Finite Group Databasebeta

← C31×#24402 #21481161

Subgroups — C31×#24402 #21481161

Order 7936.

1358 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#575C211yesmaximal, characteristic, complemented
2C2×C31×#472C211yesmaximal, characteristic, complemented
3C2×C31×#471C211yesmaximal, characteristic, complemented
4C31×#3006C211yesmaximal, characteristic, complemented
5C2×C31×#449C211yesmaximal, characteristic, complemented
6C31×#2880C211yesmaximal, characteristic, complemented
7C31×#2052C211yesmaximal, characteristic, complemented
8C31×#2051C211yesmaximal, characteristic, complemented
9C31×#2019C211yesmaximal, characteristic, complemented
10C31×#2018C211yesmaximal, characteristic, complemented
11C31×#1908C211yesmaximal, characteristic, complemented
12C31×#1907C211yesmaximal, characteristic, complemented
13C31×#1900C211yesmaximal, characteristic, complemented
14C31×#1855C211yesmaximal, characteristic, complemented
15C31×#1785C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C22×#41×C31C2211yescharacteristic
18C31×#575—24no—
19C31×#575—24no—
20C2×C31×#137—21no—
21C2×C31×#137C2211yescharacteristic
22C2×C31×#137C2211yescharacteristic
23C2×C31×AGL(1,ℤ/8)—21no—
24C2×C31×AGL(1,ℤ/8)C2211yescharacteristic
25C2×C31×AGL(1,ℤ/8)C2211yescharacteristic
26C2×C31×AGL(1,ℤ/8)C2211yescharacteristic
27C2×C31×AGL(1,ℤ/8)C2211yescharacteristic
28C2×C31×#135—21no—
29C2×C31×#135—21no—
30C22×SD16×C31C2211yescharacteristic, complemented
31C22×D8×C31C2211yescharacteristic, complemented
32C2×C31×#131C2211yescharacteristic
33C2×C31×#131C2211yescharacteristic
34C22×M16×C31C2211yescharacteristic
35C2×C31×#121C2211yescharacteristic
36C31×#472—24no—
37C31×#471—24no—
38C31×#449—21no—
39C31×#449—21no—
40C31×#449—21no—
41C31×#449—21no—
42C31×#449—21no—
43C31×#449—21no—
44C31×#448—21no—
45C31×#447—21no—
46C2×C31×#108C2211yescharacteristic, complemented
47C2×C31×#108C2211yescharacteristic, complemented
48C31×#417C2211yescharacteristic
49C31×#417C2211yescharacteristic
50C2×C31×#103C2211yescharacteristic, complemented
51C2×C31×#102C2211yescharacteristic, complemented
52C2×C31×#101C2211yescharacteristic, complemented
53C2×C31×#101C2211yescharacteristic, complemented
54C2×C31×#100C2211yescharacteristic, complemented
55C2×C31×#100C2211yescharacteristic, complemented
56C2×C31×#100C2211yescharacteristic, complemented
57C2×C31×#100C2211yescharacteristic, complemented
58C31×#408—21no—
59C31×#408—21no—
60C31×#408C2211yescharacteristic
61C31×#408C2211yescharacteristic
62C31×#407—21no—
63C31×#407C2211yescharacteristic
64C31×#407C2211yescharacteristic
65C2×C31×C22⋊C8—21no—
66C2×C31×C22⋊C8C2211yescharacteristic
67C31×#343C2211yescharacteristic, complemented
68C31×#343C2211yescharacteristic, complemented
69C31×#341C2211yescharacteristic, complemented
70C31×#341C2211yescharacteristic, complemented
71C2×#41×C31—21no—
72C2×#41×C31—21no—
73C2×#41×C31—22no—
