Finite Group Databasebeta

← C31×#24471 #21481230

Subgroups — C31×#24471 #21481230

Order 7936.

1444 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3488C211yesmaximal, characteristic
2C31×#3056C211yesmaximal, characteristic, complemented
3C2×C31×#455C211yesmaximal, characteristic, complemented
4C31×#3007C211yesmaximal, characteristic, complemented
5C2×C31×#421C211yesmaximal, characteristic, complemented
6C31×#2620C211yesmaximal, characteristic, complemented
7C31×#2039C211yesmaximal, characteristic, complemented
8C31×#2037C211yesmaximal, characteristic, complemented
9C31×#2007C211yesmaximal, characteristic, complemented
10C31×#2004C211yesmaximal, characteristic, complemented
11C31×#1900C211yesmaximal, characteristic, complemented
12C31×#1897C211yesmaximal, characteristic, complemented
13C31×#1882C211yesmaximal, characteristic, complemented
14C31×#1859C211yesmaximal, characteristic, complemented
15C31×#1792C211yesmaximal, characteristic, complemented
16C2×C31×H(5,𝔽2)C2211yescharacteristic
17C22×#41×C31C2211yescharacteristic
18C2×C31×#137C2211yescharacteristic
19C2×C31×#137C2211yescharacteristic, complemented
20C2×C31×#137C2211yescharacteristic, complemented
21C22×M16×C31C2211yescharacteristic, complemented
22C31×#550—21no—
23C31×#548—21no—
24C31×#546—21no—
25C31×#546—22no—
26D42×C31—22no—
27D42×C31—21no—
28C31×#537—21no—
29C31×#537C2211yescharacteristic
30C31×#535—21no—
31C31×#535C2211yescharacteristic
32C2×C31×#124C2211yescharacteristic, complemented
33C31×#525—21no—
34C31×#525C2211yescharacteristic
35C2×C31×C22⋊Q8C2211yescharacteristic, complemented
36C2×C31×#121—21no—
37C2×C31×#121C2211yescharacteristic
38C31×#520C2211yescharacteristic
39C2×C31×#117C2211yescharacteristic, complemented
40C31×#470—21no—
41C31×#468—21no—
42C31×#467—21no—
43C31×#465—21no—
44C31×#455—24no—
45C31×#452—21no—
46C31×#452—21no—
47C31×#451—21no—
48C31×#450—21no—
49C31×#428C2211yescharacteristic, complemented
50C31×#421—24no—
51C2×C31×#104C2211yescharacteristic
52C2×C31×#104C2211yescharacteristic
53C2×C31×#104C2211yescharacteristic, complemented
54C2×C31×#104C2211yescharacteristic, complemented
55C2×C31×#104C2211yescharacteristic, complemented
56C2×C31×#104C2211yescharacteristic, complemented
57C31×#419C2211yescharacteristic, complemented
58C31×#417C2211yescharacteristic
59C31×#417C2211yescharacteristic, complemented
60C31×#417C2211yescharacteristic, complemented
61C2×C31×#100C2211yescharacteristic, complemented
62C2×C31×#100C2211yescharacteristic, complemented
63C31×#407C2211yescharacteristic, complemented
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×H(5,𝔽2)—22no—
74C31×H(5,𝔽2)—22no—
75C31×H(5,𝔽2)—41no—
76C31×H(5,𝔽2)—41no—
77C2×#41×C31—21no—
78C2×#41×C31—21no—
79C2×#41×C31—21no—
80C2×#41×C31—21no—
81C2×#41×C31—22no—
82C2×#41×C31—22no—
83C2×#41×C31—41no—
84C2×#41×C31—41no—
85C2×#41×C31D411yescharacteristic
86C2×#41×C31D411yescharacteristic
