Finite Group Databasebeta

← C31×#9230 #21465989

Subgroups — C31×#9230 #21465989

Order 7936.

570 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#460C211yesmaximal, characteristic
2C2×C31×#446C211yesmaximal, characteristic, complemented
3C31×#1957C211yesmaximal, characteristic
4C31×#1803C211yesmaximal, characteristic, complemented
5C2×C31×#331C211yesmaximal, characteristic
6C31×#1296C211yesmaximal, characteristic, complemented
7C31×#1277C211yesmaximal, characteristic, complemented
8C22×SD16×C31—21no—
9C2×C31×#127C2211yescharacteristic
10C2×C4×Q8×C31C2211yescharacteristic
11C31×#460—22no—
12C31×#460C414yescomplemented
13C31×#446—22no—
14C31×#446—22no—
15C2×C31×C4⋊C8—21no—
16C2×C31×C4⋊C8C2211yescharacteristic
17C2×C31×C4⋊C8C2211yescharacteristic
18C2×C31×C4⋊C8C2211yescharacteristic
19C2×C31×#103—21no—
20C2×C31×#102—21no—
21C2×C31×#102—21no—
22C2×C31×#102—21no—
23C2×C31×#97—21no—
24C2×C4×C8×C31C2211yescharacteristic
25C31×#384C2211yescharacteristic
26C31×#340—21no—
27C31×#331—22no—
28C22×Q8×C31D411yescharacteristic
29C22×D4×C31—21no—
30C22×D4×C31—21no—
31C22×D4×C31—21no—
32C2×SD16×C31—24no—
33C2×SD16×C31—42no—
34C2×SD16×C31—42no—
35C22×C8×C31—21no—
36C22×C8×C31—21no—
37C22×C8×C31—21no—
38C22×C8×C31D411yescharacteristic
39C22×C8×C31D411yescharacteristic
40C31×#127—21no—
41C31×#127—21no—
42C31×#127—21no—
43C31×#127C2×C412yes—
44C4×Q8×C31—21no—
45C4×Q8×C31—21no—
46C4×Q8×C31C2×C412yes—
47C4×Q8×C31D412yes—
48C2×C4⋊C4×C31—21no—
49C2×C4⋊C4×C31—21no—
50C2×C4⋊C4×C31—21no—
51C2×C4⋊C4×C31—21no—
52C2×C4⋊C4×C31D411yescharacteristic
53C2×C42×C31—21no—
54C2×C42×C31C2311yescharacteristic
55C31×C4⋊C8—24no—
56C31×C4⋊C8—21no—
57C31×C4⋊C8—21no—
58C31×C4⋊C8—21no—
59C31×C4⋊C8—21no—
60C31×C4⋊C8C2×C412yes—
61C31×C4⋊C8D412yes—
62C31×#103—42no—
63C31×#102—24no—
64C31×#102—42no—
65C31×#102—42no—
66C31×#97—24no—
67C4×C8×C31—21no—
68C4×C8×C31—21no—
69C24×C31—41no—
70C2×Q8×C31—21no—
71C2×Q8×C31—21no—
72C2×Q8×C31—21no—
73C2×Q8×C31—21no—
74C2×Q8×C31—21no—
75C2×Q8×C31C22⋊C412yes—
76C2×D4×C31—22no—
77C2×D4×C31—22no—
78C2×D4×C31—22no—
79C2×D4×C31—41no—
80C2×D4×C31—41no—
81C2×D4×C31—41no—
82C2×D4×C31—41no—
83C2×D4×C31—41no—
84C2×D4×C31—41no—
85C2×D4×C31—41no—
86C2×D4×C31—41no—
87C2×D4×C31—41no—
88C2×D4×C31—41no—
89C2×D4×C31—41no—
90C2×D4×C31—81no—
91C2×D4×C31—81no—
92C22×C4×C31—21no—
93C22×C4×C31—21no—
94C22×C4×C31—41no—
95C22×C4×C31C2×D411yescharacteristic
96C22×C4×C31C2×D411yescharacteristic
97C22×C4×C31#4111yescharacteristic
98SD16×C31—48no—
99C2×C8×C31—21no—
100C2×C8×C31—21no—
101C2×C8×C31—22no—
102C2×C8×C31—21no—
103C2×C8×C31—22no—
104C2×C8×C31—21no—
105C2×C8×C31—21no—
106C2×C8×C31—41no—
107C2×C8×C31—41no—
108C2×C8×C31—41no—
109C2×C8×C31—41no—
110C2×C8×C31—41no—
111C2×C8×C31—41no—
112C2×C8×C31—41no—
113C2×C8×C31SD1612yescomplemented
114C4⋊C4×C31—22no—
115C4⋊C4×C31—21no—
116C4⋊C4×C31—22no—
117C4⋊C4×C31—41no—
118C4⋊C4×C31—41no—
119C4⋊C4×C31—41no—
120C4⋊C4×C31—41no—
121C4⋊C4×C31—81no—
122C4⋊C4×C31C22⋊C412yes—
123C42×C31—22no—
124C42×C31—22no—
125C42×C31C22×C411yescharacteristic
126C42×C31C2×D411yescharacteristic
127C42×C31C2×D411yescharacteristic
128C42×C31#4111yescharacteristic
129#9230C3111yesmaximal, characteristic, direct product factor, Sylow
130C23×C31—42no—
131C23×C31—81no—
132C23×C31—81no—
133C23×C31—81no—
134C23×C31—81no—
135C23×C31—81no—
136C23×C31—81no—
137C23×C31#12111yescharacteristic
138Q8×C31—22no—
139Q8×C31—22no—
140Q8×C31—41no—
141Q8×C31—41no—
142D4×C31—42no—
143D4×C31—42no—
144D4×C31—42no—
145D4×C31—42no—
146D4×C31—82no—
