Finite Group Databasebeta

← C31×#9320 #21466079

Subgroups — C31×#9320 #21466079

Order 7936.

490 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
1C31×#3039C211yesmaximal, characteristic
2C31×#2989C211yesmaximal, characteristic
3C31×#1988C211yesmaximal, characteristic, complemented
4C31×#1806C211yesmaximal, characteristic
5C31×#1546C211yesmaximal, characteristic, complemented
6C31×#1303C211yesmaximal, characteristic, complemented
7C31×#1292C211yesmaximal, characteristic, complemented
8C2×C31×#137—21no—
9C2×C31×C4⋊Q8C2211yescharacteristic
10C4×#41×C31C2211yescharacteristic
11C31×#462—21no—
12C31×#462C412yescomplemented
13C31×#461—21no—
14C31×#461C412yescomplemented
15C31×#446—21no—
16C31×#436—21no—
17C31×#435—22no—
18C31×#432—21no—
19C31×#431C2211yescharacteristic
20C31×#423—21no—
21C31×#423C2211yescharacteristic
22C31×#423C2211yescharacteristic
23C2×C31×C4⋊C8C2211yescharacteristic
24C2×C31×#104—21no—
25C31×#419—21no—
26C4×C4⋊C4×C31C2211yescharacteristic
27C31×#340—22no—
28C31×#339—21no—
29C31×#332—21no—
30C31×#332—21no—
31C2×#41×C31D411yescharacteristic
32C22×Q8×C31—21no—
33C31×#137—42no—
34C31×#137—42no—
35C2×Q16×C31—22no—
36C2×SD16×C31—22no—
37C2×M16×C31—21no—
38C2×M16×C31—22no—
39C2×M16×C31—21no—
40C22×C8×C31D412yes—
41C31×C4⋊Q8—21no—
42C31×C4⋊Q8—21no—
43C31×C4⋊Q8—21no—
44C31×C4⋊Q8C2×C412yes—
45C4×Q8×C31C2×C411yescharacteristic
46C4×Q8×C31D411yescharacteristic
47C4×D4×C31—21no—
48C4×D4×C31—21no—
49C4×D4×C31C2×C411yescharacteristic
50C4×D4×C31D411yescharacteristic
51C31×#117—21no—
52C31×#117D411yescharacteristic
53C2×C4⋊C4×C31—21no—
54C2×C4⋊C4×C31—21no—
55C2×C4⋊C4×C31—21no—
56C2×C42×C31—21no—
57C2×C42×C31—21no—
58C2×C42×C31C2311yescharacteristic
59C31×C4⋊C8—22no—
60C31×C4⋊C8—21no—
61C31×C4⋊C8—21no—
62C31×C4⋊C8—21no—
63C31×C4⋊C8—21no—
64C31×C4⋊C8—21no—
65C31×C4⋊C8C2×C412yes—
66C31×C4⋊C8D411yescharacteristic
67C31×C4⋊C8D411yescharacteristic
68C31×#104—42no—
69C31×#103—22no—
70C31×#103—22no—
71C31×C22⋊C8—22no—
72C31×C22⋊C8—21no—
73C31×#97—22no—
74C4×C8×C31—21no—
75C31×#95—21no—
76#41×C31—21no—
77#41×C31—21no—
78#41×C31—21no—
79#41×C31—21no—
80C2×Q8×C31—22no—
81C2×Q8×C31—41no—
82C2×Q8×C31—41no—
83C2×Q8×C31—41no—
84C2×Q8×C31—41no—
85C2×Q8×C31—41no—
86C2×Q8×C31C22⋊C411yescharacteristic
87C2×D4×C31—21no—
88C2×D4×C31C22⋊C411yescharacteristic
89C22×C4×C31—21no—
90C22×C4×C31—21no—
91C22×C4×C31—21no—
92C22×C4×C31—41no—
93C22×C4×C31—41no—
94C22×C4×C31C2×D411yescharacteristic
95C22×C4×C31C2×D411yescharacteristic
96C22×C4×C31#4111yescharacteristic
97Q16×C31—44no—
98SD16×C31—44no—
99M16×C31—41no—
100M16×C31—41no—
101M16×C31—41no—
102M16×C31—41no—
103M16×C31—82no—
104C2×C8×C31—22no—
105C2×C8×C31—21no—
106C2×C8×C31—21no—
107C2×C8×C31—22no—
108C2×C8×C31—42no—
109C2×C8×C31—41no—
110C4⋊C4×C31—21no—
111C4⋊C4×C31—21no—
112C4⋊C4×C31—22no—
113C4⋊C4×C31—22no—
114C4⋊C4×C31—22no—
115C4⋊C4×C31—41no—
116C4⋊C4×C31—41no—
117C4⋊C4×C31—41no—
118C4⋊C4×C31C22⋊C411yescharacteristic
119C4⋊C4×C31C22⋊C411yescharacteristic
120C22⋊C4×C31—21no—
121C22⋊C4×C31—21no—
122C22⋊C4×C31—21no—
123C42×C31—21no—
124C42×C31—21no—
125C42×C31—21no—
126C42×C31—41no—
127C42×C31—41no—
128C42×C31C22×C411yescharacteristic
129C42×C31C2×D411yescharacteristic
130C42×C31C2×D411yescharacteristic
131C42×C31#4111yescharacteristic
