Finite Group Databasebeta

← C31×#29237 #21485996

Subgroups — C31×#29237 #21485996

Order 7936.

926 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C31×#121C211yesmaximal, characteristic
2C2×C31×#389C211yesmaximal, characteristic, complemented
3C31×#2087C212yesmaximal, complemented
4C31×#2065C212yesmaximal, complemented
5C31×#1919C212yesmaximal, complemented
6C31×#1874C211yesmaximal, characteristic
7C31×#1874C211yesmaximal, characteristic
8C31×#1862C212yesmaximal, complemented
9C31×#1853C211yesmaximal, characteristic, complemented
10C31×#1852C211yesmaximal, characteristic, complemented
11C31×#1797C211yesmaximal, characteristic, complemented
12C2×C31×#121C2211yescharacteristic
13C2×C4×D4×C31—21no—
14C2×C4×D4×C31C2211yescharacteristic
15C22×C4⋊C4×C31—21no—
16C22×C4⋊C4×C31C2211yescharacteristic
17C22×C4⋊C4×C31C2211yescharacteristic
18C22×C42×C31C2211yescharacteristic
19C2×C31×#107C2212yes—
20C2×C31×#106C2212yes—
21C2×C31×C4⋊C8C2212yes—
22C2×C31×#102C2212yes—
23C2×C31×#102C2212yes—
24C2×C31×C22⋊C8C2211yescharacteristic
25C2×C31×C22⋊C8C2211yescharacteristic
26C31×#390C2211yescharacteristic
27C31×#389—21no—
28C31×#389—21no—
29C31×#389C2212yes—
30C31×#389C2211yescharacteristic
31C31×#389C2212yes—
32C31×#388—21no—
33C31×#386—21no—
34C31×#380C2211yescharacteristic
35C4×C4⋊C4×C31C2211yescharacteristic
36C4×C22⋊C4×C31—21no—
37C2×C31×#95—21no—
38C31×#340C2212yes—
39C31×#340C2212yes—
40C31×#340C2212yes—
41C31×#340C2212yes—
42C31×#336C2212yes—
43C22×D4×C31—21no—
44C22×D4×C31C2311yescharacteristic
45C23×C4×C31—21no—
46C23×C4×C31—21no—
47C23×C4×C31—21no—
48C23×C4×C31D411yescharacteristic
49C23×C4×C31D411yescharacteristic
50C23×C4×C31C2311yescharacteristic
51C22×C8×C31C2312yes—
52C22×C8×C31C2312yes—
53C31×#121—22no—
54C31×#121Q814yes—
55C4×D4×C31—42no—
56C4×D4×C31—44no—
57C2×C4⋊C4×C31—21no—
58C2×C4⋊C4×C31—24no—
59C2×C4⋊C4×C31—22no—
60C2×C4⋊C4×C31—22no—
61C2×C4⋊C4×C31—21no—
62C2×C4⋊C4×C31—21no—
63C2×C4⋊C4×C31—42no—
64C2×C4⋊C4×C31—44no—
65C2×C4⋊C4×C31C2312yes—
66C2×C4⋊C4×C31C2311yescharacteristic
67C2×C4⋊C4×C31C2311yescharacteristic
68C2×C4⋊C4×C31C2311yescharacteristic
69C2×C4⋊C4×C31C2312yes—
70C2×C22⋊C4×C31—21no—
71C2×C22⋊C4×C31—21no—
72C2×C22⋊C4×C31—21no—
73C2×C22⋊C4×C31—21no—
74C2×C22⋊C4×C31—21no—
75C2×C42×C31—21no—
76C2×C42×C31—42no—
77C2×C42×C31D411yescharacteristic
78C2×C42×C31D411yescharacteristic
79C2×C42×C31C2311yescharacteristic
80C2×C42×C31C2311yescharacteristic
81C31×#107—42no—
82C31×#106—24no—
83C31×C4⋊C8—42no—
84C31×#102—24no—
85C31×#102—42no—
86C31×C22⋊C8—22no—
87C31×C22⋊C8—22no—
88C31×#95—22no—
89C31×#95—22no—
90C31×#95—21no—
91C31×#95—21no—
92C31×#95—21no—
93C24×C31—21no—
94C24×C31C2×D411yescharacteristic
95C2×D4×C31—24no—
96C2×D4×C31—22no—
97C2×D4×C31—21no—
98C2×D4×C31—22no—
99C2×D4×C31—42no—
100C2×D4×C31—42no—
101C2×D4×C31C2×Q812yes—
102C22×C4×C31—22no—
103C22×C4×C31—22no—
104C22×C4×C31—24no—
105C22×C4×C31—22no—
106C22×C4×C31—22no—
107C22×C4×C31—21no—
108C22×C4×C31—22no—
109C22×C4×C31—22no—
110C22×C4×C31—22no—
111C22×C4×C31—21no—
112C22×C4×C31—21no—
113C22×C4×C31—22no—
114C22×C4×C31—41no—
115C22×C4×C31—41no—
