Finite Group Databasebeta

← C31×#25854 #21482613

Subgroups — C31×#25854 #21482613

Order 7936.

1094 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3501C211yesmaximal, characteristic
2C31×#2583C212yesmaximal, complemented
3C31×#2579C211yesmaximal, characteristic
4C31×#2062C212yesmaximal, complemented
5C31×#2062C212yesmaximal, complemented
6C31×#1996C212yesmaximal, complemented
7C31×#1867C212yesmaximal
8C31×#1867C212yesmaximal
9C4×C31×#99C211yesmaximal, characteristic
10C31×#554—22no—
11C31×#554—24no—
12D4×Q8×C31—22no—
13C31×#544—21no—
14C31×#543—21no—
15C31×#543C2212yes—
16C31×#533—21no—
17C2×C31×C22⋊Q8—21no—
18C2×C31×C22⋊Q8C2212yes—
19C31×#518C2212yes—
20C2×C4×D4×C31C2211yescharacteristic
21C22×C4⋊C4×C31C2211yescharacteristic
22C2×C31×#99C2212yes—
23C31×#398—21no—
24C31×#398—22no—
25C31×#396—21no—
26C31×#395—22no—
27C31×#389—24no—
28C31×#387—21no—
29C31×#386C2211yescharacteristic
30C31×#386C2211yescharacteristic
31C31×#385—21no—
32C31×#385C2211yescharacteristic
33C31×#385C2211yescharacteristic
34C31×#385C2214yes—
35C31×#385C2214yes—
36C31×#380C2211yescharacteristic
37C4×C22⋊C4×C31C2212yes—
38C31×#342C2212yes—
39C31×#342C2214yes—
40C31×#342C2214yes—
41C22×Q8×C31—21no—
42C22×Q8×C31D412yes—
43C22×D4×C31C2311yescharacteristic
44C23×C4×C31D411yescharacteristic
45C23×C4×C31C2311yescharacteristic
46C23×C4×C31C2311yescharacteristic
47C23×C4×C31C2311yescharacteristic
48C31×C4⋊Q8—21no—
49C31×C4⋊Q8—21no—
50C31×C4⋊Q8—24no—
51C31×#125—22no—
52C31×#125—24no—
53C31×C22⋊Q8—22no—
54C31×C22⋊Q8—22no—
55C31×C22⋊Q8—24no—
56C31×C22⋊Q8—24no—
57C31×C22⋊Q8—22no—
58C31×C22⋊Q8—22no—
59C31×C22⋊Q8—22no—
60C31×C22⋊Q8—22no—
61C31×C22⋊Q8—22no—
62C31×C22⋊Q8—22no—
63C31×C22⋊Q8—24no—
64C31×C22⋊Q8—24no—
65C4×Q8×C31—22no—
66C4×Q8×C31—22no—
67C4×D4×C31—22no—
68C4×D4×C31—22no—
69C4×D4×C31—24no—
70C4×D4×C31—24no—
71C31×#117—22no—
72C2×C4⋊C4×C31—21no—
73C2×C4⋊C4×C31—22no—
74C2×C4⋊C4×C31—22no—
75C2×C4⋊C4×C31—21no—
76C2×C4⋊C4×C31—21no—
77C2×C4⋊C4×C31—24no—
78C2×C4⋊C4×C31—21no—
79C2×C4⋊C4×C31—22no—
80C2×C4⋊C4×C31—24no—
81C2×C4⋊C4×C31—21no—
82C2×C4⋊C4×C31—21no—
83C2×C4⋊C4×C31D411yescharacteristic
84C2×C4⋊C4×C31D412yes—
85C2×C4⋊C4×C31D414yes—
86C2×C22⋊C4×C31—22no—
87C2×C22⋊C4×C31—21no—
88C2×C22⋊C4×C31—21no—
89C2×C22⋊C4×C31D411yescharacteristic
90C2×C22⋊C4×C31C2311yescharacteristic
91C2×C22⋊C4×C31C2311yescharacteristic
92C2×C22⋊C4×C31C2311yescharacteristic
93C2×C22⋊C4×C31C2314yes—
94C2×C22⋊C4×C31C2314yes—
95C2×C42×C31—22no—
96C2×C42×C31D411yescharacteristic
97C31×#99Q818yescomplemented
98C31×#95—22no—
99C31×#95—24no—
100C31×#95—21no—
101C31×#95—21no—
102C31×#95—24no—
103C31×#95—21no—
104C31×#95—21no—
105C31×#95—21no—
106C24×C31C2×D411yescharacteristic
107C24×C31C2411yescharacteristic
108C2×Q8×C31—22no—
109C2×Q8×C31—22no—
110C2×Q8×C31—22no—
111C2×Q8×C31—22no—
112C2×Q8×C31—82no—
113C2×Q8×C31—82no—
114C2×D4×C31—22no—
115C2×D4×C31—22no—
