Finite Group Databasebeta

← C31×#24469 #21481228

Subgroups — C31×#24469 #21481228

Order 7936.

1402 conjugacy classes of subgroups.

The subgroup lattice has 1052 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3489C211yesmaximal, characteristic, complemented
2C31×#3055C211yesmaximal, characteristic, complemented
3C2×C31×#454C211yesmaximal, characteristic, complemented
4C31×#3006C211yesmaximal, characteristic, complemented
5C2×C31×#421C211yesmaximal, characteristic, complemented
6C31×#2620C211yesmaximal, characteristic, complemented
7C31×#2039C211yesmaximal, characteristic, complemented
8C31×#2038C211yesmaximal, characteristic, complemented
9C31×#2006C211yesmaximal, characteristic, complemented
10C31×#2003C211yesmaximal, characteristic, complemented
11C31×#1901C211yesmaximal, characteristic, complemented
12C31×#1897C211yesmaximal, characteristic, complemented
13C31×#1883C211yesmaximal, characteristic, complemented
14C31×#1859C211yesmaximal, characteristic, complemented
15C31×#1793C211yesmaximal, characteristic, complemented
16C2×C31×2−1+4C2211yescharacteristic
17C22×#41×C31C2211yescharacteristic
18C2×C31×AGL(1,ℤ/8)C2211yescharacteristic
19C2×C31×AGL(1,ℤ/8)C2211yescharacteristic
20C2×C31×AGL(1,ℤ/8)C2211yescharacteristic, complemented
21C22×M16×C31C2211yescharacteristic
22D4×Q8×C31—21no—
23C31×#548—21no—
24C31×#547—21no—
25C31×#547—22no—
26C31×#546—21no—
27C31×#546—22no—
28C31×#537—21no—
29C31×#537C2211yescharacteristic
30C31×#536—21no—
31C31×#536C2211yescharacteristic
32C2×C31×#124C2211yescharacteristic, complemented
33C31×#525—21no—
34C31×#525C2211yescharacteristic
35C2×C31×C22⋊Q8—21no—
36C2×C31×C22⋊Q8C2211yescharacteristic
37C2×C31×#121C2211yescharacteristic
38C31×#520C2211yescharacteristic
39C2×C31×#117C2211yescharacteristic
40C31×#469—21no—
41C31×#468—21no—
42C31×#466—21no—
43C31×#465—21no—
44C31×#454—24no—
45C31×#449—21no—
46C31×#449—21no—
47C31×#448—21no—
48C31×#447—21no—
49C31×#428C2211yescharacteristic, complemented
50C31×#421—24no—
51C2×C31×#104C2211yescharacteristic
52C2×C31×#104C2211yescharacteristic
53C2×C31×#104C2211yescharacteristic
54C2×C31×#104C2211yescharacteristic
55C2×C31×#104C2211yescharacteristic, complemented
56C2×C31×#104C2211yescharacteristic, complemented
57C31×#418C2211yescharacteristic, complemented
58C31×#417C2211yescharacteristic
59C31×#417C2211yescharacteristic
60C31×#417C2211yescharacteristic, complemented
61C2×C31×#101C2211yescharacteristic, complemented
62C2×C31×#101C2211yescharacteristic, complemented
63C31×#407C2211yescharacteristic
64C31×#396—22no—
65C31×#394—22no—
66C31×#391C2211yescharacteristic, complemented
67C31×#390C2211yescharacteristic, complemented
68C31×#384C2211yescharacteristic, complemented
69C31×#343C2211yescharacteristic, complemented
70C31×#343C2211yescharacteristic, complemented
71C31×#339C2211yescharacteristic, complemented
72C31×#339C2211yescharacteristic, complemented
73C31×2−1+4—22no—
74C31×2−1+4—22no—
75C31×2−1+4—41no—
76C31×2−1+4—41no—
77C2×#41×C31—21no—
78C2×#41×C31—21no—
79C2×#41×C31—21no—
80C2×#41×C31—22no—
81C2×#41×C31—21no—
