Finite Group Databasebeta

← #26236591

Subgroups — #26236591

Order 12032.

1386 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689257C211yesmaximal, characteristic
2C2×#15689233C211yesmaximal, characteristic, complemented
3C22×#13093945C211yesmaximal, characteristic, complemented
4#20246402C211yesmaximal, characteristic, complemented
5#20244263C211yesmaximal, characteristic, complemented
6#20244088C211yesmaximal, characteristic, complemented
7#20244012C211yesmaximal, characteristic, complemented
8#20243814C211yesmaximal, characteristic, complemented
9#20243739C211yesmaximal, characteristic, complemented
10#20243736C211yesmaximal, characteristic, complemented
11#20243649C211yesmaximal, characteristic, complemented
12#20243580C211yesmaximal, characteristic, complemented
13#20243213C211yesmaximal, characteristic, complemented
14#20243166C211yesmaximal, characteristic, complemented
15D4×C22⋊C4×C47C211yesmaximal, characteristic, complemented
16C22×#10625334C2211yescharacteristic
17C22×#10625334C2211yescharacteristic
18C23×C47⋊C8C2211yescharacteristic
19C2×#13093998C2211yescharacteristic
20C2×C4×D188C2211yescharacteristic, complemented
21C2×(C22⋊D47)⋊C4—21no—
22C22×C4⋊Dic47C2211yescharacteristic
23#15689257C418yescomplemented
24#15689233—24no—
25C2×#13093955C2211yescharacteristic, complemented
26C2×#13093955C2211yescharacteristic, complemented
27C2×#13093945—24no—
28C2×#13093945C2211yescharacteristic
29C2×#13093945C2211yescharacteristic
30C2×#13093945C2211yescharacteristic
31C2×#13093945C2211yescharacteristic
32C2×#13093945C2211yescharacteristic
33C2×#13093945C2211yescharacteristic
34C2×#13093944C2211yescharacteristic, complemented
35C2×#13093944C2211yescharacteristic, complemented
36C2×C22⋊(C47⋊C8)C2211yescharacteristic
37C2×#13093935C2211yescharacteristic, complemented
38C2×#13093935C2211yescharacteristic, complemented
39#15689025C2211yescharacteristic, complemented
40#15689021C2211yescharacteristic, complemented
41#15689015—21no—
42#15689000—21no—
43#15688997—21no—
44C4×C4⋊Dic47C2211yescharacteristic, complemented
45#15688885C2211yescharacteristic, complemented
46#15688885C2211yescharacteristic, complemented
47#15688885C2211yescharacteristic, complemented
48#15688885C2211yescharacteristic, complemented
49#15688878C2211yescharacteristic, complemented
50#15688878C2211yescharacteristic, complemented
51C23×D4×C47C2211yescharacteristic
52C2×C4×D4×C47C2211yescharacteristic
53C2×C4×D4×C47C2211yescharacteristic
54C22×C22⋊C4×C47—21no—
55C47×#390C2211yescharacteristic
56C47×#390C2211yescharacteristic
57C47×#386—21no—
58C47×#386—21no—
59C47×#380C2211yescharacteristic
60C47×#379—21no—
61C4×C22⋊C4×C47C2211yescharacteristic
62C22×D188C2311yescharacteristic
