Finite Group Databasebeta

← #26215820

Subgroups — #26215820

Order 12032.

1482 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689591C211yesmaximal, characteristic
2C2×#15689146C211yesmaximal, characteristic, complemented
3C2×#15689141C211yesmaximal, characteristic
4C2×#15689139C211yesmaximal, characteristic
5#20245791C211yesmaximal, characteristic, complemented
6#20243407C218yesmaximal, complemented
7#20243097C211yesmaximal, characteristic, complemented
8C47×#1733C211yesmaximal, characteristic, complemented
9C22×#10625350C2211yescharacteristic
10C22×#10625329C2211yescharacteristic
11#15689591—21no—
12#15689591—21no—
13#15689591—22no—
14#15689591C412yescomplemented
15#15689591C412yescomplemented
16#15689591C2214yes—
17C2×#13093989C412yescomplemented
18C2×#13093986C412yescomplemented
19C2×(C22⋊D47)⋊C4—22no—
20C2×#13093983C2211yescharacteristic
21C2×#13093981—21no—
22C22×C4×Dic47C2211yescharacteristic
23C2×C42×D47—21no—
24#15689146—21no—
25#15689146—21no—
26#15689146C2214yescomplemented
27C2×Dic47⋊C8—22no—
28#15689141—24no—
29#15689139—24no—
30C2×#13093952C2214yes—
31C2×#13093950C2214yes—
32#15688992—21no—
33#15688988—21no—
34#15688981—22no—
35C4×Dic47⋊C4C2214yescomplemented
36#15688882C2214yescomplemented
37C22×M16×C47C2211yescharacteristic
38C2×#117×C47C2211yescharacteristic
39C2×#117×C47C2211yescharacteristic
40C47×#339C2214yescomplemented
41C2×#10625350—21no—
42C2×#10625350—21no—
43C2×#10625350—22no—
44C2×#10625350—22no—
45C2×#10625350C2×C412yes—
46C2×#10625350D414yes—
47C2×#10625350Q814yes—
48C2×#10625350C2312yes—
49C22×Dic94C2×C411yescharacteristic
50C22×D188C2×C411yescharacteristic
51C22×C22⋊D47—21no—
52C23×Dic47D412yes—
53C22×C4×D47—21no—
54C22×C4×D47—22no—
55C2×#10625329—21no—
56C2×#10625329—22no—
57C2×#10625329—22no—
58C2×#10625329C2312yes—
59C22×C47⋊C8—21no—
60#13093989—22no—
61#13093989—22no—
62#13093989C2×C414yes—
63#13093989C2×C414yes—
64#13093986—22no—
65#13093986—22no—
66#13093986C2×C414yes—
67#13093986C2×C414yes—
68(C22⋊D47)⋊C4—24no—
69(C22⋊D47)⋊C4—24no—
70(C22⋊D47)⋊C4—24no—
71(C22⋊D47)⋊C4—24no—
72#13093983—22no—
73#13093983—22no—
74#13093981—22no—
75#13093981—22no—
76#13093981—24no—
77C2×C4⋊Dic47—21no—
78C2×Dic47⋊C4—22no—
79C2×Dic47⋊C4—24no—
80C2×C22⋊Dic47—21no—
81C2×(C2×D47)⋊C4—22no—
82C2×C4×Dic47—22no—
83C2×C4×Dic47C2×C412yes—
84C2×C4×Dic47C2×C411yescharacteristic
85C2×C4×Dic47C2×C411yescharacteristic
86C2×C4×Dic47D411yescharacteristic
87C2×C4×Dic47D411yescharacteristic
88C2×C4×Dic47D411yescharacteristic
89C2×C4×Dic47D411yescharacteristic
90C2×C4×Dic47D412yes—
91C2×C4×Dic47C2312yes—
92C2×C4×Dic47C2312yes—
93C42×D47—22no—
94C42×D47—22no—
95C42×D47—24no—
96Dic47⋊C8—24no—
97Dic47⋊C8—24no—
98#13093952—28no—
99#13093950—28no—
100C47⋊#95—24no—
101C23×C4×C47C2311yescharacteristic
102C2×M16×C47—21no—
103C2×M16×C47—22no—
104C2×M16×C47—22no—
105C2×M16×C47C2312yes—
106C22×C8×C47—21no—
