Finite Group Databasebeta

← C31×#24472 #21481231

Subgroups — C31×#24472 #21481231

Order 7936.

1372 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3585C211yesmaximal, characteristic, complemented
2C31×#3068C211yesmaximal, characteristic, complemented
3C31×#3038C211yesmaximal, characteristic, complemented
4C31×#3021C211yesmaximal, characteristic, complemented
5C2×C31×#453C211yesmaximal, characteristic, complemented
6C31×#2901C211yesmaximal, characteristic, complemented
7C31×#2050C211yesmaximal, characteristic, complemented
8C31×#2048C211yesmaximal, characteristic, complemented
9C31×#2008C211yesmaximal, characteristic, complemented
10C31×#2002C211yesmaximal, characteristic, complemented
11C31×#1906C211yesmaximal, characteristic, complemented
12C31×#1903C211yesmaximal, characteristic, complemented
13C31×#1903C211yesmaximal, characteristic, complemented
14C31×#1861C211yesmaximal, characteristic, complemented
15C31×#1795C211yesmaximal, characteristic, complemented
16C31×#585C2211yescharacteristic
17C2×C31×H(5,𝔽2)C2211yescharacteristic
18C31×#577—22no—
19C31×#577—22no—
20C31×#576—22no—
21C31×#576—22no—
22C31×#575—22no—
23C31×#575C2211yescharacteristic
24C31×#575C2211yescharacteristic
25C2×C31×AGL(1,ℤ/8)—22no—
26C2×C31×AGL(1,ℤ/8)C2211yescharacteristic
27C2×C31×AGL(1,ℤ/8)C2211yescharacteristic
28C2×C31×AGL(1,ℤ/8)C2211yescharacteristic
29C2×C31×AGL(1,ℤ/8)C2211yescharacteristic, complemented
30C2×C31×AGL(1,ℤ/8)C2211yescharacteristic, complemented
31C31×#568C2211yescharacteristic
32C31×#568C2211yescharacteristic, complemented
33C31×#535C2211yescharacteristic, complemented
34C2×C31×#127C2211yescharacteristic, complemented
35C4×#41×C31C2211yescharacteristic, complemented
36C31×#472—22no—
37C31×#471—22no—
38C31×#460—22no—
39C31×#459—22no—
40C31×#454—22no—
41C31×#453—22no—
42C31×#453—22no—
43C31×#453—22no—
44C31×#430C2211yescharacteristic, complemented
45C31×#423C2211yescharacteristic, complemented
46C31×#421—22no—
47C31×#421C2211yescharacteristic
48C31×#421C2211yescharacteristic
49C31×#421C2211yescharacteristic, complemented
50C31×#421C2211yescharacteristic, complemented
51C2×C31×#104—22no—
52C2×C31×#104C2211yescharacteristic
53C2×C31×#104C2211yescharacteristic, complemented
54C2×C31×#104C2211yescharacteristic, complemented
55C31×#418C2211yescharacteristic, complemented
56C31×#418C2211yescharacteristic, complemented
57C31×#418C2211yescharacteristic, complemented
58C31×#413C2211yescharacteristic, complemented
59C31×#413C2211yescharacteristic, complemented
60C2×C31×#100C2211yescharacteristic, complemented
61C2×C31×#100C2211yescharacteristic, complemented
62C31×#410C2211yescharacteristic, complemented
63C31×#344C2211yescharacteristic, complemented
64C31×#344C2211yescharacteristic, complemented
65C31×#339C2211yescharacteristic, complemented
