Finite Group Databasebeta

← #26185629

Subgroups — #26185629

Order 12032.

592 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252517C211yesmaximal, characteristic
2#20252515C211yesmaximal, characteristic
3#20252352C211yesmaximal, characteristic
4#20242178C211yesmaximal, characteristic, complemented
5#20242178C211yesmaximal, characteristic, complemented
6#20242165C211yesmaximal, characteristic, complemented
7#20242159C211yesmaximal, characteristic, complemented
8#20242157C211yesmaximal, characteristic, complemented
9#20242156C211yesmaximal, characteristic, complemented
10#20242154C211yesmaximal, characteristic, complemented
11#20242142C211yesmaximal, characteristic, complemented
12#20242141C211yesmaximal, characteristic, complemented
13#20242139C211yesmaximal, characteristic, complemented
14#20242133C211yesmaximal, characteristic, complemented
15C47×#1572C211yesmaximal, characteristic, complemented
16C4×#10625350C2211yescharacteristic
17#15689252C411yescharacteristic
18#15689252C411yescharacteristic
19#15689251—21no—
20C8×Dic94—21no—
21#15689202—21no—
22#15689198—21no—
23#15689198—21no—
24#15689198C411yescharacteristic
25#15689198C411yescharacteristic
26#15689197C411yescharacteristic
27#15689197C411yescharacteristic
28#15689196—21no—
29#15689193C411yescharacteristic
30#15689193C411yescharacteristic
31#15689191—21no—
32(C22⋊D47)⋊C8—21no—
33#15689179C2211yescharacteristic
34#15689175C2211yescharacteristic
35#15689175C2211yescharacteristic
36#15689175C2211yescharacteristic
37#15689174C2211yescharacteristic
38#15689174C2211yescharacteristic
39#15689147C2211yescharacteristic
40#15689145C2211yescharacteristic
41#15689145C2211yescharacteristic
42#15689145C2211yescharacteristic
43C2×C4⋊(C47⋊C8)C2211yescharacteristic
44C4⋊C8×D47C2211yescharacteristic
45C4×#10625329C2211yescharacteristic
46C4×#10625324C2211yescharacteristic
47C4×C8×D47C2211yescharacteristic
48#15688875C2211yescharacteristic
49#15688875C2211yescharacteristic
50#15688875C2211yescharacteristic
51#15688875C2211yescharacteristic
52#15688874C2211yescharacteristic
53#15688874C2211yescharacteristic
54#15688874C2211yescharacteristic
55#15688874C2211yescharacteristic
56#15688873C2211yescharacteristic
57#15688873C2211yescharacteristic
58#15688873C2211yescharacteristic
59#15688873C2211yescharacteristic
60C47×#432C2211yescharacteristic
61C47×#431C2211yescharacteristic
62C47×#431C2211yescharacteristic
63C47×#335C2211yescharacteristic
64C47×#335C2211yescharacteristic
65C47×#334C2211yescharacteristic
66C47×#334C2211yescharacteristic
67C2×#10625350Q811yescharacteristic
68C2×#10625329—21no—
69C2×#10625329C2×C411yescharacteristic
70C2×#10625329C2×C411yescharacteristic
71C2×#10625324—21no—
72C2×#10625324—21no—
73C2×#10625324—21no—
74C2×#10625324C2×C411yescharacteristic
75C2×#10625324C2×C411yescharacteristic
76C22×C47⋊C8—21no—
77C2×C8×D47—21no—
78C2×C8×D47C2×C411yescharacteristic
79C2×C8×D47C2×C411yescharacteristic
80C4×Dic94C2×C411yescharacteristic
