Finite Group Databasebeta

← C31×#25124 #21481883

Subgroups — C31×#25124 #21481883

Order 7936.

1362 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#469C211yesmaximal, characteristic, complemented
2C2×C31×#447C211yesmaximal, characteristic, complemented
3C2×C31×#435C211yesmaximal, characteristic, complemented
4C22×C31×#102C211yesmaximal, characteristic, complemented
5C31×#2416C211yesmaximal, characteristic, complemented
6C31×#2408C211yesmaximal, characteristic, complemented
7C31×#2065C211yesmaximal, characteristic, complemented
8C31×#2054C211yesmaximal, characteristic, complemented
9C31×#2034C211yesmaximal, characteristic, complemented
10C31×#1999C211yesmaximal, characteristic, complemented
11C31×#1972C211yesmaximal, characteristic, complemented
12C31×#1936C211yesmaximal, characteristic, complemented
13C31×#1895C211yesmaximal, characteristic, complemented
14C31×#1893C211yesmaximal, characteristic, complemented
15C31×#1853C211yesmaximal, characteristic, complemented
16C23×D4×C31C2211yescharacteristic
17C22×D8×C31C2211yescharacteristic
18C22×D8×C31C2211yescharacteristic
19C22×M16×C31C2211yescharacteristic, complemented
20C23×C8×C31C2211yescharacteristic
21C2×C31×#121—21no—
22C2×C31×#121C2211yescharacteristic
23C2×C31×#121C2211yescharacteristic
24C2×C31×#121C2211yescharacteristic
25C2×C31×#121C2211yescharacteristic, complemented
26C2×C31×#120—21no—
27C2×C4×D4×C31C2211yescharacteristic
28C22×C4⋊C4×C31C2211yescharacteristic
29C31×#469—24no—
30C31×#447—24no—
31C31×#435—24no—
32C2×C31×#106C2211yescharacteristic, complemented
33C2×C31×#106C2211yescharacteristic, complemented
34C2×C31×C4⋊C8C2211yescharacteristic, complemented
35C2×C31×#102—24no—
36C2×C31×#102C2211yescharacteristic
37C2×C31×#102C2211yescharacteristic
38C2×C31×#102C2211yescharacteristic
39C2×C31×#102C2211yescharacteristic
40C2×C31×#102C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic, complemented
43C2×C31×#102C2211yescharacteristic, complemented
44C2×C31×C22⋊C8C2211yescharacteristic
45C2×C31×C22⋊C8C2211yescharacteristic, complemented
46C2×C31×#97C2211yescharacteristic, complemented
47C31×#396—21no—
48C31×#394—21no—
49C31×#394—21no—
50C31×#392—21no—
51C31×#390C2211yescharacteristic
52C31×#390C2211yescharacteristic
53C31×#390C2211yescharacteristic, complemented
54C31×#389C2211yescharacteristic, complemented
55C31×#386—21no—
56C31×#380C2211yescharacteristic
57C31×#380C2211yescharacteristic, complemented
58C31×#379—21no—
59C31×#340C2211yescharacteristic, complemented
60C31×#340C2211yescharacteristic, complemented
61C31×#340C2211yescharacteristic, complemented
62C31×#340C2211yescharacteristic, complemented
63C25×C31—21no—
64C22×D4×C31—22no—
65C22×D4×C31—22no—
66C22×D4×C31—21no—
67C22×D4×C31—21no—
68C22×D4×C31—21no—
69C22×D4×C31—21no—
70C22×D4×C31—22no—
71C22×D4×C31—21no—
72C22×D4×C31—22no—
73C22×D4×C31—41no—
74C22×D4×C31—41no—
75C22×D4×C31D411yescharacteristic