63C22×C22⋊D47—21no—
64C23×Dic47—21no—
65C22×C4×D47—21no—
66C2×#10625334—22no—
67C2×#10625334—22no—
68C2×#10625334—41no—
69C2×#10625334—41no—
70C2×#10625334C2×C414yescomplemented
71C2×#10625334C2×C414yescomplemented
72C22×C47⋊C8—22no—
73C22×C47⋊C8—22no—
74C22×C47⋊C8—41no—
75C22×C47⋊C8C2311yescharacteristic
76C22×C47⋊C8C2311yescharacteristic
77C22×C47⋊C8C2311yescharacteristic
78C22×C47⋊C8C2311yescharacteristic
79#13093998—22no—
80#13093998C2×C414yescomplemented
81C4×D188—22no—
82C4×D188—41no—
83(C22⋊D47)⋊C4—44no—
84C2×C4⋊Dic47—22no—
85C2×C4⋊Dic47—21no—
86C2×C4⋊Dic47—41no—
87C2×C4⋊Dic47C2311yescharacteristic
88C2×C4⋊Dic47C2311yescharacteristic
89C2×C4⋊Dic47C2311yescharacteristic
90C2×Dic47⋊C4—21no—
91C2×(C2×D47)⋊C4—21no—
92C2×(C2×D47)⋊C4—21no—
93C2×(C2×D47)⋊C4—21no—
94C2×(C2×D47)⋊C4—21no—
95C2×C4×Dic47—21no—
96#13093955—22no—
97#13093955—41no—
98#13093945—22no—
99#13093945—22no—
100#13093945—22no—
101#13093945C2×C414yescomplemented
102#13093945C2×C414yescomplemented
103#13093945D414yescomplemented
104#13093944—22no—
105#13093944—41no—
106C22⋊(C47⋊C8)C2×C414yescomplemented
107#13093935—22no—
108#13093935—41no—
109C47⋊#95—21no—
110C47⋊#95—21no—
111C25×C47—21no—
112C22×D4×C47—22no—
113C22×D4×C47—22no—
114C22×D4×C47—21no—
115C22×D4×C47—22no—
116C22×D4×C47—41no—
117C22×D4×C47—41no—
118C22×D4×C47C2×C414yescomplemented
119C22×D4×C47C2311yescharacteristic
120C22×D4×C47C2311yescharacteristic
121C23×C4×C47—21no—
122C23×C4×C47—21no—
123C23×C4×C47C2311yescharacteristic
124C4×D4×C47—22no—
125C4×D4×C47—22no—
126C4×D4×C47—41no—
127C4×D4×C47—41no—
128C2×C4⋊C4×C47C2311yescharacteristic
129C2×C4⋊C4×C47C2311yescharacteristic
130C2×C22⋊C4×C47—21no—
131C2×C22⋊C4×C47—21no—
132C2×C22⋊C4×C47—21no—
133C2×C22⋊C4×C47—21no—
134C2×C22⋊C4×C47—21no—
135C2×C22⋊C4×C47—21no—
136C2×C22⋊C4×C47—21no—
137C2×C22⋊C4×C47—44no—
138C2×C22⋊C4×C47D411yescharacteristic
139C2×C22⋊C4×C47D411yescharacteristic
140C2×C42×C47C2311yescharacteristic
141C2×C42×C47C2311yescharacteristic
142#95×C47—21no—
143#95×C47D411yescharacteristic
144#95×C47D411yescharacteristic
145C24×C47—21no—
146C24×C47—21no—
147C24×C47—24no—
148C24×C47—42no—
149C24×C47—42no—
150C24×C47—42no—
151C24×C47—42no—
152C24×C47—81no—
153C24×C47—81no—
154C24×C47C2×D411yescharacteristic
155C23×D47—21no—
156C2×D4×C47—28no—
157C2×D4×C47—24no—
158C2×D4×C47—21no—
159C2×D4×C47—21no—
160C2×D4×C47—21no—
161C2×D4×C47—21no—
162C2×D4×C47—21no—
163C2×D4×C47—21no—
164C2×D4×C47—21no—
165C2×D4×C47—21no—
166C2×D4×C47—44no—
167C2×D4×C47—44no—
168C2×D4×C47—44no—
169C2×D4×C47—42no—
170C2×D4×C47—42no—
171C2×D4×C47C22×C412yes—
172C2×D4×C47C22×C412yes—
173C2×D4×C47C2×D412yes—
174C2×D4×C47#4112yes—
175C22×C4×C47—21no—
176C22×C4×C47—21no—
177C22×C4×C47—21no—
178C22×C4×C47—21no—
