Finite Group Databasebeta

← C31×#9471 #21466230

Subgroups — C31×#9471 #21466230

Order 7936.

716 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2973C211yesmaximal, characteristic
2C31×#2409C211yesmaximal, characteristic
3C31×#1799C211yesmaximal, characteristic
4C31×#1787C212yesmaximal, complemented
5C31×#1289C212yesmaximal, complemented
6C23×Q8×C31C2211yescharacteristic
7C2×C31×C22⋊Q8—21no—
8C2×C4×D4×C31C2211yescharacteristic
9C31×#435—24no—
10C31×#432—21no—
11C2×C31×#103—24no—
12C2×C31×#99—21no—
13C31×#407—21no—
14C2×C31×C22⋊C8C2212yes—
15C31×#395C412yescomplemented
16C31×#393C412yescomplemented
17C31×#391—21no—
18C31×#386—21no—
19C31×#385—21no—
20C31×#380C2212yes—
21C31×#380C2211yescharacteristic
22C31×#342—21no—
23C22×Q8×C31—21no—
24C22×Q8×C31—22no—
25C22×Q8×C31—22no—
26C22×Q8×C31—44no—
27C22×Q8×C31C2×C412yes—
28C22×D4×C31D411yescharacteristic
29C23×C4×C31—21no—
30C23×C4×C31D411yescharacteristic
31C23×C4×C31C2311yescharacteristic
32C2×M16×C31—22no—
33C22×C8×C31D414yes—
34C31×C22⋊Q8—44no—
35C4×D4×C31—22no—
36C4×D4×C31—22no—
37C2×C4⋊C4×C31—22no—
38C2×C4⋊C4×C31—21no—
39C2×C4⋊C4×C31—22no—
40C2×C4⋊C4×C31C2×C411yescharacteristic
41C2×C22⋊C4×C31—22no—
42C2×C22⋊C4×C31—21no—
43C2×C22⋊C4×C31—22no—
44C2×C22⋊C4×C31C2×C411yescharacteristic
45C2×C22⋊C4×C31D411yescharacteristic
46C2×C42×C31D411yescharacteristic
47C31×C4⋊C8—22no—
48C31×#103—48no—
49C31×#99—42no—
50C31×C22⋊C8—22no—
51C31×C22⋊C8—22no—
52C31×C22⋊C8—22no—
53C31×#97—22no—
54C31×#95—22no—
55C31×#95—22no—
56C31×#95—22no—
57C31×#95C2×C412yes—
58C24×C31C22⋊C411yescharacteristic
59C24×C31C2×D411yescharacteristic
60C2×Q8×C31—24no—
61C2×Q8×C31—28no—
62C2×Q8×C31—24no—
63C2×Q8×C31—44no—
64C2×Q8×C31—44no—
65C2×Q8×C31—42no—
66C2×Q8×C31—48no—
67C2×Q8×C31—41no—
68C2×Q8×C31—41no—
69C2×D4×C31—22no—
70C2×D4×C31—21no—
71C2×D4×C31—21no—
72C2×D4×C31—22no—
73C22×C4×C31—22no—
74C22×C4×C31—21no—
75C22×C4×C31—21no—
76C22×C4×C31—22no—
77C22×C4×C31—42no—
78C22×C4×C31—44no—
79C22×C4×C31—42no—
80C22×C4×C31—42no—
81C22×C4×C31—42no—
82C22×C4×C31C22⋊C411yescharacteristic
83C22×C4×C31C22⋊C411yescharacteristic
84C22×C4×C31C22⋊C411yescharacteristic
85C22×C4×C31C22×C411yescharacteristic
86C22×C4×C31C2×D412yes—
87C22×C4×C31C2×D411yescharacteristic
88C22×C4×C31#4112yes—
89M16×C31—82no—
90C2×C8×C31—24no—
91C2×C8×C31—44no—
92C4⋊C4×C31—22no—
93C4⋊C4×C31—42no—
94C4⋊C4×C31—44no—
95C4⋊C4×C31—44no—
96C22⋊C4×C31—22no—
97C22⋊C4×C31—22no—
98C22⋊C4×C31—44no—
99C22⋊C4×C31—41no—
100C22⋊C4×C31—41no—
101C22⋊C4×C31—42no—
102C22⋊C4×C31—42no—
103C42×C31—21no—
104C42×C31—21no—
105#9471C3111yesmaximal, characteristic, direct product factor, Sylow
106C23×C31—21no—
107C23×C31—21no—
108C23×C31—21no—
109C23×C31—41no—
110C23×C31—41no—
111C23×C31—41no—
