Finite Group Databasebeta

← C31×#23510 #21480269

Subgroups — C31×#23510 #21480269

Order 7936.

1414 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#536C211yesmaximal, characteristic
2C2×C31×#417C211yesmaximal, characteristic
3C2×C31×#419C211yesmaximal, characteristic, complemented
4C2×C31×#416C211yesmaximal, characteristic
5C22×C31×#103C211yesmaximal, characteristic, complemented
6C31×#2317C211yesmaximal, characteristic, complemented
7C31×#2043C214yesmaximal, complemented
8C31×#2042C214yesmaximal, complemented
9C31×#1729C211yesmaximal, characteristic, complemented
10C22×#41×C31C2211yescharacteristic
11C23×Q8×C31C2211yescharacteristic
12C22×M16×C31C2211yescharacteristic
13C23×C8×C31C2211yescharacteristic
14C31×#536—24no—
15C31×#536—24no—
16C2×C31×C4⋊Q8C2212yes—
17C2×C31×#124C2212yes—
18C2×C31×#123—22no—
19C2×C31×C22⋊Q8—21no—
20C2×C31×C22⋊Q8—21no—
21C2×C31×#117C2211yescharacteristic
22C2×C31×#117C2211yescharacteristic
23C22×C4⋊C4×C31C2211yescharacteristic
24C31×#419—24no—
25C31×#417—24no—
26C31×#416—24no—
27C2×C31×#103—24no—
28C2×C31×#103C2214yes—
29C2×C31×#103C2212yes—
30C2×C31×#103C2214yes—
31C2×C31×#103C2212yes—
32C2×C31×#102C2212yes—
33C2×C31×#102C2212yes—
34C31×#389C2214yes—
35C31×#385—22no—
36C31×#384—21no—
37C31×#382—21no—
38C31×#336C2214yes—
39C2×#41×C31—22no—
40C2×#41×C31—22no—
41C2×#41×C31—22no—
42C2×#41×C31—22no—
43C2×#41×C31—22no—
44C2×#41×C31D414yes—
45C22×Q8×C31—21no—
46C22×Q8×C31—22no—
47C22×Q8×C31—22no—
48C22×Q8×C31—22no—
49C22×Q8×C31—22no—
50C22×Q8×C31—22no—
51C22×Q8×C31D414yes—
52C22×Q8×C31C2312yes—
53C22×Q8×C31C2311yescharacteristic
54C22×D4×C31—21no—
55C22×D4×C31C2311yescharacteristic
56C23×C4×C31—21no—
57C23×C4×C31—21no—
58C23×C4×C31—21no—
59C23×C4×C31C2311yescharacteristic
60C2×M16×C31—22no—
61C2×M16×C31—22no—
62C2×M16×C31—22no—
63C22×C8×C31—22no—
64C22×C8×C31—22no—
65C22×C8×C31—22no—
66C22×C8×C31C2312yes—
67C22×C8×C31C2312yes—
68C31×C4⋊Q8—24no—
69C31×C4⋊Q8—24no—
70C31×#124—24no—
71C31×#124—24no—
72C31×#123—216no—
73C31×C22⋊Q8—28no—
74C31×C22⋊Q8—28no—
75C31×#117—22no—
76C31×#117—22no—
77C31×#117—22no—
78C31×#117D414yes—
79C2×C4⋊C4×C31—22no—
80C2×C4⋊C4×C31—22no—
81C2×C4⋊C4×C31—22no—
82C2×C4⋊C4×C31—22no—
83C2×C4⋊C4×C31—21no—
84C2×C4⋊C4×C31—24no—
85C2×C4⋊C4×C31D411yescharacteristic
86C2×C4⋊C4×C31D411yescharacteristic
87C2×C4⋊C4×C31C2312yes—
88C2×C4⋊C4×C31C2312yes—
89C2×C22⋊C4×C31—21no—
90C2×C22⋊C4×C31—22no—
91C2×C22⋊C4×C31—22no—
92C2×C22⋊C4×C31D412yes—
93C2×C42×C31—21no—
94C2×C42×C31C2312yes—
95C31×#103—28no—
96C31×#103—24no—
97C31×#103—24no—
98C31×#103—28no—
99C31×#102—24no—
100C31×#102—24no—
101C31×#95—24no—
102C24×C31—21no—
103C24×C31C2×D411yescharacteristic
104#41×C31—28no—
105#41×C31—28no—
106#41×C31—44no—
107#41×C31—44no—
108C2×Q8×C31—24no—
109C2×Q8×C31—22no—
110C2×Q8×C31—21no—
111C2×Q8×C31—28no—
112C2×Q8×C31—28no—
113C2×Q8×C31—22no—
114C2×Q8×C31—21no—
115C2×Q8×C31—22no—
116C2×Q8×C31—22no—
117C2×Q8×C31—22no—
118C2×Q8×C31—21no—
119C2×Q8×C31—21no—
120C2×Q8×C31—21no—
121C2×Q8×C31—42no—
122C2×Q8×C31—44no—
123C2×Q8×C31—44no—
124C2×Q8×C31—42no—
125C2×Q8×C31C2×D414yes—
126C2×Q8×C31C2×D412yes—
