Finite Group Databasebeta

← C31×#16362 #21473121

Subgroups — C31×#16362 #21473121

Order 7936.

2226 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#121C211yesmaximal, characteristic
2C2×C31×#397C212yesmaximal, complemented
3C2×C31×#380C211yesmaximal, characteristic, complemented
4C31×#1442C212yesmaximal, complemented
5C31×#1439C212yesmaximal, complemented
6C31×#1438C212yesmaximal, complemented
7C31×#1438C214yesmaximal, complemented
8C31×C22⋊#95C211yesmaximal, characteristic, complemented
9C23×D4×C31C2212yes—
10C23×D4×C31C2211yescharacteristic
11C24×C4×C31C2211yescharacteristic
12C2×C31×#121—24no—
13C2×C31×#121—28no—
14C22×C4⋊C4×C31C2211yescharacteristic
15C22×C4⋊C4×C31C2211yescharacteristic
16C22×C4⋊C4×C31C2211yescharacteristic
17C22×C22⋊C4×C31C2212yes—
18C22×C22⋊C4×C31C2214yes—
19C22×C22⋊C4×C31C2212yes—
20C22×C22⋊C4×C31C2212yes—
21C22×C22⋊C4×C31C2214yes—
22C31×#397—28no—
23C31×#380—24no—
24C2×C31×#95C2212yes—
25C2×C31×#95C2214yes—
26C2×C31×#95C2212yes—
27C2×C31×#95C2212yes—
28C2×C31×#95C2214yes—
29C25×C31C2312yes—
30C25×C31C2311yescharacteristic
31C22×D4×C31—24no—
32C22×D4×C31—24no—
33C22×D4×C31—24no—
34C22×D4×C31—28no—
35C22×D4×C31—24no—
36C22×D4×C31—22no—
37C22×D4×C31—24no—
38C22×D4×C31—42no—
39C22×D4×C31—44no—
40C23×C4×C31—24no—
41C23×C4×C31—24no—
42C23×C4×C31—42no—
43C23×C4×C31D414yes—
44C23×C4×C31C2312yes—
45C23×C4×C31C2312yes—
46C23×C4×C31C2314yes—
47C23×C4×C31C2312yes—
48C23×C4×C31C2311yescharacteristic
49C23×C4×C31C2311yescharacteristic
50C31×#121—232no—
51C2×C4⋊C4×C31—24no—
52C2×C4⋊C4×C31—22no—
53C2×C4⋊C4×C31—24no—
54C2×C4⋊C4×C31—22no—
55C2×C4⋊C4×C31—22no—
56C2×C4⋊C4×C31—42no—
57C2×C22⋊C4×C31—24no—
58C2×C22⋊C4×C31—24no—
59C2×C22⋊C4×C31—28no—
60C2×C22⋊C4×C31—24no—
61C2×C22⋊C4×C31—24no—
62C2×C22⋊C4×C31—42no—
63C2×C22⋊C4×C31—44no—
64C2×C22⋊C4×C31—42no—
65C2×C22⋊C4×C31—44no—
66C2×C22⋊C4×C31—44no—
67C2×C22⋊C4×C31—44no—
68C2×C22⋊C4×C31—44no—
69C2×C22⋊C4×C31—44no—
70C2×C22⋊C4×C31D418yes—
71C31×#95—24no—
72C31×#95—28no—
73C31×#95—24no—
74C31×#95—24no—
75C31×#95—44no—
76C24×C31—22no—
77C24×C31—22no—
78C24×C31—22no—
79C24×C31—21no—
80C24×C31—22no—
81C24×C31—22no—
82C24×C31—21no—
83C24×C31—22no—
84C24×C31—22no—
85C24×C31—24no—
86C24×C31—24no—
87C24×C31—22no—
88C24×C31—22no—
89C24×C31—22no—
90C24×C31—24no—
91C24×C31—24no—
92C24×C31—22no—
93C24×C31C2×D414yes—
94C24×C31C2×D412yes—
95C24×C31#4114yes—
96C24×C31C2411yescharacteristic
97C2×D4×C31—28no—
98C2×D4×C31—216no—
99C2×D4×C31—416no—
100C2×D4×C31—416no—
101C2×D4×C31—44no—
102C2×D4×C31—416no—
103C2×D4×C31—48no—
104C2×D4×C31—48no—
105C2×D4×C31—44no—
106C22×C4×C31—22no—
107C22×C4×C31—22no—
108C22×C4×C31—22no—
109C22×C4×C31—22no—
110C22×C4×C31—22no—
111C22×C4×C31—22no—
112C22×C4×C31—24no—
113C22×C4×C31—24no—
114C22×C4×C31—28no—
115C22×C4×C31—28no—
116C22×C4×C31—24no—
117C22×C4×C31—22no—
118C22×C4×C31—24no—
119C22×C4×C31—22no—
120C22×C4×C31—24no—
121C22×C4×C31—24no—
122C22×C4×C31—22no—
123C22×C4×C31—24no—
124C22×C4×C31—22no—
125C22×C4×C31—24no—
126C22×C4×C31—24no—
127C22×C4×C31—24no—
128C22×C4×C31—24no—
