Finite Group Databasebeta

← #27081068

Subgroups — #27081068

Order 12032.

2590 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×C4×D4×D47C211yesmaximal, characteristic
2#20252427C212yesmaximal, complemented
3#20252418C218yesmaximal, complemented
4#20252417C211yesmaximal, characteristic, complemented
5#20252416C212yesmaximal, complemented
6#20252410C212yesmaximal, complemented
7#20252121C218yesmaximal, complemented
8#20252018C212yesmaximal, complemented
9C2×#15689085C212yesmaximal, complemented
10#407×D47C212yesmaximal, complemented
11C47×#2973C211yesmaximal, characteristic, complemented
12C22×D4×D47C411yescharacteristic
13C23×C4×D47C2211yescharacteristic
14C23×C4×D47C2211yescharacteristic
15C22×#10625324C2214yescomplemented
16C2×M16×D47C2214yescomplemented
17C2×C4×D188C2211yescharacteristic
18C2×D4×Dic47C411yescharacteristic
19C2×#13093986C411yescharacteristic
20C2×C4×C22⋊D47C2211yescharacteristic
21C2×C4×C22⋊D47C2211yescharacteristic
22C2×(C22⋊D47)⋊C4C411yescharacteristic
23C2×(C22⋊D47)⋊C4C411yescharacteristic
24C4×D4×D47C414yes—
25C4×D4×D47C414yes—
26C4×D4×D47C2214yes—
27C4×D4×D47C2214yes—
28C2×C4⋊C4×D47C411yescharacteristic
29C2×C22⋊C4×D47C411yescharacteristic
30C2×C22⋊C4×D47C411yescharacteristic
31C2×C42×D47C2211yescharacteristic
32#15689199C2218yescomplemented
33#15689198C2218yescomplemented
34#15689196C2218yescomplemented
35#15689195C2218yescomplemented
36#15689193C2218yescomplemented
37C8×C22⋊D47C2218yescomplemented
38(C22⋊D47)⋊C8C2218yescomplemented
39#15689180C2212yescomplemented
40#15689178C2214yescomplemented
41#15689175C2214yescomplemented
42#15689173C2214yescomplemented
43#15689145C2214yescomplemented
44#15689087C2212yescomplemented
45#15689086C2214yescomplemented
46#15689085C2214yes—
47#15689085C2214yescomplemented
48#15689085C2214yescomplemented
49#15689085C2214yescomplemented
50#15689085C2214yescomplemented
51C2×C22⋊(C47⋊C8)C2212yescomplemented
52C2×(C2×D47)⋊C8C2214yescomplemented
53C22⋊C8×D47C2214yescomplemented
54C22⋊C8×D47C2214yescomplemented
55#15689075C2214yescomplemented
56C2×C4×D4×C47C2211yescharacteristic
57C47×#435C2218yescomplemented
58C47×#432C2212yescomplemented
59C47×#407C2212yescomplemented
60C2×C22⋊C8×C47C2212yescomplemented
61C24×D47C2×C411yescharacteristic
62C24×D47C2×C411yescharacteristic
63C22×D188C2×C411yescharacteristic
64C22×C22⋊D47C2×C411yescharacteristic
65C22×C22⋊D47C2×C411yescharacteristic
66C2×D4×D47—28no—
67C2×D4×D47C2×C414yes—
68C2×D4×D47C2×C414yes—
69C23×Dic47C2×C411yescharacteristic
70C23×Dic47C2×C411yescharacteristic
71C22×C4×D47—44no—
72C22×C4×D47—44no—
73C22×C4×D47C2×C411yescharacteristic
74C22×C4×D47C2×C411yescharacteristic
75C22×C4×D47C2×C411yescharacteristic
76C22×C4×D47C2×C411yescharacteristic
77C22×C4×D47C2×C412yes—
78C22×C4×D47C2×C412yes—
