Finite Group Databasebeta

← C31×#24406 #21481165

Subgroups — C31×#24406 #21481165

Order 7936.

1620 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3485C211yesmaximal, characteristic, complemented
2C2×C31×B(4,𝔽2)C211yesmaximal, characteristic, complemented
3C2×C31×#410C211yesmaximal, characteristic, complemented
4C31×#2411C212yesmaximal, complemented
5C31×#2404C211yesmaximal, characteristic, complemented
6C31×#2044C212yesmaximal, complemented
7C31×#2021C212yesmaximal, complemented
8C31×#1899C212yesmaximal, complemented
9C31×#1889C211yesmaximal, characteristic, complemented
10C31×#1867C211yesmaximal, characteristic, complemented
11C31×#1790C211yesmaximal, characteristic, complemented
12C2×C31×H(5,𝔽2)C2211yescharacteristic
13C22×#41×C31C2211yescharacteristic
14C31×#547—22no—
15C31×#547—22no—
16C31×#546—22no—
17C31×#546—22no—
18C31×#536—21no—
19C31×#534—21no—
20C31×#534C2212yes—
21C31×#525—21no—
22C2×C31×#123—21no—
23C2×C31×#123C2212yes—
24C2×C31×#120C2211yescharacteristic
25C2×C31×#120C2212yes—
26C2×C31×#120C2211yescharacteristic, complemented
27C31×#518C2211yescharacteristic
28C2×C31×#117C2212yescomplemented
29C22×C22⋊C4×C31C2211yescharacteristic, complemented
30C31×B(4,𝔽2)—24no—
31C31×#410—24no—
32C2×C31×#99C2211yescharacteristic
33C2×C31×#99C2212yes—
34C2×C31×#99C2212yes—
35C2×C31×#99C2211yescharacteristic
36C2×C31×#99C2212yescomplemented
37C31×#396—22no—
38C31×#394—22no—
39C31×#393—21no—
40C31×#392—21no—
41C31×#390—22no—
42C31×#388—22no—
43C31×#386—21no—
44C31×#386—21no—
45C31×#386C2211yescharacteristic
46C31×#386C2212yes—
47C31×#386C2211yescharacteristic, complemented
48C31×#385C2212yescomplemented
49C31×#381C2211yescharacteristic, complemented
50C31×#379C2212yescomplemented
51C31×#342C2212yescomplemented
52C31×#342C2212yescomplemented
53C25×C31C2311yescharacteristic
54C31×H(5,𝔽2)—22no—
55C31×H(5,𝔽2)—22no—
56C31×H(5,𝔽2)—42no—
57C2×#41×C31—22no—
58C2×#41×C31—22no—
59C2×#41×C31—21no—
60C2×#41×C31—22no—
61C2×#41×C31—22no—
62C2×#41×C31—22no—
63C2×#41×C31—42no—
64C22×Q8×C31D411yescharacteristic, complemented
65C22×D4×C31—21no—
66C22×D4×C31—22no—
67C22×D4×C31—21no—
68C22×D4×C31—22no—
69C22×D4×C31—21no—
70C22×D4×C31D411yescharacteristic, complemented
71C22×D4×C31C2312yes—
72C22×D4×C31C2311yescharacteristic
73C22×D4×C31C2311yescharacteristic
74C23×C4×C31D411yescharacteristic, complemented
75C23×C4×C31D411yescharacteristic, complemented
76C23×C4×C31C2311yescharacteristic
77C23×C4×C31C2311yescharacteristic
78C31×C4⋊Q8—22no—
79C31×#124—22no—
80C31×#123—22no—
81C31×#123—22no—
82C31×#123—22no—
83C31×#123—22no—
84C31×#123—22no—
85C31×#123—22no—
86C31×#123—22no—
87C31×#123—22no—
88C31×#123—22no—
89C31×C22⋊Q8—21no—
90C31×C22⋊Q8—21no—
91C31×C22⋊Q8—22no—
92C31×C22⋊Q8—22no—
93C31×#121—21no—
94C31×#121—21no—
95C31×#121—22no—
96C31×#121—22no—
97C31×#121—22no—
98C31×#121—22no—
99C31×#120—22no—