179C22×C4×C47—21no—
180C22×C4×C47—21no—
181C22×C4×C47—42no—
182C22×C4×C47—42no—
183C22×C4×C47—42no—
184C22×C4×C47—42no—
185C22×C4×C47—81no—
186C22×C4×C47—81no—
187C22×C4×C47C22×C412yes—
188C22×C4×C47C2×D411yescharacteristic
189C22×C4×C47C2×D411yescharacteristic
190C22×C4×C47C2×D411yescharacteristic
191C22×C4×C47C2×D411yescharacteristic
192C22×C4×C47C2×D411yescharacteristic
193C22×C4×C47#4112yes—
194C22×C4×C47C2411yescharacteristic
195C2×C22⋊D47—24no—
196C2×C22⋊D47—42no—
197C2×C22⋊D47—42no—
198C22×Dic47—21no—
199C22×Dic47—21no—
200C22×Dic47—21no—
201C22×Dic47—42no—
202C22×Dic47—42no—
203C22×Dic47—81no—
204C2×D188—21no—
205C2×D188—21no—
206C2×D188—21no—
207C2×D188—21no—
208C2×D188—21no—
209C2×D188C22×C412yes—
210C2×C4×D47—42no—
211C2×C4×D47—42no—
212C2×C4×D47—81no—
213C4⋊C4×C47—21no—
214C4⋊C4×C47—21no—
215C4⋊C4×C47—21no—
216C4⋊C4×C47—21no—
217C22⋊C4×C47—22no—
218C22⋊C4×C47—22no—
219C22⋊C4×C47—42no—
220C22⋊C4×C47—42no—
221C22⋊C4×C47—42no—
222C22⋊C4×C47—42no—
223C22⋊C4×C47—42no—
224C22⋊C4×C47—81no—
225C22⋊C4×C47—81no—
226C42×C47—21no—
227C42×C47—21no—
228C42×C47—21no—
229C42×C47—21no—
230#10625334—28no—
231#10625334—44no—
232(C2×D47)⋊C4—24no—
233(C2×D47)⋊C4—42no—
234(C2×D47)⋊C4—42no—
235(C2×D47)⋊C4—81no—
236C4⋊Dic47—21no—
237C4⋊Dic47—21no—
238C4⋊Dic47—21no—
239C4⋊Dic47—21no—
240C4⋊Dic47—42no—
241C4⋊Dic47C22×C412yes—
242C4⋊Dic47C2×D412yes—
243Dic47⋊C4—42no—
244C4×Dic47—42no—
245C2×C47⋊C8—21no—
246C2×C47⋊C8—21no—
247C2×C47⋊C8—21no—
248C2×C47⋊C8—21no—
249C2×C47⋊C8—21no—
250C2×C47⋊C8—21no—
251C2×C47⋊C8—21no—
252C2×C47⋊C8—21no—
253C2×C47⋊C8—21no—
254C2×C47⋊C8—44no—
255C2×C47⋊C8C22×C412yes—
256C2×C47⋊C8C22×C412yes—
257C2×C47⋊C8C2×D412yes—
258C23×C47—21no—
259C23×C47—21no—
260C23×C47—21no—
261C23×C47—21no—
262C23×C47—22no—
263C23×C47—22no—
264C23×C47—22no—
265C23×C47—22no—
266C23×C47—48no—
267C23×C47—41no—
268C23×C47—41no—
269C23×C47—41no—
270C23×C47—41no—
271C23×C47—41no—
272C23×C47—41no—
273C23×C47—41no—
274C23×C47—41no—
275C23×C47—41no—
276C23×C47—41no—
277C23×C47—48no—
278C23×C47—84no—
279C23×C47—84no—
280C23×C47—84no—
281C23×C47—84no—
282C23×C47—84no—
283C23×C47C4×D412yes—
284C23×C47AGL(1,ℤ/8)12yes—
285C23×C47AGL(1,ℤ/8)12yes—
286C23×C47C22×D411yescharacteristic
287C22×D47—22no—
288C22×D47—41no—
289C22×D47—41no—
290C22×D47—41no—
291C22×D47—41no—
292C22×D47—41no—
293C22×D47—41no—
294D4×C47—22no—
295D4×C47—22no—
296D4×C47—22no—
297D4×C47—22no—
298D4×C47—22no—
299D4×C47—48no—
300D4×C47—41no—
301D4×C47—41no—
302D4×C47C4×D414yescomplemented
303C2×C4×C47—21no—
304C2×C4×C47—21no—
305C2×C4×C47—22no—
306C2×C4×C47—22no—
307C2×C4×C47—22no—
308C2×C4×C47—22no—
309C2×C4×C47—21no—
310C2×C4×C47—21no—
311C2×C4×C47—21no—
312C2×C4×C47—21no—
313C2×C4×C47—21no—
314C2×C4×C47—21no—
