Finite Group Databasebeta

← C31×#23594 #21480353

Subgroups — C31×#23594 #21480353

Order 7936.

1038 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3461C211yesmaximal, characteristic
2C4×C31×#137C212yesmaximal, complemented
3C31×#2327C211yesmaximal, characteristic, complemented
4C31×#2061C211yesmaximal, characteristic, complemented
5C31×#2040C211yesmaximal, characteristic
6C31×#2038C212yesmaximal, complemented
7C31×#2028C211yesmaximal, characteristic, complemented
8C31×#2007C211yesmaximal, characteristic
9C31×#2005C212yesmaximal, complemented
10C31×#1759C212yesmaximal, complemented
11C4×C31×#101C211yesmaximal, characteristic, complemented
12C2×C31×#137C2212yes—
13C31×#544C2211yescharacteristic
14C31×#542—22no—
15C31×#541—22no—
16C31×#539—22no—
17C31×#537C2211yescharacteristic
18C31×#536C2212yes—
19C31×#533—22no—
20C2×C31×C4⋊Q8C2211yescharacteristic
21C31×#529—22no—
22C31×#529—22no—
23C4×#41×C31C2212yes—
24C2×C4×Q8×C31C2211yescharacteristic
25C2×C4×Q8×C31C2211yescharacteristic
26C31×#441—22no—
27C31×#440—22no—
28C4×Q16×C31—22no—
29C4×SD16×C31—22no—
30C31×#428C2212yes—
31C2×C31×#104C2212yes—
32C2×C31×#104C2212yes—
33C31×#419C2212yes—
34C31×#417C2212yes—
35C2×C31×#101C2212yes—
36C4×M16×C31C2212yes—
37C31×#391C2211yescharacteristic
38C31×#391C2211yescharacteristic
39C31×#387—22no—
40C31×#387—22no—
41C31×#382C2211yescharacteristic
42C31×#376C2211yescharacteristic
43C31×#343C2211yescharacteristic
44C31×#343C2211yescharacteristic
45C31×#339C2212yes—
46C31×#339C2212yes—
47C2×#41×C31C2312yes—
48C22×Q8×C31C2311yescharacteristic
49C22×Q8×C31C2311yescharacteristic
50C31×#137—24no—
51C31×#137—24no—
52C2×Q16×C31—22no—
53C2×SD16×C31—22no—
54C2×M16×C31C2312yes—
55C2×M16×C31C2312yes—
56C31×C4⋊Q8—22no—
57C31×C4⋊Q8—22no—
58C31×C4⋊Q8—22no—
59C31×C4⋊Q8—22no—
60C31×#126—24no—
61C31×#126—24no—
62C31×#125—22no—
63C31×#125—24no—
64C31×#125—22no—
65C31×#124—22no—
66C31×#124—22no—
67C31×#123—24no—
68C31×#123—24no—
69C31×C22⋊Q8—24no—
70C31×C22⋊Q8—22no—
71C31×C22⋊Q8—22no—
72C31×C22⋊Q8—22no—
73C31×C22⋊Q8—22no—
74C31×#121—22no—
75C31×#121—22no—
76C4×Q8×C31—22no—
77C4×Q8×C31—22no—
78C4×Q8×C31—22no—
79C4×Q8×C31—22no—
80C4×Q8×C31—22no—
81C4×Q8×C31D412yes—
82C4×Q8×C31D412yes—
83C4×D4×C31—22no—
84C4×D4×C31—22no—
85C4×D4×C31—22no—
86C4×D4×C31D412yes—
87C4×D4×C31D412yes—
88C31×#117—24no—
89C31×#117—22no—
90C31×#117C2312yes—
91C2×C4⋊C4×C31—22no—
92C2×C4⋊C4×C31—21no—
93C2×C4⋊C4×C31D412yes—
94C2×C4⋊C4×C31C2311yescharacteristic
95C2×C4⋊C4×C31C2311yescharacteristic
96C2×C42×C31—22no—
97C2×C42×C31—21no—
98C2×C42×C31D412yes—
99C2×C42×C31C2311yescharacteristic
100C2×C42×C31C2311yescharacteristic
101C2×C42×C31C2311yescharacteristic
102C31×#107—22no—
103C31×#106—22no—
104C31×#104—24no—
105C31×#104—24no—
106C31×#103—22no—
107C31×#103—22no—
108C31×#103—22no—
109C31×#102—22no—
110C31×#101—24no—
111C31×#97—22no—
112C4×C8×C31—22no—
113C31×#95—21no—
114C31×#95—21no—
115C31×#95—22no—
