Finite Group Databasebeta

← C31×#21455 #21478214

Subgroups — C31×#21455 #21478214

Order 7936.

1436 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Q8×C31C211yesmaximal, characteristic
2C2×C31×#451C211yesmaximal, characteristic
3C2×C31×#441C212yesmaximal, complemented
4C4×C31×C22⋊Q8C211yesmaximal, characteristic
5C31×#1878C212yesmaximal, complemented
6C31×#1872C211yesmaximal, characteristic
7C31×#1865C212yesmaximal, complemented
8C31×#1853C211yesmaximal, characteristic
9C31×#1787C211yesmaximal, characteristic
10C31×#1763C212yesmaximal, complemented
11C31×#1749C211yesmaximal, characteristic
12C23×Q8×C31C2211yescharacteristic
13C22×Q16×C31C2212yes—
14C2×C31×C22⋊Q8C2211yescharacteristic
15C2×C4×Q8×C31—28no—
16C2×C4×Q8×C31—21no—
17C2×C4×Q8×C31—21no—
18C2×C4×Q8×C31C2212yes—
19C2×C4×Q8×C31C2211yescharacteristic
20C2×C4×Q8×C31C2212yes—
21C22×C4⋊C4×C31—21no—
22C22×C4⋊C4×C31C2211yescharacteristic
23C22×C42×C31—21no—
24C22×C42×C31C2211yescharacteristic
25C31×#451C418yescomplemented
26C31×#441—28no—
27C2×C31×#106C2212yes—
28C2×C31×#103C2212yes—
29C2×C31×#103C2212yes—
30C2×C31×#103C2212yes—
31C2×C31×#103C2212yes—
32C2×C31×C22⋊C8C2211yescharacteristic
33C2×C31×C22⋊C8C2211yescharacteristic
34C2×C31×#97C2212yes—
35C31×#391C2211yescharacteristic
36C31×#389C2211yescharacteristic
37C31×#387—21no—
38C31×#385—21no—
39C31×#380C2211yescharacteristic
40C4×C4⋊C4×C31—21no—
41C4×C4⋊C4×C31C2211yescharacteristic
42C4×C22⋊C4×C31—21no—
43C31×#340C2212yes—
44C31×#340C2212yes—
45C31×#336C2212yes—
46C22×Q8×C31—24no—
47C22×Q8×C31—24no—
48C22×Q8×C31—21no—
49C22×Q8×C31—22no—
50C22×Q8×C31C2×C414yes—
51C22×Q8×C31C2311yescharacteristic
52C22×Q8×C31C2312yes—
53C23×C4×C31—21no—
54C23×C4×C31—21no—
55C23×C4×C31D411yescharacteristic
56C23×C4×C31D411yescharacteristic
57C23×C4×C31C2311yescharacteristic
58C2×Q16×C31—24no—
59C2×Q16×C31—24no—
60C2×Q16×C31C2×C418yescomplemented
61C22×C8×C31C2312yes—
62C22×C8×C31C2312yes—
63C31×C22⋊Q8—22no—
64C31×C22⋊Q8C2×C414yes—
65C4×Q8×C31—28no—
66C4×Q8×C31—28no—
67C4×Q8×C31—24no—
68C4×Q8×C31—24no—
69C4×Q8×C31—24no—
70C4×Q8×C31—24no—
71C4×Q8×C31D418yes—
72C2×C4⋊C4×C31—28no—
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—21no—
80C2×C4⋊C4×C31C2311yescharacteristic
81C2×C4⋊C4×C31C2311yescharacteristic
82C2×C4⋊C4×C31C2311yescharacteristic
83C2×C4⋊C4×C31C2312yes—
84C2×C22⋊C4×C31—21no—
85C2×C22⋊C4×C31—21no—
86C2×C42×C31—28no—
87C2×C42×C31—22no—
88C2×C42×C31—22no—
89C2×C42×C31—24no—
90C2×C42×C31—21no—
91C2×C42×C31—21no—
92C2×C42×C31D411yescharacteristic
93C2×C42×C31D411yescharacteristic
94C2×C42×C31C2311yescharacteristic
95C2×C42×C31C2311yescharacteristic