107#117×C47—21no—
108#117×C47—21no—
109#117×C47—22no—
110#117×C47—22no—
111#117×C47C2×C412yes—
112#117×C47C2312yes—
113C2×C4⋊C4×C47—21no—
114C2×C4⋊C4×C47C2×C412yes—
115C2×C22⋊C4×C47—21no—
116C2×C22⋊C4×C47—21no—
117C2×C42×C47—21no—
118C2×C42×C47C2312yes—
119C24×C47C2×D411yescharacteristic
120C23×D47—21no—
121C22×C4×C47—22no—
122C22×C4×C47—22no—
123C22×C4×C47C22×C411yescharacteristic
124C22×C4×C47C22×C411yescharacteristic
125C22×C4×C47C2×D411yescharacteristic
126C22×C4×C47C2×D411yescharacteristic
127C22×C4×C47C2×D411yescharacteristic
128C22×C4×C47C2×D412yes—
129C22×C4×C47C2×Q812yes—
130C22×C4×C47#4112yes—
131C22×C4×C47#4112yes—
132C22×C4×C47C2411yescharacteristic
133C2×C22⋊D47—22no—
134C2×C22⋊D47—24no—
135C2×C22⋊D47—24no—
136C2×C22⋊D47—22no—
137C22×Dic47—21no—
138C22×Dic47—22no—
139C22×Dic47—44no—
140C22×Dic47C22⋊C412yes—
141C22×Dic47C22⋊C412yes—
142C22×Dic47C22⋊C412yes—
143C22×Dic47C22⋊C412yes—
144C22×Dic47C2×D412yes—
145C22×Dic47C2×D412yes—
146#10625350—24no—
147#10625350—24no—
148#10625350—24no—
149#10625350—24no—
150#10625350—24no—
151#10625350—22no—
152#10625350—22no—
153#10625350C4⋊C418yescomplemented
154#10625350C2×D414yes—
155#10625350C2×Q814yes—
156C2×D188—21no—
157C2×D188—22no—
158C2×D188C4⋊C414yescomplemented
159C2×D188C22×C412yes—
160C2×C4×D47—22no—
161C2×C4×D47—24no—
162C2×C4×D47—24no—
163C2×C4×D47—22no—
164C2×C4×D47—24no—
165C2×C4×D47—24no—
166C2×C4×D47—48no—
167C2×Dic94—21no—
168C2×Dic94—22no—
169C2×Dic94C4⋊C414yescomplemented
170C2×Dic94C22×C412yes—
171M16×C47—22no—
172M16×C47—22no—
173M16×C47—42no—
174C2×C8×C47—22no—
175C2×C8×C47—42no—
176C4⋊C4×C47—22no—
177C4⋊C4×C47—42no—
178C4⋊C4×C47C22×C414yes—
179C22⋊C4×C47—22no—
180C22⋊C4×C47—22no—
181C22⋊C4×C47—42no—
182C42×C47—22no—
183C42×C47—22no—
184C42×C47—22no—
185C42×C47—22no—
186C22⋊Dic47—42no—
187(C2×D47)⋊C4—24no—
188(C2×D47)⋊C4—24no—
189C4⋊Dic47—42no—
190Dic47⋊C4—24no—
191Dic47⋊C4—24no—
192Dic47⋊C4—48no—
193C4×Dic47—24no—
194C4×Dic47—24no—
195C4×Dic47—22no—
196C4×Dic47—22no—
197C4×Dic47C22⋊C411yescharacteristic
198C4×Dic47C22⋊C411yescharacteristic
199C4×Dic47C22⋊C411yescharacteristic
200C4×Dic47C22⋊C411yescharacteristic
201C4×Dic47C22⋊C412yes—
202C4×Dic47C22⋊C412yes—
203C4×Dic47C22×C412yes—
204C4×Dic47C22×C412yes—
205C4×Dic47C2×D412yes—
206C4×Dic47C2×D412yes—
207#10625329—22no—
208#10625329—22no—
209#10625329—42no—
210C2×C47⋊C8—22no—
211C2×C47⋊C8—42no—
212C23×C47—42no—
213C23×C47C2×C22⋊C411yescharacteristic
214C23×C47C2×C22⋊C411yescharacteristic
215C23×C47#12112yes—
216C23×C47C22⋊Q812yes—
217C23×C47C22×D411yescharacteristic
218C22×D47—22no—
219C22×D47—24no—
220C22×D47—44no—
221C2×C4×C47—24no—
222C2×C4×C47—44no—
223C2×C4×C47—44no—
224C2×C4×C47—42no—
225C2×C4×C47C2×C22⋊C411yescharacteristic
226C2×C4×C47C2×C22⋊C411yescharacteristic
227C2×C4×C47C2×C4⋊C412yes—
228C2×C4×C47C2×C4⋊C412yes—
229C2×C4×C47#11712yes—
230C2×C4×C47#11712yes—
