Finite Group Databasebeta

← C31×#13940 #21470699

Subgroups — C31×#13940 #21470699

Order 7936.

2230 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C31C211yesmaximal, characteristic
2C2×C31×#381C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊C4×C31C211yesmaximal, characteristic, complemented
4C31×#1440C212yesmaximal, complemented
5C31×#1438C212yesmaximal
6C31×#1437C212yesmaximal, complemented
7C31×#1436C212yesmaximal, complemented
8C31×#1434C212yesmaximal, complemented
9C31×C22⋊#95C212yesmaximal, complemented
10C23×D4×C31C2211yescharacteristic
11C24×C4×C31C2211yescharacteristic
12C24×C4×C31C2211yescharacteristic
13C2×C4×D4×C31—24no—
14C2×C4×D4×C31—24no—
15C2×C4×D4×C31C418yescomplemented
16C22×C4⋊C4×C31C2211yescharacteristic
17C22×C22⋊C4×C31C2212yes—
18C22×C22⋊C4×C31C2214yes—
19C22×C22⋊C4×C31C2211yescharacteristic
20C22×C22⋊C4×C31C2211yescharacteristic
21C22×C22⋊C4×C31C2212yes—
22C22×C42×C31C2211yescharacteristic
23C22×C42×C31C2212yes—
24C31×#381—24no—
25C4×C22⋊C4×C31—24no—
26C2×C31×#95C2212yes—
27C2×C31×#95C2212yes—
28C2×C31×#95C2214yes—
29C2×C31×#95C2214yes—
30C2×C31×#95C2212yes—
31C2×C31×#95C2214yes—
32C25×C31C2311yescharacteristic
33C25×C31C2311yescharacteristic
34C22×D4×C31—22no—
35C22×D4×C31—22no—
36C22×D4×C31—24no—
37C22×D4×C31—24no—
38C22×D4×C31C2×C414yes—
39C23×C4×C31—22no—
40C23×C4×C31—22no—
41C23×C4×C31—44no—
42C23×C4×C31—44no—
43C23×C4×C31C2×C414yes—
44C23×C4×C31C2×C414yes—
45C23×C4×C31D414yes—
46C23×C4×C31D414yes—
47C23×C4×C31C2314yes—
48C23×C4×C31C2311yescharacteristic
49C23×C4×C31C2311yescharacteristic
50C23×C4×C31C2314yes—
51C23×C4×C31C2311yescharacteristic
52C23×C4×C31C2311yescharacteristic
53C23×C4×C31C2311yescharacteristic
54C4×D4×C31—232no—
55C2×C4⋊C4×C31—22no—
56C2×C4⋊C4×C31—22no—
57C2×C4⋊C4×C31C2×C414yes—
58C2×C22⋊C4×C31—22no—
59C2×C22⋊C4×C31—22no—
60C2×C22⋊C4×C31—24no—
61C2×C22⋊C4×C31—22no—
62C2×C22⋊C4×C31—22no—
63C2×C22⋊C4×C31—28no—
64C2×C22⋊C4×C31—24no—
65C2×C22⋊C4×C31—28no—
66C2×C22⋊C4×C31—28no—
67C2×C22⋊C4×C31—44no—
68C2×C22⋊C4×C31—44no—
69C2×C22⋊C4×C31C2×C414yes—
70C2×C22⋊C4×C31C2×C414yes—
71C2×C42×C31—22no—
72C2×C42×C31—22no—
73C2×C42×C31—24no—
74C2×C42×C31—44no—
75C2×C42×C31C2×C414yes—
76C31×#95—24no—
77C31×#95—24no—
78C31×#95—24no—
79C31×#95—28no—
80C31×#95—28no—
81C31×#95—44no—
82C24×C31—21no—
83C24×C31—21no—
84C24×C31—24no—
85C24×C31—24no—
86C24×C31—22no—
87C24×C31—22no—
88C24×C31—22no—
89C24×C31—24no—
90C24×C31—24no—
91C24×C31C22×C412yes—
92C24×C31C22×C412yes—
93C24×C31C2×D412yes—
94C24×C31C2×D412yes—
95C24×C31#4114yes—
96C24×C31C2411yescharacteristic
97C2×D4×C31—216no—
98C2×D4×C31—216no—
99C2×D4×C31—28no—
100C2×D4×C31—28no—
101C2×D4×C31—28no—
102C22×C4×C31—21no—
103C22×C4×C31—21no—
104C22×C4×C31—22no—
105C22×C4×C31—24no—
106C22×C4×C31—24no—
107C22×C4×C31—24no—
108C22×C4×C31—21no—
109C22×C4×C31—21no—
110C22×C4×C31—21no—
111C22×C4×C31—21no—
112C22×C4×C31—24no—
113C22×C4×C31—24no—
114C22×C4×C31—24no—
115C22×C4×C31—24no—
116C22×C4×C31—24no—
117C22×C4×C31—24no—
118C22×C4×C31—24no—
119C22×C4×C31—28no—
