Finite Group Databasebeta

← C31×#24465 #21481224

Subgroups — C31×#24465 #21481224

Order 7936.

1444 conjugacy classes of subgroups.

The subgroup lattice has 1056 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
5C22×C31×#104C211yesmaximal, characteristic, complemented
6C31×#2850C211yesmaximal, characteristic, complemented
7C31×#2040C211yesmaximal, characteristic, complemented
8C31×#2038C211yesmaximal, characteristic, complemented
9C31×#2006C211yesmaximal, characteristic, complemented
10C31×#2003C211yesmaximal, characteristic, complemented
11C31×#1901C211yesmaximal, characteristic, complemented
12C31×#1896C211yesmaximal, characteristic, complemented
13C31×#1883C211yesmaximal, characteristic, complemented
14C31×#1860C211yesmaximal, 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
39C22×C42×C31C2211yescharacteristic
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
50C2×C31×#104—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×#391C2211yescharacteristic, complemented
65C31×#390C2211yescharacteristic, complemented
66C31×#388—22no—
67C31×#386—22no—
68C31×#382C2211yescharacteristic, 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×C31—21no—
101C23×C4×C31C2311yescharacteristic
102C31×AGL(1,ℤ/8)—22no—
103C31×AGL(1,ℤ/8)—22no—
104C31×AGL(1,ℤ/8)—22no—
105C31×AGL(1,ℤ/8)—41no—
106C31×AGL(1,ℤ/8)—41no—
107C31×AGL(1,ℤ/8)—41no—
108C2×SD16×C31—21no—
109C2×SD16×C31—21no—
110C2×SD16×C31—21no—
111C2×D8×C31—21no—
112C2×D8×C31—21no—
113C2×D8×C31—21no—
114C2×M16×C31—21no—
115C2×M16×C31—22no—
116C2×M16×C31—41no—
117C2×M16×C31C2311yescharacteristic
118C2×M16×C31C2311yescharacteristic
119C2×M16×C31C2311yescharacteristic
120C2×M16×C31C2311yescharacteristic
121C22×C8×C31—21no—
122C31×C4⋊Q8—22no—
123C31×C4⋊Q8—21no—
124C31×#124—22no—
125C31×#124—21no—
126C31×#124—22no—
127C31×#124—41no—
128C31×#123—22no—
129C31×#123—22no—
130C31×#123—22no—
131C31×#123—21no—
132C31×#123—22no—
133C31×C22⋊Q8—22no—
134C31×C22⋊Q8—22no—
135C31×C22⋊Q8—22no—
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⋊Q8—21no—
144C31×C22⋊Q8D411yescharacteristic
145C31×C22⋊Q8D411yescharacteristic
146C31×#121—22no—
147C31×#121—22no—
148C31×#121—22no—
149C31×#121—21no—
150C31×#121—21no—
151C31×#121—22no—
152C31×#121—21no—
153C31×#121—21no—
154C31×#121—21no—
155C31×#121—21no—
156C31×#121D411yescharacteristic
157C31×#121D411yescharacteristic
158C31×#120—22no—
159C31×#120—21no—
160C4×Q8×C31—21no—
161C4×D4×C31—22no—
162C4×D4×C31—22no—
163C4×D4×C31—21no—
164C4×D4×C31—22no—
165C4×D4×C31—21no—
166C4×D4×C31—21no—
167C31×#117—21no—
168C31×#117C2311yescharacteristic
169C2×C4⋊C4×C31—22no—
170C2×C4⋊C4×C31—21no—
171C2×C4⋊C4×C31D412yes—
172C2×C4⋊C4×C31C2311yescharacteristic
173C2×C4⋊C4×C31C2311yescharacteristic
174C2×C22⋊C4×C31—22no—
175C2×C22⋊C4×C31—21no—
176C2×C22⋊C4×C31—22no—
177C2×C22⋊C4×C31—22no—
178C2×C22⋊C4×C31D412yes—
179C2×C42×C31—22no—
