Finite Group Databasebeta

← C31×#24467 #21481226

Subgroups — C31×#24467 #21481226

Order 7936.

1486 conjugacy classes of subgroups.

The subgroup lattice has 1068 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
5C22×C31×#104C211yesmaximal, characteristic, complemented
6C31×#2850C211yesmaximal, characteristic, complemented
7C31×#2040C211yesmaximal, characteristic, complemented
8C31×#2037C211yesmaximal, characteristic, complemented
9C31×#2007C211yesmaximal, characteristic, complemented
10C31×#2004C211yesmaximal, characteristic, complemented
11C31×#1900C211yesmaximal, characteristic, complemented
12C31×#1896C211yesmaximal, characteristic, complemented
13C31×#1882C211yesmaximal, characteristic, complemented
14C31×#1860C211yesmaximal, 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
39C22×C42×C31C2211yescharacteristic, 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
50C2×C31×#104—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×#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×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×C31—21no—
102C23×C4×C31C2311yescharacteristic
103C31×#137—22no—
104C31×#137—22no—
105C31×#137—22no—
106C31×#137—41no—
107C31×#137—41no—
108C31×#137—41no—
109C2×Q16×C31—21no—
110C2×Q16×C31—21no—
111C2×Q16×C31—21no—
112C2×SD16×C31—21no—
113C2×SD16×C31—21no—
114C2×SD16×C31—21no—
115C2×M16×C31—21no—
116C2×M16×C31—22no—
117C2×M16×C31—41no—
118C2×M16×C31C2311yescharacteristic
119C2×M16×C31C2311yescharacteristic
120C2×M16×C31C2311yescharacteristic
121C2×M16×C31C2311yescharacteristic
122C22×C8×C31—21no—
123C31×#127—22no—
124C31×#127—21no—
125C31×#124—22no—
126C31×#124—21no—
127C31×#124—22no—
128C31×#124—41no—
129C31×#123—22no—
130C31×#123—21no—
131C31×C22⋊Q8—22no—
132C31×C22⋊Q8—21no—
133C31×C22⋊Q8—21no—
134C31×C22⋊Q8—21no—
135C31×C22⋊Q8—21no—
136C31×C22⋊Q8—21no—
137C31×C22⋊Q8—21no—
138C31×C22⋊Q8D411yescharacteristic
139C31×C22⋊Q8D411yescharacteristic
140C31×#121—22no—
141C31×#121—22no—
142C31×#121—22no—
143C31×#121—22no—
144C31×#121—22no—
145C31×#121—21no—
146C31×#121—21no—
147C31×#121—21no—
148C31×#121—21no—
149C31×#121—21no—
150C31×#121—21no—
151C31×#121—22no—
152C31×#121—21no—
153C31×#121—21no—
154C31×#121D411yescharacteristic
155C31×#121D411yescharacteristic
156C31×#120—22no—
157C31×#120—22no—
158C31×#120—22no—
159C31×#120—21no—
160C31×#120—22no—
161C4×Q8×C31—21no—
162C4×D4×C31—22no—
163C4×D4×C31—22no—
164C4×D4×C31—21no—
165C4×D4×C31—22no—
166C4×D4×C31—21no—
167C4×D4×C31—21no—
168C31×#117—21no—
169C31×#117C2311yescharacteristic
170C2×C4⋊C4×C31—21no—
171C2×C4⋊C4×C31—21no—
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×#103—21no—
196C31×#103—21no—
197C31×#102—21no—
198C31×#102—21no—
199C31×#102—21no—
200C31×#100—22no—
201C31×#100—41no—
202C31×C22⋊C8—21no—
203C31×C22⋊C8—21no—
204C31×#95—22no—
205C31×#95—22no—
206C24×C31—22no—
207C24×C31—21no—
