Finite Group Databasebeta

← C31×#10993 #21467752

Subgroups — C31×#10993 #21467752

Order 7936.

1458 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#525C211yesmaximal, characteristic
2C2×C31×#413C211yesmaximal, characteristic, complemented
3C31×#2879C211yesmaximal, characteristic, complemented
4C2×C31×#407C212yesmaximal, complemented
5C2×C31×#344C212yesmaximal, complemented
6C22×#41×C31C2211yescharacteristic
7C24×C4×C31C2211yescharacteristic
8C22×M16×C31C2212yes—
9C22×M16×C31C2212yes—
10C31×#525—24no—
11C31×#525—24no—
12C2×C31×#123C412yes—
13C2×C31×C22⋊Q8—21no—
14C2×C31×#121—21no—
15C2×C31×#120C412yes—
16C2×C4×D4×C31—22no—
17C2×C31×#117C2211yescharacteristic
18C31×#413—24no—
19C2×C31×#101—21no—
20C2×C31×#100—21no—
21C31×#408—24no—
22C31×#407—24no—
23C31×#407—22no—
24C31×#407—24no—
25C2×C31×C22⋊C8—24no—
26C31×#344—24no—
27C25×C31C2×C411yescharacteristic
28C2×#41×C31—22no—
29C2×#41×C31—22no—
30C2×#41×C31—22no—
31C2×#41×C31—22no—
32C2×#41×C31—22no—
33C2×#41×C31—22no—
34C22×Q8×C31D411yescharacteristic
35C22×D4×C31—22no—
36C22×D4×C31C2×C412yes—
37C22×D4×C31D411yescharacteristic
38C23×C4×C31—22no—
39C23×C4×C31—22no—
40C23×C4×C31—21no—
41C23×C4×C31—21no—
42C23×C4×C31—22no—
43C23×C4×C31—22no—
44C23×C4×C31—22no—
45C23×C4×C31C2×C411yescharacteristic
46C23×C4×C31D412yes—
47C23×C4×C31D414yes—
48C23×C4×C31C2311yescharacteristic
49C2×M16×C31—22no—
50C2×M16×C31—22no—
51C2×M16×C31—22no—
52C2×M16×C31—22no—
53C2×M16×C31—22no—
54C2×M16×C31—22no—
55C2×M16×C31—22no—
56C2×M16×C31—22no—
57C2×M16×C31—22no—
58C2×M16×C31—22no—
59C2×M16×C31—22no—
60C2×M16×C31D414yescomplemented
61C22×C8×C31—22no—
62C22×C8×C31D414yescomplemented
63C31×#123—24no—
64C31×#123—24no—
65C31×C22⋊Q8—28no—
66C31×#121—28no—
67C31×#120—24no—
68C31×#120—24no—
69C4×D4×C31—216no—
70C31×#117—22no—
71C31×#117D414yes—
72C2×C4⋊C4×C31—22no—
73C2×C4⋊C4×C31—21no—
74C2×C22⋊C4×C31—22no—
75C2×C22⋊C4×C31—22no—
76C2×C22⋊C4×C31C2×C412yes—
77C2×C42×C31—21no—
78C31×#101—24no—
79C31×#100—24no—
80C31×C22⋊C8—216no—
81C31×C22⋊C8—28no—
82C24×C31—21no—
83C24×C31—22no—
84C24×C31—21no—
85C24×C31—22no—
86C24×C31—44no—
87C24×C31C22⋊C412yes—
88C24×C31C22⋊C412yes—
89C24×C31C22×C411yescharacteristic
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—
98C2×Q8×C31—21no—
99C2×Q8×C31—22no—
100C2×Q8×C31—22no—
101C2×Q8×C31—21no—
102C2×D4×C31—28no—
103C2×D4×C31—22no—
104C2×D4×C31—22no—
105C2×D4×C31—24no—
106C2×D4×C31—24no—
107C2×D4×C31—21no—
108C2×D4×C31—22no—
109C2×D4×C31—22no—
110C2×D4×C31—21no—
111C2×D4×C31—48no—
112C22×C4×C31—22no—
113C22×C4×C31—21no—
114C22×C4×C31—21no—
115C22×C4×C31—22no—
116C22×C4×C31—22no—
117C22×C4×C31—24no—
118C22×C4×C31—24no—
119C22×C4×C31—24no—
120C22×C4×C31—24no—
121C22×C4×C31—22no—
122C22×C4×C31—24no—
123C22×C4×C31—24no—
124C22×C4×C31—24no—
125C22×C4×C31—24no—
126C22×C4×C31—22no—
127C22×C4×C31—41no—
128C22×C4×C31—41no—
129C22×C4×C31—42no—
130C22×C4×C31—42no—
