Finite Group Databasebeta

← C31×#13045 #21469804

Subgroups — C31×#13045 #21469804

Order 7936.

654 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3025C211yesmaximal, characteristic
2C31×#2977C211yesmaximal, characteristic, complemented
3C31×#2120C211yesmaximal, characteristic, complemented
4C31×#1794C211yesmaximal, characteristic, complemented
5C31×#1791C211yesmaximal, characteristic, complemented
6C31×#1395C211yesmaximal, characteristic, complemented
7C31×#1391C211yesmaximal, characteristic, complemented
8C31×#585C2211yescharacteristic
9C31×#525—21no—
10C31×#525C2211yescharacteristic
11C31×#458—21no—
12C31×#458C412yescomplemented
13C31×B(4,𝔽2)—21no—
14C31×B(4,𝔽2)C412yescomplemented
15C31×#435—21no—
16C31×#435—21no—
17C8×D4×C31—21no—
18C8×D4×C31—21no—
19C31×#433—21no—
20C31×#421—21no—
21C31×#416—21no—
22C31×#413—21no—
23C31×#413C2211yescharacteristic
24C31×#410—21no—
25C31×#410C2211yescharacteristic
26C31×#410C2211yescharacteristic
27C31×#408—21no—
28C31×#408C2211yescharacteristic
29C31×#408C2211yescharacteristic
30C2×C31×C22⋊C8—21no—
31C31×#352—21no—
32C31×AΣL(1,𝔽16)—21no—
33C31×2−1+4—21no—
34C31×2−1+4—41no—
35C31×H(5,𝔽2)—21no—
36C31×H(5,𝔽2)—21no—
37C31×H(5,𝔽2)—41no—
38C31×H(5,𝔽2)C2×C412yes—
39C2×#41×C31—21no—
40C2×#41×C31—21no—
41C2×#41×C31—21no—
42C2×#41×C31—42no—
43C2×#41×C31C2311yescharacteristic
44C23×C4×C31D411yescharacteristic
45C2×M16×C31—21no—
46C2×M16×C31D411yescharacteristic, complemented
47C2×M16×C31D411yescharacteristic, complemented
48C22×C8×C31—21no—
49C22×C8×C31—21no—
50C22×C8×C31D411yescharacteristic, complemented
51C22×C8×C31D411yescharacteristic, complemented
52C31×#123—22no—
53C31×#123C2×C411yescharacteristic
54C31×#123D411yescharacteristic
55C31×C22⋊Q8—21no—
56C31×C22⋊Q8—41no—
57C31×#121—21no—
58C31×#121—41no—
59C31×#120—22no—
60C31×#120C2×C411yescharacteristic
61C31×#120D411yescharacteristic
62C4×D4×C31—21no—
63C4×D4×C31—21no—
64C4×D4×C31—42no—
65C31×#117—21no—
66C31×#117—21no—
67C31×#117D411yescharacteristic
68C31×C4⋊C8—21no—
69C31×C4⋊C8—21no—
70C31×#104—42no—
71C31×#103—41no—
72C31×#102—41no—
73C31×#101—21no—
74C31×#101—41no—
75C31×#100—21no—
76C31×#100—41no—
77C31×#99—21no—
78C31×#99—22no—
79C31×#99—22no—
80C31×#99—21no—
81C31×#99—21no—
82C31×#99C2×C412yes—
83C31×C22⋊C8—21no—
84C31×C22⋊C8—21no—
85C31×C22⋊C8—21no—
86C31×C22⋊C8—21no—
87C31×C22⋊C8—21no—
88C31×C22⋊C8—21no—
89C31×C22⋊C8—42no—
90C31×#97—21no—
91C4×C8×C31—21no—
92C24×C31C22⋊C411yescharacteristic
93#41×C31—22no—
94#41×C31—22no—
95#41×C31—41no—
96#41×C31—41no—
97#41×C31—42no—
98#41×C31—41no—
99#41×C31—41no—
100#41×C31—41no—
101#41×C31—41no—
102#41×C31—41no—
103#41×C31—42no—
104#41×C31—42no—
105#41×C31—42no—
106#41×C31—41no—
107#41×C31—41no—
108#41×C31—41no—
109C2×Q8×C31—21no—
110C2×Q8×C31—21no—
111C2×Q8×C31—21no—
112C2×Q8×C31—42no—
113C2×Q8×C31#4111yescharacteristic
114C2×D4×C31—21no—
115C2×D4×C31—21no—
116C2×D4×C31—21no—
117C2×D4×C31—22no—
118C2×D4×C31—21no—
119C2×D4×C31—22no—
120C2×D4×C31—21no—
