Finite Group Databasebeta

← #26121669

Subgroups — #26121669

Order 12032.

1210 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689889C211yesmaximal, characteristic
2C2×#15689105C211yesmaximal, characteristic
3#20245976C211yesmaximal, characteristic
4C2×#15688893C211yesmaximal, characteristic, complemented
5C2×#15688891C211yesmaximal, characteristic, complemented
6C2×#15688891C211yesmaximal, characteristic, complemented
7C2×C47×#344C211yesmaximal, characteristic, complemented
8C22×#10625350C2211yescharacteristic
9#15689889—22no—
10#15689889—22no—
11#15689889—22no—
12#15689889C414yescomplemented
13C2×#13094032—22no—
14C2×#13094030—22no—
15C22×#10625329C2211yescharacteristic
16C22×#10625329C2211yescharacteristic
17C2×M16×D47—22no—
18C22×C4⋊Dic47C2211yescharacteristic
19#15689105—22no—
20#15689105C414yescomplemented
21C2×#13093942—21no—
22C2×#13093940—21no—
23#15689029—21no—
24#15689025—21no—
25#15689000C414yes—
26#15688980—22no—
27#15688893—22no—
28#15688891—22no—
29#15688891—22no—
30C22×M16×C47C2211yescharacteristic
31C22×M16×C47C2211yescharacteristic
32C2×#117×C47C2211yescharacteristic
33C47×#344—22no—
34C2×#10625350—21no—
35C2×#10625350—21no—
36C2×#10625350—21no—
37C2×#10625350—21no—
38C2×#10625350—21no—
39C2×#10625350—21no—
40C2×#10625350—21no—
41C2×#10625350—21no—
42C2×#10625350C2×C412yes—
43C2×#10625350C2×C412yes—
44C2×#10625350D412yes—
45C2×#10625350Q812yes—
46C22×Dic94D411yescharacteristic
47C22×D188D411yescharacteristic
48C22×C22⋊D47C2×C412yes—
49C23×Dic47C2×C412yes—
50C22×C4×D47D412yes—
51#13094032—28no—
52#13094032—28no—
53#13094030—28no—
54#13094030—28no—
55C2×#10625329—21no—
56C2×#10625329—21no—
57C2×#10625329—21no—
58C2×#10625329—21no—
59C2×#10625329—21no—
60C2×#10625329—21no—
61C2×#10625329—21no—
62C2×#10625329—21no—
63C2×#10625329C2×C412yes—
64C2×#10625329C2×C412yes—
65C2×#10625329D412yes—
66C2×#10625329D412yes—
67C2×#10625324—24no—
68M16×D47—28no—
69M16×D47—28no—
70C22×C47⋊C8—21no—
71C22×C47⋊C8—21no—
72C2×C8×D47—24no—
73C2×C4⋊Dic47—21no—
74C2×C4⋊Dic47—21no—
75C2×C4⋊Dic47—21no—
76C2×C4⋊Dic47—21no—
77C2×C4⋊Dic47—21no—
78C2×C4⋊Dic47—21no—
79C2×(C2×D47)⋊C4—24no—
80#13093942—24no—
81#13093940—24no—
82C47⋊#95—24no—
83C23×C4×C47C2311yescharacteristic
84C2×M16×C47—21no—
85C2×M16×C47—21no—
86C2×M16×C47—21no—
87C2×M16×C47—21no—
88C2×M16×C47—21no—
89C2×M16×C47—21no—
90C2×M16×C47—21no—
91C2×M16×C47—21no—
92C2×M16×C47C2×C412yes—
93C2×M16×C47C2×C412yes—
94C2×M16×C47D412yes—
95C2×M16×C47D412yes—
96C22×C8×C47—21no—
97C22×C8×C47—21no—
98#117×C47—21no—
99#117×C47—21no—
100#117×C47—21no—
101#117×C47—21no—
102C2×C4⋊C4×C47—21no—
103C2×C22⋊C4×C47C2×C412yes—
104C2×C42×C47—21no—
105C24×C47C22×C411yescharacteristic
106C23×D47C22⋊C412yes—
107C22×C4×C47—22no—
108C22×C4×C47C22×C411yescharacteristic
109C22×C4×C47C22×C411yescharacteristic
110C22×C4×C47C2×D411yescharacteristic
111C22×C4×C47C2×D411yescharacteristic
112C22×C4×C47C2×D411yescharacteristic
113C22×C4×C47C2×D411yescharacteristic
114C22×C4×C47C2×D411yescharacteristic
115C22×C4×C47C2×D411yescharacteristic
116C22×C4×C47C2×D411yescharacteristic
