Finite Group Databasebeta

← C31×#24435 #21481194

Subgroups — C31×#24435 #21481194

Order 7936.

1550 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#550C211yesmaximal, characteristic, complemented
2C2×C31×#466C211yesmaximal, characteristic, complemented
3C2×C31×#449C211yesmaximal, characteristic, complemented
4C2×C31×#449C211yesmaximal, characteristic, complemented
5C2×C31×#416C211yesmaximal, characteristic, complemented
6C31×#2414C211yesmaximal, characteristic, complemented
7C31×#2041C211yesmaximal, characteristic, complemented
8C31×#2033C211yesmaximal, characteristic, complemented
9C31×#2011C211yesmaximal, characteristic, complemented
10C31×#1999C211yesmaximal, characteristic, complemented
11C31×#1880C211yesmaximal, characteristic, complemented
12C31×#1875C211yesmaximal, characteristic, complemented
13C31×#1869C211yesmaximal, characteristic, complemented
14C31×#1863C211yesmaximal, characteristic, complemented
15C31×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C22×#41×C31C2211yescharacteristic
18C22×SD16×C31C2211yescharacteristic
19C22×D8×C31C2211yescharacteristic
20C22×D8×C31C2211yescharacteristic
21C23×C8×C31C2211yescharacteristic
22C31×#550—24no—
23C31×#550—24no—
24C2×C31×#127—21no—
25C2×C31×#127C2211yescharacteristic
26C2×C31×#121—21no—
27C2×C31×#121—21no—
28C2×C31×#121C2211yescharacteristic
29C2×C31×#121C2211yescharacteristic
30C2×C31×#121C2211yescharacteristic
31C2×C31×#121C2211yescharacteristic
32C2×C4×Q8×C31C2211yescharacteristic
33C2×C4×D4×C31—21no—
34C2×C4×D4×C31C2211yescharacteristic
35C2×C31×#117C2211yescharacteristic
36C31×#466—24no—
37C31×#449—24no—
38C31×#449—24no—
39C2×C31×#107C2211yescharacteristic
40C31×#416—24no—
41C2×C31×#103C2211yescharacteristic
42C2×C31×#103C2211yescharacteristic
43C2×C31×#103C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×#102C2211yescharacteristic
46C2×C31×#102C2211yescharacteristic
47C2×C31×#102C2211yescharacteristic
48C2×C31×#102C2211yescharacteristic
49C2×C31×#102C2211yescharacteristic
50C2×C31×#102C2211yescharacteristic
51C2×C31×C22⋊C8C2211yescharacteristic
52C2×C31×C22⋊C8C2211yescharacteristic
53C2×C31×C22⋊C8C2211yescharacteristic
54C31×#394—21no—
55C31×#392—21no—
56C31×#390—21no—
57C31×#390C2211yescharacteristic
58C31×#389C2211yescharacteristic
59C31×#388—21no—
60C31×#380C2211yescharacteristic
61C31×#340C2211yescharacteristic
62C31×#340C2211yescharacteristic
63C31×#336C2211yescharacteristic
64C31×#336C2211yescharacteristic
65C2×#41×C31—22no—
66C2×#41×C31—22no—
67C2×#41×C31—22no—
68C2×#41×C31—22no—
69C2×#41×C31—22no—
70C2×#41×C31—22no—
71C2×#41×C31—22no—
72C2×#41×C31—41no—
73C2×#41×C31—41no—
74C2×#41×C31—41no—
75C2×#41×C31—41no—
76C2×#41×C31D414yescomplemented
77C22×Q8×C31C2311yescharacteristic
78C22×D4×C31—21no—
79C22×D4×C31—21no—
80C22×D4×C31—21no—
81C22×D4×C31—21no—
82C22×D4×C31—21no—
83C22×D4×C31—21no—
84C22×D4×C31—21no—
85C22×D4×C31—21no—
86C22×D4×C31D411yescharacteristic
87C22×D4×C31C2311yescharacteristic
