Finite Group Databasebeta

← C31×#23634 #21480393

Subgroups — C31×#23634 #21480393

Order 7936.

1010 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#417C211yesmaximal, characteristic
2C2×C31×#416C211yesmaximal, characteristic
3C31×#2317C211yesmaximal, characteristic, complemented
4C31×#2311C211yesmaximal, characteristic
5C31×#2074C212yesmaximal, complemented
6C31×#2073C212yesmaximal, complemented
7C31×#2072C212yesmaximal, complemented
8C31×#2071C212yesmaximal, complemented
9C31×#1736C211yesmaximal, characteristic, complemented
10C2×C31×#340C211yesmaximal, characteristic, complemented
11C31×#1729C211yesmaximal, characteristic, complemented
12C22×#41×C31C2211yescharacteristic
13C22×M16×C31C2211yescharacteristic
14C23×C8×C31C2211yescharacteristic
15C2×C31×#117C2211yescharacteristic
16C2×C31×#117C2211yescharacteristic
17C22×C4⋊C4×C31C2211yescharacteristic
18C22×C4⋊C4×C31C2211yescharacteristic
19C31×#417—24no—
20C31×#416—24no—
21C2×C31×#103C2211yescharacteristic
22C2×C31×#103C2212yes—
23C2×C31×#103C2211yescharacteristic
24C2×C31×#102C2211yescharacteristic
25C2×C31×#102C2212yes—
26C2×C31×#102C2211yescharacteristic
27C31×#391C2212yes—
28C31×#390C2212yes—
29C31×#389—21no—
30C31×#389—21no—
31C31×#386—22no—
32C31×#385—22no—
33C31×#384C2212yes—
34C31×#382C2212yes—
35C31×#380—21no—
36C31×#380—21no—
37C31×#340C2212yes—
38C31×#340C2212yes—
39C31×#340C2212yes—
40C31×#340C2212yes—
41C31×#336C2212yes—
42C31×#336C2212yes—
43C2×#41×C31—22no—
44C2×#41×C31—22no—
45C2×#41×C31—22no—
46C2×#41×C31—22no—
47C2×#41×C31—22no—
48C2×#41×C31D414yes—
49C22×Q8×C31C2311yescharacteristic
50C22×D4×C31—21no—
51C22×D4×C31C2311yescharacteristic
52C23×C4×C31—21no—
53C23×C4×C31—21no—
54C23×C4×C31—21no—
55C23×C4×C31C2311yescharacteristic
56C2×M16×C31—22no—
57C2×M16×C31—22no—
58C2×M16×C31—22no—
59C22×C8×C31—22no—
60C22×C8×C31—22no—
61C22×C8×C31—22no—
62C22×C8×C31C2311yescharacteristic
63C22×C8×C31C2311yescharacteristic
64C22×C8×C31C2312yes—
65C31×#117—22no—
66C31×#117—22no—
67C31×#117—22no—
68C31×#117—22no—
69C2×C4⋊C4×C31—22no—
70C2×C4⋊C4×C31—22no—
71C2×C4⋊C4×C31—22no—
72C2×C4⋊C4×C31—22no—
73C2×C4⋊C4×C31—21no—
74C2×C4⋊C4×C31—21no—
75C2×C4⋊C4×C31—22no—
76C2×C4⋊C4×C31—22no—
77C2×C4⋊C4×C31D411yescharacteristic
78C2×C4⋊C4×C31D411yescharacteristic
79C2×C4⋊C4×C31C2312yes—
80C2×C4⋊C4×C31C2311yescharacteristic
81C2×C4⋊C4×C31C2311yescharacteristic
82C2×C4⋊C4×C31C2312yes—
83C2×C22⋊C4×C31—21no—
84C2×C22⋊C4×C31—22no—
85C2×C22⋊C4×C31—22no—
86C2×C22⋊C4×C31D412yes—
87C2×C42×C31—21no—
88C2×C42×C31C2312yes—
89C31×#103—22no—
90C31×#103—22no—
91C31×#103—24no—
92C31×#102—22no—
93C31×#102—22no—
94C31×#102—24no—
95C31×#95—22no—
96C31×#95—22no—
97C31×#95—22no—
98C31×#95—22no—
99C24×C31—21no—
100C24×C31C2×D411yescharacteristic
101#41×C31—28no—
102#41×C31—28no—
103#41×C31—44no—
104#41×C31—44no—
105C2×Q8×C31—21no—
106C2×Q8×C31—21no—
107C2×Q8×C31—21no—
108C2×Q8×C31—21no—
109C2×Q8×C31—21no—
110C2×Q8×C31C2×D412yes—
111C2×D4×C31—24no—
112C2×D4×C31—21no—
113C2×D4×C31—21no—
114C2×D4×C31—21no—
115C2×D4×C31—21no—
116C2×D4×C31—21no—
117C2×D4×C31—42no—
118C2×D4×C31—42no—
119C2×D4×C31C2×D412yes—
120C22×C4×C31—21no—
121C22×C4×C31—24no—
122C22×C4×C31—21no—
123C22×C4×C31—22no—
124C22×C4×C31—22no—
