Finite Group Databasebeta

← C31×#24456 #21481215

Subgroups — C31×#24456 #21481215

Order 7936.

1410 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#576C211yesmaximal, characteristic, complemented
2C2×C31×#472C211yesmaximal, characteristic, complemented
3C31×#3045C211yesmaximal, characteristic, complemented
4C2×C31×#453C211yesmaximal, characteristic, complemented
5C31×#3008C211yesmaximal, characteristic, complemented
6C31×#2897C211yesmaximal, characteristic, complemented
7C31×#2051C211yesmaximal, characteristic, complemented
8C31×#2045C211yesmaximal, characteristic, complemented
9C31×#2011C211yesmaximal, characteristic, complemented
10C31×#2002C211yesmaximal, characteristic, complemented
11C31×#1907C211yesmaximal, characteristic, complemented
12C31×#1883C211yesmaximal, characteristic, complemented
13C31×#1876C211yesmaximal, characteristic, complemented
14C31×#1866C211yesmaximal, characteristic, complemented
15C31×#1792C211yesmaximal, characteristic, complemented
16C2×C31×H(5,𝔽2)C2211yescharacteristic
17C2×C31×H(5,𝔽2)C2211yescharacteristic
18C31×#576—24no—
19C31×#576—24no—
20C2×C31×AGL(1,ℤ/8)—21no—
21C2×C31×AGL(1,ℤ/8)—21no—
22C2×C31×AGL(1,ℤ/8)C2211yescharacteristic
23C2×C31×AGL(1,ℤ/8)C2211yescharacteristic
24C2×C31×AGL(1,ℤ/8)C2211yescharacteristic
25C2×C31×AGL(1,ℤ/8)C2211yescharacteristic, complemented
26C2×C31×#135—21no—
27C2×C31×#135C2211yescharacteristic
28C22×D8×C31—21no—
29C22×D8×C31C2211yescharacteristic
30C22×D8×C31C2211yescharacteristic, complemented
31C2×C31×#131C2211yescharacteristic
32C2×C31×#131C2211yescharacteristic, complemented
33C31×#535C2211yescharacteristic, complemented
34C2×C31×#127C2211yescharacteristic, complemented
35C31×#520C2211yescharacteristic, complemented
36C31×#472—24no—
37C31×#464—21no—
38C31×#463—21no—
39C31×#460—21no—
40C31×#459—21no—
41C31×#453—24no—
42C31×#449—21no—
43C31×#449—21no—
44C31×#447—21no—
45C31×#447—21no—
46C2×C31×#108C2211yescharacteristic, complemented
47C31×#424C2211yescharacteristic, complemented
48C2×C31×#104C2211yescharacteristic
49C2×C31×#104C2211yescharacteristic, complemented
50C2×C31×#104C2211yescharacteristic, complemented
51C31×#418—21no—
52C31×#418C2211yescharacteristic, complemented
53C31×#418C2211yescharacteristic, complemented
54C31×#417—21no—
55C31×#417C2211yescharacteristic
56C31×#417C2211yescharacteristic, complemented
57C31×#416—21no—
58C31×#416C2211yescharacteristic
59C2×C31×#102—21no—
60C2×C31×#102C2211yescharacteristic, complemented
61C2×C31×#102C2211yescharacteristic, complemented
62C2×C31×#100C2211yescharacteristic, complemented
63C2×C31×#100C2211yescharacteristic, complemented
64C2×C31×#100C2211yescharacteristic, complemented
65C31×#408C2211yescharacteristic, complemented
66C31×#390C2211yescharacteristic, complemented
67C31×#343C2211yescharacteristic, complemented
68C31×#341C2211yescharacteristic, complemented
69C31×#339C2211yescharacteristic, complemented
70C31×#336C2211yescharacteristic, complemented
71C31×H(5,𝔽2)—22no—
