Finite Group Databasebeta

← C31×#8873 #21465632

Subgroups — C31×#8873 #21465632

Order 7936.

702 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2325C211yesmaximal, characteristic
2C31×#1874C211yesmaximal, characteristic
3C31×#1853C211yesmaximal, characteristic, complemented
4C2×C31×#327C211yesmaximal, characteristic
5C31×#1444C211yesmaximal, characteristic, complemented
6C31×#1294C211yesmaximal, characteristic, complemented
7C31×#1280C211yesmaximal, characteristic, complemented
8C2×C31×#121C2211yescharacteristic
9C2×C4×D4×C31—21no—
10C22×C4⋊C4×C31—21no—
11C22×C4⋊C4×C31C2211yescharacteristic
12C2×C31×#106—21no—
13C2×C31×#102—21no—
14C2×C31×C22⋊C8C2211yescharacteristic
15C2×C31×C22⋊C8C2211yescharacteristic
16C31×#388—21no—
17C31×#387—21no—
18C31×#386—21no—
19C31×#386—21no—
20C31×#385—21no—
21C31×#380C2211yescharacteristic
22C2×C31×#95—21no—
23C2×C31×#95C2211yescharacteristic
24C2×C31×#95C2211yescharacteristic
25C31×#340—21no—
26C31×#340—21no—
27C31×#327C414yescomplemented
28C22×D4×C31—21no—
29C22×D4×C31D411yescharacteristic
30C23×C4×C31—21no—
31C23×C4×C31—21no—
32C23×C4×C31—21no—
33C23×C4×C31D411yescharacteristic
34C23×C4×C31D411yescharacteristic
35C23×C4×C31C2311yescharacteristic
36C22×C8×C31—21no—
37C22×C8×C31—21no—
38C31×#121—21no—
39C31×#121—21no—
40C31×#121C2×C412yes—
41C31×#121Q812yes—
42C4×D4×C31—42no—
43C4×D4×C31—42no—
44C2×C4⋊C4×C31—21no—
45C2×C4⋊C4×C31—21no—
46C2×C4⋊C4×C31—21no—
47C2×C4⋊C4×C31—42no—
48C2×C4⋊C4×C31—42no—
49C2×C4⋊C4×C31—42no—
50C2×C4⋊C4×C31—42no—
51C2×C4⋊C4×C31D411yescharacteristic
52C2×C4⋊C4×C31D411yescharacteristic
53C2×C4⋊C4×C31D411yescharacteristic
54C2×C22⋊C4×C31—21no—
55C2×C22⋊C4×C31—21no—
56C2×C22⋊C4×C31—21no—
57C2×C22⋊C4×C31—21no—
58C2×C22⋊C4×C31—21no—
59C2×C42×C31—21no—
60C31×#106—42no—
61C31×#102—42no—
62C31×C22⋊C8—21no—
63C31×C22⋊C8—21no—
64C31×C22⋊C8—21no—
65C31×C22⋊C8C2×C412yescomplemented
66C31×#95—21no—
67C31×#95—21no—
68C31×#95—21no—
69C31×#95—21no—
70C31×#95—21no—
71C31×#95—21no—
72C31×#95—42no—
73C31×#95C2×C412yescomplemented
74C24×C31—21no—
75C24×C31C2×D411yescharacteristic
76C2×D4×C31—22no—
77C2×D4×C31—22no—
78C2×D4×C31—21no—
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×C31C4⋊C412yescomplemented
86C22×C4×C31—22no—
87C22×C4×C31—22no—
88C22×C4×C31—22no—
89C22×C4×C31—21no—
90C22×C4×C31—21no—
91C22×C4×C31—21no—
92C22×C4×C31—22no—
93C22×C4×C31—21no—
94C22×C4×C31—21no—
95C22×C4×C31—21no—
96C22×C4×C31—21no—
97C22×C4×C31—21no—
98C22×C4×C31—41no—
99C22×C4×C31—41no—
100C22×C4×C31—42no—
101C22×C4×C31—41no—
102C22×C4×C31—41no—
103C22×C4×C31—41no—
104C22×C4×C31—41no—
105C22×C4×C31—41no—
106C22×C4×C31—41no—
107C22×C4×C31—41no—
108C22×C4×C31—41no—
109C22×C4×C31—41no—
110C22×C4×C31—41no—
111C22×C4×C31—41no—
112C22×C4×C31—41no—
113C22×C4×C31—41no—
114C22×C4×C31—41no—
115C22×C4×C31—81no—
116C22×C4×C31—81no—
117C22×C4×C31SD1612yes—
118C22×C4×C31C22×C411yescharacteristic
119C22×C4×C31C2×D411yescharacteristic
120C22×C4×C31C2×D411yescharacteristic
