Finite Group Databasebeta

← #26185538

Subgroups — #26185538

Order 12032.

588 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252355C211yesmaximal, characteristic
2#20252054C211yesmaximal, characteristic
3#20242179C211yesmaximal, characteristic, complemented
4#20242176C211yesmaximal, characteristic, complemented
5#20242174C211yesmaximal, characteristic, complemented
6#20242171C211yesmaximal, characteristic, complemented
7#20242169C211yesmaximal, characteristic, complemented
8#20242166C211yesmaximal, characteristic, complemented
9#20242156C211yesmaximal, characteristic, complemented
10#20242153C211yesmaximal, characteristic, complemented
11#20242149C211yesmaximal, characteristic, complemented
12#20242141C211yesmaximal, characteristic, complemented
13#20242138C211yesmaximal, characteristic, complemented
14#20242134C211yesmaximal, characteristic, complemented
15C47×#2925C211yesmaximal, characteristic
16#15689254C411yescharacteristic
17#15689254C411yescharacteristic
18#15689201C411yescharacteristic
19#15689201C411yescharacteristic
20#15689195C411yescharacteristic
21#15689195C411yescharacteristic
22#15689195C411yescharacteristic
23#15689195C411yescharacteristic
24#15689184—21no—
25#15689184—21no—
26#15689180C2211yescharacteristic
27#15689180C2211yescharacteristic
28#15689176C2211yescharacteristic
29#15689176C2211yescharacteristic
30#15689176C2211yescharacteristic
31#15689176C2211yescharacteristic
32#15689176C2211yescharacteristic
33#15689147C2211yescharacteristic
34C2×C4⋊(C47⋊C8)C2211yescharacteristic
35#15689090—21no—
36#15689079—21no—
37C4×#10625329C2211yescharacteristic
38C4×#10625329C2211yescharacteristic
39C2×C4×C47⋊C8C2211yescharacteristic
40#15688875C2211yescharacteristic
41#15688875C2211yescharacteristic
42#15688875C2211yescharacteristic
43#15688875C2211yescharacteristic
44#15688875C2211yescharacteristic
45#15688875C2211yescharacteristic
46#15688875C2211yescharacteristic
47#15688875C2211yescharacteristic
48#15688873C2211yescharacteristic
49#15688873C2211yescharacteristic
50#15688873C2211yescharacteristic
51#15688873C2211yescharacteristic
52#15688873C2211yescharacteristic
53#15688873C2211yescharacteristic
54#15688873C2211yescharacteristic
55#15688873C2211yescharacteristic
56C4×#41×C47C2211yescharacteristic
57C47×#433—21no—
58C47×#433—21no—
59C47×#432C2211yescharacteristic
60C47×#432C2211yescharacteristic
61C47×#431C2211yescharacteristic
62C47×#431C2211yescharacteristic
63C47×#423C2211yescharacteristic
64C2×C4⋊C8×C47C2211yescharacteristic
65C47×#408—21no—
66C47×#405—21no—
67C2×#10625329—21no—
68C2×#10625329C2×C411yescharacteristic
69C2×#10625329C2×C411yescharacteristic
70C2×#10625329C2×C411yescharacteristic
71C2×#10625329C2×C411yescharacteristic
72C22×C47⋊C8—21no—
73C22×C47⋊C8C2×C411yescharacteristic
74C22×C47⋊C8C2×C411yescharacteristic
75C4⋊(C47⋊C8)—21no—
76C4⋊(C47⋊C8)—21no—
77C4⋊(C47⋊C8)C2×C411yescharacteristic
78C4⋊(C47⋊C8)C2×C411yescharacteristic
79C4⋊(C47⋊C8)C2×C411yescharacteristic
80C4⋊(C47⋊C8)C2×C411yescharacteristic
81C4⋊(C47⋊C8)C2×C411yescharacteristic
82C4⋊(C47⋊C8)C2×C411yescharacteristic