76C22×D4×C31C2311yescharacteristic
77C22×D4×C31C2311yescharacteristic
78C22×D4×C31C2311yescharacteristic
79C23×C4×C31—21no—
80C23×C4×C31C2311yescharacteristic
81C23×C4×C31C2311yescharacteristic
82C2×D8×C31—22no—
83C2×D8×C31—22no—
84C2×D8×C31—22no—
85C2×D8×C31—22no—
86C2×D8×C31—41no—
87C2×D8×C31—41no—
88C2×M16×C31—22no—
89C2×M16×C31—22no—
90C2×M16×C31—41no—
91C22×C8×C31—22no—
92C22×C8×C31—22no—
93C22×C8×C31—41no—
94C22×C8×C31C2311yescharacteristic
95C22×C8×C31C2311yescharacteristic
96C22×C8×C31C2311yescharacteristic
97C22×C8×C31C2311yescharacteristic
98C31×#121—22no—
99C31×#121—22no—
100C31×#121—22no—
101C31×#121—22no—
102C31×#121—22no—
103C31×#121—41no—
104C31×#121—41no—
105C31×#121—41no—
106C31×#121—44no—
107C31×#120—44no—
108C4×D4×C31—22no—
109C4×D4×C31—22no—
110C2×C4⋊C4×C31—22no—
111C2×C4⋊C4×C31—21no—
112C2×C4⋊C4×C31—21no—
113C2×C4⋊C4×C31—41no—
114C2×C4⋊C4×C31D411yescharacteristic
115C2×C4⋊C4×C31C2311yescharacteristic
116C2×C4⋊C4×C31C2311yescharacteristic
117C2×C4⋊C4×C31C2311yescharacteristic
118C2×C4⋊C4×C31C2311yescharacteristic
119C2×C4⋊C4×C31C2311yescharacteristic
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×C31—21no—
128C2×C22⋊C4×C31—21no—
129C2×C22⋊C4×C31—21no—
130C2×C22⋊C4×C31—21no—
131C2×C22⋊C4×C31—21no—
132C2×C22⋊C4×C31D411yescharacteristic
133C2×C22⋊C4×C31D411yescharacteristic
134C2×C42×C31C2311yescharacteristic
135C31×#106—22no—
136C31×#106—41no—
137C31×C4⋊C8—22no—
138C31×#102—22no—
139C31×#102—22no—
140C31×#102—22no—
141C31×#102—22no—
142C31×#102—22no—
143C31×#102—22no—
144C31×#102—41no—
145C31×#102D414yescomplemented
146C31×C22⋊C8—22no—
147C31×C22⋊C8D414yescomplemented
148C31×#97—22no—
149C31×#95—21no—
150C31×#95—21no—
151C31×#95—21no—
152C24×C31—21no—
153C24×C31—21no—
154C24×C31—21no—
155C24×C31—42no—
156C24×C31—42no—
157C24×C31—42no—
158C24×C31—42no—
159C24×C31—42no—
160C24×C31—81no—
161C24×C31—81no—
162C24×C31C2×D411yescharacteristic
163C24×C31C2×D411yescharacteristic
164C2×D4×C31—28no—
165C2×D4×C31—22no—
166C2×D4×C31—22no—
167C2×D4×C31—22no—
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—21no—
183C2×D4×C31—21no—
184C2×D4×C31—44no—
185C2×D4×C31—44no—
186C2×D4×C31—42no—
187C2×D4×C31—42no—
188C2×D4×C31—44no—
189C2×D4×C31—42no—
190C2×D4×C31—42no—
191C2×D4×C31—42no—
192C2×D4×C31—42no—
193C2×D4×C31—42no—
194C2×D4×C31—42no—
195C2×D4×C31—42no—
196C2×D4×C31—42no—
197C2×D4×C31—42no—
198C2×D4×C31—42no—
199C2×D4×C31—81no—
200C2×D4×C31—81no—
201C2×D4×C31—81no—
202C2×D4×C31C2×D412yes—
203C2×D4×C31#4112yes—
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—21no—
211C22×C4×C31—21no—
212C22×C4×C31—21no—
213C22×C4×C31—21no—
214C22×C4×C31—21no—
215C22×C4×C31—21no—
216C22×C4×C31—21no—
217C22×C4×C31—21no—
218C22×C4×C31—21no—
219C22×C4×C31—42no—
220C22×C4×C31—42no—
221C22×C4×C31—81no—
222C22×C4×C31C2×D411yescharacteristic
223C22×C4×C31C2×D411yescharacteristic
224C22×C4×C31C2×D411yescharacteristic