82C2×#41×C31—22no—
83C2×#41×C31—22no—
84C2×#41×C31—41no—
85C2×#41×C31—41no—
86C2×#41×C31D411yescharacteristic
87C2×#41×C31D411yescharacteristic
88C2×#41×C31C2311yescharacteristic
89C2×#41×C31C2311yescharacteristic
90C2×#41×C31C2311yescharacteristic
91C22×Q8×C31—21no—
92C22×Q8×C31—21no—
93C22×Q8×C31D411yescharacteristic
94C22×Q8×C31C2311yescharacteristic
95C22×D4×C31—21no—
96C22×D4×C31—21no—
97C22×D4×C31D411yescharacteristic
98C22×D4×C31C2311yescharacteristic
99C23×C4×C31—21no—
100C23×C4×C31C2311yescharacteristic
101C31×AGL(1,ℤ/8)—22no—
102C31×AGL(1,ℤ/8)—22no—
103C31×AGL(1,ℤ/8)—22no—
104C31×AGL(1,ℤ/8)—41no—
105C31×AGL(1,ℤ/8)—41no—
106C31×AGL(1,ℤ/8)—41no—
107C2×SD16×C31—21no—
108C2×SD16×C31—21no—
109C2×SD16×C31—21no—
110C2×D8×C31—21no—
111C2×D8×C31—21no—
112C2×D8×C31—21no—
113C2×M16×C31—21no—
114C2×M16×C31—22no—
115C2×M16×C31—41no—
116C2×M16×C31C2311yescharacteristic
117C2×M16×C31C2311yescharacteristic
118C2×M16×C31C2311yescharacteristic
119C2×M16×C31C2311yescharacteristic
120C22×C8×C31—21no—
121C31×C4⋊Q8—22no—
122C31×C4⋊Q8—21no—
123C31×#124—22no—
124C31×#124—21no—
125C31×#124—22no—
126C31×#124—41no—
127C31×#123—22no—
128C31×#123—22no—
129C31×#123—22no—
130C31×#123—21no—
131C31×#123—22no—
132C31×C22⋊Q8—22no—
133C31×C22⋊Q8—22no—
134C31×C22⋊Q8—22no—
135C31×C22⋊Q8—21no—
136C31×C22⋊Q8—21no—
137C31×C22⋊Q8—21no—
138C31×C22⋊Q8—21no—
139C31×C22⋊Q8—21no—
140C31×C22⋊Q8—21no—
141C31×C22⋊Q8—21no—
142C31×C22⋊Q8—21no—
143C31×C22⋊Q8D411yescharacteristic
144C31×C22⋊Q8D411yescharacteristic
145C31×#121—22no—
146C31×#121—22no—
147C31×#121—22no—
148C31×#121—21no—
149C31×#121—21no—
150C31×#121—22no—
151C31×#121—21no—
152C31×#121—21no—
153C31×#121—21no—
154C31×#121—21no—
155C31×#121D411yescharacteristic
156C31×#121D411yescharacteristic
157C31×#120—22no—
158C31×#120—21no—
159C4×Q8×C31—21no—
160C4×D4×C31—22no—
161C4×D4×C31—22no—
162C4×D4×C31—21no—
163C4×D4×C31—22no—
164C4×D4×C31—21no—
165C4×D4×C31—21no—
166C31×#117—21no—
167C31×#117—22no—
168C31×#117—41no—
169C31×#117C2311yescharacteristic
170C2×C4⋊C4×C31—22no—
171C2×C4⋊C4×C31—21no—
172C2×C4⋊C4×C31—21no—
173C2×C4⋊C4×C31—22no—
174C2×C4⋊C4×C31D412yes—
175C2×C4⋊C4×C31C2311yescharacteristic
176C2×C4⋊C4×C31C2311yescharacteristic
177C2×C22⋊C4×C31—22no—
178C2×C22⋊C4×C31—21no—
179C2×C22⋊C4×C31—21no—
180C2×C22⋊C4×C31—22no—
181C2×C22⋊C4×C31—22no—
182C2×C22⋊C4×C31D412yes—
183C2×C42×C31C2311yescharacteristic
184C2×C42×C31C2311yescharacteristic
185C31×#107—21no—
186C31×#106—21no—
187C31×#104—22no—
188C31×#104—22no—
189C31×#104—22no—
190C31×#104—22no—
191C31×#104—41no—
192C31×#104D414yescomplemented
193C31×#103—21no—
194C31×#103—21no—
195C31×#103—21no—
196C31×#102—21no—
197C31×#102—21no—
198C31×#102—21no—
199C31×#102—21no—
200C31×#102—21no—
201C31×#101—22no—
202C31×#101—41no—
203C31×C22⋊C8—21no—
204C31×C22⋊C8—21no—
205C31×#95—22no—
206C24×C31—21no—
207C24×C31—21no—
208C24×C31C2×D411yescharacteristic
209#41×C31—21no—
210#41×C31—21no—
211#41×C31—22no—
212#41×C31—22no—
213#41×C31—21no—
214#41×C31—21no—
215#41×C31—21no—
216#41×C31—21no—
217#41×C31—21no—
218#41×C31—21no—
219#41×C31—21no—
220#41×C31—21no—
