Finite Group Databasebeta

← #26232900

Subgroups — #26232900

Order 12032.

1110 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689829C211yesmaximal, characteristic
2C2×#15689251C211yesmaximal, characteristic, complemented
3#20246300C211yesmaximal, characteristic, complemented
4#20244355C211yesmaximal, characteristic, complemented
5#20244347C211yesmaximal, characteristic, complemented
6#20244346C211yesmaximal, characteristic, complemented
7#20244342C211yesmaximal, characteristic, complemented
8#20244334C211yesmaximal, characteristic, complemented
9#20243387C211yesmaximal, characteristic
10#20243387C211yesmaximal, characteristic
11#20243385C211yesmaximal, characteristic
12#20243214C211yesmaximal, characteristic
13#20243212C211yesmaximal, characteristic
14#20243202C211yesmaximal, characteristic
15C47×#1992C211yesmaximal, characteristic, complemented
16#15689829—24no—
17#15689829C418yescomplemented
18C2×#13094023C2211yescharacteristic
19C2×#13094015C2211yescharacteristic
20C2×#13094004—21no—
21C2×#13094002—21no—
22C2×#13094002—21no—
23C2×C4×Dic94C2211yescharacteristic
24C2×#13093989—21no—
25C2×C4×D188C2211yescharacteristic
26C2×#13093986C2211yescharacteristic
27C2×#13093986C2211yescharacteristic
28C2×C4⋊C4×D47—21no—
29#15689251—24no—
30C2×C4⋊(C47⋊C8)C2211yescharacteristic
31C2×Dic47⋊C8C2211yescharacteristic
32C2×Dic47⋊C8C2211yescharacteristic
33C2×#13093946C2211yescharacteristic
34C2×#13093946C2211yescharacteristic
35C2×#13093944C2211yescharacteristic
36C2×#13093944C2211yescharacteristic
37C2×#13093934C2211yescharacteristic
38C2×C8×Dic47C2211yescharacteristic
39#15689019—21no—
40#15689018—21no—
41#15689018—21no—
42#15688992C2211yescharacteristic
43#15688992C2211yescharacteristic
44C4⋊C4×Dic47C2211yescharacteristic
45C4⋊C4×Dic47C2211yescharacteristic
46C4×C4⋊Dic47C2211yescharacteristic
47#15688886C2211yescharacteristic
48#15688886C2211yescharacteristic
49#15688885C2211yescharacteristic
50#15688885C2211yescharacteristic
51#15688885C2211yescharacteristic
52#15688885C2211yescharacteristic
53#15688885C2211yescharacteristic
54#15688885C2211yescharacteristic
55C2×#125×C47C2211yescharacteristic
56C2×#97×C47C2211yescharacteristic
57C47×#384C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#340C2211yescharacteristic
62C22×Dic94—21no—
63C22×Dic94D411yescharacteristic
64C22×D188C2311yescharacteristic
65C22×C4×D47—21no—
66C22×C4×D47—21no—
67C22×C4×D47—21no—
68C22×C47⋊C8C2311yescharacteristic
69C22×C47⋊C8C2311yescharacteristic
70#13094023—22no—
71#13094023C2×C414yes—
72#13094015—22no—
73#13094015C2×C414yes—
74#13094004—28no—
75#13094002—28no—
76#13094002—28no—
77C4×Dic94C2×C414yes—
78C4×Dic94D414yes—
79#13093989—44no—
80C4×D188—22no—
81C4×D188C2×C414yes—
82#13093986—22no—
83#13093986—22no—
84#13093986C2×C414yes—
85#13093986C2×C414yes—
86C2×C4⋊Dic47—21no—
87C2×C4⋊Dic47D411yescharacteristic
88C2×C4⋊Dic47C2311yescharacteristic
89C2×C4⋊Dic47C2311yescharacteristic
90C2×C4⋊Dic47C2311yescharacteristic
91C2×Dic47⋊C4—21no—
92C2×Dic47⋊C4—21no—
93C2×Dic47⋊C4—21no—
