Finite Group Databasebeta

← C31×#11691 #21468450

Subgroups — C31×#11691 #21468450

Order 7936.

552 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2392C211yesmaximal, characteristic
2C31×#1740C211yesmaximal, characteristic, complemented
3C31×#1458C211yesmaximal, characteristic, complemented
4C31×#1344C212yesmaximal, complemented
5C31×#1343C212yesmaximal
6C2×C4×D4×C31—21no—
7C2×C4×D4×C31C411yescharacteristic, complemented
8C2×C31×#117—21no—
9C2×C31×#117C2211yescharacteristic
10C31×#431—21no—
11C31×#398C411yescharacteristic, complemented
12C31×#397C2211yescharacteristic
13C31×#396—21no—
14C31×#394—21no—
15C31×#394C411yescharacteristic, complemented
16C31×#392C2211yescharacteristic
17C4×C4⋊C4×C31C411yescharacteristic, complemented
18C4×C22⋊C4×C31—21no—
19C31×#342—21no—
20C31×#342C2212yes—
21C31×#324—21no—
22C31×#323C2212yes—
23C22×D4×C31—21no—
24C22×D4×C31C2×C411yescharacteristic
25C23×C4×C31—21no—
26C23×C4×C31D411yescharacteristic
27C4×D4×C31—41no—
28C4×D4×C31—41no—
29C4×D4×C31—42no—
30C4×D4×C31—42no—
31C31×#117—24no—
32C31×#117—41no—
33C31×#117—41no—
34C31×#117—42no—
35C2×C4⋊C4×C31—21no—
36C2×C4⋊C4×C31—21no—
37C2×C4⋊C4×C31—41no—
38C2×C4⋊C4×C31C2×C411yescharacteristic
39C2×C4⋊C4×C31C2×C411yescharacteristic
40C2×C4⋊C4×C31D411yescharacteristic
41C2×C22⋊C4×C31—22no—
42C2×C22⋊C4×C31—21no—
43C2×C22⋊C4×C31—21no—
44C2×C22⋊C4×C31—21no—
45C2×C22⋊C4×C31—21no—
46C2×C22⋊C4×C31—21no—
47C2×C22⋊C4×C31D411yescharacteristic
48C2×C22⋊C4×C31C2311yescharacteristic
49C2×C42×C31—21no—
50C2×C42×C31—41no—
51C2×C42×C31C2×C411yescharacteristic
52C2×C42×C31D411yescharacteristic
53C31×C4⋊C8—41no—
54C31×C22⋊C8—22no—
55C4×C8×C31—41no—
56C31×#95—21no—
57C31×#95—21no—
58C31×#95C2×C411yescharacteristic
59C31×#95C2×C411yescharacteristic
60C24×C31—21no—
61C24×C31C2×D411yescharacteristic
62C2×D4×C31—42no—
63C2×D4×C31—41no—
64C2×D4×C31—42no—
65C2×D4×C31—41no—
66C2×D4×C31—41no—
67C2×D4×C31—42no—
68C22×C4×C31—21no—
69C22×C4×C31—21no—
70C22×C4×C31—22no—
71C22×C4×C31—21no—
72C22×C4×C31—21no—
73C22×C4×C31—21no—
74C22×C4×C31—42no—
75C22×C4×C31—41no—
76C22×C4×C31—41no—
77C22×C4×C31—42no—
78C22×C4×C31—42no—
79C22×C4×C31C22⋊C411yescharacteristic
80C22×C4×C31C22⋊C411yescharacteristic
81C22×C4×C31C22⋊C411yescharacteristic
82C22×C4×C31C22⋊C411yescharacteristic
83C22×C4×C31D812yes—
84C22×C4×C31SD1612yes—
85C22×C4×C31C22×C411yescharacteristic
86C22×C4×C31C2×D411yescharacteristic
87C2×C8×C31—42no—
88C4⋊C4×C31—41no—
89C4⋊C4×C31—41no—
90C4⋊C4×C31—42no—
91C4⋊C4×C31—44no—
92C4⋊C4×C31—41no—
93C4⋊C4×C31—42no—
94C22⋊C4×C31—24no—
95C22⋊C4×C31—41no—
96C22⋊C4×C31—41no—
97C22⋊C4×C31—42no—
98C22⋊C4×C31—42no—
99C22⋊C4×C31—42no—
100C22⋊C4×C31—42no—
101C22⋊C4×C31—41no—
102C22⋊C4×C31—41no—
103C22⋊C4×C31—42no—
104C42×C31—21no—
105C42×C31—21no—
106C42×C31—21no—
107C42×C31—21no—
108C42×C31—44no—
109C42×C31—42no—
110#11691C3111yesmaximal, characteristic, direct product factor, Sylow
111C23×C31—21no—
112C23×C31—21no—
113C23×C31—22no—
114C23×C31—41no—
115C23×C31—41no—
116C23×C31—41no—
117C23×C31—41no—
118C23×C31—41no—
119C23×C31—41no—
120C23×C31—41no—
