Finite Group Databasebeta

← C31×#9231 #21465990

Subgroups — C31×#9231 #21465990

Order 7936.

686 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3101C211yesmaximal, characteristic
2C42×D4×C31C211yesmaximal, characteristic
3C31×#1994C211yesmaximal, characteristic, complemented
4C31×#1503C211yesmaximal, characteristic, complemented
5C31×#1486C211yesmaximal, characteristic
6C31×#1303C211yesmaximal, characteristic, complemented
7C31×#1276C211yesmaximal, characteristic, complemented
8C31×#533C2211yescharacteristic
9C2×C4×D4×C31—21no—
10C2×C4×D4×C31C2211yescharacteristic
11C22×C42×C31—21no—
12C31×#483—21no—
13C31×#476C412yescomplemented
14C31×#461C412yescomplemented
15C31×#450—21no—
16C4×SD16×C31—22no—
17C31×#431C2211yescharacteristic
18C31×#431C2211yescharacteristic
19C31×#423C2211yescharacteristic
20C4×C4⋊C4×C31—21no—
21C4×C4⋊C4×C31C2211yescharacteristic
22C4×C22⋊C4×C31—21no—
23C4×C22⋊C4×C31—22no—
24C43×C31C2211yescharacteristic
25C31×#339—21no—
26C31×#339—21no—
27C31×#328—22no—
28C31×D4⋊C8—22no—
29C22×D4×C31D411yescharacteristic
30C23×C4×C31—22no—
31C23×C4×C31—21no—
32C2×SD16×C31—22no—
33C2×M16×C31—21no—
34C31×C4⋊Q8C2×C411yescharacteristic, complemented
35C31×C4⋊Q8C2×C411yescharacteristic, complemented
36C31×#125—21no—
37C31×C22⋊Q8—21no—
38C31×C22⋊Q8—21no—
39C4×Q8×C31—21no—
40C4×Q8×C31—21no—
41C4×D4×C31—28no—
42C4×D4×C31—21no—
43C4×D4×C31—21no—
44C4×D4×C31C2×C412yes—
45C4×D4×C31D412yes—
46C31×#117—21no—
47C2×C4⋊C4×C31—21no—
48C2×C4⋊C4×C31D411yescharacteristic
49C2×C22⋊C4×C31—22no—
50C2×C22⋊C4×C31—21no—
51C2×C42×C31—21no—
52C2×C42×C31—22no—
53C2×C42×C31—21no—
54C2×C42×C31—21no—
55C2×C42×C31—42no—
56C2×C42×C31—42no—
57C2×C42×C31D411yescharacteristic
58C2×C42×C31D411yescharacteristic
59C2×C42×C31C2311yescharacteristic
60C31×#106—22no—
61C31×C4⋊C8—21no—
62C31×C4⋊C8—21no—
63C31×C4⋊C8—21no—
64C31×C4⋊C8C2×C412yescomplemented
65C31×#103—22no—
66C31×#102—22no—
67C31×C22⋊C8—21no—
68C31×C22⋊C8—21no—
69C4×C8×C31—21no—
70C4×C8×C31—21no—
71C31×#95—22no—
72C31×#95D412yes—
73C24×C31—21no—
74C2×Q8×C31—21no—
75C2×Q8×C31—21no—
76C2×D4×C31—24no—
77C2×D4×C31—21no—
78C2×D4×C31C22⋊C412yes—
79C22×C4×C31—21no—
80C22×C4×C31—28no—
81C22×C4×C31—21no—
82C22×C4×C31—21no—
83C22×C4×C31—22no—
84C22×C4×C31—22no—
85C22×C4×C31—22no—
86C22×C4×C31—44no—
87C22×C4×C31—44no—
88C22×C4×C31—41no—
89C22×C4×C31—41no—
90C22×C4×C31—41no—
91C22×C4×C31—41no—
92C22×C4×C31C2×D411yescharacteristic
93C22×C4×C31C2×D411yescharacteristic
94C22×C4×C31C2×D411yescharacteristic
95SD16×C31—44no—
96M16×C31—41no—
97M16×C31—41no—
98C2×C8×C31—22no—
99C2×C8×C31—41no—
100C2×C8×C31—41no—
101C4⋊C4×C31—24no—
102C4⋊C4×C31—21no—
103C4⋊C4×C31—21no—
104C4⋊C4×C31—21no—
105C4⋊C4×C31—21no—
106C4⋊C4×C31—21no—
107C4⋊C4×C31—41no—
108C4⋊C4×C31—41no—
109C4⋊C4×C31C22⋊C412yes—
110C22⋊C4×C31—28no—
111C22⋊C4×C31—22no—
112C22⋊C4×C31—22no—
113C22⋊C4×C31—41no—
114C42×C31—24no—
115C42×C31—21no—
116C42×C31—21no—
117C42×C31—21no—
118C42×C31—42no—
119C42×C31—44no—
120C42×C31—41no—
121C42×C31—41no—
122C42×C31—41no—
123C42×C31SD1612yescomplemented
124C42×C31C22×C411yescharacteristic
125C42×C31C2×D411yescharacteristic
126C42×C31#4111yescharacteristic
127C42×C31#4111yescharacteristic
128#9231C3111yesmaximal, characteristic, direct product factor, Sylow
129C23×C31—24no—
130C23×C31—22no—
131C23×C31—42no—
