Finite Group Databasebeta

← C31×#9243 #21466002

Subgroups — C31×#9243 #21466002

Order 7936.

514 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#463C211yesmaximal, characteristic
2C31×#2974C211yesmaximal, characteristic, complemented
3C31×#1527C211yesmaximal, characteristic, complemented
4C31×#1490C211yesmaximal, characteristic, complemented
5C31×#1469C211yesmaximal, characteristic, complemented
6C31×#1290C211yesmaximal, characteristic, complemented
7C31×#1283C211yesmaximal, characteristic, complemented
8C22×SD16×C31C411yescharacteristic
9C22×D8×C31C411yescharacteristic
10C2×C31×#124C2211yescharacteristic
11C2×C4×D4×C31C2211yescharacteristic
12C31×#463—21no—
13C31×#463—21no—
14C31×#463—21no—
15C31×#463—21no—
16C31×#436—21no—
17C31×#435—22no—
18C8×D4×C31—21no—
19C31×#432C2211yescharacteristic
20C31×#432C2211yescharacteristic
21C31×#431C2211yescharacteristic
22C2×C31×C4⋊C8C2211yescharacteristic
23C2×C31×#103C411yescharacteristic
24C2×C31×#102C411yescharacteristic
25C31×#407—21no—
26C2×C31×C22⋊C8—21no—
27C4×M16×C31C2211yescharacteristic
28C31×#329—22no—
29C31×D4⋊C8—21no—
30C31×D4⋊C8—21no—
31C31×#323—21no—
32C31×#323—21no—
33C22×Q8×C31C2×C411yescharacteristic
34C22×D4×C31C2×C411yescharacteristic
35C22×D4×C31C2×C411yescharacteristic
36C23×C4×C31—21no—
37C2×SD16×C31—21no—
38C2×SD16×C31—21no—
39C2×SD16×C31—42no—
40C2×D8×C31—21no—
41C2×D8×C31—21no—
42C2×D8×C31—42no—
43C2×M16×C31—22no—
44C2×M16×C31—21no—
45C22×C8×C31—22no—
46C22×C8×C31C2×C411yescharacteristic
47C22×C8×C31C2×C411yescharacteristic
48C31×#124—21no—
49C31×#124—21no—
50C31×#124—21no—
51C31×#124—21no—
52C4×D4×C31—21no—
53C4×D4×C31—21no—
54C4×D4×C31D411yescharacteristic
55C4×D4×C31D411yescharacteristic
56C4×D4×C31D411yescharacteristic
57C4×D4×C31D411yescharacteristic
58C2×C4⋊C4×C31C2×C411yescharacteristic
59C2×C22⋊C4×C31—21no—
60C2×C22⋊C4×C31—21no—
61C2×C22⋊C4×C31—21no—
62C2×C42×C31C2311yescharacteristic
63C31×C4⋊C8—21no—
64C31×C4⋊C8—21no—
65C31×C4⋊C8—21no—
66C31×C4⋊C8—21no—
67C31×C4⋊C8—21no—
68C31×#103—21no—
69C31×#103—21no—
70C31×#102—21no—
71C31×#102—21no—
72C31×C22⋊C8—22no—
73C31×C22⋊C8—22no—
74C31×C22⋊C8—21no—
75C31×C22⋊C8—21no—
76C31×C22⋊C8D411yescharacteristic
77C31×C22⋊C8D411yescharacteristic
78C31×#97—21no—
79C31×#97—21no—
80C31×#97D412yes—
81C4×C8×C31—21no—
82C4×C8×C31—21no—
83C24×C31—21no—
84C24×C31—21no—
85C2×Q8×C31—21no—
86C2×Q8×C31—21no—
87C2×Q8×C31—41no—
88C2×Q8×C31—41no—
89C2×D4×C31—22no—
90C2×D4×C31—21no—
91C2×D4×C31—21no—
92C2×D4×C31—21no—
93C2×D4×C31—41no—
94C2×D4×C31—41no—
95C2×D4×C31—41no—
96C2×D4×C31C22⋊C411yescharacteristic
97C2×D4×C31C22⋊C411yescharacteristic
