Finite Group Databasebeta

← #26185613

Subgroups — #26185613

Order 12032.

594 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#20252513C211yesmaximal, characteristic
2#20252355C211yesmaximal, characteristic
3#20242174C211yesmaximal, characteristic, complemented
4#20242171C211yesmaximal, characteristic, complemented
5#20242169C211yesmaximal, characteristic, complemented
6#20242166C211yesmaximal, characteristic, complemented
7#20242164C211yesmaximal, characteristic, complemented
8#20242162C211yesmaximal, characteristic, complemented
9#20242156C211yesmaximal, characteristic, complemented
10#20242153C211yesmaximal, characteristic, complemented
11#20242149C211yesmaximal, characteristic, complemented
12#20242141C211yesmaximal, characteristic, complemented
13#20242138C211yesmaximal, characteristic, complemented
14C2×#15688875C211yesmaximal, characteristic, complemented
15C47×#2990C211yesmaximal, characteristic
16#15689254—21no—
17#15689254C411yescharacteristic
18#15689254C411yescharacteristic
19#15689201C411yescharacteristic
20#15689201C411yescharacteristic
21#15689195—21no—
22#15689195—21no—
23#15689195C411yescharacteristic
24#15689195C411yescharacteristic
25#15689195C411yescharacteristic
26#15689195C411yescharacteristic
27D4×C47⋊C8—21no—
28#15689180C2211yescharacteristic
29#15689180C2211yescharacteristic
30#15689176C2211yescharacteristic
31#15689176C2211yescharacteristic
32#15689176C2211yescharacteristic
33#15689176C2211yescharacteristic
34#15689147C2211yescharacteristic
35C2×C4⋊(C47⋊C8)C2211yescharacteristic
36C2×C4⋊(C47⋊C8)C2211yescharacteristic
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#15688875C2211yescharacteristic
49#15688875C2211yescharacteristic
50#15688873C2211yescharacteristic
51#15688873C2211yescharacteristic
52#15688873C2211yescharacteristic
53#15688873C2211yescharacteristic
54#15688873C2211yescharacteristic
55#15688873C2211yescharacteristic
56C4×#41×C47C2211yescharacteristic
57C47×#446—21no—
58C47×#435—21no—
59C47×#435—21no—
60C8×D4×C47—21no—
61C47×#432C2211yescharacteristic
62C47×#432C2211yescharacteristic
63C47×#431C2211yescharacteristic
64C47×#423C2211yescharacteristic
65C2×C4⋊C8×C47C2211yescharacteristic
66C2×C4⋊C8×C47C2211yescharacteristic
67C2×#10625329—21no—
68C2×#10625329C2×C411yescharacteristic
69C2×#10625329C2×C411yescharacteristic
70C2×#10625329C2×C411yescharacteristic
71C2×#10625329C2×C411yescharacteristic
72C22×C47⋊C8—21no—
73C22×C47⋊C8—21no—
74C22×C47⋊C8C2×C411yescharacteristic
75C22×C47⋊C8C2×C411yescharacteristic
76C4⋊(C47⋊C8)—21no—
77C4⋊(C47⋊C8)—21no—
78C4⋊(C47⋊C8)—21no—
79C4⋊(C47⋊C8)C2×C411yescharacteristic
80C4⋊(C47⋊C8)C2×C411yescharacteristic
81C4⋊(C47⋊C8)C2×C411yescharacteristic
82C4⋊(C47⋊C8)C2×C411yescharacteristic
83C4⋊(C47⋊C8)C2×C411yescharacteristic
84C4⋊(C47⋊C8)C2×C411yescharacteristic
85C4⋊(C47⋊C8)C2311yescharacteristic
86C4⋊(C47⋊C8)C2311yescharacteristic
87C4⋊(C47⋊C8)C2311yescharacteristic
88C4⋊(C47⋊C8)C2311yescharacteristic
89C22⋊(C47⋊C8)—21no—
90C22⋊(C47⋊C8)—21no—
91C22⋊(C47⋊C8)—21no—
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
97C22⋊(C47⋊C8)C2×C411yescharacteristic
98#13093935—21no—
