Finite Group Databasebeta

← C31×#25132 #21481891

Subgroups — C31×#25132 #21481891

Order 7936.

1314 conjugacy classes of subgroups.

The subgroup lattice has 892 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×#436C211yesmaximal, characteristic, complemented
4C2×C31×#418C211yesmaximal, characteristic, complemented
5C31×#2414C211yesmaximal, characteristic, complemented
6C31×#2408C211yesmaximal, characteristic, complemented
7C31×#2065C211yesmaximal, characteristic, complemented
8C31×#2054C211yesmaximal, characteristic, complemented
9C31×#2033C211yesmaximal, characteristic, complemented
10C31×#1999C211yesmaximal, characteristic, complemented
11C31×#1970C211yesmaximal, characteristic, complemented
12C31×#1934C211yesmaximal, characteristic, complemented
13C31×#1895C211yesmaximal, characteristic, complemented
14C31×#1895C211yesmaximal, characteristic, complemented
15C31×#1854C211yesmaximal, characteristic, complemented
16C23×D4×C31C2211yescharacteristic
17C22×D8×C31C2211yescharacteristic
18C22×D8×C31C2211yescharacteristic
19C22×M16×C31C2211yescharacteristic
20C22×M16×C31C2211yescharacteristic, complemented
21C2×C31×#121C2211yescharacteristic
22C2×C31×#121C2211yescharacteristic
23C2×C31×#121C2211yescharacteristic
24C2×C31×#121C2211yescharacteristic, complemented
25C2×C31×#120—21no—
26C2×C4×D4×C31C2211yescharacteristic
27C2×C31×#117C2211yescharacteristic
28C31×#469—24no—
29C31×#447—24no—
30C31×#436—24no—
31C2×C31×#107C2211yescharacteristic, complemented
32C2×C31×#106C2211yescharacteristic, complemented
33C2×C31×C4⋊C8C2211yescharacteristic, complemented
34C31×#418—24no—
35C2×C31×#102C2211yescharacteristic
36C2×C31×#102C2211yescharacteristic
37C2×C31×#102C2211yescharacteristic
38C2×C31×#102C2211yescharacteristic
39C2×C31×#102C2211yescharacteristic
40C2×C31×#102C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic, complemented
42C2×C31×#102C2211yescharacteristic, complemented
43C2×C31×C22⋊C8C2211yescharacteristic
44C2×C31×C22⋊C8C2211yescharacteristic, complemented
45C2×C4×C8×C31C2211yescharacteristic, complemented
46C31×#394—21no—
47C31×#394—21no—
48C31×#392—21no—
49C31×#392—21no—
50C31×#390—21no—
51C31×#390C2211yescharacteristic
52C31×#390C2211yescharacteristic
53C31×#390C2211yescharacteristic, complemented
54C31×#389C2211yescharacteristic, complemented
55C31×#388—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×C31C2311yescharacteristic
80C23×C4×C31C2311yescharacteristic
81C2×D8×C31—22no—
82C2×D8×C31—22no—
83C2×D8×C31—22no—
84C2×D8×C31—22no—
85C2×D8×C31—41no—
86C2×D8×C31—41no—
87C2×M16×C31—22no—
88C2×M16×C31—22no—
89C2×M16×C31—22no—
90C2×M16×C31—22no—
91C2×M16×C31—41no—
92C2×M16×C31—41no—
93C22×C8×C31C2311yescharacteristic
94C22×C8×C31C2311yescharacteristic
95C22×C8×C31C2311yescharacteristic
96C22×C8×C31C2311yescharacteristic
97C31×#121—22no—
98C31×#121—22no—
99C31×#121—22no—
100C31×#121—22no—
101C31×#121—22no—
102C31×#121—41no—
103C31×#121—41no—
104C31×#121—41no—
105C31×#120—44no—
106C4×D4×C31—22no—
107C4×D4×C31—22no—
108C31×#117—22no—
109C31×#117—41no—
