Finite Group Databasebeta

← C31×#17134 #21473893

Subgroups — C31×#17134 #21473893

Order 7936.

1138 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#400C212yesmaximal
2C2×C31×#398C212yesmaximal
3C31×#1445C211yesmaximal, characteristic
4C31×#1444C211yesmaximal, characteristic
5C31×#1442C211yesmaximal, characteristic
6C31×#1441C212yesmaximal
7C31×#1441C212yesmaximal
8C31×#1441C212yesmaximal
9C31×#1441C212yesmaximal
10C22×C4⋊C4×C31C2212yes—
11C22×C4⋊C4×C31C2212yes—
12C22×C4⋊C4×C31C2212yes—
13C22×C4⋊C4×C31C2212yes—
14C22×C4⋊C4×C31C2211yescharacteristic
15C22×C4⋊C4×C31C2211yescharacteristic
16C22×C4⋊C4×C31C2211yescharacteristic
17C31×#400—28no—
18C31×#398—28no—
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×#95C2212yes—
28C2×C31×#95C2212yes—
29C2×C31×#95C2211yescharacteristic
30C2×C31×#95C2211yescharacteristic
31C2×C31×#95C2211yescharacteristic
32C2×C31×#95C2211yescharacteristic
33C23×C4×C31C2312yes—
34C23×C4×C31C2312yes—
35C23×C4×C31C2312yes—
36C23×C4×C31C2312yes—
37C23×C4×C31C2311yescharacteristic
38C23×C4×C31C2311yescharacteristic
39C23×C4×C31C2312yes—
40C23×C4×C31C2311yescharacteristic
41C23×C4×C31C2312yes—
42C2×C4⋊C4×C31—24no—
43C2×C4⋊C4×C31—24no—
44C2×C4⋊C4×C31—24no—
45C2×C4⋊C4×C31—24no—
46C2×C4⋊C4×C31—24no—
47C2×C4⋊C4×C31—24no—
48C2×C4⋊C4×C31—24no—
49C2×C4⋊C4×C31—24no—
50C2×C4⋊C4×C31—24no—
51C2×C4⋊C4×C31—41no—
52C2×C4⋊C4×C31—41no—
53C2×C4⋊C4×C31—41no—
54C2×C4⋊C4×C31—42no—
55C2×C4⋊C4×C31—42no—
56C2×C4⋊C4×C31—42no—
57C2×C4⋊C4×C31—42no—
58C2×C4⋊C4×C31—41no—
59C2×C4⋊C4×C31—42no—
60C2×C4⋊C4×C31Q814yes—
61C31×#95—24no—
62C31×#95—24no—
63C31×#95—24no—
64C31×#95—24no—
65C31×#95—24no—
66C31×#95—24no—
67C31×#95—42no—
68C31×#95—42no—
69C31×#95—42no—
70C31×#95—41no—
71C31×#95—42no—
72C31×#95—41no—
73C31×#95D414yes—
74C31×#95D414yes—
75C24×C31C2411yescharacteristic
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—22no—
88C22×C4×C31—22no—
89C22×C4×C31—21no—
90C22×C4×C31—21no—
91C22×C4×C31—22no—
92C22×C4×C31—21no—
93C22×C4×C31—21no—
94C22×C4×C31—22no—
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—21no—
105C22×C4×C31—21no—
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×C31—22no—
125C22×C4×C31—22no—
126C22×C4×C31C2×D412yes—
127C22×C4×C31C2×D414yes—
128C22×C4×C31C2×D412yes—
129C22×C4×C31C2×D414yes—
130C22×C4×C31C2×Q812yes—
131C22×C4×C31C2×Q814yes—
132C22×C4×C31#4114yes—
133C4⋊C4×C31—44no—
134C4⋊C4×C31—48no—
135C4⋊C4×C31—48no—
136C4⋊C4×C31—48no—
137C4⋊C4×C31—48no—
138C4⋊C4×C31—44no—
139C4⋊C4×C31—44no—
140#17134C3111yesmaximal, characteristic, direct product factor, Sylow
141C23×C31C22×D411yescharacteristic
142C23×C31C22×D411yescharacteristic
143C23×C31C22×Q811yescharacteristic
144C23×C31C2×#4112yes—
145C23×C31H(5,𝔽2)11yescharacteristic
146C23×C31H(5,𝔽2)12yes—
147C23×C31H(5,𝔽2)11yescharacteristic
148C23×C312−1+412yes—
149C23×C312−1+412yes—
150C23×C312−1+411yescharacteristic
151C23×C312−1+411yescharacteristic
152C2×C4×C31—24no—
153C2×C4×C31—24no—
154C2×C4×C31—22no—
155C2×C4×C31—22no—
156C2×C4×C31—24no—
157C2×C4×C31—22no—
158C2×C4×C31—24no—