121C2×D4×C31—42no—
122C2×D4×C31—42no—
123C2×D4×C31—42no—
124C2×D4×C31—41no—
125C2×D4×C31—42no—
126C2×D4×C31C22×C411yescharacteristic
127C2×D4×C31C2×D411yescharacteristic
128C2×D4×C31#4111yescharacteristic
129C22×C4×C31—22no—
130C22×C4×C31—22no—
131C22×C4×C31—21no—
132C22×C4×C31—21no—
133C22×C4×C31—41no—
134C22×C4×C31—41no—
135C22×C4×C31—41no—
136C22×C4×C31C22⋊C411yescharacteristic
137C22×C4×C31C2×D411yescharacteristic
138C22×C4×C31C2×D411yescharacteristic
139C22×C4×C31C2×D411yescharacteristic
140M16×C31—41no—
141M16×C31—41no—
142M16×C31—41no—
143M16×C31—41no—
144C2×C8×C31—21no—
145C2×C8×C31—21no—
146C2×C8×C31—21no—
147C2×C8×C31—21no—
148C2×C8×C31—41no—
149C2×C8×C31—41no—
150C2×C8×C31—41no—
151C2×C8×C31—81no—
152C2×C8×C31—81no—
153C4⋊C4×C31—21no—
154C4⋊C4×C31—21no—
155C4⋊C4×C31—21no—
156C4⋊C4×C31—41no—
157C4⋊C4×C31—42no—
158C4⋊C4×C31—41no—
159C22⋊C4×C31—21no—
160C22⋊C4×C31—21no—
161C22⋊C4×C31—21no—
162C22⋊C4×C31—21no—
163C22⋊C4×C31—22no—
164C22⋊C4×C31—42no—
165C22⋊C4×C31—42no—
166C22⋊C4×C31—41no—
167C22⋊C4×C31C22⋊C411yescharacteristic
168C22⋊C4×C31C22⋊C411yescharacteristic
169C42×C31—21no—
170C42×C31—41no—
171C42×C31—41no—
172#13045C3111yesmaximal, characteristic, direct product factor, Sylow
173C23×C31—21no—
174C23×C31—22no—
175C23×C31—22no—
176C23×C31—41no—
177C23×C31—42no—
178C23×C31—41no—
179C23×C31C2×C22⋊C411yescharacteristic
180C23×C31C4×D411yescharacteristic
181C23×C31#12111yescharacteristic
182Q8×C31—22no—
183Q8×C31—41no—
184Q8×C31—41no—
185Q8×C31—41no—
186Q8×C31—41no—
187D4×C31—22no—
188D4×C31—41no—
189D4×C31—41no—
190D4×C31—41no—
191D4×C31—41no—
192D4×C31—41no—
193D4×C31—42no—
194D4×C31—42no—
195D4×C31—42no—
196D4×C31—42no—
197D4×C31—42no—
198D4×C31—42no—
199D4×C31—41no—
200D4×C31—84no—
201C2×C4×C31—21no—
202C2×C4×C31—21no—
203C2×C4×C31—21no—
204C2×C4×C31—21no—
205C2×C4×C31—21no—
206C2×C4×C31—21no—
207C2×C4×C31—22no—
208C2×C4×C31—22no—
209C2×C4×C31—21no—
210C2×C4×C31—21no—
211C2×C4×C31—21no—
212C2×C4×C31—42no—
213C2×C4×C31—42no—
214C2×C4×C31—42no—
215C2×C4×C31—41no—
216C2×C4×C31—41no—
217C2×C4×C31—41no—
218C2×C4×C31—42no—
219C2×C4×C31—41no—
220C2×C4×C31—42no—
221C2×C4×C31—81no—
222C2×C4×C31—81no—
223C2×C4×C31C4×D411yescharacteristic
224C2×C4×C31#12011yescharacteristic
225C2×C4×C31#12111yescharacteristic
226C2×C4×C31#12311yescharacteristic
227C8×C31—41no—
228C8×C31—41no—
229C8×C31—41no—
230C8×C31—41no—
231C8×C31—81no—
232#3025C2×C3111yescharacteristic
233#2977C2×C3111yescharacteristic, complemented
234#2120C2×C3111yescharacteristic, complemented
235#1794C2×C3111yescharacteristic, complemented
236#1791C2×C3111yescharacteristic, complemented
237#1395C2×C3111yescharacteristic, complemented
238#1391C2×C3111yescharacteristic, complemented
239C22×C31—22no—
240C22×C31—21no—
241C22×C31—21no—
242C22×C31—21no—
243C22×C31—41no—
244C22×C31—41no—
245C22×C31—41no—
246C22×C31—41no—
247C22×C31—42no—
248C22×C31—41no—
249C22×C31—42no—
250C22×C31—81no—
251C22×C31—82no—
252C22×C31—82no—
