Finite Group Databasebeta

← C31×#13603 #21470362

Subgroups — C31×#13603 #21470362

Order 7936.

334 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 90 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
2C2×C31×#355C211yesmaximal, characteristic
3C2×C31×#354C211yesmaximal, characteristic
4C31×#1414C214yesmaximal, complemented
5C31×#533C411yescharacteristic, complemented
6C2×C31×#124C2211yescharacteristic
7C31×#489—21no—
8C31×#489—21no—
9C31×#488C412yescomplemented
10C31×#488C2212yes—
11C31×#419—21no—
12C31×#418—21no—
13C2×C31×#101—21no—
14C2×C31×#99—21no—
15C4×M16×C31C411yescharacteristic, complemented
16C31×#355—21no—
17C31×#355C2212yes—
18C31×#354—21no—
19C31×#354C2212yes—
20C22×Q8×C31D411yescharacteristic
21C22×D4×C31D411yescharacteristic
22C2×M16×C31—21no—
23C2×M16×C31—41no—
24C31×C4⋊Q8—21no—
25C31×#125C2×C412yescomplemented
26C31×#124—41no—
27C31×#124C2×C411yescharacteristic
28C31×#124D411yescharacteristic
29C31×#124D411yescharacteristic
30C31×#124C2311yescharacteristic
31C31×C22⋊Q8—41no—
32C4×Q8×C31—41no—
33C31×#117—21no—
34C2×C22⋊C4×C31—41no—
35C2×C22⋊C4×C31—41no—
36C2×C42×C31C2×C411yescharacteristic
37C31×#103—22no—
38C31×#103—22no—
39C31×#102—22no—
40C31×#102—22no—
41C31×#101—22no—
42C31×#101—41no—
43C31×#99—22no—
44C31×#99—41no—
45C31×#97—21no—
46C4×C8×C31C2×C412yescomplemented
47C24×C31—21no—
48C2×Q8×C31—21no—
49C2×Q8×C31—41no—
50C2×Q8×C31—41no—
51C2×Q8×C31—41no—
52C2×Q8×C31C22⋊C411yescharacteristic
53C2×Q8×C31C2×D411yescharacteristic
54C2×D4×C31—21no—
55C2×D4×C31—41no—
56C2×D4×C31—41no—
57C2×D4×C31C22⋊C411yescharacteristic
58C2×D4×C31C2×D411yescharacteristic
59C22×C4×C31—21no—
60C22×C4×C31—21no—
61C22×C4×C31—81no—
62C22×C4×C31C22⋊C411yescharacteristic
63M16×C31—41no—
64M16×C31—41no—
65M16×C31—42no—
66M16×C31—81no—
67C2×C8×C31—22no—
68C2×C8×C31—81no—
69C4⋊C4×C31—22no—
70C4⋊C4×C31—41no—
71C4⋊C4×C31—42no—
72C22⋊C4×C31—41no—
73C22⋊C4×C31—41no—
74C22⋊C4×C31—41no—
75C22⋊C4×C31—41no—
76C22⋊C4×C31—41no—
77C22⋊C4×C31—42no—
78C22⋊C4×C31—81no—
79C42×C31—21no—
80C42×C31—41no—
81C42×C31C22⋊C411yescharacteristic
82C42×C31C22×C411yescharacteristic
83#13603C3111yesmaximal, characteristic, direct product factor, Sylow
84C23×C31—21no—
85C23×C31—21no—
86C23×C31—41no—
87C23×C31—41no—
88C23×C31—82no—
89C23×C31#9911yescharacteristic
90Q8×C31—41no—
91Q8×C31—41no—
92Q8×C31—81no—
93Q8×C31—82no—
94D4×C31—41no—
95D4×C31—41no—
96D4×C31—81no—
97C2×C4×C31—21no—
98C2×C4×C31—21no—
99C2×C4×C31—21no—
100C2×C4×C31—21no—
101C2×C4×C31—21no—
102C2×C4×C31—21no—
103C2×C4×C31—41no—
104C2×C4×C31—41no—
105C2×C4×C31—42no—
106C2×C4×C31—81no—
107C2×C4×C31—82no—
108C2×C4×C31—162no—
109C2×C4×C31#9911yescharacteristic
110C2×C4×C31C2×C22⋊C411yescharacteristic
111C8×C31—42no—
112C8×C31—82no—
113#3140C2×C3111yescharacteristic
114C2×#355C2×C3111yescharacteristic
115C2×#354C2×C3111yescharacteristic
116#1414C2×C3114yescomplemented
117C22×C31—41no—
118C22×C31—41no—
119C22×C31—41no—
120C22×C31—81no—
121C22×C31—81no—
122C22×C31—82no—
123C22×C31—161no—
124C22×C31#35411yescharacteristic
125C22×C31#35411yescharacteristic
126C22×C31C2×#9911yescharacteristic
127C4×C31—21no—
128C4×C31—21no—
129C4×C31—41no—
130C4×C31—41no—
131C4×C31—41no—
132C4×C31—41no—
133C4×C31—82no—
134C4×C31—162no—
135#533C4×C3111yescharacteristic, complemented
136C2×#124C22×C3111yescharacteristic