112C23×C31—41no—
113C23×C31C2×C22⋊C411yescharacteristic
114C23×C31#12112yes—
115C23×C31AGL(1,ℤ/8)11yescharacteristic
116C23×C31#13711yescharacteristic
117C23×C31#13712yes—
118Q8×C31—28no—
119Q8×C31—44no—
120Q8×C31—44no—
121Q8×C31—44no—
122D4×C31—42no—
123D4×C31—42no—
124C2×C4×C31—24no—
125C2×C4×C31—22no—
126C2×C4×C31—24no—
127C2×C4×C31—21no—
128C2×C4×C31—21no—
129C2×C4×C31—21no—
130C2×C4×C31—21no—
131C2×C4×C31—21no—
132C2×C4×C31—41no—
133C2×C4×C31—42no—
134C2×C4×C31—42no—
135C2×C4×C31—48no—
136C2×C4×C31—42no—
137C2×C4×C31—42no—
138C2×C4×C31—41no—
139C2×C4×C31—41no—
140C2×C4×C31—42no—
141C2×C4×C31—42no—
142C2×C4×C31—42no—
143C2×C4×C31—81no—
144C2×C4×C31—82no—
145C2×C4×C31—82no—
146C2×C4×C31—82no—
147C2×C4×C31C4×D412yes—
148C2×C4×C31#12011yescharacteristic
149C2×C4×C31#12311yescharacteristic
150C8×C31—44no—
151#2973C2×C3111yescharacteristic
152#2409C2×C3111yescharacteristic
153#1799C2×C3111yescharacteristic
154#1787C2×C3112yescomplemented
155#1289C2×C3112yescomplemented
156C22×C31—21no—
157C22×C31—22no—
158C22×C31—21no—
159C22×C31—22no—
160C22×C31—41no—
161C22×C31—41no—
162C22×C31—42no—
163C22×C31—42no—
164C22×C31—41no—
165C22×C31—41no—
166C22×C31—41no—
167C22×C31—81no—
168C22×C31#38611yescharacteristic
169C22×C31#41711yescharacteristic
170C22×C31#41911yescharacteristic
171C22×C31#46812yes—
172C22×C31#47012yes—
173C4×C31—21no—
174C4×C31—22no—
175C4×C31—44no—
176C4×C31—41no—
177C4×C31—41no—
178C4×C31—41no—
179C4×C31—82no—
180C4×C31—162no—
181C4×C31B(4,𝔽2)12yes—
182C23×Q8C22×C3111yescharacteristic
183C2×C22⋊Q8—21no—
184C2×C4×D4C22×C3111yescharacteristic
185#435—24no—
186#432—21no—
187C2×#103—24no—
188C2×#99—21no—
189#407—21no—
190C2×C22⋊C8C22×C3112yes—
191#395C4×C3112yescomplemented
192#393C4×C3112yescomplemented
193#391—21no—
194#386—21no—
195#385—21no—
196#380C22×C3112yes—
197#380C22×C3111yescharacteristic
198#342—21no—
199C2×C31—21no—
200C2×C31—22no—
201C2×C31—21no—
202C2×C31—22no—
203C2×C31—81no—
204C2×C31#188911yescharacteristic
205C2×C31#189411yescharacteristic
206C2×C31#190911yescharacteristic
207C22×Q8—21no—
208C22×Q8—22no—
209C22×Q8—22no—
210C22×Q8—44no—
211C22×Q8C2×C4×C3112yes—
212C22×D4D4×C3111yescharacteristic
213C23×C4—21no—
214C23×C4D4×C3111yescharacteristic
215C23×C4C23×C3111yescharacteristic
216C2×M16—22no—
217C22×C8D4×C3114yes—
218C22⋊Q8—44no—
219C4×D4—22no—
220C4×D4—22no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—22no—
224C2×C4⋊C4C2×C4×C3111yescharacteristic
225C2×C22⋊C4—22no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—22no—
228C2×C22⋊C4C2×C4×C3111yescharacteristic
229C2×C22⋊C4D4×C3111yescharacteristic
230C2×C42D4×C3111yescharacteristic
231C4⋊C8—22no—
232#103—48no—
233#99—42no—
234C22⋊C8—22no—
235C22⋊C8—22no—
236C22⋊C8—22no—
