Finite Group Databasebeta

← C31×#24404 #21481163

Subgroups — C31×#24404 #21481163

Order 7936.

2010 conjugacy classes of subgroups.

The subgroup lattice has 1046 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3484C211yesmaximal, characteristic, complemented
2C2×C31×B(4,𝔽2)C211yesmaximal, characteristic, complemented
3C22×C31×#99C211yesmaximal, characteristic, complemented
4C31×#2410C212yesmaximal, complemented
5C31×#2403C211yesmaximal, characteristic, complemented
6C31×#2044C212yesmaximal, complemented
7C31×#2021C212yesmaximal, complemented
8C31×#1898C212yesmaximal, complemented
9C31×#1889C211yesmaximal, characteristic, complemented
10C31×#1867C211yesmaximal, characteristic, complemented
11C31×#1790C211yesmaximal, characteristic, complemented
12C2×C31×H(5,𝔽2)C2211yescharacteristic
13C23×D4×C31C2211yescharacteristic
14C23×D4×C31C2211yescharacteristic, complemented
15C31×#546—22no—
16C31×#546—22no—
17D42×C31—22no—
18D42×C31—22no—
19C31×#535—21no—
20C31×#534—21no—
21C31×#534C2212yes—
22C31×#525—21no—
23C2×C31×#121—22no—
24C2×C31×#120—21no—
25C2×C31×#120—21no—
26C2×C31×#120C2211yescharacteristic
27C2×C31×#120C2212yes—
28C2×C31×#120C2212yescomplemented
29C2×C31×#120C2211yescharacteristic, complemented
30C31×#518C2211yescharacteristic
31C22×C22⋊C4×C31C2212yescomplemented
32C31×B(4,𝔽2)—24no—
33C2×C31×#99—24no—
34C2×C31×#99C2211yescharacteristic
35C2×C31×#99C2211yescharacteristic
36C2×C31×#99C2212yescomplemented
37C2×C31×#99C2212yescomplemented
38C2×C31×#99C2212yescomplemented
39C31×#394—22no—
40C31×#392—21no—
41C31×#392—21no—
42C31×#392—22no—
43C31×#386—21no—
44C31×#386—22no—
45C31×#386C2211yescharacteristic
46C31×#386C2211yescharacteristic, complemented
47C31×#386C2212yescomplemented
48C31×#385C2212yescomplemented
49C31×#379C2212yescomplemented
50C31×#379C2211yescharacteristic, complemented
51C31×#342C2212yescomplemented
52C31×#342C2212yescomplemented
53C25×C31D411yescharacteristic, complemented
54C25×C31C2311yescharacteristic
55C25×C31C2311yescharacteristic
56C31×H(5,𝔽2)—22no—
57C31×H(5,𝔽2)—22no—
58C31×H(5,𝔽2)—42no—
59C2×#41×C31—21no—
60C2×#41×C31—22no—
61C22×D4×C31—21no—
62C22×D4×C31—21no—
63C22×D4×C31—22no—
64C22×D4×C31—22no—
65C22×D4×C31—22no—
66C22×D4×C31—22no—
67C22×D4×C31—21no—
68C22×D4×C31—21no—
69C22×D4×C31—22no—
70C22×D4×C31—22no—
71C22×D4×C31—21no—
72C22×D4×C31—22no—
73C22×D4×C31—21no—
74C22×D4×C31—21no—
75C22×D4×C31—22no—
76C22×D4×C31—44no—
77C22×D4×C31—42no—
78C22×D4×C31D411yescharacteristic, complemented
79C22×D4×C31D411yescharacteristic, complemented
80C22×D4×C31D412yescomplemented
81C22×D4×C31D412yescomplemented
82C22×D4×C31C2312yes—
83C22×D4×C31C2311yescharacteristic
84C22×D4×C31C2311yescharacteristic
85C23×C4×C31—22no—
86C23×C4×C31D411yescharacteristic, complemented
87C23×C4×C31C2311yescharacteristic
88C31×#127—22no—
89C31×#124—22no—
90C31×#123—22no—
91C31×#123—22no—
92C31×#123—22no—