180C2×C42×C31—21no—
181C2×C42×C31—41no—
182C2×C42×C31C2311yescharacteristic
183C2×C42×C31C2311yescharacteristic
184C31×#107—21no—
185C31×#106—21no—
186C31×#104—22no—
187C31×#104—22no—
188C31×#104—22no—
189C31×#104—22no—
190C31×#104—41no—
191C31×#104D414yescomplemented
192C31×#103—21no—
193C31×#103—21no—
194C31×#103—21no—
195C31×#102—21no—
196C31×#102—21no—
197C31×#102—21no—
198C31×#102—21no—
199C31×#102—21no—
200C31×#101—22no—
201C31×#101—41no—
202C31×C22⋊C8—21no—
203C31×C22⋊C8—21no—
204C31×#95—22no—
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—44no—
273C2×D4×C31—41no—
274C2×D4×C31—41no—
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—21no—
288C22×C4×C31—22no—
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×C31—42no—
297C22×C4×C31—42no—
298C22×C4×C31—42no—
299C22×C4×C31C2×D412yes—
300C22×C4×C31C2×D411yescharacteristic
301C22×C4×C31C2×D411yescharacteristic
302C22×C4×C31C2×D411yescharacteristic
303C22×C4×C31C2×D411yescharacteristic
304C22×C4×C31C2×D411yescharacteristic
305C22×C4×C31C2×D412yes—
306C22×C4×C31C2411yescharacteristic
307SD16×C31—42no—
308SD16×C31—42no—
309SD16×C31—42no—
310D8×C31—42no—
311D8×C31—42no—
312D8×C31—42no—
313M16×C31—21no—
314M16×C31—21no—
315M16×C31—21no—
316M16×C31—21no—
317M16×C31—21no—
318M16×C31—21no—
319M16×C31—21no—
320M16×C31—42no—
321M16×C31C2×D412yes—
322C2×C8×C31—21no—
323C2×C8×C31—21no—
324C2×C8×C31—21no—
325C2×C8×C31—21no—
326C2×C8×C31—42no—
327C4⋊C4×C31—22no—
328C4⋊C4×C31—22no—
329C4⋊C4×C31—22no—
330C4⋊C4×C31—22no—
331C4⋊C4×C31—21no—
332C4⋊C4×C31—22no—
333C4⋊C4×C31—22no—
334C4⋊C4×C31—21no—
335C4⋊C4×C31—21no—
336C4⋊C4×C31—21no—
337C4⋊C4×C31—21no—
338C4⋊C4×C31—21no—
339C4⋊C4×C31C2×D411yescharacteristic
340C4⋊C4×C31C2×D411yescharacteristic
341C22⋊C4×C31—22no—
342C22⋊C4×C31—22no—
343C22⋊C4×C31—22no—
344C22⋊C4×C31—22no—
345C22⋊C4×C31—22no—
346C22⋊C4×C31—21no—
347C22⋊C4×C31—22no—
348C22⋊C4×C31—22no—
349C22⋊C4×C31—21no—
350C22⋊C4×C31—21no—
351C22⋊C4×C31—21no—
352C22⋊C4×C31—21no—
353C22⋊C4×C31—44no—
354C22⋊C4×C31—44no—
355C22⋊C4×C31—41no—
356C22⋊C4×C31—41no—
357C42×C31—22no—
358C42×C31—21no—
359C42×C31—21no—
360C42×C31—21no—
361C42×C31—21no—
362C42×C31—42no—
363C42×C31C2×D412yes—
364#24465C3111yesmaximal, characteristic, direct product factor, Sylow
365C23×C31—21no—
366C23×C31—21no—
367C23×C31—21no—
368C23×C31—22no—
369C23×C31—21no—
370C23×C31—21no—
371C23×C31—41no—
372C23×C31—42no—
373C23×C31—42no—
374C23×C31—42no—
375C23×C31—42no—
376C23×C31—41no—
377C23×C31—41no—
378C23×C31—41no—
379C23×C31—81no—
380C23×C31#12011yescharacteristic
381C23×C31#12011yescharacteristic
382C23×C31C22×D411yescharacteristic
383Q8×C31—21no—
384Q8×C31—21no—
385Q8×C31—21no—
386Q8×C31—21no—
387Q8×C31—21no—
388Q8×C31—42no—
389Q8×C31—44no—
390Q8×C31—41no—
391Q8×C31—41no—
392Q8×C31—41no—
393Q8×C31—41no—
394Q8×C31#12112yes—
395D4×C31—22no—
396D4×C31—22no—
