Finite Group Databasebeta

← C31×#9473 #21466232

Subgroups — C31×#9473 #21466232

Order 7936.

556 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2973C211yesmaximal, characteristic
2C31×#2487C211yesmaximal, characteristic
3C31×#1824C212yesmaximal, complemented
4C31×#1799C211yesmaximal, characteristic
5C31×#1289C212yesmaximal, complemented
6C2×C4×D4×C31C2211yescharacteristic
7C22×C4⋊C4×C31C2211yescharacteristic
8C31×#435—24no—
9C31×#432—21no—
10C2×C31×#99—21no—
11C31×#407—21no—
12C2×C31×C22⋊C8C2212yes—
13C31×#400C412yescomplemented
14C31×#399C412yescomplemented
15C31×#389—21no—
16C31×#386—21no—
17C31×#385—21no—
18C31×#380—21no—
19C31×#380C2212yes—
20C31×#380C2211yescharacteristic
21C31×#342—21no—
22C31×#340—24no—
23C22×D4×C31D411yescharacteristic
24C23×C4×C31—21no—
25C23×C4×C31D411yescharacteristic
26C23×C4×C31C2311yescharacteristic
27C2×M16×C31—22no—
28C22×C8×C31D414yes—
29C4×D4×C31—22no—
30C4×D4×C31—22no—
31C2×C4⋊C4×C31—22no—
32C2×C4⋊C4×C31—22no—
33C2×C4⋊C4×C31—21no—
34C2×C4⋊C4×C31—21no—
35C2×C4⋊C4×C31—22no—
36C2×C4⋊C4×C31—22no—
37C2×C4⋊C4×C31C2×C412yes—
38C2×C4⋊C4×C31C2×C411yescharacteristic
39C2×C22⋊C4×C31—21no—
40C2×C22⋊C4×C31—22no—
41C2×C22⋊C4×C31—22no—
42C2×C22⋊C4×C31C2×C411yescharacteristic
43C2×C22⋊C4×C31D411yescharacteristic
44C2×C42×C31D411yescharacteristic
45C31×C4⋊C8—22no—
46C31×#99—42no—
47C31×C22⋊C8—22no—
48C31×C22⋊C8—22no—
49C31×C22⋊C8—22no—
50C31×#97—22no—
51C31×#95—22no—
52C31×#95—22no—
53C31×#95—22no—
54C31×#95C2×C412yes—
55C24×C31C22⋊C411yescharacteristic
56C24×C31C2×D411yescharacteristic
57C2×D4×C31—22no—
58C2×D4×C31—21no—
59C2×D4×C31—21no—
60C2×D4×C31—22no—
61C22×C4×C31—21no—
62C22×C4×C31—21no—
63C22×C4×C31—22no—
64C22×C4×C31—22no—
65C22×C4×C31—42no—
66C22×C4×C31—42no—
67C22×C4×C31—42no—
68C22×C4×C31—42no—
69C22×C4×C31—82no—
70C22×C4×C31C22⋊C411yescharacteristic
71C22×C4×C31C22⋊C411yescharacteristic
72C22×C4×C31C22⋊C411yescharacteristic
73C22×C4×C31C22×C411yescharacteristic
74C22×C4×C31C2×D412yes—
75C22×C4×C31C2×D411yescharacteristic
76C22×C4×C31#4112yes—
77M16×C31—82no—
78C2×C8×C31—24no—
79C2×C8×C31—44no—
80C4⋊C4×C31—22no—
81C4⋊C4×C31—24no—
82C4⋊C4×C31—42no—
83C4⋊C4×C31—44no—
84C4⋊C4×C31—41no—
85C4⋊C4×C31—41no—
86C4⋊C4×C31—82no—
87C22⋊C4×C31—22no—
88C22⋊C4×C31—22no—
89C22⋊C4×C31—41no—
90C22⋊C4×C31—41no—
91C22⋊C4×C31—42no—
92C22⋊C4×C31—42no—
93C22⋊C4×C31—82no—
94C42×C31—21no—
95C42×C31—21no—
96#9473C3111yesmaximal, characteristic, direct product factor, Sylow
97C23×C31—21no—
98C23×C31—21no—
99C23×C31—21no—
100C23×C31—41no—
101C23×C31—41no—
102C23×C31—41no—