93C31×C22⋊Q8—21no—
94C31×C22⋊Q8—21no—
95C31×#121—21no—
96C31×#121—21no—
97C31×#121—22no—
98C31×#121—22no—
99C31×#121—22no—
100C31×#121—22no—
101C31×#121—22no—
102C31×#121—22no—
103C31×#121—48no—
104C31×#120—22no—
105C31×#120—22no—
106C31×#120—22no—
107C31×#120—22no—
108C31×#120—22no—
109C31×#120—22no—
110C31×#120—22no—
111C31×#120—22no—
112C31×#120—22no—
113C31×#120—22no—
114C31×#120—22no—
115C31×#120—24no—
116C31×#120—42no—
117C31×#120—42no—
118C31×#120—44no—
119C4×D4×C31—22no—
120C4×D4×C31—22no—
121C4×D4×C31—22no—
122C4×D4×C31—22no—
123C31×#117—21no—
124C2×C4⋊C4×C31—22no—
125C2×C22⋊C4×C31—21no—
126C2×C22⋊C4×C31—21no—
127C2×C22⋊C4×C31—21no—
128C2×C22⋊C4×C31—24no—
129C2×C22⋊C4×C31—22no—
130C2×C22⋊C4×C31—21no—
131C2×C22⋊C4×C31—21no—
132C2×C22⋊C4×C31—21no—
133C2×C22⋊C4×C31—22no—
134C2×C22⋊C4×C31—21no—
135C2×C22⋊C4×C31—21no—
136C2×C22⋊C4×C31—22no—
137C2×C22⋊C4×C31—22no—
138C2×C22⋊C4×C31—21no—
139C2×C22⋊C4×C31—22no—
140C2×C22⋊C4×C31—42no—
141C2×C22⋊C4×C31D412yescomplemented
142C2×C22⋊C4×C31D412yescomplemented
143C2×C22⋊C4×C31C2312yes—
144C2×C22⋊C4×C31C2311yescharacteristic
145C2×C22⋊C4×C31C2311yescharacteristic
146C2×C22⋊C4×C31C2312yes—
147C2×C22⋊C4×C31C2312yes—
148C31×#99—22no—
149C31×#99—24no—
150C31×#99—24no—
151C31×#99—42no—
152C31×#99D414yescomplemented
153C31×#95—22no—
154C31×#95—21no—
155C31×#95—21no—
156C31×#95—22no—
157C24×C31—21no—
158C24×C31—21no—
159C24×C31—22no—
160C24×C31—21no—
161C24×C31—22no—
162C24×C31—21no—
163C24×C31—21no—
164C24×C31—21no—
165C24×C31—22no—
166C24×C31—21no—
167C24×C31—21no—
168C24×C31—22no—
169C24×C31—41no—
170C24×C31—42no—
171C24×C31—42no—
172C24×C31—42no—
173C24×C31—81no—
174C24×C31—81no—
175C24×C31—81no—
176C24×C31C2×D411yescharacteristic
177C24×C31C2×D412yes—
178C24×C31C2×D411yescharacteristic
179C24×C31C2×D412yes—
180C24×C31C2×D412yes—
181C24×C31C2×D411yescharacteristic
182C24×C31C2×D411yescharacteristic
183C24×C31C2411yescharacteristic
184#41×C31—44no—
185#41×C31—44no—
186#41×C31—42no—
187#41×C31—42no—
188C2×Q8×C31—21no—
189C2×D4×C31—22no—
190C2×D4×C31—22no—
191C2×D4×C31—22no—
192C2×D4×C31—24no—
193C2×D4×C31—21no—
194C2×D4×C31—28no—
195C2×D4×C31—22no—
196C2×D4×C31—22no—
197C2×D4×C31—22no—
198C2×D4×C31—22no—
199C2×D4×C31—22no—
200C2×D4×C31—21no—
201C2×D4×C31—22no—
202C2×D4×C31—22no—
203C2×D4×C31—22no—
204C2×D4×C31—22no—
205C2×D4×C31—21no—
206C2×D4×C31—22no—
207C2×D4×C31—22no—
208C2×D4×C31—22no—
209C2×D4×C31—22no—
210C2×D4×C31—22no—
211C2×D4×C31—22no—
212C2×D4×C31—22no—
213C2×D4×C31—22no—
214C2×D4×C31—22no—
215C2×D4×C31—41no—
216C2×D4×C31—41no—
217C2×D4×C31—42no—
218C2×D4×C31—44no—
219C2×D4×C31—44no—
220C2×D4×C31—44no—
221C2×D4×C31—44no—
222C2×D4×C31—44no—
223C2×D4×C31—44no—
224C2×D4×C31—44no—
225C2×D4×C31—44no—
226C2×D4×C31—44no—
227C2×D4×C31—42no—
228C2×D4×C31—42no—
229C2×D4×C31—44no—
230C2×D4×C31—42no—
231C2×D4×C31—41no—
232C2×D4×C31—42no—
233C2×D4×C31—41no—
