Finite Group Databasebeta

← C31×#25585 #21482344

Subgroups — C31×#25585 #21482344

Order 7936.

1636 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3505C211yesmaximal, characteristic, complemented
2C31×#2435C211yesmaximal, characteristic, complemented
3C31×#2433C211yesmaximal, characteristic, complemented
4C31×#2408C211yesmaximal, characteristic, complemented
5C31×#2021C214yesmaximal, complemented
6C31×#1996C211yesmaximal, characteristic, complemented
7C31×#1964C211yesmaximal, characteristic, complemented
8C31×#1889C214yesmaximal, complemented
9C4×C31×#99C211yesmaximal, characteristic, complemented
10C23×D4×C31C2211yescharacteristic
11C31×#553—21no—
12C31×#553—22no—
13C31×#552—21no—
14C31×#551—22no—
15C31×#548—21no—
16C31×#546—21no—
17C31×#539—21no—
18C31×#538—21no—
19C31×#534C2212yes—
20C2×C31×#127—21no—
21C31×#529—21no—
22C2×C31×#124—21no—
23C31×#525—21no—
24C2×C31×C22⋊Q8C2211yescharacteristic
25C2×C31×#121—21no—
26C2×C31×#121C2211yescharacteristic
27C2×C31×#120C2214yes—
28C2×C31×#120C2212yes—
29C31×#518C2212yes—
30C2×C4×D4×C31C2211yescharacteristic
31C2×C31×#99C2212yes—
32C2×C31×#99C2214yes—
33C31×#394—21no—
34C31×#394—22no—
35C31×#392—21no—
36C31×#392—22no—
37C31×#390—21no—
38C31×#390—21no—
39C31×#390—21no—
40C31×#380C2211yescharacteristic
41C31×#379C2212yes—
42C31×#379C2214yes—
43C4×C22⋊C4×C31C2211yescharacteristic
44C4×C22⋊C4×C31C2211yescharacteristic
45C31×#342C2212yes—
46C31×#342C2214yes—
47C25×C31C2312yes—
48C2×#41×C31—21no—
49C22×Q8×C31D411yescharacteristic, complemented
50C22×D4×C31—22no—
51C22×D4×C31—24no—
52C22×D4×C31—21no—
53C22×D4×C31—21no—
54C22×D4×C31—21no—
55C22×D4×C31—21no—
56C22×D4×C31—21no—
57C22×D4×C31—21no—
58C22×D4×C31—44no—
59C22×D4×C31D411yescharacteristic, complemented
60C22×D4×C31C2311yescharacteristic
61C22×D4×C31C2312yes—
62C23×C4×C31D411yescharacteristic, complemented
63C23×C4×C31C2311yescharacteristic
64C31×#127—44no—
65C31×#126—22no—
66C31×#126—22no—
67C31×#126—22no—
68C31×#125—21no—
69C31×#125—22no—
70C31×#124—21no—
71C31×#124—22no—
72C31×#124—44no—
73C31×#123—22no—
74C31×#123—22no—
75C31×#123—22no—
76C31×#123—22no—
77C31×#123—22no—
78C31×C22⋊Q8—21no—
79C31×C22⋊Q8—22no—
80C31×C22⋊Q8—21no—
81C31×C22⋊Q8—21no—
82C31×C22⋊Q8—21no—
83C31×C22⋊Q8—21no—
84C31×#121—21no—
85C31×#121—22no—
86C31×#121—21no—
87C31×#121—21no—
88C31×#121—21no—
89C31×#121—21no—
90C31×#121—22no—
91C31×#121—22no—
92C31×#121—44no—
93C31×#120—22no—
94C31×#120—22no—
95C31×#120—28no—
96C31×#120—44no—
97C31×#120—44no—
98C4×Q8×C31—21no—
99C4×D4×C31—22no—
100C4×D4×C31—21no—
101C4×D4×C31—21no—
102C4×D4×C31—21no—
103C4×D4×C31—21no—
104C4×D4×C31—21no—
105C4×D4×C31—22no—
106C4×D4×C31—22no—
107C4×D4×C31—22no—
108C4×D4×C31—22no—
109C31×#117—21no—
110C31×#117—22no—
111C31×#117—22no—
112C2×C4⋊C4×C31—21no—
