Finite Group Databasebeta

← C2×C31×#1436 #21470517

Subgroups — C2×C31×#1436 #21470517

Order 7936.

3550 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4⋊C4×C31C211yesmaximal, characteristic
2C23×C42×C31C211yesmaximal, characteristic
3C22×C31×#95C212yesmaximal
4C22×C31×#95C211yesmaximal, characteristic
5C22×C31×#95C212yesmaximal
6C31×#1436C218yesmaximal, direct product factor
7C24×C4×C31C2211yescharacteristic
8C24×C4×C31C2212yes—
9C24×C4×C31C2211yescharacteristic
10C24×C4×C31C2211yescharacteristic
11C24×C4×C31C2212yes—
12C22×C4⋊C4×C31—24no—
13C22×C4⋊C4×C31—24no—
14C22×C4⋊C4×C31C418yescomplemented
15C22×C4⋊C4×C31C2214yes—
16C22×C42×C31—24no—
17C22×C42×C31—28no—
18C22×C42×C31C2214yes—
19C2×C31×#95—24no—
20C2×C31×#95—28no—
21C2×C31×#95C4116yescomplemented
22C2×C31×#95C2218yes—
23C2×C31×#95C2214yes—
24C2×C31×#95C2218yes—
25C25×C31C2311yescharacteristic
26C23×C4×C31—24no—
27C23×C4×C31—24no—
28C23×C4×C31—24no—
29C23×C4×C31—22no—
30C23×C4×C31—22no—
31C23×C4×C31—24no—
32C23×C4×C31—24no—
33C23×C4×C31—24no—
34C23×C4×C31—24no—
35C23×C4×C31—22no—
36C23×C4×C31—22no—
37C23×C4×C31—24no—
38C23×C4×C31—24no—
39C23×C4×C31—24no—
40C23×C4×C31—24no—
41C23×C4×C31—24no—
42C23×C4×C31—24no—
43C23×C4×C31—24no—
44C23×C4×C31—24no—
45C23×C4×C31C2×C414yes—
46C23×C4×C31C2×C418yes—
47C23×C4×C31C2×C414yes—
48C23×C4×C31C2×C418yes—
49C23×C4×C31C2×C414yes—
50C23×C4×C31C2×C418yes—
51C23×C4×C31D414yes—
52C23×C4×C31D414yes—
53C23×C4×C31D418yes—
54C23×C4×C31Q818yes—
55C23×C4×C31C2312yes—
56C23×C4×C31C2314yes—
57C23×C4×C31C2312yes—
58C23×C4×C31C2312yes—
59C23×C4×C31C2314yes—
60C2×C4⋊C4×C31—232no—
61C2×C4⋊C4×C31—28no—
62C2×C4⋊C4×C31—28no—
63C2×C4⋊C4×C31C2×C4116yescomplemented
64C2×C42×C31—232no—
65C2×C42×C31—28no—
66C2×C42×C31—216no—
67C31×#95—28no—
68C31×#95—216no—
69C31×#95C2×C4132yescomplemented
70C24×C31C22×C412yes—
71C24×C31C22×C414yes—
72C24×C31C2×D412yes—
73C24×C31C2×D412yes—
74C24×C31C2×D414yes—
75C24×C31C2×Q814yes—
76C24×C31#4114yes—
77C24×C31#4114yes—
78C24×C31#4114yes—
79C24×C31C2411yescharacteristic
80C22×C4×C31—28no—
81C22×C4×C31—28no—
82C22×C4×C31—216no—
83C22×C4×C31—216no—
84C22×C4×C31—216no—
85C22×C4×C31—216no—
86C22×C4×C31—216no—
87C22×C4×C31—216no—
88C22×C4×C31—28no—
89C22×C4×C31—216no—
90C22×C4×C31—216no—
91C22×C4×C31—216no—
92C22×C4×C31—216no—
93C22×C4×C31—28no—
94C22×C4×C31—24no—
95C22×C4×C31—24no—
96C22×C4×C31—24no—
97C22×C4×C31—22no—
98C22×C4×C31—22no—
99C22×C4×C31—24no—
100C22×C4×C31—24no—
101C22×C4×C31—24no—
102C22×C4×C31—24no—
103C22×C4×C31—28no—