147D4×C31—82no—
148D4×C31—81no—
149D4×C31—81no—
150D4×C31—81no—
151D4×C31—81no—
152C2×C4×C31—21no—
153C2×C4×C31—21no—
154C2×C4×C31—22no—
155C2×C4×C31—22no—
156C2×C4×C31—41no—
157C2×C4×C31—41no—
158C2×C4×C31—41no—
159C2×C4×C31—41no—
160C2×C4×C31—81no—
161C2×C4×C31—81no—
162C2×C4×C31—81no—
163C2×C4×C31C2×C22⋊C411yescharacteristic
164C2×C4×C31C4×D411yescharacteristic
165C2×C4×C31C4×D411yescharacteristic
166C2×C4×C31#12011yescharacteristic
167C2×C4×C31#12111yescharacteristic
168C2×C4×C31#12311yescharacteristic
169C2×C4×C31C2×SD1611yescharacteristic
170C2×C4×C31#13511yescharacteristic
171C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
174C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
175C2×C4×C31#13711yescharacteristic
176C2×C4×C31#13711yescharacteristic
177C8×C31—22no—
178C8×C31—42no—
179C8×C31—41no—
180C8×C31—42no—
181C8×C31—81no—
182C2×#460C2×C3111yescharacteristic
183C2×#446C2×C3111yescharacteristic, complemented
184#1957C2×C3111yescharacteristic
185#1803C2×C3111yescharacteristic, complemented
186C2×#331C2×C3111yescharacteristic
187#1296C2×C3111yescharacteristic, complemented
188#1277C2×C3111yescharacteristic, complemented
189C22×C31—82no—
190C22×C31—82no—
191C22×C31—82no—
192C22×C31—161no—
193C22×C31—161no—
194C22×C31—161no—
195C22×C31—161no—
196C22×C31#38611yescharacteristic
197C22×C31#46011yescharacteristic
198C22×C31#46411yescharacteristic
199C22×C31#46811yescharacteristic
200C22×C31#46911yescharacteristic
201C22×C31#47111yescharacteristic
202C22×C31#47211yescharacteristic
203C4×C31—21no—
204C4×C31—21no—
205C4×C31—42no—
206C4×C31—42no—
207C4×C31—161no—
208C4×C31#41711yescharacteristic
209C4×C31#41811yescharacteristic
210C4×C31C4×SD1611yescharacteristic
211C4×C31#44011yescharacteristic
212C4×C31#44811yescharacteristic
213C4×C31#44911yescharacteristic
214C4×C31#46811yescharacteristic
215C4×C31#46911yescharacteristic
216C22×SD16—21no—
217C2×#127C22×C3111yescharacteristic
218C2×C4×Q8C22×C3111yescharacteristic
219#460—22no—
220#460C4×C3114yescomplemented
221#446—22no—
222#446—22no—
223C2×C4⋊C8—21no—
224C2×C4⋊C8C22×C3111yescharacteristic
225C2×C4⋊C8C22×C3111yescharacteristic
226C2×C4⋊C8C22×C3111yescharacteristic
227C2×#103—21no—
228C2×#102—21no—
229C2×#102—21no—
230C2×#102—21no—
231C2×#97—21no—
232C2×C4×C8C22×C3111yescharacteristic
233#384C22×C3111yescharacteristic
234#340—21no—
235#331—22no—
236C2×C31—162no—
237C2×C31#168611yescharacteristic
238C2×C31#168811yescharacteristic
239C2×C31#169811yescharacteristic
240C2×C31#170211yescharacteristic
241C2×C31#188011yescharacteristic
242C2×C31#189511yescharacteristic
243C2×C31#190711yescharacteristic
244C22×Q8D4×C3111yescharacteristic
245C22×D4—21no—
246C22×D4—21no—
247C22×D4—21no—
248C2×SD16—24no—
249C2×SD16—42no—
250C2×SD16—42no—
251C22×C8—21no—
252C22×C8—21no—
253C22×C8—21no—
254C22×C8D4×C3111yescharacteristic
255C22×C8D4×C3111yescharacteristic
256#127—21no—
257#127—21no—
258#127—21no—
259#127C2×C4×C3112yes—
260C4×Q8—21no—
261C4×Q8—21no—
262C4×Q8C2×C4×C3112yes—
263C4×Q8D4×C3112yes—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4D4×C3111yescharacteristic
269C2×C42—21no—
270C2×C42C23×C3111yescharacteristic
271C4⋊C8—24no—
272C4⋊C8—21no—
273C4⋊C8—21no—
274C4⋊C8—21no—
275C4⋊C8—21no—
276C4⋊C8C2×C4×C3112yes—
277C4⋊C8D4×C3112yes—
278#103—42no—
279#102—24no—
280#102—42no—
281#102—42no—
282#97—24no—
283C4×C8—21no—
284C4×C8—21no—
285C31#923011yescharacteristic, direct product factor, Sylow
286C24—41no—
287C2×Q8—21no—
288C2×Q8—21no—
289C2×Q8—21no—
290C2×Q8—21no—
291C2×Q8—21no—
