Finite Group Databasebeta

← C31×#24979 #21481738

Subgroups — C31×#24979 #21481738

Order 7936.

828 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2536C211yesmaximal, characteristic
2D4×C4⋊C4×C31C211yesmaximal, characteristic
3C31×#2077C211yesmaximal, characteristic, complemented
4C31×#2075C211yesmaximal, characteristic, complemented
5C31×#2036C211yesmaximal, characteristic, complemented
6C31×#2035C211yesmaximal, characteristic, complemented
7C31×#1955C211yesmaximal, characteristic
8C31×#1949C211yesmaximal, characteristic, complemented
9C31×#1872C211yesmaximal, characteristic, complemented
10C31×#1872C211yesmaximal, characteristic, complemented
11C31×#1836C211yesmaximal, characteristic, complemented
12C31×#1824C211yesmaximal, characteristic, complemented
13C31×#1823C211yesmaximal, characteristic, complemented
14C31×#1803C211yesmaximal, characteristic, complemented
15C31×#1763C211yesmaximal, characteristic, complemented
16C2×C31×C22⋊Q8C2211yescharacteristic
17C2×C31×C22⋊Q8C2211yescharacteristic
18C2×C4×Q8×C31C2211yescharacteristic
19C2×C4×D4×C31—21no—
20C2×C4×D4×C31C2211yescharacteristic
21C22×C4⋊C4×C31C2211yescharacteristic
22C22×C4⋊C4×C31C2211yescharacteristic
23C2×C31×#107C2211yescharacteristic
24C2×C31×#106C2211yescharacteristic
25C2×C31×C4⋊C8C2211yescharacteristic
26C2×C31×#103C2211yescharacteristic
27C2×C31×#103C2211yescharacteristic
28C2×C31×#103C2211yescharacteristic
29C2×C31×#103C2211yescharacteristic
30C2×C31×C22⋊C8C2211yescharacteristic
31C2×C31×C22⋊C8C2211yescharacteristic
32C2×C31×C22⋊C8C2211yescharacteristic
33C2×C31×C22⋊C8C2211yescharacteristic
34C2×C31×#97C2211yescharacteristic
35C31×#398—21no—
36C31×#394—21no—
37C31×#389—21no—
38C31×#388—21no—
39C31×#388—21no—
40C31×#385—21no—
41C31×#385—21no—
42C31×#384C2211yescharacteristic
43C31×#382C2211yescharacteristic
44C31×#380C2211yescharacteristic
45C31×#380C2211yescharacteristic
46C31×#380C2211yescharacteristic
47C31×#380C2211yescharacteristic
48C4×C4⋊C4×C31C2211yescharacteristic
49C31×#340C2211yescharacteristic
50C31×#340C2211yescharacteristic
51C31×#340C2211yescharacteristic
52C31×#340C2211yescharacteristic
53C31×#340C2211yescharacteristic
54C31×#340C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C22×Q8×C31C2311yescharacteristic
60C22×D4×C31D411yescharacteristic
61C23×C4×C31—21no—
62C23×C4×C31—21no—
63C23×C4×C31C2311yescharacteristic
64C23×C4×C31C2311yescharacteristic
65C22×C8×C31C2311yescharacteristic
66C22×C8×C31C2311yescharacteristic
67C22×C8×C31C2311yescharacteristic
68C22×C8×C31C2311yescharacteristic
69C31×C22⋊Q8—22no—
70C31×C22⋊Q8—22no—
71C31×C22⋊Q8—41no—
72C31×C22⋊Q8—41no—
73C4×Q8×C31—22no—
74C4×Q8×C31—22no—
75C4×D4×C31—22no—
76C4×D4×C31—22no—
77C4×D4×C31—44no—
78C2×C4⋊C4×C31—22no—
79C2×C4⋊C4×C31—22no—
80C2×C4⋊C4×C31—21no—
81C2×C4⋊C4×C31—21no—
82C2×C4⋊C4×C31—21no—
83C2×C4⋊C4×C31—21no—
84C2×C4⋊C4×C31—21no—
85C2×C4⋊C4×C31—21no—
86C2×C4⋊C4×C31—21no—
87C2×C4⋊C4×C31—41no—
88C2×C4⋊C4×C31—41no—
89C2×C4⋊C4×C31D411yescharacteristic
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×C4⋊C4×C31C2311yescharacteristic
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×C31C2311yescharacteristic
108C31×#107—41no—
109C31×#106—41no—
110C31×C4⋊C8—22no—
111C31×#103—22no—
112C31×#103—22no—
113C31×#103—41no—
114C31×#103—41no—
115C31×C22⋊C8—41no—
116C31×C22⋊C8—41no—
117C31×C22⋊C8—41no—
118C31×C22⋊C8—41no—
119C31×#97—22no—
120C31×#95—21no—
121C31×#95—21no—
122C31×#95—21no—
123C31×#95—21no—
124C31×#95—21no—