66C31×#338C2211yescharacteristic, complemented
67C31×2−1+4—21no—
68C31×2−1+4—21no—
69C31×2−1+4D412yescomplemented
70C31×H(5,𝔽2)—22no—
71C31×H(5,𝔽2)—21no—
72C31×H(5,𝔽2)—22no—
73C31×H(5,𝔽2)—21no—
74C31×H(5,𝔽2)—22no—
75C31×H(5,𝔽2)—41no—
76C31×H(5,𝔽2)—41no—
77C31×H(5,𝔽2)D412yescomplemented
78C2×#41×C31—22no—
79C2×#41×C31—22no—
80C2×#41×C31—21no—
81C2×#41×C31—21no—
82C2×#41×C31—41no—
83C2×#41×C31C2311yescharacteristic
84C2×#41×C31C2311yescharacteristic
85C2×#41×C31C2311yescharacteristic
86C2×#41×C31C2311yescharacteristic
87C22×D4×C31—21no—
88C22×D4×C31—21no—
89C22×D4×C31—41no—
90C22×D4×C31—41no—
91C22×D4×C31C2311yescharacteristic
92C22×D4×C31C2311yescharacteristic
93C31×#137—24no—
94C31×#137—21no—
95C31×#137—21no—
96C31×#137—21no—
97C31×#137D412yescomplemented
98C31×AGL(1,ℤ/8)—24no—
99C31×AGL(1,ℤ/8)—24no—
100C31×AGL(1,ℤ/8)—24no—
101C31×AGL(1,ℤ/8)—22no—
102C31×AGL(1,ℤ/8)—22no—
103C31×AGL(1,ℤ/8)—21no—
104C31×AGL(1,ℤ/8)—22no—
105C31×AGL(1,ℤ/8)—21no—
106C31×AGL(1,ℤ/8)—21no—
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)—22no—
112C31×AGL(1,ℤ/8)—22no—
113C31×AGL(1,ℤ/8)—41no—
114C31×AGL(1,ℤ/8)D412yescomplemented
115C31×#135—24no—
116C31×#135—24no—
117C31×#135—22no—
118C31×#135—22no—
119C2×SD16×C31—24no—
120C2×SD16×C31—21no—
121C2×SD16×C31—21no—
122C2×SD16×C31—21no—
123C2×SD16×C31—21no—
124C2×SD16×C31D412yescomplemented
125C2×D8×C31—24no—
126C2×D8×C31—21no—
127C2×D8×C31—21no—
128C2×D8×C31—21no—
129C2×D8×C31—21no—
130C2×D8×C31D412yescomplemented
131C31×#131—22no—
132C31×#131—22no—
133C31×#131—22no—
134C31×#131—41no—
135C2×M16×C31—22no—
136C2×M16×C31—22no—
137C2×M16×C31C2311yescharacteristic
138C2×M16×C31C2311yescharacteristic
139C2×M16×C31C2311yescharacteristic
140C2×M16×C31C2311yescharacteristic
141C2×M16×C31C2311yescharacteristic
142C2×M16×C31C2311yescharacteristic
143C31×#127—21no—
144C31×#127—22no—
145C31×#127—21no—
146C31×#127—21no—
147C31×#124—21no—
148C31×#121—41no—
149C31×#120—41no—
150C4×Q8×C31—21no—
151C4×D4×C31—21no—
152C4×D4×C31—41no—
153C31×#117—21no—
154C31×#117C2311yescharacteristic
155C31×#117C2311yescharacteristic
156C2×C42×C31—21no—
157C2×C42×C31C2311yescharacteristic
158C31×#108—22no—
159C31×C4⋊C8—22no—
160C31×#104—22no—
161C31×#104—22no—
162C31×#104—22no—
163C31×#104—22no—
164C31×#104—21no—
165C31×#104—21no—
166C31×#104—21no—
167C31×#104—21no—
168C31×#104D412yescomplemented
169C31×#104D412yescomplemented
170C31×#102—22no—
171C31×#102—22no—
172C31×#102—41no—
173C31×#101—21no—
174C31×#101—21no—
175C31×#100—21no—
176C31×#100—21no—
177C31×#100—22no—
178C31×#100—22no—
179C31×#99—41no—
180C24×C31—21no—
181C24×C31—21no—
182C24×C31—41no—
183#41×C31—21no—
184#41×C31—21no—
185#41×C31—21no—
186#41×C31—21no—
187#41×C31—24no—
188#41×C31—22no—
189#41×C31—22no—
190#41×C31—22no—
191#41×C31—22no—
192#41×C31—21no—
193#41×C31—21no—