208C24×C31C2×D411yescharacteristic
209C24×C31C2×D412yes—
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—44no—
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—21no—
291C22×C4×C31—22no—
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×C31—42no—
301C22×C4×C31—42no—
302C22×C4×C31—42no—
303C22×C4×C31C2×D411yescharacteristic
304C22×C4×C31C2×D411yescharacteristic
305C22×C4×C31C2×D411yescharacteristic
306C22×C4×C31C2×D411yescharacteristic
307C22×C4×C31C2×D411yescharacteristic
308C22×C4×C31C2×D412yes—
309C22×C4×C31C2411yescharacteristic
310Q16×C31—42no—
311Q16×C31—42no—
312Q16×C31—42no—
313SD16×C31—42no—
314SD16×C31—42no—
315SD16×C31—42no—
316M16×C31—21no—
317M16×C31—21no—
318M16×C31—21no—
319M16×C31—21no—
320M16×C31—21no—
321M16×C31—21no—
322M16×C31—21no—
323M16×C31—42no—
324M16×C31C2×D412yescomplemented
325C2×C8×C31—21no—
326C2×C8×C31—21no—
327C2×C8×C31—21no—
328C2×C8×C31—21no—
329C2×C8×C31—42no—
330C4⋊C4×C31—22no—
331C4⋊C4×C31—22no—
332C4⋊C4×C31—21no—
333C4⋊C4×C31—21no—
334C4⋊C4×C31—21no—
335C4⋊C4×C31—21no—
336C4⋊C4×C31—21no—
337C4⋊C4×C31—21no—
338C4⋊C4×C31—41no—
339C4⋊C4×C31—41no—
340C4⋊C4×C31C2×D411yescharacteristic
341C4⋊C4×C31C2×D411yescharacteristic
342C22⋊C4×C31—22no—
343C22⋊C4×C31—22no—
344C22⋊C4×C31—22no—
345C22⋊C4×C31—22no—
346C22⋊C4×C31—22no—
347C22⋊C4×C31—21no—
348C22⋊C4×C31—21no—
349C22⋊C4×C31—21no—
350C22⋊C4×C31—21no—
351C22⋊C4×C31—22no—
352C22⋊C4×C31—22no—
353C22⋊C4×C31—21no—
354C22⋊C4×C31—44no—
355C22⋊C4×C31—44no—
356C22⋊C4×C31—41no—
357C22⋊C4×C31—41no—
358C42×C31—22no—
359C42×C31—21no—
360C42×C31—21no—
361C42×C31—21no—
362C42×C31—21no—
363C42×C31—42no—
364C42×C31C2×D412yescomplemented
365#24467C3111yesmaximal, characteristic, direct product factor, Sylow
366C23×C31—21no—
367C23×C31—21no—
368C23×C31—21no—
369C23×C31—22no—
370C23×C31—22no—
371C23×C31—21no—
372C23×C31—21no—
373C23×C31—22no—
374C23×C31—22no—
375C23×C31—41no—
376C23×C31—42no—
377C23×C31—44no—
378C23×C31—42no—
379C23×C31—42no—
380C23×C31—42no—
381C23×C31—81no—
382C23×C31—82no—
383C23×C31—82no—
384C23×C31#12011yescharacteristic
385C23×C31#12011yescharacteristic
386C23×C31C22×D411yescharacteristic
387Q8×C31—21no—
388Q8×C31—21no—
389Q8×C31—21no—
390Q8×C31—21no—
391Q8×C31—21no—
392Q8×C31—42no—
393Q8×C31—41no—
394Q8×C31—41no—
395Q8×C31—41no—
396Q8×C31—41no—
397Q8×C31#12112yes—
398D4×C31—22no—
399D4×C31—22no—
400D4×C31—21no—
401D4×C31—21no—
402D4×C31—21no—
403D4×C31—21no—
404D4×C31—21no—
405D4×C31—42no—
406D4×C31—42no—
407D4×C31—44no—
408D4×C31—42no—
409D4×C31—44no—
410D4×C31—41no—
411D4×C31—41no—
412D4×C31—41no—
413D4×C31—41no—
414D4×C31—44no—
415D4×C31—42no—
416D4×C31—41no—
417D4×C31—41no—
418D4×C31—41no—
419D4×C31—41no—
420D4×C31—81no—
421D4×C31—82no—
422D4×C31—82no—
423D4×C31—82no—
424D4×C31—82no—
425D4×C31#12112yes—
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—21no—
435C2×C4×C31—22no—
