Finite Group Databasebeta

← C31×#26788 #21483547

Subgroups — C31×#26788 #21483547

Order 7936.

882 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#481C211yesmaximal, characteristic
2C2×C31×#475C211yesmaximal, characteristic, complemented
3C31×#2491C211yesmaximal, characteristic
4C31×#2360C211yesmaximal, characteristic, complemented
5C31×#2065C211yesmaximal, characteristic, complemented
6C31×#2058C211yesmaximal, characteristic, complemented
7C31×#2035C211yesmaximal, characteristic, complemented
8C31×#2000C211yesmaximal, characteristic
9C31×#1968C211yesmaximal, characteristic, complemented
10C31×#1927C211yesmaximal, characteristic, complemented
11C31×#1926C211yesmaximal, characteristic, complemented
12C31×#1923C211yesmaximal, characteristic, complemented
13C31×#1880C211yesmaximal, characteristic, complemented
14C31×#1853C211yesmaximal, characteristic, complemented
15C4×C31×#106C211yesmaximal, characteristic, complemented
16C22×SD16×C31C2211yescharacteristic
17C2×C31×C4⋊Q8C2211yescharacteristic
18C2×C31×#124—21no—
19C2×C31×C22⋊Q8C2211yescharacteristic
20C2×C31×#121C2211yescharacteristic
21C2×C4×Q8×C31C2211yescharacteristic
22C22×C4⋊C4×C31C2211yescharacteristic
23C31×#481—24no—
24C31×#475—24no—
25C2×C31×#106C2211yescharacteristic
26C2×C31×#106C2211yescharacteristic
27C2×C31×#106C2211yescharacteristic
28C2×C31×#106C2211yescharacteristic
29C2×C31×#106C2211yescharacteristic
30C2×C31×C4⋊C8C2211yescharacteristic
31C2×C31×#103C2211yescharacteristic
32C2×C31×#103C2211yescharacteristic
33C2×C31×#103C2211yescharacteristic
34C2×C31×#102C2211yescharacteristic
35C2×C31×#102C2211yescharacteristic
36C2×C31×#102C2211yescharacteristic
37C2×C31×C22⋊C8C2211yescharacteristic
38C2×C31×C22⋊C8C2211yescharacteristic
39C2×C4×C8×C31C2211yescharacteristic
40C31×#394—21no—
41C31×#393—21no—
42C31×#391C2211yescharacteristic
43C31×#390C2211yescharacteristic
44C31×#390C2211yescharacteristic
45C31×#389—21no—
46C31×#389C2211yescharacteristic
47C31×#388—21no—
48C31×#387—21no—
49C31×#385—21no—
50C31×#380C2211yescharacteristic
51C4×C4⋊C4×C31C2211yescharacteristic
52C4×C4⋊C4×C31C2211yescharacteristic
53C4×C22⋊C4×C31—21no—
54C4×C22⋊C4×C31C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#336C2211yescharacteristic
60C31×#336C2211yescharacteristic
61C22×Q8×C31—21no—
62C22×Q8×C31C2311yescharacteristic
63C22×D4×C31—21no—
64C22×D4×C31C2311yescharacteristic
65C23×C4×C31—21no—
66C23×C4×C31C2311yescharacteristic
67C2×SD16×C31—22no—
68C2×SD16×C31—22no—
69C2×SD16×C31—41no—
70C22×C8×C31C2311yescharacteristic
71C22×C8×C31C2311yescharacteristic
72C22×C8×C31C2311yescharacteristic
73C22×C8×C31C2311yescharacteristic
74C31×C4⋊Q8—22no—
75C31×C4⋊Q8—41no—
76C31×#124—44no—
77C31×C22⋊Q8—22no—
78C31×C22⋊Q8—22no—
79C31×#121—22no—
80C31×#121—41no—
81C4×Q8×C31—22no—
82C4×Q8×C31—41no—
83C2×C4⋊C4×C31—21no—
84C2×C4⋊C4×C31—22no—
85C2×C4⋊C4×C31—21no—
86C2×C4⋊C4×C31—21no—
87C2×C4⋊C4×C31—21no—
88C2×C4⋊C4×C31—21no—
89C2×C4⋊C4×C31—41no—
90C2×C4⋊C4×C31C2311yescharacteristic
