Finite Group Databasebeta

← C31×#18410 #21475169

Subgroups — C31×#18410 #21475169

Order 7936.

906 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3502C211yesmaximal, characteristic
2C31×#3229C212yesmaximal
3C31×#2546C211yesmaximal, characteristic
4C31×#1611C218yesmaximal
5C31×#1503C212yesmaximal
6C31×#1461C211yesmaximal, characteristic
7Q82×C31—22no—
8C31×#557—22no—
9C31×#557—24no—
10C31×#544—21no—
11C31×#544C2214yes—
12C31×#533—22no—
13C31×#533C2212yes—
14C2×C31×C4⋊Q8—21no—
15C2×C31×C4⋊Q8C2211yescharacteristic
16C31×#519—21no—
17C2×C4×Q8×C31C2211yescharacteristic
18C31×#498—22no—
19C31×#487—22no—
20C31×#483C2218yes—
21C31×#475—24no—
22C31×#431C2212yes—
23C31×#398C2214yes—
24C31×#391—21no—
25C31×#389—22no—
26C4×C4⋊C4×C31C2211yescharacteristic
27C31×#328C2218yes—
28C31×#324C2214yes—
29C22×Q8×C31—21no—
30C22×Q8×C31D411yescharacteristic
31C31×C4⋊Q8—22no—
32C31×C4⋊Q8—22no—
33C31×C4⋊Q8—24no—
34C31×C4⋊Q8—28no—
35C31×C4⋊Q8—22no—
36C31×C4⋊Q8—22no—
37C31×C4⋊Q8—44no—
38C31×C4⋊Q8D412yes—
39C31×C4⋊Q8D412yes—
40C31×#125—24no—
41C31×#125—24no—
42C31×#125—28no—
43C31×#125—22no—
44C31×C22⋊Q8—22no—
45C31×C22⋊Q8—24no—
46C31×C22⋊Q8C2314yes—
47C4×Q8×C31—24no—
48C4×Q8×C31—24no—
49C4×Q8×C31—24no—
50C4×Q8×C31—24no—
51C4×Q8×C31—22no—
52C4×Q8×C31—22no—
53C4×Q8×C31—22no—
54C4×Q8×C31D414yes—
55C31×#117—24no—
56C31×#117—22no—
57C2×C4⋊C4×C31—21no—
58C2×C4⋊C4×C31—24no—
59C2×C4⋊C4×C31—21no—
60C2×C4⋊C4×C31D411yescharacteristic
61C2×C4⋊C4×C31C2312yes—
62C2×C4⋊C4×C31C2312yes—
63C2×C42×C31—21no—
64C2×C42×C31D412yes—
65C2×C42×C31C2311yescharacteristic
66C31×#106—28no—
67C31×C4⋊C8—22no—
68C31×#103—28no—
69C31×C22⋊C8C2314yes—
70C4×C8×C31—22no—
71C31×#95—24no—
72C31×#95C2312yes—
73C2×Q8×C31—24no—
74C2×Q8×C31—22no—
75C2×Q8×C31—22no—
76C2×Q8×C31—22no—
77C2×Q8×C31—42no—
78C2×Q8×C31—42no—
79C2×Q8×C31—42no—
80C2×Q8×C31SD1614yes—
81C2×Q8×C31C2×D414yes—
82C22×C4×C31—22no—
83C22×C4×C31—22no—
84C22×C4×C31C2×D411yescharacteristic
85C22×C4×C31C2×D412yes—
86C22×C4×C31C2×D412yes—
87C22×C4×C31C2×D411yescharacteristic
88C22×C4×C31C2411yescharacteristic
89C2×C8×C31—24no—
90C4⋊C4×C31—24no—
91C4⋊C4×C31—24no—
92C4⋊C4×C31—24no—
93C4⋊C4×C31—24no—
94C4⋊C4×C31—28no—
95C4⋊C4×C31—22no—
96C4⋊C4×C31—22no—
97C4⋊C4×C31—22no—
98C4⋊C4×C31—22no—
99C4⋊C4×C31—24no—
100C4⋊C4×C31—24no—
101C4⋊C4×C31—24no—
102C4⋊C4×C31—24no—
103C4⋊C4×C31—41no—
104C4⋊C4×C31—41no—
105C4⋊C4×C31—48no—
106C4⋊C4×C31C2×D414yes—
107C22⋊C4×C31—24no—
108C42×C31—28no—
109C42×C31—22no—
110C42×C31—22no—
111C42×C31—24no—
112C42×C31—42no—
113C42×C31C2×D412yes—
114C42×C31C2×D412yes—
115#18410C3111yesmaximal, characteristic, direct product factor, Sylow
116C23×C31C22×D411yescharacteristic
117Q8×C31—28no—
118Q8×C31—44no—
119Q8×C31—44no—
120Q8×C31—84no—
121Q8×C31—84no—
122C2×C4×C31—22no—
123C2×C4×C31—22no—
124C2×C4×C31—22no—
125C2×C4×C31—24no—
126C2×C4×C31—24no—
127C2×C4×C31—24no—
128C2×C4×C31—22no—
129C2×C4×C31—41no—
130C2×C4×C31—42no—
131C2×C4×C31—42no—
132C2×C4×C31—42no—
133C2×C4×C31—42no—
134C2×C4×C31—42no—
135C2×C4×C31—42no—
136C2×C4×C31#12011yescharacteristic
137C2×C4×C31#12012yes—
138C2×C4×C31#12011yescharacteristic
139C2×C4×C31C2×SD1614yes—
140C2×C4×C31C2×SD1612yes—
141C2×C4×C31#13712yes—
142C2×C4×C31C22×D412yes—
143C8×C31—44no—
144#3502C2×C3111yescharacteristic
145#3229C2×C3112yes—
146#2546C2×C3111yescharacteristic
147#1611C2×C3118yes—
148#1503C2×C3112yes—
149#1461C2×C3111yescharacteristic
150C22×C31—21no—
151C22×C31—21no—
152C22×C31C2×#12011yescharacteristic
153C22×C31C22×SD1611yescharacteristic
154C22×C31C2×#13711yescharacteristic
155C4×C31—24no—