225C22×C4×C31C2×D411yescharacteristic
226C22×C4×C31C2×D412yes—
227C22×C4×C31#4112yes—
228C22×C4×C31C2411yescharacteristic
229D8×C31—44no—
230D8×C31—44no—
231M16×C31—44no—
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×C31—44no—
242C2×C8×C31C2×D412yes—
243C2×C8×C31C2×D412yes—
244C2×C8×C31C2×D412yes—
245C4⋊C4×C31—22no—
246C4⋊C4×C31—21no—
247C4⋊C4×C31—21no—
248C4⋊C4×C31—21no—
249C4⋊C4×C31—21no—
250C4⋊C4×C31—21no—
251C4⋊C4×C31—21no—
252C4⋊C4×C31—21no—
253C4⋊C4×C31—21no—
254C4⋊C4×C31—21no—
255C4⋊C4×C31—42no—
256C4⋊C4×C31—42no—
257C4⋊C4×C31C2×D412yes—
258C22⋊C4×C31—22no—
259C22⋊C4×C31—22no—
260C22⋊C4×C31—42no—
261C22⋊C4×C31—42no—
262C22⋊C4×C31—42no—
263C22⋊C4×C31—42no—
264C22⋊C4×C31—42no—
265C22⋊C4×C31—42no—
266C22⋊C4×C31—42no—
267C22⋊C4×C31—42no—
268C22⋊C4×C31—42no—
269C22⋊C4×C31—81no—
270C22⋊C4×C31—81no—
271C22⋊C4×C31—81no—
272C42×C31—21no—
273C42×C31—21no—
274#25124C3111yesmaximal, characteristic, direct product factor, Sylow
275C23×C31—21no—
276C23×C31—21no—
277C23×C31—21no—
278C23×C31—21no—
279C23×C31—21no—
280C23×C31—22no—
281C23×C31—21no—
282C23×C31—22no—
283C23×C31—21no—
284C23×C31—21no—
285C23×C31—21no—
286C23×C31—21no—
287C23×C31—21no—
288C23×C31—48no—
289C23×C31—41no—
290C23×C31—41no—
291C23×C31—41no—
292C23×C31—41no—
293C23×C31—41no—
294C23×C31—41no—
295C23×C31—41no—
296C23×C31—41no—
297C23×C31—41no—
298C23×C31—41no—
299C23×C31—41no—
300C23×C31—41no—
301C23×C31—41no—
302C23×C31—41no—
303C23×C31—41no—
304C23×C31—41no—
305C23×C31—41no—
306C23×C31—41no—
307C23×C31—41no—
308C23×C31—84no—
309C23×C31—84no—
310C23×C31—84no—
311C23×C31—84no—
312C23×C31—84no—
313C23×C31—84no—
314C23×C31#12112yes—
315C23×C31AGL(1,ℤ/8)12yes—
316C23×C31AGL(1,ℤ/8)12yes—
317C23×C31C22×D411yescharacteristic
318D4×C31—22no—
319D4×C31—22no—
320D4×C31—22no—
321D4×C31—22no—
322D4×C31—48no—
323D4×C31—44no—
324D4×C31—41no—
325D4×C31—41no—
326D4×C31—41no—
327D4×C31—41no—
328D4×C31—41no—
329D4×C31—41no—
330D4×C31—41no—
331D4×C31—41no—
332D4×C31—84no—
333D4×C31—84no—
334D4×C31—84no—
335D4×C31—84no—
336C2×C4×C31—21no—
337C2×C4×C31—21no—
338C2×C4×C31—22no—
339C2×C4×C31—22no—
340C2×C4×C31—22no—
341C2×C4×C31—22no—
342C2×C4×C31—21no—
343C2×C4×C31—21no—
344C2×C4×C31—21no—
345C2×C4×C31—21no—
346C2×C4×C31—22no—
347C2×C4×C31—21no—
348C2×C4×C31—21no—
349C2×C4×C31—21no—
350C2×C4×C31—21no—
351C2×C4×C31—21no—
352C2×C4×C31—41no—
353C2×C4×C31—41no—
354C2×C4×C31—41no—
355C2×C4×C31—41no—
356C2×C4×C31—41no—
357C2×C4×C31—41no—
358C2×C4×C31—41no—
359C2×C4×C31—41no—
360C2×C4×C31—41no—
361C2×C4×C31—41no—
362C2×C4×C31—41no—
363C2×C4×C31—41no—
364C2×C4×C31—41no—
365C2×C4×C31—41no—
366C2×C4×C31—41no—
367C2×C4×C31—41no—
368C2×C4×C31—41no—
369C2×C4×C31—41no—
370C2×C4×C31—84no—
371C2×C4×C31#12112yes—
372C2×C4×C31C22×D411yescharacteristic
373C2×C4×C31C22×D411yescharacteristic
374C2×C4×C31C2×#4111yescharacteristic
375C2×C4×C31C2×#4111yescharacteristic
376C2×C4×C31H(5,𝔽2)11yescharacteristic
