Finite Group Databasebeta

← C31×#24451 #21481210

Subgroups — C31×#24451 #21481210

Order 7936.

1580 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#550C211yesmaximal, characteristic, complemented
2C2×C31×#469C211yesmaximal, characteristic, complemented
3C2×C31×#449C211yesmaximal, characteristic, complemented
4C2×C31×#449C211yesmaximal, characteristic, complemented
5C2×C31×#417C211yesmaximal, characteristic, complemented
6C31×#2416C211yesmaximal, characteristic, complemented
7C31×#2041C211yesmaximal, characteristic, complemented
8C31×#2034C211yesmaximal, characteristic, complemented
9C31×#2011C211yesmaximal, characteristic, complemented
10C31×#1999C211yesmaximal, characteristic, complemented
11C31×#1880C211yesmaximal, characteristic, complemented
12C31×#1874C211yesmaximal, characteristic, complemented
13C31×#1870C211yesmaximal, characteristic, complemented
14C31×#1865C211yesmaximal, characteristic, complemented
15C31×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C22×#41×C31C2211yescharacteristic
18C22×SD16×C31C2211yescharacteristic
19C22×D8×C31C2211yescharacteristic
20C22×D8×C31C2211yescharacteristic
21C22×M16×C31C2211yescharacteristic
22C31×#550—24no—
23C31×#550—24no—
24C2×C31×#127—21no—
25C2×C31×#127C2211yescharacteristic
26C2×C31×#121—21no—
27C2×C31×#121—21no—
28C2×C31×#121—21no—
29C2×C31×#121C2211yescharacteristic
30C2×C31×#121C2211yescharacteristic
31C2×C31×#121C2211yescharacteristic
32C2×C31×#121C2211yescharacteristic
33C2×C4×Q8×C31C2211yescharacteristic
34C2×C4×D4×C31—21no—
35C2×C4×D4×C31C2211yescharacteristic
36C22×C4⋊C4×C31C2211yescharacteristic
37C31×#469—24no—
38C31×#449—24no—
39C31×#449—24no—
40C2×C31×#106C2211yescharacteristic
41C31×#417—24no—
42C2×C31×#103C2211yescharacteristic
43C2×C31×#103C2211yescharacteristic
44C2×C31×#103C2211yescharacteristic
45C2×C31×#102C2211yescharacteristic
46C2×C31×#102C2211yescharacteristic
47C2×C31×#102C2211yescharacteristic
48C2×C31×#102C2211yescharacteristic
49C2×C31×#102C2211yescharacteristic
50C2×C31×#102C2211yescharacteristic
51C2×C31×#102C2211yescharacteristic
52C2×C31×C22⋊C8C2211yescharacteristic
53C2×C31×C22⋊C8C2211yescharacteristic
54C2×C31×C22⋊C8C2211yescharacteristic
55C31×#396—21no—
56C31×#394—21no—
57C31×#390C2211yescharacteristic
58C31×#389C2211yescharacteristic
59C31×#386—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×C31—21no—
93C23×C4×C31C2311yescharacteristic
94C23×C4×C31C2311yescharacteristic
95C2×SD16×C31—22no—
96C2×SD16×C31—22no—
97C2×SD16×C31—22no—
98C2×D8×C31—22no—
99C2×D8×C31—22no—
100C2×D8×C31—22no—
101C2×D8×C31—41no—
102C2×D8×C31—41no—
103C2×D8×C31—41no—
104C2×M16×C31—22no—
105C2×M16×C31—22no—
106C2×M16×C31—41no—
107C22×C8×C31C2311yescharacteristic
108C22×C8×C31C2311yescharacteristic
109C22×C8×C31C2311yescharacteristic
110C22×C8×C31C2311yescharacteristic
111C31×#127—28no—
112C31×#127—22no—
113C31×#127—22no—
114C31×#121—28no—
115C31×#121—28no—
116C31×#121—22no—
117C31×#121—22no—
118C31×#121—22no—
119C31×#121—22no—
120C31×#121—22no—
121C31×#121—22no—
122C31×#121—41no—
123C31×#121—44no—
124C31×#121D414yescomplemented
125C4×Q8×C31—22no—
126C4×Q8×C31—22no—
127C4×D4×C31—28no—