221#41×C31—42no—
222#41×C31—42no—
223#41×C31—41no—
224#41×C31—41no—
225#41×C31—42no—
226#41×C31—42no—
227#41×C31—42no—
228#41×C31—42no—
229#41×C31—44no—
230#41×C31—44no—
231#41×C31—42no—
232#41×C31—42no—
233#41×C31C2×D412yes—
234#41×C31#4112yes—
235C2×Q8×C31—22no—
236C2×Q8×C31—21no—
237C2×Q8×C31—21no—
238C2×Q8×C31—21no—
239C2×Q8×C31—21no—
240C2×Q8×C31—21no—
241C2×Q8×C31—21no—
242C2×Q8×C31—21no—
243C2×Q8×C31—22no—
244C2×Q8×C31—41no—
245C2×Q8×C31—42no—
246C2×Q8×C31—42no—
247C2×Q8×C31—42no—
248C2×Q8×C31—42no—
249C2×Q8×C31C2×D411yescharacteristic
250C2×Q8×C31C2×D411yescharacteristic
251C2×Q8×C31C2×D411yescharacteristic
252C2×D4×C31—21no—
253C2×D4×C31—22no—
254C2×D4×C31—22no—
255C2×D4×C31—21no—
256C2×D4×C31—21no—
257C2×D4×C31—21no—
258C2×D4×C31—21no—
259C2×D4×C31—21no—
260C2×D4×C31—22no—
261C2×D4×C31—21no—
262C2×D4×C31—21no—
263C2×D4×C31—21no—
264C2×D4×C31—21no—
265C2×D4×C31—21no—
266C2×D4×C31—21no—
267C2×D4×C31—21no—
268C2×D4×C31—21no—
269C2×D4×C31—41no—
270C2×D4×C31—42no—
271C2×D4×C31—42no—
272C2×D4×C31—41no—
273C2×D4×C31—41no—
274C2×D4×C31—82no—
275C2×D4×C31C2×D411yescharacteristic
276C2×D4×C31C2×D411yescharacteristic
277C2×D4×C31C2×D411yescharacteristic
278C22×C4×C31—21no—
279C22×C4×C31—21no—
280C22×C4×C31—21no—
281C22×C4×C31—21no—
282C22×C4×C31—21no—
283C22×C4×C31—22no—
284C22×C4×C31—22no—
285C22×C4×C31—21no—
286C22×C4×C31—21no—
287C22×C4×C31—22no—
288C22×C4×C31—21no—
289C22×C4×C31—21no—
290C22×C4×C31—21no—
291C22×C4×C31—21no—
292C22×C4×C31—21no—
293C22×C4×C31—21no—
294C22×C4×C31—42no—
295C22×C4×C31—42no—
296C22×C4×C31C2×D412yes—
297C22×C4×C31C2×D411yescharacteristic
298C22×C4×C31C2×D411yescharacteristic
299C22×C4×C31C2×D411yescharacteristic
300C22×C4×C31C2×D411yescharacteristic
301C22×C4×C31C2×D411yescharacteristic
302C22×C4×C31C2×D412yes—
303C22×C4×C31C2411yescharacteristic
304SD16×C31—42no—
305SD16×C31—42no—
306SD16×C31—42no—
307D8×C31—42no—
308D8×C31—42no—
309D8×C31—42no—
310M16×C31—21no—
311M16×C31—21no—
312M16×C31—21no—
313M16×C31—21no—
314M16×C31—21no—
315M16×C31—21no—
316M16×C31—21no—
317M16×C31—42no—
318M16×C31C2×D412yes—
319C2×C8×C31—21no—
320C2×C8×C31—21no—
321C2×C8×C31—21no—
322C2×C8×C31—21no—
323C2×C8×C31—42no—
324C4⋊C4×C31—22no—
325C4⋊C4×C31—22no—
326C4⋊C4×C31—22no—
327C4⋊C4×C31—22no—
328C4⋊C4×C31—21no—
329C4⋊C4×C31—22no—
330C4⋊C4×C31—22no—
331C4⋊C4×C31—21no—
332C4⋊C4×C31—21no—
333C4⋊C4×C31—21no—
334C4⋊C4×C31—21no—
335C4⋊C4×C31—21no—
336C4⋊C4×C31—42no—
337C4⋊C4×C31—82no—
338C4⋊C4×C31C2×D411yescharacteristic
339C4⋊C4×C31C2×D411yescharacteristic
340C22⋊C4×C31—22no—
341C22⋊C4×C31—22no—
342C22⋊C4×C31—22no—
343C22⋊C4×C31—22no—
344C22⋊C4×C31—22no—
345C22⋊C4×C31—21no—
346C22⋊C4×C31—22no—
347C22⋊C4×C31—22no—
348C22⋊C4×C31—21no—
349C22⋊C4×C31—21no—
350C22⋊C4×C31—21no—
351C22⋊C4×C31—21no—
352C22⋊C4×C31—44no—
353C22⋊C4×C31—42no—
354C22⋊C4×C31—41no—
355C22⋊C4×C31—41no—
356C22⋊C4×C31—82no—
357C42×C31—22no—
358C42×C31—21no—
359C42×C31—21no—
360C42×C31—21no—
361C42×C31—21no—
362C42×C31C2×D412yes—
363#24469C3111yesmaximal, characteristic, direct product factor, Sylow
364C23×C31—21no—
365C23×C31—21no—
