Finite Group Databasebeta

← C31×#11703 #21468462

Subgroups — C31×#11703 #21468462

Order 7936.

466 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3050C211yesmaximal, characteristic
2C2×C31×C22⋊C16C211yesmaximal, characteristic, complemented
3C31×#1735C211yesmaximal, characteristic, complemented
4C31×#1348C212yesmaximal, complemented
5C31×#1347C212yesmaximal, complemented
6C2×C31×#135C411yescharacteristic, complemented
7C23×C8×C31C2211yescharacteristic
8C31×#525—21no—
9C2×C31×#117—21no—
10C22×C16×C31—21no—
11C31×#467C411yescharacteristic, complemented
12C31×#467C2211yescharacteristic
13C31×#466C411yescharacteristic, complemented
14C31×#466C2211yescharacteristic
15C31×#465—21no—
16C31×#465—21no—
17C31×#427C411yescharacteristic, complemented
18C31×#416—21no—
19C31×C22⋊C16—21no—
20C31×C22⋊C16C2212yes—
21C31×#340—21no—
22C31×#340C2212yes—
23C2×#41×C31—21no—
24C23×C4×C31D411yescharacteristic
25C31×#135—42no—
26C2×Q16×C31C2×C411yescharacteristic
27C2×SD16×C31—21no—
28C2×D8×C31C2×C411yescharacteristic
29C22×C8×C31—42no—
30C22×C8×C31C2×C411yescharacteristic
31C22×C8×C31C2×C411yescharacteristic
32C22×C8×C31D411yescharacteristic
33C22×C8×C31D411yescharacteristic
34C22×C8×C31D411yescharacteristic
35C22×C8×C31C2311yescharacteristic
36C31×#123—41no—
37C31×C22⋊Q8—21no—
38C31×C22⋊Q8—21no—
39C31×#121—21no—
40C31×#121—21no—
41C31×#120—41no—
42C4×D4×C31—41no—
43C4×D4×C31—41no—
44C31×#117—24no—
45C31×#117—21no—
46C31×#117—42no—
47C2×C4⋊C4×C31—22no—
48C2×C22⋊C4×C31—41no—
49C2×C42×C31—41no—
50C2×C16×C31—22no—
51C2×C16×C31—42no—
52C31×#107C2×C411yescharacteristic
53C31×#107C2×C411yescharacteristic
54C31×#106—21no—
55C31×#103—21no—
56C31×#103—21no—
57C31×#102—21no—
58C31×#102—21no—
59C24×C31D811yescharacteristic
60#41×C31—42no—
61#41×C31—42no—
62C2×Q8×C31—21no—
63C2×D4×C31—21no—
64C2×D4×C31—41no—
65C2×D4×C31—41no—
66C2×D4×C31—41no—
67C22×C4×C31—22no—
68C22×C4×C31—22no—
69C22×C4×C31—42no—
70C22×C4×C31—41no—
71C22×C4×C31C22⋊C411yescharacteristic
72C22×C4×C31C22⋊C411yescharacteristic
73C22×C4×C31D811yescharacteristic
74C22×C4×C31SD1611yescharacteristic
75C22×C4×C31SD1611yescharacteristic
76C22×C4×C31C2×D411yescharacteristic
77Q16×C31—41no—
78SD16×C31—42no—
79D8×C31—41no—
80C2×C8×C31—22no—
81C2×C8×C31—22no—
82C2×C8×C31—41no—
83C2×C8×C31—41no—
84C2×C8×C31—41no—
85C2×C8×C31—41no—
86C2×C8×C31C22⋊C411yescharacteristic
87C2×C8×C31C22⋊C411yescharacteristic
88C2×C8×C31C22×C411yescharacteristic
89C2×C8×C31C2×D411yescharacteristic
90C4⋊C4×C31—24no—
91C4⋊C4×C31—21no—
92C4⋊C4×C31—21no—
93C4⋊C4×C31—42no—
94C4⋊C4×C31—41no—
95C4⋊C4×C31—41no—
96C22⋊C4×C31—44no—
97C22⋊C4×C31—41no—
98C22⋊C4×C31—41no—
99C22⋊C4×C31—41no—
100C22⋊C4×C31—41no—
101C22⋊C4×C31—41no—
102C42×C31—44no—
103C42×C31—41no—
104C16×C31—42no—
105#11703C3111yesmaximal, characteristic, direct product factor, Sylow
106C23×C31—22no—
107C23×C31—22no—
108C23×C31—41no—
109C23×C31—41no—
110C23×C31#10211yescharacteristic