194#41×C31—21no—
195#41×C31—21no—
196#41×C31—21no—
197#41×C31—21no—
198#41×C31—21no—
199#41×C31—21no—
200#41×C31—42no—
201#41×C31—42no—
202#41×C31—42no—
203#41×C31—42no—
204#41×C31—42no—
205#41×C31—42no—
206#41×C31—41no—
207#41×C31—41no—
208#41×C31—42no—
209#41×C31C2×D412yes—
210#41×C31C2×D412yes—
211#41×C31C2×D412yes—
212#41×C31C2×D412yes—
213C2×Q8×C31—22no—
214C2×Q8×C31—22no—
215C2×Q8×C31—41no—
216C2×Q8×C31C2×D411yescharacteristic
217C2×Q8×C31C2×D411yescharacteristic
218C2×Q8×C31C2×D411yescharacteristic
219C2×Q8×C31#4111yescharacteristic
220C2×D4×C31—21no—
221C2×D4×C31—21no—
222C2×D4×C31—24no—
223C2×D4×C31—22no—
224C2×D4×C31—22no—
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—21no—
238C2×D4×C31—42no—
239C2×D4×C31—41no—
240C2×D4×C31—41no—
241C2×D4×C31—42no—
242C2×D4×C31—42no—
243C2×D4×C31—42no—
244C2×D4×C31—42no—
245C2×D4×C31—41no—
246C2×D4×C31—44no—
247C2×D4×C31—42no—
248C2×D4×C31—42no—
249C2×D4×C31—44no—
250C2×D4×C31—42no—
251C2×D4×C31—42no—
252C2×D4×C31—84no—
253C2×D4×C31C2×D411yescharacteristic
254C2×D4×C31C2×D411yescharacteristic
255C2×D4×C31C2×D412yes—
256C2×D4×C31C2×D411yescharacteristic
257C2×D4×C31#4111yescharacteristic
258C22×C4×C31—21no—
259C22×C4×C31—21no—
260C22×C4×C31—21no—
261C22×C4×C31—21no—
262C22×C4×C31—21no—
263C22×C4×C31—41no—
264C22×C4×C31—42no—
265C22×C4×C31—41no—
266C22×C4×C31C2411yescharacteristic
267Q16×C31—22no—
268Q16×C31—22no—
269SD16×C31—24no—
270SD16×C31—22no—
271SD16×C31—22no—
272SD16×C31—22no—
273SD16×C31—24no—
274SD16×C31—22no—
275SD16×C31—42no—
276SD16×C31—42no—
277SD16×C31—42no—
278D8×C31—24no—
279D8×C31—22no—
280D8×C31—22no—
281D8×C31—24no—
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—21no—
294M16×C31—21no—
295M16×C31—21no—
296M16×C31—42no—
297M16×C31C2×D412yes—
298M16×C31C2×D412yes—
299C2×C8×C31—24no—
300C2×C8×C31—21no—
301C2×C8×C31—21no—
302C2×C8×C31—21no—
303C2×C8×C31—21no—
304C2×C8×C31—21no—
305C2×C8×C31—42no—
306C2×C8×C31C2×D412yes—
307C4⋊C4×C31—21no—
308C4⋊C4×C31—21no—
309C4⋊C4×C31—41no—
310C22⋊C4×C31—21no—
311C22⋊C4×C31—21no—
312C22⋊C4×C31—41no—
313C22⋊C4×C31—42no—
314C42×C31—21no—
315C42×C31—21no—
316C42×C31—21no—
317C42×C31—41no—
318C42×C31C2×D411yescharacteristic
319C42×C31C2×D411yescharacteristic
320#24472C3111yesmaximal, characteristic, direct product factor, Sylow
321C23×C31—21no—
322C23×C31—21no—
323C23×C31—21no—
324C23×C31—22no—
325C23×C31—21no—
326C23×C31—42no—
327C23×C31—44no—
328C23×C31—41no—
329C23×C31—41no—
330C23×C31—41no—
331C23×C31—41no—
332C23×C31—41no—
333C23×C31—82no—
334C23×C31—82no—
335C23×C31—162no—
336C23×C31H(5,𝔽2)11yescharacteristic
337Q8×C31—21no—
338Q8×C31—21no—
339Q8×C31—21no—
340Q8×C31—21no—
341Q8×C31—21no—
342Q8×C31—21no—
343Q8×C31—42no—
344Q8×C31#12012yes—
345Q8×C31#12112yes—
346D4×C31—22no—
347D4×C31—22no—
348D4×C31—22no—
349D4×C31—22no—