100C31×#120—22no—
101C31×#120—22no—
102C31×#120—22no—
103C31×#120—22no—
104C31×#120—24no—
105C31×#120—42no—
106C31×#120—42no—
107C4×D4×C31—22no—
108C4×D4×C31—22no—
109C4×D4×C31—22no—
110C4×D4×C31—22no—
111C31×#117—21no—
112C31×#117—24no—
113C31×#117—42no—
114C2×C4⋊C4×C31—21no—
115C2×C4⋊C4×C31—21no—
116C2×C4⋊C4×C31—22no—
117C2×C4⋊C4×C31—22no—
118C2×C4⋊C4×C31D412yescomplemented
119C2×C4⋊C4×C31D412yescomplemented
120C2×C22⋊C4×C31—21no—
121C2×C22⋊C4×C31—21no—
122C2×C22⋊C4×C31—21no—
123C2×C22⋊C4×C31—22no—
124C2×C22⋊C4×C31—22no—
125C2×C22⋊C4×C31—21no—
126C2×C22⋊C4×C31—22no—
127C2×C22⋊C4×C31—21no—
128C2×C22⋊C4×C31—21no—
129C2×C22⋊C4×C31—21no—
130C2×C22⋊C4×C31—22no—
131C2×C22⋊C4×C31—21no—
132C2×C22⋊C4×C31—21no—
133C2×C22⋊C4×C31—22no—
134C2×C22⋊C4×C31—22no—
135C2×C22⋊C4×C31D412yescomplemented
136C2×C22⋊C4×C31D412yescomplemented
137C2×C22⋊C4×C31C2312yes—
138C2×C22⋊C4×C31C2311yescharacteristic
139C2×C22⋊C4×C31C2311yescharacteristic
140C2×C22⋊C4×C31C2312yes—
141C2×C22⋊C4×C31C2312yes—
142C2×C42×C31—22no—
143C31×#99—22no—
144C31×#99—24no—
145C31×#99—24no—
146C31×#99—42no—
147C31×#99D414yescomplemented
148C31×#95—22no—
149C31×#95—21no—
150C31×#95—21no—
151C31×#95—22no—
152C31×#95—21no—
153C31×#95—21no—
154C24×C31—21no—
155C24×C31—22no—
156C24×C31—21no—
157C24×C31—21no—
158C24×C31—21no—
159C24×C31—22no—
160C24×C31—42no—
161C24×C31—81no—
162C24×C31C2×D412yes—
163C24×C31C2×D411yescharacteristic
164C24×C31C2×D411yescharacteristic
165C24×C31C2411yescharacteristic
166#41×C31—44no—
167#41×C31—44no—
168#41×C31—44no—
169#41×C31—44no—
170#41×C31—44no—
171#41×C31—44no—
172#41×C31—42no—
173#41×C31—42no—
174C2×Q8×C31—21no—
175C2×Q8×C31—22no—
176C2×Q8×C31—22no—
177C2×Q8×C31—41no—
178C2×D4×C31—22no—
179C2×D4×C31—22no—
180C2×D4×C31—22no—
181C2×D4×C31—21no—
182C2×D4×C31—22no—
183C2×D4×C31—21no—
184C2×D4×C31—22no—
185C2×D4×C31—22no—
186C2×D4×C31—22no—
187C2×D4×C31—22no—
188C2×D4×C31—21no—
189C2×D4×C31—22no—
190C2×D4×C31—22no—
191C2×D4×C31—22no—
192C2×D4×C31—22no—
193C2×D4×C31—22no—
194C2×D4×C31—22no—
195C2×D4×C31—22no—
196C2×D4×C31—41no—
197C2×D4×C31—44no—
198C2×D4×C31—44no—
199C2×D4×C31—44no—
200C2×D4×C31—42no—
201C2×D4×C31—42no—
202C2×D4×C31—42no—
203C2×D4×C31—44no—
204C2×D4×C31—42no—
205C2×D4×C31—42no—
206C2×D4×C31—42no—
207C2×D4×C31—82no—
208C2×D4×C31—81no—
209C2×D4×C31—81no—
210C2×D4×C31C2×D412yes—
211C2×D4×C31#4112yes—
212C22×C4×C31—21no—
213C22×C4×C31—21no—
214C22×C4×C31—22no—
215C22×C4×C31—21no—
216C22×C4×C31—22no—
217C22×C4×C31—22no—
218C22×C4×C31—22no—
219C22×C4×C31—21no—
220C22×C4×C31—21no—
221C22×C4×C31—21no—
222C22×C4×C31—21no—
223C22×C4×C31—21no—
224C22×C4×C31—21no—
225C22×C4×C31—22no—
226C22×C4×C31—21no—
227C22×C4×C31—21no—
228C22×C4×C31—21no—
229C22×C4×C31—22no—
230C22×C4×C31—22no—
231C22×C4×C31—41no—
232C22×C4×C31—41no—
233C22×C4×C31—81no—
234C22×C4×C31C2×D412yes—
235C22×C4×C31C2×D411yescharacteristic
