Finite Group Databasebeta

← C2×C31×#1339 #21468442

Subgroups — C2×C31×#1339 #21468442

Order 7936.

496 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#469C211yesmaximal, characteristic
2C2×C31×#349C211yesmaximal, characteristic, complemented
3C2×C31×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
4C31×#1339C214yesmaximal, direct product factor
5C22×D8×C31C411yescharacteristic, complemented
6C22×M16×C31C2211yescharacteristic
7C2×C31×#121—21no—
8C2×C31×#117—21no—
9C2×C31×M32—21no—
10C31×#469—21no—
11C31×#469—21no—
12C31×#469C412yescomplemented
13C31×#469C2212yes—
14C2×C31×#106C411yescharacteristic, complemented
15C2×C31×#102—21no—
16C31×#349—21no—
17C31×#349C2212yescomplemented
18C31×H(3,ℤ/4)—21no—
19C31×H(3,ℤ/4)C2212yescomplemented
20C22×D4×C31—21no—
21C22×D4×C31—41no—
22C23×C4×C31D411yescharacteristic
23C2×D8×C31—21no—
24C2×D8×C31—41no—
25C2×D8×C31—41no—
26C2×D8×C31C2×C412yescomplemented
27C2×M16×C31—41no—
28C2×M16×C31—41no—
29C2×M16×C31C2×C411yescharacteristic
30C2×M16×C31D411yescharacteristic
31C2×M16×C31D411yescharacteristic
32C2×M16×C31C2311yescharacteristic
33C22×C8×C31C2×C411yescharacteristic
34C22×C8×C31D411yescharacteristic
35C31×#121—22no—
36C31×#121—22no—
37C31×#121—41no—
38C31×#121—41no—
39C31×#117—22no—
40C31×#117—22no—
41C31×#117—41no—
42C31×#117—41no—
43C2×C4⋊C4×C31—21no—
44C2×C4⋊C4×C31—41no—
45C2×C22⋊C4×C31—41no—
46C2×C22⋊C4×C31—41no—
47C2×C42×C31—22no—
48C31×M32—22no—
49C31×M32—41no—
50C2×C16×C31—41no—
51C31×#106—21no—
52C31×#106C2×C412yescomplemented
53C31×#102—22no—
54C31×#102—22no—
55C24×C31—41no—
56C24×C31D811yescharacteristic
57C2×D4×C31—22no—
58C2×D4×C31—42no—
59C2×D4×C31—42no—
60C2×D4×C31—41no—
61C2×D4×C31—41no—
62C2×D4×C31—41no—
63C2×D4×C31—41no—
64C2×D4×C31—41no—
65C2×D4×C31—84no—
66C22×C4×C31—21no—
67C22×C4×C31—21no—
68C22×C4×C31—21no—
69C22×C4×C31—21no—
70C22×C4×C31—42no—
71C22×C4×C31—41no—
72C22×C4×C31C22⋊C411yescharacteristic
73C22×C4×C31C22⋊C411yescharacteristic
74C22×C4×C31D811yescharacteristic
75C22×C4×C31SD1611yescharacteristic
76C22×C4×C31SD1611yescharacteristic
77C22×C4×C31C2×D411yescharacteristic
78D8×C31—42no—
79D8×C31—42no—
80M16×C31—41no—
81M16×C31—41no—
82M16×C31—41no—
83M16×C31—41no—
84C2×C8×C31—21no—
85C2×C8×C31—21no—
86C2×C8×C31—21no—
87C2×C8×C31—21no—
88C2×C8×C31C22⋊C411yescharacteristic
89C2×C8×C31C22⋊C411yescharacteristic
90C2×C8×C31C22×C411yescharacteristic
91C2×C8×C31C2×D411yescharacteristic
92C4⋊C4×C31—22no—
93C4⋊C4×C31—42no—
94C4⋊C4×C31—42no—
95C4⋊C4×C31—41no—
96C22⋊C4×C31—42no—
97C22⋊C4×C31—42no—
98C22⋊C4×C31—42no—
99C22⋊C4×C31—42no—
100C42×C31—24no—
101C42×C31—42no—
102C16×C31—42no—
103C2×#1339C3111yesmaximal, characteristic, direct product factor, Sylow
104C23×C31—21no—
105C23×C31—21no—
106C23×C31—42no—
107C23×C31—42no—
108C23×C31—82no—
109C23×C31—82no—
110C23×C31—81no—
111C23×C31—81no—
112C23×C31#10211yescharacteristic
113C23×C31#10211yescharacteristic
114C23×C31C2×D811yescharacteristic
115D4×C31—42no—
116D4×C31—42no—
117D4×C31—84no—
118D4×C31—84no—
