Finite Group Databasebeta

← C31×#24031 #21480790

Subgroups — C31×#24031 #21480790

Order 7936.

1334 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3488C211yesmaximal, characteristic
2C31×#3093C211yesmaximal, characteristic, complemented
3C31×#2896C211yesmaximal, characteristic, complemented
4C31×#2500C211yesmaximal, characteristic, complemented
5C31×#2040C211yesmaximal, characteristic, complemented
6C31×#2039C211yesmaximal, characteristic, complemented
7C31×#2037C211yesmaximal, characteristic, complemented
8C31×#2037C211yesmaximal, characteristic, complemented
9C31×#1900C211yesmaximal, characteristic, complemented
10C31×#1871C211yesmaximal, characteristic, complemented
11C31×#1860C211yesmaximal, characteristic, complemented
12C31×#1859C211yesmaximal, characteristic, complemented
13C31×#1792C211yesmaximal, characteristic, complemented
14C31×#1792C211yesmaximal, characteristic, complemented
15C31×#1789C211yesmaximal, characteristic, complemented
16C2×C31×H(5,𝔽2)C2211yescharacteristic
17C22×#41×C31C2211yescharacteristic
18C22×M16×C31C2211yescharacteristic, complemented
19C31×#550—21no—
20C31×#548—21no—
21C31×#546—21no—
22C31×#546—22no—
23D42×C31—22no—
24D42×C31—21no—
25C31×#537—21no—
26C31×#537C2211yescharacteristic
27C31×#535—21no—
28C31×#535C2211yescharacteristic
29C31×#525—21no—
30C31×#525C2211yescharacteristic
31C2×C31×#121—21no—
32C2×C31×#121C2211yescharacteristic
33C31×#520C2211yescharacteristic
34C2×C31×#117C2211yescharacteristic, complemented
35C31×#485—21no—
36C31×#485—21no—
37C31×#482—21no—
38C31×#482—21no—
39C31×#428C2211yescharacteristic, complemented
40C31×#428C2211yescharacteristic, complemented
41C2×C31×#104C2211yescharacteristic
42C2×C31×#104C2211yescharacteristic
43C2×C31×#104C2211yescharacteristic, complemented
44C2×C31×#104C2211yescharacteristic, complemented
45C2×C31×#104C2211yescharacteristic, complemented
46C2×C31×#104C2211yescharacteristic, complemented
47C31×#419—21no—
48C31×#418—21no—
49C31×#417C2211yescharacteristic
50C31×#417C2211yescharacteristic
51C31×#417C2211yescharacteristic, complemented
52C31×#417C2211yescharacteristic, complemented
53C31×#417C2211yescharacteristic, complemented
54C31×#417C2211yescharacteristic, complemented
55C31×#416—21no—
56C31×#416—21no—
57C2×C31×#100C2211yescharacteristic, complemented
58C2×C31×#100C2211yescharacteristic, complemented
59C31×#407C2211yescharacteristic, complemented
60C31×#394—22no—
61C31×#390C2211yescharacteristic, complemented
62C31×#390C2211yescharacteristic, complemented
63C31×#388—22no—
64C31×#384C2211yescharacteristic, complemented
65C31×#382C2211yescharacteristic, complemented
66C4×C22⋊C4×C31C2211yescharacteristic, complemented
67C31×#343C2211yescharacteristic, complemented
68C31×#343C2211yescharacteristic, complemented
69C31×#339C2211yescharacteristic, complemented
70C31×#339C2211yescharacteristic, complemented
71C31×H(5,𝔽2)—22no—
72C31×H(5,𝔽2)—22no—
73C31×H(5,𝔽2)—41no—
74C31×H(5,𝔽2)—41no—
75C2×#41×C31—21no—
76C2×#41×C31—21no—
