Finite Group Databasebeta

← C31×#25162 #21481921

Subgroups — C31×#25162 #21481921

Order 7936.

1240 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#459C211yesmaximal, characteristic, complemented
2C2×C31×#449C211yesmaximal, characteristic, complemented
3C2×C31×#449C211yesmaximal, characteristic, complemented
4C2×C4×D8×C31C211yesmaximal, characteristic, complemented
5C31×#2428C211yesmaximal, characteristic, complemented
6C31×#2339C211yesmaximal, characteristic, complemented
7C31×#2068C211yesmaximal, characteristic, complemented
8C31×#2034C211yesmaximal, characteristic, complemented
9C31×#2033C211yesmaximal, characteristic, complemented
10C31×#2014C211yesmaximal, characteristic, complemented
11C31×#1968C211yesmaximal, characteristic, complemented
12C31×#1923C211yesmaximal, characteristic, complemented
13C31×#1879C211yesmaximal, characteristic, complemented
14C31×#1877C211yesmaximal, characteristic, complemented
15C31×#1864C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C22×SD16×C31C2211yescharacteristic
18C22×SD16×C31C2211yescharacteristic
19C22×D8×C31C2211yescharacteristic
20C22×D8×C31C2211yescharacteristic
21C2×C31×#127C2211yescharacteristic
22C2×C31×#121—21no—
23C2×C31×#121C2211yescharacteristic
24C2×C31×#121C2211yescharacteristic
25C2×C4×D4×C31C2211yescharacteristic
26C2×C4×D4×C31C2211yescharacteristic
27C2×C4×D4×C31C2211yescharacteristic
28C31×#459—24no—
29C31×#449—24no—
30C31×#449—24no—
31C4×D8×C31—24no—
32C2×C31×#107C2211yescharacteristic
33C2×C31×#106C2211yescharacteristic
34C2×C31×C4⋊C8C2211yescharacteristic
35C2×C31×#103C2211yescharacteristic
36C2×C31×#103C2211yescharacteristic
37C2×C31×#102C2211yescharacteristic
38C2×C31×#102C2211yescharacteristic
39C2×C31×#102C2211yescharacteristic
40C2×C31×#102C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×C22⋊C8C2211yescharacteristic
44C2×C31×C22⋊C8C2211yescharacteristic
45C2×C4×C8×C31C2211yescharacteristic
46C31×#394—21no—
47C31×#392—21no—
48C31×#391C2211yescharacteristic
49C31×#391C2211yescharacteristic
50C31×#390C2211yescharacteristic
51C31×#389C2211yescharacteristic
52C31×#386—21no—
53C31×#386—21no—
54C31×#386—21no—
55C31×#381—21no—
56C31×#380C2211yescharacteristic
57C4×C22⋊C4×C31C2211yescharacteristic
58C2×C31×#95—21no—
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×C31—21no—
82C23×C4×C31C2311yescharacteristic
83C2×SD16×C31—22no—
84C2×SD16×C31—22no—
85C2×SD16×C31—22no—
86C2×SD16×C31—22no—
87C2×SD16×C31—41no—
88C2×SD16×C31—41no—
89C2×D8×C31—22no—
90C2×D8×C31—22no—
91C2×D8×C31—22no—
92C2×D8×C31—22no—
93C2×D8×C31—22no—
94C2×D8×C31D414yescomplemented
95C22×C8×C31C2311yescharacteristic
96C22×C8×C31C2311yescharacteristic
97C22×C8×C31C2311yescharacteristic
98C22×C8×C31C2311yescharacteristic
99C31×#127—22no—
100C31×#127—41no—
101C31×#121—22no—
102C31×#121—22no—
103C31×#121—44no—
104C31×#121—41no—
105C31×#121—41no—
106C4×D4×C31—22no—
107C4×D4×C31—22no—
108C4×D4×C31—22no—
109C4×D4×C31—41no—
110C4×D4×C31—41no—
111C4×D4×C31—41no—
112C2×C4⋊C4×C31—21no—
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×C31D411yescharacteristic
126C2×C22⋊C4×C31D411yescharacteristic
127C2×C42×C31C2311yescharacteristic
128C2×C42×C31C2311yescharacteristic