397D4×C31—21no—
398D4×C31—21no—
399D4×C31—21no—
400D4×C31—21no—
401D4×C31—21no—
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—42no—
411D4×C31—41no—
412D4×C31—41no—
413D4×C31—41no—
414D4×C31—41no—
415D4×C31—81no—
416D4×C31—82no—
417D4×C31—82no—
418D4×C31—82no—
419D4×C31#12112yes—
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—21no—
429C2×C4×C31—22no—
430C2×C4×C31—21no—
431C2×C4×C31—21no—
432C2×C4×C31—22no—
433C2×C4×C31—22no—
434C2×C4×C31—21no—
435C2×C4×C31—22no—
436C2×C4×C31—21no—
437C2×C4×C31—21no—
438C2×C4×C31—22no—
439C2×C4×C31—21no—
440C2×C4×C31—22no—
441C2×C4×C31—22no—
442C2×C4×C31—22no—
443C2×C4×C31—42no—
444C2×C4×C31—42no—
445C2×C4×C31—42no—
446C2×C4×C31—44no—
447C2×C4×C31—41no—
448C2×C4×C31—41no—
449C2×C4×C31—41no—
450C2×C4×C31—44no—
451C2×C4×C31—48no—
452C2×C4×C31—41no—
453C2×C4×C31—41no—
454C2×C4×C31—41no—
455C2×C4×C31—41no—
456C2×C4×C31—41no—
457C2×C4×C31—42no—
458C2×C4×C31—42no—
459C2×C4×C31—41no—
460C2×C4×C31—82no—
461C2×C4×C31#12011yescharacteristic
462C2×C4×C31#12011yescharacteristic
463C2×C4×C31C22×D411yescharacteristic
464C2×C4×C31C22×D411yescharacteristic
465C2×C4×C31C22×D411yescharacteristic
466C2×C4×C31C2×#4111yescharacteristic
467C2×C4×C31H(5,𝔽2)11yescharacteristic
468C2×C4×C31H(5,𝔽2)11yescharacteristic
469C8×C31—22no—
470C8×C31—41no—
471C8×C31—41no—
472C8×C31—41no—
473#3489C2×C3111yescharacteristic, complemented
474#3055C2×C3111yescharacteristic, complemented
475C2×#454C2×C3111yescharacteristic, complemented
476#3006C2×C3111yescharacteristic, complemented
477C22×#104C2×C3111yescharacteristic, complemented
478#2850C2×C3111yescharacteristic, complemented
479#2040C2×C3111yescharacteristic, complemented
480#2038C2×C3111yescharacteristic, complemented
481#2006C2×C3111yescharacteristic, complemented
482#2003C2×C3111yescharacteristic, complemented
483#1901C2×C3111yescharacteristic, complemented
484#1896C2×C3111yescharacteristic, complemented
485#1883C2×C3111yescharacteristic, complemented
486#1860C2×C3111yescharacteristic, complemented
487#1793C2×C3111yescharacteristic, complemented
488C22×C31—21no—
489C22×C31—21no—
490C22×C31—21no—
491C22×C31—21no—
492C22×C31—21no—
493C22×C31—22no—
494C22×C31—21no—
495C22×C31—21no—
496C22×C31—42no—
497C22×C31—42no—
498C22×C31—41no—
499C22×C31—41no—
500C22×C31—41no—
501C22×C31—41no—
502C22×C31—41no—
503C22×C31—41no—
504C22×C31—41no—
505C22×C31—41no—
506C22×C31—84no—
507C22×C31—82no—
508C22×C31—82no—
509C22×C31—81no—
510C22×C31—81no—
511C22×C31—81no—
512C22×C31#45412yescomplemented
513C22×C31C2×#12011yescharacteristic
514C22×C31D4211yescharacteristic
515C22×C31#54611yescharacteristic
516C4×C31—21no—
517C4×C31—21no—
518C4×C31—22no—
519C4×C31—42no—
520C4×C31—42no—
521C4×C31—42no—
522C4×C31—41no—
523C4×C31—41no—
524C4×C31—41no—
525C4×C31—42no—
526C4×C31—41no—
527C4×C31—81no—
528C4×C31C2×#12111yescharacteristic
529C4×C31#53411yescharacteristic