436C2×C4×C31—21no—
437C2×C4×C31—21no—
438C2×C4×C31—22no—
439C2×C4×C31—22no—
440C2×C4×C31—21no—
441C2×C4×C31—22no—
442C2×C4×C31—21no—
443C2×C4×C31—21no—
444C2×C4×C31—21no—
445C2×C4×C31—22no—
446C2×C4×C31—42no—
447C2×C4×C31—42no—
448C2×C4×C31—42no—
449C2×C4×C31—44no—
450C2×C4×C31—41no—
451C2×C4×C31—41no—
452C2×C4×C31—41no—
453C2×C4×C31—48no—
454C2×C4×C31—41no—
455C2×C4×C31—41no—
456C2×C4×C31—41no—
457C2×C4×C31—41no—
458C2×C4×C31—41no—
459C2×C4×C31—42no—
460C2×C4×C31—42no—
461C2×C4×C31—41no—
462C2×C4×C31—41no—
463C2×C4×C31—41no—
464C2×C4×C31—41no—
465C2×C4×C31—82no—
466C2×C4×C31#12011yescharacteristic
467C2×C4×C31#12011yescharacteristic
468C2×C4×C31C22×D411yescharacteristic
469C2×C4×C31C22×D411yescharacteristic
470C2×C4×C31C22×D411yescharacteristic
471C2×C4×C31C2×#4111yescharacteristic
472C2×C4×C31H(5,𝔽2)11yescharacteristic
473C2×C4×C31H(5,𝔽2)11yescharacteristic
474C8×C31—22no—
475C8×C31—41no—
476C8×C31—41no—
477C8×C31—41no—
478#3488C2×C3111yescharacteristic
479#3056C2×C3111yescharacteristic, complemented
480C2×#455C2×C3111yescharacteristic, complemented
481#3007C2×C3111yescharacteristic, complemented
482C22×#104C2×C3111yescharacteristic, complemented
483#2850C2×C3111yescharacteristic, complemented
484#2040C2×C3111yescharacteristic, complemented
485#2037C2×C3111yescharacteristic, complemented
486#2007C2×C3111yescharacteristic, complemented
487#2004C2×C3111yescharacteristic, complemented
488#1900C2×C3111yescharacteristic, complemented
489#1896C2×C3111yescharacteristic, complemented
490#1882C2×C3111yescharacteristic, complemented
491#1860C2×C3111yescharacteristic, complemented
492#1792C2×C3111yescharacteristic, complemented
493C22×C31—21no—
494C22×C31—21no—
495C22×C31—21no—
496C22×C31—21no—
497C22×C31—21no—
498C22×C31—22no—
499C22×C31—21no—
500C22×C31—21no—
501C22×C31—42no—
502C22×C31—42no—
503C22×C31—41no—
504C22×C31—41no—
505C22×C31—41no—
506C22×C31—41no—
507C22×C31—42no—
508C22×C31—42no—
509C22×C31—41no—
510C22×C31—41no—
511C22×C31—41no—
512C22×C31—42no—
513C22×C31—41no—
514C22×C31—84no—
515C22×C31—82no—
516C22×C31—82no—
517C22×C31—164no—
518C22×C31#45512yescomplemented
519C22×C31C2×#12011yescharacteristic
520C22×C31D4211yescharacteristic
521C22×C31#54611yescharacteristic
522C4×C31—21no—
523C4×C31—21no—
524C4×C31—22no—
525C4×C31—42no—
526C4×C31—42no—
527C4×C31—41no—
528C4×C31—41no—
529C4×C31—42no—
530C4×C31—41no—
531C4×C31—41no—
532C4×C31—81no—
533C4×C31—81no—
534C4×C31C2×#12111yescharacteristic
535C4×C31#53411yescharacteristic
536C4×C31D4211yescharacteristic
537C4×C31#54611yescharacteristic
538C2×H(5,𝔽2)C22×C3111yescharacteristic
539C22×#41C22×C3111yescharacteristic
540C2×#137C22×C3111yescharacteristic
541C2×#137C22×C3111yescharacteristic, complemented
542C2×#137C22×C3111yescharacteristic, complemented
543C22×M16C22×C3111yescharacteristic, complemented
544#550—21no—
545#548—21no—
546#546—21no—