110C2×C4⋊C4×C31—21no—
111C2×C4⋊C4×C31D411yescharacteristic
112C2×C4⋊C4×C31C2311yescharacteristic
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×C31—21no—
128C2×C22⋊C4×C31—21no—
129C2×C22⋊C4×C31—21no—
130C2×C22⋊C4×C31D411yescharacteristic
131C2×C22⋊C4×C31D411yescharacteristic
132C2×C42×C31—21no—
133C2×C42×C31C2311yescharacteristic
134C31×#107—41no—
135C31×#106—22no—
136C31×C4⋊C8—22no—
137C31×#102—22no—
138C31×#102—22no—
139C31×#102—22no—
140C31×#102—22no—
141C31×#102—22no—
142C31×#102—22no—
143C31×#102—41no—
144C31×#102D414yescomplemented
145C31×C22⋊C8—22no—
146C31×C22⋊C8D414yescomplemented
147C4×C8×C31—22no—
148C31×#95—21no—
149C31×#95—21no—
150C31×#95—21no—
151C24×C31—21no—
152C24×C31—21no—
153C24×C31—21no—
154C24×C31—42no—
155C24×C31—42no—
156C24×C31—42no—
157C24×C31—42no—
158C24×C31—42no—
159C24×C31—81no—
160C24×C31—81no—
161C24×C31C2×D411yescharacteristic
162C24×C31C2×D411yescharacteristic
163C2×D4×C31—28no—
164C2×D4×C31—22no—
165C2×D4×C31—22no—
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—44no—
183C2×D4×C31—44no—
184C2×D4×C31—41no—
185C2×D4×C31—42no—
186C2×D4×C31—42no—
187C2×D4×C31—44no—
188C2×D4×C31—42no—
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—81no—
197C2×D4×C31—81no—
198C2×D4×C31—81no—
199C2×D4×C31—81no—
200C2×D4×C31—81no—
201C2×D4×C31C2×D412yes—
202C2×D4×C31#4112yes—
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—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×C31C2×D411yescharacteristic
219C22×C4×C31C2×D411yescharacteristic
220C22×C4×C31C2×D411yescharacteristic
221C22×C4×C31C2×D412yes—
222C22×C4×C31C2×D411yescharacteristic
223C22×C4×C31#4112yes—
224C22×C4×C31C2411yescharacteristic
225D8×C31—44no—
226D8×C31—44no—
227M16×C31—44no—
228M16×C31—44no—
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×C31C2×D412yes—
239C2×C8×C31C2×D412yes—
240C2×C8×C31C2×D412yes—
241C4⋊C4×C31—22no—
242C4⋊C4×C31—21no—
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—21no—
251C4⋊C4×C31—81no—
252C4⋊C4×C31C2×D412yes—
253C22⋊C4×C31—22no—
254C22⋊C4×C31—22no—
255C22⋊C4×C31—42no—
256C22⋊C4×C31—42no—
257C22⋊C4×C31—42no—
258C22⋊C4×C31—42no—
259C22⋊C4×C31—42no—
260C22⋊C4×C31—42no—
261C22⋊C4×C31—42no—
262C22⋊C4×C31—42no—
263C22⋊C4×C31—42no—
264C22⋊C4×C31—81no—
265C22⋊C4×C31—81no—
266C22⋊C4×C31—81no—
267C22⋊C4×C31—81no—
268C42×C31—21no—
269C42×C31—21no—
270C42×C31—42no—
271#25132C3111yesmaximal, characteristic, direct product factor, Sylow
272C23×C31—21no—
273C23×C31—21no—
274C23×C31—21no—
275C23×C31—21no—
276C23×C31—21no—
277C23×C31—21no—
278C23×C31—21no—
279C23×C31—22no—
280C23×C31—21no—
281C23×C31—22no—
282C23×C31—21no—
283C23×C31—21no—
284C23×C31—21no—
285C23×C31—21no—
286C23×C31—21no—
287C23×C31—48no—
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—84no—
308C23×C31—84no—
309C23×C31—84no—
310C23×C31—84no—
311C23×C31—84no—
312C23×C31—84no—
313C23×C31#12112yes—
314C23×C31C22×D411yescharacteristic
315D4×C31—22no—
316D4×C31—22no—
317D4×C31—22no—
318D4×C31—22no—
319D4×C31—44no—
320D4×C31—48no—
321D4×C31—41no—
322D4×C31—41no—
323D4×C31—41no—
