Finite Group Databasebeta

← C31×#11394 #21468153

Subgroups — C31×#11394 #21468153

Order 7936.

1090 conjugacy classes of subgroups; only the 254 normal subgroups are shown.

normal subgroups only

This group has 1090 conjugacy classes of subgroups — too many to draw. Only its 254 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
1C2×C31×#543C211yesmaximal, characteristic
2C2×C31×#342C213yesmaximal
3C2×C31×#342C213yesmaximal
4C31×#543—26no—
5C31×#543C414yescomplemented
6C2×C31×C22⋊Q8—26no—
7C22×C22⋊C4×C31C2211yescharacteristic
8C22×C22⋊C4×C31C2213yes—
9C22×C22⋊C4×C31C2213yes—
10C31×#342—26no—
11C31×#342—26no—
12C25×C31C2311yescharacteristic
13C22×Q8×C31—22no—
14C23×C4×C31—23no—
15C23×C4×C31—23no—
16C23×C4×C31Q812yescomplemented
17C31×C22⋊Q8—224no—
18C31×C22⋊Q8—224no—
19C2×C4⋊C4×C31—26no—
20C2×C22⋊C4×C31—23no—
21C2×C22⋊C4×C31—23no—
22C2×C22⋊C4×C31—23no—
23C2×C22⋊C4×C31—23no—
24C2×C22⋊C4×C31—23no—
25C2×C22⋊C4×C31—23no—
26C2×C22⋊C4×C31—23no—
27C2×C22⋊C4×C31—23no—
28C2×C22⋊C4×C31—23no—
29C2×C22⋊C4×C31—23no—
30C2×C22⋊C4×C31C2×C416yes—
31C2×C22⋊C4×C31D416yes—
32C2×C22⋊C4×C31D416yes—
33C2×C22⋊C4×C31Q816yescomplemented
34C24×C31—82no—
35C24×C31C22×C411yescharacteristic
36C24×C31C2×D413yes—
37C24×C31C2×D413yes—
38C24×C31C2×Q811yescharacteristic
39C24×C31C2×Q813yes—
40C24×C31#4113yes—
41C24×C31#4111yescharacteristic
42C2×Q8×C31—28no—
43C2×Q8×C31—84no—
44C22×C4×C31—26no—
45C22×C4×C31—26no—
46C22×C4×C31—26no—
47C22×C4×C31—26no—
48C22×C4×C31—26no—
49C22×C4×C31—43no—
50C22×C4×C31—43no—
51C22×C4×C31—86no—
52C22×C4×C31—86no—
53C22×C4×C31—82no—
54C4⋊C4×C31—224no—
55C22⋊C4×C31—26no—
56C22⋊C4×C31—26no—
57C22⋊C4×C31—26no—
58C22⋊C4×C31—26no—
59C22⋊C4×C31—26no—
60C22⋊C4×C31—43no—
61C22⋊C4×C31—41no—
62C22⋊C4×C31—43no—
63C22⋊C4×C31—43no—
64C22⋊C4×C31C22⋊C4112yes—
65#11394C3111yesmaximal, characteristic, direct product factor, Sylow
66C23×C31—46no—
67C23×C31—42no—
68C23×C31—46no—
69C23×C31—81no—
70C23×C31—83no—
71C23×C31—83no—
72C23×C31—81no—
73C23×C31C2×C22⋊C413yes—
74C23×C31C4×Q811yescharacteristic
75C23×C31C4×Q813yes—
76C23×C31#12011yescharacteristic
77C23×C31#12013yes—
78C23×C31C22⋊Q813yes—
79C23×C31C22⋊Q813yes—
80C23×C31C22⋊Q813yes—
81C23×C31C22⋊Q813yes—
82C23×C31#12413yes—
83C23×C31#12413yes—
84C23×C31C4⋊Q813yes—
85C23×C31C4⋊Q813yes—
86Q8×C31—88no—
87C2×C4×C31—212no—
88C2×C4×C31—412no—
89C2×C4×C31—46no—
90C2×C4×C31—42no—
91C2×C4×C31—86no—
92C2×C4×C31—86no—
93C2×C4×C31—86no—
94C2×C4×C31—86no—
95C2×C4×C31—86no—
96C2×C4×C31—86no—
97C2×#543C2×C3111yescharacteristic
98C2×#342C2×C3113yes—
99C2×#342C2×C3113yes—
100C22×C31—22no—
101C22×C31—26no—
102C22×C31—26no—
103C22×C31—43no—
104C22×C31—43no—
105C22×C31—43no—
106C22×C31—43no—
107C22×C31—41no—
108C22×C31—43no—
109C22×C31—43no—
110C22×C31—43no—
111C22×C31—43no—
112C22×C31—43no—
113C22×C31#37911yescharacteristic
114C22×C31#39113yes—
115C22×C31#39113yes—
116C22×C31#39313yes—
117C22×C31#39311yescharacteristic
118C22×C31#39511yescharacteristic
119C22×C31#39513yes—
120C4×C31—412no—
121C4×C31—86no—
122C4×C31—82no—
123#543—26no—
124#543C4×C3114yescomplemented
