Finite Group Databasebeta

← #26275142

Subgroups — #26275142

Order 12032.

818 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689531C211yesmaximal, characteristic, complemented
2C2×#15689166C211yesmaximal, characteristic
3#20247095C211yesmaximal, characteristic
4#20247091C211yesmaximal, characteristic
5#20244868C211yesmaximal, characteristic, complemented
6#20244862C211yesmaximal, characteristic, complemented
7#20244725C211yesmaximal, characteristic, complemented
8#20244719C211yesmaximal, characteristic, complemented
9#20244125C211yesmaximal, characteristic, complemented
10#20244120C211yesmaximal, characteristic, complemented
11#20243583C211yesmaximal, characteristic
12#20243543C211yesmaximal, characteristic, complemented
13#20243419C211yesmaximal, characteristic
14#20243174C211yesmaximal, characteristic
15C47×#1854C211yesmaximal, characteristic
16C22×#10625329C2211yescharacteristic
17C2×#13094023C2211yescharacteristic
18C2×#13094015C2211yescharacteristic
19C2×#13094001—21no—
20C22×C4⋊Dic47C2211yescharacteristic
21#15689531—24no—
22#15689166—24no—
23C2×#13093957C2211yescharacteristic
24C2×#13093957C2211yescharacteristic
25C2×#13093957C2211yescharacteristic
26C2×#13093956C2211yescharacteristic
27C2×#13093956C2211yescharacteristic
28C2×#13093955C2211yescharacteristic
29C2×#13093955C2211yescharacteristic
30C2×#13093955C2211yescharacteristic
31C2×#13093934C2211yescharacteristic
32C2×C8×Dic47C2211yescharacteristic
33#15689059—21no—
34#15689057—21no—
35#15689046—21no—
36#15689044—21no—
37#15689022C2211yescharacteristic
38#15689022C2211yescharacteristic
39#15689021—21no—
40#15689019C2211yescharacteristic
41#15689019C2211yescharacteristic
42#15689007—21no—
43#15688995—21no—
44#15688992C2211yescharacteristic
45#15688992C2211yescharacteristic
46#15688983C2211yescharacteristic
47C4×C22⋊Dic47C2211yescharacteristic
48#15688886C2211yescharacteristic
49#15688886C2211yescharacteristic
50#15688885C2211yescharacteristic
51#15688885C2211yescharacteristic
52#15688877C2211yescharacteristic
53#15688877C2211yescharacteristic
54C2×#117×C47C2211yescharacteristic
55C2×#107×C47C2211yescharacteristic
56C2×#106×C47C2211yescharacteristic
57C2×C22⋊C8×C47C2211yescharacteristic
58C47×#380C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C22×Dic94—21no—
62C23×Dic47—21no—
63C2×#10625329—22no—
64C2×#10625329—22no—
65C2×#10625329Q814yescomplemented
66C22×C47⋊C8C2311yescharacteristic
67C22×C47⋊C8C2311yescharacteristic
68#13094023—22no—
69#13094023—41no—
70#13094015—22no—
71#13094015—41no—
72#13094001—44no—
73C2×C4⋊Dic47—22no—
74C2×C4⋊Dic47—21no—
75C2×C4⋊Dic47—21no—
76C2×C4⋊Dic47—21no—
77C2×C4⋊Dic47—21no—
78C2×C4⋊Dic47—41no—
79C2×C4⋊Dic47C2311yescharacteristic
80C2×C4⋊Dic47C2311yescharacteristic
81C2×C4⋊Dic47C2311yescharacteristic
82C2×C4⋊Dic47C2311yescharacteristic
83C2×Dic47⋊C4—21no—
84C2×Dic47⋊C4—21no—
