Finite Group Databasebeta

← #26186336

Subgroups — #26186336

Order 12032.

648 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253437C211yesmaximal, characteristic
2#20252533C211yesmaximal, characteristic, complemented
3#20252411C211yesmaximal, characteristic, complemented
4#20242251C211yesmaximal, characteristic, complemented
5#20242244C211yesmaximal, characteristic, complemented
6#20242223C211yesmaximal, characteristic, complemented
7#20242216C211yesmaximal, characteristic, complemented
8#20242211C211yesmaximal, characteristic, complemented
9#20242199C211yesmaximal, characteristic, complemented
10#20242187C211yesmaximal, characteristic, complemented
11#20242182C211yesmaximal, characteristic, complemented
12#20241812C211yesmaximal, characteristic, complemented
13#20241794C211yesmaximal, characteristic, complemented
14#20241688C211yesmaximal, characteristic, complemented
15C47×#1574C211yesmaximal, characteristic, complemented
16#15689657C2211yescharacteristic
17C2×C4×D188C2211yescharacteristic
18#15689459C411yescharacteristic
19#15689442C411yescharacteristic
20#15689424C411yescharacteristic
21#15689424C411yescharacteristic
22#15689339C411yescharacteristic
23#15689339C411yescharacteristic
24#15689276C411yescharacteristic
25#15689259C411yescharacteristic
26#15689250C2211yescharacteristic, complemented
27#15689247C2211yescharacteristic, complemented
28C4×#10625325C2211yescharacteristic
29C4×#10625325C2211yescharacteristic
30C4×D376C2211yescharacteristic
31C4×D376C2211yescharacteristic
32#15689200C2211yescharacteristic, complemented
33#15689199—21no—
34#15689192—21no—
35C8×D188—21no—
36C8×D188—21no—
37#15689188C2211yescharacteristic
38#15689188C2211yescharacteristic
39#15689188C2211yescharacteristic
40#15689188C2211yescharacteristic
41#15689188C2211yescharacteristic, complemented
42#15689183—21no—
43#15689176C2211yescharacteristic
44#15689176C2211yescharacteristic
45#15689148—21no—
46C22⋊C8×D47—21no—
47C22⋊C8×D47—21no—
48#15688853C2211yescharacteristic, complemented
49#15688853C2211yescharacteristic, complemented
50#15688850C2211yescharacteristic
51#15688850C2211yescharacteristic
52#15688850C2211yescharacteristic
53#15688850C2211yescharacteristic
54#15688850C2211yescharacteristic, complemented
55#15688850C2211yescharacteristic, complemented
56#15688845C2211yescharacteristic, complemented
57#15688845C2211yescharacteristic, complemented
58#15688844C2211yescharacteristic, complemented
59C8×C47⋊C8C2211yescharacteristic, complemented
60C47×#431C2211yescharacteristic
61C47×#431C2211yescharacteristic
62C47×#423C2211yescharacteristic
63C47×#335C2211yescharacteristic, complemented
64C47×#335C2211yescharacteristic, complemented
65C47×#334C2211yescharacteristic, complemented
66C47×#334C2211yescharacteristic, complemented
67C22×D188C2×C411yescharacteristic
68C22×C4×D47—21no—
69C2×#10625325C2×C411yescharacteristic
70C2×#10625325C2×C411yescharacteristic
71C2×D376C2×C411yescharacteristic
72C2×D376C2×C411yescharacteristic
73C2×#10625324—21no—
74C2×C8×D47—21no—
75C2×C8×D47—21no—
76C2×C8×D47—21no—
77C2×C8×D47—21no—
78C2×C8×D47—21no—
79#13094018—21no—
80#13094016C2×C411yescharacteristic
81#13094012C2×C411yescharacteristic
82#13094007—21no—
83#13094003C2×C411yescharacteristic
84#13093998C2×C411yescharacteristic
85C4×Dic94C2311yescharacteristic
86C4×D188—21no—
87C4×D188—21no—
88C4×D188C2×C411yescharacteristic
89C4×D188C2×C411yescharacteristic
90C4×D188C2311yescharacteristic
91C4×D188C2311yescharacteristic
92C4×D188C2311yescharacteristic
93C4×C22⋊D47—21no—
94#13093981—21no—
95C2×C4⋊Dic47C2×C411yescharacteristic