72C31×H(5,𝔽2)—22no—
73C31×H(5,𝔽2)—22no—
74C31×H(5,𝔽2)—22no—
75C31×H(5,𝔽2)—22no—
76C31×H(5,𝔽2)—41no—
77C31×H(5,𝔽2)—41no—
78C31×H(5,𝔽2)D414yescomplemented
79C2×#41×C31—21no—
80C2×#41×C31—21no—
81C2×#41×C31—21no—
82C2×#41×C31—21no—
83C2×#41×C31C2311yescharacteristic
84C2×#41×C31C2311yescharacteristic
85C2×#41×C31C2311yescharacteristic
86C22×D4×C31—21no—
87C22×D4×C31—21no—
88C22×D4×C31—21no—
89C22×D4×C31—21no—
90C22×D4×C31—41no—
91C22×D4×C31—41no—
92C22×D4×C31—41no—
93C22×D4×C31C2311yescharacteristic
94C22×D4×C31C2311yescharacteristic
95C22×D4×C31C2311yescharacteristic
96C31×AGL(1,ℤ/8)—28no—
97C31×AGL(1,ℤ/8)—28no—
98C31×AGL(1,ℤ/8)—22no—
99C31×AGL(1,ℤ/8)—22no—
100C31×AGL(1,ℤ/8)—22no—
101C31×AGL(1,ℤ/8)—22no—
102C31×AGL(1,ℤ/8)—22no—
103C31×AGL(1,ℤ/8)—22no—
104C31×AGL(1,ℤ/8)—22no—
105C31×AGL(1,ℤ/8)D414yescomplemented
106C31×#135—28no—
107C31×#135—22no—
108C31×#135—22no—
109C2×Q16×C31D411yescharacteristic, complemented
110C2×SD16×C31—21no—
111C2×SD16×C31—21no—
112C2×SD16×C31—21no—
113C2×SD16×C31—21no—
114C2×SD16×C31D411yescharacteristic, complemented
115C2×SD16×C31D411yescharacteristic, complemented
116C2×D8×C31—28no—
117C2×D8×C31—21no—
118C2×D8×C31—21no—
119C2×D8×C31—22no—
120C2×D8×C31—22no—
121C2×D8×C31—21no—
122C2×D8×C31—21no—
123C2×D8×C31—22no—
124C2×D8×C31—21no—
125C2×D8×C31—21no—
126C2×D8×C31—21no—
127C2×D8×C31—21no—
128C2×D8×C31—41no—
129C2×D8×C31D411yescharacteristic, complemented
130C31×#131—22no—
131C31×#131—22no—
132C31×#131—22no—
133C31×#131—41no—
134C2×M16×C31—21no—
135C2×M16×C31—21no—
136C2×M16×C31C2311yescharacteristic
137C2×M16×C31C2311yescharacteristic
138C2×M16×C31C2311yescharacteristic
139C2×M16×C31C2311yescharacteristic
140C22×C8×C31—21no—
141C22×C8×C31—21no—
142C22×C8×C31C2311yescharacteristic
143C22×C8×C31C2311yescharacteristic
144C31×#127—22no—
145C31×#127—21no—
146C31×#127—41no—
147C31×#124—21no—
148C31×#121—21no—
149C31×#121—21no—
150C31×#120—41no—
151C4×Q8×C31—21no—
152C4×D4×C31—21no—
153C4×D4×C31—41no—
154C31×#117—21no—
155C31×#117C2311yescharacteristic
156C2×C4⋊C4×C31—21no—
157C2×C4⋊C4×C31C2311yescharacteristic
158C2×C22⋊C4×C31—41no—
159C2×C42×C31C2311yescharacteristic
160C31×#108—22no—
161C31×C4⋊C8—21no—
162C31×C4⋊C8—21no—
163C31×#104—22no—
164C31×#104—22no—
165C31×#104—41no—
166C31×#103—21no—
167C31×#103—21no—
168C31×#103D411yescharacteristic, complemented
169C31×#103D411yescharacteristic, complemented
170C31×#102—21no—
171C31×#102—21no—
172C31×#102—21no—
173C31×#102—21no—
174C31×#102—21no—
175C31×#102—21no—
176C31×#102—21no—
177C31×#102—21no—
178C31×#102—21no—
179C31×#102—21no—
180C31×#102D411yescharacteristic, complemented
181C31×#102D411yescharacteristic, complemented
182C31×#100—22no—
183C31×#100—22no—
184C31×#100—22no—
185C31×C22⋊C8—21no—
186C31×C22⋊C8—21no—
187C24×C31—21no—
188C24×C31—21no—
189C24×C31—21no—
190C24×C31—41no—
191C24×C31—41no—
192#41×C31—21no—
193#41×C31—21no—
194#41×C31—21no—
195#41×C31—21no—
196#41×C31—24no—
197#41×C31—24no—
198#41×C31—24no—
199#41×C31—21no—