81C4×Dic94D411yescharacteristic
82C4×D188C2×C411yescharacteristic
83C4×D188D411yescharacteristic
84C4×C22⋊D47C2×C411yescharacteristic
85C4×C22⋊D47C2×C411yescharacteristic
86C4×C22⋊D47D411yescharacteristic
87C4×C22⋊D47D411yescharacteristic
88#13093983Q811yescharacteristic
89#13093981Q811yescharacteristic
90#13093981Q811yescharacteristic
91C42×D47C2311yescharacteristic
92C42×D47C2311yescharacteristic
93C4⋊(C47⋊C8)—21no—
94C4⋊(C47⋊C8)—21no—
95C4⋊(C47⋊C8)C2311yescharacteristic
96C4⋊(C47⋊C8)C2311yescharacteristic
97C4⋊(C47⋊C8)C2311yescharacteristic
98C4⋊(C47⋊C8)C2311yescharacteristic
99Dic47⋊C8—21no—
100Dic47⋊C8—21no—
101Dic47⋊C8—21no—
102Dic47⋊C8—21no—
103Dic47⋊C8C2×C411yescharacteristic
104Dic47⋊C8C2×C411yescharacteristic
105Dic47⋊C8C2×C411yescharacteristic
106Dic47⋊C8C2×C411yescharacteristic
107(C2×D47)⋊C8—21no—
108(C2×D47)⋊C8—21no—
109(C2×D47)⋊C8—21no—
110(C2×D47)⋊C8—21no—
111(C2×D47)⋊C8C2×C411yescharacteristic
112(C2×D47)⋊C8C2×C411yescharacteristic
113(C2×D47)⋊C8C2×C411yescharacteristic
114(C2×D47)⋊C8C2×C411yescharacteristic
115#13093935C2×C411yescharacteristic
116#13093935C2×C411yescharacteristic
117#13093934—21no—
118#13093934C2×C411yescharacteristic
119#13093934C2×C411yescharacteristic
120C4×C47⋊C8C2311yescharacteristic
121C4×C47⋊C8C2311yescharacteristic
122C8×Dic47—21no—
123C8×Dic47—21no—
124C8×Dic47—21no—
125C8×Dic47C2×C411yescharacteristic
126C8×Dic47C2×C411yescharacteristic
127C2×C42×C47C2311yescharacteristic
128C4⋊C8×C47C2×C411yescharacteristic
129C4⋊C8×C47C2×C411yescharacteristic
130C4⋊C8×C47C2311yescharacteristic
131C4⋊C8×C47C2311yescharacteristic
132C4⋊C8×C47C2311yescharacteristic
133C4⋊C8×C47C2311yescharacteristic
134C22⋊C8×C47—21no—
135C22⋊C8×C47—21no—
136C22⋊C8×C47C2×C411yescharacteristic
137C22⋊C8×C47C2×C411yescharacteristic
138#97×C47—21no—
139C4×C8×C47—21no—
140C4×C8×C47C2311yescharacteristic
141C4×C8×C47C2311yescharacteristic
142C22×C4×C47C22×C411yescharacteristic
143C22×C4×C47C2×D411yescharacteristic
144C22×C4×C47C2×Q811yescharacteristic
145C2×C22⋊D47C4⋊C411yescharacteristic
146C2×C22⋊D47C4⋊C411yescharacteristic
147#10625350—42no—
148C2×D188C4⋊C411yescharacteristic
149C2×C4×D47C22×C411yescharacteristic
150C2×C4×D47C22×C411yescharacteristic
151C2×C4×D47C2×D411yescharacteristic
152C2×C4×D47C2×D411yescharacteristic
153C2×C4×D47C2×Q811yescharacteristic
154C2×C4×D47C2×Q811yescharacteristic
155C2×Dic94C4⋊C411yescharacteristic
156C2×C8×C47—21no—
157C2×C8×C47—21no—
158C2×C8×C47—21no—
159C2×C8×C47—21no—
160C2×C8×C47C22×C411yescharacteristic
161C2×C8×C47C22×C411yescharacteristic
162C2×C8×C47C22×C411yescharacteristic
163C2×C8×C47C22×C411yescharacteristic
164C42×C47C22×C411yescharacteristic
165C42×C47C2×D411yescharacteristic
166C42×C47C2×Q811yescharacteristic
167C42×C47C2411yescharacteristic
168C22⋊Dic47C4⋊C411yescharacteristic
169C22⋊Dic47C4⋊C411yescharacteristic
170(C2×D47)⋊C4C4⋊C411yescharacteristic
171(C2×D47)⋊C4C4⋊C411yescharacteristic
172(C2×D47)⋊C4C4⋊C411yescharacteristic
173(C2×D47)⋊C4C4⋊C411yescharacteristic