113C2×C4⋊C4×C31D411yescharacteristic, complemented
114C2×C4⋊C4×C31D411yescharacteristic, complemented
115C2×C4⋊C4×C31D411yescharacteristic, complemented
116C2×C4⋊C4×C31D412yescomplemented
117C2×C22⋊C4×C31—22no—
118C2×C22⋊C4×C31—24no—
119C2×C22⋊C4×C31—22no—
120C2×C22⋊C4×C31—22no—
121C2×C22⋊C4×C31—24no—
122C2×C22⋊C4×C31—22no—
123C2×C22⋊C4×C31—24no—
124C2×C22⋊C4×C31D411yescharacteristic, complemented
125C2×C22⋊C4×C31D412yescomplemented
126C2×C22⋊C4×C31C2312yes—
127C2×C22⋊C4×C31C2312yes—
128C2×C22⋊C4×C31C2311yescharacteristic
129C2×C22⋊C4×C31C2312yes—
130C2×C22⋊C4×C31C2312yes—
131C2×C42×C31—21no—
132C2×C42×C31—21no—
133C2×C42×C31D411yescharacteristic, complemented
134C31×#99—24no—
135C31×#99—44no—
136C31×#95—21no—
137C31×#95—21no—
138C31×#95—21no—
139C24×C31—22no—
140C24×C31—22no—
141C24×C31—22no—
142C24×C31—24no—
143C24×C31—24no—
144C24×C31—44no—
145C24×C31—82no—
146C24×C31C2×D412yes—
147C24×C31C2×D411yescharacteristic
148C24×C31C2411yescharacteristic
149#41×C31—82no—
150C2×Q8×C31—21no—
151C2×Q8×C31—21no—
152C2×Q8×C31—42no—
153C2×D4×C31—24no—
154C2×D4×C31—24no—
155C2×D4×C31—24no—
156C2×D4×C31—21no—
157C2×D4×C31—22no—
158C2×D4×C31—21no—
159C2×D4×C31—22no—
160C2×D4×C31—22no—
161C2×D4×C31—24no—
162C2×D4×C31—24no—
163C2×D4×C31—22no—
164C2×D4×C31—22no—
165C2×D4×C31—22no—
166C2×D4×C31—21no—
167C2×D4×C31—21no—
168C2×D4×C31—42no—
169C2×D4×C31—42no—
170C2×D4×C31—42no—
171C2×D4×C31—42no—
172C2×D4×C31—48no—
173C2×D4×C31—44no—
174C2×D4×C31—44no—
175C2×D4×C31—44no—
176C2×D4×C31—44no—
177C2×D4×C31—44no—
178C2×D4×C31—48no—
179C2×D4×C31—41no—
180C2×D4×C31—41no—
181C2×D4×C31—41no—
182C2×D4×C31—41no—
183C2×D4×C31—84no—
184C2×D4×C31—82no—
185C22×C4×C31—22no—
186C22×C4×C31—22no—
187C22×C4×C31—22no—
188C22×C4×C31—21no—
189C22×C4×C31—21no—
190C22×C4×C31—22no—
191C22×C4×C31—22no—
192C22×C4×C31—42no—
193C22×C4×C31—42no—
194C22×C4×C31C2×D411yescharacteristic
195C22×C4×C31C2×D412yes—
196C22×C4×C31C2×D411yescharacteristic
197C22×C4×C31C2×D411yescharacteristic
198C22×C4×C31C2×D411yescharacteristic
199C22×C4×C31C2×D411yescharacteristic
200C22×C4×C31C2×D412yes—
201C22×C4×C31C2×D411yescharacteristic
202C22×C4×C31C2×D412yes—
203C22×C4×C31C2×D411yescharacteristic
204C22×C4×C31C2×D411yescharacteristic
205C22×C4×C31C2×D411yescharacteristic
206C4⋊C4×C31—22no—
207C4⋊C4×C31—22no—
208C4⋊C4×C31—22no—
209C4⋊C4×C31—22no—
210C4⋊C4×C31—21no—
211C4⋊C4×C31—22no—
212C4⋊C4×C31—21no—
213C4⋊C4×C31—21no—
214C4⋊C4×C31—21no—
215C4⋊C4×C31—21no—
216C4⋊C4×C31—22no—
217C4⋊C4×C31—21no—
218C4⋊C4×C31—42no—
219C22⋊C4×C31—22no—
220C22⋊C4×C31—22no—
221C22⋊C4×C31—22no—
222C22⋊C4×C31—22no—
223C22⋊C4×C31—22no—
224C22⋊C4×C31—22no—
225C22⋊C4×C31—21no—
226C22⋊C4×C31—22no—
227C22⋊C4×C31—21no—
228C22⋊C4×C31—22no—
229C22⋊C4×C31—22no—
230C22⋊C4×C31—22no—