132C23×C31—41no—
133C23×C31—41no—
134C23×C31#12011yescharacteristic
135Q8×C31—42no—
136Q8×C31—81no—
137D4×C31—24no—
138D4×C31—22no—
139D4×C31#10414yes—
140C2×C4×C31—22no—
141C2×C4×C31—22no—
142C2×C4×C31—22no—
143C2×C4×C31—22no—
144C2×C4×C31—22no—
145C2×C4×C31—24no—
146C2×C4×C31—22no—
147C2×C4×C31—41no—
148C2×C4×C31—416no—
149C2×C4×C31—41no—
150C2×C4×C31—42no—
151C2×C4×C31—42no—
152C2×C4×C31—41no—
153C2×C4×C31—41no—
154C2×C4×C31—41no—
155C2×C4×C31—42no—
156C2×C4×C31—42no—
157C2×C4×C31—42no—
158C2×C4×C31—42no—
159C2×C4×C31—41no—
160C2×C4×C31—41no—
161C2×C4×C31C2×C22⋊C411yescharacteristic
162C2×C4×C31C4×D411yescharacteristic
163C2×C4×C31C4×D411yescharacteristic
164C2×C4×C31#12111yescharacteristic
165C2×C4×C31#12111yescharacteristic
166C2×C4×C31#12311yescharacteristic
167C2×C4×C31C2×SD1611yescharacteristic
168C2×C4×C31#13511yescharacteristic
169C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C31#13711yescharacteristic
171C8×C31—42no—
172C8×C31—81no—
173C8×C31—81no—
174#3101C2×C3111yescharacteristic
175C42×D4C2×C3111yescharacteristic
176#1994C2×C3111yescharacteristic, complemented
177#1503C2×C3111yescharacteristic, complemented
178#1486C2×C3111yescharacteristic
179#1303C2×C3111yescharacteristic, complemented
180#1276C2×C3111yescharacteristic, complemented
181C22×C31—21no—
182C22×C31—21no—
183C22×C31—24no—
184C22×C31—44no—
185C22×C31—44no—
186C22×C31—42no—
187C22×C31—42no—
188C22×C31#38611yescharacteristic
189C22×C31#45011yescharacteristic
190C22×C31#45211yescharacteristic
191C4×C31—24no—
192C4×C31—21no—
193C4×C31—21no—
194C4×C31—21no—
195C4×C31—42no—
196C4×C31—44no—
197C4×C31—42no—
198C4×C31—81no—
199C4×C31—81no—
200C4×C31C2×#10412yes—
201C4×C31C4×SD1611yescharacteristic
202C4×C31#44011yescharacteristic
203C4×C31#46111yescharacteristic
204C4×C31#46311yescharacteristic
205#533C22×C3111yescharacteristic
206C2×C4×D4—21no—
207C2×C4×D4C22×C3111yescharacteristic
208C22×C42—21no—
209#483—21no—
210#476C4×C3112yescomplemented
211#461C4×C3112yescomplemented
212#450—21no—
213C4×SD16—22no—
214#431C22×C3111yescharacteristic
215#431C22×C3111yescharacteristic
216#423C22×C3111yescharacteristic
217C4×C4⋊C4—21no—
218C4×C4⋊C4C22×C3111yescharacteristic
219C4×C22⋊C4—21no—
220C4×C22⋊C4—22no—
221C43C22×C3111yescharacteristic
222#339—21no—
223#339—21no—
224#328—22no—
225D4⋊C8—22no—
226C2×C31—21no—
227C2×C31—21no—
228C2×C31—44no—
229C2×C31#187711yescharacteristic
230C2×C31#189611yescharacteristic
231C2×C31#190611yescharacteristic
232C22×D4D4×C3111yescharacteristic
233C23×C4—22no—
234C23×C4—21no—
235C2×SD16—22no—
236C2×M16—21no—
237C4⋊Q8C2×C4×C3111yescharacteristic, complemented
238C4⋊Q8C2×C4×C3111yescharacteristic, complemented
239#125—21no—
240C22⋊Q8—21no—
241C22⋊Q8—21no—
242C4×Q8—21no—
243C4×Q8—21no—
244C4×D4—28no—
245C4×D4—21no—
246C4×D4—21no—
247C4×D4C2×C4×C3112yes—
248C4×D4D4×C3112yes—
249#117—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4D4×C3111yescharacteristic
252C2×C22⋊C4—22no—
253C2×C22⋊C4—21no—
254C2×C42—21no—
255C2×C42—22no—
256C2×C42—21no—
257C2×C42—21no—
258C2×C42—42no—
259C2×C42—42no—
260C2×C42D4×C3111yescharacteristic
261C2×C42D4×C3111yescharacteristic
262C2×C42C23×C3111yescharacteristic
263#106—22no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8C2×C4×C3112yescomplemented
268#103—22no—
269#102—22no—
270C22⋊C8—21no—