200#41×C31—21no—
201#41×C31—21no—
202#41×C31—21no—
203#41×C31—42no—
204#41×C31—42no—
205#41×C31—42no—
206#41×C31—42no—
207#41×C31—42no—
208#41×C31C2×D412yes—
209#41×C31C2×D412yes—
210#41×C31C2×D412yes—
211#41×C31#4112yes—
212C2×Q8×C31C2×D411yescharacteristic
213C2×Q8×C31C2×D411yescharacteristic
214C2×Q8×C31C2×D411yescharacteristic
215C2×D4×C31—21no—
216C2×D4×C31—21no—
217C2×D4×C31—24no—
218C2×D4×C31—24no—
219C2×D4×C31—24no—
220C2×D4×C31—21no—
221C2×D4×C31—21no—
222C2×D4×C31—21no—
223C2×D4×C31—21no—
224C2×D4×C31—21no—
225C2×D4×C31—21no—
226C2×D4×C31—21no—
227C2×D4×C31—21no—
228C2×D4×C31—21no—
229C2×D4×C31—21no—
230C2×D4×C31—21no—
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—42no—
238C2×D4×C31—42no—
239C2×D4×C31—42no—
240C2×D4×C31—41no—
241C2×D4×C31—41no—
242C2×D4×C31—41no—
243C2×D4×C31—41no—
244C2×D4×C31—41no—
245C2×D4×C31—41no—
246C2×D4×C31—44no—
247C2×D4×C31—42no—
248C2×D4×C31—44no—
249C2×D4×C31—44no—
250C2×D4×C31—44no—
251C2×D4×C31—42no—
252C2×D4×C31—44no—
253C2×D4×C31—82no—
254C2×D4×C31—82no—
255C2×D4×C31C2×D412yes—
256C2×D4×C31C2×D412yes—
257C2×D4×C31C2×D411yescharacteristic
258C2×D4×C31C2×D411yescharacteristic
259C2×D4×C31C2×D411yescharacteristic
260C22×C4×C31—21no—
261C22×C4×C31—21no—
262C22×C4×C31—21no—
263C22×C4×C31—21no—
264C22×C4×C31—21no—
265C22×C4×C31—41no—
266C22×C4×C31—41no—
267C22×C4×C31—41no—
268C22×C4×C31C2411yescharacteristic
269Q16×C31—22no—
270SD16×C31—24no—
271SD16×C31—24no—
272SD16×C31—22no—
273SD16×C31—22no—
274SD16×C31—42no—
275SD16×C31—42no—
276D8×C31—24no—
277D8×C31—24no—
278D8×C31—24no—
279D8×C31—22no—
280D8×C31—24no—
281D8×C31—42no—
282D8×C31—42no—
283D8×C31—42no—
284D8×C31—42no—
285M16×C31—24no—
286M16×C31—21no—
287M16×C31—21no—
288M16×C31—21no—
289M16×C31—21no—
290M16×C31—21no—
291M16×C31—21no—
292M16×C31—21no—
293M16×C31—42no—
294M16×C31C2×D412yes—
295C2×C8×C31—24no—
296C2×C8×C31—21no—
297C2×C8×C31—21no—
298C2×C8×C31—21no—
299C2×C8×C31—21no—
300C2×C8×C31—21no—
301C2×C8×C31—21no—
302C2×C8×C31—21no—
303C2×C8×C31—21no—
304C2×C8×C31—42no—
305C2×C8×C31C2×D411yescharacteristic
306C2×C8×C31C2×D411yescharacteristic
307C2×C8×C31C2×D411yescharacteristic
308C2×C8×C31C2×D411yescharacteristic
309C4⋊C4×C31—21no—
310C4⋊C4×C31—21no—
311C4⋊C4×C31—41no—
312C4⋊C4×C31C2×D411yescharacteristic
313C4⋊C4×C31C2×D411yescharacteristic
314C22⋊C4×C31—21no—
315C22⋊C4×C31—41no—
316C22⋊C4×C31—41no—
317C22⋊C4×C31—41no—
318C22⋊C4×C31—82no—
319C42×C31—21no—
320C42×C31—21no—
321C42×C31—21no—
322C42×C31—41no—
323#24456C3111yesmaximal, characteristic, direct product factor, Sylow
324C23×C31—21no—
325C23×C31—21no—
326C23×C31—21no—
327C23×C31—22no—
328C23×C31—22no—
329C23×C31—44no—
330C23×C31—44no—
331C23×C31—41no—
332C23×C31—41no—
333C23×C31—41no—
334C23×C31—41no—
335C23×C31—41no—
336C23×C31—41no—
337C23×C31—41no—
338C23×C31—81no—
339C23×C31—81no—
340C23×C31—81no—
341C23×C31—81no—
342C23×C31—81no—
343C23×C31—81no—
344C23×C31—161no—
345C23×C31—161no—
346C23×C31—161no—
347C23×C31—161no—
