Finite Group Databasebeta

← C31×#16605 #21473364

Subgroups — C31×#16605 #21473364

Order 7936.

1382 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#125C211yesmaximal, characteristic
2C2×C31×#398C212yesmaximal
3C2×C31×#387C211yesmaximal, characteristic
4C31×#1444C211yesmaximal, characteristic
5C31×#1442C211yesmaximal, characteristic
6C31×#1442C212yesmaximal
7C31×#1441C212yesmaximal
8C31×#1441C211yesmaximal, characteristic
9C31×#1441C211yesmaximal, characteristic
10C31×#1441C212yesmaximal
11C31×C4⋊#95C211yesmaximal, characteristic
12C2×C31×#125—28no—
13C2×C31×#125—24no—
14C22×C4⋊C4×C31C2211yescharacteristic
15C22×C4⋊C4×C31C2212yes—
16C22×C4⋊C4×C31C2211yescharacteristic
17C22×C4⋊C4×C31C2211yescharacteristic
18C22×C4⋊C4×C31C2212yes—
19C22×C4⋊C4×C31C2212yes—
20C22×C4⋊C4×C31C2212yes—
21C22×C4⋊C4×C31C2211yescharacteristic
22C22×C42×C31C2211yescharacteristic
23C31×#398—28no—
24C31×#387—24no—
25C2×C31×#95C2212yes—
26C2×C31×#95C2212yes—
27C2×C31×#95C2212yes—
28C2×C31×#95C2211yescharacteristic
29C2×C31×#95C2211yescharacteristic
30C2×C31×#95C2211yescharacteristic
31C2×C31×#95C2211yescharacteristic
32C2×C31×#95C2212yes—
33C2×C31×#95C2211yescharacteristic
34C2×C31×#95C2211yescharacteristic
35C2×C31×#95C2212yes—
36C2×C31×#95C2212yes—
37C2×C31×#95C2212yes—
38C2×C31×#95C2212yes—
39C23×C4×C31C2311yescharacteristic
40C23×C4×C31C2312yes—
41C23×C4×C31C2311yescharacteristic
42C23×C4×C31C2311yescharacteristic
43C23×C4×C31C2312yes—
44C23×C4×C31C2312yes—
45C23×C4×C31C2311yescharacteristic
46C23×C4×C31C2311yescharacteristic
47C23×C4×C31C2312yes—
48C23×C4×C31C2311yescharacteristic
49C23×C4×C31C2311yescharacteristic
50C31×#125—232no—
51C2×C4⋊C4×C31—24no—
52C2×C4⋊C4×C31—24no—
53C2×C4⋊C4×C31—24no—
54C2×C4⋊C4×C31—24no—
55C2×C4⋊C4×C31—24no—
56C2×C4⋊C4×C31—22no—
57C2×C4⋊C4×C31—22no—
58C2×C4⋊C4×C31—24no—
59C2×C4⋊C4×C31—24no—
60C2×C4⋊C4×C31—22no—
61C2×C4⋊C4×C31—22no—
62C2×C4⋊C4×C31—24no—
63C2×C4⋊C4×C31—24no—
64C2×C4⋊C4×C31—24no—
65C2×C4⋊C4×C31—22no—
66C2×C4⋊C4×C31—24no—
67C2×C4⋊C4×C31—24no—
68C2×C4⋊C4×C31—42no—
69C2×C4⋊C4×C31—42no—
70C2×C4⋊C4×C31D418yes—
71C2×C4⋊C4×C31Q814yes—
72C2×C42×C31—24no—
73C2×C42×C31D414yes—
74C31×#95—24no—
75C31×#95—24no—
76C31×#95—24no—
77C31×#95—22no—
78C31×#95—22no—
79C31×#95—22no—
80C31×#95—22no—
81C31×#95—22no—
82C31×#95—24no—
83C31×#95—22no—
84C31×#95—42no—
85C31×#95—42no—
86C31×#95—42no—
87C31×#95—42no—
88C24×C31C2411yescharacteristic
89C22×C4×C31—22no—
90C22×C4×C31—22no—
91C22×C4×C31—21no—
92C22×C4×C31—22no—
93C22×C4×C31—21no—
94C22×C4×C31—21no—
95C22×C4×C31—22no—
96C22×C4×C31—21no—
97C22×C4×C31—22no—
98C22×C4×C31—22no—
99C22×C4×C31—22no—
100C22×C4×C31—22no—
101C22×C4×C31—22no—
102C22×C4×C31—22no—
103C22×C4×C31—22no—
104C22×C4×C31—22no—
105C22×C4×C31—21no—
106C22×C4×C31—21no—
107C22×C4×C31—22no—
108C22×C4×C31—21no—
109C22×C4×C31—22no—
110C22×C4×C31—22no—
111C22×C4×C31—21no—
112C22×C4×C31—21no—
