Finite Group Databasebeta

← C31×#17003 #21473762

Subgroups — C31×#17003 #21473762

Order 7936.

1090 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#1445C212yesmaximal
2C31×#1444C212yesmaximal
3C31×#1444C212yesmaximal
4C31×#1441C212yesmaximal
5C31×#1441C211yesmaximal, characteristic
6C31×#1441C211yesmaximal, characteristic
7C31×#1441C212yesmaximal
8C31×#1436C212yesmaximal
9C31×C4⋊#95C211yesmaximal, characteristic
10C22×C4⋊C4×C31C2211yescharacteristic
11C22×C4⋊C4×C31C2211yescharacteristic
12C22×C4⋊C4×C31C2211yescharacteristic
13C22×C4⋊C4×C31C2212yes—
14C22×C4⋊C4×C31C2212yes—
15C22×C4⋊C4×C31C2211yescharacteristic
16C22×C4⋊C4×C31C2212yes—
17C22×C42×C31C2211yescharacteristic
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×#95C2212yes—
29C2×C31×#95C2212yes—
30C2×C31×#95C2211yescharacteristic
31C23×C4×C31C2312yes—
32C23×C4×C31C2312yes—
33C23×C4×C31C2312yes—
34C23×C4×C31C2311yescharacteristic
35C23×C4×C31C2312yes—
36C23×C4×C31C2311yescharacteristic
37C23×C4×C31C2312yes—
38C23×C4×C31C2312yes—
39C23×C4×C31C2311yescharacteristic
40C2×C4⋊C4×C31—24no—
41C2×C4⋊C4×C31—22no—
42C2×C4⋊C4×C31—41no—
43C2×C4⋊C4×C31—41no—
44C2×C4⋊C4×C31—42no—
45C2×C4⋊C4×C31—42no—
46C2×C4⋊C4×C31—41no—
47C2×C4⋊C4×C31—41no—
48C2×C4⋊C4×C31—41no—
49C2×C4⋊C4×C31—42no—
50C2×C4⋊C4×C31—42no—
51C2×C4⋊C4×C31—42no—
52C2×C4⋊C4×C31—42no—
53C2×C4⋊C4×C31—42no—
54C2×C4⋊C4×C31—41no—
55C2×C4⋊C4×C31—42no—
56C2×C4⋊C4×C31—42no—
57C2×C4⋊C4×C31Q818yes—
58C2×C4⋊C4×C31Q814yes—
59C2×C42×C31—22no—
60C2×C42×C31—41no—
61C2×C42×C31—41no—
62C31×#95—24no—
63C31×#95—24no—
64C31×#95—24no—
65C31×#95—24no—
66C31×#95—42no—
67C31×#95—42no—
68C31×#95—42no—
69C31×#95—42no—
70C31×#95—42no—
71C31×#95—41no—
72C31×#95—41no—
73C31×#95—42no—
74C31×#95—42no—
75C24×C31C2411yescharacteristic
76C22×C4×C31—21no—
77C22×C4×C31—21no—
78C22×C4×C31—21no—
79C22×C4×C31—21no—
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—22no—
90C22×C4×C31—22no—
91C22×C4×C31—22no—
92C22×C4×C31—22no—
93C22×C4×C31—22no—
94C22×C4×C31—22no—
95C22×C4×C31—22no—
96C22×C4×C31—22no—
97C22×C4×C31—22no—
98C22×C4×C31—21no—
99C22×C4×C31—21no—
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—21no—
107C22×C4×C31—21no—
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×Q814yes—
127C22×C4×C31C2×Q812yes—
128C22×C4×C31C2×Q812yes—
129C22×C4×C31C2×Q814yes—
130C22×C4×C31C2×Q814yes—
131C22×C4×C31C2×Q812yes—
132C22×C4×C31#4114yes—
133C22×C4×C31#4112yes—
134C22×C4×C31#4112yes—
135C4⋊C4×C31—44no—
136C4⋊C4×C31—48no—
137C4⋊C4×C31—44no—
138C4⋊C4×C31—44no—
139C4⋊C4×C31—44no—
140C4⋊C4×C31—48no—
141C4⋊C4×C31—48no—
142C42×C31—44no—
143#17003C3111yesmaximal, characteristic, direct product factor, Sylow
144C23×C31C22×Q811yescharacteristic
145C23×C31C22×Q812yes—
146C23×C31C2×#4111yescharacteristic
147C23×C31C2×#4111yescharacteristic
148C23×C31C2×#4112yes—
149C23×C31H(5,𝔽2)11yescharacteristic
150C23×C31H(5,𝔽2)11yescharacteristic
151C23×C31H(5,𝔽2)11yescharacteristic
152C23×C31H(5,𝔽2)12yes—
153C23×C31H(5,𝔽2)12yes—
154C23×C312−1+411yescharacteristic
155C2×C4×C31—22no—
156C2×C4×C31—22no—
157C2×C4×C31—22no—
158C2×C4×C31—22no—
159C2×C4×C31—22no—
160C2×C4×C31—22no—
161C2×C4×C31—24no—
162C2×C4×C31—24no—