377C2×C4×C31H(5,𝔽2)11yescharacteristic
378C8×C31—22no—
379C8×C31—22no—
380C8×C31—22no—
381C8×C31—41no—
382C2×#469C2×C3111yescharacteristic, complemented
383C2×#447C2×C3111yescharacteristic, complemented
384C2×#435C2×C3111yescharacteristic, complemented
385C22×#102C2×C3111yescharacteristic, complemented
386#2416C2×C3111yescharacteristic, complemented
387#2408C2×C3111yescharacteristic, complemented
388#2065C2×C3111yescharacteristic, complemented
389#2054C2×C3111yescharacteristic, complemented
390#2034C2×C3111yescharacteristic, complemented
391#1999C2×C3111yescharacteristic, complemented
392#1972C2×C3111yescharacteristic, complemented
393#1936C2×C3111yescharacteristic, complemented
394#1895C2×C3111yescharacteristic, complemented
395#1893C2×C3111yescharacteristic, complemented
396#1853C2×C3111yescharacteristic, complemented
397C22×C31—22no—
398C22×C31—22no—
399C22×C31—22no—
400C22×C31—22no—
401C22×C31—22no—
402C22×C31—22no—
403C22×C31—41no—
404C22×C31—42no—
405C22×C31—42no—
406C22×C31—41no—
407C22×C31—42no—
408C22×C31—41no—
409C22×C31—42no—
410C22×C31—41no—
411C22×C31—42no—
412C22×C31—41no—
413C22×C31—41no—
414C22×C31—41no—
415C22×C31—42no—
416C22×C31—816no—
417C22×C31—81no—
418C22×C31—81no—
419C22×C31—81no—
420C22×C31—81no—
421C22×C31—81no—
422C22×C31—81no—
423C22×C31—81no—
424C22×C31—81no—
425C22×C31—81no—
426C22×C31—81no—
427C22×C31—81no—
428C22×C31—81no—
429C22×C31—81no—
430C22×C31—81no—
431C22×C31—81no—
432C22×C31#46914yescomplemented
433C22×C31C2×#12111yescharacteristic
434C22×C31D4211yescharacteristic
435C22×C31#54611yescharacteristic
436C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
437C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
438C22×C31#57611yescharacteristic
439C22×C31#57711yescharacteristic
440C4×C31—22no—
441C4×C31—41no—
442C4×C31—42no—
443C4×C31—41no—
444C4×C31—41no—
445C4×C31—81no—
446C4×C31—81no—
447C4×C31—81no—
448C4×C31—81no—
449C4×C31#52511yescharacteristic
450C4×C31#53811yescharacteristic
451C4×C31D4211yescharacteristic
452C4×C31#54611yescharacteristic
453C23×D4C22×C3111yescharacteristic
454C22×D8C22×C3111yescharacteristic
455C22×D8C22×C3111yescharacteristic
456C22×M16C22×C3111yescharacteristic, complemented
457C23×C8C22×C3111yescharacteristic
458C2×#121—21no—
459C2×#121C22×C3111yescharacteristic
460C2×#121C22×C3111yescharacteristic
461C2×#121C22×C3111yescharacteristic
462C2×#121C22×C3111yescharacteristic, complemented
463C2×#120—21no—
464C2×C4×D4C22×C3111yescharacteristic
465C22×C4⋊C4C22×C3111yescharacteristic
466#469—24no—
467#447—24no—
468#435—24no—
469C2×#106C22×C3111yescharacteristic, complemented
470C2×#106C22×C3111yescharacteristic, complemented
471C2×C4⋊C8C22×C3111yescharacteristic, complemented
472C2×#102—24no—
473C2×#102C22×C3111yescharacteristic
474C2×#102C22×C3111yescharacteristic
475C2×#102C22×C3111yescharacteristic
476C2×#102C22×C3111yescharacteristic
477C2×#102C22×C3111yescharacteristic
