Finite Group Databasebeta

← C31×#8512 #21465271

Subgroups — C31×#8512 #21465271

Order 7936.

652 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3563C211yesmaximal, characteristic
2C31×#1989C211yesmaximal, characteristic, complemented
3C31×#1986C211yesmaximal, characteristic, complemented
4C31×#1552C211yesmaximal, characteristic, complemented
5C31×#1528C211yesmaximal, characteristic, complemented
6C31×#1509C211yesmaximal, characteristic
7C31×#1483C211yesmaximal, characteristic
8C31×#564C412yescomplemented
9C31×#563C412yescomplemented
10C31×#557—21no—
11C31×#554—21no—
12C31×#552—21no—
13C31×#552—22no—
14C31×#552—21no—
15C31×#544—21no—
16C31×#544—21no—
17C31×#541—21no—
18C31×#541—22no—
19C31×#539—21no—
20C31×#533C2211yescharacteristic
21C31×#529C2211yescharacteristic
22C2×C31×#125C2211yescharacteristic
23C31×#432C2211yescharacteristic
24C2×C31×C4⋊C8C2211yescharacteristic
25C4×M16×C31C2211yescharacteristic
26C4×C4⋊C4×C31C2211yescharacteristic
27C31×#340—21no—
28C31×#340—21no—
29C31×#339—22no—
30C31×#332—21no—
31C31×#332—21no—
32C31×#330—22no—
33C31×#328—21no—
34C31×#327—21no—
35C31×Q8⋊C8—21no—
36C31×D4⋊C8—21no—
37C2×M16×C31—21no—
38C22×C8×C31—21no—
39C31×C4⋊Q8—22no—
40C31×C4⋊Q8—21no—
41C31×C4⋊Q8—22no—
42C31×C4⋊Q8D411yescharacteristic
43C31×C4⋊Q8D411yescharacteristic
44C31×#126—22no—
45C31×#126—22no—
46C31×#126—22no—
47C31×#126—22no—
48C31×#126—21no—
49C31×#125—22no—
50C31×#125—22no—
51C31×#125—21no—
52C31×#125—22no—
53C31×#125—22no—
54C31×#125—22no—
55C31×#125—22no—
56C31×#125—22no—
57C31×#125—22no—
58C31×#125—21no—
59C31×#125—21no—
60C31×#125C2×C412yes—
61C31×#125C2×C411yescharacteristic
62C31×#125C2×C412yes—
63C31×#125D412yes—
64C31×#124C2×C411yescharacteristic
65C31×#123—22no—
66C31×#123—22no—
67C31×#123—21no—
68C31×C22⋊Q8—22no—
69C31×C22⋊Q8—21no—
70C31×C22⋊Q8—21no—
71C31×C22⋊Q8—22no—
72C31×C22⋊Q8—21no—
73C31×C22⋊Q8—21no—
74C31×C22⋊Q8—22no—
75C31×C22⋊Q8—22no—
76C31×C22⋊Q8D411yescharacteristic
77C31×#121D411yescharacteristic
78C4×Q8×C31—21no—
79C4×Q8×C31—22no—
80C4×Q8×C31—21no—
81C4×Q8×C31—21no—
82C4×Q8×C31—21no—
83C4×Q8×C31D411yescharacteristic
84C4×D4×C31—22no—
85C4×D4×C31—21no—
86C4×D4×C31D411yescharacteristic
87C31×#117—22no—
88C31×#117—21no—
89C31×#117—22no—
90C31×#117—21no—
91C31×#117D412yes—
92C2×C4⋊C4×C31—21no—
93C2×C4⋊C4×C31—21no—
94C2×C4⋊C4×C31—21no—
95C2×C4⋊C4×C31—21no—
96C2×C4⋊C4×C31D411yescharacteristic
97C2×C4⋊C4×C31D411yescharacteristic
98C2×C42×C31—21no—
99C2×C42×C31C2311yescharacteristic
100C31×C4⋊C8—21no—
101C31×C4⋊C8—21no—
102C31×C4⋊C8—21no—
103C31×C22⋊C8—21no—
104C31×#97—21no—
105C31×#97—21no—
106C4×C8×C31—21no—
107C31×#95—21no—
108C2×Q8×C31—22no—
109C2×Q8×C31—21no—
110C2×Q8×C31—21no—
111C2×Q8×C31C22⋊C411yescharacteristic
112C2×D4×C31—21no—
113C2×D4×C31C22⋊C411yescharacteristic