96C2×(C2×D47)⋊C4—21no—
97#13093958C2×C411yescharacteristic
98#13093958C2×C411yescharacteristic
99#13093956C2×C411yescharacteristic
100#13093956C2×C411yescharacteristic
101C4⋊(C47⋊C8)—21no—
102C4⋊(C47⋊C8)D411yescharacteristic
103C4⋊(C47⋊C8)D411yescharacteristic
104Dic47⋊C8—21no—
105Dic47⋊C8—21no—
106#13093949C2×C411yescharacteristic
107#13093949C2×C411yescharacteristic
108#13093946C2×C411yescharacteristic
109#13093946C2×C411yescharacteristic
110#13093946C2×C411yescharacteristic
111#13093946C2×C411yescharacteristic
112#13093946C2×C411yescharacteristic
113#13093946C2×C411yescharacteristic
114C22⋊(C47⋊C8)—21no—
115C22⋊(C47⋊C8)D411yescharacteristic
116C22⋊(C47⋊C8)D411yescharacteristic
117(C2×D47)⋊C8—21no—
118(C2×D47)⋊C8—21no—
119(C2×D47)⋊C8—21no—
120(C2×D47)⋊C8—21no—
121(C2×D47)⋊C8—21no—
122(C2×D47)⋊C8—21no—
123#13093934—21no—
124C4×C47⋊C8C2311yescharacteristic
125C4×C47⋊C8C2311yescharacteristic
126C4×C47⋊C8C2311yescharacteristic
127C4×C47⋊C8C2311yescharacteristic
128C8×Dic47—21no—
129C2×M16×C47—21no—
130C2×C42×C47C2311yescharacteristic
131C4⋊C8×C47—21no—
132C4⋊C8×C47C2×C411yescharacteristic
133C4⋊C8×C47C2×C411yescharacteristic
134C4⋊C8×C47C2311yescharacteristic
135C4⋊C8×C47C2311yescharacteristic
136C4⋊C8×C47C2311yescharacteristic
137C4⋊C8×C47C2311yescharacteristic
138C22⋊C8×C47—21no—
139C22⋊C8×C47C2×C411yescharacteristic
140C22⋊C8×C47C2×C411yescharacteristic
141C4×C8×C47—21no—
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C23×D47—21no—
145C22×C4×C47C22×C411yescharacteristic
146C22×C4×C47C2×D411yescharacteristic
147C22×C4×C47#4111yescharacteristic
148C2×C22⋊D47—21no—
149C22×Dic47—21no—
150C2×D188—21no—
151C2×D188—22no—
152C2×D188—22no—
153C2×D188C22×C411yescharacteristic
154C2×D188C22×C411yescharacteristic
155C2×D188C22×C411yescharacteristic
156C2×C4×D47—21no—
157C2×C4×D47—21no—
158C2×C4×D47—21no—
159C2×C4×D47—21no—
160C2×C4×D47—21no—
161C2×C4×D47—81no—
162C2×C4×D47—81no—
163C2×Dic94C22×C411yescharacteristic
164M16×C47—81no—
165C2×C8×C47—21no—
166C2×C8×C47—21no—
167C2×C8×C47—21no—
168C2×C8×C47—21no—
169C2×C8×C47C22×C411yescharacteristic
170C2×C8×C47C22×C411yescharacteristic
171C2×C8×C47C22×C411yescharacteristic
172C2×C8×C47C22×C411yescharacteristic
173C42×C47C22×C411yescharacteristic
174C42×C47C2×D411yescharacteristic
175C42×C47#4111yescharacteristic
176C42×C47C2411yescharacteristic
177C22⋊Dic47—21no—
178(C2×D47)⋊C4—21no—
179(C2×D47)⋊C4—21no—
180(C2×D47)⋊C4—21no—
181(C2×D47)⋊C4—21no—
182(C2×D47)⋊C4—21no—
183(C2×D47)⋊C4—21no—
184(C2×D47)⋊C4—21no—
185(C2×D47)⋊C4—21no—
186C4⋊Dic47—21no—
187C4⋊Dic47C22×C411yescharacteristic
188C4⋊Dic47C22×C411yescharacteristic
189C4⋊Dic47C22×C411yescharacteristic
190C4⋊Dic47C22×C411yescharacteristic
191Dic47⋊C4—21no—
192Dic47⋊C4—21no—
193Dic47⋊C4—21no—
194Dic47⋊C4—21no—
195C4×Dic47—21no—
196C2×C47⋊C8—21no—
197C2×C47⋊C8—21no—
198C2×C47⋊C8C2×D411yescharacteristic
199C2×C47⋊C8C2×D411yescharacteristic
200C2×C47⋊C8C2×D411yescharacteristic
201C2×C47⋊C8C2×D411yescharacteristic
202D376—22no—
203D376—22no—
204#10625325—22no—
205#10625325—22no—
206#10625324—81no—
207C8×D47—81no—
208C8×D47—81no—
209C8×D47—81no—
210C8×D47—81no—
211C8×D47—81no—
212C23×C47C4×D411yescharacteristic
213C22×D47—21no—
214C22×D47—21no—
215C22×D47—24no—
216C22×D47—21no—
217C22×D47—81no—
218C22×D47—81no—
219C2×C4×C47—21no—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—41no—
224C2×C4×C47C4×D411yescharacteristic
225C2×C4×C47C4×D411yescharacteristic
226C2×C4×C47C4×D411yescharacteristic
227C2×C4×C47C23×C411yescharacteristic
228C2×C4×C47C22×D411yescharacteristic
229C2×C4×C47C2×#4111yescharacteristic
