Finite Group Databasebeta

← C31×#13920 #21470679

Subgroups — C31×#13920 #21470679

Order 7936.

2458 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×D4×C31C211yesmaximal, characteristic
2C2×C31×#390C212yesmaximal
3C2×C31×#389C212yesmaximal, complemented
4C2×C31×#380C212yesmaximal, complemented
5C31×#1439C214yesmaximal, complemented
6C31×C4⋊#95C211yesmaximal, characteristic, complemented
7C31×C22⋊#95C212yesmaximal, complemented
8C4×C31×#95C211yesmaximal, characteristic, complemented
9C23×D4×C31C2211yescharacteristic
10C24×C4×C31C2212yes—
11C2×C4×D4×C31—28no—
12C2×C4×D4×C31C418yescomplemented
13C22×C4⋊C4×C31C2212yes—
14C22×C4⋊C4×C31C2214yes—
15C22×C4⋊C4×C31C2211yescharacteristic
16C22×C22⋊C4×C31C2214yes—
17C22×C22⋊C4×C31C2214yes—
18C22×C22⋊C4×C31C2212yes—
19C22×C42×C31C2212yes—
20C22×C42×C31C2211yescharacteristic
21C31×#390—28no—
22C31×#389—28no—
23C31×#380—28no—
24C2×C31×#95C2211yescharacteristic
25C2×C31×#95C2212yes—
26C2×C31×#95C2212yes—
27C2×C31×#95C2214yes—
28C2×C31×#95C2212yes—
29C2×C31×#95C2211yescharacteristic
30C25×C31C2312yes—
31C22×D4×C31—24no—
32C22×D4×C31—24no—
33C22×D4×C31C2×C414yes—
34C22×D4×C31D414yes—
35C22×D4×C31Q814yes—
36C23×C4×C31—28no—
37C23×C4×C31—24no—
38C23×C4×C31—24no—
39C23×C4×C31—44no—
40C23×C4×C31C2×C418yes—
41C23×C4×C31C2314yes—
42C23×C4×C31C2311yescharacteristic
43C23×C4×C31C2312yes—
44C23×C4×C31C2312yes—
45C23×C4×C31C2312yes—
46C23×C4×C31C2311yescharacteristic
47C23×C4×C31C2311yescharacteristic
48C4×D4×C31—232no—
49C2×C4⋊C4×C31—28no—
50C2×C4⋊C4×C31—28no—
51C2×C4⋊C4×C31—24no—
52C2×C4⋊C4×C31—24no—
53C2×C4⋊C4×C31—24no—
54C2×C4⋊C4×C31—44no—
55C2×C4⋊C4×C31C2×C414yes—
56C2×C4⋊C4×C31D418yes—
57C2×C22⋊C4×C31—28no—
58C2×C22⋊C4×C31—28no—
59C2×C22⋊C4×C31—28no—
60C2×C22⋊C4×C31—28no—
61C2×C22⋊C4×C31—28no—
62C2×C22⋊C4×C31—44no—
63C2×C22⋊C4×C31—44no—
64C2×C22⋊C4×C31C2×C418yes—
65C2×C42×C31—24no—
66C2×C42×C31—24no—
67C2×C42×C31—24no—
68C2×C42×C31—24no—
69C2×C42×C31C2×C414yes—
70C31×#95—24no—
71C31×#95—28no—
72C31×#95—24no—
73C31×#95—22no—
74C31×#95—42no—
75C31×#95D414yescomplemented
76C24×C31—22no—
77C24×C31—24no—
78C24×C31—24no—
79C24×C31—22no—
80C24×C31—24no—
81C24×C31—22no—
82C24×C31—24no—
83C24×C31—22no—
84C24×C31C22×C414yes—
85C24×C31C2×D414yes—
86C24×C31C2×Q814yes—
87C24×C31C2411yescharacteristic
88C2×D4×C31—28no—
89C2×D4×C31—28no—
90C2×D4×C31—216no—
91C2×D4×C31—216no—
92C2×D4×C31C4⋊C4116yescomplemented
93C22×C4×C31—22no—
94C22×C4×C31—22no—
95C22×C4×C31—22no—
96C22×C4×C31—24no—
97C22×C4×C31—22no—
98C22×C4×C31—22no—
99C22×C4×C31—22no—
100C22×C4×C31—22no—
101C22×C4×C31—22no—
102C22×C4×C31—22no—
