Finite Group Databasebeta

← C31×#9552 #21466311

Subgroups — C31×#9552 #21466311

Order 7936.

366 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C31×#100C211yesmaximal, characteristic
2C31×#1565C211yesmaximal, characteristic, complemented
3C31×#1478C211yesmaximal, characteristic
4C2×C31×D4⋊C8C211yesmaximal, characteristic
5C31×#1451C211yesmaximal, characteristic, complemented
6C31×#1283C211yesmaximal, characteristic, complemented
7C31×#1278C211yesmaximal, characteristic, complemented
8C2×C4×D4×C31C2211yescharacteristic
9C31×#431C2211yescharacteristic
10C31×#431C2211yescharacteristic
11C2×C31×C4⋊C8C2211yescharacteristic
12C2×C31×#100C411yescharacteristic
13C2×C31×#100C411yescharacteristic
14C4×M16×C31C2211yescharacteristic
15C4×M16×C31C2211yescharacteristic
16C2×C4×C8×C31C2211yescharacteristic
17C31×#343C411yescharacteristic
18C31×#343C411yescharacteristic
19C31×#335—21no—
20C31×#334—21no—
21C31×D4⋊C8—21no—
22C31×D4⋊C8—21no—
23C31×D4⋊C8—21no—
24C31×D4⋊C8—21no—
25C31×#322—21no—
26C31×#322—21no—
27C22×D4×C31C2×C411yescharacteristic
28C23×C4×C31—21no—
29C2×M16×C31C2×C411yescharacteristic
30C2×M16×C31C2×C411yescharacteristic
31C2×M16×C31C2×C411yescharacteristic
32C2×M16×C31C2×C411yescharacteristic
33C22×C8×C31—21no—
34C22×C8×C31—21no—
35C4×D4×C31—21no—
36C4×D4×C31—21no—
37C4×D4×C31—21no—
38C4×D4×C31—21no—
39C2×C4⋊C4×C31C2×C411yescharacteristic
40C2×C22⋊C4×C31—21no—
41C2×C42×C31C2311yescharacteristic
42C31×C4⋊C8—21no—
43C31×C4⋊C8—21no—
44C31×C4⋊C8—21no—
45C31×C4⋊C8D411yescharacteristic
46C31×C4⋊C8D411yescharacteristic
47C31×#100—22no—
48C31×#100—22no—
49C31×C22⋊C8—21no—
50C31×C22⋊C8—21no—
51C31×#97—21no—
52C31×#97—21no—
53C4×C8×C31—21no—
54C4×C8×C31—21no—
55C4×C8×C31—21no—
56C4×C8×C31—21no—
57C4×C8×C31—21no—
58C4×C8×C31D411yescharacteristic
59C4×C8×C31D411yescharacteristic
60C24×C31—21no—
61C2×D4×C31—21no—
62C2×D4×C31—21no—
63C2×D4×C31—21no—
64C2×D4×C31—21no—
65C2×D4×C31—21no—
66C2×D4×C31M1612yes—
67C22×C4×C31—21no—
68C22×C4×C31—41no—
69C22×C4×C31—41no—
70C22×C4×C31—81no—
71C22×C4×C31—81no—
72C22×C4×C31C22×C411yescharacteristic
73C22×C4×C31#4111yescharacteristic
74C22×C4×C31#4111yescharacteristic
75M16×C31—21no—
76M16×C31—21no—
77M16×C31—21no—
78M16×C31—21no—
79M16×C31—21no—
80M16×C31—21no—
81M16×C31—21no—
82M16×C31M1612yes—
83C2×C8×C31—21no—
84C2×C8×C31—21no—
85C2×C8×C31—21no—
86C2×C8×C31—21no—
87C2×C8×C31—21no—
88C2×C8×C31—21no—
89C2×C8×C31—21no—
90C2×C8×C31—21no—
91C2×C8×C31—42no—
92C2×C8×C31—41no—
93C2×C8×C31—41no—
94C2×C8×C31—81no—
95C4⋊C4×C31—21no—
96C4⋊C4×C31—21no—
97C22⋊C4×C31—41no—
98C22⋊C4×C31—41no—
99C42×C31C2×D411yescharacteristic
100C42×C31C2×D411yescharacteristic
101C42×C31#4111yescharacteristic
102C42×C31#4111yescharacteristic
103#9552C3111yesmaximal, characteristic, direct product factor, Sylow
104C23×C31—22no—
105C23×C31—41no—
106C23×C31—41no—
107C23×C31—81no—
108C23×C31—81no—