348C23×C31H(5,𝔽2)11yescharacteristic
349Q8×C31—21no—
350Q8×C31—21no—
351Q8×C31—21no—
352Q8×C31—21no—
353Q8×C31#12012yes—
354Q8×C31#12112yes—
355D4×C31—22no—
356D4×C31—22no—
357D4×C31—22no—
358D4×C31—22no—
359D4×C31—22no—
360D4×C31—22no—
361D4×C31—21no—
362D4×C31—22no—
363D4×C31—21no—
364D4×C31—22no—
365D4×C31—21no—
366D4×C31—21no—
367D4×C31—44no—
368D4×C31—44no—
369D4×C31—44no—
370D4×C31—44no—
371D4×C31—41no—
372D4×C31—41no—
373D4×C31—41no—
374D4×C31—41no—
375D4×C31—41no—
376D4×C31—41no—
377D4×C31—41no—
378D4×C31—41no—
379D4×C31—41no—
380D4×C31—41no—
381D4×C31—88no—
382D4×C31—161no—
383D4×C31—161no—
384D4×C31#12012yes—
385D4×C31#12112yes—
386C2×C4×C31—21no—
387C2×C4×C31—21no—
388C2×C4×C31—22no—
389C2×C4×C31—22no—
390C2×C4×C31—22no—
391C2×C4×C31—22no—
392C2×C4×C31—22no—
393C2×C4×C31—21no—
394C2×C4×C31—21no—
395C2×C4×C31—21no—
396C2×C4×C31—44no—
397C2×C4×C31—44no—
398C2×C4×C31—41no—
399C2×C4×C31—41no—
400C2×C4×C31—41no—
401C2×C4×C31—41no—
402C2×C4×C31—41no—
403C2×C4×C31—81no—
404C2×C4×C31—161no—
405C2×C4×C31C22×D411yescharacteristic
406C2×C4×C31C22×D411yescharacteristic
407C2×C4×C31C22×D411yescharacteristic
408C2×C4×C31C22×D411yescharacteristic
409C2×C4×C31C2×#4111yescharacteristic
410C2×C4×C31H(5,𝔽2)11yescharacteristic
411C8×C31—21no—
412C8×C31—22no—
413C8×C31—21no—
414C8×C31—21no—
415C8×C31—21no—
416C8×C31—41no—
417C8×C31—41no—
418C8×C31—41no—
419C2×#576C2×C3111yescharacteristic, complemented
420C2×#472C2×C3111yescharacteristic, complemented
421#3045C2×C3111yescharacteristic, complemented
422C2×#453C2×C3111yescharacteristic, complemented
423#3008C2×C3111yescharacteristic, complemented
424#2897C2×C3111yescharacteristic, complemented
425#2051C2×C3111yescharacteristic, complemented
426#2045C2×C3111yescharacteristic, complemented
427#2011C2×C3111yescharacteristic, complemented
428#2002C2×C3111yescharacteristic, complemented
429#1907C2×C3111yescharacteristic, complemented
430#1883C2×C3111yescharacteristic, complemented
431#1876C2×C3111yescharacteristic, complemented
432#1866C2×C3111yescharacteristic, complemented
433#1792C2×C3111yescharacteristic, complemented
434C22×C31—21no—
435C22×C31—21no—
436C22×C31—22no—
437C22×C31—22no—
438C22×C31—41no—
439C22×C31—41no—
440C22×C31—41no—
441C22×C31—41no—
442C22×C31—41no—
443C22×C31—42no—
444C22×C31—42no—
445C22×C31—41no—
446C22×C31—41no—
447C22×C31—82no—
448C22×C31—82no—
449C22×C31—82no—
450C22×C31—81no—
451C22×C31—81no—
452C22×C31—81no—
453C22×C31—81no—
454C22×C31—81no—
455C22×C31—81no—
456C22×C31—81no—
457C22×C31—161no—
458C22×C31—161no—
459C22×C31—161no—
460C22×C31—164no—
461C22×C31—164no—
462C22×C31#53411yescharacteristic
463C22×C31D4211yescharacteristic
464C22×C31#54611yescharacteristic
465C4×C31—22no—
466C4×C31—22no—
467C4×C31—42no—
468C4×C31—41no—
469C4×C31—41no—
470C4×C31—41no—
471C4×C31—81no—
472C4×C31C2×#12011yescharacteristic
473C4×C31C2×#12111yescharacteristic
474C4×C31D4211yescharacteristic
475C4×C31#54611yescharacteristic
476C2×H(5,𝔽2)C22×C3111yescharacteristic
