Finite Group Databasebeta

← C31×#10979 #21467738

Subgroups — C31×#10979 #21467738

Order 7936.

1382 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#532C211yesmaximal, characteristic
2C2×C31×#421C212yesmaximal, complemented
3C2×C31×#410C211yesmaximal, characteristic, complemented
4C31×#2879C211yesmaximal, characteristic, complemented
5C2×C31×#339C212yesmaximal, complemented
6C22×#41×C31C2211yescharacteristic
7C22×#41×C31C2211yescharacteristic
8C22×M16×C31C2212yes—
9C31×#532—24no—
10C31×#532—24no—
11C2×C31×C4⋊Q8C411yescharacteristic, complemented
12C2×C31×#127C411yescharacteristic, complemented
13C2×C31×#124C411yescharacteristic, complemented
14C2×C31×#124C411yescharacteristic, complemented
15C2×C31×#121—22no—
16C2×C4×D4×C31—22no—
17C2×C31×#117C2212yes—
18C22×C42×C31C2211yescharacteristic
19C31×#421—24no—
20C31×#421—24no—
21C2×C31×#104—24no—
22C31×#410—24no—
23C2×C31×#99—22no—
24C31×#408—24no—
25C31×#407—22no—
26C31×#339—24no—
27C2×#41×C31—22no—
28C2×#41×C31—22no—
29C2×#41×C31—22no—
30C2×#41×C31—22no—
31C2×#41×C31—22no—
32C2×#41×C31—22no—
33C2×#41×C31—22no—
34C2×#41×C31—22no—
35C2×#41×C31—22no—
36C2×#41×C31—22no—
37C2×#41×C31—22no—
38C2×#41×C31D414yes—
39C22×Q8×C31C2×C411yescharacteristic
40C22×Q8×C31C2×C411yescharacteristic
41C22×D4×C31—22no—
42C22×D4×C31—21no—
43C22×D4×C31C2×C411yescharacteristic
44C22×D4×C31C2×C411yescharacteristic
45C22×D4×C31D412yes—
46C23×C4×C31—21no—
47C23×C4×C31—21no—
48C23×C4×C31D412yes—
49C23×C4×C31C2311yescharacteristic
50C2×M16×C31—22no—
51C2×M16×C31—22no—
52C2×M16×C31—22no—
53C2×M16×C31—22no—
54C2×M16×C31—22no—
55C2×M16×C31D414yescomplemented
56C22×C8×C31—22no—
57C31×C4⋊Q8—22no—
58C31×C4⋊Q8—22no—
59C31×#127—22no—
60C31×#127—22no—
61C31×#124—22no—
62C31×#124—22no—
63C31×#124—22no—
64C31×#124—22no—
65C31×#121—216no—
66C4×D4×C31—216no—
67C31×#117—22no—
68C31×#117—22no—
69C31×#117—22no—
70C31×#117D414yescomplemented
71C2×C4⋊C4×C31—22no—
72C2×C4⋊C4×C31—22no—
73C2×C22⋊C4×C31—22no—
74C2×C22⋊C4×C31—22no—
75C2×C22⋊C4×C31—22no—
76C2×C42×C31—21no—
77C2×C42×C31—22no—
78C2×C42×C31—22no—
79C2×C42×C31C2×C411yescharacteristic
80C2×C42×C31C2×C411yescharacteristic
81C2×C42×C31D414yes—
82C31×#104—216no—
83C31×#99—28no—
84C31×C22⋊C8—28no—
85C24×C31—21no—
86C24×C31C22⋊C412yes—
87C24×C31C2×D411yescharacteristic
88#41×C31—24no—
89#41×C31—24no—
90#41×C31—24no—
91#41×C31—24no—
92#41×C31—42no—
93#41×C31—42no—
94#41×C31—42no—
95#41×C31—42no—
96#41×C31—42no—
97#41×C31—42no—
98#41×C31—42no—
99#41×C31—42no—
100#41×C31—42no—
101#41×C31—42no—
102#41×C31—42no—
103#41×C31—42no—
104C2×Q8×C31—21no—
105C2×Q8×C31—21no—
106C2×Q8×C31—21no—
107C2×Q8×C31—22no—
108C2×Q8×C31—22no—
109C2×Q8×C31—22no—
110C2×Q8×C31—22no—
111C2×Q8×C31C22⋊C412yes—
112C2×D4×C31—28no—
113C2×D4×C31—22no—
114C2×D4×C31—24no—
115C2×D4×C31—24no—
116C2×D4×C31—24no—
117C2×D4×C31—22no—
118C2×D4×C31—21no—
119C2×D4×C31—21no—
120C2×D4×C31—21no—
121C2×D4×C31—22no—
122C2×D4×C31—22no—
123C2×D4×C31—22no—
124C2×D4×C31—22no—
125C2×D4×C31—48no—
126C2×D4×C31—41no—
