Finite Group Databasebeta

← C31×#25097 #21481856

Subgroups — C31×#25097 #21481856

Order 7936.

1378 conjugacy classes of subgroups.

The subgroup lattice has 904 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×#447C211yesmaximal, characteristic, complemented
4C2×C31×#418C211yesmaximal, characteristic, complemented
5C31×#2433C211yesmaximal, characteristic, complemented
6C31×#2363C211yesmaximal, characteristic, complemented
7C31×#2065C211yesmaximal, characteristic, complemented
8C31×#2054C211yesmaximal, characteristic, complemented
9C31×#2041C211yesmaximal, characteristic, complemented
10C31×#2011C211yesmaximal, characteristic, complemented
11C31×#1982C211yesmaximal, characteristic, complemented
12C31×#1926C211yesmaximal, characteristic, complemented
13C31×#1879C211yesmaximal, characteristic, complemented
14C31×#1875C211yesmaximal, characteristic, complemented
15C31×#1851C211yesmaximal, characteristic, complemented
16C23×D4×C31C2211yescharacteristic
17C22×D8×C31C2211yescharacteristic
18C22×D8×C31C2211yescharacteristic
19C22×D8×C31C2211yescharacteristic, complemented
20C22×M16×C31C2211yescharacteristic
21C2×C31×#127C2211yescharacteristic
22C2×C31×#127C2211yescharacteristic
23C2×C31×#121C2211yescharacteristic
24C2×C31×#121C2211yescharacteristic
25C2×C31×#120—21no—
26C2×C31×#120—21no—
27C2×C4×D4×C31C2211yescharacteristic, complemented
28C2×C31×#117C2211yescharacteristic
29C31×#469—24no—
30C31×#459—24no—
31C31×#447—24no—
32C2×C31×#106C2211yescharacteristic, complemented
33C2×C31×C4⋊C8C2211yescharacteristic, complemented
34C2×C31×C4⋊C8C2211yescharacteristic, complemented
35C31×#418—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×#102C2211yescharacteristic, complemented
45C2×C31×#102C2211yescharacteristic, complemented
46C2×C31×C22⋊C8C2211yescharacteristic
47C31×#392—21no—
48C31×#392—21no—
49C31×#390—21no—
50C31×#390C2211yescharacteristic
51C31×#390C2211yescharacteristic
52C31×#390C2211yescharacteristic, complemented
53C31×#389C2211yescharacteristic, complemented
54C31×#388—21no—
55C31×#386—21no—
56C4×C4⋊C4×C31C2211yescharacteristic, complemented
57C4×C22⋊C4×C31—21no—
58C4×C22⋊C4×C31C2211yescharacteristic
59C31×#340C2211yescharacteristic, complemented
60C31×#340C2211yescharacteristic, complemented
61C31×#336C2211yescharacteristic, complemented
62C31×#336C2211yescharacteristic, complemented
63C25×C31—21no—
64C22×D4×C31—22no—
65C22×D4×C31—22no—
66C22×D4×C31—21no—
67C22×D4×C31—21no—
68C22×D4×C31—22no—
69C22×D4×C31—21no—
70C22×D4×C31—21no—
71C22×D4×C31—21no—
72C22×D4×C31—21no—
73C22×D4×C31—21no—
74C22×D4×C31—22no—
75C22×D4×C31—41no—
76C22×D4×C31—41no—
77C22×D4×C31C2311yescharacteristic
78C22×D4×C31C2311yescharacteristic
79C22×D4×C31C2311yescharacteristic
80C22×D4×C31C2311yescharacteristic
81C23×C4×C31—21no—
82C23×C4×C31C2311yescharacteristic
83C2×D8×C31—22no—
84C2×D8×C31—22no—
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×D8×C31—41no—
92C2×M16×C31—22no—
93C2×M16×C31—22no—
94C2×M16×C31—41no—
95C22×C8×C31C2311yescharacteristic
96C22×C8×C31C2311yescharacteristic
97C22×C8×C31C2311yescharacteristic
98C22×C8×C31C2311yescharacteristic
