Finite Group Databasebeta

← C31×#10625 #21467384

Subgroups — C31×#10625 #21467384

Order 7936.

402 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#1954C211yesmaximal, characteristic
2C31×#1834C211yesmaximal, characteristic, complemented
3C31×#1802C211yesmaximal, characteristic
4C31×#1802C211yesmaximal, characteristic
5C31×#1296C211yesmaximal, characteristic, complemented
6C31×#1296C211yesmaximal, characteristic, complemented
7C31×#1277C211yesmaximal, characteristic, complemented
8C2×C4×D4×C31C2211yescharacteristic
9C2×C31×C4⋊C8C2211yescharacteristic
10C2×C31×C4⋊C8C2211yescharacteristic
11C2×C31×C4⋊C8C2211yescharacteristic
12C2×C31×#102—21no—
13C2×C31×#102—21no—
14C2×C31×C22⋊C8—21no—
15C2×C31×C22⋊C8—21no—
16C2×C4×C8×C31C2211yescharacteristic
17C31×#384C2211yescharacteristic
18C31×#384C2211yescharacteristic
19C31×#340—21no—
20C31×#340—21no—
21C31×#340—21no—
22C31×#340—21no—
23C22×D4×C31D411yescharacteristic
24C23×C4×C31—21no—
25C22×C8×C31—21no—
26C22×C8×C31—21no—
27C22×C8×C31—21no—
28C22×C8×C31D411yescharacteristic
29C22×C8×C31D411yescharacteristic
30C4×D4×C31—21no—
31C4×D4×C31—21no—
32C4×D4×C31—21no—
33C4×D4×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×C31D411yescharacteristic
41C2×C22⋊C4×C31—21no—
42C2×C42×C31C2311yescharacteristic
43C31×C4⋊C8—21no—
44C31×C4⋊C8—21no—
45C31×C4⋊C8—21no—
46C31×C4⋊C8—21no—
47C31×C4⋊C8—21no—
48C31×C4⋊C8—21no—
49C31×#102—42no—
50C31×#102—42no—
51C31×C22⋊C8—42no—
52C31×C22⋊C8—42no—
53C4×C8×C31—21no—
54C4×C8×C31—21no—
55C24×C31—21no—
56C2×D4×C31—21no—
57C2×D4×C31—21no—
58C2×D4×C31—21no—
59C2×D4×C31—21no—
60C2×D4×C31—21no—
61C2×D4×C31SD1612yes—
62C22×C4×C31—21no—
63C22×C4×C31—41no—
64C22×C4×C31—41no—
65C22×C4×C31—41no—
66C22×C4×C31—41no—
67C22×C4×C31—41no—
68C22×C4×C31—41no—
69C22×C4×C31—41no—
70C22×C4×C31—41no—
71C22×C4×C31C2×D411yescharacteristic
72C22×C4×C31C2×D411yescharacteristic
73C22×C4×C31#4111yescharacteristic
74C2×C8×C31—21no—
75C2×C8×C31—21no—
76C2×C8×C31—21no—
77C2×C8×C31—21no—
78C2×C8×C31—21no—
79C2×C8×C31—21no—
80C2×C8×C31—41no—
81C2×C8×C31—41no—
82C2×C8×C31—41no—
83C2×C8×C31—41no—
84C2×C8×C31—41no—
85C2×C8×C31—41no—
86C2×C8×C31—41no—
87C2×C8×C31—41no—
88C2×C8×C31—41no—
89C4⋊C4×C31—21no—
90C4⋊C4×C31—21no—
91C4⋊C4×C31—41no—
92C4⋊C4×C31—41no—
93C4⋊C4×C31—41no—
94C4⋊C4×C31—41no—
95C4⋊C4×C31—41no—
96C4⋊C4×C31—41no—
97C4⋊C4×C31—41no—
98C4⋊C4×C31—41no—
99C4⋊C4×C31—81no—
100C4⋊C4×C31—81no—
101C22⋊C4×C31—41no—
102C22⋊C4×C31—41no—
103C42×C31#4111yescharacteristic
104C42×C31#4111yescharacteristic
105C42×C31#4111yescharacteristic
106C42×C31#4111yescharacteristic
107#10625C3111yesmaximal, characteristic, direct product factor, Sylow
108C23×C31—22no—
109C23×C31—41no—
110C23×C31—41no—
111C23×C31—41no—
112C23×C31—41no—
113C23×C31—41no—
114C23×C31—41no—
115C23×C31#12111yescharacteristic
116D4×C31—22no—
117D4×C31—22no—
118D4×C31—41no—
119D4×C31—41no—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—41no—
123C2×C4×C31—41no—
124C2×C4×C31—41no—
125C2×C4×C31—81no—
