Finite Group Databasebeta

← C31×#25136 #21481895

Subgroups — C31×#25136 #21481895

Order 7936.

1264 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#468C211yesmaximal, characteristic, complemented
2C2×C31×#450C211yesmaximal, characteristic, complemented
3C2×C31×#436C211yesmaximal, characteristic, complemented
4C2×C31×#418C211yesmaximal, characteristic, complemented
5C31×#2415C211yesmaximal, characteristic, complemented
6C31×#2408C211yesmaximal, characteristic
7C31×#2067C211yesmaximal, characteristic, complemented
8C31×#2055C211yesmaximal, characteristic, complemented
9C31×#2034C211yesmaximal, characteristic, complemented
10C31×#2000C211yesmaximal, characteristic, complemented
11C31×#1968C211yesmaximal, characteristic, complemented
12C31×#1934C211yesmaximal, characteristic, complemented
13C31×#1895C211yesmaximal, characteristic, complemented
14C31×#1894C211yesmaximal, characteristic, complemented
15C31×#1854C211yesmaximal, characteristic, complemented
16C23×D4×C31C2211yescharacteristic
17C22×SD16×C31C2211yescharacteristic
18C22×SD16×C31C2211yescharacteristic
19C22×M16×C31C2211yescharacteristic
20C22×M16×C31C2211yescharacteristic, complemented
21C2×C31×C22⋊Q8C2211yescharacteristic
22C2×C31×C22⋊Q8C2211yescharacteristic, complemented
23C2×C31×#121C2211yescharacteristic
24C2×C31×#121C2211yescharacteristic
25C2×C31×#120—21no—
26C2×C4×D4×C31C2211yescharacteristic
27C2×C31×#117C2211yescharacteristic
28C31×#468—24no—
29C31×#450—24no—
30C31×#436—24no—
31C2×C31×#107C2211yescharacteristic, complemented
32C2×C31×#106C2211yescharacteristic, complemented
33C2×C31×C4⋊C8C2211yescharacteristic, complemented
34C31×#418—24no—
35C2×C31×#103C2211yescharacteristic, complemented
36C2×C31×#103C2211yescharacteristic, complemented
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, complemented
45C2×C4×C8×C31C2211yescharacteristic, complemented
46C31×#397—21no—
47C31×#394—21no—
48C31×#394—21no—
49C31×#392—21no—
50C31×#391C2211yescharacteristic, complemented
51C31×#390C2211yescharacteristic
52C31×#390C2211yescharacteristic
53C31×#389—21no—
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×Q8×C31C2311yescharacteristic
65C22×D4×C31—22no—
66C22×D4×C31—22no—
67C22×D4×C31—21no—
68C22×D4×C31—21no—
69C22×D4×C31—22no—
70C22×D4×C31—21no—
71C22×D4×C31—22no—
72C22×D4×C31—41no—
73C22×D4×C31—41no—
74C22×D4×C31D411yescharacteristic
75C22×D4×C31C2311yescharacteristic
76C22×D4×C31C2311yescharacteristic
77C23×C4×C31C2311yescharacteristic
78C23×C4×C31C2311yescharacteristic
79C2×SD16×C31—22no—
80C2×SD16×C31—22no—
81C2×SD16×C31—22no—
82C2×SD16×C31—22no—
83C2×SD16×C31—41no—
84C2×SD16×C31—41no—
85C2×M16×C31—22no—
86C2×M16×C31—22no—
87C2×M16×C31—22no—
88C2×M16×C31—22no—
89C2×M16×C31—41no—
90C2×M16×C31—41no—
91C22×C8×C31C2311yescharacteristic
92C22×C8×C31C2311yescharacteristic
93C22×C8×C31C2311yescharacteristic
94C22×C8×C31C2311yescharacteristic
95C31×C22⋊Q8—22no—
96C31×C22⋊Q8—22no—
97C31×C22⋊Q8—22no—
98C31×C22⋊Q8—41no—
99C31×#121—22no—
100C31×#121—22no—