315C2×C4×C47—21no—
316C2×C4×C47—21no—
317C2×C4×C47—21no—
318C2×C4×C47—21no—
319C2×C4×C47—21no—
320C2×C4×C47—21no—
321C2×C4×C47—41no—
322C2×C4×C47—41no—
323C2×C4×C47—41no—
324C2×C4×C47—41no—
325C2×C4×C47—41no—
326C2×C4×C47—41no—
327C2×C4×C47—84no—
328C2×C4×C47—84no—
329C2×C4×C47C4×D412yes—
330C2×C4×C47C23×C411yescharacteristic
331C2×C4×C47C22×D411yescharacteristic
332C2×C4×C47C2×#4111yescharacteristic
333C2×C4×C47C2×#4111yescharacteristic
334C2×C4×C47H(5,𝔽2)11yescharacteristic
335C2×C4×C47H(5,𝔽2)11yescharacteristic
336C22⋊D47—48no—
337C2×Dic47—22no—
338C2×Dic47—22no—
339C2×Dic47—41no—
340C2×Dic47—41no—
341C2×Dic47—41no—
342C2×Dic47—41no—
343C2×Dic47—41no—
344C2×Dic47—41no—
345C2×Dic47—41no—
346C2×Dic47—84no—
347D188—22no—
348D188—22no—
349D188—41no—
350D188—41no—
351C4×D47—84no—
352C47⋊C8—22no—
353C47⋊C8—22no—
354C47⋊C8—22no—
355C47⋊C8—41no—
356#22858—471nomaximal, Sylow
357C22×C47—22no—
358C22×C47—22no—
359C22×C47—22no—
360C22×C47—22no—
361C22×C47—22no—
362C22×C47—22no—
363C22×C47—24no—
364C22×C47—42no—
365C22×C47—42no—
366C22×C47—42no—
367C22×C47—42no—
368C22×C47—42no—
369C22×C47—42no—
370C22×C47—42no—
371C22×C47—42no—
372C22×C47—42no—
373C22×C47—816no—
374C22×C47—81no—
375C22×C47—81no—
376C22×C47—81no—
377C22×C47—81no—
378C22×C47#44214yescomplemented
379C22×C47C2×C4×D411yescharacteristic
380C22×C47D4211yescharacteristic
381C22×C47#54611yescharacteristic
382C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
383C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
384C22×C47#57611yescharacteristic
385C22×C47#57711yescharacteristic
386C2×D47—42no—
387C2×D47—42no—
388C2×D47—42no—
389C2×D47—81no—
390C2×D47—81no—
391C2×D47—81no—
392C2×D47—81no—
393C4×C47—22no—
394C4×C47—41no—
395C4×C47—41no—
396C4×C47—41no—
397C4×C47—41no—
398C4×C47—81no—
399C4×C47—81no—
400C4×C47C2×C4×D411yescharacteristic
401C4×C47#51811yescharacteristic
402C4×C47#54611yescharacteristic
403C4×C47#55111yescharacteristic
404Dic47—42no—
405Dic47—42no—
406Dic47—81no—
407C2×#447—471no—
408C2×#442—471no—
409C22×#102—471no—
410#2361—471no—
411D4×C22⋊C4D4711yescharacteristic, complemented
412#1972—471no—
413#1936—471no—
414#1926—471no—
415#1893—471no—
416#1879—471no—
417#1879—471no—
418#1864—471no—
419#1853—471no—
420#1762—471no—
421#1752—471no—
422C2×C47—24no—
423C2×C47—44no—
424C2×C47—82no—
425C2×C47#235811yescharacteristic
426C2×C47C2×#44211yescharacteristic
427C2×C47#294611yescharacteristic
428C2×C47#326411yescharacteristic
429C2×C47#326511yescharacteristic
430C2×C47#330611yescharacteristic
431C2×C47#331811yescharacteristic
432D47—82no—
433C23×D4C2×D4711yescharacteristic
434C22×D8—471no—
435C22×D8—471no—
436C23×C8—471no—
437C2×#121—471no—
438C2×C4×D4—471no—
439C2×C4×D4—941no—