234C2×D4×C31—42no—
235C2×D4×C31—44no—
236C2×D4×C31—42no—
237C2×D4×C31—42no—
238C2×D4×C31—42no—
239C2×D4×C31—44no—
240C2×D4×C31—42no—
241C2×D4×C31—82no—
242C2×D4×C31—82no—
243C2×D4×C31—81no—
244C2×D4×C31—81no—
245C2×D4×C31—82no—
246C2×D4×C31—82no—
247C2×D4×C31C2×D412yes—
248C2×D4×C31#4112yes—
249C22×C4×C31—21no—
250C22×C4×C31—22no—
251C22×C4×C31—21no—
252C22×C4×C31—21no—
253C22×C4×C31—21no—
254C22×C4×C31—22no—
255C22×C4×C31—22no—
256C22×C4×C31—21no—
257C22×C4×C31—21no—
258C22×C4×C31—22no—
259C22×C4×C31—22no—
260C22×C4×C31—21no—
261C22×C4×C31—21no—
262C22×C4×C31—42no—
263C22×C4×C31—41no—
264C22×C4×C31—44no—
265C22×C4×C31—44no—
266C22×C4×C31—82no—
267C22×C4×C31C2×D412yes—
268C22×C4×C31C2×D411yescharacteristic
269C22×C4×C31C2×D411yescharacteristic
270C22×C4×C31C2×D412yes—
271C22×C4×C31C2×D412yes—
272C4⋊C4×C31—21no—
273C4⋊C4×C31—21no—
274C4⋊C4×C31—22no—
275C4⋊C4×C31—22no—
276C4⋊C4×C31—44no—
277C22⋊C4×C31—22no—
278C22⋊C4×C31—22no—
279C22⋊C4×C31—22no—
280C22⋊C4×C31—22no—
281C22⋊C4×C31—22no—
282C22⋊C4×C31—22no—
283C22⋊C4×C31—22no—
284C22⋊C4×C31—22no—
285C22⋊C4×C31—22no—
286C22⋊C4×C31—22no—
287C22⋊C4×C31—22no—
288C22⋊C4×C31—22no—
289C22⋊C4×C31—22no—
290C22⋊C4×C31—21no—
291C22⋊C4×C31—21no—
292C22⋊C4×C31—22no—
293C22⋊C4×C31—22no—
294C22⋊C4×C31—44no—
295C22⋊C4×C31—44no—
296C22⋊C4×C31—42no—
297C22⋊C4×C31—42no—
298C22⋊C4×C31—42no—
299C22⋊C4×C31—44no—
300C22⋊C4×C31—42no—
301C22⋊C4×C31—44no—
302C22⋊C4×C31—42no—
303C22⋊C4×C31—82no—
304C22⋊C4×C31—81no—
305C22⋊C4×C31C2×D414yescomplemented
306C42×C31—22no—
307#24404C3111yesmaximal, characteristic, direct product factor, Sylow
308C23×C31—21no—
309C23×C31—21no—
310C23×C31—21no—
311C23×C31—22no—
312C23×C31—22no—
313C23×C31—22no—
314C23×C31—24no—
315C23×C31—21no—
316C23×C31—21no—
317C23×C31—21no—
318C23×C31—22no—
319C23×C31—22no—
320C23×C31—24no—
321C23×C31—22no—
322C23×C31—21no—
323C23×C31—22no—
324C23×C31—21no—
325C23×C31—21no—
326C23×C31—22no—
327C23×C31—22no—
328C23×C31—41no—
329C23×C31—42no—
330C23×C31—41no—
331C23×C31—41no—
332C23×C31—41no—
333C23×C31—42no—
334C23×C31—41no—
335C23×C31—42no—
336C23×C31—42no—
337C23×C31—42no—
338C23×C31—41no—
339C23×C31—41no—
340C23×C31—41no—
341C23×C31—41no—
342C23×C31—42no—
343C23×C31—42no—
344C23×C31—41no—
345C23×C31—42no—
346C23×C31—41no—
347C23×C31—41no—
348C23×C31—42no—
349C23×C31—42no—
350C23×C31—42no—
351C23×C31—42no—
352C23×C31—41no—
353C23×C31—41no—
354C23×C31—41no—
355C23×C31—42no—
356C23×C31—42no—
357C23×C31—42no—
358C23×C31—81no—
359C23×C31—81no—
360C23×C31—82no—
361C23×C31—82no—
362C23×C31—82no—
363C23×C31—82no—
364C23×C31—84no—
365C23×C31—84no—
366C23×C31—81no—
367C23×C31—81no—
368C23×C31—84no—
369C23×C31—84no—
370C23×C31#12011yescharacteristic
371C23×C31#12012yes—
372C23×C31#12011yescharacteristic
373C23×C31#12112yescomplemented
374C23×C31C22×D411yescharacteristic
375C23×C31C22×D412yes—
376C23×C31C22×D411yescharacteristic