91C2×C4⋊C4×C31C2311yescharacteristic
92C2×C4⋊C4×C31C2311yescharacteristic
93C2×C4⋊C4×C31C2311yescharacteristic
94C2×C4⋊C4×C31C2311yescharacteristic
95C2×C4⋊C4×C31C2311yescharacteristic
96C2×C22⋊C4×C31—21no—
97C2×C22⋊C4×C31—21no—
98C2×C22⋊C4×C31—21no—
99C2×C22⋊C4×C31—21no—
100C2×C22⋊C4×C31—21no—
101C2×C22⋊C4×C31—21no—
102C2×C22⋊C4×C31—21no—
103C2×C22⋊C4×C31D411yescharacteristic
104C2×C22⋊C4×C31D411yescharacteristic
105C2×C42×C31—21no—
106C2×C42×C31—21no—
107C2×C42×C31—21no—
108C2×C42×C31C2311yescharacteristic
109C2×C42×C31C2311yescharacteristic
110C31×#106—22no—
111C31×#106—22no—
112C31×#106—22no—
113C31×#106—41no—
114C31×#106D414yes—
115C31×C4⋊C8—22no—
116C31×#103—22no—
117C31×#103—22no—
118C31×#103—22no—
119C31×#102—22no—
120C31×#102—22no—
121C31×#102—22no—
122C31×C22⋊C8—22no—
123C31×C22⋊C8—22no—
124C4×C8×C31—22no—
125C31×#95—21no—
126C31×#95—21no—
127C31×#95—21no—
128C31×#95—21no—
129C31×#95—21no—
130C31×#95—21no—
131C31×#95D411yescharacteristic
132C31×#95D411yescharacteristic
133C24×C31—21no—
134C24×C31C2×D411yescharacteristic
135C2×Q8×C31—21no—
136C2×Q8×C31—21no—
137C2×Q8×C31—21no—
138C2×Q8×C31—21no—
139C2×Q8×C31—21no—
140C2×Q8×C31—42no—
141C2×Q8×C31—42no—
142C2×Q8×C31—81no—
143C2×Q8×C31#4112yes—
144C2×D4×C31—21no—
145C2×D4×C31—21no—
146C2×D4×C31—21no—
147C2×D4×C31—21no—
148C2×D4×C31—21no—
149C2×D4×C31—21no—
150C2×D4×C31—42no—
151C2×D4×C31—42no—
152C2×D4×C31—81no—
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—21no—
162C22×C4×C31—21no—
163C22×C4×C31—21no—
164C22×C4×C31—21no—
165C22×C4×C31—21no—
166C22×C4×C31—42no—
167C22×C4×C31—42no—
168C22×C4×C31—81no—
169C22×C4×C31C2×D411yescharacteristic
170C22×C4×C31C2×D411yescharacteristic
171C22×C4×C31C2×D411yescharacteristic
172C22×C4×C31C2×D411yescharacteristic
173C22×C4×C31C2×D411yescharacteristic
174C22×C4×C31C2411yescharacteristic
175SD16×C31—44no—
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×C31—21no—
183C2×C8×C31—21no—
184C2×C8×C31—21no—
185C2×C8×C31—21no—
186C2×C8×C31C2×D412yes—
187C2×C8×C31#4112yes—
188C4⋊C4×C31—24no—
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—21no—
198C4⋊C4×C31—42no—
199C4⋊C4×C31—42no—
200C4⋊C4×C31—42no—
201C4⋊C4×C31—81no—
202C4⋊C4×C31C2×D412yes—
203C4⋊C4×C31C2×D412yes—
204C4⋊C4×C31#4112yes—
205C22⋊C4×C31—24no—
206C22⋊C4×C31—41no—
207C22⋊C4×C31—42no—
208C22⋊C4×C31—42no—
209C22⋊C4×C31—42no—
210C22⋊C4×C31—42no—
211C22⋊C4×C31—42no—
212C22⋊C4×C31—81no—
213C22⋊C4×C31SD1614yescomplemented
214C42×C31—21no—
215C42×C31—21no—
216C42×C31—21no—
217C42×C31—21no—
218C42×C31—42no—
219C42×C31—42no—
220C42×C31—81no—
221#26788C3111yesmaximal, characteristic, direct product factor, Sylow
222C23×C31—21no—
223C23×C31—21no—
224C23×C31—21no—
225C23×C31—21no—
226C23×C31—21no—
227C23×C31—21no—
228C23×C31—41no—
229C23×C31—41no—
230C23×C31—41no—
231C23×C31—41no—
232C23×C31—41no—
233C23×C31—41no—
234C23×C31—41no—
235C23×C31C2×SD1612yes—
236C23×C31C22×D411yescharacteristic
237Q8×C31—22no—
238Q8×C31—22no—
239Q8×C31—41no—
240Q8×C31—41no—
241Q8×C31—84no—
242D4×C31—41no—
243D4×C31—41no—