440C2×C4×D4C2×D4711yescharacteristic
441C2×C4×D4C2×D4711yescharacteristic
442C22×C4⋊C4—471no—
443C22×C22⋊C4—21no—
444#447—478no—
445#442—944no—
446C2×#106—471no—
447C2×#106—471no—
448C2×#102—471no—
449C2×#102—471no—
450C2×#102—471no—
451C2×#102—471no—
452C2×#102—471no—
453C2×#102—471no—
454C2×#102—471no—
455C2×#102—471no—
456C2×#102—944no—
457C2×C22⋊C8—471no—
458C2×#97—471no—
459C2×#97—471no—
460#390—471no—
461#390C2×D4711yescharacteristic
462#390C2×D4711yescharacteristic
463#389—471no—
464#388—941no—
465#386—21no—
466#386—21no—
467#386—941no—
468#385—941no—
469#380C2×D4711yescharacteristic
470#379—21no—
471C4×C4⋊C4—471no—
472C4×C22⋊C4C2×D4711yescharacteristic
473#340—471no—
474#340—471no—
475#340—471no—
476#340—471no—
477#336—471no—
478#336—471no—
479C47#2285811yescharacteristic, complemented, Sylow
480C25—21no—
481C22×D4—22no—
482C22×D4—22no—
483C22×D4—22no—
484C22×D4—21no—
485C22×D4—41no—
486C22×D4—41no—
487C22×D4—471no—
488C22×D4—941no—
489C22×D4C4×D4714yescomplemented
490C22×D4C22×D4711yescharacteristic
491C22×D4C22×D4711yescharacteristic
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—941no—
495C23×C4—941no—
496C23×C4C22×D4711yescharacteristic
497C2×D8—474no—
498C2×D8—474no—
499C2×D8—942no—
500C2×D8—942no—
501C2×D8—1881no—
502C2×D8—1881no—
503C22×C8—471no—
504C22×C8—471no—
505C22×C8—471no—
506C22×C8—471no—
507C22×C8—942no—
508C22×C8—942no—
509C22×C8—1881no—
510#121—474no—
511#121—942no—
512C4×D4—22no—
513C4×D4—22no—
514C4×D4—41no—
515C4×D4—41no—
516C4×D4—942no—
517C4×D4—1881no—
518C4×D4—1884no—
519C2×C4⋊C4—471no—
520C2×C4⋊C4—471no—
521C2×C4⋊C4—471no—
522C2×C4⋊C4—942no—
523C2×C4⋊C4—941no—
524C2×C4⋊C4—941no—
525C2×C4⋊C4—1881no—
526C2×C4⋊C4C22×D4711yescharacteristic
527C2×C4⋊C4C22×D4711yescharacteristic
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—44no—
536C2×C22⋊C4—941no—
537C2×C22⋊C4—941no—
538C2×C22⋊C4—941no—
539C2×C22⋊C4—941no—
540C2×C22⋊C4C22⋊D4711yescharacteristic
541C2×C22⋊C4C22⋊D4711yescharacteristic
542C2×C42—941no—
543C2×C42C22×D4711yescharacteristic
544C2×C42C22×D4711yescharacteristic
545#106—942no—
546#106—1881no—
547#102—474no—
548#102—474no—
549#102—474no—
550#102—942no—
551#102—942no—
552#102—942no—
553#102—942no—
554#102—1881no—
555C22⋊C8—474no—
556#97—942no—
557#97—1881no—
558#95—21no—
559#95—941no—
560#95—941no—
561#95C22⋊D4711yescharacteristic
562#95C22⋊D4711yescharacteristic
563C24—21no—
564C24—21no—
565C24—24no—
566C24—42no—
567C24—42no—
568C24—42no—
569C24—42no—
570C24—81no—
571C24—81no—
572C24—941no—
573C24C2×C22⋊D4711yescharacteristic
574C2×D4—28no—
575C2×D4—24no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—44no—
585C2×D4—44no—
586C2×D4—44no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4—472no—
590C2×D4—944no—