377C23×C31C2×#4111yescharacteristic
378C23×C31H(5,𝔽2)12yes—
379Q8×C31—42no—
380D4×C31—24no—
381D4×C31—24no—
382D4×C31—44no—
383D4×C31—42no—
384D4×C31—44no—
385D4×C31—48no—
386D4×C31—44no—
387D4×C31—44no—
388D4×C31—44no—
389D4×C31—42no—
390D4×C31—42no—
391D4×C31—42no—
392D4×C31—42no—
393D4×C31—42no—
394D4×C31—42no—
395D4×C31—44no—
396D4×C31—44no—
397D4×C31—82no—
398D4×C31—82no—
399D4×C31—82no—
400D4×C31—82no—
401D4×C31—88no—
402D4×C31—84no—
403D4×C31—84no—
404C2×C4×C31—21no—
405C2×C4×C31—21no—
406C2×C4×C31—22no—
407C2×C4×C31—24no—
408C2×C4×C31—22no—
409C2×C4×C31—22no—
410C2×C4×C31—22no—
411C2×C4×C31—21no—
412C2×C4×C31—21no—
413C2×C4×C31—21no—
414C2×C4×C31—24no—
415C2×C4×C31—22no—
416C2×C4×C31—22no—
417C2×C4×C31—42no—
418C2×C4×C31—42no—
419C2×C4×C31—44no—
420C2×C4×C31—42no—
421C2×C4×C31—42no—
422C2×C4×C31—41no—
423C2×C4×C31—42no—
424C2×C4×C31—42no—
425C2×C4×C31—41no—
426C2×C4×C31—42no—
427C2×C4×C31—42no—
428C2×C4×C31—42no—
429C2×C4×C31—41no—
430C2×C4×C31—41no—
431C2×C4×C31—42no—
432C2×C4×C31—41no—
433C2×C4×C31—41no—
434C2×C4×C31—41no—
435C2×C4×C31—41no—
436C2×C4×C31—42no—
437C2×C4×C31—81no—
438C2×C4×C31—81no—
439C2×C4×C31—88no—
440C2×C4×C31#12112yescomplemented
441#3484C2×C3111yescharacteristic, complemented
442C2×B(4,𝔽2)C2×C3111yescharacteristic, complemented
443C22×#99C2×C3111yescharacteristic, complemented
444#2410C2×C3112yescomplemented
445#2403C2×C3111yescharacteristic, complemented
446#2044C2×C3112yescomplemented
447#2021C2×C3112yescomplemented
448#1898C2×C3112yescomplemented
449#1889C2×C3111yescharacteristic, complemented
450#1867C2×C3111yescharacteristic, complemented
451#1790C2×C3111yescharacteristic, complemented
452C22×C31—21no—
453C22×C31—22no—
454C22×C31—21no—
455C22×C31—22no—
456C22×C31—21no—
457C22×C31—21no—
458C22×C31—21no—
459C22×C31—22no—
460C22×C31—22no—
461C22×C31—22no—
462C22×C31—21no—
463C22×C31—21no—
464C22×C31—22no—
465C22×C31—41no—
466C22×C31—41no—
467C22×C31—42no—
468C22×C31—44no—
469C22×C31—44no—
470C22×C31—42no—
471C22×C31—42no—
472C22×C31—42no—
473C22×C31—44no—
474C22×C31—42no—
475C22×C31—42no—
476C22×C31—42no—
477C22×C31—44no—
478C22×C31—41no—
479C22×C31—41no—
480C22×C31—42no—
481C22×C31—41no—
482C22×C31—42no—
483C22×C31—42no—
484C22×C31—41no—
485C22×C31—42no—
486C22×C31—41no—
487C22×C31—82no—
488C22×C31—81no—
489C22×C31—81no—
490C22×C31—81no—
491C22×C31—82no—
492C22×C31—84no—
493C22×C31—82no—
494C22×C31—82no—
495C22×C31—81no—
496C22×C31—82no—
497C22×C31—81no—
498C22×C31—81no—
499C22×C31—82no—
500C22×C31—84no—
501C22×C31—81no—
502C22×C31—81no—
503C22×C31—162no—
504C22×C31B(4,𝔽2)12yescomplemented
505C22×C31C2×#12011yescharacteristic
506C22×C31C2×#12111yescharacteristic
507C22×C31#53411yescharacteristic
508C22×C31D4212yes—
509C22×C31#54612yes—
510C4×C31—22no—
511C4×C31—44no—
512C4×C31—41no—
513C4×C31—42no—
514C4×C31—42no—
515C4×C31—42no—
516C4×C31—42no—
517C4×C31—82no—
518C4×C31—81no—
