Finite Group Databasebeta

← C31×#26151 #21482910

Subgroups — C31×#26151 #21482910

Order 7936.

854 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#485C211yesmaximal, characteristic, complemented
2C2×C31×#428C211yesmaximal, characteristic, complemented
3C31×#2417C211yesmaximal, characteristic
4C31×#2354C211yesmaximal, characteristic
5C31×#2095C211yesmaximal, characteristic, complemented
6C31×#2083C211yesmaximal, characteristic, complemented
7C31×#2075C211yesmaximal, characteristic, complemented
8C31×#2036C211yesmaximal, characteristic, complemented
9C31×#1927C211yesmaximal, characteristic, complemented
10C31×#1920C211yesmaximal, characteristic, complemented
11C31×#1894C211yesmaximal, characteristic, complemented
12C31×#1873C211yesmaximal, characteristic, complemented
13C31×#1870C211yesmaximal, characteristic
14C31×#1854C211yesmaximal, characteristic, complemented
15C31×#1852C211yesmaximal, characteristic, complemented
16C22×M16×C31C2211yescharacteristic
17C2×C31×C22⋊Q8C2211yescharacteristic
18C2×C31×C22⋊Q8C2211yescharacteristic
19C2×C4×D4×C31C2211yescharacteristic
20C2×C31×#117C2211yescharacteristic
21C2×C31×#117C2211yescharacteristic
22C22×C4⋊C4×C31C2211yescharacteristic
23C31×#485—24no—
24C31×#428—24no—
25C2×C31×#107C2211yescharacteristic
26C2×C31×#107C2211yescharacteristic
27C2×C31×#107C2211yescharacteristic
28C2×C31×#107C2211yescharacteristic
29C2×C31×#106C2211yescharacteristic
30C2×C31×#106C2211yescharacteristic
31C2×C31×#103C2211yescharacteristic
32C2×C31×#103C2211yescharacteristic
33C2×C31×#103C2211yescharacteristic
34C2×C31×#103C2211yescharacteristic
35C2×C31×C22⋊C8C2211yescharacteristic
36C2×C31×C22⋊C8C2211yescharacteristic
37C2×C31×C22⋊C8C2211yescharacteristic
38C31×#398—21no—
39C31×#396—21no—
40C31×#391C2211yescharacteristic
41C31×#390—21no—
42C31×#389C2211yescharacteristic
43C31×#388—21no—
44C31×#388—21no—
45C31×#386—21no—
46C31×#384C2211yescharacteristic
47C31×#380—21no—
48C31×#380C2211yescharacteristic
49C31×#380C2211yescharacteristic
50C31×#380C2211yescharacteristic
51C4×C4⋊C4×C31—21no—
52C4×C4⋊C4×C31C2211yescharacteristic
53C31×#340C2211yescharacteristic
54C31×#340C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#336C2211yescharacteristic
60C31×#336C2211yescharacteristic
61C22×Q8×C31C2311yescharacteristic
62C22×D4×C31D411yescharacteristic
63C23×C4×C31—21no—
64C23×C4×C31C2311yescharacteristic
65C23×C4×C31C2311yescharacteristic
66C2×M16×C31—22no—
67C2×M16×C31—22no—
68C2×M16×C31—22no—
69C22×C8×C31C2311yescharacteristic
70C22×C8×C31C2311yescharacteristic
71C22×C8×C31C2311yescharacteristic
72C22×C8×C31C2311yescharacteristic
73C31×C22⋊Q8—22no—
74C31×C22⋊Q8—22no—
75C31×C22⋊Q8—22no—
76C31×C22⋊Q8—41no—
77C4×D4×C31—22no—
78C4×D4×C31—22no—
79C31×#117—22no—
80C31×#117—22no—
81C31×#117—41no—
82C31×#117—41no—
83C2×C4⋊C4×C31—22no—
84C2×C4⋊C4×C31—21no—
85C2×C4⋊C4×C31—21no—
86C2×C4⋊C4×C31—21no—
87C2×C4⋊C4×C31—21no—
88C2×C4⋊C4×C31—21no—
89C2×C4⋊C4×C31—21no—
90C2×C4⋊C4×C31—41no—
91C2×C4⋊C4×C31D411yescharacteristic
92C2×C4⋊C4×C31C2311yescharacteristic
93C2×C4⋊C4×C31C2311yescharacteristic
94C2×C4⋊C4×C31C2311yescharacteristic