117C22×C4×C47C2×Q811yescharacteristic
118C22×C4×C47#4111yescharacteristic
119C22×C4×C47#4111yescharacteristic
120C22×C4×C47#4111yescharacteristic
121C22×C4×C47#4111yescharacteristic
122C2×C22⋊D47—22no—
123C2×C22⋊D47—22no—
124C2×C22⋊D47—22no—
125C2×C22⋊D47—22no—
126C2×C22⋊D47C4214yes—
127C2×C22⋊D47C4⋊C414yes—
128C22×Dic47—22no—
129C22×Dic47—22no—
130C22×Dic47—22no—
131C22×Dic47—82no—
132C22×Dic47C22⋊C412yes—
133#10625350—22no—
134#10625350—22no—
135#10625350—22no—
136#10625350—22no—
137#10625350—22no—
138#10625350—22no—
139#10625350—22no—
140#10625350—22no—
141#10625350—22no—
142#10625350—22no—
143#10625350—22no—
144#10625350—22no—
145#10625350—22no—
146#10625350—22no—
147#10625350—22no—
148#10625350—22no—
149C2×D188—21no—
150C2×D188—21no—
151C2×D188—21no—
152C2×D188—21no—
153C2×D188C22⋊C412yes—
154C2×D188C4⋊C412yes—
155C2×C4×D47—22no—
156C2×C4×D47—22no—
157C2×C4×D47—22no—
158C2×C4×D47—22no—
159C2×C4×D47C22⋊C414yes—
160C2×C4×D47C4⋊C414yes—
161C2×Dic94—21no—
162C2×Dic94—21no—
163C2×Dic94—21no—
164C2×Dic94—21no—
165C2×Dic94C22⋊C412yes—
166C2×Dic94C4⋊C412yes—
167M16×C47—22no—
168M16×C47—22no—
169M16×C47—22no—
170M16×C47—22no—
171M16×C47—22no—
172M16×C47—41no—
173M16×C47—41no—
174M16×C47C22⋊C414yescomplemented
175C2×C8×C47—22no—
176C2×C8×C47—22no—
177C2×C8×C47—22no—
178C2×C8×C47—22no—
179C2×C8×C47—41no—
180C2×C8×C47—41no—
181C4⋊C4×C47—41no—
182C4⋊C4×C47—41no—
183C22⋊C4×C47—22no—
184C22⋊C4×C47—22no—
185C42×C47—41no—
186C42×C47—41no—
187(C2×D47)⋊C4—84no—
188C4⋊Dic47—41no—
189C4⋊Dic47—41no—
190C4⋊Dic47—41no—
191C4⋊Dic47—41no—
192#10625329—22no—
193#10625329—22no—
194#10625329—22no—
195#10625329—22no—
196#10625329—22no—
197#10625329—41no—
198#10625329—41no—
199#10625329C22⋊C414yescomplemented
200C2×C47⋊C8—22no—
201C2×C47⋊C8—22no—
202C2×C47⋊C8—22no—
203C2×C47⋊C8—22no—
204C2×C47⋊C8—41no—
205C2×C47⋊C8—41no—
206#10625324—216no—
207C8×D47—216no—
208C23×C47—41no—
209C23×C47—41no—
210C23×C47C2×C4211yescharacteristic
211C23×C47C2×C22⋊C411yescharacteristic
212C23×C47C2×C4⋊C411yescharacteristic
213C23×C47C4×D411yescharacteristic
214C23×C47C4×D411yescharacteristic
215C23×C47C4×D411yescharacteristic
216C23×C47C4×D411yescharacteristic
217C22×D47—22no—
218C22×D47—22no—
219C22×D47—42no—
220C22×D47—42no—
221C22×D47#9514yes—
222C2×C4×C47—42no—
223C2×C4×C47—42no—
224C2×C4×C47—42no—
225C2×C4×C47C2×C22⋊C411yescharacteristic
226C2×C4×C47C2×C22⋊C411yescharacteristic
227C2×C4×C47C2×C22⋊C411yescharacteristic
228C2×C4×C47C2×C22⋊C411yescharacteristic
229C2×C4×C47C2×C4⋊C411yescharacteristic
230C2×C4×C47C2×C4⋊C411yescharacteristic
231C2×C4×C47#11711yescharacteristic
232C2×C4×C47#11711yescharacteristic
233C2×C4×C47C4×D411yescharacteristic
234C2×C4×C47C4×D411yescharacteristic
235C2×C4×C47C4×D411yescharacteristic
236C2×C4×C47C4×D411yescharacteristic
237C2×C4×C47#12011yescharacteristic
238C2×C4×C47#12011yescharacteristic
239C2×C4×C47#12011yescharacteristic
240C2×C4×C47#12011yescharacteristic
241C2×C4×C47#12111yescharacteristic
242C2×C4×C47#12111yescharacteristic
243C2×C4×C47#12111yescharacteristic
244C2×C4×C47#12111yescharacteristic