128C4×D4×C31—22no—
129C4×D4×C31—22no—
130C2×C4⋊C4×C31—21no—
131C2×C4⋊C4×C31—22no—
132C2×C4⋊C4×C31—21no—
133C2×C4⋊C4×C31—21no—
134C2×C4⋊C4×C31—41no—
135C2×C4⋊C4×C31D411yescharacteristic
136C2×C4⋊C4×C31C2311yescharacteristic
137C2×C4⋊C4×C31C2311yescharacteristic
138C2×C4⋊C4×C31C2311yescharacteristic
139C2×C4⋊C4×C31C2311yescharacteristic
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×C31—21no—
146C2×C22⋊C4×C31—21no—
147C2×C22⋊C4×C31D411yescharacteristic
148C2×C22⋊C4×C31D411yescharacteristic
149C2×C42×C31—21no—
150C2×C42×C31C2311yescharacteristic
151C31×#106—22no—
152C31×#103—22no—
153C31×#103—22no—
154C31×#103D414yescomplemented
155C31×#102—22no—
156C31×#102—22no—
157C31×#102—22no—
158C31×#102—22no—
159C31×#102—22no—
160C31×#102—22no—
161C31×#102—41no—
162C31×C22⋊C8—22no—
163C31×C22⋊C8—22no—
164C31×C22⋊C8—41no—
165C31×#95—21no—
166C31×#95—21no—
167C24×C31—21no—
168C24×C31—21no—
169C24×C31—21no—
170C24×C31C2×D411yescharacteristic
171C24×C31C2×D411yescharacteristic
172#41×C31—28no—
173#41×C31—44no—
174#41×C31—44no—
175#41×C31—44no—
176#41×C31—44no—
177#41×C31—44no—
178#41×C31—44no—
179#41×C31—44no—
180C2×Q8×C31—21no—
181C2×Q8×C31—21no—
182C2×Q8×C31—21no—
183C2×Q8×C31C2×D412yes—
184C2×Q8×C31C2×D412yes—
185C2×Q8×C31#4112yes—
186C2×D4×C31—24no—
187C2×D4×C31—24no—
188C2×D4×C31—22no—
189C2×D4×C31—24no—
190C2×D4×C31—24no—
191C2×D4×C31—24no—
192C2×D4×C31—24no—
193C2×D4×C31—22no—
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—21no—
210C2×D4×C31—41no—
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—42no—
220C2×D4×C31—42no—
221C2×D4×C31—42no—
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×C31—81no—
229C2×D4×C31C2×D412yes—
230C2×D4×C31C2×D412yes—
231C22×C4×C31—21no—
232C22×C4×C31—21no—
233C22×C4×C31—21no—
234C22×C4×C31—21no—
235C22×C4×C31—21no—
236C22×C4×C31—24no—
237C22×C4×C31—21no—
238C22×C4×C31—21no—
239C22×C4×C31—24no—
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—21no—
248C22×C4×C31—42no—
249C22×C4×C31—42no—
250C22×C4×C31—42no—
251C22×C4×C31—42no—
252C22×C4×C31—42no—
253C22×C4×C31—42no—
254C22×C4×C31—81no—
255C22×C4×C31C2×D411yescharacteristic
256C22×C4×C31C2×D411yescharacteristic
257C22×C4×C31C2×D411yescharacteristic
258C22×C4×C31C2×D412yes—
259C22×C4×C31C2×D412yes—
260C22×C4×C31C2×D411yescharacteristic
261C22×C4×C31C2411yescharacteristic
262SD16×C31—44no—
263D8×C31—44no—
264D8×C31—44no—
265M16×C31—44no—
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—21no—
273C2×C8×C31—21no—
274C2×C8×C31—21no—
275C2×C8×C31—21no—
276C2×C8×C31—21no—
277C2×C8×C31C2×D412yes—
278C4⋊C4×C31—24no—
279C4⋊C4×C31—22no—
280C4⋊C4×C31—21no—
281C4⋊C4×C31—21no—
282C4⋊C4×C31—21no—
283C4⋊C4×C31—21no—
284C4⋊C4×C31—21no—
285C4⋊C4×C31—21no—
286C4⋊C4×C31—42no—
287C4⋊C4×C31—42no—
288C4⋊C4×C31C2×D412yes—
289C4⋊C4×C31C2×D412yes—
290C22⋊C4×C31—24no—
291C22⋊C4×C31—22no—
292C22⋊C4×C31—24no—
293C22⋊C4×C31—22no—
294C22⋊C4×C31—42no—
295C22⋊C4×C31—42no—
296C22⋊C4×C31—42no—
297C22⋊C4×C31—42no—
298C22⋊C4×C31—81no—
299C42×C31—24no—
300C42×C31—21no—
301C42×C31—21no—
302#24451C3111yesmaximal, characteristic, direct product factor, Sylow
303C23×C31—21no—
304C23×C31—21no—
