Finite Group Databasebeta

← C31×#19080 #21475839

Subgroups — C31×#19080 #21475839

Order 7936.

936 conjugacy classes of subgroups; only the 230 normal subgroups are shown.

normal subgroups only

This group has 936 conjugacy classes of subgroups — too many to draw. Only its 230 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×#3548C211yesmaximal, characteristic
2C31×#3141C212yesmaximal, complemented
3C31×#3139C211yesmaximal, characteristic, complemented
4C31×#1662C218yesmaximal, complemented
5C31×#1526C211yesmaximal, characteristic, complemented
6C31×#1525C212yesmaximal, complemented
7C31×#562C2214yes—
8C31×#554—22no—
9C31×#550—22no—
10C31×#547—22no—
11C31×#540—22no—
12C31×#537—24no—
13C31×#533C2211yescharacteristic
14C31×#532C2212yes—
15C2×C31×C4⋊Q8C2211yescharacteristic
16C31×#491C2214yes—
17C31×#489C2218yes—
18C31×#487—22no—
19C31×#487—22no—
20C31×#486—22no—
21C31×#419—22no—
22C31×#417—24no—
23C4×M16×C31C2211yescharacteristic
24C4×M16×C31C2212yes—
25C31×#330C2214yes—
26C31×#329C2218yes—
27C2×#41×C31—24no—
28C2×#41×C31D414yes—
29C22×Q8×C31—21no—
30C2×M16×C31—22no—
31C2×M16×C31—21no—
32C31×C4⋊Q8—22no—
33C31×C4⋊Q8—21no—
34C31×C4⋊Q8D412yes—
35C31×C4⋊Q8D412yes—
36C31×C4⋊Q8C2312yes—
37C31×#127—22no—
38C31×#127D412yes—
39C31×#125—22no—
40C31×#125C2312yes—
41C31×#124C2314yes—
42C31×#123—28no—
43C31×C22⋊Q8—24no—
44C31×C22⋊Q8—28no—
45C31×C22⋊Q8—22no—
46C31×#121—28no—
47C31×#121—24no—
48C31×#121—28no—
49C31×#121—22no—
50C31×#121—22no—
51C4×Q8×C31—22no—
52C4×D4×C31—24no—
53C4×D4×C31—22no—
54C4×D4×C31—22no—
55C31×#117D412yes—
56C2×C4⋊C4×C31—24no—
57C2×C4⋊C4×C31—22no—
58C2×C42×C31C2311yescharacteristic
59C31×#103—28no—
60C31×#103—28no—
61C31×#102—28no—
62C31×#97C2314yes—
63C31×#97C2312yes—
64C4×C8×C31—22no—
65C4×C8×C31—21no—
66#41×C31—48no—
67#41×C31—88no—
68C2×Q8×C31—22no—
69C2×Q8×C31—22no—
70C2×Q8×C31—44no—
71C2×Q8×C31—41no—
72C2×Q8×C31C2×D414yes—
73C2×D4×C31—28no—
74C2×D4×C31—24no—
75C2×D4×C31—22no—
76C2×D4×C31—22no—
77C2×D4×C31C2×D414yes—
78C22×C4×C31—28no—
79C22×C4×C31—24no—
80C22×C4×C31—41no—
81C22×C4×C31C2×D412yes—
82C22×C4×C31C2×D411yescharacteristic
83M16×C31—42no—
84M16×C31—44no—
85C2×C8×C31—24no—
86C2×C8×C31—22no—
87C4⋊C4×C31—28no—
88C4⋊C4×C31—22no—
89C4⋊C4×C31—22no—
90C4⋊C4×C31—22no—
91C4⋊C4×C31—24no—
92C4⋊C4×C31—24no—
93C4⋊C4×C31—42no—
94C4⋊C4×C31C2×D414yes—
95C22⋊C4×C31—28no—
96C22⋊C4×C31—22no—
97C22⋊C4×C31—24no—
98C22⋊C4×C31—24no—
99C42×C31—22no—
100C42×C31C2×D411yescharacteristic
101C42×C31C2×D412yes—
102C42×C31C2411yescharacteristic
103#19080C3111yesmaximal, characteristic, direct product factor, Sylow
104C23×C31—24no—
105C23×C31#12011yescharacteristic
106Q8×C31—44no—
107Q8×C31—44no—
108Q8×C31—44no—
109Q8×C31—82no—
110D4×C31—44no—
111D4×C31—44no—
112D4×C31—44no—
113D4×C31—84no—
114D4×C31—88no—
115C2×C4×C31—22no—
116C2×C4×C31—24no—
117C2×C4×C31—24no—
118C2×C4×C31—24no—
119C2×C4×C31—48no—
120C2×C4×C31—42no—
121C2×C4×C31—88no—
122C2×C4×C31—82no—
123C2×C4×C31#12011yescharacteristic
124C2×C4×C31#12012yes—
125C2×C4×C31C22×D411yescharacteristic
126C2×C4×C31C22×D412yes—
127C8×C31—44no—
128C8×C31—42no—
129#3548C2×C3111yescharacteristic
130#3141C2×C3112yescomplemented
131#3139C2×C3111yescharacteristic, complemented
132#1662C2×C3118yescomplemented
133#1526C2×C3111yescharacteristic, complemented
134#1525C2×C3112yescomplemented
135C22×C31—22no—
136C22×C31—21no—
137C22×C31—44no—
