Finite Group Databasebeta

← C31×#13303 #21470062

Subgroups — C31×#13303 #21470062

Order 7936.

396 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2565C211yesmaximal, characteristic
2C31×#1801C211yesmaximal, characteristic
3C4×C31×#101C211yesmaximal, characteristic
4C31×#1394C212yesmaximal
5C31×#1394C212yesmaximal
6C2×C31×#125C411yescharacteristic
7C2×C4×Q8×C31C2211yescharacteristic
8C31×#423—21no—
9C2×C31×#101C2212yes—
10C2×C31×#101C2212yes—
11C4×M16×C31—21no—
12C31×#398—21no—
13C31×#398—21no—
14C31×#391C2211yescharacteristic
15C31×#391C2211yescharacteristic
16C31×#387—21no—
17C31×#387—21no—
18C31×#384C411yescharacteristic
19C31×#382C411yescharacteristic
20C4×C4⋊C4×C31C411yescharacteristic
21C31×#343—21no—
22C31×#343—21no—
23C22×Q8×C31C2311yescharacteristic
24C2×M16×C31—22no—
25C2×M16×C31—22no—
26C31×#125—41no—
27C31×#125—41no—
28C4×Q8×C31—41no—
29C4×Q8×C31—41no—
30C2×C4⋊C4×C31—21no—
31C2×C4⋊C4×C31—21no—
32C2×C4⋊C4×C31—21no—
33C2×C4⋊C4×C31—21no—
34C2×C4⋊C4×C31—21no—
35C2×C4⋊C4×C31C2×C411yescharacteristic
36C2×C4⋊C4×C31C2×C411yescharacteristic
37C2×C4⋊C4×C31C2×C411yescharacteristic
38C2×C4⋊C4×C31D411yescharacteristic
39C2×C4⋊C4×C31D411yescharacteristic
40C2×C42×C31C2×C411yescharacteristic
41C2×C42×C31C2×C411yescharacteristic
42C2×C42×C31C2×C411yescharacteristic
43C2×C42×C31D411yescharacteristic
44C2×C42×C31D411yescharacteristic
45C31×C4⋊C8—41no—
46C31×C4⋊C8—41no—
47C31×#101—22no—
48C31×#101—24no—
49C31×#101Q814yes—
50C31×#97—41no—
51C4×C8×C31—41no—
52C31×#95—21no—
53C31×#95—21no—
54C31×#95—21no—
55C31×#95—21no—
56C31×#95—21no—
57C31×#95—21no—
58C31×#95—21no—
59C2×Q8×C31—41no—
60C2×Q8×C31—41no—
61C2×Q8×C31C2×Q812yes—
62C2×Q8×C31#4112yes—
63C22×C4×C31—21no—
64C22×C4×C31—21no—
65C22×C4×C31—21no—
66C22×C4×C31—21no—
67C22×C4×C31C22⋊C411yescharacteristic
68C22×C4×C31C22⋊C411yescharacteristic
69C22×C4×C31C22⋊C411yescharacteristic
70C22×C4×C31C22⋊C411yescharacteristic
71C22×C4×C31C22×C411yescharacteristic
72C22×C4×C31C2×D411yescharacteristic
73C22×C4×C31C2×D411yescharacteristic
74M16×C31—24no—
75M16×C31—42no—
76M16×C31—42no—
77M16×C31—42no—
78C2×C8×C31—42no—
79C2×C8×C31—42no—
80C4⋊C4×C31—41no—
81C4⋊C4×C31—41no—
82C4⋊C4×C31—41no—
83C4⋊C4×C31—42no—
84C4⋊C4×C31—42no—
85C4⋊C4×C31—42no—
86C4⋊C4×C31—42no—
87C4⋊C4×C31—41no—
88C4⋊C4×C31—41no—
89C4⋊C4×C31—41no—
90C4⋊C4×C31—41no—
91C42×C31—21no—
92C42×C31—21no—
93C42×C31—21no—
94C42×C31—21no—
95C42×C31—21no—
96C42×C31—21no—
97C42×C31—41no—
98C42×C31—41no—
99#13303C3111yesmaximal, characteristic, direct product factor, Sylow
100C23×C31C2×C22⋊C411yescharacteristic
101Q8×C31—42no—
102Q8×C31—42no—
103C2×C4×C31—21no—
104C2×C4×C31—21no—
105C2×C4×C31—21no—
106C2×C4×C31—21no—
107C2×C4×C31—21no—
108C2×C4×C31—21no—
109C2×C4×C31—22no—
110C2×C4×C31—21no—
111C2×C4×C31—21no—
112C2×C4×C31—21no—
113C2×C4×C31—41no—
114C2×C4×C31—41no—
115C2×C4×C31—41no—
116C2×C4×C31—41no—
117C2×C4×C31—41no—
118C2×C4×C31—41no—
119C2×C4×C31—41no—
120C2×C4×C31—41no—
121C2×C4×C31—41no—
122C2×C4×C31—41no—
123C2×C4×C31—42no—
124C2×C4×C31—41no—
125C2×C4×C31—41no—
126C2×C4×C31—41no—
127C2×C4×C31#9911yescharacteristic
128C2×C4×C31#9911yescharacteristic
129C2×C4×C31C4×Q812yes—
130C2×C4×C31C22⋊Q812yes—
131C2×C4×C31#12411yescharacteristic
132C2×C4×C31C4⋊Q811yescharacteristic
133C8×C31—44no—
134C8×C31—82no—
135#2565C2×C3111yescharacteristic
136#1801C2×C3111yescharacteristic
137C4×#101C2×C3111yescharacteristic
138#1394C2×C3112yes—
139#1394C2×C3112yes—
140C22×C31—21no—
141C22×C31—21no—
142C22×C31#39111yescharacteristic
143C22×C31C2×#9911yescharacteristic
144C22×C31#41011yescharacteristic