236C22×C4×C31C2×D411yescharacteristic
237C22×C4×C31C2×D411yescharacteristic
238C22×C4×C31C2×D412yes—
239C22×C4×C31C2×D412yes—
240C22×C4×C31C2×D411yescharacteristic
241C22×C4×C31C2×D412yes—
242C22×C4×C31C2×D412yes—
243C4⋊C4×C31—22no—
244C4⋊C4×C31—22no—
245C4⋊C4×C31—21no—
246C4⋊C4×C31—21no—
247C4⋊C4×C31—22no—
248C4⋊C4×C31—22no—
249C4⋊C4×C31—22no—
250C4⋊C4×C31—22no—
251C4⋊C4×C31—44no—
252C4⋊C4×C31—82no—
253C22⋊C4×C31—22no—
254C22⋊C4×C31—22no—
255C22⋊C4×C31—22no—
256C22⋊C4×C31—22no—
257C22⋊C4×C31—22no—
258C22⋊C4×C31—22no—
259C22⋊C4×C31—22no—
260C22⋊C4×C31—22no—
261C22⋊C4×C31—22no—
262C22⋊C4×C31—22no—
263C22⋊C4×C31—22no—
264C22⋊C4×C31—22no—
265C22⋊C4×C31—22no—
266C22⋊C4×C31—21no—
267C22⋊C4×C31—21no—
268C22⋊C4×C31—22no—
269C22⋊C4×C31—22no—
270C22⋊C4×C31—44no—
271C22⋊C4×C31—42no—
272C22⋊C4×C31—44no—
273C22⋊C4×C31—41no—
274C22⋊C4×C31—41no—
275C22⋊C4×C31—42no—
276C22⋊C4×C31—42no—
277C22⋊C4×C31—82no—
278C22⋊C4×C31—82no—
279C22⋊C4×C31—81no—
280C22⋊C4×C31—81no—
281C22⋊C4×C31C2×D414yes—
282C42×C31—22no—
283C42×C31—44no—
284#24406C3111yesmaximal, characteristic, direct product factor, Sylow
285C23×C31—21no—
286C23×C31—21no—
287C23×C31—24no—
288C23×C31—22no—
289C23×C31—22no—
290C23×C31—21no—
291C23×C31—21no—
292C23×C31—21no—
293C23×C31—22no—
294C23×C31—22no—
295C23×C31—41no—
296C23×C31—41no—
297C23×C31—41no—
298C23×C31—41no—
299C23×C31—41no—
300C23×C31—41no—
301C23×C31—42no—
302C23×C31—42no—
303C23×C31—41no—
304C23×C31—41no—
305C23×C31—42no—
306C23×C31—41no—
307C23×C31—42no—
308C23×C31—42no—
309C23×C31—42no—
310C23×C31—41no—
311C23×C31—41no—
312C23×C31—41no—
313C23×C31—42no—
314C23×C31—42no—
315C23×C31—82no—
316C23×C31—82no—
317C23×C31—84no—
318C23×C31—81no—
319C23×C31—81no—
320C23×C31#12112yes—
321C23×C31C22×D411yescharacteristic
322C23×C31C22×D412yes—
323C23×C31C22×D411yescharacteristic
324C23×C31C2×#4111yescharacteristic
325C23×C31H(5,𝔽2)12yes—
326Q8×C31—44no—
327Q8×C31—42no—
328D4×C31—24no—
329D4×C31—24no—
330D4×C31—44no—
331D4×C31—42no—
332D4×C31—44no—
333D4×C31—42no—
334D4×C31—42no—
335D4×C31—42no—
336D4×C31—42no—
337D4×C31—42no—
338D4×C31—42no—
339D4×C31—82no—
340D4×C31—82no—
341D4×C31—88no—
342D4×C31—84no—
343D4×C31—84no—
344C2×C4×C31—21no—
345C2×C4×C31—21no—
346C2×C4×C31—21no—
347C2×C4×C31—21no—
348C2×C4×C31—21no—
349C2×C4×C31—21no—
350C2×C4×C31—22no—
351C2×C4×C31—22no—
352C2×C4×C31—22no—
353C2×C4×C31—22no—
354C2×C4×C31—22no—
355C2×C4×C31—22no—
356C2×C4×C31—21no—
357C2×C4×C31—22no—
358C2×C4×C31—21no—
359C2×C4×C31—21no—
360C2×C4×C31—24no—
361C2×C4×C31—22no—
362C2×C4×C31—22no—
363C2×C4×C31—42no—
364C2×C4×C31—42no—
365C2×C4×C31—42no—
366C2×C4×C31—42no—
367C2×C4×C31—44no—
368C2×C4×C31—42no—
369C2×C4×C31—42no—
370C2×C4×C31—42no—
371C2×C4×C31—42no—
372C2×C4×C31—42no—
373C2×C4×C31—42no—
374C2×C4×C31—42no—
375C2×C4×C31—42no—
376C2×C4×C31—41no—
377C2×C4×C31—41no—
378C2×C4×C31—41no—