231C22⋊C4×C31—21no—
232C22⋊C4×C31—21no—
233C22⋊C4×C31—22no—
234C22⋊C4×C31—22no—
235C22⋊C4×C31—22no—
236C22⋊C4×C31—24no—
237C22⋊C4×C31—48no—
238C22⋊C4×C31—44no—
239C22⋊C4×C31—44no—
240C22⋊C4×C31—48no—
241C22⋊C4×C31—84no—
242C22⋊C4×C31—82no—
243C22⋊C4×C31#4114yescomplemented
244C42×C31—22no—
245C42×C31—22no—
246C42×C31—21no—
247C42×C31—21no—
248C42×C31—42no—
249C42×C31—42no—
250#25585C3111yesmaximal, characteristic, direct product factor, Sylow
251C23×C31—24no—
252C23×C31—24no—
253C23×C31—24no—
254C23×C31—21no—
255C23×C31—22no—
256C23×C31—21no—
257C23×C31—21no—
258C23×C31—24no—
259C23×C31—41no—
260C23×C31—41no—
261C23×C31—41no—
262C23×C31—41no—
263C23×C31—44no—
264C23×C31—42no—
265C23×C31—42no—
266C23×C31—42no—
267C23×C31—42no—
268C23×C31—42no—
269C23×C31—44no—
270C23×C31—42no—
271C23×C31—42no—
272C23×C31—42no—
273C23×C31—42no—
274C23×C31—42no—
275C23×C31—44no—
276C23×C31—44no—
277C23×C31—88no—
278C23×C31—88no—
279C23×C31C22×D411yescharacteristic
280C23×C31C22×D411yescharacteristic
281C23×C31C22×D411yescharacteristic
282C23×C31C2×#4112yes—
283C23×C31H(5,𝔽2)12yes—
284Q8×C31—42no—
285Q8×C31—81no—
286D4×C31—44no—
287D4×C31—44no—
288D4×C31—44no—
289D4×C31—42no—
290D4×C31—42no—
291D4×C31—42no—
292D4×C31—42no—
293D4×C31—44no—
294D4×C31—44no—
295D4×C31—42no—
296D4×C31—81no—
297D4×C31—82no—
298D4×C31—82no—
299D4×C31—816no—
300D4×C31—88no—
301C2×C4×C31—22no—
302C2×C4×C31—22no—
303C2×C4×C31—22no—
304C2×C4×C31—21no—
305C2×C4×C31—22no—
306C2×C4×C31—21no—
307C2×C4×C31—21no—
308C2×C4×C31—22no—
309C2×C4×C31—22no—
310C2×C4×C31—21no—
311C2×C4×C31—21no—
312C2×C4×C31—24no—
313C2×C4×C31—24no—
314C2×C4×C31—41no—
315C2×C4×C31—41no—
316C2×C4×C31—41no—
317C2×C4×C31—42no—
318C2×C4×C31—42no—
319C2×C4×C31—42no—
320C2×C4×C31—41no—
321C2×C4×C31—42no—
322C2×C4×C31—41no—
323C2×C4×C31—42no—
324C2×C4×C31—42no—
325C2×C4×C31—42no—
326C2×C4×C31—42no—
327C2×C4×C31—42no—
328C2×C4×C31—42no—
329C2×C4×C31—42no—
330C2×C4×C31—81no—
331C2×C4×C31—82no—
332C2×C4×C31—82no—
333C2×C4×C31#12011yescharacteristic
334C2×C4×C31#12011yescharacteristic
335C2×C4×C31#12011yescharacteristic
336C2×C4×C31#12011yescharacteristic
337#3505C2×C3111yescharacteristic, complemented
338#2435C2×C3111yescharacteristic, complemented
339#2433C2×C3111yescharacteristic, complemented
340#2408C2×C3111yescharacteristic, complemented
341#2021C2×C3114yescomplemented
342#1996C2×C3111yescharacteristic, complemented
343#1964C2×C3111yescharacteristic, complemented
344#1889C2×C3114yescomplemented
345C4×#99C2×C3111yescharacteristic, complemented
346C22×C31—21no—
347C22×C31—21no—
348C22×C31—21no—
349C22×C31—21no—
350C22×C31—21no—
351C22×C31—21no—
352C22×C31—42no—
353C22×C31—42no—
354C22×C31—42no—
355C22×C31—48no—
356C22×C31—44no—
357C22×C31—48no—
358C22×C31—44no—
