Finite Group Databasebeta

← #26226643

Subgroups — #26226643

Order 12032.

790 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689185C211yesmaximal, characteristic
2C2×#15689183C211yesmaximal, characteristic
3#20245868C211yesmaximal, characteristic
4#20244111C211yesmaximal, characteristic, complemented
5#20244110C211yesmaximal, characteristic, complemented
6#20244108C211yesmaximal, characteristic, complemented
7#20244107C211yesmaximal, characteristic, complemented
8#20244105C211yesmaximal, characteristic, complemented
9#20244104C211yesmaximal, characteristic, complemented
10#20244103C211yesmaximal, characteristic, complemented
11#20243371C211yesmaximal, characteristic
12#20243369C211yesmaximal, characteristic
13#20243367C211yesmaximal, characteristic
14#20243365C211yesmaximal, characteristic
15C47×#1940C211yesmaximal, characteristic, complemented
16C2×#13093981C2211yescharacteristic
17C2×#13093981C2211yescharacteristic
18C2×C42×D47C2211yescharacteristic
19#15689185—24no—
20#15689183—24no—
21C2×C4⋊(C47⋊C8)C2211yescharacteristic
22C2×C4⋊(C47⋊C8)C2211yescharacteristic
23C2×C4⋊(C47⋊C8)C2211yescharacteristic
24C2×Dic47⋊C8C2211yescharacteristic
25C2×Dic47⋊C8C2211yescharacteristic
26C2×Dic47⋊C8C2211yescharacteristic
27C2×Dic47⋊C8C2211yescharacteristic
28C2×Dic47⋊C8C2211yescharacteristic
29C2×Dic47⋊C8C2211yescharacteristic
30C2×(C2×D47)⋊C8C2211yescharacteristic
31C2×(C2×D47)⋊C8C2211yescharacteristic
32C2×(C2×D47)⋊C8C2211yescharacteristic
33C2×(C2×D47)⋊C8C2211yescharacteristic
34C2×#13093934C2211yescharacteristic
35C2×C4×C47⋊C8C2211yescharacteristic
36C2×C8×Dic47C2211yescharacteristic
37#15689020C411yescharacteristic
38#15689020C411yescharacteristic
39#15689018C411yescharacteristic
40#15689018C411yescharacteristic
41#15688997C411yescharacteristic
42#15688997C411yescharacteristic
43#15688994C411yescharacteristic
44#15688994C411yescharacteristic
45C4×Dic47⋊C4C2211yescharacteristic
46C4×Dic47⋊C4C2211yescharacteristic
47C4×C4⋊Dic47C2211yescharacteristic
48#15688878C2211yescharacteristic
49#15688878C2211yescharacteristic
50#15688877C2211yescharacteristic
51#15688877C2211yescharacteristic
52#15688877C2211yescharacteristic
53#15688877C2211yescharacteristic
54C2×C4⋊C8×C47C2211yescharacteristic
55C2×C4⋊C8×C47C2211yescharacteristic
56C2×C4⋊C8×C47C2211yescharacteristic
57C2×#97×C47C2211yescharacteristic
58C4×C4⋊C4×C47C2211yescharacteristic
59C47×#336C2211yescharacteristic
60C47×#336C2211yescharacteristic
61C22×C4×D47C2×C411yescharacteristic
62C22×C4×D47C2×C411yescharacteristic
63C22×C4×D47C2311yescharacteristic