104C22×C4×C31—216no—
105C22×C4×C31—216no—
106C22×C4×C31—216no—
107C22×C4×C31—216no—
108C22×C4×C31—24no—
109C22×C4×C31—24no—
110C22×C4×C31—24no—
111C22×C4×C31—22no—
112C22×C4×C31—22no—
113C22×C4×C31—24no—
114C22×C4×C31—24no—
115C22×C4×C31—24no—
116C22×C4×C31—24no—
117C22×C4×C31—24no—
118C22×C4×C31—44no—
119C22×C4×C31—48no—
120C22×C4×C31—48no—
121C22×C4×C31—44no—
122C22×C4×C31—48no—
123C22×C4×C31—48no—
124C22×C4×C31—48no—
125C22×C4×C31C42116yescomplemented
126C22×C4×C31C22⋊C4116yes—
127C22×C4×C31C4⋊C4132yescomplemented
128C22×C4×C31C22×C418yes—
129C22×C4×C31C22×C414yes—
130C22×C4×C31C22×C418yes—
131C22×C4×C31C22×C414yes—
132C22×C4×C31C22×C414yes—
133C22×C4×C31C22×C418yes—
134C22×C4×C31C2×D414yes—
135C22×C4×C31C2×D414yes—
136C22×C4×C31C2×D418yes—
137C22×C4×C31C2×Q818yes—
138C4⋊C4×C31—232no—
139C42×C31—232no—
140C2×#1436C3111yesmaximal, characteristic, direct product factor, Sylow
141C23×C31C2×C4214yes—
142C23×C31C2×C22⋊C414yes—
143C23×C31C2×C4⋊C418yes—
144C23×C31#11714yes—
145C23×C31#11718yes—
146C23×C31C4×D418yes—
147C23×C31C4×D418yes—
148C23×C31C4×D418yes—
149C23×C31C4×D418yes—
150C23×C31C4×Q818yes—
151C23×C31C4×Q818yes—
152C23×C31#12014yes—
153C23×C31#12118yes—
154C23×C31C22⋊Q818yes—
155C23×C31C22⋊Q818yes—
156C23×C31#12318yes—
157C23×C31#12314yes—
158C23×C31#12414yes—
159C23×C31#12518yes—
160C23×C31#12618yes—
161C23×C31C4⋊Q814yes—
162C23×C31C23×C411yescharacteristic
163C23×C31C23×C412yes—
164C23×C31C22×D411yescharacteristic
165C23×C31C22×D411yescharacteristic
166C23×C31C22×D412yes—
167C23×C31C22×Q812yes—
168C23×C31C2×#4112yes—
169C23×C31C2×#4112yes—
170C23×C31C2×#4112yes—
171C2×C4×C31—24no—
172C2×C4×C31—24no—
173C2×C4×C31—28no—
174C2×C4×C31—28no—
175C2×C4×C31—28no—
176C2×C4×C31—28no—
177C2×C4×C31—28no—
178C2×C4×C31—28no—
179C2×C4×C31—24no—
180C2×C4×C31—28no—
181C2×C4×C31—28no—
182C2×C4×C31—28no—
183C2×C4×C31—28no—
184C2×C4×C31—24no—
185C2×C4×C31—232no—
186C2×C4×C31—264no—
187C2×C4×C31—232no—
188C2×C4×C31—24no—
189C2×C4×C31—28no—
190C2×C4×C31—28no—
191C2×C4×C31—28no—
192C2×C4×C31—28no—
193C2×C4×C31—42no—
194C2×C4×C31—44no—
195C2×C4×C31—44no—
196C2×C4×C31—42no—
197C2×C4×C31—44no—
198C2×C4×C31—44no—
199C2×C4×C31—44no—
200C2×C4×C31—416no—
201C2×C4×C31—432no—
202C2×C4×C31C2×C4218yescomplemented
203C2×C4×C31C2×C22⋊C418yes—
204C2×C4×C31C2×C4⋊C4116yescomplemented
205C23×C4⋊C4C2×C3111yescharacteristic
206C23×C42C2×C3111yescharacteristic
207C22×#95C2×C3112yes—
208C22×#95C2×C3111yescharacteristic
209C22×#95C2×C3112yes—
210#1436C2×C3118yesdirect product factor