478C2×#102C22×C3111yescharacteristic
479C2×#102C22×C3111yescharacteristic, complemented
480C2×#102C22×C3111yescharacteristic, complemented
481C2×C22⋊C8C22×C3111yescharacteristic
482C2×C22⋊C8C22×C3111yescharacteristic, complemented
483C2×#97C22×C3111yescharacteristic, complemented
484#396—21no—
485#394—21no—
486#394—21no—
487#392—21no—
488#390C22×C3111yescharacteristic
489#390C22×C3111yescharacteristic
490#390C22×C3111yescharacteristic, complemented
491#389C22×C3111yescharacteristic, complemented
492#386—21no—
493#380C22×C3111yescharacteristic
494#380C22×C3111yescharacteristic, complemented
495#379—21no—
496#340C22×C3111yescharacteristic, complemented
497#340C22×C3111yescharacteristic, complemented
498#340C22×C3111yescharacteristic, complemented
499#340C22×C3111yescharacteristic, complemented
500C2×C31—24no—
501C2×C31—81no—
502C2×C31—82no—
503C2×C31—82no—
504C2×C31—161no—
505C2×C31#242411yescharacteristic
506C2×C31C2×#46911yescharacteristic
507C2×C31#306211yescharacteristic
508C2×C31#326411yescharacteristic
509C2×C31#326511yescharacteristic
510C2×C31#330611yescharacteristic
511C2×C31#331811yescharacteristic
512C25—21no—
513C22×D4—22no—
514C22×D4—22no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—22no—
520C22×D4—21no—
521C22×D4—22no—
522C22×D4—41no—
523C22×D4—41no—
524C22×D4D4×C3111yescharacteristic
525C22×D4C23×C3111yescharacteristic
526C22×D4C23×C3111yescharacteristic
527C22×D4C23×C3111yescharacteristic
528C23×C4—21no—
529C23×C4C23×C3111yescharacteristic
530C23×C4C23×C3111yescharacteristic
531C2×D8—22no—
532C2×D8—22no—
533C2×D8—22no—
534C2×D8—22no—
535C2×D8—41no—
536C2×D8—41no—
537C2×M16—22no—
538C2×M16—22no—
539C2×M16—41no—
540C22×C8—22no—
541C22×C8—22no—
542C22×C8—41no—
543C22×C8C23×C3111yescharacteristic
544C22×C8C23×C3111yescharacteristic
545C22×C8C23×C3111yescharacteristic
546C22×C8C23×C3111yescharacteristic
547#121—22no—
548#121—22no—
549#121—22no—
550#121—22no—
551#121—22no—
552#121—41no—
553#121—41no—
554#121—41no—
555#121—44no—
556#120—44no—
557C4×D4—22no—
558C4×D4—22no—
559C2×C4⋊C4—22no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—41no—
563C2×C4⋊C4D4×C3111yescharacteristic
564C2×C4⋊C4C23×C3111yescharacteristic
565C2×C4⋊C4C23×C3111yescharacteristic
566C2×C4⋊C4C23×C3111yescharacteristic
567C2×C4⋊C4C23×C3111yescharacteristic
568C2×C4⋊C4C23×C3111yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—21no—
580C2×C22⋊C4—21no—
581C2×C22⋊C4D4×C3111yescharacteristic
582C2×C22⋊C4D4×C3111yescharacteristic
583C2×C42C23×C3111yescharacteristic
584#106—22no—
585#106—41no—
586C4⋊C8—22no—
587#102—22no—
588#102—22no—
589#102—22no—
590#102—22no—
591#102—22no—
592#102—22no—
593#102—41no—
594#102D4×C3114yescomplemented
595C22⋊C8—22no—
596C22⋊C8D4×C3114yescomplemented
597#97—22no—
598#95—21no—
599#95—21no—
600#95—21no—
601C31#2512411yescharacteristic, direct product factor, Sylow
602C24—21no—
603C24—21no—
604C24—21no—
605C24—42no—