64C22×C47⋊C8C2311yescharacteristic
65C22×C47⋊C8C2311yescharacteristic
66C22×C47⋊C8C2311yescharacteristic
67C22×C47⋊C8C2311yescharacteristic
68#13093981—41no—
69#13093981—41no—
70#13093981D414yes—
71#13093981Q814yes—
72C2×C4⋊Dic47C2×C411yescharacteristic
73C2×C4⋊Dic47C2×C411yescharacteristic
74C2×Dic47⋊C4C2×C411yescharacteristic
75C2×Dic47⋊C4C2×C411yescharacteristic
76C2×Dic47⋊C4C2×C411yescharacteristic
77C2×Dic47⋊C4C2×C411yescharacteristic
78C2×Dic47⋊C4C2×C411yescharacteristic
79C2×Dic47⋊C4C2×C411yescharacteristic
80C2×Dic47⋊C4C2×C411yescharacteristic
81C2×Dic47⋊C4C2×C411yescharacteristic
82C2×(C2×D47)⋊C4C2×C411yescharacteristic
83C2×(C2×D47)⋊C4C2×C411yescharacteristic
84C2×(C2×D47)⋊C4C2×C411yescharacteristic
85C2×(C2×D47)⋊C4C2×C411yescharacteristic
86C2×C4×Dic47C2×C411yescharacteristic
87C2×C4×Dic47C2×C411yescharacteristic
88C2×C4×Dic47C2311yescharacteristic
89C2×C4×Dic47C2311yescharacteristic
90C2×C4×Dic47C2311yescharacteristic
91C42×D47—41no—
92C42×D47—41no—
93C4⋊(C47⋊C8)—22no—
94C4⋊(C47⋊C8)—41no—
95C4⋊(C47⋊C8)—41no—
96Dic47⋊C8—22no—
97Dic47⋊C8—22no—
98Dic47⋊C8—41no—
99Dic47⋊C8—41no—
100Dic47⋊C8—41no—
101Dic47⋊C8—41no—
102(C2×D47)⋊C8—22no—
103(C2×D47)⋊C8—22no—
104(C2×D47)⋊C8—22no—
105(C2×D47)⋊C8—22no—
106#13093934—22no—
107C4×C47⋊C8—22no—
108C8×Dic47—22no—
109C47⋊#95C2×C411yescharacteristic
110C47⋊#95C2×C411yescharacteristic
111C47⋊#95C2×C411yescharacteristic
112C47⋊#95C2×C411yescharacteristic
113C47⋊#95C2×C411yescharacteristic
114C47⋊#95C2×C411yescharacteristic
115C22×C8×C47C2311yescharacteristic
116C22×C8×C47C2311yescharacteristic
117C22×C8×C47C2311yescharacteristic
118C22×C8×C47C2311yescharacteristic
119C2×C4⋊C4×C47C2×C411yescharacteristic
120C2×C4⋊C4×C47C2×C411yescharacteristic
121C2×C42×C47C2311yescharacteristic
122C2×C42×C47C2311yescharacteristic
123C2×C42×C47C2311yescharacteristic
124C4⋊C8×C47—22no—
125C4⋊C8×C47—41no—
126C4⋊C8×C47—41no—
127#97×C47—22no—
128#95×C47C2×C411yescharacteristic
129#95×C47C2×C411yescharacteristic
130C23×D47C22×C411yescharacteristic
131C22×C4×C47C22×C411yescharacteristic
132C22×C4×C47C22×C411yescharacteristic
133C22×C4×C47C22×C411yescharacteristic
134C22×C4×C47C22×C411yescharacteristic
135C22×C4×C47C22×C411yescharacteristic
136C22×C4×C47C22×C411yescharacteristic
137C22×C4×C47C2411yescharacteristic
138C22×Dic47C22×C411yescharacteristic
139C22×Dic47C22×C411yescharacteristic
140C22×Dic47C22×C411yescharacteristic
141C22×Dic47C22×C411yescharacteristic
142C22×Dic47C22×C411yescharacteristic
143C22×Dic47C22×C411yescharacteristic