85C2×Dic47⋊C4—21no—
86C2×Dic47⋊C4—21no—
87C2×Dic47⋊C4—21no—
88C2×Dic47⋊C4—21no—
89C2×Dic47⋊C4—21no—
90C2×Dic47⋊C4—21no—
91C2×C22⋊Dic47—21no—
92C2×C22⋊Dic47D411yescharacteristic
93C2×C22⋊Dic47D411yescharacteristic
94C2×C4×Dic47C2311yescharacteristic
95C2×C4×Dic47C2311yescharacteristic
96#13093957—22no—
97#13093957—22no—
98#13093957D414yes—
99#13093956—22no—
100#13093956—41no—
101#13093955—22no—
102#13093955—22no—
103#13093955—22no—
104#13093934—22no—
105C8×Dic47—22no—
106C47⋊#95—21no—
107C47⋊#95—21no—
108C47⋊#95—21no—
109C47⋊#95—21no—
110C47⋊#95—21no—
111C47⋊#95D411yescharacteristic
112C47⋊#95D411yescharacteristic
113C23×C4×C47C2311yescharacteristic
114C22×C8×C47C2311yescharacteristic
115C22×C8×C47C2311yescharacteristic
116#117×C47—22no—
117#117×C47—41no—
118C2×C4⋊C4×C47C2311yescharacteristic
119C2×C4⋊C4×C47C2311yescharacteristic
120C2×C4⋊C4×C47C2311yescharacteristic
121C2×C4⋊C4×C47C2311yescharacteristic
122C2×C22⋊C4×C47—21no—
123C2×C22⋊C4×C47—21no—
124C2×C42×C47—21no—
125#107×C47—22no—
126#106×C47—41no—
127C22⋊C8×C47Q814yescomplemented
128#95×C47—21no—
129C24×C47C2×D411yescharacteristic
130C22×C4×C47—21no—
131C22×C4×C47—21no—
132C22×C4×C47—21no—
133C22×C4×C47—21no—
134C22×C4×C47—21no—
135C22×C4×C47—21no—
136C22×C4×C47—21no—
137C22×C4×C47—21no—
138C22×C4×C47C2×D411yescharacteristic
139C22×C4×C47C2×Q812yes—
140C22×C4×C47C2×Q812yes—
141C22×C4×C47C2411yescharacteristic
142C22×Dic47—21no—
143C22×Dic47—21no—
144C22×Dic47—21no—
145C22×Dic47—21no—
146C22×Dic47—42no—
147C22×Dic47—42no—
148C22×Dic47—81no—
149C22×Dic47C2×D411yescharacteristic
150C22×Dic47C2×D411yescharacteristic
151C22×Dic47C2×D411yescharacteristic
152C22×Dic47C2×D411yescharacteristic
153C2×Dic94—42no—
154C2×Dic94—42no—
155C2×Dic94—81no—
156C2×C8×C47—21no—
157C2×C8×C47—21no—
158C2×C8×C47—21no—
159C2×C8×C47—21no—
160C2×C8×C47C2×Q812yes—
161C2×C8×C47C2×Q812yes—
162C4⋊C4×C47—21no—
163C4⋊C4×C47—21no—
164C4⋊C4×C47—21no—
165C4⋊C4×C47—21no—
166C4⋊C4×C47—21no—
167C4⋊C4×C47—21no—
168C4⋊C4×C47—21no—
169C4⋊C4×C47C2×D412yes—
170C22⋊C4×C47—42no—
171C22⋊C4×C47—42no—
172C42×C47—42no—
173C22⋊Dic47—22no—
174C22⋊Dic47—22no—
175C22⋊Dic47—81no—
176C4⋊Dic47—21no—
177C4⋊Dic47—21no—
178C4⋊Dic47—21no—
179C4⋊Dic47—21no—
180C4⋊Dic47—21no—
181C4⋊Dic47—21no—
182C4⋊Dic47—21no—
183C4⋊Dic47—42no—
184C4⋊Dic47—42no—
185C4⋊Dic47—42no—
186C4⋊Dic47—42no—
187C4⋊Dic47C2×D412yes—
188Dic47⋊C4—42no—
189Dic47⋊C4—42no—
190Dic47⋊C4—42no—
191Dic47⋊C4—42no—
192Dic47⋊C4—42no—
193Dic47⋊C4—81no—
194Dic47⋊C4—81no—
195Dic47⋊C4—81no—
196C4×Dic47—21no—
197C4×Dic47—21no—
198C4×Dic47—21no—
199C4×Dic47—21no—
200#10625329—28no—
201C2×C47⋊C8—21no—
202C2×C47⋊C8—21no—
203C2×C47⋊C8C2×D412yes—
204C2×C47⋊C8C2×Q812yes—
205C2×C47⋊C8C2×Q812yes—
206C2×C47⋊C8#4112yes—
207C23×C47—21no—
208C23×C47—21no—
209C23×C47—21no—
210C23×C47—21no—
211C23×C47—21no—
212C23×C47—21no—
213C23×C47C4⋊Q812yes—
