Finite Group Databasebeta

← C31×#25092 #21481851

Subgroups — C31×#25092 #21481851

Order 7936.

1230 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#469C211yesmaximal, characteristic, complemented
2C2×C31×#459C211yesmaximal, characteristic, complemented
3C2×C31×#449C211yesmaximal, characteristic, complemented
4C2×C31×#417C211yesmaximal, characteristic, complemented
5C31×#2431C211yesmaximal, characteristic, complemented
6C31×#2361C211yesmaximal, characteristic, complemented
7C31×#2066C211yesmaximal, characteristic, complemented
8C31×#2054C211yesmaximal, characteristic, complemented
9C31×#2041C211yesmaximal, characteristic, complemented
10C31×#2012C211yesmaximal, characteristic, complemented
11C31×#1983C211yesmaximal, characteristic, complemented
12C31×#1926C211yesmaximal, characteristic, complemented
13C31×#1877C211yesmaximal, characteristic, complemented
14C31×#1874C211yesmaximal, characteristic, complemented
15C31×#1851C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C22×SD16×C31C2211yescharacteristic
18C22×D8×C31C2211yescharacteristic
19C22×D8×C31C2211yescharacteristic
20C22×M16×C31C2211yescharacteristic
21C2×C31×#127C2211yescharacteristic
22C2×C31×#124C2211yescharacteristic
23C2×C31×#121C2211yescharacteristic
24C2×C31×#121C2211yescharacteristic
25C2×C4×D4×C31—21no—
26C2×C4×D4×C31C2211yescharacteristic
27C22×C4⋊C4×C31C2211yescharacteristic
28C31×#469—24no—
29C31×#459—24no—
30C31×#449—24no—
31C2×C31×#106C2211yescharacteristic
32C2×C31×C4⋊C8C2211yescharacteristic
33C2×C31×C4⋊C8C2211yescharacteristic
34C31×#417—24no—
35C2×C31×#103C2211yescharacteristic
36C2×C31×#103C2211yescharacteristic
37C2×C31×#103C2211yescharacteristic
38C2×C31×#102C2211yescharacteristic
39C2×C31×#102C2211yescharacteristic
40C2×C31×#102C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×C22⋊C8C2211yescharacteristic
46C31×#392—21no—
47C31×#392—21no—
48C31×#391C2211yescharacteristic
49C31×#390C2211yescharacteristic
50C31×#390C2211yescharacteristic
51C31×#389C2211yescharacteristic
52C31×#388—21no—
53C31×#386—21no—
54C31×#386—21no—
55C31×#386—21no—
56C31×#385—21no—
57C4×C4⋊C4×C31C2211yescharacteristic
58C4×C22⋊C4×C31C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C31×#336C2211yescharacteristic
63C2×#41×C31—22no—
64C2×#41×C31—22no—
65C2×#41×C31—22no—
66C2×#41×C31—22no—
67C2×#41×C31—41no—
68C2×#41×C31—41no—
69C22×Q8×C31C2311yescharacteristic
70C22×D4×C31—21no—
71C22×D4×C31—21no—
72C22×D4×C31—21no—
73C22×D4×C31—21no—
74C22×D4×C31—21no—
75C22×D4×C31C2311yescharacteristic
76C22×D4×C31C2311yescharacteristic
77C22×D4×C31C2311yescharacteristic
78C23×C4×C31—21no—
79C23×C4×C31—21no—
80C23×C4×C31—21no—
81C23×C4×C31C2311yescharacteristic
82C2×SD16×C31—22no—
83C2×SD16×C31—22no—
84C2×SD16×C31—41no—
85C2×D8×C31—22no—
86C2×D8×C31—22no—
87C2×D8×C31—22no—
88C2×D8×C31—22no—
89C2×D8×C31—41no—
90C2×D8×C31—41no—
91C2×M16×C31—22no—
92C2×M16×C31—22no—
93C2×M16×C31—41no—
94C22×C8×C31C2311yescharacteristic
95C22×C8×C31C2311yescharacteristic
96C22×C8×C31C2311yescharacteristic
