Finite Group Databasebeta

← C31×#9343 #21466102

Subgroups — C31×#9343 #21466102

Order 7936.

576 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3192C211yesmaximal, characteristic
2C31×#2377C211yesmaximal, characteristic, complemented
3C31×#1964C211yesmaximal, characteristic, complemented
4C31×#1510C211yesmaximal, characteristic, complemented
5C31×#1507C211yesmaximal, characteristic, complemented
6C31×#1305C211yesmaximal, characteristic, complemented
7C31×#1284C211yesmaximal, characteristic, complemented
8C2×C31×#121C2211yescharacteristic
9C2×C31×#121C2211yescharacteristic
10C31×#481—21no—
11C31×#481C412yescomplemented
12C31×#469—22no—
13C31×#447—21no—
14C31×#447C412yescomplemented
15C2×C31×#99—21no—
16C2×C31×#99—21no—
17C31×#407C2211yescharacteristic
18C31×#407C2211yescharacteristic
19C31×#390—21no—
20C31×#388—21no—
21C31×#387—21no—
22C31×#386—21no—
23C31×#386—21no—
24C31×#385—21no—
25C31×#381C2211yescharacteristic
26C31×#380C2211yescharacteristic
27C4×C22⋊C4×C31C2211yescharacteristic
28C31×#327—22no—
29C31×#327—21no—
30C31×#327—21no—
31C22×D4×C31—21no—
32C22×D4×C31—21no—
33C22×D4×C31C2×C411yescharacteristic, complemented
34C22×D4×C31D411yescharacteristic
35C23×C4×C31—21no—
36C23×C4×C31C2311yescharacteristic
37C2×D8×C31—22no—
38C2×M16×C31—21no—
39C2×M16×C31—21no—
40C31×#121—21no—
41C31×#121—21no—
42C31×#121—21no—
43C31×#121—21no—
44C31×#121—21no—
45C31×#121—21no—
46C31×#121C2×C412yes—
47C31×#121D412yes—
48C2×C4⋊C4×C31—21no—
49C2×C4⋊C4×C31—21no—
50C2×C4⋊C4×C31C2×C411yescharacteristic, complemented
51C2×C4⋊C4×C31D411yescharacteristic
52C2×C22⋊C4×C31—21no—
53C2×C22⋊C4×C31—21no—
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×C22⋊C4×C31D411yescharacteristic
60C2×C22⋊C4×C31D411yescharacteristic
61C2×C42×C31—21no—
62C2×C42×C31—21no—
63C31×#106—22no—
64C31×#102—22no—
65C31×#102—22no—
66C31×#99—42no—
67C31×#99—42no—
68C31×C22⋊C8—21no—
69C31×C22⋊C8—21no—
70C31×C22⋊C8—21no—
71C31×C22⋊C8C2×C412yescomplemented
72C31×#95—21no—
73C31×#95—21no—
74C31×#95—21no—
75C31×#95—21no—
76C31×#95—21no—
77C31×#95D411yescharacteristic
78C31×#95D411yescharacteristic
79C24×C31—21no—
80C24×C31—21no—
81C24×C31C2×D411yescharacteristic
82C2×D4×C31—22no—
83C2×D4×C31—22no—
84C2×D4×C31—21no—
85C2×D4×C31—21no—
86C2×D4×C31—21no—
87C2×D4×C31—41no—
88C2×D4×C31—41no—
89C2×D4×C31—41no—
90C2×D4×C31—41no—
91C2×D4×C31—41no—
92C2×D4×C31—41no—
93C2×D4×C31—81no—
94C2×D4×C31—81no—
95C2×D4×C31—81no—
96C2×D4×C31—81no—
97C2×D4×C31C22⋊C412yes—
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—41no—
105C22×C4×C31—81no—
106C22×C4×C31—81no—
107C22×C4×C31—81no—
108C22×C4×C31—81no—
109C22×C4×C31C22×C411yescharacteristic
