Finite Group Databasebeta

← C31×#9439 #21466198

Subgroups — C31×#9439 #21466198

Order 7936.

490 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 118 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3140C211yesmaximal, characteristic
2C31×#2372C211yesmaximal, characteristic
3C31×#1533C211yesmaximal, characteristic
4C31×#1506C212yesmaximal, complemented
5C31×#1300C212yesmaximal, complemented
6C31×#533C2211yescharacteristic
7C2×C31×#124C2211yescharacteristic
8C31×#489C414yescomplemented
9C31×#488—22no—
10C31×#432C2212yes—
11C31×#419—21no—
12C31×#418—21no—
13C4×M16×C31C2211yescharacteristic
14C31×#391—21no—
15C31×#388—22no—
16C31×#386—21no—
17C4×C22⋊C4×C31—22no—
18C31×#376C2212yes—
19C31×#329—22no—
20C31×#328—22no—
21C31×#328—22no—
22C22×Q8×C31D411yescharacteristic
23C22×D4×C31D411yescharacteristic
24C23×C4×C31—21no—
25C2×M16×C31—21no—
26C31×C4⋊Q8C2×C412yescomplemented
27C31×#125—21no—
28C31×#124—22no—
29C31×#124C2×C412yes—
30C31×#124D412yes—
31C31×C22⋊Q8—22no—
32C4×Q8×C31—22no—
33C31×#117—21no—
34C2×C4⋊C4×C31—21no—
35C2×C22⋊C4×C31—22no—
36C2×C22⋊C4×C31—22no—
37C2×C22⋊C4×C31—21no—
38C2×C42×C31—22no—
39C2×C42×C31—21no—
40C2×C42×C31C2311yescharacteristic
41C31×C4⋊C8—22no—
42C31×#103—24no—
43C31×#102—24no—
44C31×C22⋊C8—22no—
45C31×#97—22no—
46C31×#97C2×C412yescomplemented
47C4×C8×C31—21no—
48C31×#95—22no—
49C31×#95—22no—
50C31×#95D412yes—
51C31×#95D412yes—
52C24×C31—21no—
53C2×Q8×C31—21no—
54C2×Q8×C31—22no—
55C2×Q8×C31—41no—
56C2×Q8×C31—41no—
57C2×Q8×C31C22⋊C412yes—
58C2×D4×C31—21no—
59C2×D4×C31—41no—
60C2×D4×C31—41no—
61C2×D4×C31C22⋊C412yes—
62C22×C4×C31—22no—
63C22×C4×C31—21no—
64C22×C4×C31—22no—
65C22×C4×C31—44no—
66C22×C4×C31—81no—
67C22×C4×C31C2×D411yescharacteristic
68C22×C4×C31C2×D412yes—
69M16×C31—41no—
70M16×C31—41no—
71C2×C8×C31—22no—
72C2×C8×C31—42no—
73C4⋊C4×C31—22no—
74C4⋊C4×C31—22no—
75C4⋊C4×C31—42no—
76C4⋊C4×C31—81no—
77C22⋊C4×C31—24no—
78C22⋊C4×C31—24no—
79C22⋊C4×C31—44no—
80C22⋊C4×C31—41no—
81C22⋊C4×C31—81no—
82C42×C31—44no—
83C42×C31—41no—
84C42×C31—81no—
85C42×C31C22×C411yescharacteristic
86C42×C31C2×D411yescharacteristic
87C42×C31#4112yes—
88#9439C3111yesmaximal, characteristic, direct product factor, Sylow
89C23×C31—22no—
90C23×C31—42no—
91C23×C31—42no—
92C23×C31—41no—
93C23×C31—41no—
94C23×C31#12011yescharacteristic
95Q8×C31—42no—
96Q8×C31—81no—
97Q8×C31—82no—
98D4×C31—42no—
99D4×C31—81no—
100C2×C4×C31—21no—
101C2×C4×C31—21no—
102C2×C4×C31—24no—
103C2×C4×C31—22no—
104C2×C4×C31—42no—
105C2×C4×C31—42no—
106C2×C4×C31—42no—
107C2×C4×C31—41no—
108C2×C4×C31—41no—
109C2×C4×C31—42no—
110C2×C4×C31—42no—
111C2×C4×C31—42no—
112C2×C4×C31—42no—
113C2×C4×C31—84no—
114C2×C4×C31C2×C22⋊C411yescharacteristic
115C2×C4×C31C4×D412yes—
116C2×C4×C31#12112yes—
117C2×C4×C31#12311yescharacteristic
118C8×C31—42no—
119C8×C31—82no—
120#3140C2×C3111yescharacteristic
121#2372C2×C3111yescharacteristic
122#1533C2×C3111yescharacteristic
123#1506C2×C3112yescomplemented
124#1300C2×C3112yescomplemented
125C22×C31—22no—
126C22×C31—42no—
127C22×C31—44no—
128C22×C31—81no—
129C22×C31—81no—
130C22×C31—82no—
131C22×C31#38611yescharacteristic
132C22×C31#45511yescharacteristic
133C22×C31#45511yescharacteristic
134C4×C31—21no—
135C4×C31—21no—
