Finite Group Databasebeta

← C31×#24034 #21480793

Subgroups — C31×#24034 #21480793

Order 7936.

1380 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#550C211yesmaximal, characteristic
2C2×C31×#482C211yesmaximal, characteristic, complemented
3C2×C31×#416C211yesmaximal, characteristic, complemented
4C31×#2485C211yesmaximal, characteristic, complemented
5C31×#2041C211yesmaximal, characteristic, complemented
6C31×#2041C211yesmaximal, characteristic, complemented
7C31×#2034C211yesmaximal, characteristic, complemented
8C31×#2033C211yesmaximal, characteristic, complemented
9C31×#1893C211yesmaximal, characteristic, complemented
10C31×#1869C211yesmaximal, characteristic, complemented
11C31×#1865C211yesmaximal, characteristic, complemented
12C31×#1863C211yesmaximal, characteristic, complemented
13C31×#1788C211yesmaximal, characteristic, complemented
14C31×#1788C211yesmaximal, characteristic, complemented
15C31×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C22×#41×C31C2211yescharacteristic
18C23×C8×C31C2211yescharacteristic
19C31×#550—24no—
20C31×#550—24no—
21C2×C31×#127—21no—
22C2×C31×#127C2211yescharacteristic
23C2×C31×#121—21no—
24C2×C31×#121—21no—
25C2×C31×#121C2211yescharacteristic
26C2×C31×#121C2211yescharacteristic
27C2×C4×Q8×C31C2211yescharacteristic
28C2×C4×D4×C31—21no—
29C2×C4×D4×C31C2211yescharacteristic
30C2×C31×#117C2211yescharacteristic
31C31×#482—24no—
32C2×C31×#107C2211yescharacteristic
33C2×C31×#106C2211yescharacteristic
34C31×#416—24no—
35C2×C31×#103C2211yescharacteristic
36C2×C31×#103C2211yescharacteristic
37C2×C31×#103C2211yescharacteristic
38C2×C31×#103C2211yescharacteristic
39C2×C31×#102C2211yescharacteristic
40C2×C31×#102C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×#102C2211yescharacteristic
46C2×C31×#102C2211yescharacteristic
47C2×C31×C22⋊C8C2211yescharacteristic
48C2×C31×C22⋊C8C2211yescharacteristic
49C2×C31×C22⋊C8C2211yescharacteristic
50C31×#397—21no—
51C31×#394—21no—
52C31×#389C2211yescharacteristic
53C31×#389C2211yescharacteristic
54C31×#388—21no—
55C31×#387—21no—
56C31×#380C2211yescharacteristic
57C31×#380C2211yescharacteristic
58C31×#380C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C31×#336C2211yescharacteristic
63C2×#41×C31—22no—
64C2×#41×C31—22no—
65C2×#41×C31—22no—
66C2×#41×C31—22no—
67C2×#41×C31—22no—
68C2×#41×C31—22no—
69C2×#41×C31—22no—
70C2×#41×C31—41no—
71C2×#41×C31—41no—
72C2×#41×C31—41no—
73C2×#41×C31—41no—
74C2×#41×C31D414yes—
75C22×Q8×C31C2311yescharacteristic
76C22×D4×C31—21no—
77C22×D4×C31—21no—
78C22×D4×C31—21no—
79C22×D4×C31—21no—
80C22×D4×C31—21no—
81C22×D4×C31—21no—
82C22×D4×C31D411yescharacteristic
83C22×D4×C31C2311yescharacteristic
84C22×D4×C31C2311yescharacteristic
85C23×C4×C31—21no—
86C23×C4×C31—21no—
87C23×C4×C31C2311yescharacteristic
88C23×C4×C31C2311yescharacteristic
89C22×C8×C31—22no—
90C22×C8×C31—41no—
91C22×C8×C31—41no—
92C22×C8×C31C2311yescharacteristic
93C22×C8×C31C2311yescharacteristic
94C22×C8×C31C2311yescharacteristic
95C22×C8×C31C2311yescharacteristic
96C31×#127—28no—
97C31×#127—22no—
