Finite Group Databasebeta

← C31×#12965 #21469724

Subgroups — C31×#12965 #21469724

Order 7936.

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

normal subgroups only

This group has 536 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×#2372C211yesmaximal, characteristic
2C2×C31×#354C211yesmaximal, characteristic
3C31×#1885C211yesmaximal, characteristic
4C31×#1867C212yesmaximal
5C31×#1390C212yesmaximal
6C2×C31×#124C2211yescharacteristic
7C31×#518C2211yescharacteristic
8C31×#419—21no—
9C2×C31×#100C2211yescharacteristic
10C2×C31×#99C2212yes—
11C31×#391—21no—
12C31×#388—22no—
13C31×#386C2212yes—
14C31×#385—22no—
15C4×C22⋊C4×C31—22no—
16C31×#376—21no—
17C31×#354C414yescomplemented
18C31×#342—22no—
19C31×#339—21no—
20C22×Q8×C31D411yescharacteristic
21C22×D4×C31C2311yescharacteristic
22C23×C4×C31D412yes—
23C2×M16×C31—21no—
24C31×#124—22no—
25C31×#124C2×C412yes—
26C31×#124Q812yes—
27C4×D4×C31—42no—
28C31×#117—21no—
29C2×C4⋊C4×C31—21no—
30C2×C4⋊C4×C31—42no—
31C2×C22⋊C4×C31—22no—
32C2×C22⋊C4×C31—22no—
33C2×C22⋊C4×C31—22no—
34C2×C22⋊C4×C31—22no—
35C2×C22⋊C4×C31D412yes—
36C2×C42×C31—22no—
37C2×C42×C31—21no—
38C2×C42×C31D411yescharacteristic
39C31×#103—42no—
40C31×#100—22no—
41C31×#99—22no—
42C31×#99C2×C414yes—
43C31×#95—21no—
44C31×#95—21no—
45C31×#95—22no—
46C31×#95—22no—
47C31×#95—42no—
48C24×C31C2×D412yes—
49C2×Q8×C31—21no—
50C2×Q8×C31—41no—
51C2×Q8×C31—41no—
52C2×Q8×C31C4⋊C412yescomplemented
53C2×D4×C31—41no—
54C2×D4×C31—41no—
55C2×D4×C31C22×C411yescharacteristic
56C2×D4×C31C2×Q811yescharacteristic
57C2×D4×C31#4112yes—
58C22×C4×C31—22no—
59C22×C4×C31—21no—
60C22×C4×C31—21no—
61C22×C4×C31—22no—
62C22×C4×C31—22no—
63C22×C4×C31—22no—
64C22×C4×C31—44no—
65C22×C4×C31—42no—
66C22×C4×C31—42no—
67C22×C4×C31C2×D411yescharacteristic
68M16×C31—41no—
69M16×C31—41no—
70C2×C8×C31—41no—
71C4⋊C4×C31—22no—
72C4⋊C4×C31—81no—
73C4⋊C4×C31—84no—
74C22⋊C4×C31—24no—
75C22⋊C4×C31—24no—
76C22⋊C4×C31—24no—
77C22⋊C4×C31—44no—
78C22⋊C4×C31—42no—
79C22⋊C4×C31—42no—
80C22⋊C4×C31—41no—
81C22⋊C4×C31—42no—
82C42×C31—21no—
83C42×C31—44no—
84C42×C31—41no—
85C42×C31—81no—
86C42×C31C4⋊C412yescomplemented
87#12965C3111yesmaximal, characteristic, direct product factor, Sylow
88C23×C31—22no—
89C23×C31—22no—
90C23×C31—42no—
91C23×C31—42no—
92C23×C31C4×D412yes—
93C23×C31#12011yescharacteristic
94C23×C31C22⋊Q812yes—
95Q8×C31—42no—
96Q8×C31—81no—
97D4×C31—41no—
98D4×C31—41no—
99D4×C31—42no—
100C2×C4×C31—21no—
101C2×C4×C31—21no—
102C2×C4×C31—24no—
103C2×C4×C31—22no—
104C2×C4×C31—22no—
105C2×C4×C31—42no—
106C2×C4×C31—42no—
107C2×C4×C31—42no—
108C2×C4×C31—41no—
109C2×C4×C31—41no—
110C2×C4×C31—44no—
111C2×C4×C31—42no—
112C2×C4×C31—44no—
113C2×C4×C31—42no—
114C2×C4×C31—42no—
115C2×C4×C31—42no—
116C2×C4×C31—82no—
117C2×C4×C31—82no—
118C2×C4×C31—82no—
119C2×C4×C31—82no—
120C2×C4×C31—82no—
121C2×C4×C31C2×C4⋊C411yescharacteristic
122C2×C4×C31#12311yescharacteristic
123C8×C31—81no—
124#2372C2×C3111yescharacteristic
125C2×#354C2×C3111yescharacteristic
126#1885C2×C3111yescharacteristic
127#1867C2×C3112yes—
128#1390C2×C3112yes—
129C22×C31—22no—
130C22×C31—22no—
131C22×C31—22no—
132C22×C31—42no—
133C22×C31—42no—
134C22×C31—42no—
135C22×C31—42no—
136C22×C31—82no—
137C22×C31#38511yescharacteristic
138C22×C31B(4,𝔽2)11yescharacteristic
139C22×C31#45811yescharacteristic
140C4×C31—21no—
141C4×C31—21no—
