Finite Group Databasebeta

← C31×#14264 #21471023

Subgroups — C31×#14264 #21471023

Order 7936.

1926 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#117C211yesmaximal, characteristic
2C2×C31×#389C212yesmaximal, complemented
3C2×C31×#380C211yesmaximal, characteristic
4C2×C31×#380C211yesmaximal, characteristic
5C31×#1444C212yesmaximal, complemented
6C31×#1442C212yesmaximal, complemented
7C31×#1439C214yesmaximal
8C31×C4⋊#95C212yesmaximal, complemented
9C24×C4×C31C2211yescharacteristic
10C2×C31×#117—24no—
11C2×C31×#117—28no—
12C22×C4⋊C4×C31C2211yescharacteristic
13C22×C4⋊C4×C31C2211yescharacteristic
14C22×C4⋊C4×C31C2211yescharacteristic
15C22×C4⋊C4×C31C2211yescharacteristic
16C22×C4⋊C4×C31C2212yes—
17C22×C4⋊C4×C31C2214yes—
18C22×C22⋊C4×C31C2212yes—
19C22×C22⋊C4×C31C2212yes—
20C22×C22⋊C4×C31C2212yes—
21C22×C42×C31C2212yes—
22C31×#389—28no—
23C31×#380—24no—
24C31×#380C418yescomplemented
25C2×C31×#95C2214yes—
26C2×C31×#95C2212yes—
27C2×C31×#95C2214yes—
28C2×C31×#95C2214yes—
29C2×C31×#95C2212yes—
30C25×C31C2311yescharacteristic
31C23×C4×C31—24no—
32C23×C4×C31—24no—
33C23×C4×C31C2×C414yes—
34C23×C4×C31D414yes—
35C23×C4×C31Q814yes—
36C23×C4×C31C2312yes—
37C23×C4×C31C2312yes—
38C23×C4×C31C2314yes—
39C23×C4×C31C2312yes—
40C23×C4×C31C2312yes—
41C23×C4×C31C2311yescharacteristic
42C23×C4×C31C2311yescharacteristic
43C31×#117—232no—
44C2×C4⋊C4×C31—24no—
45C2×C4⋊C4×C31—24no—
46C2×C4⋊C4×C31—22no—
47C2×C4⋊C4×C31—22no—
48C2×C4⋊C4×C31—24no—
49C2×C4⋊C4×C31—24no—
50C2×C4⋊C4×C31—22no—
51C2×C4⋊C4×C31—22no—
52C2×C4⋊C4×C31—28no—
53C2×C4⋊C4×C31—24no—
54C2×C4⋊C4×C31—24no—
55C2×C4⋊C4×C31—44no—
56C2×C4⋊C4×C31—44no—
57C2×C4⋊C4×C31C2×C418yes—
58C2×C22⋊C4×C31—24no—
59C2×C22⋊C4×C31—24no—
60C2×C22⋊C4×C31—24no—
61C2×C22⋊C4×C31—24no—
62C2×C22⋊C4×C31—42no—
63C2×C22⋊C4×C31—42no—
64C2×C22⋊C4×C31—44no—
65C2×C22⋊C4×C31C2×C418yes—
66C2×C42×C31—24no—
67C2×C42×C31—24no—
68C2×C42×C31D418yes—
69C31×#95—24no—
70C31×#95—28no—
71C31×#95—44no—
72C31×#95—44no—
73C31×#95C2×C418yes—
74C24×C31—22no—
75C24×C31—22no—
76C24×C31—21no—
77C24×C31—21no—
78C24×C31—22no—
79C24×C31—21no—
80C24×C31—21no—
81C24×C31—22no—
82C24×C31C22×C412yes—
83C24×C31C2×D412yes—
84C24×C31C2×Q812yes—
85C24×C31C2411yescharacteristic
86C22×C4×C31—22no—
87C22×C4×C31—22no—
88C22×C4×C31—216no—
89C22×C4×C31—28no—
90C22×C4×C31—216no—
91C22×C4×C31—28no—
92C22×C4×C31—24no—
93C22×C4×C31—22no—
94C22×C4×C31—22no—
95C22×C4×C31—22no—
96C22×C4×C31—22no—
97C22×C4×C31—24no—
98C22×C4×C31—22no—
99C22×C4×C31—22no—
100C22×C4×C31—24no—
101C22×C4×C31—24no—
102C22×C4×C31—24no—
103C22×C4×C31—22no—
104C22×C4×C31—22no—
105C22×C4×C31—24no—
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—22no—
115C22×C4×C31—24no—
116C22×C4×C31—24no—
117C22×C4×C31—22no—
118C22×C4×C31—22no—
119C22×C4×C31—22no—
120C22×C4×C31C4⋊C4116yescomplemented
121C22×C4×C31C22×C418yes—
122C22×C4×C31C22×C412yes—
123C22×C4×C31C22×C412yes—
124C22×C4×C31C2×D414yes—
125C22×C4×C31C2×D414yes—
126C22×C4×C31C2×D412yes—
127C22×C4×C31C2×D412yes—
128C22×C4×C31C2×D414yes—
129C22×C4×C31C2×Q812yes—
