Finite Group Databasebeta

← C31×#9654 #21466413

Subgroups — C31×#9654 #21466413

Order 7936.

640 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#389C211yesmaximal, characteristic
2C31×#1797C211yesmaximal, characteristic
3C31×#1749C211yesmaximal, characteristic
4C2×C31×#324C214yesmaximal
5C22×C4⋊C4×C31C411yescharacteristic
6C22×C4⋊C4×C31C411yescharacteristic
7C22×C4⋊C4×C31C2212yes—
8C22×C42×C31C2211yescharacteristic
9C2×C31×C4⋊C8—21no—
10C2×C31×C22⋊C8C2212yes—
11C2×C31×C22⋊C8C2212yes—
12C2×C31×#97—21no—
13C31×#389—21no—
14C31×#389—21no—
15C31×#389—21no—
16C31×#389—21no—
17C2×C31×#95C412yes—
18C31×#336—21no—
19C31×#336—21no—
20C31×#324—28no—
21C23×C4×C31C2×C411yescharacteristic
22C23×C4×C31C2×C412yes—
23C23×C4×C31C2×C411yescharacteristic
24C23×C4×C31C2×C412yes—
25C23×C4×C31C2311yescharacteristic
26C22×C8×C31—22no—
27C22×C8×C31—22no—
28C2×C4⋊C4×C31—21no—
29C2×C4⋊C4×C31—21no—
30C2×C4⋊C4×C31—24no—
31C2×C4⋊C4×C31—21no—
32C2×C4⋊C4×C31—21no—
33C2×C4⋊C4×C31—24no—
34C2×C4⋊C4×C31—22no—
35C2×C4⋊C4×C31—22no—
36C2×C4⋊C4×C31—24no—
37C2×C4⋊C4×C31—42no—
38C2×C42×C31—42no—
39C2×C42×C31D411yescharacteristic
40C2×C42×C31D411yescharacteristic
41C2×C42×C31D411yescharacteristic
42C2×C42×C31D411yescharacteristic
43C31×C4⋊C8—42no—
44C31×C22⋊C8—22no—
45C31×C22⋊C8—24no—
46C31×C22⋊C8D414yes—
47C31×#97—42no—
48C31×#95—22no—
49C31×#95—22no—
50C24×C31C22×C411yescharacteristic
51C22×C4×C31—22no—
52C22×C4×C31—22no—
53C22×C4×C31—22no—
54C22×C4×C31—22no—
55C22×C4×C31—24no—
56C22×C4×C31—22no—
57C22×C4×C31—22no—
58C22×C4×C31—24no—
59C22×C4×C31—22no—
60C22×C4×C31—22no—
61C22×C4×C31—24no—
62C22×C4×C31—41no—
63C22×C4×C31—41no—
64C22×C4×C31—41no—
65C22×C4×C31—42no—
66C22×C4×C31—42no—
67C22×C4×C31C22⋊C411yescharacteristic
68C22×C4×C31C22⋊C411yescharacteristic
69C22×C4×C31C22⋊C411yescharacteristic
70C22×C4×C31C22⋊C411yescharacteristic
71C22×C4×C31M1614yes—
72C22×C4×C31C2×D411yescharacteristic
73C22×C4×C31C2×D411yescharacteristic
74C22×C4×C31C2×D412yes—
75C22×C4×C31#4112yes—
76C2×C8×C31—24no—
77C2×C8×C31—42no—
78C2×C8×C31—42no—
79C2×C8×C31—42no—
80C2×C8×C31—42no—
81C2×C8×C31—42no—
82C4⋊C4×C31—24no—
83C4⋊C4×C31—24no—
84C4⋊C4×C31—42no—
85C4⋊C4×C31—42no—
86C4⋊C4×C31—44no—
87C4⋊C4×C31—42no—
88C4⋊C4×C31—42no—
89C42×C31—22no—
90C42×C31—22no—
91C42×C31—41no—
92C42×C31—41no—
93#9654C3111yesmaximal, characteristic, direct product factor, Sylow
94C23×C31—21no—
95C23×C31—21no—
96C23×C31—21no—
97C23×C31—21no—
98C23×C31C2×C22⋊C411yescharacteristic
99C23×C31C4×D412yes—
100C23×C31C2×M1612yes—
101C23×C31#13112yes—
102C2×C4×C31—28no—
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—21no—
110C2×C4×C31—21no—
111C2×C4×C31—21no—
112C2×C4×C31—21no—
113C2×C4×C31—24no—
114C2×C4×C31—21no—
115C2×C4×C31—21no—
116C2×C4×C31—21no—
117C2×C4×C31—28no—
118C2×C4×C31—42no—
119C2×C4×C31—42no—
120C2×C4×C31—44no—
121C2×C4×C31—42no—
122C2×C4×C31—42no—
123C2×C4×C31—44no—
124C2×C4×C31—42no—
125C2×C4×C31—42no—
126C2×C4×C31—42no—
127C2×C4×C31—84no—
128C2×C4×C31#9912yes—
129C2×C4×C31#10112yes—
130C2×C4×C31#10112yes—
131C2×C4×C31#12112yes—
132C2×C4×C31#12411yescharacteristic
133C2×C4×C31#12711yescharacteristic
134C8×C31—44no—
135C8×C31—82no—
136C2×#389C2×C3111yescharacteristic
137#1797C2×C3111yescharacteristic
138#1749C2×C3111yescharacteristic
139C2×#324C2×C3114yes—
140C22×C31—22no—
141C22×C31—22no—
142C22×C31—22no—
143C22×C31—22no—
144C22×C31—22no—
145C22×C31—22no—
146C22×C31#39011yescharacteristic
147C22×C31#40711yescharacteristic
148C22×C31#40811yescharacteristic
149C22×C31C2×#9911yescharacteristic
150C22×C31#41011yescharacteristic
151C22×C31C2×#10111yescharacteristic
152C22×C31C2×#10111yescharacteristic
153C22×C31#43514yes—
154C4×C31—22no—
155C4×C31—21no—
156C4×C31—21no—
157C4×C31—22no—
158C4×C31—22no—
159C4×C31—22no—
160C4×C31—44no—
161C4×C31—41no—
162C4×C31—82no—
