Finite Group Databasebeta

← C31×#25159 #21481918

Subgroups — C31×#25159 #21481918

Order 7936.

1212 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#460C211yesmaximal, characteristic, complemented
2C2×C31×#449C211yesmaximal, characteristic, complemented
3C2×C31×#449C211yesmaximal, characteristic, complemented
4C2×C4×SD16×C31C211yesmaximal, characteristic, complemented
5C31×#2428C211yesmaximal, characteristic, complemented
6C31×#2341C211yesmaximal, characteristic, complemented
7C31×#2065C211yesmaximal, characteristic, complemented
8C31×#2034C211yesmaximal, characteristic, complemented
9C31×#2033C211yesmaximal, characteristic, complemented
10C31×#2011C211yesmaximal, characteristic, complemented
11C31×#1970C211yesmaximal, characteristic, complemented
12C31×#1923C211yesmaximal, characteristic, complemented
13C31×#1880C211yesmaximal, characteristic, complemented
14C31×#1879C211yesmaximal, characteristic, complemented
15C31×#1863C211yesmaximal, 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×Q8×C31C2211yescharacteristic
26C2×C4×Q8×C31C2211yescharacteristic
27C2×C4×D4×C31C2211yescharacteristic
28C31×#460—24no—
29C31×#449—24no—
30C31×#449—24no—
31C4×SD16×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×#390—21no—
49C31×#390—21no—
50C31×#390C2211yescharacteristic
51C31×#390C2211yescharacteristic
52C31×#390C2211yescharacteristic
53C31×#389C2211yescharacteristic
54C31×#386—21no—
55C31×#380—21no—
56C31×#380C2211yescharacteristic
57C4×C22⋊C4×C31—21no—
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×C31C2311yescharacteristic
81C2×SD16×C31—22no—
82C2×SD16×C31—22no—
83C2×SD16×C31—22no—
84C2×SD16×C31—22no—
85C2×SD16×C31—22no—
86C2×SD16×C31D414yescomplemented
87C2×D8×C31—22no—
88C2×D8×C31—22no—
89C2×D8×C31—22no—
90C2×D8×C31—22no—
91C2×D8×C31—41no—
92C2×D8×C31—41no—
93C22×C8×C31C2311yescharacteristic
94C22×C8×C31C2311yescharacteristic
95C22×C8×C31C2311yescharacteristic
96C22×C8×C31C2311yescharacteristic
97C31×#127—22no—
98C31×#127—41no—
99C31×#121—22no—
100C31×#121—22no—
101C31×#121—44no—
102C31×#121—41no—
103C31×#121—41no—
104C4×Q8×C31—22no—
105C4×Q8×C31—22no—
106C4×Q8×C31—41no—
107C4×Q8×C31—41no—
108C4×D4×C31—22no—
109C4×D4×C31—41no—
110C2×C4⋊C4×C31—21no—
111C2×C4⋊C4×C31—21no—
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×C31—21no—
126C2×C22⋊C4×C31—21no—
127C2×C22⋊C4×C31D411yescharacteristic
128C2×C22⋊C4×C31D411yescharacteristic
129C2×C42×C31—21no—
130C2×C42×C31—21no—
131C2×C42×C31C2311yescharacteristic
132C2×C42×C31C2311yescharacteristic
133C31×#107—41no—
134C31×#106—22no—
135C31×C4⋊C8—22no—
136C31×#103—22no—
137C31×#103D414yescomplemented
138C31×#102—22no—
139C31×#102—22no—
140C31×#102—22no—
141C31×#102—22no—
142C31×#102—22no—
143C31×#102—41no—
144C31×C22⋊C8—22no—
145C31×C22⋊C8—22no—
146C4×C8×C31—22no—
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×C31C2×D412yes—
163C2×Q8×C31C2×D412yes—
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×C31#4112yes—
198C22×C4×C31—21no—
199C22×C4×C31—24no—