477C2×H(5,𝔽2)C22×C3111yescharacteristic
478#576—24no—
479#576—24no—
480C2×AGL(1,ℤ/8)—21no—
481C2×AGL(1,ℤ/8)—21no—
482C2×AGL(1,ℤ/8)C22×C3111yescharacteristic
483C2×AGL(1,ℤ/8)C22×C3111yescharacteristic
484C2×AGL(1,ℤ/8)C22×C3111yescharacteristic
485C2×AGL(1,ℤ/8)C22×C3111yescharacteristic, complemented
486C2×#135—21no—
487C2×#135C22×C3111yescharacteristic
488C22×D8—21no—
489C22×D8C22×C3111yescharacteristic
490C22×D8C22×C3111yescharacteristic, complemented
491C2×#131C22×C3111yescharacteristic
492C2×#131C22×C3111yescharacteristic, complemented
493#535C22×C3111yescharacteristic, complemented
494C2×#127C22×C3111yescharacteristic, complemented
495#520C22×C3111yescharacteristic, complemented
496#472—24no—
497#464—21no—
498#463—21no—
499#460—21no—
500#459—21no—
501#453—24no—
502#449—21no—
503#449—21no—
504#447—21no—
505#447—21no—
506C2×#108C22×C3111yescharacteristic, complemented
507#424C22×C3111yescharacteristic, complemented
508C2×#104C22×C3111yescharacteristic
509C2×#104C22×C3111yescharacteristic, complemented
510C2×#104C22×C3111yescharacteristic, complemented
511#418—21no—
512#418C22×C3111yescharacteristic, complemented
513#418C22×C3111yescharacteristic, complemented
514#417—21no—
515#417C22×C3111yescharacteristic
516#417C22×C3111yescharacteristic, complemented
517#416—21no—
518#416C22×C3111yescharacteristic
519C2×#102—21no—
520C2×#102C22×C3111yescharacteristic, complemented
521C2×#102C22×C3111yescharacteristic, complemented
522C2×#100C22×C3111yescharacteristic, complemented
523C2×#100C22×C3111yescharacteristic, complemented
524C2×#100C22×C3111yescharacteristic, complemented
525#408C22×C3111yescharacteristic, complemented
526#390C22×C3111yescharacteristic, complemented
527#343C22×C3111yescharacteristic, complemented
528#341C22×C3111yescharacteristic, complemented
529#339C22×C3111yescharacteristic, complemented
530#336C22×C3111yescharacteristic, complemented
531C2×C31—21no—
532C2×C31—21no—
533C2×C31—42no—
534C2×C31—42no—
535C2×C31—81no—
536C2×C31—82no—
537C2×C31—82no—
538C2×C31—161no—
539C2×C31#241011yescharacteristic
540C2×C31#328811yescharacteristic
541C2×C31#329211yescharacteristic
542H(5,𝔽2)—22no—
543H(5,𝔽2)—22no—
544H(5,𝔽2)—22no—
545H(5,𝔽2)—22no—
546H(5,𝔽2)—22no—
547H(5,𝔽2)—41no—
548H(5,𝔽2)—41no—
549H(5,𝔽2)D4×C3114yescomplemented
550C2×#41—21no—
551C2×#41—21no—
552C2×#41—21no—
553C2×#41—21no—
554C2×#41C23×C3111yescharacteristic
555C2×#41C23×C3111yescharacteristic
556C2×#41C23×C3111yescharacteristic
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—41no—
562C22×D4—41no—
563C22×D4—41no—
564C22×D4C23×C3111yescharacteristic
565C22×D4C23×C3111yescharacteristic
566C22×D4C23×C3111yescharacteristic
567AGL(1,ℤ/8)—28no—
568AGL(1,ℤ/8)—28no—
569AGL(1,ℤ/8)—22no—
570AGL(1,ℤ/8)—22no—
571AGL(1,ℤ/8)—22no—
572AGL(1,ℤ/8)—22no—
573AGL(1,ℤ/8)—22no—
574AGL(1,ℤ/8)—22no—
575AGL(1,ℤ/8)—22no—
576AGL(1,ℤ/8)D4×C3114yescomplemented
577#135—28no—
578#135—22no—
579#135—22no—
580C2×Q16D4×C3111yescharacteristic, complemented