379C2×C4×C31—41no—
380C2×C4×C31—42no—
381C2×C4×C31—41no—
382C2×C4×C31—41no—
383C2×C4×C31—41no—
384C2×C4×C31—41no—
385C2×C4×C31—41no—
386C2×C4×C31—42no—
387C2×C4×C31—81no—
388C2×C4×C31—81no—
389C2×C4×C31#12011yescharacteristic
390C2×C4×C31#12011yescharacteristic
391C2×C4×C31#12012yes—
392C2×C4×C31#12112yes—
393#3485C2×C3111yescharacteristic, complemented
394C2×B(4,𝔽2)C2×C3111yescharacteristic, complemented
395C2×#410C2×C3111yescharacteristic, complemented
396#2411C2×C3112yescomplemented
397#2404C2×C3111yescharacteristic, complemented
398#2044C2×C3112yescomplemented
399#2021C2×C3112yescomplemented
400#1899C2×C3112yescomplemented
401#1889C2×C3111yescharacteristic, complemented
402#1867C2×C3111yescharacteristic, complemented
403#1790C2×C3111yescharacteristic, complemented
404C22×C31—22no—
405C22×C31—21no—
406C22×C31—22no—
407C22×C31—21no—
408C22×C31—22no—
409C22×C31—41no—
410C22×C31—41no—
411C22×C31—42no—
412C22×C31—42no—
413C22×C31—42no—
414C22×C31—44no—
415C22×C31—42no—
416C22×C31—42no—
417C22×C31—44no—
418C22×C31—41no—
419C22×C31—41no—
420C22×C31—41no—
421C22×C31—42no—
422C22×C31—41no—
423C22×C31—42no—
424C22×C31—42no—
425C22×C31—41no—
426C22×C31—42no—
427C22×C31—81no—
428C22×C31—82no—
429C22×C31—81no—
430C22×C31—82no—
431C22×C31—82no—
432C22×C31—81no—
433C22×C31—81no—
434C22×C31—82no—
435C22×C31—81no—
436C22×C31—81no—
437C22×C31—162no—
438C22×C31C2×#12011yescharacteristic
439C22×C31C2×#12111yescharacteristic
440C22×C31#53411yescharacteristic
441C22×C31D4212yes—
442C22×C31#54612yes—
443C4×C31—21no—
444C4×C31—21no—
445C4×C31—22no—
446C4×C31—22no—
447C4×C31—44no—
448C4×C31—42no—
449C4×C31—41no—
450C4×C31—42no—
451C4×C31—42no—
452C4×C31—82no—
453C4×C31—81no—
454C4×C31—81no—
455C4×C31—81no—
456C2×H(5,𝔽2)C22×C3111yescharacteristic
457C22×#41C22×C3111yescharacteristic
458#547—22no—
459#547—22no—
460#546—22no—
461#546—22no—
462#536—21no—
463#534—21no—
464#534C22×C3112yes—
465#525—21no—
466C2×#123—21no—
467C2×#123C22×C3112yes—
468C2×#120C22×C3111yescharacteristic
469C2×#120C22×C3112yes—
470C2×#120C22×C3111yescharacteristic, complemented
471#518C22×C3111yescharacteristic
472C2×#117C22×C3112yescomplemented
473C22×C22⋊C4C22×C3111yescharacteristic, complemented
474B(4,𝔽2)—24no—
475#410—24no—
476C2×#99C22×C3111yescharacteristic
477C2×#99C22×C3112yes—
478C2×#99C22×C3112yes—
479C2×#99C22×C3111yescharacteristic
480C2×#99C22×C3112yescomplemented
481#396—22no—
482#394—22no—
483#393—21no—
484#392—21no—
485#390—22no—
486#388—22no—
487#386—21no—
488#386—21no—
489#386C22×C3111yescharacteristic
490#386C22×C3112yes—
491#386C22×C3111yescharacteristic, complemented
492#385C22×C3112yescomplemented
493#381C22×C3111yescharacteristic, complemented
494#379C22×C3112yescomplemented
495#342C22×C3112yescomplemented
496#342C22×C3112yescomplemented
497C2×C31—22no—
498C2×C31—21no—
499C2×C31—21no—
500C2×C31—22no—