144C22×Dic47C22×C411yescharacteristic
145C2×C4×D47—21no—
146C2×C4×D47—21no—
147C2×C4×D47—21no—
148C2×C4×D47—21no—
149C2×C4×D47—22no—
150C2×C4×D47—22no—
151C2×C4×D47—41no—
152C2×C4×D47—41no—
153C2×C4×D47—41no—
154C2×C4×D47—41no—
155C2×C4×D47C2×D412yes—
156C2×C4×D47C2×Q812yes—
157C2×C8×C47—21no—
158C2×C8×C47—21no—
159C2×C8×C47—21no—
160C2×C8×C47—21no—
161C2×C8×C47—21no—
162C2×C8×C47—21no—
163C2×C8×C47—21no—
164C2×C8×C47—21no—
165C2×C8×C47—21no—
166C2×C8×C47—21no—
167C2×C8×C47—21no—
168C2×C8×C47—21no—
169C4⋊C4×C47—22no—
170C4⋊C4×C47—41no—
171C42×C47—21no—
172C42×C47—21no—
173C42×C47—21no—
174C42×C47—21no—
175C42×C47C2×D412yes—
176C42×C47C2×Q812yes—
177(C2×D47)⋊C4—41no—
178(C2×D47)⋊C4—41no—
179(C2×D47)⋊C4C4⋊C414yes—
180(C2×D47)⋊C4C4⋊C414yes—
181C4⋊Dic47—22no—
182C4⋊Dic47—41no—
183Dic47⋊C4—22no—
184Dic47⋊C4—22no—
185Dic47⋊C4—41no—
186Dic47⋊C4—41no—
187Dic47⋊C4—41no—
188Dic47⋊C4—41no—
189Dic47⋊C4C4⋊C414yes—
190Dic47⋊C4C4⋊C414yes—
191C4×Dic47—21no—
192C4×Dic47—21no—
193C4×Dic47—21no—
194C4×Dic47—21no—
195C4×Dic47—41no—
196C4×Dic47—41no—
197C4×Dic47C2×D412yes—
198C4×Dic47C2×Q812yes—
199C2×C47⋊C8—21no—
200C2×C47⋊C8—21no—
201C2×C47⋊C8—21no—
202C2×C47⋊C8—21no—
203C2×C47⋊C8—21no—
204C2×C47⋊C8—21no—
205C2×C47⋊C8—21no—
206C2×C47⋊C8—21no—
207C2×C47⋊C8—21no—
208C2×C47⋊C8—21no—
209C2×C47⋊C8—21no—
210C2×C47⋊C8—21no—
211C23×C47C23×C411yescharacteristic
212C22×D47—21no—
213C22×D47—21no—
214C22×D47—21no—
215C22×D47—21no—
216C22×D47—21no—
217C22×D47—21no—
218C22×D47C2×C4⋊C412yes—
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—21no—
227C2×C4×C47—21no—
228C2×C4×C47—21no—
229C2×C4×C47—21no—
230C2×C4×C47—21no—
231C2×C4×C47—21no—
232C2×C4×C47—21no—
233C2×C4×C47—21no—
234C2×C4×C47C2×C4⋊C412yes—
235C2×C4×C47C2×C4⋊C412yes—
236C2×C4×C47#13112yes—
237C2×C4×C47C22×D411yescharacteristic
238C2×C4×C47C22×Q811yescharacteristic
239C2×C4×C47H(5,𝔽2)11yescharacteristic
240C2×C4×C47H(5,𝔽2)11yescharacteristic
241C2×C4×C472−1+411yescharacteristic
242C2×C4×C472−1+411yescharacteristic
243C2×Dic47—21no—
244C2×Dic47—21no—
245C2×Dic47—21no—
246C2×Dic47—21no—
247C2×Dic47—21no—
248C2×Dic47—21no—
249C2×Dic47—21no—
250C2×Dic47—21no—
251C2×Dic47—21no—
252C2×Dic47—21no—
253C2×Dic47—21no—
254C2×Dic47—21no—
255C2×Dic47—21no—
256C2×Dic47—21no—
257C2×Dic47—21no—
258C2×Dic47—21no—
259C2×Dic47—21no—
260C2×Dic47C2×C4⋊C412yes—
261C2×Dic47C2×C4⋊C412yes—
262C2×Dic47C2×C4⋊C412yes—
263C2×Dic47#13112yes—
264C4×D47—22no—
265C4×D47—22no—
266C4×D47—22no—
267C4×D47—22no—
268C4×D47—44no—
269C4×D47—44no—
270C8×C47—41no—
271C8×C47—41no—
272C8×C47—41no—
273C8×C47—41no—