97C22×C8×C31C2311yescharacteristic
98C31×#127—22no—
99C31×#127—41no—
100C31×#124—22no—
101C31×#124—41no—
102C31×#121—22no—
103C31×#121—22no—
104C31×#121—22no—
105C31×#121D414yescomplemented
106C4×D4×C31—22no—
107C4×D4×C31—41no—
108C4×D4×C31—44no—
109C2×C4⋊C4×C31—22no—
110C2×C4⋊C4×C31—21no—
111C2×C4⋊C4×C31—21no—
112C2×C4⋊C4×C31—41no—
113C2×C4⋊C4×C31C2311yescharacteristic
114C2×C4⋊C4×C31C2311yescharacteristic
115C2×C4⋊C4×C31C2311yescharacteristic
116C2×C4⋊C4×C31C2311yescharacteristic
117C2×C22⋊C4×C31—21no—
118C2×C22⋊C4×C31—21no—
119C2×C22⋊C4×C31—21no—
120C2×C22⋊C4×C31—21no—
121C2×C22⋊C4×C31—21no—
122C2×C22⋊C4×C31—21no—
123C2×C22⋊C4×C31—21no—
124C2×C22⋊C4×C31—21no—
125C2×C22⋊C4×C31—21no—
126C2×C22⋊C4×C31D411yescharacteristic
127C2×C22⋊C4×C31D411yescharacteristic
128C2×C42×C31—21no—
129C2×C42×C31C2311yescharacteristic
130C2×C42×C31C2311yescharacteristic
131C31×#106—22no—
132C31×C4⋊C8—22no—
133C31×C4⋊C8—41no—
134C31×#103—22no—
135C31×#103—22no—
136C31×#103—22no—
137C31×#102—22no—
138C31×#102—22no—
139C31×#102—22no—
140C31×#102—22no—
141C31×#102—22no—
142C31×#102—41no—
143C31×#102D414yescomplemented
144C31×C22⋊C8—22no—
145C31×#95—21no—
146C31×#95—21no—
147C31×#95—21no—
148C31×#95—21no—
149C31×#95D411yescharacteristic
150C31×#95D411yescharacteristic
151C24×C31—21no—
152C24×C31—21no—
153C24×C31—21no—
154C24×C31C2×D411yescharacteristic
155#41×C31—28no—
156#41×C31—44no—
157#41×C31—44no—
158#41×C31—44no—
159C2×Q8×C31—21no—
160C2×Q8×C31—21no—
161C2×Q8×C31—21no—
162C2×Q8×C31—21no—
163C2×Q8×C31—21no—
164C2×Q8×C31#4112yes—
165C2×D4×C31—24no—
166C2×D4×C31—21no—
167C2×D4×C31—21no—
168C2×D4×C31—21no—
169C2×D4×C31—21no—
170C2×D4×C31—21no—
171C2×D4×C31—21no—
172C2×D4×C31—21no—
173C2×D4×C31—21no—
174C2×D4×C31—21no—
175C2×D4×C31—21no—
176C2×D4×C31—21no—
177C2×D4×C31—21no—
178C2×D4×C31—21no—
179C2×D4×C31—21no—
180C2×D4×C31—21no—
181C2×D4×C31—21no—
182C2×D4×C31—42no—
183C2×D4×C31—42no—
184C2×D4×C31—42no—
185C2×D4×C31—42no—
186C2×D4×C31—42no—
187C2×D4×C31—42no—
188C2×D4×C31—42no—
189C2×D4×C31—42no—
190C2×D4×C31—42no—
191C2×D4×C31—42no—
192C2×D4×C31—81no—
193C2×D4×C31—81no—
194C2×D4×C31—81no—
195C2×D4×C31—81no—
196C2×D4×C31C2×D412yes—
197C2×D4×C31C2×D412yes—
198C22×C4×C31—21no—
199C22×C4×C31—21no—
200C22×C4×C31—21no—
201C22×C4×C31—21no—
202C22×C4×C31—21no—
203C22×C4×C31—21no—
204C22×C4×C31—21no—
205C22×C4×C31—21no—
206C22×C4×C31—21no—
207C22×C4×C31—42no—
208C22×C4×C31—42no—
209C22×C4×C31—42no—
210C22×C4×C31—42no—
211C22×C4×C31—42no—
212C22×C4×C31—42no—
213C22×C4×C31—42no—
214C22×C4×C31—81no—
215C22×C4×C31—81no—
216C22×C4×C31C2×D411yescharacteristic
217C22×C4×C31C2×D411yescharacteristic
218C22×C4×C31C2×D411yescharacteristic
219C22×C4×C31C2×D411yescharacteristic
220C22×C4×C31C2×D412yes—
221C22×C4×C31C2×D411yescharacteristic
222C22×C4×C31#4112yes—
223C22×C4×C31C2411yescharacteristic
224SD16×C31—44no—
225D8×C31—44no—
226D8×C31—44no—
227M16×C31—44no—
228C2×C8×C31—21no—
229C2×C8×C31—21no—
230C2×C8×C31—21no—
231C2×C8×C31—21no—
232C2×C8×C31—21no—
233C2×C8×C31—21no—
234C2×C8×C31—21no—