87C2×#41×C31C2311yescharacteristic
88C2×#41×C31C2311yescharacteristic
89C2×#41×C31C2311yescharacteristic
90C22×Q8×C31D411yescharacteristic
91C22×Q8×C31C2311yescharacteristic
92C22×D4×C31—21no—
93C22×D4×C31—22no—
94C22×D4×C31—22no—
95C22×D4×C31—21no—
96C22×D4×C31—21no—
97C22×D4×C31D411yescharacteristic
98C22×D4×C31D412yes—
99C22×D4×C31C2311yescharacteristic
100C23×C4×C31—21no—
101C23×C4×C31C2311yescharacteristic
102C31×#137—22no—
103C31×#137—22no—
104C31×#137—22no—
105C31×#137—41no—
106C31×#137—41no—
107C31×#137—41no—
108C2×Q16×C31—21no—
109C2×Q16×C31—21no—
110C2×Q16×C31—21no—
111C2×SD16×C31—21no—
112C2×SD16×C31—21no—
113C2×SD16×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×#127—22no—
123C31×#127—21no—
124C31×#124—22no—
125C31×#124—21no—
126C31×#124—22no—
127C31×#124—41no—
128C31×#123—22no—
129C31×#123—21no—
130C31×C22⋊Q8—22no—
131C31×C22⋊Q8—21no—
132C31×C22⋊Q8—21no—
133C31×C22⋊Q8—21no—
134C31×C22⋊Q8—21no—
135C31×C22⋊Q8—21no—
136C31×C22⋊Q8—21no—
137C31×C22⋊Q8D411yescharacteristic
138C31×C22⋊Q8D411yescharacteristic
139C31×#121—22no—
140C31×#121—22no—
141C31×#121—22no—
142C31×#121—22no—
143C31×#121—22no—
144C31×#121—21no—
145C31×#121—21no—
146C31×#121—21no—
147C31×#121—21no—
148C31×#121—21no—
149C31×#121—21no—
150C31×#121—22no—
151C31×#121—21no—
152C31×#121—21no—
153C31×#121D411yescharacteristic
154C31×#121D411yescharacteristic
155C31×#120—22no—
156C31×#120—22no—
157C31×#120—22no—
158C31×#120—21no—
159C31×#120—22no—
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×#117—22no—
169C31×#117—41no—
170C31×#117C2311yescharacteristic
171C2×C4⋊C4×C31—21no—
172C2×C4⋊C4×C31—21no—
173C2×C4⋊C4×C31—21no—
174C2×C4⋊C4×C31—22no—
175C2×C4⋊C4×C31C2311yescharacteristic
176C2×C4⋊C4×C31C2311yescharacteristic
177C2×C22⋊C4×C31—22no—
178C2×C22⋊C4×C31—22no—
179C2×C22⋊C4×C31—21no—
180C2×C22⋊C4×C31—21no—
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×#103—21no—
197C31×#103—21no—
198C31×#102—21no—
199C31×#102—21no—
200C31×#102—21no—
201C31×#100—22no—
202C31×#100—41no—
203C31×C22⋊C8—21no—
204C31×C22⋊C8—21no—
205C31×#95—22no—
206C24×C31—22no—
207C24×C31—21no—
208C24×C31C2×D412yes—
209C24×C31C2×D411yescharacteristic
210#41×C31—21no—
211#41×C31—21no—
212#41×C31—22no—
213#41×C31—22no—
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—21no—
222#41×C31—42no—
223#41×C31—42no—
224#41×C31—41no—
225#41×C31—41no—
226#41×C31—42no—
227#41×C31—42no—
228#41×C31—42no—
229#41×C31—42no—
230#41×C31—42no—
231#41×C31—42no—
232#41×C31C2×D412yes—
233#41×C31#4112yes—
234C2×Q8×C31—21no—
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—41no—
243C2×Q8×C31C2×D411yescharacteristic
244C2×Q8×C31C2×D411yescharacteristic
245C2×Q8×C31C2×D411yescharacteristic
246C2×D4×C31—21no—
247C2×D4×C31—22no—
248C2×D4×C31—22no—
249C2×D4×C31—22no—
250C2×D4×C31—22no—
251C2×D4×C31—21no—
252C2×D4×C31—21no—
253C2×D4×C31—21no—
254C2×D4×C31—21no—
255C2×D4×C31—21no—
256C2×D4×C31—22no—