121C22×C4×C31C2×Q811yescharacteristic
122C22×C4×C31#4111yescharacteristic
123C22×C4×C31#4111yescharacteristic
124C2×C8×C31—22no—
125C2×C8×C31—41no—
126C2×C8×C31—41no—
127C2×C8×C31—41no—
128C2×C8×C31—41no—
129C2×C8×C31—41no—
130C4⋊C4×C31—21no—
131C4⋊C4×C31—22no—
132C4⋊C4×C31—22no—
133C4⋊C4×C31—41no—
134C4⋊C4×C31—41no—
135C4⋊C4×C31—42no—
136C4⋊C4×C31—41no—
137C4⋊C4×C31—41no—
138C4⋊C4×C31—48no—
139C4⋊C4×C31C4⋊C412yescomplemented
140C22⋊C4×C31—22no—
141C22⋊C4×C31—22no—
142C22⋊C4×C31—42no—
143C22⋊C4×C31—41no—
144C22⋊C4×C31—41no—
145C22⋊C4×C31—81no—
146C22⋊C4×C31—81no—
147C42×C31—42no—
148#8873C3111yesmaximal, characteristic, direct product factor, Sylow
149C23×C31—21no—
150C23×C31—21no—
151C23×C31—21no—
152C23×C31—21no—
153C23×C31—22no—
154C23×C31—41no—
155C23×C31—41no—
156C23×C31—41no—
157C23×C31—41no—
158C23×C31—41no—
159C23×C31—41no—
160C23×C31C4×D411yescharacteristic
161C23×C31#12011yescharacteristic
162C23×C31C22⋊Q811yescharacteristic
163C23×C31C2×SD1611yescharacteristic
164C23×C31#13511yescharacteristic
165C23×C31AGL(1,ℤ/8)11yescharacteristic
166C23×C31AGL(1,ℤ/8)11yescharacteristic
167D4×C31—42no—
168D4×C31—42no—
169D4×C31—42no—
170D4×C31—42no—
171D4×C31—42no—
172D4×C31—81no—
173C2×C4×C31—21no—
174C2×C4×C31—21no—
175C2×C4×C31—21no—
176C2×C4×C31—21no—
177C2×C4×C31—24no—
178C2×C4×C31—22no—
179C2×C4×C31—22no—
180C2×C4×C31—41no—
181C2×C4×C31—41no—
182C2×C4×C31—41no—
183C2×C4×C31—41no—
184C2×C4×C31—42no—
185C2×C4×C31—42no—
186C2×C4×C31—42no—
187C2×C4×C31—42no—
188C2×C4×C31—42no—
189C2×C4×C31—42no—
190C2×C4×C31—41no—
191C2×C4×C31—41no—
192C2×C4×C31—41no—
193C2×C4×C31—41no—
194C2×C4×C31—42no—
195C2×C4×C31—42no—
196C2×C4×C31—42no—
197C2×C4×C31—42no—
198C2×C4×C31—41no—
199C2×C4×C31—41no—
200C2×C4×C31—41no—
201C2×C4×C31—41no—
202C2×C4×C31—41no—
203C2×C4×C31—41no—
204C2×C4×C31—41no—
205C2×C4×C31—41no—
206C2×C4×C31—42no—
207C2×C4×C31—41no—
208C2×C4×C31—81no—
209C2×C4×C31—84no—
210C2×C4×C31—81no—
211C2×C4×C31—81no—
212C2×C4×C31—81no—
213C2×C4×C31—81no—
214C2×C4×C31—81no—
215C2×C4×C31C2×C4⋊C411yescharacteristic
216C2×C4×C31C4×D411yescharacteristic
217C2×C4×C31C22⋊Q811yescharacteristic
218C2×C4×C31#12311yescharacteristic
219C8×C31—42no—
220C8×C31—81no—
221#2325C2×C3111yescharacteristic
222#1874C2×C3111yescharacteristic
223#1853C2×C3111yescharacteristic, complemented
224C2×#327C2×C3111yescharacteristic
225#1444C2×C3111yescharacteristic, complemented
226#1294C2×C3111yescharacteristic, complemented
227#1280C2×C3111yescharacteristic, complemented
228C22×C31—21no—
229C22×C31—21no—
230C22×C31—21no—
231C22×C31—21no—
232C22×C31—21no—
233C22×C31—21no—
234C22×C31—21no—
235C22×C31—21no—
236C22×C31—21no—
237C22×C31—21no—
238C22×C31—21no—
239C22×C31—21no—
240C22×C31—42no—
241C22×C31—42no—
242C22×C31—42no—
243C22×C31—81no—
244C22×C31—81no—
245C22×C31—81no—
246C22×C31—81no—
247C22×C31#38511yescharacteristic
248C22×C31C4×SD1611yescharacteristic
249C22×C31#44211yescharacteristic