132#9320C3111yesmaximal, characteristic, direct product factor, Sylow
133C23×C31—21no—
134C23×C31#12111yescharacteristic
135Q8×C31—21no—
136Q8×C31—21no—
137Q8×C31—42no—
138Q8×C31—42no—
139Q8×C31—81no—
140Q8×C31—81no—
141D4×C31—21no—
142D4×C31—21no—
143D4×C31—41no—
144D4×C31—41no—
145C2×C4×C31—21no—
146C2×C4×C31—21no—
147C2×C4×C31—21no—
148C2×C4×C31—21no—
149C2×C4×C31—21no—
150C2×C4×C31—41no—
151C2×C4×C31—41no—
152C2×C4×C31—41no—
153C2×C4×C31—41no—
154C2×C4×C31—41no—
155C2×C4×C31—42no—
156C2×C4×C31—42no—
157C2×C4×C31—81no—
158C2×C4×C31—81no—
159C2×C4×C31—81no—
160C2×C4×C31—81no—
161C2×C4×C31—81no—
162C2×C4×C31C2×C22⋊C411yescharacteristic
163C2×C4×C31C4×D411yescharacteristic
164C2×C4×C31C4×D411yescharacteristic
165C2×C4×C31#12011yescharacteristic
166C2×C4×C31#12111yescharacteristic
167C2×C4×C31#12311yescharacteristic
168C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
169C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C31#13711yescharacteristic
172C8×C31—42no—
173C8×C31—42no—
174C8×C31—41no—
175C8×C31—41no—
176C8×C31—81no—
177#3039C2×C3111yescharacteristic
178#2989C2×C3111yescharacteristic
179#1988C2×C3111yescharacteristic, complemented
180#1806C2×C3111yescharacteristic
181#1546C2×C3111yescharacteristic, complemented
182#1303C2×C3111yescharacteristic, complemented
183#1292C2×C3111yescharacteristic, complemented
184C22×C31—21no—
185C22×C31—21no—
186C22×C31—41no—
187C22×C31—41no—
188C22×C31—41no—
189C22×C31#38611yescharacteristic
190C22×C31#46811yescharacteristic
191C22×C31#46911yescharacteristic
192C4×C31—21no—
193C4×C31—21no—
194C4×C31—21no—
195C4×C31—41no—
196C4×C31—41no—
197C4×C31—41no—
198C4×C31—82no—
199C4×C31—82no—
200C4×C31#41711yescharacteristic
201C4×C31#41811yescharacteristic
202C4×C31#45511yescharacteristic
203C4×C31#45611yescharacteristic
204C4×C31#46811yescharacteristic
205C4×C31#46911yescharacteristic
206C2×#137—21no—
207C2×C4⋊Q8C22×C3111yescharacteristic
208C4×#41C22×C3111yescharacteristic
209#462—21no—
210#462C4×C3112yescomplemented
211#461—21no—
212#461C4×C3112yescomplemented
213#446—21no—
214#436—21no—
215#435—22no—
216#432—21no—
217#431C22×C3111yescharacteristic
218#423—21no—
219#423C22×C3111yescharacteristic
220#423C22×C3111yescharacteristic
221C2×C4⋊C8C22×C3111yescharacteristic
222C2×#104—21no—
223#419—21no—
224C4×C4⋊C4C22×C3111yescharacteristic
225#340—22no—
226#339—21no—
227#332—21no—
228#332—21no—
229C2×C31—21no—
230C2×C31—21no—
231C2×C31—81no—
232C2×C31#188211yescharacteristic
233C2×C31#189511yescharacteristic
234C2×C31#190211yescharacteristic
235C2×#41D4×C3111yescharacteristic
236C22×Q8—21no—
237#137—42no—
238#137—42no—
239C2×Q16—22no—
240C2×SD16—22no—
241C2×M16—21no—
242C2×M16—22no—
243C2×M16—21no—
244C22×C8D4×C3112yes—
245C4⋊Q8—21no—
246C4⋊Q8—21no—
247C4⋊Q8—21no—
248C4⋊Q8C2×C4×C3112yes—
249C4×Q8C2×C4×C3111yescharacteristic
250C4×Q8D4×C3111yescharacteristic
251C4×D4—21no—
252C4×D4—21no—
253C4×D4C2×C4×C3111yescharacteristic
254C4×D4D4×C3111yescharacteristic
255#117—21no—
256#117D4×C3111yescharacteristic
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C42—21no—
261C2×C42—21no—
262C2×C42C23×C3111yescharacteristic
263C4⋊C8—22no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8—21no—
269C4⋊C8C2×C4×C3112yes—
270C4⋊C8D4×C3111yescharacteristic
271C4⋊C8D4×C3111yescharacteristic