359C22×C31—41no—
360C22×C31—42no—
361C22×C31—41no—
362C22×C31—42no—
363C22×C31—44no—
364C22×C31—42no—
365C22×C31—41no—
366C22×C31—84no—
367C22×C31—81no—
368C22×C31—84no—
369C22×C31—82no—
370C22×C31—84no—
371C22×C31—82no—
372C22×C31—82no—
373C22×C31—82no—
374C22×C31C2×#12011yescharacteristic
375C22×C31#53211yescharacteristic
376C22×C31#53511yescharacteristic
377C22×C31#54612yes—
378C22×C31#55012yes—
379C4×C31—21no—
380C4×C31—21no—
381C4×C31—21no—
382C4×C31—44no—
383C4×C31—41no—
384C4×C31—42no—
385C4×C31—41no—
386C4×C31—42no—
387C4×C31—41no—
388C4×C31—42no—
389C4×C31—82no—
390C4×C31—82no—
391C4×C31B(4,𝔽2)12yes—
392C23×D4C22×C3111yescharacteristic
393#553—21no—
394#553—22no—
395#552—21no—
396#551—22no—
397#548—21no—
398#546—21no—
399#539—21no—
400#538—21no—
401#534C22×C3112yes—
402C2×#127—21no—
403#529—21no—
404C2×#124—21no—
405#525—21no—
406C2×C22⋊Q8C22×C3111yescharacteristic
407C2×#121—21no—
408C2×#121C22×C3111yescharacteristic
409C2×#120C22×C3114yes—
410C2×#120C22×C3112yes—
411#518C22×C3112yes—
412C2×C4×D4C22×C3111yescharacteristic
413C2×#99C22×C3112yes—
414C2×#99C22×C3114yes—
415#394—21no—
416#394—22no—
417#392—21no—
418#392—22no—
419#390—21no—
420#390—21no—
421#390—21no—
422#380C22×C3111yescharacteristic
423#379C22×C3112yes—
424#379C22×C3114yes—
425C4×C22⋊C4C22×C3111yescharacteristic
426C4×C22⋊C4C22×C3111yescharacteristic
427#342C22×C3112yes—
428#342C22×C3114yes—
429C2×C31—22no—
430C2×C31—21no—
431C2×C31—22no—
432C2×C31—21no—
433C2×C31—84no—
434C2×C31—81no—
435C2×C31—82no—
436C2×C31#243111yescharacteristic
437C2×C31C2×B(4,𝔽2)11yescharacteristic
438C2×C31#302711yescharacteristic
439C25C23×C3112yes—
440C2×#41—21no—
441C22×Q8D4×C3111yescharacteristic, complemented
442C22×D4—22no—
443C22×D4—24no—
444C22×D4—21no—
445C22×D4—21no—
446C22×D4—21no—
447C22×D4—21no—
448C22×D4—21no—
449C22×D4—21no—
450C22×D4—44no—
451C22×D4D4×C3111yescharacteristic, complemented
452C22×D4C23×C3111yescharacteristic
453C22×D4C23×C3112yes—
454C23×C4D4×C3111yescharacteristic, complemented
455C23×C4C23×C3111yescharacteristic
456#127—44no—
457#126—22no—
458#126—22no—
459#126—22no—
460#125—21no—
461#125—22no—
462#124—21no—
463#124—22no—
464#124—44no—
465#123—22no—
466#123—22no—
467#123—22no—
468#123—22no—
469#123—22no—
470C22⋊Q8—21no—
471C22⋊Q8—22no—
472C22⋊Q8—21no—
473C22⋊Q8—21no—
474C22⋊Q8—21no—
475C22⋊Q8—21no—
476#121—21no—
477#121—22no—
478#121—21no—
479#121—21no—
480#121—21no—
481#121—21no—
482#121—22no—
483#121—22no—
484#121—44no—
485#120—22no—
486#120—22no—
487#120—28no—
488#120—44no—
489#120—44no—
490C4×Q8—21no—
491C4×D4—22no—
492C4×D4—21no—
493C4×D4—21no—
494C4×D4—21no—
495C4×D4—21no—
496C4×D4—21no—
497C4×D4—22no—
498C4×D4—22no—
499C4×D4—22no—
500C4×D4—22no—
501#117—21no—
502#117—22no—