101C31×#121—41no—
102C31×#121—41no—
103C31×#120—44no—
104C4×D4×C31—22no—
105C4×D4×C31—22no—
106C31×#117—22no—
107C31×#117—41no—
108C2×C4⋊C4×C31—21no—
109C2×C4⋊C4×C31—21no—
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×C31D411yescharacteristic
129C2×C22⋊C4×C31D411yescharacteristic
130C2×C42×C31—21no—
131C2×C42×C31C2311yescharacteristic
132C31×#107—22no—
133C31×#106—41no—
134C31×C4⋊C8—22no—
135C31×#103—22no—
136C31×#103—41no—
137C31×#102—22no—
138C31×#102—22no—
139C31×#102—22no—
140C31×#102—22no—
141C31×#102—22no—
142C31×#102D414yescomplemented
143C31×C22⋊C8—22no—
144C31×C22⋊C8D414yescomplemented
145C4×C8×C31—22no—
146C31×#95—21no—
147C31×#95—21no—
148C31×#95—21no—
149C31×#95—21no—
150C31×#95—21no—
151C24×C31—21no—
152C24×C31—21no—
153C24×C31—42no—
154C24×C31—42no—
155C24×C31—42no—
156C24×C31—42no—
157C24×C31—42no—
158C24×C31—81no—
159C24×C31—81no—
160C24×C31C2×D411yescharacteristic
161C24×C31C2×D411yescharacteristic
162C2×Q8×C31—21no—
163C2×Q8×C31—21no—
164C2×Q8×C31—21no—
165C2×Q8×C31—21no—
166C2×Q8×C31—21no—
167C2×Q8×C31—21no—
168C2×D4×C31—28no—
169C2×D4×C31—22no—
170C2×D4×C31—22no—
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—44no—
182C2×D4×C31—44no—
183C2×D4×C31—41no—
184C2×D4×C31—42no—
185C2×D4×C31—42no—
186C2×D4×C31—44no—
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×C31C2×D412yes—
195C2×D4×C31#4112yes—
196C22×C4×C31—21no—
197C22×C4×C31—21no—
198C22×C4×C31—21no—
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—21no—
211C22×C4×C31—21no—
212C22×C4×C31C2×D411yescharacteristic
213C22×C4×C31C2×D411yescharacteristic
214C22×C4×C31C2×D411yescharacteristic
215C22×C4×C31C2×D412yes—
216C22×C4×C31C2×D411yescharacteristic
217C22×C4×C31#4112yes—
218C22×C4×C31C2411yescharacteristic
219SD16×C31—44no—
220SD16×C31—44no—
221M16×C31—44no—
222M16×C31—44no—
223C2×C8×C31—21no—
224C2×C8×C31—21no—
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×C31C2×D412yes—
233C2×C8×C31C2×D412yes—
234C2×C8×C31C2×D412yes—
235C4⋊C4×C31—22no—
236C4⋊C4×C31—21no—
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—21no—
245C4⋊C4×C31—42no—
246C4⋊C4×C31—42no—
247C4⋊C4×C31—42no—
248C4⋊C4×C31C2×D412yes—
249C22⋊C4×C31—22no—
250C22⋊C4×C31—22no—
251C22⋊C4×C31—42no—
252C22⋊C4×C31—42no—
253C22⋊C4×C31—42no—
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—42no—
265#25136C3111yesmaximal, characteristic, direct product factor, Sylow
266C23×C31—21no—
267C23×C31—21no—
268C23×C31—21no—
269C23×C31—21no—
270C23×C31—21no—
271C23×C31—21no—
272C23×C31—21no—
273C23×C31—21no—
274C23×C31—22no—
275C23×C31—22no—
276C23×C31—21no—
277C23×C31—21no—
278C23×C31—21no—
279C23×C31—21no—
280C23×C31—21no—
281C23×C31—48no—
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—84no—
295C23×C31—84no—
296C23×C31—84no—
297C23×C31—84no—
298C23×C31—84no—
299C23×C31—84no—
300C23×C31#12112yes—
301C23×C31C22×D411yescharacteristic
302Q8×C31—41no—
303Q8×C31—41no—
304Q8×C31—41no—
305Q8×C31—41no—
306D4×C31—22no—
307D4×C31—22no—
308D4×C31—22no—
309D4×C31—22no—