214C23×C47C22×D411yescharacteristic
215C2×C4×C47—21no—
216C2×C4×C47—21no—
217C2×C4×C47—22no—
218C2×C4×C47—22no—
219C2×C4×C47—22no—
220C2×C4×C47—22no—
221C2×C4×C47—22no—
222C2×C4×C47—41no—
223C2×C4×C47—41no—
224C2×C4×C47—41no—
225C2×C4×C47—41no—
226C2×C4×C47—41no—
227C2×C4×C47—41no—
228C2×C4×C47—41no—
229C2×C4×C47—41no—
230C2×C4×C47—41no—
231C2×C4×C47—41no—
232C2×C4×C47—41no—
233C2×C4×C47C4⋊Q812yes—
234C2×C4×C47C22×D411yescharacteristic
235C2×C4×C47C22×Q811yescharacteristic
236C2×C4×C47C22×Q811yescharacteristic
237C2×C4×C47C2×#4111yescharacteristic
238C2×C4×C47H(5,𝔽2)11yescharacteristic
239C2×C4×C472−1+411yescharacteristic
240C2×Dic47—21no—
241C2×Dic47—21no—
242C2×Dic47—21no—
243C2×Dic47—21no—
244C2×Dic47—21no—
245C2×Dic47—21no—
246C2×Dic47—22no—
247C2×Dic47—21no—
248C2×Dic47—21no—
249C2×Dic47—21no—
250C2×Dic47—21no—
251C2×Dic47—41no—
252C2×Dic47—41no—
253C2×Dic47—41no—
254C2×Dic47—41no—
255C2×Dic47—41no—
256C2×Dic47—41no—
257C2×Dic47—41no—
258C2×Dic47—41no—
259C2×Dic47—41no—
260C2×Dic47—41no—
261C2×Dic47—41no—
262C2×Dic47—84no—
263C2×Dic47AGL(1,ℤ/8)12yes—
264C2×Dic47#13712yes—
265Dic94—84no—
266C8×C47—22no—
267C8×C47—22no—
268C47⋊C8—22no—
269C47⋊C8C22⋊Q814yescomplemented
270#26078—471nomaximal, Sylow
271C22×C47—22no—
272C22×C47—22no—
273C22×C47—22no—
274C22×C47—41no—
275C22×C47—41no—
276C22×C47—41no—
277C22×C47—41no—
278C22×C47C2×C4⋊Q811yescharacteristic
279C22×C47D4211yescharacteristic
280C22×C47#54711yescharacteristic
281C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
282C22×C47C2×#13711yescharacteristic
283C22×C47#57711yescharacteristic
284C22×C47#57711yescharacteristic
285C4×C47—22no—
286C4×C47—42no—
287C4×C47—81no—
288C4×C47—81no—
289C4×C47—81no—
290C4×C47C2×C22⋊Q811yescharacteristic
291C4×C47#54411yescharacteristic
292C4×C47D4×Q811yescharacteristic
293C4×C47#55411yescharacteristic
294Dic47—22no—
295Dic47—22no—
296Dic47—41no—
297Dic47—42no—
298Dic47—41no—
299Dic47—81no—
300Dic47—81no—
301Dic47—81no—
302C2×#501—471no—
303C2×#428—471no—
304#2441—471no—
305#2440—471no—
306#2084—471no—
307#2083—471no—
308#2059—471no—
309#2058—471no—
310#1943—471no—
311#1942—471no—
312#1854D4711yescharacteristic
313#1853—471no—
314#1844—471no—
315#1809—471no—
316#1753—471no—
317C2×C47—42no—
318C2×C47#244011yescharacteristic
319C2×C47#316311yescharacteristic
320C2×C47#316511yescharacteristic
321C2×C47#327211yescharacteristic
322C2×C47#327811yescharacteristic
323C2×C47#334411yescharacteristic
324C2×C47#334511yescharacteristic
325C22×M16—471no—
326C2×C4⋊Q8—471no—
327C2×#125—471no—
328C2×C22⋊Q8—941no—
329C2×#117C2×D4711yescharacteristic
330C22×C4⋊C4—471no—
331#501—944no—
332#428—944no—
333C2×#107—471no—
334C2×#107—471no—
335C2×#107—471no—
336C2×#107C2×D4711yescharacteristic
337C2×#106—471no—
338C2×#106—471no—
339C2×#106—471no—
340C2×#106—471no—
341C2×#106—471no—
342C2×#106C2×D4711yescharacteristic