98C22×C4×C31—21no—
99C22×C4×C31—21no—
100C22×C4×C31—21no—
101C22×C4×C31—21no—
102C22×C4×C31—21no—
103C22×C4×C31—21no—
104C22×C4×C31—82no—
105C22×C4×C31C22×C411yescharacteristic
106C22×C4×C31C2×D411yescharacteristic
107C22×C4×C31#4111yescharacteristic
108SD16×C31—42no—
109SD16×C31—42no—
110D8×C31—42no—
111D8×C31—42no—
112M16×C31—22no—
113M16×C31—41no—
114M16×C31—82no—
115C2×C8×C31—21no—
116C2×C8×C31—21no—
117C2×C8×C31—21no—
118C2×C8×C31—21no—
119C2×C8×C31—22no—
120C2×C8×C31—41no—
121C2×C8×C31—41no—
122C2×C8×C31—41no—
123C2×C8×C31—41no—
124C2×C8×C31—82no—
125C4⋊C4×C31—21no—
126C4⋊C4×C31C22⋊C411yescharacteristic
127C4⋊C4×C31C22⋊C411yescharacteristic
128C22⋊C4×C31—21no—
129C22⋊C4×C31—21no—
130C22⋊C4×C31—21no—
131C22⋊C4×C31—21no—
132C22⋊C4×C31—41no—
133C22⋊C4×C31—41no—
134C22⋊C4×C31—41no—
135C22⋊C4×C31—41no—
136C42×C31C2×D411yescharacteristic
137C42×C31C2×D411yescharacteristic
138C42×C31C2×D411yescharacteristic
139C42×C31#4111yescharacteristic
140#9243C3111yesmaximal, characteristic, direct product factor, Sylow
141C23×C31—21no—
142C23×C31—21no—
143C23×C31—42no—
144C23×C31—41no—
145C23×C31—41no—
146C23×C31—41no—
147C23×C31—41no—
148C23×C31—41no—
149C23×C31—81no—
150C23×C31—81no—
151C23×C31—81no—
152C23×C31C4×D411yescharacteristic
153Q8×C31—41no—
154Q8×C31—41no—
155Q8×C31—81no—
156D4×C31—21no—
157D4×C31—21no—
158D4×C31—21no—
159D4×C31—42no—
160D4×C31—41no—
161D4×C31—41no—
162D4×C31—81no—
163D4×C31#10012yes—
164C2×C4×C31—21no—
165C2×C4×C31—21no—
166C2×C4×C31—21no—
167C2×C4×C31—21no—
168C2×C4×C31—21no—
169C2×C4×C31—21no—
170C2×C4×C31—41no—
171C2×C4×C31—42no—
172C2×C4×C31—42no—
173C2×C4×C31—41no—
174C2×C4×C31—81no—
175C2×C4×C31—81no—
176C2×C4×C31—81no—
177C2×C4×C31—81no—
178C2×C4×C31C2×C22⋊C411yescharacteristic
179C2×C4×C31C4×D411yescharacteristic
180C2×C4×C31#12011yescharacteristic
181C2×C4×C31#12111yescharacteristic
182C2×C4×C31#12111yescharacteristic
183C2×C4×C31#12311yescharacteristic
184C8×C31—41no—
185C8×C31—42no—
186C8×C31—41no—
187C8×C31—42no—
188C8×C31—41no—
189C8×C31—41no—
190C8×C31—81no—
191C2×#463C2×C3111yescharacteristic
192#2974C2×C3111yescharacteristic, complemented
193#1527C2×C3111yescharacteristic, complemented
194#1490C2×C3111yescharacteristic, complemented
195#1469C2×C3111yescharacteristic, complemented
196#1290C2×C3111yescharacteristic, complemented
197#1283C2×C3111yescharacteristic, complemented
198C22×C31—21no—
199C22×C31—21no—
200C22×C31—22no—
201C22×C31—41no—
202C22×C31—41no—
203C22×C31—41no—
204C22×C31—41no—
205C22×C31—41no—
206C22×C31—82no—
207C22×C31—82no—
208C22×C31—81no—
209C22×C31—81no—
210C22×C31—81no—