324D4×C31—41no—
325D4×C31—41no—
326D4×C31—41no—
327D4×C31—41no—
328D4×C31—41no—
329D4×C31—84no—
330D4×C31—84no—
331D4×C31—84no—
332D4×C31—84no—
333C2×C4×C31—21no—
334C2×C4×C31—21no—
335C2×C4×C31—21no—
336C2×C4×C31—21no—
337C2×C4×C31—22no—
338C2×C4×C31—22no—
339C2×C4×C31—22no—
340C2×C4×C31—22no—
341C2×C4×C31—21no—
342C2×C4×C31—21no—
343C2×C4×C31—22no—
344C2×C4×C31—21no—
345C2×C4×C31—21no—
346C2×C4×C31—21no—
347C2×C4×C31—21no—
348C2×C4×C31—41no—
349C2×C4×C31—41no—
350C2×C4×C31—41no—
351C2×C4×C31—41no—
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#12112yes—
367C2×C4×C31AGL(1,ℤ/8)12yes—
368C2×C4×C31C22×D411yescharacteristic
369C2×C4×C31C22×D411yescharacteristic
370C2×C4×C31C2×#4111yescharacteristic
371C2×C4×C31C2×#4111yescharacteristic
372C2×C4×C31H(5,𝔽2)11yescharacteristic
373C2×C4×C31H(5,𝔽2)11yescharacteristic
374C8×C31—22no—
375C8×C31—22no—
376C8×C31—22no—
377C8×C31—41no—
378C2×#469C2×C3111yescharacteristic, complemented
379C2×#447C2×C3111yescharacteristic, complemented
380C2×#436C2×C3111yescharacteristic, complemented
381C2×#418C2×C3111yescharacteristic, complemented
382#2414C2×C3111yescharacteristic, complemented
383#2408C2×C3111yescharacteristic, complemented
384#2065C2×C3111yescharacteristic, complemented
385#2054C2×C3111yescharacteristic, complemented
386#2033C2×C3111yescharacteristic, complemented
387#1999C2×C3111yescharacteristic, complemented
388#1970C2×C3111yescharacteristic, complemented
389#1934C2×C3111yescharacteristic, complemented
390#1895C2×C3111yescharacteristic, complemented
391#1895C2×C3111yescharacteristic, complemented
392#1854C2×C3111yescharacteristic, complemented
393C22×C31—22no—
394C22×C31—22no—
395C22×C31—22no—
396C22×C31—41no—
397C22×C31—41no—
398C22×C31—41no—
399C22×C31—41no—
400C22×C31—41no—
401C22×C31—42no—
402C22×C31—42no—
403C22×C31—41no—
404C22×C31—42no—
405C22×C31—41no—
406C22×C31—42no—
407C22×C31—41no—
408C22×C31—41no—
409C22×C31—41no—
410C22×C31—42no—
411C22×C31—41no—
412C22×C31—42no—
413C22×C31—816no—
414C22×C31—81no—
415C22×C31—81no—
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×C31C2×#12111yescharacteristic
430C22×C31D4211yescharacteristic
431C22×C31#54611yescharacteristic
432C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
433C22×C31#57511yescharacteristic
434C22×C31#57611yescharacteristic
435C22×C31#57611yescharacteristic
436C4×C31—22no—
437C4×C31—22no—
438C4×C31—41no—
439C4×C31—42no—
440C4×C31—41no—
441C4×C31—81no—
442C4×C31—81no—
443C4×C31—81no—
444C4×C31—81no—
445C4×C31#52511yescharacteristic
446C4×C31#53811yescharacteristic
447C4×C31D4211yescharacteristic
448C4×C31#54611yescharacteristic
449C23×D4C22×C3111yescharacteristic
450C22×D8C22×C3111yescharacteristic
451C22×D8C22×C3111yescharacteristic
452C22×M16C22×C3111yescharacteristic
453C22×M16C22×C3111yescharacteristic, complemented
454C2×#121C22×C3111yescharacteristic
455C2×#121C22×C3111yescharacteristic
456C2×#121C22×C3111yescharacteristic
457C2×#121C22×C3111yescharacteristic, complemented
458C2×#120—21no—
459C2×C4×D4C22×C3111yescharacteristic
460C2×#117C22×C3111yescharacteristic