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—24no—
166C2×C4×C31—24no—
167C2×C4×C31—24no—
168C2×C4×C31—24no—
169C2×C4×C31—24no—
170C2×C4×C31—42no—
171C2×C4×C31—42no—
172C2×C4×C31—42no—
173C2×C4×C31—42no—
174C2×C4×C31—42no—
175C2×C4×C31—42no—
176C2×C4×C31—42no—
177C2×C4×C31—42no—
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—41no—
185C2×C4×C31—41no—
186C2×C4×C31—41no—
187C2×C4×C31—41no—
188C2×C4×C31—42no—
189C2×C4×C31—42no—
190C2×C4×C31—42no—
191C2×C4×C31—42no—
192C2×C4×C31—41no—
193C2×C4×C31—42no—
194C2×C4×C31—41no—
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—42no—
208C2×C4×C31—42no—
209C2×#400C2×C3112yes—
210C2×#398C2×C3112yes—
211#1445C2×C3111yescharacteristic
212#1444C2×C3111yescharacteristic
213#1442C2×C3111yescharacteristic
214#1441C2×C3112yes—
215#1441C2×C3112yes—
216#1441C2×C3112yes—
217#1441C2×C3112yes—
218C22×C31#53612yes—
219C22×C31#53711yescharacteristic
220C22×C31#53712yes—
221C22×C31#53711yescharacteristic
222C22×C31#53912yes—
223C22×C31#54112yes—
224C22×C31#54212yes—
225C22×C31#54311yescharacteristic
226C22×C31#54412yes—
227C22×C31D4211yescharacteristic
228C22×C31#54612yes—
229C22×C31#54712yes—
230C22×C31D4×Q811yescharacteristic
231C22×C31D4×Q811yescharacteristic
232C22×C31#55111yescharacteristic
233C22×C31#55712yes—
234C22×C31#56011yescharacteristic
235C22×C31#56212yes—
236C22×C31#56311yescharacteristic
237C22×C31#56311yescharacteristic
238C22×C31#56312yes—
239C22×C31#56311yescharacteristic
240C22×C31#56412yes—
241C4×C31—42no—
242C4×C31—44no—
243C4×C31—44no—
244C4×C31—44no—
245C4×C31—42no—
246C4×C31—44no—
247C4×C31—42no—
248C4×C31—82no—
249C4×C31—82no—
250C22×C4⋊C4C22×C3112yes—
251C22×C4⋊C4C22×C3112yes—
252C22×C4⋊C4C22×C3112yes—
253C22×C4⋊C4C22×C3112yes—
254C22×C4⋊C4C22×C3111yescharacteristic
255C22×C4⋊C4C22×C3111yescharacteristic
256C22×C4⋊C4C22×C3111yescharacteristic
257#400—28no—
258#398—28no—
259C2×#95C22×C3112yes—
260C2×#95C22×C3112yes—
261C2×#95C22×C3112yes—
262C2×#95C22×C3112yes—
263C2×#95C22×C3112yes—
264C2×#95C22×C3112yes—
265C2×#95C22×C3112yes—
266C2×#95C22×C3112yes—
267C2×#95C22×C3112yes—
268C2×#95C22×C3112yes—
269C2×#95C22×C3111yescharacteristic
270C2×#95C22×C3111yescharacteristic
271C2×#95C22×C3111yescharacteristic
272C2×#95C22×C3111yescharacteristic
273C2×C31#267212yes—
274C2×C31#268311yescharacteristic
275C2×C31#269311yescharacteristic
276C2×C31#271312yes—
277C2×C31#272211yescharacteristic
278C2×C31#272612yes—
279C2×C31#279911yescharacteristic
280C2×C31#282211yescharacteristic
281C2×C31#282311yescharacteristic
282C2×C31#283912yes—
283C2×C31#284111yescharacteristic
284C23×C4C23×C3112yes—
285C23×C4C23×C3112yes—
286C23×C4C23×C3112yes—
287C23×C4C23×C3112yes—
288C23×C4C23×C3111yescharacteristic
289C23×C4C23×C3111yescharacteristic
290C23×C4C23×C3112yes—
291C23×C4C23×C3111yescharacteristic
292C23×C4C23×C3112yes—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—41no—
303C2×C4⋊C4—41no—
304C2×C4⋊C4—41no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—41no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4Q8×C3114yes—
