Finite Group Databasebeta

← C31×#13408 #21470167

Subgroups — C31×#13408 #21470167

Order 7936.

482 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#495C211yesmaximal, characteristic
2C2×C31×#358C211yesmaximal, characteristic, complemented
3C2×C31×#358C211yesmaximal, characteristic, complemented
4C2×C31×#357C211yesmaximal, characteristic
5C2×C31×#357C211yesmaximal, characteristic
6C31×#1942C211yesmaximal, characteristic, complemented
7C31×#1374C211yesmaximal, characteristic, complemented
8C22×Q16×C31C2211yescharacteristic
9C22×SD16×C31—21no—
10C22×D8×C31C2211yescharacteristic
11C2×C31×#124—21no—
12C22×C16×C31C2211yescharacteristic
13C22×C16×C31C2211yescharacteristic
14C31×#495—22no—
15C31×#495—22no—
16C2×C31×#107C2211yescharacteristic
17C2×C31×#107C2211yescharacteristic
18C2×C4×C8×C31C2211yescharacteristic
19C31×#389—21no—
20C31×#358—22no—
21C31×#358—22no—
22C31×#357—22no—
23C31×#357—22no—
24C31×#340—21no—
25C22×Q8×C31—21no—
26C22×D4×C31—21no—
27C2×Q16×C31—21no—
28C2×Q16×C31—21no—
29C2×Q16×C31—21no—
30C2×Q16×C31—21no—
31C2×Q16×C31—21no—
32C2×Q16×C31D412yes—
33C2×SD16×C31—24no—
34C2×SD16×C31—42no—
35C2×SD16×C31—42no—
36C2×D8×C31—21no—
37C2×D8×C31—21no—
38C2×D8×C31—21no—
39C2×D8×C31—21no—
40C2×D8×C31—21no—
41C2×D8×C31D412yes—
42C22×C8×C31D411yescharacteristic
43C22×C8×C31C2311yescharacteristic
44C31×#124—24no—
45C31×#124—42no—
46C2×C4⋊C4×C31—21no—
47C2×C4⋊C4×C31—21no—
48C2×C4⋊C4×C31—41no—
49C2×C22⋊C4×C31—41no—
50C2×C22⋊C4×C31—41no—
51C2×C42×C31D411yescharacteristic
52C2×C16×C31—21no—
53C2×C16×C31—21no—
54C2×C16×C31—21no—
55C2×C16×C31—21no—
56C2×C16×C31—21no—
57C2×C16×C31—21no—
58C31×#107—21no—
59C31×#107—21no—
60C31×#107—21no—
61C31×#107D412yes—
62C4×C8×C31—21no—
63C4×C8×C31—21no—
64C31×#95—41no—
65C24×C31—41no—
66C2×Q8×C31—22no—
67C2×Q8×C31—41no—
68C2×Q8×C31—41no—
69C2×Q8×C31—41no—
70C2×Q8×C31—41no—
71C2×Q8×C31—41no—
72C2×D4×C31—22no—
73C2×D4×C31—41no—
74C2×D4×C31—41no—
75C2×D4×C31—41no—
76C2×D4×C31—41no—
77C2×D4×C31—41no—
78C22×C4×C31—41no—
79C22×C4×C31—41no—
80C22×C4×C31—41no—
81C22×C4×C31D811yescharacteristic
82C22×C4×C31D811yescharacteristic
83C22×C4×C31C2×D411yescharacteristic
84Q16×C31—22no—
85Q16×C31—22no—
86Q16×C31—41no—
87Q16×C31—41no—
88SD16×C31—48no—
89D8×C31—22no—
90D8×C31—22no—
91D8×C31—41no—
92D8×C31—41no—
93C2×C8×C31—21no—
94C2×C8×C31—21no—
95C2×C8×C31SD1612yes—
96C2×C8×C31C2×D411yescharacteristic
97C2×C8×C31C2×D411yescharacteristic
98C2×C8×C31C2×D411yescharacteristic
99C2×C8×C31#4111yescharacteristic
100C2×C8×C31#4111yescharacteristic
101C2×C8×C31#4111yescharacteristic
102C4⋊C4×C31—22no—
103C4⋊C4×C31—41no—
104C4⋊C4×C31—41no—
105C4⋊C4×C31—41no—
106C4⋊C4×C31—82no—
107C22⋊C4×C31—44no—
108C22⋊C4×C31—44no—
109C42×C31—21no—
110C42×C31—21no—
111C16×C31—41no—
112C16×C31—41no—
113#13408C3111yesmaximal, characteristic, direct product factor, Sylow
114C23×C31—42no—
115C23×C31—81no—
116C23×C31—81no—
117C23×C31—81no—
118C23×C31—81no—
119C23×C31—81no—
120C23×C31—81no—
121C23×C31C2×D811yescharacteristic
122Q8×C31—42no—
123Q8×C31—42no—
