Finite Group Databasebeta

← C31×#10238 #21466997

Subgroups — C31×#10238 #21466997

Order 7936.

794 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3205C211yesmaximal, characteristic, complemented
2C31×#3036C211yesmaximal, characteristic, complemented
3C31×#2541C211yesmaximal, characteristic, complemented
4C31×#1545C211yesmaximal, characteristic, complemented
5C31×#1502C211yesmaximal, characteristic, complemented
6C31×#1478C211yesmaximal, characteristic, complemented
7C31×#1303C211yesmaximal, characteristic, complemented
8C2×C31×AGL(1,ℤ/8)—21no—
9C31×#532C2211yescharacteristic
10C2×C31×#127—21no—
11C2×C31×#127C2211yescharacteristic
12C2×C31×#121—22no—
13C2×C4×D4×C31C2211yescharacteristic
14C31×#493—21no—
15C31×#486—21no—
16C31×#463—22no—
17C31×#461—21no—
18C31×#459—21no—
19C31×#459—22no—
20C31×#447—22no—
21C31×#431C2211yescharacteristic
22C31×#431C2211yescharacteristic
23C31×#423C2211yescharacteristic
24C31×#417—21no—
25C31×#392—22no—
26C31×#390—21no—
27C4×C4⋊C4×C31C2211yescharacteristic
28C31×#331—22no—
29C31×#327—22no—
30C31×D4⋊C8—22no—
31C2×#41×C31—21no—
32C22×D4×C31—24no—
33C22×D4×C31—21no—
34C22×D4×C31—21no—
35C22×D4×C31D411yescharacteristic
36C22×D4×C31D412yes—
37C23×C4×C31—21no—
38C31×AGL(1,ℤ/8)—42no—
39C31×AGL(1,ℤ/8)—42no—
40C2×SD16×C31—22no—
41C2×D8×C31—22no—
42C2×D8×C31—24no—
43C2×M16×C31—21no—
44C31×C4⋊Q8D411yescharacteristic, complemented
45C31×#127—21no—
46C31×#127—21no—
47C31×#127—21no—
48C31×#127—21no—
49C31×#127—42no—
50C31×#127—42no—
51C31×#127D411yescharacteristic, complemented
52C31×#124—21no—
53C31×#121—21no—
54C31×#121—21no—
55C31×#121—48no—
56C4×D4×C31—21no—
57C4×D4×C31—21no—
58C4×D4×C31—21no—
59C4×D4×C31—21no—
60C4×D4×C31—21no—
61C4×D4×C31—21no—
62C2×C4⋊C4×C31—21no—
63C2×C4⋊C4×C31D411yescharacteristic
64C2×C22⋊C4×C31—24no—
65C2×C22⋊C4×C31—21no—
66C2×C42×C31—21no—
67C2×C42×C31C2311yescharacteristic
68C31×C4⋊C8—21no—
69C31×C4⋊C8—21no—
70C31×C4⋊C8D412yescomplemented
71C31×C4⋊C8D412yescomplemented
72C31×#103—22no—
73C31×#102—22no—
74C31×#102—24no—
75C31×C22⋊C8—21no—
76C31×C22⋊C8—21no—
77C4×C8×C31—21no—
78C4×C8×C31—21no—
79C31×#95D412yes—
80C24×C31—21no—
81C24×C31—22no—
82#41×C31—41no—
83#41×C31—41no—
84#41×C31—41no—
85#41×C31—41no—
86C2×Q8×C31—21no—
87C2×D4×C31—21no—
88C2×D4×C31—21no—
89C2×D4×C31—22no—
90C2×D4×C31—21no—
91C2×D4×C31—21no—
92C2×D4×C31—21no—
93C2×D4×C31—22no—
94C2×D4×C31—21no—
95C2×D4×C31—21no—
96C2×D4×C31—21no—
97C2×D4×C31—44no—
98C2×D4×C31—48no—
99C2×D4×C31—48no—
100C2×D4×C31—41no—
101C2×D4×C31—41no—
102C2×D4×C31—41no—
103C2×D4×C31—41no—
104C2×D4×C31—41no—
105C2×D4×C31—41no—
106C2×D4×C31—41no—
107C2×D4×C31—41no—
108C2×D4×C31—41no—
109C2×D4×C31—82no—
110C2×D4×C31—84no—
111C2×D4×C31D812yescomplemented
112C22×C4×C31—22no—
113C22×C4×C31—21no—
114C22×C4×C31—44no—
115C22×C4×C31—41no—