125C2×C22⋊Q8—26no—
126C22×C22⋊C4C22×C3111yescharacteristic
127C22×C22⋊C4C22×C3113yes—
128C22×C22⋊C4C22×C3113yes—
129#342—26no—
130#342—26no—
131C2×C31—21no—
132C2×C31—23no—
133C2×C31—23no—
134C2×C31—23no—
135C2×C31—21no—
136C2×C31—23no—
137C2×C31#144611yescharacteristic
138C2×C31#203212yes—
139C25C23×C3111yescharacteristic
140C22×Q8—22no—
141C23×C4—23no—
142C23×C4—23no—
143C23×C4Q8×C3112yescomplemented
144C22⋊Q8—224no—
145C22⋊Q8—224no—
146C2×C4⋊C4—26no—
147C2×C22⋊C4—23no—
148C2×C22⋊C4—23no—
149C2×C22⋊C4—23no—
150C2×C22⋊C4—23no—
151C2×C22⋊C4—23no—
152C2×C22⋊C4—23no—
153C2×C22⋊C4—23no—
154C2×C22⋊C4—23no—
155C2×C22⋊C4—23no—
156C2×C22⋊C4—23no—
157C2×C22⋊C4C2×C4×C3116yes—
158C2×C22⋊C4D4×C3116yes—
159C2×C22⋊C4D4×C3116yes—
160C2×C22⋊C4Q8×C3116yescomplemented
161C31#1139411yescharacteristic, direct product factor, Sylow
162C24—82no—
163C24C22×C4×C3111yescharacteristic
164C24C2×D4×C3113yes—
165C24C2×D4×C3113yes—
166C24C2×Q8×C3111yescharacteristic
167C24C2×Q8×C3113yes—
168C24#41×C3113yes—
169C24#41×C3111yescharacteristic
170C2×Q8—28no—
171C2×Q8—84no—
172C22×C4—26no—
173C22×C4—26no—
174C22×C4—26no—
175C22×C4—26no—
176C22×C4—26no—
177C22×C4—43no—
178C22×C4—43no—
179C22×C4—86no—
180C22×C4—86no—
181C22×C4—82no—
182C4⋊C4—224no—
183C22⋊C4—26no—
184C22⋊C4—26no—
185C22⋊C4—26no—
186C22⋊C4—26no—
187C22⋊C4—26no—
188C22⋊C4—43no—
189C22⋊C4—41no—
190C22⋊C4—43no—
191C22⋊C4—43no—
192C22⋊C4C22⋊C4×C31112yes—
193C23—46no—
194C23—42no—
195C23—46no—
196C23—81no—
197C23—83no—
198C23—83no—
199C23—81no—
200C23C2×C22⋊C4×C3113yes—
201C23C4×Q8×C3111yescharacteristic
202C23C4×Q8×C3113yes—
203C23C31×#12011yescharacteristic
204C23C31×#12013yes—
205C23C31×C22⋊Q813yes—
206C23C31×C22⋊Q813yes—
207C23C31×C22⋊Q813yes—
208C23C31×C22⋊Q813yes—
209C23C31×#12413yes—
210C23C31×#12413yes—
211C23C31×C4⋊Q813yes—
212C23C31×C4⋊Q813yes—
213Q8—88no—
214C2×C4—212no—
215C2×C4—412no—
216C2×C4—46no—
217C2×C4—42no—
218C2×C4—86no—
219C2×C4—86no—
220C2×C4—86no—
221C2×C4—86no—
222C2×C4—86no—
223C2×C4—86no—
224C22—22no—
225C22—26no—
226C22—26no—
227C22—43no—
228C22—43no—
229C22—43no—
230C22—43no—
231C22—41no—
232C22—43no—
233C22—43no—
234C22—43no—
235C22—43no—
236C22—43no—
237C22C31×#37911yescharacteristic
238C22C31×#39113yes—
239C22C31×#39113yes—
240C22C31×#39313yes—
241C22C31×#39311yescharacteristic
242C22C31×#39511yescharacteristic
243C22C31×#39513yes—
244C4—412no—
245C4—86no—
246C4—82no—
247C2—21no—
248C2—23no—
249C2—21no—
250C2—23no—
251C2—23no—
252C2—23no—
253C2C31×#144611yescharacteristic
254C2C31×#203212yes—
subgroupG/H
center, socleC22×C31#393
commutatorC24C22×C4×C31
Frattini, cosocleC25C23×C31
prime radicalC25×C31C23
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C25×C31 ◁ G

Complements

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

NH ≅ G/Ntype
5. C31×#543C4semidirect
16. C23×C4×C31Q8semidirect
33. C2×C22⋊C4×C31Q8semidirect
65. #11394C31direct (N × H)
124. #543C4×C31semidirect
143. C23×C4Q8×C31semidirect
160. C2×C22⋊C4Q8×C31semidirect
161. C31#11394direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5432
C2×C31×#3422
#1139431