519C4×C31—81no—
520C2×H(5,𝔽2)C22×C3111yescharacteristic
521C23×D4C22×C3111yescharacteristic
522C23×D4C22×C3111yescharacteristic, complemented
523#546—22no—
524#546—22no—
525D42—22no—
526D42—22no—
527#535—21no—
528#534—21no—
529#534C22×C3112yes—
530#525—21no—
531C2×#121—22no—
532C2×#120—21no—
533C2×#120—21no—
534C2×#120C22×C3111yescharacteristic
535C2×#120C22×C3112yes—
536C2×#120C22×C3112yescomplemented
537C2×#120C22×C3111yescharacteristic, complemented
538#518C22×C3111yescharacteristic
539C22×C22⋊C4C22×C3112yescomplemented
540B(4,𝔽2)—24no—
541C2×#99—24no—
542C2×#99C22×C3111yescharacteristic
543C2×#99C22×C3111yescharacteristic
544C2×#99C22×C3112yescomplemented
545C2×#99C22×C3112yescomplemented
546C2×#99C22×C3112yescomplemented
547#394—22no—
548#392—21no—
549#392—21no—
550#392—22no—
551#386—21no—
552#386—22no—
553#386C22×C3111yescharacteristic
554#386C22×C3111yescharacteristic, complemented
555#386C22×C3112yescomplemented
556#385C22×C3112yescomplemented
557#379C22×C3112yescomplemented
558#379C22×C3111yescharacteristic, complemented
559#342C22×C3112yescomplemented
560#342C22×C3112yescomplemented
561C2×C31—22no—
562C2×C31—21no—
563C2×C31—21no—
564C2×C31—22no—
565C2×C31—22no—
566C2×C31—42no—
567C2×C31—41no—
568C2×C31—42no—
569C2×C31—82no—
570C2×C31—81no—
571C2×C31—82no—
572C2×C31#241011yescharacteristic
573C2×C31C2×B(4,𝔽2)11yescharacteristic
574C2×C31#302611yescharacteristic
575C25D4×C3111yescharacteristic, complemented
576C25C23×C3111yescharacteristic
577C25C23×C3111yescharacteristic
578H(5,𝔽2)—22no—
579H(5,𝔽2)—22no—
580H(5,𝔽2)—42no—
581C2×#41—21no—
582C2×#41—22no—
583C22×D4—21no—
584C22×D4—21no—
585C22×D4—22no—
586C22×D4—22no—
587C22×D4—22no—
588C22×D4—22no—
589C22×D4—21no—
590C22×D4—21no—
591C22×D4—22no—
592C22×D4—22no—
593C22×D4—21no—
594C22×D4—22no—
595C22×D4—21no—
596C22×D4—21no—
597C22×D4—22no—
598C22×D4—44no—
599C22×D4—42no—
600C22×D4D4×C3111yescharacteristic, complemented
601C22×D4D4×C3111yescharacteristic, complemented
602C22×D4D4×C3112yescomplemented
603C22×D4D4×C3112yescomplemented
604C22×D4C23×C3112yes—
605C22×D4C23×C3111yescharacteristic
606C22×D4C23×C3111yescharacteristic
607C23×C4—22no—
608C23×C4D4×C3111yescharacteristic, complemented
609C23×C4C23×C3111yescharacteristic
610#127—22no—
611#124—22no—
612#123—22no—
613#123—22no—
614#123—22no—
615C22⋊Q8—21no—
616C22⋊Q8—21no—
617#121—21no—
618#121—21no—
619#121—22no—
620#121—22no—
621#121—22no—
622#121—22no—
623#121—22no—
624#121—22no—
625#121—48no—
626#120—22no—
627#120—22no—
628#120—22no—
629#120—22no—
630#120—22no—
631#120—22no—
632#120—22no—
633#120—22no—
634#120—22no—
635#120—22no—
636#120—22no—
637#120—24no—
638#120—42no—
639#120—42no—
640#120—44no—
641C4×D4—22no—
642C4×D4—22no—
643C4×D4—22no—
644C4×D4—22no—
645#117—21no—
646C2×C4⋊C4—22no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—24no—