125C22×C4×C31—21no—
126C22×C4×C31—42no—
127C22×C4×C31—42no—
128C22×C4×C31—42no—
129C22×C4×C31—42no—
130C22×C4×C31—81no—
131C22×C4×C31—81no—
132C22×C4×C31—81no—
133C22×C4×C31—81no—
134C22×C4×C31C2×D412yes—
135C22×C4×C31C2×D412yes—
136C22×C4×C31C2×D411yescharacteristic
137C22×C4×C31C2×D412yes—
138C22×C4×C31#4112yes—
139C22×C4×C31#4112yes—
140C22×C4×C31#4112yes—
141C22×C4×C31#4112yes—
142C22×C4×C31#4112yes—
143C22×C4×C31C2411yescharacteristic
144M16×C31—44no—
145C2×C8×C31—21no—
146C2×C8×C31—21no—
147C2×C8×C31—22no—
148C2×C8×C31—21no—
149C2×C8×C31—21no—
150C2×C8×C31—21no—
151C2×C8×C31—21no—
152C2×C8×C31—22no—
153C2×C8×C31—22no—
154C2×C8×C31—44no—
155C4⋊C4×C31—22no—
156C4⋊C4×C31—22no—
157C4⋊C4×C31—22no—
158C4⋊C4×C31—21no—
159C4⋊C4×C31—21no—
160C4⋊C4×C31—22no—
161C4⋊C4×C31—22no—
162C4⋊C4×C31—22no—
163C4⋊C4×C31—21no—
164C4⋊C4×C31—21no—
165C4⋊C4×C31—42no—
166C4⋊C4×C31—42no—
167C4⋊C4×C31—82no—
168C4⋊C4×C31—82no—
169C22⋊C4×C31—24no—
170C22⋊C4×C31—42no—
171C22⋊C4×C31—82no—
172C22⋊C4×C31—82no—
173C42×C31—22no—
174C42×C31—22no—
175C42×C31—42no—
176#23634C3111yesmaximal, characteristic, direct product factor, Sylow
177C23×C31—21no—
178C23×C31—21no—
179C23×C31—21no—
180C23×C31—21no—
181C23×C31—22no—
182C23×C31—41no—
183C23×C31—41no—
184C23×C31—41no—
185C23×C31—41no—
186C23×C31—41no—
187C23×C31—41no—
188C23×C31#12112yes—
189C23×C31#12312yes—
190C23×C31#12412yes—
191C23×C31C22×D411yescharacteristic
192Q8×C31—22no—
193Q8×C31—22no—
194Q8×C31—41no—
195Q8×C31—41no—
196D4×C31—22no—
197D4×C31—22no—
198D4×C31—48no—
199D4×C31—41no—
200D4×C31—41no—
201C2×C4×C31—22no—
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—41no—
209C2×C4×C31—41no—
210C2×C4×C31—48no—
211C2×C4×C31—41no—
212C2×C4×C31—41no—
213C2×C4×C31—42no—
214C2×C4×C31—42no—
215C2×C4×C31—42no—
216C2×C4×C31—41no—
217C2×C4×C31—42no—
218C2×C4×C31—42no—
219C2×C4×C31—41no—
220C2×C4×C31—42no—
221C2×C4×C31—41no—
222C2×C4×C31—41no—
223C2×C4×C31—84no—
224C2×C4×C31—84no—
225C2×C4×C31#12112yes—
226C2×C4×C31#12314yes—
227C2×C4×C31#12314yes—
228C2×C4×C31#12312yes—
229C2×C4×C31#12412yes—
230C2×C4×C31#12614yes—
231C2×C4×C31#12614yes—
232C2×C4×C31C22×D411yescharacteristic
233C2×C4×C31C2×#4111yescharacteristic
234C2×C4×C31C2×#4111yescharacteristic
235C2×C4×C31C2×#4111yescharacteristic
236C2×C4×C31C2×#4111yescharacteristic
237C2×C4×C31C2×#4111yescharacteristic
238C8×C31—41no—
239C8×C31—41no—
240C8×C31—42no—
241C2×#417C2×C3111yescharacteristic
242C2×#416C2×C3111yescharacteristic
243#2317C2×C3111yescharacteristic, complemented
244#2311C2×C3111yescharacteristic
245#2074C2×C3112yescomplemented
246#2073C2×C3112yescomplemented
247#2072C2×C3112yescomplemented
248#2071C2×C3112yescomplemented
249#1736C2×C3111yescharacteristic, complemented
250C2×#340C2×C3111yescharacteristic, complemented
251#1729C2×C3111yescharacteristic, complemented
252C22×C31—22no—
253C22×C31—22no—
254C22×C31—22no—
255C22×C31—22no—
256C22×C31—22no—
257C22×C31—22no—
258C22×C31—42no—
259C22×C31—42no—
260C22×C31—42no—
261C22×C31—81no—
262C22×C31—81no—
263C22×C31—81no—
264C22×C31—81no—
265C22×C31#39714yes—
266C22×C31C2×#12111yescharacteristic
267C22×C31C2×#12311yescharacteristic
268C22×C31C2×#12411yescharacteristic
269C22×C31#57611yescharacteristic