116C22×C4×C31—42no—
117C22×C4×C31—42no—
118C22×C4×C31—42no—
119C22×C4×C31—42no—
120C22×C4×C31—42no—
121C22×C4×C31—42no—
122C22×C4×C31—42no—
123C22×C4×C31—42no—
124C22×C4×C31C2×D411yescharacteristic
125C22×C4×C31C2×D411yescharacteristic
126C22×C4×C31C2×D411yescharacteristic
127C22×C4×C31C2×D411yescharacteristic
128C22×C4×C31C2×D411yescharacteristic
129C22×C4×C31C2×Q812yes—
130C22×C4×C31#4112yes—
131C22×C4×C31C2411yescharacteristic
132C2×C8×C31—22no—
133C2×C8×C31—22no—
134C2×C8×C31—22no—
135C2×C8×C31—22no—
136C2×C8×C31—22no—
137C2×C8×C31—22no—
138C4⋊C4×C31—24no—
139C4⋊C4×C31—22no—
140C4⋊C4×C31—21no—
141C4⋊C4×C31—22no—
142C4⋊C4×C31—22no—
143C4⋊C4×C31—22no—
144C4⋊C4×C31—22no—
145C4⋊C4×C31—42no—
146C4⋊C4×C31—44no—
147C4⋊C4×C31—42no—
148C4⋊C4×C31—44no—
149C4⋊C4×C31C2×Q812yes—
150C4⋊C4×C31#4114yes—
151C22⋊C4×C31—24no—
152C22⋊C4×C31—42no—
153C22⋊C4×C31—42no—
154C22⋊C4×C31—42no—
155C22⋊C4×C31—42no—
156C42×C31—22no—
157C42×C31—22no—
158C42×C31—41no—
159C42×C31—41no—
160C42×C31—42no—
161#29237C3111yesmaximal, characteristic, direct product factor, Sylow
162C23×C31—21no—
163C23×C31—21no—
164C23×C31—21no—
165C23×C31—21no—
166C23×C31—22no—
167C23×C31—41no—
168C23×C31—41no—
169C23×C31—41no—
170C23×C31—41no—
171C23×C31—41no—
172C23×C31—41no—
173C23×C31C22⋊Q812yes—
174C23×C31#13512yes—
175C23×C31AGL(1,ℤ/8)12yes—
176C23×C31C22×D411yescharacteristic
177D4×C31—24no—
178D4×C31—48no—
179D4×C31—42no—
180C2×C4×C31—21no—
181C2×C4×C31—21no—
182C2×C4×C31—21no—
183C2×C4×C31—21no—
184C2×C4×C31—21no—
185C2×C4×C31—21no—
186C2×C4×C31—24no—
187C2×C4×C31—24no—
188C2×C4×C31—22no—
189C2×C4×C31—24no—
190C2×C4×C31—21no—
191C2×C4×C31—21no—
192C2×C4×C31—21no—
193C2×C4×C31—21no—
194C2×C4×C31—21no—
195C2×C4×C31—21no—
196C2×C4×C31—44no—
197C2×C4×C31—44no—
198C2×C4×C31—48no—
199C2×C4×C31—42no—
200C2×C4×C31—41no—
201C2×C4×C31—41no—
202C2×C4×C31—42no—
203C2×C4×C31—41no—
204C2×C4×C31—41no—
205C2×C4×C31—42no—
206C2×C4×C31—41no—
207C2×C4×C31—41no—
208C2×C4×C31—42no—
209C2×C4×C31—42no—
210C2×C4×C31—41no—
211C2×C4×C31—41no—
212C2×C4×C31—84no—
213C2×C4×C31—84no—
214C2×C4×C31C22⋊Q812yes—
215C2×C4×C31AGL(1,ℤ/8)12yes—
216C2×C4×C31#13712yes—
217C2×C4×C31C22×Q811yescharacteristic
218C2×C4×C31C2×#4111yescharacteristic
219C2×C4×C31C2×#4112yes—
220C2×C4×C31H(5,𝔽2)12yes—
221C8×C31—42no—
222C8×C31—42no—
223C4×#121C2×C3111yescharacteristic
224C2×#389C2×C3111yescharacteristic, complemented
225#2087C2×C3112yescomplemented
226#2065C2×C3112yescomplemented
227#1919C2×C3112yescomplemented
228#1874C2×C3111yescharacteristic
229#1874C2×C3111yescharacteristic
230#1862C2×C3112yescomplemented
231#1853C2×C3111yescharacteristic, complemented
232#1852C2×C3111yescharacteristic, complemented
233#1797C2×C3111yescharacteristic, complemented
234C22×C31—22no—
235C22×C31—22no—
236C22×C31—22no—
237C22×C31—22no—
238C22×C31—22no—
239C22×C31—22no—
240C22×C31—42no—
241C22×C31—42no—
242C22×C31—42no—
243C22×C31—81no—
244C22×C31—81no—
245C22×C31—81no—
246C22×C31—81no—
247C22×C31#47814yes—
248C22×C31C2×C22⋊Q811yescharacteristic
249C22×C31#52511yescharacteristic
250C22×C31#53411yescharacteristic
251C22×C31C2×#13511yescharacteristic