125C31×#95—21no—
126C31×#95—21no—
127C24×C31C2×D411yescharacteristic
128C24×C31C2×D411yescharacteristic
129C2×Q8×C31—21no—
130C2×Q8×C31—21no—
131C2×Q8×C31—21no—
132C2×Q8×C31—21no—
133C2×Q8×C31—21no—
134C2×Q8×C31#4112yes—
135C2×D4×C31—22no—
136C2×D4×C31—22no—
137C2×D4×C31—22no—
138C22×C4×C31—21no—
139C22×C4×C31—21no—
140C22×C4×C31—21no—
141C22×C4×C31—21no—
142C22×C4×C31—21no—
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—42no—
159C22×C4×C31—42no—
160C22×C4×C31—42no—
161C22×C4×C31—42no—
162C22×C4×C31—81no—
163C22×C4×C31—81no—
164C22×C4×C31C2×D411yescharacteristic
165C22×C4×C31C2×D411yescharacteristic
166C22×C4×C31C2×D411yescharacteristic
167C22×C4×C31C2×D411yescharacteristic
168C22×C4×C31C2411yescharacteristic
169C2×C8×C31—21no—
170C2×C8×C31—21no—
171C2×C8×C31—21no—
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—
181C4⋊C4×C31—22no—
182C4⋊C4×C31—21no—
183C4⋊C4×C31—21no—
184C4⋊C4×C31—21no—
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—42no—
196C4⋊C4×C31—42no—
197C4⋊C4×C31—42no—
198C4⋊C4×C31—42no—
199C4⋊C4×C31—42no—
200C4⋊C4×C31—42no—
201C4⋊C4×C31—81no—
202C4⋊C4×C31#4112yes—
203C22⋊C4×C31—22no—
204C22⋊C4×C31—22no—
205C22⋊C4×C31—42no—
206C22⋊C4×C31—42no—
207C22⋊C4×C31—42no—
208C22⋊C4×C31—42no—
209C22⋊C4×C31—42no—
210C22⋊C4×C31—42no—
211C42×C31—42no—
212C42×C31—42no—
213C42×C31#4112yes—
214C42×C31#4112yes—
215#24979C3111yesmaximal, characteristic, direct product factor, Sylow
216C23×C31—21no—
217C23×C31—21no—
218C23×C31—21no—
219C23×C31—21no—
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×C31AGL(1,ℤ/8)12yes—
229C23×C31#13712yes—
230C23×C31C22×D411yescharacteristic
231Q8×C31—22no—
232Q8×C31—22no—
233Q8×C31—41no—
234Q8×C31—41no—
235D4×C31—28no—
236C2×C4×C31—21no—
237C2×C4×C31—21no—
238C2×C4×C31—21no—
239C2×C4×C31—21no—
240C2×C4×C31—21no—
241C2×C4×C31—21no—
242C2×C4×C31—22no—
243C2×C4×C31—22no—
244C2×C4×C31—21no—
245C2×C4×C31—21no—
246C2×C4×C31—21no—
247C2×C4×C31—21no—
248C2×C4×C31—41no—
249C2×C4×C31—41no—
250C2×C4×C31—41no—
251C2×C4×C31—41no—
252C2×C4×C31—41no—
253C2×C4×C31—41no—
254C2×C4×C31—41no—
255C2×C4×C31—41no—
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—84no—
279C2×C4×C31—84no—
280C2×C4×C31#12312yes—
281C2×C4×C31#12312yes—
282C2×C4×C31C2×#4111yescharacteristic
283C2×C4×C31C2×#4111yescharacteristic
284C2×C4×C31C2×#4111yescharacteristic
285C2×C4×C31C2×#4111yescharacteristic
286C2×C4×C31H(5,𝔽2)11yescharacteristic
287C2×C4×C31H(5,𝔽2)11yescharacteristic
288C8×C31—41no—
289C8×C31—41no—
290C8×C31—41no—
291C8×C31—41no—
292#2536C2×C3111yescharacteristic
293D4×C4⋊C4C2×C3111yescharacteristic
294#2077C2×C3111yescharacteristic, complemented
295#2075C2×C3111yescharacteristic, complemented
296#2036C2×C3111yescharacteristic, complemented
297#2035C2×C3111yescharacteristic, complemented
298#1955C2×C3111yescharacteristic
299#1949C2×C3111yescharacteristic, complemented
300#1872C2×C3111yescharacteristic, complemented
301#1872C2×C3111yescharacteristic, complemented
302#1836C2×C3111yescharacteristic, complemented
303#1824C2×C3111yescharacteristic, complemented
304#1823C2×C3111yescharacteristic, complemented
305#1803C2×C3111yescharacteristic, complemented
306#1763C2×C3111yescharacteristic, complemented
307C22×C31—22no—
308C22×C31—22no—
309C22×C31—22no—
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×C31C2×#12311yescharacteristic
322C22×C31#54611yescharacteristic
323C22×C31#54611yescharacteristic
324C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