120C22×C4×C31—24no—
121C22×C4×C31—24no—
122C22×C4×C31—24no—
123C22×C4×C31—24no—
124C22×C4×C31—24no—
125C22×C4×C31—24no—
126C22×C4×C31—24no—
127C22×C4×C31—48no—
128C22×C4×C31—48no—
129C22×C4×C31—48no—
130C22×C4×C31—48no—
131C22×C4×C31—48no—
132C22×C4×C31—48no—
133C22×C4×C31C22⋊C4116yescomplemented
134C22×C4×C31C22×C412yes—
135C22×C4×C31C22×C412yes—
136C22×C4×C31C22×C412yes—
137C22×C4×C31C22×C412yes—
138C22×C4×C31C22×C412yes—
139C22×C4×C31C2×D412yes—
140C22×C4×C31C2×D412yes—
141C22×C4×C31C2×D412yes—
142C22×C4×C31C2×D412yes—
143C22×C4×C31#4118yes—
144C22×C4×C31#4114yes—
145C4⋊C4×C31—28no—
146C22⋊C4×C31—216no—
147C22⋊C4×C31—28no—
148C22⋊C4×C31—28no—
149C22⋊C4×C31—416no—
150C22⋊C4×C31—48no—
151C42×C31—28no—
152C42×C31—48no—
153#13940C3111yesmaximal, characteristic, direct product factor, Sylow
154C23×C31—22no—
155C23×C31—22no—
156C23×C31—22no—
157C23×C31—22no—
158C23×C31—24no—
159C23×C31—24no—
160C23×C31—24no—
161C23×C31—24no—
162C23×C31—24no—
163C23×C31—24no—
164C23×C31—24no—
165C23×C31—24no—
166C23×C31—24no—
167C23×C31—24no—
168C23×C31—24no—
169C23×C31—24no—
170C23×C31—28no—
171C23×C31—28no—
172C23×C31—42no—
173C23×C31—42no—
174C23×C31—42no—
175C23×C31—42no—
176C23×C31—44no—
177C23×C31—44no—
178C23×C31—44no—
179C23×C31—44no—
180C23×C31—44no—
181C23×C31—44no—
182C23×C31C2×C22⋊C414yes—
183C23×C31#11714yes—
184C23×C31C23×C411yescharacteristic
185C23×C31C22×D411yescharacteristic
186C23×C31C22×D411yescharacteristic
187C23×C31C2×#4112yes—
188C23×C31C2×#4112yes—
189C23×C31C2×#4114yes—
190C23×C31H(5,𝔽2)14yes—
191D4×C31—232no—
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—24no—
201C2×C4×C31—24no—
202C2×C4×C31—22no—
203C2×C4×C31—22no—
204C2×C4×C31—24no—
205C2×C4×C31—24no—
206C2×C4×C31—28no—
207C2×C4×C31—28no—
208C2×C4×C31—28no—
209C2×C4×C31—416no—
210C2×C4×C31—416no—
211C2×C4×C31—44no—
212C2×C4×C31—42no—
213C2×C4×C31—42no—
214C2×C4×C31—44no—
215C2×C4×C31—42no—
216C2×C4×C31—42no—
217C2×C4×C31—44no—
218C2×C4×C31—44no—
219C2×C4×C31—44no—
220C2×C4×C31—44no—
221C2×C4×C31—44no—
222C2×C4×C31—44no—
223C2×C4×C31—44no—
224C2×C4×C31—44no—
225C2×C4×C31—44no—
226C2×C4×C31C2×C22⋊C414yes—
227C2×C4×C31C2×C22⋊C414yes—
228C2×C4×C31#11714yes—
229C22×C4×D4C2×C3111yescharacteristic
230C2×#381C2×C3111yescharacteristic, complemented
231C2×C4×C22⋊C4C2×C3111yescharacteristic, complemented
232#1440C2×C3112yescomplemented
233#1438C2×C3112yes—
234#1437C2×C3112yescomplemented
235#1436C2×C3112yescomplemented
236#1434C2×C3112yescomplemented
237C22⋊#95C2×C3112yescomplemented
238C22×C31—24no—
239C22×C31—28no—
240C22×C31—24no—
241C22×C31—24no—
242C22×C31—24no—
243C22×C31—42no—
244C22×C31—48no—
245C22×C31—48no—
246C22×C31—48no—
247C22×C31—48no—
248C22×C31—44no—
249C22×C31—44no—
250C22×C31—44no—
251C22×C31—42no—
252C22×C31C22×C22⋊C411yescharacteristic
253C22×C31C2×#11711yescharacteristic
254C22×C31C2×#11711yescharacteristic
255C22×C31C4×#4112yes—
256C22×C31#51812yes—
257C22×C31#52512yes—
258C22×C31#52512yes—
259C22×C31#52512yes—
260C22×C31#53212yes—
261C22×C31#53412yes—