305C23×C31—21no—
306C23×C31—21no—
307C23×C31—21no—
308C23×C31—21no—
309C23×C31—21no—
310C23×C31—22no—
311C23×C31—22no—
312C23×C31—21no—
313C23×C31—21no—
314C23×C31—21no—
315C23×C31—21no—
316C23×C31—21no—
317C23×C31—21no—
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—41no—
335C23×C31—41no—
336C23×C31—41no—
337C23×C31#12012yes—
338C23×C31C22×D411yescharacteristic
339Q8×C31—22no—
340Q8×C31—22no—
341Q8×C31—22no—
342Q8×C31#12114yescomplemented
343D4×C31—22no—
344D4×C31—22no—
345D4×C31—22no—
346D4×C31—22no—
347D4×C31—44no—
348D4×C31—48no—
349D4×C31—48no—
350D4×C31—48no—
351D4×C31—41no—
352D4×C31—41no—
353D4×C31—41no—
354D4×C31—41no—
355D4×C31—41no—
356D4×C31—41no—
357D4×C31—41no—
358D4×C31—41no—
359D4×C31—84no—
360D4×C31—84no—
361D4×C31—84no—
362D4×C31—84no—
363D4×C31—84no—
364C2×C4×C31—21no—
365C2×C4×C31—22no—
366C2×C4×C31—21no—
367C2×C4×C31—22no—
368C2×C4×C31—21no—
369C2×C4×C31—22no—
370C2×C4×C31—21no—
371C2×C4×C31—22no—
372C2×C4×C31—22no—
373C2×C4×C31—22no—
374C2×C4×C31—22no—
375C2×C4×C31—21no—
376C2×C4×C31—22no—
377C2×C4×C31—21no—
378C2×C4×C31—21no—
379C2×C4×C31—22no—
380C2×C4×C31—21no—
381C2×C4×C31—21no—
382C2×C4×C31—21no—
383C2×C4×C31—48no—
384C2×C4×C31—48no—
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—41no—
397C2×C4×C31—41no—
398C2×C4×C31—41no—
399C2×C4×C31—84no—
400C2×C4×C31#12012yes—
401C2×C4×C31AGL(1,ℤ/8)12yes—
402C2×C4×C31C22×D411yescharacteristic
403C2×C4×C31C22×D411yescharacteristic
404C2×C4×C31C22×D411yescharacteristic
405C2×C4×C31C2×#4111yescharacteristic
406C2×C4×C31H(5,𝔽2)11yescharacteristic
407C2×C4×C31H(5,𝔽2)11yescharacteristic
408C8×C31—22no—
409C8×C31—41no—
410C8×C31—41no—
411C8×C31—41no—
412C2×#550C2×C3111yescharacteristic, complemented
413C2×#469C2×C3111yescharacteristic, complemented
414C2×#449C2×C3111yescharacteristic, complemented
415C2×#449C2×C3111yescharacteristic, complemented
416C2×#417C2×C3111yescharacteristic, complemented
417#2416C2×C3111yescharacteristic, complemented
418#2041C2×C3111yescharacteristic, complemented
419#2034C2×C3111yescharacteristic, complemented
420#2011C2×C3111yescharacteristic, complemented
421#1999C2×C3111yescharacteristic, complemented
422#1880C2×C3111yescharacteristic, complemented
423#1874C2×C3111yescharacteristic, complemented
424#1870C2×C3111yescharacteristic, complemented
425#1865C2×C3111yescharacteristic, complemented
426#1788C2×C3111yescharacteristic, complemented
427C22×C31—22no—
428C22×C31—22no—
429C22×C31—22no—
430C22×C31—41no—
431C22×C31—41no—
432C22×C31—41no—
433C22×C31—41no—
434C22×C31—41no—
435C22×C31—42no—
436C22×C31—42no—
437C22×C31—41no—
438C22×C31—41no—
439C22×C31—42no—
440C22×C31—42no—
441C22×C31—41no—
442C22×C31—42no—
443C22×C31—42no—
444C22×C31—41no—
445C22×C31—41no—
446C22×C31—41no—
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×C31—81no—
459C22×C31—81no—
460C22×C31—81no—
461C22×C31—81no—
462C22×C31C2×#12011yescharacteristic
463C22×C31D4211yescharacteristic
464C22×C31#54611yescharacteristic
465C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
466C22×C31#57511yescharacteristic
467C22×C31#57611yescharacteristic
468C22×C31#57711yescharacteristic
469C4×C31—22no—
