Finite Group Databasebeta

← C31×#10572 #21467331

Subgroups — C31×#10572 #21467331

Order 7936.

560 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2646C211yesmaximal, characteristic
2C31×#1853C211yesmaximal, characteristic
3C31×#1852C211yesmaximal, characteristic
4C31×#1444C211yesmaximal, characteristic
5C31×#1294C211yesmaximal, characteristic
6C31×#1294C211yesmaximal, characteristic
7C31×#1280C211yesmaximal, characteristic
8C22×C4⋊C4×C31—21no—
9C22×C4⋊C4×C31C2211yescharacteristic
10C2×C31×#107—21no—
11C2×C31×#106—21no—
12C2×C31×C22⋊C8C2211yescharacteristic
13C2×C31×C22⋊C8C2211yescharacteristic
14C31×#400—21no—
15C31×#400—21no—
16C31×#398—21no—
17C31×#398—21no—
18C31×#385—21no—
19C31×#385—21no—
20C31×#380C2211yescharacteristic
21C31×#380C2211yescharacteristic
22C2×C31×#95—21no—
23C2×C31×#95C2211yescharacteristic
24C2×C31×#95C2211yescharacteristic
25C31×#340—21no—
26C31×#340—21no—
27C23×C4×C31—21no—
28C23×C4×C31—21no—
29C23×C4×C31D411yescharacteristic
30C23×C4×C31D411yescharacteristic
31C23×C4×C31C2311yescharacteristic
32C22×C8×C31—21no—
33C22×C8×C31—21no—
34C2×C4⋊C4×C31—21no—
35C2×C4⋊C4×C31—21no—
36C2×C4⋊C4×C31—21no—
37C2×C4⋊C4×C31—21no—
38C2×C4⋊C4×C31—21no—
39C2×C4⋊C4×C31—21no—
40C2×C4⋊C4×C31—42no—
41C2×C4⋊C4×C31—42no—
42C2×C4⋊C4×C31—42no—
43C2×C4⋊C4×C31—42no—
44C2×C4⋊C4×C31D411yescharacteristic
45C2×C4⋊C4×C31D411yescharacteristic
46C2×C4⋊C4×C31D411yescharacteristic
47C2×C4⋊C4×C31D411yescharacteristic
48C2×C22⋊C4×C31—21no—
49C2×C22⋊C4×C31—21no—
50C31×#107—42no—
51C31×#106—42no—
52C31×C22⋊C8—21no—
53C31×C22⋊C8—21no—
54C31×C22⋊C8Q812yes—
55C31×C22⋊C8Q812yes—
56C31×#95—21no—
57C31×#95—21no—
58C31×#95—21no—
59C31×#95—21no—
60C31×#95—21no—
61C31×#95—21no—
62C31×#95—21no—
63C31×#95—21no—
64C31×#95—21no—
65C31×#95—42no—
66C31×#95Q812yes—
67C24×C31C2×D411yescharacteristic
68C22×C4×C31—22no—
69C22×C4×C31—22no—
70C22×C4×C31—22no—
71C22×C4×C31—22no—
72C22×C4×C31—21no—
73C22×C4×C31—21no—
74C22×C4×C31—21no—
75C22×C4×C31—21no—
76C22×C4×C31—21no—
77C22×C4×C31—21no—
78C22×C4×C31—21no—
79C22×C4×C31—21no—
80C22×C4×C31—21no—
81C22×C4×C31—21no—
82C22×C4×C31—41no—
83C22×C4×C31—41no—
84C22×C4×C31—41no—
85C22×C4×C31—41no—
86C22×C4×C31—41no—
87C22×C4×C31—41no—
88C22×C4×C31—41no—
89C22×C4×C31—41no—
90C22×C4×C31—41no—
91C22×C4×C31—41no—
92C22×C4×C31—41no—
93C22×C4×C31—41no—
94C22×C4×C31—41no—
95C22×C4×C31—41no—
96C22×C4×C31—41no—
97C22×C4×C31—41no—
98C22×C4×C31C2×D411yescharacteristic
99C22×C4×C31C2×D411yescharacteristic
100C22×C4×C31C2×Q811yescharacteristic
101C22×C4×C31C2×Q811yescharacteristic
102C22×C4×C31C2×Q811yescharacteristic
103C22×C4×C31#4111yescharacteristic
104C2×C8×C31—22no—
105C2×C8×C31—22no—
106C2×C8×C31—41no—
107C2×C8×C31—41no—
108C2×C8×C31—41no—
109C2×C8×C31—41no—
110C4⋊C4×C31—22no—
111C4⋊C4×C31—22no—
112C4⋊C4×C31—41no—
113C4⋊C4×C31—41no—
114C4⋊C4×C31—41no—
115C4⋊C4×C31—41no—
116C4⋊C4×C31—41no—
117C4⋊C4×C31—41no—
118C4⋊C4×C31—48no—
119C4⋊C4×C31—81no—
120C4⋊C4×C31—81no—
121C4⋊C4×C31—81no—
122C4⋊C4×C31—81no—
123C22⋊C4×C31—41no—
124C22⋊C4×C31—41no—
125C22⋊C4×C31—41no—
126C22⋊C4×C31—41no—
127#10572C3111yesmaximal, characteristic, direct product factor, Sylow
128C23×C31—21no—
129C23×C31—21no—
130C23×C31—21no—
131C23×C31—21no—