129C31×#107—22no—
130C31×#106—41no—
131C31×C4⋊C8—22no—
132C31×#103—22no—
133C31×#103—22no—
134C31×#102—22no—
135C31×#102—22no—
136C31×#102—22no—
137C31×#102—22no—
138C31×#102—41no—
139C31×#102D414yescomplemented
140C31×C22⋊C8—22no—
141C31×C22⋊C8—22no—
142C4×C8×C31—22no—
143C31×#95—21no—
144C31×#95—21no—
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—44no—
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—42no—
181C2×D4×C31—42no—
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—81no—
191C2×D4×C31—81no—
192C2×D4×C31—81no—
193C2×D4×C31—81no—
194C2×D4×C31C2×D412yes—
195C2×D4×C31C2×D412yes—
196C2×D4×C31C2×D412yes—
197C2×D4×C31#4112yes—
198C22×C4×C31—24no—
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—21no—
208C22×C4×C31—21no—
209C22×C4×C31—21no—
210C22×C4×C31—42no—
211C22×C4×C31—42no—
212C22×C4×C31—42no—
213C22×C4×C31—42no—
214C22×C4×C31—42no—
215C22×C4×C31—42no—
216C22×C4×C31—42no—
217C22×C4×C31—42no—
218C22×C4×C31—81no—
219C22×C4×C31—81no—
220C22×C4×C31—81no—
221C22×C4×C31C2×D411yescharacteristic
222C22×C4×C31C2×D411yescharacteristic
223C22×C4×C31C2×D411yescharacteristic
224C22×C4×C31C2×D411yescharacteristic
225C22×C4×C31C2×D411yescharacteristic
226C22×C4×C31C2411yescharacteristic
227SD16×C31—44no—
228SD16×C31—44no—
229D8×C31—28no—
230D8×C31—44no—
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×C31—21no—
240C2×C8×C31—21no—
241C2×C8×C31C2×D412yes—
242C2×C8×C31C2×D412yes—
243C4⋊C4×C31—21no—
244C4⋊C4×C31—21no—
245C4⋊C4×C31—21no—
246C4⋊C4×C31—21no—
247C4⋊C4×C31—21no—
248C4⋊C4×C31—21no—
249C4⋊C4×C31—21no—
250C4⋊C4×C31—42no—
251C4⋊C4×C31C2×D412yes—
252C22⋊C4×C31—22no—
253C22⋊C4×C31—22no—
254C22⋊C4×C31—42no—
255C22⋊C4×C31—42no—
256C22⋊C4×C31—42no—
257C22⋊C4×C31—42no—
258C22⋊C4×C31—42no—
259C22⋊C4×C31—42no—
260C22⋊C4×C31—81no—
261C22⋊C4×C31—81no—
262C42×C31—21no—
263C42×C31—21no—
264C42×C31—21no—
265C42×C31—21no—
266#25162C3111yesmaximal, characteristic, direct product factor, Sylow
267C23×C31—22no—
268C23×C31—22no—
269C23×C31—22no—
270C23×C31—21no—
271C23×C31—22no—
272C23×C31—21no—
273C23×C31—21no—
274C23×C31—21no—
275C23×C31—21no—
276C23×C31—21no—
277C23×C31—21no—
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—41no—
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—22no—
305D4×C31—48no—
306D4×C31—41no—
307D4×C31—41no—
308D4×C31—41no—
309D4×C31—41no—
310D4×C31—41no—
311D4×C31—41no—
312D4×C31—84no—
313D4×C31—84no—
314D4×C31—84no—
315D4×C31—84no—
316D4×C31#12114yescomplemented
317C2×C4×C31—21no—
318C2×C4×C31—21no—
319C2×C4×C31—21no—
320C2×C4×C31—21no—
321C2×C4×C31—21no—
322C2×C4×C31—22no—
323C2×C4×C31—21no—
324C2×C4×C31—21no—
325C2×C4×C31—22no—
326C2×C4×C31—21no—
327C2×C4×C31—21no—
328C2×C4×C31—21no—
329C2×C4×C31—21no—
330C2×C4×C31—21no—
331C2×C4×C31—21no—
332C2×C4×C31—48no—
333C2×C4×C31—41no—
334C2×C4×C31—41no—
335C2×C4×C31—41no—
336C2×C4×C31—41no—
337C2×C4×C31—41no—
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—84no—
353C2×C4×C31#13512yes—
354C2×C4×C31AGL(1,ℤ/8)12yes—
355C2×C4×C31C22×D411yescharacteristic
356C2×C4×C31C22×D411yescharacteristic
357C2×C4×C31C2×#4111yescharacteristic
358C2×C4×C31C2×#4111yescharacteristic
359C2×C4×C31H(5,𝔽2)11yescharacteristic