530C4×C31D4211yescharacteristic
531C4×C31#54611yescharacteristic
532C2×2−1+4C22×C3111yescharacteristic
533C22×#41C22×C3111yescharacteristic
534C2×AGL(1,ℤ/8)C22×C3111yescharacteristic
535C2×AGL(1,ℤ/8)C22×C3111yescharacteristic
536C2×AGL(1,ℤ/8)C22×C3111yescharacteristic, complemented
537C22×M16C22×C3111yescharacteristic
538D4×Q8—21no—
539#548—21no—
540#547—21no—
541#547—22no—
542#546—21no—
543#546—22no—
544#537—21no—
545#537C22×C3111yescharacteristic
546#536—21no—
547#536C22×C3111yescharacteristic
548C2×#124C22×C3111yescharacteristic, complemented
549#525—21no—
550#525C22×C3111yescharacteristic
551C2×C22⋊Q8—21no—
552C2×C22⋊Q8C22×C3111yescharacteristic
553C2×#121C22×C3111yescharacteristic
554#520C22×C3111yescharacteristic
555C22×C42C22×C3111yescharacteristic
556#469—21no—
557#468—21no—
558#466—21no—
559#465—21no—
560#454—24no—
561#449—21no—
562#449—21no—
563#448—21no—
564#447—21no—
565#428C22×C3111yescharacteristic, complemented
566C2×#104—24no—
567C2×#104C22×C3111yescharacteristic
568C2×#104C22×C3111yescharacteristic
569C2×#104C22×C3111yescharacteristic
570C2×#104C22×C3111yescharacteristic
571C2×#104C22×C3111yescharacteristic, complemented
572C2×#104C22×C3111yescharacteristic, complemented
573#418C22×C3111yescharacteristic, complemented
574#417C22×C3111yescharacteristic
575#417C22×C3111yescharacteristic
576#417C22×C3111yescharacteristic, complemented
577C2×#101C22×C3111yescharacteristic, complemented
578C2×#101C22×C3111yescharacteristic, complemented
579#407C22×C3111yescharacteristic
580#391C22×C3111yescharacteristic, complemented
581#390C22×C3111yescharacteristic, complemented
582#388—22no—
583#386—22no—
584#382C22×C3111yescharacteristic, complemented
585#343C22×C3111yescharacteristic, complemented
586#343C22×C3111yescharacteristic, complemented
587#339C22×C3111yescharacteristic, complemented
588#339C22×C3111yescharacteristic, complemented
589C2×C31—21no—
590C2×C31—21no—
591C2×C31—22no—
592C2×C31—41no—
593C2×C31—42no—
594C2×C31—81no—
595C2×C31—81no—
596C2×C31—161no—
597C2×C31#241011yescharacteristic
598C2×C31C2×#45411yescharacteristic
599C2×C31#301811yescharacteristic
6002−1+4—22no—
6012−1+4—22no—
6022−1+4—41no—
6032−1+4—41no—
604C2×#41—21no—
605C2×#41—21no—
606C2×#41—21no—
607C2×#41—22no—
608C2×#41—21no—
609C2×#41—22no—
610C2×#41—22no—
611C2×#41—41no—
612C2×#41—41no—
613C2×#41D4×C3111yescharacteristic
614C2×#41D4×C3111yescharacteristic
615C2×#41C23×C3111yescharacteristic
616C2×#41C23×C3111yescharacteristic
617C2×#41C23×C3111yescharacteristic
618C22×Q8—21no—
619C22×Q8—21no—
620C22×Q8D4×C3111yescharacteristic
621C22×Q8C23×C3111yescharacteristic
622C22×D4—21no—
623C22×D4—21no—
624C22×D4D4×C3111yescharacteristic
625C22×D4C23×C3111yescharacteristic
626C23×C4—21no—
627C23×C4—21no—
628C23×C4C23×C3111yescharacteristic
629AGL(1,ℤ/8)—22no—
630AGL(1,ℤ/8)—22no—
631AGL(1,ℤ/8)—22no—
