Finite Group Databasebeta

← #26232928

Subgroups — #26232928

Order 12032.

1034 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×#15689850C211yesmaximal, characteristic
2C2×#15689252C211yesmaximal, characteristic
3C4⋊C4×Dic94C211yesmaximal, characteristic
4#20244358C211yesmaximal, characteristic
5#20244355C211yesmaximal, characteristic
6#20244347C211yesmaximal, characteristic
7#20244344C211yesmaximal, characteristic
8#20244338C211yesmaximal, characteristic
9#20243394C211yesmaximal, characteristic
10#20243392C211yesmaximal, characteristic
11#20243392C211yesmaximal, characteristic
12#20243221C211yesmaximal, characteristic
13#20243217C211yesmaximal, characteristic
14#20243207C211yesmaximal, characteristic
15C47×#1989C211yesmaximal, characteristic
16#15689850—24no—
17#15689850C418yescomplemented
18C2×#13094023—21no—
19C2×#13094023C2211yescharacteristic
20C2×#13094015C2211yescharacteristic
21C2×#13094014—21no—
22C2×#13094014—21no—
23C2×C4×Dic94—21no—
24C2×C4×Dic94C2211yescharacteristic
25C2×C4×Dic94C2211yescharacteristic
26C2×#13093989—21no—
27C2×#13093989C2211yescharacteristic
28C2×#13093989C2211yescharacteristic
29#15689252—24no—
30C2×Dic47⋊C8C2211yescharacteristic
31C2×Dic47⋊C8C2211yescharacteristic
32C2×#13093949C2211yescharacteristic
33C2×#13093949C2211yescharacteristic
34C2×#13093947C2211yescharacteristic
35C2×#13093947C2211yescharacteristic
36C2×#13093935C2211yescharacteristic
37C2×#13093934C2211yescharacteristic
38C2×C8×Dic47C2211yescharacteristic
39#15689021—21no—
40#15689020—21no—
41#15689020—21no—
42#15688993C2211yescharacteristic
43#15688992C2211yescharacteristic
44#15688992C2211yescharacteristic
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×C4⋊C8×C47C2211yescharacteristic
57C4×C4⋊C4×C47C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#340C2211yescharacteristic
62C22×Dic94—21no—
63C22×Dic94D411yescharacteristic
64C22×Dic94C2311yescharacteristic
65C22×C47⋊C8C2311yescharacteristic
66C22×C47⋊C8C2311yescharacteristic
67#13094023—28no—
68#13094023—22no—
69#13094023C2×C414yes—
70#13094015—22no—
71#13094015C2×C414yes—
72#13094014—28no—
73#13094014—28no—
74C4×Dic94—22no—
75C4×Dic94—44no—
76C4×Dic94C2×C414yes—
77C4×Dic94C2×C414yes—
78C4×Dic94D414yes—
79#13093989—28no—
80#13093989—22no—
81#13093989—22no—
82#13093989C2×C414yes—
83#13093989C2×C414yes—
84C2×C4⋊Dic47—21no—
85C2×C4⋊Dic47—21no—
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⋊C4—21no—
98C2×Dic47⋊C4—21no—
99C2×Dic47⋊C4—21no—
100C2×Dic47⋊C4D411yescharacteristic
101C2×Dic47⋊C4D411yescharacteristic
102C2×C4×Dic47—21no—
103C2×C4×Dic47—21no—
104C2×C4×Dic47—21no—