129C22×C4×C31—22no—
130C22×C4×C31—24no—
131C22×C4×C31—24no—
132C22×C4×C31—22no—
133C22×C4×C31—44no—
134C22×C4×C31—416no—
135C22×C4×C31C2×D414yes—
136C22×C4×C31C2×D414yes—
137C22×C4×C31C2×D412yes—
138C22×C4×C31C2×D412yes—
139C22×C4×C31#4114yes—
140C4⋊C4×C31—28no—
141C4⋊C4×C31—44no—
142C4⋊C4×C31—44no—
143C22⋊C4×C31—216no—
144C22⋊C4×C31—48no—
145C22⋊C4×C31—416no—
146C22⋊C4×C31—48no—
147C22⋊C4×C31—416no—
148#16362C3111yesmaximal, characteristic, direct product factor, Sylow
149C23×C31—22no—
150C23×C31—22no—
151C23×C31—22no—
152C23×C31—22no—
153C23×C31—22no—
154C23×C31—22no—
155C23×C31—24no—
156C23×C31—24no—
157C23×C31—28no—
158C23×C31—28no—
159C23×C31—24no—
160C23×C31—24no—
161C23×C31—24no—
162C23×C31—28no—
163C23×C31—28no—
164C23×C31—42no—
165C23×C31—42no—
166C23×C31—42no—
167C23×C31—42no—
168C23×C31—44no—
169C23×C31—44no—
170C23×C31—42no—
171C23×C31—42no—
172C23×C31—42no—
173C23×C31—42no—
174C23×C31—42no—
175C23×C31—42no—
176C23×C31—42no—
177C23×C31—42no—
178C23×C31—44no—
179C23×C31—44no—
180C23×C31—44no—
181C23×C31—44no—
182C23×C31—44no—
183C23×C31—44no—
184C23×C31—44no—
185C23×C31—44no—
186C23×C31—44no—
187C23×C31—44no—
188C23×C31#12414yes—
189C23×C31C22×D411yescharacteristic
190C23×C31C22×D412yes—
191C23×C31C2×#4112yes—
192C23×C31C2×#4112yes—
193C23×C31H(5,𝔽2)12yes—
194C23×C31H(5,𝔽2)11yescharacteristic
195C23×C31H(5,𝔽2)12yes—
196C23×C31H(5,𝔽2)12yes—
197C23×C312−1+411yescharacteristic
198D4×C31—416no—
199D4×C31—432no—
200C2×C4×C31—22no—
201C2×C4×C31—22no—
202C2×C4×C31—22no—
203C2×C4×C31—22no—
204C2×C4×C31—28no—
205C2×C4×C31—28no—
206C2×C4×C31—24no—
207C2×C4×C31—28no—
208C2×C4×C31—416no—
209C2×C4×C31—42no—
210C2×C4×C31—42no—
211C2×C4×C31—44no—
212C2×C4×C31—42no—
213C2×C4×C31—42no—
214C2×C4×C31—44no—
215C2×C4×C31—42no—
216C2×C4×C31—44no—
217C2×C4×C31—42no—
218C2×C4×C31—42no—
219C2×C4×C31—42no—
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×C31—44no—
227C2×C4×C31—44no—
228C2×C4×C31—44no—
229C2×C4×C31#12014yes—
230C2×C4×C31#12314yes—
231C22×#121C2×C3111yescharacteristic
232C2×#397C2×C3112yescomplemented
233C2×#380C2×C3111yescharacteristic, complemented
234#1442C2×C3112yescomplemented
235#1439C2×C3112yescomplemented
236#1438C2×C3112yescomplemented
237#1438C2×C3114yescomplemented
238C22⋊#95C2×C3111yescharacteristic, complemented
239C22×C31—24no—
240C22×C31—24no—
241C22×C31—24no—
242C22×C31—42no—
243C22×C31—42no—
244C22×C31—42no—
245C22×C31—48no—
246C22×C31—48no—
247C22×C31—42no—
248C22×C31—44no—
249C22×C31—44no—
250C22×C31—44no—
251C22×C31—48no—
252C22×C31—48no—
253C22×C31—82no—
254C22×C31—82no—
255C22×C31—84no—
256C22×C31—84no—
257C22×C31—82no—
258C22×C31—82no—
259C22×C31C2×#12011yescharacteristic
260C22×C31C2×#12311yescharacteristic
261C22×C31C2×#12411yescharacteristic
262C22×C31#53411yescharacteristic
263C22×C31#53512yes—
264C22×C31#53511yescharacteristic
265C22×C31#53511yescharacteristic
266C22×C31#53711yescharacteristic
267C22×C31#53712yes—
268C22×C31#53812yes—
269C22×C31#53912yes—
270C22×C31#54012yes—
271C22×C31#54212yes—
272C22×C31#54614yes—
273C22×C31#54614yes—