244D4×C31—41no—
245D4×C31—41no—
246D4×C31—84no—
247C2×C4×C31—21no—
248C2×C4×C31—21no—
249C2×C4×C31—21no—
250C2×C4×C31—21no—
251C2×C4×C31—22no—
252C2×C4×C31—22no—
253C2×C4×C31—21no—
254C2×C4×C31—21no—
255C2×C4×C31—22no—
256C2×C4×C31—21no—
257C2×C4×C31—22no—
258C2×C4×C31—21no—
259C2×C4×C31—21no—
260C2×C4×C31—21no—
261C2×C4×C31—21no—
262C2×C4×C31—21no—
263C2×C4×C31—21no—
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—41no—
283C2×C4×C31—41no—
284C2×C4×C31—41no—
285C2×C4×C31—84no—
286C2×C4×C31C2×SD1612yes—
287C2×C4×C31C2×SD1612yes—
288C2×C4×C31C22×D411yescharacteristic
289C2×C4×C31C2×#4111yescharacteristic
290C2×C4×C31C2×#4111yescharacteristic
291C2×C4×C31C2×#4111yescharacteristic
292C2×C4×C31H(5,𝔽2)11yescharacteristic
293C2×C4×C312−1+411yescharacteristic
294C8×C31—22no—
295C8×C31—22no—
296C8×C31—41no—
297C8×C31—41no—
298C2×#481C2×C3111yescharacteristic
299C2×#475C2×C3111yescharacteristic, complemented
300#2491C2×C3111yescharacteristic
301#2360C2×C3111yescharacteristic, complemented
302#2065C2×C3111yescharacteristic, complemented
303#2058C2×C3111yescharacteristic, complemented
304#2035C2×C3111yescharacteristic, complemented
305#2000C2×C3111yescharacteristic
306#1968C2×C3111yescharacteristic, complemented
307#1927C2×C3111yescharacteristic, complemented
308#1926C2×C3111yescharacteristic, complemented
309#1923C2×C3111yescharacteristic, complemented
310#1880C2×C3111yescharacteristic, complemented
311#1853C2×C3111yescharacteristic, complemented
312C4×#106C2×C3111yescharacteristic, complemented
313C22×C31—22no—
314C22×C31—22no—
315C22×C31—22no—
316C22×C31—41no—
317C22×C31—41no—
318C22×C31—41no—
319C22×C31—41no—
320C22×C31—81no—
321C22×C31—81no—
322C22×C31—81no—
323C22×C31—81no—
324C22×C31—81no—
325C22×C31—81no—
326C22×C31—81no—
327C22×C31#52511yescharacteristic
328C22×C31D4211yescharacteristic
329C22×C31#54711yescharacteristic
330C22×C31C22×SD1611yescharacteristic
331C22×C31#57511yescharacteristic
332C22×C31#57711yescharacteristic
333C22×C31#57711yescharacteristic
334C4×C31—22no—
335C4×C31—22no—
336C4×C31—41no—
337C4×C31—42no—
338C4×C31—41no—
339C4×C31—42no—
340C4×C31—41no—
341C4×C31—42no—
342C4×C31—42no—
343C4×C31—81no—
344C4×C31—81no—
345C4×C31—81no—
346C4×C31#53211yescharacteristic
347C4×C31#54211yescharacteristic
348C4×C31#54811yescharacteristic
349C4×C31#55111yescharacteristic
350C22×SD16C22×C3111yescharacteristic
351C2×C4⋊Q8C22×C3111yescharacteristic
352C2×#124—21no—
353C2×C22⋊Q8C22×C3111yescharacteristic
354C2×#121C22×C3111yescharacteristic
355C2×C4×Q8C22×C3111yescharacteristic
356C22×C4⋊C4C22×C3111yescharacteristic
357#481—24no—
358#475—24no—
359C2×#106C22×C3111yescharacteristic
360C2×#106C22×C3111yescharacteristic
361C2×#106C22×C3111yescharacteristic
362C2×#106C22×C3111yescharacteristic
363C2×#106C22×C3111yescharacteristic
364C2×C4⋊C8C22×C3111yescharacteristic
365C2×#103C22×C3111yescharacteristic
366C2×#103C22×C3111yescharacteristic
367C2×#103C22×C3111yescharacteristic
368C2×#102C22×C3111yescharacteristic