116C31×#95—22no—
117C31×#95—22no—
118#41×C31—22no—
119#41×C31—22no—
120#41×C31—22no—
121#41×C31—22no—
122C2×Q8×C31—22no—
123C2×Q8×C31—22no—
124C2×Q8×C31—22no—
125C2×Q8×C31—21no—
126C2×Q8×C31—21no—
127C2×Q8×C31—21no—
128C2×Q8×C31—22no—
129C2×Q8×C31—22no—
130C2×Q8×C31C2×D412yes—
131C2×Q8×C31#4112yes—
132C2×D4×C31—22no—
133C2×D4×C31—22no—
134C2×D4×C31C2×D412yes—
135C22×C4×C31—21no—
136C22×C4×C31—21no—
137C22×C4×C31—22no—
138C22×C4×C31—22no—
139C22×C4×C31—22no—
140C22×C4×C31—21no—
141C22×C4×C31—21no—
142C22×C4×C31C2×D412yes—
143C22×C4×C31C2×D412yes—
144C22×C4×C31C2×D411yescharacteristic
145C22×C4×C31C2×D411yescharacteristic
146C22×C4×C31C2411yescharacteristic
147Q16×C31—28no—
148SD16×C31—28no—
149M16×C31—22no—
150M16×C31—22no—
151M16×C31—22no—
152M16×C31#4114yes—
153C2×C8×C31—22no—
154C2×C8×C31—22no—
155C4⋊C4×C31—28no—
156C4⋊C4×C31—24no—
157C4⋊C4×C31—24no—
158C4⋊C4×C31—22no—
159C4⋊C4×C31—22no—
160C4⋊C4×C31—24no—
161C4⋊C4×C31—24no—
162C4⋊C4×C31—22no—
163C4⋊C4×C31—22no—
164C4⋊C4×C31—22no—
165C4⋊C4×C31—22no—
166C4⋊C4×C31—41no—
167C4⋊C4×C31—41no—
168C4⋊C4×C31C2×D412yes—
169C4⋊C4×C31C2×D412yes—
170C22⋊C4×C31—24no—
171C22⋊C4×C31—24no—
172C22⋊C4×C31—24no—
173C22⋊C4×C31—22no—
174C22⋊C4×C31—22no—
175C22⋊C4×C31—22no—
176C42×C31—22no—
177C42×C31—22no—
178C42×C31—22no—
179C42×C31—22no—
180C42×C31—22no—
181C42×C31—21no—
182C42×C31—22no—
183C42×C31—42no—
184C42×C31C2×D412yes—
185C42×C31C2×D412yes—
186C42×C31#4112yes—
187#23594C3111yesmaximal, characteristic, direct product factor, Sylow
188C23×C31—22no—
189C23×C31C22×D411yescharacteristic
190Q8×C31—24no—
191Q8×C31—22no—
192Q8×C31—22no—
193Q8×C31—42no—
194Q8×C31—42no—
195Q8×C31—42no—
196Q8×C31—82no—
197D4×C31—22no—
198D4×C31—22no—
199D4×C31—42no—
200D4×C31—42no—
201D4×C31—82no—
202C2×C4×C31—22no—
203C2×C4×C31—22no—
204C2×C4×C31—22no—
205C2×C4×C31—22no—
206C2×C4×C31—22no—
207C2×C4×C31—22no—
208C2×C4×C31—22no—
209C2×C4×C31—22no—
210C2×C4×C31—22no—
211C2×C4×C31—41no—
212C2×C4×C31—41no—
213C2×C4×C31—44no—
214C2×C4×C31—41no—
215C2×C4×C31—41no—
216C2×C4×C31—41no—
217C2×C4×C31—41no—
218C2×C4×C31—42no—
219C2×C4×C31—42no—
220C2×C4×C31—42no—
221C2×C4×C31—41no—
222C2×C4×C31—41no—
223C2×C4×C31—42no—
224C2×C4×C31—41no—
225C2×C4×C31—41no—
226C2×C4×C31—82no—
227C2×C4×C31#12011yescharacteristic
228C2×C4×C31#12011yescharacteristic
229C2×C4×C31#12012yes—
230C2×C4×C31C22×D412yes—
231C2×C4×C31C2×#4111yescharacteristic
232C2×C4×C31C2×#4112yes—
233C2×C4×C31C2×#4111yescharacteristic
234C8×C31—24no—
235C8×C31—42no—
236#3461C2×C3111yescharacteristic
237C4×#137C2×C3112yescomplemented
238#2327C2×C3111yescharacteristic, complemented
239#2061C2×C3111yescharacteristic, complemented
240#2040C2×C3111yescharacteristic
241#2038C2×C3112yescomplemented
242#2028C2×C3111yescharacteristic, complemented
243#2007C2×C3111yescharacteristic
244#2005C2×C3112yescomplemented
245#1759C2×C3112yescomplemented
246C4×#101C2×C3111yescharacteristic, complemented