231C2×C4×C47#12112yes—
232C2×C4×C47#12112yes—
233C2×C4×C47#12112yes—
234C2×C4×C47C22⋊Q812yes—
235C2×C4×C47C22⋊Q812yes—
236C2×C4×C47C22⋊Q812yes—
237C2×C4×C47C23×C411yescharacteristic
238C2×C4×C47C22×D411yescharacteristic
239C2×C4×C47C22×D411yescharacteristic
240C2×C4×C47C22×Q811yescharacteristic
241C2×C4×C47C2×#4111yescharacteristic
242C2×C4×C47C2×#4111yescharacteristic
243C22⋊D47—24no—
244C22⋊D47—24no—
245C22⋊D47—28no—
246C2×Dic47—22no—
247C2×Dic47—24no—
248C2×Dic47—24no—
249C2×Dic47—24no—
250C2×Dic47—24no—
251C2×Dic47—42no—
252C2×Dic47—42no—
253C2×Dic47—42no—
254C2×Dic47—44no—
255C2×Dic47—42no—
256C2×Dic47C2×C22⋊C412yes—
257C2×Dic47C2×C22⋊C412yes—
258C2×Dic47C2×C22⋊C412yes—
259C2×Dic47C2×C22⋊C412yes—
260D188—22no—
261D188—24no—
262D188C2×C4⋊C414yes—
263C4×D47—24no—
264C4×D47—24no—
265C4×D47—28no—
266C4×D47—48no—
267C4×D47—48no—
268Dic94—22no—
269Dic94—24no—
270Dic94C2×C4⋊C414yes—
271C8×C47—42no—
272C47⋊C8—42no—
273#20654—471nomaximal, Sylow
274C22×C47—22no—
275C22×C47—22no—
276C22×C47—22no—
277C22×C47—42no—
278C22×C47—42no—
279C22×C47#38012yes—
280C22×C47#38012yes—
281C22×C47C22×C22⋊C411yescharacteristic
282C22×C47C2×#12111yescharacteristic
283C22×C47C2×C22⋊Q811yescharacteristic
284C2×D47—24no—
285C2×D47—48no—
286C2×D47—44no—
287C4×C47—44no—
288C4×C47—82no—
289C4×C47#38012yes—
290C4×C47#38012yes—
291C4×C47C22×C4⋊C411yescharacteristic
292C4×C47C2×#11711yescharacteristic
293C4×C47C2×#12111yescharacteristic
294C4×C47C2×C22⋊Q811yescharacteristic
295Dic47—22no—
296Dic47—22no—
297Dic47—22no—
298Dic47—24no—
299Dic47—82no—
300Dic47#42114yescomplemented
301C2×C4×#41—471no—
302C2×#423—471no—
303C2×#421—471no—
304C2×#421—471no—
305#2285—471no—
306#1806—478no—
307#1733—471no—
308#1733D4711yescharacteristic, complemented
309C2×C47—21no—
310C2×C47—22no—
311C2×C47—21no—
312C2×C47—22no—
313C2×C47C2×#38011yescharacteristic
314C2×C47C2×#42112yes—
315D47—44no—
316C22×#41—471no—
317C22×M16—471no—
318C22×M16C2×D4711yescharacteristic
319C4×#41—472no—
320C4×#41—472no—
321C4×#41—474no—
322C4×#41—941no—
323C4×#41—941no—
324C4×#41—942no—
325C2×C4×Q8—472no—
326C2×C4×D4—472no—
327C2×C4×D4—942no—
328C2×#117—471no—
329C2×#117—941no—
330C2×#117C2×D4711yescharacteristic
331C2×#117C2×D4711yescharacteristic
332C22×C42—471no—
333C22×C42—941no—
334#423—474no—
335#423—941no—
336#423—941no—
337C2×C4⋊C8—942no—
338#421—944no—
339#421—944no—
340C2×#104—474no—
341C2×#104—474no—
342#384—941no—
343#382—941no—
344#380—942no—
345C4×C4⋊C4—474no—
346#339—474no—
347#339C2×D4714yescomplemented
348C47#2065411yescharacteristic, complemented, Sylow
349C2×#41—472no—
350C2×#41—474no—
351C2×#41—474no—
352C2×#41—472no—
353C2×#41—942no—
354C2×#41—942no—
355C2×#41—941no—
356C2×#41—941no—
357C22×Q8—471no—
358C22×D4—471no—
359C22×D4—941no—
360C23×C4—472no—
361C23×C4—942no—
362C23×C4—941no—
363C23×C4C22×D4711yescharacteristic
364C2×M16—21no—