138C22×C31—44no—
139C22×C31—44no—
140C22×C31C2×#12011yescharacteristic
141C4×C31—22no—
142C4×C31—21no—
143C4×C31—44no—
144C4×C31—44no—
145C4×C31—82no—
146C4×C31#45412yes—
147C4×C31#45514yes—
148#562C22×C3114yes—
149#554—22no—
150#550—22no—
151#547—22no—
152#540—22no—
153#537—24no—
154#533C22×C3111yescharacteristic
155#532C22×C3112yes—
156C2×C4⋊Q8C22×C3111yescharacteristic
157#491C22×C3114yes—
158#489C22×C3118yes—
159#487—22no—
160#487—22no—
161#486—22no—
162#419—22no—
163#417—24no—
164C4×M16C22×C3111yescharacteristic
165C4×M16C22×C3112yes—
166#330C22×C3114yes—
167#329C22×C3118yes—
168C2×C31—41no—
169C2×C31—84no—
170C2×C31C2×#45512yes—
171C2×C31C2×#45411yescharacteristic
172C2×#41—24no—
173C2×#41D4×C3114yes—
174C22×Q8—21no—
175C2×M16—22no—
176C2×M16—21no—
177C4⋊Q8—22no—
178C4⋊Q8—21no—
179C4⋊Q8D4×C3112yes—
180C4⋊Q8D4×C3112yes—
181C4⋊Q8C23×C3112yes—
182#127—22no—
183#127D4×C3112yes—
184#125—22no—
185#125C23×C3112yes—
186#124C23×C3114yes—
187#123—28no—
188C22⋊Q8—24no—
189C22⋊Q8—28no—
190C22⋊Q8—22no—
191#121—28no—
192#121—24no—
193#121—28no—
194#121—22no—
195#121—22no—
196C4×Q8—22no—
197C4×D4—24no—
198C4×D4—22no—
199C4×D4—22no—
200#117D4×C3112yes—
201C2×C4⋊C4—24no—
202C2×C4⋊C4—22no—
203C2×C42C23×C3111yescharacteristic
204#103—28no—
205#103—28no—
206#102—28no—
207#97C23×C3112yes—
208#97C23×C3114yes—
209C4×C8—22no—
210C4×C8—21no—
211C31#1908011yescharacteristic, direct product factor, Sylow
212#41—48no—
213#41—88no—
214C2×Q8—22no—
215C2×Q8—22no—
216C2×Q8—44no—
217C2×Q8—41no—
218C2×Q8C2×D4×C3114yes—
219C2×D4—28no—
220C2×D4—24no—
221C2×D4—22no—
222C2×D4—22no—
223C2×D4C2×D4×C3114yes—
224C22×C4—28no—
225C22×C4—24no—
226C22×C4—41no—
227C22×C4C2×D4×C3112yes—
228C22×C4C2×D4×C3111yescharacteristic
229M16—42no—
230M16—44no—
231C2×C8—24no—
232C2×C8—22no—
233C4⋊C4—28no—
234C4⋊C4—22no—
235C4⋊C4—22no—
236C4⋊C4—22no—
237C4⋊C4—24no—
238C4⋊C4—24no—
239C4⋊C4—42no—
240C4⋊C4C2×D4×C3114yes—
241C22⋊C4—28no—
242C22⋊C4—22no—
243C22⋊C4—24no—
244C22⋊C4—24no—
245C42—22no—
246C42C2×D4×C3111yescharacteristic
247C42C2×D4×C3112yes—
248C42C24×C3111yescharacteristic
249C23—24no—
250C23C31×#12011yescharacteristic
251Q8—44no—
252Q8—44no—
253Q8—44no—
254Q8—82no—
255D4—44no—
256D4—44no—
257D4—44no—
258D4—84no—
259D4—88no—
260C2×C4—22no—
261C2×C4—24no—
262C2×C4—24no—
263C2×C4—24no—
264C2×C4—48no—
265C2×C4—42no—
266C2×C4—88no—
267C2×C4—82no—
268C2×C4C31×#12011yescharacteristic
269C2×C4C31×#12012yes—
270C2×C4C22×D4×C3111yescharacteristic
271C2×C4C22×D4×C3112yes—
272C8—44no—
273C8—42no—
274C22—22no—
275C22—21no—
276C22—44no—
277C22—44no—
278C22—44no—
279C22C2×C31×#12011yescharacteristic
280C4—22no—
281C4—21no—
282C4—44no—
283C4—44no—
284C4—82no—
285C4C31×#45412yes—
286C4C31×#45514yes—
287C2—41no—
288C2—84no—
289C2C2×C31×#45512yes—
290C2C2×C31×#45411yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC42C24×C31
prime radicalC31×#3548C2
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
2. C31×#3141C2semidirect
3. C31×#3139C2semidirect
4. C31×#1662C2semidirect
5. C31×#1526C2semidirect
6. C31×#1525C2semidirect
103. #19080C31direct (N × H)
130. #3141C2×C31semidirect
131. #3139C2×C31semidirect
132. #1662C2×C31semidirect
133. #1526C2×C31semidirect
134. #1525C2×C31semidirect
211. C31#19080direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35482
C31×#31412
C31×#31392
C31×#16622
C31×#15262
C31×#15252
#1908031