Finite Group Databasebeta

← C31×#10986 #21467745

Subgroups — C31×#10986 #21467745

Order 7936.

1334 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×#537C211yesmaximal, characteristic
2C2×C31×#421C212yesmaximal, complemented
3C2×C31×#413C211yesmaximal, characteristic, complemented
4C2×C31×#410C211yesmaximal, characteristic, complemented
5C31×#1736C212yesmaximal, complemented
6C22×#41×C31C2211yescharacteristic
7C22×#41×C31C2211yescharacteristic
8C22×M16×C31C2212yes—
9C31×#537—24no—
10C31×#537—24no—
11C2×C31×C22⋊Q8—21no—
12C2×C31×C22⋊Q8C412yescomplemented
13C2×C31×#121—21no—
14C2×C31×#121—22no—
15C2×C31×#121C412yescomplemented
16C2×C31×#117C2212yes—
17C22×C4⋊C4×C31C2211yescharacteristic
18C31×#421—24no—
19C31×#421—24no—
20C2×C31×#104—24no—
21C31×#413—24no—
22C2×C31×#101—21no—
23C2×C31×#100—21no—
24C31×#410—24no—
25C2×C31×#99—22no—
26C31×#340—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×C31D411yescharacteristic
41C22×D4×C31—21no—
42C22×D4×C31—22no—
43C22×D4×C31C2×C411yescharacteristic
44C22×D4×C31D412yes—
45C22×D4×C31D411yescharacteristic
46C23×C4×C31—21no—
47C23×C4×C31—21no—
48C23×C4×C31C2×C412yes—
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×C22⋊Q8—28no—
58C31×C22⋊Q8—24no—
59C31×C22⋊Q8—24no—
60C31×#121—216no—
61C31×#121—28no—
62C31×#121—24no—
63C31×#121—24no—
64C31×#117—22no—
65C31×#117—22no—
66C31×#117—22no—
67C31×#117D414yescomplemented
68C2×C4⋊C4×C31—22no—
69C2×C4⋊C4×C31—21no—
70C2×C4⋊C4×C31—22no—
71C2×C4⋊C4×C31—22no—
72C2×C4⋊C4×C31C2×C412yes—
73C2×C4⋊C4×C31D414yes—
74C2×C22⋊C4×C31—22no—
75C2×C22⋊C4×C31—22no—
76C2×C22⋊C4×C31—22no—
77C2×C42×C31—22no—
78C31×#104—216no—
79C31×#101—24no—
80C31×#100—24no—
81C31×#99—28no—
82C24×C31—21no—
83C24×C31C22⋊C412yes—
84C24×C31C2×D411yescharacteristic
85#41×C31—24no—
86#41×C31—24no—
87#41×C31—24no—
88#41×C31—24no—
89#41×C31—42no—
90#41×C31—42no—
91#41×C31—42no—
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—
101C2×Q8×C31—21no—
102C2×Q8×C31—21no—
103C2×Q8×C31—22no—
104C2×Q8×C31—22no—
105C2×Q8×C31—21no—
106C2×Q8×C31—22no—
107C2×Q8×C31—22no—
108C2×Q8×C31C22⋊C412yes—
109C2×D4×C31—22no—
110C2×D4×C31—24no—
111C2×D4×C31—24no—
112C2×D4×C31—24no—
113C2×D4×C31—22no—
114C2×D4×C31—28no—
115C2×D4×C31—21no—
116C2×D4×C31—22no—
117C2×D4×C31—22no—
118C2×D4×C31—21no—
119C2×D4×C31—22no—
120C2×D4×C31—22no—
121C2×D4×C31—21no—
122C2×D4×C31—41no—
123C2×D4×C31—42no—
124C2×D4×C31—41no—
125C2×D4×C31—84no—
126C2×D4×C31C22⋊C412yes—
127C22×C4×C31—22no—
128C22×C4×C31—21no—
129C22×C4×C31—24no—
130C22×C4×C31—22no—
131C22×C4×C31—22no—
132C22×C4×C31—24no—
133C22×C4×C31—24no—
134C22×C4×C31—24no—
135C22×C4×C31—41no—
136C22×C4×C31—42no—
137C22×C4×C31—41no—
138C22×C4×C31—42no—
139C22×C4×C31—82no—
