Finite Group Databasebeta

← C31×#16933 #21473692

Subgroups — C31×#16933 #21473692

Order 7936.

1002 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#1445C212yesmaximal
2C31×#1443C212yesmaximal
3C31×#1442C212yesmaximal
4C31×#1442C212yesmaximal
5C31×#1441C212yesmaximal
6C31×#1441C211yesmaximal, characteristic
7C31×#1441C211yesmaximal, characteristic
8C31×#1436C212yesmaximal
9C31×C4⋊#95C211yesmaximal, characteristic
10C22×C4⋊C4×C31C2212yes—
11C22×C4⋊C4×C31C2211yescharacteristic
12C22×C4⋊C4×C31C2211yescharacteristic
13C22×C4⋊C4×C31C2211yescharacteristic
14C22×C4⋊C4×C31C2211yescharacteristic
15C22×C42×C31C2211yescharacteristic
16C2×C31×#95C2212yes—
17C2×C31×#95C2212yes—
18C2×C31×#95C2212yes—
19C2×C31×#95C2212yes—
20C2×C31×#95C2212yes—
21C2×C31×#95C2212yes—
22C2×C31×#95C2212yes—
23C2×C31×#95C2212yes—
24C2×C31×#95C2212yes—
25C2×C31×#95C2212yes—
26C2×C31×#95C2212yes—
27C2×C31×#95C2211yescharacteristic
28C2×C31×#95C2211yescharacteristic
29C2×C31×#95C2212yes—
30C2×C31×#95C2212yes—
31C23×C4×C31C2312yes—
32C23×C4×C31C2312yes—
33C23×C4×C31C2312yes—
34C23×C4×C31C2312yes—
35C23×C4×C31C2311yescharacteristic
36C23×C4×C31C2311yescharacteristic
37C23×C4×C31C2312yes—
38C23×C4×C31C2312yes—
39C23×C4×C31C2311yescharacteristic
40C2×C4⋊C4×C31—24no—
41C2×C4⋊C4×C31—24no—
42C2×C4⋊C4×C31—24no—
43C2×C4⋊C4×C31—22no—
44C2×C4⋊C4×C31—41no—
45C2×C4⋊C4×C31—41no—
46C2×C4⋊C4×C31—41no—
47C2×C4⋊C4×C31—42no—
48C2×C4⋊C4×C31—41no—
49C2×C4⋊C4×C31—41no—
50C2×C4⋊C4×C31—42no—
51C2×C4⋊C4×C31—41no—
52C2×C4⋊C4×C31Q814yes—
53C2×C42×C31—22no—
54C2×C42×C31—41no—
55C2×C42×C31—41no—
56C31×#95—24no—
57C31×#95—24no—
58C31×#95—24no—
59C31×#95—24no—
60C31×#95—24no—
61C31×#95—42no—
62C31×#95—42no—
63C31×#95—42no—
64C31×#95—42no—
65C31×#95—41no—
66C31×#95—41no—
67C31×#95—42no—
68C31×#95—42no—
69C31×#95—42no—
70C31×#95—42no—
71C24×C31C2411yescharacteristic
72C22×C4×C31—21no—
73C22×C4×C31—21no—
74C22×C4×C31—21no—
75C22×C4×C31—21no—
76C22×C4×C31—22no—
77C22×C4×C31—22no—
78C22×C4×C31—22no—
79C22×C4×C31—22no—
80C22×C4×C31—22no—
81C22×C4×C31—22no—
82C22×C4×C31—22no—
83C22×C4×C31—22no—
84C22×C4×C31—22no—
85C22×C4×C31—22no—
86C22×C4×C31—22no—
87C22×C4×C31—21no—
88C22×C4×C31—21no—
89C22×C4×C31—22no—
90C22×C4×C31—22no—
91C22×C4×C31—22no—
92C22×C4×C31—22no—
93C22×C4×C31—21no—
94C22×C4×C31—21no—
95C22×C4×C31—22no—
96C22×C4×C31—22no—
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—22no—
106C22×C4×C31—22no—
107C22×C4×C31—22no—
108C22×C4×C31—22no—
109C22×C4×C31—22no—
110C22×C4×C31—22no—
111C22×C4×C31—22no—
112C22×C4×C31—22no—
113C22×C4×C31—22no—
114C22×C4×C31—22no—
115C22×C4×C31—22no—
116C22×C4×C31—22no—
117C22×C4×C31—22no—
118C22×C4×C31—22no—
119C22×C4×C31—22no—
120C22×C4×C31—22no—
121C22×C4×C31—22no—
122C22×C4×C31—22no—
123C22×C4×C31—22no—
124C22×C4×C31C2×Q812yes—
125C22×C4×C31C2×Q812yes—
126C22×C4×C31C2×Q812yes—
127C22×C4×C31#4114yes—
128C22×C4×C31#4114yes—
129C22×C4×C31#4112yes—
130C22×C4×C31#4112yes—
131C4⋊C4×C31—44no—
132C4⋊C4×C31—44no—
133C4⋊C4×C31—48no—
134C4⋊C4×C31—44no—
135C4⋊C4×C31—44no—
136C42×C31—44no—
137#16933C3111yesmaximal, characteristic, direct product factor, Sylow
138C23×C31C22×Q811yescharacteristic
139C23×C31C2×#4111yescharacteristic
140C23×C31C2×#4111yescharacteristic