103C22×C4×C31—22no—
104C22×C4×C31—22no—
105C22×C4×C31—22no—
106C22×C4×C31—22no—
107C22×C4×C31—22no—
108C22×C4×C31—21no—
109C22×C4×C31—22no—
110C22×C4×C31—22no—
111C22×C4×C31—22no—
112C22×C4×C31—21no—
113C22×C4×C31—22no—
114C22×C4×C31—216no—
115C22×C4×C31—216no—
116C22×C4×C31—24no—
117C22×C4×C31—24no—
118C22×C4×C31—24no—
119C22×C4×C31—24no—
120C22×C4×C31—24no—
121C22×C4×C31—24no—
122C22×C4×C31—24no—
123C22×C4×C31—48no—
124C22×C4×C31—416no—
125C22×C4×C31—416no—
126C22×C4×C31C22×C412yes—
127C22×C4×C31C22×C414yes—
128C22×C4×C31C22×C412yes—
129C22×C4×C31C22×C412yes—
130C22×C4×C31C2×D414yes—
131C22×C4×C31C2×D418yes—
132C22×C4×C31C2×D412yes—
133C22×C4×C31C2×D414yes—
134C22×C4×C31C2×D412yes—
135C22×C4×C31C2×Q812yes—
136C22×C4×C31#4114yes—
137C22×C4×C31#4112yes—
138C22×C4×C31#4114yes—
139C4⋊C4×C31—416no—
140C4⋊C4×C31—48no—
141C4⋊C4×C31C22⋊C4116yescomplemented
142C22⋊C4×C31—216no—
143C22⋊C4×C31—416no—
144C22⋊C4×C31—416no—
145C42×C31—28no—
146C42×C31—48no—
147#13920C3111yesmaximal, characteristic, direct product factor, Sylow
148C23×C31—24no—
149C23×C31—24no—
150C23×C31—24no—
151C23×C31—24no—
152C23×C31—24no—
153C23×C31—24no—
154C23×C31—28no—
155C23×C31—28no—
156C23×C31—24no—
157C23×C31—28no—
158C23×C31—24no—
159C23×C31—24no—
160C23×C31—24no—
161C23×C31—28no—
162C23×C31—44no—
163C23×C31—44no—
164C23×C31—44no—
165C23×C31—44no—
166C23×C31—44no—
167C23×C31—44no—
168C23×C31—44no—
169C23×C31—44no—
170C23×C31C2×C4⋊C418yes—
171C23×C31C23×C411yescharacteristic
172C23×C31C22×D412yes—
173C23×C31C22×D411yescharacteristic
174C23×C31C22×D411yescharacteristic
175C23×C31C22×Q811yescharacteristic
176C23×C31C2×#4112yes—
177C23×C31C2×#4111yescharacteristic
178C23×C31C2×#4112yes—
179C23×C31H(5,𝔽2)12yes—
180C23×C31H(5,𝔽2)11yescharacteristic
181C23×C312−1+411yescharacteristic
182D4×C31—232no—
183C2×C4×C31—22no—
184C2×C4×C31—24no—
185C2×C4×C31—22no—
186C2×C4×C31—24no—
187C2×C4×C31—28no—
188C2×C4×C31—24no—
189C2×C4×C31—24no—
190C2×C4×C31—28no—
191C2×C4×C31—22no—
192C2×C4×C31—22no—
193C2×C4×C31—22no—
194C2×C4×C31—24no—
195C2×C4×C31—24no—
196C2×C4×C31—24no—
197C2×C4×C31—24no—
198C2×C4×C31—24no—
199C2×C4×C31—24no—
200C2×C4×C31—432no—
201C2×C4×C31—42no—
202C2×C4×C31—42no—
203C2×C4×C31—42no—
204C2×C4×C31—42no—
205C2×C4×C31—42no—
206C2×C4×C31—42no—
207C2×C4×C31—42no—
208C2×C4×C31—42no—
209C2×C4×C31—42no—
210C2×C4×C31—42no—
211C2×C4×C31—44no—
212C2×C4×C31—44no—
213C2×C4×C31—44no—
214C2×C4×C31—44no—
215C2×C4×C31—44no—
216C2×C4×C31—44no—
217C2×C4×C31—44no—
218C2×C4×C31C2×C22⋊C418yes—
219C2×C4×C31C2×C22⋊C414yes—
220C2×C4×C31C2×C4⋊C414yes—
221C2×C4×C31#11714yes—