116C22×C4×C31—41no—
117C22×C4×C31—41no—
118C22×C4×C31C2×D411yescharacteristic
119C22×C4×C31C2×D411yescharacteristic
120C22×C4×C31C2×D411yescharacteristic
121SD16×C31—44no—
122D8×C31—44no—
123D8×C31—84no—
124M16×C31—41no—
125M16×C31—41no—
126C2×C8×C31—22no—
127C2×C8×C31—22no—
128C2×C8×C31—41no—
129C4⋊C4×C31—24no—
130C4⋊C4×C31—21no—
131C4⋊C4×C31—21no—
132C4⋊C4×C31—21no—
133C4⋊C4×C31—21no—
134C22⋊C4×C31—48no—
135C22⋊C4×C31—41no—
136C22⋊C4×C31—41no—
137C22⋊C4×C31—41no—
138C22⋊C4×C31—41no—
139C42×C31—41no—
140C42×C31—41no—
141C42×C31C2×D411yescharacteristic
142C42×C31C2×D411yescharacteristic
143C42×C31C2×D411yescharacteristic
144C42×C31#4111yescharacteristic
145#10238C3111yesmaximal, characteristic, direct product factor, Sylow
146C23×C31—22no—
147C23×C31—42no—
148C23×C31—42no—
149C23×C31—44no—
150C23×C31—44no—
151C23×C31—41no—
152C23×C31—41no—
153C23×C31—41no—
154C23×C31—42no—
155C23×C31—42no—
156C23×C31—42no—
157C23×C31#12011yescharacteristic
158Q8×C31—41no—
159Q8×C31—41no—
160D4×C31—22no—
161D4×C31—22no—
162D4×C31—41no—
163D4×C31—41no—
164D4×C31—41no—
165D4×C31—42no—
166D4×C31—44no—
167D4×C31—41no—
168D4×C31—81no—
169D4×C31—82no—
170D4×C31—82no—
171D4×C31—82no—
172D4×C31—816no—
173D4×C31—81no—
174D4×C31—81no—
175D4×C31—81no—
176D4×C31—81no—
177D4×C31—81no—
178D4×C31—81no—
179C2×C4×C31—22no—
180C2×C4×C31—24no—
181C2×C4×C31—41no—
182C2×C4×C31—42no—
183C2×C4×C31—42no—
184C2×C4×C31—42no—
185C2×C4×C31—41no—
186C2×C4×C31—41no—
187C2×C4×C31—82no—
188C2×C4×C31—82no—
189C2×C4×C31—81no—
190C2×C4×C31—81no—
191C2×C4×C31#12011yescharacteristic
192C2×C4×C31#12011yescharacteristic
193C2×C4×C31#12111yescharacteristic
194C2×C4×C31#12111yescharacteristic
195C2×C4×C31#12111yescharacteristic
196C2×C4×C31#12711yescharacteristic
197C2×C4×C31C2×D811yescharacteristic
198C2×C4×C31#13511yescharacteristic
199C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
200C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
201C8×C31—42no—
202C8×C31—42no—
203C8×C31—81no—
204#3205C2×C3111yescharacteristic, complemented
205#3036C2×C3111yescharacteristic, complemented
206#2541C2×C3111yescharacteristic, complemented
207#1545C2×C3111yescharacteristic, complemented
208#1502C2×C3111yescharacteristic, complemented
209#1478C2×C3111yescharacteristic, complemented
210#1303C2×C3111yescharacteristic, complemented
211C22×C31—21no—
212C22×C31—21no—
213C22×C31—44no—
214C22×C31—42no—
215C22×C31—82no—
216C22×C31—84no—
217C22×C31—84no—
218C22×C31—81no—
219C22×C31—81no—
220C22×C31—81no—
221C22×C31—82no—
222C22×C31—82no—
223C22×C31—81no—
224C22×C31—82no—
225C22×C31—81no—
226C22×C31#39211yescharacteristic
227C22×C31#44711yescharacteristic
228C22×C31#44911yescharacteristic
229C4×C31—21no—
230C4×C31—21no—
231C4×C31—21no—
232C4×C31—44no—
233C4×C31—81no—
234C4×C31—81no—
235C4×C31#44711yescharacteristic