257C2×D4×C31—22no—
258C2×D4×C31—22no—
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—41no—
269C2×D4×C31—42no—
270C2×D4×C31—42no—
271C2×D4×C31—42no—
272C2×D4×C31—42no—
273C2×D4×C31—44no—
274C2×D4×C31—44no—
275C2×D4×C31—42no—
276C2×D4×C31—42no—
277C2×D4×C31—82no—
278C2×D4×C31—84no—
279C2×D4×C31C2×D411yescharacteristic
280C2×D4×C31C2×D411yescharacteristic
281C2×D4×C31C2×D411yescharacteristic
282C22×C4×C31—21no—
283C22×C4×C31—21no—
284C22×C4×C31—21no—
285C22×C4×C31—21no—
286C22×C4×C31—21no—
287C22×C4×C31—22no—
288C22×C4×C31—21no—
289C22×C4×C31—21no—
290C22×C4×C31—22no—
291C22×C4×C31—21no—
292C22×C4×C31—21no—
293C22×C4×C31—21no—
294C22×C4×C31—21no—
295C22×C4×C31—21no—
296C22×C4×C31—21no—
297C22×C4×C31—21no—
298C22×C4×C31—42no—
299C22×C4×C31—42no—
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
307Q16×C31—42no—
308Q16×C31—42no—
309Q16×C31—42no—
310SD16×C31—42no—
311SD16×C31—42no—
312SD16×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×D412yescomplemented
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—21no—
330C4⋊C4×C31—21no—
331C4⋊C4×C31—21no—
332C4⋊C4×C31—21no—
333C4⋊C4×C31—21no—
334C4⋊C4×C31—21no—
335C4⋊C4×C31—42no—
336C4⋊C4×C31—41no—
337C4⋊C4×C31—41no—
338C4⋊C4×C31—82no—
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—21no—
348C22⋊C4×C31—21no—
349C22⋊C4×C31—21no—
350C22⋊C4×C31—22no—
351C22⋊C4×C31—22no—
352C22⋊C4×C31—21no—
353C22⋊C4×C31—42no—
354C22⋊C4×C31—44no—
355C22⋊C4×C31—41no—
356C22⋊C4×C31—41no—
357C22⋊C4×C31—82no—
358C42×C31—22no—
359C42×C31—21no—
360C42×C31—21no—
361C42×C31—21no—
362C42×C31—21no—
363C42×C31C2×D412yescomplemented
364#24471C3111yesmaximal, 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—22no—
372C23×C31—22no—
373C23×C31—41no—
374C23×C31—41no—
375C23×C31—42no—
376C23×C31—42no—
377C23×C31—44no—
378C23×C31—42no—
379C23×C31—42no—
380C23×C31—81no—
381C23×C31—82no—
382C23×C31—82no—
383C23×C31#12011yescharacteristic
384C23×C31#12011yescharacteristic
385C23×C31C22×D411yescharacteristic
386Q8×C31—21no—
387Q8×C31—21no—
388Q8×C31—21no—
389Q8×C31—21no—
390Q8×C31—21no—
391Q8×C31—42no—
392Q8×C31—41no—
393Q8×C31—41no—
394Q8×C31—41no—
395Q8×C31—41no—
396Q8×C31#12112yes—
397D4×C31—22no—
398D4×C31—22no—
399D4×C31—21no—
400D4×C31—21no—
401D4×C31—21no—
402D4×C31—21no—
403D4×C31—21no—
404D4×C31—42no—
405D4×C31—42no—
406D4×C31—44no—
407D4×C31—42no—
408D4×C31—44no—
409D4×C31—44no—
410D4×C31—42no—
411D4×C31—41no—
412D4×C31—41no—
413D4×C31—41no—
414D4×C31—41no—
415D4×C31—41no—
416D4×C31—41no—
417D4×C31—41no—
418D4×C31—41no—
419D4×C31—81no—
420D4×C31—82no—
421D4×C31—82no—
422D4×C31—82no—
423D4×C31—82no—
424D4×C31#12112yes—
425C2×C4×C31—21no—
426C2×C4×C31—21no—
427C2×C4×C31—21no—
428C2×C4×C31—21no—
429C2×C4×C31—21no—
430C2×C4×C31—21no—
431C2×C4×C31—21no—
432C2×C4×C31—21no—
433C2×C4×C31—21no—
434C2×C4×C31—22no—
435C2×C4×C31—21no—
436C2×C4×C31—21no—
437C2×C4×C31—22no—
438C2×C4×C31—21no—