130C22×C4×C31C2×Q812yes—
131C22×C4×C31#4114yes—
132C4⋊C4×C31—28no—
133C4⋊C4×C31—28no—
134C4⋊C4×C31—216no—
135C4⋊C4×C31—416no—
136C4⋊C4×C31—44no—
137C4⋊C4×C31—44no—
138C22⋊C4×C31—216no—
139C22⋊C4×C31—48no—
140C22⋊C4×C31—48no—
141C42×C31—216no—
142#14264C3111yesmaximal, characteristic, direct product factor, Sylow
143C23×C31—24no—
144C23×C31—22no—
145C23×C31—22no—
146C23×C31—24no—
147C23×C31—22no—
148C23×C31—24no—
149C23×C31—22no—
150C23×C31—22no—
151C23×C31—22no—
152C23×C31—22no—
153C23×C31—22no—
154C23×C31—22no—
155C23×C31—22no—
156C23×C31—24no—
157C23×C31—42no—
158C23×C31—42no—
159C23×C31—42no—
160C23×C31—42no—
161C23×C31—42no—
162C23×C31—42no—
163C23×C31—42no—
164C23×C31—42no—
165C23×C31C2×C4⋊C414yes—
166C23×C31C23×C411yescharacteristic
167C23×C31C22×D411yescharacteristic
168C23×C31C22×D412yes—
169C23×C31C22×Q811yescharacteristic
170C23×C31C2×#4112yes—
171C23×C31H(5,𝔽2)11yescharacteristic
172C23×C31H(5,𝔽2)11yescharacteristic
173C23×C31H(5,𝔽2)12yes—
174C23×C312−1+411yescharacteristic
175C23×C312−1+411yescharacteristic
176C23×C312−1+412yes—
177C2×C4×C31—24no—
178C2×C4×C31—22no—
179C2×C4×C31—24no—
180C2×C4×C31—22no—
181C2×C4×C31—232no—
182C2×C4×C31—28no—
183C2×C4×C31—28no—
184C2×C4×C31—28no—
185C2×C4×C31—24no—
186C2×C4×C31—24no—
187C2×C4×C31—24no—
188C2×C4×C31—24no—
189C2×C4×C31—24no—
190C2×C4×C31—24no—
191C2×C4×C31—44no—
192C2×C4×C31—42no—
193C2×C4×C31—42no—
194C2×C4×C31—42no—
195C2×C4×C31—42no—
196C2×C4×C31—44no—
197C2×C4×C31—42no—
198C2×C4×C31—42no—
199C2×C4×C31—42no—
200C2×C4×C31—42no—
201C2×C4×C31—44no—
202C2×C4×C31—44no—
203C2×C4×C31—42no—
204C2×C4×C31—42no—
205C2×C4×C31—42no—
206C2×C4×C31—42no—
207C2×C4×C31—44no—
208C2×C4×C31—42no—
209C2×C4×C31—44no—
210C2×C4×C31—42no—
211C2×C4×C31—44no—
212C2×C4×C31—44no—
213C2×C4×C31C2×C4⋊C414yes—
214C2×C4×C31C2×C4⋊C414yes—
215C2×C4×C31C4×D418yes—
216C2×C4×C31#12014yes—
217C2×C4×C31C22⋊Q818yes—
218C2×C4×C31#12314yes—
219C22×#117C2×C3111yescharacteristic
220C2×#389C2×C3112yescomplemented
221C2×#380C2×C3111yescharacteristic
222C2×#380C2×C3111yescharacteristic
223#1444C2×C3112yescomplemented
224#1442C2×C3112yescomplemented
225#1439C2×C3114yes—
226C4⋊#95C2×C3112yescomplemented
227C22×C31—24no—
228C22×C31—24no—
229C22×C31—24no—
230C22×C31—44no—
231C22×C31—44no—
232C22×C31—42no—
233C22×C31—42no—
234C22×C31—42no—
235C22×C31—42no—
236C22×C31—44no—
237C22×C31—44no—
238C22×C31C22×C4⋊C411yescharacteristic
239C22×C31C2×C4×D412yes—
240C22×C31#51811yescharacteristic
241C22×C31#51911yescharacteristic
242C22×C31#52012yes—
243C22×C31C2×#12011yescharacteristic
244C22×C31C2×C22⋊Q812yes—
245C22×C31C2×#12311yescharacteristic
246C22×C31#53511yescharacteristic
247C22×C31#53512yes—
248C22×C31#53611yescharacteristic
249C22×C31#53612yes—
250C22×C31#53711yescharacteristic
251C22×C31#53711yescharacteristic
252C22×C31#53712yes—
253C22×C31#53712yes—
254C22×C31#54012yes—
255C22×C31#54112yes—
256C22×C31#54212yes—
257C22×C31#54212yes—
258C22×C31#54411yescharacteristic
259C22×C31#54411yescharacteristic
260C22×C31#54412yes—
261C4×C31—24no—
262C4×C31—48no—
263C4×C31—44no—