360C2×C4×C31H(5,𝔽2)11yescharacteristic
361C8×C31—22no—
362C8×C31—22no—
363C8×C31—41no—
364C8×C31—41no—
365C2×#459C2×C3111yescharacteristic, complemented
366C2×#449C2×C3111yescharacteristic, complemented
367C2×#449C2×C3111yescharacteristic, complemented
368C2×C4×D8C2×C3111yescharacteristic, complemented
369#2428C2×C3111yescharacteristic, complemented
370#2339C2×C3111yescharacteristic, complemented
371#2068C2×C3111yescharacteristic, complemented
372#2034C2×C3111yescharacteristic, complemented
373#2033C2×C3111yescharacteristic, complemented
374#2014C2×C3111yescharacteristic, complemented
375#1968C2×C3111yescharacteristic, complemented
376#1923C2×C3111yescharacteristic, complemented
377#1879C2×C3111yescharacteristic, complemented
378#1877C2×C3111yescharacteristic, complemented
379#1864C2×C3111yescharacteristic, complemented
380C22×C31—24no—
381C22×C31—42no—
382C22×C31—42no—
383C22×C31—42no—
384C22×C31—42no—
385C22×C31—42no—
386C22×C31—42no—
387C22×C31—41no—
388C22×C31—41no—
389C22×C31—41no—
390C22×C31—42no—
391C22×C31—41no—
392C22×C31—41no—
393C22×C31—42no—
394C22×C31—42no—
395C22×C31—41no—
396C22×C31—41no—
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×C31—81no—
408C22×C31#52511yescharacteristic
409C22×C31D4211yescharacteristic
410C22×C31D4211yescharacteristic
411C22×C31C2×#13511yescharacteristic
412C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
413C22×C31#57611yescharacteristic
414C22×C31#57711yescharacteristic
415C4×C31—22no—
416C4×C31—22no—
417C4×C31—41no—
418C4×C31—42no—
419C4×C31—42no—
420C4×C31—41no—
421C4×C31—41no—
422C4×C31—81no—
423C4×C31—81no—
424C4×C31—81no—
425C4×C31C2×#12111yescharacteristic
426C4×C31#53811yescharacteristic
427C4×C31#54611yescharacteristic
428C4×C31#54611yescharacteristic
429C22×#41C22×C3111yescharacteristic
430C22×SD16C22×C3111yescharacteristic
431C22×SD16C22×C3111yescharacteristic
432C22×D8C22×C3111yescharacteristic
433C22×D8C22×C3111yescharacteristic
434C2×#127C22×C3111yescharacteristic
435C2×#121—21no—
436C2×#121C22×C3111yescharacteristic
437C2×#121C22×C3111yescharacteristic
438C2×C4×D4C22×C3111yescharacteristic
439C2×C4×D4C22×C3111yescharacteristic
440C2×C4×D4C22×C3111yescharacteristic
441#459—24no—
442#449—24no—
443#449—24no—
444C4×D8—24no—
445C2×#107C22×C3111yescharacteristic
446C2×#106C22×C3111yescharacteristic
447C2×C4⋊C8C22×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×C22⋊C8C22×C3111yescharacteristic
457C2×C22⋊C8C22×C3111yescharacteristic
458C2×C4×C8C22×C3111yescharacteristic
459#394—21no—
460#392—21no—
461#391C22×C3111yescharacteristic
462#391C22×C3111yescharacteristic
463#390C22×C3111yescharacteristic
464#389C22×C3111yescharacteristic
465#386—21no—
466#386—21no—
467#386—21no—
468#381—21no—
469#380C22×C3111yescharacteristic
470C4×C22⋊C4C22×C3111yescharacteristic
471C2×#95—21no—
472#340C22×C3111yescharacteristic
473#340C22×C3111yescharacteristic
474#336C22×C3111yescharacteristic
475#336C22×C3111yescharacteristic
476C2×C31—44no—
477C2×C31—81no—
478C2×C31—82no—
479C2×C31—161no—
480C2×C31#242411yescharacteristic
481C2×C31#310611yescharacteristic
482C2×C31#311911yescharacteristic
483C2×C31#326411yescharacteristic
484C2×C31#327211yescharacteristic
