Finite Group Databasebeta

← C31×#9152 #21465911

Subgroups — C31×#9152 #21465911

Order 7936.

630 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
1C31×#2855C211yesmaximal, characteristic
2C2×C31×#382C211yesmaximal, characteristic
3C31×#1817C211yesmaximal, characteristic
4C2×C31×#328C212yesmaximal
5C31×#1294C212yesmaximal
6C2×C31×C22⋊Q8C2211yescharacteristic
7C22×C4⋊C4×C31—21no—
8C22×C42×C31C2211yescharacteristic
9C2×C31×C22⋊C8C2212yes—
10C31×#391C412yescomplemented
11C31×#389C412yescomplemented
12C31×#387—22no—
13C31×#385—21no—
14C31×#382—24no—
15C31×#381—21no—
16C31×#380C2211yescharacteristic
17C2×C31×#95—21no—
18C2×C31×#95C2212yes—
19C31×#336—22no—
20C31×#328—24no—
21C22×Q8×C31C2×C411yescharacteristic
22C23×C4×C31—22no—
23C23×C4×C31D411yescharacteristic
24C23×C4×C31D411yescharacteristic
25C23×C4×C31C2311yescharacteristic
26C22×C8×C31—22no—
27C31×C22⋊Q8—22no—
28C31×C22⋊Q8—22no—
29C2×C4⋊C4×C31—24no—
30C2×C4⋊C4×C31—22no—
31C2×C4⋊C4×C31—21no—
32C2×C4⋊C4×C31—42no—
33C2×C4⋊C4×C31—42no—
34C2×C4⋊C4×C31C2×C411yescharacteristic
35C2×C4⋊C4×C31C2×C412yes—
36C2×C22⋊C4×C31—21no—
37C2×C22⋊C4×C31—21no—
38C2×C42×C31—22no—
39C2×C42×C31—22no—
40C2×C42×C31C2×C412yes—
41C2×C42×C31D412yes—
42C31×C22⋊C8—22no—
43C31×C22⋊C8—22no—
44C31×#95—24no—
45C31×#95—22no—
46C31×#95—22no—
47C31×#95—22no—
48C31×#95—22no—
49C31×#95—21no—
50C31×#95D414yes—
51C24×C31C2×D411yescharacteristic
52C2×Q8×C31—22no—
53C2×Q8×C31—42no—
54C22×C4×C31—21no—
55C22×C4×C31—21no—
56C22×C4×C31—21no—
57C22×C4×C31—21no—
58C22×C4×C31—21no—
59C22×C4×C31—21no—
60C22×C4×C31—22no—
61C22×C4×C31—21no—
62C22×C4×C31—21no—
63C22×C4×C31—24no—
64C22×C4×C31—42no—
65C22×C4×C31—42no—
66C22×C4×C31—44no—
67C22×C4×C31—44no—
68C22×C4×C31—42no—
69C22×C4×C31—42no—
70C22×C4×C31C22⋊C412yes—
71C22×C4×C31C22⋊C412yes—
72C22×C4×C31SD1612yes—
73C22×C4×C31Q1612yes—
74C22×C4×C31C22×C411yescharacteristic
75C22×C4×C31C2×D411yescharacteristic
76C22×C4×C31C2×D412yes—
77C22×C4×C31#4112yes—
78C2×C8×C31—44no—
79C2×C8×C31—42no—
80C4⋊C4×C31—22no—
81C4⋊C4×C31—44no—
82C4⋊C4×C31—48no—
83C4⋊C4×C31—42no—
84C4⋊C4×C31—42no—
85C22⋊C4×C31—41no—
86C22⋊C4×C31—41no—
87C22⋊C4×C31—41no—
88C22⋊C4×C31—41no—
89C42×C31—24no—
90C42×C31—24no—
91#9152C3111yesmaximal, characteristic, direct product factor, Sylow
92C23×C31—22no—
93C23×C31—22no—
94C23×C31C2×C22⋊C411yescharacteristic
95C23×C31#12011yescharacteristic
96C23×C31#12311yescharacteristic
97C23×C31C2×SD1611yescharacteristic
98C23×C31C2×Q1611yescharacteristic
99C23×C31AGL(1,ℤ/8)11yescharacteristic
100C23×C31#13711yescharacteristic
101Q8×C31—82no—
102C2×C4×C31—22no—
103C2×C4×C31—22no—
104C2×C4×C31—22no—
105C2×C4×C31—22no—
106C2×C4×C31—22no—
107C2×C4×C31—22no—
108C2×C4×C31—22no—
109C2×C4×C31—22no—
110C2×C4×C31—22no—
111C2×C4×C31—22no—
112C2×C4×C31—22no—
113C2×C4×C31—42no—
114C2×C4×C31—42no—
115C2×C4×C31—42no—
116C2×C4×C31—42no—
117C2×C4×C31—44no—
118C2×C4×C31—44no—
119C2×C4×C31—41no—
120C2×C4×C31—41no—
121C2×C4×C31—42no—
122C2×C4×C31—42no—
123C2×C4×C31—42no—
124C2×C4×C31—42no—
125C2×C4×C31—42no—
126C2×C4×C31—44no—
127C2×C4×C31—84no—
128C2×C4×C31—84no—
129C2×C4×C31#10314yes—
130C2×C4×C31C4×D412yes—
131C2×C4×C31#12112yes—
132C8×C31—82no—
133#2855C2×C3111yescharacteristic
134C2×#382C2×C3111yescharacteristic
135#1817C2×C3111yescharacteristic
136C2×#328C2×C3112yes—
137#1294C2×C3112yes—
138C22×C31—21no—
139C22×C31—21no—
140C22×C31—21no—
141C22×C31—21no—
142C22×C31—22no—
143C22×C31—22no—
144C22×C31—22no—
145C22×C31—22no—
146C22×C31#38611yescharacteristic
147C22×C31#41012yes—
148C22×C31C2×#10311yescharacteristic
149C22×C31#41711yescharacteristic
150C22×C31#42112yes—
151C22×C31#45011yescharacteristic
152C22×C31#45111yescharacteristic
153C22×C31#48311yescharacteristic