325C22×C31C2×#13711yescharacteristic
326C22×C31#57711yescharacteristic
327C22×C31#57811yescharacteristic
328C4×C31—22no—
329C4×C31—22no—
330C4×C31—41no—
331C4×C31—41no—
332C4×C31—42no—
333C4×C31—42no—
334C4×C31—81no—
335C4×C31—81no—
336C4×C31—81no—
337C4×C31—81no—
338C4×C31—81no—
339C4×C31—81no—
340C4×C31#52911yescharacteristic
341C4×C31#54011yescharacteristic
342C4×C31#55311yescharacteristic
343C4×C31#55511yescharacteristic
344C2×C22⋊Q8C22×C3111yescharacteristic
345C2×C22⋊Q8C22×C3111yescharacteristic
346C2×C4×Q8C22×C3111yescharacteristic
347C2×C4×D4—21no—
348C2×C4×D4C22×C3111yescharacteristic
349C22×C4⋊C4C22×C3111yescharacteristic
350C22×C4⋊C4C22×C3111yescharacteristic
351C2×#107C22×C3111yescharacteristic
352C2×#106C22×C3111yescharacteristic
353C2×C4⋊C8C22×C3111yescharacteristic
354C2×#103C22×C3111yescharacteristic
355C2×#103C22×C3111yescharacteristic
356C2×#103C22×C3111yescharacteristic
357C2×#103C22×C3111yescharacteristic
358C2×C22⋊C8C22×C3111yescharacteristic
359C2×C22⋊C8C22×C3111yescharacteristic
360C2×C22⋊C8C22×C3111yescharacteristic
361C2×C22⋊C8C22×C3111yescharacteristic
362C2×#97C22×C3111yescharacteristic
363#398—21no—
364#394—21no—
365#389—21no—
366#388—21no—
367#388—21no—
368#385—21no—
369#385—21no—
370#384C22×C3111yescharacteristic
371#382C22×C3111yescharacteristic
372#380C22×C3111yescharacteristic
373#380C22×C3111yescharacteristic
374#380C22×C3111yescharacteristic
375#380C22×C3111yescharacteristic
376C4×C4⋊C4C22×C3111yescharacteristic
377#340C22×C3111yescharacteristic
378#340C22×C3111yescharacteristic
379#340C22×C3111yescharacteristic
380#340C22×C3111yescharacteristic
381#340C22×C3111yescharacteristic
382#340C22×C3111yescharacteristic
383#340C22×C3111yescharacteristic
384#340C22×C3111yescharacteristic
385#340C22×C3111yescharacteristic
386#340C22×C3111yescharacteristic
387C2×C31—42no—
388C2×C31—42no—
389C2×C31#242011yescharacteristic
390C2×C31#309211yescharacteristic
391C2×C31#309711yescharacteristic
392C2×C31#330811yescharacteristic
393C2×C31#331011yescharacteristic
394C2×C31#331211yescharacteristic
395C2×C31#331611yescharacteristic
396C22×Q8C23×C3111yescharacteristic
397C22×D4D4×C3111yescharacteristic
398C23×C4—21no—
399C23×C4—21no—
400C23×C4C23×C3111yescharacteristic
401C23×C4C23×C3111yescharacteristic
402C22×C8C23×C3111yescharacteristic
403C22×C8C23×C3111yescharacteristic
404C22×C8C23×C3111yescharacteristic
405C22×C8C23×C3111yescharacteristic
406C22⋊Q8—22no—
407C22⋊Q8—22no—
408C22⋊Q8—41no—
409C22⋊Q8—41no—
410C4×Q8—22no—
411C4×Q8—22no—
412C4×D4—22no—
413C4×D4—22no—
414C4×D4—44no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—41no—
425C2×C4⋊C4—41no—
426C2×C4⋊C4D4×C3111yescharacteristic
427C2×C4⋊C4C23×C3111yescharacteristic
428C2×C4⋊C4C23×C3111yescharacteristic
429C2×C4⋊C4C23×C3111yescharacteristic
430C2×C4⋊C4C23×C3111yescharacteristic
431C2×C4⋊C4C23×C3111yescharacteristic
432C2×C4⋊C4C23×C3111yescharacteristic
433C2×C4⋊C4C23×C3111yescharacteristic
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4D4×C3111yescharacteristic
441C2×C22⋊C4D4×C3111yescharacteristic
442C2×C42—21no—
443C2×C42—21no—
444C2×C42C23×C3111yescharacteristic
445#107—41no—
446#106—41no—
447C4⋊C8—22no—
448#103—22no—
449#103—22no—
450#103—41no—
451#103—41no—
452C22⋊C8—41no—
453C22⋊C8—41no—
454C22⋊C8—41no—
455C22⋊C8—41no—
456#97—22no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464C31#2497911yescharacteristic, direct product factor, Sylow
465C24C2×D4×C3111yescharacteristic
466C24C2×D4×C3111yescharacteristic