145C4×C31—21no—
146C4×C31—21no—
147C4×C31—22no—
148C4×C31—21no—
149C4×C31—22no—
150C4×C31—21no—
151C4×C31—42no—
152C4×C31—41no—
153C4×C31—41no—
154C4×C31—41no—
155C4×C31—81no—
156C4×C31—81no—
157C4×C31—81no—
158C2×#125C4×C3111yescharacteristic
159C2×C4×Q8C22×C3111yescharacteristic
160#423—21no—
161C2×#101C22×C3112yes—
162C2×#101C22×C3112yes—
163C4×M16—21no—
164#398—21no—
165#398—21no—
166#391C22×C3111yescharacteristic
167#391C22×C3111yescharacteristic
168#387—21no—
169#387—21no—
170#384C4×C3111yescharacteristic
171#382C4×C3111yescharacteristic
172C4×C4⋊C4C4×C3111yescharacteristic
173#343—21no—
174#343—21no—
175C2×C31—21no—
176C2×C31—21no—
177C2×C31#199611yescharacteristic
178C2×C31#213211yescharacteristic
179C2×C31#213311yescharacteristic
180C22×Q8C23×C3111yescharacteristic
181C2×M16—22no—
182C2×M16—22no—
183#125—41no—
184#125—41no—
185C4×Q8—41no—
186C4×Q8—41no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4C2×C4×C3111yescharacteristic
193C2×C4⋊C4C2×C4×C3111yescharacteristic
194C2×C4⋊C4C2×C4×C3111yescharacteristic
195C2×C4⋊C4D4×C3111yescharacteristic
196C2×C4⋊C4D4×C3111yescharacteristic
197C2×C42C2×C4×C3111yescharacteristic
198C2×C42C2×C4×C3111yescharacteristic
199C2×C42C2×C4×C3111yescharacteristic
200C2×C42D4×C3111yescharacteristic
201C2×C42D4×C3111yescharacteristic
202C4⋊C8—41no—
203C4⋊C8—41no—
204#101—22no—
205#101—24no—
206#101Q8×C3114yes—
207#97—41no—
208C4×C8—41no—
209#95—21no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—21no—
216C31#1330311yescharacteristic, direct product factor, Sylow
217C2×Q8—41no—
218C2×Q8—41no—
219C2×Q8C2×Q8×C3112yes—
220C2×Q8#41×C3112yes—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4C22⋊C4×C3111yescharacteristic
226C22×C4C22⋊C4×C3111yescharacteristic
227C22×C4C22⋊C4×C3111yescharacteristic
228C22×C4C22⋊C4×C3111yescharacteristic
229C22×C4C22×C4×C3111yescharacteristic
230C22×C4C2×D4×C3111yescharacteristic
231C22×C4C2×D4×C3111yescharacteristic
232M16—24no—
233M16—42no—
234M16—42no—
235M16—42no—
236C2×C8—42no—
237C2×C8—42no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—42no—
244C4⋊C4—42no—
245C4⋊C4—42no—
246C4⋊C4—42no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C42—21no—
250C42—21no—
251C42—21no—
252C42—21no—
253C42—21no—
254C42—21no—
255C42—41no—
256C42—41no—
257C23C2×C22⋊C4×C3111yescharacteristic
258Q8—42no—
259Q8—42no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—22no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—42no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4C31×#9911yescharacteristic
285C2×C4C31×#9911yescharacteristic
286C2×C4C4×Q8×C3112yes—
287C2×C4C31×C22⋊Q812yes—
288C2×C4C31×#12411yescharacteristic
289C2×C4C31×C4⋊Q811yescharacteristic
290C8—44no—
291C8—82no—
292C22—21no—
293C22—21no—
294C22C31×#39111yescharacteristic
295C22C2×C31×#9911yescharacteristic
296C22C31×#41011yescharacteristic
297C4—21no—
298C4—21no—
299C4—22no—
300C4—21no—
301C4—22no—
302C4—21no—
303C4—42no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—81no—
308C4—81no—
309C4—81no—
310C2—21no—
311C2—21no—
312C2C31×#199611yescharacteristic
313C2C31×#213211yescharacteristic
314C2C31×#213311yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC22×C4C22×C4×C31
Frattini, cosocleC22×Q8C23×C31
prime radicalC23×C31C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C4×C31 ◁ C2×C4×Q8×C31 ◁ G

Complements

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

NH ≅ G/Ntype
99. #13303C31direct (N × H)
216. C31#13303direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#25652
C31×#18012
C4×C31×#1012
C31×#13942
#1330331