88C22×D4×C31C2311yescharacteristic
89C22×D4×C31C2311yescharacteristic
90C23×C4×C31—21no—
91C23×C4×C31—21no—
92C23×C4×C31C2311yescharacteristic
93C23×C4×C31C2311yescharacteristic
94C2×SD16×C31—22no—
95C2×SD16×C31—22no—
96C2×SD16×C31—22no—
97C2×D8×C31—22no—
98C2×D8×C31—22no—
99C2×D8×C31—22no—
100C2×D8×C31—41no—
101C2×D8×C31—41no—
102C2×D8×C31—41no—
103C22×C8×C31—22no—
104C22×C8×C31—22no—
105C22×C8×C31—41no—
106C22×C8×C31C2311yescharacteristic
107C22×C8×C31C2311yescharacteristic
108C22×C8×C31C2311yescharacteristic
109C22×C8×C31C2311yescharacteristic
110C31×#127—28no—
111C31×#127—22no—
112C31×#127—22no—
113C31×#121—28no—
114C31×#121—28no—
115C31×#121—22no—
116C31×#121—22no—
117C31×#121—22no—
118C31×#121—22no—
119C31×#121—22no—
120C31×#121—22no—
121C31×#121—41no—
122C31×#121D414yescomplemented
123C4×Q8×C31—22no—
124C4×Q8×C31—22no—
125C4×D4×C31—28no—
126C4×D4×C31—22no—
127C4×D4×C31—22no—
128C31×#117—22no—
129C31×#117—41no—
130C2×C4⋊C4×C31—21no—
131C2×C4⋊C4×C31—21no—
132C2×C4⋊C4×C31D411yescharacteristic
133C2×C4⋊C4×C31C2311yescharacteristic
134C2×C4⋊C4×C31C2311yescharacteristic
135C2×C4⋊C4×C31C2311yescharacteristic
136C2×C4⋊C4×C31C2311yescharacteristic
137C2×C22⋊C4×C31—21no—
138C2×C22⋊C4×C31—21no—
139C2×C22⋊C4×C31—21no—
140C2×C22⋊C4×C31—21no—
141C2×C22⋊C4×C31—21no—
142C2×C22⋊C4×C31—21no—
143C2×C22⋊C4×C31—21no—
144C2×C22⋊C4×C31—21no—
145C2×C22⋊C4×C31D411yescharacteristic
146C2×C22⋊C4×C31D411yescharacteristic
147C2×C42×C31—21no—
148C2×C42×C31—21no—
149C2×C42×C31C2311yescharacteristic
150C31×#107—22no—
151C31×#103—22no—
152C31×#103—22no—
153C31×#103D414yescomplemented
154C31×#102—22no—
155C31×#102—22no—
156C31×#102—22no—
157C31×#102—22no—
158C31×#102—22no—
159C31×#102—22no—
160C31×#102—41no—
161C31×C22⋊C8—22no—
162C31×C22⋊C8—22no—
163C31×C22⋊C8—41no—
164C31×#95—21no—
165C31×#95—21no—
166C24×C31—21no—
167C24×C31—21no—
168C24×C31—21no—
169C24×C31C2×D411yescharacteristic
170C24×C31C2×D411yescharacteristic
171#41×C31—28no—
172#41×C31—44no—
173#41×C31—44no—
174#41×C31—44no—
175#41×C31—44no—
176#41×C31—44no—
177#41×C31—44no—
178#41×C31—44no—
179C2×Q8×C31—21no—
180C2×Q8×C31—21no—
181C2×Q8×C31—21no—
182C2×Q8×C31C2×D412yes—
183C2×Q8×C31C2×D412yes—
184C2×Q8×C31#4112yes—
185C2×D4×C31—24no—
186C2×D4×C31—24no—
187C2×D4×C31—22no—
188C2×D4×C31—24no—
189C2×D4×C31—24no—
190C2×D4×C31—24no—
191C2×D4×C31—24no—
192C2×D4×C31—22no—
193C2×D4×C31—21no—
194C2×D4×C31—21no—
195C2×D4×C31—21no—
196C2×D4×C31—21no—
197C2×D4×C31—21no—
198C2×D4×C31—21no—
199C2×D4×C31—21no—
200C2×D4×C31—21no—
201C2×D4×C31—21no—
202C2×D4×C31—21no—
203C2×D4×C31—21no—
204C2×D4×C31—21no—
205C2×D4×C31—21no—
206C2×D4×C31—21no—
207C2×D4×C31—21no—
208C2×D4×C31—21no—
209C2×D4×C31—41no—
210C2×D4×C31—42no—
211C2×D4×C31—42no—
212C2×D4×C31—42no—
213C2×D4×C31—42no—
214C2×D4×C31—42no—
215C2×D4×C31—42no—
216C2×D4×C31—42no—
217C2×D4×C31—42no—
218C2×D4×C31—42no—
219C2×D4×C31—81no—
220C2×D4×C31—81no—
221C2×D4×C31—81no—
