Finite Group Databasebeta

← C31×#26128 #21482887

Subgroups — C31×#26128 #21482887

Order 7936.

938 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#483C211yesmaximal, characteristic, complemented
2C22×C31×#106C211yesmaximal, characteristic, complemented
3C31×#2417C211yesmaximal, characteristic
4D4×C4⋊C4×C31C211yesmaximal, characteristic
5C31×#2096C211yesmaximal, characteristic, complemented
6C31×#2084C211yesmaximal, characteristic, complemented
7C31×#2077C211yesmaximal, characteristic, complemented
8C31×#2035C211yesmaximal, characteristic, complemented
9C31×#1927C211yesmaximal, characteristic, complemented
10C31×#1920C211yesmaximal, characteristic, complemented
11C31×#1892C211yesmaximal, characteristic, complemented
12C31×#1872C211yesmaximal, characteristic, complemented
13C31×#1869C211yesmaximal, characteristic
14C31×#1853C211yesmaximal, characteristic, complemented
15C31×#1853C211yesmaximal, characteristic, complemented
16C23×C8×C31C2211yescharacteristic
17C2×C31×C22⋊Q8C2211yescharacteristic
18C2×C31×C22⋊Q8C2211yescharacteristic
19C2×C4×D4×C31—21no—
20C2×C4×D4×C31C2211yescharacteristic
21C22×C4⋊C4×C31C2211yescharacteristic
22C22×C4⋊C4×C31C2211yescharacteristic
23C22×C4⋊C4×C31C2211yescharacteristic
24C31×#483—24no—
25C2×C31×#106—24no—
26C2×C31×#106C2211yescharacteristic
27C2×C31×#106C2211yescharacteristic
28C2×C31×#106C2211yescharacteristic
29C2×C31×#106C2211yescharacteristic
30C2×C31×#106C2211yescharacteristic
31C2×C31×#106C2211yescharacteristic
32C2×C31×#103C2211yescharacteristic
33C2×C31×#103C2211yescharacteristic
34C2×C31×#103C2211yescharacteristic
35C2×C31×#103C2211yescharacteristic
36C2×C31×C22⋊C8C2211yescharacteristic
37C2×C31×C22⋊C8C2211yescharacteristic
38C2×C31×C22⋊C8C2211yescharacteristic
39C31×#398—21no—
40C31×#396—21no—
41C31×#391C2211yescharacteristic
42C31×#389—21no—
43C31×#389C2211yescharacteristic
44C31×#386—21no—
45C31×#385—21no—
46C31×#385—21no—
47C31×#384C2211yescharacteristic
48C31×#380—21no—
49C31×#380C2211yescharacteristic
50C31×#380C2211yescharacteristic
51C31×#380C2211yescharacteristic
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×C31—21no—
65C23×C4×C31—21no—
66C23×C4×C31C2311yescharacteristic
67C23×C4×C31C2311yescharacteristic
68C22×C8×C31—22no—
69C22×C8×C31—22no—
70C22×C8×C31—22no—
71C22×C8×C31C2311yescharacteristic
72C22×C8×C31C2311yescharacteristic
73C22×C8×C31C2311yescharacteristic
74C22×C8×C31C2311yescharacteristic
75C31×C22⋊Q8—22no—
76C31×C22⋊Q8—22no—
77C31×C22⋊Q8—22no—
78C31×C22⋊Q8—41no—
79C4×D4×C31—22no—
80C4×D4×C31—22no—
81C4×D4×C31—44no—
82C2×C4⋊C4×C31—22no—
83C2×C4⋊C4×C31—22no—
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—21no—
90C2×C4⋊C4×C31—21no—
91C2×C4⋊C4×C31—21no—
92C2×C4⋊C4×C31—21no—
93C2×C4⋊C4×C31—41no—
94C2×C4⋊C4×C31—41no—
95C2×C4⋊C4×C31—41no—
96C2×C4⋊C4×C31D411yescharacteristic
97C2×C4⋊C4×C31C2311yescharacteristic
98C2×C4⋊C4×C31C2311yescharacteristic
99C2×C4⋊C4×C31C2311yescharacteristic
100C2×C4⋊C4×C31C2311yescharacteristic