439C2×C4×C31—22no—
440C2×C4×C31—21no—
441C2×C4×C31—21no—
442C2×C4×C31—21no—
443C2×C4×C31—22no—
444C2×C4×C31—42no—
445C2×C4×C31—42no—
446C2×C4×C31—42no—
447C2×C4×C31—44no—
448C2×C4×C31—41no—
449C2×C4×C31—41no—
450C2×C4×C31—41no—
451C2×C4×C31—41no—
452C2×C4×C31—41no—
453C2×C4×C31—41no—
454C2×C4×C31—42no—
455C2×C4×C31—41no—
456C2×C4×C31—42no—
457C2×C4×C31—41no—
458C2×C4×C31—41no—
459C2×C4×C31—41no—
460C2×C4×C31—41no—
461C2×C4×C31—41no—
462C2×C4×C31—41no—
463C2×C4×C31—82no—
464C2×C4×C31#12011yescharacteristic
465C2×C4×C31#12011yescharacteristic
466C2×C4×C31C22×D411yescharacteristic
467C2×C4×C31C22×D411yescharacteristic
468C2×C4×C31C22×D411yescharacteristic
469C2×C4×C31C2×#4111yescharacteristic
470C2×C4×C31H(5,𝔽2)11yescharacteristic
471C2×C4×C31H(5,𝔽2)11yescharacteristic
472C8×C31—22no—
473C8×C31—41no—
474C8×C31—41no—
475C8×C31—41no—
476#3488C2×C3111yescharacteristic
477#3056C2×C3111yescharacteristic, complemented
478C2×#455C2×C3111yescharacteristic, complemented
479#3007C2×C3111yescharacteristic, complemented
480C2×#421C2×C3111yescharacteristic, complemented
481#2620C2×C3111yescharacteristic, complemented
482#2039C2×C3111yescharacteristic, complemented
483#2037C2×C3111yescharacteristic, complemented
484#2007C2×C3111yescharacteristic, complemented
485#2004C2×C3111yescharacteristic, complemented
486#1900C2×C3111yescharacteristic, complemented
487#1897C2×C3111yescharacteristic, complemented
488#1882C2×C3111yescharacteristic, complemented
489#1859C2×C3111yescharacteristic, complemented
490#1792C2×C3111yescharacteristic, complemented
491C22×C31—21no—
492C22×C31—21no—
493C22×C31—21no—
494C22×C31—21no—
495C22×C31—22no—
496C22×C31—21no—
497C22×C31—21no—
498C22×C31—21no—
499C22×C31—21no—
500C22×C31—41no—
501C22×C31—41no—
502C22×C31—41no—
503C22×C31—41no—
504C22×C31—42no—
505C22×C31—42no—
506C22×C31—41no—
507C22×C31—41no—
508C22×C31—41no—
509C22×C31—42no—
510C22×C31—41no—
511C22×C31—81no—
512C22×C31—81no—
513C22×C31—82no—
514C22×C31—82no—
515C22×C31—84no—
516C22×C31—164no—
517C22×C31C2×#12011yescharacteristic
518C22×C31D4211yescharacteristic
519C22×C31#54611yescharacteristic
520C4×C31—21no—
521C4×C31—21no—
522C4×C31—22no—
523C4×C31—42no—
524C4×C31—41no—
525C4×C31—41no—
526C4×C31—42no—
527C4×C31—41no—
528C4×C31—41no—
529C4×C31—81no—
530C4×C31—81no—
531C4×C31—81no—
532C4×C31C2×#12111yescharacteristic
533C4×C31#53411yescharacteristic
534C4×C31D4211yescharacteristic
535C4×C31#54611yescharacteristic
536C2×H(5,𝔽2)C22×C3111yescharacteristic
537C22×#41C22×C3111yescharacteristic
538C2×#137C22×C3111yescharacteristic
539C2×#137C22×C3111yescharacteristic, complemented
540C2×#137C22×C3111yescharacteristic, complemented
541C22×M16C22×C3111yescharacteristic, complemented
542#550—21no—
543#548—21no—
544#546—21no—
545#546—22no—
546D42—22no—
547D42—21no—
548#537—21no—
549#537C22×C3111yescharacteristic
550#535—21no—
551#535C22×C3111yescharacteristic