470C4×C31—24no—
471C4×C31—22no—
472C4×C31—41no—
473C4×C31—41no—
474C4×C31—42no—
475C4×C31—42no—
476C4×C31—81no—
477C4×C31—81no—
478C4×C31C2×#12111yescharacteristic
479C4×C31#53411yescharacteristic
480C4×C31D4211yescharacteristic
481C4×C31#54611yescharacteristic
482C22×#41C22×C3111yescharacteristic
483C22×#41C22×C3111yescharacteristic
484C22×SD16C22×C3111yescharacteristic
485C22×D8C22×C3111yescharacteristic
486C22×D8C22×C3111yescharacteristic
487C22×M16C22×C3111yescharacteristic
488#550—24no—
489#550—24no—
490C2×#127—21no—
491C2×#127C22×C3111yescharacteristic
492C2×#121—21no—
493C2×#121—21no—
494C2×#121—21no—
495C2×#121C22×C3111yescharacteristic
496C2×#121C22×C3111yescharacteristic
497C2×#121C22×C3111yescharacteristic
498C2×#121C22×C3111yescharacteristic
499C2×C4×Q8C22×C3111yescharacteristic
500C2×C4×D4—21no—
501C2×C4×D4C22×C3111yescharacteristic
502C22×C4⋊C4C22×C3111yescharacteristic
503#469—24no—
504#449—24no—
505#449—24no—
506C2×#106C22×C3111yescharacteristic
507#417—24no—
508C2×#103C22×C3111yescharacteristic
509C2×#103C22×C3111yescharacteristic
510C2×#103C22×C3111yescharacteristic
511C2×#102C22×C3111yescharacteristic
512C2×#102C22×C3111yescharacteristic
513C2×#102C22×C3111yescharacteristic
514C2×#102C22×C3111yescharacteristic
515C2×#102C22×C3111yescharacteristic
516C2×#102C22×C3111yescharacteristic
517C2×#102C22×C3111yescharacteristic
518C2×C22⋊C8C22×C3111yescharacteristic
519C2×C22⋊C8C22×C3111yescharacteristic
520C2×C22⋊C8C22×C3111yescharacteristic
521#396—21no—
522#394—21no—
523#390C22×C3111yescharacteristic
524#389C22×C3111yescharacteristic
525#386—21no—
526#380C22×C3111yescharacteristic
527#340C22×C3111yescharacteristic
528#340C22×C3111yescharacteristic
529#336C22×C3111yescharacteristic
530#336C22×C3111yescharacteristic
531C2×C31—42no—
532C2×C31—81no—
533C2×C31—82no—
534C2×C31—82no—
535C2×C31—161no—
536C2×C31#241011yescharacteristic
537C2×C31#300611yescharacteristic
538C2×C31#301211yescharacteristic
539C2×C31#327111yescharacteristic
540C2×C31#327411yescharacteristic
541C2×C31#330911yescharacteristic
542C2×C31#333211yescharacteristic
543C2×#41—22no—
544C2×#41—22no—
545C2×#41—22no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—41no—
551C2×#41—41no—
552C2×#41—41no—
553C2×#41—41no—
554C2×#41D4×C3114yescomplemented
555C22×Q8C23×C3111yescharacteristic
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—21no—
563C22×D4—21no—
564C22×D4D4×C3111yescharacteristic
565C22×D4C23×C3111yescharacteristic
566C22×D4C23×C3111yescharacteristic
567C22×D4C23×C3111yescharacteristic
568C23×C4—21no—
569C23×C4—21no—
570C23×C4—21no—
571C23×C4C23×C3111yescharacteristic
572C23×C4C23×C3111yescharacteristic
573C2×SD16—22no—
574C2×SD16—22no—
575C2×SD16—22no—
576C2×D8—22no—
577C2×D8—22no—
578C2×D8—22no—
579C2×D8—41no—
580C2×D8—41no—
581C2×D8—41no—
582C2×M16—22no—
583C2×M16—22no—
584C2×M16—41no—
585C22×C8C23×C3111yescharacteristic
586C22×C8C23×C3111yescharacteristic
587C22×C8C23×C3111yescharacteristic
588C22×C8C23×C3111yescharacteristic
589#127—28no—
590#127—22no—
591#127—22no—
592#121—28no—
593#121—28no—
594#121—22no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—22no—