99#13093935—21no—
100#13093935C2×C411yescharacteristic
101#13093935C2×C411yescharacteristic
102#13093935C2×C411yescharacteristic
103#13093935C2×C411yescharacteristic
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×C47Q811yescharacteristic
112C2×M16×C47—21no—
113C22×C8×C47—21no—
114C22×C8×C47—21no—
115C4×Q8×C47C2×C411yescharacteristic
116C4×Q8×C47D411yescharacteristic
117C4×D4×C47C2×C411yescharacteristic
118C4×D4×C47C2×C411yescharacteristic
119C4×D4×C47C2×C411yescharacteristic
120C4×D4×C47D411yescharacteristic
121C4×D4×C47D411yescharacteristic
122C4×D4×C47D411yescharacteristic
123#117×C47Q811yescharacteristic
124#117×C47Q811yescharacteristic
125#117×C47Q811yescharacteristic
126C2×C42×C47C2311yescharacteristic
127C2×C42×C47C2311yescharacteristic
128C2×C42×C47C2311yescharacteristic
129C4⋊C8×C47—21no—
130C4⋊C8×C47—21no—
131C4⋊C8×C47—21no—
132C4⋊C8×C47C2311yescharacteristic
133C4⋊C8×C47C2311yescharacteristic
134C4⋊C8×C47C2311yescharacteristic
135C4⋊C8×C47C2311yescharacteristic
136C22⋊C8×C47—21no—
137C22⋊C8×C47—21no—
138C22⋊C8×C47—21no—
139#97×C47—21no—
140#97×C47—21no—
141C4×C8×C47—21no—
142#41×C47—42no—
143C2×Q8×C47C4⋊C411yescharacteristic
144C2×D4×C47C4⋊C411yescharacteristic
145C2×D4×C47C4⋊C411yescharacteristic
146C2×D4×C47C4⋊C411yescharacteristic
147C22×C4×C47C22×C411yescharacteristic
148C22×C4×C47C22×C411yescharacteristic
149C22×C4×C47C22×C411yescharacteristic
150C22×C4×C47C2×D411yescharacteristic
151C22×C4×C47C2×D411yescharacteristic
152C22×C4×C47C2×D411yescharacteristic
153C22×C4×C47C2×Q811yescharacteristic
154C22×C4×C47C2×Q811yescharacteristic
155C22×C4×C47C2×Q811yescharacteristic
156M16×C47—81no—
157C2×C8×C47—21no—
158C2×C8×C47—21no—
159C2×C8×C47—21no—
160C2×C8×C47—21no—
161C2×C8×C47—81no—
162C2×C8×C47—81no—
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—81no—
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—81no—
197C2×C47⋊C8—81no—
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
205C2×C47⋊C8C22×C411yescharacteristic
206C23×C47C2×C4⋊C411yescharacteristic
207C23×C47C2×C4⋊C411yescharacteristic
208C23×C47C2×C4⋊C411yescharacteristic
209Q8×C47—41no—
210D4×C47—22no—
211D4×C47—22no—
212D4×C47—41no—
213C2×C4×C47—22no—
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—21no—
225C2×C4×C47—21no—
226C2×C4×C47—41no—
227C2×C4×C47—41no—
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×C47C2×C4⋊C411yescharacteristic
237C2×C4×C47C23×C411yescharacteristic
238C2×C4×C47C22×D411yescharacteristic
239C2×C4×C47C22×Q811yescharacteristic
240C8×C47—41no—
241C8×C47—41no—
242C8×C47—41no—
243C8×C47—41no—
244C47⋊C8—21no—
245C47⋊C8—21no—
246C47⋊C8—21no—
247C47⋊C8—21no—
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#17840—471nomaximal, Sylow
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×C47#43012yes—
266C22×C47C22×C4⋊C411yescharacteristic
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×C47—21no—
277C4×C47C2×#13111yescharacteristic
278C4×C47#56811yescharacteristic
279C4×C47#57611yescharacteristic
280C4×C47#57811yescharacteristic
281#2990—471no—
282#2990D4711yescharacteristic
283#2965—471no—
284#1573—471no—
285#1573—471no—
286#1572—471no—