236C4×C31#44911yescharacteristic
237C4×C31#45312yes—
238C4×C31#46611yescharacteristic
239C4×C31#46911yescharacteristic
240C2×AGL(1,ℤ/8)—21no—
241#532C22×C3111yescharacteristic
242C2×#127—21no—
243C2×#127C22×C3111yescharacteristic
244C2×#121—22no—
245C2×C4×D4C22×C3111yescharacteristic
246#493—21no—
247#486—21no—
248#463—22no—
249#461—21no—
250#459—21no—
251#459—22no—
252#447—22no—
253#431C22×C3111yescharacteristic
254#431C22×C3111yescharacteristic
255#423C22×C3111yescharacteristic
256#417—21no—
257#392—22no—
258#390—21no—
259C4×C4⋊C4C22×C3111yescharacteristic
260#331—22no—
261#327—22no—
262D4⋊C8—22no—
263C2×C31—21no—
264C2×C31—21no—
265C2×C31—82no—
266C2×C31—161no—
267C2×C31—162no—
268C2×C31#199911yescharacteristic
269C2×C31#200211yescharacteristic
270C2×C31#200811yescharacteristic
271C2×#41—21no—
272C22×D4—24no—
273C22×D4—21no—
274C22×D4—21no—
275C22×D4D4×C3111yescharacteristic
276C22×D4D4×C3112yes—
277C23×C4—21no—
278AGL(1,ℤ/8)—42no—
279AGL(1,ℤ/8)—42no—
280C2×SD16—22no—
281C2×D8—22no—
282C2×D8—24no—
283C2×M16—21no—
284C4⋊Q8D4×C3111yescharacteristic, complemented
285#127—21no—
286#127—21no—
287#127—21no—
288#127—21no—
289#127—42no—
290#127—42no—
291#127D4×C3111yescharacteristic, complemented
292#124—21no—
293#121—21no—
294#121—21no—
295#121—48no—
296C4×D4—21no—
297C4×D4—21no—
298C4×D4—21no—
299C4×D4—21no—
300C4×D4—21no—
301C4×D4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4D4×C3111yescharacteristic
304C2×C22⋊C4—24no—
305C2×C22⋊C4—21no—
306C2×C42—21no—
307C2×C42C23×C3111yescharacteristic
308C4⋊C8—21no—
309C4⋊C8—21no—
310C4⋊C8D4×C3112yescomplemented
311C4⋊C8D4×C3112yescomplemented
312#103—22no—
313#102—22no—
314#102—24no—
315C22⋊C8—21no—
316C22⋊C8—21no—
317C4×C8—21no—
318C4×C8—21no—
319#95D4×C3112yes—
320C31#1023811yescharacteristic, direct product factor, Sylow
321C24—21no—
322C24—22no—
323#41—41no—
324#41—41no—
325#41—41no—
326#41—41no—
327C2×Q8—21no—
328C2×D4—21no—
329C2×D4—21no—
330C2×D4—22no—
331C2×D4—21no—
332C2×D4—21no—
333C2×D4—21no—
334C2×D4—22no—
335C2×D4—21no—
336C2×D4—21no—
337C2×D4—21no—
338C2×D4—44no—
339C2×D4—48no—
340C2×D4—48no—
341C2×D4—41no—
342C2×D4—41no—
343C2×D4—41no—
344C2×D4—41no—
345C2×D4—41no—
346C2×D4—41no—
347C2×D4—41no—
348C2×D4—41no—
349C2×D4—41no—
350C2×D4—82no—
351C2×D4—84no—
352C2×D4D8×C3112yescomplemented
353C22×C4—22no—
354C22×C4—21no—
355C22×C4—44no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4C2×D4×C3111yescharacteristic
360C22×C4C2×D4×C3111yescharacteristic
361C22×C4C2×D4×C3111yescharacteristic
362SD16—44no—
363D8—44no—
364D8—84no—
365M16—41no—
366M16—41no—
367C2×C8—22no—
368C2×C8—22no—
369C2×C8—41no—
370C4⋊C4—24no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C22⋊C4—48no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—41no—
379C22⋊C4—41no—
380C42—41no—
381C42—41no—