96C31×#106—24no—
97C31×#103—24no—
98C31×#103—24no—
99C31×#103—24no—
100C31×#103C2×C418yescomplemented
101C31×C22⋊C8—22no—
102C31×C22⋊C8C2×C414yes—
103C31×#97—24no—
104C31×#95—21no—
105C31×#95—21no—
106C31×#95—21no—
107C31×#95—21no—
108C31×#95—21no—
109C24×C31C2×D411yescharacteristic
110C2×Q8×C31—24no—
111C2×Q8×C31—216no—
112C2×Q8×C31—24no—
113C2×Q8×C31—216no—
114C2×Q8×C31—24no—
115C2×Q8×C31—22no—
116C2×Q8×C31—22no—
117C2×Q8×C31—22no—
118C2×Q8×C31—21no—
119C2×Q8×C31—22no—
120C2×Q8×C31—22no—
121C2×Q8×C31C22×C412yes—
122C2×Q8×C31C22×C414yes—
123C2×Q8×C31C2×D414yes—
124C2×Q8×C31#4114yes—
125C22×C4×C31—24no—
126C22×C4×C31—24no—
127C22×C4×C31—24no—
128C22×C4×C31—22no—
129C22×C4×C31—22no—
130C22×C4×C31—22no—
131C22×C4×C31—22no—
132C22×C4×C31—22no—
133C22×C4×C31—22no—
134C22×C4×C31—24no—
135C22×C4×C31—22no—
136C22×C4×C31—21no—
137C22×C4×C31—21no—
138C22×C4×C31—22no—
139C22×C4×C31—22no—
140C22×C4×C31—21no—
141C22×C4×C31—21no—
142C22×C4×C31—41no—
143C22×C4×C31—42no—
144C22×C4×C31—42no—
145C22×C4×C31C22×C412yes—
146C22×C4×C31C2×D411yescharacteristic
147C22×C4×C31C2×D411yescharacteristic
148C22×C4×C31C2×D411yescharacteristic
149C22×C4×C31C2×D411yescharacteristic
150C22×C4×C31C2×D411yescharacteristic
151C22×C4×C31#4112yes—
152C22×C4×C31C2411yescharacteristic
153Q16×C31—216no—
154C2×C8×C31—22no—
155C2×C8×C31—22no—
156C2×C8×C31—22no—
157C2×C8×C31—22no—
158C2×C8×C31—22no—
159C2×C8×C31C22×C414yes—
160C4⋊C4×C31—28no—
161C4⋊C4×C31—24no—
162C4⋊C4×C31—24no—
163C4⋊C4×C31—28no—
164C4⋊C4×C31—22no—
165C4⋊C4×C31—21no—
166C4⋊C4×C31—22no—
167C4⋊C4×C31—22no—
168C4⋊C4×C31—42no—
169C4⋊C4×C31—42no—
170C4⋊C4×C31C22×C412yes—
171C4⋊C4×C31C2×D414yes—
172C22⋊C4×C31—24no—
173C22⋊C4×C31—42no—
174C42×C31—28no—
175C42×C31—28no—
176C42×C31—22no—
177C42×C31—22no—
178C42×C31—22no—
179C42×C31—42no—
180C42×C31—42no—
181C42×C31C2×D414yes—
182#21455C3111yesmaximal, characteristic, direct product factor, Sylow
183C23×C31—21no—
184C23×C31—21no—
185C23×C31—21no—
186C23×C31—21no—
187C23×C31C4×D412yes—
188C23×C31#13712yes—
189C23×C31#13712yes—
190C23×C31C22×D411yescharacteristic
191Q8×C31—216no—
192Q8×C31—24no—
193Q8×C31—24no—
194Q8×C31—24no—
195Q8×C31—24no—
196Q8×C31—42no—
197Q8×C31C4×D418yes—
198C2×C4×C31—28no—
199C2×C4×C31—216no—
200C2×C4×C31—24no—
201C2×C4×C31—21no—
202C2×C4×C31—24no—
203C2×C4×C31—21no—
204C2×C4×C31—24no—
205C2×C4×C31—21no—
206C2×C4×C31—21no—
207C2×C4×C31—21no—
208C2×C4×C31—21no—
209C2×C4×C31—21no—
210C2×C4×C31—21no—
211C2×C4×C31—24no—
212C2×C4×C31—24no—
213C2×C4×C31—22no—
214C2×C4×C31—22no—
215C2×C4×C31—21no—
216C2×C4×C31—24no—
217C2×C4×C31—21no—
