Finite Group Databasebeta

← C31×#12974 #21469733

Subgroups — C31×#12974 #21469733

Order 7936.

408 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 114 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×#2980C211yesmaximal, characteristic
2C31×#2132C211yesmaximal, characteristic
3C31×#1884C211yesmaximal, characteristic
4C31×#1858C212yesmaximal, complemented
5C31×#1395C212yesmaximal, complemented
6C31×#568C2211yescharacteristic
7C31×#532C2211yescharacteristic
8C31×#435—22no—
9C31×#435—22no—
10C31×#432—21no—
11C31×#430—22no—
12C31×#421—21no—
13C31×#413C2212yes—
14C31×#410C2211yescharacteristic
15C31×#408—21no—
16C31×#408C2212yes—
17C31×#356C412yescomplemented
18C31×#355C412yescomplemented
19C31×#341—22no—
20C31×#339—21no—
21C2×#41×C31D411yescharacteristic
22C2×#41×C31C2311yescharacteristic
23C31×#131—42no—
24C2×M16×C31—21no—
25C2×M16×C31—22no—
26C2×M16×C31—21no—
27C2×M16×C31—22no—
28C2×M16×C31D412yes—
29C22×C8×C31—21no—
30C22×C8×C31D412yes—
31C31×C4⋊Q8C2×C411yescharacteristic
32C31×#127Q811yescharacteristic
33C31×#124C2×C411yescharacteristic
34C31×#124Q811yescharacteristic
35C31×#121—22no—
36C4×D4×C31—22no—
37C31×#117—21no—
38C2×C42×C31D411yescharacteristic
39C31×#108—44no—
40C31×C4⋊C8—21no—
41C31×C4⋊C8—21no—
42C31×#104—42no—
43C31×#101C2×C414yes—
44C31×#100—22no—
45C31×#99—22no—
46C31×C22⋊C8—22no—
47C31×C22⋊C8—22no—
48C31×C22⋊C8—22no—
49C31×#97—22no—
50#41×C31—41no—
51#41×C31—41no—
52#41×C31—41no—
53#41×C31—41no—
54C2×Q8×C31C4⋊C411yescharacteristic
55C2×Q8×C31C22×C411yescharacteristic
56C2×D4×C31—22no—
57C2×D4×C31—21no—
58C2×D4×C31C4⋊C411yescharacteristic
59C2×D4×C31C2×Q811yescharacteristic
60C2×D4×C31#4112yes—
61C22×C4×C31—21no—
62C22×C4×C31—21no—
63C22×C4×C31C2×D411yescharacteristic
64C22×C4×C31C2×D412yes—
65M16×C31—22no—
66M16×C31—24no—
67M16×C31—24no—
68M16×C31—42no—
69M16×C31—41no—
70M16×C31—42no—
71M16×C31—81no—
72C2×C8×C31—22no—
73C2×C8×C31—22no—
74C2×C8×C31—42no—
75C2×C8×C31—41no—
76C2×C8×C31—42no—
77C2×C8×C31—42no—
78C2×C8×C31—81no—
79C4⋊C4×C31—22no—
80C4⋊C4×C31—41no—
81C22⋊C4×C31—22no—
82C22⋊C4×C31—22no—
83C22⋊C4×C31—41no—
84C42×C31—21no—
85C42×C31—41no—
86C42×C31C4⋊C411yescharacteristic
87C42×C31C4⋊C411yescharacteristic
88#12974C3111yesmaximal, characteristic, direct product factor, Sylow
89C23×C31—21no—
90C23×C31C22⋊Q812yes—
91C23×C31#12311yescharacteristic
92Q8×C31—41no—
93Q8×C31—41no—
94D4×C31—41no—
95D4×C31—42no—
96D4×C31—41no—
97D4×C31—81no—
98D4×C31—82no—
99C2×C4×C31—21no—
100C2×C4×C31—22no—
101C2×C4×C31—21no—
102C2×C4×C31—22no—
103C2×C4×C31—21no—
104C2×C4×C31—21no—
105C2×C4×C31—21no—
106C2×C4×C31—41no—
107C2×C4×C31—41no—
108C2×C4×C31—81no—
109C2×C4×C31—81no—
110C2×C4×C31C2×C4⋊C411yescharacteristic
111C2×C4×C31C4×D412yes—
112C2×C4×C31#12011yescharacteristic
113C8×C31—44no—
114C8×C31—42no—
115C8×C31—42no—
116C8×C31—42no—
117#2980C2×C3111yescharacteristic
118#2132C2×C3111yescharacteristic
119#1884C2×C3111yescharacteristic
120#1858C2×C3112yescomplemented
121#1395C2×C3112yescomplemented
122C22×C31—21no—
123C22×C31—22no—
124C22×C31—41no—
125C22×C31—42no—
126C22×C31—42no—
127C22×C31—41no—
128C22×C31#38511yescharacteristic
129C4×C31—22no—
130C4×C31—21no—
131C4×C31—41no—
132C4×C31—41no—
133C4×C31—41no—
134C4×C31—161no—