230C22⋊D47—81no—
231C2×Dic47—21no—
232C2×Dic47—21no—
233C2×Dic47—21no—
234C2×Dic47—21no—
235C2×Dic47—21no—
236C2×Dic47—81no—
237D188—24no—
238D188—21no—
239D188—21no—
240D188—21no—
241D188—21no—
242D188#13112yes—
243D188#13112yes—
244C4×D47—41no—
245C4×D47—41no—
246C4×D47—41no—
247C4×D47—41no—
248C4×D47—41no—
249C4×D47—41no—
250C4×D47—81no—
251C4×D47—81no—
252Dic94—21no—
253Dic94—21no—
254C8×C47—21no—
255C8×C47—21no—
256C8×C47—21no—
257C8×C47—21no—
258C8×C47—41no—
259C8×C47—41no—
260C8×C47—41no—
261C8×C47—41no—
262C47⋊C8—21no—
263C47⋊C8—21no—
264C47⋊C8—21no—
265C47⋊C8—21no—
266C47⋊C8—41no—
267C47⋊C8—41no—
268#17918—471nomaximal, Sylow
269C22×C47—21no—
270C22×C47—21no—
271C22×C47—21no—
272C22×C47C2×C4×D411yescharacteristic
273C2×D47—22no—
274C2×D47—22no—
275C2×D47—41no—
276C2×D47—41no—
277C2×D47—41no—
278C2×D47—41no—
279C2×D47—41no—
280C2×D47—41no—
281C2×D47—41no—
282C2×D47—84no—
283C4×C47—21no—
284C4×C47—21no—
285C4×C47—21no—
286C4×C47—21no—
287C4×C47C2×#13111yescharacteristic
288C4×C47C2×#13111yescharacteristic
289C4×C47#57611yescharacteristic
290C4×C47#57711yescharacteristic
291Dic47—41no—
292Dic47—41no—
293Dic47—41no—
294Dic47—41no—
295Dic47—41no—
296#3105—471no—
297#2993—471no—
298#2972—471no—
299#1586—471no—
300#1585—471no—
301#1582—471no—
302#1581—471no—
303#1580—471no—
304SD16⋊C8—471no—
305C8×SD16—471no—
306C8×D8—471no—
307#1574D4711yescharacteristic, complemented
308#1486—471no—
309#1482—471no—
310#1454—471no—
311C2×C47—41no—
312C2×C47#292911yescharacteristic
313C2×C47#294611yescharacteristic
314C2×C47#295711yescharacteristic
315D47—42no—
316D47—42no—
317D47—81no—
318#529—471no—
319C2×C4×D4—471no—
320#484—471no—
321#481—471no—
322#478—471no—
323#478—471no—
324#463—471no—
325#463—471no—
326#450—471no—
327#447—471no—
328#446—471no—
329C8×Q8—471no—
330C4×SD16—471no—
331C4×SD16—471no—
332C4×D8—471no—
333C4×D8—471no—
334#436—471no—
335#436—941no—
336#435—941no—
337C8×D4—471no—
338C8×D4—471no—
339C8×D4—471no—
340C8×D4—471no—
341C8×D4—471no—
342C8×D4—941no—
343C8×D4—941no—
344#433—941no—
345#431—471no—
346#431—471no—
347#431C2×D4711yescharacteristic
348#431C2×D4711yescharacteristic
349#424—941no—
350#423C2×D4711yescharacteristic
351C2×C22⋊C8—941no—
352C2×C22⋊C8—941no—
353#335C2×D4711yescharacteristic, complemented
354#335C2×D4711yescharacteristic, complemented
355#334C2×D4711yescharacteristic, complemented
356#334C2×D4711yescharacteristic, complemented
357Q8⋊C8—471no—
358Q8⋊C8—471no—
359D4⋊C8—471no—
360D4⋊C8—471no—
361D4⋊C8—471no—
362D4⋊C8—471no—
363D4⋊C8—471no—
364D4⋊C8—471no—
365#322—471no—
366#322—471no—
367#322—471no—
368C82—471no—
369C47#1791811yescharacteristic, complemented, Sylow
370C22×D4—471no—
371C23×C4—941no—
372C2×SD16—471no—
373C2×SD16—471no—
374C2×D8—471no—
375C2×D8—471no—
376C2×M16—21no—
377C2×M16—941no—
378C22×C8—941no—
379C22×C8—941no—
380C22×C8—941no—
381C22×C8—941no—
382C22×C8—941no—
383#126—941no—
384#125—471no—
385#124—471no—
386#123—941no—
387C22⋊Q8—471no—
388#121—471no—
389C4×Q8—471no—
390C4×D4—471no—
391C4×D4—471no—
392C4×D4—471no—
393C4×D4—471no—
394C4×D4—471no—
395C4×D4—941no—
396C4×D4—941no—
397C4×D4—941no—
398#117—941no—
399C2×C4⋊C4—471no—
400C2×C22⋊C4—941no—
401C2×C42C22×D4711yescharacteristic
402#107—471no—
403#107—471no—
404#106—471no—
405#106—471no—
406C4⋊C8—21no—
407C4⋊C8—471no—
408C4⋊C8—471no—
409C4⋊C8—941no—
410C4⋊C8—941no—
411C4⋊C8—941no—
412C4⋊C8C4×D4711yescharacteristic
413C4⋊C8C4×D4711yescharacteristic
414C4⋊C8C22×D4711yescharacteristic
415C4⋊C8C22×D4711yescharacteristic
416C4⋊C8C22×D4711yescharacteristic
417C4⋊C8C22×D4711yescharacteristic
418#103—471no—
419#103—471no—