461#469—24no—
462#447—24no—
463#436—24no—
464C2×#107C22×C3111yescharacteristic, complemented
465C2×#106C22×C3111yescharacteristic, complemented
466C2×C4⋊C8C22×C3111yescharacteristic, complemented
467#418—24no—
468C2×#102C22×C3111yescharacteristic
469C2×#102C22×C3111yescharacteristic
470C2×#102C22×C3111yescharacteristic
471C2×#102C22×C3111yescharacteristic
472C2×#102C22×C3111yescharacteristic
473C2×#102C22×C3111yescharacteristic
474C2×#102C22×C3111yescharacteristic, complemented
475C2×#102C22×C3111yescharacteristic, complemented
476C2×C22⋊C8C22×C3111yescharacteristic
477C2×C22⋊C8C22×C3111yescharacteristic, complemented
478C2×C4×C8C22×C3111yescharacteristic, complemented
479#394—21no—
480#394—21no—
481#392—21no—
482#392—21no—
483#390—21no—
484#390C22×C3111yescharacteristic
485#390C22×C3111yescharacteristic
486#390C22×C3111yescharacteristic, complemented
487#389C22×C3111yescharacteristic, complemented
488#388—21no—
489#380C22×C3111yescharacteristic
490#380C22×C3111yescharacteristic, complemented
491#379—21no—
492#340C22×C3111yescharacteristic, complemented
493#340C22×C3111yescharacteristic, complemented
494#340C22×C3111yescharacteristic, complemented
495#340C22×C3111yescharacteristic, complemented
496C2×C31—42no—
497C2×C31—81no—
498C2×C31—82no—
499C2×C31—82no—
500C2×C31—161no—
501C2×C31#242411yescharacteristic
502C2×C31#305511yescharacteristic
503C2×C31#305811yescharacteristic
504C2×C31#327311yescharacteristic
505C2×C31#327411yescharacteristic
506C2×C31#332211yescharacteristic
507C2×C31#332511yescharacteristic
508C25—21no—
509C22×D4—22no—
510C22×D4—22no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—22no—
516C22×D4—21no—
517C22×D4—22no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4D4×C3111yescharacteristic
521C22×D4C23×C3111yescharacteristic
522C22×D4C23×C3111yescharacteristic
523C22×D4C23×C3111yescharacteristic
524C23×C4C23×C3111yescharacteristic
525C23×C4C23×C3111yescharacteristic
526C2×D8—22no—
527C2×D8—22no—
528C2×D8—22no—
529C2×D8—22no—
530C2×D8—41no—
531C2×D8—41no—
532C2×M16—22no—
533C2×M16—22no—
534C2×M16—22no—
535C2×M16—22no—
536C2×M16—41no—
537C2×M16—41no—
538C22×C8C23×C3111yescharacteristic
539C22×C8C23×C3111yescharacteristic
540C22×C8C23×C3111yescharacteristic
541C22×C8C23×C3111yescharacteristic
542#121—22no—
543#121—22no—
544#121—22no—
545#121—22no—
546#121—22no—
547#121—41no—
548#121—41no—
549#121—41no—
550#120—44no—
551C4×D4—22no—
552C4×D4—22no—
553#117—22no—
554#117—41no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4D4×C3111yescharacteristic
557C2×C4⋊C4C23×C3111yescharacteristic
558C2×C4⋊C4C23×C3111yescharacteristic
559C2×C4⋊C4C23×C3111yescharacteristic
560C2×C4⋊C4C23×C3111yescharacteristic
561C2×C4⋊C4C23×C3111yescharacteristic
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
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⋊C4D4×C3111yescharacteristic
576C2×C22⋊C4D4×C3111yescharacteristic
577C2×C42—21no—
578C2×C42C23×C3111yescharacteristic
579#107—41no—
580#106—22no—
581C4⋊C8—22no—
582#102—22no—
583#102—22no—