131C22×C4×C31—42no—
132C22×C4×C31—42no—
133C22×C4×C31—41no—
134C22×C4×C31—41no—
135C22×C4×C31—42no—
136C22×C4×C31—42no—
137C22×C4×C31C22⋊C412yes—
138C22×C4×C31C22⋊C412yes—
139C22×C4×C31C2×D411yescharacteristic
140C22×C4×C31C2×D412yes—
141C22×C4×C31C2×D411yescharacteristic
142C22×C4×C31C2×D412yes—
143C22×C4×C31C2×D412yes—
144C22×C4×C31C2×D412yes—
145C22×C4×C31#4112yes—
146C22×C4×C31#4112yes—
147M16×C31—24no—
148M16×C31—24no—
149M16×C31—42no—
150M16×C31—42no—
151M16×C31—42no—
152M16×C31—42no—
153M16×C31—42no—
154M16×C31—42no—
155C2×C8×C31—24no—
156C2×C8×C31—24no—
157C2×C8×C31—24no—
158C2×C8×C31—24no—
159C2×C8×C31—42no—
160C2×C8×C31—42no—
161C4⋊C4×C31—28no—
162C4⋊C4×C31—24no—
163C22⋊C4×C31—28no—
164C22⋊C4×C31—28no—
165C22⋊C4×C31—22no—
166C22⋊C4×C31C22⋊C414yes—
167C42×C31—24no—
168#10993C3111yesmaximal, characteristic, direct product factor, Sylow
169C23×C31—24no—
170C23×C31—28no—
171C23×C31—22no—
172C23×C31—24no—
173C23×C31—22no—
174C23×C31—22no—
175C23×C31—22no—
176C23×C31—44no—
177C23×C31—42no—
178C23×C31—42no—
179C23×C31—44no—
180C23×C31—44no—
181C23×C31—48no—
182C23×C31—44no—
183C23×C31—41no—
184C23×C31—41no—
185C23×C31—42no—
186C23×C31C2×C22⋊C411yescharacteristic
187C23×C31C2×C22⋊C411yescharacteristic
188C23×C31C2×C22⋊C411yescharacteristic
189C23×C31C4×D412yes—
190C23×C31C4×D412yes—
191Q8×C31—42no—
192Q8×C31—42no—
193D4×C31—416no—
194D4×C31—44no—
195D4×C31—44no—
196D4×C31—42no—
197D4×C31—42no—
198C2×C4×C31—24no—
199C2×C4×C31—22no—
200C2×C4×C31—22no—
201C2×C4×C31—24no—
202C2×C4×C31—22no—
203C2×C4×C31—22no—
204C2×C4×C31—44no—
205C2×C4×C31—41no—
206C2×C4×C31—41no—
207C2×C4×C31—42no—
208C2×C4×C31—44no—
209C2×C4×C31—44no—
210C2×C4×C31—44no—
211C2×C4×C31—44no—
212C2×C4×C31—44no—
213C2×C4×C31—44no—
214C2×C4×C31#12012yes—
215C2×C4×C31#12011yescharacteristic
216C2×C4×C31#12012yes—
217C2×C4×C31#12012yes—
218C2×C4×C31#12011yescharacteristic
219C2×C4×C31#12112yes—
220C2×C4×C31#12112yes—
221C2×C4×C31#12112yes—
222C2×C4×C31#12112yes—
223C2×C4×C31#12112yes—
224C2×C4×C31#12112yes—
225C2×C4×C31#12311yescharacteristic
226C2×C4×C31#12312yes—
227C2×C4×C31#12311yescharacteristic
228C2×C4×C31#12412yes—
229C2×C4×C31#12712yes—
230C8×C31—44no—
231C8×C31—44no—
232C2×#525C2×C3111yescharacteristic
233C2×#413C2×C3111yescharacteristic, complemented
234#2879C2×C3111yescharacteristic, complemented
235C2×#407C2×C3112yescomplemented
236C2×#344C2×C3112yescomplemented
237C22×C31—22no—
238C22×C31—24no—
239C22×C31—24no—
240C22×C31—28no—
241C22×C31—41no—
242C22×C31—41no—
243C22×C31—42no—
244C22×C31—42no—
245C22×C31—44no—
246C22×C31—44no—
247C22×C31—48no—
248C22×C31—44no—
249C22×C31—44no—
250C22×C31—42no—
251C22×C31—44no—
252C22×C31—42no—
253C22×C31—82no—
254C22×C31#37911yescharacteristic
255C22×C31#38611yescharacteristic
256C22×C31#38612yes—
257C22×C31#38611yescharacteristic
258C22×C31#39012yes—
259C4×C31—44no—
260C4×C31—42no—
261C4×C31—42no—