101C2×C4⋊C4×C31C2311yescharacteristic
102C2×C4⋊C4×C31C2311yescharacteristic
103C2×C4⋊C4×C31C2311yescharacteristic
104C2×C22⋊C4×C31—21no—
105C2×C22⋊C4×C31—21no—
106C2×C22⋊C4×C31—21no—
107C2×C22⋊C4×C31—21no—
108C2×C22⋊C4×C31—21no—
109C2×C22⋊C4×C31D411yescharacteristic
110C2×C22⋊C4×C31D411yescharacteristic
111C2×C42×C31—21no—
112C2×C42×C31C2311yescharacteristic
113C31×#106—22no—
114C31×#106—22no—
115C31×#106—22no—
116C31×#106—22no—
117C31×#106—41no—
118C31×#106D414yescomplemented
119C31×#103—22no—
120C31×#103—22no—
121C31×#103—22no—
122C31×#103—41no—
123C31×C22⋊C8—22no—
124C31×C22⋊C8—22no—
125C31×C22⋊C8—22no—
126C31×#95—21no—
127C31×#95—21no—
128C31×#95—21no—
129C31×#95—21no—
130C31×#95—21no—
131C31×#95—21no—
132C31×#95—21no—
133C24×C31C2×D411yescharacteristic
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—21no—
141C2×D4×C31—22no—
142C2×D4×C31—22no—
143C2×D4×C31SD1614yes—
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—21no—
162C22×C4×C31—42no—
163C22×C4×C31—42no—
164C22×C4×C31—42no—
165C22×C4×C31—42no—
166C22×C4×C31—42no—
167C22×C4×C31—42no—
168C22×C4×C31—81no—
169C22×C4×C31—81no—
170C22×C4×C31—81no—
171C22×C4×C31C2×D411yescharacteristic
172C22×C4×C31C2×D411yescharacteristic
173C22×C4×C31C2×D411yescharacteristic
174C22×C4×C31C2×D411yescharacteristic
175C22×C4×C31#4112yes—
176C22×C4×C31#4112yes—
177C22×C4×C31C2411yescharacteristic
178C2×C8×C31—28no—
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×C31—21no—
187C2×C8×C31—21no—
188C2×C8×C31—21no—
189C2×C8×C31C2×D412yes—
190C2×C8×C31#4112yes—
191C4⋊C4×C31—22no—
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—21no—
199C4⋊C4×C31—21no—
200C4⋊C4×C31—21no—
201C4⋊C4×C31—21no—
202C4⋊C4×C31—21no—
203C4⋊C4×C31—21no—
204C4⋊C4×C31—42no—
205C4⋊C4×C31—42no—
206C4⋊C4×C31—42no—
207C4⋊C4×C31—42no—
208C4⋊C4×C31—42no—
209C4⋊C4×C31—42no—
210C4⋊C4×C31—81no—
211C4⋊C4×C31—81no—
212C4⋊C4×C31C2×D412yes—
213C4⋊C4×C31C2×D412yes—
214C22⋊C4×C31—22no—
215C22⋊C4×C31—22no—
216C22⋊C4×C31—42no—
217C22⋊C4×C31—42no—
218C22⋊C4×C31—42no—
219C22⋊C4×C31—42no—
220C22⋊C4×C31—81no—
221C42×C31—21no—
222C42×C31—21no—
223C42×C31—42no—
224#26128C3111yesmaximal, characteristic, direct product factor, Sylow
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—21no—
234C23×C31—21no—
235C23×C31#12312yes—
236C23×C31C2×SD1612yes—
237C23×C31C2×SD1612yes—
238C23×C31#13712yes—
239C23×C31C22×D411yescharacteristic
240Q8×C31—41no—
241Q8×C31—41no—
242Q8×C31—41no—
243Q8×C31—41no—
244D4×C31—28no—
245C2×C4×C31—21no—
246C2×C4×C31—21no—
247C2×C4×C31—21no—
248C2×C4×C31—21no—
249C2×C4×C31—22no—
250C2×C4×C31—22no—
251C2×C4×C31—22no—
252C2×C4×C31—22no—
253C2×C4×C31—21no—
254C2×C4×C31—21no—
255C2×C4×C31—22no—
256C2×C4×C31—22no—
257C2×C4×C31—21no—
258C2×C4×C31—21no—
259C2×C4×C31—21no—
260C2×C4×C31—21no—
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—41no—
283C2×C4×C31—41no—
284C2×C4×C31—41no—
285C2×C4×C31—41no—
286C2×C4×C31—41no—
287C2×C4×C31—84no—
288C2×C4×C31—84no—