245C2×C4×C47C22⋊Q811yescharacteristic
246C2×C4×C47C22⋊Q811yescharacteristic
247C2×C4×C47C22⋊Q811yescharacteristic
248C2×C4×C47C22⋊Q811yescharacteristic
249C2×C4×C47#12311yescharacteristic
250C2×C4×C47#12311yescharacteristic
251C2×C4×C47#12311yescharacteristic
252C2×C4×C47#12311yescharacteristic
253C22⋊D47—24no—
254C22⋊D47—24no—
255C22⋊D47—24no—
256C22⋊D47—24no—
257C2×Dic47—22no—
258C2×Dic47—22no—
259C2×Dic47—44no—
260C2×Dic47—42no—
261C2×Dic47—82no—
262C2×Dic47—82no—
263C2×Dic47#9514yes—
264D188—22no—
265D188—22no—
266D188—22no—
267D188—22no—
268C4×D47—24no—
269C4×D47—24no—
270C4×D47—24no—
271C4×D47—24no—
272Dic94—22no—
273Dic94—22no—
274Dic94—22no—
275Dic94—22no—
276C8×C47—24no—
277C8×C47—42no—
278C47⋊C8—24no—
279C47⋊C8—42no—
280#10755—471nomaximal, Sylow
281C22×C47—21no—
282C22×C47—21no—
283C22×C47—21no—
284C22×C47—21no—
285C22×C47—21no—
286C22×C47—21no—
287C22×C47—41no—
288C22×C47—41no—
289C22×C47—41no—
290C22×C47—41no—
291C22×C47C2×#9511yescharacteristic
292C22×C47C4×C22⋊C411yescharacteristic
293C22×C47C4×C22⋊C411yescharacteristic
294C22×C47#38511yescharacteristic
295C22×C47#38511yescharacteristic
296C22×C47#38611yescharacteristic
297C22×C47#38611yescharacteristic
298C2×D47—24no—
299C2×D47—42no—
300C2×D47—42no—
301C2×D47—44no—
302C2×D47—82no—
303C4×C47—82no—
304C4×C47#37911yescharacteristic
305C4×C47#38011yescharacteristic
306C4×C47#38011yescharacteristic
307C4×C47#38111yescharacteristic
308C4×C47#38511yescharacteristic
309C4×C47#38511yescharacteristic
310C4×C47#38611yescharacteristic
311C4×C47#38611yescharacteristic
312Dic47—24no—
313Dic47—82no—
314C2×#568—471no—
315C2×#413—471no—
316#2311—471no—
317C2×#344—471no—
318C2×#344D4711yescharacteristic, complemented
319C2×#343—471no—
320C2×#343—471no—
321C2×C47—21no—
322C2×C47—21no—
323C2×C47—21no—
324C2×C47—21no—
325C2×C47—21no—
326C2×C47—21no—
327C2×C47C22⋊#9511yescharacteristic
328C2×C47#191411yescharacteristic
329C2×C47#191511yescharacteristic
330D47—44no—
331C22×#41—471no—
332#568—474no—
333#568—942no—
334#568—942no—
335#568—942no—
336C2×#131—942no—
337C2×#131—942no—
338C22×M16—471no—
339C22×M16—471no—
340C22×M16—942no—
341C22×M16C2×D4711yescharacteristic
342C22×M16C2×D4711yescharacteristic
343C2×#117C2×D4711yescharacteristic
344C22×C4⋊C4—471no—
345#413—474no—
346#413—942no—
347C2×#101—941no—
348C2×#100—941no—
349#391—941no—
350#390—941no—
351#386—474no—
352#380—942no—
353#344—22no—
354#344—942no—
355#343—942no—
356#343—942no—
357C47#1075511yescharacteristic, complemented, Sylow
358C2×#41—472no—
359C2×#41—472no—
360C2×#41—472no—
361C2×#41—472no—
362C2×#41—941no—
363C2×#41—941no—
364C2×#41—941no—
365C2×#41—941no—
366C2×#41—941no—
367C2×#41—941no—
368C2×#41—941no—
369C2×#41—941no—
370C22×Q8—471no—
371C22×D4—472no—
372C22×D4—471no—
373C23×C4—472no—
374C23×C4—472no—
375C23×C4C22×D4711yescharacteristic
376#131—948no—
377#131—948no—
378#131—948no—
379#131—948no—
380C2×M16—21no—
381C2×M16—21no—
382C2×M16—21no—
383C2×M16—21no—
384C2×M16—21no—
385C2×M16—21no—
386C2×M16—21no—
387C2×M16—21no—
388C2×M16—472no—
389C2×M16—472no—
390C2×M16—472no—