127C2×D4×C31—42no—
128C2×D4×C31—41no—
129C2×D4×C31C22⋊C412yes—
130C22×C4×C31—21no—
131C22×C4×C31—21no—
132C22×C4×C31—21no—
133C22×C4×C31—24no—
134C22×C4×C31—24no—
135C22×C4×C31—24no—
136C22×C4×C31—22no—
137C22×C4×C31—24no—
138C22×C4×C31—22no—
139C22×C4×C31—44no—
140C22×C4×C31—41no—
141C22×C4×C31—42no—
142C22×C4×C31—41no—
143C22×C4×C31—42no—
144C22×C4×C31C22⋊C412yes—
145C22×C4×C31C22×C411yescharacteristic
146C22×C4×C31C2×D412yes—
147C22×C4×C31C2×D412yes—
148C22×C4×C31C2×D412yes—
149C22×C4×C31C2×D412yes—
150C22×C4×C31C2×D411yescharacteristic
151C22×C4×C31#4112yes—
152C22×C4×C31#4112yes—
153M16×C31—24no—
154M16×C31—24no—
155M16×C31—42no—
156M16×C31—42no—
157C2×C8×C31—24no—
158C2×C8×C31—42no—
159C2×C8×C31—42no—
160C4⋊C4×C31—28no—
161C4⋊C4×C31—24no—
162C4⋊C4×C31—42no—
163C22⋊C4×C31—28no—
164C22⋊C4×C31—28no—
165C22⋊C4×C31—24no—
166C22⋊C4×C31—42no—
167C42×C31—21no—
168C42×C31—21no—
169C42×C31—24no—
170C42×C31—24no—
171C42×C31—42no—
172C42×C31C22⋊C412yes—
173C42×C31C22⋊C412yes—
174#10979C3111yesmaximal, characteristic, direct product factor, Sylow
175C23×C31—22no—
176C23×C31—22no—
177C23×C31—22no—
178C23×C31—22no—
179C23×C31—42no—
180C23×C31—44no—
181C23×C31—44no—
182C23×C31—41no—
183C23×C31—41no—
184C23×C31C2×C22⋊C411yescharacteristic
185C23×C31#12012yes—
186C23×C31#12011yescharacteristic
187C23×C31#12112yes—
188C23×C31#12311yescharacteristic
189Q8×C31—24no—
190Q8×C31—42no—
191Q8×C31—42no—
192Q8×C31—42no—
193D4×C31—24no—
194D4×C31—416no—
195D4×C31—44no—
196D4×C31—44no—
197D4×C31—44no—
198D4×C31—44no—
199D4×C31—42no—
200D4×C31—42no—
201D4×C31—42no—
202C2×C4×C31—24no—
203C2×C4×C31—22no—
204C2×C4×C31—22no—
205C2×C4×C31—22no—
206C2×C4×C31—22no—
207C2×C4×C31—22no—
208C2×C4×C31—22no—
209C2×C4×C31—48no—
210C2×C4×C31—42no—
211C2×C4×C31—41no—
212C2×C4×C31—41no—
213C2×C4×C31—44no—
214C2×C4×C31—44no—
215C2×C4×C31—44no—
216C2×C4×C31—44no—
217C2×C4×C31—44no—
218C2×C4×C31—84no—
219C2×C4×C31C2×C22⋊C411yescharacteristic
220C2×C4×C31C2×C22⋊C411yescharacteristic
221C2×C4×C31C4×D412yes—
222C2×C4×C31C4×D412yes—
223C2×C4×C31#12012yes—
224C2×C4×C31#12012yes—
225C2×C4×C31#12011yescharacteristic
226C2×C4×C31#12112yes—
227C2×C4×C31#12112yes—
228C2×C4×C31#12112yes—
229C2×C4×C31#12112yes—
230C2×C4×C31#12112yes—
231C2×C4×C31#12312yes—
232C2×C4×C31#12311yescharacteristic
233C2×C4×C31#12412yes—
234C2×C4×C31#12712yes—
235C8×C31—44no—
236C2×#532C2×C3111yescharacteristic
237C2×#421C2×C3112yescomplemented
238C2×#410C2×C3111yescharacteristic, complemented
239#2879C2×C3111yescharacteristic, complemented
240C2×#339C2×C3112yescomplemented
241C22×C31—22no—
242C22×C31—24no—
243C22×C31—42no—
244C22×C31—41no—
245C22×C31—41no—
246C22×C31—44no—
247C22×C31—44no—
248C22×C31—44no—
249C22×C31—42no—
250C22×C31—42no—
251C22×C31—82no—
252C22×C31—82no—
253C22×C31—82no—
254C22×C31#37911yescharacteristic
255C22×C31#38611yescharacteristic
256C22×C31#38611yescharacteristic
257C22×C31#39212yes—
258C22×C31#39412yes—
259C4×C31—24no—
260C4×C31—42no—
261C4×C31—42no—