83C4⋊(C47⋊C8)C2311yescharacteristic
84C4⋊(C47⋊C8)C2311yescharacteristic
85C4⋊(C47⋊C8)C2311yescharacteristic
86C4⋊(C47⋊C8)C2311yescharacteristic
87C22⋊(C47⋊C8)—21no—
88C22⋊(C47⋊C8)—21no—
89C22⋊(C47⋊C8)—21no—
90C22⋊(C47⋊C8)—21no—
91C22⋊(C47⋊C8)C2×C411yescharacteristic
92C22⋊(C47⋊C8)C2×C411yescharacteristic
93C22⋊(C47⋊C8)C2×C411yescharacteristic
94C22⋊(C47⋊C8)C2×C411yescharacteristic
95C22⋊(C47⋊C8)C2×C411yescharacteristic
96C22⋊(C47⋊C8)C2×C411yescharacteristic
97#13093935—21no—
98#13093935—21no—
99#13093935C2×C411yescharacteristic
100#13093935C2×C411yescharacteristic
101#13093935C2×C411yescharacteristic
102#13093935C2×C411yescharacteristic
103C4×C47⋊C8—21no—
104C4×C47⋊C8—21no—
105C4×C47⋊C8C2×C411yescharacteristic
106C4×C47⋊C8C2×C411yescharacteristic
107C4×C47⋊C8C2311yescharacteristic
108C4×C47⋊C8C2311yescharacteristic
109C4×C47⋊C8C2311yescharacteristic
110C4×C47⋊C8C2311yescharacteristic
111C2×#41×C47D411yescharacteristic
112C2×M16×C47—21no—
113C22×C8×C47—21no—
114C4×Q8×C47C2×C411yescharacteristic
115C4×Q8×C47Q811yescharacteristic
116C4×D4×C47C2×C411yescharacteristic
117C4×D4×C47C2×C411yescharacteristic
118C4×D4×C47C2×C411yescharacteristic
119C4×D4×C47Q811yescharacteristic
120C4×D4×C47Q811yescharacteristic
121C4×D4×C47Q811yescharacteristic
122#117×C47D411yescharacteristic
123#117×C47D411yescharacteristic
124#117×C47D411yescharacteristic
125C2×C42×C47C2311yescharacteristic
126C2×C42×C47C2311yescharacteristic
127C2×C42×C47C2311yescharacteristic
128C4⋊C8×C47—21no—
129C4⋊C8×C47—21no—
130C4⋊C8×C47C2311yescharacteristic
131C4⋊C8×C47C2311yescharacteristic
132C4⋊C8×C47C2311yescharacteristic
133C4⋊C8×C47C2311yescharacteristic
134C22⋊C8×C47—21no—
135C22⋊C8×C47—21no—
136C22⋊C8×C47—21no—
137C22⋊C8×C47—21no—
138#97×C47—21no—
139#97×C47—21no—
140C4×C8×C47—21no—
141C4×C8×C47—21no—
142#41×C47—41no—
143#41×C47—41no—
144C2×Q8×C47C4⋊C411yescharacteristic
145C2×D4×C47C4⋊C411yescharacteristic
146C2×D4×C47C4⋊C411yescharacteristic
147C2×D4×C47C4⋊C411yescharacteristic
148C22×C4×C47C22×C411yescharacteristic
149C22×C4×C47C22×C411yescharacteristic
150C22×C4×C47C22×C411yescharacteristic
151C22×C4×C47C2×D411yescharacteristic
152C22×C4×C47C2×D411yescharacteristic
153C22×C4×C47C2×D411yescharacteristic
154C22×C4×C47C2×Q811yescharacteristic
155C22×C4×C47C2×Q811yescharacteristic
156C22×C4×C47C2×Q811yescharacteristic
157M16×C47—42no—
158C2×C8×C47—21no—
159C2×C8×C47—21no—
160C2×C8×C47—21no—
161C2×C8×C47—21no—
162C2×C8×C47—42no—
163C4⋊C4×C47C4⋊C411yescharacteristic
164C4⋊C4×C47C4⋊C411yescharacteristic
165C4⋊C4×C47C4⋊C411yescharacteristic
166C4⋊C4×C47C4⋊C411yescharacteristic
167C4⋊C4×C47C4⋊C411yescharacteristic
168C4⋊C4×C47C4⋊C411yescharacteristic
169C22⋊C4×C47C4⋊C411yescharacteristic
170C22⋊C4×C47C4⋊C411yescharacteristic
171C22⋊C4×C47C4⋊C411yescharacteristic
172C22⋊C4×C47C4⋊C411yescharacteristic
173C22⋊C4×C47C4⋊C411yescharacteristic
174C22⋊C4×C47C4⋊C411yescharacteristic
175C42×C47C22×C411yescharacteristic
176C42×C47C22×C411yescharacteristic
177C42×C47C22×C411yescharacteristic
178C42×C47C2×D411yescharacteristic