289C2×C4×C31—84no—
290C2×C4×C31#12312yes—
291C2×C4×C31C2×SD1612yes—
292C2×C4×C31C22×D411yescharacteristic
293C2×C4×C31C2×#4111yescharacteristic
294C2×C4×C31C2×#4111yescharacteristic
295C2×C4×C31C2×#4111yescharacteristic
296C2×C4×C31H(5,𝔽2)11yescharacteristic
297C2×C4×C312−1+411yescharacteristic
298C8×C31—22no—
299C8×C31—22no—
300C8×C31—41no—
301C8×C31—41no—
302C2×#483C2×C3111yescharacteristic, complemented
303C22×#106C2×C3111yescharacteristic, complemented
304#2417C2×C3111yescharacteristic
305D4×C4⋊C4C2×C3111yescharacteristic
306#2096C2×C3111yescharacteristic, complemented
307#2084C2×C3111yescharacteristic, complemented
308#2077C2×C3111yescharacteristic, complemented
309#2035C2×C3111yescharacteristic, complemented
310#1927C2×C3111yescharacteristic, complemented
311#1920C2×C3111yescharacteristic, complemented
312#1892C2×C3111yescharacteristic, complemented
313#1872C2×C3111yescharacteristic, complemented
314#1869C2×C3111yescharacteristic
315#1853C2×C3111yescharacteristic, complemented
316#1853C2×C3111yescharacteristic, complemented
317C22×C31—22no—
318C22×C31—22no—
319C22×C31—22no—
320C22×C31—22no—
321C22×C31—22no—
322C22×C31—22no—
323C22×C31—22no—
324C22×C31—22no—
325C22×C31—22no—
326C22×C31—41no—
327C22×C31—41no—
328C22×C31—41no—
329C22×C31—41no—
330C22×C31#48314yescomplemented
331C22×C31C2×#12311yescharacteristic
332C22×C31D4211yescharacteristic
333C22×C31#54711yescharacteristic
334C22×C31C22×SD1611yescharacteristic
335C22×C31C2×#13711yescharacteristic
336C22×C31#57711yescharacteristic
337C22×C31#57711yescharacteristic
338C4×C31—22no—
339C4×C31—22no—
340C4×C31—41no—
341C4×C31—41no—
342C4×C31—42no—
343C4×C31—42no—
344C4×C31—81no—
345C4×C31—81no—
346C4×C31—81no—
347C4×C31—81no—
348C4×C31—81no—
349C4×C31—81no—
350C4×C31#52511yescharacteristic
351C4×C31#53911yescharacteristic
352C4×C31#54811yescharacteristic
353C4×C31#55311yescharacteristic
354C23×C8C22×C3111yescharacteristic
355C2×C22⋊Q8C22×C3111yescharacteristic
356C2×C22⋊Q8C22×C3111yescharacteristic
357C2×C4×D4—21no—
358C2×C4×D4C22×C3111yescharacteristic
359C22×C4⋊C4C22×C3111yescharacteristic
360C22×C4⋊C4C22×C3111yescharacteristic
361C22×C4⋊C4C22×C3111yescharacteristic
362#483—24no—
363C2×#106—24no—
364C2×#106C22×C3111yescharacteristic
365C2×#106C22×C3111yescharacteristic
366C2×#106C22×C3111yescharacteristic
367C2×#106C22×C3111yescharacteristic
368C2×#106C22×C3111yescharacteristic
369C2×#106C22×C3111yescharacteristic
370C2×#103C22×C3111yescharacteristic
371C2×#103C22×C3111yescharacteristic
372C2×#103C22×C3111yescharacteristic
373C2×#103C22×C3111yescharacteristic
374C2×C22⋊C8C22×C3111yescharacteristic
375C2×C22⋊C8C22×C3111yescharacteristic
376C2×C22⋊C8C22×C3111yescharacteristic
377#398—21no—
378#396—21no—
379#391C22×C3111yescharacteristic
380#389—21no—
381#389C22×C3111yescharacteristic
382#386—21no—
383#385—21no—
384#385—21no—
385#384C22×C3111yescharacteristic
386#380—21no—
387#380C22×C3111yescharacteristic
388#380C22×C3111yescharacteristic