252C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
253C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
254C22×C31C2×#13711yescharacteristic
255C4×C31—22no—
256C4×C31—22no—
257C4×C31—22no—
258C4×C31—42no—
259C4×C31—44no—
260C4×C31—41no—
261C4×C31—41no—
262C4×C31—81no—
263C4×C31—81no—
264C4×C31—82no—
265C4×C31#55312yes—
266C4×C31#55412yes—
267C2×#121C22×C3111yescharacteristic
268C2×C4×D4—21no—
269C2×C4×D4C22×C3111yescharacteristic
270C22×C4⋊C4—21no—
271C22×C4⋊C4C22×C3111yescharacteristic
272C22×C4⋊C4C22×C3111yescharacteristic
273C22×C42C22×C3111yescharacteristic
274C2×#107C22×C3112yes—
275C2×#106C22×C3112yes—
276C2×C4⋊C8C22×C3112yes—
277C2×#102C22×C3112yes—
278C2×#102C22×C3112yes—
279C2×C22⋊C8C22×C3111yescharacteristic
280C2×C22⋊C8C22×C3111yescharacteristic
281#390C22×C3111yescharacteristic
282#389—21no—
283#389—21no—
284#389C22×C3112yes—
285#389C22×C3111yescharacteristic
286#389C22×C3112yes—
287#388—21no—
288#386—21no—
289#380C22×C3111yescharacteristic
290C4×C4⋊C4C22×C3111yescharacteristic
291C4×C22⋊C4—21no—
292C2×#95—21no—
293#340C22×C3112yes—
294#340C22×C3112yes—
295#340C22×C3112yes—
296#340C22×C3112yes—
297#336C22×C3112yes—
298C2×C31—24no—
299C2×C31—82no—
300C2×C31#257911yescharacteristic
301C2×C31C2×#47811yescharacteristic
302C2×C31#307911yescharacteristic
303C2×C31#310511yescharacteristic
304C2×C31#311211yescharacteristic
305C2×C31#319011yescharacteristic
306C2×C31#319211yescharacteristic
307C22×D4—21no—
308C22×D4C23×C3111yescharacteristic
309C23×C4—21no—
310C23×C4—21no—
311C23×C4—21no—
312C23×C4D4×C3111yescharacteristic
313C23×C4D4×C3111yescharacteristic
314C23×C4C23×C3111yescharacteristic
315C22×C8C23×C3112yes—
316C22×C8C23×C3112yes—
317#121—22no—
318#121Q8×C3114yes—
319C4×D4—42no—
320C4×D4—44no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—44no—
329C2×C4⋊C4C23×C3112yes—
330C2×C4⋊C4C23×C3111yescharacteristic
331C2×C4⋊C4C23×C3111yescharacteristic
332C2×C4⋊C4C23×C3111yescharacteristic
333C2×C4⋊C4C23×C3112yes—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—21no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C42—21no—
340C2×C42—42no—
341C2×C42D4×C3111yescharacteristic
342C2×C42D4×C3111yescharacteristic
343C2×C42C23×C3111yescharacteristic
344C2×C42C23×C3111yescharacteristic
345#107—42no—
346#106—24no—
347C4⋊C8—42no—
348#102—24no—
349#102—42no—
350C22⋊C8—22no—
351C22⋊C8—22no—
352#95—22no—
353#95—22no—
354#95—21no—
355#95—21no—
356#95—21no—
357C31#2923711yescharacteristic, direct product factor, Sylow
358C24—21no—
359C24C2×D4×C3111yescharacteristic
360C2×D4—24no—
361C2×D4—22no—
362C2×D4—21no—
363C2×D4—22no—
364C2×D4—42no—
365C2×D4—42no—
366C2×D4C2×Q8×C3112yes—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—24no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—21no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—42no—
382C22×C4—42no—
383C22×C4—42no—
384C22×C4—42no—
385C22×C4—42no—
386C22×C4—42no—
387C22×C4—42no—
388C22×C4—42no—
389C22×C4C2×D4×C3111yescharacteristic
390C22×C4C2×D4×C3111yescharacteristic
391C22×C4C2×D4×C3111yescharacteristic
392C22×C4C2×D4×C3111yescharacteristic