137#489—21no—
138#489—21no—
139#488C4×C3112yescomplemented
140#488C22×C3112yes—
141#419—21no—
142#418—21no—
143C2×#101—21no—
144C2×#99—21no—
145C4×M16C4×C3111yescharacteristic, complemented
146#355—21no—
147#355C22×C3112yes—
148#354—21no—
149#354C22×C3112yes—
150C2×C31—21no—
151C2×C31—21no—
152C2×C31—21no—
153C2×C31—81no—
154C2×C31—81no—
155C2×C31C2×#35411yescharacteristic
156C22×Q8D4×C3111yescharacteristic
157C22×D4D4×C3111yescharacteristic
158C2×M16—21no—
159C2×M16—41no—
160C4⋊Q8—21no—
161#125C2×C4×C3112yescomplemented
162#124—41no—
163#124C2×C4×C3111yescharacteristic
164#124D4×C3111yescharacteristic
165#124D4×C3111yescharacteristic
166#124C23×C3111yescharacteristic
167C22⋊Q8—41no—
168C4×Q8—41no—
169#117—21no—
170C2×C22⋊C4—41no—
171C2×C22⋊C4—41no—
172C2×C42C2×C4×C3111yescharacteristic
173#103—22no—
174#103—22no—
175#102—22no—
176#102—22no—
177#101—22no—
178#101—41no—
179#99—22no—
180#99—41no—
181#97—21no—
182C4×C8C2×C4×C3112yescomplemented
183C31#1360311yescharacteristic, direct product factor, Sylow
184C24—21no—
185C2×Q8—21no—
186C2×Q8—41no—
187C2×Q8—41no—
188C2×Q8—41no—
189C2×Q8C22⋊C4×C3111yescharacteristic
190C2×Q8C2×D4×C3111yescharacteristic
191C2×D4—21no—
192C2×D4—41no—
193C2×D4—41no—
194C2×D4C22⋊C4×C3111yescharacteristic
195C2×D4C2×D4×C3111yescharacteristic
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—81no—
199C22×C4C22⋊C4×C3111yescharacteristic
200M16—41no—
201M16—41no—
202M16—42no—
203M16—81no—
204C2×C8—22no—
205C2×C8—81no—
206C4⋊C4—22no—
207C4⋊C4—42no—
208C4⋊C4—41no—
209C22⋊C4—41no—
210C22⋊C4—41no—
211C22⋊C4—41no—
212C22⋊C4—41no—
213C22⋊C4—41no—
214C22⋊C4—42no—
215C22⋊C4—81no—
216C42—21no—
217C42—41no—
218C42C22⋊C4×C3111yescharacteristic
219C42C22×C4×C3111yescharacteristic
220C23—21no—
221C23—21no—
222C23—41no—
223C23—41no—
224C23—82no—
225C23C31×#9911yescharacteristic
226Q8—41no—
227Q8—41no—
228Q8—81no—
229Q8—82no—
230D4—41no—
231D4—41no—
232D4—81no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—81no—
243C2×C4—82no—
244C2×C4—162no—
245C2×C4C31×#9911yescharacteristic
246C2×C4C2×C22⋊C4×C3111yescharacteristic
247C8—42no—
248C8—82no—
249C22—41no—
250C22—41no—
251C22—41no—
252C22—81no—
253C22—81no—
254C22—82no—
255C22—161no—
256C22C31×#35411yescharacteristic
257C22C31×#35411yescharacteristic
258C22C2×C31×#9911yescharacteristic
259C4—21no—
260C4—21no—
261C4—41no—
262C4—41no—
263C4—41no—
264C4—41no—
265C4—82no—
266C4—162no—
267C2—21no—
268C2—21no—
269C2—21no—
270C2—81no—
271C2—81no—
272C2C2×C31×#35411yescharacteristic
subgroupG/H
center, socleC2×C31C2×#354
commutatorC42C22×C4×C31
Frattini, cosocle#124C23×C31
prime radicalC22×D4×C31D4
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C31 ◁ C23×C31 ◁ C22×C4×C31 ◁ C2×C31×#124 ◁ G

Complements

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

NH ≅ G/Ntype
4. C31×#1414C2semidirect
5. C31×#533C4semidirect
9. C31×#488C4semidirect
15. C4×M16×C31C4semidirect
25. C31×#125C2×C4semidirect
46. C4×C8×C31C2×C4semidirect
83. #13603C31direct (N × H)
116. #1414C2×C31semidirect
135. #533C4×C31semidirect
139. #488C4×C31semidirect
145. C4×M16C4×C31semidirect
161. #125C2×C4×C31semidirect
182. C4×C8C2×C4×C31semidirect
183. C31#13603direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#31402
C2×C31×#3552
C2×C31×#3542
C31×#14142
#1360331