222C2×C4×C31C4×D414yes—
223C2×C4×C31#12118yes—
224C2×C4×C31C22⋊Q818yes—
225C22×C4×D4C2×C3111yescharacteristic
226C2×#390C2×C3112yes—
227C2×#389C2×C3112yescomplemented
228C2×#380C2×C3112yescomplemented
229#1439C2×C3114yescomplemented
230C4⋊#95C2×C3111yescharacteristic, complemented
231C22⋊#95C2×C3112yescomplemented
232C4×#95C2×C3111yescharacteristic, complemented
233C22×C31—28no—
234C22×C31—28no—
235C22×C31—28no—
236C22×C31—44no—
237C22×C31—44no—
238C22×C31—44no—
239C22×C31—48no—
240C22×C31—48no—
241C22×C31—48no—
242C22×C31—48no—
243C22×C31—44no—
244C22×C31C22×C22⋊C411yescharacteristic
245C22×C31C22×C4⋊C411yescharacteristic
246C22×C31C2×#11711yescharacteristic
247C22×C31C2×C4×D411yescharacteristic
248C22×C31C4×#4111yescharacteristic
249C22×C31#51811yescharacteristic
250C22×C31#52011yescharacteristic
251C22×C31C2×#12112yes—
252C22×C31C2×C22⋊Q812yes—
253C22×C31#52912yes—
254C22×C31#53212yes—
255C22×C31#54012yes—
256C22×C31#54212yes—
257C22×C31D4212yes—
258C22×C31D4211yescharacteristic
259C22×C31#54612yes—
260C22×C31#54612yes—
261C22×C31#54711yescharacteristic
262C22×C31#54812yes—
263C22×C31D4×Q811yescharacteristic
264C22×C31#55012yes—
265C22×C31#55411yescharacteristic
266C22×C31#55412yes—
267C4×C31—24no—
268C4×C31—28no—
269C4×C31—42no—
270C4×C31—44no—
271C4×C31—44no—
272C4×C31—84no—
273C4×C31#38018yescomplemented
274C23×D4C22×C3111yescharacteristic
275C24×C4C22×C3112yes—
276C2×C4×D4—28no—
277C2×C4×D4C4×C3118yescomplemented
278C22×C4⋊C4C22×C3112yes—
279C22×C4⋊C4C22×C3114yes—
280C22×C4⋊C4C22×C3111yescharacteristic
281C22×C22⋊C4C22×C3114yes—
282C22×C22⋊C4C22×C3114yes—
283C22×C22⋊C4C22×C3112yes—
284C22×C42C22×C3112yes—
285C22×C42C22×C3111yescharacteristic
286#390—28no—
287#389—28no—
288#380—28no—
289C2×#95C22×C3111yescharacteristic
290C2×#95C22×C3112yes—
291C2×#95C22×C3112yes—
292C2×#95C22×C3114yes—
293C2×#95C22×C3112yes—
294C2×#95C22×C3111yescharacteristic
295C2×C31—48no—
296C2×C31C2×#38011yescharacteristic
297C2×C31#229311yescharacteristic
298C2×C31#231911yescharacteristic
299C2×C31D4×C22⋊C411yescharacteristic
300C2×C31#234111yescharacteristic
301C2×C31D4×C4⋊C411yescharacteristic
302C2×C31#234911yescharacteristic
303C2×C31#242712yes—
304C2×C31#242812yes—
305C2×C31#245212yes—
306C2×C31#245412yes—
307C25C23×C3112yes—
308C22×D4—24no—
309C22×D4—24no—
310C22×D4C2×C4×C3114yes—
311C22×D4D4×C3114yes—
312C22×D4Q8×C3114yes—
313C23×C4—28no—
314C23×C4—24no—
315C23×C4—24no—
316C23×C4—44no—
317C23×C4C2×C4×C3118yes—
318C23×C4C23×C3114yes—
319C23×C4C23×C3111yescharacteristic
320C23×C4C23×C3112yes—
321C23×C4C23×C3112yes—
322C23×C4C23×C3112yes—