98C31×#127—22no—
99C31×#121—28no—
100C31×#121—28no—
101C31×#121—22no—
102C31×#121—22no—
103C31×#121—22no—
104C31×#121D414yes—
105C4×Q8×C31—22no—
106C4×Q8×C31—22no—
107C4×D4×C31—28no—
108C4×D4×C31—22no—
109C4×D4×C31—22no—
110C31×#117—22no—
111C31×#117—22no—
112C2×C4⋊C4×C31—21no—
113C2×C4⋊C4×C31—21no—
114C2×C4⋊C4×C31—21no—
115C2×C4⋊C4×C31D411yescharacteristic
116C2×C4⋊C4×C31C2311yescharacteristic
117C2×C4⋊C4×C31C2311yescharacteristic
118C2×C4⋊C4×C31C2311yescharacteristic
119C2×C4⋊C4×C31C2311yescharacteristic
120C2×C4⋊C4×C31C2311yescharacteristic
121C2×C22⋊C4×C31—21no—
122C2×C22⋊C4×C31—21no—
123C2×C22⋊C4×C31—21no—
124C2×C22⋊C4×C31—21no—
125C2×C22⋊C4×C31—21no—
126C2×C22⋊C4×C31—21no—
127C2×C22⋊C4×C31D411yescharacteristic
128C2×C22⋊C4×C31D411yescharacteristic
129C2×C42×C31—21no—
130C2×C42×C31—21no—
131C2×C42×C31C2311yescharacteristic
132C31×#107—22no—
133C31×#106—22no—
134C31×#103—22no—
135C31×#103—22no—
136C31×#103—22no—
137C31×#103—22no—
138C31×#102—22no—
139C31×#102—22no—
140C31×#102—22no—
141C31×#102—22no—
142C31×#102—41no—
143C31×#102—41no—
144C31×#102—41no—
145C31×#102—41no—
146C31×C22⋊C8—22no—
147C31×C22⋊C8—41no—
148C31×C22⋊C8—41no—
149C31×#95—21no—
150C31×#95—21no—
151C31×#95—21no—
152C31×#95—21no—
153C31×#95—21no—
154C24×C31—21no—
155C24×C31—21no—
156C24×C31C2×D411yescharacteristic
157C24×C31C2×D411yescharacteristic
158#41×C31—28no—
159#41×C31—44no—
160#41×C31—44no—
161#41×C31—44no—
162#41×C31—44no—
163#41×C31—44no—
164#41×C31—44no—
165#41×C31—44no—
166C2×Q8×C31—21no—
167C2×Q8×C31—21no—
168C2×Q8×C31—21no—
169C2×Q8×C31C2×D412yes—
170C2×Q8×C31#4112yes—
171C2×Q8×C31#4112yes—
172C2×D4×C31—24no—
173C2×D4×C31—24no—
174C2×D4×C31—22no—
175C2×D4×C31—24no—
176C2×D4×C31—24no—
177C2×D4×C31—24no—
178C2×D4×C31—24no—
179C2×D4×C31—22no—
180C2×D4×C31—21no—
181C2×D4×C31—21no—
182C2×D4×C31—21no—
183C2×D4×C31—21no—
184C2×D4×C31—21no—
185C2×D4×C31—21no—
186C2×D4×C31—21no—
187C2×D4×C31—21no—
188C2×D4×C31—21no—
189C2×D4×C31—21no—
190C2×D4×C31—41no—
191C2×D4×C31—42no—
192C2×D4×C31—42no—
193C2×D4×C31—42no—
194C2×D4×C31—42no—
195C2×D4×C31—42no—
196C2×D4×C31—42no—
197C2×D4×C31—81no—
198C2×D4×C31—81no—
199C2×D4×C31—81no—
200C2×D4×C31—81no—
201C2×D4×C31—81no—
202C2×D4×C31—81no—
203C2×D4×C31C2×D412yes—
204C2×D4×C31C2×D412yes—
205C22×C4×C31—21no—
206C22×C4×C31—21no—
207C22×C4×C31—21no—
208C22×C4×C31—21no—
209C22×C4×C31—21no—
210C22×C4×C31—24no—
211C22×C4×C31—21no—
212C22×C4×C31—24no—
213C22×C4×C31—21no—
214C22×C4×C31—21no—
215C22×C4×C31—21no—
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—21no—
223C22×C4×C31—42no—
224C22×C4×C31—42no—
225C22×C4×C31—42no—
226C22×C4×C31—42no—
227C22×C4×C31C2×D411yescharacteristic
228C22×C4×C31C2×D411yescharacteristic
229C22×C4×C31C2×D411yescharacteristic
230C22×C4×C31C2×D412yes—
231C22×C4×C31C2×D412yes—
232C22×C4×C31C2×D411yescharacteristic
233C22×C4×C31C2411yescharacteristic
234C2×C8×C31—21no—
235C2×C8×C31—21no—
236C2×C8×C31—21no—
237C2×C8×C31—21no—
238C2×C8×C31—21no—
239C2×C8×C31—21no—
240C2×C8×C31—21no—
241C2×C8×C31—21no—
242C2×C8×C31—21no—
243C2×C8×C31—21no—
244C2×C8×C31—21no—