99C31×#127—22no—
100C31×#127—22no—
101C31×#127—41no—
102C31×#127—41no—
103C31×#121—22no—
104C31×#121—22no—
105C31×#121—22no—
106C31×#121D414yescomplemented
107C31×#120—44no—
108C31×#120—44no—
109C4×D4×C31—22no—
110C4×D4×C31—41no—
111C31×#117—22no—
112C31×#117—41no—
113C2×C4⋊C4×C31—21no—
114C2×C4⋊C4×C31C2311yescharacteristic
115C2×C4⋊C4×C31C2311yescharacteristic
116C2×C4⋊C4×C31C2311yescharacteristic
117C2×C4⋊C4×C31C2311yescharacteristic
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×C31—21no—
128C2×C22⋊C4×C31D411yescharacteristic
129C2×C22⋊C4×C31D411yescharacteristic
130C2×C42×C31—21no—
131C2×C42×C31—21no—
132C2×C42×C31C2311yescharacteristic
133C2×C42×C31C2311yescharacteristic
134C31×#106—22no—
135C31×C4⋊C8—22no—
136C31×C4⋊C8—41no—
137C31×#102—22no—
138C31×#102—22no—
139C31×#102—22no—
140C31×#102—22no—
141C31×#102—22no—
142C31×#102—22no—
143C31×#102—22no—
144C31×#102—22no—
145C31×#102—41no—
146C31×#102D414yescomplemented
147C31×C22⋊C8—22no—
148C31×#95—21no—
149C31×#95—21no—
150C31×#95D411yescharacteristic
151C31×#95D411yescharacteristic
152C24×C31—21no—
153C24×C31—21no—
154C24×C31—21no—
155C24×C31—21no—
156C24×C31—42no—
157C24×C31—42no—
158C24×C31—42no—
159C24×C31—42no—
160C24×C31—42no—
161C24×C31—81no—
162C24×C31—81no—
163C24×C31C2×D411yescharacteristic
164C2×D4×C31—28no—
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—21no—
183C2×D4×C31—21no—
184C2×D4×C31—21no—
185C2×D4×C31—21no—
186C2×D4×C31—21no—
187C2×D4×C31—44no—
188C2×D4×C31—44no—
189C2×D4×C31—42no—
190C2×D4×C31—42no—
191C2×D4×C31—44no—
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—42no—
200C2×D4×C31—42no—
201C2×D4×C31—42no—
202C2×D4×C31—42no—
203C2×D4×C31—42no—
204C2×D4×C31—81no—
205C2×D4×C31—81no—
206C2×D4×C31—81no—
207C2×D4×C31—81no—
208C2×D4×C31—81no—
209C2×D4×C31—81no—
210C2×D4×C31C2×D412yes—
211C2×D4×C31C2×D412yes—
212C2×D4×C31#4112yes—
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—21no—
220C22×C4×C31—21no—
221C22×C4×C31—42no—
222C22×C4×C31—42no—
223C22×C4×C31—81no—
224C22×C4×C31C2×D411yescharacteristic
225C22×C4×C31C2×D411yescharacteristic
226C22×C4×C31C2×D411yescharacteristic
227C22×C4×C31C2×D412yes—
228C22×C4×C31C2×D411yescharacteristic
229C22×C4×C31C2×D411yescharacteristic
230C22×C4×C31#4112yes—
231C22×C4×C31C2411yescharacteristic
232D8×C31—44no—
233D8×C31—44no—
234D8×C31—44no—
235M16×C31—44no—
236C2×C8×C31—21no—
237C2×C8×C31—21no—
238C2×C8×C31—21no—
239C2×C8×C31—21no—
240C2×C8×C31—21no—
241C2×C8×C31—21no—
242C2×C8×C31—21no—
243C2×C8×C31—21no—
244C2×C8×C31—21no—
245C2×C8×C31—21no—
246C2×C8×C31—21no—
247C2×C8×C31C2×D412yes—
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—81no—
255C4⋊C4×C31C2×D412yes—
256C4⋊C4×C31C2×D412yes—
257C22⋊C4×C31—24no—
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—81no—
269C42×C31—21no—
270C42×C31—21no—
271C42×C31—21no—
272C42×C31—21no—
273C42×C31—42no—
274C42×C31—81no—
275#25097C3111yesmaximal, characteristic, direct product factor, Sylow
276C23×C31—21no—
277C23×C31—21no—
278C23×C31—21no—
279C23×C31—21no—
280C23×C31—21no—
281C23×C31—21no—
282C23×C31—22no—
283C23×C31—22no—
284C23×C31—22no—
285C23×C31—48no—