310D4×C31—44no—
311D4×C31—48no—
312D4×C31—41no—
313D4×C31—41no—
314D4×C31—41no—
315D4×C31—41no—
316D4×C31—84no—
317D4×C31—84no—
318C2×C4×C31—21no—
319C2×C4×C31—21no—
320C2×C4×C31—21no—
321C2×C4×C31—21no—
322C2×C4×C31—22no—
323C2×C4×C31—22no—
324C2×C4×C31—22no—
325C2×C4×C31—22no—
326C2×C4×C31—21no—
327C2×C4×C31—21no—
328C2×C4×C31—22no—
329C2×C4×C31—21no—
330C2×C4×C31—21no—
331C2×C4×C31—21no—
332C2×C4×C31—21no—
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—41no—
351C2×C4×C31—41no—
352C2×C4×C31—41no—
353C2×C4×C31—41no—
354C2×C4×C31#12112yes—
355C2×C4×C31AGL(1,ℤ/8)12yes—
356C2×C4×C31C22×D411yescharacteristic
357C2×C4×C31C22×D411yescharacteristic
358C2×C4×C31C2×#4111yescharacteristic
359C2×C4×C31C2×#4111yescharacteristic
360C2×C4×C31H(5,𝔽2)11yescharacteristic
361C2×C4×C31H(5,𝔽2)11yescharacteristic
362C8×C31—22no—
363C8×C31—22no—
364C8×C31—22no—
365C8×C31—41no—
366C2×#468C2×C3111yescharacteristic, complemented
367C2×#450C2×C3111yescharacteristic, complemented
368C2×#436C2×C3111yescharacteristic, complemented
369C2×#418C2×C3111yescharacteristic, complemented
370#2415C2×C3111yescharacteristic, complemented
371#2408C2×C3111yescharacteristic
372#2067C2×C3111yescharacteristic, complemented
373#2055C2×C3111yescharacteristic, complemented
374#2034C2×C3111yescharacteristic, complemented
375#2000C2×C3111yescharacteristic, complemented
376#1968C2×C3111yescharacteristic, complemented
377#1934C2×C3111yescharacteristic, complemented
378#1895C2×C3111yescharacteristic, complemented
379#1894C2×C3111yescharacteristic, complemented
380#1854C2×C3111yescharacteristic, complemented
381C22×C31—22no—
382C22×C31—22no—
383C22×C31—22no—
384C22×C31—41no—
385C22×C31—41no—
386C22×C31—41no—
387C22×C31—41no—
388C22×C31—41no—
389C22×C31—42no—
390C22×C31—42no—
391C22×C31—41no—
392C22×C31—42no—
393C22×C31—41no—
394C22×C31—42no—
395C22×C31—41no—
396C22×C31—41no—
397C22×C31—41no—
398C22×C31—42no—
399C22×C31—41no—
400C22×C31—42no—
401C22×C31—816no—
402C22×C31—81no—
403C22×C31—81no—
404C22×C31—81no—
405C22×C31—81no—
406C22×C31—81no—
407C22×C31—81no—
408C22×C31—81no—
409C22×C31—81no—
410C22×C31C2×#12111yescharacteristic
411C22×C31D4211yescharacteristic
412C22×C31#54611yescharacteristic
413C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
414C22×C31#57511yescharacteristic
415C22×C31#57711yescharacteristic
416C22×C31#57711yescharacteristic
417C4×C31—22no—
418C4×C31—22no—
419C4×C31—41no—
420C4×C31—42no—
421C4×C31—41no—
422C4×C31—81no—
423C4×C31—81no—
424C4×C31—81no—
425C4×C31—81no—
426C4×C31—81no—
427C4×C31#52511yescharacteristic
428C4×C31#53811yescharacteristic
429C4×C31D4211yescharacteristic
430C4×C31#54611yescharacteristic
431C23×D4C22×C3111yescharacteristic
432C22×SD16C22×C3111yescharacteristic
433C22×SD16C22×C3111yescharacteristic
434C22×M16C22×C3111yescharacteristic
435C22×M16C22×C3111yescharacteristic, complemented
436C2×C22⋊Q8C22×C3111yescharacteristic
437C2×C22⋊Q8C22×C3111yescharacteristic, complemented
438C2×#121C22×C3111yescharacteristic