222C2×D4×C31—81no—
223C2×D4×C31—81no—
224C2×D4×C31—81no—
225C2×D4×C31—81no—
226C2×D4×C31—81no—
227C2×D4×C31—81no—
228C2×D4×C31C2×D412yes—
229C2×D4×C31C2×D412yes—
230C22×C4×C31—21no—
231C22×C4×C31—21no—
232C22×C4×C31—21no—
233C22×C4×C31—21no—
234C22×C4×C31—21no—
235C22×C4×C31—24no—
236C22×C4×C31—21no—
237C22×C4×C31—21no—
238C22×C4×C31—24no—
239C22×C4×C31—21no—
240C22×C4×C31—21no—
241C22×C4×C31—21no—
242C22×C4×C31—21no—
243C22×C4×C31—21no—
244C22×C4×C31—21no—
245C22×C4×C31—21no—
246C22×C4×C31—21no—
247C22×C4×C31—42no—
248C22×C4×C31—42no—
249C22×C4×C31—42no—
250C22×C4×C31—42no—
251C22×C4×C31C2×D411yescharacteristic
252C22×C4×C31C2×D411yescharacteristic
253C22×C4×C31C2×D411yescharacteristic
254C22×C4×C31C2×D412yes—
255C22×C4×C31C2×D412yes—
256C22×C4×C31C2×D411yescharacteristic
257C22×C4×C31C2411yescharacteristic
258SD16×C31—44no—
259D8×C31—44no—
260D8×C31—44no—
261C2×C8×C31—21no—
262C2×C8×C31—21no—
263C2×C8×C31—21no—
264C2×C8×C31—21no—
265C2×C8×C31—21no—
266C2×C8×C31—21no—
267C2×C8×C31—21no—
268C2×C8×C31—21no—
269C2×C8×C31—21no—
270C2×C8×C31—21no—
271C2×C8×C31—21no—
272C2×C8×C31—44no—
273C2×C8×C31C2×D412yes—
274C4⋊C4×C31—24no—
275C4⋊C4×C31—22no—
276C4⋊C4×C31—21no—
277C4⋊C4×C31—21no—
278C4⋊C4×C31—21no—
279C4⋊C4×C31—21no—
280C4⋊C4×C31—21no—
281C4⋊C4×C31—21no—
282C4⋊C4×C31—81no—
283C4⋊C4×C31C2×D412yes—
284C4⋊C4×C31C2×D412yes—
285C22⋊C4×C31—24no—
286C22⋊C4×C31—22no—
287C22⋊C4×C31—24no—
288C22⋊C4×C31—22no—
289C22⋊C4×C31—42no—
290C22⋊C4×C31—42no—
291C22⋊C4×C31—42no—
292C22⋊C4×C31—42no—
293C22⋊C4×C31—81no—
294C22⋊C4×C31—81no—
295C42×C31—24no—
296C42×C31—21no—
297C42×C31—21no—
298C42×C31—42no—
299#24435C3111yesmaximal, characteristic, direct product factor, Sylow
300C23×C31—21no—
301C23×C31—21no—
302C23×C31—21no—
303C23×C31—21no—
304C23×C31—21no—
305C23×C31—21no—
306C23×C31—21no—
307C23×C31—22no—
308C23×C31—22no—
309C23×C31—21no—
310C23×C31—21no—
311C23×C31—21no—
312C23×C31—21no—
313C23×C31—21no—
314C23×C31—21no—
315C23×C31—41no—
316C23×C31—41no—
317C23×C31—41no—
318C23×C31—41no—
319C23×C31—41no—
320C23×C31—41no—
321C23×C31—41no—
322C23×C31—41no—
323C23×C31—41no—
324C23×C31—41no—
325C23×C31—41no—
326C23×C31—41no—
327C23×C31—41no—
328C23×C31—41no—
329C23×C31—41no—
330C23×C31—41no—
331C23×C31—41no—
332C23×C31—41no—
333C23×C31—41no—
334C23×C31#12012yes—
335C23×C31C22×D411yescharacteristic
336Q8×C31—22no—
337Q8×C31—22no—
338Q8×C31—22no—
339Q8×C31#12114yes—
340D4×C31—22no—
341D4×C31—22no—
342D4×C31—22no—
343D4×C31—22no—
344D4×C31—44no—
345D4×C31—48no—
346D4×C31—48no—
347D4×C31—48no—
348D4×C31—41no—
349D4×C31—41no—
350D4×C31—41no—
351D4×C31—41no—
352D4×C31—41no—
353D4×C31—41no—
354D4×C31—41no—
355D4×C31—41no—
356D4×C31—84no—
357D4×C31—84no—
358D4×C31—84no—
359D4×C31—84no—
360D4×C31—84no—
361C2×C4×C31—21no—
362C2×C4×C31—22no—
363C2×C4×C31—21no—
364C2×C4×C31—22no—
365C2×C4×C31—21no—
366C2×C4×C31—22no—
367C2×C4×C31—21no—
368C2×C4×C31—22no—
369C2×C4×C31—22no—
370C2×C4×C31—22no—
371C2×C4×C31—22no—