323C23×C4C23×C3111yescharacteristic
324C23×C4C23×C3111yescharacteristic
325C4×D4—232no—
326C2×C4⋊C4—28no—
327C2×C4⋊C4—28no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—44no—
332C2×C4⋊C4C2×C4×C3114yes—
333C2×C4⋊C4D4×C3118yes—
334C2×C22⋊C4—28no—
335C2×C22⋊C4—28no—
336C2×C22⋊C4—28no—
337C2×C22⋊C4—28no—
338C2×C22⋊C4—28no—
339C2×C22⋊C4—44no—
340C2×C22⋊C4—44no—
341C2×C22⋊C4C2×C4×C3118yes—
342C2×C42—24no—
343C2×C42—24no—
344C2×C42—24no—
345C2×C42—24no—
346C2×C42C2×C4×C3114yes—
347#95—24no—
348#95—28no—
349#95—24no—
350#95—22no—
351#95—42no—
352#95D4×C3114yescomplemented
353C31#1392011yescharacteristic, direct product factor, Sylow
354C24—22no—
355C24—24no—
356C24—24no—
357C24—22no—
358C24—24no—
359C24—22no—
360C24—24no—
361C24—22no—
362C24C22×C4×C3114yes—
363C24C2×D4×C3114yes—
364C24C2×Q8×C3114yes—
365C24C24×C3111yescharacteristic
366C2×D4—28no—
367C2×D4—28no—
368C2×D4—216no—
369C2×D4—216no—
370C2×D4C4⋊C4×C31116yescomplemented
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—24no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—21no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—216no—
393C22×C4—216no—
394C22×C4—24no—
395C22×C4—24no—
396C22×C4—24no—
397C22×C4—24no—
398C22×C4—24no—
399C22×C4—24no—
400C22×C4—24no—
401C22×C4—48no—
402C22×C4—416no—
403C22×C4—416no—
404C22×C4C22×C4×C3112yes—
405C22×C4C22×C4×C3114yes—
406C22×C4C22×C4×C3112yes—
407C22×C4C22×C4×C3112yes—
408C22×C4C2×D4×C3114yes—
409C22×C4C2×D4×C3118yes—
410C22×C4C2×D4×C3112yes—
411C22×C4C2×D4×C3114yes—
412C22×C4C2×D4×C3112yes—
413C22×C4C2×Q8×C3112yes—
414C22×C4#41×C3114yes—
415C22×C4#41×C3112yes—
416C22×C4#41×C3114yes—
417C4⋊C4—416no—
418C4⋊C4—48no—
419C4⋊C4C22⋊C4×C31116yescomplemented
420C22⋊C4—216no—
421C22⋊C4—416no—
422C22⋊C4—416no—
423C42—28no—
424C42—48no—
425C23—24no—
426C23—24no—
427C23—24no—
428C23—24no—
429C23—24no—
430C23—24no—
431C23—28no—
432C23—28no—
433C23—24no—
434C23—28no—
435C23—24no—
436C23—24no—
437C23—24no—
438C23—28no—
439C23—44no—
440C23—44no—
441C23—44no—
442C23—44no—
443C23—44no—
444C23—44no—
445C23—44no—
446C23—44no—
447C23C2×C4⋊C4×C3118yes—
448C23C23×C4×C3111yescharacteristic
449C23C22×D4×C3112yes—
450C23C22×D4×C3111yescharacteristic
451C23C22×D4×C3111yescharacteristic
452C23C22×Q8×C3111yescharacteristic
453C23C2×#41×C3112yes—
454C23C2×#41×C3111yescharacteristic
455C23C2×#41×C3112yes—
456C23C31×H(5,𝔽2)12yes—
457C23C31×H(5,𝔽2)11yescharacteristic
458C23C31×2−1+411yescharacteristic
459D4—232no—
460C2×C4—22no—
461C2×C4—24no—
462C2×C4—22no—
463C2×C4—24no—