111C23×C31#10211yescharacteristic
112C23×C31C2×D811yescharacteristic
113Q8×C31—41no—
114Q8×C31—41no—
115D4×C31—41no—
116D4×C31—41no—
117D4×C31—82no—
118D4×C31—82no—
119D4×C31—82no—
120C2×C4×C31—22no—
121C2×C4×C31—22no—
122C2×C4×C31—22no—
123C2×C4×C31—21no—
124C2×C4×C31—21no—
125C2×C4×C31—21no—
126C2×C4×C31—21no—
127C2×C4×C31—44no—
128C2×C4×C31—41no—
129C2×C4×C31—41no—
130C2×C4×C31—41no—
131C2×C4×C31—82no—
132C2×C4×C31—82no—
133C2×C4×C31—82no—
134C2×C4×C31#9912yes—
135C2×C4×C31#10211yescharacteristic
136C2×C4×C31#10211yescharacteristic
137C2×C4×C31#10412yes—
138C2×C4×C31C2×C22⋊C411yescharacteristic
139C2×C4×C31C2×SD1611yescharacteristic
140C8×C31—21no—
141C8×C31—21no—
142C8×C31—21no—
143C8×C31—21no—
144#3050C2×C3111yescharacteristic
145C2×C22⋊C16C2×C3111yescharacteristic, complemented
146#1735C2×C3111yescharacteristic, complemented
147#1348C2×C3112yescomplemented
148#1347C2×C3112yescomplemented
149C22×C31—21no—
150C22×C31—21no—
151C22×C31—21no—
152C22×C31—21no—
153C22×C31—21no—
154C22×C31—21no—
155C22×C31—21no—
156C22×C31—44no—
157C22×C31—81no—
158C22×C31—81no—
159C22×C31—81no—
160C22×C31#32712yes—
161C22×C31C2×#10211yescharacteristic
162C22×C31#50812yes—
163C4×C31—21no—
164C4×C31—21no—
165C4×C31—84no—
166C4×C31—81no—
167C4×C31—81no—
168C4×C31—81no—
169C4×C31#32712yes—
170C4×C31C2×#9911yescharacteristic
171C4×C31C2×#10411yescharacteristic
172C2×#135C4×C3111yescharacteristic, complemented
173C23×C8C22×C3111yescharacteristic
174#525—21no—
175C2×#117—21no—
176C22×C16—21no—
177#467C4×C3111yescharacteristic, complemented
178#467C22×C3111yescharacteristic
179#466C4×C3111yescharacteristic, complemented
180#466C22×C3111yescharacteristic
181#465—21no—
182#465—21no—
183#427C4×C3111yescharacteristic, complemented
184#416—21no—
185C22⋊C16—21no—
186C22⋊C16C22×C3112yes—
187#340—21no—
188#340C22×C3112yes—
189C2×C31—22no—
190C2×C31—22no—
191C2×C31—41no—
192C2×C31—161no—
193C2×C31C2×#32711yescharacteristic
194C2×C31#213811yescharacteristic
195C2×C31#214511yescharacteristic
196C2×#41—21no—
197C23×C4D4×C3111yescharacteristic
198#135—42no—
199C2×Q16C2×C4×C3111yescharacteristic
200C2×SD16—21no—
201C2×D8C2×C4×C3111yescharacteristic
202C22×C8—42no—
203C22×C8C2×C4×C3111yescharacteristic
204C22×C8C2×C4×C3111yescharacteristic
205C22×C8D4×C3111yescharacteristic
206C22×C8D4×C3111yescharacteristic
207C22×C8D4×C3111yescharacteristic
208C22×C8C23×C3111yescharacteristic
209#123—41no—
210C22⋊Q8—21no—
211C22⋊Q8—21no—
212#121—21no—
213#121—21no—
214#120—41no—
215C4×D4—41no—
216C4×D4—41no—
217#117—24no—
218#117—21no—
219#117—42no—
220C2×C4⋊C4—22no—
221C2×C22⋊C4—41no—
222C2×C42—41no—
223C2×C16—22no—
224C2×C16—42no—
225#107C2×C4×C3111yescharacteristic
226#107C2×C4×C3111yescharacteristic
227#106—21no—
228#103—21no—
229#103—21no—
230#102—21no—
231#102—21no—
232C31#1170311yescharacteristic, direct product factor, Sylow
233C24D8×C3111yescharacteristic
234#41—42no—