391C2×M16—472no—
392C2×M16—944no—
393C2×M16—948no—
394C2×M16—948no—
395C2×M16—941no—
396C2×M16—941no—
397C2×M16—941no—
398C2×M16—941no—
399C2×M16—941no—
400C2×M16—941no—
401C2×M16—941no—
402C2×M16—941no—
403C2×M16C4×D4712yes—
404C2×M16C4×D4712yes—
405C2×M16D18812yes—
406C2×M16C22⋊D4712yes—
407C22×C8—21no—
408C22×C8—21no—
409C22×C8—944no—
410C22×C8—941no—
411C22×C8—941no—
412#117—21no—
413#117—21no—
414#117—21no—
415#117—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—941no—
418C2×C4⋊C4—941no—
419C2×C4⋊C4—941no—
420C2×C4⋊C4—941no—
421C2×C4⋊C4—941no—
422C2×C4⋊C4—941no—
423C2×C22⋊C4—944no—
424C2×C22⋊C4C4×D4712yes—
425C2×C42—21no—
426#101—944no—
427#100—944no—
428#95—944no—
429C24—472no—
430C24C2×C4×D4711yescharacteristic
431#41—942no—
432#41—942no—
433#41—942no—
434#41—942no—
435#41—942no—
436#41—942no—
437#41—942no—
438#41—942no—
439#41—942no—
440#41—942no—
441#41—942no—
442#41—942no—
443#41—942no—
444#41—942no—
445#41—942no—
446#41—942no—
447C2×Q8—472no—
448C2×Q8—472no—
449C2×Q8—941no—
450C2×Q8—941no—
451C2×Q8—941no—
452C2×Q8—941no—
453C2×D4—474no—
454C2×D4—474no—
455C2×D4—472no—
456C2×D4—472no—
457C2×D4—942no—
458C2×D4—942no—
459C2×D4—942no—
460C2×D4—942no—
461C2×D4—941no—
462C2×D4—941no—
463C2×D4—941no—
464C2×D4—941no—
465C22×C4—22no—
466C22×C4—472no—
467C22×C4—474no—
468C22×C4—474no—
469C22×C4—942no—
470C22×C4—942no—
471C22×C4—942no—
472C22×C4—942no—
473C22×C4—942no—
474C22×C4—942no—
475C22×C4—942no—
476C22×C4—3762no—
477C22×C4C2×C4×D4711yescharacteristic
478C22×C4C2×C4×D4711yescharacteristic
479C22×C4C2×D18811yescharacteristic
480C22×C4#1062535011yescharacteristic
481C22×C4#1062535011yescharacteristic
482C22×C4D4×D4711yescharacteristic
483C22×C4D4×D4711yescharacteristic
484C22×C4D4×D4711yescharacteristic
485C22×C4D4×D4711yescharacteristic
486C22×C4D4×D4711yescharacteristic
487C22×C4#1062535211yescharacteristic
488C22×C4Q8×D4711yescharacteristic
489C22×C4#1062535411yescharacteristic
490C22×C4C2×C22⋊D4711yescharacteristic
491M16—22no—
492M16—22no—
493M16—22no—
494M16—22no—
495M16—22no—
496M16—41no—
497M16—41no—
498M16—474no—
499M16—9416no—
500M16—942no—
501M16—942no—
502M16—942no—
503M16—942no—
504M16—942no—
505M16—1881no—
506M16—1881no—
507M16(C2×D47)⋊C414yescomplemented
508C2×C8—22no—
509C2×C8—22no—
510C2×C8—22no—
511C2×C8—22no—
512C2×C8—41no—
513C2×C8—41no—
514C2×C8—9416no—
515C2×C8—942no—
516C2×C8—942no—
517C2×C8—942no—
518C2×C8—942no—
519C2×C8—1881no—
520C2×C8—1881no—
521C4⋊C4—41no—
522C4⋊C4—41no—
523C4⋊C4—1881no—
524C4⋊C4—1881no—
525C4⋊C4—1881no—
526C4⋊C4—1881no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—3764no—
530C42—41no—
531C42—41no—
532C23—41no—
533C23—41no—
534C23—474no—
535C23—942no—
536C23—942no—
537C23—1882no—
538C23—1882no—
539C23C42×D4711yescharacteristic
540C23C22⋊C4×D4711yescharacteristic
541C23C4⋊C4×D4711yescharacteristic
542C23(C22⋊D47)⋊C411yescharacteristic
543C23C4×C22⋊D4711yescharacteristic
544C23#1309398611yescharacteristic
545C23C4×D18811yescharacteristic
546Q8—942no—
547Q8—942no—
548Q8—942no—
549Q8—942no—
550D4—944no—
551D4—944no—