163C2×C4×C31—24no—
164C2×C4×C31—22no—
165C2×C4×C31—22no—
166C2×C4×C31—24no—
167C2×C4×C31—24no—
168C2×C4×C31—24no—
169C2×C4×C31—24no—
170C2×C4×C31—24no—
171C2×C4×C31—24no—
172C2×C4×C31—24no—
173C2×C4×C31—24no—
174C2×C4×C31—24no—
175C2×C4×C31—24no—
176C2×C4×C31—24no—
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—42no—
185C2×C4×C31—42no—
186C2×C4×C31—42no—
187C2×C4×C31—42no—
188C2×C4×C31—42no—
189C2×C4×C31—41no—
190C2×C4×C31—41no—
191C2×C4×C31—42no—
192C2×C4×C31—42no—
193C2×C4×C31—42no—
194C2×C4×C31—41no—
195C2×C4×C31—42no—
196C2×C4×C31—41no—
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×C4×C31—42no—
210C2×C4×C31—42no—
211C2×C4×C31—42no—
212C2×C4×C31—42no—
213C2×C4×C31#12514yes—
214#1445C2×C3112yes—
215#1444C2×C3112yes—
216#1444C2×C3112yes—
217#1441C2×C3112yes—
218#1441C2×C3111yescharacteristic
219#1441C2×C3111yescharacteristic
220#1441C2×C3112yes—
221#1436C2×C3112yes—
222C4⋊#95C2×C3111yescharacteristic
223C22×C31C2×#12511yescharacteristic
224C22×C31#53312yes—
225C22×C31#53811yescharacteristic
226C22×C31#53811yescharacteristic
227C22×C31#53911yescharacteristic
228C22×C31#53911yescharacteristic
229C22×C31#53912yes—
230C22×C31#54012yes—
231C22×C31#54012yes—
232C22×C31#54311yescharacteristic
233C22×C31#54312yes—
234C22×C31#54411yescharacteristic
235C22×C31#54412yes—
236C22×C31#55111yescharacteristic
237C22×C31#55312yes—
238C22×C31#55412yes—
239C22×C31#55412yes—
240C22×C31#55412yes—
241C22×C31Q8211yescharacteristic
242C22×C31Q8212yes—
243C22×C31#56011yescharacteristic
244C22×C31#56012yes—
245C22×C31H(3,𝔽4)11yescharacteristic
246C4×C31—24no—
247C4×C31—44no—
248C4×C31—42no—
249C4×C31—42no—
250C4×C31—44no—
251C4×C31—44no—
252C4×C31—44no—
253C4×C31—82no—
254C4×C31—82no—
255C22×C4⋊C4C22×C3111yescharacteristic
256C22×C4⋊C4C22×C3111yescharacteristic
257C22×C4⋊C4C22×C3111yescharacteristic
258C22×C4⋊C4C22×C3112yes—
259C22×C4⋊C4C22×C3112yes—
260C22×C4⋊C4C22×C3111yescharacteristic
261C22×C4⋊C4C22×C3112yes—
262C22×C42C22×C3111yescharacteristic
263C2×#95C22×C3112yes—
264C2×#95C22×C3112yes—
265C2×#95C22×C3112yes—
266C2×#95C22×C3112yes—
267C2×#95C22×C3112yes—
268C2×#95C22×C3112yes—
269C2×#95C22×C3112yes—
270C2×#95C22×C3112yes—
271C2×#95C22×C3112yes—
272C2×#95C22×C3111yescharacteristic
273C2×#95C22×C3112yes—
274C2×#95C22×C3112yes—
275C2×#95C22×C3111yescharacteristic
276C2×C31#250712yes—
277C2×C31#258611yescharacteristic
278C2×C31#264611yescharacteristic
279C2×C31#266712yes—
280C2×C31#274811yescharacteristic
281C2×C31#278012yes—
282C2×C31#278211yescharacteristic
283C2×C31#279211yescharacteristic
284C2×C31#279212yes—
285C2×C31#281111yescharacteristic
286C2×C31#282811yescharacteristic
287C23×C4C23×C3112yes—
288C23×C4C23×C3112yes—
289C23×C4C23×C3111yescharacteristic
290C23×C4C23×C3112yes—
291C23×C4C23×C3111yescharacteristic
292C23×C4C23×C3112yes—
293C23×C4C23×C3112yes—
294C23×C4C23×C3112yes—
295C23×C4C23×C3111yescharacteristic
296C2×C4⋊C4—24no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—41no—
299C2×C4⋊C4—41no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—42no—
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—42no—
310C2×C4⋊C4—41no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4Q8×C3118yes—