485C2×C31#328011yescharacteristic
486C2×C31#328411yescharacteristic
487C2×#41—22no—
488C2×#41—22no—
489C2×#41—22no—
490C2×#41—22no—
491C2×#41—41no—
492C2×#41—41no—
493C22×Q8C23×C3111yescharacteristic
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4C23×C3111yescharacteristic
500C22×D4C23×C3111yescharacteristic
501C22×D4C23×C3111yescharacteristic
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4C23×C3111yescharacteristic
507C2×SD16—22no—
508C2×SD16—22no—
509C2×SD16—22no—
510C2×SD16—22no—
511C2×SD16—41no—
512C2×SD16—41no—
513C2×D8—22no—
514C2×D8—22no—
515C2×D8—22no—
516C2×D8—22no—
517C2×D8—22no—
518C2×D8D4×C3114yescomplemented
519C22×C8C23×C3111yescharacteristic
520C22×C8C23×C3111yescharacteristic
521C22×C8C23×C3111yescharacteristic
522C22×C8C23×C3111yescharacteristic
523#127—22no—
524#127—41no—
525#121—22no—
526#121—22no—
527#121—44no—
528#121—41no—
529#121—41no—
530C4×D4—22no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—41no—
534C4×D4—41no—
535C4×D4—41no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4C23×C3111yescharacteristic
538C2×C4⋊C4C23×C3111yescharacteristic
539C2×C4⋊C4C23×C3111yescharacteristic
540C2×C4⋊C4C23×C3111yescharacteristic
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×C42C23×C3111yescharacteristic
552C2×C42C23×C3111yescharacteristic
553#107—22no—
554#106—41no—
555C4⋊C8—22no—
556#103—22no—
557#103—22no—
558#102—22no—
559#102—22no—
560#102—22no—
561#102—22no—
562#102—41no—
563#102D4×C3114yescomplemented
564C22⋊C8—22no—
565C22⋊C8—22no—
566C4×C8—22no—
567#95—21no—
568#95—21no—
569#95—21no—
570#95—21no—
571#95—21no—
572#95—21no—
573#95D4×C3111yescharacteristic
574#95D4×C3111yescharacteristic
575C31#2516211yescharacteristic, direct product factor, Sylow
576C24—21no—
577C24—21no—
578C24—21no—
579C24C2×D4×C3111yescharacteristic
580#41—44no—
581#41—44no—
582#41—44no—
583#41—44no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8#41×C3112yes—
590C2×D4—24no—
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—42no—
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—81no—
616C2×D4—81no—
617C2×D4—81no—
618C2×D4—81no—
619C2×D4C2×D4×C3112yes—
620C2×D4C2×D4×C3112yes—
621C2×D4C2×D4×C3112yes—
622C2×D4#41×C3112yes—
623C22×C4—24no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—81no—
644C22×C4—81no—
645C22×C4—81no—
646C22×C4C2×D4×C3111yescharacteristic
647C22×C4C2×D4×C3111yescharacteristic
648C22×C4C2×D4×C3111yescharacteristic
649C22×C4C2×D4×C3111yescharacteristic
650C22×C4C2×D4×C3111yescharacteristic
651C22×C4C24×C3111yescharacteristic
652SD16—44no—
653SD16—44no—
654D8—28no—
655D8—44no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8C2×D4×C3112yes—
667C2×C8C2×D4×C3112yes—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—42no—
676C4⋊C4C2×D4×C3112yes—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—81no—
686C22⋊C4—81no—
687C42—21no—
688C42—21no—
689C42—21no—
690C42—21no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—21no—
695C23—22no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
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—
717C23—41no—
718C23—41no—
719C23C22×D4×C3111yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—41no—
723Q8—41no—