132C23×C31#12011yescharacteristic
133C23×C31C22⋊Q811yescharacteristic
134C23×C31C4⋊Q811yescharacteristic
135C23×C31#13511yescharacteristic
136C23×C31#13511yescharacteristic
137C23×C31AGL(1,ℤ/8)11yescharacteristic
138C23×C31#13711yescharacteristic
139C2×C4×C31—21no—
140C2×C4×C31—21no—
141C2×C4×C31—21no—
142C2×C4×C31—21no—
143C2×C4×C31—24no—
144C2×C4×C31—41no—
145C2×C4×C31—41no—
146C2×C4×C31—41no—
147C2×C4×C31—41no—
148C2×C4×C31—42no—
149C2×C4×C31—42no—
150C2×C4×C31—42no—
151C2×C4×C31—42no—
152C2×C4×C31—42no—
153C2×C4×C31—42no—
154C2×C4×C31—42no—
155C2×C4×C31—42no—
156C2×C4×C31—42no—
157C2×C4×C31—42no—
158C2×C4×C31—41no—
159C2×C4×C31—41no—
160C2×C4×C31—41no—
161C2×C4×C31—41no—
162C2×C4×C31—41no—
163C2×C4×C31—41no—
164C2×C4×C31—41no—
165C2×C4×C31—41no—
166C2×C4×C31—41no—
167C2×C4×C31—41no—
168C2×C4×C31—41no—
169C2×C4×C31—41no—
170C2×C4×C31—42no—
171C2×C4×C31—41no—
172C2×C4×C31—41no—
173C2×C4×C31—41no—
174C2×C4×C31—41no—
175C2×C4×C31—41no—
176C2×C4×C31—41no—
177C2×C4×C31—81no—
178C2×C4×C31—81no—
179C2×C4×C31—81no—
180C2×C4×C31—81no—
181C2×C4×C31—81no—
182C2×C4×C31—81no—
183C2×C4×C31C22⋊Q811yescharacteristic
184C2×C4×C31C22⋊Q811yescharacteristic
185C2×C4×C31C4⋊Q811yescharacteristic
186C2×C4×C31C4⋊Q811yescharacteristic
187C8×C31—42no—
188C8×C31—42no—
189#2646C2×C3111yescharacteristic
190#1853C2×C3111yescharacteristic
191#1852C2×C3111yescharacteristic
192#1444C2×C3111yescharacteristic
193#1294C2×C3111yescharacteristic
194#1294C2×C3111yescharacteristic
195#1280C2×C3111yescharacteristic
196C22×C31—21no—
197C22×C31—21no—
198C22×C31—21no—
199C22×C31—21no—
200C22×C31—21no—
201C22×C31—21no—
202C22×C31—21no—
203C22×C31—21no—
204C22×C31—21no—
205C22×C31—21no—
206C22×C31—21no—
207C22×C31—21no—
208C22×C31#39511yescharacteristic
209C22×C31#44911yescharacteristic
210C22×C31#45211yescharacteristic
211C22×C31#45311yescharacteristic
212C22×C31#45611yescharacteristic
213C22×C31B(4,𝔽2)11yescharacteristic
214C22×C31#45811yescharacteristic
215C22×C31#47811yescharacteristic
216C22×C31#47911yescharacteristic
217C22×C31#49911yescharacteristic
218C22×C31#50111yescharacteristic
219C4×C31—21no—
220C4×C31—21no—
221C4×C31—21no—
222C4×C31—21no—
223C4×C31—44no—
224C4×C31—81no—
225C4×C31—81no—
226C4×C31—82no—
227C4×C31—81no—
228C4×C31—81no—
229C4×C31—81no—
230C4×C31—81no—
231C22×C4⋊C4—21no—
232C22×C4⋊C4C22×C3111yescharacteristic
233C2×#107—21no—
234C2×#106—21no—
235C2×C22⋊C8C22×C3111yescharacteristic
236C2×C22⋊C8C22×C3111yescharacteristic
237#400—21no—
238#400—21no—
239#398—21no—
240#398—21no—
241#385—21no—
242#385—21no—
243#380C22×C3111yescharacteristic
244#380C22×C3111yescharacteristic
245C2×#95—21no—
246C2×#95C22×C3111yescharacteristic
247C2×#95C22×C3111yescharacteristic
248#340—21no—
249#340—21no—
250C2×C31—21no—
251C2×C31—21no—
252C2×C31—21no—
253C2×C31—21no—
254C2×C31#160011yescharacteristic
255C2×C31#160311yescharacteristic
256C2×C31#160911yescharacteristic
257C2×C31#161811yescharacteristic
258C2×C31#205911yescharacteristic
259C2×C31#206011yescharacteristic
260C2×C31#206211yescharacteristic
261C23×C4—21no—
262C23×C4—21no—
263C23×C4D4×C3111yescharacteristic
264C23×C4D4×C3111yescharacteristic
265C23×C4C23×C3111yescharacteristic
266C22×C8—21no—