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—81no—
215C22×C4×C31C2×D411yescharacteristic
216C22×C4×C31C2×D411yescharacteristic
217C22×C4×C31C2×D411yescharacteristic
218C22×C4×C31C2×D411yescharacteristic
219C22×C4×C31C2×D411yescharacteristic
220C22×C4×C31C2411yescharacteristic
221SD16×C31—28no—
222SD16×C31—44no—
223D8×C31—44no—
224D8×C31—44no—
225C2×C8×C31—21no—
226C2×C8×C31—21no—
227C2×C8×C31—21no—
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×C31C2×D412yes—
236C2×C8×C31C2×D412yes—
237C4⋊C4×C31—21no—
238C4⋊C4×C31—21no—
239C4⋊C4×C31—21no—
240C4⋊C4×C31—21no—
241C4⋊C4×C31—21no—
242C4⋊C4×C31—21no—
243C4⋊C4×C31—21no—
244C4⋊C4×C31—42no—
245C4⋊C4×C31—42no—
246C4⋊C4×C31—42no—
247C4⋊C4×C31C2×D412yes—
248C22⋊C4×C31—22no—
249C22⋊C4×C31—22no—
250C22⋊C4×C31—42no—
251C22⋊C4×C31—42no—
252C22⋊C4×C31—42no—
253C22⋊C4×C31—42no—
254C22⋊C4×C31—42no—
255C22⋊C4×C31—42no—
256C22⋊C4×C31—81no—
257C22⋊C4×C31—81no—
258C22⋊C4×C31—81no—
259C22⋊C4×C31—81no—
260C42×C31—21no—
261C42×C31—21no—
262C42×C31—21no—
263C42×C31—21no—
264C42×C31—42no—
265C42×C31—42no—
266#25159C3111yesmaximal, characteristic, direct product factor, Sylow
267C23×C31—21no—
268C23×C31—22no—
269C23×C31—22no—
270C23×C31—21no—
271C23×C31—21no—
272C23×C31—21no—
273C23×C31—21no—
274C23×C31—21no—
275C23×C31—21no—
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—41no—
295C23×C31C22×D411yescharacteristic
296Q8×C31—22no—
297Q8×C31—22no—
298Q8×C31—22no—
299Q8×C31#12114yescomplemented
300D4×C31—22no—
301D4×C31—22no—
302D4×C31—22no—
303D4×C31—22no—
304D4×C31—48no—
305D4×C31—41no—
306D4×C31—41no—
307D4×C31—41no—
308D4×C31—41no—
309D4×C31—41no—
310D4×C31—41no—
311D4×C31—41no—
312D4×C31—41no—
313D4×C31—84no—
314D4×C31—84no—
315D4×C31—84no—
316D4×C31—84no—
317C2×C4×C31—22no—
318C2×C4×C31—21no—
319C2×C4×C31—21no—
320C2×C4×C31—22no—
321C2×C4×C31—22no—
322C2×C4×C31—21no—
323C2×C4×C31—21no—
324C2×C4×C31—21no—
325C2×C4×C31—21no—
326C2×C4×C31—21no—
327C2×C4×C31—22no—
328C2×C4×C31—21no—
329C2×C4×C31—21no—
330C2×C4×C31—21no—
331C2×C4×C31—21no—
332C2×C4×C31—21no—
333C2×C4×C31—21no—
334C2×C4×C31—48no—
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#13512yes—
352C2×C4×C31AGL(1,ℤ/8)12yes—
353C2×C4×C31C22×D411yescharacteristic
354C2×C4×C31C22×D411yescharacteristic
355C2×C4×C31C2×#4111yescharacteristic
356C2×C4×C31C2×#4111yescharacteristic
357C2×C4×C31H(5,𝔽2)11yescharacteristic
358C2×C4×C31H(5,𝔽2)11yescharacteristic
359C8×C31—22no—
360C8×C31—22no—
361C8×C31—41no—
362C8×C31—41no—
363C2×#460C2×C3111yescharacteristic, complemented
364C2×#449C2×C3111yescharacteristic, complemented
365C2×#449C2×C3111yescharacteristic, complemented
366C2×C4×SD16C2×C3111yescharacteristic, complemented
367#2428C2×C3111yescharacteristic, complemented
368#2341C2×C3111yescharacteristic, complemented
369#2065C2×C3111yescharacteristic, complemented
370#2034C2×C3111yescharacteristic, complemented
371#2033C2×C3111yescharacteristic, complemented
372#2011C2×C3111yescharacteristic, complemented
373#1970C2×C3111yescharacteristic, complemented
