Finite Group Databasebeta

← C31×#7572 #21464331

Subgroups — C31×#7572 #21464331

Order 7936.

884 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#390C211yesmaximal, characteristic
2C31×#1797C211yesmaximal, characteristic, complemented
3C4×C31×C22⋊C8C211yesmaximal, characteristic, complemented
4C31×#1270C214yesmaximal, complemented
5C23×D4×C31C411yescharacteristic
6C22×C4⋊C4×C31C411yescharacteristic
7C22×C22⋊C4×C31—21no—
8C22×C22⋊C4×C31—21no—
9C22×C42×C31C2211yescharacteristic
10C2×C31×C4⋊C8—21no—
11C2×C31×C22⋊C8—21no—
12C2×C31×C22⋊C8—21no—
13C2×C4×C8×C31—21no—
14C31×#390—21no—
15C31×#390—21no—
16C31×#390C412yes—
17C31×#390C2212yes—
18C31×#336C2212yescomplemented
19C31×#336C2212yescomplemented
20C25×C31—21no—
21C22×D4×C31—21no—
22C22×D4×C31—22no—
23C22×D4×C31—42no—
24C22×D4×C31—42no—
25C22×D4×C31C814yescomplemented
26C22×D4×C31C2×C412yes—
27C23×C4×C31—21no—
28C23×C4×C31C2×C411yescharacteristic
29C23×C4×C31D411yescharacteristic
30C23×C4×C31D411yescharacteristic
31C22×C8×C31—22no—
32C22×C8×C31—22no—
33C2×C4⋊C4×C31—21no—
34C2×C4⋊C4×C31—42no—
35C2×C4⋊C4×C31C2×C412yes—
36C2×C22⋊C4×C31—22no—
37C2×C22⋊C4×C31—22no—
38C2×C22⋊C4×C31—22no—
39C2×C22⋊C4×C31—22no—
40C2×C22⋊C4×C31—44no—
41C2×C22⋊C4×C31—42no—
42C2×C22⋊C4×C31—42no—
43C2×C42×C31—42no—
44C2×C42×C31C2×C411yescharacteristic
45C2×C42×C31D411yescharacteristic
46C2×C42×C31D411yescharacteristic
47C2×C42×C31C2311yescharacteristic
48C31×C4⋊C8—42no—
49C31×C22⋊C8—24no—
50C31×C22⋊C8—42no—
51C4×C8×C31—42no—
52C24×C31—24no—
53C24×C31—22no—
54C24×C31—42no—
55C24×C31—42no—
56C24×C31—42no—
57C24×C31—42no—
58C24×C31—42no—
59C24×C31—42no—
60C24×C31C22⋊C411yescharacteristic
61C2×D4×C31—24no—
62C2×D4×C31—22no—
63C2×D4×C31—48no—
64C2×D4×C31—42no—
65C2×D4×C31—42no—
66C2×D4×C31—48no—
67C2×D4×C31—42no—
68C2×D4×C31—42no—
69C2×D4×C31C2×C814yes—
70C22×C4×C31—22no—
71C22×C4×C31—22no—
72C22×C4×C31—22no—
73C22×C4×C31—22no—
74C22×C4×C31—22no—
75C22×C4×C31—41no—
76C22×C4×C31—41no—
77C22×C4×C31—41no—
78C22×C4×C31—42no—
79C22×C4×C31—42no—
80C22×C4×C31—42no—
81C22×C4×C31C22⋊C411yescharacteristic
82C22×C4×C31C22⋊C411yescharacteristic
83C22×C4×C31C22⋊C411yescharacteristic
84C22×C4×C31C2×C812yes—
85C22×C4×C31M1612yes—
86C22×C4×C31D812yes—
87C22×C4×C31SD1612yes—
88C22×C4×C31C22×C411yescharacteristic
89C22×C4×C31C2×D411yescharacteristic
90C22×C4×C31C2×D411yescharacteristic
91C2×C8×C31—24no—
92C2×C8×C31—42no—
93C2×C8×C31—42no—
94C2×C8×C31—42no—
95C2×C8×C31—42no—
96C2×C8×C31—42no—
97C4⋊C4×C31—42no—
98C4⋊C4×C31—42no—
99C22⋊C4×C31—44no—
100C22⋊C4×C31—44no—
101C22⋊C4×C31—42no—
102C22⋊C4×C31—42no—
103C22⋊C4×C31—44no—
104C42×C31—22no—
105C42×C31—22no—
106C42×C31—41no—
107C42×C31—41no—
108#7572C3111yesmaximal, characteristic, direct product factor, Sylow
109C23×C31—21no—
110C23×C31—21no—
111C23×C31—21no—
112C23×C31—21no—
113C23×C31—24no—
114C23×C31—48no—
115C23×C31—48no—
116C23×C31—48no—
117C23×C31—42no—
118C23×C31—42no—
119C23×C31—42no—
120C23×C31—42no—
121C23×C31—42no—
122C23×C31—42no—
123C23×C31—84no—
124C23×C31—84no—
125C23×C31—84no—
126C23×C31—84no—
127C23×C31C22⋊C812yes—
128C23×C31#10212yes—
129C23×C31#10412yes—
130C23×C31C2×C22⋊C411yescharacteristic