343C2×C22⋊C8C2×D4711yescharacteristic
344C2×#97—471no—
345C2×C4×C8—471no—
346#399—941no—
347#398—941no—
348#396—941no—
349#395—941no—
350#389—471no—
351#389—471no—
352#389—471no—
353#389—471no—
354#389—941no—
355#387—941no—
356#385—941no—
357#384—471no—
358#384—471no—
359#380—471no—
360#380C2×D4711yescharacteristic
361C4×C22⋊C4—471no—
362#340—471no—
363#340—471no—
364#340—471no—
365#340—471no—
366#340C2×D4711yescharacteristic
367#340C2×D4711yescharacteristic
368#336—471no—
369#336—471no—
370C47#2607811yescharacteristic, complemented, Sylow
371C22×Q8—941no—
372C23×C4—941no—
373C23×C4C22×D4711yescharacteristic
374C2×M16—474no—
375C2×M16—942no—
376C2×M16—942no—
377C22×C8—471no—
378C22×C8—471no—
379C22×C8C22×D4711yescharacteristic
380C22×C8C22×D4711yescharacteristic
381C4⋊Q8—942no—
382C4⋊Q8—1881no—
383#125—942no—
384#125—1881no—
385C22⋊Q8—1884no—
386#117—22no—
387#117—41no—
388C2×C4⋊C4—471no—
389C2×C4⋊C4—471no—
390C2×C4⋊C4—471no—
391C2×C4⋊C4—471no—
392C2×C4⋊C4—942no—
393C2×C4⋊C4—941no—
394C2×C4⋊C4—941no—
395C2×C4⋊C4—941no—
396C2×C4⋊C4—941no—
397C2×C4⋊C4—941no—
398C2×C4⋊C4—941no—
399C2×C4⋊C4—941no—
400C2×C4⋊C4—941no—
401C2×C4⋊C4—941no—
402C2×C4⋊C4—941no—
403C2×C4⋊C4—941no—
404C2×C4⋊C4—941no—
405C2×C4⋊C4—1881no—
406C2×C4⋊C4C22×D4711yescharacteristic
407C2×C4⋊C4C22×D4711yescharacteristic
408C2×C4⋊C4C22×D4711yescharacteristic
409C2×C4⋊C4C22×D4711yescharacteristic
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—471no—
413C2×C22⋊C4—471no—
414C2×C22⋊C4—941no—
415C2×C42—21no—
416C2×C42—471no—
417C2×C42—471no—
418#107—22no—
419#107—474no—
420#107—942no—
421#107—942no—
422#106—41no—
423#106—942no—
424#106—942no—
425#106—942no—
426#106—942no—
427#106—1881no—
428C22⋊C8Dic9414yescomplemented
429#97—942no—
430C4×C8—942no—
431#95—21no—
432#95—471no—
433#95—471no—
434#95—941no—
435#95—941no—
436#95—941no—
437#95—941no—
438#95—941no—
439C24D4×D4711yescharacteristic
440C2×Q8—3761no—
441C2×Q8—1882no—
442C2×Q8—1882no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—471no—
452C22×C4—471no—
453C22×C4—471no—
454C22×C4—471no—
455C22×C4—941no—
456C22×C4—941no—
457C22×C4—941no—
458C22×C4—941no—
459C22×C4—3761no—
460C22×C4—1882no—
461C22×C4—1882no—
462C22×C4C2×Dic9412yes—
463C22×C4D4×D4711yescharacteristic
464C22×C4Q8×D4712yes—
465C22×C4C23×D4711yescharacteristic
466M16—948no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—472no—
472C2×C8—472no—
473C2×C8—472no—
474C2×C8—472no—
475C2×C8—941no—
476C2×C8—941no—
477C2×C8C2×Dic9412yes—
478C2×C8C2×Dic9412yes—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—472no—
487C4⋊C4—941no—
488C4⋊C4—941no—
489C4⋊C4—941no—
490C4⋊C4—941no—
491C4⋊C4—941no—
492C4⋊C4—941no—
493C4⋊C4—941no—
494C4⋊C4—3761no—
495C4⋊C4—3761no—
496C4⋊C4—3761no—
497C4⋊C4—1882no—
498C4⋊C4—1882no—
499C4⋊C4—1882no—
500C4⋊C4—1882no—
501C4⋊C4—1882no—
502C4⋊C4—1882no—
503C4⋊C4—1882no—
504C4⋊C4—1882no—