271C22⋊C8—21no—
272C4×C8—21no—
273C4×C8—21no—
274#95—22no—
275#95D4×C3112yes—
276C31#923111yescharacteristic, direct product factor, Sylow
277C24—21no—
278C2×Q8—21no—
279C2×Q8—21no—
280C2×D4—24no—
281C2×D4—21no—
282C2×D4C22⋊C4×C3112yes—
283C22×C4—21no—
284C22×C4—28no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—44no—
291C22×C4—44no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4—41no—
295C22×C4—41no—
296C22×C4C2×D4×C3111yescharacteristic
297C22×C4C2×D4×C3111yescharacteristic
298C22×C4C2×D4×C3111yescharacteristic
299SD16—44no—
300M16—41no—
301M16—41no—
302C2×C8—22no—
303C2×C8—41no—
304C2×C8—41no—
305C4⋊C4—24no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4C22⋊C4×C3112yes—
314C22⋊C4—28no—
315C22⋊C4—22no—
316C22⋊C4—22no—
317C22⋊C4—41no—
318C42—24no—
319C42—21no—
320C42—21no—
321C42—21no—
322C42—42no—
323C42—44no—
324C42—41no—
325C42—41no—
326C42—41no—
327C42SD16×C3112yescomplemented
328C42C22×C4×C3111yescharacteristic
329C42C2×D4×C3111yescharacteristic
330C42#41×C3111yescharacteristic
331C42#41×C3111yescharacteristic
332C23—24no—
333C23—22no—
334C23—42no—
335C23—41no—
336C23—41no—
337C23C31×#12011yescharacteristic
338Q8—42no—
339Q8—81no—
340D4—24no—
341D4—22no—
342D4C31×#10414yes—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—24no—
349C2×C4—22no—
350C2×C4—41no—
351C2×C4—416no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4C2×C22⋊C4×C3111yescharacteristic
365C2×C4C4×D4×C3111yescharacteristic
366C2×C4C4×D4×C3111yescharacteristic
367C2×C4C31×#12111yescharacteristic
368C2×C4C31×#12111yescharacteristic
369C2×C4C31×#12311yescharacteristic
370C2×C4C2×SD16×C3111yescharacteristic
371C2×C4C31×#13511yescharacteristic
372C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
373C2×C4C31×#13711yescharacteristic
374C8—42no—
375C8—81no—
376C8—81no—
377C22—21no—
378C22—21no—
379C22—24no—
380C22—44no—
381C22—44no—
382C22—42no—
383C22—42no—
384C22C31×#38611yescharacteristic
385C22C31×#45011yescharacteristic
386C22C31×#45211yescharacteristic
387C4—24no—
388C4—21no—
389C4—21no—
390C4—21no—
391C4—44no—
392C4—42no—
393C4—42no—
394C4—81no—
395C4—81no—
396C4C2×C31×#10412yes—
397C4C4×SD16×C3111yescharacteristic
398C4C31×#44011yescharacteristic
399C4C31×#46111yescharacteristic
400C4C31×#46311yescharacteristic
401C2—21no—
402C2—21no—
403C2—44no—
404C2C31×#187711yescharacteristic
405C2C31×#189611yescharacteristic
406C2C31×#190611yescharacteristic
subgroupG/H
centerC2×C4×C31#121
commutatorC42C22×C4×C31
Frattini, cosocleC2×C42C23×C31
socleC22×C31#386
prime radicalC22×D4×C31D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#1994C2semidirect
4. C31×#1503C2semidirect
6. C31×#1303C2semidirect
7. C31×#1276C2semidirect
13. C31×#476C4semidirect
14. C31×#461C4semidirect
34. C31×C4⋊Q8C2×C4semidirect
35. C31×C4⋊Q8C2×C4semidirect
64. C31×C4⋊C8C2×C4semidirect
123. C42×C31SD16semidirect
128. #9231C31direct (N × H)
176. #1994C2×C31semidirect
177. #1503C2×C31semidirect
179. #1303C2×C31semidirect
180. #1276C2×C31semidirect
210. #476C4×C31semidirect
211. #461C4×C31semidirect
237. C4⋊Q8C2×C4×C31semidirect
238. C4⋊Q8C2×C4×C31semidirect
267. C4⋊C8C2×C4×C31semidirect
276. C31#9231direct (N × H)
327. C42SD16×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#31012
C42×D4×C312
C31×#19942
C31×#15032
C31×#14862
C31×#13032
C31×#12762
#923131