372C2×C4×C31—21no—
373C2×C4×C31—22no—
374C2×C4×C31—21no—
375C2×C4×C31—22no—
376C2×C4×C31—21no—
377C2×C4×C31—21no—
378C2×C4×C31—21no—
379C2×C4×C31—21no—
380C2×C4×C31—48no—
381C2×C4×C31—48no—
382C2×C4×C31—41no—
383C2×C4×C31—41no—
384C2×C4×C31—41no—
385C2×C4×C31—41no—
386C2×C4×C31—41no—
387C2×C4×C31—41no—
388C2×C4×C31—41no—
389C2×C4×C31—41no—
390C2×C4×C31—41no—
391C2×C4×C31—41no—
392C2×C4×C31—41no—
393C2×C4×C31—41no—
394C2×C4×C31—41no—
395C2×C4×C31—41no—
396C2×C4×C31#12012yes—
397C2×C4×C31#13512yes—
398C2×C4×C31C22×D411yescharacteristic
399C2×C4×C31C22×D411yescharacteristic
400C2×C4×C31C22×D411yescharacteristic
401C2×C4×C31C2×#4111yescharacteristic
402C2×C4×C31H(5,𝔽2)11yescharacteristic
403C2×C4×C31H(5,𝔽2)11yescharacteristic
404C8×C31—22no—
405C8×C31—41no—
406C8×C31—41no—
407C8×C31—41no—
408C2×#550C2×C3111yescharacteristic, complemented
409C2×#466C2×C3111yescharacteristic, complemented
410C2×#449C2×C3111yescharacteristic, complemented
411C2×#449C2×C3111yescharacteristic, complemented
412C2×#416C2×C3111yescharacteristic, complemented
413#2414C2×C3111yescharacteristic, complemented
414#2041C2×C3111yescharacteristic, complemented
415#2033C2×C3111yescharacteristic, complemented
416#2011C2×C3111yescharacteristic, complemented
417#1999C2×C3111yescharacteristic, complemented
418#1880C2×C3111yescharacteristic, complemented
419#1875C2×C3111yescharacteristic, complemented
420#1869C2×C3111yescharacteristic, complemented
421#1863C2×C3111yescharacteristic, complemented
422#1788C2×C3111yescharacteristic, complemented
423C22×C31—22no—
424C22×C31—22no—
425C22×C31—22no—
426C22×C31—41no—
427C22×C31—41no—
428C22×C31—41no—
429C22×C31—41no—
430C22×C31—42no—
431C22×C31—42no—
432C22×C31—41no—
433C22×C31—41no—
434C22×C31—42no—
435C22×C31—42no—
436C22×C31—41no—
437C22×C31—42no—
438C22×C31—42no—
439C22×C31—41no—
440C22×C31—41no—
441C22×C31—41no—
442C22×C31—41no—
443C22×C31—81no—
444C22×C31—81no—
445C22×C31—81no—
446C22×C31—81no—
447C22×C31—81no—
448C22×C31—81no—
449C22×C31—81no—
450C22×C31—81no—
451C22×C31—81no—
452C22×C31—81no—
453C22×C31—81no—
454C22×C31—81no—
455C22×C31—81no—
456C22×C31—81no—
457C22×C31—81no—
458C22×C31C2×#12011yescharacteristic
459C22×C31D4211yescharacteristic
460C22×C31#54611yescharacteristic
461C22×C31C2×#13511yescharacteristic
462C22×C31#57511yescharacteristic
463C22×C31#57611yescharacteristic
464C22×C31#57611yescharacteristic
465C4×C31—22no—
466C4×C31—24no—
467C4×C31—22no—
468C4×C31—41no—
469C4×C31—41no—
470C4×C31—42no—
471C4×C31—42no—
472C4×C31—81no—
473C4×C31—81no—
474C4×C31C2×#12111yescharacteristic
475C4×C31#53411yescharacteristic
476C4×C31D4211yescharacteristic
477C4×C31#54611yescharacteristic
478C22×#41C22×C3111yescharacteristic
479C22×#41C22×C3111yescharacteristic
480C22×SD16C22×C3111yescharacteristic
481C22×D8C22×C3111yescharacteristic
482C22×D8C22×C3111yescharacteristic
483C23×C8C22×C3111yescharacteristic
484#550—24no—
485#550—24no—
486C2×#127—21no—