141C23×C31C2×#4112yes—
142C23×C31C2×#4112yes—
143C23×C31H(5,𝔽2)11yescharacteristic
144C23×C31H(5,𝔽2)11yescharacteristic
145C23×C31H(5,𝔽2)11yescharacteristic
146C23×C31H(5,𝔽2)12yes—
147C23×C312−1+411yescharacteristic
148C23×C312−1+412yes—
149C2×C4×C31—22no—
150C2×C4×C31—22no—
151C2×C4×C31—22no—
152C2×C4×C31—22no—
153C2×C4×C31—22no—
154C2×C4×C31—22no—
155C2×C4×C31—24no—
156C2×C4×C31—24no—
157C2×C4×C31—22no—
158C2×C4×C31—22no—
159C2×C4×C31—24no—
160C2×C4×C31—24no—
161C2×C4×C31—24no—
162C2×C4×C31—24no—
163C2×C4×C31—24no—
164C2×C4×C31—24no—
165C2×C4×C31—42no—
166C2×C4×C31—42no—
167C2×C4×C31—42no—
168C2×C4×C31—42no—
169C2×C4×C31—42no—
170C2×C4×C31—42no—
171C2×C4×C31—41no—
172C2×C4×C31—42no—
173C2×C4×C31—41no—
174C2×C4×C31—42no—
175C2×C4×C31—42no—
176C2×C4×C31—41no—
177C2×C4×C31—41no—
178C2×C4×C31—42no—
179C2×C4×C31—42no—
180C2×C4×C31—42no—
181C2×C4×C31—42no—
182C2×C4×C31—42no—
183C2×C4×C31—42no—
184C2×C4×C31—42no—
185C2×C4×C31—42no—
186C2×C4×C31—42no—
187C2×C4×C31—42no—
188C2×C4×C31—42no—
189C2×C4×C31—42no—
190C2×C4×C31—42no—
191C2×C4×C31—42no—
192C2×C4×C31—42no—
193C2×C4×C31—42no—
194C2×C4×C31—42no—
195C2×C4×C31—42no—
196C2×C4×C31—42no—
197C2×C4×C31—42no—
198C2×C4×C31—42no—
199C2×C4×C31—42no—
200C2×C4×C31—42no—
201C2×C4×C31—42no—
202C2×C4×C31—42no—
203C2×C4×C31—42no—
204C2×C4×C31—42no—
205C2×C4×C31—42no—
206C2×C4×C31—42no—
207C2×C4×C31#12514yes—
208#1445C2×C3112yes—
209#1443C2×C3112yes—
210#1442C2×C3112yes—
211#1442C2×C3112yes—
212#1441C2×C3112yes—
213#1441C2×C3111yescharacteristic
214#1441C2×C3111yescharacteristic
215#1436C2×C3112yes—
216C4⋊#95C2×C3111yescharacteristic
217C22×C31C2×#12511yescharacteristic
218C22×C31#52912yes—
219C22×C31#53811yescharacteristic
220C22×C31#53811yescharacteristic
221C22×C31#53911yescharacteristic
222C22×C31#53911yescharacteristic
223C22×C31#53912yes—
224C22×C31#54012yes—
225C22×C31#54112yes—
226C22×C31#54212yes—
227C22×C31#54212yes—
228C22×C31#54311yescharacteristic
229C22×C31#54411yescharacteristic
230C22×C31#55111yescharacteristic
231C22×C31#55112yes—
232C22×C31#55312yes—
233C22×C31#55412yes—
234C22×C31#55511yescharacteristic
235C22×C31#55612yes—
236C22×C31#55712yes—
237C22×C31#56011yescharacteristic
238C22×C31#56212yes—
239C22×C31#56311yescharacteristic
240C4×C31—24no—
241C4×C31—44no—
242C4×C31—42no—
243C4×C31—42no—
244C4×C31—44no—
245C4×C31—82no—
246C4×C31—82no—
247C4×C31—82no—
248C4×C31—82no—
249C22×C4⋊C4C22×C3112yes—
250C22×C4⋊C4C22×C3111yescharacteristic
251C22×C4⋊C4C22×C3111yescharacteristic
252C22×C4⋊C4C22×C3111yescharacteristic
253C22×C4⋊C4C22×C3111yescharacteristic
254C22×C42C22×C3111yescharacteristic
255C2×#95C22×C3112yes—
256C2×#95C22×C3112yes—
257C2×#95C22×C3112yes—
258C2×#95C22×C3112yes—
259C2×#95C22×C3112yes—
260C2×#95C22×C3112yes—
261C2×#95C22×C3112yes—
262C2×#95C22×C3112yes—
263C2×#95C22×C3112yes—
264C2×#95C22×C3112yes—
265C2×#95C22×C3112yes—
266C2×#95C22×C3111yescharacteristic
267C2×#95C22×C3111yescharacteristic
268C2×#95C22×C3112yes—
269C2×#95C22×C3112yes—
270C2×C31#250912yes—
271C2×C31#257211yescharacteristic
272C2×C31#264611yescharacteristic
273C2×C31#265412yes—
274C2×C31#274811yescharacteristic
275C2×C31#275512yes—
276C2×C31#278612yes—
277C2×C31#278911yescharacteristic