606C24—42no—
607C24—42no—
608C24—42no—
609C24—42no—
610C24—81no—
611C24—81no—
612C24C2×D4×C3111yescharacteristic
613C24C2×D4×C3111yescharacteristic
614C2×D4—28no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—22no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—44no—
635C2×D4—44no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4—44no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—42no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4—42no—
649C2×D4—81no—
650C2×D4—81no—
651C2×D4—81no—
652C2×D4C2×D4×C3112yes—
653C2×D4#41×C3112yes—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—81no—
672C22×C4C2×D4×C3111yescharacteristic
673C22×C4C2×D4×C3111yescharacteristic
674C22×C4C2×D4×C3111yescharacteristic
675C22×C4C2×D4×C3111yescharacteristic
676C22×C4C2×D4×C3112yes—
677C22×C4#41×C3112yes—
678C22×C4C24×C3111yescharacteristic
679D8—44no—
680D8—44no—
681M16—44no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—44no—
692C2×C8C2×D4×C3112yes—
693C2×C8C2×D4×C3112yes—
694C2×C8C2×D4×C3112yes—
695C4⋊C4—22no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—42no—
706C4⋊C4—42no—
707C4⋊C4C2×D4×C3112yes—
708C22⋊C4—22no—
709C22⋊C4—22no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C22⋊C4—42no—
713C22⋊C4—42no—
714C22⋊C4—42no—
715C22⋊C4—42no—
716C22⋊C4—42no—
717C22⋊C4—42no—
718C22⋊C4—42no—
719C22⋊C4—81no—
720C22⋊C4—81no—
721C22⋊C4—81no—
722C42—21no—
723C42—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—22no—
730C23—21no—
731C23—22no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—48no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—84no—
758C23—84no—
759C23—84no—
760C23—84no—
761C23—84no—
762C23—84no—
763C23C31×#12112yes—
764C23C31×AGL(1,ℤ/8)12yes—
765C23C31×AGL(1,ℤ/8)12yes—
766C23C22×D4×C3111yescharacteristic
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—48no—
772D4—44no—
773D4—41no—
774D4—41no—
775D4—41no—
776D4—41no—
777D4—41no—
778D4—41no—
779D4—41no—
780D4—41no—
781D4—84no—
782D4—84no—
783D4—84no—
784D4—84no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—22no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—84no—
820C2×C4C31×#12112yes—
821C2×C4C22×D4×C3111yescharacteristic
822C2×C4C22×D4×C3111yescharacteristic
823C2×C4C2×#41×C3111yescharacteristic
824C2×C4C2×#41×C3111yescharacteristic
825C2×C4C31×H(5,𝔽2)11yescharacteristic
826C2×C4C31×H(5,𝔽2)11yescharacteristic
827C8—22no—
828C8—22no—
829C8—22no—
830C8—41no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—41no—
838C22—42no—
839C22—42no—
840C22—41no—
841C22—42no—
842C22—41no—
843C22—42no—
844C22—41no—
845C22—42no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22—42no—
850C22—816no—
851C22—81no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22C31×#46914yescomplemented
867C22C2×C31×#12111yescharacteristic
868C22D42×C3111yescharacteristic
869C22C31×#54611yescharacteristic
870C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