274C22×C31#55314yes—
275C22×C31#56014yes—
276C4×C31—24no—
277C4×C31—24no—
278C4×C31—44no—
279C4×C31—82no—
280C4×C31—84no—
281C4×C31—82no—
282C23×D4C22×C3112yes—
283C23×D4C22×C3111yescharacteristic
284C24×C4C22×C3111yescharacteristic
285C2×#121—24no—
286C2×#121—28no—
287C22×C4⋊C4C22×C3111yescharacteristic
288C22×C4⋊C4C22×C3111yescharacteristic
289C22×C4⋊C4C22×C3111yescharacteristic
290C22×C22⋊C4C22×C3112yes—
291C22×C22⋊C4C22×C3114yes—
292C22×C22⋊C4C22×C3112yes—
293C22×C22⋊C4C22×C3112yes—
294C22×C22⋊C4C22×C3114yes—
295#397—28no—
296#380—24no—
297C2×#95C22×C3112yes—
298C2×#95C22×C3114yes—
299C2×#95C22×C3112yes—
300C2×#95C22×C3112yes—
301C2×#95C22×C3114yes—
302C2×C31—44no—
303C2×C31—84no—
304C2×C31#240511yescharacteristic
305C2×C31#243511yescharacteristic
306C2×C31#250411yescharacteristic
307C2×C31#261511yescharacteristic
308C2×C31#262411yescharacteristic
309C2×C31#263911yescharacteristic
310C2×C31#269114yes—
311C2×C31#270314yes—
312C2×C31#281511yescharacteristic
313C25C23×C3112yes—
314C25C23×C3111yescharacteristic
315C22×D4—24no—
316C22×D4—24no—
317C22×D4—24no—
318C22×D4—28no—
319C22×D4—24no—
320C22×D4—22no—
321C22×D4—24no—
322C22×D4—42no—
323C22×D4—44no—
324C23×C4—24no—
325C23×C4—24no—
326C23×C4—42no—
327C23×C4D4×C3114yes—
328C23×C4C23×C3112yes—
329C23×C4C23×C3112yes—
330C23×C4C23×C3114yes—
331C23×C4C23×C3112yes—
332C23×C4C23×C3111yescharacteristic
333C23×C4C23×C3111yescharacteristic
334#121—232no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—42no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—28no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—44no—
348C2×C22⋊C4—42no—
349C2×C22⋊C4—44no—
350C2×C22⋊C4—44no—
351C2×C22⋊C4—44no—
352C2×C22⋊C4—44no—
353C2×C22⋊C4—44no—
354C2×C22⋊C4D4×C3118yes—
355#95—24no—
356#95—24no—
357#95—28no—
358#95—24no—
359#95—44no—
360C31#1636211yescharacteristic, direct product factor, Sylow
361C24—22no—
362C24—22no—
363C24—22no—
364C24—21no—
365C24—22no—
366C24—22no—
367C24—21no—
368C24—22no—
369C24—22no—
370C24—24no—
371C24—24no—
372C24—22no—
373C24—22no—
374C24—22no—
375C24—24no—
376C24—24no—
377C24—22no—
378C24C2×D4×C3114yes—
379C24C2×D4×C3112yes—
380C24#41×C3114yes—
381C24C24×C3111yescharacteristic
382C2×D4—28no—
383C2×D4—216no—
384C2×D4—416no—
385C2×D4—416no—
386C2×D4—44no—
387C2×D4—416no—
388C2×D4—48no—
389C2×D4—48no—
390C2×D4—44no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—24no—
398C22×C4—24no—
399C22×C4—28no—
400C22×C4—28no—
401C22×C4—24no—
402C22×C4—22no—
403C22×C4—24no—
404C22×C4—22no—
405C22×C4—24no—
406C22×C4—24no—
407C22×C4—22no—
408C22×C4—24no—
409C22×C4—22no—
410C22×C4—24no—
411C22×C4—24no—
412C22×C4—24no—
413C22×C4—24no—
414C22×C4—22no—
415C22×C4—24no—
416C22×C4—24no—
417C22×C4—22no—
418C22×C4—44no—
419C22×C4—416no—
420C22×C4C2×D4×C3114yes—
421C22×C4C2×D4×C3114yes—
422C22×C4C2×D4×C3112yes—
423C22×C4C2×D4×C3112yes—
424C22×C4#41×C3114yes—
425C4⋊C4—28no—
426C4⋊C4—44no—
427C4⋊C4—44no—
428C22⋊C4—216no—
429C22⋊C4—48no—
430C22⋊C4—416no—
431C22⋊C4—48no—
432C22⋊C4—416no—
433C23—22no—
434C23—22no—
435C23—22no—