600#121—41no—
601#121—44no—
602#121D4×C3114yescomplemented
603C4×Q8—22no—
604C4×Q8—22no—
605C4×D4—28no—
606C4×D4—22no—
607C4×D4—22no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—41no—
613C2×C4⋊C4D4×C3111yescharacteristic
614C2×C4⋊C4C23×C3111yescharacteristic
615C2×C4⋊C4C23×C3111yescharacteristic
616C2×C4⋊C4C23×C3111yescharacteristic
617C2×C4⋊C4C23×C3111yescharacteristic
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4D4×C3111yescharacteristic
626C2×C22⋊C4D4×C3111yescharacteristic
627C2×C42—21no—
628C2×C42C23×C3111yescharacteristic
629#106—22no—
630#103—22no—
631#103—22no—
632#103D4×C3114yescomplemented
633#102—22no—
634#102—22no—
635#102—22no—
636#102—22no—
637#102—22no—
638#102—22no—
639#102—41no—
640C22⋊C8—22no—
641C22⋊C8—22no—
642C22⋊C8—41no—
643#95—21no—
644#95—21no—
645C31#2445111yescharacteristic, direct product factor, Sylow
646C24—21no—
647C24—21no—
648C24—21no—
649C24C2×D4×C3111yescharacteristic
650C24C2×D4×C3111yescharacteristic
651#41—28no—
652#41—44no—
653#41—44no—
654#41—44no—
655#41—44no—
656#41—44no—
657#41—44no—
658#41—44no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8C2×D4×C3112yes—
663C2×Q8C2×D4×C3112yes—
664C2×Q8#41×C3112yes—
665C2×D4—24no—
666C2×D4—24no—
667C2×D4—22no—
668C2×D4—24no—
669C2×D4—24no—
670C2×D4—24no—
671C2×D4—24no—
672C2×D4—22no—
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—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—41no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—42no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—81no—
702C2×D4—81no—
703C2×D4—81no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4C2×D4×C3112yes—
709C2×D4C2×D4×C3112yes—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—24no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—24no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—42no—
728C22×C4—42no—
729C22×C4—42no—
730C22×C4—42no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—81no—
734C22×C4C2×D4×C3111yescharacteristic
735C22×C4C2×D4×C3111yescharacteristic
736C22×C4C2×D4×C3111yescharacteristic
737C22×C4C2×D4×C3112yes—
738C22×C4C2×D4×C3112yes—
739C22×C4C2×D4×C3111yescharacteristic
740C22×C4C24×C3111yescharacteristic
741SD16—44no—
742D8—44no—
743D8—44no—
744M16—44no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8C2×D4×C3112yes—
757C4⋊C4—24no—
758C4⋊C4—22no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—42no—
766C4⋊C4—42no—
767C4⋊C4C2×D4×C3112yes—
768C4⋊C4C2×D4×C3112yes—
769C22⋊C4—24no—
770C22⋊C4—22no—
771C22⋊C4—24no—
772C22⋊C4—22no—
773C22⋊C4—42no—
774C22⋊C4—42no—
775C22⋊C4—42no—
776C22⋊C4—42no—
777C22⋊C4—81no—
778C42—24no—
779C42—21no—
780C42—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—22no—
789C23—22no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23C31×#12012yes—
816C23C22×D4×C3111yescharacteristic
817Q8—22no—
818Q8—22no—
819Q8—22no—
820Q8C31×#12114yescomplemented
821D4—22no—
822D4—22no—
823D4—22no—
824D4—22no—
825D4—44no—
826D4—48no—
827D4—48no—
828D4—48no—
829D4—41no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4—41no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—84no—
838D4—84no—
839D4—84no—