581C2×SD16—21no—
582C2×SD16—21no—
583C2×SD16—21no—
584C2×SD16—21no—
585C2×SD16D4×C3111yescharacteristic, complemented
586C2×SD16D4×C3111yescharacteristic, complemented
587C2×D8—28no—
588C2×D8—21no—
589C2×D8—21no—
590C2×D8—22no—
591C2×D8—22no—
592C2×D8—22no—
593C2×D8—21no—
594C2×D8—21no—
595C2×D8—21no—
596C2×D8—21no—
597C2×D8—21no—
598C2×D8—21no—
599C2×D8—41no—
600C2×D8D4×C3111yescharacteristic, complemented
601#131—22no—
602#131—22no—
603#131—22no—
604#131—41no—
605C2×M16—21no—
606C2×M16—21no—
607C2×M16C23×C3111yescharacteristic
608C2×M16C23×C3111yescharacteristic
609C2×M16C23×C3111yescharacteristic
610C2×M16C23×C3111yescharacteristic
611C22×C8—21no—
612C22×C8—21no—
613C22×C8C23×C3111yescharacteristic
614C22×C8C23×C3111yescharacteristic
615#127—22no—
616#127—21no—
617#127—41no—
618#124—21no—
619#121—21no—
620#121—21no—
621#120—41no—
622C4×Q8—21no—
623C4×D4—21no—
624C4×D4—41no—
625#117—21no—
626#117C23×C3111yescharacteristic
627C2×C4⋊C4—21no—
628C2×C4⋊C4C23×C3111yescharacteristic
629C2×C22⋊C4—41no—
630C2×C42C23×C3111yescharacteristic
631#108—22no—
632C4⋊C8—21no—
633C4⋊C8—21no—
634#104—22no—
635#104—22no—
636#104—41no—
637#103—21no—
638#103—21no—
639#103D4×C3111yescharacteristic, complemented
640#103D4×C3111yescharacteristic, complemented
641#102—21no—
642#102—21no—
643#102—21no—
644#102—21no—
645#102—21no—
646#102—21no—
647#102—21no—
648#102—21no—
649#102—21no—
650#102—21no—
651#102D4×C3111yescharacteristic, complemented
652#102D4×C3111yescharacteristic, complemented
653#100—22no—
654#100—22no—
655#100—22no—
656C22⋊C8—21no—
657C22⋊C8—21no—
658C31#2445611yescharacteristic, direct product factor, Sylow
659C24—21no—
660C24—21no—
661C24—21no—
662C24—41no—
663C24—41no—
664#41—21no—
665#41—21no—
666#41—21no—
667#41—21no—
668#41—24no—
669#41—24no—
670#41—24no—
671#41—21no—
672#41—21no—
673#41—21no—
674#41—21no—
675#41—42no—
676#41—42no—
677#41—42no—
678#41—42no—
679#41—42no—
680#41C2×D4×C3112yes—
681#41C2×D4×C3112yes—
682#41C2×D4×C3112yes—
683#41#41×C3112yes—
684C2×Q8C2×D4×C3111yescharacteristic
685C2×Q8C2×D4×C3111yescharacteristic
686C2×Q8C2×D4×C3111yescharacteristic
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—24no—
690C2×D4—24no—
691C2×D4—24no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—42no—
710C2×D4—42no—
711C2×D4—42no—
712C2×D4—41no—
713C2×D4—41no—
714C2×D4—41no—
715C2×D4—41no—
716C2×D4—41no—
717C2×D4—41no—
718C2×D4—44no—
719C2×D4—42no—
720C2×D4—44no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—42no—
724C2×D4—44no—
725C2×D4—82no—
726C2×D4—82no—
727C2×D4C2×D4×C3112yes—
728C2×D4C2×D4×C3112yes—
729C2×D4C2×D4×C3111yescharacteristic
730C2×D4C2×D4×C3111yescharacteristic
731C2×D4C2×D4×C3111yescharacteristic
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—41no—
738C22×C4—41no—
739C22×C4—41no—
740C22×C4C24×C3111yescharacteristic
741Q16—22no—
742SD16—24no—
743SD16—24no—
744SD16—22no—
745SD16—22no—
746SD16—42no—
747SD16—42no—
748D8—24no—
749D8—24no—
750D8—24no—
751D8—22no—