116C2×D4×C31C2×Q814yes—
117C22×C4×C31—24no—
118C22×C4×C31—21no—
119C22×C4×C31—22no—
120C22×C4×C31—22no—
121C22×C4×C31—22no—
122C22×C4×C31—21no—
123C22×C4×C31—21no—
124C22×C4×C31—21no—
125C22×C4×C31—21no—
126C22×C4×C31—21no—
127C22×C4×C31—22no—
128C22×C4×C31—42no—
129C22×C4×C31—81no—
130C22×C4×C31—81no—
131C22×C4×C31—81no—
132C22×C4×C31C2×D411yescharacteristic
133C22×C4×C31C2×D411yescharacteristic
134C22×C4×C31C2×D414yes—
135C22×C4×C31C2×D414yes—
136C22×C4×C31C2×D411yescharacteristic
137C22×C4×C31C2×D411yescharacteristic
138C22×C4×C31C2×D412yes—
139C22×C4×C31C2×D412yes—
140C22×C4×C31C2×D411yescharacteristic
141C4⋊C4×C31—22no—
142C4⋊C4×C31—24no—
143C4⋊C4×C31—22no—
144C4⋊C4×C31—22no—
145C4⋊C4×C31—24no—
146C4⋊C4×C31—22no—
147C4⋊C4×C31—24no—
148C4⋊C4×C31—22no—
149C4⋊C4×C31—22no—
150C4⋊C4×C31—22no—
151C4⋊C4×C31—24no—
152C4⋊C4×C31—42no—
153C4⋊C4×C31—48no—
154C4⋊C4×C31—41no—
155C4⋊C4×C31—41no—
156C4⋊C4×C31—42no—
157C4⋊C4×C31—81no—
158C4⋊C4×C31—84no—
159C4⋊C4×C31—81no—
160C22⋊C4×C31—24no—
161C22⋊C4×C31—24no—
162C22⋊C4×C31—22no—
163C22⋊C4×C31—24no—
164C22⋊C4×C31—24no—
165C22⋊C4×C31—22no—
166C22⋊C4×C31—22no—
167C22⋊C4×C31—22no—
168C22⋊C4×C31—42no—
169C22⋊C4×C31—81no—
170C22⋊C4×C31C2×Q818yescomplemented
171C42×C31—24no—
172C42×C31—21no—
173C42×C31—21no—
174C42×C31—82no—
175#25854C3111yesmaximal, characteristic, direct product factor, Sylow
176C23×C31—21no—
177C23×C31—21no—
178C23×C31—41no—
179C23×C31—41no—
180C23×C31—41no—
181C23×C31—41no—
182C23×C31C4⋊Q812yes—
183C23×C31C22×D411yescharacteristic
184C23×C31C22×D412yes—
185C23×C31C22×Q812yes—
186C23×C312−1+412yes—
187Q8×C31—44no—
188Q8×C31—82no—
189Q8×C31—82no—
190Q8×C31—82no—
191D4×C31—28no—
192C2×C4×C31—21no—
193C2×C4×C31—21no—
194C2×C4×C31—22no—
195C2×C4×C31—24no—
196C2×C4×C31—21no—
197C2×C4×C31—24no—
198C2×C4×C31—24no—
199C2×C4×C31—21no—
200C2×C4×C31—28no—
201C2×C4×C31—42no—
202C2×C4×C31—41no—
203C2×C4×C31—41no—
204C2×C4×C31—42no—
205C2×C4×C31—42no—
206C2×C4×C31—44no—
207C2×C4×C31—44no—
208C2×C4×C31—42no—
209C2×C4×C31—41no—
210C2×C4×C31—41no—
211C2×C4×C31—44no—
212C2×C4×C31—41no—
213C2×C4×C31—41no—
214C2×C4×C31—44no—
215C2×C4×C31—41no—
216C2×C4×C31—41no—
217C2×C4×C31—41no—
218C2×C4×C31—41no—
219C2×C4×C31—41no—
220C2×C4×C31—44no—
221C2×C4×C31—41no—
222C2×C4×C31—41no—
223C2×C4×C31—41no—
224C2×C4×C31—41no—
225C2×C4×C31—81no—
226C2×C4×C31—82no—
227C2×C4×C31—82no—
228C2×C4×C31#12011yescharacteristic
229C2×C4×C31#12011yescharacteristic
230C2×C4×C31#12012yes—
231C2×C4×C31C4⋊Q812yes—
232#3501C2×C3111yescharacteristic
233#2583C2×C3112yescomplemented
234#2579C2×C3111yescharacteristic
235#2062C2×C3112yescomplemented
236#2062C2×C3112yescomplemented
237#1996C2×C3112yescomplemented
238#1867C2×C3112yes—
239#1867C2×C3112yes—
240C4×#99C2×C3111yescharacteristic
241C22×C31—22no—
242C22×C31—21no—
243C22×C31—22no—
244C22×C31—21no—
245C22×C31—22no—
246C22×C31—42no—
247C22×C31—42no—