110C22×C4×C31C2×D411yescharacteristic
111C22×C4×C31C2×D411yescharacteristic
112C22×C4×C31C2×D411yescharacteristic
113C22×C4×C31#4111yescharacteristic
114C22×C4×C31#4111yescharacteristic
115D8×C31—82no—
116M16×C31—81no—
117M16×C31—81no—
118C2×C8×C31—22no—
119C2×C8×C31—41no—
120C4⋊C4×C31—21no—
121C4⋊C4×C31—21no—
122C4⋊C4×C31—21no—
123C4⋊C4×C31—81no—
124C4⋊C4×C31—81no—
125C4⋊C4×C31C22⋊C412yes—
126C22⋊C4×C31—22no—
127C22⋊C4×C31—22no—
128C22⋊C4×C31—22no—
129C22⋊C4×C31—41no—
130C22⋊C4×C31—41no—
131C22⋊C4×C31—41no—
132C22⋊C4×C31—41no—
133C22⋊C4×C31—41no—
134C22⋊C4×C31—81no—
135C22⋊C4×C31—81no—
136C22⋊C4×C31—81no—
137C22⋊C4×C31—81no—
138C42×C31—81no—
139C42×C31—81no—
140#9343C3111yesmaximal, characteristic, direct product factor, Sylow
141C23×C31—21no—
142C23×C31—21no—
143C23×C31—22no—
144C23×C31—41no—
145C23×C31—41no—
146C23×C31—41no—
147C23×C31—41no—
148C23×C31—41no—
149C23×C31—41no—
150C23×C31—41no—
151C23×C31—41no—
152C23×C31—41no—
153C23×C31—41no—
154C23×C31—41no—
155C23×C31—81no—
156C23×C31—81no—
157C23×C31C4×D411yescharacteristic
158C23×C31#12011yescharacteristic
159C23×C31#12111yescharacteristic
160D4×C31—42no—
161D4×C31—42no—
162D4×C31—81no—
163D4×C31—81no—
164D4×C31—82no—
165D4×C31—82no—
166D4×C31—81no—
167D4×C31—81no—
168D4×C31—81no—
169D4×C31—81no—
170C2×C4×C31—22no—
171C2×C4×C31—41no—
172C2×C4×C31—41no—
173C2×C4×C31—41no—
174C2×C4×C31—41no—
175C2×C4×C31—41no—
176C2×C4×C31—41no—
177C2×C4×C31—41no—
178C2×C4×C31—41no—
179C2×C4×C31—41no—
180C2×C4×C31—41no—
181C2×C4×C31—42no—
182C2×C4×C31—41no—
183C2×C4×C31—41no—
184C2×C4×C31—41no—
185C2×C4×C31—41no—
186C2×C4×C31—41no—
187C2×C4×C31—41no—
188C2×C4×C31—41no—
189C2×C4×C31—41no—
190C2×C4×C31—41no—
191C2×C4×C31—41no—
192C2×C4×C31—41no—
193C2×C4×C31—41no—
194C2×C4×C31—41no—
195C2×C4×C31—81no—
196C2×C4×C31—81no—
197C2×C4×C31—84no—
198C2×C4×C31C2×C22⋊C411yescharacteristic
199C2×C4×C31C4×D411yescharacteristic
200C2×C4×C31#12111yescharacteristic
201C2×C4×C31#12311yescharacteristic
202C8×C31—42no—
203C8×C31—81no—
204#3192C2×C3111yescharacteristic
205#2377C2×C3111yescharacteristic, complemented
206#1964C2×C3111yescharacteristic, complemented
207#1510C2×C3111yescharacteristic, complemented
208#1507C2×C3111yescharacteristic, complemented
209#1305C2×C3111yescharacteristic, complemented
210#1284C2×C3111yescharacteristic, complemented
211C22×C31—21no—
212C22×C31—21no—
213C22×C31—21no—
214C22×C31—21no—
215C22×C31—21no—
216C22×C31—21no—
217C22×C31—21no—
218C22×C31—21no—
219C22×C31—42no—
220C22×C31—42no—
221C22×C31—42no—
222C22×C31—81no—
223C22×C31—81no—
224C22×C31—81no—
225C22×C31—81no—
226C22×C31—81no—
227C22×C31—81no—
228C22×C31—81no—
229C22×C31—81no—
230C22×C31—81no—