247C22×C31—21no—
248C22×C31—21no—
249C22×C31—42no—
250C22×C31—42no—
251C22×C31—42no—
252C22×C31C2×#12011yescharacteristic
253C22×C31#52511yescharacteristic
254C22×C31#53211yescharacteristic
255C4×C31—21no—
256C4×C31—21no—
257C4×C31—22no—
258C4×C31—42no—
259C4×C31—42no—
260C4×C31—42no—
261C4×C31—42no—
262C4×C31—42no—
263C4×C31—42no—
264C4×C31—42no—
265C4×C31—81no—
266C4×C31—81no—
267C4×C31#52512yes—
268C4×C31#53212yes—
269C2×#137C22×C3112yes—
270#544C22×C3111yescharacteristic
271#542—22no—
272#541—22no—
273#539—22no—
274#537C22×C3111yescharacteristic
275#536C22×C3112yes—
276#533—22no—
277C2×C4⋊Q8C22×C3111yescharacteristic
278#529—22no—
279#529—22no—
280C4×#41C22×C3112yes—
281C2×C4×Q8C22×C3111yescharacteristic
282C2×C4×Q8C22×C3111yescharacteristic
283#441—22no—
284#440—22no—
285C4×Q16—22no—
286C4×SD16—22no—
287#428C22×C3112yes—
288C2×#104C22×C3112yes—
289C2×#104C22×C3112yes—
290#419C22×C3112yes—
291#417C22×C3112yes—
292C2×#101C22×C3112yes—
293C4×M16C22×C3112yes—
294#391C22×C3111yescharacteristic
295#391C22×C3111yescharacteristic
296#387—22no—
297#387—22no—
298#382C22×C3111yescharacteristic
299#376C22×C3111yescharacteristic
300#343C22×C3111yescharacteristic
301#343C22×C3111yescharacteristic
302#339C22×C3112yes—
303#339C22×C3112yes—
304C2×C31—21no—
305C2×C31—21no—
306C2×C31—82no—
307C2×C31#238811yescharacteristic
308C2×C31#302011yescharacteristic
309C2×C31#302211yescharacteristic
310C2×#41C23×C3112yes—
311C22×Q8C23×C3111yescharacteristic
312C22×Q8C23×C3111yescharacteristic
313#137—24no—
314#137—24no—
315C2×Q16—22no—
316C2×SD16—22no—
317C2×M16C23×C3112yes—
318C2×M16C23×C3112yes—
319C4⋊Q8—22no—
320C4⋊Q8—22no—
321C4⋊Q8—22no—
322C4⋊Q8—22no—
323#126—24no—
324#126—24no—
325#125—22no—
326#125—24no—
327#125—22no—
328#124—22no—
329#124—22no—
330#123—24no—
331#123—24no—
332C22⋊Q8—24no—
333C22⋊Q8—22no—
334C22⋊Q8—22no—
335C22⋊Q8—22no—
336C22⋊Q8—22no—
337#121—22no—
338#121—22no—
339C4×Q8—22no—
340C4×Q8—22no—
341C4×Q8—22no—
342C4×Q8—22no—
343C4×Q8—22no—
344C4×Q8D4×C3112yes—
345C4×Q8D4×C3112yes—
346C4×D4—22no—
347C4×D4—22no—
348C4×D4—22no—
349C4×D4D4×C3112yes—
350C4×D4D4×C3112yes—
351#117—24no—
352#117—22no—
353#117C23×C3112yes—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4D4×C3112yes—
357C2×C4⋊C4C23×C3111yescharacteristic
358C2×C4⋊C4C23×C3111yescharacteristic
359C2×C42—22no—
360C2×C42—21no—
361C2×C42D4×C3112yes—
362C2×C42C23×C3111yescharacteristic
363C2×C42C23×C3111yescharacteristic
364C2×C42C23×C3111yescharacteristic
365#107—22no—
366#106—22no—
367#104—24no—
368#104—24no—
369#103—22no—
370#103—22no—
371#103—22no—
372#102—22no—
373#101—24no—
374#97—22no—
375C4×C8—22no—
376#95—21no—
377#95—21no—
378#95—22no—
379#95—22no—
380#95—22no—
381C31#2359411yescharacteristic, direct product factor, Sylow
382#41—22no—
383#41—22no—
384#41—22no—
385#41—22no—
386C2×Q8—22no—
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8—21no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8—22no—