547#546—22no—
548D42—22no—
549D42—21no—
550#537—21no—
551#537C22×C3111yescharacteristic
552#535—21no—
553#535C22×C3111yescharacteristic
554C2×#124C22×C3111yescharacteristic, complemented
555#525—21no—
556#525C22×C3111yescharacteristic
557C2×C22⋊Q8C22×C3111yescharacteristic, complemented
558C2×#121—21no—
559C2×#121C22×C3111yescharacteristic
560#520C22×C3111yescharacteristic
561C22×C42C22×C3111yescharacteristic, complemented
562#470—21no—
563#468—21no—
564#467—21no—
565#465—21no—
566#455—24no—
567#452—21no—
568#452—21no—
569#451—21no—
570#450—21no—
571#428C22×C3111yescharacteristic, complemented
572C2×#104—24no—
573C2×#104C22×C3111yescharacteristic
574C2×#104C22×C3111yescharacteristic
575C2×#104C22×C3111yescharacteristic, complemented
576C2×#104C22×C3111yescharacteristic, complemented
577C2×#104C22×C3111yescharacteristic, complemented
578C2×#104C22×C3111yescharacteristic, complemented
579#419C22×C3111yescharacteristic, complemented
580#417C22×C3111yescharacteristic
581#417C22×C3111yescharacteristic, complemented
582#417C22×C3111yescharacteristic, complemented
583C2×#100C22×C3111yescharacteristic, complemented
584C2×#100C22×C3111yescharacteristic, complemented
585#407C22×C3111yescharacteristic, complemented
586#391C22×C3111yescharacteristic, complemented
587#390C22×C3111yescharacteristic, complemented
588#388—22no—
589#386—22no—
590#382C22×C3111yescharacteristic, complemented
591#343C22×C3111yescharacteristic, complemented
592#343C22×C3111yescharacteristic, complemented
593#339C22×C3111yescharacteristic, complemented
594#339C22×C3111yescharacteristic, complemented
595C2×C31—21no—
596C2×C31—21no—
597C2×C31—22no—
598C2×C31—41no—
599C2×C31—42no—
600C2×C31—81no—
601C2×C31—82no—
602C2×C31—81no—
603C2×C31#241011yescharacteristic
604C2×C31C2×#45511yescharacteristic
605C2×C31#301811yescharacteristic
606H(5,𝔽2)—22no—
607H(5,𝔽2)—22no—
608H(5,𝔽2)—41no—
609H(5,𝔽2)—41no—
610C2×#41—21no—
611C2×#41—21no—
612C2×#41—21no—
613C2×#41—21no—
614C2×#41—22no—
615C2×#41—22no—
616C2×#41—41no—
617C2×#41—41no—
618C2×#41D4×C3111yescharacteristic
619C2×#41D4×C3111yescharacteristic
620C2×#41C23×C3111yescharacteristic
621C2×#41C23×C3111yescharacteristic
622C2×#41C23×C3111yescharacteristic
623C22×Q8D4×C3111yescharacteristic
624C22×Q8C23×C3111yescharacteristic
625C22×D4—21no—
626C22×D4—22no—
627C22×D4—22no—
628C22×D4—21no—
629C22×D4—21no—
630C22×D4D4×C3111yescharacteristic
631C22×D4D4×C3112yes—
632C22×D4C23×C3111yescharacteristic
633C23×C4—21no—
634C23×C4—21no—
635C23×C4C23×C3111yescharacteristic
636#137—22no—
637#137—22no—
638#137—22no—
639#137—41no—
640#137—41no—
641#137—41no—
642C2×Q16—21no—
643C2×Q16—21no—
644C2×Q16—21no—
645C2×SD16—21no—
646C2×SD16—21no—
647C2×SD16—21no—
648C2×M16—21no—
649C2×M16—22no—
650C2×M16—41no—
651C2×M16C23×C3111yescharacteristic
652C2×M16C23×C3111yescharacteristic
653C2×M16C23×C3111yescharacteristic