245C2×C8×C31—21no—
246C2×C8×C31—44no—
247C4⋊C4×C31—24no—
248C4⋊C4×C31—22no—
249C4⋊C4×C31—21no—
250C4⋊C4×C31—21no—
251C4⋊C4×C31—21no—
252C4⋊C4×C31—21no—
253C4⋊C4×C31—21no—
254C4⋊C4×C31—21no—
255C4⋊C4×C31—21no—
256C4⋊C4×C31—21no—
257C4⋊C4×C31—21no—
258C4⋊C4×C31—42no—
259C4⋊C4×C31—81no—
260C4⋊C4×C31C2×D412yes—
261C22⋊C4×C31—24no—
262C22⋊C4×C31—22no—
263C22⋊C4×C31—24no—
264C22⋊C4×C31—22no—
265C22⋊C4×C31—42no—
266C22⋊C4×C31—42no—
267C22⋊C4×C31—81no—
268C22⋊C4×C31—81no—
269C42×C31—24no—
270C42×C31—21no—
271C42×C31—21no—
272C42×C31—42no—
273#24034C3111yesmaximal, characteristic, direct product factor, Sylow
274C23×C31—21no—
275C23×C31—21no—
276C23×C31—21no—
277C23×C31—21no—
278C23×C31—21no—
279C23×C31—21no—
280C23×C31—21no—
281C23×C31—22no—
282C23×C31—22no—
283C23×C31—21no—
284C23×C31—21no—
285C23×C31—21no—
286C23×C31—21no—
287C23×C31—21no—
288C23×C31—21no—
289C23×C31—41no—
290C23×C31—41no—
291C23×C31—41no—
292C23×C31—41no—
293C23×C31—41no—
294C23×C31—41no—
295C23×C31—41no—
296C23×C31—41no—
297C23×C31—41no—
298C23×C31—41no—
299C23×C31—41no—
300C23×C31—41no—
301C23×C31#12012yes—
302C23×C31C22×D411yescharacteristic
303Q8×C31—22no—
304Q8×C31—22no—
305Q8×C31—22no—
306Q8×C31#12314yes—
307D4×C31—22no—
308D4×C31—22no—
309D4×C31—22no—
310D4×C31—22no—
311D4×C31—44no—
312D4×C31—48no—
313D4×C31—48no—
314D4×C31—48no—
315D4×C31—41no—
316D4×C31—41no—
317D4×C31—41no—
318D4×C31—41no—
319D4×C31—84no—
320D4×C31—84no—
321D4×C31—84no—
322C2×C4×C31—21no—
323C2×C4×C31—22no—
324C2×C4×C31—21no—
325C2×C4×C31—21no—
326C2×C4×C31—22no—
327C2×C4×C31—22no—
328C2×C4×C31—21no—
329C2×C4×C31—22no—
330C2×C4×C31—22no—
331C2×C4×C31—22no—
332C2×C4×C31—22no—
333C2×C4×C31—21no—
334C2×C4×C31—22no—
335C2×C4×C31—21no—
336C2×C4×C31—21no—
337C2×C4×C31—21no—
338C2×C4×C31—21no—
339C2×C4×C31—21no—
340C2×C4×C31—48no—
341C2×C4×C31—48no—
342C2×C4×C31—41no—
343C2×C4×C31—41no—
344C2×C4×C31—41no—
345C2×C4×C31—41no—
346C2×C4×C31—41no—
347C2×C4×C31—41no—
348C2×C4×C31—41no—
349C2×C4×C31—41no—
350C2×C4×C31—41no—
351C2×C4×C31—41no—
352C2×C4×C31—41no—
353C2×C4×C31—41no—
354C2×C4×C31—41no—
355C2×C4×C31—41no—
356C2×C4×C31—41no—
357C2×C4×C31—41no—
358C2×C4×C31—41no—
359C2×C4×C31—41no—
360C2×C4×C31#12012yes—
361C2×C4×C31#13512yes—
362C2×C4×C31C22×D411yescharacteristic
363C2×C4×C31C22×D411yescharacteristic
364C2×C4×C31C2×#4111yescharacteristic
365C2×C4×C31C2×#4111yescharacteristic
366C2×C4×C31H(5,𝔽2)11yescharacteristic
367C2×C4×C31H(5,𝔽2)11yescharacteristic
368C8×C31—41no—
369C8×C31—41no—
370C8×C31—41no—
371C8×C31—41no—
372C2×#550C2×C3111yescharacteristic
373C2×#482C2×C3111yescharacteristic, complemented
374C2×#416C2×C3111yescharacteristic, complemented
375#2485C2×C3111yescharacteristic, complemented
376#2041C2×C3111yescharacteristic, complemented
377#2041C2×C3111yescharacteristic, complemented
378#2034C2×C3111yescharacteristic, complemented
379#2033C2×C3111yescharacteristic, complemented
380#1893C2×C3111yescharacteristic, complemented
381#1869C2×C3111yescharacteristic, complemented
382#1865C2×C3111yescharacteristic, complemented