350D4×C31—21no—
351D4×C31—21no—
352D4×C31—22no—
353D4×C31—21no—
354D4×C31—21no—
355D4×C31—21no—
356D4×C31—21no—
357D4×C31—22no—
358D4×C31—42no—
359D4×C31—42no—
360D4×C31—44no—
361D4×C31—42no—
362D4×C31—44no—
363D4×C31—41no—
364D4×C31—41no—
365D4×C31—41no—
366D4×C31—41no—
367D4×C31—41no—
368D4×C31—41no—
369D4×C31—41no—
370D4×C31—41no—
371D4×C31—41no—
372D4×C31—41no—
373D4×C31—84no—
374D4×C31—84no—
375D4×C31—162no—
376D4×C31#12012yes—
377D4×C31#12112yes—
378C2×C4×C31—21no—
379C2×C4×C31—21no—
380C2×C4×C31—21no—
381C2×C4×C31—22no—
382C2×C4×C31—22no—
383C2×C4×C31—22no—
384C2×C4×C31—22no—
385C2×C4×C31—21no—
386C2×C4×C31—21no—
387C2×C4×C31—21no—
388C2×C4×C31—42no—
389C2×C4×C31—42no—
390C2×C4×C31—42no—
391C2×C4×C31—42no—
392C2×C4×C31—44no—
393C2×C4×C31—41no—
394C2×C4×C31—41no—
395C2×C4×C31—41no—
396C2×C4×C31—41no—
397C2×C4×C31—41no—
398C2×C4×C31—41no—
399C2×C4×C31—82no—
400C2×C4×C31C22×D411yescharacteristic
401C2×C4×C31C22×D411yescharacteristic
402C2×C4×C31C22×D411yescharacteristic
403C2×C4×C31C22×D411yescharacteristic
404C2×C4×C31C2×#4111yescharacteristic
405C2×C4×C31H(5,𝔽2)11yescharacteristic
406C8×C31—22no—
407C8×C31—22no—
408C8×C31—22no—
409C8×C31—41no—
410C8×C31—41no—
411C8×C31—41no—
412#3585C2×C3111yescharacteristic, complemented
413#3068C2×C3111yescharacteristic, complemented
414#3038C2×C3111yescharacteristic, complemented
415#3021C2×C3111yescharacteristic, complemented
416C2×#453C2×C3111yescharacteristic, complemented
417#2901C2×C3111yescharacteristic, complemented
418#2050C2×C3111yescharacteristic, complemented
419#2048C2×C3111yescharacteristic, complemented
420#2008C2×C3111yescharacteristic, complemented
421#2002C2×C3111yescharacteristic, complemented
422#1906C2×C3111yescharacteristic, complemented
423#1903C2×C3111yescharacteristic, complemented
424#1903C2×C3111yescharacteristic, complemented
425#1861C2×C3111yescharacteristic, complemented
426#1795C2×C3111yescharacteristic, complemented
427C22×C31—22no—
428C22×C31—22no—
429C22×C31—41no—
430C22×C31—41no—
431C22×C31—42no—
432C22×C31—41no—
433C22×C31—81no—
434C22×C31—81no—
435C22×C31—82no—
436C22×C31—81no—
437C22×C31—81no—
438C22×C31—82no—
439C22×C31—82no—
440C22×C31—82no—
441C22×C31—81no—
442C22×C31—161no—
443C22×C31—161no—
444C22×C31—162no—
445C22×C31—164no—
446C22×C31#53411yescharacteristic
447C22×C31D4211yescharacteristic
448C22×C31#54611yescharacteristic
449C4×C31—22no—
450C4×C31—22no—
451C4×C31—22no—
452C4×C31—41no—
453C4×C31—41no—
454C4×C31—41no—
455C4×C31—81no—
456C4×C31—81no—
457C4×C31C2×#12011yescharacteristic
458C4×C31C2×#12111yescharacteristic
459C4×C31D4211yescharacteristic
460C4×C31#54611yescharacteristic
461#585C22×C3111yescharacteristic
462C2×H(5,𝔽2)C22×C3111yescharacteristic
463#577—22no—
464#577—22no—
465#576—22no—
466#576—22no—
467#575—22no—
468#575C22×C3111yescharacteristic