503#117—22no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4D4×C3111yescharacteristic, complemented
506C2×C4⋊C4D4×C3111yescharacteristic, complemented
507C2×C4⋊C4D4×C3111yescharacteristic, complemented
508C2×C4⋊C4D4×C3112yescomplemented
509C2×C22⋊C4—22no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4D4×C3111yescharacteristic, complemented
517C2×C22⋊C4D4×C3112yescomplemented
518C2×C22⋊C4C23×C3112yes—
519C2×C22⋊C4C23×C3112yes—
520C2×C22⋊C4C23×C3111yescharacteristic
521C2×C22⋊C4C23×C3112yes—
522C2×C22⋊C4C23×C3112yes—
523C2×C42—21no—
524C2×C42—21no—
525C2×C42D4×C3111yescharacteristic, complemented
526#99—24no—
527#99—44no—
528#95—21no—
529#95—21no—
530#95—21no—
531C31#2558511yescharacteristic, direct product factor, Sylow
532C24—22no—
533C24—22no—
534C24—22no—
535C24—24no—
536C24—24no—
537C24—44no—
538C24—82no—
539C24C2×D4×C3112yes—
540C24C2×D4×C3111yescharacteristic
541C24C24×C3111yescharacteristic
542#41—82no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—42no—
546C2×D4—24no—
547C2×D4—24no—
548C2×D4—24no—
549C2×D4—21no—
550C2×D4—22no—
551C2×D4—21no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—24no—
555C2×D4—24no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—48no—
566C2×D4—44no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—44no—
571C2×D4—48no—
572C2×D4—41no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—84no—
577C2×D4—82no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4C2×D4×C3111yescharacteristic
588C22×C4C2×D4×C3112yes—
589C22×C4C2×D4×C3111yescharacteristic
590C22×C4C2×D4×C3111yescharacteristic
591C22×C4C2×D4×C3111yescharacteristic
592C22×C4C2×D4×C3111yescharacteristic
593C22×C4C2×D4×C3112yes—
594C22×C4C2×D4×C3111yescharacteristic
595C22×C4C2×D4×C3112yes—
596C22×C4C2×D4×C3111yescharacteristic
597C22×C4C2×D4×C3111yescharacteristic
598C22×C4C2×D4×C3111yescharacteristic
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—21no—
604C4⋊C4—22no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—22no—
610C4⋊C4—21no—
611C4⋊C4—42no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—21no—
619C22⋊C4—22no—
620C22⋊C4—21no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—24no—
630C22⋊C4—48no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C22⋊C4—48no—
634C22⋊C4—84no—
635C22⋊C4—82no—
636C22⋊C4#41×C3114yescomplemented
637C42—22no—
638C42—22no—
639C42—21no—
640C42—21no—
641C42—42no—
642C42—42no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—21no—
647C23—22no—
648C23—21no—
649C23—21no—
650C23—24no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—44no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—44no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—44no—
668C23—44no—
669C23—88no—
670C23—88no—
671C23C22×D4×C3111yescharacteristic
672C23C22×D4×C3111yescharacteristic