179C42×C47C2×D411yescharacteristic
180C42×C47C2×D411yescharacteristic
181C42×C47C2×Q811yescharacteristic
182C42×C47C2×Q811yescharacteristic
183C42×C47C2×Q811yescharacteristic
184C42×C47C2411yescharacteristic
185#10625329—22no—
186#10625329—22no—
187#10625329—41no—
188#10625329—41no—
189#10625329—42no—
190C2×C47⋊C8—22no—
191C2×C47⋊C8—21no—
192C2×C47⋊C8—21no—
193C2×C47⋊C8—21no—
194C2×C47⋊C8—21no—
195C2×C47⋊C8—41no—
196C2×C47⋊C8—42no—
197C2×C47⋊C8C22×C411yescharacteristic
198C2×C47⋊C8C22×C411yescharacteristic
199C2×C47⋊C8C22×C411yescharacteristic
200C2×C47⋊C8C22×C411yescharacteristic
201C2×C47⋊C8C22×C411yescharacteristic
202C2×C47⋊C8C22×C411yescharacteristic
203C2×C47⋊C8C22×C411yescharacteristic
204C2×C47⋊C8C22×C411yescharacteristic
205C23×C47C2×C4⋊C411yescharacteristic
206C23×C47C2×C4⋊C411yescharacteristic
207C23×C47C2×C4⋊C411yescharacteristic
208Q8×C47—41no—
209D4×C47—41no—
210D4×C47—41no—
211D4×C47—41no—
212C2×C4×C47—21no—
213C2×C4×C47—21no—
214C2×C4×C47—21no—
215C2×C4×C47—21no—
216C2×C4×C47—21no—
217C2×C4×C47—21no—
218C2×C4×C47—21no—
219C2×C4×C47—21no—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—41no—
225C2×C4×C47—41no—
226C2×C4×C47—41no—
227C2×C4×C47C2×C4⋊C411yescharacteristic
228C2×C4×C47C2×C4⋊C411yescharacteristic
229C2×C4×C47C2×C4⋊C411yescharacteristic
230C2×C4×C47C2×C4⋊C411yescharacteristic
231C2×C4×C47C2×C4⋊C411yescharacteristic
232C2×C4×C47C2×C4⋊C411yescharacteristic
233C2×C4×C47C2×C4⋊C411yescharacteristic
234C2×C4×C47C2×C4⋊C411yescharacteristic
235C2×C4×C47C2×C4⋊C411yescharacteristic
236C2×C4×C47C23×C411yescharacteristic
237C2×C4×C47C22×D411yescharacteristic
238C2×C4×C47C22×Q811yescharacteristic
239C8×C47—41no—
240C8×C47—41no—
241C8×C47—41no—
242C8×C47—41no—
243C47⋊C8—21no—
244C47⋊C8—21no—
245C47⋊C8—21no—
246C47⋊C8—21no—
247C47⋊C8—21no—
248C47⋊C8—21no—
249C47⋊C8—21no—
250C47⋊C8—41no—
251C47⋊C8—41no—
252C47⋊C8—41no—
253C47⋊C8—41no—
254C47⋊C8#13112yes—
255#17831—471nomaximal, Sylow
256C22×C47—21no—
257C22×C47—21no—
258C22×C47—21no—
259C22×C47—21no—
260C22×C47—21no—
261C22×C47—21no—
262C22×C47—21no—
263C22×C47—21no—
264C22×C47—21no—
265C22×C47C22×C4⋊C411yescharacteristic
266C4×C47—21no—
267C4×C47—21no—
268C4×C47—21no—
269C4×C47—21no—
270C4×C47—21no—
271C4×C47—21no—
272C4×C47—21no—
273C4×C47—21no—
274C4×C47—21no—
275C4×C47—21no—
276C4×C47C2×#13111yescharacteristic
277C4×C47#56811yescharacteristic
278C4×C47#57511yescharacteristic
279C4×C47#57511yescharacteristic
280#2965—471no—
281#2925—471no—
282#2925D4711yescharacteristic
283#1574—471no—
284#1574—471no—
285#1573—471no—
286#1573—471no—
287#1572—471no—
288#1572—471no—
289#1569—471no—
290#1569—471no—
291#1568—471no—
292#1565—471no—
293#1565—471no—
294#1564—471no—
295C2×C47—41no—
296C2×C47—41no—
297C2×C47—41no—
298C2×C47#290611yescharacteristic
299C2×C47#291111yescharacteristic
300C2×C47#291611yescharacteristic
301C4×#41C2×D4711yescharacteristic
302#446—471no—
303#446—471no—
304#436—471no—
305#436—471no—
306#435—471no—
307#435—471no—
308#435—471no—
309#435—471no—
310#433—21no—
311#433—21no—
312#433—941no—
313#433—941no—
314#432—471no—