74C2×#41×C31—22no—
75C2×#41×C31—22no—
76C2×#41×C31—22no—
77C2×#41×C31—21no—
78C2×#41×C31—21no—
79C2×#41×C31—21no—
80C2×#41×C31—21no—
81C2×#41×C31—41no—
82C2×#41×C31—41no—
83C2×#41×C31—41no—
84C2×#41×C31—41no—
85C2×#41×C31D411yescharacteristic
86C2×#41×C31D411yescharacteristic
87C2×#41×C31C2311yescharacteristic
88C2×#41×C31C2311yescharacteristic
89C22×Q8×C31D411yescharacteristic
90C22×Q8×C31C2311yescharacteristic
91C22×D4×C31—21no—
92C22×D4×C31—21no—
93C22×D4×C31—21no—
94C22×D4×C31D411yescharacteristic
95C22×D4×C31C2311yescharacteristic
96C22×D4×C31C2311yescharacteristic
97C23×C4×C31—21no—
98C23×C4×C31—21no—
99C23×C4×C31C2311yescharacteristic
100C31×#137—28no—
101C31×#137—22no—
102C31×#137—22no—
103C31×#137—22no—
104C31×#137D414yescomplemented
105C31×AGL(1,ℤ/8)—28no—
106C31×AGL(1,ℤ/8)—22no—
107C31×AGL(1,ℤ/8)—22no—
108C31×AGL(1,ℤ/8)—22no—
109C31×AGL(1,ℤ/8)—22no—
110C31×AGL(1,ℤ/8)—22no—
111C31×AGL(1,ℤ/8)—41no—
112C31×AGL(1,ℤ/8)—41no—
113C31×AGL(1,ℤ/8)D414yescomplemented
114C31×#135—28no—
115C31×#135—28no—
116C2×Q16×C31—21no—
117C2×Q16×C31—21no—
118C2×SD16×C31—21no—
119C2×SD16×C31—21no—
120C2×SD16×C31—21no—
121C2×SD16×C31—21no—
122C2×SD16×C31—21no—
123C2×SD16×C31—21no—
124C2×SD16×C31—22no—
125C2×SD16×C31—21no—
126C2×SD16×C31—21no—
127C2×SD16×C31—41no—
128C2×D8×C31—21no—
129C2×D8×C31—21no—
130C2×D8×C31—21no—
131C2×D8×C31—21no—
132C2×D8×C31—22no—
133C2×D8×C31—21no—
134C2×D8×C31—21no—
135C2×D8×C31—41no—
136C31×#131—22no—
137C31×#131—22no—
138C31×#131—41no—
139C31×#131—41no—
140C2×M16×C31—21no—
141C2×M16×C31—22no—
142C2×M16×C31—22no—
143C2×M16×C31—21no—
144C2×M16×C31—21no—
145C2×M16×C31C2311yescharacteristic
146C2×M16×C31C2311yescharacteristic
147C2×M16×C31C2311yescharacteristic
148C2×M16×C31C2311yescharacteristic
149C2×M16×C31C2311yescharacteristic
150C2×M16×C31C2311yescharacteristic
151C22×C8×C31—21no—
152C22×C8×C31—21no—
153C22×C8×C31—21no—
154C22×C8×C31C2311yescharacteristic
155C22×C8×C31C2311yescharacteristic
156C31×#121—21no—
157C31×#121—21no—
158C31×#121—21no—
159C31×#121—21no—
160C2×C4⋊C4×C31C2311yescharacteristic
161C2×C22⋊C4×C31—21no—
162C31×#108—22no—
163C31×#108—22no—
164C31×#103—21no—
165C31×#103—21no—
166C31×#103—21no—
167C31×#103—21no—
168C31×#102—21no—
169C31×#102—21no—
170C31×#102—21no—
171C31×#102—21no—
172C31×#101—22no—
173C31×#101—41no—
174C31×#100—22no—
175C31×#100—22no—
176C31×#100—22no—
177C31×#100—41no—
178C31×C22⋊C8—21no—
179C31×C22⋊C8—21no—
180C31×C22⋊C8—21no—
181C31×C22⋊C8—21no—
182C31×C22⋊C8—21no—
183C31×C22⋊C8—21no—
184C31×C22⋊C8—21no—
185C31×C22⋊C8—21no—
186C31×C22⋊C8D411yescharacteristic
187C31×C22⋊C8D411yescharacteristic
188C31×C22⋊C8D411yescharacteristic
189C31×C22⋊C8D411yescharacteristic
190C24×C31—21no—
191C24×C31—21no—
192C24×C31—21no—
193C24×C31#4111yescharacteristic
194#41×C31—21no—
195#41×C31—21no—
196#41×C31—24no—
197#41×C31—24no—
198#41×C31—22no—
199#41×C31—22no—
200#41×C31—21no—
201#41×C31—21no—