142C4×C31—42no—
143C4×C31—42no—
144C4×C31—44no—
145C4×C31—82no—
146C4×C31—84no—
147C4×C31—82no—
148C2×#124C22×C3111yescharacteristic
149#518C22×C3111yescharacteristic
150#419—21no—
151C2×#100C22×C3111yescharacteristic
152C2×#99C22×C3112yes—
153#391—21no—
154#388—22no—
155#386C22×C3112yes—
156#385—22no—
157C4×C22⋊C4—22no—
158#376—21no—
159#354C4×C3114yescomplemented
160#342—22no—
161#339—21no—
162C2×C31—21no—
163C2×C31—21no—
164C2×C31—42no—
165C2×C31—42no—
166C2×C31#186711yescharacteristic
167C2×C31#219712yes—
168C22×Q8D4×C3111yescharacteristic
169C22×D4C23×C3111yescharacteristic
170C23×C4D4×C3112yes—
171C2×M16—21no—
172#124—22no—
173#124C2×C4×C3112yes—
174#124Q8×C3112yes—
175C4×D4—42no—
176#117—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—42no—
179C2×C22⋊C4—22no—
180C2×C22⋊C4—22no—
181C2×C22⋊C4—22no—
182C2×C22⋊C4—22no—
183C2×C22⋊C4D4×C3112yes—
184C2×C42—22no—
185C2×C42—21no—
186C2×C42D4×C3111yescharacteristic
187#103—42no—
188#100—22no—
189#99—22no—
190#99C2×C4×C3114yes—
191#95—21no—
192#95—21no—
193#95—22no—
194#95—22no—
195#95—42no—
196C31#1296511yescharacteristic, direct product factor, Sylow
197C24C2×D4×C3112yes—
198C2×Q8—21no—
199C2×Q8—41no—
200C2×Q8—41no—
201C2×Q8C4⋊C4×C3112yescomplemented
202C2×D4—41no—
203C2×D4—41no—
204C2×D4C22×C4×C3111yescharacteristic
205C2×D4C2×Q8×C3111yescharacteristic
206C2×D4#41×C3112yes—
207C22×C4—22no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—44no—
214C22×C4—42no—
215C22×C4—42no—
216C22×C4C2×D4×C3111yescharacteristic
217M16—41no—
218M16—41no—
219C2×C8—41no—
220C4⋊C4—22no—
221C4⋊C4—81no—
222C4⋊C4—84no—
223C22⋊C4—24no—
224C22⋊C4—24no—
225C22⋊C4—24no—
226C22⋊C4—44no—
227C22⋊C4—42no—
228C22⋊C4—42no—
229C22⋊C4—41no—
230C22⋊C4—42no—
231C42—21no—
232C42—44no—
233C42—41no—
234C42—81no—
235C42C4⋊C4×C3112yescomplemented
236C23—22no—
237C23—22no—
238C23—42no—
239C23—42no—
240C23C4×D4×C3112yes—
241C23C31×#12011yescharacteristic
242C23C31×C22⋊Q812yes—
243Q8—42no—
244Q8—81no—
245D4—41no—
246D4—41no—
247D4—42no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—24no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—44no—
259C2×C4—42no—
260C2×C4—44no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—82no—
265C2×C4—82no—
266C2×C4—82no—
267C2×C4—82no—
268C2×C4—82no—
269C2×C4C2×C4⋊C4×C3111yescharacteristic
270C2×C4C31×#12311yescharacteristic
271C8—81no—
272C22—22no—
273C22—22no—
274C22—22no—
275C22—42no—
276C22—42no—
277C22—42no—
278C22—42no—
279C22—82no—
280C22C31×#38511yescharacteristic
281C22C31×B(4,𝔽2)11yescharacteristic
282C22C31×#45811yescharacteristic
283C4—21no—
284C4—21no—
285C4—42no—
286C4—42no—
287C4—44no—
288C4—82no—
289C4—84no—
290C4—82no—
291C2—21no—
292C2—21no—
293C2—42no—
294C2—42no—
295C2C31×#186711yescharacteristic
296C2C31×#219712yes—
subgroupG/H
center, socleC22×C31B(4,𝔽2)
commutatorC2×D4C22×C4×C31
Frattini, cosocleC22×D4C23×C31
prime radicalC22×D4×C31C23
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C31 ◁ C22×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
17. C31×#354C4semidirect
52. C2×Q8×C31C4⋊C4semidirect
86. C42×C31C4⋊C4semidirect
87. #12965C31direct (N × H)
159. #354C4×C31semidirect
196. C31#12965direct (N × H)
201. C2×Q8C4⋊C4×C31semidirect
235. C42C4⋊C4×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#23722
C2×C31×#3542
C31×#18852
C31×#18672
C31×#13902
#1296531