369C2×#102C22×C3111yescharacteristic
370C2×#102C22×C3111yescharacteristic
371C2×C22⋊C8C22×C3111yescharacteristic
372C2×C22⋊C8C22×C3111yescharacteristic
373C2×C4×C8C22×C3111yescharacteristic
374#394—21no—
375#393—21no—
376#391C22×C3111yescharacteristic
377#390C22×C3111yescharacteristic
378#390C22×C3111yescharacteristic
379#389—21no—
380#389C22×C3111yescharacteristic
381#388—21no—
382#387—21no—
383#385—21no—
384#380C22×C3111yescharacteristic
385C4×C4⋊C4C22×C3111yescharacteristic
386C4×C4⋊C4C22×C3111yescharacteristic
387C4×C22⋊C4—21no—
388C4×C22⋊C4C22×C3111yescharacteristic
389#340C22×C3111yescharacteristic
390#340C22×C3111yescharacteristic
391#340C22×C3111yescharacteristic
392#340C22×C3111yescharacteristic
393#336C22×C3111yescharacteristic
394#336C22×C3111yescharacteristic
395C2×C31—42no—
396C2×C31—161no—
397C2×C31#246111yescharacteristic
398C2×C31#310311yescharacteristic
399C2×C31#312511yescharacteristic
400C2×C31#327511yescharacteristic
401C2×C31D4×SD1611yescharacteristic
402C2×C31#333511yescharacteristic
403C2×C31#334811yescharacteristic
404C22×Q8—21no—
405C22×Q8C23×C3111yescharacteristic
406C22×D4—21no—
407C22×D4C23×C3111yescharacteristic
408C23×C4—21no—
409C23×C4C23×C3111yescharacteristic
410C2×SD16—22no—
411C2×SD16—22no—
412C2×SD16—41no—
413C22×C8C23×C3111yescharacteristic
414C22×C8C23×C3111yescharacteristic
415C22×C8C23×C3111yescharacteristic
416C22×C8C23×C3111yescharacteristic
417C4⋊Q8—22no—
418C4⋊Q8—41no—
419#124—44no—
420C22⋊Q8—22no—
421C22⋊Q8—22no—
422#121—22no—
423#121—41no—
424C4×Q8—22no—
425C4×Q8—41no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—41no—
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
452C2×C42C23×C3111yescharacteristic
453#106—22no—
454#106—22no—
455#106—22no—
456#106—41no—
457#106D4×C3114yes—
458C4⋊C8—22no—
459#103—22no—
460#103—22no—
461#103—22no—
462#102—22no—
463#102—22no—
464#102—22no—
465C22⋊C8—22no—
466C22⋊C8—22no—
467C4×C8—22no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95D4×C3111yescharacteristic
475#95D4×C3111yescharacteristic
476C31#2678811yescharacteristic, direct product factor, Sylow
477C24—21no—
478C24C2×D4×C3111yescharacteristic
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—42no—
485C2×Q8—42no—
486C2×Q8—81no—
487C2×Q8#41×C3112yes—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—42no—
495C2×D4—42no—
496C2×D4—81no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—81no—
513C22×C4C2×D4×C3111yescharacteristic
514C22×C4C2×D4×C3111yescharacteristic
515C22×C4C2×D4×C3111yescharacteristic
516C22×C4C2×D4×C3111yescharacteristic
517C22×C4C2×D4×C3111yescharacteristic
518C22×C4C24×C3111yescharacteristic
519SD16—44no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8C2×D4×C3112yes—
531C2×C8#41×C3112yes—
532C4⋊C4—24no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—42no—
543C4⋊C4—42no—
544C4⋊C4—42no—
545C4⋊C4—81no—
546C4⋊C4C2×D4×C3112yes—
547C4⋊C4C2×D4×C3112yes—
548C4⋊C4#41×C3112yes—
549C22⋊C4—24no—
550C22⋊C4—41no—
551C22⋊C4—42no—
552C22⋊C4—42no—