113C22×C4×C31—22no—
114C22×C4×C31—22no—
115C22×C4×C31—22no—
116C22×C4×C31—22no—
117C22×C4×C31—22no—
118C22×C4×C31—21no—
119C22×C4×C31—22no—
120C22×C4×C31—22no—
121C22×C4×C31—21no—
122C22×C4×C31—21no—
123C22×C4×C31—22no—
124C22×C4×C31—22no—
125C22×C4×C31—22no—
126C22×C4×C31—21no—
127C22×C4×C31—21no—
128C22×C4×C31—22no—
129C22×C4×C31—22no—
130C22×C4×C31—22no—
131C22×C4×C31—22no—
132C22×C4×C31—22no—
133C22×C4×C31—22no—
134C22×C4×C31—21no—
135C22×C4×C31—22no—
136C22×C4×C31—22no—
137C22×C4×C31—21no—
138C22×C4×C31—22no—
139C22×C4×C31—21no—
140C22×C4×C31—21no—
141C22×C4×C31—22no—
142C22×C4×C31—22no—
143C22×C4×C31C2×D412yes—
144C22×C4×C31C2×D414yes—
145C22×C4×C31C2×D414yes—
146C22×C4×C31C2×D412yes—
147C22×C4×C31C2×D414yes—
148C22×C4×C31C2×D412yes—
149C22×C4×C31C2×Q812yes—
150C22×C4×C31C2×Q812yes—
151C22×C4×C31C2×Q812yes—
152C22×C4×C31#4114yes—
153C22×C4×C31#4112yes—
154C4⋊C4×C31—28no—
155C4⋊C4×C31—28no—
156C4⋊C4×C31—216no—
157C4⋊C4×C31—216no—
158C4⋊C4×C31—28no—
159C4⋊C4×C31—48no—
160C4⋊C4×C31—48no—
161C4⋊C4×C31—44no—
162C42×C31—28no—
163#16605C3111yesmaximal, characteristic, direct product factor, Sylow
164C23×C31C22×D411yescharacteristic
165C23×C31C22×D412yes—
166C23×C31C22×Q811yescharacteristic
167C23×C31C2×#4111yescharacteristic
168C23×C31C2×#4112yes—
169C23×C31H(5,𝔽2)11yescharacteristic
170C23×C31H(5,𝔽2)11yescharacteristic
171C23×C312−1+411yescharacteristic
172C23×C312−1+412yes—
173C23×C312−1+412yes—
174C23×C312−1+411yescharacteristic
175C2×C4×C31—22no—
176C2×C4×C31—22no—
177C2×C4×C31—22no—
178C2×C4×C31—22no—
179C2×C4×C31—24no—
180C2×C4×C31—24no—
181C2×C4×C31—24no—
182C2×C4×C31—24no—
183C2×C4×C31—22no—
184C2×C4×C31—24no—
185C2×C4×C31—24no—
186C2×C4×C31—22no—
187C2×C4×C31—22no—
188C2×C4×C31—22no—
189C2×C4×C31—24no—
190C2×C4×C31—22no—
191C2×C4×C31—24no—
192C2×C4×C31—24no—
193C2×C4×C31—22no—
194C2×C4×C31—22no—
195C2×C4×C31—24no—
196C2×C4×C31—24no—
197C2×C4×C31—24no—
198C2×C4×C31—24no—
199C2×C4×C31—24no—
200C2×C4×C31—41no—
201C2×C4×C31—42no—
202C2×C4×C31—42no—
203C2×C4×C31—42no—
204C2×C4×C31—42no—
205C2×C4×C31—41no—
206C2×C4×C31—42no—
207C2×C4×C31—42no—
208C2×C4×C31—42no—
209C2×C4×C31—41no—
210C2×C4×C31—41no—
211C2×C4×C31—42no—
212C2×C4×C31—42no—
213C2×C4×C31—41no—
214C2×C4×C31—42no—
215C2×C4×C31—41no—
216C2×C4×C31—42no—
217C2×C4×C31—42no—
218C2×C4×C31—42no—
219C2×C4×C31—42no—
220C2×C4×C31—42no—
221C2×C4×C31—41no—
222C2×C4×C31—41no—
223C2×C4×C31—41no—
224C2×C4×C31—41no—
225C2×C4×C31—41no—
226C2×C4×C31—41no—
227C2×C4×C31—42no—
228C2×C4×C31—42no—
229C2×C4×C31—42no—
230C2×C4×C31—42no—
231C2×C4×C31—42no—
232C2×C4×C31—42no—
233C2×C4×C31—42no—
234C2×C4×C31—42no—
235C2×C4×C31—42no—
236C2×C4×C31—42no—
237C2×C4×C31—42no—
238C2×C4×C31#12014yes—
239C2×C4×C31C22⋊Q814yes—
240C22×#125C2×C3111yescharacteristic
241C2×#398C2×C3112yes—
242C2×#387C2×C3111yescharacteristic
243#1444C2×C3111yescharacteristic
244#1442C2×C3111yescharacteristic