77C2×#41×C31—21no—
78C2×#41×C31—21no—
79C2×#41×C31—22no—
80C2×#41×C31—22no—
81C2×#41×C31—41no—
82C2×#41×C31—41no—
83C2×#41×C31D411yescharacteristic
84C2×#41×C31D411yescharacteristic
85C2×#41×C31C2311yescharacteristic
86C2×#41×C31C2311yescharacteristic
87C2×#41×C31C2311yescharacteristic
88C22×Q8×C31D411yescharacteristic
89C22×D4×C31—21no—
90C22×D4×C31—22no—
91C22×D4×C31—22no—
92C22×D4×C31—21no—
93C22×D4×C31—21no—
94C22×D4×C31D411yescharacteristic
95C22×D4×C31D412yes—
96C22×D4×C31C2311yescharacteristic
97C23×C4×C31—21no—
98C23×C4×C31C2311yescharacteristic
99C2×M16×C31—21no—
100C2×M16×C31—41no—
101C2×M16×C31—41no—
102C2×M16×C31C2311yescharacteristic
103C2×M16×C31C2311yescharacteristic
104C2×M16×C31C2311yescharacteristic
105C2×M16×C31C2311yescharacteristic
106C22×C8×C31—21no—
107C31×#127—22no—
108C31×#127—21no—
109C31×#124—22no—
110C31×#124—21no—
111C31×#123—22no—
112C31×#123—21no—
113C31×C22⋊Q8—22no—
114C31×C22⋊Q8—21no—
115C31×C22⋊Q8—21no—
116C31×C22⋊Q8D411yescharacteristic
117C31×C22⋊Q8D411yescharacteristic
118C31×#121—22no—
119C31×#121—22no—
120C31×#121—22no—
121C31×#121—22no—
122C31×#121—22no—
123C31×#121—21no—
124C31×#121—21no—
125C31×#121—21no—
126C31×#121—21no—
127C31×#121—21no—
128C31×#121—21no—
129C31×#121—22no—
130C31×#121—21no—
131C31×#121—21no—
132C31×#121D411yescharacteristic
133C31×#121D411yescharacteristic
134C31×#120—22no—
135C31×#120—22no—
136C31×#120—22no—
137C31×#120—21no—
138C31×#120—22no—
139C4×Q8×C31—21no—
140C4×D4×C31—22no—
141C4×D4×C31—22no—
142C4×D4×C31—21no—
143C4×D4×C31—22no—
144C4×D4×C31—21no—
145C4×D4×C31—21no—
146C31×#117—21no—
147C31×#117—21no—
148C31×#117—21no—
149C31×#117—21no—
150C31×#117—21no—
151C31×#117C2311yescharacteristic
152C2×C4⋊C4×C31—21no—
153C2×C4⋊C4×C31—22no—
154C2×C4⋊C4×C31C2311yescharacteristic
155C2×C4⋊C4×C31C2311yescharacteristic
156C2×C4⋊C4×C31C2311yescharacteristic
157C2×C22⋊C4×C31—22no—
158C2×C22⋊C4×C31—21no—
159C2×C22⋊C4×C31—21no—
160C2×C22⋊C4×C31—22no—
161C2×C22⋊C4×C31—22no—
162C2×C22⋊C4×C31D412yes—
163C2×C42×C31—21no—
164C2×C42×C31C2311yescharacteristic
165C2×C42×C31C2311yescharacteristic
166C31×#107—21no—
167C31×#107—21no—
168C31×#106—21no—
169C31×#106—21no—
170C31×#104—22no—
171C31×#104—22no—
172C31×#104—41no—
173C31×#104—41no—
174C31×#104—41no—
175C31×#104—41no—
176C31×#103—21no—
177C31×#103—21no—
178C31×#103—21no—
179C31×#103—21no—
180C31×#103—21no—
181C31×#103—21no—
182C31×#102—21no—
183C31×#102—21no—
184C31×#102—21no—
185C31×#102—21no—
186C31×#102—21no—
187C31×#102—21no—
188C31×#100—41no—
189C31×#100—41no—
190C31×C22⋊C8—21no—
191C31×C22⋊C8—21no—
192C31×#95—21no—
193C31×#95—22no—
194C24×C31—22no—
195C24×C31—21no—
196C24×C31C2×D412yes—
197C24×C31C2×D411yescharacteristic
198#41×C31—21no—
199#41×C31—21no—
200#41×C31—22no—
201#41×C31—22no—
202#41×C31—21no—
203#41×C31—21no—
204#41×C31—21no—
205#41×C31—21no—
206#41×C31—21no—
207#41×C31—21no—
208#41×C31—21no—
209#41×C31—21no—
210#41×C31—42no—
211#41×C31—42no—
212#41×C31—41no—
213#41×C31—41no—
214#41×C31—42no—
215#41×C31—42no—