374#1923C2×C3111yescharacteristic, complemented
375#1880C2×C3111yescharacteristic, complemented
376#1879C2×C3111yescharacteristic, complemented
377#1863C2×C3111yescharacteristic, complemented
378C22×C31—41no—
379C22×C31—42no—
380C22×C31—41no—
381C22×C31—42no—
382C22×C31—42no—
383C22×C31—41no—
384C22×C31—42no—
385C22×C31—41no—
386C22×C31—41no—
387C22×C31—42no—
388C22×C31—42no—
389C22×C31—41no—
390C22×C31—41no—
391C22×C31—81no—
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#52511yescharacteristic
407C22×C31D4211yescharacteristic
408C22×C31D4211yescharacteristic
409C22×C31C2×#13511yescharacteristic
410C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
411C22×C31#57611yescharacteristic
412C22×C31#57711yescharacteristic
413C4×C31—24no—
414C4×C31—22no—
415C4×C31—22no—
416C4×C31—41no—
417C4×C31—42no—
418C4×C31—41no—
419C4×C31—41no—
420C4×C31—81no—
421C4×C31—81no—
422C4×C31—81no—
423C4×C31C2×#12111yescharacteristic
424C4×C31#53811yescharacteristic
425C4×C31#54611yescharacteristic
426C4×C31#54611yescharacteristic
427C22×#41C22×C3111yescharacteristic
428C22×SD16C22×C3111yescharacteristic
429C22×SD16C22×C3111yescharacteristic
430C22×D8C22×C3111yescharacteristic
431C22×D8C22×C3111yescharacteristic
432C2×#127C22×C3111yescharacteristic
433C2×#121—21no—
434C2×#121C22×C3111yescharacteristic
435C2×#121C22×C3111yescharacteristic
436C2×C4×Q8C22×C3111yescharacteristic
437C2×C4×Q8C22×C3111yescharacteristic
438C2×C4×D4C22×C3111yescharacteristic
439#460—24no—
440#449—24no—
441#449—24no—
442C4×SD16—24no—
443C2×#107C22×C3111yescharacteristic
444C2×#106C22×C3111yescharacteristic
445C2×C4⋊C8C22×C3111yescharacteristic
446C2×#103C22×C3111yescharacteristic
447C2×#103C22×C3111yescharacteristic
448C2×#102C22×C3111yescharacteristic
449C2×#102C22×C3111yescharacteristic
450C2×#102C22×C3111yescharacteristic
451C2×#102C22×C3111yescharacteristic
452C2×#102C22×C3111yescharacteristic
453C2×#102C22×C3111yescharacteristic
454C2×C22⋊C8C22×C3111yescharacteristic
455C2×C22⋊C8C22×C3111yescharacteristic
456C2×C4×C8C22×C3111yescharacteristic
457#394—21no—
458#392—21no—
459#390—21no—
460#390—21no—
461#390C22×C3111yescharacteristic
462#390C22×C3111yescharacteristic
463#390C22×C3111yescharacteristic
464#389C22×C3111yescharacteristic
465#386—21no—
466#380—21no—
467#380C22×C3111yescharacteristic
468C4×C22⋊C4—21no—
469C4×C22⋊C4C22×C3111yescharacteristic
470#340C22×C3111yescharacteristic
471#340C22×C3111yescharacteristic
472#336C22×C3111yescharacteristic
473#336C22×C3111yescharacteristic
474C2×C31—81no—
475C2×C31—82no—
476C2×C31—82no—
477C2×C31—161no—
478C2×C31#242411yescharacteristic
479C2×C31#310611yescharacteristic
480C2×C31#311911yescharacteristic
481C2×C31#326511yescharacteristic
482C2×C31#327411yescharacteristic
483C2×C31#328211yescharacteristic
484C2×C31#328711yescharacteristic
485C2×#41—22no—
486C2×#41—22no—
487C2×#41—22no—
488C2×#41—22no—
489C2×#41—41no—
490C2×#41—41no—
491C22×Q8C23×C3111yescharacteristic
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4C23×C3111yescharacteristic