126C2×C4×C31—81no—
127C2×C4×C31—81no—
128C2×C4×C31—81no—
129C2×C4×C31—81no—
130C2×C4×C31—81no—
131C2×C4×C31—81no—
132C2×C4×C31—81no—
133C2×C4×C31—81no—
134C2×C4×C31—81no—
135C2×C4×C31#12311yescharacteristic
136C2×C4×C31#12311yescharacteristic
137C2×C4×C31#12311yescharacteristic
138C2×C4×C31#12411yescharacteristic
139C2×C4×C31#12611yescharacteristic
140C2×C4×C31#12611yescharacteristic
141C2×C4×C31C2×SD1611yescharacteristic
142C2×C4×C31#13511yescharacteristic
143C2×C4×C31#13511yescharacteristic
144C2×C4×C31#13511yescharacteristic
145C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C31#13711yescharacteristic
149C8×C31—41no—
150C8×C31—41no—
151C8×C31—81no—
152C8×C31—81no—
153C8×C31—81no—
154#1954C2×C3111yescharacteristic
155#1834C2×C3111yescharacteristic, complemented
156#1802C2×C3111yescharacteristic
157#1802C2×C3111yescharacteristic
158#1296C2×C3111yescharacteristic, complemented
159#1296C2×C3111yescharacteristic, complemented
160#1277C2×C3111yescharacteristic, complemented
161C22×C31—42no—
162C22×C31—42no—
163C22×C31—42no—
164C22×C31—81no—
165C22×C31—81no—
166C22×C31—81no—
167C22×C31—81no—
168C22×C31#39711yescharacteristic
169C22×C31#46311yescharacteristic
170C22×C31#46311yescharacteristic
171C22×C31#46511yescharacteristic
172C22×C31#46811yescharacteristic
173C22×C31#47211yescharacteristic
174C22×C31#47311yescharacteristic
175C4×C31—21no—
176C4×C31—21no—
177C4×C31—81no—
178C4×C31—161no—
179C4×C31—161no—
180C4×C31#48111yescharacteristic
181C4×C31#48211yescharacteristic
182C4×C31#48211yescharacteristic
183C4×C31#48211yescharacteristic
184C4×C31#48311yescharacteristic
185C4×C31#48511yescharacteristic
186C4×C31#48811yescharacteristic
187C4×C31#49011yescharacteristic
188C2×C4×D4C22×C3111yescharacteristic
189C2×C4⋊C8C22×C3111yescharacteristic
190C2×C4⋊C8C22×C3111yescharacteristic
191C2×C4⋊C8C22×C3111yescharacteristic
192C2×#102—21no—
193C2×#102—21no—
194C2×C22⋊C8—21no—
195C2×C22⋊C8—21no—
196C2×C4×C8C22×C3111yescharacteristic
197#384C22×C3111yescharacteristic
198#384C22×C3111yescharacteristic
199#340—21no—
200#340—21no—
201#340—21no—
202#340—21no—
203C2×C31—82no—
204C2×C31#167711yescharacteristic
205C2×C31#167911yescharacteristic
206C2×C31#169711yescharacteristic
207C2×C31#169911yescharacteristic
208C2×C31#207311yescharacteristic
209C2×C31#207711yescharacteristic
210C2×C31#207811yescharacteristic
211C22×D4D4×C3111yescharacteristic
212C23×C4—21no—
213C22×C8—21no—
214C22×C8—21no—
215C22×C8—21no—
216C22×C8D4×C3111yescharacteristic
217C22×C8D4×C3111yescharacteristic
218C4×D4—21no—
219C4×D4—21no—
220C4×D4—21no—
221C4×D4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4D4×C3111yescharacteristic
229C2×C22⋊C4—21no—
230C2×C42C23×C3111yescharacteristic
231C4⋊C8—21no—
232C4⋊C8—21no—
233C4⋊C8—21no—
234C4⋊C8—21no—
235C4⋊C8—21no—
236C4⋊C8—21no—
237#102—42no—
238#102—42no—
239C22⋊C8—42no—
240C22⋊C8—42no—
241C4×C8—21no—
242C4×C8—21no—
243C31#1062511yescharacteristic, direct product factor, Sylow
