Finite Group Databasebeta

← C31×#16093 #21472852

Subgroups — C31×#16093 #21472852

Order 7936.

1602 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×C4⋊Q8C211yesmaximal, characteristic
2C2×C31×#391C211yesmaximal, characteristic
3C2×C31×#387C212yesmaximal
4C31×#1446C212yesmaximal
5C31×#1446C211yesmaximal, characteristic
6C31×#1442C212yesmaximal
7C31×#1441C212yesmaximal
8C31×#1441C212yesmaximal
9C31×#1436C212yesmaximal
10C23×Q8×C31C2211yescharacteristic
11C23×Q8×C31C2211yescharacteristic
12C2×C31×C4⋊Q8—24no—
13C2×C31×C4⋊Q8—28no—
14C22×C4⋊C4×C31C2212yes—
15C22×C4⋊C4×C31C2212yes—
16C22×C4⋊C4×C31C2212yes—
17C22×C4⋊C4×C31C2211yescharacteristic
18C22×C42×C31C2211yescharacteristic
19C22×C42×C31C2211yescharacteristic
20C31×#391—24no—
21C31×#387—28no—
22C2×C31×#95C2212yes—
23C2×C31×#95C2212yes—
24C2×C31×#95C2212yes—
25C2×C31×#95C2212yes—
26C2×C31×#95C2212yes—
27C2×C31×#95C2212yes—
28C2×C31×#95C2212yes—
29C2×C31×#95C2212yes—
30C2×C31×#95C2212yes—
31C2×C31×#95C2212yes—
32C2×C31×#95C2211yescharacteristic
33C2×C31×#95C2212yes—
34C2×C31×#95C2211yescharacteristic
35C22×Q8×C31—24no—
36C22×Q8×C31—24no—
37C22×Q8×C31—22no—
38C22×Q8×C31—24no—
39C22×Q8×C31—24no—
40C22×Q8×C31—41no—
41C22×Q8×C31—41no—
42C22×Q8×C31—41no—
43C22×Q8×C31—41no—
44C22×Q8×C31D414yes—
45C23×C4×C31C2312yes—
46C23×C4×C31C2312yes—
47C23×C4×C31C2311yescharacteristic
48C23×C4×C31C2312yes—
49C23×C4×C31C2312yes—
50C23×C4×C31C2312yes—
51C23×C4×C31C2311yescharacteristic
52C23×C4×C31C2312yes—
53C23×C4×C31C2311yescharacteristic
54C31×C4⋊Q8—232no—
55C2×C4⋊C4×C31—24no—
56C2×C4⋊C4×C31—24no—
57C2×C4⋊C4×C31—24no—
58C2×C4⋊C4×C31—24no—
59C2×C4⋊C4×C31—24no—
60C2×C4⋊C4×C31—24no—
61C2×C4⋊C4×C31—24no—
62C2×C4⋊C4×C31—22no—
63C2×C4⋊C4×C31—41no—
64C2×C4⋊C4×C31—41no—
65C2×C4⋊C4×C31D418yes—
66C2×C4⋊C4×C31Q818yescomplemented
67C2×C42×C31—22no—
68C2×C42×C31—24no—
69C2×C42×C31—24no—
70C2×C42×C31—22no—
71C31×#95—24no—
72C31×#95—24no—
73C31×#95—24no—
74C31×#95—24no—
75C31×#95—24no—
76C31×#95—24no—
77C31×#95—24no—
78C31×#95—24no—
79C31×#95—24no—
80C31×#95—41no—
81C31×#95—42no—
82C31×#95—41no—
83C31×#95—42no—
84C24×C31C2411yescharacteristic
85C2×Q8×C31—28no—
86C2×Q8×C31—28no—
87C2×Q8×C31—28no—
88C2×Q8×C31—44no—
89C2×Q8×C31—48no—
90C2×Q8×C31—48no—
91C2×Q8×C31—48no—
92C2×Q8×C31—48no—
93C2×Q8×C31—44no—
94C2×Q8×C31—44no—
95C22×C4×C31—22no—
96C22×C4×C31—22no—
97C22×C4×C31—22no—
98C22×C4×C31—22no—
99C22×C4×C31—21no—
100C22×C4×C31—21no—
101C22×C4×C31—21no—
102C22×C4×C31—21no—
103C22×C4×C31—22no—
104C22×C4×C31—22no—
105C22×C4×C31—22no—