365C2×M16—22no—
366C2×M16—22no—
367C2×M16—472no—
368C2×M16—941no—
369C2×M16—942no—
370C2×M16—942no—
371C2×M16C22×D4712yes—
372C22×C8—21no—
373C22×C8—941no—
374C4×Q8—474no—
375C4×Q8—474no—
376C4×Q8—942no—
377C4×Q8—942no—
378C4×D4—474no—
379C4×D4—474no—
380C4×D4—942no—
381C4×D4—942no—
382C4×D4—944no—
383C4×D4—944no—
384C4×D4—944no—
385C4×D4—944no—
386#117—21no—
387#117—21no—
388#117—22no—
389#117—22no—
390#117—942no—
391#117—942no—
392#117—944no—
393#117—942no—
394#117—942no—
395#117C4×D4712yes—
396#117C22×D4712yes—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—942no—
399C2×C4⋊C4—944no—
400C2×C4⋊C4—941no—
401C2×C4⋊C4C4×D4712yes—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—942no—
405C2×C22⋊C4—941no—
406C2×C42—21no—
407C2×C42—472no—
408C2×C42—471no—
409C2×C42—471no—
410C2×C42—471no—
411C2×C42—471no—
412C2×C42—471no—
413C2×C42—472no—
414C2×C42—471no—
415C2×C42—472no—
416C2×C42—472no—
417C2×C42—942no—
418C2×C42—942no—
419C2×C42—944no—
420C2×C42—942no—
421C2×C42C22×D4712yes—
422C4⋊C8—944no—
423C4⋊C8—944no—
424#104—948no—
425#104—948no—
426#95—944no—
427C24—941no—
428C24D4×D4711yescharacteristic
429#41—478no—
430#41—474no—
431#41—474no—
432#41—944no—
433#41—944no—
434#41—944no—
435#41—944no—
436#41—944no—
437#41—942no—
438#41—942no—
439C2×Q8—474no—
440C2×Q8—472no—
441C2×Q8—941no—
442C2×Q8—942no—
443C2×D4—474no—
444C2×D4—472no—
445C2×D4—942no—
446C2×D4—944no—
447C2×D4—944no—
448C2×D4—942no—
449C2×D4—941no—
450C2×D4—942no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—472no—
454C22×C4—472no—
455C22×C4—472no—
456C22×C4—472no—
457C22×C4—472no—
458C22×C4—472no—
459C22×C4—944no—
460C22×C4—944no—
461C22×C4—941no—
462C22×C4—942no—
463C22×C4—944no—
464C22×C4—944no—
465C22×C4—942no—
466C22×C4—942no—
467C22×C4—1888no—
468C22×C4—1884no—
469C22×C4C2×C4×D4711yescharacteristic
470C22×C4C2×C4×D4711yescharacteristic
471C22×C4#1062535012yes—
472C22×C4#1062535012yes—
473C22×C4D4×D4711yescharacteristic
474C22×C4D4×D4711yescharacteristic
475C22×C4D4×D4711yescharacteristic
476C22×C4D4×D4712yes—
477C22×C4Q8×D4712yes—
478C22×C4C23×D4711yescharacteristic
479M16—22no—
480M16—22no—
481M16—42no—
482M16—942no—
483M16—942no—
484M16—1882no—
485C2×C8—22no—
486C2×C8—42no—
487C2×C8—942no—
488C2×C8—1882no—
489C4⋊C4—22no—
490C4⋊C4—42no—
491C4⋊C4—944no—
492C4⋊C4—944no—
493C4⋊C4—1888no—
494C4⋊C4—1882no—
495C4⋊C4C2×C4×D4714yes—
496C22⋊C4—22no—
497C22⋊C4—22no—
498C22⋊C4—42no—
499C22⋊C4—944no—
500C22⋊C4—944no—
501C22⋊C4—1882no—
502C42—22no—
503C42—22no—
504C42—22no—
505C42—22no—
506C42—471no—
507C42—471no—
508C42—471no—
509C42—471no—
510C42—472no—
511C42—472no—
512C42—472no—
513C42—472no—
514C42—472no—
515C42—472no—
516C42—944no—
517C42—944no—
518C42—942no—
519C42—942no—
520C23—42no—
521C23—944no—
522C23—942no—
523C23—1884no—
524C23C22⋊C4×D4711yescharacteristic
525C23C22⋊C4×D4711yescharacteristic
526C23#1309399712yes—