420#102—471no—
421#102—471no—
422#102—471no—
423#102—471no—
424#102—471no—
425#102—471no—
426C22⋊C8—21no—
427C22⋊C8—471no—
428C22⋊C8—471no—
429C22⋊C8—941no—
430C22⋊C8—941no—
431C22⋊C8—941no—
432C22⋊C8—941no—
433C22⋊C8—941no—
434C22⋊C8—941no—
435C22⋊C8—941no—
436C22⋊C8C4×D4711yescharacteristic
437C22⋊C8C4×D4711yescharacteristic
438#97—941no—
439C4×C8—21no—
440C4×C8—471no—
441C4×C8—471no—
442C4×C8—471no—
443C4×C8—471no—
444C4×C8—941no—
445C4×C8C22×D4711yescharacteristic
446C4×C8C22×D4711yescharacteristic
447C24—941no—
448C2×Q8—471no—
449C2×D4—471no—
450C2×D4—471no—
451C2×D4—471no—
452C2×D4—942no—
453C2×D4—942no—
454C2×D4—941no—
455C2×D4—941no—
456C22×C4—941no—
457C22×C4—941no—
458C22×C4—941no—
459C22×C4—941no—
460C22×C4—941no—
461C22×C4—941no—
462C22×C4—3761no—
463C22×C4—3761no—
464C22×C4C2×C4×D4711yescharacteristic
465C22×C4D4×D4711yescharacteristic
466C22×C4#1062535411yescharacteristic
467SD16—942no—
468SD16—942no—
469D8—942no—
470D8—942no—
471M16—81no—
472M16—3761no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—471no—
478C2×C8—471no—
479C2×C8—471no—
480C2×C8—471no—
481C2×C8—941no—
482C2×C8—941no—
483C2×C8—3761no—
484C2×C8—3761no—
485C2×C8—3761no—
486C2×C8—3761no—
487C2×C8—3761no—
488C2×C8C2×C4×D4711yescharacteristic
489C2×C8C2×C4×D4711yescharacteristic
490C2×C8C2×C4×D4711yescharacteristic
491C2×C8C2×C4×D4711yescharacteristic
492C4⋊C4—471no—
493C4⋊C4—471no—
494C4⋊C4—471no—
495C4⋊C4—471no—
496C4⋊C4—941no—
497C4⋊C4—941no—
498C4⋊C4—941no—
499C4⋊C4—941no—
500C4⋊C4—941no—
501C22⋊C4—941no—
502C22⋊C4—941no—
503C22⋊C4—941no—
504C22⋊C4—941no—
505C22⋊C4—941no—
506C22⋊C4—941no—
507C22⋊C4—941no—
508C22⋊C4—941no—
509C22⋊C4—941no—
510C42—941no—
511C42C2×C4×D4711yescharacteristic
512C42D4×D4711yescharacteristic
513C42#1062535411yescharacteristic
514C42C23×D4711yescharacteristic
515C23—944no—
516C23—941no—
517C23—941no—
518C23—941no—
519C23—3761no—
520C23—3761no—
521C23#1309398611yescharacteristic
522Q8—941no—
523Q8—941no—
524D4—472no—
525D4—472no—
526D4—944no—
527D4—941no—
528D4—941no—
529D4—941no—
530D4—941no—
531D4—3761no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—941no—
538C2×C4—941no—
539C2×C4—941no—
540C2×C4—941no—
541C2×C4—941no—
542C2×C4—3761no—
543C2×C4—3761no—
544C2×C4—3761no—
545C2×C4—1881no—
546C2×C4—1881no—
547C2×C4—1881no—
548C2×C4—1881no—
549C2×C4—1881no—
550C2×C4—1881no—
551C2×C4#1309398611yescharacteristic
552C2×C4#1309398611yescharacteristic
553C2×C4#1309398611yescharacteristic
554C2×C4C22×C4×D4711yescharacteristic
555C2×C4C2×D4×D4711yescharacteristic
556C2×C4C2×#1062535411yescharacteristic
557C8—21no—
558C8—21no—
559C8—21no—
560C8—21no—
561C8—41no—
562C8—41no—
563C8—41no—
564C8—41no—
565C8—941no—
566C8—941no—
567C8—941no—
568C8—941no—
569C8—1881no—
570C8—1881no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—942no—
575C22—942no—
576C22—3764no—
577C22—1881no—
578C22—1881no—
579C22—1881no—
580C22—1881no—
581C22—1881no—
582C22—1881no—
583C22—1881no—
584C22C2×#1309398611yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—1881no—
590C4—1881no—
591C4—1881no—
592C4—1881no—
593C4—1881no—
594C4#131×D4711yescharacteristic
595C4#131×D4711yescharacteristic
596C4#1568992711yescharacteristic
597C4#1568993211yescharacteristic
598C2—41no—
599C2—3761no—
600C2—1882no—
601C2—1882no—
602C2#2025208111yescharacteristic
603C2#2025221811yescharacteristic
604C2#2025230411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1574C2
socleC22×C47C2×C4×D4
prime radical#15689259C4
cosocleC42×C47C24
hypercenter#1574D47
hypocenterC47#17918
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1574