724D4—22no—
725D4—22no—
726D4—22no—
727D4—22no—
728D4—22no—
729D4—48no—
730D4—41no—
731D4—41no—
732D4—41no—
733D4—41no—
734D4—41no—
735D4—41no—
736D4—84no—
737D4—84no—
738D4—84no—
739D4—84no—
740D4C31×#12114yescomplemented
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—22no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—22no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—48no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
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—41no—
774C2×C4—84no—
775C2×C4—84no—
776C2×C4—84no—
777C2×C4C31×#13512yes—
778C2×C4C31×AGL(1,ℤ/8)12yes—
779C2×C4C22×D4×C3111yescharacteristic
780C2×C4C22×D4×C3111yescharacteristic
781C2×C4C2×#41×C3111yescharacteristic
782C2×C4C2×#41×C3111yescharacteristic
783C2×C4C31×H(5,𝔽2)11yescharacteristic
784C2×C4C31×H(5,𝔽2)11yescharacteristic
785C8—22no—
786C8—22no—
787C8—41no—
788C8—41no—
789C22—24no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—42no—
800C22—41no—
801C22—41no—
802C22—42no—
803C22—42no—
804C22—41no—
805C22—41no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22C31×#52511yescharacteristic
818C22D42×C3111yescharacteristic
819C22D42×C3111yescharacteristic
820C22C2×C31×#13511yescharacteristic
821C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
822C22C31×#57611yescharacteristic
823C22C31×#57711yescharacteristic
824C4—22no—
825C4—22no—
826C4—41no—
827C4—42no—
828C4—42no—
829C4—41no—
830C4—41no—
831C4—81no—
832C4—81no—
833C4—81no—
834C4C2×C31×#12111yescharacteristic
835C4C31×#53811yescharacteristic
836C4C31×#54611yescharacteristic
837C4C31×#54611yescharacteristic
838C2—44no—
839C2—81no—
840C2—82no—
841C2—161no—
842C2C31×#242411yescharacteristic
843C2C31×#310611yescharacteristic
844C2C31×#311911yescharacteristic
845C2C31×#326411yescharacteristic
846C2C31×#327211yescharacteristic
847C2C31×#328011yescharacteristic
848C2C31×#328411yescharacteristic
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×#459C2semidirect
2. C2×C31×#449C2semidirect
3. C2×C31×#449C2semidirect
4. C2×C4×D8×C31C2semidirect
5. C31×#2428C2semidirect
6. C31×#2339C2semidirect
7. C31×#2068C2semidirect
8. C31×#2034C2semidirect
9. C31×#2033C2semidirect
10. C31×#2014C2semidirect
11. C31×#1968C2semidirect
12. C31×#1923C2semidirect
13. C31×#1879C2semidirect
14. C31×#1877C2semidirect
15. C31×#1864C2semidirect
94. C2×D8×C31D4semidirect
139. C31×#102D4semidirect
266. #25162C31direct (N × H)
316. D4×C31#121semidirect
365. C2×#459C2×C31semidirect
366. C2×#449C2×C31semidirect
367. C2×#449C2×C31semidirect
368. C2×C4×D8C2×C31semidirect
369. #2428C2×C31semidirect
370. #2339C2×C31semidirect
371. #2068C2×C31semidirect
372. #2034C2×C31semidirect
373. #2033C2×C31semidirect
374. #2014C2×C31semidirect
375. #1968C2×C31semidirect
376. #1923C2×C31semidirect
377. #1879C2×C31semidirect
378. #1877C2×C31semidirect
379. #1864C2×C31semidirect
518. C2×D8D4×C31semidirect
563. #102D4×C31semidirect
575. C31#25162direct (N × H)
740. D4C31×#121semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4592
C2×C31×#4492
C2×C4×D8×C312
C31×#24282
C31×#23392
C31×#20682
C31×#20342
C31×#20332
C31×#20142
C31×#19682
C31×#19232
C31×#18792
C31×#18772
C31×#18642
#2516231