121C23×C31—41no—
122C23×C31C2×C22⋊C411yescharacteristic
123C23×C31C2×D811yescharacteristic
124C23×C31C2×SD1611yescharacteristic
125D4×C31—42no—
126D4×C31—44no—
127D4×C31—44no—
128D4×C31—42no—
129C2×C4×C31—21no—
130C2×C4×C31—21no—
131C2×C4×C31—22no—
132C2×C4×C31—22no—
133C2×C4×C31—22no—
134C2×C4×C31—22no—
135C2×C4×C31—22no—
136C2×C4×C31—21no—
137C2×C4×C31—21no—
138C2×C4×C31—21no—
139C2×C4×C31—21no—
140C2×C4×C31—41no—
141C2×C4×C31—41no—
142C2×C4×C31—41no—
143C2×C4×C31—41no—
144C2×C4×C31—41no—
145C2×C4×C31—41no—
146C2×C4×C31—44no—
147C2×C4×C31—41no—
148C2×C4×C31—41no—
149C2×C4×C31—41no—
150C2×C4×C31—41no—
151C2×C4×C31—41no—
152C2×C4×C31—41no—
153C2×C4×C31—82no—
154C2×C4×C31—82no—
155C2×C4×C31—82no—
156C2×C4×C31—82no—
157C2×C4×C31#9911yescharacteristic
158C2×C4×C31#9911yescharacteristic
159C2×C4×C31#10212yes—
160C2×C4×C31#10212yes—
161C2×C4×C31#10412yes—
162C8×C31—82no—
163#2392C2×C3111yescharacteristic
164#1740C2×C3111yescharacteristic, complemented
165#1458C2×C3111yescharacteristic, complemented
166#1344C2×C3112yescomplemented
167#1343C2×C3112yes—
168C22×C31—21no—
169C22×C31—21no—
170C22×C31—21no—
171C22×C31—21no—
172C22×C31—41no—
173C22×C31—41no—
174C22×C31—42no—
175C22×C31—42no—
176C22×C31—41no—
177C22×C31—41no—
178C22×C31—42no—
179C22×C31—81no—
180C22×C31—81no—
181C22×C31—81no—
182C22×C31—81no—
183C22×C31—81no—
184C22×C31C2×#9911yescharacteristic
185C22×C31C2×#10211yescharacteristic
186C22×C31C2×#10411yescharacteristic
187C4×C31—22no—
188C4×C31—42no—
189C4×C31—41no—
190C4×C31—41no—
191C4×C31—41no—
192C4×C31—41no—
193C4×C31—81no—
194C4×C31—84no—
195C4×C31—81no—
196C4×C31#32712yes—
197C4×C31#32712yes—
198C2×C4×D4—21no—
199C2×C4×D4C4×C3111yescharacteristic, complemented
200C2×#117—21no—
201C2×#117C22×C3111yescharacteristic
202#431—21no—
203#398C4×C3111yescharacteristic, complemented
204#397C22×C3111yescharacteristic
205#396—21no—
206#394—21no—
207#394C4×C3111yescharacteristic, complemented
208#392C22×C3111yescharacteristic
209C4×C4⋊C4C4×C3111yescharacteristic, complemented
210C4×C22⋊C4—21no—
211#342—21no—
212#342C22×C3112yes—
213#324—21no—
214#323C22×C3112yes—
215C2×C31—21no—
216C2×C31—21no—
217C2×C31—41no—
218C2×C31—41no—
219C2×C31—82no—
220C2×C31C2×#32711yescharacteristic
221C2×C31#212011yescharacteristic
222C2×C31#212611yescharacteristic
223C22×D4—21no—
224C22×D4C2×C4×C3111yescharacteristic
225C23×C4—21no—
226C23×C4D4×C3111yescharacteristic
227C4×D4—41no—
228C4×D4—41no—
229C4×D4—42no—
230C4×D4—42no—
231#117—24no—
232#117—41no—
233#117—41no—
234#117—42no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—41no—
238C2×C4⋊C4C2×C4×C3111yescharacteristic
239C2×C4⋊C4C2×C4×C3111yescharacteristic
240C2×C4⋊C4D4×C3111yescharacteristic
241C2×C22⋊C4—22no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—21no—
247C2×C22⋊C4D4×C3111yescharacteristic
248C2×C22⋊C4C23×C3111yescharacteristic
249C2×C42—21no—
250C2×C42—41no—
251C2×C42C2×C4×C3111yescharacteristic
252C2×C42D4×C3111yescharacteristic
253C4⋊C8—41no—
254C22⋊C8—22no—
255C4×C8—41no—
256#95—21no—
257#95—21no—
258#95C2×C4×C3111yescharacteristic