124Q8×C31—81no—
125Q8×C31—81no—
126D4×C31—42no—
127D4×C31—42no—
128D4×C31—81no—
129D4×C31—81no—
130C2×C4×C31—21no—
131C2×C4×C31—21no—
132C2×C4×C31—21no—
133C2×C4×C31—21no—
134C2×C4×C31—21no—
135C2×C4×C31—21no—
136C2×C4×C31—42no—
137C2×C4×C31—42no—
138C2×C4×C31—81no—
139C2×C4×C31—81no—
140C2×C4×C31—81no—
141C2×C4×C31—81no—
142C2×C4×C31—81no—
143C2×C4×C31—81no—
144C2×C4×C31—81no—
145C2×C4×C31#12011yescharacteristic
146C2×C4×C31#12111yescharacteristic
147C2×C4×C31#12411yescharacteristic
148C2×C4×C31C2×SD1611yescharacteristic
149C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
151C8×C31—22no—
152C8×C31#12111yescharacteristic
153C8×C31#12111yescharacteristic
154C8×C31#12311yescharacteristic
155C8×C31#12311yescharacteristic
156C2×#495C2×C3111yescharacteristic
157C2×#358C2×C3111yescharacteristic, complemented
158C2×#358C2×C3111yescharacteristic, complemented
159C2×#357C2×C3111yescharacteristic
160C2×#357C2×C3111yescharacteristic
161#1942C2×C3111yescharacteristic, complemented
162#1374C2×C3111yescharacteristic, complemented
163C22×C31—82no—
164C22×C31—82no—
165C22×C31—82no—
166C22×C31—161no—
167C22×C31—161no—
168C22×C31—161no—
169C22×C31—161no—
170C22×C31#44711yescharacteristic
171C22×C31#45911yescharacteristic
172C22×C31#48611yescharacteristic
173C22×C31#50811yescharacteristic
174C22×C31#50811yescharacteristic
175C22×C31#50911yescharacteristic
176C22×C31#51011yescharacteristic
177C4×C31—41no—
178C4×C31—41no—
179C4×C31—82no—
180C4×C31—82no—
181C4×C31—161no—
182C4×C31#39411yescharacteristic
183C4×C31#45011yescharacteristic
184C4×C31#46011yescharacteristic
185C4×C31#49011yescharacteristic
186C22×Q16C22×C3111yescharacteristic
187C22×SD16—21no—
188C22×D8C22×C3111yescharacteristic
189C2×#124—21no—
190C22×C16C22×C3111yescharacteristic
191C22×C16C22×C3111yescharacteristic
192#495—22no—
193#495—22no—
194C2×#107C22×C3111yescharacteristic
195C2×#107C22×C3111yescharacteristic
196C2×C4×C8C22×C3111yescharacteristic
197#389—21no—
198#358—22no—
199#358—22no—
200#357—22no—
201#357—22no—
202#340—21no—
203C2×C31—162no—
204C2×C31#204111yescharacteristic
205C2×C31#218611yescharacteristic
206C2×C31#218911yescharacteristic
207C2×C31#221011yescharacteristic
208C2×C31#221111yescharacteristic
209C2×C31#224211yescharacteristic
210C2×C31#224311yescharacteristic
211C22×Q8—21no—
212C22×D4—21no—
213C2×Q16—21no—
214C2×Q16—21no—
215C2×Q16—21no—
216C2×Q16—21no—
217C2×Q16—21no—
218C2×Q16D4×C3112yes—
219C2×SD16—24no—
220C2×SD16—42no—
221C2×SD16—42no—
222C2×D8—21no—
223C2×D8—21no—
224C2×D8—21no—
225C2×D8—21no—
226C2×D8—21no—
227C2×D8D4×C3112yes—
228C22×C8D4×C3111yescharacteristic
229C22×C8C23×C3111yescharacteristic
230#124—24no—
231#124—42no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—41no—
235C2×C22⋊C4—41no—
236C2×C22⋊C4—41no—
237C2×C42D4×C3111yescharacteristic
238C2×C16—21no—
239C2×C16—21no—
240C2×C16—21no—
241C2×C16—21no—
242C2×C16—21no—
243C2×C16—21no—
244#107—21no—
245#107—21no—
246#107—21no—
247#107D4×C3112yes—
248C4×C8—21no—
249C4×C8—21no—
250#95—41no—