105C2×C4×Dic47—21no—
106C2×C4×Dic47—21no—
107C2×C4×Dic47C2311yescharacteristic
108C2×C4×Dic47C2311yescharacteristic
109Dic47⋊C8—22no—
110Dic47⋊C8—22no—
111#13093949—22no—
112#13093949—22no—
113#13093947—22no—
114#13093947Q814yescomplemented
115#13093935—22no—
116#13093934—22no—
117C8×Dic47—22no—
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×C47C2311yescharacteristic
127C2×C4⋊C4×C47C2311yescharacteristic
128C2×C4⋊C4×C47C2311yescharacteristic
129C2×C4⋊C4×C47C2311yescharacteristic
130C2×C42×C47—21no—
131C2×C42×C47C2311yescharacteristic
132C4⋊C8×C47—22no—
133#95×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×D411yescharacteristic
140C22×C4×C47C2411yescharacteristic
141C22×Dic47—21no—
142C22×Dic47—21no—
143C22×Dic47—21no—
144C22×Dic47—21no—
145C22×Dic47C2×D411yescharacteristic
146C22×Dic47C2×D411yescharacteristic
147C22×Dic47C2×D411yescharacteristic
148C22×Dic47C2×D411yescharacteristic
149C2×Dic94—21no—
150C2×Dic94—21no—
151C2×Dic94—21no—
152C2×Dic94—22no—
153C2×Dic94—22no—
154C2×Dic94—24no—
155C2×Dic94—42no—
156C2×Dic94—42no—
157C2×Dic94C22⋊C414yes—
158C2×Dic94C22×C412yes—
159C2×Dic94C2×Q812yes—
160C2×Dic94#4112yes—
161C2×C8×C47—21no—
162C2×C8×C47—21no—
163C2×C8×C47—21no—
164C2×C8×C47—21no—
165C2×C8×C47—21no—
166C2×C8×C47—21no—
167C4⋊C4×C47—24no—
168C4⋊C4×C47—24no—
169C4⋊C4×C47—21no—
170C4⋊C4×C47—21no—
171C4⋊C4×C47—21no—
172C4⋊C4×C47—21no—
173C4⋊C4×C47—21no—
174C4⋊C4×C47C22×C412yes—
175C4⋊C4×C47C22×C412yes—
176C4⋊C4×C47C2×Q812yes—
177C42×C47—42no—
178C42×C47C22×C412yes—
179C42×C47C2×D412yes—
180C4⋊Dic47—21no—
181C4⋊Dic47—24no—
182C4⋊Dic47—21no—
183C4⋊Dic47—21no—
184C4⋊Dic47—21no—
185C4⋊Dic47—21no—
186C4⋊Dic47—42no—
187C4⋊Dic47—81no—
188C4⋊Dic47C22⋊C414yes—
189C4⋊Dic47C22×C412yes—
190Dic47⋊C4—24no—
191Dic47⋊C4—24no—
192Dic47⋊C4—24no—
193Dic47⋊C4—24no—
194Dic47⋊C4—24no—
195Dic47⋊C4—42no—
196Dic47⋊C4—42no—
197Dic47⋊C4—81no—
198Dic47⋊C4—81no—
199Dic47⋊C4C22⋊C414yes—
200Dic47⋊C4C22⋊C414yes—
201C4×Dic47—24no—
202C4×Dic47—24no—
203C4×Dic47—24no—
204C4×Dic47—42no—
205C4×Dic47—42no—
206C4×Dic47C22×C412yes—
207C4×Dic47C22×C412yes—
208C4×Dic47C2×D412yes—
209C4×Dic47C2×D412yes—
210C2×C47⋊C8—21no—
211C2×C47⋊C8—21no—
212C2×C47⋊C8—21no—
213C2×C47⋊C8—21no—
214C2×C47⋊C8—21no—
215C2×C47⋊C8C2×Q812yes—
216C23×C47C22×D411yescharacteristic
217C2×C4×C47—21no—
218C2×C4×C47—21no—
219C2×C4×C47—21no—
220C2×C4×C47—21no—
221C2×C4×C47—22no—
222C2×C4×C47—22no—
223C2×C4×C47—22no—
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×C47C2×C22⋊C412yes—
234C2×C4×C47C2×C22⋊C412yes—
235C2×C4×C47C23×C411yescharacteristic
236C2×C4×C47C22×D411yescharacteristic