235C2×C8×C31—21no—
236C2×C8×C31—21no—
237C2×C8×C31—21no—
238C2×C8×C31—21no—
239C2×C8×C31C2×D412yes—
240C4⋊C4×C31—21no—
241C4⋊C4×C31—21no—
242C4⋊C4×C31—21no—
243C4⋊C4×C31—21no—
244C4⋊C4×C31—21no—
245C4⋊C4×C31—21no—
246C4⋊C4×C31—42no—
247C4⋊C4×C31—42no—
248C4⋊C4×C31C2×D412yes—
249C4⋊C4×C31C2×D412yes—
250C22⋊C4×C31—24no—
251C22⋊C4×C31—22no—
252C22⋊C4×C31—41no—
253C22⋊C4×C31—42no—
254C22⋊C4×C31—42no—
255C22⋊C4×C31—42no—
256C22⋊C4×C31—42no—
257C22⋊C4×C31—42no—
258C22⋊C4×C31—81no—
259C22⋊C4×C31—81no—
260C22⋊C4×C31—81no—
261C42×C31—21no—
262C42×C31—21no—
263C42×C31—21no—
264C42×C31—21no—
265C42×C31—42no—
266#25092C3111yesmaximal, characteristic, direct product factor, Sylow
267C23×C31—21no—
268C23×C31—21no—
269C23×C31—21no—
270C23×C31—21no—
271C23×C31—21no—
272C23×C31—21no—
273C23×C31—22no—
274C23×C31—22no—
275C23×C31—41no—
276C23×C31—41no—
277C23×C31—41no—
278C23×C31—41no—
279C23×C31—41no—
280C23×C31—41no—
281C23×C31—41no—
282C23×C31—41no—
283C23×C31—41no—
284C23×C31—41no—
285C23×C31—41no—
286C23×C31—41no—
287C23×C31—41no—
288C23×C31—41no—
289C23×C31—41no—
290C23×C31—41no—
291C23×C31—41no—
292C23×C31—41no—
293C23×C31—41no—
294C23×C31#12112yes—
295C23×C31C22×D411yescharacteristic
296Q8×C31—22no—
297Q8×C31—22no—
298Q8×C31—41no—
299Q8×C31—41no—
300D4×C31—22no—
301D4×C31—22no—
302D4×C31—22no—
303D4×C31—22no—
304D4×C31—48no—
305D4×C31—48no—
306D4×C31—41no—
307D4×C31—41no—
308D4×C31—41no—
309D4×C31—41no—
310D4×C31—41no—
311D4×C31—41no—
312D4×C31—41no—
313D4×C31—41no—
314D4×C31—84no—
315D4×C31—84no—
316D4×C31—84no—
317C2×C4×C31—21no—
318C2×C4×C31—21no—
319C2×C4×C31—21no—
320C2×C4×C31—21no—
321C2×C4×C31—22no—
322C2×C4×C31—22no—
323C2×C4×C31—22no—
324C2×C4×C31—22no—
325C2×C4×C31—22no—
326C2×C4×C31—21no—
327C2×C4×C31—22no—
328C2×C4×C31—21no—
329C2×C4×C31—21no—
330C2×C4×C31—22no—
331C2×C4×C31—21no—
332C2×C4×C31—21no—
333C2×C4×C31—21no—
334C2×C4×C31—21no—
335C2×C4×C31—21no—
336C2×C4×C31—21no—
337C2×C4×C31—48no—
338C2×C4×C31—41no—
339C2×C4×C31—41no—
340C2×C4×C31—41no—
341C2×C4×C31—41no—
342C2×C4×C31—41no—
343C2×C4×C31—41no—
344C2×C4×C31—41no—
345C2×C4×C31—41no—
346C2×C4×C31—41no—
347C2×C4×C31—41no—
348C2×C4×C31—41no—
349C2×C4×C31—41no—
350C2×C4×C31—84no—
351C2×C4×C31—84no—
352C2×C4×C31#12112yes—
353C2×C4×C31AGL(1,ℤ/8)12yes—
354C2×C4×C31C22×D411yescharacteristic
355C2×C4×C31C22×D411yescharacteristic
356C2×C4×C31C2×#4111yescharacteristic
357C2×C4×C31C2×#4111yescharacteristic
358C2×C4×C31H(5,𝔽2)11yescharacteristic
359C2×C4×C31H(5,𝔽2)11yescharacteristic
360C8×C31—22no—
361C8×C31—41no—
362C8×C31—41no—
363C8×C31—41no—
364C2×#469C2×C3111yescharacteristic, complemented
365C2×#459C2×C3111yescharacteristic, complemented
366C2×#449C2×C3111yescharacteristic, complemented
367C2×#417C2×C3111yescharacteristic, complemented
368#2431C2×C3111yescharacteristic, complemented
369#2361C2×C3111yescharacteristic, complemented
370#2066C2×C3111yescharacteristic, complemented
371#2054C2×C3111yescharacteristic, complemented
372#2041C2×C3111yescharacteristic, complemented