202#41×C31—21no—
203#41×C31—21no—
204#41×C31—42no—
205#41×C31—42no—
206#41×C31—41no—
207#41×C31—41no—
208#41×C31—42no—
209#41×C31—42no—
210#41×C31—42no—
211#41×C31—42no—
212#41×C31—42no—
213#41×C31—42no—
214#41×C31—42no—
215#41×C31—42no—
216#41×C31C2×D412yes—
217#41×C31C2×D412yes—
218C2×Q8×C31—21no—
219C2×Q8×C31—21no—
220C2×Q8×C31—22no—
221C2×Q8×C31—21no—
222C2×Q8×C31—21no—
223C2×Q8×C31—21no—
224C2×Q8×C31—21no—
225C2×Q8×C31—41no—
226C2×Q8×C31C2×D412yes—
227C2×Q8×C31C2×D411yescharacteristic
228C2×Q8×C31C2×D411yescharacteristic
229C2×D4×C31—21no—
230C2×D4×C31—22no—
231C2×D4×C31—21no—
232C2×D4×C31—21no—
233C2×D4×C31—21no—
234C2×D4×C31—21no—
235C2×D4×C31—21no—
236C2×D4×C31—21no—
237C2×D4×C31—21no—
238C2×D4×C31—21no—
239C2×D4×C31—21no—
240C2×D4×C31—21no—
241C2×D4×C31—21no—
242C2×D4×C31—21no—
243C2×D4×C31—21no—
244C2×D4×C31—21no—
245C2×D4×C31—21no—
246C2×D4×C31—41no—
247C2×D4×C31—42no—
248C2×D4×C31—42no—
249C2×D4×C31—42no—
250C2×D4×C31—42no—
251C2×D4×C31—41no—
252C2×D4×C31—41no—
253C2×D4×C31—41no—
254C2×D4×C31—41no—
255C2×D4×C31—82no—
256C2×D4×C31C2×D412yes—
257C2×D4×C31C2×D411yescharacteristic
258C2×D4×C31C2×D411yescharacteristic
259C22×C4×C31—21no—
260C22×C4×C31—21no—
261C22×C4×C31—21no—
262C22×C4×C31—21no—
263C22×C4×C31—21no—
264C22×C4×C31—21no—
265C22×C4×C31—21no—
266C22×C4×C31—21no—
267C22×C4×C31—21no—
268C22×C4×C31—21no—
269C22×C4×C31—21no—
270C22×C4×C31—42no—
271C22×C4×C31—42no—
272C22×C4×C31—42no—
273C22×C4×C31—42no—
274C22×C4×C31—41no—
275C22×C4×C31—41no—
276C22×C4×C31C2×D411yescharacteristic
277C22×C4×C31C2×D411yescharacteristic
278C22×C4×C31C2×D411yescharacteristic
279C22×C4×C31C2×D411yescharacteristic
280C22×C4×C31#4111yescharacteristic
281C22×C4×C31C2411yescharacteristic
282Q16×C31—24no—
283Q16×C31—24no—
284SD16×C31—24no—
285SD16×C31—24no—
286SD16×C31—24no—
287SD16×C31—24no—
288SD16×C31—42no—
289SD16×C31—42no—
290SD16×C31—42no—
291SD16×C31—42no—
292D8×C31—24no—
293D8×C31—24no—
294D8×C31—42no—
295D8×C31—42no—
296D8×C31—42no—
297D8×C31—42no—
298M16×C31—24no—
299M16×C31—21no—
300M16×C31—21no—
301M16×C31—21no—
302M16×C31—21no—
303M16×C31—21no—
304M16×C31—21no—
305M16×C31—21no—
306M16×C31—21no—
307M16×C31—21no—
308M16×C31—21no—
309M16×C31—42no—
310M16×C31—42no—
311M16×C31C2×D412yes—
312M16×C31C2×D412yes—
313C2×C8×C31—24no—
314C2×C8×C31—21no—
315C2×C8×C31—21no—
316C2×C8×C31—21no—
317C2×C8×C31—21no—
318C2×C8×C31—21no—
319C2×C8×C31—21no—
320C2×C8×C31—21no—
321C2×C8×C31—21no—
322C2×C8×C31—21no—
323C2×C8×C31—21no—
324C2×C8×C31—42no—
325C2×C8×C31—42no—
326C2×C8×C31C2×D411yescharacteristic
327C2×C8×C31C2×D411yescharacteristic
328C2×C8×C31C2×D411yescharacteristic
329C2×C8×C31C2×D411yescharacteristic
330C4⋊C4×C31—21no—
331C4⋊C4×C31—21no—
332C22⋊C4×C31—41no—
333C22⋊C4×C31—41no—
334#24402C3111yesmaximal, characteristic, direct product factor, Sylow
335C23×C31—21no—
336C23×C31—21no—
337C23×C31—21no—
338C23×C31—21no—