262C4×C31#39212yes—
263C4×C31#39212yes—
264C4×C31#39412yes—
265C4×C31#39412yes—
266C22×#41C22×C3111yescharacteristic
267C24×C4C22×C3111yescharacteristic
268C22×M16C22×C3112yes—
269C22×M16C22×C3112yes—
270#525—24no—
271#525—24no—
272C2×#123C4×C3112yes—
273C2×C22⋊Q8—21no—
274C2×#121—21no—
275C2×#120C4×C3112yes—
276C2×C4×D4—22no—
277C2×#117C22×C3111yescharacteristic
278#413—24no—
279C2×#101—21no—
280C2×#100—21no—
281#408—24no—
282#407—24no—
283#407—22no—
284#407—24no—
285C2×C22⋊C8—24no—
286#344—24no—
287C2×C31—21no—
288C2×C31—22no—
289C2×C31—21no—
290C2×C31—22no—
291C2×C31—44no—
292C2×C31—82no—
293C2×C31#143811yescharacteristic
294C2×C31#189112yes—
295C25C2×C4×C3111yescharacteristic
296C2×#41—22no—
297C2×#41—22no—
298C2×#41—22no—
299C2×#41—22no—
300C2×#41—22no—
301C2×#41—22no—
302C22×Q8D4×C3111yescharacteristic
303C22×D4—22no—
304C22×D4C2×C4×C3112yes—
305C22×D4D4×C3111yescharacteristic
306C23×C4—21no—
307C23×C4—21no—
308C23×C4—22no—
309C23×C4—22no—
310C23×C4—22no—
311C23×C4—22no—
312C23×C4—22no—
313C23×C4C2×C4×C3111yescharacteristic
314C23×C4D4×C3112yes—
315C23×C4D4×C3114yes—
316C23×C4C23×C3111yescharacteristic
317C2×M16—22no—
318C2×M16—22no—
319C2×M16—22no—
320C2×M16—22no—
321C2×M16—22no—
322C2×M16—22no—
323C2×M16—22no—
324C2×M16—22no—
325C2×M16—22no—
326C2×M16—22no—
327C2×M16—22no—
328C2×M16D4×C3114yescomplemented
329C22×C8—22no—
330C22×C8D4×C3114yescomplemented
331#123—24no—
332#123—24no—
333C22⋊Q8—28no—
334#121—28no—
335#120—24no—
336#120—24no—
337C4×D4—216no—
338#117—22no—
339#117D4×C3114yes—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—21no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4C2×C4×C3112yes—
345C2×C42—21no—
346#101—24no—
347#100—24no—
348C22⋊C8—216no—
349C22⋊C8—28no—
350C31#1099311yescharacteristic, direct product factor, Sylow
351C24—21no—
352C24—22no—
353C24—21no—
354C24—22no—
355C24—44no—
356C24C22⋊C4×C3112yes—
357C24C22⋊C4×C3112yes—
358C24C22×C4×C3111yescharacteristic
359#41—42no—
360#41—42no—
361#41—42no—
362#41—42no—
363#41—42no—
364#41—42no—
365#41—42no—
366#41—42no—
367C2×Q8—21no—
368C2×Q8—22no—
369C2×Q8—22no—
370C2×Q8—21no—
371C2×D4—28no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—24no—
375C2×D4—24no—
376C2×D4—21no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—21no—
380C2×D4—48no—
381C22×C4—22no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—24no—
387C22×C4—22no—
388C22×C4—24no—
389C22×C4—24no—
390C22×C4—24no—
391C22×C4—24no—
392C22×C4—24no—
393C22×C4—24no—
394C22×C4—24no—
395C22×C4—22no—
396C22×C4—41no—
397C22×C4—41no—
398C22×C4—42no—
399C22×C4—42no—
400C22×C4—42no—
401C22×C4—42no—
402C22×C4—41no—
403C22×C4—41no—
404C22×C4—42no—
405C22×C4—42no—
406C22×C4C22⋊C4×C3112yes—
407C22×C4C22⋊C4×C3112yes—
408C22×C4C2×D4×C3111yescharacteristic
409C22×C4C2×D4×C3111yescharacteristic
410C22×C4C2×D4×C3112yes—
411C22×C4C2×D4×C3112yes—
412C22×C4C2×D4×C3112yes—