262C4×C31—42no—
263C4×C31—84no—
264C4×C31#38612yes—
265C4×C31#39012yes—
266C4×C31#39212yes—
267C4×C31#39412yes—
268C22×#41C22×C3111yescharacteristic
269C22×#41C22×C3111yescharacteristic
270C22×M16C22×C3112yes—
271#532—24no—
272#532—24no—
273C2×C4⋊Q8C4×C3111yescharacteristic, complemented
274C2×#127C4×C3111yescharacteristic, complemented
275C2×#124C4×C3111yescharacteristic, complemented
276C2×#124C4×C3111yescharacteristic, complemented
277C2×#121—22no—
278C2×C4×D4—22no—
279C2×#117C22×C3112yes—
280C22×C42C22×C3111yescharacteristic
281#421—24no—
282#421—24no—
283C2×#104—24no—
284#410—24no—
285C2×#99—22no—
286#408—24no—
287#407—22no—
288#339—24no—
289C2×C31—21no—
290C2×C31—22no—
291C2×C31—21no—
292C2×C31—22no—
293C2×C31—82no—
294C2×C31—82no—
295C2×C31#143811yescharacteristic
296C2×C31#188412yes—
297C2×#41—22no—
298C2×#41—22no—
299C2×#41—22no—
300C2×#41—22no—
301C2×#41—22no—
302C2×#41—22no—
303C2×#41—22no—
304C2×#41—22no—
305C2×#41—22no—
306C2×#41—22no—
307C2×#41—22no—
308C2×#41D4×C3114yes—
309C22×Q8C2×C4×C3111yescharacteristic
310C22×Q8C2×C4×C3111yescharacteristic
311C22×D4—22no—
312C22×D4—21no—
313C22×D4C2×C4×C3111yescharacteristic
314C22×D4C2×C4×C3111yescharacteristic
315C22×D4D4×C3112yes—
316C23×C4—21no—
317C23×C4—21no—
318C23×C4D4×C3112yes—
319C23×C4C23×C3111yescharacteristic
320C2×M16—22no—
321C2×M16—22no—
322C2×M16—22no—
323C2×M16—22no—
324C2×M16—22no—
325C2×M16D4×C3114yescomplemented
326C22×C8—22no—
327C4⋊Q8—22no—
328C4⋊Q8—22no—
329#127—22no—
330#127—22no—
331#124—22no—
332#124—22no—
333#124—22no—
334#124—22no—
335#121—216no—
336C4×D4—216no—
337#117—22no—
338#117—22no—
339#117—22no—
340#117D4×C3114yescomplemented
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—22no—
346C2×C42—21no—
347C2×C42—22no—
348C2×C42—22no—
349C2×C42C2×C4×C3111yescharacteristic
350C2×C42C2×C4×C3111yescharacteristic
351C2×C42D4×C3114yes—
352#104—216no—
353#99—28no—
354C22⋊C8—28no—
355C31#1097911yescharacteristic, direct product factor, Sylow
356C24—21no—
357C24C22⋊C4×C3112yes—
358C24C2×D4×C3111yescharacteristic
359#41—24no—
360#41—24no—
361#41—24no—
362#41—24no—
363#41—42no—
364#41—42no—
365#41—42no—
366#41—42no—
367#41—42no—
368#41—42no—
369#41—42no—
370#41—42no—
371#41—42no—
372#41—42no—
373#41—42no—
374#41—42no—
375C2×Q8—21no—
376C2×Q8—21no—
377C2×Q8—21no—
378C2×Q8—22no—
379C2×Q8—22no—
380C2×Q8—22no—
381C2×Q8—22no—
382C2×Q8C22⋊C4×C3112yes—
383C2×D4—28no—
384C2×D4—22no—
385C2×D4—24no—
386C2×D4—24no—
387C2×D4—24no—
388C2×D4—22no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—48no—
397C2×D4—41no—
398C2×D4—42no—
399C2×D4—41no—
400C2×D4C22⋊C4×C3112yes—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—24no—
405C22×C4—22no—
406C22×C4—24no—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—22no—
410C22×C4—44no—
411C22×C4—41no—
412C22×C4—42no—
413C22×C4—41no—
414C22×C4—42no—
415C22×C4C22⋊C4×C3112yes—
416C22×C4C22×C4×C3111yescharacteristic
417C22×C4C2×D4×C3112yes—
418C22×C4C2×D4×C3112yes—
419C22×C4C2×D4×C3112yes—
420C22×C4C2×D4×C3112yes—