127C2×D4×C31—24no—
128C2×D4×C31—21no—
129C2×D4×C31—21no—
130C2×D4×C31—21no—
131C2×D4×C31—21no—
132C2×D4×C31—21no—
133C2×D4×C31—42no—
134C2×D4×C31—42no—
135C2×D4×C31C2×D412yes—
136C22×C4×C31—24no—
137C22×C4×C31—22no—
138C22×C4×C31—22no—
139C22×C4×C31—21no—
140C22×C4×C31—24no—
141C22×C4×C31—22no—
142C22×C4×C31—42no—
143C22×C4×C31—42no—
144C22×C4×C31—42no—
145C22×C4×C31—42no—
146C22×C4×C31—42no—
147C22×C4×C31—82no—
148C22×C4×C31C2×D412yes—
149C22×C4×C31C2×D412yes—
150C22×C4×C31C2×D411yescharacteristic
151C22×C4×C31C2×D412yes—
152C22×C4×C31C2×D412yes—
153C22×C4×C31C2×D412yes—
154C22×C4×C31#4112yes—
155C22×C4×C31#4112yes—
156C22×C4×C31#4112yes—
157C22×C4×C31C2411yescharacteristic
158M16×C31—44no—
159C2×C8×C31—22no—
160C2×C8×C31—22no—
161C2×C8×C31—22no—
162C2×C8×C31—22no—
163C2×C8×C31—22no—
164C2×C8×C31—22no—
165C2×C8×C31—44no—
166C4⋊C4×C31—28no—
167C4⋊C4×C31—28no—
168C4⋊C4×C31—22no—
169C4⋊C4×C31—22no—
170C4⋊C4×C31—22no—
171C4⋊C4×C31—22no—
172C4⋊C4×C31—22no—
173C4⋊C4×C31—42no—
174C4⋊C4×C31—84no—
175C4⋊C4×C31C2×D414yes—
176C22⋊C4×C31—28no—
177C22⋊C4×C31—28no—
178C22⋊C4×C31—24no—
179C22⋊C4×C31—24no—
180C42×C31—24no—
181C42×C31—22no—
182C42×C31—22no—
183#23510C3111yesmaximal, characteristic, direct product factor, Sylow
184C23×C31—22no—
185C23×C31—22no—
186C23×C31—22no—
187C23×C31—41no—
188C23×C31—41no—
189C23×C31—42no—
190C23×C31—42no—
191C23×C31#12012yes—
192C23×C31#12112yes—
193C23×C31#12412yes—
194C23×C31C22×D411yescharacteristic
195Q8×C31—24no—
196Q8×C31—22no—
197Q8×C31—24no—
198Q8×C31—22no—
199Q8×C31—42no—
200Q8×C31—41no—
201Q8×C31—42no—
202Q8×C31—41no—
203Q8×C31—48no—
204D4×C31—22no—
205D4×C31—22no—
206D4×C31—48no—
207D4×C31—41no—
208D4×C31—41no—
209C2×C4×C31—22no—
210C2×C4×C31—22no—
211C2×C4×C31—24no—
212C2×C4×C31—22no—
213C2×C4×C31—24no—
214C2×C4×C31—24no—
215C2×C4×C31—24no—
216C2×C4×C31—41no—
217C2×C4×C31—42no—
218C2×C4×C31—41no—
219C2×C4×C31—42no—
220C2×C4×C31—42no—
221C2×C4×C31—42no—
222C2×C4×C31—48no—
223C2×C4×C31—48no—
224C2×C4×C31—42no—
225C2×C4×C31—44no—
226C2×C4×C31—84no—
227C2×C4×C31#12012yes—
228C2×C4×C31#12114yes—
229C2×C4×C31#12114yes—
230C2×C4×C31#12112yes—
231C2×C4×C31#12314yes—
232C2×C4×C31#12314yes—
233C2×C4×C31#12412yes—
234C2×C4×C31C22×D411yescharacteristic
235C2×C4×C31C22×D411yescharacteristic
236C2×C4×C31C22×D411yescharacteristic
237C2×C4×C31C2×#4111yescharacteristic
238C2×C4×C31C2×#4111yescharacteristic
239C2×C4×C31C2×#4111yescharacteristic
240C8×C31—42no—
241C8×C31—42no—
242C2×#536C2×C3111yescharacteristic
243C2×#417C2×C3111yescharacteristic
244C2×#419C2×C3111yescharacteristic, complemented
245C2×#416C2×C3111yescharacteristic
246C22×#103C2×C3111yescharacteristic, complemented
247#2317C2×C3111yescharacteristic, complemented
248#2043C2×C3114yescomplemented
249#2042C2×C3114yescomplemented
250#1729C2×C3111yescharacteristic, complemented
251C22×C31—24no—
252C22×C31—22no—
253C22×C31—22no—
254C22×C31—24no—
255C22×C31—42no—
256C22×C31—42no—
257C22×C31—42no—
258C22×C31—82no—
259C22×C31—82no—
260C22×C31#39414yes—
261C22×C31C2×#12011yescharacteristic
262C22×C31C2×#12111yescharacteristic