278C2×C31#279511yescharacteristic
279C2×C31#280911yescharacteristic
280C2×C31#283011yescharacteristic
281C23×C4C23×C3112yes—
282C23×C4C23×C3112yes—
283C23×C4C23×C3112yes—
284C23×C4C23×C3112yes—
285C23×C4C23×C3111yescharacteristic
286C23×C4C23×C3111yescharacteristic
287C23×C4C23×C3112yes—
288C23×C4C23×C3112yes—
289C23×C4C23×C3111yescharacteristic
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—41no—
295C2×C4⋊C4—41no—
296C2×C4⋊C4—41no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—41no—
299C2×C4⋊C4—41no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—41no—
302C2×C4⋊C4Q8×C3114yes—
303C2×C42—22no—
304C2×C42—41no—
305C2×C42—41no—
306#95—24no—
307#95—24no—
308#95—24no—
309#95—24no—
310#95—24no—
311#95—42no—
312#95—42no—
313#95—42no—
314#95—42no—
315#95—41no—
316#95—41no—
317#95—42no—
318#95—42no—
319#95—42no—
320#95—42no—
321C31#1693311yescharacteristic, direct product factor, Sylow
322C24C24×C3111yescharacteristic
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4C2×Q8×C3112yes—
376C22×C4C2×Q8×C3112yes—
377C22×C4C2×Q8×C3112yes—
378C22×C4#41×C3114yes—
379C22×C4#41×C3114yes—
380C22×C4#41×C3112yes—
381C22×C4#41×C3112yes—
382C4⋊C4—44no—
383C4⋊C4—44no—
384C4⋊C4—48no—
385C4⋊C4—44no—
386C4⋊C4—44no—
387C42—44no—
388C23C22×Q8×C3111yescharacteristic
389C23C2×#41×C3111yescharacteristic
390C23C2×#41×C3111yescharacteristic
391C23C2×#41×C3112yes—
392C23C2×#41×C3112yes—
393C23C31×H(5,𝔽2)11yescharacteristic
394C23C31×H(5,𝔽2)11yescharacteristic
395C23C31×H(5,𝔽2)11yescharacteristic
396C23C31×H(5,𝔽2)12yes—
397C23C31×2−1+411yescharacteristic
398C23C31×2−1+412yes—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—24no—
406C2×C4—24no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—24no—
410C2×C4—24no—
411C2×C4—24no—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—41no—
422C2×C4—42no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4C31×#12514yes—
458C22C2×C31×#12511yescharacteristic
459C22C31×#52912yes—
460C22C31×#53811yescharacteristic
461C22C31×#53811yescharacteristic
462C22C31×#53911yescharacteristic
463C22C31×#53911yescharacteristic
464C22C31×#53912yes—
465C22C31×#54012yes—
466C22C31×#54112yes—
467C22C31×#54212yes—
468C22C31×#54212yes—
469C22C31×#54311yescharacteristic
470C22C31×#54411yescharacteristic
471C22C31×#55111yescharacteristic
472C22C31×#55112yes—
473C22C31×#55312yes—
474C22C31×#55412yes—
475C22C31×#55511yescharacteristic
476C22C31×#55612yes—
477C22C31×#55712yes—
478C22C31×#56011yescharacteristic
479C22C31×#56212yes—
480C22C31×#56311yescharacteristic
481C4—24no—
482C4—44no—
483C4—42no—
484C4—42no—
485C4—44no—
486C4—82no—
487C4—82no—
488C4—82no—
489C4—82no—
490C2C31×#250912yes—
491C2C31×#257211yescharacteristic
492C2C31×#264611yescharacteristic
493C2C31×#265412yes—
494C2C31×#274811yescharacteristic
495C2C31×#275512yes—
496C2C31×#278612yes—
497C2C31×#278911yescharacteristic
498C2C31×#279511yescharacteristic
499C2C31×#280911yescharacteristic
500C2C31×#283011yescharacteristic
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
137. #16933C31direct (N × H)
321. C31#16933direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#14452
C31×#14432
C31×#14422
C31×#14412
C31×#14362
C31×C4⋊#952
#1693331