109C23×C31#11711yescharacteristic
110D4×C31—22no—
111D4×C31—22no—
112D4×C31—41no—
113D4×C31—41no—
114C2×C4×C31—21no—
115C2×C4×C31—21no—
116C2×C4×C31—41no—
117C2×C4×C31—41no—
118C2×C4×C31—82no—
119C2×C4×C31—81no—
120C2×C4×C31—81no—
121C2×C4×C31—81no—
122C2×C4×C31C4×D411yescharacteristic
123C2×C4×C31C4×D411yescharacteristic
124C2×C4×C31#12111yescharacteristic
125C2×C4×C31#12311yescharacteristic
126C2×C4×C31#12411yescharacteristic
127C2×C4×C31#12611yescharacteristic
128C2×C4×C31C2×M1611yescharacteristic
129C2×C4×C31C2×M1611yescharacteristic
130C2×C4×C31#13111yescharacteristic
131C2×C4×C31#13111yescharacteristic
132C8×C31—22no—
133C8×C31—22no—
134C8×C31—41no—
135C8×C31—41no—
136C8×C31—41no—
137C8×C31—41no—
138C8×C31—41no—
139C8×C31—41no—
140C8×C31—81no—
141C8×C31—81no—
142C4×#100C2×C3111yescharacteristic
143#1565C2×C3111yescharacteristic, complemented
144#1478C2×C3111yescharacteristic
145C2×D4⋊C8C2×C3111yescharacteristic
146#1451C2×C3111yescharacteristic, complemented
147#1283C2×C3111yescharacteristic, complemented
148#1278C2×C3111yescharacteristic, complemented
149C22×C31—21no—
150C22×C31—21no—
151C22×C31—42no—
152C22×C31—82no—
153C22×C31—82no—
154C22×C31—81no—
155C22×C31—81no—
156C22×C31#38811yescharacteristic
157C22×C31#43211yescharacteristic
158C22×C31#43311yescharacteristic
159C4×C31—21no—
160C4×C31—21no—
161C4×C31—21no—
162C4×C31—81no—
163C4×C31#43511yescharacteristic
164C4×C31#43511yescharacteristic
165C4×C31#43511yescharacteristic
166C4×C31#43611yescharacteristic
167C4×C31#47111yescharacteristic
168C4×C31#47211yescharacteristic
169C2×C4×D4C22×C3111yescharacteristic
170#431C22×C3111yescharacteristic
171#431C22×C3111yescharacteristic
172C2×C4⋊C8C22×C3111yescharacteristic
173C2×#100C4×C3111yescharacteristic
174C2×#100C4×C3111yescharacteristic
175C4×M16C22×C3111yescharacteristic
176C4×M16C22×C3111yescharacteristic
177C2×C4×C8C22×C3111yescharacteristic
178#343C4×C3111yescharacteristic
179#343C4×C3111yescharacteristic
180#335—21no—
181#334—21no—
182D4⋊C8—21no—
183D4⋊C8—21no—
184D4⋊C8—21no—
185D4⋊C8—21no—
186#322—21no—
187#322—21no—
188C2×C31—21no—
189C2×C31—21no—
190C2×C31—82no—
191C2×C31#192411yescharacteristic
192C2×C31#193111yescharacteristic
193C2×C31#193211yescharacteristic
194C22×D4C2×C4×C3111yescharacteristic
195C23×C4—21no—
196C2×M16C2×C4×C3111yescharacteristic
197C2×M16C2×C4×C3111yescharacteristic
198C2×M16C2×C4×C3111yescharacteristic
199C2×M16C2×C4×C3111yescharacteristic
200C22×C8—21no—
201C22×C8—21no—
202C4×D4—21no—
203C4×D4—21no—
204C4×D4—21no—
205C4×D4—21no—
206C2×C4⋊C4C2×C4×C3111yescharacteristic
207C2×C22⋊C4—21no—
208C2×C42C23×C3111yescharacteristic
209C4⋊C8—21no—
210C4⋊C8—21no—
211C4⋊C8—21no—
212C4⋊C8D4×C3111yescharacteristic
213C4⋊C8D4×C3111yescharacteristic
214#100—22no—
215#100—22no—
216C22⋊C8—21no—
217C22⋊C8—21no—
218#97—21no—
219#97—21no—
220C4×C8—21no—
221C4×C8—21no—
222C4×C8—21no—