366C23×C31—21no—
367C23×C31—21no—
368C23×C31—21no—
369C23×C31—41no—
370C23×C31—41no—
371C23×C31—42no—
372C23×C31—42no—
373C23×C31—42no—
374C23×C31—42no—
375C23×C31—41no—
376C23×C31—41no—
377C23×C31—41no—
378C23×C31—81no—
379C23×C31#12011yescharacteristic
380C23×C31#12011yescharacteristic
381C23×C31C22×D411yescharacteristic
382Q8×C31—21no—
383Q8×C31—21no—
384Q8×C31—21no—
385Q8×C31—21no—
386Q8×C31—21no—
387Q8×C31—42no—
388Q8×C31—44no—
389Q8×C31—41no—
390Q8×C31—41no—
391Q8×C31—41no—
392Q8×C31—41no—
393Q8×C31#12112yes—
394D4×C31—22no—
395D4×C31—22no—
396D4×C31—21no—
397D4×C31—21no—
398D4×C31—21no—
399D4×C31—21no—
400D4×C31—21no—
401D4×C31—42no—
402D4×C31—42no—
403D4×C31—42no—
404D4×C31—42no—
405D4×C31—44no—
406D4×C31—41no—
407D4×C31—41no—
408D4×C31—41no—
409D4×C31—41no—
410D4×C31—41no—
411D4×C31—41no—
412D4×C31—41no—
413D4×C31—41no—
414D4×C31—81no—
415D4×C31—82no—
416D4×C31—82no—
417D4×C31—82no—
418D4×C31#12112yes—
419C2×C4×C31—21no—
420C2×C4×C31—21no—
421C2×C4×C31—21no—
422C2×C4×C31—21no—
423C2×C4×C31—21no—
424C2×C4×C31—21no—
425C2×C4×C31—21no—
426C2×C4×C31—21no—
427C2×C4×C31—21no—
428C2×C4×C31—22no—
429C2×C4×C31—21no—
430C2×C4×C31—21no—
431C2×C4×C31—22no—
432C2×C4×C31—21no—
433C2×C4×C31—22no—
434C2×C4×C31—21no—
435C2×C4×C31—21no—
436C2×C4×C31—22no—
437C2×C4×C31—21no—
438C2×C4×C31—22no—
439C2×C4×C31—22no—
440C2×C4×C31—22no—
441C2×C4×C31—42no—
442C2×C4×C31—42no—
443C2×C4×C31—42no—
444C2×C4×C31—44no—
445C2×C4×C31—41no—
446C2×C4×C31—41no—
447C2×C4×C31—44no—
448C2×C4×C31—41no—
449C2×C4×C31—41no—
450C2×C4×C31—41no—
451C2×C4×C31—41no—
452C2×C4×C31—42no—
453C2×C4×C31—41no—
454C2×C4×C31—42no—
455C2×C4×C31—41no—
456C2×C4×C31—41no—
457C2×C4×C31—41no—
458C2×C4×C31—82no—
459C2×C4×C31#12011yescharacteristic
460C2×C4×C31#12011yescharacteristic
461C2×C4×C31C22×D411yescharacteristic
462C2×C4×C31C22×D411yescharacteristic
463C2×C4×C31C22×D411yescharacteristic
464C2×C4×C31C2×#4111yescharacteristic
465C2×C4×C31H(5,𝔽2)11yescharacteristic
466C2×C4×C31H(5,𝔽2)11yescharacteristic
467C8×C31—22no—
468C8×C31—41no—
469C8×C31—41no—
470C8×C31—41no—
471#3489C2×C3111yescharacteristic, complemented
472#3055C2×C3111yescharacteristic, complemented
473C2×#454C2×C3111yescharacteristic, complemented
474#3006C2×C3111yescharacteristic, complemented
475C2×#421C2×C3111yescharacteristic, complemented
476#2620C2×C3111yescharacteristic, complemented
477#2039C2×C3111yescharacteristic, complemented
478#2038C2×C3111yescharacteristic, complemented
479#2006C2×C3111yescharacteristic, complemented
480#2003C2×C3111yescharacteristic, complemented
481#1901C2×C3111yescharacteristic, complemented
482#1897C2×C3111yescharacteristic, complemented
483#1883C2×C3111yescharacteristic, complemented
484#1859C2×C3111yescharacteristic, complemented
485#1793C2×C3111yescharacteristic, complemented
486C22×C31—21no—
487C22×C31—21no—
488C22×C31—21no—
489C22×C31—21no—
490C22×C31—22no—
491C22×C31—21no—
492C22×C31—21no—
493C22×C31—21no—
494C22×C31—21no—
495C22×C31—41no—
496C22×C31—41no—
497C22×C31—41no—
498C22×C31—41no—
499C22×C31—41no—
500C22×C31—41no—
501C22×C31—41no—