373#2012C2×C3111yescharacteristic, complemented
374#1983C2×C3111yescharacteristic, complemented
375#1926C2×C3111yescharacteristic, complemented
376#1877C2×C3111yescharacteristic, complemented
377#1874C2×C3111yescharacteristic, complemented
378#1851C2×C3111yescharacteristic, complemented
379C22×C31—22no—
380C22×C31—22no—
381C22×C31—22no—
382C22×C31—41no—
383C22×C31—41no—
384C22×C31—41no—
385C22×C31—41no—
386C22×C31—42no—
387C22×C31—42no—
388C22×C31—42no—
389C22×C31—42no—
390C22×C31—42no—
391C22×C31—42no—
392C22×C31—81no—
393C22×C31—81no—
394C22×C31—81no—
395C22×C31—81no—
396C22×C31—81no—
397C22×C31—81no—
398C22×C31—81no—
399C22×C31—81no—
400C22×C31—81no—
401C22×C31—81no—
402C22×C31—81no—
403C22×C31—81no—
404C22×C31—81no—
405C22×C31—81no—
406C22×C31—81no—
407C22×C31C2×#12111yescharacteristic
408C22×C31D4211yescharacteristic
409C22×C31#54611yescharacteristic
410C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
411C22×C31#57511yescharacteristic
412C22×C31#57611yescharacteristic
413C22×C31#57711yescharacteristic
414C4×C31—22no—
415C4×C31—22no—
416C4×C31—41no—
417C4×C31—42no—
418C4×C31—42no—
419C4×C31—41no—
420C4×C31—42no—
421C4×C31—41no—
422C4×C31—81no—
423C4×C31—81no—
424C4×C31#52511yescharacteristic
425C4×C31#53811yescharacteristic
426C4×C31D4211yescharacteristic
427C4×C31#54611yescharacteristic
428C22×#41C22×C3111yescharacteristic
429C22×SD16C22×C3111yescharacteristic
430C22×D8C22×C3111yescharacteristic
431C22×D8C22×C3111yescharacteristic
432C22×M16C22×C3111yescharacteristic
433C2×#127C22×C3111yescharacteristic
434C2×#124C22×C3111yescharacteristic
435C2×#121C22×C3111yescharacteristic
436C2×#121C22×C3111yescharacteristic
437C2×C4×D4—21no—
438C2×C4×D4C22×C3111yescharacteristic
439C22×C4⋊C4C22×C3111yescharacteristic
440#469—24no—
441#459—24no—
442#449—24no—
443C2×#106C22×C3111yescharacteristic
444C2×C4⋊C8C22×C3111yescharacteristic
445C2×C4⋊C8C22×C3111yescharacteristic
446#417—24no—
447C2×#103C22×C3111yescharacteristic
448C2×#103C22×C3111yescharacteristic
449C2×#103C22×C3111yescharacteristic
450C2×#102C22×C3111yescharacteristic
451C2×#102C22×C3111yescharacteristic
452C2×#102C22×C3111yescharacteristic
453C2×#102C22×C3111yescharacteristic
454C2×#102C22×C3111yescharacteristic
455C2×#102C22×C3111yescharacteristic
456C2×#102C22×C3111yescharacteristic
457C2×C22⋊C8C22×C3111yescharacteristic
458#392—21no—
459#392—21no—
460#391C22×C3111yescharacteristic
461#390C22×C3111yescharacteristic
462#390C22×C3111yescharacteristic
463#389C22×C3111yescharacteristic
464#388—21no—
465#386—21no—
466#386—21no—
467#386—21no—
468#385—21no—
469C4×C4⋊C4C22×C3111yescharacteristic
470C4×C22⋊C4C22×C3111yescharacteristic
471#340C22×C3111yescharacteristic
472#340C22×C3111yescharacteristic
473#336C22×C3111yescharacteristic
474#336C22×C3111yescharacteristic
475C2×C31—42no—
476C2×C31—82no—
477C2×C31—82no—
478C2×C31—161no—
479C2×C31#242411yescharacteristic
480C2×C31#303611yescharacteristic
481C2×C31#304511yescharacteristic
482C2×C31#326411yescharacteristic
483C2×C31#327511yescharacteristic