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—22no—
113C22×C4×C31—22no—
114C22×C4×C31—22no—
115C22×C4×C31—22no—
116C22×C4×C31—22no—
117C22×C4×C31—22no—
118C22×C4×C31—22no—
119C22×C4×C31—22no—
120C22×C4×C31—21no—
121C22×C4×C31—21no—
122C22×C4×C31—22no—
123C22×C4×C31—22no—
124C22×C4×C31—22no—
125C22×C4×C31—22no—
126C22×C4×C31—22no—
127C22×C4×C31—22no—
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—22no—
135C22×C4×C31—22no—
136C22×C4×C31—22no—
137C22×C4×C31—22no—
138C22×C4×C31—22no—
139C22×C4×C31—22no—
140C22×C4×C31—22no—
141C22×C4×C31C2×D412yes—
142C22×C4×C31C2×D414yes—
143C22×C4×C31C2×D414yes—
144C22×C4×C31C2×D412yes—
145C22×C4×C31C2×D414yes—
146C22×C4×C31C2×D412yes—
147C22×C4×C31C2×Q814yes—
148C22×C4×C31C2×Q814yes—
149C22×C4×C31C2×Q814yes—
150C22×C4×C31#4114yes—
151C22×C4×C31#4114yes—
152C4⋊C4×C31—216no—
153C4⋊C4×C31—216no—
154C4⋊C4×C31—216no—
155C4⋊C4×C31—44no—
156C42×C31—28no—
157C42×C31—44no—
158#16093C3111yesmaximal, characteristic, direct product factor, Sylow
159C23×C31C22×D412yes—
160C23×C31C22×D411yescharacteristic
161C23×C31C22×Q812yes—
162C23×C31C2×#4112yes—
163C23×C31C2×#4112yes—
164C23×C31H(5,𝔽2)11yescharacteristic
165C23×C31H(5,𝔽2)11yescharacteristic
166C23×C312−1+412yes—
167C23×C312−1+412yes—
168Q8×C31—416no—
169Q8×C31—416no—
170C2×C4×C31—24no—
171C2×C4×C31—22no—
172C2×C4×C31—22no—
173C2×C4×C31—22no—
174C2×C4×C31—22no—
175C2×C4×C31—24no—
176C2×C4×C31—24no—
177C2×C4×C31—24no—
178C2×C4×C31—24no—
179C2×C4×C31—24no—
180C2×C4×C31—24no—
181C2×C4×C31—24no—
182C2×C4×C31—24no—
183C2×C4×C31—24no—
184C2×C4×C31—22no—
185C2×C4×C31—24no—
186C2×C4×C31—24no—
187C2×C4×C31—24no—
188C2×C4×C31—22no—
189C2×C4×C31—24no—
190C2×C4×C31—22no—
191C2×C4×C31—24no—
192C2×C4×C31—24no—
193C2×C4×C31—24no—
194C2×C4×C31—24no—
195C2×C4×C31—24no—
196C2×C4×C31—42no—
197C2×C4×C31—42no—
198C2×C4×C31—42no—
199C2×C4×C31—42no—
200C2×C4×C31—42no—
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—42no—
212C2×C4×C31—42no—
213C2×C4×C31—42no—
214C2×C4×C31—42no—
215C2×C4×C31—42no—
216C2×C4×C31—42no—
217C2×C4×C31—42no—
218C2×C4×C31—42no—
219C2×C4×C31—42no—
220C2×C4×C31—42no—
221C2×C4×C31—42no—
222C2×C4×C31—42no—
223C2×C4×C31—42no—
224C2×C4×C31#12014yes—
225C2×C4×C31C22⋊Q818yes—
226C2×C4×C31#12314yes—
227C22×C4⋊Q8C2×C3111yescharacteristic
228C2×#391C2×C3111yescharacteristic
229C2×#387C2×C3112yes—
230#1446C2×C3112yes—
231#1446C2×C3111yescharacteristic
232#1442C2×C3112yes—
233#1441C2×C3112yes—
234#1441C2×C3112yes—
235#1436C2×C3112yes—
236C22×C31C2×#12011yescharacteristic
237C22×C31C2×C22⋊Q812yes—
238C22×C31C2×#12311yescharacteristic