274C47⋊C8—41no—
275C47⋊C8—41no—
276C47⋊C8—41no—
277C47⋊C8—41no—
278#21958—471nomaximal, Sylow
279C22×C47C22×C4⋊C411yescharacteristic
280C22×C47#51811yescharacteristic
281C22×C47#51911yescharacteristic
282C22×C47C2×#13111yescharacteristic
283C22×C47C2×#13111yescharacteristic
284C22×C47#56811yescharacteristic
285C22×C47#56811yescharacteristic
286C2×D47—22no—
287C2×D47—22no—
288C2×D47—22no—
289C2×D47—41no—
290C2×D47—41no—
291C2×D47—41no—
292C2×D47—41no—
293C4×C47—22no—
294C4×C47—22no—
295C4×C47—22no—
296C4×C47—41no—
297C4×C47—41no—
298C4×C47—41no—
299C4×C47#53711yescharacteristic
300C4×C47#53711yescharacteristic
301C4×C47#54411yescharacteristic
302C4×C47#54411yescharacteristic
303Dic47—22no—
304Dic47—22no—
305Dic47—22no—
306Dic47—22no—
307Dic47—41no—
308Dic47—41no—
309Dic47—41no—
310C2×#433—471no—
311C2×#433—471no—
312#2296—471no—
313#1940—471no—
314#1940—471no—
315#1940—471no—
316#1940D4711yescharacteristic, complemented
317#1939—471no—
318#1939—471no—
319#1939—471no—
320#1939—471no—
321#1798—471no—
322#1798—471no—
323#1797—471no—
324#1797—471no—
325C2×C47#231611yescharacteristic
326C2×C47#290611yescharacteristic
327C2×C47#290611yescharacteristic
328C2×C47#297711yescharacteristic
329C2×C47#297811yescharacteristic
330C2×C47#298511yescharacteristic
331C2×C47#298511yescharacteristic
332D47—42no—
333C2×#117—471no—
334C2×#117—471no—
335C22×C42—471no—
336#433—944no—
337#433—944no—
338C2×C4⋊C8—471no—
339C2×C4⋊C8—471no—
340C2×C4⋊C8—471no—
341C2×C4⋊C8—471no—
342C2×C4⋊C8—471no—
343C2×C4⋊C8—471no—
344C2×C4⋊C8—471no—
345C2×C4⋊C8—471no—
346C2×C4⋊C8—471no—
347C2×C4⋊C8C2×D4711yescharacteristic
348C2×C4⋊C8C2×D4711yescharacteristic
349C2×C4⋊C8C2×D4711yescharacteristic
350C2×C22⋊C8—471no—
351C2×C22⋊C8—471no—
352C2×C22⋊C8—471no—
353C2×C22⋊C8—471no—
354C2×#97—471no—
355C2×#97C2×D4711yescharacteristic
356C2×C4×C8—471no—
357C2×C4×C8—471no—
358#389—471no—
359#389—471no—
360#389—471no—
361#389—471no—
362#385—471no—
363#385—471no—
364#385—471no—
365#385—471no—
366C4×C4⋊C4—471no—
367C4×C4⋊C4—471no—
368C4×C4⋊C4—471no—
369C4×C4⋊C4C2×D4711yescharacteristic
370#336—471no—
371#336—471no—
372#336—471no—
373#336—471no—
374#336—471no—
375#336—471no—
376#336C2×D4711yescharacteristic
377#336C2×D4711yescharacteristic
378C47#2195811yescharacteristic, complemented, Sylow
379C23×C4—471no—
380C23×C4—471no—
381C23×C4—471no—
382C22×C8—471no—
383C22×C8—471no—
384C22×C8—471no—
385C22×C8—471no—
386C22×C8C22×D4711yescharacteristic
387C22×C8C22×D4711yescharacteristic
388C22×C8C22×D4711yescharacteristic
389C22×C8C22×D4711yescharacteristic