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×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—41no—
309C23×C31—41no—
310C23×C31—41no—
311C23×C31—84no—
312C23×C31—84no—
313C23×C31—84no—
314C23×C31—84no—
315C23×C31—84no—
316C23×C31—84no—
317C23×C31#12112yes—
318C23×C31C22×D411yescharacteristic
319D4×C31—22no—
320D4×C31—22no—
321D4×C31—22no—
322D4×C31—22no—
323D4×C31—22no—
324D4×C31—22no—
325D4×C31—48no—
326D4×C31—41no—
327D4×C31—41no—
328D4×C31—41no—
329D4×C31—41no—
330D4×C31—41no—
331D4×C31—41no—
332D4×C31—41no—
333D4×C31—41no—
334D4×C31—41no—
335D4×C31—41no—
336D4×C31—84no—
337D4×C31—84no—
338D4×C31—84no—
339D4×C31—84no—
340D4×C31—84no—
341D4×C31—84no—
342C2×C4×C31—21no—
343C2×C4×C31—21no—
344C2×C4×C31—21no—
345C2×C4×C31—21no—
346C2×C4×C31—21no—
347C2×C4×C31—21no—
348C2×C4×C31—22no—
349C2×C4×C31—22no—
350C2×C4×C31—22no—
351C2×C4×C31—22no—
352C2×C4×C31—22no—
353C2×C4×C31—21no—
354C2×C4×C31—22no—
355C2×C4×C31—21no—
356C2×C4×C31—21no—
357C2×C4×C31—21no—
358C2×C4×C31—21no—
359C2×C4×C31—21no—
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×C31AGL(1,ℤ/8)12yes—
373C2×C4×C31AGL(1,ℤ/8)12yes—
374C2×C4×C31C22×D411yescharacteristic
375C2×C4×C31C22×D411yescharacteristic
376C2×C4×C31C2×#4111yescharacteristic
377C2×C4×C31C2×#4111yescharacteristic
378C2×C4×C31H(5,𝔽2)11yescharacteristic
379C2×C4×C31H(5,𝔽2)11yescharacteristic
380C8×C31—22no—
381C8×C31—41no—
382C8×C31—41no—
383C8×C31—41no—
384C2×#469C2×C3111yescharacteristic, complemented
385C2×#459C2×C3111yescharacteristic, complemented
386C2×#447C2×C3111yescharacteristic, complemented
387C2×#418C2×C3111yescharacteristic, complemented
388#2433C2×C3111yescharacteristic, complemented
389#2363C2×C3111yescharacteristic, complemented
390#2065C2×C3111yescharacteristic, complemented
391#2054C2×C3111yescharacteristic, complemented
392#2041C2×C3111yescharacteristic, complemented
393#2011C2×C3111yescharacteristic, complemented
394#1982C2×C3111yescharacteristic, complemented
395#1926C2×C3111yescharacteristic, complemented
396#1879C2×C3111yescharacteristic, complemented
397#1875C2×C3111yescharacteristic, complemented
398#1851C2×C3111yescharacteristic, complemented
399C22×C31—22no—
400C22×C31—22no—
401C22×C31—22no—
402C22×C31—41no—
403C22×C31—41no—
404C22×C31—41no—
405C22×C31—41no—
406C22×C31—42no—
407C22×C31—42no—
408C22×C31—42no—
409C22×C31—42no—
410C22×C31—42no—
411C22×C31—42no—
412C22×C31—42no—
413C22×C31—42no—
414C22×C31—42no—
415C22×C31—816no—
416C22×C31—81no—
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—81no—
433C22×C31—81no—
434C22×C31—81no—
435C22×C31C2×#12111yescharacteristic
436C22×C31D4211yescharacteristic
437C22×C31#54611yescharacteristic
438C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
439C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
440C22×C31#57611yescharacteristic
441C22×C31#57611yescharacteristic
442C4×C31—22no—
443C4×C31—22no—
444C4×C31—22no—
445C4×C31—42no—
446C4×C31—41no—
447C4×C31—42no—
448C4×C31—41no—
449C4×C31—81no—
450C4×C31—81no—
451C4×C31#52511yescharacteristic
452C4×C31#53811yescharacteristic
453C4×C31D4211yescharacteristic
454C4×C31#54611yescharacteristic