262C22×C31#53412yes—
263C22×C31#55114yes—
264C22×C31#55314yes—
265C22×C31#55314yes—
266C22×C31#55914yes—
267C4×C31—24no—
268C4×C31—24no—
269C4×C31—24no—
270C4×C31—42no—
271C4×C31—48no—
272C4×C31—42no—
273C4×C31—84no—
274C23×D4C22×C3111yescharacteristic
275C24×C4C22×C3111yescharacteristic
276C24×C4C22×C3111yescharacteristic
277C2×C4×D4—24no—
278C2×C4×D4—24no—
279C2×C4×D4C4×C3118yescomplemented
280C22×C4⋊C4C22×C3111yescharacteristic
281C22×C22⋊C4C22×C3112yes—
282C22×C22⋊C4C22×C3114yes—
283C22×C22⋊C4C22×C3111yescharacteristic
284C22×C22⋊C4C22×C3111yescharacteristic
285C22×C22⋊C4C22×C3112yes—
286C22×C42C22×C3111yescharacteristic
287C22×C42C22×C3112yes—
288#381—24no—
289C4×C22⋊C4—24no—
290C2×#95C22×C3112yes—
291C2×#95C22×C3112yes—
292C2×#95C22×C3114yes—
293C2×#95C22×C3114yes—
294C2×#95C22×C3112yes—
295C2×#95C22×C3114yes—
296C2×C31—44no—
297C2×C31—44no—
298C2×C31#228011yescharacteristic
299C2×C31#229711yescharacteristic
300C2×C31#230811yescharacteristic
301C2×C31#235312yes—
302C2×C31#235712yes—
303C2×C31#260014yes—
304C2×C31#260214yes—
305C25C23×C3111yescharacteristic
306C25C23×C3111yescharacteristic
307C22×D4—22no—
308C22×D4—22no—
309C22×D4—24no—
310C22×D4—24no—
311C22×D4C2×C4×C3114yes—
312C23×C4—22no—
313C23×C4—22no—
314C23×C4—44no—
315C23×C4—44no—
316C23×C4C2×C4×C3114yes—
317C23×C4C2×C4×C3114yes—
318C23×C4D4×C3114yes—
319C23×C4D4×C3114yes—
320C23×C4C23×C3114yes—
321C23×C4C23×C3111yescharacteristic
322C23×C4C23×C3111yescharacteristic
323C23×C4C23×C3114yes—
324C23×C4C23×C3111yescharacteristic
325C23×C4C23×C3111yescharacteristic
326C23×C4C23×C3111yescharacteristic
327C4×D4—232no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4C2×C4×C3114yes—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—28no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—28no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—44no—
341C2×C22⋊C4—44no—
342C2×C22⋊C4C2×C4×C3114yes—
343C2×C22⋊C4C2×C4×C3114yes—
344C2×C42—22no—
345C2×C42—22no—
346C2×C42—24no—
347C2×C42—44no—
348C2×C42C2×C4×C3114yes—
349#95—24no—
350#95—24no—
351#95—24no—
352#95—28no—
353#95—28no—
354#95—44no—
355C31#1394011yescharacteristic, direct product factor, Sylow
356C24—21no—
357C24—21no—
358C24—24no—
359C24—24no—
360C24—22no—
361C24—22no—
362C24—22no—
363C24—24no—
364C24—24no—
365C24C22×C4×C3112yes—
366C24C22×C4×C3112yes—
367C24C2×D4×C3112yes—
368C24C2×D4×C3112yes—
369C24#41×C3114yes—
370C24C24×C3111yescharacteristic
371C2×D4—216no—
372C2×D4—216no—
373C2×D4—28no—
374C2×D4—28no—
375C2×D4—28no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—24no—
380C22×C4—24no—
381C22×C4—24no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—24no—
387C22×C4—24no—
388C22×C4—24no—
389C22×C4—24no—
390C22×C4—24no—
391C22×C4—24no—
392C22×C4—24no—
393C22×C4—28no—
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—48no—
403C22×C4—48no—
404C22×C4—48no—
405C22×C4—48no—
406C22×C4—48no—
407C22×C4C22⋊C4×C31116yescomplemented
408C22×C4C22×C4×C3112yes—
409C22×C4C22×C4×C3112yes—
410C22×C4C22×C4×C3112yes—
411C22×C4C22×C4×C3112yes—