315#432—471no—
316#432C2×D4711yescharacteristic
317#432C2×D4711yescharacteristic
318#431—471no—
319#431—471no—
320#431—471no—
321#431—471no—
322#431—471no—
323#431C2×D4711yescharacteristic
324#431C2×D4711yescharacteristic
325#423—471no—
326#423C2×D4711yescharacteristic
327C2×C4⋊C8—471no—
328C2×C4⋊C8C2×D4711yescharacteristic
329#408—21no—
330#408—941no—
331#405—21no—
332#405—941no—
333C4×M16—471no—
334C4×M16—471no—
335C2×C4×C8—471no—
336#335—471no—
337#335—471no—
338#335—471no—
339#335—471no—
340#335—471no—
341#335—471no—
342#335—471no—
343#335—471no—
344#334—471no—
345#334—471no—
346#334—471no—
347#334—471no—
348#334—471no—
349#334—471no—
350#334—471no—
351#334—471no—
352C47#1783111yescharacteristic, complemented, Sylow
353C2×#41C22⋊D4711yescharacteristic
354C2×M16—21no—
355C2×M16—471no—
356C2×M16—471no—
357C2×M16—471no—
358C2×M16—471no—
359C2×M16—941no—
360C22×C8—21no—
361C22×C8—471no—
362C22×C8—471no—
363C22×C8—941no—
364C4×Q8Dic9411yescharacteristic
365C4×Q8C4×D4711yescharacteristic
366C4×D4Dic9411yescharacteristic
367C4×D4Dic9411yescharacteristic
368C4×D4Dic9411yescharacteristic
369C4×D4C4×D4711yescharacteristic
370C4×D4C4×D4711yescharacteristic
371C4×D4C4×D4711yescharacteristic
372#117C22⋊D4711yescharacteristic
373#117C22⋊D4711yescharacteristic
374#117C22⋊D4711yescharacteristic
375C2×C42C22×D4711yescharacteristic
376C2×C42C22×D4711yescharacteristic
377C2×C42C22×D4711yescharacteristic
378C4⋊C8—21no—
379C4⋊C8—21no—
380C4⋊C8—471no—
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—471no—
390C4⋊C8—941no—
391C4⋊C8—941no—
392C4⋊C8C22×D4711yescharacteristic
393C4⋊C8C22×D4711yescharacteristic
394C4⋊C8C22×D4711yescharacteristic
395C4⋊C8C22×D4711yescharacteristic
396C22⋊C8—21no—
397C22⋊C8—21no—
398C22⋊C8—21no—
399C22⋊C8—21no—
400C22⋊C8—471no—
401C22⋊C8—471no—
402C22⋊C8—471no—
403C22⋊C8—471no—
404C22⋊C8—471no—
405C22⋊C8—471no—
406C22⋊C8—941no—
407C22⋊C8—941no—
408C22⋊C8—941no—
409C22⋊C8—941no—
410#97—21no—
411#97—21no—
412#97—471no—
413#97—471no—
414#97—471no—
415#97—471no—
416#97—941no—
417#97—941no—
418C4×C8—21no—
419C4×C8—21no—
420C4×C8—471no—
421C4×C8—471no—
422C4×C8—471no—
423C4×C8—471no—
424C4×C8—471no—
425C4×C8—471no—
426C4×C8—941no—
427C4×C8—941no—
428#41—41no—
429#41—41no—
430C2×Q8Dic47⋊C411yescharacteristic
431C2×D4Dic47⋊C411yescharacteristic
432C2×D4Dic47⋊C411yescharacteristic
433C2×D4Dic47⋊C411yescharacteristic
434C22×C4C2×Dic9411yescharacteristic
435C22×C4C2×Dic9411yescharacteristic
436C22×C4C2×Dic9411yescharacteristic
437C22×C4C2×C4×D4711yescharacteristic
438C22×C4C2×C4×D4711yescharacteristic
439C22×C4C2×C4×D4711yescharacteristic
440C22×C4C2×C22⋊D4711yescharacteristic
441C22×C4C2×C22⋊D4711yescharacteristic
442C22×C4C2×C22⋊D4711yescharacteristic
443M16—42no—
444M16—942no—
445M16—942no—
446M16—1881no—
447M16—1881no—
448M16—1882no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—42no—
454C2×C8—471no—
455C2×C8—471no—
456C2×C8—471no—
457C2×C8—471no—
458C2×C8—471no—
459C2×C8—471no—
460C2×C8—471no—
461C2×C8—471no—
462C2×C8—942no—
463C2×C8—941no—
464C2×C8—941no—
465C2×C8—941no—
466C2×C8—941no—