383#1863C2×C3111yescharacteristic, complemented
384#1788C2×C3111yescharacteristic, complemented
385#1788C2×C3111yescharacteristic, complemented
386#1788C2×C3111yescharacteristic, complemented
387C22×C31—22no—
388C22×C31—22no—
389C22×C31—22no—
390C22×C31—41no—
391C22×C31—41no—
392C22×C31—41no—
393C22×C31—41no—
394C22×C31—42no—
395C22×C31—42no—
396C22×C31—41no—
397C22×C31—41no—
398C22×C31—42no—
399C22×C31—42no—
400C22×C31—41no—
401C22×C31—42no—
402C22×C31—42no—
403C22×C31—41no—
404C22×C31—41no—
405C22×C31—41no—
406C22×C31—41no—
407C22×C31—81no—
408C22×C31—81no—
409C22×C31—81no—
410C22×C31—81no—
411C22×C31—81no—
412C22×C31—81no—
413C22×C31—81no—
414C22×C31—81no—
415C22×C31C2×#12011yescharacteristic
416C22×C31#54611yescharacteristic
417C22×C31#54611yescharacteristic
418C22×C31C2×#13511yescharacteristic
419C22×C31#57511yescharacteristic
420C22×C31#57611yescharacteristic
421C22×C31#57711yescharacteristic
422C4×C31—22no—
423C4×C31—24no—
424C4×C31—22no—
425C4×C31—41no—
426C4×C31—41no—
427C4×C31—42no—
428C4×C31—81no—
429C4×C31—81no—
430C4×C31—81no—
431C4×C31—81no—
432C4×C31C2×#12311yescharacteristic
433C4×C31#53411yescharacteristic
434C4×C31#54611yescharacteristic
435C4×C31#54611yescharacteristic
436C22×#41C22×C3111yescharacteristic
437C22×#41C22×C3111yescharacteristic
438C23×C8C22×C3111yescharacteristic
439#550—24no—
440#550—24no—
441C2×#127—21no—
442C2×#127C22×C3111yescharacteristic
443C2×#121—21no—
444C2×#121—21no—
445C2×#121C22×C3111yescharacteristic
446C2×#121C22×C3111yescharacteristic
447C2×C4×Q8C22×C3111yescharacteristic
448C2×C4×D4—21no—
449C2×C4×D4C22×C3111yescharacteristic
450C2×#117C22×C3111yescharacteristic
451#482—24no—
452C2×#107C22×C3111yescharacteristic
453C2×#106C22×C3111yescharacteristic
454#416—24no—
455C2×#103C22×C3111yescharacteristic
456C2×#103C22×C3111yescharacteristic
457C2×#103C22×C3111yescharacteristic
458C2×#103C22×C3111yescharacteristic
459C2×#102C22×C3111yescharacteristic
460C2×#102C22×C3111yescharacteristic
461C2×#102C22×C3111yescharacteristic
462C2×#102C22×C3111yescharacteristic
463C2×#102C22×C3111yescharacteristic
464C2×#102C22×C3111yescharacteristic
465C2×#102C22×C3111yescharacteristic
466C2×#102C22×C3111yescharacteristic
467C2×C22⋊C8C22×C3111yescharacteristic
468C2×C22⋊C8C22×C3111yescharacteristic
469C2×C22⋊C8C22×C3111yescharacteristic
470#397—21no—
471#394—21no—
472#389C22×C3111yescharacteristic
473#389C22×C3111yescharacteristic
474#388—21no—
475#387—21no—
476#380C22×C3111yescharacteristic
477#380C22×C3111yescharacteristic
478#380C22×C3111yescharacteristic
479#340C22×C3111yescharacteristic
480#340C22×C3111yescharacteristic
481#336C22×C3111yescharacteristic
482#336C22×C3111yescharacteristic
483C2×C31—42no—
484C2×C31—81no—
485C2×C31—82no—
486C2×C31—82no—
487C2×C31#240511yescharacteristic
488C2×C31#300211yescharacteristic
489C2×C31#301211yescharacteristic
490C2×C31#330411yescharacteristic
491C2×C31#330511yescharacteristic
492C2×C31#330911yescharacteristic
493C2×C31#331711yescharacteristic
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41D4×C3114yes—