501C2×C31—42no—
502C2×C31—82no—
503C2×C31—81no—
504C2×C31—82no—
505C2×C31#241011yescharacteristic
506C2×C31#302511yescharacteristic
507C2×C31#302711yescharacteristic
508C25C23×C3111yescharacteristic
509H(5,𝔽2)—22no—
510H(5,𝔽2)—22no—
511H(5,𝔽2)—42no—
512C2×#41—22no—
513C2×#41—22no—
514C2×#41—21no—
515C2×#41—22no—
516C2×#41—22no—
517C2×#41—22no—
518C2×#41—42no—
519C22×Q8D4×C3111yescharacteristic, complemented
520C22×D4—21no—
521C22×D4—22no—
522C22×D4—21no—
523C22×D4—22no—
524C22×D4—21no—
525C22×D4D4×C3111yescharacteristic, complemented
526C22×D4C23×C3112yes—
527C22×D4C23×C3111yescharacteristic
528C22×D4C23×C3111yescharacteristic
529C23×C4D4×C3111yescharacteristic, complemented
530C23×C4D4×C3111yescharacteristic, complemented
531C23×C4C23×C3111yescharacteristic
532C23×C4C23×C3111yescharacteristic
533C4⋊Q8—22no—
534#124—22no—
535#123—22no—
536#123—22no—
537#123—22no—
538#123—22no—
539#123—22no—
540#123—22no—
541#123—22no—
542#123—22no—
543#123—22no—
544C22⋊Q8—21no—
545C22⋊Q8—21no—
546C22⋊Q8—22no—
547C22⋊Q8—22no—
548#121—21no—
549#121—21no—
550#121—22no—
551#121—22no—
552#121—22no—
553#121—22no—
554#120—22no—
555#120—22no—
556#120—22no—
557#120—22no—
558#120—22no—
559#120—24no—
560#120—42no—
561#120—42no—
562C4×D4—22no—
563C4×D4—22no—
564C4×D4—22no—
565C4×D4—22no—
566#117—21no—
567#117—24no—
568#117—42no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—22no—
572C2×C4⋊C4—22no—
573C2×C4⋊C4D4×C3112yescomplemented
574C2×C4⋊C4D4×C3112yescomplemented
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—22no—
580C2×C22⋊C4—21no—
581C2×C22⋊C4—22no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—22no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—22no—
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—22no—
589C2×C22⋊C4—22no—
590C2×C22⋊C4D4×C3112yescomplemented
591C2×C22⋊C4D4×C3112yescomplemented
592C2×C22⋊C4C23×C3112yes—
593C2×C22⋊C4C23×C3111yescharacteristic
594C2×C22⋊C4C23×C3111yescharacteristic
595C2×C22⋊C4C23×C3112yes—
596C2×C22⋊C4C23×C3112yes—
597C2×C42—22no—
598#99—22no—
599#99—24no—
600#99—24no—
601#99—42no—
602#99D4×C3114yescomplemented
603#95—21no—
604#95—21no—
605#95—22no—
606#95—21no—
607#95—21no—
608#95—22no—
609C31#2440611yescharacteristic, direct product factor, Sylow
610C24—21no—
611C24—22no—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—22no—
616C24—42no—
617C24—81no—
618C24C2×D4×C3112yes—
619C24C2×D4×C3111yescharacteristic
620C24C2×D4×C3111yescharacteristic
621C24C24×C3111yescharacteristic
622#41—44no—
623#41—44no—
624#41—44no—
625#41—44no—
626#41—44no—
627#41—44no—
628#41—42no—
629#41—42no—
630C2×Q8—21no—
631C2×Q8—22no—
632C2×Q8—22no—
633C2×Q8—41no—
634C2×D4—22no—
635C2×D4—22no—
636C2×D4—22no—
637C2×D4—21no—
638C2×D4—22no—
639C2×D4—21no—
640C2×D4—22no—
641C2×D4—22no—
642C2×D4—22no—
643C2×D4—22no—
644C2×D4—21no—
645C2×D4—22no—
646C2×D4—22no—