390#117—474no—
391#117—474no—
392#117—1881no—
393#117—1881no—
394C2×C4⋊C4—471no—
395C2×C4⋊C4—471no—
396C2×C4⋊C4—471no—
397C2×C4⋊C4—471no—
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⋊C4C4×D4711yescharacteristic
405C2×C4⋊C4C4×D4711yescharacteristic
406C2×C22⋊C4—471no—
407C2×C22⋊C4—471no—
408C2×C22⋊C4—471no—
409C2×C22⋊C4—471no—
410C2×C42—471no—
411C2×C42—471no—
412C2×C42—471no—
413C2×C42—471no—
414C2×C42—471no—
415C2×C42—1881no—
416C2×C42—1881no—
417C2×C42C22×D4711yescharacteristic
418C2×C42C22×D4711yescharacteristic
419C2×C42C22×D4711yescharacteristic
420C4⋊C8—22no—
421C4⋊C8—41no—
422C4⋊C8—41no—
423C4⋊C8—942no—
424C4⋊C8—942no—
425C4⋊C8—942no—
426C4⋊C8—1881no—
427C4⋊C8—1881no—
428C4⋊C8—1881no—
429C4⋊C8—1881no—
430C4⋊C8—1881no—
431C4⋊C8—1881no—
432C22⋊C8—942no—
433C22⋊C8—942no—
434C22⋊C8—942no—
435C22⋊C8—942no—
436#97—22no—
437#97—942no—
438C4×C8—942no—
439C4×C8—942no—
440#95—471no—
441#95—471no—
442#95—471no—
443#95—471no—
444#95—471no—
445#95—471no—
446#95C4×D4711yescharacteristic
447#95C4×D4711yescharacteristic
448C24—471no—
449C22×C4—471no—
450C22×C4—471no—
451C22×C4—471no—
452C22×C4—471no—
453C22×C4—472no—
454C22×C4—472no—
455C22×C4—471no—
456C22×C4—471no—
457C22×C4—471no—
458C22×C4—942no—
459C22×C4—941no—
460C22×C4—941no—
461C22×C4—941no—
462C22×C4—941no—
463C22×C4—942no—
464C22×C4—1881no—
465C22×C4—1881no—
466C22×C4—1881no—
467C22×C4—1881no—
468C22×C4C2×C4×D4711yescharacteristic
469C22×C4C2×C4×D4711yescharacteristic
470C22×C4C2×C4×D4711yescharacteristic
471C22×C4C2×C4×D4711yescharacteristic
472C22×C4C2×C4×D4711yescharacteristic
473C22×C4C2×C4×D4711yescharacteristic
474C22×C4C23×D4711yescharacteristic
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—941no—
488C2×C8—941no—
489C2×C8—941no—
490C2×C8—941no—
491C2×C8—941no—
492C2×C8—941no—
493C2×C8—941no—
494C2×C8—941no—
495C2×C8—941no—
496C2×C8—941no—
497C2×C8—941no—
498C2×C8—941no—
499C4⋊C4—22no—
500C4⋊C4—41no—
501C4⋊C4—474no—
502C4⋊C4—474no—
503C4⋊C4—942no—
504C4⋊C4—942no—
505C4⋊C4—942no—
506C4⋊C4—1881no—
507C4⋊C4—1881no—
508C4⋊C4—1881no—
509C4⋊C4—1881no—
510C4⋊C4—1881no—
511C22⋊C4—474no—
512C22⋊C4—474no—
513C22⋊C4—1881no—
514C22⋊C4—1881no—
515C42—21no—
516C42—21no—
517C42—21no—
518C42—21no—
519C42—472no—
520C42—472no—
521C42—941no—
522C42—941no—
523C42—941no—
524C42—941no—
525C42—1881no—
526C42—1881no—
527C42D4×D4712yes—
528C42Q8×D4712yes—
529C23—472no—
530C23—941no—
531C23—941no—
532C23—941no—
533C23—941no—
534C23—941no—
535C23—941no—
536C23C22×C4×D4711yescharacteristic
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—472no—