216#41×C31—42no—
217#41×C31—42no—
218#41×C31—42no—
219#41×C31—42no—
220#41×C31#4112yes—
221#41×C31#4112yes—
222C2×Q8×C31—21no—
223C2×Q8×C31—22no—
224C2×Q8×C31—41no—
225C2×Q8×C31C2×D411yescharacteristic
226C2×Q8×C31C2×D411yescharacteristic
227C2×Q8×C31C2×D411yescharacteristic
228C2×D4×C31—21no—
229C2×D4×C31—22no—
230C2×D4×C31—22no—
231C2×D4×C31—22no—
232C2×D4×C31—22no—
233C2×D4×C31—21no—
234C2×D4×C31—21no—
235C2×D4×C31—21no—
236C2×D4×C31—21no—
237C2×D4×C31—21no—
238C2×D4×C31—22no—
239C2×D4×C31—22no—
240C2×D4×C31—22no—
241C2×D4×C31—21no—
242C2×D4×C31—22no—
243C2×D4×C31—21no—
244C2×D4×C31—21no—
245C2×D4×C31—21no—
246C2×D4×C31—21no—
247C2×D4×C31—21no—
248C2×D4×C31—21no—
249C2×D4×C31—21no—
250C2×D4×C31—41no—
251C2×D4×C31—42no—
252C2×D4×C31—42no—
253C2×D4×C31—42no—
254C2×D4×C31—42no—
255C2×D4×C31—44no—
256C2×D4×C31—44no—
257C2×D4×C31—42no—
258C2×D4×C31—42no—
259C2×D4×C31—82no—
260C2×D4×C31—84no—
261C2×D4×C31C2×D411yescharacteristic
262C2×D4×C31C2×D411yescharacteristic
263C2×D4×C31C2×D411yescharacteristic
264C22×C4×C31—21no—
265C22×C4×C31—21no—
266C22×C4×C31—21no—
267C22×C4×C31—21no—
268C22×C4×C31—21no—
269C22×C4×C31—22no—
270C22×C4×C31—21no—
271C22×C4×C31—21no—
272C22×C4×C31—22no—
273C22×C4×C31—21no—
274C22×C4×C31—21no—
275C22×C4×C31—21no—
276C22×C4×C31—21no—
277C22×C4×C31—21no—
278C22×C4×C31—21no—
279C22×C4×C31—21no—
280C22×C4×C31—42no—
281C22×C4×C31—42no—
282C22×C4×C31C2×D411yescharacteristic
283C22×C4×C31C2×D411yescharacteristic
284C22×C4×C31C2×D411yescharacteristic
285C22×C4×C31C2×D411yescharacteristic
286C22×C4×C31C2×D411yescharacteristic
287C22×C4×C31C2×D412yes—
288C22×C4×C31C2411yescharacteristic
289M16×C31—21no—
290M16×C31—21no—
291M16×C31—21no—
292M16×C31—21no—
293M16×C31—21no—
294M16×C31—21no—
295M16×C31—21no—
296M16×C31—21no—
297M16×C31—42no—
298C2×C8×C31—21no—
299C2×C8×C31—21no—
300C2×C8×C31—21no—
301C2×C8×C31—21no—
302C2×C8×C31—42no—
303C4⋊C4×C31—22no—
304C4⋊C4×C31—22no—
305C4⋊C4×C31—21no—
306C4⋊C4×C31—21no—
307C4⋊C4×C31—21no—
308C4⋊C4×C31—21no—
309C4⋊C4×C31—21no—
310C4⋊C4×C31—21no—
311C4⋊C4×C31—21no—
312C4⋊C4×C31—21no—
313C4⋊C4×C31—82no—
314C4⋊C4×C31C2×D411yescharacteristic
315C4⋊C4×C31C2×D411yescharacteristic
316C22⋊C4×C31—22no—
317C22⋊C4×C31—22no—
318C22⋊C4×C31—22no—
319C22⋊C4×C31—22no—
320C22⋊C4×C31—22no—
321C22⋊C4×C31—21no—
322C22⋊C4×C31—21no—
323C22⋊C4×C31—21no—
324C22⋊C4×C31—21no—
325C22⋊C4×C31—22no—
326C22⋊C4×C31—22no—
327C22⋊C4×C31—21no—
328C22⋊C4×C31—42no—
329C22⋊C4×C31—44no—
330C22⋊C4×C31—41no—
331C22⋊C4×C31—41no—
332C22⋊C4×C31—82no—
333C42×C31—22no—
334C42×C31—21no—
335C42×C31—21no—
336C42×C31—21no—
337C42×C31—21no—
338C42×C31—21no—
339C42×C31—41no—
340C42×C31—41no—
341#24031C3111yesmaximal, characteristic, direct product factor, Sylow
342C23×C31—21no—
343C23×C31—21no—
344C23×C31—21no—
345C23×C31—22no—
346C23×C31—21no—
347C23×C31—21no—
348C23×C31—22no—
349C23×C31—22no—
350C23×C31—41no—
351C23×C31—41no—
352C23×C31—42no—
353C23×C31—42no—
354C23×C31—44no—
355C23×C31—42no—
356C23×C31—42no—