223C4×C8—21no—
224C4×C8—21no—
225C4×C8D4×C3111yescharacteristic
226C4×C8D4×C3111yescharacteristic
227C31#955211yescharacteristic, direct product factor, Sylow
228C24—21no—
229C2×D4—21no—
230C2×D4—21no—
231C2×D4—21no—
232C2×D4—21no—
233C2×D4—21no—
234C2×D4M16×C3112yes—
235C22×C4—21no—
236C22×C4—41no—
237C22×C4—41no—
238C22×C4—81no—
239C22×C4—81no—
240C22×C4C22×C4×C3111yescharacteristic
241C22×C4#41×C3111yescharacteristic
242C22×C4#41×C3111yescharacteristic
243M16—21no—
244M16—21no—
245M16—21no—
246M16—21no—
247M16—21no—
248M16—21no—
249M16—21no—
250M16M16×C3112yes—
251C2×C8—21no—
252C2×C8—21no—
253C2×C8—21no—
254C2×C8—21no—
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—21no—
258C2×C8—21no—
259C2×C8—42no—
260C2×C8—41no—
261C2×C8—41no—
262C2×C8—81no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C22⋊C4—41no—
266C22⋊C4—41no—
267C42C2×D4×C3111yescharacteristic
268C42C2×D4×C3111yescharacteristic
269C42#41×C3111yescharacteristic
270C42#41×C3111yescharacteristic
271C23—22no—
272C23—41no—
273C23—41no—
274C23—81no—
275C23—81no—
276C23C31×#11711yescharacteristic
277D4—22no—
278D4—22no—
279D4—41no—
280D4—41no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—82no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4C4×D4×C3111yescharacteristic
290C2×C4C4×D4×C3111yescharacteristic
291C2×C4C31×#12111yescharacteristic
292C2×C4C31×#12311yescharacteristic
293C2×C4C31×#12411yescharacteristic
294C2×C4C31×#12611yescharacteristic
295C2×C4C2×M16×C3111yescharacteristic
296C2×C4C2×M16×C3111yescharacteristic
297C2×C4C31×#13111yescharacteristic
298C2×C4C31×#13111yescharacteristic
299C8—22no—
300C8—22no—
301C8—41no—
302C8—41no—
303C8—41no—
304C8—41no—
305C8—41no—
306C8—41no—
307C8—81no—
308C8—81no—
309C22—21no—
310C22—21no—
311C22—42no—
312C22—82no—
313C22—82no—
314C22—81no—
315C22—81no—
316C22C31×#38811yescharacteristic
317C22C31×#43211yescharacteristic
318C22C31×#43311yescharacteristic
319C4—21no—
320C4—21no—
321C4—21no—
322C4—81no—
323C4C31×#43511yescharacteristic
324C4C31×#43511yescharacteristic
325C4C31×#43511yescharacteristic
326C4C31×#43611yescharacteristic
327C4C31×#47111yescharacteristic
328C4C31×#47211yescharacteristic
329C2—21no—
330C2—21no—
331C2—82no—
332C2C31×#192411yescharacteristic
333C2C31×#193111yescharacteristic
334C2C31×#193211yescharacteristic
subgroupG/H
centerC2×C4×C31#121
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
socleC22×C31#388
prime radicalC22×D4×C31C2×C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1565C2semidirect
5. C31×#1451C2semidirect
6. C31×#1283C2semidirect
7. C31×#1278C2semidirect
103. #9552C31direct (N × H)
143. #1565C2×C31semidirect
146. #1451C2×C31semidirect
147. #1283C2×C31semidirect
148. #1278C2×C31semidirect
227. C31#9552direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C31×#1002
C31×#15652
C31×#14782
C2×C31×D4⋊C82
C31×#14512
C31×#12832
C31×#12782
#955231