Finite Group Databasebeta

← C31×#9235 #21465994

Subgroups — C31×#9235 #21465994

Order 7936.

550 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3101C211yesmaximal, characteristic
2C31×#2293C211yesmaximal, 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×C31C2211yescharacteristic
10C2×C31×#117—21no—
11C31×#483—21no—
12C31×#476C412yescomplemented
13C31×#461C412yescomplemented
14C31×#450—21no—
15C4×SD16×C31—22no—
16C31×#431C2211yescharacteristic
17C31×#431C2211yescharacteristic
18C31×#423C2211yescharacteristic
19C31×#390—21no—
20C31×#389—21no—
21C31×#388—22no—
22C4×C4⋊C4×C31C2211yescharacteristic
23C4×C22⋊C4×C31—21no—
24C43×C31C2211yescharacteristic
25C31×#339—21no—
26C31×#339—21no—
27C31×#328—22no—
28C31×D4⋊C8—22no—
29C22×D4×C31D411yescharacteristic
30C23×C4×C31—21no—
31C2×SD16×C31—22no—
32C2×M16×C31—21no—
33C31×C4⋊Q8C2×C411yescharacteristic
34C31×C4⋊Q8C2×C411yescharacteristic
35C31×#125—21no—
36C31×C22⋊Q8—21no—
37C31×C22⋊Q8—21no—
38C4×Q8×C31—21no—
39C4×Q8×C31—21no—
40C4×D4×C31—21no—
41C4×D4×C31—21no—
42C4×D4×C31C2×C412yes—
43C4×D4×C31D412yes—
44C31×#117—21no—
45C31×#117—42no—
46C31×#117—42no—
47C2×C4⋊C4×C31—22no—
48C2×C4⋊C4×C31—21no—
49C2×C4⋊C4×C31D411yescharacteristic
50C2×C22⋊C4×C31—21no—
51C2×C22⋊C4×C31—22no—
52C2×C22⋊C4×C31—22no—
53C2×C42×C31—21no—
54C2×C42×C31—21no—
55C2×C42×C31—21no—
56C2×C42×C31D411yescharacteristic
57C2×C42×C31D411yescharacteristic
58C2×C42×C31C2311yescharacteristic
59C31×#106—22no—
60C31×C4⋊C8—21no—
61C31×C4⋊C8—21no—
62C31×C4⋊C8—21no—
63C31×C4⋊C8C2×C412yes—
64C31×#103—22no—
65C31×#102—22no—
66C31×C22⋊C8—21no—
67C31×C22⋊C8—21no—
68C4×C8×C31—21no—
69C4×C8×C31—21no—
70C31×#95—22no—
71C31×#95D412yes—
72C24×C31—21no—
73C2×Q8×C31—21no—
74C2×Q8×C31—21no—
75C2×D4×C31—21no—
76C2×D4×C31—42no—
77C2×D4×C31C22⋊C412yes—
78C22×C4×C31—21no—
79C22×C4×C31—21no—
80C22×C4×C31—21no—
81C22×C4×C31—22no—
82C22×C4×C31—22no—
83C22×C4×C31—22no—
84C22×C4×C31—41no—
85C22×C4×C31—41no—
86C22×C4×C31—41no—
87C22×C4×C31—41no—
88C22×C4×C31C2×D411yescharacteristic
89C22×C4×C31C2×D411yescharacteristic
90C22×C4×C31C2×D411yescharacteristic
91SD16×C31—44no—
92M16×C31—41no—
93M16×C31—41no—
94C2×C8×C31—22no—
95C2×C8×C31—41no—
96C2×C8×C31—41no—
97C4⋊C4×C31—21no—
98C4⋊C4×C31—21no—
99C4⋊C4×C31—21no—
100C4⋊C4×C31—21no—
101C4⋊C4×C31—21no—
102C4⋊C4×C31—42no—
103C4⋊C4×C31—44no—
104C4⋊C4×C31—41no—
105C4⋊C4×C31—41no—
106C4⋊C4×C31C22⋊C412yes—
107C22⋊C4×C31—22no—
108C22⋊C4×C31—22no—
109C22⋊C4×C31—44no—
110C22⋊C4×C31—44no—
111C22⋊C4×C31—41no—
112C42×C31—21no—
113C42×C31—21no—
114C42×C31—21no—
115C42×C31—42no—
116C42×C31—42no—
117C42×C31—41no—
118C42×C31—41no—
119C42×C31—41no—
120C42×C31SD1612yescomplemented
121C42×C31C22×C411yescharacteristic
122C42×C31C2×D411yescharacteristic
123C42×C31#4111yescharacteristic
124C42×C31#4111yescharacteristic
125#9235C3111yesmaximal, characteristic, direct product factor, Sylow
126C23×C31—22no—
127C23×C31—42no—
128C23×C31—42no—
129C23×C31—41no—
