Finite Group Databasebeta

← C31×#10992 #21467751

Subgroups — C31×#10992 #21467751

Order 7936.

1658 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#123C211yesmaximal, characteristic
2C22×C31×#99C211yesmaximal, characteristic
3C31×#2308C211yesmaximal, characteristic
4C2×C31×#381C212yesmaximal, complemented
5C2×C31×#342C212yesmaximal, complemented
6C23×D4×C31C2211yescharacteristic
7C24×C4×C31C2211yescharacteristic
8C2×C31×#123—22no—
9C2×C31×#123—24no—
10C2×C31×#123—24no—
11C2×C31×#123C414yescomplemented
12C22×C4⋊C4×C31—21no—
13C22×C22⋊C4×C31—21no—
14C22×C22⋊C4×C31C2212yes—
15C22×C22⋊C4×C31C2212yes—
16C22×C22⋊C4×C31C2211yescharacteristic
17C2×C31×#99—22no—
18C2×C31×#99—24no—
19C31×#386—24no—
20C31×#381—21no—
21C31×#381—24no—
22C31×#381—24no—
23C31×#379—21no—
24C2×C31×#95—24no—
25C31×#342—24no—
26C25×C31D411yescharacteristic
27C25×C31C2311yescharacteristic
28C22×D4×C31—22no—
29C22×D4×C31—22no—
30C22×D4×C31—22no—
31C22×D4×C31—22no—
32C22×D4×C31—22no—
33C22×D4×C31—22no—
34C22×D4×C31C2×C412yes—
35C22×D4×C31D412yes—
36C23×C4×C31—21no—
37C23×C4×C31—21no—
38C23×C4×C31—21no—
39C23×C4×C31—22no—
40C23×C4×C31—22no—
41C23×C4×C31—22no—
42C23×C4×C31—22no—
43C23×C4×C31—22no—
44C23×C4×C31—22no—
45C23×C4×C31C2×C412yes—
46C23×C4×C31D411yescharacteristic
47C23×C4×C31D414yes—
48C23×C4×C31D414yes—
49C31×#123—216no—
50C31×#123—28no—
51C31×#123—28no—
52C2×C4⋊C4×C31—28no—
53C2×C4⋊C4×C31—24no—
54C2×C22⋊C4×C31—28no—
55C2×C22⋊C4×C31—24no—
56C2×C22⋊C4×C31—22no—
57C2×C22⋊C4×C31—21no—
58C2×C22⋊C4×C31—22no—
59C2×C22⋊C4×C31—22no—
60C2×C22⋊C4×C31—22no—
61C2×C22⋊C4×C31—22no—
62C2×C22⋊C4×C31—22no—
63C2×C22⋊C4×C31—22no—
64C2×C22⋊C4×C31—22no—
65C2×C22⋊C4×C31—22no—
66C2×C22⋊C4×C31—22no—
67C2×C22⋊C4×C31—22no—
68C2×C22⋊C4×C31—22no—
69C2×C22⋊C4×C31—24no—
70C2×C22⋊C4×C31C2×C412yes—
71C2×C22⋊C4×C31D414yes—
72C2×C22⋊C4×C31D414yes—
73C31×#99—28no—
74C31×#95—216no—
75C31×#95—24no—
76C24×C31—22no—
77C24×C31—21no—
78C24×C31—22no—
79C24×C31—21no—
80C24×C31—44no—
81C24×C31—44no—
82C24×C31C22⋊C412yes—
83C24×C31C22×C411yescharacteristic
84C24×C31C2×D411yescharacteristic
85C24×C31C2×D412yes—
86C24×C31C2×D411yescharacteristic
87C24×C31C2×D412yes—
88C24×C31C2×D412yes—
89C24×C31C2×D412yes—
90C24×C31#4112yes—
91C24×C31#4112yes—
92C2×D4×C31—22no—
93C2×D4×C31—22no—
94C2×D4×C31—24no—
95C2×D4×C31—24no—
96C2×D4×C31—22no—
97C2×D4×C31—24no—
98C2×D4×C31—24no—
99C2×D4×C31—22no—
100C2×D4×C31—42no—
101C2×D4×C31—42no—
102C2×D4×C31—42no—
103C2×D4×C31—42no—
104C2×D4×C31—42no—
105C2×D4×C31—42no—
106C2×D4×C31—42no—
107C2×D4×C31—42no—
108C22×C4×C31—22no—
109C22×C4×C31—22no—
110C22×C4×C31—22no—
111C22×C4×C31—24no—
112C22×C4×C31—24no—
113C22×C4×C31—24no—
114C22×C4×C31—24no—
115C22×C4×C31—24no—
116C22×C4×C31—22no—
117C22×C4×C31—24no—
118C22×C4×C31—21no—
119C22×C4×C31—24no—
120C22×C4×C31—24no—
121C22×C4×C31—22no—
122C22×C4×C31—24no—
123C22×C4×C31—21no—
124C22×C4×C31—24no—
125C22×C4×C31—24no—
126C22×C4×C31—24no—
127C22×C4×C31—24no—