654C2×M16C23×C3111yescharacteristic
655C22×C8—21no—
656#127—22no—
657#127—21no—
658#124—22no—
659#124—21no—
660#124—22no—
661#124—41no—
662#123—22no—
663#123—21no—
664C22⋊Q8—22no—
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—22no—
677#121—22no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—21no—
683#121—21no—
684#121—22no—
685#121—21no—
686#121—21no—
687#121D4×C3111yescharacteristic
688#121D4×C3111yescharacteristic
689#120—22no—
690#120—22no—
691#120—22no—
692#120—21no—
693#120—22no—
694C4×Q8—21no—
695C4×D4—22no—
696C4×D4—22no—
697C4×D4—21no—
698C4×D4—22no—
699C4×D4—21no—
700C4×D4—21no—
701#117—21no—
702#117C23×C3111yescharacteristic
703C2×C4⋊C4—21no—
704C2×C4⋊C4—21no—
705C2×C4⋊C4C23×C3111yescharacteristic
706C2×C4⋊C4C23×C3111yescharacteristic
707C2×C22⋊C4—22no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4D4×C3112yes—
712C2×C42—22no—
713C2×C42—21no—
714C2×C42—41no—
715C2×C42C23×C3111yescharacteristic
716C2×C42C23×C3111yescharacteristic
717#107—21no—
718#106—21no—
719#104—22no—
720#104—22no—
721#104—22no—
722#104—22no—
723#104—41no—
724#104D4×C3114yescomplemented
725#103—21no—
726#103—21no—
727#103—21no—
728#103—21no—
729#103—21no—
730#102—21no—
731#102—21no—
732#102—21no—
733#100—22no—
734#100—41no—
735C22⋊C8—21no—
736C22⋊C8—21no—
737#95—22no—
738#95—22no—
739C31#2446711yescharacteristic, direct product factor, Sylow
740C24—22no—
741C24—21no—
742C24C2×D4×C3111yescharacteristic
743C24C2×D4×C3112yes—
744#41—21no—
745#41—21no—
746#41—22no—
747#41—22no—
748#41—21no—
749#41—21no—
750#41—21no—
751#41—21no—
752#41—21no—
753#41—21no—
754#41—21no—
755#41—21no—
756#41—42no—
757#41—42no—
758#41—41no—
759#41—41no—
760#41—42no—
761#41—42no—
762#41—42no—
763#41—42no—
764#41—42no—
765#41—42no—
766#41C2×D4×C3112yes—
767#41#41×C3112yes—
768C2×Q8—21no—
769C2×Q8—22no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—21no—
775C2×Q8—21no—
776C2×Q8—41no—
777C2×Q8C2×D4×C3111yescharacteristic
778C2×Q8C2×D4×C3111yescharacteristic
779C2×Q8C2×D4×C3111yescharacteristic
780C2×D4—21no—
781C2×D4—22no—
782C2×D4—22no—
783C2×D4—22no—
784C2×D4—22no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—22no—
791C2×D4—22no—
792C2×D4—22no—
793C2×D4—21no—
794C2×D4—22no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—41no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—42no—
806C2×D4—42no—
807C2×D4—44no—
808C2×D4—44no—
809C2×D4—42no—
810C2×D4—42no—
811C2×D4—44no—
812C2×D4—84no—
813C2×D4C2×D4×C3111yescharacteristic
814C2×D4C2×D4×C3111yescharacteristic
815C2×D4C2×D4×C3111yescharacteristic
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—22no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—22no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4—42no—
836C22×C4—42no—
837C22×C4C2×D4×C3111yescharacteristic
838C22×C4C2×D4×C3111yescharacteristic
839C22×C4C2×D4×C3111yescharacteristic
