Finite Group Databasebeta

← C31×#9163 #21465922

Subgroups — C31×#9163 #21465922

Order 7936.

508 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3109C211yesmaximal, characteristic
2C31×#2974C211yesmaximal, characteristic, complemented
3C31×#1762C211yesmaximal, characteristic, complemented
4C31×#1530C211yesmaximal, characteristic, complemented
5C31×#1502C211yesmaximal, characteristic, complemented
6C31×#1302C211yesmaximal, characteristic, complemented
7C31×#1285C211yesmaximal, characteristic, complemented
8C31×#532C2211yescharacteristic
9C2×C4×D4×C31C2211yescharacteristic
10C31×#481—21no—
11C31×#476C411yescharacteristic, complemented
12C31×#476C411yescharacteristic, complemented
13C31×#459C411yescharacteristic, complemented
14C31×#459C411yescharacteristic, complemented
15C31×#447—21no—
16C31×#442—21no—
17C31×#442—21no—
18C31×#436—21no—
19C31×#435—22no—
20C8×D4×C31—21no—
21C31×#432C2211yescharacteristic
22C31×#432C2211yescharacteristic
23C31×#431C2211yescharacteristic
24C2×C31×#102—21no—
25C31×#407—21no—
26C2×C31×C22⋊C8—21no—
27C2×C31×#97C2211yescharacteristic
28C4×C4⋊C4×C31C2211yescharacteristic
29C31×#340—21no—
30C31×#329—22no—
31C31×#327—21no—
32C31×#327—21no—
33C2×#41×C31—21no—
34C22×D4×C31D411yescharacteristic
35C23×C4×C31—21no—
36C2×D8×C31—21no—
37C2×D8×C31—21no—
38C2×M16×C31—22no—
39C22×C8×C31—21no—
40C22×C8×C31—22no—
41C31×C4⋊Q8C2×C411yescharacteristic
42C31×#127C2×C411yescharacteristic
43C31×#124—21no—
44C31×#121—21no—
45C31×#121—21no—
46C4×D4×C31—21no—
47C4×D4×C31—21no—
48C4×D4×C31—21no—
49C4×D4×C31—21no—
50C4×D4×C31C2×C411yescharacteristic
51C4×D4×C31C2×C411yescharacteristic
52C4×D4×C31D411yescharacteristic
53C4×D4×C31D411yescharacteristic
54C2×C4⋊C4×C31—21no—
55C2×C4⋊C4×C31D411yescharacteristic
56C2×C22⋊C4×C31—21no—
57C2×C42×C31—21no—
58C2×C42×C31C2311yescharacteristic
59C31×#106—21no—
60C31×#106—21no—
61C31×C4⋊C8—21no—
62C31×C4⋊C8—21no—
63C31×C4⋊C8C2×C411yescharacteristic
64C31×C4⋊C8C2×C411yescharacteristic
65C31×#102—24no—
66C31×#102—21no—
67C31×#102—21no—
68C31×#102—21no—
69C31×#102—21no—
70C31×C22⋊C8—22no—
71C31×C22⋊C8—22no—
72C31×C22⋊C8—21no—
73C31×C22⋊C8—21no—
74C31×C22⋊C8D411yescharacteristic
75C31×C22⋊C8D411yescharacteristic
76C31×#97—21no—
77C31×#97—21no—
78C31×#97—21no—
79C31×#97D412yes—
80C4×C8×C31—21no—
81C31×#95—21no—
82C24×C31—21no—
83#41×C31—81no—
84#41×C31—81no—
85C2×Q8×C31—21no—
86C2×D4×C31—22no—
87C2×D4×C31—21no—
88C2×D4×C31—21no—
89C2×D4×C31—21no—
90C2×D4×C31—21no—
91C2×D4×C31—41no—
92C2×D4×C31—41no—
93C2×D4×C31C22⋊C411yescharacteristic
94C2×D4×C31C22⋊C411yescharacteristic
95C22×C4×C31—21no—
96C22×C4×C31—21no—
97C22×C4×C31—21no—
98C22×C4×C31—21no—
99C22×C4×C31—21no—
100C22×C4×C31—41no—
101C22×C4×C31—41no—
102C22×C4×C31—82no—
103C22×C4×C31C2×D411yescharacteristic
104C22×C4×C31C2×D411yescharacteristic
105C22×C4×C31#4111yescharacteristic
106D8×C31—42no—
107D8×C31—42no—
108M16×C31—82no—
109C2×C8×C31—22no—
110C2×C8×C31—21no—
111C2×C8×C31—21no—
112C2×C8×C31—21no—
113C2×C8×C31—21no—
114C2×C8×C31—22no—
115C2×C8×C31—41no—
116C2×C8×C31—41no—
117C2×C8×C31—82no—
118C4⋊C4×C31—21no—
119C4⋊C4×C31—22no—
120C4⋊C4×C31—21no—
121C4⋊C4×C31—21no—
122C4⋊C4×C31—41no—
123C4⋊C4×C31C22⋊C411yescharacteristic
124C4⋊C4×C31C22⋊C411yescharacteristic
125C22⋊C4×C31—21no—
126C22⋊C4×C31—21no—
127C22⋊C4×C31—21no—
128C22⋊C4×C31—21no—
129C22⋊C4×C31—41no—
130C22⋊C4×C31—41no—
131C42×C31—81no—
132C42×C31C22×C411yescharacteristic
133C42×C31C2×D411yescharacteristic
134C42×C31C2×D411yescharacteristic
135C42×C31#4111yescharacteristic