114C22×C4×C31—21no—
115C22×C4×C31—22no—
116C22×C4×C31—21no—
117C22×C4×C31—21no—
118C22×C4×C31—41no—
119C22×C4×C31C2×D411yescharacteristic
120C22×C4×C31C2×D411yescharacteristic
121C22×C4×C31C2×D411yescharacteristic
122M16×C31—22no—
123M16×C31—41no—
124C2×C8×C31—41no—
125C2×C8×C31—42no—
126C2×C8×C31—41no—
127C2×C8×C31—41no—
128C4⋊C4×C31—22no—
129C4⋊C4×C31—22no—
130C4⋊C4×C31—22no—
131C4⋊C4×C31—22no—
132C4⋊C4×C31—22no—
133C4⋊C4×C31—22no—
134C4⋊C4×C31—22no—
135C4⋊C4×C31—22no—
136C4⋊C4×C31—22no—
137C4⋊C4×C31—22no—
138C4⋊C4×C31—21no—
139C4⋊C4×C31—21no—
140C4⋊C4×C31—22no—
141C4⋊C4×C31—22no—
142C4⋊C4×C31—21no—
143C4⋊C4×C31—21no—
144C4⋊C4×C31—22no—
145C4⋊C4×C31—22no—
146C4⋊C4×C31—21no—
147C4⋊C4×C31—21no—
148C4⋊C4×C31—21no—
149C4⋊C4×C31—21no—
150C4⋊C4×C31—22no—
151C4⋊C4×C31—41no—
152C4⋊C4×C31C22⋊C412yes—
153C4⋊C4×C31C22⋊C412yes—
154C4⋊C4×C31C22⋊C412yes—
155C4⋊C4×C31C22⋊C412yes—
156C4⋊C4×C31C22⋊C411yescharacteristic
157C4⋊C4×C31C22⋊C411yescharacteristic
158C22⋊C4×C31—22no—
159C22⋊C4×C31—22no—
160C22⋊C4×C31—22no—
161C22⋊C4×C31—21no—
162C22⋊C4×C31—22no—
163C22⋊C4×C31—21no—
164C22⋊C4×C31—21no—
165C22⋊C4×C31—21no—
166C22⋊C4×C31—21no—
167C42×C31—22no—
168C42×C31—22no—
169C42×C31—22no—
170C42×C31—22no—
171C42×C31—21no—
172C42×C31—42no—
173C42×C31C22×C411yescharacteristic
174C42×C31C2×D411yescharacteristic
175C42×C31C2×D411yescharacteristic
176C42×C31C2×D411yescharacteristic
177#8512C3111yesmaximal, characteristic, direct product factor, Sylow
178C23×C31—21no—
179C23×C31#12011yescharacteristic
180Q8×C31—41no—
181Q8×C31—41no—
182Q8×C31—41no—
183Q8×C31—81no—
184Q8×C31—82no—
185D4×C31—41no—
186D4×C31—41no—
187D4×C31—41no—
188C2×C4×C31—21no—
189C2×C4×C31—21no—
190C2×C4×C31—21no—
191C2×C4×C31—21no—
192C2×C4×C31—22no—
193C2×C4×C31—21no—
194C2×C4×C31—21no—
195C2×C4×C31—21no—
196C2×C4×C31—22no—
197C2×C4×C31—22no—
198C2×C4×C31—22no—
199C2×C4×C31—41no—
200C2×C4×C31—41no—
201C2×C4×C31—41no—
202C2×C4×C31—41no—
203C2×C4×C31—41no—
204C2×C4×C31—42no—
205C2×C4×C31—81no—
206C2×C4×C31—82no—
207C2×C4×C31—81no—
208C2×C4×C31—81no—
209C2×C4×C31C2×C22⋊C411yescharacteristic
210C2×C4×C31C2×C22⋊C411yescharacteristic
211C2×C4×C31C2×C22⋊C411yescharacteristic
212C2×C4×C31#12011yescharacteristic
213C2×C4×C31#12011yescharacteristic
214C2×C4×C31#12011yescharacteristic
215C8×C31—42no—
216C8×C31—81no—
217C8×C31—81no—
218#3563C2×C3111yescharacteristic
219#1989C2×C3111yescharacteristic, complemented
220#1986C2×C3111yescharacteristic, complemented
221#1552C2×C3111yescharacteristic, complemented
222#1528C2×C3111yescharacteristic, complemented
223#1509C2×C3111yescharacteristic
224#1483C2×C3111yescharacteristic
225C22×C31—21no—
226C22×C31—21no—
227C22×C31—41no—
228C22×C31—41no—
229C22×C31—41no—
230C22×C31#37911yescharacteristic