469#575C22×C3111yescharacteristic
470C2×AGL(1,ℤ/8)—22no—
471C2×AGL(1,ℤ/8)C22×C3111yescharacteristic
472C2×AGL(1,ℤ/8)C22×C3111yescharacteristic
473C2×AGL(1,ℤ/8)C22×C3111yescharacteristic
474C2×AGL(1,ℤ/8)C22×C3111yescharacteristic, complemented
475C2×AGL(1,ℤ/8)C22×C3111yescharacteristic, complemented
476#568C22×C3111yescharacteristic
477#568C22×C3111yescharacteristic, complemented
478#535C22×C3111yescharacteristic, complemented
479C2×#127C22×C3111yescharacteristic, complemented
480C4×#41C22×C3111yescharacteristic, complemented
481#472—22no—
482#471—22no—
483#460—22no—
484#459—22no—
485#454—22no—
486#453—22no—
487#453—22no—
488#453—22no—
489#430C22×C3111yescharacteristic, complemented
490#423C22×C3111yescharacteristic, complemented
491#421—22no—
492#421C22×C3111yescharacteristic
493#421C22×C3111yescharacteristic
494#421C22×C3111yescharacteristic, complemented
495#421C22×C3111yescharacteristic, complemented
496C2×#104—22no—
497C2×#104C22×C3111yescharacteristic
498C2×#104C22×C3111yescharacteristic, complemented
499C2×#104C22×C3111yescharacteristic, complemented
500#418C22×C3111yescharacteristic, complemented
501#418C22×C3111yescharacteristic, complemented
502#418C22×C3111yescharacteristic, complemented
503#413C22×C3111yescharacteristic, complemented
504#413C22×C3111yescharacteristic, complemented
505C2×#100C22×C3111yescharacteristic, complemented
506C2×#100C22×C3111yescharacteristic, complemented
507#410C22×C3111yescharacteristic, complemented
508#344C22×C3111yescharacteristic, complemented
509#344C22×C3111yescharacteristic, complemented
510#339C22×C3111yescharacteristic, complemented
511#338C22×C3111yescharacteristic, complemented
512C2×C31—21no—
513C2×C31—21no—
514C2×C31—21no—
515C2×C31—42no—
516C2×C31—42no—
517C2×C31—82no—
518C2×C31—81no—
519C2×C31—81no—
520C2×C31—161no—
521C2×C31#241011yescharacteristic
5222−1+4—21no—
5232−1+4—21no—
5242−1+4D4×C3112yescomplemented
525H(5,𝔽2)—22no—
526H(5,𝔽2)—21no—
527H(5,𝔽2)—22no—
528H(5,𝔽2)—21no—
529H(5,𝔽2)—22no—
530H(5,𝔽2)—41no—
531H(5,𝔽2)—41no—
532H(5,𝔽2)D4×C3112yescomplemented
533C2×#41—22no—
534C2×#41—22no—
535C2×#41—21no—
536C2×#41—21no—
537C2×#41—41no—
538C2×#41C23×C3111yescharacteristic
539C2×#41C23×C3111yescharacteristic
540C2×#41C23×C3111yescharacteristic
541C2×#41C23×C3111yescharacteristic
542C22×D4—21no—
543C22×D4—21no—
544C22×D4—41no—
545C22×D4—41no—
546C22×D4C23×C3111yescharacteristic
547C22×D4C23×C3111yescharacteristic
548#137—24no—
549#137—21no—
550#137—21no—
551#137—21no—
552#137D4×C3112yescomplemented
553AGL(1,ℤ/8)—24no—
554AGL(1,ℤ/8)—24no—
555AGL(1,ℤ/8)—24no—
556AGL(1,ℤ/8)—22no—
557AGL(1,ℤ/8)—22no—
558AGL(1,ℤ/8)—21no—
559AGL(1,ℤ/8)—22no—
560AGL(1,ℤ/8)—21no—
561AGL(1,ℤ/8)—21no—
562AGL(1,ℤ/8)—22no—
563AGL(1,ℤ/8)—22no—
564AGL(1,ℤ/8)—22no—
565AGL(1,ℤ/8)—22no—
566AGL(1,ℤ/8)—22no—
