22C2×C31×#12011yescharacteristic
933C22C2×C31×#12111yescharacteristic
934C22C2×C31×#12111yescharacteristic
935C22C2×C31×#12111yescharacteristic
936C22C2×C31×#12111yescharacteristic
937C22C2×C31×#12311yescharacteristic
938C22C2×C31×#12311yescharacteristic
939C22C31×#52511yescharacteristic
940C22C2×C31×#12411yescharacteristic
941C22C31×#52911yescharacteristic
942C22C31×#52911yescharacteristic
943C22C31×#53211yescharacteristic
944C22C31×#53211yescharacteristic
945C22C31×#53511yescharacteristic
946C22C31×#53711yescharacteristic
947C22C31×#54011yescharacteristic
948C22C31×#54011yescharacteristic
949C22C31×#54211yescharacteristic
950C22C31×#54211yescharacteristic
951C22D42×C3111yescharacteristic
952C22D42×C3111yescharacteristic
953C22D42×C3111yescharacteristic
954C22C31×#54611yescharacteristic
955C22C31×#54611yescharacteristic
956C22C31×#54611yescharacteristic
957C22C31×#54611yescharacteristic
958C22C31×#54711yescharacteristic
959C22C31×#54711yescharacteristic
960C22C31×#54811yescharacteristic
961C22C31×#54811yescharacteristic
962C22C31×#55011yescharacteristic
963C22C31×#55011yescharacteristic
964C22C31×#55311yescharacteristic
965C22C31×#55311yescharacteristic
966C22C31×#55511yescharacteristic
967C4—42no—
968C4—42no—
969C4—44no—
970C4—42no—
971C4—42no—
972C4—42no—
973C4—44no—
974C4—82no—
975C4C31×#39418yescomplemented
976C2—44no—
977C2—84no—
978C2C2×C31×#39411yescharacteristic
979C2C31×#240711yescharacteristic
980C2C31×#240811yescharacteristic
981C2C31×#241411yescharacteristic
982C2C31×#241611yescharacteristic
983C2C31×#242011yescharacteristic
984C2C31×#242211yescharacteristic
985C2C31×#242611yescharacteristic
986C2C31×#242711yescharacteristic
987C2C31×#242811yescharacteristic
988C2C31×#242811yescharacteristic
989C2C31×#249011yescharacteristic
990C2C31×#249111yescharacteristic
991C2C31×#262411yescharacteristic
992C2C31×#285411yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
prime radicalC22×C31×#121C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#394C2semidirect
3. C2×C31×#390C2semidirect
4. C2×C31×#390C2semidirect
5. C2×C31×#389C2semidirect
6. C2×C31×#380C2semidirect
7. C2×C4×C22⋊C4×C31C2semidirect
8. C31×#1440C2semidirect
9. C31×#1439C2semidirect
10. C31×#1438C2semidirect
11. C31×C4⋊#95C2semidirect
88. C2×C4⋊C4×C31D4semidirect
112. C2×C22⋊C4×C31D4semidirect
254. #15126C31direct (N × H)
407. C2×#394C2×C31semidirect
408. C2×#390C2×C31semidirect
409. C2×#390C2×C31semidirect
410. C2×#389C2×C31semidirect
411. C2×#380C2×C31semidirect
412. C2×C4×C22⋊C4C2×C31semidirect
413. #1440C2×C31semidirect
414. #1439C2×C31semidirect
415. #1438C2×C31semidirect
416. C4⋊#95C2×C31semidirect
490. C4×C31#394semidirect
584. C2×C4⋊C4D4×C31semidirect
608. C2×C22⋊C4D4×C31semidirect
621. C31#15126direct (N × H)
975. C4C31×#394semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1212
C2×C31×#3942
C2×C31×#3902
C2×C31×#3892
C2×C31×#3802
C2×C4×C22⋊C4×C312
C31×#14402
C31×#14392
C31×#14382
C31×C4⋊#952
#1512631