Finite Group Databasebeta

← C31×#11907 #21468666

Subgroups — C31×#11907 #21468666

Order 7936.

372 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 118 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×#2568C211yesmaximal, characteristic
2C31×#1801C211yesmaximal, characteristic
3C31×#1461C211yesmaximal, characteristic
4C31×#1353C214yesmaximal
5C2×C31×C4⋊Q8C411yescharacteristic
6C2×C4×Q8×C31C2211yescharacteristic
7C31×#431—21no—
8C31×#423—21no—
9C2×C31×#101—21no—
10C31×#400C412yes—
11C31×#400C2212yes—
12C31×#391—21no—
13C31×#391—21no—
14C31×#391—21no—
15C31×#382—21no—
16C4×C4⋊C4×C31C411yescharacteristic
17C31×#343C2212yes—
18C31×#324—21no—
19C31×#324C2212yes—
20C22×Q8×C31—21no—
21C22×Q8×C31D411yescharacteristic
22C2×M16×C31—22no—
23C31×C4⋊Q8—41no—
24C31×C4⋊Q8—41no—
25C4×Q8×C31—41no—
26C4×Q8×C31—41no—
27C2×C4⋊C4×C31—21no—
28C2×C4⋊C4×C31—21no—
29C2×C4⋊C4×C31C2×C412yes—
30C2×C4⋊C4×C31C2×C411yescharacteristic
31C2×C4⋊C4×C31D411yescharacteristic
32C2×C4⋊C4×C31C2311yescharacteristic
33C2×C42×C31—21no—
34C2×C42×C31C2×C411yescharacteristic
35C2×C42×C31D411yescharacteristic
36C2×C42×C31D411yescharacteristic
37C31×C4⋊C8—41no—
38C31×C4⋊C8—41no—
39C31×C4⋊C8—41no—
40C31×#101—42no—
41C31×C22⋊C8—22no—
42C4×C8×C31—41no—
43C31×#95—22no—
44C31×#95—22no—
45C31×#95—22no—
46C31×#95—22no—
47C31×#95C2×C412yes—
48C2×Q8×C31—41no—
49C2×Q8×C31—41no—
50C2×Q8×C31—44no—
51C2×Q8×C31—41no—
52C2×Q8×C31—41no—
53C2×Q8×C31SD1612yes—
54C2×Q8×C31Q1612yes—
55C22×C4×C31—22no—
56C22×C4×C31—22no—
57C22×C4×C31C22⋊C411yescharacteristic
58C22×C4×C31C22⋊C411yescharacteristic
59C22×C4×C31C22⋊C411yescharacteristic
60C22×C4×C31C22⋊C411yescharacteristic
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—41no—
69C4⋊C4×C31—41no—
70C4⋊C4×C31—41no—
71C4⋊C4×C31—42no—
72C4⋊C4×C31—42no—
73C4⋊C4×C31—42no—
74C42×C31—21no—
75C42×C31—21no—
76C42×C31—21no—
77C42×C31—21no—
78C42×C31—21no—
79C42×C31—21no—
80C42×C31—42no—
81#11907C3111yesmaximal, characteristic, direct product factor, Sylow
82C23×C31C2×C22⋊C411yescharacteristic
83Q8×C31—42no—
84Q8×C31—42no—
85Q8×C31—82no—
86Q8×C31—82no—
87C2×C4×C31—21no—
88C2×C4×C31—21no—
89C2×C4×C31—21no—
90C2×C4×C31—21no—
91C2×C4×C31—21no—
92C2×C4×C31—21no—
93C2×C4×C31—22no—
94C2×C4×C31—21no—
95C2×C4×C31—21no—
96C2×C4×C31—21no—
97C2×C4×C31—41no—
98C2×C4×C31—41no—
99C2×C4×C31—41no—
100C2×C4×C31—42no—
101C2×C4×C31—42no—
102C2×C4×C31—44no—
103C2×C4×C31—42no—
104C2×C4×C31—42no—
105C2×C4×C31#9911yescharacteristic
106C2×C4×C31#9911yescharacteristic
107C2×C4×C31#10312yes—
108C2×C4×C31#10312yes—
109C2×C4×C31C2×SD1611yescharacteristic
110C2×C4×C31C2×Q1611yescharacteristic
111C8×C31—82no—
112C8×C31—82no—
113#2568C2×C3111yescharacteristic
114#1801C2×C3111yescharacteristic
115#1461C2×C3111yescharacteristic
116#1353C2×C3114yes—
117C22×C31—21no—
118C22×C31—21no—
119C22×C31C2×#9911yescharacteristic
120C22×C31C2×#10311yescharacteristic
121C22×C31#42111yescharacteristic
122C4×C31—21no—
123C4×C31—21no—
124C4×C31—22no—
125C4×C31—22no—
126C4×C31—21no—
127C4×C31—41no—
128C4×C31—41no—