95C2×C4⋊C4×C31C2311yescharacteristic
96C2×C4⋊C4×C31C2311yescharacteristic
97C2×C4⋊C4×C31C2311yescharacteristic
98C2×C4⋊C4×C31C2311yescharacteristic
99C2×C22⋊C4×C31—21no—
100C2×C22⋊C4×C31—21no—
101C2×C22⋊C4×C31—21no—
102C2×C22⋊C4×C31—21no—
103C2×C22⋊C4×C31—21no—
104C2×C22⋊C4×C31—21no—
105C2×C22⋊C4×C31—21no—
106C2×C22⋊C4×C31D411yescharacteristic
107C2×C22⋊C4×C31D411yescharacteristic
108C2×C42×C31—21no—
109C2×C42×C31—21no—
110C2×C42×C31—21no—
111C2×C42×C31C2311yescharacteristic
112C31×#107—22no—
113C31×#107—22no—
114C31×#107—22no—
115C31×#107—41no—
116C31×#106—22no—
117C31×#106D414yescomplemented
118C31×#103—22no—
119C31×#103—22no—
120C31×#103—22no—
121C31×#103—41no—
122C31×C22⋊C8—22no—
123C31×C22⋊C8—22no—
124C31×C22⋊C8—22no—
125C31×#95—21no—
126C31×#95—21no—
127C31×#95—21no—
128C31×#95—21no—
129C31×#95—21no—
130C31×#95—21no—
131C31×#95—21no—
132C24×C31C2×D411yescharacteristic
133C24×C31C2×D411yescharacteristic
134C2×Q8×C31—21no—
135C2×Q8×C31—21no—
136C2×Q8×C31—21no—
137C2×Q8×C31—21no—
138C2×Q8×C31—21no—
139C2×Q8×C31—21no—
140C2×D4×C31—22no—
141C2×D4×C31—22no—
142C2×D4×C31—41no—
143C22×C4×C31—21no—
144C22×C4×C31—21no—
145C22×C4×C31—21no—
146C22×C4×C31—21no—
147C22×C4×C31—21no—
148C22×C4×C31—21no—
149C22×C4×C31—21no—
150C22×C4×C31—21no—
151C22×C4×C31—21no—
152C22×C4×C31—21no—
153C22×C4×C31—21no—
154C22×C4×C31—21no—
155C22×C4×C31—21no—
156C22×C4×C31—21no—
157C22×C4×C31—21no—
158C22×C4×C31—21no—
159C22×C4×C31—21no—
160C22×C4×C31—21no—
161C22×C4×C31—42no—
162C22×C4×C31—42no—
163C22×C4×C31—81no—
164C22×C4×C31C2×D411yescharacteristic
165C22×C4×C31C2×D411yescharacteristic
166C22×C4×C31C2×D411yescharacteristic
167C22×C4×C31C2×D411yescharacteristic
168C22×C4×C31#4112yes—
169C22×C4×C31#4112yes—
170C22×C4×C31C2411yescharacteristic
171M16×C31—28no—
172C2×C8×C31—21no—
173C2×C8×C31—21no—
174C2×C8×C31—21no—
175C2×C8×C31—21no—
176C2×C8×C31—21no—
177C2×C8×C31—21no—
178C2×C8×C31—21no—
179C2×C8×C31—21no—
180C2×C8×C31—21no—
181C2×C8×C31—21no—
182C2×C8×C31C2×D412yes—
183C2×C8×C31#4112yes—
184C4⋊C4×C31—22no—
185C4⋊C4×C31—21no—
186C4⋊C4×C31—21no—
187C4⋊C4×C31—21no—
188C4⋊C4×C31—21no—
189C4⋊C4×C31—21no—
190C4⋊C4×C31—21no—
191C4⋊C4×C31—21no—
192C4⋊C4×C31—21no—
193C4⋊C4×C31—21no—
194C4⋊C4×C31—21no—
195C4⋊C4×C31—21no—
196C4⋊C4×C31—21no—
197C4⋊C4×C31—42no—
198C4⋊C4×C31—42no—
199C4⋊C4×C31—42no—
200C4⋊C4×C31—42no—
201C4⋊C4×C31—81no—
202C4⋊C4×C31—81no—
203C4⋊C4×C31C2×D412yes—
204C4⋊C4×C31C2×D412yes—
205C22⋊C4×C31—22no—
206C22⋊C4×C31—22no—
207C22⋊C4×C31—42no—
208C22⋊C4×C31—42no—
209C22⋊C4×C31—42no—
210C22⋊C4×C31—42no—
211C22⋊C4×C31—81no—
212C22⋊C4×C31—81no—
213C22⋊C4×C31—81no—
214C42×C31—21no—
215C42×C31—21no—
216C42×C31—42no—
217C42×C31—42no—
218C42×C31—42no—
219#26151C3111yesmaximal, characteristic, direct product factor, Sylow
220C23×C31—21no—
221C23×C31—21no—
222C23×C31—21no—
223C23×C31—21no—
224C23×C31—21no—
225C23×C31—21no—
226C23×C31—21no—
227C23×C31—21no—
228C23×C31—21no—
229C23×C31—21no—
230C23×C31—21no—
231C23×C31—21no—
232C23×C31—21no—
233C23×C31#12312yes—
234C23×C31C22×D411yescharacteristic
235Q8×C31—41no—
236Q8×C31—41no—