632AGL(1,ℤ/8)—41no—
633AGL(1,ℤ/8)—41no—
634AGL(1,ℤ/8)—41no—
635C2×SD16—21no—
636C2×SD16—21no—
637C2×SD16—21no—
638C2×D8—21no—
639C2×D8—21no—
640C2×D8—21no—
641C2×M16—21no—
642C2×M16—22no—
643C2×M16—41no—
644C2×M16C23×C3111yescharacteristic
645C2×M16C23×C3111yescharacteristic
646C2×M16C23×C3111yescharacteristic
647C2×M16C23×C3111yescharacteristic
648C22×C8—21no—
649C4⋊Q8—22no—
650C4⋊Q8—21no—
651#124—22no—
652#124—21no—
653#124—22no—
654#124—41no—
655#123—22no—
656#123—22no—
657#123—22no—
658#123—21no—
659#123—22no—
660C22⋊Q8—22no—
661C22⋊Q8—22no—
662C22⋊Q8—22no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8—21no—
668C22⋊Q8—21no—
669C22⋊Q8—21no—
670C22⋊Q8—21no—
671C22⋊Q8D4×C3111yescharacteristic
672C22⋊Q8D4×C3111yescharacteristic
673#121—22no—
674#121—22no—
675#121—22no—
676#121—21no—
677#121—21no—
678#121—22no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—21no—
683#121D4×C3111yescharacteristic
684#121D4×C3111yescharacteristic
685#120—22no—
686#120—21no—
687C4×Q8—21no—
688C4×D4—22no—
689C4×D4—22no—
690C4×D4—21no—
691C4×D4—22no—
692C4×D4—21no—
693C4×D4—21no—
694#117—21no—
695#117C23×C3111yescharacteristic
696C2×C4⋊C4—22no—
697C2×C4⋊C4—21no—
698C2×C4⋊C4D4×C3112yes—
699C2×C4⋊C4C23×C3111yescharacteristic
700C2×C4⋊C4C23×C3111yescharacteristic
701C2×C22⋊C4—22no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4D4×C3112yes—
706C2×C42—22no—
707C2×C42—21no—
708C2×C42—41no—
709C2×C42C23×C3111yescharacteristic
710C2×C42C23×C3111yescharacteristic
711#107—21no—
712#106—21no—
713#104—22no—
714#104—22no—
715#104—22no—
716#104—22no—
717#104—41no—
718#104D4×C3114yescomplemented
719#103—21no—
720#103—21no—
721#103—21no—
722#102—21no—
723#102—21no—
724#102—21no—
725#102—21no—
726#102—21no—
727#101—22no—
728#101—41no—
729C22⋊C8—21no—
730C22⋊C8—21no—
731#95—22no—
732#95—22no—
733C31#2446511yescharacteristic, direct product factor, Sylow
734C24—21no—
735C24—21no—
736C24C2×D4×C3111yescharacteristic
737#41—21no—
738#41—21no—
739#41—22no—
740#41—22no—
741#41—21no—
742#41—21no—
743#41—21no—
744#41—21no—
745#41—21no—
746#41—21no—
747#41—21no—
748#41—21no—
749#41—42no—
750#41—42no—
751#41—41no—
752#41—41no—
753#41—42no—
754#41—42no—
755#41—42no—
756#41—42no—
757#41—44no—
758#41—44no—
759#41—42no—
760#41—42no—
761#41C2×D4×C3112yes—
762#41#41×C3112yes—
763C2×Q8—22no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—22no—
772C2×Q8—41no—
773C2×Q8—42no—
774C2×Q8—42no—
775C2×Q8—42no—
776C2×Q8—42no—
777C2×Q8C2×D4×C3111yescharacteristic
778C2×Q8C2×D4×C3111yescharacteristic
779C2×Q8C2×D4×C3111yescharacteristic
780C2×D4—21no—
781C2×D4—22no—
782C2×D4—22no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—22no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—41no—
798C2×D4—42no—
799C2×D4—42no—
800C2×D4—44no—
801C2×D4—41no—
802C2×D4—41no—
803C2×D4C2×D4×C3111yescharacteristic
804C2×D4C2×D4×C3111yescharacteristic