94C2×Dic47⋊C4—21no—
95C2×Dic47⋊C4—21no—
96C2×Dic47⋊C4—21no—
97C2×Dic47⋊C4D411yescharacteristic
98C2×Dic47⋊C4D411yescharacteristic
99C4⋊C4×D47—28no—
100C2×(C2×D47)⋊C4—21no—
101C2×(C2×D47)⋊C4—21no—
102C2×(C2×D47)⋊C4—21no—
103C2×C4×Dic47—21no—
104C2×C4×Dic47—21no—
105C2×C4×Dic47—21no—
106C2×C4×Dic47C2311yescharacteristic
107C2×C4×Dic47C2311yescharacteristic
108C4⋊(C47⋊C8)—22no—
109Dic47⋊C8—22no—
110Dic47⋊C8—22no—
111#13093946—22no—
112#13093946Q814yescomplemented
113#13093944—22no—
114#13093944—22no—
115#13093934—22no—
116C8×Dic47—22no—
117C47⋊#95—21no—
118C47⋊#95—21no—
119C47⋊#95—21no—
120C22×C8×C47C2311yescharacteristic
121C22×C8×C47C2311yescharacteristic
122#125×C47—22no—
123#125×C47C2×C414yes—
124C2×C4⋊C4×C47—21no—
125C2×C4⋊C4×C47—21no—
126C2×C4⋊C4×C47—21no—
127C2×C4⋊C4×C47—21no—
128C2×C4⋊C4×C47C2311yescharacteristic
129C2×C4⋊C4×C47C2311yescharacteristic
130C2×C4⋊C4×C47C2311yescharacteristic
131C2×C4⋊C4×C47C2311yescharacteristic
132C2×C42×C47C2311yescharacteristic
133#97×C47—22no—
134C23×D47—21no—
135C22×C4×C47—21no—
136C22×C4×C47—21no—
137C22×C4×C47—21no—
138C22×C4×C47—21no—
139C22×C4×C47C2×D411yescharacteristic
140C22×C4×C47C2×D411yescharacteristic
141C22×C4×C47C2411yescharacteristic
142C22×Dic47—21no—
143C22×Dic47—21no—
144C22×Dic47—21no—
145C22×Dic47C2×D411yescharacteristic
146C22×Dic47C2×D411yescharacteristic
147C22×Dic47C2×D411yescharacteristic
148C22×Dic47C2×D411yescharacteristic
149C2×D188—21no—
150C2×D188—21no—
151C2×D188—21no—
152C2×D188C22×C412yes—
153C2×D188C2×Q812yes—
154C2×D188#4112yes—
155C2×C4×D47—24no—
156C2×C4×D47—24no—
157C2×C4×D47—24no—
158C2×C4×D47—42no—
159C2×C4×D47—42no—
160C2×C4×D47—81no—
161C2×C4×D47—81no—
162C2×C4×D47—81no—
163C2×C4×D47—81no—
164C2×Dic94—22no—
165C2×Dic94—22no—
166C2×Dic94—24no—
167C2×Dic94—81no—
168C2×Dic94—81no—
169C2×Dic94C22⋊C414yes—
170C2×C8×C47—21no—
171C2×C8×C47—21no—
172C2×C8×C47—21no—
173C2×C8×C47—21no—
174C2×C8×C47—21no—
175C2×C8×C47C2×Q812yes—
176C4⋊C4×C47—24no—
177C4⋊C4×C47—24no—
178C4⋊C4×C47—21no—
179C4⋊C4×C47—21no—
180C4⋊C4×C47—21no—
181C4⋊C4×C47—21no—
182C4⋊C4×C47—21no—
183C4⋊C4×C47—21no—
184C4⋊C4×C47—42no—
185C4⋊C4×C47—81no—
186C4⋊C4×C47C22×C412yes—
187C4⋊C4×C47C22×C412yes—
188C42×C47C22×C412yes—
189C42×C47C2×D412yes—
190(C2×D47)⋊C4—24no—
191(C2×D47)⋊C4—24no—
192(C2×D47)⋊C4—24no—
193C4⋊Dic47—21no—
194C4⋊Dic47—21no—
195C4⋊Dic47—24no—
196C4⋊Dic47—21no—
197C4⋊Dic47—21no—
198C4⋊Dic47C22⋊C414yes—
199C4⋊Dic47C22×C412yes—
200C4⋊Dic47C2×Q812yes—
201Dic47⋊C4—24no—
202Dic47⋊C4—24no—
203Dic47⋊C4—42no—
204Dic47⋊C4—42no—
205Dic47⋊C4—81no—
206Dic47⋊C4—81no—
207Dic47⋊C4C22⋊C414yes—
208Dic47⋊C4C22⋊C414yes—
209C4×Dic47—42no—
210C4×Dic47—42no—
211C4×Dic47—42no—
212C4×Dic47C22×C412yes—
213C4×Dic47C22×C412yes—
214C4×Dic47C2×D412yes—
215C4×Dic47C2×D412yes—
216C2×C47⋊C8—21no—
217C2×C47⋊C8—21no—
218C2×C47⋊C8—21no—
219C2×C47⋊C8—21no—
220C2×C47⋊C8—21no—
221C2×C47⋊C8—21no—
222C23×C47C22×D411yescharacteristic
223C22×D47—22no—
224C22×D47—22no—
225C22×D47—22no—
226C22×D47—41no—
227C22×D47—41no—
228C22×D47—41no—
