Finite Group Databasebeta

← C31×#8765 #21465524

Subgroups — C31×#8765 #21465524

Order 7936.

498 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 142 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×#2349C211yesmaximal, characteristic
2C31×#1800C211yesmaximal, characteristic
3C31×#1460C211yesmaximal, characteristic
4C31×#1303C212yesmaximal, complemented
5C31×#1286C212yesmaximal, complemented
6C2×C4×D4×C31—21no—
7C2×C4×D4×C31C2211yescharacteristic
8C31×#431C2212yes—
9C31×#423C2212yes—
10C2×C31×#100—21no—
11C31×#389—21no—
12C31×#385—22no—
13C31×#382C2211yescharacteristic
14C31×#380C412yes—
15C4×C4⋊C4×C31C2211yescharacteristic
16C2×C31×#95C412yes—
17C31×#343—21no—
18C31×#323—22no—
19C22×D4×C31D411yescharacteristic
20C23×C4×C31—22no—
21C23×C4×C31C2×C412yes—
22C2×M16×C31—22no—
23C4×D4×C31—22no—
24C4×D4×C31—22no—
25C4×D4×C31—44no—
26C2×C4⋊C4×C31—21no—
27C2×C4⋊C4×C31—21no—
28C2×C4⋊C4×C31—22no—
29C2×C4⋊C4×C31D411yescharacteristic
30C2×C22⋊C4×C31—22no—
31C2×C22⋊C4×C31D412yes—
32C2×C42×C31—21no—
33C2×C42×C31C2311yescharacteristic
34C31×C4⋊C8—22no—
35C31×C4⋊C8—22no—
36C31×C4⋊C8—22no—
37C31×#100—42no—
38C31×C22⋊C8—22no—
39C4×C8×C31—22no—
40C31×#95—22no—
41C31×#95—21no—
42C31×#95C2×C411yescharacteristic
43C31×#95C2×C412yes—
44C31×#95C2×C411yescharacteristic
45C24×C31C22⋊C412yes—
46C2×D4×C31—22no—
47C2×D4×C31—22no—
48C2×D4×C31SD1612yes—
49C2×D4×C31Q1612yes—
50C22×C4×C31—21no—
51C22×C4×C31—22no—
52C22×C4×C31—22no—
53C22×C4×C31—22no—
54C22×C4×C31—21no—
55C22×C4×C31—44no—
56C22×C4×C31—44no—
57C22×C4×C31—82no—
58C22×C4×C31—82no—
59C22×C4×C31C22⋊C412yes—
60C22×C4×C31C22×C411yescharacteristic
61C22×C4×C31C2×D411yescharacteristic
62C22×C4×C31C2×D411yescharacteristic
63M16×C31—42no—
64M16×C31—42no—
65C2×C8×C31—42no—
66C2×C8×C31—42no—
67C4⋊C4×C31—22no—
68C4⋊C4×C31—42no—
69C4⋊C4×C31—42no—
70C4⋊C4×C31—82no—
71C22⋊C4×C31—24no—
72C22⋊C4×C31—44no—
73C42×C31—42no—
74C42×C31#4112yes—
75C42×C31#4112yes—
76#8765C3111yesmaximal, characteristic, direct product factor, Sylow
77C23×C31—22no—
78C23×C31—22no—
79C23×C31—42no—
80C23×C31—42no—
81C23×C31#10314yes—
82C23×C31C2×C22⋊C411yescharacteristic
83D4×C31—24no—
84D4×C31—24no—
85C2×C4×C31—22no—
86C2×C4×C31—22no—
87C2×C4×C31—41no—
88C2×C4×C31—41no—
89C2×C4×C31—41no—
90C2×C4×C31—41no—
91C2×C4×C31—42no—
92C2×C4×C31—41no—
93C2×C4×C31—41no—
94C2×C4×C31—42no—
95C2×C4×C31—42no—
96C2×C4×C31—41no—
97C2×C4×C31—42no—
98C2×C4×C31—82no—
99C2×C4×C31—82no—
100C2×C4×C31—88no—
101C2×C4×C31#11711yescharacteristic
102C2×C4×C31#11711yescharacteristic
103C2×C4×C31#12312yes—
104C2×C4×C31#12312yes—
105C2×C4×C31C2×SD1611yescharacteristic
106C2×C4×C31C2×Q1611yescharacteristic
107C2×C4×C31AGL(1,ℤ/8)12yes—
108C8×C31—82no—
109C8×C31—82no—
110#2349C2×C3111yescharacteristic
111#1800C2×C3111yescharacteristic
112#1460C2×C3111yescharacteristic
113#1303C2×C3112yescomplemented
114#1286C2×C3112yescomplemented
115C22×C31—21no—
116C22×C31—21no—
117C22×C31—24no—
118C22×C31—44no—
119C22×C31—44no—
120C22×C31—42no—
121C22×C31—42no—
122C22×C31#38111yescharacteristic
123C22×C31C2×#10311yescharacteristic
124C22×C31#41811yescharacteristic
125C4×C31—22no—
126C4×C31—21no—
127C4×C31—21no—
128C4×C31—42no—