218C2×C4×C31—21no—
219C2×C4×C31—44no—
220C2×C4×C31—48no—
221C2×C4×C31—41no—
222C2×C4×C31—41no—
223C2×C4×C31—41no—
224C2×C4×C31—42no—
225C2×C4×C31—41no—
226C2×C4×C31—42no—
227C2×C4×C31—41no—
228C2×C4×C31—41no—
229C2×C4×C31—41no—
230C2×C4×C31—41no—
231C2×C4×C31—41no—
232C2×C4×C31—41no—
233C2×C4×C31C4×D412yes—
234C2×C4×C31#12012yes—
235C2×C4×C31#12012yes—
236C2×C4×C31#13712yes—
237C2×C4×C31C23×C411yescharacteristic
238C2×C4×C31C22×D412yes—
239C2×C4×C31C2×#4112yes—
240C2×C4×C31C2×#4111yescharacteristic
241C8×C31—24no—
242C8×C31—42no—
243C22×C4×Q8C2×C3111yescharacteristic
244C2×#451C2×C3111yescharacteristic
245C2×#441C2×C3112yescomplemented
246C4×C22⋊Q8C2×C3111yescharacteristic
247#1878C2×C3112yescomplemented
248#1872C2×C3111yescharacteristic
249#1865C2×C3112yescomplemented
250#1853C2×C3111yescharacteristic
251#1787C2×C3111yescharacteristic
252#1763C2×C3112yescomplemented
253#1749C2×C3111yescharacteristic
254C22×C31—22no—
255C22×C31—22no—
256C22×C31—22no—
257C22×C31—22no—
258C22×C31—22no—
259C22×C31—22no—
260C22×C31#44114yescomplemented
261C22×C31C2×C4×D411yescharacteristic
262C22×C31C2×#12011yescharacteristic
263C22×C31#52511yescharacteristic
264C22×C31C2×#13711yescharacteristic
265C22×C31C2×#13711yescharacteristic
266C22×C31C2×#13711yescharacteristic
267C22×C31#57511yescharacteristic
268C4×C31—22no—
269C4×C31—22no—
270C4×C31—22no—
271C4×C31—28no—
272C4×C31—22no—
273C4×C31—42no—
274C4×C31—41no—
275C4×C31—44no—
276C4×C31—42no—
277C4×C31—81no—
278C4×C31—81no—
279C4×C31C2×C4×D412yes—
280C4×C31#52512yes—
281C23×Q8C22×C3111yescharacteristic
282C22×Q16C22×C3112yes—
283C2×C22⋊Q8C22×C3111yescharacteristic
284C2×C4×Q8—28no—
285C2×C4×Q8—21no—
286C2×C4×Q8—21no—
287C2×C4×Q8C22×C3112yes—
288C2×C4×Q8C22×C3111yescharacteristic
289C2×C4×Q8C22×C3112yes—
290C22×C4⋊C4—21no—
291C22×C4⋊C4C22×C3111yescharacteristic
292C22×C42—21no—
293C22×C42C22×C3111yescharacteristic
294#451C4×C3118yescomplemented
295#441—28no—
296C2×#106C22×C3112yes—
297C2×#103C22×C3112yes—
298C2×#103C22×C3112yes—
299C2×#103C22×C3112yes—
300C2×#103C22×C3112yes—
301C2×C22⋊C8C22×C3111yescharacteristic
302C2×C22⋊C8C22×C3111yescharacteristic
303C2×#97C22×C3112yes—
304#391C22×C3111yescharacteristic
305#389C22×C3111yescharacteristic
306#387—21no—
307#385—21no—
308#380C22×C3111yescharacteristic
309C4×C4⋊C4—21no—
310C4×C4⋊C4C22×C3111yescharacteristic
311C4×C22⋊C4—21no—
312#340C22×C3112yes—
313#340C22×C3112yes—
314#336C22×C3112yes—
315C2×C31—24no—
316C2×C31C4×#12011yescharacteristic
317C2×C31C2×#44111yescharacteristic
318C2×C31C4×#13711yescharacteristic
319C2×C31#300411yescharacteristic