174C4⋊Dic47C4⋊C411yescharacteristic
175C4⋊Dic47C4⋊C411yescharacteristic
176Dic47⋊C4C4⋊C411yescharacteristic
177Dic47⋊C4C4⋊C411yescharacteristic
178Dic47⋊C4C4⋊C411yescharacteristic
179Dic47⋊C4C4⋊C411yescharacteristic
180C4×Dic47C22×C411yescharacteristic
181C4×Dic47C22×C411yescharacteristic
182C4×Dic47C2×D411yescharacteristic
183C4×Dic47C2×D411yescharacteristic
184C4×Dic47C2×Q811yescharacteristic
185C4×Dic47C2×Q811yescharacteristic
186#10625329—22no—
187#10625329—41no—
188#10625329—81no—
189C2×C47⋊C8—21no—
190C2×C47⋊C8—21no—
191C2×C47⋊C8—21no—
192C2×C47⋊C8—21no—
193C2×C47⋊C8—81no—
194C2×C47⋊C8C22×C411yescharacteristic
195C2×C47⋊C8C22×C411yescharacteristic
196C2×C47⋊C8C22×C411yescharacteristic
197C2×C47⋊C8C22×C411yescharacteristic
198#10625324—22no—
199#10625324—41no—
200#10625324—81no—
201#10625324—81no—
202#10625324—81no—
203C8×D47—22no—
204C8×D47—41no—
205C8×D47—81no—
206C23×C47C2×C4⋊C411yescharacteristic
207C22×D47C2×C4⋊C411yescharacteristic
208C22×D47C2×C4⋊C411yescharacteristic
209C2×C4×C47—21no—
210C2×C4×C47—21no—
211C2×C4×C47—21no—
212C2×C4×C47—21no—
213C2×C4×C47—41no—
214C2×C4×C47C2×C4⋊C411yescharacteristic
215C2×C4×C47C2×C4⋊C411yescharacteristic
216C2×C4×C47C2×C4⋊C411yescharacteristic
217C2×C4×C47C23×C411yescharacteristic
218C2×C4×C47C22×D411yescharacteristic
219C2×C4×C47C22×Q811yescharacteristic
220C22⋊D47—22no—
221C22⋊D47—41no—
222C2×Dic47C2×C4⋊C411yescharacteristic
223C2×Dic47C2×C4⋊C411yescharacteristic
224C2×Dic47C2×C4⋊C411yescharacteristic
225C2×Dic47C2×C4⋊C411yescharacteristic
226C2×Dic47C2×C4⋊C411yescharacteristic
227C2×Dic47C2×C4⋊C411yescharacteristic
228D188—41no—
229C4×D47—21no—
230C4×D47—21no—
231C4×D47—21no—
232C4×D47—21no—
233C4×D47—21no—
234C4×D47—21no—
235C4×D47—21no—
236C4×D47—21no—
237C4×D47—22no—
238C4×D47—41no—
239Dic94—22no—
240C8×C47—21no—
241C8×C47—21no—
242C8×C47—21no—
243C8×C47—21no—
244C8×C47—41no—
245C8×C47—41no—
246C8×C47—41no—
247C8×C47—41no—
248C47⋊C8—21no—
249C47⋊C8—21no—
250C47⋊C8—21no—
251C47⋊C8—41no—
252C47⋊C8—41no—
253C47⋊C8—41no—
254C47⋊C8—41no—
255C47⋊C8#13112yes—
256#17841—471nomaximal, Sylow
257C22×C47—21no—
258C22×C47—21no—
259C22×C47—21no—
260C22×C47C22×C4⋊C411yescharacteristic
261C2×D47—21no—
262C2×D47—21no—
263C2×D47—21no—
264C2×D47—21no—
265C2×D47—21no—
266C2×D47—21no—
267C4×C47—21no—
268C4×C47—21no—
269C4×C47—21no—
270C4×C47—21no—
271C4×C47C2×#13111yescharacteristic
272C4×C47#56811yescharacteristic
273C4×C47#57711yescharacteristic
274C4×C47#57711yescharacteristic
275Dic47—21no—
276Dic47—21no—
277Dic47—21no—
278Dic47—21no—
279Dic47—21no—
280Dic47#43012yes—
281#2991—471no—
282#2990—471no—
283#2965—471no—
284#1574—471no—
285#1574—471no—
286#1572—471no—
287#1572D4711yescharacteristic, complemented
288#1570—471no—
289#1570—471no—
290#1569—471no—
291#1569—471no—
292#1566—471no—
293#1565—471no—
294#1565—471no—
295#1564—471no—
296C2×C47—41no—
297C2×C47#290611yescharacteristic
298C2×C47#291211yescharacteristic
299C2×C47C2×#43011yescharacteristic
300D47—41no—