128C22×C4×C31—44no—
129C22×C4×C31—41no—
130C22×C4×C31—41no—
131C22×C4×C31—42no—
132C22×C4×C31—42no—
133C22×C4×C31—42no—
134C22×C4×C31—42no—
135C22×C4×C31—41no—
136C22×C4×C31—41no—
137C22×C4×C31—42no—
138C22×C4×C31—42no—
139C22×C4×C31—48no—
140C22×C4×C31—48no—
141C22×C4×C31—42no—
142C22×C4×C31—42no—
143C22×C4×C31C22⋊C412yes—
144C22×C4×C31C22⋊C414yescomplemented
145C4⋊C4×C31—216no—
146C22⋊C4×C31—216no—
147C22⋊C4×C31—22no—
148C22⋊C4×C31—24no—
149C22⋊C4×C31—24no—
150C22⋊C4×C31—24no—
151C22⋊C4×C31—42no—
152C22⋊C4×C31—42no—
153C22⋊C4×C31—42no—
154C22⋊C4×C31—42no—
155C22⋊C4×C31—42no—
156C22⋊C4×C31—42no—
157C22⋊C4×C31—84no—
158C22⋊C4×C31C22⋊C414yescomplemented
159#10992C3111yesmaximal, characteristic, direct product factor, Sylow
160C23×C31—28no—
161C23×C31—24no—
162C23×C31—22no—
163C23×C31—22no—
164C23×C31—22no—
165C23×C31—42no—
166C23×C31—42no—
167C23×C31—44no—
168C23×C31—44no—
169C23×C31—44no—
170C23×C31—44no—
171C23×C31—44no—
172C23×C31—44no—
173C23×C31—48no—
174C23×C31—42no—
175C23×C31—42no—
176C23×C31—44no—
177C23×C31—82no—
178C23×C31—84no—
179C23×C31C2×C22⋊C411yescharacteristic
180C23×C31C2×C22⋊C411yescharacteristic
181C23×C31C2×C22⋊C411yescharacteristic
182C23×C31C4×D412yes—
183C23×C31C4×D412yes—
184C23×C31#12012yes—
185C23×C31#12012yes—
186C23×C31#12012yes—
187C23×C31#12011yescharacteristic
188C23×C31#12011yescharacteristic
189C23×C31#12112yes—
190C23×C31#12112yes—
191C23×C31#12112yes—
192C23×C31#12112yes—
193C23×C31#12112yes—
194C23×C31#12112yes—
195C23×C31#12311yescharacteristic
196C23×C31#12312yes—
197C23×C31#12311yescharacteristic
198C23×C31#12412yes—
199C23×C31#12712yes—
200D4×C31—44no—
201D4×C31—44no—
202D4×C31—44no—
203D4×C31—44no—
204C2×C4×C31—24no—
205C2×C4×C31—24no—
206C2×C4×C31—22no—
207C2×C4×C31—28no—
208C2×C4×C31—22no—
209C2×C4×C31—22no—
210C2×C4×C31—44no—
211C2×C4×C31—48no—
212C2×C4×C31—42no—
213C2×C4×C31—42no—
214C2×C4×C31—44no—
215C2×C4×C31—44no—
216C2×C4×C31—44no—
217C2×C4×C31—42no—
218C2×C4×C31—44no—
219C2×C4×C31—44no—
220C2×C4×C31—42no—
221C2×C4×C31—48no—
222C2×C4×C31—48no—
223C2×C4×C31—44no—
224C2×C4×C31—44no—
225C2×C4×C31—48no—
226C2×C4×C31—84no—
227C2×C4×C31—84no—
228C2×C4×C31—84no—
229C22×#123C2×C3111yescharacteristic
230C22×#99C2×C3111yescharacteristic
231#2308C2×C3111yescharacteristic
232C2×#381C2×C3112yescomplemented
233C2×#342C2×C3112yescomplemented
234C22×C31—22no—
235C22×C31—24no—
236C22×C31—22no—
237C22×C31—24no—
238C22×C31—24no—
239C22×C31—24no—
240C22×C31—24no—
241C22×C31—24no—
242C22×C31—24no—
243C22×C31—24no—
244C22×C31—41no—
245C22×C31—41no—
246C22×C31—42no—
247C22×C31—42no—
248C22×C31—41no—
249C22×C31—42no—
250C22×C31—42no—
251C22×C31—41no—
252C22×C31—42no—
253C22×C31—42no—
254C22×C31—44no—
255C22×C31—44no—
256C22×C31—42no—
257C22×C31—82no—
258C22×C31—84no—
259C22×C31—84no—
260C22×C31#37911yescharacteristic
261C22×C31#38612yes—
262C22×C31#38611yescharacteristic
263C22×C31#38611yescharacteristic
264C22×C31#39012yes—