251C31#1340811yescharacteristic, direct product factor, Sylow
252C24—41no—
253C2×Q8—22no—
254C2×Q8—41no—
255C2×Q8—41no—
256C2×Q8—41no—
257C2×Q8—41no—
258C2×Q8—41no—
259C2×D4—22no—
260C2×D4—41no—
261C2×D4—41no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—41no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4D8×C3111yescharacteristic
269C22×C4D8×C3111yescharacteristic
270C22×C4C2×D4×C3111yescharacteristic
271Q16—22no—
272Q16—22no—
273Q16—41no—
274Q16—41no—
275SD16—48no—
276D8—22no—
277D8—22no—
278D8—41no—
279D8—41no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8SD16×C3112yes—
283C2×C8C2×D4×C3111yescharacteristic
284C2×C8C2×D4×C3111yescharacteristic
285C2×C8C2×D4×C3111yescharacteristic
286C2×C8#41×C3111yescharacteristic
287C2×C8#41×C3111yescharacteristic
288C2×C8#41×C3111yescharacteristic
289C4⋊C4—22no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—82no—
294C22⋊C4—44no—
295C22⋊C4—44no—
296C42—21no—
297C42—21no—
298C16—41no—
299C16—41no—
300C23—42no—
301C23—81no—
302C23—81no—
303C23—81no—
304C23—81no—
305C23—81no—
306C23—81no—
307C23C2×D8×C3111yescharacteristic
308Q8—42no—
309Q8—42no—
310Q8—81no—
311Q8—81no—
312D4—42no—
313D4—42no—
314D4—81no—
315D4—81no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4C31×#12011yescharacteristic
332C2×C4C31×#12111yescharacteristic
333C2×C4C31×#12411yescharacteristic
334C2×C4C2×SD16×C3111yescharacteristic
335C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
336C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
337C8—22no—
338C8C31×#12111yescharacteristic
339C8C31×#12111yescharacteristic
340C8C31×#12311yescharacteristic
341C8C31×#12311yescharacteristic
342C22—82no—
343C22—82no—
344C22—82no—
345C22—161no—
346C22—161no—
347C22—161no—
348C22—161no—
349C22C31×#44711yescharacteristic
350C22C31×#45911yescharacteristic
351C22C31×#48611yescharacteristic
352C22C31×#50811yescharacteristic
353C22C31×#50811yescharacteristic
354C22C31×#50911yescharacteristic
355C22C31×#51011yescharacteristic
356C4—41no—
357C4—41no—
358C4—82no—
359C4—82no—
360C4—161no—
361C4C31×#39411yescharacteristic
362C4C31×#45011yescharacteristic
363C4C31×#46011yescharacteristic
364C4C31×#49011yescharacteristic
365C2—162no—
366C2C31×#204111yescharacteristic
367C2C31×#218611yescharacteristic
368C2C31×#218911yescharacteristic
369C2C31×#221011yescharacteristic
370C2C31×#221111yescharacteristic
371C2C31×#224211yescharacteristic
372C2C31×#224311yescharacteristic
subgroupG/H
center, socleC23×C31C2×D8
commutator, Frattini, cosocleC22×C8C23×C31
prime radicalC22×D8×C31C22
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C42×C31 ◁ C2×C4×C8×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#358C2semidirect
3. C2×C31×#358C2semidirect
6. C31×#1942C2semidirect
7. C31×#1374C2semidirect
113. #13408C31direct (N × H)
157. C2×#358C2×C31semidirect
158. C2×#358C2×C31semidirect
161. #1942C2×C31semidirect
162. #1374C2×C31semidirect
251. C31#13408direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4952
C2×C31×#3582
C2×C31×#3572
C31×#19422
C31×#13742
#1340831