357C23×C31—81no—
358C23×C31—82no—
359C23×C31—82no—
360C23×C31#12011yescharacteristic
361C23×C31#12011yescharacteristic
362C23×C31C22×D411yescharacteristic
363Q8×C31—21no—
364Q8×C31—21no—
365Q8×C31—21no—
366Q8×C31—21no—
367Q8×C31—21no—
368Q8×C31—42no—
369Q8×C31#12312yes—
370D4×C31—22no—
371D4×C31—22no—
372D4×C31—21no—
373D4×C31—21no—
374D4×C31—21no—
375D4×C31—21no—
376D4×C31—21no—
377D4×C31—42no—
378D4×C31—42no—
379D4×C31—44no—
380D4×C31—42no—
381D4×C31—44no—
382D4×C31—44no—
383D4×C31—42no—
384D4×C31—41no—
385D4×C31—41no—
386D4×C31—41no—
387D4×C31—41no—
388D4×C31—41no—
389D4×C31—41no—
390D4×C31—41no—
391D4×C31—41no—
392D4×C31—81no—
393D4×C31—82no—
394D4×C31—82no—
395D4×C31—82no—
396D4×C31—82no—
397D4×C31#12312yes—
398C2×C4×C31—21no—
399C2×C4×C31—21no—
400C2×C4×C31—21no—
401C2×C4×C31—21no—
402C2×C4×C31—21no—
403C2×C4×C31—21no—
404C2×C4×C31—21no—
405C2×C4×C31—21no—
406C2×C4×C31—21no—
407C2×C4×C31—21no—
408C2×C4×C31—21no—
409C2×C4×C31—22no—
410C2×C4×C31—22no—
411C2×C4×C31—22no—
412C2×C4×C31—21no—
413C2×C4×C31—22no—
414C2×C4×C31—21no—
415C2×C4×C31—21no—
416C2×C4×C31—21no—
417C2×C4×C31—42no—
418C2×C4×C31—42no—
419C2×C4×C31—42no—
420C2×C4×C31—44no—
421C2×C4×C31—41no—
422C2×C4×C31—41no—
423C2×C4×C31—41no—
424C2×C4×C31—41no—
425C2×C4×C31—41no—
426C2×C4×C31—41no—
427C2×C4×C31—42no—
428C2×C4×C31—41no—
429C2×C4×C31—42no—
430C2×C4×C31—41no—
431C2×C4×C31—42no—
432C2×C4×C31—41no—
433C2×C4×C31—41no—
434C2×C4×C31—41no—
435C2×C4×C31—82no—
436C2×C4×C31#12011yescharacteristic
437C2×C4×C31#12011yescharacteristic
438C2×C4×C31C22×D411yescharacteristic
439C2×C4×C31C22×D411yescharacteristic
440C2×C4×C31C2×#4111yescharacteristic
441C2×C4×C31C2×#4111yescharacteristic
442C2×C4×C31H(5,𝔽2)11yescharacteristic
443C2×C4×C31H(5,𝔽2)11yescharacteristic
444C8×C31—41no—
445C8×C31—41no—
446C8×C31—41no—
447C8×C31—41no—
448#3488C2×C3111yescharacteristic
449#3093C2×C3111yescharacteristic, complemented
450#2896C2×C3111yescharacteristic, complemented
451#2500C2×C3111yescharacteristic, complemented
452#2040C2×C3111yescharacteristic, complemented
453#2039C2×C3111yescharacteristic, complemented
454#2037C2×C3111yescharacteristic, complemented
455#2037C2×C3111yescharacteristic, complemented
456#1900C2×C3111yescharacteristic, complemented
457#1871C2×C3111yescharacteristic, complemented
458#1860C2×C3111yescharacteristic, complemented
459#1859C2×C3111yescharacteristic, complemented
460#1792C2×C3111yescharacteristic, complemented
461#1792C2×C3111yescharacteristic, complemented
462#1789C2×C3111yescharacteristic, complemented
463C22×C31—21no—
464C22×C31—21no—
465C22×C31—21no—
466C22×C31—21no—
467C22×C31—22no—
468C22×C31—21no—
469C22×C31—21no—
470C22×C31—21no—
471C22×C31—21no—
472C22×C31—41no—
473C22×C31—41no—
474C22×C31—41no—
475C22×C31—41no—
476C22×C31—42no—
477C22×C31—41no—
478C22×C31—42no—
479C22×C31—41no—
480C22×C31—42no—
481C22×C31—41no—
482C22×C31—41no—
483C22×C31—81no—
484C22×C31—81no—
485C22×C31—82no—
486C22×C31—82no—
487C22×C31—84no—
488C22×C31—164no—