131D4×C31—44no—
132D4×C31—44no—
133D4×C31—48no—
134C2×C4×C31—21no—
135C2×C4×C31—21no—
136C2×C4×C31—21no—
137C2×C4×C31—21no—
138C2×C4×C31—21no—
139C2×C4×C31—21no—
140C2×C4×C31—21no—
141C2×C4×C31—21no—
142C2×C4×C31—24no—
143C2×C4×C31—24no—
144C2×C4×C31—21no—
145C2×C4×C31—21no—
146C2×C4×C31—21no—
147C2×C4×C31—42no—
148C2×C4×C31—42no—
149C2×C4×C31—44no—
150C2×C4×C31—42no—
151C2×C4×C31—42no—
152C2×C4×C31—42no—
153C2×C4×C31—84no—
154C2×C4×C31C22⋊C812yes—
155C2×C4×C31#9912yes—
156C2×C4×C31#10012yes—
157C2×C4×C31#10212yes—
158C2×C4×C31C22×C811yescharacteristic
159C2×C4×C31C2×M1611yescharacteristic
160C2×C4×C31C2×D811yescharacteristic
161C2×C4×C31C2×SD1611yescharacteristic
162C2×C4×C31AGL(1,ℤ/8)12yes—
163C8×C31—44no—
164C8×C31—82no—
165C2×#390C2×C3111yescharacteristic
166#1797C2×C3111yescharacteristic, complemented
167C4×C22⋊C8C2×C3111yescharacteristic, complemented
168#1270C2×C3114yescomplemented
169C22×C31—22no—
170C22×C31—22no—
171C22×C31—22no—
172C22×C31—22no—
173C22×C31—22no—
174C22×C31—22no—
175C22×C31—44no—
176C22×C31—44no—
177C22×C31—44no—
178C22×C31—816no—
179C22×C31—82no—
180C22×C31—82no—
181C22×C31—82no—
182C22×C31—82no—
183C22×C31D4⋊C814yes—
184C22×C31C2×C22⋊C811yescharacteristic
185C22×C31C2×#9911yescharacteristic
186C22×C31C2×#10011yescharacteristic
187C22×C31C2×#10211yescharacteristic
188C22×C31#41811yescharacteristic
189C22×C31C2×#10411yescharacteristic
190C22×C31#42111yescharacteristic
191C4×C31—21no—
192C4×C31—21no—
193C4×C31—22no—
194C4×C31—21no—
195C4×C31—22no—
196C4×C31—21no—
197C4×C31—41no—
198C4×C31—82no—
199C4×C31#32314yes—
200C23×D4C4×C3111yescharacteristic
201C22×C4⋊C4C4×C3111yescharacteristic
202C22×C22⋊C4—21no—
203C22×C22⋊C4—21no—
204C22×C42C22×C3111yescharacteristic
205C2×C4⋊C8—21no—
206C2×C22⋊C8—21no—
207C2×C22⋊C8—21no—
208C2×C4×C8—21no—
209#390—21no—
210#390—21no—
211#390C4×C3112yes—
212#390C22×C3112yes—
213#336C22×C3112yescomplemented
214#336C22×C3112yescomplemented
215C2×C31—24no—
216C2×C31—84no—
217C2×C31C2×#32311yescharacteristic
218C2×C31C2×D4⋊C811yescharacteristic
219C2×C31#147811yescharacteristic
220C2×C31#150711yescharacteristic
221C2×C31#151911yescharacteristic
222C2×C31#152711yescharacteristic
223C2×C31#154511yescharacteristic
224C25—21no—
225C22×D4—21no—
226C22×D4—22no—
227C22×D4—42no—
228C22×D4—42no—
229C22×D4C8×C3114yescomplemented
230C22×D4C2×C4×C3112yes—
231C23×C4—21no—
232C23×C4C2×C4×C3111yescharacteristic
233C23×C4D4×C3111yescharacteristic
234C23×C4D4×C3111yescharacteristic
235C22×C8—22no—
236C22×C8—22no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—42no—
239C2×C4⋊C4C2×C4×C3112yes—
240C2×C22⋊C4—22no—
241C2×C22⋊C4—22no—
242C2×C22⋊C4—22no—
243C2×C22⋊C4—22no—
244C2×C22⋊C4—44no—
245C2×C22⋊C4—42no—
246C2×C22⋊C4—42no—
247C2×C42—42no—
248C2×C42C2×C4×C3111yescharacteristic
249C2×C42D4×C3111yescharacteristic
250C2×C42D4×C3111yescharacteristic
251C2×C42C23×C3111yescharacteristic
252C4⋊C8—42no—
253C22⋊C8—24no—
254C22⋊C8—42no—
255C4×C8—42no—
256C31#757211yescharacteristic, direct product factor, Sylow
257C24—24no—
258C24—22no—
259C24—42no—
260C24—42no—
261C24—42no—
262C24—42no—
263C24—42no—
264C24—42no—