237Q8×C31—41no—
238Q8×C31—41no—
239D4×C31—44no—
240C2×C4×C31—21no—
241C2×C4×C31—21no—
242C2×C4×C31—21no—
243C2×C4×C31—21no—
244C2×C4×C31—22no—
245C2×C4×C31—22no—
246C2×C4×C31—22no—
247C2×C4×C31—22no—
248C2×C4×C31—21no—
249C2×C4×C31—21no—
250C2×C4×C31—22no—
251C2×C4×C31—21no—
252C2×C4×C31—22no—
253C2×C4×C31—21no—
254C2×C4×C31—21no—
255C2×C4×C31—21no—
256C2×C4×C31—41no—
257C2×C4×C31—41no—
258C2×C4×C31—41no—
259C2×C4×C31—41no—
260C2×C4×C31—41no—
261C2×C4×C31—41no—
262C2×C4×C31—41no—
263C2×C4×C31—41no—
264C2×C4×C31—41no—
265C2×C4×C31—41no—
266C2×C4×C31—41no—
267C2×C4×C31—41no—
268C2×C4×C31—41no—
269C2×C4×C31—41no—
270C2×C4×C31—41no—
271C2×C4×C31—41no—
272C2×C4×C31—41no—
273C2×C4×C31—41no—
274C2×C4×C31—41no—
275C2×C4×C31—41no—
276C2×C4×C31—41no—
277C2×C4×C31—41no—
278C2×C4×C31—41no—
279C2×C4×C31—41no—
280C2×C4×C31—41no—
281C2×C4×C31—41no—
282C2×C4×C31—84no—
283C2×C4×C31#12312yes—
284C2×C4×C31#13712yes—
285C2×C4×C31C22×D411yescharacteristic
286C2×C4×C31C2×#4111yescharacteristic
287C2×C4×C31C2×#4111yescharacteristic
288C2×C4×C31C2×#4111yescharacteristic
289C2×C4×C31H(5,𝔽2)11yescharacteristic
290C2×C4×C312−1+411yescharacteristic
291C8×C31—22no—
292C8×C31—22no—
293C8×C31—41no—
294C8×C31—41no—
295C2×#485C2×C3111yescharacteristic, complemented
296C2×#428C2×C3111yescharacteristic, complemented
297#2417C2×C3111yescharacteristic
298#2354C2×C3111yescharacteristic
299#2095C2×C3111yescharacteristic, complemented
300#2083C2×C3111yescharacteristic, complemented
301#2075C2×C3111yescharacteristic, complemented
302#2036C2×C3111yescharacteristic, complemented
303#1927C2×C3111yescharacteristic, complemented
304#1920C2×C3111yescharacteristic, complemented
305#1894C2×C3111yescharacteristic, complemented
306#1873C2×C3111yescharacteristic, complemented
307#1870C2×C3111yescharacteristic
308#1854C2×C3111yescharacteristic, complemented
309#1852C2×C3111yescharacteristic, complemented
310C22×C31—22no—
311C22×C31—22no—
312C22×C31—22no—
313C22×C31—41no—
314C22×C31—41no—
315C22×C31—41no—
316C22×C31—41no—
317C22×C31—41no—
318C22×C31—41no—
319C22×C31—41no—
320C22×C31—41no—
321C22×C31—41no—
322C22×C31—41no—
323C22×C31—41no—
324C22×C31C2×#12311yescharacteristic
325C22×C31D4211yescharacteristic
326C22×C31#54711yescharacteristic
327C22×C31C2×#13711yescharacteristic
328C22×C31#57511yescharacteristic
329C22×C31#57611yescharacteristic
330C22×C31#57811yescharacteristic
331C4×C31—22no—
332C4×C31—22no—
333C4×C31—41no—
334C4×C31—41no—
335C4×C31—42no—
336C4×C31—42no—
337C4×C31—81no—
338C4×C31—81no—
339C4×C31—81no—
340C4×C31—81no—
341C4×C31—81no—
342C4×C31—81no—
343C4×C31#52511yescharacteristic
344C4×C31#53911yescharacteristic
345C4×C31#54811yescharacteristic
346C4×C31#55311yescharacteristic
347C22×M16C22×C3111yescharacteristic
348C2×C22⋊Q8C22×C3111yescharacteristic
349C2×C22⋊Q8C22×C3111yescharacteristic
350C2×C4×D4C22×C3111yescharacteristic
351C2×#117C22×C3111yescharacteristic
352C2×#117C22×C3111yescharacteristic
353C22×C4⋊C4C22×C3111yescharacteristic
354#485—24no—
355#428—24no—
356C2×#107C22×C3111yescharacteristic
357C2×#107C22×C3111yescharacteristic