272#104—42no—
273#103—22no—
274#103—22no—
275C22⋊C8—22no—
276C22⋊C8—21no—
277#97—22no—
278C4×C8—21no—
279#95—21no—
280C31#932011yescharacteristic, direct product factor, Sylow
281#41—21no—
282#41—21no—
283#41—21no—
284#41—21no—
285C2×Q8—22no—
286C2×Q8—41no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×Q8—41no—
291C2×Q8C22⋊C4×C3111yescharacteristic
292C2×D4—21no—
293C2×D4C22⋊C4×C3111yescharacteristic
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—41no—
298C22×C4—41no—
299C22×C4C2×D4×C3111yescharacteristic
300C22×C4C2×D4×C3111yescharacteristic
301C22×C4#41×C3111yescharacteristic
302Q16—44no—
303SD16—44no—
304M16—41no—
305M16—41no—
306M16—41no—
307M16—41no—
308M16—82no—
309C2×C8—22no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—22no—
313C2×C8—42no—
314C2×C8—41no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—22no—
318C4⋊C4—22no—
319C4⋊C4—22no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4C22⋊C4×C3111yescharacteristic
324C4⋊C4C22⋊C4×C3111yescharacteristic
325C22⋊C4—21no—
326C22⋊C4—21no—
327C22⋊C4—21no—
328C42—21no—
329C42—21no—
330C42—21no—
331C42—41no—
332C42—41no—
333C42C22×C4×C3111yescharacteristic
334C42C2×D4×C3111yescharacteristic
335C42C2×D4×C3111yescharacteristic
336C42#41×C3111yescharacteristic
337C23—21no—
338C23C31×#12111yescharacteristic
339Q8—21no—
340Q8—21no—
341Q8—42no—
342Q8—42no—
343Q8—81no—
344Q8—81no—
345D4—21no—
346D4—21no—
347D4—41no—
348D4—41no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4—81no—
365C2×C4—81no—
366C2×C4C2×C22⋊C4×C3111yescharacteristic
367C2×C4C4×D4×C3111yescharacteristic
368C2×C4C4×D4×C3111yescharacteristic
369C2×C4C31×#12011yescharacteristic
370C2×C4C31×#12111yescharacteristic
371C2×C4C31×#12311yescharacteristic
372C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
373C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
374C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
375C2×C4C31×#13711yescharacteristic
376C8—42no—
377C8—42no—
378C8—41no—
379C8—41no—
380C8—81no—
381C22—21no—
382C22—21no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22C31×#38611yescharacteristic
387C22C31×#46811yescharacteristic
388C22C31×#46911yescharacteristic
389C4—21no—
390C4—21no—
391C4—21no—
392C4—41no—
393C4—41no—
394C4—41no—
395C4—82no—
396C4—82no—
397C4C31×#41711yescharacteristic
398C4C31×#41811yescharacteristic
399C4C31×#45511yescharacteristic
400C4C31×#45611yescharacteristic
401C4C31×#46811yescharacteristic
402C4C31×#46911yescharacteristic
403C2—21no—
404C2—21no—
405C2—81no—
406C2C31×#188211yescharacteristic
407C2C31×#189511yescharacteristic
408C2C31×#190211yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC42C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC2×#41×C31D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#1988C2semidirect
5. C31×#1546C2semidirect
6. C31×#1303C2semidirect
7. C31×#1292C2semidirect
12. C31×#462C4semidirect
14. C31×#461C4semidirect
132. #9320C31direct (N × H)
179. #1988C2×C31semidirect
181. #1546C2×C31semidirect
182. #1303C2×C31semidirect
183. #1292C2×C31semidirect
210. #462C4×C31semidirect
212. #461C4×C31semidirect
280. C31#9320direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#30392
C31×#29892
C31×#19882
C31×#18062
C31×#15462
C31×#13032
C31×#12922
#932031