498C22×D4C23×C3111yescharacteristic
499C22×D4C23×C3111yescharacteristic
500C23×C4—21no—
501C23×C4—21no—
502C23×C4C23×C3111yescharacteristic
503C2×SD16—22no—
504C2×SD16—22no—
505C2×SD16—22no—
506C2×SD16—22no—
507C2×SD16—22no—
508C2×SD16D4×C3114yescomplemented
509C2×D8—22no—
510C2×D8—22no—
511C2×D8—22no—
512C2×D8—22no—
513C2×D8—41no—
514C2×D8—41no—
515C22×C8C23×C3111yescharacteristic
516C22×C8C23×C3111yescharacteristic
517C22×C8C23×C3111yescharacteristic
518C22×C8C23×C3111yescharacteristic
519#127—22no—
520#127—41no—
521#121—22no—
522#121—22no—
523#121—44no—
524#121—41no—
525#121—41no—
526C4×Q8—22no—
527C4×Q8—22no—
528C4×Q8—41no—
529C4×Q8—41no—
530C4×D4—22no—
531C4×D4—41no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4C23×C3111yescharacteristic
536C2×C4⋊C4C23×C3111yescharacteristic
537C2×C4⋊C4C23×C3111yescharacteristic
538C2×C4⋊C4C23×C3111yescharacteristic
539C2×C22⋊C4—21no—
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×C42—21no—
553C2×C42C23×C3111yescharacteristic
554C2×C42C23×C3111yescharacteristic
555#107—41no—
556#106—22no—
557C4⋊C8—22no—
558#103—22no—
559#103D4×C3114yescomplemented
560#102—22no—
561#102—22no—
562#102—22no—
563#102—22no—
564#102—22no—
565#102—41no—
566C22⋊C8—22no—
567C22⋊C8—22no—
568C4×C8—22no—
569#95—21no—
570#95—21no—
571#95D4×C3111yescharacteristic
572#95D4×C3111yescharacteristic
573C31#2515911yescharacteristic, direct product factor, Sylow
574C24—21no—
575C24—21no—
576C24—21no—
577C24C2×D4×C3111yescharacteristic
578#41—44no—
579#41—44no—
580#41—44no—
581#41—44no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8C2×D4×C3112yes—
586C2×Q8C2×D4×C3112yes—
587C2×Q8#41×C3112yes—
588C2×D4—24no—
589C2×D4—21no—
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—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×D4#41×C3112yes—
621C22×C4—21no—
622C22×C4—24no—
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—21no—
632C22×C4—21no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—81no—
638C22×C4C2×D4×C3111yescharacteristic
639C22×C4C2×D4×C3111yescharacteristic
640C22×C4C2×D4×C3111yescharacteristic
641C22×C4C2×D4×C3111yescharacteristic
642C22×C4C2×D4×C3111yescharacteristic
643C22×C4C24×C3111yescharacteristic
644SD16—28no—
645SD16—44no—
646D8—44no—
647D8—44no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8C2×D4×C3112yes—
659C2×C8C2×D4×C3112yes—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4C2×D4×C3112yes—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—42no—
674C22⋊C4—42no—
675C22⋊C4—42no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—81no—
680C22⋊C4—81no—
681C22⋊C4—81no—
682C22⋊C4—81no—
683C42—21no—
684C42—21no—
685C42—21no—
686C42—21no—
687C42—42no—
688C42—42no—
689C23—21no—
690C23—22no—
691C23—22no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
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—
717C23C22×D4×C3111yescharacteristic
718Q8—22no—
719Q8—22no—
720Q8—22no—
721Q8C31×#12114yescomplemented
722D4—22no—
723D4—22no—