270C22×C31#57711yescharacteristic
271C22×C31#57711yescharacteristic
272C22×C31#57811yescharacteristic
273C4×C31—42no—
274C4×C31—42no—
275C4×C31—42no—
276C4×C31—82no—
277C4×C31—81no—
278C4×C31—82no—
279C4×C31—81no—
280C4×C31#39714yes—
281C4×C31C2×#12311yescharacteristic
282C4×C31C2×#12311yescharacteristic
283C4×C31C2×#12611yescharacteristic
284C4×C31C2×#12611yescharacteristic
285C22×#41C22×C3111yescharacteristic
286C22×M16C22×C3111yescharacteristic
287C23×C8C22×C3111yescharacteristic
288C2×#117C22×C3111yescharacteristic
289C2×#117C22×C3111yescharacteristic
290C22×C4⋊C4C22×C3111yescharacteristic
291C22×C4⋊C4C22×C3111yescharacteristic
292#417—24no—
293#416—24no—
294C2×#103C22×C3111yescharacteristic
295C2×#103C22×C3112yes—
296C2×#103C22×C3111yescharacteristic
297C2×#102C22×C3111yescharacteristic
298C2×#102C22×C3112yes—
299C2×#102C22×C3111yescharacteristic
300#391C22×C3112yes—
301#390C22×C3112yes—
302#389—21no—
303#389—21no—
304#386—22no—
305#385—22no—
306#384C22×C3112yes—
307#382C22×C3112yes—
308#380—21no—
309#380—21no—
310#340C22×C3112yes—
311#340C22×C3112yes—
312#340C22×C3112yes—
313#340C22×C3112yes—
314#336C22×C3112yes—
315#336C22×C3112yes—
316C2×C31—24no—
317C2×C31—82no—
318C2×C31C2×#39711yescharacteristic
319C2×C31#304511yescharacteristic
320C2×C31#304611yescharacteristic
321C2×C31#309811yescharacteristic
322C2×C31#309911yescharacteristic
323C2×C31#313611yescharacteristic
324C2×C31#313711yescharacteristic
325C2×#41—22no—
326C2×#41—22no—
327C2×#41—22no—
328C2×#41—22no—
329C2×#41—22no—
330C2×#41D4×C3114yes—
331C22×Q8C23×C3111yescharacteristic
332C22×D4—21no—
333C22×D4C23×C3111yescharacteristic
334C23×C4—21no—
335C23×C4—21no—
336C23×C4—21no—
337C23×C4C23×C3111yescharacteristic
338C2×M16—22no—
339C2×M16—22no—
340C2×M16—22no—
341C22×C8—22no—
342C22×C8—22no—
343C22×C8—22no—
344C22×C8C23×C3111yescharacteristic
345C22×C8C23×C3111yescharacteristic
346C22×C8C23×C3112yes—
347#117—22no—
348#117—22no—
349#117—22no—
350#117—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4D4×C3111yescharacteristic
360C2×C4⋊C4D4×C3111yescharacteristic
361C2×C4⋊C4C23×C3112yes—
362C2×C4⋊C4C23×C3112yes—
363C2×C4⋊C4C23×C3111yescharacteristic
364C2×C4⋊C4C23×C3111yescharacteristic
365C2×C22⋊C4—21no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4D4×C3112yes—
369C2×C42—21no—
370C2×C42C23×C3112yes—
371#103—22no—
372#103—22no—
373#103—24no—
374#102—22no—
375#102—22no—
376#102—24no—
377#95—22no—
378#95—22no—
379#95—22no—
380#95—22no—
381C31#2363411yescharacteristic, direct product factor, Sylow
382C24—21no—
383C24C2×D4×C3111yescharacteristic
384#41—28no—
385#41—28no—
386#41—44no—
387#41—44no—
388C2×Q8—21no—
389C2×Q8—21no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8—21no—
393C2×Q8C2×D4×C3112yes—
394C2×D4—24no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—21no—
398C2×D4—21no—
399C2×D4—21no—
400C2×D4—42no—
401C2×D4—42no—
402C2×D4C2×D4×C3112yes—
403C22×C4—21no—
404C22×C4—24no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—42no—
410C22×C4—42no—
411C22×C4—42no—
412C22×C4—42no—
413C22×C4—81no—
414C22×C4—81no—
415C22×C4—81no—
416C22×C4—81no—
417C22×C4C2×D4×C3112yes—
418C22×C4C2×D4×C3112yes—
419C22×C4C2×D4×C3111yescharacteristic
420C22×C4C2×D4×C3112yes—