505C4⋊C4—1882no—
506C4⋊C4D4×D4712yes—
507C22⋊C4—42no—
508C22⋊C4—42no—
509C22⋊C4—942no—
510C22⋊C4—942no—
511C22⋊C4—3761no—
512C42—42no—
513C42—941no—
514C42—941no—
515C42—941no—
516C42—941no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23#1309402312yes—
524C23C2×D4×D4711yescharacteristic
525Q8—3764no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—472no—
545C2×C4—472no—
546C2×C4—941no—
547C2×C4—941no—
548C2×C4—941no—
549C2×C4—941no—
550C2×C4—941no—
551C2×C4—941no—
552C2×C4—942no—
553C2×C4—941no—
554C2×C4—941no—
555C2×C4—941no—
556C2×C4—941no—
557C2×C4—3764no—
558C2×C4—1881no—
559C2×C4—1881no—
560C2×C4—1881no—
561C2×C4—1881no—
562C2×C4—1881no—
563C2×C4—1881no—
564C2×C4—1881no—
565C2×C4—1881no—
566C2×C4—1881no—
567C2×C4—1881no—
568C2×C4—1881no—
569C2×C4#1309402312yes—
570C2×C4C2×D4×D4711yescharacteristic
571C2×C4C2×Q8×D4711yescharacteristic
572C2×C4C22×Dic9411yescharacteristic
573C2×C4#41×D4711yescharacteristic
574C2×C4#1309406911yescharacteristic
575C2×C4#1309407111yescharacteristic
576C8—22no—
577C8—22no—
578C8—474no—
579C8—942no—
580C22—22no—
581C22—22no—
582C22—22no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22C2×#1309402311yescharacteristic
588C22#1568975511yescharacteristic
589C22#1568977111yescharacteristic
590C22AGL(1,ℤ/8)×D4711yescharacteristic
591C22#137×D4711yescharacteristic
592C22#1568993011yescharacteristic
593C22#1568993011yescharacteristic
594C4—22no—
595C4—42no—
596C4—81no—
597C4—81no—
598C4—81no—
599C4—942no—
600C4—942no—
601C4—3761no—
602C4—3761no—
603C4—3761no—
604C4—1881no—
605C4—1882no—
606C4—1881no—
607C4C22⋊Q8×D4711yescharacteristic
608C4#1568975211yescharacteristic
609C4D4×Dic9411yescharacteristic
610C4#1568983211yescharacteristic
611C2—42no—
612C2#2024708911yescharacteristic
613C2#2025392011yescharacteristic
614C2#2025393211yescharacteristic
615C2#2025498111yescharacteristic
616C2#2025504711yescharacteristic
617C2#2025583611yescharacteristic
618C2#2025586111yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#1854C2
socleC23×C47C22×D4
prime radicalC24×C47C2×D4
hypercenter#1854D47
hypocenterC47#26078
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1854

Complements

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

NH ≅ G/Ntype
1. C2×#15689531C2semidirect
5. #20244868C2semidirect
6. #20244862C2semidirect
7. #20244725C2semidirect
8. #20244719C2semidirect
9. #20244125C2semidirect
10. #20244120C2semidirect
12. #20243543C2semidirect
65. C2×#10625329Q8semidirect
127. C22⋊C8×C47Q8semidirect
269. C47⋊C8C22⋊Q8semidirect
370. C47#26078semidirect
428. C22⋊C8Dic94semidirect

Maximal subgroups

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

subgroupindex
C2×#156895312
C2×#156891662
#202470952
#202470912
#202448682
#202448622
#202447252
#202447192
#202441252
#202441202
#202435832
#202435432
#202434192
#202431742
C47×#18542
#2607847