259#95C2×C4×C3111yescharacteristic
260C31#1169111yescharacteristic, direct product factor, Sylow
261C24—21no—
262C24C2×D4×C3111yescharacteristic
263C2×D4—41no—
264C2×D4—42no—
265C2×D4—42no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—42no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—22no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—42no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—42no—
279C22×C4—42no—
280C22×C4C22⋊C4×C3111yescharacteristic
281C22×C4C22⋊C4×C3111yescharacteristic
282C22×C4C22⋊C4×C3111yescharacteristic
283C22×C4C22⋊C4×C3111yescharacteristic
284C22×C4D8×C3112yes—
285C22×C4SD16×C3112yes—
286C22×C4C22×C4×C3111yescharacteristic
287C22×C4C2×D4×C3111yescharacteristic
288C2×C8—42no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—42no—
293C4⋊C4—44no—
294C4⋊C4—42no—
295C22⋊C4—24no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—42no—
299C22⋊C4—42no—
300C22⋊C4—42no—
301C22⋊C4—42no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—42no—
305C42—21no—
306C42—21no—
307C42—21no—
308C42—21no—
309C42—44no—
310C42—42no—
311C23—21no—
312C23—21no—
313C23—22no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23C2×C22⋊C4×C3111yescharacteristic
323C23C2×D8×C3111yescharacteristic
324C23C2×SD16×C3111yescharacteristic
325D4—42no—
326D4—44no—
327D4—44no—
328D4—42no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—44no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—82no—
354C2×C4—82no—
355C2×C4—82no—
356C2×C4—82no—
357C2×C4C31×#9911yescharacteristic
358C2×C4C31×#9911yescharacteristic
359C2×C4C31×#10212yes—
360C2×C4C31×#10212yes—
361C2×C4C31×#10412yes—
362C8—82no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—41no—
368C22—41no—
369C22—42no—
370C22—42no—
371C22—41no—
372C22—41no—
373C22—42no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22—81no—
379C22C2×C31×#9911yescharacteristic
380C22C2×C31×#10211yescharacteristic
381C22C2×C31×#10411yescharacteristic
382C4—22no—
383C4—42no—
384C4—41no—
385C4—41no—
386C4—41no—
387C4—41no—
388C4—81no—
389C4—84no—
390C4—81no—
391C4C31×#32712yes—
392C4C31×#32712yes—
393C2—21no—
394C2—21no—
395C2—41no—
396C2—41no—
397C2—82no—
398C2C2×C31×#32711yescharacteristic
399C2C31×#212011yescharacteristic
400C2C31×#212611yescharacteristic
subgroupG/H
centerC2×C4×C31#99
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C22⋊C4C23×C31
socleC22×C31C2×#99
prime radicalC31×#392C22
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C22×C4×C31 ◁ C2×C31×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1740C2semidirect
3. C31×#1458C2semidirect
4. C31×#1344C2semidirect
7. C2×C4×D4×C31C4semidirect
11. C31×#398C4semidirect
15. C31×#394C4semidirect
17. C4×C4⋊C4×C31C4semidirect
110. #11691C31direct (N × H)
164. #1740C2×C31semidirect
165. #1458C2×C31semidirect
166. #1344C2×C31semidirect
199. C2×C4×D4C4×C31semidirect
203. #398C4×C31semidirect
207. #394C4×C31semidirect
209. C4×C4⋊C4C4×C31semidirect
260. C31#11691direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#23922
C31×#17402
C31×#14582
C31×#13442
C31×#13432
#1169131