265C24C22⋊C4×C3111yescharacteristic
266C2×D4—24no—
267C2×D4—22no—
268C2×D4—42no—
269C2×D4—42no—
270C2×D4—48no—
271C2×D4—48no—
272C2×D4—42no—
273C2×D4—42no—
274C2×D4C2×C8×C3114yes—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4C22⋊C4×C3111yescharacteristic
287C22×C4C22⋊C4×C3111yescharacteristic
288C22×C4C22⋊C4×C3111yescharacteristic
289C22×C4C2×C8×C3112yes—
290C22×C4M16×C3112yes—
291C22×C4D8×C3112yes—
292C22×C4SD16×C3112yes—
293C22×C4C22×C4×C3111yescharacteristic
294C22×C4C2×D4×C3111yescharacteristic
295C22×C4C2×D4×C3111yescharacteristic
296C2×C8—24no—
297C2×C8—42no—
298C2×C8—42no—
299C2×C8—42no—
300C2×C8—42no—
301C2×C8—42no—
302C4⋊C4—42no—
303C4⋊C4—42no—
304C22⋊C4—44no—
305C22⋊C4—44no—
306C22⋊C4—42no—
307C22⋊C4—42no—
308C22⋊C4—44no—
309C42—22no—
310C42—22no—
311C42—41no—
312C42—41no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—24no—
318C23—48no—
319C23—48no—
320C23—42no—
321C23—42no—
322C23—42no—
323C23—42no—
324C23—42no—
325C23—42no—
326C23—48no—
327C23—84no—
328C23—84no—
329C23—84no—
330C23—84no—
331C23C31×C22⋊C812yes—
332C23C31×#10212yes—
333C23C31×#10412yes—
334C23C2×C22⋊C4×C3111yescharacteristic
335D4—44no—
336D4—44no—
337D4—48no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—24no—
347C2×C4—24no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—44no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—84no—
358C2×C4C31×C22⋊C812yes—
359C2×C4C31×#9912yes—
360C2×C4C31×#10012yes—
361C2×C4C31×#10212yes—
362C2×C4C22×C8×C3111yescharacteristic
363C2×C4C2×M16×C3111yescharacteristic
364C2×C4C2×D8×C3111yescharacteristic
365C2×C4C2×SD16×C3111yescharacteristic
366C2×C4C31×AGL(1,ℤ/8)12yes—
367C8—44no—
368C8—82no—
369C22—22no—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—44no—
376C22—44no—
377C22—44no—
378C22—816no—
379C22—82no—
380C22—82no—
381C22—82no—
382C22—82no—
383C22C31×D4⋊C814yes—
384C22C2×C31×C22⋊C811yescharacteristic
385C22C2×C31×#9911yescharacteristic
386C22C2×C31×#10011yescharacteristic
387C22C2×C31×#10211yescharacteristic
388C22C31×#41811yescharacteristic
389C22C2×C31×#10411yescharacteristic
390C22C31×#42111yescharacteristic
391C4—21no—
392C4—21no—
393C4—22no—
394C4—21no—
395C4—22no—
396C4—21no—
397C4—41no—
398C4—82no—
399C4C31×#32314yes—
400C2—24no—
401C2—84no—
402C2C2×C31×#32311yescharacteristic
403C2C2×C31×D4⋊C811yescharacteristic
404C2C31×#147811yescharacteristic
405C2C31×#150711yescharacteristic
406C2C31×#151911yescharacteristic
407C2C31×#152711yescharacteristic
408C2C31×#154511yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC2×C4C22×C8×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC23×D4×C31C4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1797C2semidirect
3. C4×C31×C22⋊C8C2semidirect
4. C31×#1270C2semidirect
18. C31×#336C22semidirect
19. C31×#336C22semidirect
25. C22×D4×C31C8semidirect
108. #7572C31direct (N × H)
166. #1797C2×C31semidirect
167. C4×C22⋊C8C2×C31semidirect
168. #1270C2×C31semidirect
213. #336C22×C31semidirect
214. #336C22×C31semidirect
229. C22×D4C8×C31semidirect
256. C31#7572direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3902
C31×#17972
C4×C31×C22⋊C82
C31×#12702
#757231