229C22×D47—41no—
230C2×C4×C47—21no—
231C2×C4×C47—21no—
232C2×C4×C47—21no—
233C2×C4×C47—21no—
234C2×C4×C47—22no—
235C2×C4×C47—22no—
236C2×C4×C47—41no—
237C2×C4×C47—41no—
238C2×C4×C47—41no—
239C2×C4×C47—41no—
240C2×C4×C47—41no—
241C2×C4×C47—41no—
242C2×C4×C47—41no—
243C2×C4×C47—41no—
244C2×C4×C47—41no—
245C2×C4×C47—41no—
246C2×C4×C47C2×C22⋊C412yes—
247C2×C4×C47C2×C22⋊C412yes—
248C2×C4×C47C23×C411yescharacteristic
249C2×C4×C47C22×D411yescharacteristic
250C2×C4×C47C22×Q811yescharacteristic
251C2×C4×C47C2×#4111yescharacteristic
252C2×C4×C472−1+411yescharacteristic
253C2×C4×C472−1+411yescharacteristic
254C2×Dic47—21no—
255C2×Dic47—21no—
256C2×Dic47—21no—
257C2×Dic47—21no—
258C2×Dic47—21no—
259C2×Dic47—21no—
260C2×Dic47—22no—
261C2×Dic47—22no—
262C2×Dic47—41no—
263C2×Dic47—41no—
264C2×Dic47—41no—
265C2×Dic47—41no—
266C2×Dic47—41no—
267C2×Dic47—41no—
268C2×Dic47—41no—
269C2×Dic47C2×C22⋊C412yes—
270C2×Dic47C2×C22⋊C412yes—
271C2×Dic47C2×C22⋊C412yes—
272C2×Dic47C2×C22⋊C412yes—
273C2×Dic47AGL(1,ℤ/8)12yes—
274C2×Dic47#13712yes—
275D188—22no—
276D188—22no—
277D188—22no—
278D188C4×Q814yescomplemented
279C4×D47—48no—
280C4×D47—84no—
281C4×D47—84no—
282Dic94—28no—
283Dic94—84no—
284C8×C47—22no—
285C8×C47—41no—
286C47⋊C8—41no—
287C47⋊C8—41no—
288#22522—471nomaximal, Sylow
289C22×C47C22×C22⋊C411yescharacteristic
290C22×C47#54811yescharacteristic
291C22×C47D4×Q811yescharacteristic
292C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
293C22×C47C2×#13711yescharacteristic
294C22×C47#57611yescharacteristic
295C22×C47#57711yescharacteristic
296C2×D47—24no—
297C2×D47—42no—
298C2×D47—42no—
299C2×D47—42no—
300C2×D47—42no—
301C2×D47—42no—
302C2×D47—42no—
303C4×C47—22no—
304C4×C47—22no—
305C4×C47—42no—
306C4×C47—42no—
307C4×C47—81no—
308C4×C47—81no—
309C4×C47C2×C4×Q811yescharacteristic
310C4×C47#51911yescharacteristic
311C4×C47#54811yescharacteristic
312C4×C47D4×Q811yescharacteristic
313Dic47—22no—
314Dic47—22no—
315Dic47—22no—
316Dic47—42no—
317Dic47—42no—
318Dic47—81no—
319Dic47#41714yes—
320C2×#554—471no—
321C2×#446—471no—
322Q8×C4⋊C4—471no—
323#1992—471no—
324#1992D4711yescharacteristic, complemented
325#1990—471no—
326#1989—471no—
327#1989—471no—
328#1987—471no—
329#1802—471no—
330#1802—471no—
331#1802—471no—
332#1762—471no—
333#1762—471no—
334C4×#102—471no—
335C2×C47Q8×C22⋊C411yescharacteristic
336C2×C47C2×#41711yescharacteristic
337C2×C47#289711yescharacteristic
338C2×C47#336611yescharacteristic
339C2×C47#337211yescharacteristic
340C2×C47#338411yescharacteristic
341C2×C47#338511yescharacteristic
342D47—44no—
343#554—478no—
344#554—944no—
345C2×C4⋊Q8—471no—
346C2×#125—471no—
347C2×#125C2×D4711yescharacteristic
348C2×C22⋊Q8—941no—
349C2×C22⋊Q8—941no—
350C2×C22⋊Q8—941no—
351C2×C4×Q8—471no—
352C2×C4×Q8—941no—
353C2×C4×D4—471no—
354C2×C4×D4—471no—
355C2×C4×D4—471no—
356C22×C4⋊C4—941no—
357#446—944no—
358C2×C4⋊C8—471no—
359C2×C4⋊C8—471no—
360C2×C4⋊C8—471no—
361C2×#102—471no—
362C2×#102—471no—
363C2×#102—471no—
364C2×#102—471no—
365C2×#97—471no—
366C2×#97C2×D4711yescharacteristic