265C22×C31#39212yes—
266C22×C31#39212yes—
267C22×C31#39412yes—
268C22×C31#39412yes—
269C22×C31#45814yes—
270C4×C31—44no—
271C4×C31—44no—
272C4×C31—42no—
273C4×C31—84no—
274C4×C31—84no—
275C23×D4C22×C3111yescharacteristic
276C24×C4C22×C3111yescharacteristic
277C2×#123—22no—
278C2×#123—24no—
279C2×#123—24no—
280C2×#123C4×C3114yescomplemented
281C22×C4⋊C4—21no—
282C22×C22⋊C4—21no—
283C22×C22⋊C4C22×C3112yes—
284C22×C22⋊C4C22×C3112yes—
285C22×C22⋊C4C22×C3111yescharacteristic
286C2×#99—22no—
287C2×#99—24no—
288#386—24no—
289#381—21no—
290#381—24no—
291#381—24no—
292#379—21no—
293C2×#95—24no—
294#342—24no—
295C2×C31—21no—
296C2×C31—22no—
297C2×C31—21no—
298C2×C31—22no—
299C2×C31—22no—
300C2×C31—22no—
301C2×C31—22no—
302C2×C31—82no—
303C2×C31#143811yescharacteristic
304C2×C31#189012yes—
305C2×C31#202214yes—
306C25D4×C3111yescharacteristic
307C25C23×C3111yescharacteristic
308C22×D4—22no—
309C22×D4—22no—
310C22×D4—22no—
311C22×D4—22no—
312C22×D4—22no—
313C22×D4—22no—
314C22×D4C2×C4×C3112yes—
315C22×D4D4×C3112yes—
316C23×C4—21no—
317C23×C4—21no—
318C23×C4—21no—
319C23×C4—22no—
320C23×C4—22no—
321C23×C4—22no—
322C23×C4—22no—
323C23×C4—22no—
324C23×C4—22no—
325C23×C4C2×C4×C3112yes—
326C23×C4D4×C3111yescharacteristic
327C23×C4D4×C3114yes—
328C23×C4D4×C3114yes—
329#123—216no—
330#123—28no—
331#123—28no—
332C2×C4⋊C4—28no—
333C2×C4⋊C4—24no—
334C2×C22⋊C4—28no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4C2×C4×C3112yes—
351C2×C22⋊C4D4×C3114yes—
352C2×C22⋊C4D4×C3114yes—
353#99—28no—
354#95—216no—
355#95—24no—
356C31#1099211yescharacteristic, direct product factor, Sylow
357C24—22no—
358C24—21no—
359C24—22no—
360C24—21no—
361C24—44no—
362C24—44no—
363C24C22⋊C4×C3112yes—
364C24C22×C4×C3111yescharacteristic
365C24C2×D4×C3111yescharacteristic
366C24C2×D4×C3112yes—
367C24C2×D4×C3111yescharacteristic
368C24C2×D4×C3112yes—
369C24C2×D4×C3112yes—
370C24C2×D4×C3112yes—
371C24#41×C3112yes—
372C24#41×C3112yes—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—24no—
376C2×D4—24no—
377C2×D4—22no—
378C2×D4—24no—
379C2×D4—24no—
380C2×D4—22no—
381C2×D4—42no—
382C2×D4—42no—
383C2×D4—42no—
384C2×D4—42no—
385C2×D4—42no—
386C2×D4—42no—
387C2×D4—42no—
388C2×D4—42no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—24no—
393C22×C4—24no—
394C22×C4—24no—
395C22×C4—21no—
396C22×C4—24no—
397C22×C4—24no—
398C22×C4—22no—
399C22×C4—24no—
400C22×C4—24no—
401C22×C4—24no—
402C22×C4—22no—
403C22×C4—24no—
404C22×C4—21no—
405C22×C4—24no—
406C22×C4—24no—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—44no—
410C22×C4—41no—
411C22×C4—41no—
412C22×C4—42no—
413C22×C4—42no—
414C22×C4—42no—
415C22×C4—42no—
416C22×C4—41no—
417C22×C4—41no—
418C22×C4—42no—
419C22×C4—42no—
420C22×C4—48no—
421C22×C4—48no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4C22⋊C4×C3112yes—
425C22×C4C22⋊C4×C3114yescomplemented
426C4⋊C4—216no—
427C22⋊C4—216no—
428C22⋊C4—22no—
429C22⋊C4—24no—
430C22⋊C4—24no—
431C22⋊C4—24no—