489C22×C31C2×#12011yescharacteristic
490C22×C31#54611yescharacteristic
491C22×C31#54611yescharacteristic
492C4×C31—21no—
493C4×C31—21no—
494C4×C31—22no—
495C4×C31—42no—
496C4×C31—41no—
497C4×C31—41no—
498C4×C31—41no—
499C4×C31—42no—
500C4×C31—41no—
501C4×C31—81no—
502C4×C31—81no—
503C4×C31—81no—
504C4×C31C2×#12311yescharacteristic
505C4×C31#53411yescharacteristic
506C4×C31#54611yescharacteristic
507C4×C31#54611yescharacteristic
508C2×H(5,𝔽2)C22×C3111yescharacteristic
509C22×#41C22×C3111yescharacteristic
510C22×M16C22×C3111yescharacteristic, complemented
511#550—21no—
512#548—21no—
513#546—21no—
514#546—22no—
515D42—22no—
516D42—21no—
517#537—21no—
518#537C22×C3111yescharacteristic
519#535—21no—
520#535C22×C3111yescharacteristic
521#525—21no—
522#525C22×C3111yescharacteristic
523C2×#121—21no—
524C2×#121C22×C3111yescharacteristic
525#520C22×C3111yescharacteristic
526C2×#117C22×C3111yescharacteristic, complemented
527#485—21no—
528#485—21no—
529#482—21no—
530#482—21no—
531#428C22×C3111yescharacteristic, complemented
532#428C22×C3111yescharacteristic, complemented
533C2×#104C22×C3111yescharacteristic
534C2×#104C22×C3111yescharacteristic
535C2×#104C22×C3111yescharacteristic, complemented
536C2×#104C22×C3111yescharacteristic, complemented
537C2×#104C22×C3111yescharacteristic, complemented
538C2×#104C22×C3111yescharacteristic, complemented
539#419—21no—
540#418—21no—
541#417C22×C3111yescharacteristic
542#417C22×C3111yescharacteristic
543#417C22×C3111yescharacteristic, complemented
544#417C22×C3111yescharacteristic, complemented
545#417C22×C3111yescharacteristic, complemented
546#417C22×C3111yescharacteristic, complemented
547#416—21no—
548#416—21no—
549C2×#100C22×C3111yescharacteristic, complemented
550C2×#100C22×C3111yescharacteristic, complemented
551#407C22×C3111yescharacteristic, complemented
552#394—22no—
553#390C22×C3111yescharacteristic, complemented
554#390C22×C3111yescharacteristic, complemented
555#388—22no—
556#384C22×C3111yescharacteristic, complemented
557#382C22×C3111yescharacteristic, complemented
558C4×C22⋊C4C22×C3111yescharacteristic, complemented
559#343C22×C3111yescharacteristic, complemented
560#343C22×C3111yescharacteristic, complemented
561#339C22×C3111yescharacteristic, complemented
562#339C22×C3111yescharacteristic, complemented
563C2×C31—21no—
564C2×C31—21no—
565C2×C31—41no—
566C2×C31—41no—
567C2×C31—42no—
568C2×C31—81no—
569C2×C31—82no—
570C2×C31—81no—
571C2×C31#240511yescharacteristic
572C2×C31#301811yescharacteristic
573C2×C31#301911yescharacteristic
574H(5,𝔽2)—22no—
575H(5,𝔽2)—22no—
576H(5,𝔽2)—41no—
577H(5,𝔽2)—41no—
578C2×#41—21no—
579C2×#41—21no—
580C2×#41—21no—
581C2×#41—21no—
582C2×#41—22no—
583C2×#41—22no—
584C2×#41—41no—
585C2×#41—41no—
586C2×#41D4×C3111yescharacteristic
587C2×#41D4×C3111yescharacteristic
588C2×#41C23×C3111yescharacteristic
589C2×#41C23×C3111yescharacteristic
590C2×#41C23×C3111yescharacteristic
591C22×Q8D4×C3111yescharacteristic
592C22×D4—21no—
593C22×D4—22no—
594C22×D4—22no—