389#380C22×C3111yescharacteristic
390C4×C4⋊C4C22×C3111yescharacteristic
391#340C22×C3111yescharacteristic
392#340C22×C3111yescharacteristic
393#340C22×C3111yescharacteristic
394#340C22×C3111yescharacteristic
395#340C22×C3111yescharacteristic
396#340C22×C3111yescharacteristic
397#336C22×C3111yescharacteristic
398#336C22×C3111yescharacteristic
399C2×C31—24no—
400C2×C31—42no—
401C2×C31#244311yescharacteristic
402C2×C31C2×#48311yescharacteristic
403C2×C31#309911yescharacteristic
404C2×C31#326611yescharacteristic
405C2×C31D4×SD1611yescharacteristic
406C2×C31#333511yescharacteristic
407C2×C31#334411yescharacteristic
408C22×Q8C23×C3111yescharacteristic
409C22×D4D4×C3111yescharacteristic
410C23×C4—21no—
411C23×C4—21no—
412C23×C4—21no—
413C23×C4C23×C3111yescharacteristic
414C23×C4C23×C3111yescharacteristic
415C22×C8—22no—
416C22×C8—22no—
417C22×C8—22no—
418C22×C8C23×C3111yescharacteristic
419C22×C8C23×C3111yescharacteristic
420C22×C8C23×C3111yescharacteristic
421C22×C8C23×C3111yescharacteristic
422C22⋊Q8—22no—
423C22⋊Q8—22no—
424C22⋊Q8—22no—
425C22⋊Q8—41no—
426C4×D4—22no—
427C4×D4—22no—
428C4×D4—44no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—41no—
441C2×C4⋊C4—41no—
442C2×C4⋊C4—41no—
443C2×C4⋊C4D4×C3111yescharacteristic
444C2×C4⋊C4C23×C3111yescharacteristic
445C2×C4⋊C4C23×C3111yescharacteristic
446C2×C4⋊C4C23×C3111yescharacteristic
447C2×C4⋊C4C23×C3111yescharacteristic
448C2×C4⋊C4C23×C3111yescharacteristic
449C2×C4⋊C4C23×C3111yescharacteristic
450C2×C4⋊C4C23×C3111yescharacteristic
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4D4×C3111yescharacteristic
457C2×C22⋊C4D4×C3111yescharacteristic
458C2×C42—21no—
459C2×C42C23×C3111yescharacteristic
460#106—22no—
461#106—22no—
462#106—22no—
463#106—22no—
464#106—41no—
465#106D4×C3114yescomplemented
466#103—22no—
467#103—22no—
468#103—22no—
469#103—41no—
470C22⋊C8—22no—
471C22⋊C8—22no—
472C22⋊C8—22no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95—21no—
480C31#2612811yescharacteristic, direct product factor, Sylow
481C24C2×D4×C3111yescharacteristic
482C24C2×D4×C3111yescharacteristic
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4SD16×C3114yes—
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—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—42no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—81no—
517C22×C4—81no—
518C22×C4—81no—
519C22×C4C2×D4×C3111yescharacteristic
520C22×C4C2×D4×C3111yescharacteristic
521C22×C4C2×D4×C3111yescharacteristic
522C22×C4C2×D4×C3111yescharacteristic
523C22×C4#41×C3112yes—
524C22×C4#41×C3112yes—
525C22×C4C24×C3111yescharacteristic
526C2×C8—28no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8C2×D4×C3112yes—
538C2×C8#41×C3112yes—
539C4⋊C4—22no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—42no—
553C4⋊C4—42no—
554C4⋊C4—42no—
555C4⋊C4—42no—
556C4⋊C4—42no—
557C4⋊C4—42no—
558C4⋊C4—81no—
559C4⋊C4—81no—
560C4⋊C4C2×D4×C3112yes—
561C4⋊C4C2×D4×C3112yes—
562C22⋊C4—22no—