367C2×C4×C8—471no—
368#389—941no—
369#389—941no—
370#389—941no—
371#384—471no—
372#384—471no—
373#384C2×D4711yescharacteristic
374C4×C4⋊C4—471no—
375C4×C4⋊C4—471no—
376C4×C4⋊C4—471no—
377#340—471no—
378#340—471no—
379#340—471no—
380#340—471no—
381#340—471no—
382#340—471no—
383#340—471no—
384#340—471no—
385#340C2×D4711yescharacteristic
386#340C2×D4711yescharacteristic
387#340C2×D4711yescharacteristic
388#340C2×D4711yescharacteristic
389C47#2252211yescharacteristic, complemented, Sylow
390C22×Q8—471no—
391C22×Q8—941no—
392C22×D4—471no—
393C23×C4—941no—
394C23×C4—941no—
395C23×C4—941no—
396C22×C8—471no—
397C22×C8—471no—
398C22×C8C22×D4711yescharacteristic
399C22×C8C22×D4711yescharacteristic
400C4⋊Q8—474no—
401C4⋊Q8—942no—
402#125—22no—
403#125—474no—
404#125—942no—
405#125C4×D4714yes—
406C22⋊Q8—948no—
407C22⋊Q8—948no—
408C22⋊Q8—948no—
409C4×Q8—474no—
410C4×Q8—474no—
411C4×Q8—1884no—
412C4×D4—474no—
413C4×D4—474no—
414C4×D4—474no—
415C4×D4—942no—
416C4×D4—942no—
417C4×D4—942no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—471no—
423C2×C4⋊C4—471no—
424C2×C4⋊C4—471no—
425C2×C4⋊C4—471no—
426C2×C4⋊C4—471no—
427C2×C4⋊C4—471no—
428C2×C4⋊C4—948no—
429C2×C4⋊C4—941no—
430C2×C4⋊C4—941no—
431C2×C4⋊C4—941no—
432C2×C4⋊C4—941no—
433C2×C4⋊C4—941no—
434C2×C4⋊C4—941no—
435C2×C4⋊C4—941no—
436C2×C4⋊C4C22×D4711yescharacteristic
437C2×C4⋊C4C22×D4711yescharacteristic
438C2×C4⋊C4C22×D4711yescharacteristic
439C2×C4⋊C4C22×D4711yescharacteristic
440C2×C22⋊C4—941no—
441C2×C22⋊C4—941no—
442C2×C22⋊C4—941no—
443C2×C42—471no—
444C2×C42—471no—
445C2×C42—941no—
446C2×C42—941no—
447C2×C42—941no—
448C2×C42C22×D4711yescharacteristic
449C4⋊C8—942no—
450C4⋊C8—942no—
451C4⋊C8—942no—
452#102—474no—
453#102—942no—
454#102—942no—
455#102—942no—
456#97—22no—
457#97—942no—
458C4×C8—942no—
459#95—941no—
460#95—941no—
461#95—941no—
462C24—941no—
463C2×Q8—474no—
464C2×Q8—942no—
465C2×Q8—942no—
466C2×Q8—944no—
467C2×Q8—3761no—
468C2×Q8—3761no—
469C2×D4—472no—
470C2×D4—472no—
471C2×D4—472no—
472C2×D4—941no—
473C2×D4—941no—
474C2×D4—941no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—471no—
480C22×C4—471no—
481C22×C4—471no—
482C22×C4—471no—
483C22×C4—944no—
484C22×C4—944no—
485C22×C4—941no—
486C22×C4—941no—
487C22×C4—944no—
488C22×C4—941no—
489C22×C4—3761no—
490C22×C4—3761no—
491C22×C4—3761no—
492C22×C4—3761no—
493C22×C4—1882no—
494C22×C4—1882no—
495C22×C4D4×D4711yescharacteristic
496C22×C4D4×D4711yescharacteristic
497C22×C4C23×D4711yescharacteristic
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—941no—
504C2×C8—941no—
505C2×C8—941no—
506C2×C8—941no—
507C2×C8—941no—
508C2×C8—941no—
509C2×C8Q8×D4712yes—
510C4⋊C4—24no—
511C4⋊C4—24no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—42no—
519C4⋊C4—81no—
520C4⋊C4—474no—
521C4⋊C4—474no—
522C4⋊C4—474no—
523C4⋊C4—472no—
524C4⋊C4—472no—
525C4⋊C4—944no—
526C4⋊C4—944no—
527C4⋊C4—944no—
528C4⋊C4—941no—
529C4⋊C4—941no—
530C4⋊C4—941no—
531C4⋊C4—941no—
532C4⋊C4—3761no—
533C4⋊C4—3761no—
534C4⋊C4—1882no—
535C4⋊C4—1882no—
