Finite Group Databasebeta

← C31×#7189 #21463948

Subgroups — C31×#7189 #21463948

Order 7936.

462 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#324C212yesmaximal
2C31×C4⋊#95C211yesmaximal, characteristic
3C22×C4⋊C4×C31C411yescharacteristic
4C22×C4⋊C4×C31C2211yescharacteristic
5C22×C42×C31C411yescharacteristic
6C2×C31×C22⋊C8—22no—
7C2×C31×#95—22no—
8C31×#324—22no—
9C31×#324C414yescomplemented
10C23×C4×C31—21no—
11C23×C4×C31—21no—
12C23×C4×C31C2×C411yescharacteristic
13C23×C4×C31D412yes—
14C22×C8×C31—42no—
15C2×C4⋊C4×C31—21no—
16C2×C4⋊C4×C31—41no—
17C2×C4⋊C4×C31—41no—
18C2×C4⋊C4×C31—41no—
19C2×C4⋊C4×C31—41no—
20C2×C4⋊C4×C31C812yescomplemented
21C2×C4⋊C4×C31C2×C412yes—
22C2×C4⋊C4×C31D411yescharacteristic
23C2×C4⋊C4×C31Q811yescharacteristic
24C2×C42×C31—21no—
25C2×C42×C31—41no—
26C2×C42×C31—41no—
27C2×C42×C31C812yescomplemented
28C31×C22⋊C8—24no—
29C31×C22⋊C8—42no—
30C31×#95—44no—
31C24×C31C22⋊C411yescharacteristic
32C22×C4×C31—21no—
33C22×C4×C31—21no—
34C22×C4×C31—21no—
35C22×C4×C31—21no—
36C22×C4×C31—22no—
37C22×C4×C31—22no—
38C22×C4×C31—22no—
39C22×C4×C31—22no—
40C22×C4×C31—22no—
41C22×C4×C31—22no—
42C22×C4×C31—41no—
43C22×C4×C31—41no—
44C22×C4×C31—41no—
45C22×C4×C31—41no—
46C22×C4×C31—42no—
47C22×C4×C31—42no—
48C22×C4×C31—42no—
49C22×C4×C31—42no—
50C22×C4×C31—41no—
51C22×C4×C31—41no—
52C22×C4×C31C4211yescharacteristic
53C22×C4×C31C22⋊C412yes—
54C22×C4×C31C4⋊C411yescharacteristic
55C22×C4×C31C4⋊C412yes—
56C22×C4×C31C2×C811yescharacteristic
57C22×C4×C31C2×C811yescharacteristic
58C22×C4×C31M1611yescharacteristic
59C22×C4×C31M1611yescharacteristic
60C2×C8×C31—44no—
61C2×C8×C31—82no—
62C2×C8×C31—82no—
63C4⋊C4×C31—42no—
64C4⋊C4×C31—41no—
65C4⋊C4×C31—41no—
66C4⋊C4×C31—42no—
67C4⋊C4×C31—42no—
68C42×C31—42no—
69C42×C31—42no—
70#7189C3111yesmaximal, characteristic, direct product factor, Sylow
71C23×C31—21no—
72C23×C31—21no—
73C23×C31—21no—
74C23×C31—21no—
75C23×C31#9511yescharacteristic
76C23×C31C22⋊C811yescharacteristic
77C23×C31C22⋊C811yescharacteristic
78C23×C31#9911yescharacteristic
79C23×C31#9911yescharacteristic
80C23×C31#10011yescharacteristic
81C23×C31#10111yescharacteristic
82C2×C4×C31—21no—
83C2×C4×C31—21no—
84C2×C4×C31—21no—
85C2×C4×C31—21no—
86C2×C4×C31—21no—
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—21no—
94C2×C4×C31—24no—
95C2×C4×C31—22no—
96C2×C4×C31—22no—
97C2×C4×C31—42no—
98C2×C4×C31—42no—
99C2×C4×C31—42no—
100C2×C4×C31—42no—
101C2×C4×C31—42no—
102C2×C4×C31—42no—
103C2×C4×C31—42no—
104C2×C4×C31—42no—
105C2×C4×C31—42no—
106C2×C4×C31—42no—
107C2×C4×C31—44no—
108C2×C4×C31—42no—
109C2×C4×C31—82no—
110C2×C4×C31—82no—
111C2×C4×C31—81no—
112C2×C4×C31—81no—
113C2×C4×C31C4×C811yescharacteristic
114C2×C4×C31#9711yescharacteristic
115C2×C4×C31C4⋊C811yescharacteristic
116C2×C4×C31C4⋊C811yescharacteristic
117C8×C31—84no—
118C2×#324C2×C3112yes—
119C4⋊#95C2×C3111yescharacteristic
120C22×C31—21no—
121C22×C31—21no—
122C22×C31—21no—
123C22×C31—21no—
124C22×C31—21no—
125C22×C31—21no—
126C22×C31—21no—
127C22×C31—21no—
128C22×C31—21no—
129C22×C31—21no—
130C22×C31—21no—
131C22×C31—21no—
132C22×C31#32311yescharacteristic
133C22×C31#32311yescharacteristic
134C22×C31#32411yescharacteristic
135C22×C31#32411yescharacteristic
136C22×C31#33611yescharacteristic
137C22×C31#34211yescharacteristic
138C22×C31#34311yescharacteristic
139C22×C31#35311yescharacteristic
140C22×C31#35411yescharacteristic
141C22×C31#35511yescharacteristic
142C22×C31#35611yescharacteristic
143C4×C31—21no—
144C4×C31—21no—
145C4×C31—21no—
146C4×C31—21no—
147C4×C31—44no—
148C4×C31—42no—
149C4×C31—42no—
150C4×C31—82no—
151C22×C4⋊C4C4×C3111yescharacteristic
152C22×C4⋊C4C22×C3111yescharacteristic
153C22×C42C4×C3111yescharacteristic
154C2×C22⋊C8—22no—