651C2×C22⋊C4—22no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—22no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—22no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—22no—
662C2×C22⋊C4—42no—
663C2×C22⋊C4D4×C3112yescomplemented
664C2×C22⋊C4D4×C3112yescomplemented
665C2×C22⋊C4C23×C3112yes—
666C2×C22⋊C4C23×C3111yescharacteristic
667C2×C22⋊C4C23×C3111yescharacteristic
668C2×C22⋊C4C23×C3112yes—
669C2×C22⋊C4C23×C3112yes—
670#99—22no—
671#99—24no—
672#99—24no—
673#99—42no—
674#99D4×C3114yescomplemented
675#95—22no—
676#95—21no—
677#95—21no—
678#95—22no—
679C31#2440411yescharacteristic, direct product factor, Sylow
680C24—21no—
681C24—21no—
682C24—22no—
683C24—21no—
684C24—22no—
685C24—21no—
686C24—21no—
687C24—21no—
688C24—22no—
689C24—21no—
690C24—21no—
691C24—22no—
692C24—41no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—81no—
697C24—81no—
698C24—81no—
699C24C2×D4×C3111yescharacteristic
700C24C2×D4×C3112yes—
701C24C2×D4×C3111yescharacteristic
702C24C2×D4×C3112yes—
703C24C2×D4×C3112yes—
704C24C2×D4×C3111yescharacteristic
705C24C2×D4×C3111yescharacteristic
706C24C24×C3111yescharacteristic
707#41—44no—
708#41—44no—
709#41—42no—
710#41—42no—
711C2×Q8—21no—
712C2×D4—22no—
713C2×D4—22no—
714C2×D4—22no—
715C2×D4—24no—
716C2×D4—21no—
717C2×D4—28no—
718C2×D4—22no—
719C2×D4—22no—
720C2×D4—22no—
721C2×D4—22no—
722C2×D4—22no—
723C2×D4—21no—
724C2×D4—22no—
725C2×D4—22no—
726C2×D4—22no—
727C2×D4—22no—
728C2×D4—21no—
729C2×D4—22no—
730C2×D4—22no—
731C2×D4—22no—
732C2×D4—22no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—22no—
738C2×D4—41no—
739C2×D4—41no—
740C2×D4—42no—
741C2×D4—44no—
742C2×D4—44no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—44no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—44no—
753C2×D4—42no—
754C2×D4—41no—
755C2×D4—42no—
756C2×D4—41no—
757C2×D4—42no—
758C2×D4—44no—
759C2×D4—42no—
760C2×D4—42no—
761C2×D4—42no—
762C2×D4—44no—
763C2×D4—42no—
764C2×D4—82no—
765C2×D4—82no—
766C2×D4—81no—
767C2×D4—81no—
768C2×D4—82no—
769C2×D4—82no—
770C2×D4C2×D4×C3112yes—
771C2×D4#41×C3112yes—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—42no—
786C22×C4—41no—
787C22×C4—44no—
788C22×C4—44no—
789C22×C4—82no—
790C22×C4C2×D4×C3112yes—
791C22×C4C2×D4×C3111yescharacteristic
792C22×C4C2×D4×C3111yescharacteristic
793C22×C4C2×D4×C3112yes—
794C22×C4C2×D4×C3112yes—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—22no—
798C4⋊C4—22no—
799C4⋊C4—44no—
800C22⋊C4—22no—
801C22⋊C4—22no—
802C22⋊C4—22no—
803C22⋊C4—22no—
804C22⋊C4—22no—
805C22⋊C4—22no—
806C22⋊C4—22no—
807C22⋊C4—22no—
808C22⋊C4—22no—
809C22⋊C4—22no—
810C22⋊C4—22no—
811C22⋊C4—22no—
812C22⋊C4—22no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—22no—
816C22⋊C4—22no—
817C22⋊C4—44no—
818C22⋊C4—44no—
819C22⋊C4—42no—
820C22⋊C4—42no—
821C22⋊C4—42no—
822C22⋊C4—44no—
823C22⋊C4—42no—
824C22⋊C4—44no—
825C22⋊C4—42no—
826C22⋊C4—82no—
827C22⋊C4—81no—