301D47—41no—
302C4×#41—471no—
303#446—471no—
304#446—471no—
305#446—941no—
306C8×Q8—941no—
307#436—471no—
308#436—471no—
309#436—941no—
310#436—941no—
311#436—941no—
312#435—471no—
313#435—471no—
314#435—471no—
315#435—471no—
316#435—941no—
317#435—941no—
318C8×D4—941no—
319#432—471no—
320#432C2×D4711yescharacteristic
321#431—471no—
322#431—471no—
323#431—471no—
324#431—471no—
325#431—471no—
326#431C2×D4711yescharacteristic
327#431C2×D4711yescharacteristic
328#423—471no—
329#423—471no—
330#423—471no—
331#423—471no—
332C2×C4⋊C8—471no—
333C2×C4⋊C8—471no—
334C4×M16—471no—
335C4×M16—471no—
336C2×C4×C8—471no—
337#335—471no—
338#335—471no—
339#335—471no—
340#335—471no—
341#335C2×D4711yescharacteristic
342#335C2×D4711yescharacteristic
343#334—471no—
344#334—471no—
345#334—471no—
346#334—471no—
347#334—471no—
348#334—471no—
349#334—471no—
350#334—471no—
351#334C2×D4711yescharacteristic
352#334C2×D4711yescharacteristic
353C47#1784111yescharacteristic, complemented, Sylow
354C2×#41—471no—
355C2×M16—471no—
356C2×M16—471no—
357C2×M16—471no—
358C2×M16—471no—
359C2×M16—941no—
360C2×M16—941no—
361C2×M16—941no—
362C2×M16—941no—
363C22×C8—471no—
364C22×C8—471no—
365C22×C8—941no—
366C22×C8—941no—
367C4×Q8—471no—
368C4×Q8—471no—
369C4×D4—471no—
370C4×D4—471no—
371C4×D4—471no—
372C4×D4—471no—
373C4×D4—471no—
374C4×D4—471no—
375#117—471no—
376#117—471no—
377#117—471no—
378C2×C42—471no—
379C2×C42—471no—
380C2×C42C22×D4711yescharacteristic
381C4⋊C8—471no—
382C4⋊C8—471no—
383C4⋊C8—471no—
384C4⋊C8—471no—
385C4⋊C8—471no—
386C4⋊C8—471no—
387C4⋊C8—471no—
388C4⋊C8—471no—
389C4⋊C8—941no—
390C4⋊C8—941no—
391C4⋊C8—941no—
392C4⋊C8—941no—
393C4⋊C8—941no—
394C4⋊C8—941no—
395C4⋊C8C4×D4711yescharacteristic
396C4⋊C8C4×D4711yescharacteristic
397C4⋊C8C22×D4711yescharacteristic
398C4⋊C8C22×D4711yescharacteristic
399C4⋊C8C22×D4711yescharacteristic
400C4⋊C8C22×D4711yescharacteristic
401C22⋊C8—21no—
402C22⋊C8—21no—
403C22⋊C8—471no—
404C22⋊C8—471no—
405C22⋊C8—471no—
406C22⋊C8—471no—
407C22⋊C8—941no—
408C22⋊C8—941no—
409C22⋊C8—941no—
410C22⋊C8—941no—
411C22⋊C8C4×D4711yescharacteristic
412C22⋊C8C4×D4711yescharacteristic
413#97—21no—
414#97—471no—
415#97—471no—
416#97—471no—
417#97—471no—
418#97—941no—
419C4×C8—21no—
420C4×C8—471no—
421C4×C8—471no—
422C4×C8—471no—
423C4×C8—471no—
424C4×C8—941no—
425C4×C8—941no—
426C4×C8—941no—
427C4×C8C22×D4711yescharacteristic
428C4×C8C22×D4711yescharacteristic
429#41—1882no—
430C2×Q8—471no—
431C2×D4—471no—
432C2×D4—471no—
433C2×D4—471no—
434C22×C4—471no—
435C22×C4—471no—
436C22×C4—471no—
437C22×C4—471no—
438C22×C4—471no—
439C22×C4—471no—
440C22×C4C2×C4×D4711yescharacteristic
441C22×C4D4×D4711yescharacteristic
442C22×C4Q8×D4711yescharacteristic
443M16—942no—
444M16—942no—
445M16—3761no—
446M16—3761no—
447M16—3761no—
448M16—3761no—
449M16—1881no—
450M16—1881no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—471no—
456C2×C8—471no—
457C2×C8—471no—
458C2×C8—471no—
459C2×C8—942no—
460C2×C8—941no—
461C2×C8—941no—
