Finite Group Databasebeta

← C31×#10034 #21466793

Subgroups — C31×#10034 #21466793

Order 7936.

584 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 122 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×#3150C211yesmaximal, characteristic
2C31×#3103C212yesmaximal, complemented
3C31×#1985C211yesmaximal, characteristic, complemented
4C31×#1480C212yesmaximal, complemented
5C31×#1275C211yesmaximal, characteristic, complemented
6C2×C31×#135—22no—
7C31×#532C2212yes—
8C2×C4×Q8×C31C2211yescharacteristic
9C31×#497—22no—
10C31×#496—22no—
11C31×#481—22no—
12C31×#475—22no—
13C31×#460—22no—
14C31×#448—22no—
15C4×SD16×C31—24no—
16C31×#431C2212yes—
17C2×C31×C4⋊C8C2211yescharacteristic
18C2×C31×#97C2211yescharacteristic
19C31×#336—22no—
20C31×D4⋊C8—24no—
21C2×#41×C31—22no—
22C22×Q8×C31D411yescharacteristic
23C31×#135—44no—
24C31×#135—44no—
25C2×Q16×C31—22no—
26C2×SD16×C31—24no—
27C2×SD16×C31—24no—
28C2×D8×C31—22no—
29C22×C8×C31—21no—
30C22×C8×C31D412yes—
31C31×C4⋊Q8D412yes—
32C31×#127D412yes—
33C31×#124—22no—
34C31×#121—22no—
35C31×#121—22no—
36C4×Q8×C31—22no—
37C4×Q8×C31—22no—
38C4×D4×C31—22no—
39C4×D4×C31—22no—
40C2×C4⋊C4×C31—21no—
41C2×C4⋊C4×C31D411yescharacteristic
42C2×C42×C31—21no—
43C2×C42×C31C2311yescharacteristic
44C31×#106—24no—
45C31×C4⋊C8—22no—
46C31×C4⋊C8—22no—
47C31×#103—24no—
48C31×#102—24no—
49C31×C22⋊C8—22no—
50C31×#97—22no—
51C4×C8×C31D414yes—
52#41×C31—44no—
53#41×C31—44no—
54C2×Q8×C31—22no—
55C2×Q8×C31—22no—
56C2×Q8×C31—42no—
57C2×D4×C31—22no—
58C2×D4×C31—22no—
59C2×D4×C31—22no—
60C2×D4×C31—42no—
61C22×C4×C31—21no—
62C22×C4×C31—21no—
63C22×C4×C31—42no—
64C22×C4×C31C2×D411yescharacteristic
65C22×C4×C31C2×D411yescharacteristic
66C22×C4×C31#4111yescharacteristic
67Q16×C31—44no—
68SD16×C31—48no—
69SD16×C31—48no—
70D8×C31—44no—
71C2×C8×C31—22no—
72C2×C8×C31—22no—
73C2×C8×C31—24no—
74C2×C8×C31—41no—
75C2×C8×C31—42no—
76C2×C8×C31SD1614yescomplemented
77C4⋊C4×C31—22no—
78C4⋊C4×C31—22no—
79C4⋊C4×C31—22no—
80C4⋊C4×C31—42no—
81C22⋊C4×C31—42no—
82C22⋊C4×C31—42no—
83C42×C31—41no—
84C42×C31—41no—
85C42×C31C2×D412yes—
86C42×C31C2×D412yes—
87#10034C3111yesmaximal, characteristic, direct product factor, Sylow
88C23×C31—42no—
89C23×C31#12111yescharacteristic
90Q8×C31—24no—
91Q8×C31—42no—
92Q8×C31—44no—
93D4×C31—44no—
94D4×C31—44no—
95D4×C31—44no—
96D4×C31—84no—
97C2×C4×C31—22no—
98C2×C4×C31—41no—
99C2×C4×C31—41no—
100C2×C4×C31—41no—
101C2×C4×C31—41no—
102C2×C4×C31—42no—
103C2×C4×C31—41no—
104C2×C4×C31—42no—
105C2×C4×C31—82no—
106C2×C4×C31—82no—
107C2×C4×C31#12012yes—
108C2×C4×C31#12011yescharacteristic
109C2×C4×C31#12112yes—
110C2×C4×C31#12711yescharacteristic
111C2×C4×C31C2×SD1612yes—
112C2×C4×C31AGL(1,ℤ/8)12yes—
113C8×C31—24no—
114C8×C31—44no—
115C8×C31—81no—
116#3150C2×C3111yescharacteristic
117#3103C2×C3112yescomplemented
118#1985C2×C3111yescharacteristic, complemented
119#1480C2×C3112yescomplemented
120#1275C2×C3111yescharacteristic, complemented
121C22×C31—21no—
122C22×C31—21no—
123C22×C31—82no—
124C22×C31—82no—
125C22×C31—82no—
126C22×C31#39211yescharacteristic
127C22×C31#46012yes—
128C4×C31—22no—
129C4×C31—22no—
130C4×C31—42no—
131C4×C31—82no—
132C4×C31—81no—
133C4×C31#45012yes—
134C4×C31#49211yescharacteristic