828C22⋊C4C2×D4×C3114yescomplemented
829C42—22no—
830C23—22no—
831C23—24no—
832C23—21no—
833C23—21no—
834C23—21no—
835C23—22no—
836C23—22no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—22no—
841C23—22no—
842C23—24no—
843C23—22no—
844C23—21no—
845C23—22no—
846C23—21no—
847C23—21no—
848C23—22no—
849C23—22no—
850C23—41no—
851C23—42no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—42no—
856C23—41no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—42no—
865C23—42no—
866C23—41no—
867C23—42no—
868C23—41no—
869C23—41no—
870C23—42no—
871C23—42no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—42no—
879C23—42no—
880C23—81no—
881C23—81no—
882C23—82no—
883C23—82no—
884C23—82no—
885C23—82no—
886C23—84no—
887C23—84no—
888C23—81no—
889C23—81no—
890C23—84no—
891C23—84no—
892C23C31×#12011yescharacteristic
893C23C31×#12012yes—
894C23C31×#12011yescharacteristic
895C23C31×#12112yescomplemented
896C23C22×D4×C3111yescharacteristic
897C23C22×D4×C3112yes—
898C23C22×D4×C3111yescharacteristic
899C23C2×#41×C3111yescharacteristic
900C23C31×H(5,𝔽2)12yes—
901Q8—42no—
902D4—24no—
903D4—24no—
904D4—44no—
905D4—42no—
906D4—44no—
907D4—48no—
908D4—44no—
909D4—44no—
910D4—44no—
911D4—44no—
912D4—44no—
913D4—42no—
914D4—42no—
915D4—42no—
916D4—42no—
917D4—42no—
918D4—42no—
919D4—82no—
920D4—82no—
921D4—82no—
922D4—82no—
923D4—88no—
924D4—84no—
925D4—84no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—22no—
929C2×C4—24no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—24no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—44no—
942C2×C4—42no—
943C2×C4—42no—
944C2×C4—41no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—41no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—42no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—42no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—42no—
959C2×C4—81no—
960C2×C4—81no—
961C2×C4—88no—
962C2×C4C31×#12112yescomplemented
963C22—21no—
964C22—22no—
965C22—21no—
966C22—22no—
967C22—21no—
968C22—21no—
969C22—21no—
970C22—22no—
971C22—22no—
972C22—22no—
973C22—21no—
974C22—21no—
975C22—22no—
976C22—41no—
977C22—41no—
978C22—42no—
979C22—44no—
980C22—42no—
981C22—42no—
982C22—44no—
983C22—42no—
984C22—44no—
985C22—42no—
986C22—42no—
987C22—42no—
988C22—44no—
989C22—41no—
990C22—41no—
991C22—42no—
992C22—41no—
993C22—42no—
994C22—42no—
995C22—41no—
996C22—42no—
997C22—41no—
998C22—82no—
999C22—81no—
1000C22—81no—
1001C22—81no—
1002C22—82no—
1003C22—84no—
1004C22—82no—
1005C22—81no—
1006C22—82no—
1007C22—82no—
1008C22—81no—
1009C22—81no—
1010C22—82no—
1011C22—84no—
1012C22—81no—
1013C22—81no—
1014C22—162no—
1015C22C31×B(4,𝔽2)12yescomplemented
1016C22C2×C31×#12011yescharacteristic
1017C22C2×C31×#12111yescharacteristic
1018C22C31×#53411yescharacteristic
1019C22D42×C3112yes—
1020C22C31×#54612yes—
1021C4—22no—
1022C4—44no—
1023C4—41no—
1024C4—42no—
1025C4—42no—
1026C4—42no—
