Finite Group Databasebeta

← C31×#8764 #21465523

Subgroups — C31×#8764 #21465523

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—42no—
26C4×D4×C31—42no—
27C2×C4⋊C4×C31—21no—
28C2×C4⋊C4×C31—21no—
29C2×C4⋊C4×C31—22no—
30C2×C4⋊C4×C31D411yescharacteristic
31C2×C22⋊C4×C31—22no—
32C2×C22⋊C4×C31D412yes—
33C2×C42×C31—21no—
34C2×C42×C31C2311yescharacteristic
35C31×C4⋊C8—22no—
36C31×C4⋊C8—22no—
37C31×C4⋊C8—22no—
38C31×#100—42no—
39C31×C22⋊C8—22no—
40C4×C8×C31—22no—
41C31×#95—22no—
42C31×#95—21no—
43C31×#95C2×C411yescharacteristic
44C31×#95C2×C412yes—
45C31×#95C2×C411yescharacteristic
46C24×C31C22⋊C412yes—
47C2×D4×C31—22no—
48C2×D4×C31—22no—
49C2×D4×C31D812yes—
50C2×D4×C31SD1612yes—
51C22×C4×C31—21no—
52C22×C4×C31—22no—
53C22×C4×C31—22no—
54C22×C4×C31—22no—
55C22×C4×C31—21no—
56C22×C4×C31—44no—
57C22×C4×C31—44no—
58C22×C4×C31—82no—
59C22×C4×C31—82no—
60C22×C4×C31C22⋊C412yes—
61C22×C4×C31C22×C411yescharacteristic
62C22×C4×C31C2×D411yescharacteristic
63C22×C4×C31C2×D411yescharacteristic
64M16×C31—42no—
65M16×C31—42no—
66C2×C8×C31—42no—
67C2×C8×C31—42no—
68C4⋊C4×C31—22no—
69C4⋊C4×C31—42no—
70C4⋊C4×C31—41no—
71C4⋊C4×C31—41no—
72C4⋊C4×C31—82no—
73C22⋊C4×C31—24no—
74C22⋊C4×C31—44no—
75C42×C31—41no—
76C42×C31—41no—
77C42×C31#4112yes—
78C42×C31#4112yes—
79#8764C3111yesmaximal, characteristic, direct product factor, Sylow
80C23×C31—22no—
81C23×C31—22no—
82C23×C31—42no—
83C23×C31—42no—
84C23×C31#10214yes—
85C23×C31C2×C22⋊C411yescharacteristic
86D4×C31—24no—
87D4×C31—24no—
88C2×C4×C31—22no—
89C2×C4×C31—22no—
90C2×C4×C31—41no—
91C2×C4×C31—41no—
92C2×C4×C31—41no—
93C2×C4×C31—41no—
94C2×C4×C31—42no—
95C2×C4×C31—41no—
96C2×C4×C31—41no—
97C2×C4×C31—42no—
98C2×C4×C31—42no—
99C2×C4×C31—41no—
100C2×C4×C31—42no—
101C2×C4×C31—82no—
102C2×C4×C31—82no—
103C2×C4×C31—88no—
104C2×C4×C31#11711yescharacteristic
105C2×C4×C31#11711yescharacteristic
106C2×C4×C31#12312yes—
107C2×C4×C31#12312yes—
108C2×C4×C31C2×D811yescharacteristic
109C2×C4×C31C2×SD1611yescharacteristic
110C2×C4×C31#13712yes—
111C8×C31—82no—
112C8×C31—82no—
113#2349C2×C3111yescharacteristic
114#1800C2×C3111yescharacteristic
115#1460C2×C3111yescharacteristic
116#1303C2×C3112yescomplemented
117#1286C2×C3112yescomplemented
118C22×C31—21no—
119C22×C31—21no—
120C22×C31—24no—
121C22×C31—44no—
122C22×C31—44no—
123C22×C31—42no—
124C22×C31—42no—
125C22×C31#38111yescharacteristic
126C22×C31C2×#10211yescharacteristic
127C22×C31#41911yescharacteristic
128C4×C31—22no—
129C4×C31—21no—
130C4×C31—21no—
131C4×C31—42no—
132C4×C31—42no—
133C4×C31—81no—
134C4×C31—82no—
135C4×C31#48012yes—
136C4×C31#48312yes—
137C2×C4×D4—21no—
138C2×C4×D4C22×C3111yescharacteristic
139#431C22×C3112yes—
140#423C22×C3112yes—
141C2×#100—21no—
142#389—21no—
143#385—22no—