103C23×C31—41no—
104C23×C31C2×C22⋊C411yescharacteristic
105C23×C31#12112yes—
106C23×C31AGL(1,ℤ/8)11yescharacteristic
107C23×C31#13711yescharacteristic
108C23×C31#13712yes—
109D4×C31—42no—
110D4×C31—42no—
111C2×C4×C31—24no—
112C2×C4×C31—22no—
113C2×C4×C31—21no—
114C2×C4×C31—21no—
115C2×C4×C31—21no—
116C2×C4×C31—21no—
117C2×C4×C31—21no—
118C2×C4×C31—41no—
119C2×C4×C31—42no—
120C2×C4×C31—42no—
121C2×C4×C31—41no—
122C2×C4×C31—41no—
123C2×C4×C31—42no—
124C2×C4×C31—42no—
125C2×C4×C31—42no—
126C2×C4×C31—42no—
127C2×C4×C31—42no—
128C2×C4×C31—42no—
129C2×C4×C31—81no—
130C2×C4×C31—84no—
131C2×C4×C31—82no—
132C2×C4×C31—82no—
133C2×C4×C31—82no—
134C2×C4×C31C4×D412yes—
135C2×C4×C31#12011yescharacteristic
136C2×C4×C31#12311yescharacteristic
137C8×C31—44no—
138#2973C2×C3111yescharacteristic
139#2487C2×C3111yescharacteristic
140#1824C2×C3112yescomplemented
141#1799C2×C3111yescharacteristic
142#1289C2×C3112yescomplemented
143C22×C31—21no—
144C22×C31—22no—
145C22×C31—21no—
146C22×C31—22no—
147C22×C31—41no—
148C22×C31—41no—
149C22×C31—42no—
150C22×C31—42no—
151C22×C31—41no—
152C22×C31—41no—
153C22×C31—41no—
154C22×C31—81no—
155C22×C31#38611yescharacteristic
156C22×C31#41711yescharacteristic
157C22×C31#41911yescharacteristic
158C22×C31#46812yes—
159C22×C31#47012yes—
160C4×C31—21no—
161C4×C31—22no—
162C4×C31—41no—
163C4×C31—41no—
164C4×C31—41no—
165C4×C31—82no—
166C4×C31—82no—
167C4×C31—162no—
168C4×C31#45812yes—
169C2×C4×D4C22×C3111yescharacteristic
170C22×C4⋊C4C22×C3111yescharacteristic
171#435—24no—
172#432—21no—
173C2×#99—21no—
174#407—21no—
175C2×C22⋊C8C22×C3112yes—
176#400C4×C3112yescomplemented
177#399C4×C3112yescomplemented
178#389—21no—
179#386—21no—
180#385—21no—
181#380—21no—
182#380C22×C3112yes—
183#380C22×C3111yescharacteristic
184#342—21no—
185#340—24no—
186C2×C31—21no—
187C2×C31—22no—
188C2×C31—21no—
189C2×C31—22no—
190C2×C31—81no—
191C2×C31#189011yescharacteristic
192C2×C31#189411yescharacteristic
193C2×C31#191011yescharacteristic
194C22×D4D4×C3111yescharacteristic
195C23×C4—21no—
196C23×C4D4×C3111yescharacteristic
197C23×C4C23×C3111yescharacteristic
198C2×M16—22no—
199C22×C8D4×C3114yes—
200C4×D4—22no—
201C4×D4—22no—
202C2×C4⋊C4—22no—
203C2×C4⋊C4—22no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—22no—
207C2×C4⋊C4—22no—
208C2×C4⋊C4C2×C4×C3112yes—
209C2×C4⋊C4C2×C4×C3111yescharacteristic
210C2×C22⋊C4—21no—
211C2×C22⋊C4—22no—
212C2×C22⋊C4—22no—
213C2×C22⋊C4C2×C4×C3111yescharacteristic
214C2×C22⋊C4D4×C3111yescharacteristic
215C2×C42D4×C3111yescharacteristic
216C4⋊C8—22no—
217#99—42no—
218C22⋊C8—22no—