129C4×C31—42no—
130C4×C31—81no—
131C4×C31—82no—
132C4×C31#48112yes—
133C4×C31#48412yes—
134C2×C4×D4—21no—
135C2×C4×D4C22×C3111yescharacteristic
136#431C22×C3112yes—
137#423C22×C3112yes—
138C2×#100—21no—
139#389—21no—
140#385—22no—
141#382C22×C3111yescharacteristic
142#380C4×C3112yes—
143C4×C4⋊C4C22×C3111yescharacteristic
144C2×#95C4×C3112yes—
145#343—21no—
146#323—22no—
147C2×C31—21no—
148C2×C31—21no—
149C2×C31—44no—
150C2×C31#182411yescharacteristic
151C2×C31#182711yescharacteristic
152C2×C31#182911yescharacteristic
153C22×D4D4×C3111yescharacteristic
154C23×C4—22no—
155C23×C4C2×C4×C3112yes—
156C2×M16—22no—
157C4×D4—22no—
158C4×D4—22no—
159C4×D4—44no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4D4×C3111yescharacteristic
164C2×C22⋊C4—22no—
165C2×C22⋊C4D4×C3112yes—
166C2×C42—21no—
167C2×C42C23×C3111yescharacteristic
168C4⋊C8—22no—
169C4⋊C8—22no—
170C4⋊C8—22no—
171#100—42no—
172C22⋊C8—22no—
173C4×C8—22no—
174#95—22no—
175#95—21no—
176#95C2×C4×C3111yescharacteristic
177#95C2×C4×C3112yes—
178#95C2×C4×C3111yescharacteristic
179C31#876511yescharacteristic, direct product factor, Sylow
180C24C22⋊C4×C3112yes—
181C2×D4—22no—
182C2×D4—22no—
183C2×D4SD16×C3112yes—
184C2×D4Q16×C3112yes—
185C22×C4—21no—
186C22×C4—22no—
187C22×C4—22no—
188C22×C4—22no—
189C22×C4—21no—
190C22×C4—44no—
191C22×C4—44no—
192C22×C4—82no—
193C22×C4—82no—
194C22×C4C22⋊C4×C3112yes—
195C22×C4C22×C4×C3111yescharacteristic
196C22×C4C2×D4×C3111yescharacteristic
197C22×C4C2×D4×C3111yescharacteristic
198M16—42no—
199M16—42no—
200C2×C8—42no—
201C2×C8—42no—
202C4⋊C4—22no—
203C4⋊C4—42no—
204C4⋊C4—42no—
205C4⋊C4—82no—
206C22⋊C4—24no—
207C22⋊C4—44no—
208C42—42no—
209C42#41×C3112yes—
210C42#41×C3112yes—
211C23—22no—
212C23—22no—
213C23—42no—
214C23—42no—
215C23C31×#10314yes—
216C23C2×C22⋊C4×C3111yescharacteristic
217D4—24no—
218D4—24no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—42no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—41no—
231C2×C4—42no—
232C2×C4—82no—
233C2×C4—82no—
234C2×C4—88no—
235C2×C4C31×#11711yescharacteristic
236C2×C4C31×#11711yescharacteristic
237C2×C4C31×#12312yes—
238C2×C4C31×#12312yes—
239C2×C4C2×SD16×C3111yescharacteristic
240C2×C4C2×Q16×C3111yescharacteristic
241C2×C4C31×AGL(1,ℤ/8)12yes—
242C8—82no—
243C8—82no—
244C22—21no—
245C22—21no—
246C22—24no—
247C22—44no—
248C22—44no—
249C22—42no—
250C22—42no—
251C22C31×#38111yescharacteristic
252C22C2×C31×#10311yescharacteristic
253C22C31×#41811yescharacteristic
254C4—22no—
255C4—21no—
256C4—21no—
257C4—42no—
258C4—42no—
259C4—82no—
260C4—81no—
261C4C31×#48112yes—
262C4C31×#48412yes—
263C2—21no—
264C2—21no—
265C2—44no—
266C2C31×#182411yescharacteristic
267C2C31×#182711yescharacteristic
268C2C31×#182911yescharacteristic
subgroupG/H
center, socleC22×C31#381
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC22×D4×C31D4
LCSG ▷ C22×C4 ▷ 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×#1303C2semidirect
5. C31×#1286C2semidirect
76. #8765C31direct (N × H)
113. #1303C2×C31semidirect
114. #1286C2×C31semidirect
179. C31#8765direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#23492
C31×#18002
C31×#14602
C31×#13032
C31×#12862
#876531