156C4×C31—21no—
157C4×C31—22no—
158C4×C31—44no—
159C4×C31—44no—
160C4×C31—42no—
161C4×C31—44no—
162C4×C31—82no—
163C4×C31#44814yes—
164C4×C31#45612yes—
165Q82—22no—
166#557—22no—
167#557—24no—
168#544—21no—
169#544C22×C3114yes—
170#533—22no—
171#533C22×C3112yes—
172C2×C4⋊Q8—21no—
173C2×C4⋊Q8C22×C3111yescharacteristic
174#519—21no—
175C2×C4×Q8C22×C3111yescharacteristic
176#498—22no—
177#487—22no—
178#483C22×C3118yes—
179#475—24no—
180#431C22×C3112yes—
181#398C22×C3114yes—
182#391—21no—
183#389—22no—
184C4×C4⋊C4C22×C3111yescharacteristic
185#328C22×C3118yes—
186#324C22×C3114yes—
187C2×C31—21no—
188C2×C31—21no—
189C2×C31C2×#44811yescharacteristic
190C2×C31C2×#45611yescharacteristic
191C2×C31#302811yescharacteristic
192C22×Q8—21no—
193C22×Q8D4×C3111yescharacteristic
194C4⋊Q8—22no—
195C4⋊Q8—22no—
196C4⋊Q8—24no—
197C4⋊Q8—28no—
198C4⋊Q8—22no—
199C4⋊Q8—22no—
200C4⋊Q8—44no—
201C4⋊Q8D4×C3112yes—
202C4⋊Q8D4×C3112yes—
203#125—24no—
204#125—24no—
205#125—28no—
206#125—22no—
207C22⋊Q8—22no—
208C22⋊Q8—24no—
209C22⋊Q8C23×C3114yes—
210C4×Q8—24no—
211C4×Q8—24no—
212C4×Q8—24no—
213C4×Q8—24no—
214C4×Q8—22no—
215C4×Q8—22no—
216C4×Q8—22no—
217C4×Q8D4×C3114yes—
218#117—24no—
219#117—22no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—24no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4D4×C3111yescharacteristic
224C2×C4⋊C4C23×C3112yes—
225C2×C4⋊C4C23×C3112yes—
226C2×C42—21no—
227C2×C42D4×C3112yes—
228C2×C42C23×C3111yescharacteristic
229#106—28no—
230C4⋊C8—22no—
231#103—28no—
232C22⋊C8C23×C3114yes—
233C4×C8—22no—
234#95—24no—
235#95C23×C3112yes—
236C31#1841011yescharacteristic, direct product factor, Sylow
237C2×Q8—24no—
238C2×Q8—22no—
239C2×Q8—22no—
240C2×Q8—22no—
241C2×Q8—42no—
242C2×Q8—42no—
243C2×Q8—42no—
244C2×Q8SD16×C3114yes—
245C2×Q8C2×D4×C3114yes—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4C2×D4×C3111yescharacteristic
249C22×C4C2×D4×C3112yes—
250C22×C4C2×D4×C3112yes—
251C22×C4C2×D4×C3111yescharacteristic
252C22×C4C24×C3111yescharacteristic
253C2×C8—24no—
254C4⋊C4—24no—
255C4⋊C4—24no—
256C4⋊C4—24no—
257C4⋊C4—24no—
258C4⋊C4—28no—
259C4⋊C4—22no—
260C4⋊C4—22no—
261C4⋊C4—22no—
262C4⋊C4—22no—
263C4⋊C4—24no—
264C4⋊C4—24no—
265C4⋊C4—24no—
266C4⋊C4—24no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—48no—
270C4⋊C4C2×D4×C3114yes—
271C22⋊C4—24no—
272C42—28no—
273C42—22no—
274C42—22no—
275C42—24no—
276C42—42no—
277C42C2×D4×C3112yes—
278C42C2×D4×C3112yes—
279C23C22×D4×C3111yescharacteristic
280Q8—28no—
281Q8—44no—
282Q8—44no—
283Q8—84no—
284Q8—84no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—24no—
289C2×C4—24no—
290C2×C4—24no—
291C2×C4—22no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4C31×#12011yescharacteristic
300C2×C4C31×#12012yes—
301C2×C4C31×#12011yescharacteristic
302C2×C4C2×SD16×C3114yes—
303C2×C4C2×SD16×C3112yes—
304C2×C4C31×#13712yes—
305C2×C4C22×D4×C3112yes—
306C8—44no—
307C22—21no—
308C22—21no—
309C22C2×C31×#12011yescharacteristic
310C22C22×SD16×C3111yescharacteristic
311C22C2×C31×#13711yescharacteristic
312C4—24no—
313C4—21no—
314C4—22no—
315C4—44no—
316C4—44no—
317C4—42no—
318C4—44no—
319C4—82no—
320C4C31×#44814yes—
321C4C31×#45612yes—
322C2—21no—
323C2—21no—
324C2C2×C31×#44811yescharacteristic
325C2C2×C31×#45611yescharacteristic
326C2C31×#302811yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC23×C31C22×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
115. #18410C31direct (N × H)
236. C31#18410direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35022
C31×#32292
C31×#25462
C31×#16112
C31×#15032
C31×#14612
#1841031