502C22×C31—41no—
503C22×C31—81no—
504C22×C31—81no—
505C22×C31—82no—
506C22×C31—82no—
507C22×C31—84no—
508C22×C31—81no—
509C22×C31—81no—
510C22×C31—81no—
511C22×C31C2×#12011yescharacteristic
512C22×C31D4211yescharacteristic
513C22×C31#54611yescharacteristic
514C4×C31—21no—
515C4×C31—21no—
516C4×C31—22no—
517C4×C31—42no—
518C4×C31—42no—
519C4×C31—41no—
520C4×C31—41no—
521C4×C31—41no—
522C4×C31—42no—
523C4×C31—41no—
524C4×C31—81no—
525C4×C31—81no—
526C4×C31C2×#12111yescharacteristic
527C4×C31#53411yescharacteristic
528C4×C31D4211yescharacteristic
529C4×C31#54611yescharacteristic
530C2×2−1+4C22×C3111yescharacteristic
531C22×#41C22×C3111yescharacteristic
532C2×AGL(1,ℤ/8)C22×C3111yescharacteristic
533C2×AGL(1,ℤ/8)C22×C3111yescharacteristic
534C2×AGL(1,ℤ/8)C22×C3111yescharacteristic, complemented
535C22×M16C22×C3111yescharacteristic
536D4×Q8—21no—
537#548—21no—
538#547—21no—
539#547—22no—
540#546—21no—
541#546—22no—
542#537—21no—
543#537C22×C3111yescharacteristic
544#536—21no—
545#536C22×C3111yescharacteristic
546C2×#124C22×C3111yescharacteristic, complemented
547#525—21no—
548#525C22×C3111yescharacteristic
549C2×C22⋊Q8—21no—
550C2×C22⋊Q8C22×C3111yescharacteristic
551C2×#121C22×C3111yescharacteristic
552#520C22×C3111yescharacteristic
553C2×#117C22×C3111yescharacteristic
554#469—21no—
555#468—21no—
556#466—21no—
557#465—21no—
558#454—24no—
559#449—21no—
560#449—21no—
561#448—21no—
562#447—21no—
563#428C22×C3111yescharacteristic, complemented
564#421—24no—
565C2×#104C22×C3111yescharacteristic
566C2×#104C22×C3111yescharacteristic
567C2×#104C22×C3111yescharacteristic
568C2×#104C22×C3111yescharacteristic
569C2×#104C22×C3111yescharacteristic, complemented
570C2×#104C22×C3111yescharacteristic, complemented
571#418C22×C3111yescharacteristic, complemented
572#417C22×C3111yescharacteristic
573#417C22×C3111yescharacteristic
574#417C22×C3111yescharacteristic, complemented
575C2×#101C22×C3111yescharacteristic, complemented
576C2×#101C22×C3111yescharacteristic, complemented
577#407C22×C3111yescharacteristic
578#396—22no—
579#394—22no—
580#391C22×C3111yescharacteristic, complemented
581#390C22×C3111yescharacteristic, complemented
582#384C22×C3111yescharacteristic, complemented
583#343C22×C3111yescharacteristic, complemented
584#343C22×C3111yescharacteristic, complemented
585#339C22×C3111yescharacteristic, complemented
586#339C22×C3111yescharacteristic, complemented
587C2×C31—21no—
588C2×C31—21no—
589C2×C31—41no—
590C2×C31—41no—
591C2×C31—42no—
592C2×C31—81no—
593C2×C31—81no—
594C2×C31—161no—
595C2×C31#241011yescharacteristic
596C2×C31#302011yescharacteristic
597C2×C31#302111yescharacteristic
5982−1+4—22no—
5992−1+4—22no—
6002−1+4—41no—
6012−1+4—41no—
602C2×#41—21no—
603C2×#41—21no—
604C2×#41—21no—
605C2×#41—22no—
606C2×#41—21no—
607C2×#41—22no—
608C2×#41—22no—
609C2×#41—41no—
610C2×#41—41no—
611C2×#41D4×C3111yescharacteristic
612C2×#41D4×C3111yescharacteristic
613C2×#41C23×C3111yescharacteristic
614C2×#41C23×C3111yescharacteristic
615C2×#41C23×C3111yescharacteristic
616C22×Q8—21no—
617C22×Q8—21no—
618C22×Q8D4×C3111yescharacteristic