339C23×C31—22no—
340C23×C31—41no—
341C23×C31—41no—
342C23×C31—42no—
343C23×C31—42no—
344C23×C31—41no—
345C23×C31—41no—
346C23×C31—41no—
347C23×C31—41no—
348C23×C31—41no—
349C23×C31—81no—
350C23×C31—81no—
351C23×C31—81no—
352C23×C31—81no—
353C23×C31—81no—
354C23×C31#12111yescharacteristic
355C23×C31#12111yescharacteristic
356C23×C31C2×#4111yescharacteristic
357Q8×C31—21no—
358Q8×C31—21no—
359Q8×C31—22no—
360Q8×C31—21no—
361Q8×C31—22no—
362Q8×C31—42no—
363Q8×C31—41no—
364Q8×C31—41no—
365Q8×C31#12012yes—
366D4×C31—22no—
367D4×C31—22no—
368D4×C31—21no—
369D4×C31—22no—
370D4×C31—21no—
371D4×C31—21no—
372D4×C31—22no—
373D4×C31—42no—
374D4×C31—42no—
375D4×C31—42no—
376D4×C31—44no—
377D4×C31—44no—
378D4×C31—41no—
379D4×C31—41no—
380D4×C31—41no—
381D4×C31—41no—
382D4×C31—41no—
383D4×C31—41no—
384D4×C31—41no—
385D4×C31—41no—
386D4×C31—82no—
387D4×C31—82no—
388D4×C31#12012yes—
389C2×C4×C31—21no—
390C2×C4×C31—21no—
391C2×C4×C31—21no—
392C2×C4×C31—21no—
393C2×C4×C31—21no—
394C2×C4×C31—21no—
395C2×C4×C31—21no—
396C2×C4×C31—22no—
397C2×C4×C31—22no—
398C2×C4×C31—21no—
399C2×C4×C31—21no—
400C2×C4×C31—21no—
401C2×C4×C31—21no—
402C2×C4×C31—21no—
403C2×C4×C31—22no—
404C2×C4×C31—42no—
405C2×C4×C31—42no—
406C2×C4×C31—42no—
407C2×C4×C31—44no—
408C2×C4×C31—44no—
409C2×C4×C31—41no—
410C2×C4×C31—41no—
411C2×C4×C31—41no—
412C2×C4×C31—41no—
413C2×C4×C31—41no—
414C2×C4×C31—81no—
415C2×C4×C31#12111yescharacteristic
416C2×C4×C31#12111yescharacteristic
417C2×C4×C31C22×D411yescharacteristic
418C2×C4×C31C22×D411yescharacteristic
419C2×C4×C31C22×D411yescharacteristic
420C2×C4×C31C22×D411yescharacteristic
421C2×C4×C31H(5,𝔽2)11yescharacteristic
422C2×C4×C31H(5,𝔽2)11yescharacteristic
423C8×C31—22no—
424C8×C31—22no—
425C8×C31—21no—
426C8×C31—21no—
427C8×C31—21no—
428C8×C31—21no—
429C8×C31—41no—
430C8×C31—41no—
431C8×C31—41no—
432C8×C31—41no—
433C2×#575C2×C3111yescharacteristic, complemented
434C2×#472C2×C3111yescharacteristic, complemented
435C2×#471C2×C3111yescharacteristic, complemented
436#3006C2×C3111yescharacteristic, complemented
437C2×#449C2×C3111yescharacteristic, complemented
438#2880C2×C3111yescharacteristic, complemented
439#2052C2×C3111yescharacteristic, complemented
440#2051C2×C3111yescharacteristic, complemented
441#2019C2×C3111yescharacteristic, complemented
442#2018C2×C3111yescharacteristic, complemented
443#1908C2×C3111yescharacteristic, complemented
444#1907C2×C3111yescharacteristic, complemented
445#1900C2×C3111yescharacteristic, complemented
446#1855C2×C3111yescharacteristic, complemented
447#1785C2×C3111yescharacteristic, complemented
448C22×C31—21no—
449C22×C31—21no—
450C22×C31—21no—
451C22×C31—21no—
452C22×C31—22no—
453C22×C31—21no—
454C22×C31—21no—
455C22×C31—21no—
456C22×C31—21no—
457C22×C31—41no—
458C22×C31—41no—
459C22×C31—41no—
460C22×C31—42no—
461C22×C31—41no—
462C22×C31—41no—
463C22×C31—81no—
464C22×C31—81no—
465C22×C31—82no—