552C2×#124C22×C3111yescharacteristic, complemented
553#525—21no—
554#525C22×C3111yescharacteristic
555C2×C22⋊Q8C22×C3111yescharacteristic, complemented
556C2×#121—21no—
557C2×#121C22×C3111yescharacteristic
558#520C22×C3111yescharacteristic
559C2×#117C22×C3111yescharacteristic, complemented
560#470—21no—
561#468—21no—
562#467—21no—
563#465—21no—
564#455—24no—
565#452—21no—
566#452—21no—
567#451—21no—
568#450—21no—
569#428C22×C3111yescharacteristic, complemented
570#421—24no—
571C2×#104C22×C3111yescharacteristic
572C2×#104C22×C3111yescharacteristic
573C2×#104C22×C3111yescharacteristic, complemented
574C2×#104C22×C3111yescharacteristic, complemented
575C2×#104C22×C3111yescharacteristic, complemented
576C2×#104C22×C3111yescharacteristic, complemented
577#419C22×C3111yescharacteristic, complemented
578#417C22×C3111yescharacteristic
579#417C22×C3111yescharacteristic, complemented
580#417C22×C3111yescharacteristic, complemented
581C2×#100C22×C3111yescharacteristic, complemented
582C2×#100C22×C3111yescharacteristic, complemented
583#407C22×C3111yescharacteristic, complemented
584#396—22no—
585#394—22no—
586#391C22×C3111yescharacteristic, complemented
587#390C22×C3111yescharacteristic, complemented
588#384C22×C3111yescharacteristic, complemented
589#343C22×C3111yescharacteristic, complemented
590#343C22×C3111yescharacteristic, complemented
591#339C22×C3111yescharacteristic, complemented
592#339C22×C3111yescharacteristic, complemented
593C2×C31—21no—
594C2×C31—21no—
595C2×C31—41no—
596C2×C31—41no—
597C2×C31—42no—
598C2×C31—81no—
599C2×C31—82no—
600C2×C31—81no—
601C2×C31#241011yescharacteristic
602C2×C31#301911yescharacteristic
603C2×C31#302211yescharacteristic
604H(5,𝔽2)—22no—
605H(5,𝔽2)—22no—
606H(5,𝔽2)—41no—
607H(5,𝔽2)—41no—
608C2×#41—21no—
609C2×#41—21no—
610C2×#41—21no—
611C2×#41—21no—
612C2×#41—22no—
613C2×#41—22no—
614C2×#41—41no—
615C2×#41—41no—
616C2×#41D4×C3111yescharacteristic
617C2×#41D4×C3111yescharacteristic
618C2×#41C23×C3111yescharacteristic
619C2×#41C23×C3111yescharacteristic
620C2×#41C23×C3111yescharacteristic
621C22×Q8D4×C3111yescharacteristic
622C22×Q8C23×C3111yescharacteristic
623C22×D4—21no—
624C22×D4—22no—
625C22×D4—22no—
626C22×D4—21no—
627C22×D4—21no—
628C22×D4D4×C3111yescharacteristic
629C22×D4D4×C3112yes—
630C22×D4C23×C3111yescharacteristic
631C23×C4—21no—
632C23×C4C23×C3111yescharacteristic
633#137—22no—
634#137—22no—
635#137—22no—
636#137—41no—
637#137—41no—
638#137—41no—
639C2×Q16—21no—
640C2×Q16—21no—
641C2×Q16—21no—
642C2×SD16—21no—
643C2×SD16—21no—
644C2×SD16—21no—
645C2×M16—21no—
646C2×M16—22no—
647C2×M16—41no—
648C2×M16C23×C3111yescharacteristic
649C2×M16C23×C3111yescharacteristic
650C2×M16C23×C3111yescharacteristic
651C2×M16C23×C3111yescharacteristic
652C22×C8—21no—
653#127—22no—
654#127—21no—
655#124—22no—
656#124—21no—
657#124—22no—
658#124—41no—
659#123—22no—
660#123—21no—
661C22⋊Q8—22no—