129C4×C31—41no—
130C4×C31—82no—
131C4×C31—82no—
132C4×C31#35512yes—
133C2×C4⋊Q8C4×C3111yescharacteristic
134C2×C4×Q8C22×C3111yescharacteristic
135#431—21no—
136#423—21no—
137C2×#101—21no—
138#400C4×C3112yes—
139#400C22×C3112yes—
140#391—21no—
141#391—21no—
142#391—21no—
143#382—21no—
144C4×C4⋊C4C4×C3111yescharacteristic
145#343C22×C3112yes—
146#324—21no—
147#324C22×C3112yes—
148C2×C31—21no—
149C2×C31—21no—
150C2×C31#152011yescharacteristic
151C2×C31#212311yescharacteristic
152C2×C31C2×#35511yescharacteristic
153C22×Q8—21no—
154C22×Q8D4×C3111yescharacteristic
155C2×M16—22no—
156C4⋊Q8—41no—
157C4⋊Q8—41no—
158C4×Q8—41no—
159C4×Q8—41no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4C2×C4×C3112yes—
163C2×C4⋊C4C2×C4×C3111yescharacteristic
164C2×C4⋊C4D4×C3111yescharacteristic
165C2×C4⋊C4C23×C3111yescharacteristic
166C2×C42—21no—
167C2×C42C2×C4×C3111yescharacteristic
168C2×C42D4×C3111yescharacteristic
169C2×C42D4×C3111yescharacteristic
170C4⋊C8—41no—
171C4⋊C8—41no—
172C4⋊C8—41no—
173#101—42no—
174C22⋊C8—22no—
175C4×C8—41no—
176#95—22no—
177#95—22no—
178#95—22no—
179#95—22no—
180#95C2×C4×C3112yes—
181C31#1190711yescharacteristic, direct product factor, Sylow
182C2×Q8—41no—
183C2×Q8—41no—
184C2×Q8—44no—
185C2×Q8—41no—
186C2×Q8—41no—
187C2×Q8SD16×C3112yes—
188C2×Q8Q16×C3112yes—
189C22×C4—22no—
190C22×C4—22no—
191C22×C4C22⋊C4×C3111yescharacteristic
192C22×C4C22⋊C4×C3111yescharacteristic
193C22×C4C22⋊C4×C3111yescharacteristic
194C22×C4C22⋊C4×C3111yescharacteristic
195C22×C4C22×C4×C3111yescharacteristic
196C22×C4C2×D4×C3111yescharacteristic
197C22×C4C2×D4×C3111yescharacteristic
198M16—42no—
199M16—42no—
200C2×C8—42no—
201C2×C8—42no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—42no—
206C4⋊C4—42no—
207C4⋊C4—42no—
208C42—21no—
209C42—21no—
210C42—21no—
211C42—21no—
212C42—21no—
213C42—21no—
214C42—42no—
215C23C2×C22⋊C4×C3111yescharacteristic
216Q8—42no—
217Q8—42no—
218Q8—82no—
219Q8—82no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—44no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4C31×#9911yescharacteristic
239C2×C4C31×#9911yescharacteristic
240C2×C4C31×#10312yes—
241C2×C4C31×#10312yes—
242C2×C4C2×SD16×C3111yescharacteristic
243C2×C4C2×Q16×C3111yescharacteristic
244C8—82no—
245C8—82no—
246C22—21no—
247C22—21no—
248C22C2×C31×#9911yescharacteristic
249C22C2×C31×#10311yescharacteristic
250C22C31×#42111yescharacteristic
251C4—21no—
252C4—21no—
253C4—22no—
254C4—22no—
255C4—21no—
256C4—41no—
257C4—41no—
258C4—41no—
259C4—82no—
260C4—82no—
261C4C31×#35512yes—
262C2—21no—
263C2—21no—
264C2C31×#152011yescharacteristic
265C2C31×#212311yescharacteristic
266C2C2×C31×#35511yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C4⋊C4C23×C31
prime radicalC23×C31C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C4×C31 ◁ C2×C4×Q8×C31 ◁ G

Complements

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

NH ≅ G/Ntype
81. #11907C31direct (N × H)
181. C31#11907direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#25682
C31×#18012
C31×#14612
C31×#13532
#1190731