Finite Group Databasebeta

← C31×#9883 #21466642

Subgroups — C31×#9883 #21466642

Order 7936.

600 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
1C2×C31×#389C211yesmaximal, characteristic
2C31×#1797C211yesmaximal, characteristic
3C31×#1749C211yesmaximal, characteristic
4C31×#1280C214yesmaximal
5C22×C4⋊C4×C31C411yescharacteristic
6C22×C4⋊C4×C31C411yescharacteristic
7C22×C4⋊C4×C31C412yes—
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×#95C2212yes—
18C31×#336—21no—
19C31×#336—21no—
20C23×C4×C31C2×C411yescharacteristic
21C23×C4×C31C2×C411yescharacteristic
22C23×C4×C31C2×C412yes—
23C23×C4×C31C2×C412yes—
24C23×C4×C31C2311yescharacteristic
25C22×C8×C31—22no—
26C22×C8×C31—22no—
27C2×C4⋊C4×C31—21no—
28C2×C4⋊C4×C31—21no—
29C2×C4⋊C4×C31—24no—
30C2×C4⋊C4×C31—22no—
31C2×C4⋊C4×C31—21no—
32C2×C4⋊C4×C31—21no—
33C2×C4⋊C4×C31—22no—
34C2×C4⋊C4×C31—42no—
35C2×C4⋊C4×C31—44no—
36C2×C42×C31—42no—
37C2×C42×C31D411yescharacteristic
38C2×C42×C31D411yescharacteristic
39C2×C42×C31D411yescharacteristic
40C2×C42×C31D411yescharacteristic
41C31×C4⋊C8—42no—
42C31×C22⋊C8—22no—
43C31×C22⋊C8—24no—
44C31×C22⋊C8Q814yes—
45C31×#97—42no—
46C31×#95—22no—
47C31×#95—22no—
48C24×C31C22×C411yescharacteristic
49C22×C4×C31—22no—
50C22×C4×C31—22no—
51C22×C4×C31—22no—
52C22×C4×C31—22no—
53C22×C4×C31—22no—
54C22×C4×C31—22no—
55C22×C4×C31—22no—
56C22×C4×C31—22no—
57C22×C4×C31—24no—
58C22×C4×C31—41no—
59C22×C4×C31—41no—
60C22×C4×C31—41no—
61C22×C4×C31—42no—
62C22×C4×C31—42no—
63C22×C4×C31—42no—
64C22×C4×C31—42no—
65C22×C4×C31C22⋊C411yescharacteristic
66C22×C4×C31C22⋊C411yescharacteristic
67C22×C4×C31C22⋊C411yescharacteristic
68C22×C4×C31C22⋊C411yescharacteristic
69C22×C4×C31M1614yes—
70C22×C4×C31C2×D411yescharacteristic
71C22×C4×C31C2×D411yescharacteristic
72C22×C4×C31C2×Q812yes—
73C22×C4×C31#4112yes—
74C2×C8×C31—24no—
75C2×C8×C31—42no—
76C2×C8×C31—42no—
77C2×C8×C31—42no—
78C2×C8×C31—42no—
79C2×C8×C31—42no—
80C4⋊C4×C31—24no—
81C4⋊C4×C31—24no—
82C4⋊C4×C31—42no—
83C4⋊C4×C31—44no—
84C4⋊C4×C31—42no—
85C4⋊C4×C31—44no—
86C42×C31—22no—
87C42×C31—22no—
88C42×C31—41no—
89C42×C31—41no—
90#9883C3111yesmaximal, characteristic, direct product factor, Sylow
91C23×C31—21no—
92C23×C31—21no—
93C23×C31—21no—
94C23×C31—21no—
95C23×C31C2×C22⋊C411yescharacteristic
96C23×C31C4×Q812yes—
97C23×C31C2×M1612yes—
98C23×C31#13112yes—
99C2×C4×C31—28no—
100C2×C4×C31—21no—
101C2×C4×C31—21no—
102C2×C4×C31—21no—
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—24no—
111C2×C4×C31—21no—
112C2×C4×C31—21no—
113C2×C4×C31—21no—
114C2×C4×C31—42no—
115C2×C4×C31—42no—
116C2×C4×C31—44no—
117C2×C4×C31—44no—
118C2×C4×C31—42no—
119C2×C4×C31—42no—
120C2×C4×C31—44no—
121C2×C4×C31—42no—
122C2×C4×C31—42no—
123C2×C4×C31—42no—
124C2×C4×C31—84no—
125C2×C4×C31#9912yes—
126C2×C4×C31#10012yes—
127C2×C4×C31#10112yes—
128C2×C4×C31C22⋊Q812yes—
129C2×C4×C31#12411yescharacteristic
130C2×C4×C31C4⋊Q811yescharacteristic
131C8×C31—44no—
132C8×C31—82no—
133C2×#389C2×C3111yescharacteristic
134#1797C2×C3111yescharacteristic
135#1749C2×C3111yescharacteristic
136#1280C2×C3114yes—
137C22×C31—22no—
138C22×C31—22no—
139C22×C31—22no—
140C22×C31—22no—
141C22×C31—22no—
142C22×C31—22no—
143C22×C31#39111yescharacteristic
144C22×C31#40711yescharacteristic
145C22×C31#40811yescharacteristic
146C22×C31C2×#9911yescharacteristic
147C22×C31#41011yescharacteristic
148C22×C31C2×#10011yescharacteristic
149C22×C31C2×#10111yescharacteristic
150C22×C31#44614yes—
151C4×C31—22no—
152C4×C31—22no—
153C4×C31—22no—
154C4×C31—22no—
155C4×C31—21no—
156C4×C31—21no—
157C4×C31—44no—