487C2×#127C22×C3111yescharacteristic
488C2×#121—21no—
489C2×#121—21no—
490C2×#121C22×C3111yescharacteristic
491C2×#121C22×C3111yescharacteristic
492C2×#121C22×C3111yescharacteristic
493C2×#121C22×C3111yescharacteristic
494C2×C4×Q8C22×C3111yescharacteristic
495C2×C4×D4—21no—
496C2×C4×D4C22×C3111yescharacteristic
497C2×#117C22×C3111yescharacteristic
498#466—24no—
499#449—24no—
500#449—24no—
501C2×#107C22×C3111yescharacteristic
502#416—24no—
503C2×#103C22×C3111yescharacteristic
504C2×#103C22×C3111yescharacteristic
505C2×#103C22×C3111yescharacteristic
506C2×#102C22×C3111yescharacteristic
507C2×#102C22×C3111yescharacteristic
508C2×#102C22×C3111yescharacteristic
509C2×#102C22×C3111yescharacteristic
510C2×#102C22×C3111yescharacteristic
511C2×#102C22×C3111yescharacteristic
512C2×#102C22×C3111yescharacteristic
513C2×C22⋊C8C22×C3111yescharacteristic
514C2×C22⋊C8C22×C3111yescharacteristic
515C2×C22⋊C8C22×C3111yescharacteristic
516#394—21no—
517#392—21no—
518#390—21no—
519#390C22×C3111yescharacteristic
520#389C22×C3111yescharacteristic
521#388—21no—
522#380C22×C3111yescharacteristic
523#340C22×C3111yescharacteristic
524#340C22×C3111yescharacteristic
525#336C22×C3111yescharacteristic
526#336C22×C3111yescharacteristic
527C2×C31—42no—
528C2×C31—81no—
529C2×C31—82no—
530C2×C31—82no—
531C2×C31—161no—
532C2×C31#241011yescharacteristic
533C2×C31#300211yescharacteristic
534C2×C31#300811yescharacteristic
535C2×C31#326811yescharacteristic
536C2×C31#328711yescharacteristic
537C2×C31#330511yescharacteristic
538C2×C31#330911yescharacteristic
539C2×#41—22no—
540C2×#41—22no—
541C2×#41—22no—
542C2×#41—22no—
543C2×#41—22no—
544C2×#41—22no—
545C2×#41—22no—
546C2×#41—41no—
547C2×#41—41no—
548C2×#41—41no—
549C2×#41—41no—
550C2×#41D4×C3114yescomplemented
551C22×Q8C23×C3111yescharacteristic
552C22×D4—21no—
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—21no—
560C22×D4D4×C3111yescharacteristic
561C22×D4C23×C3111yescharacteristic
562C22×D4C23×C3111yescharacteristic
563C22×D4C23×C3111yescharacteristic
564C23×C4—21no—
565C23×C4—21no—
566C23×C4C23×C3111yescharacteristic
567C23×C4C23×C3111yescharacteristic
568C2×SD16—22no—
569C2×SD16—22no—
570C2×SD16—22no—
571C2×D8—22no—
572C2×D8—22no—
573C2×D8—22no—
574C2×D8—41no—
575C2×D8—41no—
576C2×D8—41no—
577C22×C8—22no—
578C22×C8—22no—
579C22×C8—41no—
580C22×C8C23×C3111yescharacteristic
581C22×C8C23×C3111yescharacteristic
582C22×C8C23×C3111yescharacteristic
583C22×C8C23×C3111yescharacteristic
584#127—28no—
585#127—22no—
586#127—22no—
587#121—28no—
588#121—28no—
589#121—22no—
590#121—22no—
591#121—22no—
592#121—22no—
593#121—22no—
594#121—22no—
595#121—41no—
596#121D4×C3114yescomplemented
597C4×Q8—22no—
598C4×Q8—22no—
599C4×D4—28no—
600C4×D4—22no—
601C4×D4—22no—
602#117—22no—
603#117—41no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4D4×C3111yescharacteristic
607C2×C4⋊C4C23×C3111yescharacteristic
608C2×C4⋊C4C23×C3111yescharacteristic
609C2×C4⋊C4C23×C3111yescharacteristic