439C2×#121C22×C3111yescharacteristic
440C2×#120—21no—
441C2×C4×D4C22×C3111yescharacteristic
442C2×#117C22×C3111yescharacteristic
443#468—24no—
444#450—24no—
445#436—24no—
446C2×#107C22×C3111yescharacteristic, complemented
447C2×#106C22×C3111yescharacteristic, complemented
448C2×C4⋊C8C22×C3111yescharacteristic, complemented
449#418—24no—
450C2×#103C22×C3111yescharacteristic, complemented
451C2×#103C22×C3111yescharacteristic, complemented
452C2×#102C22×C3111yescharacteristic
453C2×#102C22×C3111yescharacteristic
454C2×#102C22×C3111yescharacteristic
455C2×#102C22×C3111yescharacteristic
456C2×#102C22×C3111yescharacteristic
457C2×#102C22×C3111yescharacteristic
458C2×C22⋊C8C22×C3111yescharacteristic
459C2×C22⋊C8C22×C3111yescharacteristic, complemented
460C2×C4×C8C22×C3111yescharacteristic, complemented
461#397—21no—
462#394—21no—
463#394—21no—
464#392—21no—
465#391C22×C3111yescharacteristic, complemented
466#390C22×C3111yescharacteristic
467#390C22×C3111yescharacteristic
468#389—21no—
469#389C22×C3111yescharacteristic, complemented
470#388—21no—
471#380C22×C3111yescharacteristic
472#380C22×C3111yescharacteristic, complemented
473#379—21no—
474#340C22×C3111yescharacteristic, complemented
475#340C22×C3111yescharacteristic, complemented
476#340C22×C3111yescharacteristic, complemented
477#340C22×C3111yescharacteristic, complemented
478C2×C31—42no—
479C2×C31—81no—
480C2×C31—82no—
481C2×C31—82no—
482C2×C31#242411yescharacteristic
483C2×C31#305511yescharacteristic
484C2×C31#305711yescharacteristic
485C2×C31#327211yescharacteristic
486C2×C31#327511yescharacteristic
487C2×C31#332311yescharacteristic
488C2×C31#332411yescharacteristic
489C25—21no—
490C22×Q8C23×C3111yescharacteristic
491C22×D4—22no—
492C22×D4—22no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—22no—
496C22×D4—21no—
497C22×D4—22no—
498C22×D4—41no—
499C22×D4—41no—
500C22×D4D4×C3111yescharacteristic
501C22×D4C23×C3111yescharacteristic
502C22×D4C23×C3111yescharacteristic
503C23×C4C23×C3111yescharacteristic
504C23×C4C23×C3111yescharacteristic
505C2×SD16—22no—
506C2×SD16—22no—
507C2×SD16—22no—
508C2×SD16—22no—
509C2×SD16—41no—
510C2×SD16—41no—
511C2×M16—22no—
512C2×M16—22no—
513C2×M16—22no—
514C2×M16—22no—
515C2×M16—41no—
516C2×M16—41no—
517C22×C8C23×C3111yescharacteristic
518C22×C8C23×C3111yescharacteristic
519C22×C8C23×C3111yescharacteristic
520C22×C8C23×C3111yescharacteristic
521C22⋊Q8—22no—
522C22⋊Q8—22no—
523C22⋊Q8—22no—
524C22⋊Q8—41no—
525#121—22no—
526#121—22no—
527#121—41no—
528#121—41no—
529#120—44no—
530C4×D4—22no—
531C4×D4—22no—
532#117—22no—
533#117—41no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4D4×C3111yescharacteristic
538C2×C4⋊C4C23×C3111yescharacteristic
539C2×C4⋊C4C23×C3111yescharacteristic
540C2×C4⋊C4C23×C3111yescharacteristic
541C2×C4⋊C4C23×C3111yescharacteristic
542C2×C4⋊C4C23×C3111yescharacteristic
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⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4D4×C3111yescharacteristic