466C22×C31—82no—
467C22×C31—84no—
468C22×C31—81no—
469C22×C31—81no—
470C22×C31—81no—
471C22×C31—81no—
472C22×C31—81no—
473C22×C31—161no—
474C22×C31—161no—
475C22×C31C2×#12111yescharacteristic
476C22×C31#54611yescharacteristic
477C22×C31#54611yescharacteristic
478C4×C31—21no—
479C4×C31—21no—
480C4×C31—22no—
481C4×C31—41no—
482C4×C31—42no—
483C4×C31—81no—
484C4×C31C2×#12011yescharacteristic
485C4×C31#53411yescharacteristic
486C4×C31D4211yescharacteristic
487C4×C31D4211yescharacteristic
488C22×#41C22×C3111yescharacteristic
489C22×#41C22×C3111yescharacteristic
490#575—24no—
491#575—24no—
492C2×#137—21no—
493C2×#137C22×C3111yescharacteristic
494C2×#137C22×C3111yescharacteristic
495C2×AGL(1,ℤ/8)—21no—
496C2×AGL(1,ℤ/8)C22×C3111yescharacteristic
497C2×AGL(1,ℤ/8)C22×C3111yescharacteristic
498C2×AGL(1,ℤ/8)C22×C3111yescharacteristic
499C2×AGL(1,ℤ/8)C22×C3111yescharacteristic
500C2×#135—21no—
501C2×#135—21no—
502C22×SD16C22×C3111yescharacteristic, complemented
503C22×D8C22×C3111yescharacteristic, complemented
504C2×#131C22×C3111yescharacteristic
505C2×#131C22×C3111yescharacteristic
506C22×M16C22×C3111yescharacteristic
507C2×#121C22×C3111yescharacteristic
508#472—24no—
509#471—24no—
510#449—21no—
511#449—21no—
512#449—21no—
513#449—21no—
514#449—21no—
515#449—21no—
516#448—21no—
517#447—21no—
518C2×#108C22×C3111yescharacteristic, complemented
519C2×#108C22×C3111yescharacteristic, complemented
520#417C22×C3111yescharacteristic
521#417C22×C3111yescharacteristic
522C2×#103C22×C3111yescharacteristic, complemented
523C2×#102C22×C3111yescharacteristic, complemented
524C2×#101C22×C3111yescharacteristic, complemented
525C2×#101C22×C3111yescharacteristic, complemented
526C2×#100C22×C3111yescharacteristic, complemented
527C2×#100C22×C3111yescharacteristic, complemented
528C2×#100C22×C3111yescharacteristic, complemented
529C2×#100C22×C3111yescharacteristic, complemented
530#408—21no—
531#408—21no—
532#408C22×C3111yescharacteristic
533#408C22×C3111yescharacteristic
534#407—21no—
535#407C22×C3111yescharacteristic
536#407C22×C3111yescharacteristic
537C2×C22⋊C8—21no—
538C2×C22⋊C8C22×C3111yescharacteristic
539#343C22×C3111yescharacteristic, complemented
540#343C22×C3111yescharacteristic, complemented
541#341C22×C3111yescharacteristic, complemented
542#341C22×C3111yescharacteristic, complemented
543C2×C31—21no—
544C2×C31—21no—
545C2×C31—41no—
546C2×C31—41no—
547C2×C31—42no—
548C2×C31—81no—
549C2×C31—82no—
550C2×C31—161no—
551C2×C31#241011yescharacteristic
552C2×C31#306711yescharacteristic
553C2×C31#306811yescharacteristic
554C2×#41—21no—
555C2×#41—21no—
556C2×#41—22no—
557C2×#41—22no—
558C2×#41—22no—
559C2×#41—22no—
560C2×#41—21no—
561C2×#41—21no—
562C2×#41—21no—
563C2×#41—21no—
564C2×#41—41no—
565C2×#41—41no—
566C2×#41—41no—
567C2×#41—41no—
568C2×#41D4×C3111yescharacteristic
569C2×#41D4×C3111yescharacteristic
570C2×#41C23×C3111yescharacteristic