140C22×C4×C31C22⋊C412yes—
141C22×C4×C31C22×C411yescharacteristic
142C22×C4×C31C2×D412yes—
143C22×C4×C31C2×D412yes—
144C22×C4×C31C2×D412yes—
145C22×C4×C31C2×D412yes—
146C22×C4×C31C2×D411yescharacteristic
147C22×C4×C31#4112yes—
148C22×C4×C31#4112yes—
149M16×C31—24no—
150M16×C31—24no—
151M16×C31—42no—
152M16×C31—42no—
153C2×C8×C31—24no—
154C2×C8×C31—42no—
155C2×C8×C31—42no—
156C4⋊C4×C31—28no—
157C4⋊C4×C31—22no—
158C4⋊C4×C31—24no—
159C4⋊C4×C31—24no—
160C4⋊C4×C31—42no—
161C4⋊C4×C31C22⋊C414yes—
162C22⋊C4×C31—28no—
163C22⋊C4×C31—28no—
164C22⋊C4×C31—24no—
165C22⋊C4×C31—42no—
166C42×C31—24no—
167C42×C31—42no—
168#10986C3111yesmaximal, characteristic, direct product factor, Sylow
169C23×C31—22no—
170C23×C31—22no—
171C23×C31—22no—
172C23×C31—22no—
173C23×C31—41no—
174C23×C31—41no—
175C23×C31—42no—
176C23×C31—42no—
177C23×C31—42no—
178C23×C31—42no—
179C23×C31—41no—
180C23×C31—41no—
181C23×C31C2×C22⋊C411yescharacteristic
182C23×C31#12012yes—
183C23×C31#12011yescharacteristic
184C23×C31#12112yes—
185C23×C31#12311yescharacteristic
186Q8×C31—24no—
187Q8×C31—42no—
188Q8×C31—42no—
189Q8×C31—42no—
190D4×C31—24no—
191D4×C31—44no—
192D4×C31—44no—
193D4×C31—44no—
194D4×C31—44no—
195D4×C31—42no—
196D4×C31—42no—
197D4×C31—42no—
198D4×C31—88no—
199C2×C4×C31—24no—
200C2×C4×C31—22no—
201C2×C4×C31—22no—
202C2×C4×C31—22no—
203C2×C4×C31—22no—
204C2×C4×C31—44no—
205C2×C4×C31—41no—
206C2×C4×C31—41no—
207C2×C4×C31—44no—
208C2×C4×C31—44no—
209C2×C4×C31—44no—
210C2×C4×C31—44no—
211C2×C4×C31—44no—
212C2×C4×C31—84no—
213C2×C4×C31—82no—
214C2×C4×C31—82no—
215C2×C4×C31C2×C22⋊C411yescharacteristic
216C2×C4×C31C2×C22⋊C411yescharacteristic
217C2×C4×C31C4×D412yes—
218C2×C4×C31C4×D412yes—
219C2×C4×C31#12012yes—
220C2×C4×C31#12011yescharacteristic
221C2×C4×C31#12012yes—
222C2×C4×C31#12112yes—
223C2×C4×C31#12112yes—
224C2×C4×C31#12112yes—
225C2×C4×C31#12112yes—
226C2×C4×C31#12112yes—
227C2×C4×C31#12312yes—
228C2×C4×C31#12311yescharacteristic
229C2×C4×C31#12412yes—
230C2×C4×C31#12712yes—
231C8×C31—44no—
232C2×#537C2×C3111yescharacteristic
233C2×#421C2×C3112yescomplemented
234C2×#413C2×C3111yescharacteristic, complemented
235C2×#410C2×C3111yescharacteristic, complemented
236#1736C2×C3112yescomplemented
237C22×C31—21no—
238C22×C31—22no—
239C22×C31—22no—
240C22×C31—21no—
241C22×C31—41no—
242C22×C31—42no—
243C22×C31—41no—
244C22×C31—42no—
245C22×C31—42no—
246C22×C31—42no—
247C22×C31—42no—
248C22×C31—42no—
249C22×C31—42no—
250C22×C31—82no—
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—44no—
260C4×C31—42no—
261C4×C31—42no—
262C4×C31—84no—
263C4×C31#38612yes—
264C4×C31#39012yes—
265C4×C31#39212yes—
266C4×C31#39412yes—
267C22×#41C22×C3111yescharacteristic
268C22×#41C22×C3111yescharacteristic