871C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
872C22C31×#57611yescharacteristic
873C22C31×#57711yescharacteristic
874C4—22no—
875C4—41no—
876C4—42no—
877C4—41no—
878C4—41no—
879C4—81no—
880C4—81no—
881C4—81no—
882C4—81no—
883C4C31×#52511yescharacteristic
884C4C31×#53811yescharacteristic
885C4D42×C3111yescharacteristic
886C4C31×#54611yescharacteristic
887C2—24no—
888C2—81no—
889C2—82no—
890C2—82no—
891C2—161no—
892C2C31×#242411yescharacteristic
893C2C2×C31×#46911yescharacteristic
894C2C31×#306211yescharacteristic
895C2C31×#326411yescharacteristic
896C2C31×#326511yescharacteristic
897C2C31×#330611yescharacteristic
898C2C31×#331811yescharacteristic
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×#469C2semidirect
2. C2×C31×#447C2semidirect
3. C2×C31×#435C2semidirect
4. C22×C31×#102C2semidirect
5. C31×#2416C2semidirect
6. C31×#2408C2semidirect
7. C31×#2065C2semidirect
8. C31×#2054C2semidirect
9. C31×#2034C2semidirect
10. C31×#1999C2semidirect
11. C31×#1972C2semidirect
12. C31×#1936C2semidirect
13. C31×#1895C2semidirect
14. C31×#1893C2semidirect
15. C31×#1853C2semidirect
19. C22×M16×C31C22semidirect
25. C2×C31×#121C22semidirect
32. C2×C31×#106C22semidirect
33. C2×C31×#106C22semidirect
34. C2×C31×C4⋊C8C22semidirect
42. C2×C31×#102C22semidirect
43. C2×C31×#102C22semidirect
45. C2×C31×C22⋊C8C22semidirect
46. C2×C31×#97C22semidirect
53. C31×#390C22semidirect
54. C31×#389C22semidirect
57. C31×#380C22semidirect
59. C31×#340C22semidirect
60. C31×#340C22semidirect
61. C31×#340C22semidirect
62. C31×#340C22semidirect
145. C31×#102D4semidirect
147. C31×C22⋊C8D4semidirect
274. #25124C31direct (N × H)
382. C2×#469C2×C31semidirect
383. C2×#447C2×C31semidirect
384. C2×#435C2×C31semidirect
385. C22×#102C2×C31semidirect
386. #2416C2×C31semidirect
387. #2408C2×C31semidirect
388. #2065C2×C31semidirect
389. #2054C2×C31semidirect
390. #2034C2×C31semidirect
391. #1999C2×C31semidirect
392. #1972C2×C31semidirect
393. #1936C2×C31semidirect
394. #1895C2×C31semidirect
395. #1893C2×C31semidirect
396. #1853C2×C31semidirect
432. C22×C31#469semidirect
456. C22×M16C22×C31semidirect
462. C2×#121C22×C31semidirect
469. C2×#106C22×C31semidirect
470. C2×#106C22×C31semidirect
471. C2×C4⋊C8C22×C31semidirect
479. C2×#102C22×C31semidirect
480. C2×#102C22×C31semidirect
482. C2×C22⋊C8C22×C31semidirect
483. C2×#97C22×C31semidirect
490. #390C22×C31semidirect
491. #389C22×C31semidirect
494. #380C22×C31semidirect
496. #340C22×C31semidirect
497. #340C22×C31semidirect
498. #340C22×C31semidirect
499. #340C22×C31semidirect
594. #102D4×C31semidirect
596. C22⋊C8D4×C31semidirect
601. C31#25124direct (N × H)
866. C22C31×#469semidirect

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×#4472
C2×C31×#4352
C22×C31×#1022
C31×#24162
C31×#24082
C31×#20652
C31×#20542
C31×#20342
C31×#19992
C31×#19722
C31×#19362
C31×#18952
C31×#18932
C31×#18532
#2512431