555C2×C22⋊C4D4×C3111yescharacteristic
556C2×C42—21no—
557C2×C42C23×C3111yescharacteristic
558#107—22no—
559#106—41no—
560C4⋊C8—22no—
561#103—22no—
562#103—41no—
563#102—22no—
564#102—22no—
565#102—22no—
566#102—22no—
567#102—22no—
568#102D4×C3114yescomplemented
569C22⋊C8—22no—
570C22⋊C8D4×C3114yescomplemented
571C4×C8—22no—
572#95—21no—
573#95—21no—
574#95—21no—
575#95—21no—
576#95—21no—
577C31#2513611yescharacteristic, direct product factor, Sylow
578C24—21no—
579C24—21no—
580C24—42no—
581C24—42no—
582C24—42no—
583C24—42no—
584C24—42no—
585C24—81no—
586C24—81no—
587C24C2×D4×C3111yescharacteristic
588C24C2×D4×C3111yescharacteristic
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×D4—28no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—44no—
609C2×D4—44no—
610C2×D4—41no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—44no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—81no—
620C2×D4—81no—
621C2×D4C2×D4×C3112yes—
622C2×D4#41×C3112yes—
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—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4C2×D4×C3111yescharacteristic
640C22×C4C2×D4×C3111yescharacteristic
641C22×C4C2×D4×C3111yescharacteristic
642C22×C4C2×D4×C3112yes—
643C22×C4C2×D4×C3111yescharacteristic
644C22×C4#41×C3112yes—
645C22×C4C24×C3111yescharacteristic
646SD16—44no—
647SD16—44no—
648M16—44no—
649M16—44no—
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×C8—21no—
659C2×C8C2×D4×C3112yes—
660C2×C8C2×D4×C3112yes—
661C2×C8C2×D4×C3112yes—
662C4⋊C4—22no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—42no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C4⋊C4C2×D4×C3112yes—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—42no—
687C22⋊C4—81no—
688C22⋊C4—81no—
689C42—21no—
690C42—21no—
691C42—42no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—22no—
701C23—22no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—48no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—84no—
721C23—84no—
722C23—84no—
723C23—84no—
724C23—84no—
725C23—84no—
726C23C31×#12112yes—
727C23C22×D4×C3111yescharacteristic
728Q8—41no—
729Q8—41no—
730Q8—41no—
731Q8—41no—
732D4—22no—
733D4—22no—
734D4—22no—
735D4—22no—
736D4—44no—
737D4—48no—
738D4—41no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—84no—
743D4—84no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
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—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4C31×#12112yes—
781C2×C4C31×AGL(1,ℤ/8)12yes—
782C2×C4C22×D4×C3111yescharacteristic
783C2×C4C22×D4×C3111yescharacteristic
784C2×C4C2×#41×C3111yescharacteristic
785C2×C4C2×#41×C3111yescharacteristic
786C2×C4C31×H(5,𝔽2)11yescharacteristic
787C2×C4C31×H(5,𝔽2)11yescharacteristic
788C8—22no—
789C8—22no—
790C8—22no—
791C8—41no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—42no—
801C22—42no—
802C22—41no—
803C22—42no—
804C22—41no—
805C22—42no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—42no—
810C22—41no—
811C22—42no—