292C2×Q8C22⋊C4×C3112yes—
293C2×D4—22no—
294C2×D4—22no—
295C2×D4—22no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—81no—
308C2×D4—81no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—41no—
312C22×C4C2×D4×C3111yescharacteristic
313C22×C4C2×D4×C3111yescharacteristic
314C22×C4#41×C3111yescharacteristic
315SD16—48no—
316C2×C8—21no—
317C2×C8—21no—
318C2×C8—22no—
319C2×C8—21no—
320C2×C8—22no—
321C2×C8—21no—
322C2×C8—21no—
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—41no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8SD16×C3112yescomplemented
331C4⋊C4—22no—
332C4⋊C4—21no—
333C4⋊C4—22no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—81no—
339C4⋊C4C22⋊C4×C3112yes—
340C42—22no—
341C42—22no—
342C42C22×C4×C3111yescharacteristic
343C42C2×D4×C3111yescharacteristic
344C42C2×D4×C3111yescharacteristic
345C42#41×C3111yescharacteristic
346C23—42no—
347C23—81no—
348C23—81no—
349C23—81no—
350C23—81no—
351C23—81no—
352C23—81no—
353C23C31×#12111yescharacteristic
354Q8—22no—
355Q8—22no—
356Q8—41no—
357Q8—41no—
358D4—42no—
359D4—42no—
360D4—42no—
361D4—42no—
362D4—82no—
363D4—82no—
364D4—81no—
365D4—81no—
366D4—81no—
367D4—81no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—81no—
377C2×C4—81no—
378C2×C4—81no—
379C2×C4C2×C22⋊C4×C3111yescharacteristic
380C2×C4C4×D4×C3111yescharacteristic
381C2×C4C4×D4×C3111yescharacteristic
382C2×C4C31×#12011yescharacteristic
383C2×C4C31×#12111yescharacteristic
384C2×C4C31×#12311yescharacteristic
385C2×C4C2×SD16×C3111yescharacteristic
386C2×C4C31×#13511yescharacteristic
387C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
388C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
389C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
390C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
391C2×C4C31×#13711yescharacteristic
392C2×C4C31×#13711yescharacteristic
393C8—22no—
394C8—42no—
395C8—41no—
396C8—42no—
397C8—81no—
398C22—82no—
399C22—82no—
400C22—82no—
401C22—161no—
402C22—161no—
403C22—161no—
404C22—161no—
405C22C31×#38611yescharacteristic
406C22C31×#46011yescharacteristic
407C22C31×#46411yescharacteristic
408C22C31×#46811yescharacteristic
409C22C31×#46911yescharacteristic
410C22C31×#47111yescharacteristic
411C22C31×#47211yescharacteristic
412C4—21no—
413C4—21no—
414C4—42no—
415C4—42no—
416C4—161no—
417C4C31×#41711yescharacteristic
418C4C31×#41811yescharacteristic
419C4C4×SD16×C3111yescharacteristic
420C4C31×#44011yescharacteristic
421C4C31×#44811yescharacteristic
422C4C31×#44911yescharacteristic
423C4C31×#46811yescharacteristic
424C4C31×#46911yescharacteristic
425C2—162no—
426C2C31×#168611yescharacteristic
427C2C31×#168811yescharacteristic
428C2C31×#169811yescharacteristic
429C2C31×#170211yescharacteristic
430C2C31×#188011yescharacteristic
431C2C31×#189511yescharacteristic
432C2C31×#190711yescharacteristic
subgroupG/H
center, socleC23×C31#121
commutatorC42C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC2×C31×#127C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#446C2semidirect
4. C31×#1803C2semidirect
6. C31×#1296C2semidirect
7. C31×#1277C2semidirect
12. C31×#460C4semidirect
113. C2×C8×C31SD16semidirect
129. #9230C31direct (N × H)
183. C2×#446C2×C31semidirect
185. #1803C2×C31semidirect
187. #1296C2×C31semidirect
188. #1277C2×C31semidirect
220. #460C4×C31semidirect
285. C31#9230direct (N × H)
330. C2×C8SD16×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4602
C2×C31×#4462
C31×#19572
C31×#18032
C2×C31×#3312
C31×#12962
C31×#12772
#923031