584#102—22no—
585#102—22no—
586#102—22no—
587#102—22no—
588#102—41no—
589#102D4×C3114yescomplemented
590C22⋊C8—22no—
591C22⋊C8D4×C3114yescomplemented
592C4×C8—22no—
593#95—21no—
594#95—21no—
595#95—21no—
596C31#2513211yescharacteristic, direct product factor, Sylow
597C24—21no—
598C24—21no—
599C24—21no—
600C24—42no—
601C24—42no—
602C24—42no—
603C24—42no—
604C24—42no—
605C24—81no—
606C24—81no—
607C24C2×D4×C3111yescharacteristic
608C24C2×D4×C3111yescharacteristic
609C2×D4—28no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
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—44no—
629C2×D4—44no—
630C2×D4—41no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—44no—
634C2×D4—42no—
635C2×D4—42no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—81no—
643C2×D4—81no—
644C2×D4—81no—
645C2×D4—81no—
646C2×D4—81no—
647C2×D4C2×D4×C3112yes—
648C2×D4#41×C3112yes—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
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×C4C2×D4×C3111yescharacteristic
665C22×C4C2×D4×C3111yescharacteristic
666C22×C4C2×D4×C3111yescharacteristic
667C22×C4C2×D4×C3112yes—
668C22×C4C2×D4×C3111yescharacteristic
669C22×C4#41×C3112yes—
670C22×C4C24×C3111yescharacteristic
671D8—44no—
672D8—44no—
673M16—44no—
674M16—44no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8C2×D4×C3112yes—
685C2×C8C2×D4×C3112yes—
686C2×C8C2×D4×C3112yes—
687C4⋊C4—22no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—81no—
698C4⋊C4C2×D4×C3112yes—
699C22⋊C4—22no—
700C22⋊C4—22no—
701C22⋊C4—42no—
702C22⋊C4—42no—
703C22⋊C4—42no—
704C22⋊C4—42no—
705C22⋊C4—42no—
706C22⋊C4—42no—
707C22⋊C4—42no—
708C22⋊C4—42no—
709C22⋊C4—42no—
710C22⋊C4—81no—
711C22⋊C4—81no—
712C22⋊C4—81no—
713C22⋊C4—81no—
714C42—21no—
715C42—21no—
716C42—42no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—22no—
725C23—21no—
726C23—22no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—48no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
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—84no—
753C23—84no—
754C23—84no—
755C23—84no—
756C23—84no—
757C23—84no—
758C23C31×#12112yes—
759C23C22×D4×C3111yescharacteristic
760D4—22no—
761D4—22no—
762D4—22no—
763D4—22no—
764D4—44no—
765D4—48no—
766D4—41no—
767D4—41no—
768D4—41no—
769D4—41no—
770D4—41no—
771D4—41no—
772D4—41no—
773D4—41no—
774D4—84no—
775D4—84no—
776D4—84no—
777D4—84no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—22no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
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×C4C31×#12112yes—
812C2×C4C31×AGL(1,ℤ/8)12yes—
813C2×C4C22×D4×C3111yescharacteristic
814C2×C4C22×D4×C3111yescharacteristic
815C2×C4C2×#41×C3111yescharacteristic
816C2×C4C2×#41×C3111yescharacteristic
817C2×C4C31×H(5,𝔽2)11yescharacteristic
818C2×C4C31×H(5,𝔽2)11yescharacteristic
819C8—22no—
820C8—22no—
821C8—22no—
822C8—41no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—42no—
832C22—42no—
833C22—41no—
834C22—42no—
835C22—41no—
836C22—42no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—42no—
841C22—41no—