595C22×D4—21no—
596C22×D4—21no—
597C22×D4D4×C3111yescharacteristic
598C22×D4D4×C3112yes—
599C22×D4C23×C3111yescharacteristic
600C23×C4—21no—
601C23×C4C23×C3111yescharacteristic
602C2×M16—21no—
603C2×M16—41no—
604C2×M16—41no—
605C2×M16C23×C3111yescharacteristic
606C2×M16C23×C3111yescharacteristic
607C2×M16C23×C3111yescharacteristic
608C2×M16C23×C3111yescharacteristic
609C22×C8—21no—
610#127—22no—
611#127—21no—
612#124—22no—
613#124—21no—
614#123—22no—
615#123—21no—
616C22⋊Q8—22no—
617C22⋊Q8—21no—
618C22⋊Q8—21no—
619C22⋊Q8D4×C3111yescharacteristic
620C22⋊Q8D4×C3111yescharacteristic
621#121—22no—
622#121—22no—
623#121—22no—
624#121—22no—
625#121—22no—
626#121—21no—
627#121—21no—
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—22no—
633#121—21no—
634#121—21no—
635#121D4×C3111yescharacteristic
636#121D4×C3111yescharacteristic
637#120—22no—
638#120—22no—
639#120—22no—
640#120—21no—
641#120—22no—
642C4×Q8—21no—
643C4×D4—22no—
644C4×D4—22no—
645C4×D4—21no—
646C4×D4—22no—
647C4×D4—21no—
648C4×D4—21no—
649#117—21no—
650#117—21no—
651#117—21no—
652#117—21no—
653#117—21no—
654#117C23×C3111yescharacteristic
655C2×C4⋊C4—21no—
656C2×C4⋊C4—22no—
657C2×C4⋊C4C23×C3111yescharacteristic
658C2×C4⋊C4C23×C3111yescharacteristic
659C2×C4⋊C4C23×C3111yescharacteristic
660C2×C22⋊C4—22no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—22no—
664C2×C22⋊C4—22no—
665C2×C22⋊C4D4×C3112yes—
666C2×C42—21no—
667C2×C42C23×C3111yescharacteristic
668C2×C42C23×C3111yescharacteristic
669#107—21no—
670#107—21no—
671#106—21no—
672#106—21no—
673#104—22no—
674#104—22no—
675#104—41no—
676#104—41no—
677#104—41no—
678#104—41no—
679#103—21no—
680#103—21no—
681#103—21no—
682#103—21no—
683#103—21no—
684#103—21no—
685#102—21no—
686#102—21no—
687#102—21no—
688#102—21no—
689#102—21no—
690#102—21no—
691#100—41no—
692#100—41no—
693C22⋊C8—21no—
694C22⋊C8—21no—
695#95—21no—
696#95—22no—
697C31#2403111yescharacteristic, direct product factor, Sylow
698C24—22no—
699C24—21no—
700C24C2×D4×C3112yes—
701C24C2×D4×C3111yescharacteristic
702#41—21no—
703#41—21no—
704#41—22no—
705#41—22no—
706#41—21no—
707#41—21no—
708#41—21no—
709#41—21no—
710#41—21no—
711#41—21no—
712#41—21no—
713#41—21no—
714#41—42no—
715#41—42no—
716#41—41no—
717#41—41no—
718#41—42no—
719#41—42no—
720#41—42no—
721#41—42no—
722#41—42no—
723#41—42no—
724#41#41×C3112yes—
725#41#41×C3112yes—
726C2×Q8—21no—
727C2×Q8—22no—
728C2×Q8—41no—
729C2×Q8C2×D4×C3111yescharacteristic
730C2×Q8C2×D4×C3111yescharacteristic
731C2×Q8C2×D4×C3111yescharacteristic
732C2×D4—21no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—21no—
741C2×D4—21no—
742C2×D4—22no—
743C2×D4—22no—
744C2×D4—22no—
745C2×D4—21no—
746C2×D4—22no—
747C2×D4—21no—
748C2×D4—21no—
749C2×D4—21no—
750C2×D4—21no—
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—41no—
755C2×D4—42no—
756C2×D4—42no—
757C2×D4—42no—
758C2×D4—42no—
759C2×D4—44no—
760C2×D4—44no—
761C2×D4—42no—
762C2×D4—42no—
763C2×D4—82no—
764C2×D4—84no—
765C2×D4C2×D4×C3111yescharacteristic