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—22no—
674#121—22no—
675#121—21no—
676#121—21no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121—22no—
682#121—21no—
683#121—21no—
684#121D4×C3111yescharacteristic
685#121D4×C3111yescharacteristic
686#120—22no—
687#120—22no—
688#120—22no—
689#120—21no—
690#120—22no—
691C4×Q8—21no—
692C4×D4—22no—
693C4×D4—22no—
694C4×D4—21no—
695C4×D4—22no—
696C4×D4—21no—
697C4×D4—21no—
698#117—21no—
699#117—22no—
700#117—41no—
701#117C23×C3111yescharacteristic
702C2×C4⋊C4—21no—
703C2×C4⋊C4—21no—
704C2×C4⋊C4—21no—
705C2×C4⋊C4—22no—
706C2×C4⋊C4C23×C3111yescharacteristic
707C2×C4⋊C4C23×C3111yescharacteristic
708C2×C22⋊C4—22no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4D4×C3112yes—
714C2×C42C23×C3111yescharacteristic
715C2×C42C23×C3111yescharacteristic
716#107—21no—
717#106—21no—
718#104—22no—
719#104—22no—
720#104—22no—
721#104—22no—
722#104—41no—
723#104D4×C3114yescomplemented
724#103—21no—
725#103—21no—
726#103—21no—
727#103—21no—
728#103—21no—
729#102—21no—
730#102—21no—
731#102—21no—
732#100—22no—
733#100—41no—
734C22⋊C8—21no—
735C22⋊C8—21no—
736#95—22no—
737C31#2447111yescharacteristic, direct product factor, Sylow
738C24—22no—
739C24—21no—
740C24C2×D4×C3112yes—
741C24C2×D4×C3111yescharacteristic
742#41—21no—
743#41—21no—
744#41—22no—
745#41—22no—
746#41—21no—
747#41—21no—
748#41—21no—
749#41—21no—
750#41—21no—
751#41—21no—
752#41—21no—
753#41—21no—
754#41—42no—
755#41—42no—
756#41—41no—
757#41—41no—
758#41—42no—
759#41—42no—
760#41—42no—
761#41—42no—
762#41—42no—
763#41—42no—
764#41C2×D4×C3112yes—
765#41#41×C3112yes—
766C2×Q8—21no—
767C2×Q8—22no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—41no—
775C2×Q8C2×D4×C3111yescharacteristic
776C2×Q8C2×D4×C3111yescharacteristic
777C2×Q8C2×D4×C3111yescharacteristic
778C2×D4—21no—
779C2×D4—22no—
780C2×D4—22no—
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—22no—
790C2×D4—22no—
791C2×D4—21no—
792C2×D4—22no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—41no—
801C2×D4—42no—
802C2×D4—42no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—44no—
806C2×D4—44no—
807C2×D4—42no—
808C2×D4—42no—
809C2×D4—82no—
810C2×D4—84no—
811C2×D4C2×D4×C3111yescharacteristic
812C2×D4C2×D4×C3111yescharacteristic
813C2×D4C2×D4×C3111yescharacteristic
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—22no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—22no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4C2×D4×C3111yescharacteristic
833C22×C4C2×D4×C3111yescharacteristic
834C22×C4C2×D4×C3111yescharacteristic
835C22×C4C2×D4×C3111yescharacteristic
836C22×C4C2×D4×C3111yescharacteristic
837C22×C4C2×D4×C3112yes—
838C22×C4C24×C3111yescharacteristic
839Q16—42no—
840Q16—42no—
841Q16—42no—
842SD16—42no—
843SD16—42no—
844SD16—42no—
845M16—21no—
846M16—21no—
847M16—21no—
848M16—21no—
849M16—21no—
850M16—21no—
851M16—21no—
852M16—42no—