245#1442C2×C3112yes—
246#1441C2×C3112yes—
247#1441C2×C3111yescharacteristic
248#1441C2×C3111yescharacteristic
249#1441C2×C3112yes—
250C4⋊#95C2×C3111yescharacteristic
251C22×C31C2×#12011yescharacteristic
252C22×C31C2×C22⋊Q811yescharacteristic
253C22×C31#53211yescharacteristic
254C22×C31#53611yescharacteristic
255C22×C31#53611yescharacteristic
256C22×C31#53612yes—
257C22×C31#53711yescharacteristic
258C22×C31#53711yescharacteristic
259C22×C31#53712yes—
260C22×C31#53912yes—
261C22×C31#54011yescharacteristic
262C22×C31#54111yescharacteristic
263C22×C31#54112yes—
264C22×C31#54411yescharacteristic
265C22×C31#54411yescharacteristic
266C22×C31#54612yes—
267C22×C31#54712yes—
268C22×C31#54812yes—
269C22×C31D4×Q812yes—
270C22×C31#55212yes—
271C22×C31#55712yes—
272C22×C31#56312yes—
273C22×C31#56412yes—
274C4×C31—24no—
275C4×C31—24no—
276C4×C31—42no—
277C4×C31—44no—
278C4×C31—42no—
279C4×C31—42no—
280C4×C31—44no—
281C4×C31—44no—
282C4×C31—81no—
283C4×C31—81no—
284C4×C31—82no—
285C2×#125—28no—
286C2×#125—24no—
287C22×C4⋊C4C22×C3111yescharacteristic
288C22×C4⋊C4C22×C3112yes—
289C22×C4⋊C4C22×C3111yescharacteristic
290C22×C4⋊C4C22×C3111yescharacteristic
291C22×C4⋊C4C22×C3112yes—
292C22×C4⋊C4C22×C3112yes—
293C22×C4⋊C4C22×C3112yes—
294C22×C4⋊C4C22×C3111yescharacteristic
295C22×C42C22×C3111yescharacteristic
296#398—28no—
297#387—24no—
298C2×#95C22×C3112yes—
299C2×#95C22×C3112yes—
300C2×#95C22×C3112yes—
301C2×#95C22×C3111yescharacteristic
302C2×#95C22×C3111yescharacteristic
303C2×#95C22×C3111yescharacteristic
304C2×#95C22×C3111yescharacteristic
305C2×#95C22×C3112yes—
306C2×#95C22×C3111yescharacteristic
307C2×#95C22×C3111yescharacteristic
308C2×#95C22×C3112yes—
309C2×#95C22×C3112yes—
310C2×#95C22×C3112yes—
311C2×#95C22×C3112yes—
312C2×C31#240911yescharacteristic
313C2×C31#243011yescharacteristic
314C2×C31#256511yescharacteristic
315C2×C31#261611yescharacteristic
316C2×C31#262911yescharacteristic
317C2×C31#266411yescharacteristic
318C2×C31#270712yes—
319C2×C31#271312yes—
320C2×C31#271912yes—
321C2×C31#272612yes—
322C2×C31#282211yescharacteristic
323C23×C4C23×C3111yescharacteristic
324C23×C4C23×C3112yes—
325C23×C4C23×C3111yescharacteristic
326C23×C4C23×C3112yes—
327C23×C4C23×C3112yes—
328C23×C4C23×C3111yescharacteristic
329C23×C4C23×C3111yescharacteristic
330C23×C4C23×C3111yescharacteristic
331C23×C4C23×C3112yes—
332C23×C4C23×C3111yescharacteristic
333C23×C4C23×C3111yescharacteristic
334#125—232no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—42no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4D4×C3118yes—
355C2×C4⋊C4Q8×C3114yes—
356C2×C42—24no—
357C2×C42D4×C3114yes—
358#95—22no—
359#95—22no—
360#95—22no—
361#95—22no—
362#95—24no—
363#95—24no—
364#95—24no—
365#95—22no—
366#95—24no—
367#95—22no—
368#95—42no—
369#95—42no—
370#95—42no—
371#95—42no—
372C31#1660511yescharacteristic, direct product factor, Sylow