211C22×C31—161no—
212C22×C31—161no—
213C22×C31#38611yescharacteristic
214C22×C31#44311yescharacteristic
215C22×C31#44411yescharacteristic
216C4×C31—21no—
217C4×C31—21no—
218C4×C31—21no—
219C4×C31—21no—
220C4×C31—21no—
221C4×C31—41no—
222C4×C31—41no—
223C4×C31—81no—
224C4×C31C2×#10011yescharacteristic
225C4×C31#41311yescharacteristic
226C22×SD16C4×C3111yescharacteristic
227C22×D8C4×C3111yescharacteristic
228C2×#124C22×C3111yescharacteristic
229C2×C4×D4C22×C3111yescharacteristic
230#463—21no—
231#463—21no—
232#463—21no—
233#463—21no—
234#436—21no—
235#435—22no—
236C8×D4—21no—
237#432C22×C3111yescharacteristic
238#432C22×C3111yescharacteristic
239#431C22×C3111yescharacteristic
240C2×C4⋊C8C22×C3111yescharacteristic
241C2×#103C4×C3111yescharacteristic
242C2×#102C4×C3111yescharacteristic
243#407—21no—
244C2×C22⋊C8—21no—
245C4×M16C22×C3111yescharacteristic
246#329—22no—
247D4⋊C8—21no—
248D4⋊C8—21no—
249#323—21no—
250#323—21no—
251C2×C31—21no—
252C2×C31—21no—
253C2×C31—42no—
254C2×C31—81no—
255C2×C31—161no—
256C2×C31#187611yescharacteristic
257C2×C31#190011yescharacteristic
258C2×C31#190411yescharacteristic
259C22×Q8C2×C4×C3111yescharacteristic
260C22×D4C2×C4×C3111yescharacteristic
261C22×D4C2×C4×C3111yescharacteristic
262C23×C4—21no—
263C2×SD16—21no—
264C2×SD16—21no—
265C2×SD16—42no—
266C2×D8—21no—
267C2×D8—21no—
268C2×D8—42no—
269C2×M16—22no—
270C2×M16—21no—
271C22×C8—22no—
272C22×C8C2×C4×C3111yescharacteristic
273C22×C8C2×C4×C3111yescharacteristic
274#124—21no—
275#124—21no—
276#124—21no—
277#124—21no—
278C4×D4—21no—
279C4×D4—21no—
280C4×D4D4×C3111yescharacteristic
281C4×D4D4×C3111yescharacteristic
282C4×D4D4×C3111yescharacteristic
283C4×D4D4×C3111yescharacteristic
284C2×C4⋊C4C2×C4×C3111yescharacteristic
285C2×C22⋊C4—21no—
286C2×C22⋊C4—21no—
287C2×C22⋊C4—21no—
288C2×C42C23×C3111yescharacteristic
289C4⋊C8—21no—
290C4⋊C8—21no—
291C4⋊C8—21no—
292C4⋊C8—21no—
293C4⋊C8—21no—
294#103—21no—
295#103—21no—
296#102—21no—
297#102—21no—
298C22⋊C8—22no—
299C22⋊C8—22no—
300C22⋊C8—21no—
301C22⋊C8—21no—
302C22⋊C8D4×C3111yescharacteristic
303C22⋊C8D4×C3111yescharacteristic
304#97—21no—
305#97—21no—
306#97D4×C3112yes—
307C4×C8—21no—
308C4×C8—21no—
309C31#924311yescharacteristic, direct product factor, Sylow
310C24—21no—
311C24—21no—
312C2×Q8—21no—
313C2×Q8—21no—
314C2×Q8—41no—
315C2×Q8—41no—
316C2×D4—22no—
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4C22⋊C4×C3111yescharacteristic
324C2×D4C22⋊C4×C3111yescharacteristic
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—82no—
332C22×C4C22×C4×C3111yescharacteristic
333C22×C4C2×D4×C3111yescharacteristic