263C22×C31C2×#12411yescharacteristic
264C22×C31#57712yes—
265C22×C31#57812yes—
266C4×C31—42no—
267C4×C31—44no—
268C4×C31—42no—
269C4×C31—42no—
270C4×C31—44no—
271C4×C31—82no—
272C4×C31#39414yes—
273C4×C31C2×#12111yescharacteristic
274C4×C31C2×#12111yescharacteristic
275C4×C31C2×#12311yescharacteristic
276C4×C31C2×#12311yescharacteristic
277C22×#41C22×C3111yescharacteristic
278C23×Q8C22×C3111yescharacteristic
279C22×M16C22×C3111yescharacteristic
280C23×C8C22×C3111yescharacteristic
281#536—24no—
282#536—24no—
283C2×C4⋊Q8C22×C3112yes—
284C2×#124C22×C3112yes—
285C2×#123—22no—
286C2×C22⋊Q8—21no—
287C2×C22⋊Q8—21no—
288C2×#117C22×C3111yescharacteristic
289C2×#117C22×C3111yescharacteristic
290C22×C4⋊C4C22×C3111yescharacteristic
291#419—24no—
292#417—24no—
293#416—24no—
294C2×#103—24no—
295C2×#103C22×C3114yes—
296C2×#103C22×C3112yes—
297C2×#103C22×C3114yes—
298C2×#103C22×C3112yes—
299C2×#102C22×C3112yes—
300C2×#102C22×C3112yes—
301#389C22×C3114yes—
302#385—22no—
303#384—21no—
304#382—21no—
305#336C22×C3114yes—
306C2×C31—24no—
307C2×C31—82no—
308C2×C31C2×#39411yescharacteristic
309C2×C31#301011yescharacteristic
310C2×C31#301111yescharacteristic
311C2×C31#304612yes—
312C2×C31#313712yes—
313C2×#41—22no—
314C2×#41—22no—
315C2×#41—22no—
316C2×#41—22no—
317C2×#41—22no—
318C2×#41D4×C3114yes—
319C22×Q8—21no—
320C22×Q8—22no—
321C22×Q8—22no—
322C22×Q8—22no—
323C22×Q8—22no—
324C22×Q8—22no—
325C22×Q8D4×C3114yes—
326C22×Q8C23×C3112yes—
327C22×Q8C23×C3111yescharacteristic
328C22×D4—21no—
329C22×D4C23×C3111yescharacteristic
330C23×C4—21no—
331C23×C4—21no—
332C23×C4—21no—
333C23×C4C23×C3111yescharacteristic
334C2×M16—22no—
335C2×M16—22no—
336C2×M16—22no—
337C22×C8—22no—
338C22×C8—22no—
339C22×C8—22no—
340C22×C8C23×C3112yes—
341C22×C8C23×C3112yes—
342C4⋊Q8—24no—
343C4⋊Q8—24no—
344#124—24no—
345#124—24no—
346#123—216no—
347C22⋊Q8—28no—
348C22⋊Q8—28no—
349#117—22no—
350#117—22no—
351#117—22no—
352#117D4×C3114yes—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4D4×C3111yescharacteristic
360C2×C4⋊C4D4×C3111yescharacteristic
361C2×C4⋊C4C23×C3112yes—
362C2×C4⋊C4C23×C3112yes—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4D4×C3112yes—
367C2×C42—21no—
368C2×C42C23×C3112yes—
369#103—28no—
370#103—24no—
371#103—24no—
372#103—28no—
373#102—24no—
374#102—24no—
375#95—24no—
376C31#2351011yescharacteristic, direct product factor, Sylow
377C24—21no—
378C24C2×D4×C3111yescharacteristic
379#41—28no—
380#41—28no—
381#41—44no—
382#41—44no—
383C2×Q8—24no—
384C2×Q8—22no—
385C2×Q8—21no—
386C2×Q8—28no—
387C2×Q8—28no—
388C2×Q8—22no—
389C2×Q8—21no—
390C2×Q8—22no—
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8—21no—
394C2×Q8—21no—
395C2×Q8—21no—
396C2×Q8—42no—
397C2×Q8—44no—
398C2×Q8—44no—
399C2×Q8—42no—
400C2×Q8C2×D4×C3114yes—
401C2×Q8C2×D4×C3112yes—
402C2×D4—24no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—42no—
409C2×D4—42no—
410C2×D4C2×D4×C3112yes—
411C22×C4—24no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—24no—
416C22×C4—22no—
417C22×C4—42no—
418C22×C4—42no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—42no—
422C22×C4—82no—