253C22×C31—161no—
254C22×C31#38611yescharacteristic
255C4×C31—21no—
256C4×C31—21no—
257C4×C31—21no—
258C4×C31—41no—
259C4×C31—41no—
260C4×C31—42no—
261C4×C31—41no—
262C4×C31—82no—
263C4×C31—161no—
264C4×C31B(4,𝔽2)11yescharacteristic
265C4×C31B(4,𝔽2)11yescharacteristic
266#585C22×C3111yescharacteristic
267#525—21no—
268#525C22×C3111yescharacteristic
269#458—21no—
270#458C4×C3112yescomplemented
271B(4,𝔽2)—21no—
272B(4,𝔽2)C4×C3112yescomplemented
273#435—21no—
274#435—21no—
275C8×D4—21no—
276C8×D4—21no—
277#433—21no—
278#421—21no—
279#416—21no—
280#413—21no—
281#413C22×C3111yescharacteristic
282#410—21no—
283#410C22×C3111yescharacteristic
284#410C22×C3111yescharacteristic
285#408—21no—
286#408C22×C3111yescharacteristic
287#408C22×C3111yescharacteristic
288C2×C22⋊C8—21no—
289#352—21no—
290AΣL(1,𝔽16)—21no—
291C2×C31—21no—
292C2×C31—41no—
293C2×C31—41no—
294C2×C31—42no—
295C2×C31—41no—
296C2×C31—82no—
297C2×C31#188911yescharacteristic
2982−1+4—21no—
2992−1+4—41no—
300H(5,𝔽2)—21no—
301H(5,𝔽2)—21no—
302H(5,𝔽2)—41no—
303H(5,𝔽2)C2×C4×C3112yes—
304C2×#41—21no—
305C2×#41—21no—
306C2×#41—21no—
307C2×#41—42no—
308C2×#41C23×C3111yescharacteristic
309C23×C4D4×C3111yescharacteristic
310C2×M16—21no—
311C2×M16D4×C3111yescharacteristic, complemented
312C2×M16D4×C3111yescharacteristic, complemented
313C22×C8—21no—
314C22×C8—21no—
315C22×C8D4×C3111yescharacteristic, complemented
316C22×C8D4×C3111yescharacteristic, complemented
317#123—22no—
318#123C2×C4×C3111yescharacteristic
319#123D4×C3111yescharacteristic
320C22⋊Q8—21no—
321C22⋊Q8—41no—
322#121—21no—
323#121—41no—
324#120—22no—
325#120C2×C4×C3111yescharacteristic
326#120D4×C3111yescharacteristic
327C4×D4—21no—
328C4×D4—21no—
329C4×D4—42no—
330#117—21no—
331#117—21no—
332#117D4×C3111yescharacteristic
333C4⋊C8—21no—
334C4⋊C8—21no—
335#104—42no—
336#103—41no—
337#102—41no—
338#101—21no—
339#101—41no—
340#100—21no—
341#100—41no—
342#99—21no—
343#99—22no—
344#99—22no—
345#99—21no—
346#99—21no—
347#99C2×C4×C3112yes—
348C22⋊C8—21no—
349C22⋊C8—21no—
350C22⋊C8—21no—
351C22⋊C8—21no—
352C22⋊C8—21no—
353C22⋊C8—21no—
354C22⋊C8—42no—
355#97—21no—
356C4×C8—21no—
357C31#1304511yescharacteristic, direct product factor, Sylow
358C24C22⋊C4×C3111yescharacteristic
359#41—22no—
360#41—22no—
361#41—41no—
362#41—41no—
363#41—42no—
364#41—41no—
365#41—41no—
366#41—41no—
367#41—41no—
368#41—41no—
369#41—42no—
370#41—42no—
371#41—42no—
372#41—41no—
373#41—41no—
374#41—41no—
375C2×Q8—21no—
376C2×Q8—21no—
377C2×Q8—21no—
378C2×Q8—42no—
379C2×Q8#41×C3111yescharacteristic
380C2×D4—21no—
381C2×D4—21no—
382C2×D4—21no—
383C2×D4—22no—
384C2×D4—21no—
385C2×D4—22no—
386C2×D4—21no—
387C2×D4—42no—
388C2×D4—42no—
389C2×D4—42no—
390C2×D4—41no—
391C2×D4—42no—
392C2×D4C22×C4×C3111yescharacteristic
393C2×D4C2×D4×C3111yescharacteristic
394C2×D4#41×C3111yescharacteristic
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4—41no—
402C22×C4C22⋊C4×C3111yescharacteristic
403C22×C4C2×D4×C3111yescharacteristic