393C2×Q8—22no—
394C2×Q8C2×D4×C3112yes—
395C2×Q8#41×C3112yes—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4C2×D4×C3112yes—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4C2×D4×C3112yes—
407C22×C4C2×D4×C3112yes—
408C22×C4C2×D4×C3111yescharacteristic
409C22×C4C2×D4×C3111yescharacteristic
410C22×C4C24×C3111yescharacteristic
411Q16—28no—
412SD16—28no—
413M16—22no—
414M16—22no—
415M16—22no—
416M16#41×C3114yes—
417C2×C8—22no—
418C2×C8—22no—
419C4⋊C4—28no—
420C4⋊C4—24no—
421C4⋊C4—24no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—24no—
425C4⋊C4—24no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—22no—
429C4⋊C4—22no—
430C4⋊C4—41no—
431C4⋊C4—41no—
432C4⋊C4C2×D4×C3112yes—
433C4⋊C4C2×D4×C3112yes—
434C22⋊C4—24no—
435C22⋊C4—24no—
436C22⋊C4—24no—
437C22⋊C4—22no—
438C22⋊C4—22no—
439C22⋊C4—22no—
440C42—22no—
441C42—22no—
442C42—22no—
443C42—22no—
444C42—22no—
445C42—21no—
446C42—22no—
447C42—42no—
448C42C2×D4×C3112yes—
449C42C2×D4×C3112yes—
450C42#41×C3112yes—
451C23—22no—
452C23C22×D4×C3111yescharacteristic
453Q8—24no—
454Q8—22no—
455Q8—22no—
456Q8—42no—
457Q8—42no—
458Q8—42no—
459Q8—82no—
460D4—22no—
461D4—22no—
462D4—42no—
463D4—42no—
464D4—82no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—44no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—42no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—82no—
490C2×C4C31×#12011yescharacteristic
491C2×C4C31×#12011yescharacteristic
492C2×C4C31×#12012yes—
493C2×C4C22×D4×C3112yes—
494C2×C4C2×#41×C3111yescharacteristic
495C2×C4C2×#41×C3112yes—
496C2×C4C2×#41×C3111yescharacteristic
497C8—24no—
498C8—42no—
499C22—21no—
500C22—21no—
501C22—42no—
502C22—42no—
503C22—42no—
504C22C2×C31×#12011yescharacteristic
505C22C31×#52511yescharacteristic
506C22C31×#53211yescharacteristic
507C4—21no—
508C4—21no—
509C4—22no—
510C4—42no—
511C4—42no—
512C4—42no—
513C4—42no—
514C4—42no—
515C4—42no—
516C4—42no—
517C4—81no—
518C4—81no—
519C4C31×#52512yes—
520C4C31×#53212yes—
521C2—21no—
522C2—21no—
523C2—82no—
524C2C31×#238811yescharacteristic
525C2C31×#302011yescharacteristic
526C2C31×#302211yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#537C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×C31×#137C2semidirect
3. C31×#2327C2semidirect
4. C31×#2061C2semidirect
6. C31×#2038C2semidirect
7. C31×#2028C2semidirect
9. C31×#2005C2semidirect
10. C31×#1759C2semidirect
11. C4×C31×#101C2semidirect
187. #23594C31direct (N × H)
237. C4×#137C2×C31semidirect
238. #2327C2×C31semidirect
239. #2061C2×C31semidirect
241. #2038C2×C31semidirect
242. #2028C2×C31semidirect
244. #2005C2×C31semidirect
245. #1759C2×C31semidirect
246. C4×#101C2×C31semidirect
381. C31#23594direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#34612
C4×C31×#1372
C31×#23272
C31×#20612
C31×#20402
C31×#20382
C31×#20282
C31×#20072
C31×#20052
C31×#17592
C4×C31×#1012
#2359431