455C23×D4C22×C3111yescharacteristic
456C22×D8C22×C3111yescharacteristic
457C22×D8C22×C3111yescharacteristic
458C22×D8C22×C3111yescharacteristic, complemented
459C22×M16C22×C3111yescharacteristic
460C2×#127C22×C3111yescharacteristic
461C2×#127C22×C3111yescharacteristic
462C2×#121C22×C3111yescharacteristic
463C2×#121C22×C3111yescharacteristic
464C2×#120—21no—
465C2×#120—21no—
466C2×C4×D4C22×C3111yescharacteristic, complemented
467C2×#117C22×C3111yescharacteristic
468#469—24no—
469#459—24no—
470#447—24no—
471C2×#106C22×C3111yescharacteristic, complemented
472C2×C4⋊C8C22×C3111yescharacteristic, complemented
473C2×C4⋊C8C22×C3111yescharacteristic, complemented
474#418—24no—
475C2×#102C22×C3111yescharacteristic
476C2×#102C22×C3111yescharacteristic
477C2×#102C22×C3111yescharacteristic
478C2×#102C22×C3111yescharacteristic
479C2×#102C22×C3111yescharacteristic
480C2×#102C22×C3111yescharacteristic
481C2×#102C22×C3111yescharacteristic, complemented
482C2×#102C22×C3111yescharacteristic, complemented
483C2×#102C22×C3111yescharacteristic, complemented
484C2×#102C22×C3111yescharacteristic, complemented
485C2×C22⋊C8C22×C3111yescharacteristic
486#392—21no—
487#392—21no—
488#390—21no—
489#390C22×C3111yescharacteristic
490#390C22×C3111yescharacteristic
491#390C22×C3111yescharacteristic, complemented
492#389C22×C3111yescharacteristic, complemented
493#388—21no—
494#386—21no—
495C4×C4⋊C4C22×C3111yescharacteristic, complemented
496C4×C22⋊C4—21no—
497C4×C22⋊C4C22×C3111yescharacteristic
498#340C22×C3111yescharacteristic, complemented
499#340C22×C3111yescharacteristic, complemented
500#336C22×C3111yescharacteristic, complemented
501#336C22×C3111yescharacteristic, complemented
502C2×C31—42no—
503C2×C31—82no—
504C2×C31—82no—
505C2×C31—82no—
506C2×C31—161no—
507C2×C31#242411yescharacteristic
508C2×C31#303811yescharacteristic
509C2×C31#304111yescharacteristic
510C2×C31#326411yescharacteristic
511C2×C31#327411yescharacteristic
512C2×C31#331811yescharacteristic
513C2×C31#332511yescharacteristic
514C25—21no—
515C22×D4—22no—
516C22×D4—22no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—22no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—22no—
526C22×D4—41no—
527C22×D4—41no—
528C22×D4C23×C3111yescharacteristic
529C22×D4C23×C3111yescharacteristic
530C22×D4C23×C3111yescharacteristic
531C22×D4C23×C3111yescharacteristic
532C23×C4—21no—
533C23×C4C23×C3111yescharacteristic
534C2×D8—22no—
535C2×D8—22no—
536C2×D8—22no—
537C2×D8—22no—
538C2×D8—22no—
539C2×D8—22no—
540C2×D8—41no—
541C2×D8—41no—
542C2×D8—41no—
543C2×M16—22no—
544C2×M16—22no—
545C2×M16—41no—
546C22×C8C23×C3111yescharacteristic
547C22×C8C23×C3111yescharacteristic
548C22×C8C23×C3111yescharacteristic
549C22×C8C23×C3111yescharacteristic
550#127—22no—
551#127—22no—
552#127—41no—
553#127—41no—
554#121—22no—
555#121—22no—
556#121—22no—
557#121D4×C3114yescomplemented
558#120—44no—
559#120—44no—
560C4×D4—22no—
561C4×D4—41no—
562#117—22no—
563#117—41no—
564C2×C4⋊C4—21no—
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⋊C4D4×C3111yescharacteristic
580C2×C22⋊C4D4×C3111yescharacteristic
581C2×C42—21no—
582C2×C42—21no—