136#9163C3111yesmaximal, characteristic, direct product factor, Sylow
137C23×C31—21no—
138C23×C31—21no—
139C23×C31—42no—
140C23×C31—41no—
141C23×C31—41no—
142C23×C31—41no—
143C23×C31—81no—
144C23×C31#12111yescharacteristic
145Q8×C31—81no—
146D4×C31—21no—
147D4×C31—21no—
148D4×C31—21no—
149D4×C31—42no—
150D4×C31—41no—
151D4×C31—41no—
152D4×C31—81no—
153D4×C31—81no—
154D4×C31—81no—
155D4×C31—81no—
156D4×C31#10412yes—
157C2×C4×C31—21no—
158C2×C4×C31—21no—
159C2×C4×C31—21no—
160C2×C4×C31—21no—
161C2×C4×C31—21no—
162C2×C4×C31—21no—
163C2×C4×C31—41no—
164C2×C4×C31—42no—
165C2×C4×C31—42no—
166C2×C4×C31—42no—
167C2×C4×C31—41no—
168C2×C4×C31—81no—
169C2×C4×C31—81no—
170C2×C4×C31—82no—
171C2×C4×C31—81no—
172C2×C4×C31—81no—
173C2×C4×C31—81no—
174C2×C4×C31C2×C22⋊C411yescharacteristic
175C2×C4×C31C4×D411yescharacteristic
176C2×C4×C31C4×D411yescharacteristic
177C2×C4×C31#12011yescharacteristic
178C2×C4×C31#12111yescharacteristic
179C2×C4×C31#12311yescharacteristic
180C8×C31—42no—
181C8×C31—41no—
182C8×C31—42no—
183C8×C31—41no—
184C8×C31—41no—
185C8×C31—41no—
186#3109C2×C3111yescharacteristic
187#2974C2×C3111yescharacteristic, complemented
188#1762C2×C3111yescharacteristic, complemented
189#1530C2×C3111yescharacteristic, complemented
190#1502C2×C3111yescharacteristic, complemented
191#1302C2×C3111yescharacteristic, complemented
192#1285C2×C3111yescharacteristic, complemented
193C22×C31—21no—
194C22×C31—21no—
195C22×C31—22no—
196C22×C31—41no—
197C22×C31—41no—
198C22×C31—41no—
199C22×C31—41no—
200C22×C31—41no—
201C22×C31—82no—
202C22×C31—82no—
203C22×C31—81no—
204C22×C31—81no—
205C22×C31—81no—
206C22×C31#38611yescharacteristic
207C22×C31#47111yescharacteristic
208C22×C31#47211yescharacteristic
209C4×C31—21no—
210C4×C31—21no—
211C4×C31—21no—
212C4×C31—21no—
213C4×C31—21no—
214C4×C31—41no—
215C4×C31—41no—
216C4×C31—82no—
217C4×C31—81no—
218C4×C31C2×#10411yescharacteristic
219C4×C31#42111yescharacteristic
220#532C22×C3111yescharacteristic
221C2×C4×D4C22×C3111yescharacteristic
222#481—21no—
223#476C4×C3111yescharacteristic, complemented
224#476C4×C3111yescharacteristic, complemented
225#459C4×C3111yescharacteristic, complemented
226#459C4×C3111yescharacteristic, complemented
227#447—21no—
228#442—21no—
229#442—21no—
230#436—21no—
231#435—22no—
232C8×D4—21no—
233#432C22×C3111yescharacteristic
234#432C22×C3111yescharacteristic
235#431C22×C3111yescharacteristic
236C2×#102—21no—
237#407—21no—
238C2×C22⋊C8—21no—
239C2×#97C22×C3111yescharacteristic
240C4×C4⋊C4C22×C3111yescharacteristic
241#340—21no—
242#329—22no—
243#327—21no—
244#327—21no—
245C2×C31—21no—
246C2×C31—21no—
247C2×C31—42no—
248C2×C31—81no—
249C2×C31—161no—
250C2×C31#187111yescharacteristic
251C2×C31#190411yescharacteristic
252C2×C31#190711yescharacteristic
253C2×#41—21no—
254C22×D4D4×C3111yescharacteristic
255C23×C4—21no—
256C2×D8—21no—
257C2×D8—21no—
258C2×M16—22no—
259C22×C8—21no—
260C22×C8—22no—
261C4⋊Q8C2×C4×C3111yescharacteristic
262#127C2×C4×C3111yescharacteristic
263#124—21no—
264#121—21no—
265#121—21no—
266C4×D4—21no—
267C4×D4—21no—
268C4×D4—21no—
269C4×D4—21no—
270C4×D4C2×C4×C3111yescharacteristic
271C4×D4C2×C4×C3111yescharacteristic
272C4×D4D4×C3111yescharacteristic
273C4×D4D4×C3111yescharacteristic
274C2×C4⋊C4—21no—
275C2×C4⋊C4D4×C3111yescharacteristic
276C2×C22⋊C4—21no—
277C2×C42—21no—
278C2×C42C23×C3111yescharacteristic
279#106—21no—
280#106—21no—
281C4⋊C8—21no—
282C4⋊C8—21no—
283C4⋊C8C2×C4×C3111yescharacteristic
284C4⋊C8C2×C4×C3111yescharacteristic
285#102—24no—