724D4—22no—
725D4—22no—
726D4—48no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—41no—
731D4—41no—
732D4—41no—
733D4—41no—
734D4—41no—
735D4—84no—
736D4—84no—
737D4—84no—
738D4—84no—
739C2×C4—22no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
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—84no—
773C2×C4C31×#13512yes—
774C2×C4C31×AGL(1,ℤ/8)12yes—
775C2×C4C22×D4×C3111yescharacteristic
776C2×C4C22×D4×C3111yescharacteristic
777C2×C4C2×#41×C3111yescharacteristic
778C2×C4C2×#41×C3111yescharacteristic
779C2×C4C31×H(5,𝔽2)11yescharacteristic
780C2×C4C31×H(5,𝔽2)11yescharacteristic
781C8—22no—
782C8—22no—
783C8—41no—
784C8—41no—
785C22—41no—
786C22—42no—
787C22—41no—
788C22—42no—
789C22—42no—
790C22—41no—
791C22—42no—
792C22—41no—
793C22—41no—
794C22—42no—
795C22—42no—
796C22—41no—
797C22—41no—
798C22—81no—
799C22—81no—
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—
813C22C31×#52511yescharacteristic
814C22D42×C3111yescharacteristic
815C22D42×C3111yescharacteristic
816C22C2×C31×#13511yescharacteristic
817C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
818C22C31×#57611yescharacteristic
819C22C31×#57711yescharacteristic
820C4—24no—
821C4—22no—
822C4—22no—
823C4—41no—
824C4—42no—
825C4—41no—
826C4—41no—
827C4—81no—
828C4—81no—
829C4—81no—
830C4C2×C31×#12111yescharacteristic
831C4C31×#53811yescharacteristic
832C4C31×#54611yescharacteristic
833C4C31×#54611yescharacteristic
834C2—81no—
835C2—82no—
836C2—82no—
837C2—161no—
838C2C31×#242411yescharacteristic
839C2C31×#310611yescharacteristic
840C2C31×#311911yescharacteristic
841C2C31×#326511yescharacteristic
842C2C31×#327411yescharacteristic
843C2C31×#328211yescharacteristic
844C2C31×#328711yescharacteristic
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×#460C2semidirect
2. C2×C31×#449C2semidirect
3. C2×C31×#449C2semidirect
4. C2×C4×SD16×C31C2semidirect
5. C31×#2428C2semidirect
6. C31×#2341C2semidirect
7. C31×#2065C2semidirect
8. C31×#2034C2semidirect
9. C31×#2033C2semidirect
10. C31×#2011C2semidirect
11. C31×#1970C2semidirect
12. C31×#1923C2semidirect
13. C31×#1880C2semidirect
14. C31×#1879C2semidirect
15. C31×#1863C2semidirect
86. C2×SD16×C31D4semidirect
137. C31×#103D4semidirect
266. #25159C31direct (N × H)
299. Q8×C31#121semidirect
363. C2×#460C2×C31semidirect
364. C2×#449C2×C31semidirect
365. C2×#449C2×C31semidirect
366. C2×C4×SD16C2×C31semidirect
367. #2428C2×C31semidirect
368. #2341C2×C31semidirect
369. #2065C2×C31semidirect
370. #2034C2×C31semidirect
371. #2033C2×C31semidirect
372. #2011C2×C31semidirect
373. #1970C2×C31semidirect
374. #1923C2×C31semidirect
375. #1880C2×C31semidirect
376. #1879C2×C31semidirect
377. #1863C2×C31semidirect
508. C2×SD16D4×C31semidirect
559. #103D4×C31semidirect
573. C31#25159direct (N × H)
721. Q8C31×#121semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4602
C2×C31×#4492
C2×C4×SD16×C312
C31×#24282
C31×#23412
C31×#20652
C31×#20342
C31×#20332
C31×#20112
C31×#19702
C31×#19232
C31×#18802
C31×#18792
C31×#18632
#2515931