571C2×#41C23×C3111yescharacteristic
572C22×Q8D4×C3111yescharacteristic
573C22×Q8C23×C3111yescharacteristic
574C22×D4—21no—
575C22×D4—21no—
576C22×D4—21no—
577C22×D4D4×C3111yescharacteristic
578C22×D4C23×C3111yescharacteristic
579C22×D4C23×C3111yescharacteristic
580C23×C4—21no—
581C23×C4—21no—
582C23×C4C23×C3111yescharacteristic
583#137—28no—
584#137—22no—
585#137—22no—
586#137—22no—
587#137D4×C3114yescomplemented
588AGL(1,ℤ/8)—28no—
589AGL(1,ℤ/8)—22no—
590AGL(1,ℤ/8)—22no—
591AGL(1,ℤ/8)—22no—
592AGL(1,ℤ/8)—22no—
593AGL(1,ℤ/8)—22no—
594AGL(1,ℤ/8)—41no—
595AGL(1,ℤ/8)—41no—
596AGL(1,ℤ/8)D4×C3114yescomplemented
597#135—28no—
598#135—28no—
599C2×Q16—21no—
600C2×Q16—21no—
601C2×SD16—21no—
602C2×SD16—21no—
603C2×SD16—21no—
604C2×SD16—21no—
605C2×SD16—22no—
606C2×SD16—21no—
607C2×SD16—21no—
608C2×SD16—21no—
609C2×SD16—21no—
610C2×SD16—41no—
611C2×D8—21no—
612C2×D8—21no—
613C2×D8—22no—
614C2×D8—21no—
615C2×D8—21no—
616C2×D8—21no—
617C2×D8—21no—
618C2×D8—41no—
619#131—22no—
620#131—22no—
621#131—41no—
622#131—41no—
623C2×M16—21no—
624C2×M16—22no—
625C2×M16—22no—
626C2×M16—21no—
627C2×M16—21no—
628C2×M16C23×C3111yescharacteristic
629C2×M16C23×C3111yescharacteristic
630C2×M16C23×C3111yescharacteristic
631C2×M16C23×C3111yescharacteristic
632C2×M16C23×C3111yescharacteristic
633C2×M16C23×C3111yescharacteristic
634C22×C8—21no—
635C22×C8—21no—
636C22×C8—21no—
637C22×C8C23×C3111yescharacteristic
638C22×C8C23×C3111yescharacteristic
639#121—21no—
640#121—21no—
641#121—21no—
642#121—21no—
643C2×C4⋊C4C23×C3111yescharacteristic
644C2×C22⋊C4—21no—
645#108—22no—
646#108—22no—
647#103—21no—
648#103—21no—
649#103—21no—
650#103—21no—
651#102—21no—
652#102—21no—
653#102—21no—
654#102—21no—
655#101—22no—
656#101—41no—
657#100—22no—
658#100—22no—
659#100—22no—
660#100—41no—
661C22⋊C8—21no—
662C22⋊C8—21no—
663C22⋊C8—21no—
664C22⋊C8—21no—
665C22⋊C8—21no—
666C22⋊C8—21no—
667C22⋊C8—21no—
668C22⋊C8—21no—
669C22⋊C8D4×C3111yescharacteristic
670C22⋊C8D4×C3111yescharacteristic
671C22⋊C8D4×C3111yescharacteristic
672C22⋊C8D4×C3111yescharacteristic
673C31#2440211yescharacteristic, direct product factor, Sylow
674C24—21no—
675C24—21no—
676C24—21no—
677C24#41×C3111yescharacteristic
678#41—21no—
679#41—21no—
680#41—24no—
681#41—24no—
682#41—22no—
683#41—22no—
684#41—21no—
685#41—21no—
686#41—21no—
687#41—21no—
688#41—42no—
689#41—42no—
690#41—41no—
691#41—41no—
692#41—42no—
693#41—42no—
694#41—42no—
695#41—42no—
696#41—42no—
697#41—42no—
698#41—42no—
699#41—42no—
700#41C2×D4×C3112yes—
701#41C2×D4×C3112yes—
702C2×Q8—21no—
703C2×Q8—21no—
704C2×Q8—22no—
705C2×Q8—21no—
706C2×Q8—21no—
707C2×Q8—21no—
708C2×Q8—21no—
709C2×Q8—41no—
710C2×Q8C2×D4×C3112yes—
711C2×Q8C2×D4×C3111yescharacteristic
712C2×Q8C2×D4×C3111yescharacteristic
713C2×D4—21no—
714C2×D4—22no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—21no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—41no—