567AGL(1,ℤ/8)—22no—
568AGL(1,ℤ/8)—41no—
569AGL(1,ℤ/8)D4×C3112yescomplemented
570#135—24no—
571#135—24no—
572#135—22no—
573#135—22no—
574C2×SD16—24no—
575C2×SD16—21no—
576C2×SD16—21no—
577C2×SD16—21no—
578C2×SD16—21no—
579C2×SD16D4×C3112yescomplemented
580C2×D8—24no—
581C2×D8—21no—
582C2×D8—21no—
583C2×D8—21no—
584C2×D8—21no—
585C2×D8D4×C3112yescomplemented
586#131—22no—
587#131—22no—
588#131—22no—
589#131—41no—
590C2×M16—22no—
591C2×M16—22no—
592C2×M16C23×C3111yescharacteristic
593C2×M16C23×C3111yescharacteristic
594C2×M16C23×C3111yescharacteristic
595C2×M16C23×C3111yescharacteristic
596C2×M16C23×C3111yescharacteristic
597C2×M16C23×C3111yescharacteristic
598#127—22no—
599#127—21no—
600#127—21no—
601#127—21no—
602#124—21no—
603#121—41no—
604#120—41no—
605C4×Q8—21no—
606C4×D4—21no—
607C4×D4—41no—
608#117—21no—
609#117C23×C3111yescharacteristic
610#117C23×C3111yescharacteristic
611C2×C42—21no—
612C2×C42C23×C3111yescharacteristic
613#108—22no—
614C4⋊C8—22no—
615#104—22no—
616#104—22no—
617#104—22no—
618#104—22no—
619#104—21no—
620#104—21no—
621#104—21no—
622#104—21no—
623#104D4×C3112yescomplemented
624#104D4×C3112yescomplemented
625#102—22no—
626#102—22no—
627#102—41no—
628#101—21no—
629#101—21no—
630#100—21no—
631#100—21no—
632#100—22no—
633#100—22no—
634#99—41no—
635C31#2447211yescharacteristic, direct product factor, Sylow
636C24—21no—
637C24—21no—
638C24—41no—
639#41—21no—
640#41—21no—
641#41—21no—
642#41—21no—
643#41—24no—
644#41—22no—
645#41—22no—
646#41—22no—
647#41—22no—
648#41—21no—
649#41—21no—
650#41—21no—
651#41—21no—
652#41—21no—
653#41—21no—
654#41—21no—
655#41—21no—
656#41—42no—
657#41—42no—
658#41—42no—
659#41—42no—
660#41—42no—
661#41—42no—
662#41—41no—
663#41—41no—
664#41—42no—
665#41C2×D4×C3112yes—
666#41C2×D4×C3112yes—
667#41C2×D4×C3112yes—
668#41C2×D4×C3112yes—
669C2×Q8—22no—
670C2×Q8—22no—
671C2×Q8—41no—
672C2×Q8C2×D4×C3111yescharacteristic
673C2×Q8C2×D4×C3111yescharacteristic
674C2×Q8C2×D4×C3111yescharacteristic
675C2×Q8#41×C3111yescharacteristic
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—24no—
679C2×D4—22no—
680C2×D4—22no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—42no—
695C2×D4—41no—
696C2×D4—41no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—41no—
702C2×D4—44no—
703C2×D4—42no—
704C2×D4—42no—
705C2×D4—44no—
706C2×D4—42no—
707C2×D4—42no—
708C2×D4—84no—
709C2×D4C2×D4×C3111yescharacteristic
710C2×D4C2×D4×C3111yescharacteristic
711C2×D4C2×D4×C3112yes—
712C2×D4C2×D4×C3111yescharacteristic
713C2×D4#41×C3111yescharacteristic
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—41no—
720C22×C4—42no—
721C22×C4—41no—
722C22×C4C24×C3111yescharacteristic
723Q16—22no—
724Q16—22no—
725SD16—24no—
726SD16—22no—
727SD16—22no—
728SD16—22no—
729SD16—24no—
730SD16—22no—
731SD16—42no—
732SD16—42no—