211C22×C31C4×C22⋊C418yes—
212C22×C31C4×C4⋊C4116yes—
213C22×C31#385116yes—
214C22×C31#38618yes—
215C22×C31#387116yes—
216C22×C31#387116yes—
217C22×C31#388116yes—
218C22×C31#389116yes—
219C22×C31#39118yes—
220C22×C31C22×C4211yescharacteristic
221C22×C31C22×C22⋊C411yescharacteristic
222C22×C31C22×C4⋊C412yes—
223C22×C31C2×#11711yescharacteristic
224C22×C31C2×#11712yes—
225C22×C31C2×C4×D412yes—
226C22×C31C2×C4×D412yes—
227C22×C31C2×C4×D412yes—
228C22×C31C2×C4×D412yes—
229C22×C31C2×C4×Q812yes—
230C22×C31C2×C4×Q812yes—
231C22×C31C2×#12011yescharacteristic
232C22×C31C2×#12112yes—
233C22×C31C2×C22⋊Q812yes—
234C22×C31C2×C22⋊Q812yes—
235C22×C31C2×#12312yes—
236C22×C31C2×#12311yescharacteristic
237C22×C31C2×#12411yescharacteristic
238C22×C31C2×#12512yes—
239C22×C31C2×#12612yes—
240C22×C31C2×C4⋊Q811yescharacteristic
241C4×C31—28no—
242C4×C31—216no—
243C4×C31—28no—
244C4×C31—44no—
245C4×C31—48no—
246C24×C4C22×C3111yescharacteristic
247C24×C4C22×C3112yes—
248C24×C4C22×C3111yescharacteristic
249C24×C4C22×C3111yescharacteristic
250C24×C4C22×C3112yes—
251C22×C4⋊C4—24no—
252C22×C4⋊C4—24no—
253C22×C4⋊C4C4×C3118yescomplemented
254C22×C4⋊C4C22×C3114yes—
255C22×C42—24no—
256C22×C42—28no—
257C22×C42C22×C3114yes—
258C2×#95—24no—
259C2×#95—28no—
260C2×#95C4×C31116yescomplemented
261C2×#95C22×C3118yes—
262C2×#95C22×C3114yes—
263C2×#95C22×C3118yes—
264C2×C31#1436116yesdirect product factor
265C2×C31C2×C4×C22⋊C411yescharacteristic
266C2×C31C2×C4×C4⋊C412yes—
267C2×C31C2×#38512yes—
268C2×C31C2×#38611yescharacteristic
269C2×C31C2×#38712yes—
270C2×C31C2×#38712yes—
271C2×C31C2×#38812yes—
272C2×C31C2×#38912yes—
273C2×C31C2×#39111yescharacteristic
274C25C23×C3111yescharacteristic
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—24no—
278C23×C4—24no—
279C23×C4—24no—
280C23×C4—24no—
281C23×C4—24no—
282C23×C4—24no—
283C23×C4—24no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—24no—
287C23×C4—24no—
288C23×C4—24no—
289C23×C4—24no—
290C23×C4—24no—
291C23×C4—24no—
292C23×C4—24no—
293C23×C4—24no—
294C23×C4C2×C4×C3114yes—
295C23×C4C2×C4×C3118yes—
296C23×C4C2×C4×C3114yes—
297C23×C4C2×C4×C3118yes—
298C23×C4C2×C4×C3114yes—
299C23×C4C2×C4×C3118yes—
300C23×C4D4×C3114yes—
301C23×C4D4×C3114yes—
302C23×C4D4×C3118yes—
303C23×C4Q8×C3118yes—
304C23×C4C23×C3112yes—
305C23×C4C23×C3114yes—
306C23×C4C23×C3112yes—
307C23×C4C23×C3112yes—
308C23×C4C23×C3114yes—
309C2×C4⋊C4—232no—
310C2×C4⋊C4—28no—
311C2×C4⋊C4—28no—
312C2×C4⋊C4C2×C4×C31116yescomplemented
313C2×C42—232no—
314C2×C42—28no—