731C2×D4—42no—
732C2×D4—42no—
733C2×D4—42no—
734C2×D4—42no—
735C2×D4—41no—
736C2×D4—41no—
737C2×D4—41no—
738C2×D4—41no—
739C2×D4—82no—
740C2×D4C2×D4×C3112yes—
741C2×D4C2×D4×C3111yescharacteristic
742C2×D4C2×D4×C3111yescharacteristic
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—42no—
755C22×C4—42no—
756C22×C4—42no—
757C22×C4—42no—
758C22×C4—41no—
759C22×C4—41no—
760C22×C4C2×D4×C3111yescharacteristic
761C22×C4C2×D4×C3111yescharacteristic
762C22×C4C2×D4×C3111yescharacteristic
763C22×C4C2×D4×C3111yescharacteristic
764C22×C4#41×C3111yescharacteristic
765C22×C4C24×C3111yescharacteristic
766Q16—24no—
767Q16—24no—
768SD16—24no—
769SD16—24no—
770SD16—24no—
771SD16—24no—
772SD16—42no—
773SD16—42no—
774SD16—42no—
775SD16—42no—
776D8—24no—
777D8—24no—
778D8—42no—
779D8—42no—
780D8—42no—
781D8—42no—
782M16—24no—
783M16—21no—
784M16—21no—
785M16—21no—
786M16—21no—
787M16—21no—
788M16—21no—
789M16—21no—
790M16—21no—
791M16—21no—
792M16—21no—
793M16—42no—
794M16—42no—
795M16C2×D4×C3112yes—
796M16C2×D4×C3112yes—
797C2×C8—24no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—42no—
809C2×C8—42no—
810C2×C8C2×D4×C3111yescharacteristic
811C2×C8C2×D4×C3111yescharacteristic
812C2×C8C2×D4×C3111yescharacteristic
813C2×C8C2×D4×C3111yescharacteristic
814C4⋊C4—21no—
815C4⋊C4—21no—
816C22⋊C4—41no—
817C22⋊C4—41no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—22no—
823C23—41no—
824C23—41no—
825C23—42no—
826C23—42no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23—81no—
836C23—81no—
837C23C31×#12111yescharacteristic
838C23C31×#12111yescharacteristic
839C23C2×#41×C3111yescharacteristic
840Q8—21no—
841Q8—21no—
842Q8—22no—
843Q8—21no—
844Q8—22no—
845Q8—42no—
846Q8—41no—
847Q8—41no—
848Q8C31×#12012yes—
849D4—22no—
850D4—22no—
851D4—21no—
852D4—22no—
853D4—21no—
854D4—21no—
855D4—22no—
856D4—42no—
857D4—42no—
858D4—42no—
859D4—44no—
860D4—44no—
861D4—41no—
862D4—41no—
863D4—41no—
864D4—41no—
865D4—41no—
866D4—41no—
867D4—41no—
868D4—41no—
869D4—82no—
870D4—82no—
871D4C31×#12012yes—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—22no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—44no—
891C2×C4—44no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—81no—
898C2×C4C31×#12111yescharacteristic
899C2×C4C31×#12111yescharacteristic
900C2×C4C22×D4×C3111yescharacteristic
901C2×C4C22×D4×C3111yescharacteristic
902C2×C4C22×D4×C3111yescharacteristic
903C2×C4C22×D4×C3111yescharacteristic
904C2×C4C31×H(5,𝔽2)11yescharacteristic
905C2×C4C31×H(5,𝔽2)11yescharacteristic
906C8—22no—
907C8—22no—
908C8—21no—
909C8—21no—
910C8—21no—
911C8—21no—
912C8—41no—
913C8—41no—
914C8—41no—
915C8—41no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—22no—
921C22—21no—
922C22—21no—
923C22—21no—
924C22—21no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—42no—
929C22—41no—
930C22—41no—
931C22—81no—
932C22—81no—
933C22—82no—
934C22—82no—