135C4×C31#49611yescharacteristic
136C2×#135—22no—
137#532C22×C3112yes—
138C2×C4×Q8C22×C3111yescharacteristic
139#497—22no—
140#496—22no—
141#481—22no—
142#475—22no—
143#460—22no—
144#448—22no—
145C4×SD16—24no—
146#431C22×C3112yes—
147C2×C4⋊C8C22×C3111yescharacteristic
148C2×#97C22×C3111yescharacteristic
149#336—22no—
150D4⋊C8—24no—
151C2×C31—22no—
152C2×C31—162no—
153C2×C31#201011yescharacteristic
154C2×C31#201411yescharacteristic
155C2×C31#201711yescharacteristic
156C2×#41—22no—
157C22×Q8D4×C3111yescharacteristic
158#135—44no—
159#135—44no—
160C2×Q16—22no—
161C2×SD16—24no—
162C2×SD16—24no—
163C2×D8—22no—
164C22×C8—21no—
165C22×C8D4×C3112yes—
166C4⋊Q8D4×C3112yes—
167#127D4×C3112yes—
168#124—22no—
169#121—22no—
170#121—22no—
171C4×Q8—22no—
172C4×Q8—22no—
173C4×D4—22no—
174C4×D4—22no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4D4×C3111yescharacteristic
177C2×C42—21no—
178C2×C42C23×C3111yescharacteristic
179#106—24no—
180C4⋊C8—22no—
181C4⋊C8—22no—
182#103—24no—
183#102—24no—
184C22⋊C8—22no—
185#97—22no—
186C4×C8D4×C3114yes—
187C31#1003411yescharacteristic, direct product factor, Sylow
188#41—44no—
189#41—44no—
190C2×Q8—22no—
191C2×Q8—22no—
192C2×Q8—42no—
193C2×D4—22no—
194C2×D4—22no—
195C2×D4—22no—
196C2×D4—42no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—42no—
200C22×C4C2×D4×C3111yescharacteristic
201C22×C4C2×D4×C3111yescharacteristic
202C22×C4#41×C3111yescharacteristic
203Q16—44no—
204SD16—48no—
205SD16—48no—
206D8—44no—
207C2×C8—22no—
208C2×C8—22no—
209C2×C8—24no—
210C2×C8—41no—
211C2×C8—42no—
212C2×C8SD16×C3114yescomplemented
213C4⋊C4—22no—
214C4⋊C4—22no—
215C4⋊C4—22no—
216C4⋊C4—42no—
217C22⋊C4—42no—
218C22⋊C4—42no—
219C42—41no—
220C42—41no—
221C42C2×D4×C3112yes—
222C42C2×D4×C3112yes—
223C23—42no—
224C23C31×#12111yescharacteristic
225Q8—24no—
226Q8—42no—
227Q8—44no—
228D4—44no—
229D4—44no—
230D4—44no—
231D4—84no—
232C2×C4—22no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—42no—
238C2×C4—41no—
239C2×C4—42no—
240C2×C4—82no—
241C2×C4—82no—
242C2×C4C31×#12012yes—
243C2×C4C31×#12011yescharacteristic
244C2×C4C31×#12112yes—
245C2×C4C31×#12711yescharacteristic
246C2×C4C2×SD16×C3112yes—
247C2×C4C31×AGL(1,ℤ/8)12yes—
248C8—24no—
249C8—44no—
250C8—81no—
251C22—21no—
252C22—21no—
253C22—82no—
254C22—82no—
255C22—82no—
256C22C31×#39211yescharacteristic
257C22C31×#46012yes—
258C4—22no—
259C4—22no—
260C4—42no—
261C4—82no—
262C4—81no—
263C4C31×#45012yes—
264C4C31×#49211yescharacteristic
265C4C31×#49611yescharacteristic
266C2—22no—
267C2—162no—
268C2C31×#201011yescharacteristic
269C2C31×#201411yescharacteristic
270C2C31×#201711yescharacteristic
subgroupG/H
centerC2×C4×C31#127
commutator, Frattini, cosocleC2×C42C23×C31
socleC22×C31#392
prime radicalC31×#3150C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#3103C2semidirect
3. C31×#1985C2semidirect
4. C31×#1480C2semidirect
5. C31×#1275C2semidirect
76. C2×C8×C31SD16semidirect
87. #10034C31direct (N × H)
117. #3103C2×C31semidirect
118. #1985C2×C31semidirect
119. #1480C2×C31semidirect
120. #1275C2×C31semidirect
187. C31#10034direct (N × H)
212. C2×C8SD16×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#31502
C31×#31032
C31×#19852
C31×#14802
C31×#12752
#1003431