358C2×#107C22×C3111yescharacteristic
359C2×#107C22×C3111yescharacteristic
360C2×#106C22×C3111yescharacteristic
361C2×#106C22×C3111yescharacteristic
362C2×#103C22×C3111yescharacteristic
363C2×#103C22×C3111yescharacteristic
364C2×#103C22×C3111yescharacteristic
365C2×#103C22×C3111yescharacteristic
366C2×C22⋊C8C22×C3111yescharacteristic
367C2×C22⋊C8C22×C3111yescharacteristic
368C2×C22⋊C8C22×C3111yescharacteristic
369#398—21no—
370#396—21no—
371#391C22×C3111yescharacteristic
372#390—21no—
373#389C22×C3111yescharacteristic
374#388—21no—
375#388—21no—
376#386—21no—
377#384C22×C3111yescharacteristic
378#380—21no—
379#380C22×C3111yescharacteristic
380#380C22×C3111yescharacteristic
381#380C22×C3111yescharacteristic
382C4×C4⋊C4—21no—
383C4×C4⋊C4C22×C3111yescharacteristic
384#340C22×C3111yescharacteristic
385#340C22×C3111yescharacteristic
386#340C22×C3111yescharacteristic
387#340C22×C3111yescharacteristic
388#340C22×C3111yescharacteristic
389#340C22×C3111yescharacteristic
390#336C22×C3111yescharacteristic
391#336C22×C3111yescharacteristic
392C2×C31—42no—
393C2×C31—81no—
394C2×C31#244311yescharacteristic
395C2×C31#309511yescharacteristic
396C2×C31#309811yescharacteristic
397C2×C31#326811yescharacteristic
398C2×C31#327611yescharacteristic
399C2×C31#334911yescharacteristic
400C2×C31#335711yescharacteristic
401C22×Q8C23×C3111yescharacteristic
402C22×D4D4×C3111yescharacteristic
403C23×C4—21no—
404C23×C4C23×C3111yescharacteristic
405C23×C4C23×C3111yescharacteristic
406C2×M16—22no—
407C2×M16—22no—
408C2×M16—22no—
409C22×C8C23×C3111yescharacteristic
410C22×C8C23×C3111yescharacteristic
411C22×C8C23×C3111yescharacteristic
412C22×C8C23×C3111yescharacteristic
413C22⋊Q8—22no—
414C22⋊Q8—22no—
415C22⋊Q8—22no—
416C22⋊Q8—41no—
417C4×D4—22no—
418C4×D4—22no—
419#117—22no—
420#117—22no—
421#117—41no—
422#117—41no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—41no—
431C2×C4⋊C4D4×C3111yescharacteristic
432C2×C4⋊C4C23×C3111yescharacteristic
433C2×C4⋊C4C23×C3111yescharacteristic
434C2×C4⋊C4C23×C3111yescharacteristic
435C2×C4⋊C4C23×C3111yescharacteristic
436C2×C4⋊C4C23×C3111yescharacteristic
437C2×C4⋊C4C23×C3111yescharacteristic
438C2×C4⋊C4C23×C3111yescharacteristic
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4D4×C3111yescharacteristic
447C2×C22⋊C4D4×C3111yescharacteristic
448C2×C42—21no—
449C2×C42—21no—
450C2×C42—21no—
451C2×C42C23×C3111yescharacteristic
452#107—22no—
453#107—22no—
454#107—22no—
455#107—41no—
456#106—22no—
457#106D4×C3114yescomplemented
458#103—22no—
459#103—22no—
460#103—22no—
461#103—41no—
462C22⋊C8—22no—
463C22⋊C8—22no—
464C22⋊C8—22no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472C31#2615111yescharacteristic, direct product factor, Sylow
473C24C2×D4×C3111yescharacteristic
474C24C2×D4×C3111yescharacteristic
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—41no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—81no—
505C22×C4C2×D4×C3111yescharacteristic
506C22×C4C2×D4×C3111yescharacteristic
507C22×C4C2×D4×C3111yescharacteristic
508C22×C4C2×D4×C3111yescharacteristic
509C22×C4#41×C3112yes—
510C22×C4#41×C3112yes—