158C4×C31—41no—
159C4×C31—82no—
160C22×C4⋊C4C4×C3111yescharacteristic
161C22×C4⋊C4C4×C3111yescharacteristic
162C22×C4⋊C4C4×C3112yes—
163C22×C42C22×C3111yescharacteristic
164C2×C4⋊C8—21no—
165C2×C22⋊C8C22×C3112yes—
166C2×C22⋊C8C22×C3112yes—
167C2×#97—21no—
168#389—21no—
169#389—21no—
170#389—21no—
171#389—21no—
172C2×#95C22×C3112yes—
173#336—21no—
174#336—21no—
175C2×C31—24no—
176C2×C31#146311yescharacteristic
177C2×C31#146611yescharacteristic
178C2×C31#147011yescharacteristic
179C2×C31#147111yescharacteristic
180C2×C31#198511yescharacteristic
181C2×C31#199611yescharacteristic
182C2×C31#199711yescharacteristic
183C23×C4C2×C4×C3111yescharacteristic
184C23×C4C2×C4×C3111yescharacteristic
185C23×C4C2×C4×C3112yes—
186C23×C4C2×C4×C3112yes—
187C23×C4C23×C3111yescharacteristic
188C22×C8—22no—
189C22×C8—22no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—24no—
193C2×C4⋊C4—22no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4—42no—
198C2×C4⋊C4—44no—
199C2×C42—42no—
200C2×C42D4×C3111yescharacteristic
201C2×C42D4×C3111yescharacteristic
202C2×C42D4×C3111yescharacteristic
203C2×C42D4×C3111yescharacteristic
204C4⋊C8—42no—
205C22⋊C8—22no—
206C22⋊C8—24no—
207C22⋊C8Q8×C3114yes—
208#97—42no—
209#95—22no—
210#95—22no—
211C31#988311yescharacteristic, direct product factor, Sylow
212C24C22×C4×C3111yescharacteristic
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—24no—
222C22×C4—41no—
223C22×C4—41no—
224C22×C4—41no—
225C22×C4—42no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4C22⋊C4×C3111yescharacteristic
230C22×C4C22⋊C4×C3111yescharacteristic
231C22×C4C22⋊C4×C3111yescharacteristic
232C22×C4C22⋊C4×C3111yescharacteristic
233C22×C4M16×C3114yes—
234C22×C4C2×D4×C3111yescharacteristic
235C22×C4C2×D4×C3111yescharacteristic
236C22×C4C2×Q8×C3112yes—
237C22×C4#41×C3112yes—
238C2×C8—24no—
239C2×C8—42no—
240C2×C8—42no—
241C2×C8—42no—
242C2×C8—42no—
243C2×C8—42no—
244C4⋊C4—24no—
245C4⋊C4—24no—
246C4⋊C4—42no—
247C4⋊C4—44no—
248C4⋊C4—42no—
249C4⋊C4—44no—
250C42—22no—
251C42—22no—
252C42—41no—
253C42—41no—
254C23—21no—
255C23—21no—
256C23—21no—
257C23—21no—
258C23C2×C22⋊C4×C3111yescharacteristic
259C23C4×Q8×C3112yes—
260C23C2×M16×C3112yes—
261C23C31×#13112yes—
262C2×C4—28no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—24no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—44no—
280C2×C4—44no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—44no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—84no—
288C2×C4C31×#9912yes—
289C2×C4C31×#10012yes—
290C2×C4C31×#10112yes—
291C2×C4C31×C22⋊Q812yes—
292C2×C4C31×#12411yescharacteristic
293C2×C4C31×C4⋊Q811yescharacteristic
294C8—44no—
295C8—82no—
296C22—22no—
297C22—22no—
298C22—22no—
299C22—22no—
300C22—22no—
301C22—22no—
302C22C31×#39111yescharacteristic
303C22C31×#40711yescharacteristic
304C22C31×#40811yescharacteristic
305C22C2×C31×#9911yescharacteristic
306C22C31×#41011yescharacteristic
307C22C2×C31×#10011yescharacteristic
308C22C2×C31×#10111yescharacteristic
309C22C31×#44614yes—
310C4—22no—
311C4—22no—
312C4—22no—
313C4—22no—
314C4—21no—
315C4—21no—
316C4—44no—
317C4—41no—
318C4—82no—
319C2—24no—
320C2C31×#146311yescharacteristic
321C2C31×#146611yescharacteristic
322C2C31×#147011yescharacteristic
323C2C31×#147111yescharacteristic
324C2C31×#198511yescharacteristic
325C2C31×#199611yescharacteristic
326C2C31×#199711yescharacteristic
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
90. #9883C31direct (N × H)
211. C31#9883direct (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
C31×#12802
#988331