320C2×C31#300711yescharacteristic
321C2×C31#311311yescharacteristic
322C2×C31#311711yescharacteristic
323C22×Q8—24no—
324C22×Q8—24no—
325C22×Q8—21no—
326C22×Q8—22no—
327C22×Q8C2×C4×C3114yes—
328C22×Q8C23×C3111yescharacteristic
329C22×Q8C23×C3112yes—
330C23×C4—21no—
331C23×C4—21no—
332C23×C4D4×C3111yescharacteristic
333C23×C4D4×C3111yescharacteristic
334C23×C4C23×C3111yescharacteristic
335C2×Q16—24no—
336C2×Q16—24no—
337C2×Q16C2×C4×C3118yescomplemented
338C22×C8C23×C3112yes—
339C22×C8C23×C3112yes—
340C22⋊Q8—22no—
341C22⋊Q8C2×C4×C3114yes—
342C4×Q8—28no—
343C4×Q8—28no—
344C4×Q8—24no—
345C4×Q8—24no—
346C4×Q8—24no—
347C4×Q8—24no—
348C4×Q8D4×C3118yes—
349C2×C4⋊C4—28no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4C23×C3111yescharacteristic
358C2×C4⋊C4C23×C3111yescharacteristic
359C2×C4⋊C4C23×C3111yescharacteristic
360C2×C4⋊C4C23×C3112yes—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C42—28no—
364C2×C42—22no—
365C2×C42—22no—
366C2×C42—24no—
367C2×C42—21no—
368C2×C42—21no—
369C2×C42D4×C3111yescharacteristic
370C2×C42D4×C3111yescharacteristic
371C2×C42C23×C3111yescharacteristic
372C2×C42C23×C3111yescharacteristic
373#106—24no—
374#103—24no—
375#103—24no—
376#103—24no—
377#103C2×C4×C3118yescomplemented
378C22⋊C8—22no—
379C22⋊C8C2×C4×C3114yes—
380#97—24no—
381#95—21no—
382#95—21no—
383#95—21no—
384#95—21no—
385#95—21no—
386C31#2145511yescharacteristic, direct product factor, Sylow
387C24C2×D4×C3111yescharacteristic
388C2×Q8—24no—
389C2×Q8—216no—
390C2×Q8—24no—
391C2×Q8—216no—
392C2×Q8—24no—
393C2×Q8—22no—
394C2×Q8—22no—
395C2×Q8—22no—
396C2×Q8—21no—
397C2×Q8—22no—
398C2×Q8—22no—
399C2×Q8C22×C4×C3112yes—
400C2×Q8C22×C4×C3114yes—
401C2×Q8C2×D4×C3114yes—
402C2×Q8#41×C3114yes—
403C22×C4—24no—
404C22×C4—24no—
405C22×C4—24no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—24no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—41no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4C22×C4×C3112yes—
424C22×C4C2×D4×C3111yescharacteristic
425C22×C4C2×D4×C3111yescharacteristic
426C22×C4C2×D4×C3111yescharacteristic
427C22×C4C2×D4×C3111yescharacteristic
428C22×C4C2×D4×C3111yescharacteristic
429C22×C4#41×C3112yes—
430C22×C4C24×C3111yescharacteristic
431Q16—216no—
432C2×C8—22no—
433C2×C8—22no—
434C2×C8—22no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8C22×C4×C3114yes—
438C4⋊C4—28no—
439C4⋊C4—24no—
440C4⋊C4—24no—
441C4⋊C4—28no—
442C4⋊C4—22no—
443C4⋊C4—21no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—42no—
447C4⋊C4—42no—
448C4⋊C4C22×C4×C3112yes—
449C4⋊C4C2×D4×C3114yes—
450C22⋊C4—24no—
451C22⋊C4—42no—
452C42—28no—
453C42—28no—