79C22×C4×D47C2×C412yes—
80C22×C4×D47C2×C412yes—
81C22×C4×D47C2×C411yescharacteristic
82C22×C4×D47C2×C411yescharacteristic
83C22×C4×D47C2311yescharacteristic
84C22×C4×D47C2312yes—
85C22×C4×D47C2312yes—
86C22×C4×D47C2312yes—
87C22×C4×D47C2312yes—
88C22×C4×D47C2311yescharacteristic
89C22×C4×D47C2311yescharacteristic
90C2×#10625329C2314yescomplemented
91C2×#10625324—48no—
92C2×#10625324C2318yes—
93C2×#10625324C2318yescomplemented
94M16×D47—48no—
95C22×C47⋊C8C2314yescomplemented
96C2×C8×D47C2318yescomplemented
97C4×D188C2×C414yes—
98C4×D188C2314yes—
99D4×Dic47C2×C414yes—
100D4×Dic47C2×C414yes—
101#13093986C2×C414yes—
102#13093986C2×C414yes—
103C4×C22⋊D47C2×C414yes—
104C4×C22⋊D47C2×C414yes—
105C4×C22⋊D47C2314yes—
106C4×C22⋊D47C2314yes—
107(C22⋊D47)⋊C4C2×C414yes—
108(C22⋊D47)⋊C4C2×C414yes—
109(C22⋊D47)⋊C4C2×C414yes—
110(C22⋊D47)⋊C4C2×C414yes—
111C2×C4⋊Dic47C2×C411yescharacteristic
112C2×Dic47⋊C4C2×C411yescharacteristic
113C2×Dic47⋊C4C2×C411yescharacteristic
114C4⋊C4×D47C2×C414yes—
115C4⋊C4×D47C2×C414yes—
116C2×C22⋊Dic47C2×C411yescharacteristic
117C2×C22⋊Dic47C2×C411yescharacteristic
118C2×(C2×D47)⋊C4C2×C411yescharacteristic
119C2×(C2×D47)⋊C4C2×C411yescharacteristic
120C2×(C2×D47)⋊C4C2×C411yescharacteristic
121C2×(C2×D47)⋊C4C2×C411yescharacteristic
122C22⋊C4×D47C2×C414yes—
123C22⋊C4×D47C2×C414yes—
124C22⋊C4×D47C2×C414yes—
125C22⋊C4×D47C2×C414yes—
126C2×C4×Dic47C2×C411yescharacteristic
127C2×C4×Dic47C2×C411yescharacteristic
128C2×C4×Dic47C2311yescharacteristic
129C42×D47C2×C412yes—
130C42×D47C2×C412yes—
131C42×D47C2312yes—
132C42×D47C2312yes—
133C4⋊(C47⋊C8)C2314yescomplemented
134Dic47⋊C8C2318yescomplemented
135C22⋊(C47⋊C8)C2314yes—
136C22⋊(C47⋊C8)C2314yescomplemented
137C22⋊(C47⋊C8)C2314yescomplemented
138(C2×D47)⋊C8C2318yes—
139(C2×D47)⋊C8C2318yescomplemented
140(C2×D47)⋊C8C2318yescomplemented
141#13093935C2314yescomplemented
142C8×Dic47C2318yescomplemented
143C22×D4×C47C2×C411yescharacteristic
144C23×C4×C47C2311yescharacteristic
145C23×C4×C47C2311yescharacteristic
146C2×M16×C47C2314yescomplemented
147C22×C8×C47C2314yescomplemented
148C4×D4×C47C2×C414yes—
149C4×D4×C47C2314yes—
150C2×C4⋊C4×C47C2×C411yescharacteristic
151C2×C22⋊C4×C47C2×C411yescharacteristic
152C2×C22⋊C4×C47C2×C411yescharacteristic
153C2×C42×C47C2311yescharacteristic
154C4⋊C8×C47C2314yescomplemented
155C22⋊C8×C47C2314yes—
156C22⋊C8×C47C2314yescomplemented
157C22⋊C8×C47C2314yescomplemented
158#97×C47C2314yescomplemented
159C24×C47C22×C411yescharacteristic
160C24×C47C22×C411yescharacteristic
161C23×D47—24no—
162C23×D47—24no—
163C23×D47—42no—
164C23×D47—42no—
165C23×D47—42no—
166C23×D47—42no—
167C23×D47C22×C411yescharacteristic
168C23×D47C22×C412yes—
169C23×D47C22×C412yes—
170C23×D47C22×C412yes—
171C23×D47C22×C412yes—
172C23×D47C22×C411yescharacteristic