231C22×C31—161no—
232C22×C31—161no—
233C22×C31#38611yescharacteristic
234C22×C31#45311yescharacteristic
235C22×C31#45411yescharacteristic
236C4×C31—21no—
237C4×C31—21no—
238C4×C31—21no—
239C4×C31—21no—
240C4×C31—42no—
241C4×C31—81no—
242C4×C31—81no—
243C4×C31—81no—
244C4×C31—81no—
245C4×C31—82no—
246C4×C31—81no—
247C2×#121C22×C3111yescharacteristic
248C2×#121C22×C3111yescharacteristic
249#481—21no—
250#481C4×C3112yescomplemented
251#469—22no—
252#447—21no—
253#447C4×C3112yescomplemented
254C2×#99—21no—
255C2×#99—21no—
256#407C22×C3111yescharacteristic
257#407C22×C3111yescharacteristic
258#390—21no—
259#388—21no—
260#387—21no—
261#386—21no—
262#386—21no—
263#385—21no—
264#381C22×C3111yescharacteristic
265#380C22×C3111yescharacteristic
266C4×C22⋊C4C22×C3111yescharacteristic
267#327—22no—
268#327—21no—
269#327—21no—
270C2×C31—21no—
271C2×C31—21no—
272C2×C31—41no—
273C2×C31—41no—
274C2×C31—82no—
275C2×C31—161no—
276C2×C31#188311yescharacteristic
277C2×C31#190411yescharacteristic
278C2×C31#191311yescharacteristic
279C22×D4—21no—
280C22×D4—21no—
281C22×D4C2×C4×C3111yescharacteristic, complemented
282C22×D4D4×C3111yescharacteristic
283C23×C4—21no—
284C23×C4C23×C3111yescharacteristic
285C2×D8—22no—
286C2×M16—21no—
287C2×M16—21no—
288#121—21no—
289#121—21no—
290#121—21no—
291#121—21no—
292#121—21no—
293#121—21no—
294#121C2×C4×C3112yes—
295#121D4×C3112yes—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4C2×C4×C3111yescharacteristic, complemented
299C2×C4⋊C4D4×C3111yescharacteristic
300C2×C22⋊C4—21no—
301C2×C22⋊C4—21no—
302C2×C22⋊C4—21no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4D4×C3111yescharacteristic
308C2×C22⋊C4D4×C3111yescharacteristic
309C2×C42—21no—
310C2×C42—21no—
311#106—22no—
312#102—22no—
313#102—22no—
314#99—42no—
315#99—42no—
316C22⋊C8—21no—
317C22⋊C8—21no—
318C22⋊C8—21no—
319C22⋊C8C2×C4×C3112yescomplemented
320#95—21no—
321#95—21no—
322#95—21no—
323#95—21no—
324#95—21no—
325#95D4×C3111yescharacteristic
326#95D4×C3111yescharacteristic
327C31#934311yescharacteristic, direct product factor, Sylow
328C24—21no—
329C24—21no—
330C24C2×D4×C3111yescharacteristic
331C2×D4—22no—
332C2×D4—22no—
333C2×D4—21no—
334C2×D4—21no—
335C2×D4—21no—
336C2×D4—41no—
337C2×D4—41no—
338C2×D4—41no—
339C2×D4—41no—
340C2×D4—41no—
341C2×D4—41no—
342C2×D4—81no—
343C2×D4—81no—
344C2×D4—81no—
345C2×D4—81no—
346C2×D4C22⋊C4×C3112yes—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—41no—
354C22×C4—81no—
355C22×C4—81no—
356C22×C4—81no—
357C22×C4—81no—
358C22×C4C22×C4×C3111yescharacteristic
359C22×C4C2×D4×C3111yescharacteristic
360C22×C4C2×D4×C3111yescharacteristic
361C22×C4C2×D4×C3111yescharacteristic