610C2×C4⋊C4C23×C3111yescharacteristic
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4D4×C3111yescharacteristic
620C2×C22⋊C4D4×C3111yescharacteristic
621C2×C42—21no—
622C2×C42—21no—
623C2×C42C23×C3111yescharacteristic
624#107—22no—
625#103—22no—
626#103—22no—
627#103D4×C3114yescomplemented
628#102—22no—
629#102—22no—
630#102—22no—
631#102—22no—
632#102—22no—
633#102—22no—
634#102—41no—
635C22⋊C8—22no—
636C22⋊C8—22no—
637C22⋊C8—41no—
638#95—21no—
639#95—21no—
640C31#2443511yescharacteristic, direct product factor, Sylow
641C24—21no—
642C24—21no—
643C24—21no—
644C24C2×D4×C3111yescharacteristic
645C24C2×D4×C3111yescharacteristic
646#41—28no—
647#41—44no—
648#41—44no—
649#41—44no—
650#41—44no—
651#41—44no—
652#41—44no—
653#41—44no—
654C2×Q8—21no—
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8C2×D4×C3112yes—
658C2×Q8C2×D4×C3112yes—
659C2×Q8#41×C3112yes—
660C2×D4—24no—
661C2×D4—24no—
662C2×D4—22no—
663C2×D4—24no—
664C2×D4—24no—
665C2×D4—24no—
666C2×D4—24no—
667C2×D4—22no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—41no—
685C2×D4—42no—
686C2×D4—42no—
687C2×D4—42no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—81no—
695C2×D4—81no—
696C2×D4—81no—
697C2×D4—81no—
698C2×D4—81no—
699C2×D4—81no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4—81no—
703C2×D4C2×D4×C3112yes—
704C2×D4C2×D4×C3112yes—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—24no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—24no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—42no—
723C22×C4—42no—
724C22×C4—42no—
725C22×C4—42no—
726C22×C4C2×D4×C3111yescharacteristic
727C22×C4C2×D4×C3111yescharacteristic
728C22×C4C2×D4×C3111yescharacteristic
729C22×C4C2×D4×C3112yes—
730C22×C4C2×D4×C3112yes—
731C22×C4C2×D4×C3111yescharacteristic
732C22×C4C24×C3111yescharacteristic
733SD16—44no—
734D8—44no—
735D8—44no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—44no—
748C2×C8C2×D4×C3112yes—
749C4⋊C4—24no—
750C4⋊C4—22no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—81no—
758C4⋊C4C2×D4×C3112yes—
759C4⋊C4C2×D4×C3112yes—
760C22⋊C4—24no—
761C22⋊C4—22no—
762C22⋊C4—24no—
763C22⋊C4—22no—
764C22⋊C4—42no—
765C22⋊C4—42no—
766C22⋊C4—42no—
767C22⋊C4—42no—
768C22⋊C4—81no—
769C22⋊C4—81no—
770C42—24no—
771C42—21no—
772C42—21no—
773C42—42no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—22no—
782C23—22no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23C31×#12012yes—
809C23C22×D4×C3111yescharacteristic
810Q8—22no—
811Q8—22no—
812Q8—22no—
813Q8C31×#12114yes—
814D4—22no—
815D4—22no—
816D4—22no—
817D4—22no—
818D4—44no—
819D4—48no—
820D4—48no—
821D4—48no—
822D4—41no—
823D4—41no—
824D4—41no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—84no—
831D4—84no—
832D4—84no—
833D4—84no—
834D4—84no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—22no—
839C2×C4—21no—
840C2×C4—22no—
841C2×C4—21no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—21no—