250C22×C31#44911yescharacteristic
251C22×C31#45011yescharacteristic
252C22×C31#45311yescharacteristic
253C22×C31#45611yescharacteristic
254C22×C31B(4,𝔽2)11yescharacteristic
255C22×C31#45811yescharacteristic
256C22×C31#47611yescharacteristic
257C22×C31#47811yescharacteristic
258C4×C31—21no—
259C4×C31—21no—
260C4×C31—21no—
261C4×C31—21no—
262C4×C31—44no—
263C4×C31—42no—
264C4×C31—42no—
265C4×C31—81no—
266C4×C31—82no—
267C4×C31—81no—
268C4×C31—81no—
269C2×#121C22×C3111yescharacteristic
270C2×C4×D4—21no—
271C22×C4⋊C4—21no—
272C22×C4⋊C4C22×C3111yescharacteristic
273C2×#106—21no—
274C2×#102—21no—
275C2×C22⋊C8C22×C3111yescharacteristic
276C2×C22⋊C8C22×C3111yescharacteristic
277#388—21no—
278#387—21no—
279#386—21no—
280#386—21no—
281#385—21no—
282#380C22×C3111yescharacteristic
283C2×#95—21no—
284C2×#95C22×C3111yescharacteristic
285C2×#95C22×C3111yescharacteristic
286#340—21no—
287#340—21no—
288#327C4×C3114yescomplemented
289C2×C31—21no—
290C2×C31—21no—
291C2×C31—21no—
292C2×C31—21no—
293C2×C31—82no—
294C2×C31#160011yescharacteristic
295C2×C31#160411yescharacteristic
296C2×C31#160911yescharacteristic
297C2×C31#161311yescharacteristic
298C2×C31#185911yescharacteristic
299C2×C31#186411yescharacteristic
300C2×C31#186711yescharacteristic
301C22×D4—21no—
302C22×D4D4×C3111yescharacteristic
303C23×C4—21no—
304C23×C4—21no—
305C23×C4—21no—
306C23×C4D4×C3111yescharacteristic
307C23×C4D4×C3111yescharacteristic
308C23×C4C23×C3111yescharacteristic
309C22×C8—21no—
310C22×C8—21no—
311#121—21no—
312#121—21no—
313#121C2×C4×C3112yes—
314#121Q8×C3112yes—
315C4×D4—42no—
316C4×D4—42no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4D4×C3111yescharacteristic
325C2×C4⋊C4D4×C3111yescharacteristic
326C2×C4⋊C4D4×C3111yescharacteristic
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C42—21no—
333#106—42no—
334#102—42no—
335C22⋊C8—21no—
336C22⋊C8—21no—
337C22⋊C8—21no—
338C22⋊C8C2×C4×C3112yescomplemented
339#95—21no—
340#95—21no—
341#95—21no—
342#95—21no—
343#95—21no—
344#95—21no—
345#95—42no—
346#95C2×C4×C3112yescomplemented
347C31#887311yescharacteristic, direct product factor, Sylow
348C24—21no—
349C24C2×D4×C3111yescharacteristic
350C2×D4—22no—
351C2×D4—22no—
352C2×D4—21no—
353C2×D4—41no—
354C2×D4—41no—
355C2×D4—41no—
356C2×D4—41no—
357C2×D4—41no—
358C2×D4—41no—
359C2×D4C4⋊C4×C3112yescomplemented
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—22no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4—42no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4—41no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4—41no—
389C22×C4—81no—
390C22×C4—81no—
391C22×C4SD16×C3112yes—
392C22×C4C22×C4×C3111yescharacteristic
393C22×C4C2×D4×C3111yescharacteristic
394C22×C4C2×D4×C3111yescharacteristic
395C22×C4C2×Q8×C3111yescharacteristic
396C22×C4#41×C3111yescharacteristic
397C22×C4#41×C3111yescharacteristic
398C2×C8—22no—
399C2×C8—41no—
400C2×C8—41no—
401C2×C8—41no—
402C2×C8—41no—
403C2×C8—41no—