733SD16—42no—
734D8—24no—
735D8—22no—
736D8—22no—
737D8—24no—
738D8—42no—
739D8—42no—
740D8—42no—
741M16—24no—
742M16—21no—
743M16—21no—
744M16—21no—
745M16—21no—
746M16—21no—
747M16—21no—
748M16—21no—
749M16—21no—
750M16—21no—
751M16—21no—
752M16—42no—
753M16C2×D4×C3112yes—
754M16C2×D4×C3112yes—
755C2×C8—24no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—21no—
761C2×C8—42no—
762C2×C8C2×D4×C3112yes—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—41no—
766C22⋊C4—21no—
767C22⋊C4—21no—
768C22⋊C4—41no—
769C22⋊C4—42no—
770C42—21no—
771C42—21no—
772C42—21no—
773C42—41no—
774C42C2×D4×C3111yescharacteristic
775C42C2×D4×C3111yescharacteristic
776C23—21no—
777C23—21no—
778C23—21no—
779C23—22no—
780C23—21no—
781C23—42no—
782C23—44no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—82no—
789C23—82no—
790C23—162no—
791C23C31×H(5,𝔽2)11yescharacteristic
792Q8—21no—
793Q8—21no—
794Q8—21no—
795Q8—21no—
796Q8—21no—
797Q8—21no—
798Q8—42no—
799Q8C31×#12012yes—
800Q8C31×#12112yes—
801D4—22no—
802D4—22no—
803D4—22no—
804D4—22no—
805D4—21no—
806D4—21no—
807D4—22no—
808D4—21no—
809D4—21no—
810D4—21no—
811D4—21no—
812D4—22no—
813D4—42no—
814D4—42no—
815D4—44no—
816D4—42no—
817D4—44no—
818D4—41no—
819D4—41no—
820D4—41no—
821D4—41no—
822D4—41no—
823D4—41no—
824D4—41no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—84no—
829D4—84no—
830D4—162no—
831D4C31×#12012yes—
832D4C31×#12112yes—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—44no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—82no—
855C2×C4C22×D4×C3111yescharacteristic
856C2×C4C22×D4×C3111yescharacteristic
857C2×C4C22×D4×C3111yescharacteristic
858C2×C4C22×D4×C3111yescharacteristic
859C2×C4C2×#41×C3111yescharacteristic
860C2×C4C31×H(5,𝔽2)11yescharacteristic
861C8—22no—
862C8—22no—
863C8—22no—
864C8—41no—
865C8—41no—
866C8—41no—
867C22—22no—
868C22—22no—
869C22—41no—
870C22—41no—
871C22—42no—
872C22—41no—
873C22—81no—
874C22—81no—
875C22—82no—
876C22—81no—
877C22—81no—
878C22—82no—
879C22—82no—
880C22—82no—
881C22—81no—
882C22—161no—
883C22—161no—
884C22—162no—
885C22—164no—
886C22C31×#53411yescharacteristic
887C22D42×C3111yescharacteristic
888C22C31×#54611yescharacteristic
889C4—22no—
890C4—22no—
891C4—22no—
892C4—41no—
893C4—41no—
894C4—41no—
895C4—81no—
896C4—81no—
897C4C2×C31×#12011yescharacteristic
898C4C2×C31×#12111yescharacteristic
899C4D42×C3111yescharacteristic
900C4C31×#54611yescharacteristic
901C2—21no—
902C2—21no—
903C2—21no—
904C2—42no—
905C2—42no—
906C2—82no—
907C2—81no—
908C2—81no—
909C2—161no—
910C2C31×#241011yescharacteristic
subgroupG/H
center, socleC2×C31#2410
commutator, Frattini, cosocleC22×C4C24×C31
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C31 ◁ C22×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3585C2semidirect
2. C31×#3068C2semidirect