591C2×D4—941no—
592C2×D4—941no—
593C2×D4—941no—
594C2×D4—941no—
595C2×D4—941no—
596C2×D4—1882no—
597C2×D4—1882no—
598C2×D4C2×C4×D4712yes—
599C2×D4C2×C4×D4712yes—
600C2×D4D4×D4712yes—
601C2×D4#1062535212yes—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4—941no—
615C22×C4—941no—
616C22×C4—941no—
617C22×C4—3761no—
618C22×C4—3761no—
619C22×C4—1882no—
620C22×C4—1882no—
621C22×C4—1882no—
622C22×C4—1882no—
623C22×C4C2×C4×D4712yes—
624C22×C4#1062535012yes—
625C22×C4C2×C22⋊D4711yescharacteristic
626C22×C4C2×C22⋊D4711yescharacteristic
627C22×C4C2×C22⋊D4711yescharacteristic
628C22×C4C2×C22⋊D4711yescharacteristic
629C22×C4C2×C22⋊D4711yescharacteristic
630C22×C4C23×D4711yescharacteristic
631D8—948no—
632D8—1884no—
633C2×C8—472no—
634C2×C8—472no—
635C2×C8—472no—
636C2×C8—941no—
637C2×C8—941no—
638C2×C8—941no—
639C2×C8—941no—
640C2×C8—941no—
641C2×C8—941no—
642C2×C8—941no—
643C2×C8—941no—
644C2×C8—941no—
645C2×C8—1884no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—472no—
651C4⋊C4—472no—
652C4⋊C4—941no—
653C4⋊C4—941no—
654C4⋊C4—941no—
655C4⋊C4—941no—
656C4⋊C4—1882no—
657C4⋊C4—1882no—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—81no—
666C22⋊C4—81no—
667C22⋊C4—944no—
668C22⋊C4—3761no—
669C22⋊C4—1882no—
670C22⋊C4—1882no—
671C42—21no—
672C42—21no—
673C42—21no—
674C42—21no—
675C42—1882no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—48no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—48no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—84no—
697C23—84no—
698C23—84no—
699C23—84no—
700C23—84no—
701C23—942no—
702C23—1881no—
703C23—1881no—
704C23—1881no—
705C23—1881no—
706C23—1881no—
707C23—1881no—
708C23C4×C22⋊D4712yes—
709C23#1309404912yes—
710C23#1309405012yes—
711C23C22×C22⋊D4711yescharacteristic
712D4—22no—
713D4—22no—
714D4—22no—
715D4—22no—
716D4—22no—
717D4—48no—
718D4—41no—
719D4—41no—
720D4—942no—
721D4—942no—
722D4—1888no—
723D4—1881no—
724D4—1881no—
725D4(C22⋊D47)⋊C414yescomplemented
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—84no—
751C2×C4—84no—
752C2×C4—942no—
753C2×C4—942no—
754C2×C4—3764no—
755C2×C4—3764no—
756C2×C4—1881no—
757C2×C4—1881no—
758C2×C4—1881no—
759C2×C4—1881no—
760C2×C4—1881no—
761C2×C4—1881no—
762C2×C4—1881no—
763C2×C4C4×C22⋊D4712yes—
764C2×C4C22×C4×D4711yescharacteristic
765C2×C4C2×D4×D4711yescharacteristic
766C2×C4C2×#1062535211yescharacteristic
767C2×C4C2×#1062535011yescharacteristic
768C2×C4#1309406911yescharacteristic
769C2×C4#1309406911yescharacteristic
770C8—942no—
771C8—942no—
772C8—942no—
773C8—1881no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—24no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—816no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—3761no—
796C22—3761no—