421C22×C4#41×C3112yes—
422C22×C4#41×C3112yes—
423C22×C4#41×C3112yes—
424C22×C4#41×C3112yes—
425C22×C4#41×C3112yes—
426C22×C4C24×C3111yescharacteristic
427M16—44no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8—22no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—44no—
438C4⋊C4—22no—
439C4⋊C4—22no—
440C4⋊C4—22no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—42no—
449C4⋊C4—42no—
450C4⋊C4—82no—
451C4⋊C4—82no—
452C22⋊C4—24no—
453C22⋊C4—42no—
454C22⋊C4—82no—
455C22⋊C4—82no—
456C42—22no—
457C42—22no—
458C42—42no—
459C23—21no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—22no—
464C23—41no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23—41no—
469C23—41no—
470C23C31×#12112yes—
471C23C31×#12312yes—
472C23C31×#12412yes—
473C23C22×D4×C3111yescharacteristic
474Q8—22no—
475Q8—22no—
476Q8—41no—
477Q8—41no—
478D4—22no—
479D4—22no—
480D4—48no—
481D4—41no—
482D4—41no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—48no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—41no—
502C2×C4—42no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—84no—
506C2×C4—84no—
507C2×C4C31×#12112yes—
508C2×C4C31×#12312yes—
509C2×C4C31×#12314yes—
510C2×C4C31×#12314yes—
511C2×C4C31×#12412yes—
512C2×C4C31×#12614yes—
513C2×C4C31×#12614yes—
514C2×C4C22×D4×C3111yescharacteristic
515C2×C4C2×#41×C3111yescharacteristic
516C2×C4C2×#41×C3111yescharacteristic
517C2×C4C2×#41×C3111yescharacteristic
518C2×C4C2×#41×C3111yescharacteristic
519C2×C4C2×#41×C3111yescharacteristic
520C8—41no—
521C8—41no—
522C8—42no—
523C22—22no—
524C22—22no—
525C22—22no—
526C22—22no—
527C22—22no—
528C22—22no—
529C22—42no—
530C22—42no—
531C22—42no—
532C22—81no—
533C22—81no—
534C22—81no—
535C22—81no—
536C22C31×#39714yes—
537C22C2×C31×#12111yescharacteristic
538C22C2×C31×#12311yescharacteristic
539C22C2×C31×#12411yescharacteristic
540C22C31×#57611yescharacteristic
541C22C31×#57711yescharacteristic
542C22C31×#57711yescharacteristic
543C22C31×#57811yescharacteristic
544C4—42no—
545C4—42no—
546C4—42no—
547C4—82no—
548C4—82no—
549C4—81no—
550C4—81no—
551C4C31×#39714yes—
552C4C2×C31×#12311yescharacteristic
553C4C2×C31×#12311yescharacteristic
554C4C2×C31×#12611yescharacteristic
555C4C2×C31×#12611yescharacteristic
556C2—24no—
557C2—82no—
558C2C2×C31×#39711yescharacteristic
559C2C31×#304511yescharacteristic
560C2C31×#304611yescharacteristic
561C2C31×#309811yescharacteristic
562C2C31×#309911yescharacteristic
563C2C31×#313611yescharacteristic
564C2C31×#313711yescharacteristic
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. C31×#2317C2semidirect
5. C31×#2074C2semidirect
6. C31×#2073C2semidirect
7. C31×#2072C2semidirect
8. C31×#2071C2semidirect
9. C31×#1736C2semidirect
10. C2×C31×#340C2semidirect
11. C31×#1729C2semidirect
176. #23634C31direct (N × H)
243. #2317C2×C31semidirect
245. #2074C2×C31semidirect
246. #2073C2×C31semidirect
247. #2072C2×C31semidirect
248. #2071C2×C31semidirect
249. #1736C2×C31semidirect
250. C2×#340C2×C31semidirect
251. #1729C2×C31semidirect
381. C31#23634direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4172
C2×C31×#4162
C31×#23172
C31×#23112
C31×#20742
C31×#20732
C31×#20722
C31×#20712
C31×#17362
C2×C31×#3402
C31×#17292
#2363431