334C22×C4#41×C3111yescharacteristic
335SD16—42no—
336SD16—42no—
337D8—42no—
338D8—42no—
339M16—22no—
340M16—41no—
341M16—82no—
342C2×C8—21no—
343C2×C8—21no—
344C2×C8—21no—
345C2×C8—21no—
346C2×C8—22no—
347C2×C8—41no—
348C2×C8—41no—
349C2×C8—41no—
350C2×C8—41no—
351C2×C8—82no—
352C4⋊C4—21no—
353C4⋊C4C22⋊C4×C3111yescharacteristic
354C4⋊C4C22⋊C4×C3111yescharacteristic
355C22⋊C4—21no—
356C22⋊C4—21no—
357C22⋊C4—21no—
358C22⋊C4—21no—
359C22⋊C4—41no—
360C22⋊C4—41no—
361C22⋊C4—41no—
362C22⋊C4—41no—
363C42C2×D4×C3111yescharacteristic
364C42C2×D4×C3111yescharacteristic
365C42C2×D4×C3111yescharacteristic
366C42#41×C3111yescharacteristic
367C23—21no—
368C23—21no—
369C23—42no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23—41no—
375C23—81no—
376C23—81no—
377C23—81no—
378C23C4×D4×C3111yescharacteristic
379Q8—41no—
380Q8—41no—
381Q8—81no—
382D4—21no—
383D4—21no—
384D4—21no—
385D4—42no—
386D4—41no—
387D4—41no—
388D4—81no—
389D4C31×#10012yes—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—41no—
400C2×C4—81no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4C2×C22⋊C4×C3111yescharacteristic
405C2×C4C4×D4×C3111yescharacteristic
406C2×C4C31×#12011yescharacteristic
407C2×C4C31×#12111yescharacteristic
408C2×C4C31×#12111yescharacteristic
409C2×C4C31×#12311yescharacteristic
410C8—41no—
411C8—42no—
412C8—41no—
413C8—42no—
414C8—41no—
415C8—41no—
416C8—81no—
417C22—21no—
418C22—21no—
419C22—22no—
420C22—41no—
421C22—41no—
422C22—41no—
423C22—41no—
424C22—41no—
425C22—82no—
426C22—82no—
427C22—81no—
428C22—81no—
429C22—81no—
430C22—161no—
431C22—161no—
432C22C31×#38611yescharacteristic
433C22C31×#44311yescharacteristic
434C22C31×#44411yescharacteristic
435C4—21no—
436C4—21no—
437C4—21no—
438C4—21no—
439C4—21no—
440C4—41no—
441C4—41no—
442C4—81no—
443C4C2×C31×#10011yescharacteristic
444C4C31×#41311yescharacteristic
445C2—21no—
446C2—21no—
447C2—42no—
448C2—81no—
449C2—161no—
450C2C31×#187611yescharacteristic
451C2C31×#190011yescharacteristic
452C2C31×#190411yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC22×D8×C31C4
LCSG ▷ C22×C4 ▷ 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×#1527C2semidirect
4. C31×#1490C2semidirect
5. C31×#1469C2semidirect
6. C31×#1290C2semidirect
7. C31×#1283C2semidirect
140. #9243C31direct (N × H)
192. #2974C2×C31semidirect
193. #1527C2×C31semidirect
194. #1490C2×C31semidirect
195. #1469C2×C31semidirect
196. #1290C2×C31semidirect
197. #1283C2×C31semidirect
309. C31#9243direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4632
C31×#29742
C31×#15272
C31×#14902
C31×#14692
C31×#12902
C31×#12832
#924331