144#382C22×C3111yescharacteristic
145#380C4×C3112yes—
146C4×C4⋊C4C22×C3111yescharacteristic
147C2×#95C4×C3112yes—
148#343—21no—
149#323—22no—
150C2×C31—21no—
151C2×C31—21no—
152C2×C31—44no—
153C2×C31#182311yescharacteristic
154C2×C31#182711yescharacteristic
155C2×C31#182911yescharacteristic
156C22×D4D4×C3111yescharacteristic
157C23×C4—22no—
158C23×C4C2×C4×C3112yes—
159C2×M16—22no—
160C4×D4—22no—
161C4×D4—22no—
162C4×D4—42no—
163C4×D4—42no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4D4×C3111yescharacteristic
168C2×C22⋊C4—22no—
169C2×C22⋊C4D4×C3112yes—
170C2×C42—21no—
171C2×C42C23×C3111yescharacteristic
172C4⋊C8—22no—
173C4⋊C8—22no—
174C4⋊C8—22no—
175#100—42no—
176C22⋊C8—22no—
177C4×C8—22no—
178#95—22no—
179#95—21no—
180#95C2×C4×C3111yescharacteristic
181#95C2×C4×C3112yes—
182#95C2×C4×C3111yescharacteristic
183C31#876411yescharacteristic, direct product factor, Sylow
184C24C22⋊C4×C3112yes—
185C2×D4—22no—
186C2×D4—22no—
187C2×D4D8×C3112yes—
188C2×D4SD16×C3112yes—
189C22×C4—21no—
190C22×C4—22no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—21no—
194C22×C4—44no—
195C22×C4—44no—
196C22×C4—82no—
197C22×C4—82no—
198C22×C4C22⋊C4×C3112yes—
199C22×C4C22×C4×C3111yescharacteristic
200C22×C4C2×D4×C3111yescharacteristic
201C22×C4C2×D4×C3111yescharacteristic
202M16—42no—
203M16—42no—
204C2×C8—42no—
205C2×C8—42no—
206C4⋊C4—22no—
207C4⋊C4—42no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—82no—
211C22⋊C4—24no—
212C22⋊C4—44no—
213C42—41no—
214C42—41no—
215C42#41×C3112yes—
216C42#41×C3112yes—
217C23—22no—
218C23—22no—
219C23—42no—
220C23—42no—
221C23C31×#10214yes—
222C23C2×C22⋊C4×C3111yescharacteristic
223D4—24no—
224D4—24no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—42no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—41no—
237C2×C4—42no—
238C2×C4—82no—
239C2×C4—82no—
240C2×C4—88no—
241C2×C4C31×#11711yescharacteristic
242C2×C4C31×#11711yescharacteristic
243C2×C4C31×#12312yes—
244C2×C4C31×#12312yes—
245C2×C4C2×D8×C3111yescharacteristic
246C2×C4C2×SD16×C3111yescharacteristic
247C2×C4C31×#13712yes—
248C8—82no—
249C8—82no—
250C22—21no—
251C22—21no—
252C22—24no—
253C22—44no—
254C22—44no—
255C22—42no—
256C22—42no—
257C22C31×#38111yescharacteristic
258C22C2×C31×#10211yescharacteristic
259C22C31×#41911yescharacteristic
260C4—22no—
261C4—21no—
262C4—21no—
263C4—42no—
264C4—42no—
265C4—82no—
266C4—81no—
267C4C31×#48012yes—
268C4C31×#48312yes—
269C2—21no—
270C2—21no—
271C2—44no—
272C2C31×#182311yescharacteristic
273C2C31×#182711yescharacteristic
274C2C31×#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
79. #8764C31direct (N × H)
116. #1303C2×C31semidirect
117. #1286C2×C31semidirect
183. C31#8764direct (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
#876431