130C23×C31—41no—
131C23×C31#12011yescharacteristic
132Q8×C31—42no—
133Q8×C31—81no—
134D4×C31—22no—
135D4×C31—22no—
136D4×C31—42no—
137C2×C4×C31—22no—
138C2×C4×C31—22no—
139C2×C4×C31—22no—
140C2×C4×C31—22no—
141C2×C4×C31—41no—
142C2×C4×C31—41no—
143C2×C4×C31—41no—
144C2×C4×C31—41no—
145C2×C4×C31—41no—
146C2×C4×C31—41no—
147C2×C4×C31—41no—
148C2×C4×C31—42no—
149C2×C4×C31—42no—
150C2×C4×C31—42no—
151C2×C4×C31—42no—
152C2×C4×C31—42no—
153C2×C4×C31—42no—
154C2×C4×C31—41no—
155C2×C4×C31—41no—
156C2×C4×C31—42no—
157C2×C4×C31C2×C22⋊C411yescharacteristic
158C2×C4×C31C4×D411yescharacteristic
159C2×C4×C31C4×D411yescharacteristic
160C2×C4×C31#12111yescharacteristic
161C2×C4×C31#12111yescharacteristic
162C2×C4×C31#12311yescharacteristic
163C2×C4×C31C2×SD1611yescharacteristic
164C2×C4×C31#13511yescharacteristic
165C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C31#13711yescharacteristic
167C8×C31—42no—
168C8×C31—81no—
169C8×C31—81no—
170#3101C2×C3111yescharacteristic
171#2293C2×C3111yescharacteristic
172#1994C2×C3111yescharacteristic, complemented
173#1503C2×C3111yescharacteristic, complemented
174#1486C2×C3111yescharacteristic
175#1303C2×C3111yescharacteristic, complemented
176#1276C2×C3111yescharacteristic, complemented
177C22×C31—21no—
178C22×C31—21no—
179C22×C31—42no—
180C22×C31—42no—
181C22×C31—42no—
182C22×C31—82no—
183C22×C31—82no—
184C22×C31#38611yescharacteristic
185C22×C31#45011yescharacteristic
186C22×C31#45211yescharacteristic
187C4×C31—21no—
188C4×C31—21no—
189C4×C31—21no—
190C4×C31—42no—
191C4×C31—42no—
192C4×C31—42no—
193C4×C31—82no—
194C4×C31—81no—
195C4×C31—81no—
196C4×C31#42112yes—
197C4×C31C4×SD1611yescharacteristic
198C4×C31#44011yescharacteristic
199C4×C31#46111yescharacteristic
200C4×C31#46311yescharacteristic
201#533C22×C3111yescharacteristic
202C2×C4×D4C22×C3111yescharacteristic
203C2×#117—21no—
204#483—21no—
205#476C4×C3112yescomplemented
206#461C4×C3112yescomplemented
207#450—21no—
208C4×SD16—22no—
209#431C22×C3111yescharacteristic
210#431C22×C3111yescharacteristic
211#423C22×C3111yescharacteristic
212#390—21no—
213#389—21no—
214#388—22no—
215C4×C4⋊C4C22×C3111yescharacteristic
216C4×C22⋊C4—21no—
217C43C22×C3111yescharacteristic
218#339—21no—
219#339—21no—
220#328—22no—
221D4⋊C8—22no—
222C2×C31—21no—
223C2×C31—21no—
224C2×C31—82no—
225C2×C31#187711yescharacteristic
226C2×C31#189711yescharacteristic
227C2×C31#190611yescharacteristic
228C22×D4D4×C3111yescharacteristic
229C23×C4—21no—
230C2×SD16—22no—
231C2×M16—21no—
232C4⋊Q8C2×C4×C3111yescharacteristic
233C4⋊Q8C2×C4×C3111yescharacteristic
234#125—21no—
235C22⋊Q8—21no—
236C22⋊Q8—21no—
237C4×Q8—21no—
238C4×Q8—21no—
239C4×D4—21no—
240C4×D4—21no—
241C4×D4C2×C4×C3112yes—
242C4×D4D4×C3112yes—
243#117—21no—
244#117—42no—
245#117—42no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4D4×C3111yescharacteristic
249C2×C22⋊C4—21no—
250C2×C22⋊C4—22no—
251C2×C22⋊C4—22no—
252C2×C42—21no—
253C2×C42—21no—