805C2×D4C2×D4×C3111yescharacteristic
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—22no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—42no—
823C22×C4—42no—
824C22×C4—42no—
825C22×C4—42no—
826C22×C4—42no—
827C22×C4C2×D4×C3112yes—
828C22×C4C2×D4×C3111yescharacteristic
829C22×C4C2×D4×C3111yescharacteristic
830C22×C4C2×D4×C3111yescharacteristic
831C22×C4C2×D4×C3111yescharacteristic
832C22×C4C2×D4×C3111yescharacteristic
833C22×C4C2×D4×C3112yes—
834C22×C4C24×C3111yescharacteristic
835SD16—42no—
836SD16—42no—
837SD16—42no—
838D8—42no—
839D8—42no—
840D8—42no—
841M16—21no—
842M16—21no—
843M16—21no—
844M16—21no—
845M16—21no—
846M16—21no—
847M16—21no—
848M16—42no—
849M16C2×D4×C3112yes—
850C2×C8—21no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—42no—
855C4⋊C4—22no—
856C4⋊C4—22no—
857C4⋊C4—22no—
858C4⋊C4—22no—
859C4⋊C4—21no—
860C4⋊C4—22no—
861C4⋊C4—22no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4C2×D4×C3111yescharacteristic
868C4⋊C4C2×D4×C3111yescharacteristic
869C22⋊C4—22no—
870C22⋊C4—22no—
871C22⋊C4—22no—
872C22⋊C4—22no—
873C22⋊C4—22no—
874C22⋊C4—21no—
875C22⋊C4—22no—
876C22⋊C4—22no—
877C22⋊C4—21no—
878C22⋊C4—21no—
879C22⋊C4—21no—
880C22⋊C4—21no—
881C22⋊C4—44no—
882C22⋊C4—44no—
883C22⋊C4—41no—
884C22⋊C4—41no—
885C42—22no—
886C42—21no—
887C42—21no—
888C42—21no—
889C42—21no—
890C42—42no—
891C42C2×D4×C3112yes—
892C23—22no—
893C23—21no—
894C23—21no—
895C23—21no—
896C23—21no—
897C23—21no—
898C23—41no—
899C23—42no—
900C23—42no—
901C23—42no—
902C23—42no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—81no—
907C23C31×#12011yescharacteristic
908C23C31×#12011yescharacteristic
909C23C22×D4×C3111yescharacteristic
910Q8—21no—
911Q8—21no—
912Q8—21no—
913Q8—21no—
914Q8—21no—
915Q8—42no—
916Q8—44no—
917Q8—41no—
918Q8—41no—
919Q8—41no—
920Q8—41no—
921Q8C31×#12112yes—
922D4—22no—
923D4—22no—
924D4—21no—
925D4—21no—
926D4—21no—
927D4—21no—
928D4—21no—
929D4—42no—
930D4—42no—
931D4—42no—
932D4—44no—
933D4—42no—
934D4—41no—
935D4—41no—
936D4—41no—
937D4—41no—
938D4—41no—
939D4—41no—
940D4—41no—
941D4—41no—
942D4—81no—
943D4—82no—
944D4—82no—
945D4—82no—
946D4C31×#12112yes—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—22no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—21no—
962C2×C4—22no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—22no—
966C2×C4—21no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—42no—
971C2×C4—42no—
972C2×C4—42no—
973C2×C4—44no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—44no—
978C2×C4—48no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—42no—
985C2×C4—42no—
986C2×C4—41no—
987C2×C4—82no—
988C2×C4C31×#12011yescharacteristic
989C2×C4C31×#12011yescharacteristic
990C2×C4C22×D4×C3111yescharacteristic
991C2×C4C22×D4×C3111yescharacteristic
992C2×C4C22×D4×C3111yescharacteristic
993C2×C4C2×#41×C3111yescharacteristic