619C22×Q8C23×C3111yescharacteristic
620C22×D4—21no—
621C22×D4—21no—
622C22×D4D4×C3111yescharacteristic
623C22×D4C23×C3111yescharacteristic
624C23×C4—21no—
625C23×C4C23×C3111yescharacteristic
626AGL(1,ℤ/8)—22no—
627AGL(1,ℤ/8)—22no—
628AGL(1,ℤ/8)—22no—
629AGL(1,ℤ/8)—41no—
630AGL(1,ℤ/8)—41no—
631AGL(1,ℤ/8)—41no—
632C2×SD16—21no—
633C2×SD16—21no—
634C2×SD16—21no—
635C2×D8—21no—
636C2×D8—21no—
637C2×D8—21no—
638C2×M16—21no—
639C2×M16—22no—
640C2×M16—41no—
641C2×M16C23×C3111yescharacteristic
642C2×M16C23×C3111yescharacteristic
643C2×M16C23×C3111yescharacteristic
644C2×M16C23×C3111yescharacteristic
645C22×C8—21no—
646C4⋊Q8—22no—
647C4⋊Q8—21no—
648#124—22no—
649#124—21no—
650#124—22no—
651#124—41no—
652#123—22no—
653#123—22no—
654#123—22no—
655#123—21no—
656#123—22no—
657C22⋊Q8—22no—
658C22⋊Q8—22no—
659C22⋊Q8—22no—
660C22⋊Q8—21no—
661C22⋊Q8—21no—
662C22⋊Q8—21no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8—21no—
668C22⋊Q8D4×C3111yescharacteristic
669C22⋊Q8D4×C3111yescharacteristic
670#121—22no—
671#121—22no—
672#121—22no—
673#121—21no—
674#121—21no—
675#121—22no—
676#121—21no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121D4×C3111yescharacteristic
681#121D4×C3111yescharacteristic
682#120—22no—
683#120—21no—
684C4×Q8—21no—
685C4×D4—22no—
686C4×D4—22no—
687C4×D4—21no—
688C4×D4—22no—
689C4×D4—21no—
690C4×D4—21no—
691#117—21no—
692#117—22no—
693#117—41no—
694#117C23×C3111yescharacteristic
695C2×C4⋊C4—22no—
696C2×C4⋊C4—21no—
697C2×C4⋊C4—21no—
698C2×C4⋊C4—22no—
699C2×C4⋊C4D4×C3112yes—
700C2×C4⋊C4C23×C3111yescharacteristic
701C2×C4⋊C4C23×C3111yescharacteristic
702C2×C22⋊C4—22no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4D4×C3112yes—
708C2×C42C23×C3111yescharacteristic
709C2×C42C23×C3111yescharacteristic
710#107—21no—
711#106—21no—
712#104—22no—
713#104—22no—
714#104—22no—
715#104—22no—
716#104—41no—
717#104D4×C3114yescomplemented
718#103—21no—
719#103—21no—
720#103—21no—
721#102—21no—
722#102—21no—
723#102—21no—
724#102—21no—
725#102—21no—
726#101—22no—
727#101—41no—
728C22⋊C8—21no—
729C22⋊C8—21no—
730#95—22no—
731C31#2446911yescharacteristic, direct product factor, Sylow
732C24—21no—
733C24—21no—
734C24C2×D4×C3111yescharacteristic
735#41—21no—
736#41—21no—
737#41—22no—
738#41—22no—
739#41—21no—
740#41—21no—
741#41—21no—
742#41—21no—
743#41—21no—
744#41—21no—
745#41—21no—
746#41—21no—
747#41—42no—
748#41—42no—
749#41—41no—
750#41—41no—
751#41—42no—
752#41—42no—
753#41—42no—
754#41—42no—
755#41—44no—
756#41—44no—
757#41—42no—
758#41—42no—
759#41C2×D4×C3112yes—
760#41#41×C3112yes—
761C2×Q8—22no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—22no—
770C2×Q8—41no—
771C2×Q8—42no—
772C2×Q8—42no—
773C2×Q8—42no—
774C2×Q8—42no—
775C2×Q8C2×D4×C3111yescharacteristic
776C2×Q8C2×D4×C3111yescharacteristic
777C2×Q8C2×D4×C3111yescharacteristic
778C2×D4—21no—
779C2×D4—22no—
780C2×D4—22no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—22no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—41no—
796C2×D4—42no—
797C2×D4—42no—
798C2×D4—41no—
799C2×D4—41no—
800C2×D4—82no—
801C2×D4C2×D4×C3111yescharacteristic