239C22×C31#53312yes—
240C22×C31#53411yescharacteristic
241C22×C31#53612yes—
242C22×C31#54112yes—
243C22×C31#54212yes—
244C22×C31#54412yes—
245C22×C31#54612yes—
246C22×C31#54612yes—
247C22×C31#54812yes—
248C22×C31#54812yes—
249C22×C31D4×Q812yes—
250C22×C31D4×Q812yes—
251C22×C31#55511yescharacteristic
252C22×C31#55612yes—
253C22×C31#55712yes—
254C22×C31Q8211yescharacteristic
255C22×C31#56311yescharacteristic
256C22×C31#56311yescharacteristic
257C4×C31—24no—
258C4×C31—24no—
259C4×C31—28no—
260C4×C31—42no—
261C4×C31—44no—
262C4×C31—44no—
263C4×C31—44no—
264C4×C31—82no—
265C4×C31—82no—
266C23×Q8C22×C3111yescharacteristic
267C23×Q8C22×C3111yescharacteristic
268C2×C4⋊Q8—24no—
269C2×C4⋊Q8—28no—
270C22×C4⋊C4C22×C3112yes—
271C22×C4⋊C4C22×C3112yes—
272C22×C4⋊C4C22×C3112yes—
273C22×C4⋊C4C22×C3111yescharacteristic
274C22×C42C22×C3111yescharacteristic
275C22×C42C22×C3111yescharacteristic
276#391—24no—
277#387—28no—
278C2×#95C22×C3112yes—
279C2×#95C22×C3112yes—
280C2×#95C22×C3112yes—
281C2×#95C22×C3112yes—
282C2×#95C22×C3112yes—
283C2×#95C22×C3112yes—
284C2×#95C22×C3112yes—
285C2×#95C22×C3112yes—
286C2×#95C22×C3112yes—
287C2×#95C22×C3112yes—
288C2×#95C22×C3111yescharacteristic
289C2×#95C22×C3112yes—
290C2×#95C22×C3111yescharacteristic
291C2×C31#240511yescharacteristic
292C2×C31#240912yes—
293C2×C31#243912yes—
294C2×C31#244612yes—
295C2×C31#245112yes—
296C2×C31#271312yes—
297C2×C31#271612yes—
298C2×C31#273111yescharacteristic
299C2×C31#273411yescharacteristic
300C22×Q8—24no—
301C22×Q8—24no—
302C22×Q8—22no—
303C22×Q8—24no—
304C22×Q8—24no—
305C22×Q8—41no—
306C22×Q8—41no—
307C22×Q8—41no—
308C22×Q8—41no—
309C22×Q8D4×C3114yes—
310C23×C4C23×C3112yes—
311C23×C4C23×C3112yes—
312C23×C4C23×C3111yescharacteristic
313C23×C4C23×C3112yes—
314C23×C4C23×C3112yes—
315C23×C4C23×C3112yes—
316C23×C4C23×C3111yescharacteristic
317C23×C4C23×C3112yes—
318C23×C4C23×C3111yescharacteristic
319C4⋊Q8—232no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—41no—
329C2×C4⋊C4—41no—
330C2×C4⋊C4D4×C3118yes—
331C2×C4⋊C4Q8×C3118yescomplemented
332C2×C42—22no—
333C2×C42—24no—
334C2×C42—24no—
335C2×C42—22no—
336#95—24no—
337#95—24no—
338#95—24no—
339#95—24no—
340#95—24no—
341#95—24no—
342#95—24no—
343#95—24no—
344#95—24no—
345#95—41no—
346#95—42no—
347#95—41no—
348#95—42no—
349C31#1609311yescharacteristic, direct product factor, Sylow
350C24C24×C3111yescharacteristic
351C2×Q8—28no—
352C2×Q8—28no—
353C2×Q8—28no—
354C2×Q8—44no—
355C2×Q8—48no—
356C2×Q8—48no—
357C2×Q8—48no—
358C2×Q8—48no—
359C2×Q8—44no—