812C22—816no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22C2×C31×#12111yescharacteristic
822C22D42×C3111yescharacteristic
823C22C31×#54611yescharacteristic
824C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
825C22C31×#57511yescharacteristic
826C22C31×#57711yescharacteristic
827C22C31×#57711yescharacteristic
828C4—22no—
829C4—22no—
830C4—41no—
831C4—42no—
832C4—41no—
833C4—81no—
834C4—81no—
835C4—81no—
836C4—81no—
837C4—81no—
838C4C31×#52511yescharacteristic
839C4C31×#53811yescharacteristic
840C4D42×C3111yescharacteristic
841C4C31×#54611yescharacteristic
842C2—42no—
843C2—81no—
844C2—82no—
845C2—82no—
846C2C31×#242411yescharacteristic
847C2C31×#305511yescharacteristic
848C2C31×#305711yescharacteristic
849C2C31×#327211yescharacteristic
850C2C31×#327511yescharacteristic
851C2C31×#332311yescharacteristic
852C2C31×#332411yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#2408C2
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×#468C2semidirect
2. C2×C31×#450C2semidirect
3. C2×C31×#436C2semidirect
4. C2×C31×#418C2semidirect
5. C31×#2415C2semidirect
7. C31×#2067C2semidirect
8. C31×#2055C2semidirect
9. C31×#2034C2semidirect
10. C31×#2000C2semidirect
11. C31×#1968C2semidirect
12. C31×#1934C2semidirect
13. C31×#1895C2semidirect
14. C31×#1894C2semidirect
15. C31×#1854C2semidirect
20. C22×M16×C31C22semidirect
22. C2×C31×C22⋊Q8C22semidirect
31. C2×C31×#107C22semidirect
32. C2×C31×#106C22semidirect
33. C2×C31×C4⋊C8C22semidirect
35. C2×C31×#103C22semidirect
36. C2×C31×#103C22semidirect
44. C2×C31×C22⋊C8C22semidirect
45. C2×C4×C8×C31C22semidirect
50. C31×#391C22semidirect
54. C31×#389C22semidirect
57. C31×#380C22semidirect
59. C31×#340C22semidirect
60. C31×#340C22semidirect
61. C31×#340C22semidirect
62. C31×#340C22semidirect
142. C31×#102D4semidirect
144. C31×C22⋊C8D4semidirect
265. #25136C31direct (N × H)
366. C2×#468C2×C31semidirect
367. C2×#450C2×C31semidirect
368. C2×#436C2×C31semidirect
369. C2×#418C2×C31semidirect
370. #2415C2×C31semidirect
372. #2067C2×C31semidirect
373. #2055C2×C31semidirect
374. #2034C2×C31semidirect
375. #2000C2×C31semidirect
376. #1968C2×C31semidirect
377. #1934C2×C31semidirect
378. #1895C2×C31semidirect
379. #1894C2×C31semidirect
380. #1854C2×C31semidirect
435. C22×M16C22×C31semidirect
437. C2×C22⋊Q8C22×C31semidirect
446. C2×#107C22×C31semidirect
447. C2×#106C22×C31semidirect
448. C2×C4⋊C8C22×C31semidirect
450. C2×#103C22×C31semidirect
451. C2×#103C22×C31semidirect
459. C2×C22⋊C8C22×C31semidirect
460. C2×C4×C8C22×C31semidirect
465. #391C22×C31semidirect
469. #389C22×C31semidirect
472. #380C22×C31semidirect
474. #340C22×C31semidirect
475. #340C22×C31semidirect
476. #340C22×C31semidirect
477. #340C22×C31semidirect
568. #102D4×C31semidirect
570. C22⋊C8D4×C31semidirect
577. C31#25136direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4682
C2×C31×#4502
C2×C31×#4362
C2×C31×#4182
C31×#24152
C31×#24082
C31×#20672
C31×#20552
C31×#20342
C31×#20002
C31×#19682
C31×#19342
C31×#18952
C31×#18942
C31×#18542
#2513631