287#1572—471no—
288#1571—471no—
289#1571—471no—
290#1569—471no—
291#1569—471no—
292#1568—471no—
293#1565—471no—
294#1565—471no—
295C2×#335—471no—
296C2×C47—22no—
297C2×C47—41no—
298C2×C47—41no—
299C2×C47#290611yescharacteristic
300C2×C47#291311yescharacteristic
301C2×C47C2×#43011yescharacteristic
302C4×#41C2×D4711yescharacteristic
303#446—21no—
304#446—471no—
305#446—471no—
306#446—941no—
307#436—471no—
308#436—471no—
309#435—21no—
310#435—21no—
311#435—471no—
312#435—471no—
313#435—471no—
314#435—471no—
315#435—941no—
316#435—941no—
317C8×D4—21no—
318C8×D4—941no—
319#432—471no—
320#432—471no—
321#432C2×D4711yescharacteristic
322#432C2×D4711yescharacteristic
323#431—471no—
324#431—471no—
325#431—471no—
326#431—471no—
327#431C2×D4711yescharacteristic
328#423—471no—
329#423C2×D4711yescharacteristic
330C2×C4⋊C8—471no—
331C2×C4⋊C8—471no—
332C2×C4⋊C8C2×D4711yescharacteristic
333C2×C4⋊C8C2×D4711yescharacteristic
334C4×M16—471no—
335C4×M16—471no—
336C2×C4×C8—471no—
337#335—471no—
338#335—471no—
339#335—471no—
340#335—471no—
341#335—471no—
342#335—471no—
343#335—471no—
344#335—471no—
345#335—471no—
346#335—471no—
347#334—471no—
348#334—471no—
349#334—471no—
350#334—471no—
351#334—471no—
352#334—471no—
353C47#1784011yescharacteristic, complemented, Sylow
354C2×#41Dic9411yescharacteristic
355C2×M16—21no—
356C2×M16—471no—
357C2×M16—471no—
358C2×M16—471no—
359C2×M16—471no—
360C2×M16—941no—
361C22×C8—21no—
362C22×C8—21no—
363C22×C8—471no—
364C22×C8—471no—
365C22×C8—941no—
366C22×C8—941no—
367C4×Q8C4×D4711yescharacteristic
368C4×Q8C22⋊D4711yescharacteristic
369C4×D4C4×D4711yescharacteristic
370C4×D4C4×D4711yescharacteristic
371C4×D4C4×D4711yescharacteristic
372C4×D4C22⋊D4711yescharacteristic
373C4×D4C22⋊D4711yescharacteristic
374C4×D4C22⋊D4711yescharacteristic
375#117Dic9411yescharacteristic
376#117Dic9411yescharacteristic
377#117Dic9411yescharacteristic
378C2×C42C22×D4711yescharacteristic
379C2×C42C22×D4711yescharacteristic
380C2×C42C22×D4711yescharacteristic
381C4⋊C8—21no—
382C4⋊C8—21no—
383C4⋊C8—21no—
384C4⋊C8—471no—
385C4⋊C8—471no—
386C4⋊C8—471no—
387C4⋊C8—471no—
388C4⋊C8—471no—
389C4⋊C8—471no—
390C4⋊C8—471no—
391C4⋊C8—471no—
392C4⋊C8—471no—
393C4⋊C8—471no—
394C4⋊C8—941no—
395C4⋊C8—941no—
396C4⋊C8—941no—
397C4⋊C8C22×D4711yescharacteristic
398C4⋊C8C22×D4711yescharacteristic
399C4⋊C8C22×D4711yescharacteristic
400C4⋊C8C22×D4711yescharacteristic
401C22⋊C8—21no—
402C22⋊C8—21no—
403C22⋊C8—21no—
404C22⋊C8—471no—
405C22⋊C8—471no—
406C22⋊C8—471no—
407C22⋊C8—471no—
408C22⋊C8—471no—
409C22⋊C8—471no—
410C22⋊C8—941no—
411C22⋊C8—941no—
412C22⋊C8—941no—
413#97—21no—
414#97—21no—
415#97—471no—
416#97—471no—
417#97—471no—
418#97—471no—
419#97—941no—
420#97—941no—
421C4×C8—21no—
422C4×C8—471no—
423C4×C8—471no—
424C4×C8—471no—
425C4×C8—471no—
426C4×C8—471no—
427C4×C8—471no—
428C4×C8—941no—
429#41—42no—
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—81no—
444M16—942no—
445M16—942no—
446M16—3761no—
447M16—1881no—
448M16—1881no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—81no—
454C2×C8—81no—
455C2×C8—471no—
456C2×C8—471no—
457C2×C8—471no—
458C2×C8—471no—