286#102—21no—
287#102—21no—
288#102—21no—
289#102—21no—
290C22⋊C8—22no—
291C22⋊C8—22no—
292C22⋊C8—21no—
293C22⋊C8—21no—
294C22⋊C8D4×C3111yescharacteristic
295C22⋊C8D4×C3111yescharacteristic
296#97—21no—
297#97—21no—
298#97—21no—
299#97D4×C3112yes—
300C4×C8—21no—
301#95—21no—
302C31#916311yescharacteristic, direct product factor, Sylow
303C24—21no—
304#41—81no—
305#41—81no—
306C2×Q8—21no—
307C2×D4—22no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4C22⋊C4×C3111yescharacteristic
315C2×D4C22⋊C4×C3111yescharacteristic
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—82no—
324C22×C4C2×D4×C3111yescharacteristic
325C22×C4C2×D4×C3111yescharacteristic
326C22×C4#41×C3111yescharacteristic
327D8—42no—
328D8—42no—
329M16—82no—
330C2×C8—22no—
331C2×C8—21no—
332C2×C8—21no—
333C2×C8—21no—
334C2×C8—21no—
335C2×C8—22no—
336C2×C8—41no—
337C2×C8—41no—
338C2×C8—82no—
339C4⋊C4—21no—
340C4⋊C4—22no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—41no—
344C4⋊C4C22⋊C4×C3111yescharacteristic
345C4⋊C4C22⋊C4×C3111yescharacteristic
346C22⋊C4—21no—
347C22⋊C4—21no—
348C22⋊C4—21no—
349C22⋊C4—21no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C42—81no—
353C42C22×C4×C3111yescharacteristic
354C42C2×D4×C3111yescharacteristic
355C42C2×D4×C3111yescharacteristic
356C42#41×C3111yescharacteristic
357C23—21no—
358C23—21no—
359C23—42no—
360C23—41no—
361C23—41no—
362C23—41no—
363C23—81no—
364C23C31×#12111yescharacteristic
365Q8—81no—
366D4—21no—
367D4—21no—
368D4—21no—
369D4—42no—
370D4—41no—
371D4—41no—
372D4—81no—
373D4—81no—
374D4—81no—
375D4—81no—
376D4C31×#10412yes—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—41no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4—82no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4C2×C22⋊C4×C3111yescharacteristic
395C2×C4C4×D4×C3111yescharacteristic
396C2×C4C4×D4×C3111yescharacteristic
397C2×C4C31×#12011yescharacteristic
398C2×C4C31×#12111yescharacteristic
399C2×C4C31×#12311yescharacteristic
400C8—42no—
401C8—41no—
402C8—42no—
403C8—41no—
404C8—41no—
405C8—41no—
406C22—21no—
407C22—21no—
408C22—22no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—82no—
415C22—82no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22C31×#38611yescharacteristic
420C22C31×#47111yescharacteristic
421C22C31×#47211yescharacteristic
422C4—21no—
423C4—21no—
424C4—21no—
425C4—21no—
426C4—21no—
427C4—41no—
428C4—41no—
429C4—82no—
430C4—81no—
431C4C2×C31×#10411yescharacteristic
432C4C31×#42111yescharacteristic
433C2—21no—
434C2—21no—
435C2—42no—
436C2—81no—
437C2—161no—
438C2C31×#187111yescharacteristic
439C2C31×#190411yescharacteristic
440C2C31×#190711yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC42C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC31×#3109C2
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
2. C31×#2974C2semidirect
3. C31×#1762C2semidirect
4. C31×#1530C2semidirect
5. C31×#1502C2semidirect
6. C31×#1302C2semidirect
7. C31×#1285C2semidirect
11. C31×#476C4semidirect
12. C31×#476C4semidirect
13. C31×#459C4semidirect
14. C31×#459C4semidirect
136. #9163C31direct (N × H)
187. #2974C2×C31semidirect
188. #1762C2×C31semidirect
189. #1530C2×C31semidirect
190. #1502C2×C31semidirect
191. #1302C2×C31semidirect
192. #1285C2×C31semidirect
223. #476C4×C31semidirect
224. #476C4×C31semidirect
225. #459C4×C31semidirect
226. #459C4×C31semidirect
302. C31#9163direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#31092
C31×#29742
C31×#17622
C31×#15302
C31×#15022
C31×#13022
C31×#12852
#916331