Finite Group Databasebeta

← C31×#9032 #21465791

Subgroups — C31×#9032 #21465791

Order 7936.

516 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2983C211yesmaximal, characteristic, complemented
2C31×#2398C211yesmaximal, characteristic
3C4×C31×#101C211yesmaximal, characteristic, complemented
4C31×#1490C212yesmaximal
5C31×#1300C212yesmaximal, complemented
6C2×C4×Q8×C31C2211yescharacteristic
7C2×C4×D4×C31C2211yescharacteristic
8C31×#446—24no—
9C31×#432—21no—
10C31×#432C2212yes—
11C31×#431—21no—
12C2×C31×#101—21no—
13C4×M16×C31C2212yes—
14C31×#400C411yescharacteristic
15C31×#400C411yescharacteristic
16C31×#397—21no—
17C31×#394C411yescharacteristic
18C31×#394C411yescharacteristic
19C31×#393—21no—
20C4×C22⋊C4×C31—21no—
21C4×C22⋊C4×C31—21no—
22C31×#376C2211yescharacteristic
23C31×#343—21no—
24C31×D4⋊C8—24no—
25C22×Q8×C31D411yescharacteristic
26C22×D4×C31C2×C411yescharacteristic
27C23×C4×C31—21no—
28C2×M16×C31—22no—
29C4×Q8×C31—22no—
30C4×Q8×C31—22no—
31C4×D4×C31—22no—
32C4×D4×C31—22no—
33C2×C4⋊C4×C31C2×C411yescharacteristic
34C2×C4⋊C4×C31C2×C411yescharacteristic
35C2×C4⋊C4×C31C2×C411yescharacteristic
36C2×C4⋊C4×C31D411yescharacteristic
37C2×C22⋊C4×C31—21no—
38C2×C22⋊C4×C31—21no—
39C2×C22⋊C4×C31—21no—
40C2×C22⋊C4×C31—21no—
41C2×C22⋊C4×C31—21no—
42C2×C42×C31—21no—
43C2×C42×C31D411yescharacteristic
44C2×C42×C31D411yescharacteristic
45C2×C42×C31C2311yescharacteristic
46C31×C4⋊C8—22no—
47C31×C4⋊C8—22no—
48C31×C4⋊C8D414yes—
49C31×#101—24no—
50C31×C22⋊C8—22no—
51C31×#97—22no—
52C31×#97—22no—
53C31×#97—22no—
54C4×C8×C31—22no—
55C4×C8×C31—22no—
56C31×#95—21no—
57C31×#95—21no—
58C31×#95—21no—
59C31×#95—21no—
60C31×#95—21no—
61C31×#95C2×C411yescharacteristic
62C31×#95C2×C411yescharacteristic
63C24×C31—21no—
64C2×Q8×C31—22no—
65C2×Q8×C31—22no—
66C2×Q8×C31—41no—
67C2×D4×C31—22no—
68C2×D4×C31—42no—
69C22×C4×C31—21no—
70C22×C4×C31—21no—
71C22×C4×C31—21no—
72C22×C4×C31—42no—
73C22×C4×C31—42no—
74C22×C4×C31—41no—
75C22×C4×C31—41no—
76C22×C4×C31C22⋊C411yescharacteristic
77C22×C4×C31C22⋊C411yescharacteristic
78C22×C4×C31C22⋊C411yescharacteristic
79C22×C4×C31C22⋊C411yescharacteristic
80C22×C4×C31C22×C411yescharacteristic
81C22×C4×C31C2×D411yescharacteristic
82C22×C4×C31C2×D411yescharacteristic
83M16×C31—24no—
84M16×C31—42no—
85C2×C8×C31—24no—
86C2×C8×C31—42no—
87C4⋊C4×C31—22no—
88C4⋊C4×C31—22no—
89C4⋊C4×C31—22no—
90C4⋊C4×C31—22no—
91C22⋊C4×C31—42no—
92C22⋊C4×C31—42no—
93C22⋊C4×C31—42no—
94C22⋊C4×C31—42no—
95C22⋊C4×C31—42no—
96C42×C31—21no—
97C42×C31—21no—
98C42×C31—21no—
99C42×C31—21no—
100C42×C31—42no—
101C42×C31C2×D412yes—