119D4×C31—81no—
120D4×C31—81no—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31—21no—
124C2×C4×C31—21no—
125C2×C4×C31—21no—
126C2×C4×C31—21no—
127C2×C4×C31—21no—
128C2×C4×C31—21no—
129C2×C4×C31—21no—
130C2×C4×C31—21no—
131C2×C4×C31—44no—
132C2×C4×C31—42no—
133C2×C4×C31—82no—
134C2×C4×C31—84no—
135C2×C4×C31#9911yescharacteristic
136C2×C4×C31#9911yescharacteristic
137C2×C4×C31#10211yescharacteristic
138C2×C4×C31#10211yescharacteristic
139C2×C4×C31#10411yescharacteristic
140C2×C4×C31#10411yescharacteristic
141C2×C4×C31C2×C22⋊C411yescharacteristic
142C2×C4×C31C2×SD1611yescharacteristic
143C8×C31—21no—
144C8×C31—21no—
145C8×C31—21no—
146C8×C31—21no—
147C2×#469C2×C3111yescharacteristic
148C2×#349C2×C3111yescharacteristic, complemented
149C2×H(3,ℤ/4)C2×C3111yescharacteristic, complemented
150#1339C2×C3114yesdirect product factor
151C22×C31—22no—
152C22×C31—21no—
153C22×C31—21no—
154C22×C31—41no—
155C22×C31—41no—
156C22×C31—42no—
157C22×C31—81no—
158C22×C31—82no—
159C22×C31—82no—
160C22×C31—82no—
161C22×C31—162no—
162C22×C31—162no—
163C22×C31#32711yescharacteristic
164C22×C31#32711yescharacteristic
165C22×C31C2×#10211yescharacteristic
166C4×C31—21no—
167C4×C31—21no—
168C4×C31—82no—
169C4×C31—84no—
170C4×C31#32711yescharacteristic
171C4×C31#32711yescharacteristic
172C4×C31C2×#9911yescharacteristic
173C4×C31C2×#10411yescharacteristic
174C22×D8C4×C3111yescharacteristic, complemented
175C22×M16C22×C3111yescharacteristic
176C2×#121—21no—
177C2×#117—21no—
178C2×M32—21no—
179#469—21no—
180#469—21no—
181#469C4×C3112yescomplemented
182#469C22×C3112yes—
183C2×#106C4×C3111yescharacteristic, complemented
184C2×#102—21no—
185#349—21no—
186#349C22×C3112yescomplemented
187H(3,ℤ/4)—21no—
188H(3,ℤ/4)C22×C3112yescomplemented
189C2×C31—21no—
190C2×C31—21no—
191C2×C31—41no—
192C2×C31—41no—
193C2×C31—162no—
194C2×C31#133912yesdirect product factor
195C2×C31C2×#32711yescharacteristic
196C22×D4—21no—
197C22×D4—41no—
198C23×C4D4×C3111yescharacteristic
199C2×D8—21no—
200C2×D8—41no—
201C2×D8—41no—
202C2×D8C2×C4×C3112yescomplemented
203C2×M16—41no—
204C2×M16—41no—
205C2×M16C2×C4×C3111yescharacteristic
206C2×M16D4×C3111yescharacteristic
207C2×M16D4×C3111yescharacteristic
208C2×M16C23×C3111yescharacteristic
209C22×C8C2×C4×C3111yescharacteristic
210C22×C8D4×C3111yescharacteristic
211#121—22no—
212#121—22no—
213#121—41no—
214#121—41no—
215#117—22no—
216#117—22no—
217#117—41no—
218#117—41no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—41no—
221C2×C22⋊C4—41no—
222C2×C22⋊C4—41no—
223C2×C42—22no—
224M32—22no—
225M32—41no—
226C2×C16—41no—
227#106—21no—
228#106C2×C4×C3112yescomplemented
229#102—22no—
230#102—22no—
231C31C2×#133911yescharacteristic, direct product factor, Sylow
232C24—41no—
233C24D8×C3111yescharacteristic
234C2×D4—22no—
235C2×D4—42no—
236C2×D4—42no—
237C2×D4—41no—
238C2×D4—41no—
239C2×D4—41no—
240C2×D4—41no—
241C2×D4—41no—
242C2×D4—84no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—42no—
248C22×C4—41no—
249C22×C4C22⋊C4×C3111yescharacteristic