382C42C2×D4×C3111yescharacteristic
383C42C2×D4×C3111yescharacteristic
384C42C2×D4×C3111yescharacteristic
385C42#41×C3111yescharacteristic
386C23—22no—
387C23—42no—
388C23—42no—
389C23—44no—
390C23—44no—
391C23—41no—
392C23—41no—
393C23—42no—
394C23—42no—
395C23—41no—
396C23—42no—
397C23C31×#12011yescharacteristic
398Q8—41no—
399Q8—41no—
400D4—22no—
401D4—22no—
402D4—41no—
403D4—41no—
404D4—41no—
405D4—42no—
406D4—44no—
407D4—41no—
408D4—81no—
409D4—82no—
410D4—82no—
411D4—82no—
412D4—816no—
413D4—81no—
414D4—81no—
415D4—81no—
416D4—81no—
417D4—81no—
418D4—81no—
419C2×C4—22no—
420C2×C4—24no—
421C2×C4—41no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—82no—
428C2×C4—82no—
429C2×C4—81no—
430C2×C4—81no—
431C2×C4C31×#12011yescharacteristic
432C2×C4C31×#12011yescharacteristic
433C2×C4C31×#12111yescharacteristic
434C2×C4C31×#12111yescharacteristic
435C2×C4C31×#12111yescharacteristic
436C2×C4C31×#12711yescharacteristic
437C2×C4C2×D8×C3111yescharacteristic
438C2×C4C31×#13511yescharacteristic
439C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
440C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
441C8—42no—
442C8—42no—
443C8—81no—
444C22—21no—
445C22—21no—
446C22—44no—
447C22—42no—
448C22—82no—
449C22—84no—
450C22—84no—
451C22—81no—
452C22—81no—
453C22—81no—
454C22—82no—
455C22—82no—
456C22—81no—
457C22—82no—
458C22—81no—
459C22C31×#39211yescharacteristic
460C22C31×#44711yescharacteristic
461C22C31×#44911yescharacteristic
462C4—21no—
463C4—21no—
464C4—21no—
465C4—44no—
466C4—81no—
467C4—81no—
468C4C31×#44711yescharacteristic
469C4C31×#44911yescharacteristic
470C4C31×#45312yes—
471C4C31×#46611yescharacteristic
472C4C31×#46911yescharacteristic
473C2—21no—
474C2—21no—
475C2—82no—
476C2—162no—
477C2—161no—
478C2C31×#199911yescharacteristic
479C2C31×#200211yescharacteristic
480C2C31×#200811yescharacteristic
subgroupG/H
center, socleC22×C31#392
commutator, Frattini, cosocleC2×C42C23×C31
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3205C2semidirect
2. C31×#3036C2semidirect
3. C31×#2541C2semidirect
4. C31×#1545C2semidirect
5. C31×#1502C2semidirect
6. C31×#1478C2semidirect
7. C31×#1303C2semidirect
44. C31×C4⋊Q8D4semidirect
51. C31×#127D4semidirect
70. C31×C4⋊C8D4semidirect
71. C31×C4⋊C8D4semidirect
111. C2×D4×C31D8semidirect
145. #10238C31direct (N × H)
204. #3205C2×C31semidirect
205. #3036C2×C31semidirect
206. #2541C2×C31semidirect
207. #1545C2×C31semidirect
208. #1502C2×C31semidirect
209. #1478C2×C31semidirect
210. #1303C2×C31semidirect
284. C4⋊Q8D4×C31semidirect
291. #127D4×C31semidirect
310. C4⋊C8D4×C31semidirect
311. C4⋊C8D4×C31semidirect
320. C31#10238direct (N × H)
352. C2×D4D8×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#32052
C31×#30362
C31×#25412
C31×#15452
C31×#15022
C31×#14782
C31×#13032
#1023831