647C2×D4—22no—
648C2×D4—22no—
649C2×D4—22no—
650C2×D4—22no—
651C2×D4—22no—
652C2×D4—41no—
653C2×D4—44no—
654C2×D4—44no—
655C2×D4—44no—
656C2×D4—42no—
657C2×D4—42no—
658C2×D4—42no—
659C2×D4—44no—
660C2×D4—42no—
661C2×D4—42no—
662C2×D4—42no—
663C2×D4—82no—
664C2×D4—81no—
665C2×D4—81no—
666C2×D4C2×D4×C3112yes—
667C2×D4#41×C3112yes—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—22no—
671C22×C4—21no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—22no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—41no—
688C22×C4—41no—
689C22×C4—81no—
690C22×C4C2×D4×C3112yes—
691C22×C4C2×D4×C3111yescharacteristic
692C22×C4C2×D4×C3111yescharacteristic
693C22×C4C2×D4×C3111yescharacteristic
694C22×C4C2×D4×C3112yes—
695C22×C4C2×D4×C3112yes—
696C22×C4C2×D4×C3111yescharacteristic
697C22×C4C2×D4×C3112yes—
698C22×C4C2×D4×C3112yes—
699C4⋊C4—22no—
700C4⋊C4—22no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—22no—
704C4⋊C4—22no—
705C4⋊C4—22no—
706C4⋊C4—22no—
707C4⋊C4—44no—
708C4⋊C4—82no—
709C22⋊C4—22no—
710C22⋊C4—22no—
711C22⋊C4—22no—
712C22⋊C4—22no—
713C22⋊C4—22no—
714C22⋊C4—22no—
715C22⋊C4—22no—
716C22⋊C4—22no—
717C22⋊C4—22no—
718C22⋊C4—22no—
719C22⋊C4—22no—
720C22⋊C4—22no—
721C22⋊C4—22no—
722C22⋊C4—21no—
723C22⋊C4—21no—
724C22⋊C4—22no—
725C22⋊C4—22no—
726C22⋊C4—44no—
727C22⋊C4—42no—
728C22⋊C4—44no—
729C22⋊C4—41no—
730C22⋊C4—41no—
731C22⋊C4—42no—
732C22⋊C4—42no—
733C22⋊C4—82no—
734C22⋊C4—82no—
735C22⋊C4—81no—
736C22⋊C4—81no—
737C22⋊C4C2×D4×C3114yes—
738C42—22no—
739C42—44no—
740C23—21no—
741C23—21no—
742C23—24no—
743C23—22no—
744C23—22no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—22no—
749C23—22no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—42no—
757C23—42no—
758C23—41no—
759C23—41no—
760C23—42no—
761C23—41no—
762C23—42no—
763C23—42no—
764C23—42no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—42no—
769C23—42no—
770C23—82no—
771C23—82no—
772C23—84no—
773C23—81no—
774C23—81no—
775C23C31×#12112yes—
776C23C22×D4×C3111yescharacteristic
777C23C22×D4×C3112yes—
778C23C22×D4×C3111yescharacteristic
779C23C2×#41×C3111yescharacteristic
780C23C31×H(5,𝔽2)12yes—
781Q8—44no—
782Q8—42no—
783D4—24no—
784D4—24no—
785D4—44no—
786D4—42no—
787D4—44no—
788D4—42no—
789D4—42no—
790D4—42no—
791D4—42no—
792D4—42no—
793D4—42no—
794D4—82no—
795D4—82no—
796D4—88no—
797D4—84no—
798D4—84no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—24no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—44no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—42no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—42no—
842C2×C4—81no—
843C2×C4—81no—
844C2×C4C31×#12011yescharacteristic
845C2×C4C31×#12011yescharacteristic
846C2×C4C31×#12012yes—
847C2×C4C31×#12112yes—
848C22—22no—
849C22—21no—
850C22—22no—
851C22—21no—
852C22—22no—
853C22—41no—
854C22—41no—
855C22—42no—
856C22—42no—