583C2×C42C23×C3111yescharacteristic
584C2×C42C23×C3111yescharacteristic
585#106—22no—
586C4⋊C8—22no—
587C4⋊C8—41no—
588#102—22no—
589#102—22no—
590#102—22no—
591#102—22no—
592#102—22no—
593#102—22no—
594#102—22no—
595#102—22no—
596#102—41no—
597#102D4×C3114yescomplemented
598C22⋊C8—22no—
599#95—21no—
600#95—21no—
601#95D4×C3111yescharacteristic
602#95D4×C3111yescharacteristic
603C31#2509711yescharacteristic, direct product factor, Sylow
604C24—21no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—42no—
609C24—42no—
610C24—42no—
611C24—42no—
612C24—42no—
613C24—81no—
614C24—81no—
615C24C2×D4×C3111yescharacteristic
616C2×D4—28no—
617C2×D4—24no—
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—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—44no—
640C2×D4—44no—
641C2×D4—42no—
642C2×D4—42no—
643C2×D4—44no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4—42no—
649C2×D4—42no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—42no—
655C2×D4—42no—
656C2×D4—81no—
657C2×D4—81no—
658C2×D4—81no—
659C2×D4—81no—
660C2×D4—81no—
661C2×D4—81no—
662C2×D4C2×D4×C3112yes—
663C2×D4C2×D4×C3112yes—
664C2×D4#41×C3112yes—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—42no—
674C22×C4—42no—
675C22×C4—81no—
676C22×C4C2×D4×C3111yescharacteristic
677C22×C4C2×D4×C3111yescharacteristic
678C22×C4C2×D4×C3111yescharacteristic
679C22×C4C2×D4×C3112yes—
680C22×C4C2×D4×C3111yescharacteristic
681C22×C4C2×D4×C3111yescharacteristic
682C22×C4#41×C3112yes—
683C22×C4C24×C3111yescharacteristic
684D8—44no—
685D8—44no—
686D8—44no—
687M16—44no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8C2×D4×C3112yes—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—81no—
707C4⋊C4C2×D4×C3112yes—
708C4⋊C4C2×D4×C3112yes—
709C22⋊C4—24no—
710C22⋊C4—22no—
711C22⋊C4—22no—
712C22⋊C4—42no—
713C22⋊C4—42no—
714C22⋊C4—42no—
715C22⋊C4—42no—
716C22⋊C4—42no—
717C22⋊C4—42no—
718C22⋊C4—42no—
719C22⋊C4—42no—
720C22⋊C4—81no—
721C42—21no—
722C42—21no—
723C42—21no—
724C42—21no—
725C42—42no—
726C42—81no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—48no—
737C23—41no—
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—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—84no—
763C23—84no—
764C23—84no—
765C23—84no—
766C23—84no—
767C23—84no—
768C23C31×#12112yes—
769C23C22×D4×C3111yescharacteristic
770D4—22no—
771D4—22no—
772D4—22no—
773D4—22no—
774D4—22no—
775D4—22no—
776D4—48no—
777D4—41no—
778D4—41no—
779D4—41no—
780D4—41no—
781D4—41no—
782D4—41no—
783D4—41no—
784D4—41no—
785D4—41no—
786D4—41no—
787D4—84no—
788D4—84no—
789D4—84no—
790D4—84no—
791D4—84no—
792D4—84no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—21no—
805C2×C4—22no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
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—41no—
820C2×C4—41no—
821C2×C4—84no—
822C2×C4C31×#12112yes—
823C2×C4C31×AGL(1,ℤ/8)12yes—
824C2×C4C31×AGL(1,ℤ/8)12yes—
825C2×C4C22×D4×C3111yescharacteristic
826C2×C4C22×D4×C3111yescharacteristic
827C2×C4C2×#41×C3111yescharacteristic
828C2×C4C2×#41×C3111yescharacteristic
829C2×C4C31×H(5,𝔽2)11yescharacteristic
830C2×C4C31×H(5,𝔽2)11yescharacteristic
831C8—22no—