Complements

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

NH ≅ G/Ntype
2. #20252533C2semidirect
3. #20252411C2semidirect
4. #20242251C2semidirect
5. #20242244C2semidirect
6. #20242223C2semidirect
7. #20242216C2semidirect
8. #20242211C2semidirect
9. #20242199C2semidirect
10. #20242187C2semidirect
11. #20242182C2semidirect
12. #20241812C2semidirect
13. #20241794C2semidirect
14. #20241688C2semidirect
15. C47×#1574C2semidirect
26. #15689250C22semidirect
27. #15689247C22semidirect
32. #15689200C22semidirect
41. #15689188C22semidirect
48. #15688853C22semidirect
49. #15688853C22semidirect
54. #15688850C22semidirect
55. #15688850C22semidirect
56. #15688845C22semidirect
57. #15688845C22semidirect
58. #15688844C22semidirect
59. C8×C47⋊C8C22semidirect
63. C47×#335C22semidirect
64. C47×#335C22semidirect
65. C47×#334C22semidirect
66. C47×#334C22semidirect
307. #1574D47semidirect
353. #335C2×D47semidirect
354. #335C2×D47semidirect
355. #334C2×D47semidirect
356. #334C2×D47semidirect
369. C47#17918semidirect

Maximal subgroups

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

subgroupindex
#202534372
#202525332
#202524112
#202422512
#202422442
#202422232
#202422162
#202422112
#202421992
#202421872
#202421822
#202418122
#202417942
#202416882
C47×#15742
#1791847