506C22×Q8C23×C3111yescharacteristic
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4D4×C3111yescharacteristic
514C22×D4C23×C3111yescharacteristic
515C22×D4C23×C3111yescharacteristic
516C23×C4—21no—
517C23×C4—21no—
518C23×C4C23×C3111yescharacteristic
519C23×C4C23×C3111yescharacteristic
520C22×C8—22no—
521C22×C8—41no—
522C22×C8—41no—
523C22×C8C23×C3111yescharacteristic
524C22×C8C23×C3111yescharacteristic
525C22×C8C23×C3111yescharacteristic
526C22×C8C23×C3111yescharacteristic
527#127—28no—
528#127—22no—
529#127—22no—
530#121—28no—
531#121—28no—
532#121—22no—
533#121—22no—
534#121—22no—
535#121D4×C3114yes—
536C4×Q8—22no—
537C4×Q8—22no—
538C4×D4—28no—
539C4×D4—22no—
540C4×D4—22no—
541#117—22no—
542#117—22no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4D4×C3111yescharacteristic
547C2×C4⋊C4C23×C3111yescharacteristic
548C2×C4⋊C4C23×C3111yescharacteristic
549C2×C4⋊C4C23×C3111yescharacteristic
550C2×C4⋊C4C23×C3111yescharacteristic
551C2×C4⋊C4C23×C3111yescharacteristic
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4D4×C3111yescharacteristic
559C2×C22⋊C4D4×C3111yescharacteristic
560C2×C42—21no—
561C2×C42—21no—
562C2×C42C23×C3111yescharacteristic
563#107—22no—
564#106—22no—
565#103—22no—
566#103—22no—
567#103—22no—
568#103—22no—
569#102—22no—
570#102—22no—
571#102—22no—
572#102—22no—
573#102—41no—
574#102—41no—
575#102—41no—
576#102—41no—
577C22⋊C8—22no—
578C22⋊C8—41no—
579C22⋊C8—41no—
580#95—21no—
581#95—21no—
582#95—21no—
583#95—21no—
584#95—21no—
585C31#2403411yescharacteristic, direct product factor, Sylow
586C24—21no—
587C24—21no—
588C24C2×D4×C3111yescharacteristic
589C24C2×D4×C3111yescharacteristic
590#41—28no—
591#41—44no—
592#41—44no—
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—44no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8C2×D4×C3112yes—
602C2×Q8#41×C3112yes—
603C2×Q8#41×C3112yes—
604C2×D4—24no—
605C2×D4—24no—
606C2×D4—22no—
607C2×D4—24no—
608C2×D4—24no—
609C2×D4—24no—
610C2×D4—24no—
611C2×D4—22no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—41no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—81no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—81no—
633C2×D4—81no—
634C2×D4—81no—
635C2×D4C2×D4×C3112yes—
636C2×D4C2×D4×C3112yes—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—24no—
643C22×C4—21no—
644C22×C4—24no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4C2×D4×C3111yescharacteristic
660C22×C4C2×D4×C3111yescharacteristic
661C22×C4C2×D4×C3111yescharacteristic
662C22×C4C2×D4×C3112yes—
663C22×C4C2×D4×C3112yes—
664C22×C4C2×D4×C3111yescharacteristic
665C22×C4C24×C3111yescharacteristic
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—44no—
679C4⋊C4—24no—
680C4⋊C4—22no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—42no—
691C4⋊C4—81no—
692C4⋊C4C2×D4×C3112yes—
693C22⋊C4—24no—
694C22⋊C4—22no—
695C22⋊C4—24no—
696C22⋊C4—22no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—81no—
700C22⋊C4—81no—
701C42—24no—
702C42—21no—
703C42—21no—
704C42—42no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—22no—