840C22×C4C2×D4×C3111yescharacteristic
841C22×C4C2×D4×C3111yescharacteristic
842C22×C4C2×D4×C3112yes—
843C22×C4C24×C3111yescharacteristic
844Q16—42no—
845Q16—42no—
846Q16—42no—
847SD16—42no—
848SD16—42no—
849SD16—42no—
850M16—21no—
851M16—21no—
852M16—21no—
853M16—21no—
854M16—21no—
855M16—21no—
856M16—21no—
857M16—42no—
858M16C2×D4×C3112yescomplemented
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—42no—
864C4⋊C4—22no—
865C4⋊C4—22no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—41no—
873C4⋊C4—41no—
874C4⋊C4C2×D4×C3111yescharacteristic
875C4⋊C4C2×D4×C3111yescharacteristic
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—22no—
879C22⋊C4—22no—
880C22⋊C4—22no—
881C22⋊C4—21no—
882C22⋊C4—21no—
883C22⋊C4—21no—
884C22⋊C4—21no—
885C22⋊C4—22no—
886C22⋊C4—22no—
887C22⋊C4—21no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—41no—
891C22⋊C4—41no—
892C42—22no—
893C42—21no—
894C42—21no—
895C42—21no—
896C42—21no—
897C42—42no—
898C42C2×D4×C3112yescomplemented
899C23—22no—
900C23—21no—
901C23—21no—
902C23—21no—
903C23—22no—
904C23—21no—
905C23—21no—
906C23—22no—
907C23—22no—
908C23—41no—
909C23—42no—
910C23—44no—
911C23—42no—
912C23—42no—
913C23—42no—
914C23—81no—
915C23—82no—
916C23—82no—
917C23C31×#12011yescharacteristic
918C23C31×#12011yescharacteristic
919C23C22×D4×C3111yescharacteristic
920Q8—21no—
921Q8—21no—
922Q8—21no—
923Q8—21no—
924Q8—21no—
925Q8—42no—
926Q8—41no—
927Q8—41no—
928Q8—41no—
929Q8—41no—
930Q8C31×#12112yes—
931D4—22no—
932D4—22no—
933D4—21no—
934D4—21no—
935D4—21no—
936D4—21no—
937D4—21no—
938D4—42no—
939D4—42no—
940D4—44no—
941D4—42no—
942D4—44no—
943D4—44no—
944D4—42no—
945D4—41no—
946D4—41no—
947D4—41no—
948D4—41no—
949D4—41no—
950D4—41no—
951D4—41no—
952D4—41no—
953D4—81no—
954D4—82no—
955D4—82no—
956D4—82no—
957D4—82no—
958D4C31×#12112yes—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—22no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—22no—
979C2×C4—42no—
980C2×C4—42no—
981C2×C4—42no—
982C2×C4—44no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—48no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—42no—
993C2×C4—42no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—82no—
999C2×C4C31×#12011yescharacteristic
1000C2×C4C31×#12011yescharacteristic
1001C2×C4C22×D4×C3111yescharacteristic
1002C2×C4C22×D4×C3111yescharacteristic
1003C2×C4C22×D4×C3111yescharacteristic
1004C2×C4C2×#41×C3111yescharacteristic
1005C2×C4C31×H(5,𝔽2)11yescharacteristic
1006C2×C4C31×H(5,𝔽2)11yescharacteristic
1007C8—22no—
1008C8—41no—
1009C8—41no—
1010C8—41no—
1011C22—21no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—21no—
1016C22—22no—
1017C22—21no—
1018C22—21no—
1019C22—42no—
1020C22—42no—
1021C22—41no—
1022C22—41no—
1023C22—41no—
1024C22—41no—
1025C22—42no—
1026C22—42no—
1027C22—41no—
1028C22—41no—
1029C22—41no—
1030C22—42no—
1031C22—41no—
1032C22—84no—