237C2×C4×C47C22×Q811yescharacteristic
238C2×C4×C47C2×#4111yescharacteristic
239C2×C4×C472−1+411yescharacteristic
240C2×C4×C472−1+411yescharacteristic
241C2×Dic47—22no—
242C2×Dic47—22no—
243C2×Dic47—22no—
244C2×Dic47—21no—
245C2×Dic47—21no—
246C2×Dic47—21no—
247C2×Dic47—21no—
248C2×Dic47—21no—
249C2×Dic47—21no—
250C2×Dic47—22no—
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×Dic47C2×C22⋊C412yes—
260C2×Dic47C2×C22⋊C412yes—
261C2×Dic47C2×C22⋊C412yes—
262C2×Dic47C2×C22⋊C412yes—
263C2×Dic47AGL(1,ℤ/8)12yes—
264C2×Dic47#13712yes—
265Dic94—22no—
266Dic94—22no—
267Dic94—22no—
268Dic94—28no—
269Dic94—48no—
270Dic94C4×Q814yescomplemented
271C8×C47—41no—
272C8×C47—41no—
273C47⋊C8—22no—
274C47⋊C8—41no—
275#22524—471nomaximal, Sylow
276C22×C47C22×C22⋊C411yescharacteristic
277C22×C47#54811yescharacteristic
278C22×C47D4×Q811yescharacteristic
279C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
280C22×C47C2×#13711yescharacteristic
281C22×C47#57711yescharacteristic
282C22×C47#57811yescharacteristic
283C4×C47—22no—
284C4×C47—22no—
285C4×C47—42no—
286C4×C47—42no—
287C4×C47—42no—
288C4×C47—81no—
289C4×C47C2×C4×Q811yescharacteristic
290C4×C47#51911yescharacteristic
291C4×C47#54811yescharacteristic
292C4×C47D4×Q811yescharacteristic
293Dic47—24no—
294Dic47—22no—
295Dic47—22no—
296Dic47—22no—
297Dic47—42no—
298Dic47—81no—
299Dic47—81no—
300Dic47#41714yes—
301C2×#557—471no—
302C2×#446—471no—
303Q8×C4⋊C4—471no—
304#1992—471no—
305#1992—471no—
306#1990—471no—
307#1989—471no—
308#1989D4711yescharacteristic
309#1988—471no—
310#1803—471no—
311#1803—471no—
312#1803—471no—
313#1763—471no—
314#1763—471no—
315C4×#103—471no—
316C2×C47Q8×C22⋊C411yescharacteristic
317C2×C47C2×#41711yescharacteristic
318C2×C47#289811yescharacteristic
319C2×C47#336811yescharacteristic
320C2×C47#337411yescharacteristic
321C2×C47#338611yescharacteristic
322C2×C47#338711yescharacteristic
323#557—478no—
324#557—944no—
325C2×C4⋊Q8—471no—
326C2×C4⋊Q8—941no—
327C2×#125—471no—
328C2×#125—941no—
329C2×#125—941no—
330C2×#125C2×D4711yescharacteristic
331C2×C4×Q8—471no—
332C2×C4×Q8—471no—
333C2×C4×Q8—471no—
334C2×C4×Q8—471no—
335C2×C4×Q8—941no—
336C2×C4×Q8—941no—
337#446—944no—
338C2×C4⋊C8—471no—
339C2×C4⋊C8—471no—
340C2×C4⋊C8C2×D4711yescharacteristic
341C2×#103—471no—
342C2×#103—471no—
343C2×#103—471no—
344C2×#103—471no—
345C2×#97—471no—
346C2×#97—471no—
347C2×C4×C8—471no—
348#389—941no—
349#389—941no—
350#389—941no—
351#384—471no—
352#384—471no—
353#384—471no—
354C4×C4⋊C4—471no—
355C4×C4⋊C4—471no—
356C4×C4⋊C4C2×D4711yescharacteristic
357#340—471no—
358#340—471no—
359#340—471no—
360#340—471no—
361#340—471no—
362#340—471no—