412C22×C4C22×C4×C3112yes—
413C22×C4C2×D4×C3112yes—
414C22×C4C2×D4×C3112yes—
415C22×C4C2×D4×C3112yes—
416C22×C4C2×D4×C3112yes—
417C22×C4#41×C3118yes—
418C22×C4#41×C3114yes—
419C4⋊C4—28no—
420C22⋊C4—216no—
421C22⋊C4—28no—
422C22⋊C4—28no—
423C22⋊C4—416no—
424C22⋊C4—48no—
425C42—28no—
426C42—48no—
427C23—22no—
428C23—22no—
429C23—22no—
430C23—22no—
431C23—24no—
432C23—24no—
433C23—24no—
434C23—24no—
435C23—24no—
436C23—24no—
437C23—24no—
438C23—24no—
439C23—24no—
440C23—24no—
441C23—24no—
442C23—24no—
443C23—28no—
444C23—28no—
445C23—42no—
446C23—42no—
447C23—42no—
448C23—42no—
449C23—44no—
450C23—44no—
451C23—44no—
452C23—44no—
453C23—44no—
454C23—44no—
455C23C2×C22⋊C4×C3114yes—
456C23C31×#11714yes—
457C23C23×C4×C3111yescharacteristic
458C23C22×D4×C3111yescharacteristic
459C23C22×D4×C3111yescharacteristic
460C23C2×#41×C3112yes—
461C23C2×#41×C3112yes—
462C23C2×#41×C3114yes—
463C23C31×H(5,𝔽2)14yes—
464D4—232no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—28no—
480C2×C4—28no—
481C2×C4—28no—
482C2×C4—416no—
483C2×C4—416no—
484C2×C4—44no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—44no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—44no—
491C2×C4—44no—
492C2×C4—44no—
493C2×C4—44no—
494C2×C4—44no—
495C2×C4—44no—
496C2×C4—44no—
497C2×C4—44no—
498C2×C4—44no—
499C2×C4C2×C22⋊C4×C3114yes—
500C2×C4C2×C22⋊C4×C3114yes—
501C2×C4C31×#11714yes—
502C22—24no—
503C22—28no—
504C22—24no—
505C22—24no—
506C22—24no—
507C22—42no—
508C22—48no—
509C22—48no—
510C22—48no—
511C22—48no—
512C22—44no—
513C22—44no—
514C22—44no—
515C22—42no—
516C22C22×C22⋊C4×C3111yescharacteristic
517C22C2×C31×#11711yescharacteristic
518C22C2×C31×#11711yescharacteristic
519C22C4×#41×C3112yes—
520C22C31×#51812yes—
521C22C31×#52512yes—
522C22C31×#52512yes—
523C22C31×#52512yes—
524C22C31×#53212yes—
525C22C31×#53412yes—
526C22C31×#53412yes—
527C22C31×#55114yes—
528C22C31×#55314yes—
529C22C31×#55314yes—
530C22C31×#55914yes—
531C4—24no—
532C4—24no—
533C4—24no—
534C4—42no—
535C4—48no—
536C4—42no—
537C4—84no—
538C2—44no—
539C2—44no—
540C2C31×#228011yescharacteristic
541C2C31×#229711yescharacteristic
542C2C31×#230811yescharacteristic
543C2C31×#235312yes—
544C2C31×#235712yes—
545C2C31×#260014yes—
546C2C31×#260214yes—
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
2. C2×C31×#381C2semidirect
3. C2×C4×C22⋊C4×C31C2semidirect
4. C31×#1440C2semidirect
6. C31×#1437C2semidirect
7. C31×#1436C2semidirect
8. C31×#1434C2semidirect
9. C31×C22⋊#95C2semidirect
15. C2×C4×D4×C31C4semidirect
133. C22×C4×C31C22⋊C4semidirect
153. #13940C31direct (N × H)
230. C2×#381C2×C31semidirect
231. C2×C4×C22⋊C4C2×C31semidirect
232. #1440C2×C31semidirect
234. #1437C2×C31semidirect
235. #1436C2×C31semidirect
236. #1434C2×C31semidirect
237. C22⋊#95C2×C31semidirect
279. C2×C4×D4C4×C31semidirect
355. C31#13940direct (N × H)
407. C22×C4C22⋊C4×C31semidirect

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×#3812
C2×C4×C22⋊C4×C312
C31×#14402
C31×#14382
C31×#14372
C31×#14362
C31×#14342
C31×C22⋊#952
#1394031