315C2×C42—216no—
316#95—28no—
317#95—216no—
318#95C2×C4×C31132yescomplemented
319C31C2×#143611yescharacteristic, direct product factor, Sylow
320C24C22×C4×C3112yes—
321C24C22×C4×C3114yes—
322C24C2×D4×C3112yes—
323C24C2×D4×C3112yes—
324C24C2×D4×C3114yes—
325C24C2×Q8×C3114yes—
326C24#41×C3114yes—
327C24#41×C3114yes—
328C24#41×C3114yes—
329C24C24×C3111yescharacteristic
330C22×C4—28no—
331C22×C4—28no—
332C22×C4—216no—
333C22×C4—216no—
334C22×C4—216no—
335C22×C4—216no—
336C22×C4—216no—
337C22×C4—216no—
338C22×C4—28no—
339C22×C4—216no—
340C22×C4—216no—
341C22×C4—216no—
342C22×C4—216no—
343C22×C4—28no—
344C22×C4—24no—
345C22×C4—24no—
346C22×C4—24no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—24no—
350C22×C4—24no—
351C22×C4—24no—
352C22×C4—24no—
353C22×C4—28no—
354C22×C4—216no—
355C22×C4—216no—
356C22×C4—216no—
357C22×C4—216no—
358C22×C4—24no—
359C22×C4—24no—
360C22×C4—24no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—24no—
364C22×C4—24no—
365C22×C4—24no—
366C22×C4—24no—
367C22×C4—24no—
368C22×C4—44no—
369C22×C4—48no—
370C22×C4—48no—
371C22×C4—44no—
372C22×C4—48no—
373C22×C4—48no—
374C22×C4—48no—
375C22×C4C42×C31116yescomplemented
376C22×C4C22⋊C4×C31116yes—
377C22×C4C4⋊C4×C31132yescomplemented
378C22×C4C22×C4×C3118yes—
379C22×C4C22×C4×C3114yes—
380C22×C4C22×C4×C3118yes—
381C22×C4C22×C4×C3114yes—
382C22×C4C22×C4×C3114yes—
383C22×C4C22×C4×C3118yes—
384C22×C4C2×D4×C3114yes—
385C22×C4C2×D4×C3114yes—
386C22×C4C2×D4×C3118yes—
387C22×C4C2×Q8×C3118yes—
388C4⋊C4—232no—
389C42—232no—
390C23C2×C42×C3114yes—
391C23C2×C22⋊C4×C3114yes—
392C23C2×C4⋊C4×C3118yes—
393C23C31×#11714yes—
394C23C31×#11718yes—
395C23C4×D4×C3118yes—
396C23C4×D4×C3118yes—
397C23C4×D4×C3118yes—
398C23C4×D4×C3118yes—
399C23C4×Q8×C3118yes—
400C23C4×Q8×C3118yes—
401C23C31×#12014yes—
402C23C31×#12118yes—
403C23C31×C22⋊Q818yes—
404C23C31×C22⋊Q818yes—
405C23C31×#12318yes—
406C23C31×#12314yes—
407C23C31×#12414yes—
408C23C31×#12518yes—
409C23C31×#12618yes—
410C23C31×C4⋊Q814yes—
411C23C23×C4×C3111yescharacteristic
412C23C23×C4×C3112yes—
413C23C22×D4×C3111yescharacteristic
414C23C22×D4×C3111yescharacteristic
415C23C22×D4×C3112yes—
416C23C22×Q8×C3112yes—
417C23C2×#41×C3112yes—
418C23C2×#41×C3112yes—
419C23C2×#41×C3112yes—
420C2×C4—24no—
421C2×C4—24no—
422C2×C4—28no—
423C2×C4—28no—
424C2×C4—28no—
425C2×C4—28no—
426C2×C4—28no—
427C2×C4—28no—
428C2×C4—24no—
429C2×C4—28no—
430C2×C4—28no—
431C2×C4—28no—
432C2×C4—28no—
433C2×C4—24no—
434C2×C4—232no—
435C2×C4—264no—
436C2×C4—232no—
437C2×C4—24no—