797C22—3761no—
798C22—3761no—
799C22—1882no—
800C22—1882no—
801C22—1882no—
802C22#1568923314yescomplemented
803C22C2×C4×C22⋊D4711yescharacteristic
804C22D4×C22⋊D4711yescharacteristic
805C22#1568976711yescharacteristic
806C22C2×#1309404911yescharacteristic
807C22C2×#1309405011yescharacteristic
808C22#1568992611yescharacteristic
809C22#1568993411yescharacteristic
810C4—22no—
811C4—41no—
812C4—41no—
813C4—41no—
814C4—41no—
815C4—81no—
816C4—81no—
817C4—3761no—
818C4—1882no—
819C4—1882no—
820C4C2×(C22⋊D47)⋊C411yescharacteristic
821C4#1568959611yescharacteristic
822C4#1568976311yescharacteristic
823C4#1568979911yescharacteristic
824C2—24no—
825C2—44no—
826C2—82no—
827C2—3762no—
828C2#2024636711yescharacteristic
829C2C2×#1568923311yescharacteristic
830C2#2025222011yescharacteristic
831C2#2025486911yescharacteristic
832C2#2025487911yescharacteristic
833C2#2025534911yescharacteristic
834C2#2025552911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingD4×C22⋊C4×C47C2
socleC23×C47C22×D4
prime radicalC2×#15689257C2
cosocleC22×C4×C47C24
hypercenterD4×C22⋊C4D47
hypocenterC47#22858
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#15689233C2semidirect
3. C22×#13093945C2semidirect
4. #20246402C2semidirect
5. #20244263C2semidirect
6. #20244088C2semidirect
7. #20244012C2semidirect
8. #20243814C2semidirect
9. #20243739C2semidirect
10. #20243736C2semidirect
11. #20243649C2semidirect
12. #20243580C2semidirect
13. #20243213C2semidirect
14. #20243166C2semidirect
15. D4×C22⋊C4×C47C2semidirect
20. C2×C4×D188C22semidirect
23. #15689257C4semidirect
25. C2×#13093955C22semidirect
26. C2×#13093955C22semidirect
34. C2×#13093944C22semidirect
35. C2×#13093944C22semidirect
37. C2×#13093935C22semidirect
38. C2×#13093935C22semidirect
39. #15689025C22semidirect
40. #15689021C22semidirect
44. C4×C4⋊Dic47C22semidirect
45. #15688885C22semidirect
46. #15688885C22semidirect
47. #15688885C22semidirect
48. #15688885C22semidirect
49. #15688878C22semidirect
50. #15688878C22semidirect
70. C2×#10625334C2×C4semidirect
71. C2×#10625334C2×C4semidirect
80. #13093998C2×C4semidirect
101. #13093945C2×C4semidirect
102. #13093945C2×C4semidirect
103. #13093945D4semidirect
106. C22⋊(C47⋊C8)C2×C4semidirect
118. C22×D4×C47C2×C4semidirect
302. D4×C47C4×D4semidirect
378. C22×C47#442semidirect
411. D4×C22⋊C4D47semidirect
479. C47#22858semidirect
489. C22×D4C4×D47semidirect
725. D4(C22⋊D47)⋊C4semidirect
802. C22#15689233semidirect

Maximal subgroups

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

subgroupindex
C2×#156892572
C2×#156892332
C22×#130939452
#202464022
#202442632
#202440882
#202440122
#202438142
#202437392
#202437362
#202436492
#202435802
#202432132
#202431662
D4×C22⋊C4×C472
#2285847