254C2×C42—21no—
255C2×C42D4×C3111yescharacteristic
256C2×C42D4×C3111yescharacteristic
257C2×C42C23×C3111yescharacteristic
258#106—22no—
259C4⋊C8—21no—
260C4⋊C8—21no—
261C4⋊C8—21no—
262C4⋊C8C2×C4×C3112yes—
263#103—22no—
264#102—22no—
265C22⋊C8—21no—
266C22⋊C8—21no—
267C4×C8—21no—
268C4×C8—21no—
269#95—22no—
270#95D4×C3112yes—
271C31#923511yescharacteristic, direct product factor, Sylow
272C24—21no—
273C2×Q8—21no—
274C2×Q8—21no—
275C2×D4—21no—
276C2×D4—42no—
277C2×D4C22⋊C4×C3112yes—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4C2×D4×C3111yescharacteristic
289C22×C4C2×D4×C3111yescharacteristic
290C22×C4C2×D4×C3111yescharacteristic
291SD16—44no—
292M16—41no—
293M16—41no—
294C2×C8—22no—
295C2×C8—41no—
296C2×C8—41no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—42no—
303C4⋊C4—44no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4C22⋊C4×C3112yes—
307C22⋊C4—22no—
308C22⋊C4—22no—
309C22⋊C4—44no—
310C22⋊C4—44no—
311C22⋊C4—41no—
312C42—21no—
313C42—21no—
314C42—21no—
315C42—42no—
316C42—42no—
317C42—41no—
318C42—41no—
319C42—41no—
320C42SD16×C3112yescomplemented
321C42C22×C4×C3111yescharacteristic
322C42C2×D4×C3111yescharacteristic
323C42#41×C3111yescharacteristic
324C42#41×C3111yescharacteristic
325C23—22no—
326C23—42no—
327C23—42no—
328C23—41no—
329C23—41no—
330C23C31×#12011yescharacteristic
331Q8—42no—
332Q8—81no—
333D4—22no—
334D4—22no—
335D4—42no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4C2×C22⋊C4×C3111yescharacteristic
357C2×C4C4×D4×C3111yescharacteristic
358C2×C4C4×D4×C3111yescharacteristic
359C2×C4C31×#12111yescharacteristic
360C2×C4C31×#12111yescharacteristic
361C2×C4C31×#12311yescharacteristic
362C2×C4C2×SD16×C3111yescharacteristic
363C2×C4C31×#13511yescharacteristic
364C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
365C2×C4C31×#13711yescharacteristic
366C8—42no—
367C8—81no—
368C8—81no—
369C22—21no—
370C22—21no—
371C22—42no—
372C22—42no—
373C22—42no—
374C22—82no—
375C22—82no—
376C22C31×#38611yescharacteristic
377C22C31×#45011yescharacteristic
378C22C31×#45211yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—42no—
383C4—42no—
384C4—42no—
385C4—82no—
386C4—81no—
387C4—81no—
388C4C31×#42112yes—
389C4C4×SD16×C3111yescharacteristic
390C4C31×#44011yescharacteristic
391C4C31×#46111yescharacteristic
392C4C31×#46311yescharacteristic
393C2—21no—
394C2—21no—
395C2—82no—
396C2C31×#187711yescharacteristic
397C2C31×#189711yescharacteristic
398C2C31×#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
12. C31×#476C4semidirect
13. C31×#461C4semidirect
120. C42×C31SD16semidirect
125. #9235C31direct (N × H)
172. #1994C2×C31semidirect
173. #1503C2×C31semidirect
175. #1303C2×C31semidirect
176. #1276C2×C31semidirect
205. #476C4×C31semidirect
206. #461C4×C31semidirect
271. C31#9235direct (N × H)
320. C42SD16×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#31012
C31×#22932
C31×#19942
C31×#15032
C31×#14862
C31×#13032
C31×#12762
#923531