248C22×C31—42no—
249C22×C31—41no—
250C22×C31—41no—
251C22×C31—81no—
252C22×C31C2×#12011yescharacteristic
253C22×C31C2×C4⋊Q811yescharacteristic
254C22×C31#53611yescharacteristic
255C22×C31D4×Q814yes—
256C4×C31—22no—
257C4×C31—21no—
258C4×C31—21no—
259C4×C31—22no—
260C4×C31—48no—
261C4×C31—42no—
262C4×C31—44no—
263C4×C31—41no—
264C4×C31—41no—
265C4×C31—44no—
266C4×C31—81no—
267C4×C31—81no—
268C4×C31—81no—
269#554—24no—
270#554—22no—
271D4×Q8—22no—
272#544—21no—
273#543—21no—
274#543C22×C3112yes—
275#533—21no—
276C2×C22⋊Q8—21no—
277C2×C22⋊Q8C22×C3112yes—
278#518C22×C3112yes—
279C2×C4×D4C22×C3111yescharacteristic
280C22×C4⋊C4C22×C3111yescharacteristic
281C2×#99C22×C3112yes—
282#398—21no—
283#398—22no—
284#396—21no—
285#395—22no—
286#389—24no—
287#387—21no—
288#386C22×C3111yescharacteristic
289#386C22×C3111yescharacteristic
290#385—21no—
291#385C22×C3111yescharacteristic
292#385C22×C3111yescharacteristic
293#385C22×C3114yes—
294#385C22×C3114yes—
295#380C22×C3111yescharacteristic
296C4×C22⋊C4C22×C3112yes—
297#342C22×C3112yes—
298#342C22×C3114yes—
299#342C22×C3114yes—
300C2×C31—24no—
301C2×C31—21no—
302C2×C31—21no—
303C2×C31—42no—
304C2×C31#243411yescharacteristic
305C2×C31#302511yescharacteristic
306C2×C31#302611yescharacteristic
307C22×Q8—21no—
308C22×Q8D4×C3112yes—
309C22×D4C23×C3111yescharacteristic
310C23×C4D4×C3111yescharacteristic
311C23×C4C23×C3111yescharacteristic
312C23×C4C23×C3111yescharacteristic
313C23×C4C23×C3111yescharacteristic
314C4⋊Q8—21no—
315C4⋊Q8—21no—
316C4⋊Q8—24no—
317#125—22no—
318#125—24no—
319C22⋊Q8—22no—
320C22⋊Q8—22no—
321C22⋊Q8—24no—
322C22⋊Q8—24no—
323C22⋊Q8—22no—
324C22⋊Q8—22no—
325C22⋊Q8—22no—
326C22⋊Q8—22no—
327C22⋊Q8—22no—
328C22⋊Q8—22no—
329C22⋊Q8—24no—
330C22⋊Q8—24no—
331C4×Q8—22no—
332C4×Q8—22no—
333C4×D4—22no—
334C4×D4—22no—
335C4×D4—24no—
336C4×D4—24no—
337#117—22no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4D4×C3111yescharacteristic
350C2×C4⋊C4D4×C3114yes—
351C2×C4⋊C4D4×C3112yes—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4D4×C3111yescharacteristic
356C2×C22⋊C4C23×C3111yescharacteristic
357C2×C22⋊C4C23×C3111yescharacteristic
358C2×C22⋊C4C23×C3111yescharacteristic
359C2×C22⋊C4C23×C3114yes—
360C2×C22⋊C4C23×C3114yes—
361C2×C42—22no—
362C2×C42D4×C3111yescharacteristic
363#99Q8×C3118yescomplemented
364#95—22no—
365#95—21no—
366#95—21no—
367#95—21no—
368#95—24no—
369#95—24no—
370#95—21no—
371#95—21no—
372C31#2585411yescharacteristic, direct product factor, Sylow
373C24C2×D4×C3111yescharacteristic
374C24C24×C3111yescharacteristic
375C2×Q8—22no—
376C2×Q8—22no—
377C2×Q8—22no—
378C2×Q8—22no—
379C2×Q8—82no—
380C2×Q8—82no—
381C2×D4—22no—
382C2×D4—22no—
383C2×D4C2×Q8×C3114yes—
384C22×C4—24no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—42no—
396C22×C4—81no—
397C22×C4—81no—
398C22×C4—81no—
399C22×C4C2×D4×C3111yescharacteristic
400C22×C4C2×D4×C3111yescharacteristic