163C22×C4⋊C4C4×C3111yescharacteristic
164C22×C4⋊C4C4×C3111yescharacteristic
165C22×C4⋊C4C22×C3112yes—
166C22×C42C22×C3111yescharacteristic
167C2×C4⋊C8—21no—
168C2×C22⋊C8C22×C3112yes—
169C2×C22⋊C8C22×C3112yes—
170C2×#97—21no—
171#389—21no—
172#389—21no—
173#389—21no—
174#389—21no—
175C2×#95C4×C3112yes—
176#336—21no—
177#336—21no—
178#324—28no—
179C2×C31—24no—
180C2×C31#146311yescharacteristic
181C2×C31#146711yescharacteristic
182C2×C31#147011yescharacteristic
183C2×C31#147211yescharacteristic
184C2×C31#195511yescharacteristic
185C2×C31#196411yescharacteristic
186C2×C31#196611yescharacteristic
187C23×C4C2×C4×C3111yescharacteristic
188C23×C4C2×C4×C3112yes—
189C23×C4C2×C4×C3111yescharacteristic
190C23×C4C2×C4×C3112yes—
191C23×C4C23×C3111yescharacteristic
192C22×C8—22no—
193C22×C8—22no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—24no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—24no—
200C2×C4⋊C4—22no—
201C2×C4⋊C4—22no—
202C2×C4⋊C4—24no—
203C2×C4⋊C4—42no—
204C2×C42—42no—
205C2×C42D4×C3111yescharacteristic
206C2×C42D4×C3111yescharacteristic
207C2×C42D4×C3111yescharacteristic
208C2×C42D4×C3111yescharacteristic
209C4⋊C8—42no—
210C22⋊C8—22no—
211C22⋊C8—24no—
212C22⋊C8D4×C3114yes—
213#97—42no—
214#95—22no—
215#95—22no—
216C31#965411yescharacteristic, direct product factor, Sylow
217C24C22×C4×C3111yescharacteristic
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—24no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—24no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—24no—
229C22×C4—41no—
230C22×C4—41no—
231C22×C4—41no—
232C22×C4—42no—
233C22×C4—42no—
234C22×C4C22⋊C4×C3111yescharacteristic
235C22×C4C22⋊C4×C3111yescharacteristic
236C22×C4C22⋊C4×C3111yescharacteristic
237C22×C4C22⋊C4×C3111yescharacteristic
238C22×C4M16×C3114yes—
239C22×C4C2×D4×C3111yescharacteristic
240C22×C4C2×D4×C3111yescharacteristic
241C22×C4C2×D4×C3112yes—
242C22×C4#41×C3112yes—
243C2×C8—24no—
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—42no—
248C2×C8—42no—
249C4⋊C4—24no—
250C4⋊C4—24no—
251C4⋊C4—42no—
252C4⋊C4—42no—
253C4⋊C4—44no—
254C4⋊C4—42no—
255C4⋊C4—42no—
256C42—22no—
257C42—22no—
258C42—41no—
259C42—41no—
260C23—21no—
261C23—21no—
262C23—21no—
263C23—21no—
264C23C2×C22⋊C4×C3111yescharacteristic
265C23C4×D4×C3112yes—
266C23C2×M16×C3112yes—
267C23C31×#13112yes—
268C2×C4—28no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—24no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—28no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—44no—
287C2×C4—42no—
288C2×C4—44no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—84no—
294C2×C4C31×#9912yes—
295C2×C4C31×#10112yes—
296C2×C4C31×#10112yes—
297C2×C4C31×#12112yes—
298C2×C4C31×#12411yescharacteristic
299C2×C4C31×#12711yescharacteristic
300C8—44no—
301C8—82no—
302C22—22no—
303C22—22no—
304C22—22no—
305C22—22no—
306C22—22no—
307C22—22no—
308C22C31×#39011yescharacteristic
309C22C31×#40711yescharacteristic
310C22C31×#40811yescharacteristic
311C22C2×C31×#9911yescharacteristic
312C22C31×#41011yescharacteristic
313C22C2×C31×#10111yescharacteristic
314C22C2×C31×#10111yescharacteristic
315C22C31×#43514yes—
316C4—22no—
317C4—21no—
318C4—21no—
319C4—22no—
320C4—22no—
321C4—22no—
322C4—44no—
323C4—41no—
324C4—82no—
325C2—24no—
326C2C31×#146311yescharacteristic
327C2C31×#146711yescharacteristic
328C2C31×#147011yescharacteristic
329C2C31×#147211yescharacteristic
330C2C31×#195511yescharacteristic
331C2C31×#196411yescharacteristic
332C2C31×#196611yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC24C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC24×C31C22×C4
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
93. #9654C31direct (N × H)
216. C31#9654direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3892
C31×#17972
C31×#17492
C2×C31×#3242
#965431