462C2×C8—941no—
463C2×C8—941no—
464C2×C8—3761no—
465C2×C8—3761no—
466C2×C8—1881no—
467C2×C8C2×C4×D4711yescharacteristic
468C2×C8C2×C4×D4711yescharacteristic
469C2×C8C2×C4×D4711yescharacteristic
470C2×C8C2×C4×D4711yescharacteristic
471C4⋊C4—471no—
472C4⋊C4—471no—
473C4⋊C4—471no—
474C4⋊C4—471no—
475C4⋊C4—471no—
476C4⋊C4—471no—
477C22⋊C4—471no—
478C22⋊C4—471no—
479C22⋊C4—471no—
480C22⋊C4—471no—
481C22⋊C4—471no—
482C22⋊C4—471no—
483C42—471no—
484C42—471no—
485C42—471no—
486C42—471no—
487C42—471no—
488C42—471no—
489C42C2×C4×D4711yescharacteristic
490C42D4×D4711yescharacteristic
491C42Q8×D4711yescharacteristic
492C42C23×D4711yescharacteristic
493C23—471no—
494C23—471no—
495C23C4⋊C4×D4711yescharacteristic
496Q8—942no—
497D4—942no—
498D4—1881no—
499D4—1881no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—471no—
506C2×C4—471no—
507C2×C4—471no—
508C2×C4—471no—
509C2×C4—471no—
510C2×C4—471no—
511C2×C4—942no—
512C2×C4—941no—
513C2×C4—941no—
514C2×C4—941no—
515C2×C4—941no—
516C2×C4—941no—
517C2×C4—941no—
518C2×C4—941no—
519C2×C4—941no—
520C2×C4—1881no—
521C2×C4C4⋊C4×D4711yescharacteristic
522C2×C4C4⋊C4×D4711yescharacteristic
523C2×C4C4⋊C4×D4711yescharacteristic
524C2×C4C22×C4×D4711yescharacteristic
525C2×C4C2×D4×D4711yescharacteristic
526C2×C4C2×Q8×D4711yescharacteristic
527C8—21no—
528C8—21no—
529C8—21no—
530C8—21no—
531C8—41no—
532C8—41no—
533C8—41no—
534C8—41no—
535C8—472no—
536C8—941no—
537C8—941no—
538C8—941no—
539C8—1881no—
540C8—1881no—
541C8—1881no—
542C8—1881no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—941no—
547C22—941no—
548C22—941no—
549C22—941no—
550C22—941no—
551C22—941no—
552C22C2×C4⋊C4×D4711yescharacteristic
553C4—21no—
554C4—21no—
555C4—21no—
556C4—21no—
557C4—472no—
558C4—941no—
559C4—941no—
560C4—941no—
561C4—941no—
562C4—941no—
563C4#131×D4711yescharacteristic
564C4#1568988811yescharacteristic
565C4#1568993011yescharacteristic
566C4#1568993011yescharacteristic
567C2—41no—
568C2—1881no—
569C2—1881no—
570C2#2025195511yescharacteristic
571C2#2025198011yescharacteristic
572C2#430×D4711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1572C2
socleC22×C47C22×C4⋊C4
prime radicalC2×#10625350Q8
cosocleC42×C47C24
hypercenter#1572D47
hypocenterC47#17841
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1572

Complements

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

NH ≅ G/Ntype
4. #20242178C2semidirect
5. #20242178C2semidirect
6. #20242165C2semidirect
7. #20242159C2semidirect
8. #20242157C2semidirect
9. #20242156C2semidirect
10. #20242154C2semidirect
11. #20242142C2semidirect
12. #20242141C2semidirect
13. #20242139C2semidirect
14. #20242133C2semidirect
15. C47×#1572C2semidirect
287. #1572D47semidirect
353. C47#17841semidirect

Maximal subgroups

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

subgroupindex
#202525172
#202525152
#202523522
#202421782
#202421652
#202421592
#202421572
#202421562
#202421542
#202421422
#202421412
#202421392
#202421332
C47×#15722
#1784147