673C23C22×D4×C3111yescharacteristic
674C23C2×#41×C3112yes—
675C23C31×H(5,𝔽2)12yes—
676Q8—42no—
677Q8—81no—
678D4—44no—
679D4—44no—
680D4—44no—
681D4—42no—
682D4—42no—
683D4—42no—
684D4—42no—
685D4—44no—
686D4—44no—
687D4—42no—
688D4—81no—
689D4—82no—
690D4—82no—
691D4—816no—
692D4—88no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—81no—
723C2×C4—82no—
724C2×C4—82no—
725C2×C4C31×#12011yescharacteristic
726C2×C4C31×#12011yescharacteristic
727C2×C4C31×#12011yescharacteristic
728C2×C4C31×#12011yescharacteristic
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—48no—
739C22—44no—
740C22—48no—
741C22—44no—
742C22—41no—
743C22—42no—
744C22—41no—
745C22—42no—
746C22—44no—
747C22—42no—
748C22—41no—
749C22—84no—
750C22—81no—
751C22—84no—
752C22—82no—
753C22—84no—
754C22—82no—
755C22—82no—
756C22—82no—
757C22C2×C31×#12011yescharacteristic
758C22C31×#53211yescharacteristic
759C22C31×#53511yescharacteristic
760C22C31×#54612yes—
761C22C31×#55012yes—
762C4—21no—
763C4—21no—
764C4—21no—
765C4—44no—
766C4—41no—
767C4—42no—
768C4—41no—
769C4—42no—
770C4—41no—
771C4—42no—
772C4—82no—
773C4—82no—
774C4C31×B(4,𝔽2)12yes—
775C2—22no—
776C2—21no—
777C2—22no—
778C2—21no—
779C2—84no—
780C2—81no—
781C2—82no—
782C2C31×#243111yescharacteristic
783C2C2×C31×B(4,𝔽2)11yescharacteristic
784C2C31×#302711yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC24C24×C31
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3505C2semidirect
2. C31×#2435C2semidirect
3. C31×#2433C2semidirect
4. C31×#2408C2semidirect
5. C31×#2021C2semidirect
6. C31×#1996C2semidirect
7. C31×#1964C2semidirect
8. C31×#1889C2semidirect
9. C4×C31×#99C2semidirect
49. C22×Q8×C31D4semidirect
59. C22×D4×C31D4semidirect
62. C23×C4×C31D4semidirect
113. C2×C4⋊C4×C31D4semidirect
114. C2×C4⋊C4×C31D4semidirect
115. C2×C4⋊C4×C31D4semidirect
116. C2×C4⋊C4×C31D4semidirect
124. C2×C22⋊C4×C31D4semidirect
125. C2×C22⋊C4×C31D4semidirect
133. C2×C42×C31D4semidirect
243. C22⋊C4×C31#41semidirect
250. #25585C31direct (N × H)
337. #3505C2×C31semidirect
338. #2435C2×C31semidirect
339. #2433C2×C31semidirect
340. #2408C2×C31semidirect
341. #2021C2×C31semidirect
342. #1996C2×C31semidirect
343. #1964C2×C31semidirect
344. #1889C2×C31semidirect
345. C4×#99C2×C31semidirect
441. C22×Q8D4×C31semidirect
451. C22×D4D4×C31semidirect
454. C23×C4D4×C31semidirect
505. C2×C4⋊C4D4×C31semidirect
506. C2×C4⋊C4D4×C31semidirect
507. C2×C4⋊C4D4×C31semidirect
508. C2×C4⋊C4D4×C31semidirect
516. C2×C22⋊C4D4×C31semidirect
517. C2×C22⋊C4D4×C31semidirect
525. C2×C42D4×C31semidirect
531. C31#25585direct (N × H)
636. C22⋊C4#41×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#35052
C31×#24352
C31×#24332
C31×#24082
C31×#20212
C31×#19962
C31×#19642
C31×#18892
C4×C31×#992
#2558531