404C4⋊C4—21no—
405C4⋊C4—22no—
406C4⋊C4—22no—
407C4⋊C4—41no—
408C4⋊C4—41no—
409C4⋊C4—41no—
410C4⋊C4—41no—
411C4⋊C4—42no—
412C4⋊C4—48no—
413C4⋊C4C4⋊C4×C3112yescomplemented
414C22⋊C4—22no—
415C22⋊C4—22no—
416C22⋊C4—42no—
417C22⋊C4—41no—
418C22⋊C4—41no—
419C22⋊C4—81no—
420C22⋊C4—81no—
421C42—42no—
422C23—21no—
423C23—21no—
424C23—21no—
425C23—21no—
426C23—22no—
427C23—41no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23C4×D4×C3111yescharacteristic
434C23C31×#12011yescharacteristic
435C23C31×C22⋊Q811yescharacteristic
436C23C2×SD16×C3111yescharacteristic
437C23C31×#13511yescharacteristic
438C23C31×AGL(1,ℤ/8)11yescharacteristic
439C23C31×AGL(1,ℤ/8)11yescharacteristic
440D4—42no—
441D4—42no—
442D4—42no—
443D4—42no—
444D4—42no—
445D4—81no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—24no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—42no—
480C2×C4—41no—
481C2×C4—81no—
482C2×C4—84no—
483C2×C4—81no—
484C2×C4—81no—
485C2×C4—81no—
486C2×C4—81no—
487C2×C4—81no—
488C2×C4C2×C4⋊C4×C3111yescharacteristic
489C2×C4C4×D4×C3111yescharacteristic
490C2×C4C31×C22⋊Q811yescharacteristic
491C2×C4C31×#12311yescharacteristic
492C8—42no—
493C8—81no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—42no—
507C22—42no—
508C22—42no—
509C22—81no—
510C22—81no—
511C22—81no—
512C22—81no—
513C22C31×#38511yescharacteristic
514C22C4×SD16×C3111yescharacteristic
515C22C31×#44211yescharacteristic
516C22C31×#44911yescharacteristic
517C22C31×#45011yescharacteristic
518C22C31×#45311yescharacteristic
519C22C31×#45611yescharacteristic
520C22C31×B(4,𝔽2)11yescharacteristic
521C22C31×#45811yescharacteristic
522C22C31×#47611yescharacteristic
523C22C31×#47811yescharacteristic
524C4—21no—
525C4—21no—
526C4—21no—
527C4—21no—
528C4—44no—
529C4—42no—
530C4—42no—
531C4—81no—
532C4—82no—
533C4—81no—
534C4—81no—
535C2—21no—
536C2—21no—
537C2—21no—
538C2—21no—
539C2—82no—
540C2C31×#160011yescharacteristic
541C2C31×#160411yescharacteristic
542C2C31×#160911yescharacteristic
543C2C31×#161311yescharacteristic
544C2C31×#185911yescharacteristic
545C2C31×#186411yescharacteristic
546C2C31×#186711yescharacteristic
subgroupG/H
center, socleC23×C31#120
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC2×C31×#121C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#1853C2semidirect
5. C31×#1444C2semidirect
6. C31×#1294C2semidirect
7. C31×#1280C2semidirect
27. C31×#327C4semidirect
65. C31×C22⋊C8C2×C4semidirect
73. C31×#95C2×C4semidirect
85. C2×D4×C31C4⋊C4semidirect
139. C4⋊C4×C31C4⋊C4semidirect
148. #8873C31direct (N × H)
223. #1853C2×C31semidirect
225. #1444C2×C31semidirect
226. #1294C2×C31semidirect
227. #1280C2×C31semidirect
288. #327C4×C31semidirect
338. C22⋊C8C2×C4×C31semidirect
346. #95C2×C4×C31semidirect
347. C31#8873direct (N × H)
359. C2×D4C4⋊C4×C31semidirect
413. C4⋊C4C4⋊C4×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#23252
C31×#18742
C31×#18532
C2×C31×#3272
C31×#14442
C31×#12942
C31×#12802
#887331