237#97—22no—
238#95—22no—
239#95—22no—
240#95—22no—
241#95C2×C4×C3112yes—
242C31#947111yescharacteristic, direct product factor, Sylow
243C24C22⋊C4×C3111yescharacteristic
244C24C2×D4×C3111yescharacteristic
245C2×Q8—24no—
246C2×Q8—28no—
247C2×Q8—24no—
248C2×Q8—44no—
249C2×Q8—44no—
250C2×Q8—42no—
251C2×Q8—48no—
252C2×Q8—41no—
253C2×Q8—41no—
254C2×D4—22no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—22no—
258C22×C4—22no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—22no—
262C22×C4—42no—
263C22×C4—44no—
264C22×C4—42no—
265C22×C4—42no—
266C22×C4—42no—
267C22×C4C22⋊C4×C3111yescharacteristic
268C22×C4C22⋊C4×C3111yescharacteristic
269C22×C4C22⋊C4×C3111yescharacteristic
270C22×C4C22×C4×C3111yescharacteristic
271C22×C4C2×D4×C3112yes—
272C22×C4C2×D4×C3111yescharacteristic
273C22×C4#41×C3112yes—
274M16—82no—
275C2×C8—24no—
276C2×C8—44no—
277C4⋊C4—22no—
278C4⋊C4—42no—
279C4⋊C4—44no—
280C4⋊C4—44no—
281C22⋊C4—22no—
282C22⋊C4—22no—
283C22⋊C4—44no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—42no—
287C22⋊C4—42no—
288C42—21no—
289C42—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23C2×C22⋊C4×C3111yescharacteristic
298C23C31×#12112yes—
299C23C31×AGL(1,ℤ/8)11yescharacteristic
300C23C31×#13711yescharacteristic
301C23C31×#13712yes—
302Q8—28no—
303Q8—44no—
304Q8—44no—
305Q8—44no—
306D4—42no—
307D4—42no—
308C2×C4—24no—
309C2×C4—22no—
310C2×C4—24no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—41no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—48no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—81no—
328C2×C4—82no—
329C2×C4—82no—
330C2×C4—82no—
331C2×C4C4×D4×C3112yes—
332C2×C4C31×#12011yescharacteristic
333C2×C4C31×#12311yescharacteristic
334C8—44no—
335C22—21no—
336C22—22no—
337C22—21no—
338C22—22no—
339C22—41no—
340C22—41no—
341C22—42no—
342C22—42no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—81no—
347C22C31×#38611yescharacteristic
348C22C31×#41711yescharacteristic
349C22C31×#41911yescharacteristic
350C22C31×#46812yes—
351C22C31×#47012yes—
352C4—21no—
353C4—22no—
354C4—44no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—82no—
359C4—162no—
360C4C31×B(4,𝔽2)12yes—
361C2—21no—
362C2—22no—
363C2—21no—
364C2—22no—
365C2—81no—
366C2C31×#188911yescharacteristic
367C2C31×#189411yescharacteristic
368C2C31×#190911yescharacteristic
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
4. C31×#1787C2semidirect
5. C31×#1289C2semidirect
15. C31×#395C4semidirect
16. C31×#393C4semidirect
105. #9471C31direct (N × H)
154. #1787C2×C31semidirect
155. #1289C2×C31semidirect
191. #395C4×C31semidirect
192. #393C4×C31semidirect
242. C31#9471direct (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×#24092
C31×#17992
C31×#17872
C31×#12892
#947131