853M16C2×D4×C3112yescomplemented
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—42no—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—42no—
868C4⋊C4—41no—
869C4⋊C4—41no—
870C4⋊C4—82no—
871C4⋊C4C2×D4×C3111yescharacteristic
872C4⋊C4C2×D4×C3111yescharacteristic
873C22⋊C4—22no—
874C22⋊C4—22no—
875C22⋊C4—22no—
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—21no—
879C22⋊C4—21no—
880C22⋊C4—21no—
881C22⋊C4—21no—
882C22⋊C4—22no—
883C22⋊C4—22no—
884C22⋊C4—21no—
885C22⋊C4—42no—
886C22⋊C4—44no—
887C22⋊C4—41no—
888C22⋊C4—41no—
889C22⋊C4—82no—
890C42—22no—
891C42—21no—
892C42—21no—
893C42—21no—
894C42—21no—
895C42C2×D4×C3112yescomplemented
896C23—21no—
897C23—21no—
898C23—21no—
899C23—22no—
900C23—21no—
901C23—21no—
902C23—22no—
903C23—22no—
904C23—41no—
905C23—41no—
906C23—42no—
907C23—42no—
908C23—44no—
909C23—42no—
910C23—42no—
911C23—81no—
912C23—82no—
913C23—82no—
914C23C31×#12011yescharacteristic
915C23C31×#12011yescharacteristic
916C23C22×D4×C3111yescharacteristic
917Q8—21no—
918Q8—21no—
919Q8—21no—
920Q8—21no—
921Q8—21no—
922Q8—42no—
923Q8—41no—
924Q8—41no—
925Q8—41no—
926Q8—41no—
927Q8C31×#12112yes—
928D4—22no—
929D4—22no—
930D4—21no—
931D4—21no—
932D4—21no—
933D4—21no—
934D4—21no—
935D4—42no—
936D4—42no—
937D4—44no—
938D4—42no—
939D4—44no—
940D4—44no—
941D4—42no—
942D4—41no—
943D4—41no—
944D4—41no—
945D4—41no—
946D4—41no—
947D4—41no—
948D4—41no—
949D4—41no—
950D4—81no—
951D4—82no—
952D4—82no—
953D4—82no—
954D4—82no—
955D4C31×#12112yes—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—22no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—22no—
969C2×C4—21no—
970C2×C4—22no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—42no—
976C2×C4—42no—
977C2×C4—42no—
978C2×C4—44no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—42no—
986C2×C4—41no—
987C2×C4—42no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—82no—
995C2×C4C31×#12011yescharacteristic
996C2×C4C31×#12011yescharacteristic
997C2×C4C22×D4×C3111yescharacteristic
998C2×C4C22×D4×C3111yescharacteristic
999C2×C4C22×D4×C3111yescharacteristic
1000C2×C4C2×#41×C3111yescharacteristic
1001C2×C4C31×H(5,𝔽2)11yescharacteristic
1002C2×C4C31×H(5,𝔽2)11yescharacteristic
1003C8—22no—
1004C8—41no—
1005C8—41no—
1006C8—41no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—22no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—21no—
1016C22—41no—
1017C22—41no—
1018C22—41no—
1019C22—41no—
1020C22—42no—
1021C22—42no—
1022C22—41no—
1023C22—41no—
1024C22—41no—
1025C22—42no—
1026C22—41no—
1027C22—81no—
1028C22—81no—
1029C22—82no—
1030C22—82no—
1031C22—84no—
1032C22—164no—
1033C22C2×C31×#12011yescharacteristic
1034C22D42×C3111yescharacteristic
1035C22C31×#54611yescharacteristic
1036C4—21no—
1037C4—21no—
1038C4—22no—
1039C4—42no—
1040C4—41no—
1041C4—41no—
1042C4—42no—
1043C4—41no—
1044C4—41no—
1045C4—81no—
1046C4—81no—
1047C4—81no—
1048C4C2×C31×#12111yescharacteristic