552D4—944no—
553D4—944no—
554D4—942no—
555D4—942no—
556D4—942no—
557D4—942no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—474no—
562C2×C4—942no—
563C2×C4—942no—
564C2×C4—944no—
565C2×C4—944no—
566C2×C4—944no—
567C2×C4—944no—
568C2×C4—3762no—
569C2×C4—3762no—
570C2×C4—1884no—
571C2×C4—1882no—
572C2×C4C22⋊C4×D4711yescharacteristic
573C2×C4C22⋊C4×D4711yescharacteristic
574C2×C4C22⋊C4×D4711yescharacteristic
575C2×C4C2×(C2×D47)⋊C411yescharacteristic
576C2×C4C4⋊C4×D4711yescharacteristic
577C2×C4C4⋊C4×D4711yescharacteristic
578C2×C4#1309398111yescharacteristic
579C2×C4#1309398211yescharacteristic
580C2×C4(C22⋊D47)⋊C411yescharacteristic
581C2×C4C4×C22⋊D4711yescharacteristic
582C2×C4#1309398611yescharacteristic
583C2×C4C4×D18811yescharacteristic
584C2×C4#1309399211yescharacteristic
585C2×C4#1309399211yescharacteristic
586C2×C4#1309399411yescharacteristic
587C2×C4#1309399411yescharacteristic
588C2×C4#1309399511yescharacteristic
589C2×C4#1309399711yescharacteristic
590C2×C4#1309399711yescharacteristic
591C2×C4#1309399911yescharacteristic
592C2×C4#1309400011yescharacteristic
593C2×C4#1309400211yescharacteristic
594C2×C4#1309400211yescharacteristic
595C2×C4#1309400411yescharacteristic
596C2×C4#1309400611yescharacteristic
597C2×C4#1309400611yescharacteristic
598C2×C4#1309400911yescharacteristic
599C2×C4#1309400911yescharacteristic
600C8—24no—
601C8—42no—
602C8—944no—
603C8—1882no—
604C22—21no—
605C22—21no—
606C22—21no—
607C22—21no—
608C22—21no—
609C22—21no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—41no—
614C22—944no—
615C22—3762no—
616C22—1884no—
617C22—1882no—
618C22—1882no—
619C22#95×D4711yescharacteristic
620C22#1568897011yescharacteristic
621C22C4×(C2×D47)⋊C411yescharacteristic
622C22#1568899411yescharacteristic
623C22#1568899711yescharacteristic
624C22#1568899911yescharacteristic
625C22#1568900111yescharacteristic
626C4—82no—
627C4—944no—
628C4—3762no—
629C4#1568897811yescharacteristic
630C4#1568898011yescharacteristic
631C4#1568898211yescharacteristic
632C4#1568898511yescharacteristic
633C4#1568899411yescharacteristic
634C4#1568899711yescharacteristic
635C4#1568899911yescharacteristic
636C4#1568900111yescharacteristic
637C2—21no—
638C2—21no—
639C2—21no—
640C2—21no—
641C2—21no—
642C2—21no—
643C2—1884no—
644C2(C2×D47)⋊#9511yescharacteristic
645C2#2024393411yescharacteristic
646C2#2024393911yescharacteristic
subgroupG/H
centerC22#15689001
commutatorC23×C47C2×C42
FrattiniC23×C4C22×D47
FittingC2×C47×#344C2
socleC22×C47#386
prime radicalC22×#10625350C22
cosocleC23×C4×C47C23
hypercenterC2×#344D47
hypocenterC47#10755
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
4. C2×#15688893C2semidirect
5. C2×#15688891C2semidirect
6. C2×#15688891C2semidirect
7. C2×C47×#344C2semidirect
12. #15689889C4semidirect
20. #15689105C4semidirect
174. M16×C47C22⋊C4semidirect
199. #10625329C22⋊C4semidirect
318. C2×#344D47semidirect
357. C47#10755semidirect
507. M16(C2×D47)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#156898892
C2×#156891052
#202459762
C2×#156888932
C2×#156888912
C2×C47×#3442
#1075547