553C2×C4—472no—
554C2×C4—472no—
555C2×C4—472no—
556C2×C4—941no—
557C2×C4—941no—
558C2×C4—941no—
559C2×C4—941no—
560C2×C4—941no—
561C2×C4—941no—
562C2×C4—941no—
563C2×C4—941no—
564C2×C4—942no—
565C2×C4—942no—
566C2×C4—942no—
567C2×C4—942no—
568C2×C4—941no—
569C2×C4—941no—
570C2×C4—941no—
571C2×C4—941no—
572C2×C4—941no—
573C2×C4—941no—
574C2×C4—941no—
575C2×C4—941no—
576C2×C4—941no—
577C2×C4—1884no—
578C2×C4—1884no—
579C2×C4C4⋊C4×D4712yes—
580C2×C4C4⋊C4×D4712yes—
581C2×C4#1309403212yes—
582C2×C4C2×D4×D4711yescharacteristic
583C2×C4C2×Q8×D4711yescharacteristic
584C2×C4#1309406911yescharacteristic
585C2×C4#1309407011yescharacteristic
586C2×C4#1309407111yescharacteristic
587C2×C4#1309407211yescharacteristic
588C8—41no—
589C8—41no—
590C8—41no—
591C8—41no—
592C8—1881no—
593C8—1881no—
594C8—1881no—
595C8—1881no—
596C22—942no—
597C22—942no—
598C22—942no—
599C22—1881no—
600C22—1881no—
601C22—1881no—
602C22—1881no—
603C22C2×C4⋊C4×D4711yescharacteristic
604C22#1568959511yescharacteristic
605C22#1568959911yescharacteristic
606C22#131×D4711yescharacteristic
607C22C2×#1309403211yescharacteristic
608C22#1568988811yescharacteristic
609C22#1568988911yescharacteristic
610C4—22no—
611C4—22no—
612C4—22no—
613C4—41no—
614C4—41no—
615C4—41no—
616C4—942no—
617C4—942no—
618C4—942no—
619C4—942no—
620C4—1881no—
621C4—1881no—
622C4—1881no—
623C4#1568970211yescharacteristic
624C4#1568970311yescharacteristic
625C4#1568975011yescharacteristic
626C4#1568975311yescharacteristic
627C2—1882no—
628C2#2024600311yescharacteristic
629C2#2025195511yescharacteristic
630C2#2025195711yescharacteristic
631C2#2025243911yescharacteristic
632C2#2025244711yescharacteristic
633C2#2025248111yescharacteristic
634C2#2025248411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC47×#1940C2
prime radicalC23×D47C22×C4
cosocleC22×C4×C47C24
hypercenter#1940D47
hypocenterC47#21958
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #1940

Complements

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

NH ≅ G/Ntype
4. #20244111C2semidirect
5. #20244110C2semidirect
6. #20244108C2semidirect
7. #20244107C2semidirect
8. #20244105C2semidirect
9. #20244104C2semidirect
10. #20244103C2semidirect
15. C47×#1940C2semidirect
316. #1940D47semidirect
378. C47#21958semidirect

Maximal subgroups

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

subgroupindex
C2×#156891852
C2×#156891832
#202458682
#202441112
#202441102
#202441082
#202441072
#202441052
#202441042
#202441032
#202433712
#202433692
#202433672
#202433652
C47×#19402
#2195847