267C22×C8—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—42no—
275C2×C4⋊C4—42no—
276C2×C4⋊C4—42no—
277C2×C4⋊C4—42no—
278C2×C4⋊C4D4×C3111yescharacteristic
279C2×C4⋊C4D4×C3111yescharacteristic
280C2×C4⋊C4D4×C3111yescharacteristic
281C2×C4⋊C4D4×C3111yescharacteristic
282C2×C22⋊C4—21no—
283C2×C22⋊C4—21no—
284#107—42no—
285#106—42no—
286C22⋊C8—21no—
287C22⋊C8—21no—
288C22⋊C8Q8×C3112yes—
289C22⋊C8Q8×C3112yes—
290#95—21no—
291#95—21no—
292#95—21no—
293#95—21no—
294#95—21no—
295#95—21no—
296#95—21no—
297#95—21no—
298#95—21no—
299#95—42no—
300#95Q8×C3112yes—
301C31#1057211yescharacteristic, direct product factor, Sylow
302C24C2×D4×C3111yescharacteristic
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4C2×D4×C3111yescharacteristic
334C22×C4C2×D4×C3111yescharacteristic
335C22×C4C2×Q8×C3111yescharacteristic
336C22×C4C2×Q8×C3111yescharacteristic
337C22×C4C2×Q8×C3111yescharacteristic
338C22×C4#41×C3111yescharacteristic
339C2×C8—22no—
340C2×C8—22no—
341C2×C8—41no—
342C2×C8—41no—
343C2×C8—41no—
344C2×C8—41no—
345C4⋊C4—22no—
346C4⋊C4—22no—
347C4⋊C4—41no—
348C4⋊C4—41no—
349C4⋊C4—41no—
350C4⋊C4—41no—
351C4⋊C4—41no—
352C4⋊C4—41no—
353C4⋊C4—48no—
354C4⋊C4—81no—
355C4⋊C4—81no—
356C4⋊C4—81no—
357C4⋊C4—81no—
358C22⋊C4—41no—
359C22⋊C4—41no—
360C22⋊C4—41no—
361C22⋊C4—41no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23C31×#12011yescharacteristic
367C23C31×C22⋊Q811yescharacteristic
368C23C31×C4⋊Q811yescharacteristic
369C23C31×#13511yescharacteristic
370C23C31×#13511yescharacteristic
371C23C31×AGL(1,ℤ/8)11yescharacteristic
372C23C31×#13711yescharacteristic
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—24no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—42no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—81no—
412C2×C4—81no—
413C2×C4—81no—
414C2×C4—81no—
415C2×C4—81no—
416C2×C4—81no—
417C2×C4C31×C22⋊Q811yescharacteristic
418C2×C4C31×C22⋊Q811yescharacteristic
419C2×C4C31×C4⋊Q811yescharacteristic
420C2×C4C31×C4⋊Q811yescharacteristic
421C8—42no—
422C8—42no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22C31×#39511yescharacteristic
436C22C31×#44911yescharacteristic
437C22C31×#45211yescharacteristic
438C22C31×#45311yescharacteristic
439C22C31×#45611yescharacteristic
440C22C31×B(4,𝔽2)11yescharacteristic
441C22C31×#45811yescharacteristic
442C22C31×#47811yescharacteristic
443C22C31×#47911yescharacteristic
444C22C31×#49911yescharacteristic
445C22C31×#50111yescharacteristic
446C4—21no—
447C4—21no—
448C4—21no—
449C4—21no—
450C4—44no—
451C4—81no—
452C4—82no—
453C4—81no—
454C4—81no—
455C4—81no—
456C4—81no—
457C4—81no—
458C2—21no—
459C2—21no—
460C2—21no—
461C2—21no—
462C2C31×#160011yescharacteristic
463C2C31×#160311yescharacteristic
464C2C31×#160911yescharacteristic
465C2C31×#161811yescharacteristic
466C2C31×#205911yescharacteristic
467C2C31×#206011yescharacteristic
468C2C31×#206211yescharacteristic
subgroupG/H
center, socleC23×C31#120
commutator, Frattini, cosocleC23×C4C23×C31
prime radicalC24×C31C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
127. #10572C31direct (N × H)
301. C31#10572direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#26462
C31×#18532
C31×#18522
C31×#14442
C31×#12942
C31×#12802
#1057231