413C22×C4C2×D4×C3112yes—
414C22×C4#41×C3112yes—
415C22×C4#41×C3112yes—
416M16—24no—
417M16—24no—
418M16—42no—
419M16—42no—
420M16—42no—
421M16—42no—
422M16—42no—
423M16—42no—
424C2×C8—24no—
425C2×C8—24no—
426C2×C8—24no—
427C2×C8—24no—
428C2×C8—42no—
429C2×C8—42no—
430C4⋊C4—28no—
431C4⋊C4—24no—
432C22⋊C4—28no—
433C22⋊C4—28no—
434C22⋊C4—22no—
435C22⋊C4C22⋊C4×C3114yes—
436C42—24no—
437C23—24no—
438C23—28no—
439C23—22no—
440C23—24no—
441C23—22no—
442C23—22no—
443C23—22no—
444C23—44no—
445C23—42no—
446C23—42no—
447C23—44no—
448C23—44no—
449C23—48no—
450C23—44no—
451C23—41no—
452C23—41no—
453C23—42no—
454C23C2×C22⋊C4×C3111yescharacteristic
455C23C2×C22⋊C4×C3111yescharacteristic
456C23C2×C22⋊C4×C3111yescharacteristic
457C23C4×D4×C3112yes—
458C23C4×D4×C3112yes—
459Q8—42no—
460Q8—42no—
461D4—416no—
462D4—44no—
463D4—44no—
464D4—42no—
465D4—42no—
466C2×C4—24no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—24no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—44no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—42no—
476C2×C4—44no—
477C2×C4—44no—
478C2×C4—44no—
479C2×C4—44no—
480C2×C4—44no—
481C2×C4—44no—
482C2×C4C31×#12012yes—
483C2×C4C31×#12011yescharacteristic
484C2×C4C31×#12011yescharacteristic
485C2×C4C31×#12012yes—
486C2×C4C31×#12012yes—
487C2×C4C31×#12112yes—
488C2×C4C31×#12112yes—
489C2×C4C31×#12112yes—
490C2×C4C31×#12112yes—
491C2×C4C31×#12112yes—
492C2×C4C31×#12112yes—
493C2×C4C31×#12311yescharacteristic
494C2×C4C31×#12312yes—
495C2×C4C31×#12311yescharacteristic
496C2×C4C31×#12412yes—
497C2×C4C31×#12712yes—
498C8—44no—
499C8—44no—
500C22—22no—
501C22—24no—
502C22—24no—
503C22—28no—
504C22—41no—
505C22—41no—
506C22—42no—
507C22—42no—
508C22—44no—
509C22—44no—
510C22—48no—
511C22—44no—
512C22—44no—
513C22—42no—
514C22—44no—
515C22—42no—
516C22—82no—
517C22C31×#37911yescharacteristic
518C22C31×#38611yescharacteristic
519C22C31×#38612yes—
520C22C31×#38611yescharacteristic
521C22C31×#39012yes—
522C4—44no—
523C4—42no—
524C4—42no—
525C4C31×#39212yes—
526C4C31×#39212yes—
527C4C31×#39412yes—
528C4C31×#39412yes—
529C2—21no—
530C2—22no—
531C2—21no—
532C2—22no—
533C2—44no—
534C2—82no—
535C2C31×#143811yescharacteristic
536C2C31×#189112yes—
subgroupG/H
centerC2×C4×C31#120
commutatorC24C22×C4×C31
Frattini, cosocleC23×C4C23×C31
socleC22×C31#386
prime radicalC2×C31×#525C2
LCSG ▷ C24 ▷ 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×#413C2semidirect
3. C31×#2879C2semidirect
4. C2×C31×#407C2semidirect
5. C2×C31×#344C2semidirect
60. C2×M16×C31D4semidirect
62. C22×C8×C31D4semidirect
168. #10993C31direct (N × H)
233. C2×#413C2×C31semidirect
234. #2879C2×C31semidirect
235. C2×#407C2×C31semidirect
236. C2×#344C2×C31semidirect
328. C2×M16D4×C31semidirect
330. C22×C8D4×C31semidirect
350. C31#10993direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5252
C2×C31×#4132
C31×#28792
C2×C31×#4072
C2×C31×#3442
#1099331