527C23#1309400212yes—
528C23C2×D4×D4711yescharacteristic
529Q8—474no—
530Q8—944no—
531Q8—942no—
532D4—474no—
533D4—948no—
534D4—944no—
535D4—944no—
536D4—944no—
537D4—942no—
538C2×C4—24no—
539C2×C4—44no—
540C2×C4—44no—
541C2×C4—42no—
542C2×C4—472no—
543C2×C4—472no—
544C2×C4—472no—
545C2×C4—472no—
546C2×C4—944no—
547C2×C4—944no—
548C2×C4—944no—
549C2×C4—944no—
550C2×C4—942no—
551C2×C4—948no—
552C2×C4—944no—
553C2×C4—944no—
554C2×C4—1888no—
555C2×C4—1888no—
556C2×C4—1882no—
557C2×C4—1882no—
558C2×C4—1882no—
559C2×C4—1884no—
560C2×C4—1882no—
561C2×C4C22⋊C4×D4711yescharacteristic
562C2×C4C22⋊C4×D4711yescharacteristic
563C2×C4C4⋊C4×D4712yes—
564C2×C4C4⋊C4×D4712yes—
565C2×C4#1309398112yes—
566C2×C4#1309398112yes—
567C2×C4#1309399712yes—
568C2×C4#1309399712yes—
569C2×C4#1309399712yes—
570C2×C4#1309400212yes—
571C2×C4#1309400212yes—
572C2×C4#1309400212yes—
573C2×C4C22×C4×D4711yescharacteristic
574C2×C4C2×D4×D4711yescharacteristic
575C2×C4C2×D4×D4711yescharacteristic
576C2×C4C2×Q8×D4711yescharacteristic
577C2×C4C2×#1062535011yescharacteristic
578C2×C4C2×#1062535011yescharacteristic
579C8—42no—
580C8—1882no—
581C22—22no—
582C22—22no—
583C22—22no—
584C22—42no—
585C22—42no—
586C22—944no—
587C22—1888no—
588C22—1884no—
589C22#1568898212yes—
590C22#1568898212yes—
591C22C2×C22⋊C4×D4711yescharacteristic
592C22C2×#1309399711yescharacteristic
593C22C2×#1309400211yescharacteristic
594C4—44no—
595C4—82no—
596C4—474no—
597C4—944no—
598C4—942no—
599C4—942no—
600C4—942no—
601C4—3762no—
602C4#1568898212yes—
603C4#1568898212yes—
604C4C2×C4⋊C4×D4711yescharacteristic
605C4C2×#1309398111yescharacteristic
606C4C2×#1309399711yescharacteristic
607C4C2×#1309400211yescharacteristic
608C2—21no—
609C2—22no—
610C2—22no—
611C2—21no—
612C2—1884no—
613C2C2×#1568898211yescharacteristic
614C2#421×D4712yes—
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1733C2
socleC22×C47C22×C22⋊C4
prime radicalC22×#10625350C22
cosocleC22×C4×C47C24
hypercenter#1733D47
hypocenterC47#20654
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1733

Complements

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

NH ≅ G/Ntype
2. C2×#15689146C2semidirect
5. #20245791C2semidirect
6. #20243407C2semidirect
7. #20243097C2semidirect
8. C47×#1733C2semidirect
14. #15689591C4semidirect
15. #15689591C4semidirect
17. C2×#13093989C4semidirect
18. C2×#13093986C4semidirect
26. #15689146C22semidirect
35. C4×Dic47⋊C4C22semidirect
36. #15688882C22semidirect
40. C47×#339C22semidirect
153. #10625350C4⋊C4semidirect
158. C2×D188C4⋊C4semidirect
169. C2×Dic94C4⋊C4semidirect
300. Dic47#421semidirect
308. #1733D47semidirect
347. #339C2×D47semidirect
348. C47#20654semidirect

Maximal subgroups

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

subgroupindex
C2×#156895912
C2×#156891462
C2×#156891412
C2×#156891392
#202457912
#202434072
#202430972
C47×#17332
#2065447