842C22—42no—
843C22—816no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22—81no—
850C22—81no—
851C22—81no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22C2×C31×#12111yescharacteristic
860C22D42×C3111yescharacteristic
861C22C31×#54611yescharacteristic
862C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
863C22C31×#57511yescharacteristic
864C22C31×#57611yescharacteristic
865C22C31×#57611yescharacteristic
866C4—22no—
867C4—22no—
868C4—41no—
869C4—42no—
870C4—41no—
871C4—81no—
872C4—81no—
873C4—81no—
874C4—81no—
875C4C31×#52511yescharacteristic
876C4C31×#53811yescharacteristic
877C4D42×C3111yescharacteristic
878C4C31×#54611yescharacteristic
879C2—42no—
880C2—81no—
881C2—82no—
882C2—82no—
883C2—161no—
884C2C31×#242411yescharacteristic
885C2C31×#305511yescharacteristic
886C2C31×#305811yescharacteristic
887C2C31×#327311yescharacteristic
888C2C31×#327411yescharacteristic
889C2C31×#332211yescharacteristic
890C2C31×#332511yescharacteristic
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×#436C2semidirect
4. C2×C31×#418C2semidirect
5. C31×#2414C2semidirect
6. C31×#2408C2semidirect
7. C31×#2065C2semidirect
8. C31×#2054C2semidirect
9. C31×#2033C2semidirect
10. C31×#1999C2semidirect
11. C31×#1970C2semidirect
12. C31×#1934C2semidirect
13. C31×#1895C2semidirect
14. C31×#1895C2semidirect
15. C31×#1854C2semidirect
20. C22×M16×C31C22semidirect
24. C2×C31×#121C22semidirect
31. C2×C31×#107C22semidirect
32. C2×C31×#106C22semidirect
33. C2×C31×C4⋊C8C22semidirect
41. C2×C31×#102C22semidirect
42. C2×C31×#102C22semidirect
44. C2×C31×C22⋊C8C22semidirect
45. C2×C4×C8×C31C22semidirect
53. C31×#390C22semidirect
54. C31×#389C22semidirect
57. C31×#380C22semidirect
59. C31×#340C22semidirect
60. C31×#340C22semidirect
61. C31×#340C22semidirect
62. C31×#340C22semidirect
144. C31×#102D4semidirect
146. C31×C22⋊C8D4semidirect
271. #25132C31direct (N × H)
378. C2×#469C2×C31semidirect
379. C2×#447C2×C31semidirect
380. C2×#436C2×C31semidirect
381. C2×#418C2×C31semidirect
382. #2414C2×C31semidirect
383. #2408C2×C31semidirect
384. #2065C2×C31semidirect
385. #2054C2×C31semidirect
386. #2033C2×C31semidirect
387. #1999C2×C31semidirect
388. #1970C2×C31semidirect
389. #1934C2×C31semidirect
390. #1895C2×C31semidirect
391. #1895C2×C31semidirect
392. #1854C2×C31semidirect
453. C22×M16C22×C31semidirect
457. C2×#121C22×C31semidirect
464. C2×#107C22×C31semidirect
465. C2×#106C22×C31semidirect
466. C2×C4⋊C8C22×C31semidirect
474. C2×#102C22×C31semidirect
475. C2×#102C22×C31semidirect
477. C2×C22⋊C8C22×C31semidirect
478. C2×C4×C8C22×C31semidirect
486. #390C22×C31semidirect
487. #389C22×C31semidirect
490. #380C22×C31semidirect
492. #340C22×C31semidirect
493. #340C22×C31semidirect
494. #340C22×C31semidirect
495. #340C22×C31semidirect
589. #102D4×C31semidirect
591. C22⋊C8D4×C31semidirect
596. C31#25132direct (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×#4472
C2×C31×#4362
C2×C31×#4182
C31×#24142
C31×#24082
C31×#20652
C31×#20542
C31×#20332
C31×#19992
C31×#19702
C31×#19342
C31×#18952
C31×#18542
#2513231