1027C4—42no—
1028C4—82no—
1029C4—81no—
1030C4—81no—
1031C2—22no—
1032C2—21no—
1033C2—21no—
1034C2—22no—
1035C2—22no—
1036C2—41no—
1037C2—42no—
1038C2—42no—
1039C2—82no—
1040C2—81no—
1041C2—82no—
1042C2C31×#241011yescharacteristic
1043C2C2×C31×B(4,𝔽2)11yescharacteristic
1044C2C31×#302611yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC24C24×C31
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C25×C31 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C31×#3484C2semidirect
2. C2×C31×B(4,𝔽2)C2semidirect
3. C22×C31×#99C2semidirect
4. C31×#2410C2semidirect
5. C31×#2403C2semidirect
6. C31×#2044C2semidirect
7. C31×#2021C2semidirect
8. C31×#1898C2semidirect
9. C31×#1889C2semidirect
10. C31×#1867C2semidirect
11. C31×#1790C2semidirect
14. C23×D4×C31C22semidirect
28. C2×C31×#120C22semidirect
29. C2×C31×#120C22semidirect
31. C22×C22⋊C4×C31C22semidirect
36. C2×C31×#99C22semidirect
37. C2×C31×#99C22semidirect
38. C2×C31×#99C22semidirect
46. C31×#386C22semidirect
47. C31×#386C22semidirect
48. C31×#385C22semidirect
49. C31×#379C22semidirect
50. C31×#379C22semidirect
51. C31×#342C22semidirect
52. C31×#342C22semidirect
53. C25×C31D4semidirect
78. C22×D4×C31D4semidirect
79. C22×D4×C31D4semidirect
80. C22×D4×C31D4semidirect
81. C22×D4×C31D4semidirect
86. C23×C4×C31D4semidirect
141. C2×C22⋊C4×C31D4semidirect
142. C2×C22⋊C4×C31D4semidirect
152. C31×#99D4semidirect
305. C22⋊C4×C31C2×D4semidirect
307. #24404C31direct (N × H)
373. C23×C31#121semidirect
440. C2×C4×C31#121semidirect
441. #3484C2×C31semidirect
442. C2×B(4,𝔽2)C2×C31semidirect
443. C22×#99C2×C31semidirect
444. #2410C2×C31semidirect
445. #2403C2×C31semidirect
446. #2044C2×C31semidirect
447. #2021C2×C31semidirect
448. #1898C2×C31semidirect
449. #1889C2×C31semidirect
450. #1867C2×C31semidirect
451. #1790C2×C31semidirect
504. C22×C31B(4,𝔽2)semidirect
522. C23×D4C22×C31semidirect
536. C2×#120C22×C31semidirect
537. C2×#120C22×C31semidirect
539. C22×C22⋊C4C22×C31semidirect
544. C2×#99C22×C31semidirect
545. C2×#99C22×C31semidirect
546. C2×#99C22×C31semidirect
554. #386C22×C31semidirect
555. #386C22×C31semidirect
556. #385C22×C31semidirect
557. #379C22×C31semidirect
558. #379C22×C31semidirect
559. #342C22×C31semidirect
560. #342C22×C31semidirect
575. C25D4×C31semidirect
600. C22×D4D4×C31semidirect
601. C22×D4D4×C31semidirect
602. C22×D4D4×C31semidirect
603. C22×D4D4×C31semidirect
608. C23×C4D4×C31semidirect
663. C2×C22⋊C4D4×C31semidirect
664. C2×C22⋊C4D4×C31semidirect
674. #99D4×C31semidirect
679. C31#24404direct (N × H)
828. C22⋊C4C2×D4×C31semidirect
895. C23C31×#121semidirect
962. C2×C4C31×#121semidirect
1015. C22C31×B(4,𝔽2)semidirect

Maximal subgroups

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

subgroupindex
C31×#34842
C2×C31×B(4,𝔽2)2
C22×C31×#992
C31×#24102
C31×#24032
C31×#20442
C31×#20212
C31×#18982
C31×#18892
C31×#18672
C31×#17902
#2440431