438C2×C4—28no—
439C2×C4—28no—
440C2×C4—28no—
441C2×C4—28no—
442C2×C4—42no—
443C2×C4—44no—
444C2×C4—44no—
445C2×C4—42no—
446C2×C4—44no—
447C2×C4—44no—
448C2×C4—44no—
449C2×C4—416no—
450C2×C4—432no—
451C2×C4C2×C42×C3118yescomplemented
452C2×C4C2×C22⋊C4×C3118yes—
453C2×C4C2×C4⋊C4×C31116yescomplemented
454C22C4×C22⋊C4×C3118yes—
455C22C4×C4⋊C4×C31116yes—
456C22C31×#385116yes—
457C22C31×#38618yes—
458C22C31×#387116yes—
459C22C31×#387116yes—
460C22C31×#388116yes—
461C22C31×#389116yes—
462C22C31×#39118yes—
463C22C22×C42×C3111yescharacteristic
464C22C22×C22⋊C4×C3111yescharacteristic
465C22C22×C4⋊C4×C3112yes—
466C22C2×C31×#11711yescharacteristic
467C22C2×C31×#11712yes—
468C22C2×C4×D4×C3112yes—
469C22C2×C4×D4×C3112yes—
470C22C2×C4×D4×C3112yes—
471C22C2×C4×D4×C3112yes—
472C22C2×C4×Q8×C3112yes—
473C22C2×C4×Q8×C3112yes—
474C22C2×C31×#12011yescharacteristic
475C22C2×C31×#12112yes—
476C22C2×C31×C22⋊Q812yes—
477C22C2×C31×C22⋊Q812yes—
478C22C2×C31×#12312yes—
479C22C2×C31×#12311yescharacteristic
480C22C2×C31×#12411yescharacteristic
481C22C2×C31×#12512yes—
482C22C2×C31×#12612yes—
483C22C2×C31×C4⋊Q811yescharacteristic
484C4—28no—
485C4—216no—
486C4—28no—
487C4—44no—
488C4—48no—
489C2C31×#1436116yesdirect product factor
490C2C2×C4×C22⋊C4×C3111yescharacteristic
491C2C2×C4×C4⋊C4×C3112yes—
492C2C2×C31×#38512yes—
493C2C2×C31×#38611yescharacteristic
494C2C2×C31×#38712yes—
495C2C2×C31×#38712yes—
496C2C2×C31×#38812yes—
497C2C2×C31×#38912yes—
498C2C2×C31×#39111yescharacteristic
subgroupG/H
center, socle, prime radicalC25×C31C23
commutatorC22C22×C42×C31
Frattini, cosocleC24C24×C31
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C25×C31 ◁ G

Complements

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

NH ≅ G/Ntype
6. C31×#1436C2direct (N × H)
14. C22×C4⋊C4×C31C4semidirect
21. C2×C31×#95C4semidirect
63. C2×C4⋊C4×C31C2×C4semidirect
69. C31×#95C2×C4semidirect
125. C22×C4×C31C42semidirect
127. C22×C4×C31C4⋊C4semidirect
140. C2×#1436C31direct (N × H)
202. C2×C4×C31C2×C42semidirect
204. C2×C4×C31C2×C4⋊C4semidirect
210. #1436C2×C31direct (N × H)
253. C22×C4⋊C4C4×C31semidirect
260. C2×#95C4×C31semidirect
264. C2×C31#1436direct (N × H)
312. C2×C4⋊C4C2×C4×C31semidirect
318. #95C2×C4×C31semidirect
319. C31C2×#1436direct (N × H)
375. C22×C4C42×C31semidirect
377. C22×C4C4⋊C4×C31semidirect
451. C2×C4C2×C42×C31semidirect
453. C2×C4C2×C4⋊C4×C31semidirect
489. C2C31×#1436direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C4⋊C4×C312
C23×C42×C312
C22×C31×#952
C31×#14362
C2×#143631