219C22⋊C8—22no—
220C22⋊C8—22no—
221#97—22no—
222#95—22no—
223#95—22no—
224#95—22no—
225#95C2×C4×C3112yes—
226C31#947311yescharacteristic, direct product factor, Sylow
227C24C22⋊C4×C3111yescharacteristic
228C24C2×D4×C3111yescharacteristic
229C2×D4—22no—
230C2×D4—21no—
231C2×D4—21no—
232C2×D4—22no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—42no—
238C22×C4—42no—
239C22×C4—42no—
240C22×C4—42no—
241C22×C4—82no—
242C22×C4C22⋊C4×C3111yescharacteristic
243C22×C4C22⋊C4×C3111yescharacteristic
244C22×C4C22⋊C4×C3111yescharacteristic
245C22×C4C22×C4×C3111yescharacteristic
246C22×C4C2×D4×C3112yes—
247C22×C4C2×D4×C3111yescharacteristic
248C22×C4#41×C3112yes—
249M16—82no—
250C2×C8—24no—
251C2×C8—44no—
252C4⋊C4—22no—
253C4⋊C4—24no—
254C4⋊C4—42no—
255C4⋊C4—44no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—82no—
259C22⋊C4—22no—
260C22⋊C4—22no—
261C22⋊C4—41no—
262C22⋊C4—41no—
263C22⋊C4—42no—
264C22⋊C4—42no—
265C22⋊C4—82no—
266C42—21no—
267C42—21no—
268C23—21no—
269C23—21no—
270C23—21no—
271C23—41no—
272C23—41no—
273C23—41no—
274C23—41no—
275C23C2×C22⋊C4×C3111yescharacteristic
276C23C31×#12112yes—
277C23C31×AGL(1,ℤ/8)11yescharacteristic
278C23C31×#13711yescharacteristic
279C23C31×#13712yes—
280D4—42no—
281D4—42no—
282C2×C4—24no—
283C2×C4—22no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—81no—
301C2×C4—84no—
302C2×C4—82no—
303C2×C4—82no—
304C2×C4—82no—
305C2×C4C4×D4×C3112yes—
306C2×C4C31×#12011yescharacteristic
307C2×C4C31×#12311yescharacteristic
308C8—44no—
309C22—21no—
310C22—22no—
311C22—21no—
312C22—22no—
313C22—41no—
314C22—41no—
315C22—42no—
316C22—42no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—81no—
321C22C31×#38611yescharacteristic
322C22C31×#41711yescharacteristic
323C22C31×#41911yescharacteristic
324C22C31×#46812yes—
325C22C31×#47012yes—
326C4—21no—
327C4—22no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—82no—
332C4—82no—
333C4—162no—
334C4C31×#45812yes—
335C2—21no—
336C2—22no—
337C2—21no—
338C2—22no—
339C2—81no—
340C2C31×#189011yescharacteristic
341C2C31×#189411yescharacteristic
342C2C31×#191011yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC22×D4×C31D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#1824C2semidirect
5. C31×#1289C2semidirect
13. C31×#400C4semidirect
14. C31×#399C4semidirect
96. #9473C31direct (N × H)
140. #1824C2×C31semidirect
142. #1289C2×C31semidirect
176. #400C4×C31semidirect
177. #399C4×C31semidirect
226. C31#9473direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#29732
C31×#24872
C31×#18242
C31×#17992
C31×#12892
#947331