766C2×D4C2×D4×C3111yescharacteristic
767C2×D4C2×D4×C3111yescharacteristic
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—22no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—42no—
785C22×C4—42no—
786C22×C4C2×D4×C3111yescharacteristic
787C22×C4C2×D4×C3111yescharacteristic
788C22×C4C2×D4×C3111yescharacteristic
789C22×C4C2×D4×C3111yescharacteristic
790C22×C4C2×D4×C3111yescharacteristic
791C22×C4C2×D4×C3112yes—
792C22×C4C24×C3111yescharacteristic
793M16—21no—
794M16—21no—
795M16—21no—
796M16—21no—
797M16—21no—
798M16—21no—
799M16—21no—
800M16—21no—
801M16—42no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—42no—
807C4⋊C4—22no—
808C4⋊C4—22no—
809C4⋊C4—21no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—82no—
818C4⋊C4C2×D4×C3111yescharacteristic
819C4⋊C4C2×D4×C3111yescharacteristic
820C22⋊C4—22no—
821C22⋊C4—22no—
822C22⋊C4—22no—
823C22⋊C4—22no—
824C22⋊C4—22no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—21no—
828C22⋊C4—21no—
829C22⋊C4—22no—
830C22⋊C4—22no—
831C22⋊C4—21no—
832C22⋊C4—42no—
833C22⋊C4—44no—
834C22⋊C4—41no—
835C22⋊C4—41no—
836C22⋊C4—82no—
837C42—22no—
838C42—21no—
839C42—21no—
840C42—21no—
841C42—21no—
842C42—21no—
843C42—41no—
844C42—41no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—22no—
849C23—21no—
850C23—21no—
851C23—22no—
852C23—22no—
853C23—41no—
854C23—41no—
855C23—42no—
856C23—42no—
857C23—44no—
858C23—42no—
859C23—42no—
860C23—81no—
861C23—82no—
862C23—82no—
863C23C31×#12011yescharacteristic
864C23C31×#12011yescharacteristic
865C23C22×D4×C3111yescharacteristic
866Q8—21no—
867Q8—21no—
868Q8—21no—
869Q8—21no—
870Q8—21no—
871Q8—42no—
872Q8C31×#12312yes—
873D4—22no—
874D4—22no—
875D4—21no—
876D4—21no—
877D4—21no—
878D4—21no—
879D4—21no—
880D4—42no—
881D4—42no—
882D4—44no—
883D4—42no—
884D4—44no—
885D4—44no—
886D4—42no—
887D4—41no—
888D4—41no—
889D4—41no—
890D4—41no—
891D4—41no—
892D4—41no—
893D4—41no—
894D4—41no—
895D4—81no—
896D4—82no—
897D4—82no—
898D4—82no—
899D4—82no—
900D4C31×#12312yes—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—21no—
916C2×C4—22no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—42no—
921C2×C4—42no—
922C2×C4—42no—
923C2×C4—44no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—42no—
931C2×C4—41no—
932C2×C4—42no—
933C2×C4—41no—
934C2×C4—42no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—82no—
939C2×C4C31×#12011yescharacteristic
940C2×C4C31×#12011yescharacteristic
941C2×C4C22×D4×C3111yescharacteristic
942C2×C4C22×D4×C3111yescharacteristic
943C2×C4C2×#41×C3111yescharacteristic
944C2×C4C2×#41×C3111yescharacteristic
945C2×C4C31×H(5,𝔽2)11yescharacteristic
946C2×C4C31×H(5,𝔽2)11yescharacteristic
947C8—41no—
948C8—41no—
949C8—41no—
950C8—41no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—22no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—42no—
965C22—41no—
966C22—42no—
967C22—41no—
968C22—42no—
969C22—41no—
970C22—41no—
971C22—81no—
972C22—81no—
973C22—82no—
974C22—82no—
975C22—84no—
976C22—164no—
977C22C2×C31×#12011yescharacteristic