136C4×C31—22no—
137C4×C31—22no—
138C4×C31—44no—
139C4×C31—42no—
140C4×C31—82no—
141C4×C31—82no—
142#533C22×C3111yescharacteristic
143C2×#124C22×C3111yescharacteristic
144#489C4×C3114yescomplemented
145#488—22no—
146#432C22×C3112yes—
147#419—21no—
148#418—21no—
149C4×M16C22×C3111yescharacteristic
150#391—21no—
151#388—22no—
152#386—21no—
153C4×C22⋊C4—22no—
154#376C22×C3112yes—
155#329—22no—
156#328—22no—
157#328—22no—
158C2×C31—21no—
159C2×C31—21no—
160C2×C31—82no—
161C2×C31#188511yescharacteristic
162C2×C31#190612yes—
163C22×Q8D4×C3111yescharacteristic
164C22×D4D4×C3111yescharacteristic
165C23×C4—21no—
166C2×M16—21no—
167C4⋊Q8C2×C4×C3112yescomplemented
168#125—21no—
169#124—22no—
170#124C2×C4×C3112yes—
171#124D4×C3112yes—
172C22⋊Q8—22no—
173C4×Q8—22no—
174#117—21no—
175C2×C4⋊C4—21no—
176C2×C22⋊C4—22no—
177C2×C22⋊C4—22no—
178C2×C22⋊C4—21no—
179C2×C42—22no—
180C2×C42—21no—
181C2×C42C23×C3111yescharacteristic
182C4⋊C8—22no—
183#103—24no—
184#102—24no—
185C22⋊C8—22no—
186#97—22no—
187#97C2×C4×C3112yescomplemented
188C4×C8—21no—
189#95—22no—
190#95—22no—
191#95D4×C3112yes—
192#95D4×C3112yes—
193C31#943911yescharacteristic, direct product factor, Sylow
194C24—21no—
195C2×Q8—21no—
196C2×Q8—22no—
197C2×Q8—41no—
198C2×Q8—41no—
199C2×Q8C22⋊C4×C3112yes—
200C2×D4—21no—
201C2×D4—41no—
202C2×D4—41no—
203C2×D4C22⋊C4×C3112yes—
204C22×C4—22no—
205C22×C4—21no—
206C22×C4—22no—
207C22×C4—44no—
208C22×C4—81no—
209C22×C4C2×D4×C3111yescharacteristic
210C22×C4C2×D4×C3112yes—
211M16—41no—
212M16—41no—
213C2×C8—22no—
214C2×C8—42no—
215C4⋊C4—22no—
216C4⋊C4—22no—
217C4⋊C4—42no—
218C4⋊C4—81no—
219C22⋊C4—24no—
220C22⋊C4—24no—
221C22⋊C4—44no—
222C22⋊C4—41no—
223C22⋊C4—81no—
224C42—44no—
225C42—41no—
226C42—81no—
227C42C22×C4×C3111yescharacteristic
228C42C2×D4×C3111yescharacteristic
229C42#41×C3112yes—
230C23—22no—
231C23—42no—
232C23—42no—
233C23—41no—
234C23—41no—
235C23C31×#12011yescharacteristic
236Q8—42no—
237Q8—81no—
238Q8—82no—
239D4—42no—
240D4—81no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—24no—
244C2×C4—22no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—84no—
255C2×C4C2×C22⋊C4×C3111yescharacteristic
256C2×C4C4×D4×C3112yes—
257C2×C4C31×#12112yes—
258C2×C4C31×#12311yescharacteristic
259C8—42no—
260C8—82no—
261C22—22no—
262C22—42no—
263C22—44no—
264C22—81no—
265C22—81no—
266C22—82no—
267C22C31×#38611yescharacteristic
268C22C31×#45511yescharacteristic
269C22C31×#45511yescharacteristic
270C4—21no—
271C4—21no—
272C4—22no—
273C4—22no—
274C4—44no—
275C4—42no—
276C4—82no—
277C4—82no—
278C2—21no—
279C2—21no—
280C2—82no—
281C2C31×#188511yescharacteristic
282C2C31×#190612yes—
subgroupG/H
center, socleC22×C31#386
commutatorC42C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC22×D4×C31D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C31×#1506C2semidirect
5. C31×#1300C2semidirect
8. C31×#489C4semidirect
26. C31×C4⋊Q8C2×C4semidirect
46. C31×#97C2×C4semidirect
88. #9439C31direct (N × H)
123. #1506C2×C31semidirect
124. #1300C2×C31semidirect
144. #489C4×C31semidirect
167. C4⋊Q8C2×C4×C31semidirect
187. #97C2×C4×C31semidirect
193. C31#9439direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#31402
C31×#23722
C31×#15332
C31×#15062
C31×#13002
#943931