314C2×C4⋊C4Q8×C3114yes—
315C2×C42—22no—
316C2×C42—41no—
317C2×C42—41no—
318#95—24no—
319#95—24no—
320#95—24no—
321#95—24no—
322#95—42no—
323#95—42no—
324#95—42no—
325#95—42no—
326#95—42no—
327#95—41no—
328#95—41no—
329#95—42no—
330#95—42no—
331C31#1700311yescharacteristic, direct product factor, Sylow
332C24C24×C3111yescharacteristic
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
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—21no—
356C22×C4—21no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—21no—
364C22×C4—21no—
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×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4C2×Q8×C3114yes—
384C22×C4C2×Q8×C3112yes—
385C22×C4C2×Q8×C3112yes—
386C22×C4C2×Q8×C3114yes—
387C22×C4C2×Q8×C3114yes—
388C22×C4C2×Q8×C3112yes—
389C22×C4#41×C3114yes—
390C22×C4#41×C3112yes—
391C22×C4#41×C3112yes—
392C4⋊C4—44no—
393C4⋊C4—48no—
394C4⋊C4—44no—
395C4⋊C4—44no—
396C4⋊C4—44no—
397C4⋊C4—48no—
398C4⋊C4—48no—
399C42—44no—
400C23C22×Q8×C3111yescharacteristic
401C23C22×Q8×C3112yes—
402C23C2×#41×C3111yescharacteristic
403C23C2×#41×C3111yescharacteristic
404C23C2×#41×C3112yes—
405C23C31×H(5,𝔽2)11yescharacteristic
406C23C31×H(5,𝔽2)11yescharacteristic
407C23C31×H(5,𝔽2)11yescharacteristic
408C23C31×H(5,𝔽2)12yes—
409C23C31×H(5,𝔽2)12yes—
410C23C31×2−1+411yescharacteristic
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—24no—
418C2×C4—24no—
419C2×C4—24no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—24no—
423C2×C4—24no—
424C2×C4—24no—
425C2×C4—24no—
426C2×C4—24no—
427C2×C4—24no—
428C2×C4—24no—
429C2×C4—24no—
430C2×C4—24no—
431C2×C4—24no—
432C2×C4—24no—
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—41no—
446C2×C4—41no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—41no—
451C2×C4—42no—
452C2×C4—41no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4C31×#12514yes—
470C22C2×C31×#12511yescharacteristic
471C22C31×#53312yes—
472C22C31×#53811yescharacteristic
473C22C31×#53811yescharacteristic
474C22C31×#53911yescharacteristic
475C22C31×#53911yescharacteristic
476C22C31×#53912yes—
477C22C31×#54012yes—
478C22C31×#54012yes—
479C22C31×#54311yescharacteristic
480C22C31×#54312yes—
481C22C31×#54411yescharacteristic
482C22C31×#54412yes—
483C22C31×#55111yescharacteristic
484C22C31×#55312yes—
485C22C31×#55412yes—
486C22C31×#55412yes—
487C22C31×#55412yes—
488C22Q82×C3111yescharacteristic
489C22Q82×C3112yes—
490C22C31×#56011yescharacteristic
491C22C31×#56012yes—
492C22C31×H(3,𝔽4)11yescharacteristic
493C4—24no—
494C4—44no—
495C4—42no—
496C4—42no—
497C4—44no—
498C4—44no—
499C4—44no—
500C4—82no—
501C4—82no—
502C2C31×#250712yes—
503C2C31×#258611yescharacteristic
504C2C31×#264611yescharacteristic
505C2C31×#266712yes—
506C2C31×#274811yescharacteristic
507C2C31×#278012yes—
508C2C31×#278211yescharacteristic
509C2C31×#279211yescharacteristic
510C2C31×#279212yes—
511C2C31×#281111yescharacteristic
512C2C31×#282811yescharacteristic
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
143. #17003C31direct (N × H)
331. C31#17003direct (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×#14442
C31×#14412
C31×#14362
C31×C4⋊#952
#1700331