802C2×D4C2×D4×C3111yescharacteristic
803C2×D4C2×D4×C3111yescharacteristic
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—22no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—42no—
821C22×C4—42no—
822C22×C4C2×D4×C3112yes—
823C22×C4C2×D4×C3111yescharacteristic
824C22×C4C2×D4×C3111yescharacteristic
825C22×C4C2×D4×C3111yescharacteristic
826C22×C4C2×D4×C3111yescharacteristic
827C22×C4C2×D4×C3111yescharacteristic
828C22×C4C2×D4×C3112yes—
829C22×C4C24×C3111yescharacteristic
830SD16—42no—
831SD16—42no—
832SD16—42no—
833D8—42no—
834D8—42no—
835D8—42no—
836M16—21no—
837M16—21no—
838M16—21no—
839M16—21no—
840M16—21no—
841M16—21no—
842M16—21no—
843M16—42no—
844M16C2×D4×C3112yes—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—21no—
849C2×C8—42no—
850C4⋊C4—22no—
851C4⋊C4—22no—
852C4⋊C4—22no—
853C4⋊C4—22no—
854C4⋊C4—21no—
855C4⋊C4—22no—
856C4⋊C4—22no—
857C4⋊C4—21no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—42no—
863C4⋊C4—82no—
864C4⋊C4C2×D4×C3111yescharacteristic
865C4⋊C4C2×D4×C3111yescharacteristic
866C22⋊C4—22no—
867C22⋊C4—22no—
868C22⋊C4—22no—
869C22⋊C4—22no—
870C22⋊C4—22no—
871C22⋊C4—21no—
872C22⋊C4—22no—
873C22⋊C4—22no—
874C22⋊C4—21no—
875C22⋊C4—21no—
876C22⋊C4—21no—
877C22⋊C4—21no—
878C22⋊C4—44no—
879C22⋊C4—42no—
880C22⋊C4—41no—
881C22⋊C4—41no—
882C22⋊C4—82no—
883C42—22no—
884C42—21no—
885C42—21no—
886C42—21no—
887C42—21no—
888C42C2×D4×C3112yes—
889C23—21no—
890C23—21no—
891C23—21no—
892C23—21no—
893C23—21no—
894C23—41no—
895C23—41no—
896C23—42no—
897C23—42no—
898C23—42no—
899C23—42no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—81no—
904C23C31×#12011yescharacteristic
905C23C31×#12011yescharacteristic
906C23C22×D4×C3111yescharacteristic
907Q8—21no—
908Q8—21no—
909Q8—21no—
910Q8—21no—
911Q8—21no—
912Q8—42no—
913Q8—44no—
914Q8—41no—
915Q8—41no—
916Q8—41no—
917Q8—41no—
918Q8C31×#12112yes—
919D4—22no—
920D4—22no—
921D4—21no—
922D4—21no—
923D4—21no—
924D4—21no—
925D4—21no—
926D4—42no—
927D4—42no—
928D4—42no—
929D4—42no—
930D4—44no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—41no—
935D4—41no—
936D4—41no—
937D4—41no—
938D4—41no—
939D4—81no—
940D4—82no—
941D4—82no—
942D4—82no—
943D4C31×#12112yes—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—22no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—22no—
957C2×C4—21no—
958C2×C4—22no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—22no—
962C2×C4—21no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—42no—
967C2×C4—42no—
968C2×C4—42no—
969C2×C4—44no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—44no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—42no—
978C2×C4—41no—
979C2×C4—42no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—82no—
984C2×C4C31×#12011yescharacteristic
985C2×C4C31×#12011yescharacteristic
986C2×C4C22×D4×C3111yescharacteristic
987C2×C4C22×D4×C3111yescharacteristic
988C2×C4C22×D4×C3111yescharacteristic
989C2×C4C2×#41×C3111yescharacteristic
990C2×C4C31×H(5,𝔽2)11yescharacteristic
991C2×C4C31×H(5,𝔽2)11yescharacteristic
992C8—22no—
993C8—41no—
994C8—41no—
995C8—41no—