935C22—84no—
936C22—81no—
937C22—81no—
938C22—81no—
939C22—81no—
940C22—81no—
941C22—161no—
942C22—161no—
943C22C2×C31×#12111yescharacteristic
944C22C31×#54611yescharacteristic
945C22C31×#54611yescharacteristic
946C4—21no—
947C4—21no—
948C4—22no—
949C4—41no—
950C4—42no—
951C4—81no—
952C4C2×C31×#12011yescharacteristic
953C4C31×#53411yescharacteristic
954C4D42×C3111yescharacteristic
955C4D42×C3111yescharacteristic
956C2—21no—
957C2—21no—
958C2—41no—
959C2—41no—
960C2—42no—
961C2—81no—
962C2—82no—
963C2—161no—
964C2C31×#241011yescharacteristic
965C2C31×#306711yescharacteristic
966C2C31×#306811yescharacteristic
subgroupG/H
center, socleC22×C31C2×#121
commutator, Frattini, cosocleC22×C4C24×C31
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
1. C2×C31×#575C2semidirect
2. C2×C31×#472C2semidirect
3. C2×C31×#471C2semidirect
4. C31×#3006C2semidirect
5. C2×C31×#449C2semidirect
6. C31×#2880C2semidirect
7. C31×#2052C2semidirect
8. C31×#2051C2semidirect
9. C31×#2019C2semidirect
10. C31×#2018C2semidirect
11. C31×#1908C2semidirect
12. C31×#1907C2semidirect
13. C31×#1900C2semidirect
14. C31×#1855C2semidirect
15. C31×#1785C2semidirect
30. C22×SD16×C31C22semidirect
31. C22×D8×C31C22semidirect
46. C2×C31×#108C22semidirect
47. C2×C31×#108C22semidirect
50. C2×C31×#103C22semidirect
51. C2×C31×#102C22semidirect
52. C2×C31×#101C22semidirect
53. C2×C31×#101C22semidirect
54. C2×C31×#100C22semidirect
55. C2×C31×#100C22semidirect
56. C2×C31×#100C22semidirect
57. C2×C31×#100C22semidirect
67. C31×#343C22semidirect
68. C31×#343C22semidirect
69. C31×#341C22semidirect
70. C31×#341C22semidirect
104. C31×#137D4semidirect
113. C31×AGL(1,ℤ/8)D4semidirect
334. #24402C31direct (N × H)
433. C2×#575C2×C31semidirect
434. C2×#472C2×C31semidirect
435. C2×#471C2×C31semidirect
436. #3006C2×C31semidirect
437. C2×#449C2×C31semidirect
438. #2880C2×C31semidirect
439. #2052C2×C31semidirect
440. #2051C2×C31semidirect
441. #2019C2×C31semidirect
442. #2018C2×C31semidirect
443. #1908C2×C31semidirect
444. #1907C2×C31semidirect
445. #1900C2×C31semidirect
446. #1855C2×C31semidirect
447. #1785C2×C31semidirect
502. C22×SD16C22×C31semidirect
503. C22×D8C22×C31semidirect
518. C2×#108C22×C31semidirect
519. C2×#108C22×C31semidirect
522. C2×#103C22×C31semidirect
523. C2×#102C22×C31semidirect
524. C2×#101C22×C31semidirect
525. C2×#101C22×C31semidirect
526. C2×#100C22×C31semidirect
527. C2×#100C22×C31semidirect
528. C2×#100C22×C31semidirect
529. C2×#100C22×C31semidirect
539. #343C22×C31semidirect
540. #343C22×C31semidirect
541. #341C22×C31semidirect
542. #341C22×C31semidirect
587. #137D4×C31semidirect
596. AGL(1,ℤ/8)D4×C31semidirect
673. C31#24402direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5752
C2×C31×#4722
C2×C31×#4712
C31×#30062
C2×C31×#4492
C31×#28802
C31×#20522
C31×#20512
C31×#20192
C31×#20182
C31×#19082
C31×#19072
C31×#19002
C31×#18552
C31×#17852
#2440231