363#340—471no—
364#340—471no—
365#340C2×D4711yescharacteristic
366#340C2×D4711yescharacteristic
367#340C2×D4711yescharacteristic
368#340C2×D4711yescharacteristic
369C47#2252411yescharacteristic, complemented, Sylow
370C22×Q8—471no—
371C22×Q8—471no—
372C22×Q8—941no—
373C22×C8—471no—
374C22×C8—471no—
375C22×C8C22×D4711yescharacteristic
376C22×C8C22×D4711yescharacteristic
377C4⋊Q8—474no—
378C4⋊Q8—942no—
379C4⋊Q8—948no—
380#125—22no—
381#125—474no—
382#125—942no—
383#125—948no—
384#125—948no—
385#125C4×D4714yes—
386C4×Q8—474no—
387C4×Q8—474no—
388C4×Q8—474no—
389C4×Q8—474no—
390C4×Q8—474no—
391C4×Q8—942no—
392C4×Q8—942no—
393C4×Q8—948no—
394C4×Q8—942no—
395C4×Q8—1884no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—471no—
399C2×C4⋊C4—471no—
400C2×C4⋊C4—471no—
401C2×C4⋊C4—471no—
402C2×C4⋊C4—471no—
403C2×C4⋊C4—471no—
404C2×C4⋊C4—941no—
405C2×C4⋊C4—941no—
406C2×C4⋊C4—941no—
407C2×C4⋊C4—941no—
408C2×C4⋊C4—941no—
409C2×C4⋊C4—941no—
410C2×C4⋊C4—941no—
411C2×C4⋊C4—941no—
412C2×C4⋊C4—941no—
413C2×C4⋊C4—941no—
414C2×C4⋊C4—941no—
415C2×C4⋊C4—941no—
416C2×C4⋊C4C22×D4711yescharacteristic
417C2×C4⋊C4C22×D4711yescharacteristic
418C2×C4⋊C4C22×D4711yescharacteristic
419C2×C4⋊C4C22×D4711yescharacteristic
420C2×C42—21no—
421C2×C42—471no—
422C2×C42—471no—
423C2×C42—941no—
424C2×C42—941no—
425C2×C42—941no—
426C2×C42—941no—
427C2×C42—941no—
428C2×C42C22×D4711yescharacteristic
429C4⋊C8—22no—
430C4⋊C8—942no—
431C4⋊C8—942no—
432#103—474no—
433#103—942no—
434#103—942no—
435#103—942no—
436#97—942no—
437#97—942no—
438C4×C8—942no—
439#95—21no—
440#95—941no—
441#95—941no—
442C2×Q8—474no—
443C2×Q8—472no—
444C2×Q8—472no—
445C2×Q8—472no—
446C2×Q8—942no—
447C2×Q8—942no—
448C2×Q8—944no—
449C2×Q8—941no—
450C2×Q8—941no—
451C2×Q8—941no—
452C2×Q8—1882no—
453C2×Q8—1882no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—471no—
459C22×C4—471no—
460C22×C4—471no—
461C22×C4—471no—
462C22×C4—941no—
463C22×C4—941no—
464C22×C4—941no—
465C22×C4—941no—
466C22×C4D4×D4711yescharacteristic
467C22×C4D4×D4711yescharacteristic
468C22×C4C23×D4711yescharacteristic
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—472no—
476C2×C8—941no—
477C2×C8—941no—
478C2×C8—941no—
479C2×C8—941no—
480C2×C8—941no—
481C4⋊C4—24no—
482C4⋊C4—24no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—474no—
489C4⋊C4—474no—
490C4⋊C4—474no—
491C4⋊C4—472no—
492C4⋊C4—944no—
493C4⋊C4—944no—
494C4⋊C4—944no—
495C4⋊C4—944no—
496C4⋊C4—944no—
497C4⋊C4—944no—
498C4⋊C4—941no—
499C4⋊C4—941no—
500C4⋊C4—941no—
501C4⋊C4—941no—
502C4⋊C4—941no—
503C4⋊C4—3761no—
504C4⋊C4—3761no—
505C4⋊C4—3761no—
506C4⋊C4—1882no—
507C4⋊C4—1882no—