373C24C24×C3111yescharacteristic
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—21no—
377C22×C4—22no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—22no—
381C22×C4—21no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4C2×D4×C3112yes—
429C22×C4C2×D4×C3114yes—
430C22×C4C2×D4×C3114yes—
431C22×C4C2×D4×C3112yes—
432C22×C4C2×D4×C3114yes—
433C22×C4C2×D4×C3112yes—
434C22×C4C2×Q8×C3112yes—
435C22×C4C2×Q8×C3112yes—
436C22×C4C2×Q8×C3112yes—
437C22×C4#41×C3114yes—
438C22×C4#41×C3112yes—
439C4⋊C4—28no—
440C4⋊C4—28no—
441C4⋊C4—216no—
442C4⋊C4—216no—
443C4⋊C4—28no—
444C4⋊C4—48no—
445C4⋊C4—48no—
446C4⋊C4—44no—
447C42—28no—
448C23C22×D4×C3111yescharacteristic
449C23C22×D4×C3112yes—
450C23C22×Q8×C3111yescharacteristic
451C23C2×#41×C3111yescharacteristic
452C23C2×#41×C3112yes—
453C23C31×H(5,𝔽2)11yescharacteristic
454C23C31×H(5,𝔽2)11yescharacteristic
455C23C31×2−1+411yescharacteristic
456C23C31×2−1+412yes—
457C23C31×2−1+412yes—
458C23C31×2−1+411yescharacteristic
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—24no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—22no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—24no—
474C2×C4—22no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—41no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—41no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—41no—
498C2×C4—42no—
499C2×C4—41no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4C31×#12014yes—
523C2×C4C31×C22⋊Q814yes—
524C22C2×C31×#12011yescharacteristic
525C22C2×C31×C22⋊Q811yescharacteristic
526C22C31×#53211yescharacteristic
527C22C31×#53611yescharacteristic
528C22C31×#53611yescharacteristic
529C22C31×#53612yes—
530C22C31×#53711yescharacteristic
531C22C31×#53711yescharacteristic
532C22C31×#53712yes—
533C22C31×#53912yes—
534C22C31×#54011yescharacteristic
535C22C31×#54111yescharacteristic
536C22C31×#54112yes—
537C22C31×#54411yescharacteristic
538C22C31×#54411yescharacteristic
539C22C31×#54612yes—
540C22C31×#54712yes—
541C22C31×#54812yes—
542C22D4×Q8×C3112yes—
543C22C31×#55212yes—
544C22C31×#55712yes—
545C22C31×#56312yes—
546C22C31×#56412yes—
547C4—24no—
548C4—24no—
549C4—42no—
550C4—44no—
551C4—42no—
552C4—42no—
553C4—44no—
554C4—44no—
555C4—81no—
556C4—81no—
557C4—82no—
558C2C31×#240911yescharacteristic
559C2C31×#243011yescharacteristic
560C2C31×#256511yescharacteristic
561C2C31×#261611yescharacteristic
562C2C31×#262911yescharacteristic
563C2C31×#266411yescharacteristic
564C2C31×#270712yes—
565C2C31×#271312yes—
566C2C31×#271912yes—
567C2C31×#272612yes—
568C2C31×#282211yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C31C24
commutator, Frattini, cosocleC24C24×C31
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
163. #16605C31direct (N × H)
372. C31#16605direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×#1252
C2×C31×#3982
C2×C31×#3872
C31×#14442
C31×#14422
C31×#14412
C31×C4⋊#952
#1660531