244C24—21no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—21no—
248C2×D4—21no—
249C2×D4—21no—
250C2×D4SD16×C3112yes—
251C22×C4—21no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4C2×D4×C3111yescharacteristic
261C22×C4C2×D4×C3111yescharacteristic
262C22×C4#41×C3111yescharacteristic
263C2×C8—21no—
264C2×C8—21no—
265C2×C8—21no—
266C2×C8—21no—
267C2×C8—21no—
268C2×C8—21no—
269C2×C8—41no—
270C2×C8—41no—
271C2×C8—41no—
272C2×C8—41no—
273C2×C8—41no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8—41no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—81no—
289C4⋊C4—81no—
290C22⋊C4—41no—
291C22⋊C4—41no—
292C42#41×C3111yescharacteristic
293C42#41×C3111yescharacteristic
294C42#41×C3111yescharacteristic
295C42#41×C3111yescharacteristic
296C23—22no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23C31×#12111yescharacteristic
304D4—22no—
305D4—22no—
306D4—41no—
307D4—41no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4C31×#12311yescharacteristic
324C2×C4C31×#12311yescharacteristic
325C2×C4C31×#12311yescharacteristic
326C2×C4C31×#12411yescharacteristic
327C2×C4C31×#12611yescharacteristic
328C2×C4C31×#12611yescharacteristic
329C2×C4C2×SD16×C3111yescharacteristic
330C2×C4C31×#13511yescharacteristic
331C2×C4C31×#13511yescharacteristic
332C2×C4C31×#13511yescharacteristic
333C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
334C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
335C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
336C2×C4C31×#13711yescharacteristic
337C8—41no—
338C8—41no—
339C8—81no—
340C8—81no—
341C8—81no—
342C22—42no—
343C22—42no—
344C22—42no—
345C22—81no—
346C22—81no—
347C22—81no—
348C22—81no—
349C22C31×#39711yescharacteristic
350C22C31×#46311yescharacteristic
351C22C31×#46311yescharacteristic
352C22C31×#46511yescharacteristic
353C22C31×#46811yescharacteristic
354C22C31×#47211yescharacteristic
355C22C31×#47311yescharacteristic
356C4—21no—
357C4—21no—
358C4—81no—
359C4—161no—
360C4—161no—
361C4C31×#48111yescharacteristic
362C4C31×#48211yescharacteristic
363C4C31×#48211yescharacteristic
364C4C31×#48211yescharacteristic
365C4C31×#48311yescharacteristic
366C4C31×#48511yescharacteristic
367C4C31×#48811yescharacteristic
368C4C31×#49011yescharacteristic
369C2—82no—
370C2C31×#167711yescharacteristic
371C2C31×#167911yescharacteristic
372C2C31×#169711yescharacteristic
373C2C31×#169911yescharacteristic
374C2C31×#207311yescharacteristic
375C2C31×#207711yescharacteristic
376C2C31×#207811yescharacteristic
subgroupG/H
center, socleC23×C31#121
commutator, Frattini, cosocleC2×C42C23×C31
prime radicalC22×D4×C31D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1834C2semidirect
5. C31×#1296C2semidirect
6. C31×#1296C2semidirect
7. C31×#1277C2semidirect
107. #10625C31direct (N × H)
155. #1834C2×C31semidirect
158. #1296C2×C31semidirect
159. #1296C2×C31semidirect
160. #1277C2×C31semidirect
243. C31#10625direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#19542
C31×#18342
C31×#18022
C31×#12962
C31×#12772
#1062531