840D4—84no—
841D4—84no—
842C2×C4—21no—
843C2×C4—22no—
844C2×C4—21no—
845C2×C4—22no—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—21no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—21no—
854C2×C4—22no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—22no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—48no—
862C2×C4—48no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—84no—
878C2×C4C31×#12012yes—
879C2×C4C31×AGL(1,ℤ/8)12yes—
880C2×C4C22×D4×C3111yescharacteristic
881C2×C4C22×D4×C3111yescharacteristic
882C2×C4C22×D4×C3111yescharacteristic
883C2×C4C2×#41×C3111yescharacteristic
884C2×C4C31×H(5,𝔽2)11yescharacteristic
885C2×C4C31×H(5,𝔽2)11yescharacteristic
886C8—22no—
887C8—41no—
888C8—41no—
889C8—41no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—41no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—41no—
898C22—42no—
899C22—42no—
900C22—41no—
901C22—41no—
902C22—42no—
903C22—42no—
904C22—41no—
905C22—42no—
906C22—42no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22C2×C31×#12011yescharacteristic
926C22D42×C3111yescharacteristic
927C22C31×#54611yescharacteristic
928C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
929C22C31×#57511yescharacteristic
930C22C31×#57611yescharacteristic
931C22C31×#57711yescharacteristic
932C4—22no—
933C4—24no—
934C4—22no—
935C4—41no—
936C4—41no—
937C4—42no—
938C4—42no—
939C4—81no—
940C4—81no—
941C4C2×C31×#12111yescharacteristic
942C4C31×#53411yescharacteristic
943C4D42×C3111yescharacteristic
944C4C31×#54611yescharacteristic
945C2—42no—
946C2—81no—
947C2—82no—
948C2—82no—
949C2—161no—
950C2C31×#241011yescharacteristic
951C2C31×#300611yescharacteristic
952C2C31×#301211yescharacteristic
953C2C31×#327111yescharacteristic
954C2C31×#327411yescharacteristic
955C2C31×#330911yescharacteristic
956C2C31×#333211yescharacteristic
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×#469C2semidirect
3. C2×C31×#449C2semidirect
4. C2×C31×#449C2semidirect
5. C2×C31×#417C2semidirect
6. C31×#2416C2semidirect
7. C31×#2041C2semidirect
8. C31×#2034C2semidirect
9. C31×#2011C2semidirect
10. C31×#1999C2semidirect
11. C31×#1880C2semidirect
12. C31×#1874C2semidirect
13. C31×#1870C2semidirect
14. C31×#1865C2semidirect
15. C31×#1788C2semidirect
76. C2×#41×C31D4semidirect
124. C31×#121D4semidirect
154. C31×#103D4semidirect
302. #24451C31direct (N × H)
342. Q8×C31#121semidirect
412. C2×#550C2×C31semidirect
413. C2×#469C2×C31semidirect
414. C2×#449C2×C31semidirect
415. C2×#449C2×C31semidirect
416. C2×#417C2×C31semidirect
417. #2416C2×C31semidirect
418. #2041C2×C31semidirect
419. #2034C2×C31semidirect
420. #2011C2×C31semidirect
421. #1999C2×C31semidirect
422. #1880C2×C31semidirect
423. #1874C2×C31semidirect
424. #1870C2×C31semidirect
425. #1865C2×C31semidirect
426. #1788C2×C31semidirect
554. C2×#41D4×C31semidirect
602. #121D4×C31semidirect
632. #103D4×C31semidirect
645. C31#24451direct (N × H)
820. Q8C31×#121semidirect

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×#4692
C2×C31×#4492
C2×C31×#4172
C31×#24162
C31×#20412
C31×#20342
C31×#20112
C31×#19992
C31×#18802
C31×#18742
C31×#18702
C31×#18652
C31×#17882
#2445131