155C2×#95—22no—
156#324—22no—
157#324C4×C3114yescomplemented
158C2×C31—21no—
159C2×C31—21no—
160C2×C31—21no—
161C2×C31—21no—
162C2×C31#128011yescharacteristic
163C2×C31#131811yescharacteristic
164C2×C31#131911yescharacteristic
165C2×C31#132411yescharacteristic
166C2×C31#132511yescharacteristic
167C2×C31#139311yescharacteristic
168C2×C31#139411yescharacteristic
169C23×C4—21no—
170C23×C4—21no—
171C23×C4C2×C4×C3111yescharacteristic
172C23×C4D4×C3112yes—
173C22×C8—42no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—41no—
176C2×C4⋊C4—41no—
177C2×C4⋊C4—41no—
178C2×C4⋊C4—41no—
179C2×C4⋊C4C8×C3112yescomplemented
180C2×C4⋊C4C2×C4×C3112yes—
181C2×C4⋊C4D4×C3111yescharacteristic
182C2×C4⋊C4Q8×C3111yescharacteristic
183C2×C42—21no—
184C2×C42—41no—
185C2×C42—41no—
186C2×C42C8×C3112yescomplemented
187C22⋊C8—24no—
188C22⋊C8—42no—
189#95—44no—
190C31#718911yescharacteristic, direct product factor, Sylow
191C24C22⋊C4×C3111yescharacteristic
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—22no—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4—22no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4—41no—
205C22×C4—41no—
206C22×C4—42no—
207C22×C4—42no—
208C22×C4—42no—
209C22×C4—42no—
210C22×C4—41no—
211C22×C4—41no—
212C22×C4C42×C3111yescharacteristic
213C22×C4C22⋊C4×C3112yes—
214C22×C4C4⋊C4×C3111yescharacteristic
215C22×C4C4⋊C4×C3112yes—
216C22×C4C2×C8×C3111yescharacteristic
217C22×C4C2×C8×C3111yescharacteristic
218C22×C4M16×C3111yescharacteristic
219C22×C4M16×C3111yescharacteristic
220C2×C8—44no—
221C2×C8—82no—
222C2×C8—82no—
223C4⋊C4—42no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—42no—
227C4⋊C4—42no—
228C42—42no—
229C42—42no—
230C23—21no—
231C23—21no—
232C23—21no—
233C23—21no—
234C23C31×#9511yescharacteristic
235C23C31×C22⋊C811yescharacteristic
236C23C31×C22⋊C811yescharacteristic
237C23C31×#9911yescharacteristic
238C23C31×#9911yescharacteristic
239C23C31×#10011yescharacteristic
240C23C31×#10111yescharacteristic
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—24no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—44no—
267C2×C4—42no—
268C2×C4—82no—
269C2×C4—82no—
270C2×C4—81no—
271C2×C4—81no—
272C2×C4C4×C8×C3111yescharacteristic
273C2×C4C31×#9711yescharacteristic
274C2×C4C31×C4⋊C811yescharacteristic
275C2×C4C31×C4⋊C811yescharacteristic
276C8—84no—
277C22—21no—
278C22—21no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22—21no—
289C22C31×#32311yescharacteristic
290C22C31×#32311yescharacteristic
291C22C31×#32411yescharacteristic
292C22C31×#32411yescharacteristic
293C22C31×#33611yescharacteristic
294C22C31×#34211yescharacteristic
295C22C31×#34311yescharacteristic
296C22C31×#35311yescharacteristic
297C22C31×#35411yescharacteristic
298C22C31×#35511yescharacteristic
299C22C31×#35611yescharacteristic
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—44no—
305C4—42no—
306C4—42no—
307C4—82no—
308C2—21no—
309C2—21no—
310C2—21no—
311C2—21no—
312C2C31×#128011yescharacteristic
313C2C31×#131811yescharacteristic
314C2C31×#131911yescharacteristic
315C2C31×#132411yescharacteristic
316C2C31×#132511yescharacteristic
317C2C31×#139311yescharacteristic
318C2C31×#139411yescharacteristic
subgroupG/H
center, socleC23×C31#99
commutatorC2×C4C4×C8×C31
Frattini, cosocleC22×C4⋊C4C22×C31
prime radicalC24×C31C22⋊C4
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C24×C31 ◁ C22×C4⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
9. C31×#324C4semidirect
20. C2×C4⋊C4×C31C8semidirect
27. C2×C42×C31C8semidirect
70. #7189C31direct (N × H)
157. #324C4×C31semidirect
179. C2×C4⋊C4C8×C31semidirect
186. C2×C42C8×C31semidirect
190. C31#7189direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3242
C31×C4⋊#952
#718931