553C22⋊C4—42no—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—81no—
557C22⋊C4SD16×C3114yescomplemented
558C42—21no—
559C42—21no—
560C42—21no—
561C42—21no—
562C42—42no—
563C42—42no—
564C42—81no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23C2×SD16×C3112yes—
579C23C22×D4×C3111yescharacteristic
580Q8—22no—
581Q8—22no—
582Q8—41no—
583Q8—41no—
584Q8—84no—
585D4—41no—
586D4—41no—
587D4—41no—
588D4—41no—
589D4—84no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—22no—
599C2×C4—21no—
600C2×C4—22no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
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—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—84no—
629C2×C4C2×SD16×C3112yes—
630C2×C4C2×SD16×C3112yes—
631C2×C4C22×D4×C3111yescharacteristic
632C2×C4C2×#41×C3111yescharacteristic
633C2×C4C2×#41×C3111yescharacteristic
634C2×C4C2×#41×C3111yescharacteristic
635C2×C4C31×H(5,𝔽2)11yescharacteristic
636C2×C4C31×2−1+411yescharacteristic
637C8—22no—
638C8—22no—
639C8—41no—
640C8—41no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22—41no—
648C22—81no—
649C22—81no—
650C22—81no—
651C22—81no—
652C22—81no—
653C22—81no—
654C22—81no—
655C22C31×#52511yescharacteristic
656C22D42×C3111yescharacteristic
657C22C31×#54711yescharacteristic
658C22C22×SD16×C3111yescharacteristic
659C22C31×#57511yescharacteristic
660C22C31×#57711yescharacteristic
661C22C31×#57711yescharacteristic
662C4—22no—
663C4—22no—
664C4—41no—
665C4—42no—
666C4—41no—
667C4—42no—
668C4—41no—
669C4—42no—
670C4—42no—
671C4—81no—
672C4—81no—
673C4—81no—
674C4C31×#53211yescharacteristic
675C4C31×#54211yescharacteristic
676C4C31×#54811yescharacteristic
677C4C31×#55111yescharacteristic
678C2—42no—
679C2—161no—
680C2C31×#246111yescharacteristic
681C2C31×#310311yescharacteristic
682C2C31×#312511yescharacteristic
683C2C31×#327511yescharacteristic
684C2D4×SD16×C3111yescharacteristic
685C2C31×#333511yescharacteristic
686C2C31×#334811yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#121C22
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
2. C2×C31×#475C2semidirect
4. C31×#2360C2semidirect
5. C31×#2065C2semidirect
6. C31×#2058C2semidirect
7. C31×#2035C2semidirect
9. C31×#1968C2semidirect
10. C31×#1927C2semidirect
11. C31×#1926C2semidirect
12. C31×#1923C2semidirect
13. C31×#1880C2semidirect
14. C31×#1853C2semidirect
15. C4×C31×#106C2semidirect
213. C22⋊C4×C31SD16semidirect
221. #26788C31direct (N × H)
299. C2×#475C2×C31semidirect
301. #2360C2×C31semidirect
302. #2065C2×C31semidirect
303. #2058C2×C31semidirect
304. #2035C2×C31semidirect
306. #1968C2×C31semidirect
307. #1927C2×C31semidirect
308. #1926C2×C31semidirect
309. #1923C2×C31semidirect
310. #1880C2×C31semidirect
311. #1853C2×C31semidirect
312. C4×#106C2×C31semidirect
476. C31#26788direct (N × H)
557. C22⋊C4SD16×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4812
C2×C31×#4752
C31×#24912
C31×#23602
C31×#20652
C31×#20582
C31×#20352
C31×#20002
C31×#19682
C31×#19272
C31×#19262
C31×#19232
C31×#18802
C31×#18532
C4×C31×#1062
#2678831