1033C22—82no—
1034C22—82no—
1035C22—164no—
1036C22C31×#45512yescomplemented
1037C22C2×C31×#12011yescharacteristic
1038C22D42×C3111yescharacteristic
1039C22C31×#54611yescharacteristic
1040C4—21no—
1041C4—21no—
1042C4—22no—
1043C4—42no—
1044C4—42no—
1045C4—41no—
1046C4—41no—
1047C4—42no—
1048C4—41no—
1049C4—41no—
1050C4—81no—
1051C4—81no—
1052C4C2×C31×#12111yescharacteristic
1053C4C31×#53411yescharacteristic
1054C4D42×C3111yescharacteristic
1055C4C31×#54611yescharacteristic
1056C2—21no—
1057C2—22no—
1058C2—21no—
1059C2—41no—
1060C2—42no—
1061C2—81no—
1062C2—82no—
1063C2—81no—
1064C2C31×#241011yescharacteristic
1065C2C2×C31×#45511yescharacteristic
1066C2C31×#301811yescharacteristic
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. C22×C31×#104C2semidirect
6. C31×#2850C2semidirect
7. C31×#2040C2semidirect
8. C31×#2037C2semidirect
9. C31×#2007C2semidirect
10. C31×#2004C2semidirect
11. C31×#1900C2semidirect
12. C31×#1896C2semidirect
13. C31×#1882C2semidirect
14. C31×#1860C2semidirect
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. C22×C42×C31C22semidirect
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
64. C31×#391C22semidirect
65. C31×#390C22semidirect
68. C31×#382C22semidirect
69. C31×#343C22semidirect
70. C31×#343C22semidirect
71. C31×#339C22semidirect
72. C31×#339C22semidirect
191. C31×#104D4semidirect
324. M16×C31C2×D4semidirect
364. C42×C31C2×D4semidirect
365. #24467C31direct (N × H)
479. #3056C2×C31semidirect
480. C2×#455C2×C31semidirect
481. #3007C2×C31semidirect
482. C22×#104C2×C31semidirect
483. #2850C2×C31semidirect
484. #2040C2×C31semidirect
485. #2037C2×C31semidirect
486. #2007C2×C31semidirect
487. #2004C2×C31semidirect
488. #1900C2×C31semidirect
489. #1896C2×C31semidirect
490. #1882C2×C31semidirect
491. #1860C2×C31semidirect
492. #1792C2×C31semidirect
518. C22×C31#455semidirect
541. C2×#137C22×C31semidirect
542. C2×#137C22×C31semidirect
543. C22×M16C22×C31semidirect
554. C2×#124C22×C31semidirect
557. C2×C22⋊Q8C22×C31semidirect
561. C22×C42C22×C31semidirect
571. #428C22×C31semidirect
575. C2×#104C22×C31semidirect
576. C2×#104C22×C31semidirect
577. C2×#104C22×C31semidirect
578. C2×#104C22×C31semidirect
579. #419C22×C31semidirect
581. #417C22×C31semidirect
582. #417C22×C31semidirect
583. C2×#100C22×C31semidirect
584. C2×#100C22×C31semidirect
585. #407C22×C31semidirect
586. #391C22×C31semidirect
587. #390C22×C31semidirect
590. #382C22×C31semidirect
591. #343C22×C31semidirect
592. #343C22×C31semidirect
593. #339C22×C31semidirect
594. #339C22×C31semidirect
724. #104D4×C31semidirect
739. C31#24467direct (N × H)
858. M16C2×D4×C31semidirect
898. C42C2×D4×C31semidirect
1036. C22C31×#455semidirect

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
C22×C31×#1042
C31×#28502
C31×#20402
C31×#20372
C31×#20072
C31×#20042
C31×#19002
C31×#18962
C31×#18822
C31×#18602
C31×#17922
#2446731