511C22×C4C24×C3111yescharacteristic
512M16—28no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8C2×D4×C3112yes—
524C2×C8#41×C3112yes—
525C4⋊C4—22no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—42no—
539C4⋊C4—42no—
540C4⋊C4—42no—
541C4⋊C4—42no—
542C4⋊C4—81no—
543C4⋊C4—81no—
544C4⋊C4C2×D4×C3112yes—
545C4⋊C4C2×D4×C3112yes—
546C22⋊C4—22no—
547C22⋊C4—22no—
548C22⋊C4—42no—
549C22⋊C4—42no—
550C22⋊C4—42no—
551C22⋊C4—42no—
552C22⋊C4—81no—
553C22⋊C4—81no—
554C22⋊C4—81no—
555C42—21no—
556C42—21no—
557C42—42no—
558C42—42no—
559C42—42no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23C31×#12312yes—
574C23C22×D4×C3111yescharacteristic
575Q8—41no—
576Q8—41no—
577Q8—41no—
578Q8—41no—
579D4—44no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—21no—
592C2×C4—22no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—84no—
623C2×C4C31×#12312yes—
624C2×C4C31×#13712yes—
625C2×C4C22×D4×C3111yescharacteristic
626C2×C4C2×#41×C3111yescharacteristic
627C2×C4C2×#41×C3111yescharacteristic
628C2×C4C2×#41×C3111yescharacteristic
629C2×C4C31×H(5,𝔽2)11yescharacteristic
630C2×C4C31×2−1+411yescharacteristic
631C8—22no—
632C8—22no—
633C8—41no—
634C8—41no—
635C22—22no—
636C22—22no—
637C22—22no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22C2×C31×#12311yescharacteristic
650C22D42×C3111yescharacteristic
651C22C31×#54711yescharacteristic
652C22C2×C31×#13711yescharacteristic
653C22C31×#57511yescharacteristic
654C22C31×#57611yescharacteristic
655C22C31×#57811yescharacteristic
656C4—22no—
657C4—22no—
658C4—41no—
659C4—41no—
660C4—42no—
661C4—42no—
662C4—81no—
663C4—81no—
664C4—81no—
665C4—81no—
666C4—81no—
667C4—81no—
668C4C31×#52511yescharacteristic
669C4C31×#53911yescharacteristic
670C4C31×#54811yescharacteristic
671C4C31×#55311yescharacteristic
672C2—42no—
673C2—81no—
674C2C31×#244311yescharacteristic
675C2C31×#309511yescharacteristic
676C2C31×#309811yescharacteristic
677C2C31×#326811yescharacteristic
678C2C31×#327611yescharacteristic
679C2C31×#334911yescharacteristic
680C2C31×#335711yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC22×D4×C31D4
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×#485C2semidirect
2. C2×C31×#428C2semidirect
5. C31×#2095C2semidirect
6. C31×#2083C2semidirect
7. C31×#2075C2semidirect
8. C31×#2036C2semidirect
9. C31×#1927C2semidirect
10. C31×#1920C2semidirect
11. C31×#1894C2semidirect
12. C31×#1873C2semidirect
14. C31×#1854C2semidirect
15. C31×#1852C2semidirect
117. C31×#106D4semidirect
219. #26151C31direct (N × H)
295. C2×#485C2×C31semidirect
296. C2×#428C2×C31semidirect
299. #2095C2×C31semidirect
300. #2083C2×C31semidirect
301. #2075C2×C31semidirect
302. #2036C2×C31semidirect
303. #1927C2×C31semidirect
304. #1920C2×C31semidirect
305. #1894C2×C31semidirect
306. #1873C2×C31semidirect
308. #1854C2×C31semidirect
309. #1852C2×C31semidirect
457. #106D4×C31semidirect
472. C31#26151direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4852
C2×C31×#4282
C31×#24172
C31×#23542
C31×#20952
C31×#20832
C31×#20752
C31×#20362
C31×#19272
C31×#19202
C31×#18942
C31×#18732
C31×#18702
C31×#18542
C31×#18522
#2615131