1049C4C31×#53411yescharacteristic
1050C4D42×C3111yescharacteristic
1051C4C31×#54611yescharacteristic
1052C2—21no—
1053C2—21no—
1054C2—41no—
1055C2—41no—
1056C2—42no—
1057C2—81no—
1058C2—82no—
1059C2—81no—
1060C2C31×#241011yescharacteristic
1061C2C31×#301911yescharacteristic
1062C2C31×#302211yescharacteristic
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×#3056C2semidirect
3. C2×C31×#455C2semidirect
4. C31×#3007C2semidirect
5. C2×C31×#421C2semidirect
6. C31×#2620C2semidirect
7. C31×#2039C2semidirect
8. C31×#2037C2semidirect
9. C31×#2007C2semidirect
10. C31×#2004C2semidirect
11. C31×#1900C2semidirect
12. C31×#1897C2semidirect
13. C31×#1882C2semidirect
14. C31×#1859C2semidirect
15. C31×#1792C2semidirect
19. C2×C31×#137C22semidirect
20. C2×C31×#137C22semidirect
21. C22×M16×C31C22semidirect
32. C2×C31×#124C22semidirect
35. C2×C31×C22⋊Q8C22semidirect
39. C2×C31×#117C22semidirect
49. C31×#428C22semidirect
53. C2×C31×#104C22semidirect
54. C2×C31×#104C22semidirect
55. C2×C31×#104C22semidirect
56. C2×C31×#104C22semidirect
57. C31×#419C22semidirect
59. C31×#417C22semidirect
60. C31×#417C22semidirect
61. C2×C31×#100C22semidirect
62. C2×C31×#100C22semidirect
63. C31×#407C22semidirect
66. C31×#391C22semidirect
67. C31×#390C22semidirect
68. C31×#384C22semidirect
69. C31×#343C22semidirect
70. C31×#343C22semidirect
71. C31×#339C22semidirect
72. C31×#339C22semidirect
192. C31×#104D4semidirect
321. M16×C31C2×D4semidirect
363. C42×C31C2×D4semidirect
364. #24471C31direct (N × H)
477. #3056C2×C31semidirect
478. C2×#455C2×C31semidirect
479. #3007C2×C31semidirect
480. C2×#421C2×C31semidirect
481. #2620C2×C31semidirect
482. #2039C2×C31semidirect
483. #2037C2×C31semidirect
484. #2007C2×C31semidirect
485. #2004C2×C31semidirect
486. #1900C2×C31semidirect
487. #1897C2×C31semidirect
488. #1882C2×C31semidirect
489. #1859C2×C31semidirect
490. #1792C2×C31semidirect
539. C2×#137C22×C31semidirect
540. C2×#137C22×C31semidirect
541. C22×M16C22×C31semidirect
552. C2×#124C22×C31semidirect
555. C2×C22⋊Q8C22×C31semidirect
559. C2×#117C22×C31semidirect
569. #428C22×C31semidirect
573. C2×#104C22×C31semidirect
574. C2×#104C22×C31semidirect
575. C2×#104C22×C31semidirect
576. C2×#104C22×C31semidirect
577. #419C22×C31semidirect
579. #417C22×C31semidirect
580. #417C22×C31semidirect
581. C2×#100C22×C31semidirect
582. C2×#100C22×C31semidirect
583. #407C22×C31semidirect
586. #391C22×C31semidirect
587. #390C22×C31semidirect
588. #384C22×C31semidirect
589. #343C22×C31semidirect
590. #343C22×C31semidirect
591. #339C22×C31semidirect
592. #339C22×C31semidirect
723. #104D4×C31semidirect
737. C31#24471direct (N × H)
853. M16C2×D4×C31semidirect
895. C42C2×D4×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#34882
C31×#30562
C2×C31×#4552
C31×#30072
C2×C31×#4212
C31×#26202
C31×#20392
C31×#20372
C31×#20072
C31×#20042
C31×#19002
C31×#18972
C31×#18822
C31×#18592
C31×#17922
#2447131