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8#41×C3112yes—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
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—42no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—42no—
500C22×C4—81no—
501C22×C4—81no—
502C22×C4C2×D4×C3111yescharacteristic
503C22×C4C2×D4×C3111yescharacteristic
504C22×C4C2×D4×C3111yescharacteristic
505C22×C4C2×D4×C3111yescharacteristic
506C22×C4C24×C3111yescharacteristic
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C4⋊C4—22no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—42no—
534C4⋊C4—42no—
535C4⋊C4—42no—
536C4⋊C4—42no—
537C4⋊C4—42no—
538C4⋊C4—42no—
539C4⋊C4—81no—
540C4⋊C4#41×C3112yes—
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—42no—
544C22⋊C4—42no—
545C22⋊C4—42no—
546C22⋊C4—42no—
547C22⋊C4—42no—
548C22⋊C4—42no—
549C42—42no—
550C42—42no—
551C42#41×C3112yes—
552C42#41×C3112yes—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23C31×AGL(1,ℤ/8)12yes—
566C23C31×#13712yes—
567C23C22×D4×C3111yescharacteristic
568Q8—22no—
569Q8—22no—
570Q8—41no—
571Q8—41no—
572D4—28no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
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—84no—
616C2×C4—84no—
617C2×C4C31×#12312yes—
618C2×C4C31×#12312yes—
619C2×C4C2×#41×C3111yescharacteristic
620C2×C4C2×#41×C3111yescharacteristic
621C2×C4C2×#41×C3111yescharacteristic
622C2×C4C2×#41×C3111yescharacteristic
623C2×C4C31×H(5,𝔽2)11yescharacteristic
624C2×C4C31×H(5,𝔽2)11yescharacteristic
625C8—41no—
626C8—41no—
627C8—41no—
628C8—41no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—22no—
633C22—22no—
634C22—22no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22C2×C31×#12311yescharacteristic
644C22C31×#54611yescharacteristic
645C22C31×#54611yescharacteristic
646C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
647C22C2×C31×#13711yescharacteristic
648C22C31×#57711yescharacteristic
649C22C31×#57811yescharacteristic
650C4—22no—
651C4—22no—
652C4—41no—
653C4—41no—
654C4—42no—
655C4—42no—
656C4—81no—
657C4—81no—
658C4—81no—
659C4—81no—
660C4—81no—
661C4—81no—
662C4C31×#52911yescharacteristic
663C4C31×#54011yescharacteristic
664C4C31×#55311yescharacteristic
665C4C31×#55511yescharacteristic
666C2—42no—
667C2—42no—
668C2C31×#242011yescharacteristic
669C2C31×#309211yescharacteristic
670C2C31×#309711yescharacteristic
671C2C31×#330811yescharacteristic
672C2C31×#331011yescharacteristic
673C2C31×#331211yescharacteristic
674C2C31×#331611yescharacteristic
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
3. C31×#2077C2semidirect
4. C31×#2075C2semidirect
5. C31×#2036C2semidirect
6. C31×#2035C2semidirect
8. C31×#1949C2semidirect
9. C31×#1872C2semidirect
10. C31×#1872C2semidirect
11. C31×#1836C2semidirect
12. C31×#1824C2semidirect
13. C31×#1823C2semidirect
14. C31×#1803C2semidirect
15. C31×#1763C2semidirect
215. #24979C31direct (N × H)
294. #2077C2×C31semidirect
295. #2075C2×C31semidirect
296. #2036C2×C31semidirect
297. #2035C2×C31semidirect
299. #1949C2×C31semidirect
300. #1872C2×C31semidirect
301. #1872C2×C31semidirect
302. #1836C2×C31semidirect
303. #1824C2×C31semidirect
304. #1823C2×C31semidirect
305. #1803C2×C31semidirect
306. #1763C2×C31semidirect
464. C31#24979direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#25362
D4×C4⋊C4×C312
C31×#20772
C31×#20752
C31×#20362
C31×#20352
C31×#19552
C31×#19492
C31×#18722
C31×#18362
C31×#18242
C31×#18232
C31×#18032
C31×#17632
#2497931