102C42×C31#4112yes—
103#9032C3111yesmaximal, characteristic, direct product factor, Sylow
104C23×C31—22no—
105C23×C31—41no—
106C23×C31—41no—
107C23×C31—41no—
108C23×C31—41no—
109C23×C31—41no—
110C23×C31—41no—
111C23×C31C2×C22⋊C411yescharacteristic
112Q8×C31—44no—
113D4×C31—24no—
114D4×C31—42no—
115C2×C4×C31—21no—
116C2×C4×C31—21no—
117C2×C4×C31—21no—
118C2×C4×C31—21no—
119C2×C4×C31—22no—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31—21no—
124C2×C4×C31—21no—
125C2×C4×C31—41no—
126C2×C4×C31—41no—
127C2×C4×C31—41no—
128C2×C4×C31—41no—
129C2×C4×C31—41no—
130C2×C4×C31—41no—
131C2×C4×C31—41no—
132C2×C4×C31—41no—
133C2×C4×C31—41no—
134C2×C4×C31—41no—
135C2×C4×C31—41no—
136C2×C4×C31—41no—
137C2×C4×C31—82no—
138C2×C4×C31—82no—
139C2×C4×C31#10412yes—
140C2×C4×C31C4×D412yes—
141C2×C4×C31#12011yescharacteristic
142C2×C4×C31#12112yes—
143C2×C4×C31#12311yescharacteristic
144C8×C31—44no—
145C8×C31—44no—
146#2983C2×C3111yescharacteristic, complemented
147#2398C2×C3111yescharacteristic
148C4×#101C2×C3111yescharacteristic, complemented
149#1490C2×C3112yes—
150#1300C2×C3112yescomplemented
151C22×C31—21no—
152C22×C31—21no—
153C22×C31—42no—
154C22×C31—42no—
155C22×C31—42no—
156C22×C31—81no—
157C22×C31—81no—
158C22×C31—81no—
159C22×C31—81no—
160C22×C31#38611yescharacteristic
161C22×C31C2×#10411yescharacteristic
162C22×C31#42111yescharacteristic
163C4×C31—22no—
164C4×C31—22no—
165C4×C31—21no—
166C4×C31—22no—
167C4×C31—41no—
168C4×C31—41no—
169C4×C31—41no—
170C4×C31—81no—
171C4×C31—81no—
172C4×C31—81no—
173C4×C31#45412yes—
174C2×C4×Q8C22×C3111yescharacteristic
175C2×C4×D4C22×C3111yescharacteristic
176#446—24no—
177#432—21no—
178#432C22×C3112yes—
179#431—21no—
180C2×#101—21no—
181C4×M16C22×C3112yes—
182#400C4×C3111yescharacteristic
183#400C4×C3111yescharacteristic
184#397—21no—
185#394C4×C3111yescharacteristic
186#394C4×C3111yescharacteristic
187#393—21no—
188C4×C22⋊C4—21no—
189C4×C22⋊C4—21no—
190#376C22×C3111yescharacteristic
191#343—21no—
192D4⋊C8—24no—
193C2×C31—21no—
194C2×C31—21no—
195C2×C31—82no—
196C2×C31#187111yescharacteristic
197C2×C31#188811yescharacteristic
198C2×C31#189111yescharacteristic
199C22×Q8D4×C3111yescharacteristic
200C22×D4C2×C4×C3111yescharacteristic
201C23×C4—21no—
202C2×M16—22no—
203C4×Q8—22no—
204C4×Q8—22no—
205C4×D4—22no—
206C4×D4—22no—
207C2×C4⋊C4C2×C4×C3111yescharacteristic
208C2×C4⋊C4C2×C4×C3111yescharacteristic
209C2×C4⋊C4C2×C4×C3111yescharacteristic
210C2×C4⋊C4D4×C3111yescharacteristic
211C2×C22⋊C4—21no—
212C2×C22⋊C4—21no—
213C2×C22⋊C4—21no—
214C2×C22⋊C4—21no—
215C2×C22⋊C4—21no—