421C22×C4C2×D4×C3111yescharacteristic
422C22×C4#41×C3112yes—
423C22×C4#41×C3112yes—
424M16—24no—
425M16—24no—
426M16—42no—
427M16—42no—
428C2×C8—24no—
429C2×C8—42no—
430C2×C8—42no—
431C4⋊C4—28no—
432C4⋊C4—24no—
433C4⋊C4—42no—
434C22⋊C4—28no—
435C22⋊C4—28no—
436C22⋊C4—24no—
437C22⋊C4—42no—
438C42—21no—
439C42—21no—
440C42—24no—
441C42—24no—
442C42—42no—
443C42C22⋊C4×C3112yes—
444C42C22⋊C4×C3112yes—
445C23—22no—
446C23—22no—
447C23—22no—
448C23—22no—
449C23—42no—
450C23—44no—
451C23—44no—
452C23—41no—
453C23—41no—
454C23C2×C22⋊C4×C3111yescharacteristic
455C23C31×#12012yes—
456C23C31×#12011yescharacteristic
457C23C31×#12112yes—
458C23C31×#12311yescharacteristic
459Q8—24no—
460Q8—42no—
461Q8—42no—
462Q8—42no—
463D4—24no—
464D4—416no—
465D4—44no—
466D4—44no—
467D4—44no—
468D4—44no—
469D4—42no—
470D4—42no—
471D4—42no—
472C2×C4—24no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—48no—
480C2×C4—42no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—44no—
484C2×C4—44no—
485C2×C4—44no—
486C2×C4—44no—
487C2×C4—44no—
488C2×C4—84no—
489C2×C4C2×C22⋊C4×C3111yescharacteristic
490C2×C4C2×C22⋊C4×C3111yescharacteristic
491C2×C4C4×D4×C3112yes—
492C2×C4C4×D4×C3112yes—
493C2×C4C31×#12012yes—
494C2×C4C31×#12011yescharacteristic
495C2×C4C31×#12012yes—
496C2×C4C31×#12112yes—
497C2×C4C31×#12112yes—
498C2×C4C31×#12112yes—
499C2×C4C31×#12112yes—
500C2×C4C31×#12112yes—
501C2×C4C31×#12312yes—
502C2×C4C31×#12311yescharacteristic
503C2×C4C31×#12412yes—
504C2×C4C31×#12712yes—
505C8—44no—
506C22—22no—
507C22—24no—
508C22—42no—
509C22—41no—
510C22—41no—
511C22—44no—
512C22—44no—
513C22—44no—
514C22—42no—
515C22—42no—
516C22—82no—
517C22—82no—
518C22—82no—
519C22C31×#37911yescharacteristic
520C22C31×#38611yescharacteristic
521C22C31×#38611yescharacteristic
522C22C31×#39212yes—
523C22C31×#39412yes—
524C4—24no—
525C4—42no—
526C4—42no—
527C4—42no—
528C4—84no—
529C4C31×#38612yes—
530C4C31×#39012yes—
531C4C31×#39212yes—
532C4C31×#39412yes—
533C2—21no—
534C2—22no—
535C2—21no—
536C2—22no—
537C2—82no—
538C2—82no—
539C2C31×#143811yescharacteristic
540C2C31×#188412yes—
subgroupG/H
centerC2×C4×C31#120
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
socleC22×C31#386
prime radicalC2×C31×#532C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#421C2semidirect
3. C2×C31×#410C2semidirect
4. C31×#2879C2semidirect
5. C2×C31×#339C2semidirect
11. C2×C31×C4⋊Q8C4semidirect
12. C2×C31×#127C4semidirect
13. C2×C31×#124C4semidirect
14. C2×C31×#124C4semidirect
55. C2×M16×C31D4semidirect
70. C31×#117D4semidirect
174. #10979C31direct (N × H)
237. C2×#421C2×C31semidirect
238. C2×#410C2×C31semidirect
239. #2879C2×C31semidirect
240. C2×#339C2×C31semidirect
273. C2×C4⋊Q8C4×C31semidirect
274. C2×#127C4×C31semidirect
275. C2×#124C4×C31semidirect
276. C2×#124C4×C31semidirect
325. C2×M16D4×C31semidirect
340. #117D4×C31semidirect
355. C31#10979direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5322
C2×C31×#4212
C2×C31×#4102
C31×#28792
C2×C31×#3392
#1097931