135C4×C31B(4,𝔽2)11yescharacteristic
136C4×C31#45811yescharacteristic
137#568C22×C3111yescharacteristic
138#532C22×C3111yescharacteristic
139#435—22no—
140#435—22no—
141#432—21no—
142#430—22no—
143#421—21no—
144#413C22×C3112yes—
145#410C22×C3111yescharacteristic
146#408—21no—
147#408C22×C3112yes—
148#356C4×C3112yescomplemented
149#355C4×C3112yescomplemented
150#341—22no—
151#339—21no—
152C2×C31—21no—
153C2×C31—41no—
154C2×C31—42no—
155C2×C31—81no—
156C2×C31#186711yescharacteristic
157C2×#41D4×C3111yescharacteristic
158C2×#41C23×C3111yescharacteristic
159#131—42no—
160C2×M16—21no—
161C2×M16—21no—
162C2×M16—22no—
163C2×M16—22no—
164C2×M16D4×C3112yes—
165C22×C8—21no—
166C22×C8D4×C3112yes—
167C4⋊Q8C2×C4×C3111yescharacteristic
168#127Q8×C3111yescharacteristic
169#124C2×C4×C3111yescharacteristic
170#124Q8×C3111yescharacteristic
171#121—22no—
172C4×D4—22no—
173#117—21no—
174C2×C42D4×C3111yescharacteristic
175#108—44no—
176C4⋊C8—21no—
177C4⋊C8—21no—
178#104—42no—
179#101C2×C4×C3114yes—
180#100—22no—
181#99—22no—
182C22⋊C8—22no—
183C22⋊C8—22no—
184C22⋊C8—22no—
185#97—22no—
186C31#1297411yescharacteristic, direct product factor, Sylow
187#41—41no—
188#41—41no—
189#41—41no—
190#41—41no—
191C2×Q8C4⋊C4×C3111yescharacteristic
192C2×Q8C22×C4×C3111yescharacteristic
193C2×D4—22no—
194C2×D4—21no—
195C2×D4C4⋊C4×C3111yescharacteristic
196C2×D4C2×Q8×C3111yescharacteristic
197C2×D4#41×C3112yes—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4C2×D4×C3111yescharacteristic
201C22×C4C2×D4×C3112yes—
202M16—22no—
203M16—24no—
204M16—24no—
205M16—42no—
206M16—41no—
207M16—42no—
208M16—81no—
209C2×C8—22no—
210C2×C8—22no—
211C2×C8—42no—
212C2×C8—41no—
213C2×C8—42no—
214C2×C8—42no—
215C2×C8—81no—
216C4⋊C4—22no—
217C4⋊C4—41no—
218C22⋊C4—22no—
219C22⋊C4—22no—
220C22⋊C4—41no—
221C42—21no—
222C42—41no—
223C42C4⋊C4×C3111yescharacteristic
224C42C4⋊C4×C3111yescharacteristic
225C23—21no—
226C23C31×C22⋊Q812yes—
227C23C31×#12311yescharacteristic
228Q8—41no—
229Q8—41no—
230D4—41no—
231D4—42no—
232D4—41no—
233D4—81no—
234D4—82no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—81no—
245C2×C4—81no—
246C2×C4C2×C4⋊C4×C3111yescharacteristic
247C2×C4C4×D4×C3112yes—
248C2×C4C31×#12011yescharacteristic
249C8—44no—
250C8—42no—
251C8—42no—
252C8—42no—
253C22—21no—
254C22—22no—
255C22—41no—
256C22—42no—
257C22—42no—
258C22—41no—
259C22C31×#38511yescharacteristic
260C4—22no—
261C4—21no—
262C4—41no—
263C4—41no—
264C4—41no—
265C4—161no—
266C4C31×B(4,𝔽2)11yescharacteristic
267C4C31×#45811yescharacteristic
268C2—21no—
269C2—41no—
270C2—42no—
271C2—81no—
272C2C31×#186711yescharacteristic
subgroupG/H
centerC4×C31B(4,𝔽2)
commutatorC2×Q8C22×C4×C31
Frattini, cosocleC2×#41C23×C31
socleC2×C31#1867
prime radicalC31×#532C22
LCSG ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C31 ◁ C2×C4×C31 ◁ C2×#41×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C31×#1858C2semidirect
5. C31×#1395C2semidirect
17. C31×#356C4semidirect
18. C31×#355C4semidirect
88. #12974C31direct (N × H)
120. #1858C2×C31semidirect
121. #1395C2×C31semidirect
148. #356C4×C31semidirect
149. #355C4×C31semidirect
186. C31#12974direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#29802
C31×#21322
C31×#18842
C31×#18582
C31×#13952
#1297431