454C42—22no—
455C42—22no—
456C42—22no—
457C42—42no—
458C42—42no—
459C42C2×D4×C3114yes—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23C4×D4×C3112yes—
465C23C31×#13712yes—
466C23C31×#13712yes—
467C23C22×D4×C3111yescharacteristic
468Q8—216no—
469Q8—24no—
470Q8—24no—
471Q8—24no—
472Q8—24no—
473Q8—42no—
474Q8C4×D4×C3118yes—
475C2×C4—28no—
476C2×C4—216no—
477C2×C4—24no—
478C2×C4—21no—
479C2×C4—24no—
480C2×C4—21no—
481C2×C4—24no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—21no—
493C2×C4—24no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—44no—
497C2×C4—48no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—42no—
502C2×C4—41no—
503C2×C4—42no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4C4×D4×C3112yes—
511C2×C4C31×#12012yes—
512C2×C4C31×#12012yes—
513C2×C4C31×#13712yes—
514C2×C4C23×C4×C3111yescharacteristic
515C2×C4C22×D4×C3112yes—
516C2×C4C2×#41×C3112yes—
517C2×C4C2×#41×C3111yescharacteristic
518C8—24no—
519C8—42no—
520C22—22no—
521C22—22no—
522C22—22no—
523C22—22no—
524C22—22no—
525C22—22no—
526C22C31×#44114yescomplemented
527C22C2×C4×D4×C3111yescharacteristic
528C22C2×C31×#12011yescharacteristic
529C22C31×#52511yescharacteristic
530C22C2×C31×#13711yescharacteristic
531C22C2×C31×#13711yescharacteristic
532C22C2×C31×#13711yescharacteristic
533C22C31×#57511yescharacteristic
534C4—22no—
535C4—22no—
536C4—22no—
537C4—28no—
538C4—22no—
539C4—42no—
540C4—41no—
541C4—44no—
542C4—42no—
543C4—81no—
544C4—81no—
545C4C2×C4×D4×C3112yes—
546C4C31×#52512yes—
547C2—24no—
548C2C4×C31×#12011yescharacteristic
549C2C2×C31×#44111yescharacteristic
550C2C4×C31×#13711yescharacteristic
551C2C31×#300411yescharacteristic
552C2C31×#300711yescharacteristic
553C2C31×#311311yescharacteristic
554C2C31×#311711yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutatorC2×C4C23×C4×C31
Frattini, cosocleC22×C4C24×C31
prime radicalC24×C31C2×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C31×#441C2semidirect
5. C31×#1878C2semidirect
7. C31×#1865C2semidirect
10. C31×#1763C2semidirect
25. C31×#451C4semidirect
60. C2×Q16×C31C2×C4semidirect
100. C31×#103C2×C4semidirect
182. #21455C31direct (N × H)
245. C2×#441C2×C31semidirect
247. #1878C2×C31semidirect
249. #1865C2×C31semidirect
252. #1763C2×C31semidirect
260. C22×C31#441semidirect
294. #451C4×C31semidirect
337. C2×Q16C2×C4×C31semidirect
377. #103C2×C4×C31semidirect
386. C31#21455direct (N × H)
526. C22C31×#441semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Q8×C312
C2×C31×#4512
C2×C31×#4412
C4×C31×C22⋊Q82
C31×#18782
C31×#18722
C31×#18652
C31×#18532
C31×#17872
C31×#17632
C31×#17492
#2145531