235#41—42no—
236C2×Q8—21no—
237C2×D4—21no—
238C2×D4—41no—
239C2×D4—41no—
240C2×D4—41no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—42no—
244C22×C4—41no—
245C22×C4C22⋊C4×C3111yescharacteristic
246C22×C4C22⋊C4×C3111yescharacteristic
247C22×C4D8×C3111yescharacteristic
248C22×C4SD16×C3111yescharacteristic
249C22×C4SD16×C3111yescharacteristic
250C22×C4C2×D4×C3111yescharacteristic
251Q16—41no—
252SD16—42no—
253D8—41no—
254C2×C8—22no—
255C2×C8—22no—
256C2×C8—41no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8C22⋊C4×C3111yescharacteristic
261C2×C8C22⋊C4×C3111yescharacteristic
262C2×C8C22×C4×C3111yescharacteristic
263C2×C8C2×D4×C3111yescharacteristic
264C4⋊C4—24no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—42no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C22⋊C4—44no—
271C22⋊C4—41no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—41no—
276C42—44no—
277C42—41no—
278C16—42no—
279C23—22no—
280C23—22no—
281C23—41no—
282C23—41no—
283C23C31×#10211yescharacteristic
284C23C31×#10211yescharacteristic
285C23C2×D8×C3111yescharacteristic
286Q8—41no—
287Q8—41no—
288D4—41no—
289D4—41no—
290D4—82no—
291D4—82no—
292D4—82no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—44no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—82no—
305C2×C4—82no—
306C2×C4—82no—
307C2×C4C31×#9912yes—
308C2×C4C31×#10211yescharacteristic
309C2×C4C31×#10211yescharacteristic
310C2×C4C31×#10412yes—
311C2×C4C2×C22⋊C4×C3111yescharacteristic
312C2×C4C2×SD16×C3111yescharacteristic
313C8—21no—
314C8—21no—
315C8—21no—
316C8—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—44no—
325C22—81no—
326C22—81no—
327C22—81no—
328C22C31×#32712yes—
329C22C2×C31×#10211yescharacteristic
330C22C31×#50812yes—
331C4—21no—
332C4—21no—
333C4—84no—
334C4—81no—
335C4—81no—
336C4—81no—
337C4C31×#32712yes—
338C4C2×C31×#9911yescharacteristic
339C4C2×C31×#10411yescharacteristic
340C2—22no—
341C2—22no—
342C2—41no—
343C2—161no—
344C2C2×C31×#32711yescharacteristic
345C2C31×#213811yescharacteristic
346C2C31×#214511yescharacteristic
subgroupG/H
centerC2×C4×C31#102
commutatorC2×C8C22×C4×C31
Frattini, cosocleC22×C8C23×C31
socleC22×C31C2×#102
prime radicalC31×#3050C2
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C23×C4×C31 ◁ C23×C8×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×C22⋊C16C2semidirect
3. C31×#1735C2semidirect
4. C31×#1348C2semidirect
5. C31×#1347C2semidirect
6. C2×C31×#135C4semidirect
11. C31×#467C4semidirect
13. C31×#466C4semidirect
17. C31×#427C4semidirect
105. #11703C31direct (N × H)
145. C2×C22⋊C16C2×C31semidirect
146. #1735C2×C31semidirect
147. #1348C2×C31semidirect
148. #1347C2×C31semidirect
172. C2×#135C4×C31semidirect
177. #467C4×C31semidirect
179. #466C4×C31semidirect
183. #427C4×C31semidirect
232. C31#11703direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#30502
C2×C31×C22⋊C162
C31×#17352
C31×#13482
C31×#13472
#1170331