996C22—21no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—22no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—41no—
1006C22—41no—
1007C22—41no—
1008C22—41no—
1009C22—41no—
1010C22—41no—
1011C22—41no—
1012C22—41no—
1013C22—81no—
1014C22—81no—
1015C22—82no—
1016C22—82no—
1017C22—84no—
1018C22—81no—
1019C22—81no—
1020C22—81no—
1021C22C2×C31×#12011yescharacteristic
1022C22D42×C3111yescharacteristic
1023C22C31×#54611yescharacteristic
1024C4—21no—
1025C4—21no—
1026C4—22no—
1027C4—42no—
1028C4—42no—
1029C4—41no—
1030C4—41no—
1031C4—41no—
1032C4—42no—
1033C4—41no—
1034C4—81no—
1035C4—81no—
1036C4C2×C31×#12111yescharacteristic
1037C4C31×#53411yescharacteristic
1038C4D42×C3111yescharacteristic
1039C4C31×#54611yescharacteristic
1040C2—21no—
1041C2—21no—
1042C2—41no—
1043C2—41no—
1044C2—42no—
1045C2—81no—
1046C2—81no—
1047C2—161no—
1048C2C31×#241011yescharacteristic
1049C2C31×#302011yescharacteristic
1050C2C31×#302111yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
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
1. C31×#3489C2semidirect
2. C31×#3055C2semidirect
3. C2×C31×#454C2semidirect
4. C31×#3006C2semidirect
5. C2×C31×#421C2semidirect
6. C31×#2620C2semidirect
7. C31×#2039C2semidirect
8. C31×#2038C2semidirect
9. C31×#2006C2semidirect
10. C31×#2003C2semidirect
11. C31×#1901C2semidirect
12. C31×#1897C2semidirect
13. C31×#1883C2semidirect
14. C31×#1859C2semidirect
15. C31×#1793C2semidirect
20. C2×C31×AGL(1,ℤ/8)C22semidirect
32. C2×C31×#124C22semidirect
49. C31×#428C22semidirect
55. C2×C31×#104C22semidirect
56. C2×C31×#104C22semidirect
57. C31×#418C22semidirect
60. C31×#417C22semidirect
61. C2×C31×#101C22semidirect
62. C2×C31×#101C22semidirect
66. C31×#391C22semidirect
67. C31×#390C22semidirect
68. C31×#384C22semidirect
69. C31×#343C22semidirect
70. C31×#343C22semidirect
71. C31×#339C22semidirect
72. C31×#339C22semidirect
192. C31×#104D4semidirect
363. #24469C31direct (N × H)
471. #3489C2×C31semidirect
472. #3055C2×C31semidirect
473. C2×#454C2×C31semidirect
474. #3006C2×C31semidirect
475. C2×#421C2×C31semidirect
476. #2620C2×C31semidirect
477. #2039C2×C31semidirect
478. #2038C2×C31semidirect
479. #2006C2×C31semidirect
480. #2003C2×C31semidirect
481. #1901C2×C31semidirect
482. #1897C2×C31semidirect
483. #1883C2×C31semidirect
484. #1859C2×C31semidirect
485. #1793C2×C31semidirect
534. C2×AGL(1,ℤ/8)C22×C31semidirect
546. C2×#124C22×C31semidirect
563. #428C22×C31semidirect
569. C2×#104C22×C31semidirect
570. C2×#104C22×C31semidirect
571. #418C22×C31semidirect
574. #417C22×C31semidirect
575. C2×#101C22×C31semidirect
576. C2×#101C22×C31semidirect
580. #391C22×C31semidirect
581. #390C22×C31semidirect
582. #384C22×C31semidirect
583. #343C22×C31semidirect
584. #343C22×C31semidirect
585. #339C22×C31semidirect
586. #339C22×C31semidirect
717. #104D4×C31semidirect
731. C31#24469direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#34892
C31×#30552
C2×C31×#4542
C31×#30062
C2×C31×#4212
C31×#26202
C31×#20392
C31×#20382
C31×#20062
C31×#20032
C31×#19012
C31×#18972
C31×#18832
C31×#18592
C31×#17932
#2446931