360C2×Q8—44no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
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—21no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4C2×D4×C3112yes—
408C22×C4C2×D4×C3114yes—
409C22×C4C2×D4×C3114yes—
410C22×C4C2×D4×C3112yes—
411C22×C4C2×D4×C3114yes—
412C22×C4C2×D4×C3112yes—
413C22×C4C2×Q8×C3114yes—
414C22×C4C2×Q8×C3114yes—
415C22×C4C2×Q8×C3114yes—
416C22×C4#41×C3114yes—
417C22×C4#41×C3114yes—
418C4⋊C4—216no—
419C4⋊C4—216no—
420C4⋊C4—216no—
421C4⋊C4—44no—
422C42—28no—
423C42—44no—
424C23C22×D4×C3112yes—
425C23C22×D4×C3111yescharacteristic
426C23C22×Q8×C3112yes—
427C23C2×#41×C3112yes—
428C23C2×#41×C3112yes—
429C23C31×H(5,𝔽2)11yescharacteristic
430C23C31×H(5,𝔽2)11yescharacteristic
431C23C31×2−1+412yes—
432C23C31×2−1+412yes—
433Q8—416no—
434Q8—416no—
435C2×C4—24no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—24no—
441C2×C4—24no—
442C2×C4—24no—
443C2×C4—24no—
444C2×C4—24no—
445C2×C4—24no—
446C2×C4—24no—
447C2×C4—24no—
448C2×C4—24no—
449C2×C4—22no—
450C2×C4—24no—
451C2×C4—24no—
452C2×C4—24no—
453C2×C4—22no—
454C2×C4—24no—
455C2×C4—22no—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
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—42no—
489C2×C4C31×#12014yes—
490C2×C4C31×C22⋊Q818yes—
491C2×C4C31×#12314yes—
492C22C2×C31×#12011yescharacteristic
493C22C2×C31×C22⋊Q812yes—
494C22C2×C31×#12311yescharacteristic
495C22C31×#53312yes—
496C22C31×#53411yescharacteristic
497C22C31×#53612yes—
498C22C31×#54112yes—
499C22C31×#54212yes—
500C22C31×#54412yes—
501C22C31×#54612yes—
502C22C31×#54612yes—
503C22C31×#54812yes—
504C22C31×#54812yes—
505C22D4×Q8×C3112yes—
506C22D4×Q8×C3112yes—
507C22C31×#55511yescharacteristic
508C22C31×#55612yes—
509C22C31×#55712yes—
510C22Q82×C3111yescharacteristic
511C22C31×#56311yescharacteristic
512C22C31×#56311yescharacteristic
513C4—24no—
514C4—24no—
515C4—28no—
516C4—42no—
517C4—44no—
518C4—44no—
519C4—44no—
520C4—82no—
521C4—82no—
522C2C31×#240511yescharacteristic
523C2C31×#240912yes—
524C2C31×#243912yes—
525C2C31×#244612yes—
526C2C31×#245112yes—
527C2C31×#271312yes—
528C2C31×#271612yes—
529C2C31×#273111yescharacteristic
530C2C31×#273411yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C31C24
commutator, Frattini, cosocleC24C24×C31
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
66. C2×C4⋊C4×C31Q8semidirect
158. #16093C31direct (N × H)
331. C2×C4⋊C4Q8×C31semidirect
349. C31#16093direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×C4⋊Q82
C2×C31×#3912
C2×C31×#3872
C31×#14462
C31×#14422
C31×#14412
C31×#14362
#1609331