459C2×C8—471no—
460C2×C8—471no—
461C2×C8—471no—
462C2×C8—471no—
463C2×C8—942no—
464C2×C8—941no—
465C2×C8—941no—
466C2×C8—941no—
467C2×C8—941no—
468C2×C8—3761no—
469C2×C8—3761no—
470C2×C8—1881no—
471C4⋊C4Dic47⋊C411yescharacteristic
472C4⋊C4Dic47⋊C411yescharacteristic
473C4⋊C4Dic47⋊C411yescharacteristic
474C4⋊C4Dic47⋊C411yescharacteristic
475C4⋊C4Dic47⋊C411yescharacteristic
476C4⋊C4Dic47⋊C411yescharacteristic
477C22⋊C4Dic47⋊C411yescharacteristic
478C22⋊C4Dic47⋊C411yescharacteristic
479C22⋊C4Dic47⋊C411yescharacteristic
480C22⋊C4Dic47⋊C411yescharacteristic
481C22⋊C4Dic47⋊C411yescharacteristic
482C22⋊C4Dic47⋊C411yescharacteristic
483C42C2×Dic9411yescharacteristic
484C42C2×Dic9411yescharacteristic
485C42C2×Dic9411yescharacteristic
486C42C2×C4×D4711yescharacteristic
487C42C2×C4×D4711yescharacteristic
488C42C2×C4×D4711yescharacteristic
489C42C2×C22⋊D4711yescharacteristic
490C42C2×C22⋊D4711yescharacteristic
491C42C2×C22⋊D4711yescharacteristic
492C42C23×D4711yescharacteristic
493C23C2×Dic47⋊C411yescharacteristic
494C23C2×Dic47⋊C411yescharacteristic
495C23C2×Dic47⋊C411yescharacteristic
496Q8—41no—
497D4—22no—
498D4—22no—
499D4—41no—
500C2×C4—22no—
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—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—41no—
514C2×C4—41no—
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×C4C2×Dic47⋊C411yescharacteristic
523C2×C4C2×Dic47⋊C411yescharacteristic
524C2×C4C22×C4×D4711yescharacteristic
525C2×C4C22×C22⋊D4711yescharacteristic
526C2×C4C22×Dic9411yescharacteristic
527C8—41no—
528C8—41no—
529C8—41no—
530C8—41no—
531C8—472no—
532C8—941no—
533C8—941no—
534C8—941no—
535C8—941no—
536C8—941no—
537C8—941no—
538C8—941no—
539C8—1881no—
540C8—1881no—
541C8—1881no—
542C8—1881no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—21no—
549C22—21no—
550C22—21no—
551C22#1568917112yes—
552C22C22×Dic47⋊C411yescharacteristic
553C4—21no—
554C4—21no—
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4#131×D4711yescharacteristic
564C4#1568988811yescharacteristic
565C4#1568992611yescharacteristic
566C4#1568993811yescharacteristic
567C2—22no—
568C2—41no—
569C2—41no—
570C2#2025195411yescharacteristic
571C2#2025198611yescharacteristic
572C2C2×#1568917111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#2990C2
socleC22×C47C22×C4⋊C4
prime radicalC2×#41×C47Q8
cosocleC42×C47C24
hypercenter#2990D47
hypocenterC47#17840
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2990

Complements

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

NH ≅ G/Ntype
3. #20242174C2semidirect
4. #20242171C2semidirect
5. #20242169C2semidirect
6. #20242166C2semidirect
7. #20242164C2semidirect
8. #20242162C2semidirect
9. #20242156C2semidirect
10. #20242153C2semidirect
11. #20242149C2semidirect
12. #20242141C2semidirect
13. #20242138C2semidirect
14. C2×#15688875C2semidirect
353. C47#17840semidirect

Maximal subgroups

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

subgroupindex
#202525132
#202523552
#202421742
#202421712
#202421692
#202421662
#202421642
#202421622
#202421562
#202421532
#202421492
#202421412
#202421382
C2×#156888752
C47×#29902
#1784047