269C22×M16C22×C3112yes—
270#537—24no—
271#537—24no—
272C2×C22⋊Q8—21no—
273C2×C22⋊Q8C4×C3112yescomplemented
274C2×#121—21no—
275C2×#121—22no—
276C2×#121C4×C3112yescomplemented
277C2×#117C22×C3112yes—
278C22×C4⋊C4C22×C3111yescharacteristic
279#421—24no—
280#421—24no—
281C2×#104—24no—
282#413—24no—
283C2×#101—21no—
284C2×#100—21no—
285#410—24no—
286C2×#99—22no—
287#340—24no—
288C2×C31—22no—
289C2×C31—21no—
290C2×C31—21no—
291C2×C31—22no—
292C2×C31—82no—
293C2×C31—82no—
294C2×C31#143811yescharacteristic
295C2×C31#179511yescharacteristic
296C2×C31#179611yescharacteristic
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×Q8D4×C3111yescharacteristic
311C22×D4—21no—
312C22×D4—22no—
313C22×D4C2×C4×C3111yescharacteristic
314C22×D4D4×C3112yes—
315C22×D4D4×C3111yescharacteristic
316C23×C4—21no—
317C23×C4—21no—
318C23×C4C2×C4×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—
327C22⋊Q8—28no—
328C22⋊Q8—24no—
329C22⋊Q8—24no—
330#121—216no—
331#121—28no—
332#121—24no—
333#121—24no—
334#117—22no—
335#117—22no—
336#117—22no—
337#117D4×C3114yescomplemented
338C2×C4⋊C4—22no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4C2×C4×C3112yes—
343C2×C4⋊C4D4×C3114yes—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—22no—
347C2×C42—22no—
348#104—216no—
349#101—24no—
350#100—24no—
351#99—28no—
352C31#1098611yescharacteristic, direct product factor, Sylow
353C24—21no—
354C24C22⋊C4×C3112yes—
355C24C2×D4×C3111yescharacteristic
356#41—24no—
357#41—24no—
358#41—24no—
359#41—24no—
360#41—42no—
361#41—42no—
362#41—42no—
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—
372C2×Q8—21no—
373C2×Q8—21no—
374C2×Q8—22no—
375C2×Q8—22no—
376C2×Q8—21no—
377C2×Q8—22no—
378C2×Q8—22no—
379C2×Q8C22⋊C4×C3112yes—
380C2×D4—22no—
381C2×D4—24no—
382C2×D4—24no—
383C2×D4—24no—
384C2×D4—22no—
385C2×D4—28no—
386C2×D4—21no—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—21no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—21no—
393C2×D4—41no—
394C2×D4—42no—
395C2×D4—41no—
396C2×D4—84no—
397C2×D4C22⋊C4×C3112yes—
398C22×C4—22no—
399C22×C4—21no—
400C22×C4—24no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—24no—
404C22×C4—24no—
405C22×C4—24no—
406C22×C4—41no—
407C22×C4—42no—
408C22×C4—41no—
409C22×C4—42no—
410C22×C4—82no—
411C22×C4C22⋊C4×C3112yes—
412C22×C4C22×C4×C3111yescharacteristic
413C22×C4C2×D4×C3112yes—
414C22×C4C2×D4×C3112yes—
415C22×C4C2×D4×C3112yes—
416C22×C4C2×D4×C3112yes—
417C22×C4C2×D4×C3111yescharacteristic
418C22×C4#41×C3112yes—
419C22×C4#41×C3112yes—
420M16—24no—
421M16—24no—
422M16—42no—
423M16—42no—
424C2×C8—24no—
425C2×C8—42no—
426C2×C8—42no—
427C4⋊C4—28no—
428C4⋊C4—22no—
429C4⋊C4—24no—
430C4⋊C4—24no—
431C4⋊C4—42no—
432C4⋊C4C22⋊C4×C3114yes—