312#95—24no—
313#95—24no—
314#95—24no—
315#95—24no—
316#95—24no—
317#95—24no—
318#95—42no—
319#95—42no—
320#95—42no—
321#95—41no—
322#95—42no—
323#95—41no—
324#95D4×C3114yes—
325#95D4×C3114yes—
326C31#1713411yescharacteristic, direct product factor, Sylow
327C24C24×C3111yescharacteristic
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—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—21no—
342C22×C4—21no—
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—21no—
357C22×C4—21no—
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×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4C2×D4×C3112yes—
379C22×C4C2×D4×C3114yes—
380C22×C4C2×D4×C3112yes—
381C22×C4C2×D4×C3114yes—
382C22×C4C2×Q8×C3112yes—
383C22×C4C2×Q8×C3114yes—
384C22×C4#41×C3114yes—
385C4⋊C4—44no—
386C4⋊C4—48no—
387C4⋊C4—48no—
388C4⋊C4—48no—
389C4⋊C4—48no—
390C4⋊C4—44no—
391C4⋊C4—44no—
392C23C22×D4×C3111yescharacteristic
393C23C22×D4×C3111yescharacteristic
394C23C22×Q8×C3111yescharacteristic
395C23C2×#41×C3112yes—
396C23C31×H(5,𝔽2)11yescharacteristic
397C23C31×H(5,𝔽2)12yes—
398C23C31×H(5,𝔽2)11yescharacteristic
399C23C31×2−1+412yes—
400C23C31×2−1+412yes—
401C23C31×2−1+411yescharacteristic
402C23C31×2−1+411yescharacteristic
403C2×C4—24no—
404C2×C4—24no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—24no—
408C2×C4—22no—
409C2×C4—24no—
410C2×C4—24no—
411C2×C4—24no—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—24no—
416C2×C4—24no—
417C2×C4—24no—
418C2×C4—24no—
419C2×C4—24no—
420C2×C4—24no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—41no—
444C2×C4—42no—
445C2×C4—41no—
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×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C22C31×#53612yes—
461C22C31×#53711yescharacteristic
462C22C31×#53712yes—
463C22C31×#53711yescharacteristic
464C22C31×#53912yes—
465C22C31×#54112yes—
466C22C31×#54212yes—
467C22C31×#54311yescharacteristic
468C22C31×#54412yes—
469C22D42×C3111yescharacteristic
470C22C31×#54612yes—
471C22C31×#54712yes—
472C22D4×Q8×C3111yescharacteristic
473C22D4×Q8×C3111yescharacteristic
474C22C31×#55111yescharacteristic
475C22C31×#55712yes—
476C22C31×#56011yescharacteristic
477C22C31×#56212yes—
478C22C31×#56311yescharacteristic
479C22C31×#56311yescharacteristic
480C22C31×#56312yes—
481C22C31×#56311yescharacteristic
482C22C31×#56412yes—
483C4—42no—
484C4—44no—
485C4—44no—
486C4—44no—
487C4—42no—
488C4—44no—
489C4—42no—
490C4—82no—
491C4—82no—
492C2C31×#267212yes—
493C2C31×#268311yescharacteristic
494C2C31×#269311yescharacteristic
495C2C31×#271312yes—
496C2C31×#272211yescharacteristic
497C2C31×#272612yes—
498C2C31×#279911yescharacteristic
499C2C31×#282211yescharacteristic
500C2C31×#282311yescharacteristic
501C2C31×#283912yes—
502C2C31×#284111yescharacteristic
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
140. #17134C31direct (N × H)
326. C31#17134direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4002
C2×C31×#3982
C31×#14452
C31×#14442
C31×#14422
C31×#14412
#1713431