264C4×C31—44no—
265C4×C31—82no—
266C4×C31—82no—
267C4×C31#38518yes—
268C24×C4C22×C3111yescharacteristic
269C2×#117—24no—
270C2×#117—28no—
271C22×C4⋊C4C22×C3111yescharacteristic
272C22×C4⋊C4C22×C3111yescharacteristic
273C22×C4⋊C4C22×C3111yescharacteristic
274C22×C4⋊C4C22×C3111yescharacteristic
275C22×C4⋊C4C22×C3112yes—
276C22×C4⋊C4C22×C3114yes—
277C22×C22⋊C4C22×C3112yes—
278C22×C22⋊C4C22×C3112yes—
279C22×C22⋊C4C22×C3112yes—
280C22×C42C22×C3112yes—
281#389—28no—
282#380—24no—
283#380C4×C3118yescomplemented
284C2×#95C22×C3114yes—
285C2×#95C22×C3112yes—
286C2×#95C22×C3114yes—
287C2×#95C22×C3114yes—
288C2×#95C22×C3112yes—
289C2×C31—44no—
290C2×C31C2×#38511yescharacteristic
291C2×C31#231611yescharacteristic
292C2×C31#231711yescharacteristic
293C2×C31#232312yes—
294C2×C31#232412yes—
295C2×C31#261511yescharacteristic
296C2×C31#261611yescharacteristic
297C2×C31#262411yescharacteristic
298C2×C31#262511yescharacteristic
299C2×C31#262812yes—
300C2×C31#262912yes—
301C25C23×C3111yescharacteristic
302C23×C4—24no—
303C23×C4—24no—
304C23×C4C2×C4×C3114yes—
305C23×C4D4×C3114yes—
306C23×C4Q8×C3114yes—
307C23×C4C23×C3112yes—
308C23×C4C23×C3112yes—
309C23×C4C23×C3114yes—
310C23×C4C23×C3112yes—
311C23×C4C23×C3112yes—
312C23×C4C23×C3111yescharacteristic
313C23×C4C23×C3111yescharacteristic
314#117—232no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—28no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—44no—
327C2×C4⋊C4—44no—
328C2×C4⋊C4C2×C4×C3118yes—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—44no—
336C2×C22⋊C4C2×C4×C3118yes—
337C2×C42—24no—
338C2×C42—24no—
339C2×C42D4×C3118yes—
340#95—24no—
341#95—28no—
342#95—44no—
343#95—44no—
344#95C2×C4×C3118yes—
345C31#1426411yescharacteristic, direct product factor, Sylow
346C24—22no—
347C24—22no—
348C24—21no—
349C24—21no—
350C24—22no—
351C24—21no—
352C24—21no—
353C24—22no—
354C24C22×C4×C3112yes—
355C24C2×D4×C3112yes—
356C24C2×Q8×C3112yes—
357C24C24×C3111yescharacteristic
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—216no—
361C22×C4—28no—
362C22×C4—216no—
363C22×C4—28no—
364C22×C4—24no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—24no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—24no—
373C22×C4—24no—
374C22×C4—24no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—24no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—24no—
385C22×C4—24no—
386C22×C4—22no—
387C22×C4—24no—
388C22×C4—24no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4C4⋊C4×C31116yescomplemented
393C22×C4C22×C4×C3118yes—
394C22×C4C22×C4×C3112yes—
395C22×C4C22×C4×C3112yes—
396C22×C4C2×D4×C3114yes—
397C22×C4C2×D4×C3114yes—
398C22×C4C2×D4×C3112yes—
399C22×C4C2×D4×C3112yes—
400C22×C4C2×D4×C3114yes—
401C22×C4C2×Q8×C3112yes—
402C22×C4C2×Q8×C3112yes—
403C22×C4#41×C3114yes—
404C4⋊C4—28no—
405C4⋊C4—28no—
406C4⋊C4—216no—
407C4⋊C4—416no—
408C4⋊C4—44no—
409C4⋊C4—44no—
410C22⋊C4—216no—
411C22⋊C4—48no—
412C22⋊C4—48no—
413C42—216no—
414C23—24no—
415C23—22no—
416C23—22no—
417C23—24no—
418C23—22no—
419C23—24no—
420C23—22no—
421C23—22no—