432C22⋊C4—42no—
433C22⋊C4—42no—
434C22⋊C4—42no—
435C22⋊C4—42no—
436C22⋊C4—42no—
437C22⋊C4—42no—
438C22⋊C4—84no—
439C22⋊C4C22⋊C4×C3114yescomplemented
440C23—28no—
441C23—24no—
442C23—22no—
443C23—22no—
444C23—22no—
445C23—42no—
446C23—42no—
447C23—44no—
448C23—44no—
449C23—44no—
450C23—44no—
451C23—44no—
452C23—44no—
453C23—48no—
454C23—44no—
455C23—42no—
456C23—42no—
457C23—82no—
458C23—84no—
459C23C2×C22⋊C4×C3111yescharacteristic
460C23C2×C22⋊C4×C3111yescharacteristic
461C23C2×C22⋊C4×C3111yescharacteristic
462C23C4×D4×C3112yes—
463C23C4×D4×C3112yes—
464C23C31×#12012yes—
465C23C31×#12012yes—
466C23C31×#12012yes—
467C23C31×#12011yescharacteristic
468C23C31×#12011yescharacteristic
469C23C31×#12112yes—
470C23C31×#12112yes—
471C23C31×#12112yes—
472C23C31×#12112yes—
473C23C31×#12112yes—
474C23C31×#12112yes—
475C23C31×#12311yescharacteristic
476C23C31×#12312yes—
477C23C31×#12311yescharacteristic
478C23C31×#12412yes—
479C23C31×#12712yes—
480D4—44no—
481D4—44no—
482D4—44no—
483D4—44no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—22no—
487C2×C4—28no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—44no—
491C2×C4—48no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—44no—
495C2×C4—44no—
496C2×C4—44no—
497C2×C4—42no—
498C2×C4—44no—
499C2×C4—44no—
500C2×C4—42no—
501C2×C4—48no—
502C2×C4—48no—
503C2×C4—48no—
504C2×C4—44no—
505C2×C4—44no—
506C2×C4—84no—
507C2×C4—84no—
508C2×C4—84no—
509C22—22no—
510C22—24no—
511C22—22no—
512C22—24no—
513C22—24no—
514C22—24no—
515C22—24no—
516C22—24no—
517C22—24no—
518C22—24no—
519C22—41no—
520C22—41no—
521C22—42no—
522C22—42no—
523C22—41no—
524C22—42no—
525C22—42no—
526C22—41no—
527C22—42no—
528C22—42no—
529C22—44no—
530C22—44no—
531C22—42no—
532C22—82no—
533C22—84no—
534C22—84no—
535C22C31×#37911yescharacteristic
536C22C31×#38612yes—
537C22C31×#38611yescharacteristic
538C22C31×#38611yescharacteristic
539C22C31×#39012yes—
540C22C31×#39212yes—
541C22C31×#39212yes—
542C22C31×#39412yes—
543C22C31×#39412yes—
544C22C31×#45814yes—
545C4—44no—
546C4—44no—
547C4—42no—
548C4—84no—
549C4—84no—
550C2—21no—
551C2—22no—
552C2—21no—
553C2—22no—
554C2—22no—
555C2—22no—
556C2—22no—
557C2—82no—
558C2C31×#143811yescharacteristic
559C2C31×#189012yes—
560C2C31×#202214yes—
subgroupG/H
center, socleC23×C31#120
commutatorC24C22×C4×C31
Frattini, cosocleC25C23×C31
prime radicalC23×D4×C31C22
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C25×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C31×#381C2semidirect
5. C2×C31×#342C2semidirect
11. C2×C31×#123C4semidirect
144. C22×C4×C31C22⋊C4semidirect
158. C22⋊C4×C31C22⋊C4semidirect
159. #10992C31direct (N × H)
232. C2×#381C2×C31semidirect
233. C2×#342C2×C31semidirect
280. C2×#123C4×C31semidirect
356. C31#10992direct (N × H)
425. C22×C4C22⋊C4×C31semidirect
439. C22⋊C4C22⋊C4×C31semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1232
C22×C31×#992
C31×#23082
C2×C31×#3812
C2×C31×#3422
#1099231