401C22×C4C2×D4×C3114yes—
402C22×C4C2×D4×C3114yes—
403C22×C4C2×D4×C3111yescharacteristic
404C22×C4C2×D4×C3111yescharacteristic
405C22×C4C2×D4×C3112yes—
406C22×C4C2×D4×C3112yes—
407C22×C4C2×D4×C3111yescharacteristic
408C4⋊C4—22no—
409C4⋊C4—24no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—24no—
413C4⋊C4—22no—
414C4⋊C4—24no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—24no—
419C4⋊C4—42no—
420C4⋊C4—48no—
421C4⋊C4—41no—
422C4⋊C4—41no—
423C4⋊C4—42no—
424C4⋊C4—81no—
425C4⋊C4—84no—
426C4⋊C4—81no—
427C22⋊C4—24no—
428C22⋊C4—24no—
429C22⋊C4—22no—
430C22⋊C4—24no—
431C22⋊C4—24no—
432C22⋊C4—22no—
433C22⋊C4—22no—
434C22⋊C4—22no—
435C22⋊C4—42no—
436C22⋊C4—81no—
437C22⋊C4C2×Q8×C3118yescomplemented
438C42—24no—
439C42—21no—
440C42—21no—
441C42—82no—
442C23—21no—
443C23—21no—
444C23—41no—
445C23—41no—
446C23—41no—
447C23—41no—
448C23C31×C4⋊Q812yes—
449C23C22×D4×C3111yescharacteristic
450C23C22×D4×C3112yes—
451C23C22×Q8×C3112yes—
452C23C31×2−1+412yes—
453Q8—44no—
454Q8—82no—
455Q8—82no—
456Q8—82no—
457D4—28no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—22no—
461C2×C4—24no—
462C2×C4—21no—
463C2×C4—24no—
464C2×C4—24no—
465C2×C4—21no—
466C2×C4—28no—
467C2×C4—42no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—44no—
473C2×C4—44no—
474C2×C4—42no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—44no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—44no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—44no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—81no—
492C2×C4—82no—
493C2×C4—82no—
494C2×C4C31×#12011yescharacteristic
495C2×C4C31×#12011yescharacteristic
496C2×C4C31×#12012yes—
497C2×C4C31×C4⋊Q812yes—
498C22—22no—
499C22—21no—
500C22—22no—
501C22—21no—
502C22—22no—
503C22—42no—
504C22—42no—
505C22—42no—
506C22—41no—
507C22—41no—
508C22—81no—
509C22C2×C31×#12011yescharacteristic
510C22C2×C31×C4⋊Q811yescharacteristic
511C22C31×#53611yescharacteristic
512C22D4×Q8×C3114yes—
513C4—22no—
514C4—21no—
515C4—21no—
516C4—22no—
517C4—48no—
518C4—42no—
519C4—44no—
520C4—41no—
521C4—41no—
522C4—44no—
523C4—81no—
524C4—81no—
525C4—81no—
526C2—24no—
527C2—21no—
528C2—21no—
529C2—42no—
530C2C31×#243411yescharacteristic
531C2C31×#302511yescharacteristic
532C2C31×#302611yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC24C24×C31
prime radicalC22×D4×C31C23
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2583C2semidirect
4. C31×#2062C2semidirect
5. C31×#2062C2semidirect
6. C31×#1996C2semidirect
97. C31×#99Q8semidirect
170. C22⋊C4×C31C2×Q8semidirect
175. #25854C31direct (N × H)
233. #2583C2×C31semidirect
235. #2062C2×C31semidirect
236. #2062C2×C31semidirect
237. #1996C2×C31semidirect
363. #99Q8×C31semidirect
372. C31#25854direct (N × H)
437. C22⋊C4C2×Q8×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#35012
C31×#25832
C31×#25792
C31×#20622
C31×#19962
C31×#18672
C4×C31×#992
#2585431