508C4⋊C4—1882no—
509C4⋊C4C2×C4×D4712yes—
510C4⋊C4C2×C4×D4712yes—
511C4⋊C4Q8×D4712yes—
512C42—42no—
513C42—472no—
514C42—472no—
515C42—472no—
516C42—472no—
517C42—944no—
518C42—944no—
519C42—944no—
520C42—1882no—
521C42—1882no—
522C42C2×C4×D4712yes—
523C42D4×D4712yes—
524C23C2×D4×D4711yescharacteristic
525Q8—474no—
526Q8—948no—
527Q8—942no—
528Q8—942no—
529Q8—942no—
530Q8—1888no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—472no—
548C2×C4—472no—
549C2×C4—472no—
550C2×C4—472no—
551C2×C4—472no—
552C2×C4—472no—
553C2×C4—942no—
554C2×C4—942no—
555C2×C4—942no—
556C2×C4—941no—
557C2×C4—941no—
558C2×C4—941no—
559C2×C4—941no—
560C2×C4—941no—
561C2×C4—941no—
562C2×C4—942no—
563C2×C4—1881no—
564C2×C4—1881no—
565C2×C4—1881no—
566C2×C4—1881no—
567C2×C4—1881no—
568C2×C4—1881no—
569C2×C4—1881no—
570C2×C4—1881no—
571C2×C4C22⋊C4×D4712yes—
572C2×C4C22⋊C4×D4712yes—
573C2×C4C22×C4×D4711yescharacteristic
574C2×C4C2×D4×D4711yescharacteristic
575C2×C4C2×Q8×D4711yescharacteristic
576C2×C4#41×D4711yescharacteristic
577C2×C4#1309407111yescharacteristic
578C2×C4#1309407211yescharacteristic
579C8—41no—
580C8—41no—
581C8—942no—
582C8—1881no—
583C22C2×C22⋊C4×D4711yescharacteristic
584C22#1568978311yescharacteristic
585C22#1568978611yescharacteristic
586C22AGL(1,ℤ/8)×D4711yescharacteristic
587C22#137×D4711yescharacteristic
588C22#1568993011yescharacteristic
589C22#1568993711yescharacteristic
590C4—22no—
591C4—22no—
592C4—42no—
593C4—42no—
594C4—42no—
595C4—81no—
596C4—474no—
597C4—942no—
598C4—942no—
599C4—944no—
600C4—942no—
601C4—3761no—
602C4—3761no—
603C4—1882no—
604C4C4×Q8×D4711yescharacteristic
605C4#1568959911yescharacteristic
606C4#1568978111yescharacteristic
607C4#1568978811yescharacteristic
608C2#2024622211yescharacteristic
609C2#417×D4711yescharacteristic
610C2#2025191711yescharacteristic
611C2#2025612011yescharacteristic
612C2#2025619411yescharacteristic
613C2#2025630411yescharacteristic
614C2#2025632311yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1989C2
socle, prime radicalC23×C47C22×D4
cosocleC22×C4×C47C24
hypercenter#1989D47
hypocenterC47#22524
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1989

Complements

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

NH ≅ G/Ntype
17. #15689850C4semidirect
114. #13093947Q8semidirect
270. Dic94C4×Q8semidirect
369. C47#22524semidirect

Maximal subgroups

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

subgroupindex
C2×#156898502
C2×#156892522
C4⋊C4×Dic942
#202443582
#202443552
#202443472
#202443442
#202443382
#202433942
#202433922
#202432212
#202432172
#202432072
C47×#19892
#2252447