752D8—24no—
753D8—42no—
754D8—42no—
755D8—42no—
756D8—42no—
757M16—24no—
758M16—21no—
759M16—21no—
760M16—21no—
761M16—21no—
762M16—21no—
763M16—21no—
764M16—21no—
765M16—42no—
766M16C2×D4×C3112yes—
767C2×C8—24no—
768C2×C8—21no—
769C2×C8—21no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—42no—
777C2×C8C2×D4×C3111yescharacteristic
778C2×C8C2×D4×C3111yescharacteristic
779C2×C8C2×D4×C3111yescharacteristic
780C2×C8C2×D4×C3111yescharacteristic
781C4⋊C4—21no—
782C4⋊C4—21no—
783C4⋊C4—41no—
784C4⋊C4C2×D4×C3111yescharacteristic
785C4⋊C4C2×D4×C3111yescharacteristic
786C22⋊C4—21no—
787C22⋊C4—41no—
788C22⋊C4—41no—
789C22⋊C4—41no—
790C22⋊C4—82no—
791C42—21no—
792C42—21no—
793C42—21no—
794C42—41no—
795C23—21no—
796C23—21no—
797C23—21no—
798C23—22no—
799C23—22no—
800C23—44no—
801C23—44no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—81no—
810C23—81no—
811C23—81no—
812C23—81no—
813C23—81no—
814C23—81no—
815C23—161no—
816C23—161no—
817C23—161no—
818C23—161no—
819C23C31×H(5,𝔽2)11yescharacteristic
820Q8—21no—
821Q8—21no—
822Q8—21no—
823Q8—21no—
824Q8C31×#12012yes—
825Q8C31×#12112yes—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—22no—
830D4—22no—
831D4—22no—
832D4—21no—
833D4—22no—
834D4—21no—
835D4—22no—
836D4—21no—
837D4—21no—
838D4—44no—
839D4—44no—
840D4—44no—
841D4—44no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—41no—
849D4—41no—
850D4—41no—
851D4—41no—
852D4—88no—
853D4—161no—
854D4—161no—
855D4C31×#12012yes—
856D4C31×#12112yes—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—44no—
868C2×C4—44no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—81no—
875C2×C4—161no—
876C2×C4C22×D4×C3111yescharacteristic
877C2×C4C22×D4×C3111yescharacteristic
878C2×C4C22×D4×C3111yescharacteristic
879C2×C4C22×D4×C3111yescharacteristic
880C2×C4C2×#41×C3111yescharacteristic
881C2×C4C31×H(5,𝔽2)11yescharacteristic
882C8—21no—
883C8—22no—
884C8—21no—
885C8—21no—
886C8—21no—
887C8—41no—
888C8—41no—
889C8—41no—
890C22—21no—
891C22—21no—
892C22—22no—
893C22—22no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—41no—
898C22—41no—
899C22—42no—
900C22—42no—
901C22—41no—
902C22—41no—
903C22—82no—
904C22—82no—
905C22—82no—
906C22—81no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—161no—
914C22—161no—
915C22—161no—
916C22—164no—
917C22—164no—
918C22C31×#53411yescharacteristic
919C22D42×C3111yescharacteristic
920C22C31×#54611yescharacteristic
921C4—22no—
922C4—22no—
923C4—42no—
924C4—41no—
925C4—41no—
926C4—41no—
927C4—81no—
928C4C2×C31×#12011yescharacteristic
929C4C2×C31×#12111yescharacteristic
930C4D42×C3111yescharacteristic
931C4C31×#54611yescharacteristic
932C2—21no—
933C2—21no—
934C2—42no—
935C2—42no—
936C2—81no—
937C2—82no—
938C2—82no—
939C2—161no—
940C2C31×#241011yescharacteristic
941C2C31×#328811yescharacteristic
942C2C31×#329211yescharacteristic
subgroupG/H
center, socleC22×C31D42
commutator, Frattini, cosocleC22×C4C24×C31
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#576C2semidirect