404C22×C4C2×D4×C3111yescharacteristic
405C22×C4C2×D4×C3111yescharacteristic
406M16—41no—
407M16—41no—
408M16—41no—
409M16—41no—
410C2×C8—21no—
411C2×C8—21no—
412C2×C8—21no—
413C2×C8—21no—
414C2×C8—41no—
415C2×C8—41no—
416C2×C8—41no—
417C2×C8—81no—
418C2×C8—81no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—41no—
423C4⋊C4—42no—
424C4⋊C4—41no—
425C22⋊C4—21no—
426C22⋊C4—21no—
427C22⋊C4—21no—
428C22⋊C4—21no—
429C22⋊C4—22no—
430C22⋊C4—42no—
431C22⋊C4—42no—
432C22⋊C4—41no—
433C22⋊C4C22⋊C4×C3111yescharacteristic
434C22⋊C4C22⋊C4×C3111yescharacteristic
435C42—21no—
436C42—41no—
437C42—41no—
438C23—21no—
439C23—22no—
440C23—22no—
441C23—41no—
442C23—42no—
443C23—41no—
444C23C2×C22⋊C4×C3111yescharacteristic
445C23C4×D4×C3111yescharacteristic
446C23C31×#12111yescharacteristic
447Q8—22no—
448Q8—41no—
449Q8—41no—
450Q8—41no—
451Q8—41no—
452D4—22no—
453D4—41no—
454D4—41no—
455D4—41no—
456D4—41no—
457D4—41no—
458D4—42no—
459D4—42no—
460D4—42no—
461D4—42no—
462D4—42no—
463D4—42no—
464D4—41no—
465D4—84no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—42no—
484C2×C4—41no—
485C2×C4—42no—
486C2×C4—81no—
487C2×C4—81no—
488C2×C4C4×D4×C3111yescharacteristic
489C2×C4C31×#12011yescharacteristic
490C2×C4C31×#12111yescharacteristic
491C2×C4C31×#12311yescharacteristic
492C8—41no—
493C8—41no—
494C8—41no—
495C8—41no—
496C8—81no—
497C22—22no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—41no—
502C22—41no—
503C22—41no—
504C22—41no—
505C22—42no—
506C22—41no—
507C22—42no—
508C22—81no—
509C22—82no—
510C22—82no—
511C22—161no—
512C22C31×#38611yescharacteristic
513C4—21no—
514C4—21no—
515C4—21no—
516C4—41no—
517C4—41no—
518C4—42no—
519C4—41no—
520C4—82no—
521C4—161no—
522C4C31×B(4,𝔽2)11yescharacteristic
523C4C31×B(4,𝔽2)11yescharacteristic
524C2—21no—
525C2—41no—
526C2—41no—
527C2—42no—
528C2—41no—
529C2—82no—
530C2C31×#188911yescharacteristic
subgroupG/H
centerC4×C31B(4,𝔽2)
commutatorC2×D4C22×C4×C31
Frattini, cosocleC2×#41C23×C31
socleC2×C31#1889
prime radicalC31×#3025C2
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C31 ◁ C2×C4×C31 ◁ C2×#41×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2977C2semidirect
3. C31×#2120C2semidirect
4. C31×#1794C2semidirect
5. C31×#1791C2semidirect
6. C31×#1395C2semidirect
7. C31×#1391C2semidirect
12. C31×#458C4semidirect
14. C31×B(4,𝔽2)C4semidirect
46. C2×M16×C31D4semidirect
47. C2×M16×C31D4semidirect
50. C22×C8×C31D4semidirect
51. C22×C8×C31D4semidirect
172. #13045C31direct (N × H)
233. #2977C2×C31semidirect
234. #2120C2×C31semidirect
235. #1794C2×C31semidirect
236. #1791C2×C31semidirect
237. #1395C2×C31semidirect
238. #1391C2×C31semidirect
270. #458C4×C31semidirect
272. B(4,𝔽2)C4×C31semidirect
311. C2×M16D4×C31semidirect
312. C2×M16D4×C31semidirect
315. C22×C8D4×C31semidirect
316. C22×C8D4×C31semidirect
357. C31#13045direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#30252
C31×#29772
C31×#21202
C31×#17942
C31×#17912
C31×#13952
C31×#13912
#1304531