154C22×C31#48411yescharacteristic
155C4×C31—24no—
156C4×C31—22no—
157C4×C31—22no—
158C4×C31—42no—
159C4×C31—84no—
160C4×C31—81no—
161C4×C31—81no—
162C4×C31—82no—
163C2×C22⋊Q8C22×C3111yescharacteristic
164C22×C4⋊C4—21no—
165C22×C42C22×C3111yescharacteristic
166C2×C22⋊C8C22×C3112yes—
167#391C4×C3112yescomplemented
168#389C4×C3112yescomplemented
169#387—22no—
170#385—21no—
171#382—24no—
172#381—21no—
173#380C22×C3111yescharacteristic
174C2×#95—21no—
175C2×#95C22×C3112yes—
176#336—22no—
177#328—24no—
178C2×C31—21no—
179C2×C31—21no—
180C2×C31—21no—
181C2×C31—21no—
182C2×C31#151212yes—
183C2×C31#151812yes—
184C2×C31#187211yescharacteristic
185C2×C31#189711yescharacteristic
186C2×C31#189911yescharacteristic
187C22×Q8C2×C4×C3111yescharacteristic
188C23×C4—22no—
189C23×C4D4×C3111yescharacteristic
190C23×C4D4×C3111yescharacteristic
191C23×C4C23×C3111yescharacteristic
192C22×C8—22no—
193C22⋊Q8—22no—
194C22⋊Q8—22no—
195C2×C4⋊C4—24no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—42no—
199C2×C4⋊C4—42no—
200C2×C4⋊C4C2×C4×C3111yescharacteristic
201C2×C4⋊C4C2×C4×C3112yes—
202C2×C22⋊C4—21no—
203C2×C22⋊C4—21no—
204C2×C42—22no—
205C2×C42—22no—
206C2×C42C2×C4×C3112yes—
207C2×C42D4×C3112yes—
208C22⋊C8—22no—
209C22⋊C8—22no—
210#95—24no—
211#95—22no—
212#95—22no—
213#95—22no—
214#95—22no—
215#95—21no—
216#95D4×C3114yes—
217C31#915211yescharacteristic, direct product factor, Sylow
218C24C2×D4×C3111yescharacteristic
219C2×Q8—22no—
220C2×Q8—42no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—22no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—24no—
231C22×C4—42no—
232C22×C4—42no—
233C22×C4—44no—
234C22×C4—44no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4C22⋊C4×C3112yes—
238C22×C4C22⋊C4×C3112yes—
239C22×C4SD16×C3112yes—
240C22×C4Q16×C3112yes—
241C22×C4C22×C4×C3111yescharacteristic
242C22×C4C2×D4×C3111yescharacteristic
243C22×C4C2×D4×C3112yes—
244C22×C4#41×C3112yes—
245C2×C8—44no—
246C2×C8—42no—
247C4⋊C4—22no—
248C4⋊C4—42no—
249C4⋊C4—44no—
250C4⋊C4—48no—
251C4⋊C4—42no—
252C22⋊C4—41no—
253C22⋊C4—41no—
254C22⋊C4—41no—
255C22⋊C4—41no—
256C42—24no—
257C42—24no—
258C23—22no—
259C23—22no—
260C23C2×C22⋊C4×C3111yescharacteristic
261C23C31×#12011yescharacteristic
262C23C31×#12311yescharacteristic
263C23C2×SD16×C3111yescharacteristic
264C23C2×Q16×C3111yescharacteristic
265C23C31×AGL(1,ℤ/8)11yescharacteristic
266C23C31×#13711yescharacteristic
267Q8—82no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—44no—
284C2×C4—44no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—44no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—84no—
294C2×C4—84no—
295C2×C4C31×#10314yes—
296C2×C4C4×D4×C3112yes—
297C2×C4C31×#12112yes—
298C8—82no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—22no—
304C22—22no—
305C22—22no—
306C22—22no—
307C22C31×#38611yescharacteristic
308C22C31×#41012yes—
309C22C2×C31×#10311yescharacteristic
310C22C31×#41711yescharacteristic
311C22C31×#42112yes—
312C22C31×#45011yescharacteristic
313C22C31×#45111yescharacteristic
314C22C31×#48311yescharacteristic
315C22C31×#48411yescharacteristic
316C4—24no—
317C4—22no—
318C4—22no—
319C4—42no—
320C4—84no—
321C4—81no—
322C4—81no—
323C4—82no—
324C2—21no—
325C2—21no—
326C2—21no—
327C2—21no—
328C2C31×#151212yes—
329C2C31×#151812yes—
330C2C31×#187211yescharacteristic
331C2C31×#189711yescharacteristic
332C2C31×#189911yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC24×C31C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
10. C31×#391C4semidirect
11. C31×#389C4semidirect
91. #9152C31direct (N × H)
167. #391C4×C31semidirect
168. #389C4×C31semidirect
217. C31#9152direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#28552
C2×C31×#3822
C31×#18172
C2×C31×#3282
C31×#12942
#915231