536C4⋊C4C2×C4×D4712yes—
537C4⋊C4C2×C4×D4712yes—
538C22⋊C4—944no—
539C22⋊C4—944no—
540C22⋊C4—944no—
541C42—472no—
542C42—472no—
543C42—472no—
544C42—472no—
545C42—1882no—
546C42—1882no—
547C42—1882no—
548C42C2×C4×D4712yes—
549C42D4×D4712yes—
550C23—942no—
551C23—942no—
552C23—942no—
553C23—1881no—
554C23—1881no—
555C23—1881no—
556C23—1881no—
557C23C2×D4×D4711yescharacteristic
558Q8—948no—
559Q8—3764no—
560D4—474no—
561D4—942no—
562D4—942no—
563D4—942no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—472no—
581C2×C4—472no—
582C2×C4—472no—
583C2×C4—472no—
584C2×C4—472no—
585C2×C4—472no—
586C2×C4—941no—
587C2×C4—941no—
588C2×C4—941no—
589C2×C4—941no—
590C2×C4—941no—
591C2×C4—941no—
592C2×C4—942no—
593C2×C4—942no—
594C2×C4—3764no—
595C2×C4—3764no—
596C2×C4—1888no—
597C2×C4—1881no—
598C2×C4—1881no—
599C2×C4—1881no—
600C2×C4—1881no—
601C2×C4—1881no—
602C2×C4—1881no—
603C2×C4—1881no—
604C2×C4C22⋊C4×D4712yes—
605C2×C4C22⋊C4×D4712yes—
606C2×C4C22×C4×D4711yescharacteristic
607C2×C4C2×D4×D4711yescharacteristic
608C2×C4C2×Q8×D4711yescharacteristic
609C2×C4#41×D4711yescharacteristic
610C2×C4#1309407111yescharacteristic
611C2×C4#1309407211yescharacteristic
612C8—22no—
613C8—41no—
614C8—1881no—
615C8—1881no—
616C22—944no—
617C22—1882no—
618C22—1882no—
619C22—1882no—
620C22—1882no—
621C22—1882no—
622C22—1882no—
623C22C2×C22⋊C4×D4711yescharacteristic
624C22#1568978111yescharacteristic
625C22#1568978811yescharacteristic
626C22AGL(1,ℤ/8)×D4711yescharacteristic
627C22#137×D4711yescharacteristic
628C22#1568992711yescharacteristic
629C22#1568993211yescharacteristic
630C4—22no—
631C4—22no—
632C4—42no—
633C4—42no—
634C4—81no—
635C4—81no—
636C4—474no—
637C4—942no—
638C4—942no—
639C4—942no—
640C4—3761no—
641C4—1882no—
642C4—1882no—
643C4C4×Q8×D4711yescharacteristic
644C4#1568959911yescharacteristic
645C4#1568978311yescharacteristic
646C4#1568978611yescharacteristic
647C2—1884no—
648C2#2024622211yescharacteristic
649C2#417×D4711yescharacteristic
650C2#2025191211yescharacteristic
651C2#2025609211yescharacteristic
652C2#2025616611yescharacteristic
653C2#2025628411yescharacteristic
654C2#2025629511yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1992C2
socleC23×C47C22×D4
prime radicalC22×D188C23
cosocleC22×C4×C47C24
hypercenter#1992D47
hypocenterC47#22522
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1992

Complements

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

NH ≅ G/Ntype
2. C2×#15689251C2semidirect
3. #20246300C2semidirect
4. #20244355C2semidirect
5. #20244347C2semidirect
6. #20244346C2semidirect
7. #20244342C2semidirect
8. #20244334C2semidirect
15. C47×#1992C2semidirect
17. #15689829C4semidirect
112. #13093946Q8semidirect
278. D188C4×Q8semidirect
324. #1992D47semidirect
389. C47#22522semidirect

Maximal subgroups

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

subgroupindex
C2×#156898292
C2×#156892512
#202463002
#202443552
#202443472
#202443462
#202443422
#202443342
#202433872
#202433852
#202432142
#202432122
#202432022
C47×#19922
#2252247