433C22⋊C4—28no—
434C22⋊C4—28no—
435C22⋊C4—24no—
436C22⋊C4—42no—
437C42—24no—
438C42—42no—
439C23—22no—
440C23—22no—
441C23—22no—
442C23—22no—
443C23—41no—
444C23—41no—
445C23—42no—
446C23—42no—
447C23—42no—
448C23—42no—
449C23—41no—
450C23—41no—
451C23C2×C22⋊C4×C3111yescharacteristic
452C23C31×#12012yes—
453C23C31×#12011yescharacteristic
454C23C31×#12112yes—
455C23C31×#12311yescharacteristic
456Q8—24no—
457Q8—42no—
458Q8—42no—
459Q8—42no—
460D4—24no—
461D4—44no—
462D4—44no—
463D4—44no—
464D4—44no—
465D4—42no—
466D4—42no—
467D4—42no—
468D4—88no—
469C2×C4—24no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—44no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—44no—
478C2×C4—44no—
479C2×C4—44no—
480C2×C4—44no—
481C2×C4—44no—
482C2×C4—84no—
483C2×C4—82no—
484C2×C4—82no—
485C2×C4C2×C22⋊C4×C3111yescharacteristic
486C2×C4C2×C22⋊C4×C3111yescharacteristic
487C2×C4C4×D4×C3112yes—
488C2×C4C4×D4×C3112yes—
489C2×C4C31×#12012yes—
490C2×C4C31×#12011yescharacteristic
491C2×C4C31×#12012yes—
492C2×C4C31×#12112yes—
493C2×C4C31×#12112yes—
494C2×C4C31×#12112yes—
495C2×C4C31×#12112yes—
496C2×C4C31×#12112yes—
497C2×C4C31×#12312yes—
498C2×C4C31×#12311yescharacteristic
499C2×C4C31×#12412yes—
500C2×C4C31×#12712yes—
501C8—44no—
502C22—21no—
503C22—22no—
504C22—22no—
505C22—21no—
506C22—41no—
507C22—42no—
508C22—41no—
509C22—42no—
510C22—42no—
511C22—42no—
512C22—42no—
513C22—42no—
514C22—42no—
515C22—82no—
516C22—82no—
517C22—82no—
518C22—82no—
519C22C31×#37911yescharacteristic
520C22C31×#38611yescharacteristic
521C22C31×#38611yescharacteristic
522C22C31×#39212yes—
523C22C31×#39412yes—
524C4—44no—
525C4—42no—
526C4—42no—
527C4—84no—
528C4C31×#38612yes—
529C4C31×#39012yes—
530C4C31×#39212yes—
531C4C31×#39412yes—
532C2—22no—
533C2—21no—
534C2—21no—
535C2—22no—
536C2—82no—
537C2—82no—
538C2C31×#143811yescharacteristic
539C2C31×#179511yescharacteristic
540C2C31×#179611yescharacteristic
subgroupG/H
center, socleC22×C31#379
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC2×C31×#537C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×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×#413C2semidirect
4. C2×C31×#410C2semidirect
5. C31×#1736C2semidirect
12. C2×C31×C22⋊Q8C4semidirect
15. C2×C31×#121C4semidirect
55. C2×M16×C31D4semidirect
67. C31×#117D4semidirect
168. #10986C31direct (N × H)
233. C2×#421C2×C31semidirect
234. C2×#413C2×C31semidirect
235. C2×#410C2×C31semidirect
236. #1736C2×C31semidirect
273. C2×C22⋊Q8C4×C31semidirect
276. C2×#121C4×C31semidirect
325. C2×M16D4×C31semidirect
337. #117D4×C31semidirect
352. C31#10986direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5372
C2×C31×#4212
C2×C31×#4132
C2×C31×#4102
C31×#17362
#1098631