3. C31×#3038C2semidirect
4. C31×#3021C2semidirect
5. C2×C31×#453C2semidirect
6. C31×#2901C2semidirect
7. C31×#2050C2semidirect
8. C31×#2048C2semidirect
9. C31×#2008C2semidirect
10. C31×#2002C2semidirect
11. C31×#1906C2semidirect
12. C31×#1903C2semidirect
13. C31×#1903C2semidirect
14. C31×#1861C2semidirect
15. C31×#1795C2semidirect
29. C2×C31×AGL(1,ℤ/8)C22semidirect
30. C2×C31×AGL(1,ℤ/8)C22semidirect
32. C31×#568C22semidirect
33. C31×#535C22semidirect
34. C2×C31×#127C22semidirect
35. C4×#41×C31C22semidirect
44. C31×#430C22semidirect
45. C31×#423C22semidirect
49. C31×#421C22semidirect
50. C31×#421C22semidirect
53. C2×C31×#104C22semidirect
54. C2×C31×#104C22semidirect
55. C31×#418C22semidirect
56. C31×#418C22semidirect
57. C31×#418C22semidirect
58. C31×#413C22semidirect
59. C31×#413C22semidirect
60. C2×C31×#100C22semidirect
61. C2×C31×#100C22semidirect
62. C31×#410C22semidirect
63. C31×#344C22semidirect
64. C31×#344C22semidirect
65. C31×#339C22semidirect
66. C31×#338C22semidirect
69. C31×2−1+4D4semidirect
77. C31×H(5,𝔽2)D4semidirect
97. C31×#137D4semidirect
114. C31×AGL(1,ℤ/8)D4semidirect
124. C2×SD16×C31D4semidirect
130. C2×D8×C31D4semidirect
168. C31×#104D4semidirect
169. C31×#104D4semidirect
320. #24472C31direct (N × H)
412. #3585C2×C31semidirect
413. #3068C2×C31semidirect
414. #3038C2×C31semidirect
415. #3021C2×C31semidirect
416. C2×#453C2×C31semidirect
417. #2901C2×C31semidirect
418. #2050C2×C31semidirect
419. #2048C2×C31semidirect
420. #2008C2×C31semidirect
421. #2002C2×C31semidirect
422. #1906C2×C31semidirect
423. #1903C2×C31semidirect
424. #1903C2×C31semidirect
425. #1861C2×C31semidirect
426. #1795C2×C31semidirect
474. C2×AGL(1,ℤ/8)C22×C31semidirect
475. C2×AGL(1,ℤ/8)C22×C31semidirect
477. #568C22×C31semidirect
478. #535C22×C31semidirect
479. C2×#127C22×C31semidirect
480. C4×#41C22×C31semidirect
489. #430C22×C31semidirect
490. #423C22×C31semidirect
494. #421C22×C31semidirect
495. #421C22×C31semidirect
498. C2×#104C22×C31semidirect
499. C2×#104C22×C31semidirect
500. #418C22×C31semidirect
501. #418C22×C31semidirect
502. #418C22×C31semidirect
503. #413C22×C31semidirect
504. #413C22×C31semidirect
505. C2×#100C22×C31semidirect
506. C2×#100C22×C31semidirect
507. #410C22×C31semidirect
508. #344C22×C31semidirect
509. #344C22×C31semidirect
510. #339C22×C31semidirect
511. #338C22×C31semidirect
524. 2−1+4D4×C31semidirect
532. H(5,𝔽2)D4×C31semidirect
552. #137D4×C31semidirect
569. AGL(1,ℤ/8)D4×C31semidirect
579. C2×SD16D4×C31semidirect
585. C2×D8D4×C31semidirect
623. #104D4×C31semidirect
624. #104D4×C31semidirect
635. C31#24472direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35852
C31×#30682
C31×#30382
C31×#30212
C2×C31×#4532
C31×#29012
C31×#20502
C31×#20482
C31×#20082
C31×#20022
C31×#19062
C31×#19032
C31×#18612
C31×#17952
#2447231