362C22×C4#41×C3111yescharacteristic
363C22×C4#41×C3111yescharacteristic
364D8—82no—
365M16—81no—
366M16—81no—
367C2×C8—22no—
368C2×C8—41no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—81no—
373C4⋊C4—81no—
374C4⋊C4C22⋊C4×C3112yes—
375C22⋊C4—22no—
376C22⋊C4—22no—
377C22⋊C4—22no—
378C22⋊C4—41no—
379C22⋊C4—41no—
380C22⋊C4—41no—
381C22⋊C4—41no—
382C22⋊C4—41no—
383C22⋊C4—81no—
384C22⋊C4—81no—
385C22⋊C4—81no—
386C22⋊C4—81no—
387C42—81no—
388C42—81no—
389C23—21no—
390C23—21no—
391C23—22no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23—41no—
403C23—81no—
404C23—81no—
405C23C4×D4×C3111yescharacteristic
406C23C31×#12011yescharacteristic
407C23C31×#12111yescharacteristic
408D4—42no—
409D4—42no—
410D4—81no—
411D4—81no—
412D4—82no—
413D4—82no—
414D4—81no—
415D4—81no—
416D4—81no—
417D4—81no—
418C2×C4—22no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—42no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—81no—
444C2×C4—81no—
445C2×C4—84no—
446C2×C4C2×C22⋊C4×C3111yescharacteristic
447C2×C4C4×D4×C3111yescharacteristic
448C2×C4C31×#12111yescharacteristic
449C2×C4C31×#12311yescharacteristic
450C8—42no—
451C8—81no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—42no—
461C22—42no—
462C22—42no—
463C22—81no—
464C22—81no—
465C22—81no—
466C22—81no—
467C22—81no—
468C22—81no—
469C22—81no—
470C22—81no—
471C22—81no—
472C22—161no—
473C22—161no—
474C22C31×#38611yescharacteristic
475C22C31×#45311yescharacteristic
476C22C31×#45411yescharacteristic
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—42no—
482C4—81no—
483C4—81no—
484C4—81no—
485C4—81no—
486C4—82no—
487C4—81no—
488C2—21no—
489C2—21no—
490C2—41no—
491C2—41no—
492C2—82no—
493C2—161no—
494C2C31×#188311yescharacteristic
495C2C31×#190411yescharacteristic
496C2C31×#191311yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC31×#3192C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2377C2semidirect
3. C31×#1964C2semidirect
4. C31×#1510C2semidirect
5. C31×#1507C2semidirect
6. C31×#1305C2semidirect
7. C31×#1284C2semidirect
11. C31×#481C4semidirect
14. C31×#447C4semidirect
33. C22×D4×C31C2×C4semidirect
50. C2×C4⋊C4×C31C2×C4semidirect
71. C31×C22⋊C8C2×C4semidirect
140. #9343C31direct (N × H)
205. #2377C2×C31semidirect
206. #1964C2×C31semidirect
207. #1510C2×C31semidirect
208. #1507C2×C31semidirect
209. #1305C2×C31semidirect
210. #1284C2×C31semidirect
250. #481C4×C31semidirect
253. #447C4×C31semidirect
281. C22×D4C2×C4×C31semidirect
298. C2×C4⋊C4C2×C4×C31semidirect
319. C22⋊C8C2×C4×C31semidirect
327. C31#9343direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#31922
C31×#23772
C31×#19642
C31×#15102
C31×#15072
C31×#13052
C31×#12842
#934331