563C22⋊C4—22no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—42no—
567C22⋊C4—42no—
568C22⋊C4—81no—
569C42—21no—
570C42—21no—
571C42—42no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23C31×#12312yes—
583C23C2×SD16×C3112yes—
584C23C2×SD16×C3112yes—
585C23C31×#13712yes—
586C23C22×D4×C3111yescharacteristic
587Q8—41no—
588Q8—41no—
589Q8—41no—
590Q8—41no—
591D4—28no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
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—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—84no—
635C2×C4—84no—
636C2×C4—84no—
637C2×C4C31×#12312yes—
638C2×C4C2×SD16×C3112yes—
639C2×C4C22×D4×C3111yescharacteristic
640C2×C4C2×#41×C3111yescharacteristic
641C2×C4C2×#41×C3111yescharacteristic
642C2×C4C2×#41×C3111yescharacteristic
643C2×C4C31×H(5,𝔽2)11yescharacteristic
644C2×C4C31×2−1+411yescharacteristic
645C8—22no—
646C8—22no—
647C8—41no—
648C8—41no—
649C22—22no—
650C22—22no—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—22no—
655C22—22no—
656C22—22no—
657C22—22no—
658C22—41no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22C31×#48314yescomplemented
663C22C2×C31×#12311yescharacteristic
664C22D42×C3111yescharacteristic
665C22C31×#54711yescharacteristic
666C22C22×SD16×C3111yescharacteristic
667C22C2×C31×#13711yescharacteristic
668C22C31×#57711yescharacteristic
669C22C31×#57711yescharacteristic
670C4—22no—
671C4—22no—
672C4—41no—
673C4—41no—
674C4—42no—
675C4—42no—
676C4—81no—
677C4—81no—
678C4—81no—
679C4—81no—
680C4—81no—
681C4—81no—
682C4C31×#52511yescharacteristic
683C4C31×#53911yescharacteristic
684C4C31×#54811yescharacteristic
685C4C31×#55311yescharacteristic
686C2—24no—
687C2—42no—
688C2C31×#244311yescharacteristic
689C2C2×C31×#48311yescharacteristic
690C2C31×#309911yescharacteristic
691C2C31×#326611yescharacteristic
692C2D4×SD16×C3111yescharacteristic
693C2C31×#333511yescharacteristic
694C2C31×#334411yescharacteristic
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×#483C2semidirect
2. C22×C31×#106C2semidirect
5. C31×#2096C2semidirect
6. C31×#2084C2semidirect
7. C31×#2077C2semidirect
8. C31×#2035C2semidirect
9. C31×#1927C2semidirect
10. C31×#1920C2semidirect
11. C31×#1892C2semidirect
12. C31×#1872C2semidirect
14. C31×#1853C2semidirect
15. C31×#1853C2semidirect
118. C31×#106D4semidirect
224. #26128C31direct (N × H)
302. C2×#483C2×C31semidirect
303. C22×#106C2×C31semidirect
306. #2096C2×C31semidirect
307. #2084C2×C31semidirect
308. #2077C2×C31semidirect
309. #2035C2×C31semidirect
310. #1927C2×C31semidirect
311. #1920C2×C31semidirect
312. #1892C2×C31semidirect
313. #1872C2×C31semidirect
315. #1853C2×C31semidirect
316. #1853C2×C31semidirect
330. C22×C31#483semidirect
465. #106D4×C31semidirect
480. C31#26128direct (N × H)
662. C22C31×#483semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4832
C22×C31×#1062
C31×#24172
D4×C4⋊C4×C312
C31×#20962
C31×#20842
C31×#20772
C31×#20352
C31×#19272
C31×#19202
C31×#18922
C31×#18722
C31×#18692
C31×#18532
#2612831