216C2×C42—21no—
217C2×C42D4×C3111yescharacteristic
218C2×C42D4×C3111yescharacteristic
219C2×C42C23×C3111yescharacteristic
220C4⋊C8—22no—
221C4⋊C8—22no—
222C4⋊C8D4×C3114yes—
223#101—24no—
224C22⋊C8—22no—
225#97—22no—
226#97—22no—
227#97—22no—
228C4×C8—22no—
229C4×C8—22no—
230#95—21no—
231#95—21no—
232#95—21no—
233#95—21no—
234#95—21no—
235#95C2×C4×C3111yescharacteristic
236#95C2×C4×C3111yescharacteristic
237C31#903211yescharacteristic, direct product factor, Sylow
238C24—21no—
239C2×Q8—22no—
240C2×Q8—22no—
241C2×Q8—41no—
242C2×D4—22no—
243C2×D4—42no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4C22⋊C4×C3111yescharacteristic
252C22×C4C22⋊C4×C3111yescharacteristic
253C22×C4C22⋊C4×C3111yescharacteristic
254C22×C4C22⋊C4×C3111yescharacteristic
255C22×C4C22×C4×C3111yescharacteristic
256C22×C4C2×D4×C3111yescharacteristic
257C22×C4C2×D4×C3111yescharacteristic
258M16—24no—
259M16—42no—
260C2×C8—24no—
261C2×C8—42no—
262C4⋊C4—22no—
263C4⋊C4—22no—
264C4⋊C4—22no—
265C4⋊C4—22no—
266C22⋊C4—42no—
267C22⋊C4—42no—
268C22⋊C4—42no—
269C22⋊C4—42no—
270C22⋊C4—42no—
271C42—21no—
272C42—21no—
273C42—21no—
274C42—21no—
275C42—42no—
276C42C2×D4×C3112yes—
277C42#41×C3112yes—
278C23—22no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23C2×C22⋊C4×C3111yescharacteristic
286Q8—44no—
287D4—24no—
288D4—42no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—82no—
312C2×C4—82no—
313C2×C4C31×#10412yes—
314C2×C4C4×D4×C3112yes—
315C2×C4C31×#12011yescharacteristic
316C2×C4C31×#12112yes—
317C2×C4C31×#12311yescharacteristic
318C8—44no—
319C8—44no—
320C22—21no—
321C22—21no—
322C22—42no—
323C22—42no—
324C22—42no—
325C22—81no—
326C22—81no—
327C22—81no—
328C22—81no—
329C22C31×#38611yescharacteristic
330C22C2×C31×#10411yescharacteristic
331C22C31×#42111yescharacteristic
332C4—22no—
333C4—22no—
334C4—21no—
335C4—22no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—81no—
340C4—81no—
341C4—81no—
342C4C31×#45412yes—
343C2—21no—
344C2—21no—
345C2—82no—
346C2C31×#187111yescharacteristic
347C2C31×#188811yescharacteristic
348C2C31×#189111yescharacteristic
subgroupG/H
centerC2×C4×C31#120
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
socleC22×C31#386
prime radicalC22×D4×C31C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#2983C2semidirect
3. C4×C31×#101C2semidirect
5. C31×#1300C2semidirect
103. #9032C31direct (N × H)
146. #2983C2×C31semidirect
148. C4×#101C2×C31semidirect
150. #1300C2×C31semidirect
237. C31#9032direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#29832
C31×#23982
C4×C31×#1012
C31×#14902
C31×#13002
#903231