857C22—44no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—44no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—42no—
866C22—41no—
867C22—42no—
868C22—42no—
869C22—41no—
870C22—42no—
871C22—81no—
872C22—82no—
873C22—81no—
874C22—82no—
875C22—82no—
876C22—81no—
877C22—81no—
878C22—82no—
879C22—81no—
880C22—81no—
881C22—162no—
882C22C2×C31×#12011yescharacteristic
883C22C2×C31×#12111yescharacteristic
884C22C31×#53411yescharacteristic
885C22D42×C3112yes—
886C22C31×#54612yes—
887C4—21no—
888C4—21no—
889C4—22no—
890C4—22no—
891C4—44no—
892C4—42no—
893C4—41no—
894C4—42no—
895C4—42no—
896C4—81no—
897C4—81no—
898C4—82no—
899C4—81no—
900C2—22no—
901C2—21no—
902C2—21no—
903C2—22no—
904C2—42no—
905C2—82no—
906C2—81no—
907C2—82no—
908C2C31×#241011yescharacteristic
909C2C31×#302511yescharacteristic
910C2C31×#302711yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC24C24×C31
LCSG ▷ C24 ▷ 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×#3485C2semidirect
2. C2×C31×B(4,𝔽2)C2semidirect
3. C2×C31×#410C2semidirect
4. C31×#2411C2semidirect
5. C31×#2404C2semidirect
6. C31×#2044C2semidirect
7. C31×#2021C2semidirect
8. C31×#1899C2semidirect
9. C31×#1889C2semidirect
10. C31×#1867C2semidirect
11. C31×#1790C2semidirect
26. C2×C31×#120C22semidirect
28. C2×C31×#117C22semidirect
29. C22×C22⋊C4×C31C22semidirect
36. C2×C31×#99C22semidirect
47. C31×#386C22semidirect
48. C31×#385C22semidirect
49. C31×#381C22semidirect
50. C31×#379C22semidirect
51. C31×#342C22semidirect
52. C31×#342C22semidirect
64. C22×Q8×C31D4semidirect
70. C22×D4×C31D4semidirect
74. C23×C4×C31D4semidirect
75. C23×C4×C31D4semidirect
118. C2×C4⋊C4×C31D4semidirect
119. C2×C4⋊C4×C31D4semidirect
135. C2×C22⋊C4×C31D4semidirect
136. C2×C22⋊C4×C31D4semidirect
147. C31×#99D4semidirect
284. #24406C31direct (N × H)
393. #3485C2×C31semidirect
394. C2×B(4,𝔽2)C2×C31semidirect
395. C2×#410C2×C31semidirect
396. #2411C2×C31semidirect
397. #2404C2×C31semidirect
398. #2044C2×C31semidirect
399. #2021C2×C31semidirect
400. #1899C2×C31semidirect
401. #1889C2×C31semidirect
402. #1867C2×C31semidirect
403. #1790C2×C31semidirect
470. C2×#120C22×C31semidirect
472. C2×#117C22×C31semidirect
473. C22×C22⋊C4C22×C31semidirect
480. C2×#99C22×C31semidirect
491. #386C22×C31semidirect
492. #385C22×C31semidirect
493. #381C22×C31semidirect
494. #379C22×C31semidirect
495. #342C22×C31semidirect
496. #342C22×C31semidirect
519. C22×Q8D4×C31semidirect
525. C22×D4D4×C31semidirect
529. C23×C4D4×C31semidirect
530. C23×C4D4×C31semidirect
573. C2×C4⋊C4D4×C31semidirect
574. C2×C4⋊C4D4×C31semidirect
590. C2×C22⋊C4D4×C31semidirect
591. C2×C22⋊C4D4×C31semidirect
602. #99D4×C31semidirect
609. C31#24406direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#34852
C2×C31×B(4,𝔽2)2
C2×C31×#4102
C31×#24112
C31×#24042
C31×#20442
C31×#20212
C31×#18992
C31×#18892
C31×#18672
C31×#17902
#2440631