231C22×C31#45411yescharacteristic
232C22×C31#45611yescharacteristic
233C4×C31—21no—
234C4×C31—21no—
235C4×C31—21no—
236C4×C31—21no—
237C4×C31—21no—
238C4×C31—42no—
239C4×C31—41no—
240C4×C31—41no—
241C4×C31—42no—
242C4×C31—42no—
243C4×C31—42no—
244C4×C31—41no—
245C4×C31—82no—
246C4×C31#45411yescharacteristic
247C4×C31#45611yescharacteristic
248#564C4×C3112yescomplemented
249#563C4×C3112yescomplemented
250#557—21no—
251#554—21no—
252#552—21no—
253#552—22no—
254#552—21no—
255#544—21no—
256#544—21no—
257#541—21no—
258#541—22no—
259#539—21no—
260#533C22×C3111yescharacteristic
261#529C22×C3111yescharacteristic
262C2×#125C22×C3111yescharacteristic
263#432C22×C3111yescharacteristic
264C2×C4⋊C8C22×C3111yescharacteristic
265C4×M16C22×C3111yescharacteristic
266C4×C4⋊C4C22×C3111yescharacteristic
267#340—21no—
268#340—21no—
269#339—22no—
270#332—21no—
271#332—21no—
272#330—22no—
273#328—21no—
274#327—21no—
275Q8⋊C8—21no—
276D4⋊C8—21no—
277C2×C31—21no—
278C2×C31—21no—
279C2×C31—81no—
280C2×C31#179311yescharacteristic
281C2×C31#179311yescharacteristic
282C2×C31#179411yescharacteristic
283C2×M16—21no—
284C22×C8—21no—
285C4⋊Q8—22no—
286C4⋊Q8—21no—
287C4⋊Q8—22no—
288C4⋊Q8D4×C3111yescharacteristic
289C4⋊Q8D4×C3111yescharacteristic
290#126—22no—
291#126—22no—
292#126—22no—
293#126—22no—
294#126—21no—
295#125—22no—
296#125—22no—
297#125—21no—
298#125—22no—
299#125—22no—
300#125—22no—
301#125—22no—
302#125—22no—
303#125—22no—
304#125—21no—
305#125—21no—
306#125C2×C4×C3112yes—
307#125C2×C4×C3111yescharacteristic
308#125C2×C4×C3112yes—
309#125D4×C3112yes—
310#124C2×C4×C3111yescharacteristic
311#123—22no—
312#123—22no—
313#123—21no—
314C22⋊Q8—22no—
315C22⋊Q8—21no—
316C22⋊Q8—21no—
317C22⋊Q8—22no—
318C22⋊Q8—21no—
319C22⋊Q8—21no—
320C22⋊Q8—22no—
321C22⋊Q8—22no—
322C22⋊Q8D4×C3111yescharacteristic
323#121D4×C3111yescharacteristic
324C4×Q8—21no—
325C4×Q8—22no—
326C4×Q8—21no—
327C4×Q8—21no—
328C4×Q8—21no—
329C4×Q8D4×C3111yescharacteristic
330C4×D4—22no—
331C4×D4—21no—
332C4×D4D4×C3111yescharacteristic
333#117—22no—
334#117—21no—
335#117—22no—
336#117—21no—
337#117D4×C3112yes—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4D4×C3111yescharacteristic
343C2×C4⋊C4D4×C3111yescharacteristic
344C2×C42—21no—
345C2×C42C23×C3111yescharacteristic
346C4⋊C8—21no—
347C4⋊C8—21no—
348C4⋊C8—21no—
349C22⋊C8—21no—
350#97—21no—
351#97—21no—
352C4×C8—21no—
353#95—21no—
354C31#851211yescharacteristic, direct product factor, Sylow
355C2×Q8—22no—
356C2×Q8—21no—
357C2×Q8—21no—
358C2×Q8C22⋊C4×C3111yescharacteristic
359C2×D4—21no—
360C2×D4C22⋊C4×C3111yescharacteristic
361C22×C4—21no—
362C22×C4—22no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—41no—
366C22×C4C2×D4×C3111yescharacteristic
367C22×C4C2×D4×C3111yescharacteristic
368C22×C4C2×D4×C3111yescharacteristic