436C23—22no—
437C23—22no—
438C23—22no—
439C23—24no—
440C23—24no—
441C23—28no—
442C23—28no—
443C23—24no—
444C23—24no—
445C23—24no—
446C23—28no—
447C23—28no—
448C23—42no—
449C23—42no—
450C23—42no—
451C23—42no—
452C23—44no—
453C23—44no—
454C23—42no—
455C23—42no—
456C23—42no—
457C23—42no—
458C23—42no—
459C23—42no—
460C23—42no—
461C23—42no—
462C23—44no—
463C23—44no—
464C23—44no—
465C23—44no—
466C23—44no—
467C23—44no—
468C23—44no—
469C23—44no—
470C23—44no—
471C23—44no—
472C23C31×#12414yes—
473C23C22×D4×C3111yescharacteristic
474C23C22×D4×C3112yes—
475C23C2×#41×C3112yes—
476C23C2×#41×C3112yes—
477C23C31×H(5,𝔽2)12yes—
478C23C31×H(5,𝔽2)11yescharacteristic
479C23C31×H(5,𝔽2)12yes—
480C23C31×H(5,𝔽2)12yes—
481C23C31×2−1+411yescharacteristic
482D4—416no—
483D4—432no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—28no—
489C2×C4—28no—
490C2×C4—24no—
491C2×C4—28no—
492C2×C4—416no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—44no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—44no—
499C2×C4—42no—
500C2×C4—44no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—44no—
505C2×C4—44no—
506C2×C4—44no—
507C2×C4—44no—
508C2×C4—44no—
509C2×C4—44no—
510C2×C4—44no—
511C2×C4—44no—
512C2×C4—44no—
513C2×C4C31×#12014yes—
514C2×C4C31×#12314yes—
515C22—24no—
516C22—24no—
517C22—24no—
518C22—42no—
519C22—42no—
520C22—42no—
521C22—48no—
522C22—48no—
523C22—42no—
524C22—44no—
525C22—44no—
526C22—44no—
527C22—48no—
528C22—48no—
529C22—82no—
530C22—82no—
531C22—84no—
532C22—84no—
533C22—82no—
534C22—82no—
535C22C2×C31×#12011yescharacteristic
536C22C2×C31×#12311yescharacteristic
537C22C2×C31×#12411yescharacteristic
538C22C31×#53411yescharacteristic
539C22C31×#53512yes—
540C22C31×#53511yescharacteristic
541C22C31×#53511yescharacteristic
542C22C31×#53711yescharacteristic
543C22C31×#53712yes—
544C22C31×#53812yes—
545C22C31×#53912yes—
546C22C31×#54012yes—
547C22C31×#54212yes—
548C22C31×#54614yes—
549C22C31×#54614yes—
550C22C31×#55314yes—
551C22C31×#56014yes—
552C4—24no—
553C4—24no—
554C4—44no—
555C4—82no—
556C4—84no—
557C4—82no—
558C2—44no—
559C2—84no—
560C2C31×#240511yescharacteristic
561C2C31×#243511yescharacteristic
562C2C31×#250411yescharacteristic
563C2C31×#261511yescharacteristic
564C2C31×#262411yescharacteristic
565C2C31×#263911yescharacteristic
566C2C31×#269114yes—
567C2C31×#270314yes—
568C2C31×#281511yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
prime radicalC22×C31×#121C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#397C2semidirect
3. C2×C31×#380C2semidirect
4. C31×#1442C2semidirect
5. C31×#1439C2semidirect
6. C31×#1438C2semidirect
7. C31×#1438C2semidirect
8. C31×C22⋊#95C2semidirect
148. #16362C31direct (N × H)
232. C2×#397C2×C31semidirect
233. C2×#380C2×C31semidirect
234. #1442C2×C31semidirect
235. #1439C2×C31semidirect
236. #1438C2×C31semidirect
237. #1438C2×C31semidirect
238. C22⋊#95C2×C31semidirect
360. C31#16362direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×#1212
C2×C31×#3972
C2×C31×#3802
C31×#14422
C31×#14392
C31×#14382
C31×C22⋊#952
#1636231