250C22×C4C22⋊C4×C3111yescharacteristic
251C22×C4D8×C3111yescharacteristic
252C22×C4SD16×C3111yescharacteristic
253C22×C4SD16×C3111yescharacteristic
254C22×C4C2×D4×C3111yescharacteristic
255D8—42no—
256D8—42no—
257M16—41no—
258M16—41no—
259M16—41no—
260M16—41no—
261C2×C8—21no—
262C2×C8—21no—
263C2×C8—21no—
264C2×C8—21no—
265C2×C8C22⋊C4×C3111yescharacteristic
266C2×C8C22⋊C4×C3111yescharacteristic
267C2×C8C22×C4×C3111yescharacteristic
268C2×C8C2×D4×C3111yescharacteristic
269C4⋊C4—22no—
270C4⋊C4—42no—
271C4⋊C4—42no—
272C4⋊C4—41no—
273C22⋊C4—42no—
274C22⋊C4—42no—
275C22⋊C4—42no—
276C22⋊C4—42no—
277C42—24no—
278C42—42no—
279C16—42no—
280C23—21no—
281C23—21no—
282C23—42no—
283C23—42no—
284C23—82no—
285C23—82no—
286C23—81no—
287C23—81no—
288C23C31×#10211yescharacteristic
289C23C31×#10211yescharacteristic
290C23C2×D8×C3111yescharacteristic
291D4—42no—
292D4—42no—
293D4—84no—
294D4—84no—
295D4—81no—
296D4—81no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—44no—
308C2×C4—42no—
309C2×C4—82no—
310C2×C4—84no—
311C2×C4C31×#9911yescharacteristic
312C2×C4C31×#9911yescharacteristic
313C2×C4C31×#10211yescharacteristic
314C2×C4C31×#10211yescharacteristic
315C2×C4C31×#10411yescharacteristic
316C2×C4C31×#10411yescharacteristic
317C2×C4C2×C22⋊C4×C3111yescharacteristic
318C2×C4C2×SD16×C3111yescharacteristic
319C8—21no—
320C8—21no—
321C8—21no—
322C8—21no—
323C22—22no—
324C22—21no—
325C22—21no—
326C22—41no—
327C22—41no—
328C22—42no—
329C22—81no—
330C22—82no—
331C22—82no—
332C22—82no—
333C22—162no—
334C22—162no—
335C22C31×#32711yescharacteristic
336C22C31×#32711yescharacteristic
337C22C2×C31×#10211yescharacteristic
338C4—21no—
339C4—21no—
340C4—82no—
341C4—84no—
342C4C31×#32711yescharacteristic
343C4C31×#32711yescharacteristic
344C4C2×C31×#9911yescharacteristic
345C4C2×C31×#10411yescharacteristic
346C2—21no—
347C2—21no—
348C2—41no—
349C2—41no—
350C2—162no—
351C2C31×#133912yesdirect product factor
352C2C2×C31×#32711yescharacteristic
subgroupG/H
center, socleC22×C31#327
commutatorC2×C8C22×C4×C31
Frattini, cosocleC2×M16C23×C31
prime radicalC2×C31×#469C2
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C4×C31 ◁ C22×M16×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#349C2semidirect
3. C2×C31×H(3,ℤ/4)C2semidirect
4. C31×#1339C2direct (N × H)
5. C22×D8×C31C4semidirect
12. C31×#469C4semidirect
14. C2×C31×#106C4semidirect
17. C31×#349C22semidirect
19. C31×H(3,ℤ/4)C22semidirect
26. C2×D8×C31C2×C4semidirect
52. C31×#106C2×C4semidirect
103. C2×#1339C31direct (N × H)
148. C2×#349C2×C31semidirect
149. C2×H(3,ℤ/4)C2×C31semidirect
150. #1339C2×C31direct (N × H)
174. C22×D8C4×C31semidirect
181. #469C4×C31semidirect
183. C2×#106C4×C31semidirect
186. #349C22×C31semidirect
188. H(3,ℤ/4)C22×C31semidirect
194. C2×C31#1339direct (N × H)
202. C2×D8C2×C4×C31semidirect
228. #106C2×C4×C31semidirect
231. C31C2×#1339direct (N × H)
351. C2C31×#1339direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4692
C2×C31×#3492
C2×C31×H(3,ℤ/4)2
C31×#13392
C2×#133931