422C23—22no—
423C23—22no—
424C23—22no—
425C23—22no—
426C23—22no—
427C23—24no—
428C23—42no—
429C23—42no—
430C23—42no—
431C23—42no—
432C23—42no—
433C23—42no—
434C23—42no—
435C23—42no—
436C23C2×C4⋊C4×C3114yes—
437C23C23×C4×C3111yescharacteristic
438C23C22×D4×C3111yescharacteristic
439C23C22×D4×C3112yes—
440C23C22×Q8×C3111yescharacteristic
441C23C2×#41×C3112yes—
442C23C31×H(5,𝔽2)11yescharacteristic
443C23C31×H(5,𝔽2)11yescharacteristic
444C23C31×H(5,𝔽2)12yes—
445C23C31×2−1+411yescharacteristic
446C23C31×2−1+411yescharacteristic
447C23C31×2−1+412yes—
448C2×C4—24no—
449C2×C4—22no—
450C2×C4—24no—
451C2×C4—22no—
452C2×C4—232no—
453C2×C4—28no—
454C2×C4—28no—
455C2×C4—28no—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—24no—
462C2×C4—44no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—44no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—44no—
473C2×C4—44no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—44no—
479C2×C4—42no—
480C2×C4—44no—
481C2×C4—42no—
482C2×C4—44no—
483C2×C4—44no—
484C2×C4C2×C4⋊C4×C3114yes—
485C2×C4C2×C4⋊C4×C3114yes—
486C2×C4C4×D4×C3118yes—
487C2×C4C31×#12014yes—
488C2×C4C31×C22⋊Q818yes—
489C2×C4C31×#12314yes—
490C22—24no—
491C22—24no—
492C22—24no—
493C22—44no—
494C22—44no—
495C22—42no—
496C22—42no—
497C22—42no—
498C22—42no—
499C22—44no—
500C22—44no—
501C22C22×C4⋊C4×C3111yescharacteristic
502C22C2×C4×D4×C3112yes—
503C22C31×#51811yescharacteristic
504C22C31×#51911yescharacteristic
505C22C31×#52012yes—
506C22C2×C31×#12011yescharacteristic
507C22C2×C31×C22⋊Q812yes—
508C22C2×C31×#12311yescharacteristic
509C22C31×#53511yescharacteristic
510C22C31×#53512yes—
511C22C31×#53611yescharacteristic
512C22C31×#53612yes—
513C22C31×#53711yescharacteristic
514C22C31×#53711yescharacteristic
515C22C31×#53712yes—
516C22C31×#53712yes—
517C22C31×#54012yes—
518C22C31×#54112yes—
519C22C31×#54212yes—
520C22C31×#54212yes—
521C22C31×#54411yescharacteristic
522C22C31×#54411yescharacteristic
523C22C31×#54412yes—
524C4—24no—
525C4—48no—
526C4—44no—
527C4—44no—
528C4—82no—
529C4—82no—
530C4C31×#38518yes—
531C2—44no—
532C2C2×C31×#38511yescharacteristic
533C2C31×#231611yescharacteristic
534C2C31×#231711yescharacteristic
535C2C31×#232312yes—
536C2C31×#232412yes—
537C2C31×#261511yescharacteristic
538C2C31×#261611yescharacteristic
539C2C31×#262411yescharacteristic
540C2C31×#262511yescharacteristic
541C2C31×#262812yes—
542C2C31×#262912yes—
subgroupG/H
center, socleC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC25×C31C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#389C2semidirect
5. C31×#1444C2semidirect
6. C31×#1442C2semidirect
8. C31×C4⋊#95C2semidirect
24. C31×#380C4semidirect
120. C22×C4×C31C4⋊C4semidirect
142. #14264C31direct (N × H)
220. C2×#389C2×C31semidirect
223. #1444C2×C31semidirect
224. #1442C2×C31semidirect
226. C4⋊#95C2×C31semidirect
283. #380C4×C31semidirect
345. C31#14264direct (N × H)
392. C22×C4C4⋊C4×C31semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1172
C2×C31×#3892
C2×C31×#3802
C31×#14442
C31×#14422
C31×#14392
C31×C4⋊#952
#1426431