484C2×C31#330911yescharacteristic
485C2×C31#333211yescharacteristic
486C2×#41—22no—
487C2×#41—22no—
488C2×#41—22no—
489C2×#41—22no—
490C2×#41—41no—
491C2×#41—41no—
492C22×Q8C23×C3111yescharacteristic
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4C23×C3111yescharacteristic
499C22×D4C23×C3111yescharacteristic
500C22×D4C23×C3111yescharacteristic
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—21no—
504C23×C4C23×C3111yescharacteristic
505C2×SD16—22no—
506C2×SD16—22no—
507C2×SD16—41no—
508C2×D8—22no—
509C2×D8—22no—
510C2×D8—22no—
511C2×D8—22no—
512C2×D8—41no—
513C2×D8—41no—
514C2×M16—22no—
515C2×M16—22no—
516C2×M16—41no—
517C22×C8C23×C3111yescharacteristic
518C22×C8C23×C3111yescharacteristic
519C22×C8C23×C3111yescharacteristic
520C22×C8C23×C3111yescharacteristic
521#127—22no—
522#127—41no—
523#124—22no—
524#124—41no—
525#121—22no—
526#121—22no—
527#121—22no—
528#121D4×C3114yescomplemented
529C4×D4—22no—
530C4×D4—41no—
531C4×D4—44no—
532C2×C4⋊C4—22no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—41no—
536C2×C4⋊C4C23×C3111yescharacteristic
537C2×C4⋊C4C23×C3111yescharacteristic
538C2×C4⋊C4C23×C3111yescharacteristic
539C2×C4⋊C4C23×C3111yescharacteristic
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4D4×C3111yescharacteristic
550C2×C22⋊C4D4×C3111yescharacteristic
551C2×C42—21no—
552C2×C42C23×C3111yescharacteristic
553C2×C42C23×C3111yescharacteristic
554#106—22no—
555C4⋊C8—22no—
556C4⋊C8—41no—
557#103—22no—
558#103—22no—
559#103—22no—
560#102—22no—
561#102—22no—
562#102—22no—
563#102—22no—
564#102—22no—
565#102—41no—
566#102D4×C3114yescomplemented
567C22⋊C8—22no—
568#95—21no—
569#95—21no—
570#95—21no—
571#95—21no—
572#95D4×C3111yescharacteristic
573#95D4×C3111yescharacteristic
574C31#2509211yescharacteristic, direct product factor, Sylow
575C24—21no—
576C24—21no—
577C24—21no—
578C24C2×D4×C3111yescharacteristic
579#41—28no—
580#41—44no—
581#41—44no—
582#41—44no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8#41×C3112yes—
589C2×D4—24no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—81no—
617C2×D4—81no—
618C2×D4—81no—
619C2×D4—81no—
620C2×D4C2×D4×C3112yes—
621C2×D4C2×D4×C3112yes—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—81no—
639C22×C4—81no—
640C22×C4C2×D4×C3111yescharacteristic
641C22×C4C2×D4×C3111yescharacteristic
642C22×C4C2×D4×C3111yescharacteristic
643C22×C4C2×D4×C3111yescharacteristic
644C22×C4C2×D4×C3112yes—
645C22×C4C2×D4×C3111yescharacteristic
646C22×C4#41×C3112yes—
647C22×C4C24×C3111yescharacteristic
648SD16—44no—
649D8—44no—
650D8—44no—
651M16—44no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8C2×D4×C3112yes—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4C2×D4×C3112yes—
673C4⋊C4C2×D4×C3112yes—
674C22⋊C4—24no—
675C22⋊C4—22no—
676C22⋊C4—41no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—81no—
683C22⋊C4—81no—
684C22⋊C4—81no—
685C42—21no—
686C42—21no—
687C42—21no—
688C42—21no—
689C42—42no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—22no—