2. C2×C31×#472C2semidirect
3. C31×#3045C2semidirect
4. C2×C31×#453C2semidirect
5. C31×#3008C2semidirect
6. C31×#2897C2semidirect
7. C31×#2051C2semidirect
8. C31×#2045C2semidirect
9. C31×#2011C2semidirect
10. C31×#2002C2semidirect
11. C31×#1907C2semidirect
12. C31×#1883C2semidirect
13. C31×#1876C2semidirect
14. C31×#1866C2semidirect
15. C31×#1792C2semidirect
25. C2×C31×AGL(1,ℤ/8)C22semidirect
30. C22×D8×C31C22semidirect
32. C2×C31×#131C22semidirect
33. C31×#535C22semidirect
34. C2×C31×#127C22semidirect
35. C31×#520C22semidirect
46. C2×C31×#108C22semidirect
47. C31×#424C22semidirect
49. C2×C31×#104C22semidirect
50. C2×C31×#104C22semidirect
52. C31×#418C22semidirect
53. C31×#418C22semidirect
56. C31×#417C22semidirect
60. C2×C31×#102C22semidirect
61. C2×C31×#102C22semidirect
62. C2×C31×#100C22semidirect
63. C2×C31×#100C22semidirect
64. C2×C31×#100C22semidirect
65. C31×#408C22semidirect
66. C31×#390C22semidirect
67. C31×#343C22semidirect
68. C31×#341C22semidirect
69. C31×#339C22semidirect
70. C31×#336C22semidirect
78. C31×H(5,𝔽2)D4semidirect
105. C31×AGL(1,ℤ/8)D4semidirect
109. C2×Q16×C31D4semidirect
114. C2×SD16×C31D4semidirect
115. C2×SD16×C31D4semidirect
129. C2×D8×C31D4semidirect
168. C31×#103D4semidirect
169. C31×#103D4semidirect
180. C31×#102D4semidirect
181. C31×#102D4semidirect
323. #24456C31direct (N × H)
419. C2×#576C2×C31semidirect
420. C2×#472C2×C31semidirect
421. #3045C2×C31semidirect
422. C2×#453C2×C31semidirect
423. #3008C2×C31semidirect
424. #2897C2×C31semidirect
425. #2051C2×C31semidirect
426. #2045C2×C31semidirect
427. #2011C2×C31semidirect
428. #2002C2×C31semidirect
429. #1907C2×C31semidirect
430. #1883C2×C31semidirect
431. #1876C2×C31semidirect
432. #1866C2×C31semidirect
433. #1792C2×C31semidirect
485. C2×AGL(1,ℤ/8)C22×C31semidirect
490. C22×D8C22×C31semidirect
492. C2×#131C22×C31semidirect
493. #535C22×C31semidirect
494. C2×#127C22×C31semidirect
495. #520C22×C31semidirect
506. C2×#108C22×C31semidirect
507. #424C22×C31semidirect
509. C2×#104C22×C31semidirect
510. C2×#104C22×C31semidirect
512. #418C22×C31semidirect
513. #418C22×C31semidirect
516. #417C22×C31semidirect
520. C2×#102C22×C31semidirect
521. C2×#102C22×C31semidirect
522. C2×#100C22×C31semidirect
523. C2×#100C22×C31semidirect
524. C2×#100C22×C31semidirect
525. #408C22×C31semidirect
526. #390C22×C31semidirect
527. #343C22×C31semidirect
528. #341C22×C31semidirect
529. #339C22×C31semidirect
530. #336C22×C31semidirect
549. H(5,𝔽2)D4×C31semidirect
576. AGL(1,ℤ/8)D4×C31semidirect
580. C2×Q16D4×C31semidirect
585. C2×SD16D4×C31semidirect
586. C2×SD16D4×C31semidirect
600. C2×D8D4×C31semidirect
639. #103D4×C31semidirect
640. #103D4×C31semidirect
651. #102D4×C31semidirect
652. #102D4×C31semidirect
658. C31#24456direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5762
C2×C31×#4722
C31×#30452
C2×C31×#4532
C31×#30082
C31×#28972
C31×#20512
C31×#20452
C31×#20112
C31×#20022
C31×#19072
C31×#18832
C31×#18762
C31×#18662
C31×#17922
#2445631