369M16—22no—
370M16—41no—
371C2×C8—41no—
372C2×C8—42no—
373C2×C8—41no—
374C2×C8—41no—
375C4⋊C4—22no—
376C4⋊C4—22no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4—22no—
383C4⋊C4—22no—
384C4⋊C4—22no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—22no—
388C4⋊C4—22no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—22no—
392C4⋊C4—22no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—22no—
398C4⋊C4—41no—
399C4⋊C4C22⋊C4×C3112yes—
400C4⋊C4C22⋊C4×C3112yes—
401C4⋊C4C22⋊C4×C3112yes—
402C4⋊C4C22⋊C4×C3112yes—
403C4⋊C4C22⋊C4×C3111yescharacteristic
404C4⋊C4C22⋊C4×C3111yescharacteristic
405C22⋊C4—22no—
406C22⋊C4—22no—
407C22⋊C4—22no—
408C22⋊C4—21no—
409C22⋊C4—22no—
410C22⋊C4—21no—
411C22⋊C4—21no—
412C22⋊C4—21no—
413C22⋊C4—21no—
414C42—22no—
415C42—22no—
416C42—22no—
417C42—22no—
418C42—21no—
419C42—42no—
420C42C22×C4×C3111yescharacteristic
421C42C2×D4×C3111yescharacteristic
422C42C2×D4×C3111yescharacteristic
423C42C2×D4×C3111yescharacteristic
424C23—21no—
425C23C31×#12011yescharacteristic
426Q8—41no—
427Q8—41no—
428Q8—41no—
429Q8—81no—
430Q8—82no—
431D4—41no—
432D4—41no—
433D4—41no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—22no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—42no—
451C2×C4—81no—
452C2×C4—82no—
453C2×C4—81no—
454C2×C4—81no—
455C2×C4C2×C22⋊C4×C3111yescharacteristic
456C2×C4C2×C22⋊C4×C3111yescharacteristic
457C2×C4C2×C22⋊C4×C3111yescharacteristic
458C2×C4C31×#12011yescharacteristic
459C2×C4C31×#12011yescharacteristic
460C2×C4C31×#12011yescharacteristic
461C8—42no—
462C8—81no—
463C8—81no—
464C22—21no—
465C22—21no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22C31×#37911yescharacteristic
470C22C31×#45411yescharacteristic
471C22C31×#45611yescharacteristic
472C4—21no—
473C4—21no—
474C4—21no—
475C4—21no—
476C4—21no—
477C4—42no—
478C4—41no—
479C4—41no—
480C4—42no—
481C4—42no—
482C4—42no—
483C4—41no—
484C4—82no—
485C4C31×#45411yescharacteristic
486C4C31×#45611yescharacteristic
487C2—21no—
488C2—21no—
489C2—81no—
490C2C31×#179311yescharacteristic
491C2C31×#179311yescharacteristic
492C2C31×#179411yescharacteristic
subgroupG/H
center, socleC22×C31#379
commutatorC42C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC31×#121D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1989C2semidirect
3. C31×#1986C2semidirect
4. C31×#1552C2semidirect
5. C31×#1528C2semidirect
8. C31×#564C4semidirect
9. C31×#563C4semidirect
177. #8512C31direct (N × H)
219. #1989C2×C31semidirect
220. #1986C2×C31semidirect
221. #1552C2×C31semidirect
222. #1528C2×C31semidirect
248. #564C4×C31semidirect
249. #563C4×C31semidirect
354. C31#8512direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35632
C31×#19892
C31×#19862
C31×#15522
C31×#15282
C31×#15092
C31×#14832
#851231