697C23—22no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23C31×#12112yes—
718C23C22×D4×C3111yescharacteristic
719Q8—22no—
720Q8—22no—
721Q8—41no—
722Q8—41no—
723D4—22no—
724D4—22no—
725D4—22no—
726D4—22no—
727D4—48no—
728D4—48no—
729D4—41no—
730D4—41no—
731D4—41no—
732D4—41no—
733D4—41no—
734D4—41no—
735D4—41no—
736D4—41no—
737D4—84no—
738D4—84no—
739D4—84no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—21no—
750C2×C4—22no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—48no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—84no—
774C2×C4—84no—
775C2×C4C31×#12112yes—
776C2×C4C31×AGL(1,ℤ/8)12yes—
777C2×C4C22×D4×C3111yescharacteristic
778C2×C4C22×D4×C3111yescharacteristic
779C2×C4C2×#41×C3111yescharacteristic
780C2×C4C2×#41×C3111yescharacteristic
781C2×C4C31×H(5,𝔽2)11yescharacteristic
782C2×C4C31×H(5,𝔽2)11yescharacteristic
783C8—22no—
784C8—41no—
785C8—41no—
786C8—41no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22C2×C31×#12111yescharacteristic
816C22D42×C3111yescharacteristic
817C22C31×#54611yescharacteristic
818C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
819C22C31×#57511yescharacteristic
820C22C31×#57611yescharacteristic
821C22C31×#57711yescharacteristic
822C4—22no—
823C4—22no—
824C4—41no—
825C4—42no—
826C4—42no—
827C4—41no—
828C4—42no—
829C4—41no—
830C4—81no—
831C4—81no—
832C4C31×#52511yescharacteristic
833C4C31×#53811yescharacteristic
834C4D42×C3111yescharacteristic
835C4C31×#54611yescharacteristic
836C2—42no—
837C2—82no—
838C2—82no—
839C2—161no—
840C2C31×#242411yescharacteristic
841C2C31×#303611yescharacteristic
842C2C31×#304511yescharacteristic
843C2C31×#326411yescharacteristic
844C2C31×#327511yescharacteristic
845C2C31×#330911yescharacteristic
846C2C31×#333211yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C4×C22⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#469C2semidirect
2. C2×C31×#459C2semidirect
3. C2×C31×#449C2semidirect
4. C2×C31×#417C2semidirect
5. C31×#2431C2semidirect
6. C31×#2361C2semidirect
7. C31×#2066C2semidirect
8. C31×#2054C2semidirect
9. C31×#2041C2semidirect
10. C31×#2012C2semidirect
11. C31×#1983C2semidirect
12. C31×#1926C2semidirect
13. C31×#1877C2semidirect
14. C31×#1874C2semidirect
15. C31×#1851C2semidirect
105. C31×#121D4semidirect
143. C31×#102D4semidirect
266. #25092C31direct (N × H)
364. C2×#469C2×C31semidirect
365. C2×#459C2×C31semidirect
366. C2×#449C2×C31semidirect
367. C2×#417C2×C31semidirect
368. #2431C2×C31semidirect
369. #2361C2×C31semidirect
370. #2066C2×C31semidirect
371. #2054C2×C31semidirect
372. #2041C2×C31semidirect
373. #2012C2×C31semidirect
374. #1983C2×C31semidirect
375. #1926C2×C31semidirect
376. #1877C2×C31semidirect
377. #1874C2×C31semidirect
378. #1851C2×C31semidirect
528. #121D4×C31semidirect
566. #102D4×C31semidirect
574. C31#25092direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4692
C2×C31×#4592
C2×C31×#4492
C2×C31×#4172
C31×#24312
C31×#23612
C31×#20662
C31×#20542
C31×#20412
C31×#20122
C31×#19832
C31×#19262
C31×#18772
C31×#18742
C31×#18512
#2509231