978C22C31×#54611yescharacteristic
979C22C31×#54611yescharacteristic
980C4—21no—
981C4—21no—
982C4—22no—
983C4—42no—
984C4—41no—
985C4—41no—
986C4—41no—
987C4—42no—
988C4—41no—
989C4—81no—
990C4—81no—
991C4—81no—
992C4C2×C31×#12311yescharacteristic
993C4C31×#53411yescharacteristic
994C4C31×#54611yescharacteristic
995C4C31×#54611yescharacteristic
996C2—21no—
997C2—21no—
998C2—41no—
999C2—41no—
1000C2—42no—
1001C2—81no—
1002C2—82no—
1003C2—81no—
1004C2C31×#240511yescharacteristic
1005C2C31×#301811yescharacteristic
1006C2C31×#301911yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#3488C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#3093C2semidirect
3. C31×#2896C2semidirect
4. C31×#2500C2semidirect
5. C31×#2040C2semidirect
6. C31×#2039C2semidirect
7. C31×#2037C2semidirect
8. C31×#2037C2semidirect
9. C31×#1900C2semidirect
10. C31×#1871C2semidirect
11. C31×#1860C2semidirect
12. C31×#1859C2semidirect
13. C31×#1792C2semidirect
14. C31×#1792C2semidirect
15. C31×#1789C2semidirect
18. C22×M16×C31C22semidirect
34. C2×C31×#117C22semidirect
39. C31×#428C22semidirect
40. C31×#428C22semidirect
43. C2×C31×#104C22semidirect
44. C2×C31×#104C22semidirect
45. C2×C31×#104C22semidirect
46. C2×C31×#104C22semidirect
51. C31×#417C22semidirect
52. C31×#417C22semidirect
53. C31×#417C22semidirect
54. C31×#417C22semidirect
57. C2×C31×#100C22semidirect
58. C2×C31×#100C22semidirect
59. C31×#407C22semidirect
61. C31×#390C22semidirect
62. C31×#390C22semidirect
64. C31×#384C22semidirect
65. C31×#382C22semidirect
66. C4×C22⋊C4×C31C22semidirect
67. C31×#343C22semidirect
68. C31×#343C22semidirect
69. C31×#339C22semidirect
70. C31×#339C22semidirect
341. #24031C31direct (N × H)
449. #3093C2×C31semidirect
450. #2896C2×C31semidirect
451. #2500C2×C31semidirect
452. #2040C2×C31semidirect
453. #2039C2×C31semidirect
454. #2037C2×C31semidirect
455. #2037C2×C31semidirect
456. #1900C2×C31semidirect
457. #1871C2×C31semidirect
458. #1860C2×C31semidirect
459. #1859C2×C31semidirect
460. #1792C2×C31semidirect
461. #1792C2×C31semidirect
462. #1789C2×C31semidirect
510. C22×M16C22×C31semidirect
526. C2×#117C22×C31semidirect
531. #428C22×C31semidirect
532. #428C22×C31semidirect
535. C2×#104C22×C31semidirect
536. C2×#104C22×C31semidirect
537. C2×#104C22×C31semidirect
538. C2×#104C22×C31semidirect
543. #417C22×C31semidirect
544. #417C22×C31semidirect
545. #417C22×C31semidirect
546. #417C22×C31semidirect
549. C2×#100C22×C31semidirect
550. C2×#100C22×C31semidirect
551. #407C22×C31semidirect
553. #390C22×C31semidirect
554. #390C22×C31semidirect
556. #384C22×C31semidirect
557. #382C22×C31semidirect
558. C4×C22⋊C4C22×C31semidirect
559. #343C22×C31semidirect
560. #343C22×C31semidirect
561. #339C22×C31semidirect
562. #339C22×C31semidirect
697. C31#24031direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#34882
C31×#30932
C31×#28962
C31×#25002
C31×#20402
C31×#20392
C31×#20372
C31×#19002
C31×#18712
C31×#18602
C31×#18592
C31×#17922
C31×#17892
#2403131