832C8—41no—
833C8—41no—
834C8—41no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—816no—
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—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—81no—
871C22C2×C31×#12111yescharacteristic
872C22D42×C3111yescharacteristic
873C22C31×#54611yescharacteristic
874C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
875C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
876C22C31×#57611yescharacteristic
877C22C31×#57611yescharacteristic
878C4—22no—
879C4—22no—
880C4—22no—
881C4—42no—
882C4—41no—
883C4—42no—
884C4—41no—
885C4—81no—
886C4—81no—
887C4C31×#52511yescharacteristic
888C4C31×#53811yescharacteristic
889C4D42×C3111yescharacteristic
890C4C31×#54611yescharacteristic
891C2—42no—
892C2—82no—
893C2—82no—
894C2—82no—
895C2—161no—
896C2C31×#242411yescharacteristic
897C2C31×#303811yescharacteristic
898C2C31×#304111yescharacteristic
899C2C31×#326411yescharacteristic
900C2C31×#327411yescharacteristic
901C2C31×#331811yescharacteristic
902C2C31×#332511yescharacteristic
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×#447C2semidirect
4. C2×C31×#418C2semidirect
5. C31×#2433C2semidirect
6. C31×#2363C2semidirect
7. C31×#2065C2semidirect
8. C31×#2054C2semidirect
9. C31×#2041C2semidirect
10. C31×#2011C2semidirect
11. C31×#1982C2semidirect
12. C31×#1926C2semidirect
13. C31×#1879C2semidirect
14. C31×#1875C2semidirect
15. C31×#1851C2semidirect
19. C22×D8×C31C22semidirect
27. C2×C4×D4×C31C22semidirect
32. C2×C31×#106C22semidirect
33. C2×C31×C4⋊C8C22semidirect
34. C2×C31×C4⋊C8C22semidirect
42. C2×C31×#102C22semidirect
43. C2×C31×#102C22semidirect
44. C2×C31×#102C22semidirect
45. C2×C31×#102C22semidirect
52. C31×#390C22semidirect
53. C31×#389C22semidirect
56. C4×C4⋊C4×C31C22semidirect
59. C31×#340C22semidirect
60. C31×#340C22semidirect
61. C31×#336C22semidirect
62. C31×#336C22semidirect
106. C31×#121D4semidirect
146. C31×#102D4semidirect
275. #25097C31direct (N × H)
384. C2×#469C2×C31semidirect
385. C2×#459C2×C31semidirect
386. C2×#447C2×C31semidirect
387. C2×#418C2×C31semidirect
388. #2433C2×C31semidirect
389. #2363C2×C31semidirect
390. #2065C2×C31semidirect
391. #2054C2×C31semidirect
392. #2041C2×C31semidirect
393. #2011C2×C31semidirect
394. #1982C2×C31semidirect
395. #1926C2×C31semidirect
396. #1879C2×C31semidirect
397. #1875C2×C31semidirect
398. #1851C2×C31semidirect
458. C22×D8C22×C31semidirect
466. C2×C4×D4C22×C31semidirect
471. C2×#106C22×C31semidirect
472. C2×C4⋊C8C22×C31semidirect
473. C2×C4⋊C8C22×C31semidirect
481. C2×#102C22×C31semidirect
482. C2×#102C22×C31semidirect
483. C2×#102C22×C31semidirect
484. C2×#102C22×C31semidirect
491. #390C22×C31semidirect
492. #389C22×C31semidirect
495. C4×C4⋊C4C22×C31semidirect
498. #340C22×C31semidirect
499. #340C22×C31semidirect
500. #336C22×C31semidirect
501. #336C22×C31semidirect
557. #121D4×C31semidirect
597. #102D4×C31semidirect
603. C31#25097direct (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×#4472
C2×C31×#4182
C31×#24332
C31×#23632
C31×#20652
C31×#20542
C31×#20412
C31×#20112
C31×#19822
C31×#19262
C31×#18792
C31×#18752
C31×#18512
#2509731