849C2×C4—22no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—48no—
855C2×C4—48no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4C31×#12012yes—
871C2×C4C31×#13512yes—
872C2×C4C22×D4×C3111yescharacteristic
873C2×C4C22×D4×C3111yescharacteristic
874C2×C4C22×D4×C3111yescharacteristic
875C2×C4C2×#41×C3111yescharacteristic
876C2×C4C31×H(5,𝔽2)11yescharacteristic
877C2×C4C31×H(5,𝔽2)11yescharacteristic
878C8—22no—
879C8—41no—
880C8—41no—
881C8—41no—
882C22—22no—
883C22—22no—
884C22—22no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—41no—
889C22—42no—
890C22—42no—
891C22—41no—
892C22—41no—
893C22—42no—
894C22—42no—
895C22—41no—
896C22—42no—
897C22—42no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—81no—
903C22—81no—
904C22—81no—
905C22—81no—
906C22—81no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22C2×C31×#12011yescharacteristic
918C22D42×C3111yescharacteristic
919C22C31×#54611yescharacteristic
920C22C2×C31×#13511yescharacteristic
921C22C31×#57511yescharacteristic
922C22C31×#57611yescharacteristic
923C22C31×#57611yescharacteristic
924C4—22no—
925C4—24no—
926C4—22no—
927C4—41no—
928C4—41no—
929C4—42no—
930C4—42no—
931C4—81no—
932C4—81no—
933C4C2×C31×#12111yescharacteristic
934C4C31×#53411yescharacteristic
935C4D42×C3111yescharacteristic
936C4C31×#54611yescharacteristic
937C2—42no—
938C2—81no—
939C2—82no—
940C2—82no—
941C2—161no—
942C2C31×#241011yescharacteristic
943C2C31×#300211yescharacteristic
944C2C31×#300811yescharacteristic
945C2C31×#326811yescharacteristic
946C2C31×#328711yescharacteristic
947C2C31×#330511yescharacteristic
948C2C31×#330911yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C4×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#550C2semidirect
2. C2×C31×#466C2semidirect
3. C2×C31×#449C2semidirect
4. C2×C31×#449C2semidirect
5. C2×C31×#416C2semidirect
6. C31×#2414C2semidirect
7. C31×#2041C2semidirect
8. C31×#2033C2semidirect
9. C31×#2011C2semidirect
10. C31×#1999C2semidirect
11. C31×#1880C2semidirect
12. C31×#1875C2semidirect
13. C31×#1869C2semidirect
14. C31×#1863C2semidirect
15. C31×#1788C2semidirect
76. C2×#41×C31D4semidirect
122. C31×#121D4semidirect
153. C31×#103D4semidirect
299. #24435C31direct (N × H)
408. C2×#550C2×C31semidirect
409. C2×#466C2×C31semidirect
410. C2×#449C2×C31semidirect
411. C2×#449C2×C31semidirect
412. C2×#416C2×C31semidirect
413. #2414C2×C31semidirect
414. #2041C2×C31semidirect
415. #2033C2×C31semidirect
416. #2011C2×C31semidirect
417. #1999C2×C31semidirect
418. #1880C2×C31semidirect
419. #1875C2×C31semidirect
420. #1869C2×C31semidirect
421. #1863C2×C31semidirect
422. #1788C2×C31semidirect
550. C2×#41D4×C31semidirect
596. #121D4×C31semidirect
627. #103D4×C31semidirect
640. C31#24435direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5502
C2×C31×#4662
C2×C31×#4492
C2×C31×#4162
C31×#24142
C31×#20412
C31×#20332
C31×#20112
C31×#19992
C31×#18802
C31×#18752
C31×#18692
C31×#18632
C31×#17882
#2443531