464C2×C4—28no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—28no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—432no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—44no—
489C2×C4—44no—
490C2×C4—44no—
491C2×C4—44no—
492C2×C4—44no—
493C2×C4—44no—
494C2×C4—44no—
495C2×C4C2×C22⋊C4×C3118yes—
496C2×C4C2×C22⋊C4×C3114yes—
497C2×C4C2×C4⋊C4×C3114yes—
498C2×C4C31×#11714yes—
499C2×C4C4×D4×C3114yes—
500C2×C4C31×#12118yes—
501C2×C4C31×C22⋊Q818yes—
502C22—28no—
503C22—28no—
504C22—28no—
505C22—44no—
506C22—44no—
507C22—44no—
508C22—48no—
509C22—48no—
510C22—48no—
511C22—48no—
512C22—44no—
513C22C22×C22⋊C4×C3111yescharacteristic
514C22C22×C4⋊C4×C3111yescharacteristic
515C22C2×C31×#11711yescharacteristic
516C22C2×C4×D4×C3111yescharacteristic
517C22C4×#41×C3111yescharacteristic
518C22C31×#51811yescharacteristic
519C22C31×#52011yescharacteristic
520C22C2×C31×#12112yes—
521C22C2×C31×C22⋊Q812yes—
522C22C31×#52912yes—
523C22C31×#53212yes—
524C22C31×#54012yes—
525C22C31×#54212yes—
526C22D42×C3112yes—
527C22D42×C3111yescharacteristic
528C22C31×#54612yes—
529C22C31×#54612yes—
530C22C31×#54711yescharacteristic
531C22C31×#54812yes—
532C22D4×Q8×C3111yescharacteristic
533C22C31×#55012yes—
534C22C31×#55411yescharacteristic
535C22C31×#55412yes—
536C4—24no—
537C4—28no—
538C4—42no—
539C4—44no—
540C4—44no—
541C4—84no—
542C4C31×#38018yescomplemented
543C2—48no—
544C2C2×C31×#38011yescharacteristic
545C2C31×#229311yescharacteristic
546C2C31×#231911yescharacteristic
547C2D4×C22⋊C4×C3111yescharacteristic
548C2C31×#234111yescharacteristic
549C2D4×C4⋊C4×C3111yescharacteristic
550C2C31×#234911yescharacteristic
551C2C31×#242712yes—
552C2C31×#242812yes—
553C2C31×#245212yes—
554C2C31×#245412yes—
subgroupG/H
center, socleC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC23×D4×C31C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C31×#389C2semidirect
4. C2×C31×#380C2semidirect
5. C31×#1439C2semidirect
6. C31×C4⋊#95C2semidirect
7. C31×C22⋊#95C2semidirect
8. C4×C31×#95C2semidirect
12. C2×C4×D4×C31C4semidirect
75. C31×#95D4semidirect
92. C2×D4×C31C4⋊C4semidirect
141. C4⋊C4×C31C22⋊C4semidirect
147. #13920C31direct (N × H)
227. C2×#389C2×C31semidirect
228. C2×#380C2×C31semidirect
229. #1439C2×C31semidirect
230. C4⋊#95C2×C31semidirect
231. C22⋊#95C2×C31semidirect
232. C4×#95C2×C31semidirect
273. C4×C31#380semidirect
277. C2×C4×D4C4×C31semidirect
352. #95D4×C31semidirect
353. C31#13920direct (N × H)
370. C2×D4C4⋊C4×C31semidirect
419. C4⋊C4C22⋊C4×C31semidirect
542. C4C31×#380semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D4×C312
C2×C31×#3902
C2×C31×#3892
C2×C31×#3802
C31×#14392
C31×C4⋊#952
C31×C22⋊#952
C4×C31×#952
#1392031