713C23—22no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23C31×#12012yes—
733C23C22×D4×C3111yescharacteristic
734Q8—22no—
735Q8—22no—
736Q8—22no—
737Q8C31×#12314yes—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—22no—
742D4—44no—
743D4—48no—
744D4—48no—
745D4—48no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—84no—
751D4—84no—
752D4—84no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—21no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—21no—
765C2×C4—22no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—48no—
772C2×C4—48no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4C31×#12012yes—
792C2×C4C31×#13512yes—
793C2×C4C22×D4×C3111yescharacteristic
794C2×C4C22×D4×C3111yescharacteristic
795C2×C4C2×#41×C3111yescharacteristic
796C2×C4C2×#41×C3111yescharacteristic
797C2×C4C31×H(5,𝔽2)11yescharacteristic
798C2×C4C31×H(5,𝔽2)11yescharacteristic
799C8—41no—
800C8—41no—
801C8—41no—
802C8—41no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—42no—
811C22—42no—
812C22—41no—
813C22—41no—
814C22—42no—
815C22—42no—
816C22—41no—
817C22—42no—
818C22—42no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22C2×C31×#12011yescharacteristic
832C22C31×#54611yescharacteristic
833C22C31×#54611yescharacteristic
834C22C2×C31×#13511yescharacteristic
835C22C31×#57511yescharacteristic
836C22C31×#57611yescharacteristic
837C22C31×#57711yescharacteristic
838C4—22no—
839C4—24no—
840C4—22no—
841C4—41no—
842C4—41no—
843C4—42no—
844C4—81no—
845C4—81no—
846C4—81no—
847C4—81no—
848C4C2×C31×#12311yescharacteristic
849C4C31×#53411yescharacteristic
850C4C31×#54611yescharacteristic
851C4C31×#54611yescharacteristic
852C2—42no—
853C2—81no—
854C2—82no—
855C2—82no—
856C2C31×#240511yescharacteristic
857C2C31×#300211yescharacteristic
858C2C31×#301211yescharacteristic
859C2C31×#330411yescharacteristic
860C2C31×#330511yescharacteristic
861C2C31×#330911yescharacteristic
862C2C31×#331711yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#550C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C4×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#482C2semidirect
3. C2×C31×#416C2semidirect
4. C31×#2485C2semidirect
5. C31×#2041C2semidirect
6. C31×#2041C2semidirect
7. C31×#2034C2semidirect
8. C31×#2033C2semidirect
9. C31×#1893C2semidirect
10. C31×#1869C2semidirect
11. C31×#1865C2semidirect
12. C31×#1863C2semidirect
13. C31×#1788C2semidirect
14. C31×#1788C2semidirect
15. C31×#1788C2semidirect
273. #24034C31direct (N × H)
373. C2×#482C2×C31semidirect
374. C2×#416C2×C31semidirect
375. #2485C2×C31semidirect
376. #2041C2×C31semidirect
377. #2041C2×C31semidirect
378. #2034C2×C31semidirect
379. #2033C2×C31semidirect
380. #1893C2×C31semidirect
381. #1869C2×C31semidirect
382. #1865C2×C31semidirect
383. #1863C2×C31semidirect
384. #1788C2×C31semidirect
385. #1788C2×C31semidirect
386. #1788C2×C31semidirect
585. C31#24034direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5502
C2×C31×#4822
C2×C31×#4162
C31×#24852
C31×#20412
C31×#20342
C31×#20332
C31×#18932
C31×#18692
C31×#18652
C31×#18632
C31×#17882
#2403431