467C2×C8—1881no—
468C2×C8—1882no—
469C4⋊C4Dic47⋊C411yescharacteristic
470C4⋊C4Dic47⋊C411yescharacteristic
471C4⋊C4Dic47⋊C411yescharacteristic
472C4⋊C4Dic47⋊C411yescharacteristic
473C4⋊C4Dic47⋊C411yescharacteristic
474C4⋊C4Dic47⋊C411yescharacteristic
475C22⋊C4Dic47⋊C411yescharacteristic
476C22⋊C4Dic47⋊C411yescharacteristic
477C22⋊C4Dic47⋊C411yescharacteristic
478C22⋊C4Dic47⋊C411yescharacteristic
479C22⋊C4Dic47⋊C411yescharacteristic
480C22⋊C4Dic47⋊C411yescharacteristic
481C42C2×Dic9411yescharacteristic
482C42C2×Dic9411yescharacteristic
483C42C2×Dic9411yescharacteristic
484C42C2×C4×D4711yescharacteristic
485C42C2×C4×D4711yescharacteristic
486C42C2×C4×D4711yescharacteristic
487C42C2×C22⋊D4711yescharacteristic
488C42C2×C22⋊D4711yescharacteristic
489C42C2×C22⋊D4711yescharacteristic
490C42C23×D4711yescharacteristic
491C23C2×Dic47⋊C411yescharacteristic
492C23C2×Dic47⋊C411yescharacteristic
493C23C2×Dic47⋊C411yescharacteristic
494Q8—41no—
495D4—41no—
496D4—41no—
497D4—41no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4C2×Dic47⋊C411yescharacteristic
514C2×C4C2×Dic47⋊C411yescharacteristic
515C2×C4C2×Dic47⋊C411yescharacteristic
516C2×C4C2×Dic47⋊C411yescharacteristic
517C2×C4C2×Dic47⋊C411yescharacteristic
518C2×C4C2×Dic47⋊C411yescharacteristic
519C2×C4C2×Dic47⋊C411yescharacteristic
520C2×C4C2×Dic47⋊C411yescharacteristic
521C2×C4C2×Dic47⋊C411yescharacteristic
522C2×C4C22×C4×D4711yescharacteristic
523C2×C4C22×C22⋊D4711yescharacteristic
524C2×C4C22×Dic9411yescharacteristic
525C8—41no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—472no—
530C8—941no—
531C8—941no—
532C8—941no—
533C8—941no—
534C8—941no—
535C8—941no—
536C8—941no—
537C8—1881no—
538C8—1881no—
539C8—1881no—
540C8—1881no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—21no—
549C22—21no—
550C22C22×Dic47⋊C411yescharacteristic
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—21no—
560C4—21no—
561C4#131×D4711yescharacteristic
562C4#1568988811yescharacteristic
563C4#1568992111yescharacteristic
564C4#1568992111yescharacteristic
565C2—41no—
566C2—41no—
567C2—41no—
568C2#2025195411yescharacteristic
569C2#2025197711yescharacteristic
570C2#2025199711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#2925C2
socleC22×C47C22×C4⋊C4
prime radicalC2×#41×C47D4
cosocleC42×C47C24
hypercenter#2925D47
hypocenterC47#17831
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2925

Complements

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

NH ≅ G/Ntype
3. #20242179C2semidirect
4. #20242176C2semidirect
5. #20242174C2semidirect
6. #20242171C2semidirect
7. #20242169C2semidirect
8. #20242166C2semidirect
9. #20242156C2semidirect
10. #20242153C2semidirect
11. #20242149C2semidirect
12. #20242141C2semidirect
13. #20242138C2semidirect
14. #20242134C2semidirect
352. C47#17831semidirect

Maximal subgroups

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

subgroupindex
#202523552
#202520542
#202421792
#202421762
#202421742
#202421712
#202421692
#202421662
#202421562
#202421532
#202421492
#202421412
#202421382
#202421342
C47×#29252
#1783147