393C22×C4C2×D4×C3111yescharacteristic
394C22×C4C2×Q8×C3112yes—
395C22×C4#41×C3112yes—
396C22×C4C24×C3111yescharacteristic
397C2×C8—22no—
398C2×C8—22no—
399C2×C8—22no—
400C2×C8—22no—
401C2×C8—22no—
402C2×C8—22no—
403C4⋊C4—24no—
404C4⋊C4—22no—
405C4⋊C4—21no—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—42no—
411C4⋊C4—44no—
412C4⋊C4—42no—
413C4⋊C4—44no—
414C4⋊C4C2×Q8×C3112yes—
415C4⋊C4#41×C3114yes—
416C22⋊C4—24no—
417C22⋊C4—42no—
418C22⋊C4—42no—
419C22⋊C4—42no—
420C22⋊C4—42no—
421C42—22no—
422C42—22no—
423C42—41no—
424C42—41no—
425C42—42no—
426C23—21no—
427C23—21no—
428C23—21no—
429C23—21no—
430C23—22no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23—41no—
437C23C31×C22⋊Q812yes—
438C23C31×#13512yes—
439C23C31×AGL(1,ℤ/8)12yes—
440C23C22×D4×C3111yescharacteristic
441D4—24no—
442D4—48no—
443D4—42no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—24no—
451C2×C4—24no—
452C2×C4—22no—
453C2×C4—24no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—44no—
461C2×C4—44no—
462C2×C4—48no—
463C2×C4—42no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—42no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—42no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—42no—
473C2×C4—41no—
474C2×C4—42no—
475C2×C4—41no—
476C2×C4—84no—
477C2×C4—84no—
478C2×C4C31×C22⋊Q812yes—
479C2×C4C31×AGL(1,ℤ/8)12yes—
480C2×C4C31×#13712yes—
481C2×C4C22×Q8×C3111yescharacteristic
482C2×C4C2×#41×C3111yescharacteristic
483C2×C4C2×#41×C3112yes—
484C2×C4C31×H(5,𝔽2)12yes—
485C8—42no—
486C8—42no—
487C22—22no—
488C22—22no—
489C22—22no—
490C22—22no—
491C22—22no—
492C22—22no—
493C22—42no—
494C22—42no—
495C22—42no—
496C22—81no—
497C22—81no—
498C22—81no—
499C22—81no—
500C22C31×#47814yes—
501C22C2×C31×C22⋊Q811yescharacteristic
502C22C31×#52511yescharacteristic
503C22C31×#53411yescharacteristic
504C22C2×C31×#13511yescharacteristic
505C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
506C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
507C22C2×C31×#13711yescharacteristic
508C4—22no—
509C4—22no—
510C4—22no—
511C4—44no—
512C4—41no—
513C4—41no—
514C4—42no—
515C4—81no—
516C4—81no—
517C4—82no—
518C4C31×#55312yes—
519C4C31×#55412yes—
520C2—24no—
521C2—82no—
522C2C31×#257911yescharacteristic
523C2C2×C31×#47811yescharacteristic
524C2C31×#307911yescharacteristic
525C2C31×#310511yescharacteristic
526C2C31×#311211yescharacteristic
527C2C31×#319011yescharacteristic
528C2C31×#319211yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#389C2semidirect
3. C31×#2087C2semidirect
4. C31×#2065C2semidirect
5. C31×#1919C2semidirect
8. C31×#1862C2semidirect
9. C31×#1853C2semidirect
10. C31×#1852C2semidirect
11. C31×#1797C2semidirect
161. #29237C31direct (N × H)
224. C2×#389C2×C31semidirect
225. #2087C2×C31semidirect
226. #2065C2×C31semidirect
227. #1919C2×C31semidirect
230. #1862C2×C31semidirect
231. #1853C2×C31semidirect
232. #1852C2×C31semidirect
233. #1797C2×C31semidirect
357. C31#29237direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C31×#1212
C2×C31×#3892
C31×#20872
C31×#20652
C31×#19192
C31×#18742
C31×#18622
C31×#18532
C31×#18522
C31×#17972
#2923731