423C22×C4C2×D4×C3112yes—
424C22×C4C2×D4×C3112yes—
425C22×C4C2×D4×C3111yescharacteristic
426C22×C4C2×D4×C3112yes—
427C22×C4C2×D4×C3112yes—
428C22×C4C2×D4×C3112yes—
429C22×C4#41×C3112yes—
430C22×C4#41×C3112yes—
431C22×C4#41×C3112yes—
432C22×C4C24×C3111yescharacteristic
433M16—44no—
434C2×C8—22no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—22no—
438C2×C8—22no—
439C2×C8—22no—
440C2×C8—44no—
441C4⋊C4—28no—
442C4⋊C4—28no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—42no—
449C4⋊C4—84no—
450C4⋊C4C2×D4×C3114yes—
451C22⋊C4—28no—
452C22⋊C4—28no—
453C22⋊C4—24no—
454C22⋊C4—24no—
455C42—24no—
456C42—22no—
457C42—22no—
458C23—22no—
459C23—22no—
460C23—22no—
461C23—41no—
462C23—41no—
463C23—42no—
464C23—42no—
465C23C31×#12012yes—
466C23C31×#12112yes—
467C23C31×#12412yes—
468C23C22×D4×C3111yescharacteristic
469Q8—24no—
470Q8—22no—
471Q8—24no—
472Q8—22no—
473Q8—42no—
474Q8—41no—
475Q8—42no—
476Q8—41no—
477Q8—48no—
478D4—22no—
479D4—22no—
480D4—48no—
481D4—41no—
482D4—41no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—24no—
486C2×C4—22no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—41no—
491C2×C4—42no—
492C2×C4—41no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—48no—
497C2×C4—48no—
498C2×C4—42no—
499C2×C4—44no—
500C2×C4—84no—
501C2×C4C31×#12012yes—
502C2×C4C31×#12114yes—
503C2×C4C31×#12114yes—
504C2×C4C31×#12112yes—
505C2×C4C31×#12314yes—
506C2×C4C31×#12314yes—
507C2×C4C31×#12412yes—
508C2×C4C22×D4×C3111yescharacteristic
509C2×C4C22×D4×C3111yescharacteristic
510C2×C4C22×D4×C3111yescharacteristic
511C2×C4C2×#41×C3111yescharacteristic
512C2×C4C2×#41×C3111yescharacteristic
513C2×C4C2×#41×C3111yescharacteristic
514C8—42no—
515C8—42no—
516C22—24no—
517C22—22no—
518C22—22no—
519C22—24no—
520C22—42no—
521C22—42no—
522C22—42no—
523C22—82no—
524C22—82no—
525C22C31×#39414yes—
526C22C2×C31×#12011yescharacteristic
527C22C2×C31×#12111yescharacteristic
528C22C2×C31×#12411yescharacteristic
529C22C31×#57712yes—
530C22C31×#57812yes—
531C4—42no—
532C4—44no—
533C4—42no—
534C4—42no—
535C4—44no—
536C4—82no—
537C4C31×#39414yes—
538C4C2×C31×#12111yescharacteristic
539C4C2×C31×#12111yescharacteristic
540C4C2×C31×#12311yescharacteristic
541C4C2×C31×#12311yescharacteristic
542C2—24no—
543C2—82no—
544C2C2×C31×#39411yescharacteristic
545C2C31×#301011yescharacteristic
546C2C31×#301111yescharacteristic
547C2C31×#304612yes—
548C2C31×#313712yes—
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC22×#41×C31C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C31×#117 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C31×#419C2semidirect
5. C22×C31×#103C2semidirect
6. C31×#2317C2semidirect
7. C31×#2043C2semidirect
8. C31×#2042C2semidirect
9. C31×#1729C2semidirect
183. #23510C31direct (N × H)
244. C2×#419C2×C31semidirect
246. C22×#103C2×C31semidirect
247. #2317C2×C31semidirect
248. #2043C2×C31semidirect
249. #2042C2×C31semidirect
250. #1729C2×C31semidirect
376. C31#23510direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5362
C2×C31×#4172
C2×C31×#4192
C2×C31×#4162
C22×C31×#1032
C31×#23172
C31×#20432
C31×#20422
C31×#17292
#2351031