994C2×C4C31×H(5,𝔽2)11yescharacteristic
995C2×C4C31×H(5,𝔽2)11yescharacteristic
996C8—22no—
997C8—41no—
998C8—41no—
999C8—41no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—22no—
1006C22—21no—
1007C22—21no—
1008C22—42no—
1009C22—42no—
1010C22—41no—
1011C22—41no—
1012C22—41no—
1013C22—41no—
1014C22—41no—
1015C22—41no—
1016C22—41no—
1017C22—41no—
1018C22—84no—
1019C22—82no—
1020C22—82no—
1021C22—81no—
1022C22—81no—
1023C22—81no—
1024C22C31×#45412yescomplemented
1025C22C2×C31×#12011yescharacteristic
1026C22D42×C3111yescharacteristic
1027C22C31×#54611yescharacteristic
1028C4—21no—
1029C4—21no—
1030C4—22no—
1031C4—42no—
1032C4—42no—
1033C4—42no—
1034C4—41no—
1035C4—41no—
1036C4—41no—
1037C4—42no—
1038C4—41no—
1039C4—81no—
1040C4C2×C31×#12111yescharacteristic
1041C4C31×#53411yescharacteristic
1042C4D42×C3111yescharacteristic
1043C4C31×#54611yescharacteristic
1044C2—21no—
1045C2—22no—
1046C2—21no—
1047C2—41no—
1048C2—42no—
1049C2—81no—
1050C2—81no—
1051C2—161no—
1052C2C31×#241011yescharacteristic
1053C2C2×C31×#45411yescharacteristic
1054C2C31×#301811yescharacteristic
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. C22×C31×#104C2semidirect
6. C31×#2850C2semidirect
7. C31×#2040C2semidirect
8. C31×#2038C2semidirect
9. C31×#2006C2semidirect
10. C31×#2003C2semidirect
11. C31×#1901C2semidirect
12. C31×#1896C2semidirect
13. C31×#1883C2semidirect
14. C31×#1860C2semidirect
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
64. C31×#391C22semidirect
65. C31×#390C22semidirect
68. C31×#382C22semidirect
69. C31×#343C22semidirect
70. C31×#343C22semidirect
71. C31×#339C22semidirect
72. C31×#339C22semidirect
191. C31×#104D4semidirect
364. #24465C31direct (N × H)
473. #3489C2×C31semidirect
474. #3055C2×C31semidirect
475. C2×#454C2×C31semidirect
476. #3006C2×C31semidirect
477. C22×#104C2×C31semidirect
478. #2850C2×C31semidirect
479. #2040C2×C31semidirect
480. #2038C2×C31semidirect
481. #2006C2×C31semidirect
482. #2003C2×C31semidirect
483. #1901C2×C31semidirect
484. #1896C2×C31semidirect
485. #1883C2×C31semidirect
486. #1860C2×C31semidirect
487. #1793C2×C31semidirect
512. C22×C31#454semidirect
536. C2×AGL(1,ℤ/8)C22×C31semidirect
548. C2×#124C22×C31semidirect
565. #428C22×C31semidirect
571. C2×#104C22×C31semidirect
572. C2×#104C22×C31semidirect
573. #418C22×C31semidirect
576. #417C22×C31semidirect
577. C2×#101C22×C31semidirect
578. C2×#101C22×C31semidirect
580. #391C22×C31semidirect
581. #390C22×C31semidirect
584. #382C22×C31semidirect
585. #343C22×C31semidirect
586. #343C22×C31semidirect
587. #339C22×C31semidirect
588. #339C22×C31semidirect
718. #104D4×C31semidirect
733. C31#24465direct (N × H)
1024. C22C31×#454semidirect

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
C22×C31×#1042
C31×#28502
C31×#20402
C31×#20382
C31×#20062
C31×#20032
C31×#19012
C31×#18962
C31×#18832
C31×#18602
C31×#17932
#2446531