173C23×D47C22×C411yescharacteristic
174C2×D4×C47—24no—
175C2×D4×C47C22×C414yes—
176C22×C4×C47—42no—
177C22×C4×C47—42no—
178C22×C4×C47C22×C411yescharacteristic
179C22×C4×C47C22×C411yescharacteristic
180C22×C4×C47C22×C411yescharacteristic
181C22×C4×C47C22×C411yescharacteristic
182C22×C4×C47C22×C412yes—
183C22×C4×C47C22×C412yes—
184C22×C4×C47C2411yescharacteristic
185C22×C4×C47C2412yes—
186C22×C4×C47C2412yes—
187C2×C22⋊D47—24no—
188C2×C22⋊D47M1618yescomplemented
189C2×C22⋊D47C22×C414yes—
190C2×C22⋊D47C22×C414yes—
191C22×Dic47—42no—
192C22×Dic47—42no—
193C22×Dic47C22×C411yescharacteristic
194C22×Dic47C22×C412yes—
195C22×Dic47C22×C412yes—
196C22×Dic47C22×C411yescharacteristic
197C22×Dic47C22×C411yescharacteristic
198C22×Dic47C22×C411yescharacteristic
199C22×Dic47C22×C412yes—
200C22×Dic47C22×C412yes—
201C22×Dic47C22×C411yescharacteristic
202D4×D47—216no—
203D4×D47—216no—
204C2×D188—24no—
205C2×D188C22×C414yes—
206C2×C4×D47—24no—
207C2×C4×D47—28no—
208C2×C4×D47—28no—
209C2×C4×D47—24no—
210C2×C4×D47—44no—
211C2×C4×D47—44no—
212C2×C4×D47—42no—
213C2×C4×D47—42no—
214C2×C4×D47—42no—
215C2×C4×D47—44no—
216C2×C4×D47—42no—
217C2×C4×D47—44no—
218C2×C4×D47—44no—
219C2×C4×D47—44no—
220C2×C4×D47—42no—
221C2×C4×D47—42no—
222C2×C4×D47—42no—
223C2×C4×D47C22×C411yescharacteristic
224C2×C4×D47C22×C411yescharacteristic
225C2×C4×D47C22×C412yes—
226C2×C4×D47C22×C412yes—
227C2×C4×D47C22×C412yes—
228C2×C4×D47C22×C412yes—
229C2×C4×D47C22×C412yes—
230C2×C4×D47C22×C412yes—
231C2×C4×D47C22×C412yes—
232C2×C4×D47C22×C412yes—
233C2×C4×D47C22×C412yes—
234C2×C4×D47C22×C412yes—
235C2×C4×D47C22×C412yes—
236C2×C4×D47C22×C412yes—
237C2×C4×D47C22×C412yes—
238C2×C4×D47C22×C412yes—
239C2×C4×D47C2411yescharacteristic
240C2×C4×D47C2412yes—
241C2×C4×D47C2412yes—
242C2×C4×D47C2411yescharacteristic
243M16×C47—44no—
244C2×C8×C47—44no—
245C2×C8×C47C2418yes—
246C4⋊C4×C47C22×C414yes—
247C22⋊C4×C47C22×C414yes—
248C22⋊C4×C47C22×C414yes—
249C42×C47C22×C412yes—
250C42×C47C2412yes—
251C22⋊Dic47C22×C414yes—
252C22⋊Dic47C22×C414yes—
253(C2×D47)⋊C4C22×C414yes—
254(C2×D47)⋊C4C22×C414yes—
255(C2×D47)⋊C4C22×C414yes—
256(C2×D47)⋊C4C22×C414yes—
257C4⋊Dic47C22×C414yes—
258Dic47⋊C4C22×C414yes—
259Dic47⋊C4C22×C414yes—
260C4×Dic47C22×C412yes—
261C4×Dic47C22×C412yes—
262C4×Dic47C22×C412yes—
263C4×Dic47C22×C412yes—
264C4×Dic47C22×C412yes—
265C4×Dic47C2412yes—
266#10625329—44no—
267C2×C47⋊C8—44no—
268C2×C47⋊C8C2418yes—
269#10625324—216no—
270#10625324—48no—
271C8×D47—48no—
272C23×C47—22no—
273C23×C47—41no—
274C23×C47—41no—
275C23×C47—41no—
276C23×C47—41no—
277C23×C47C2×M1614yescomplemented
278C23×C47C23×C412yes—
279C23×C47C23×C412yes—
280C23×C47C23×C411yescharacteristic
281C22×D47—22no—
282C22×D47—22no—
283C22×D47—22no—
284C22×D47—22no—
285C22×D47—24no—
286C22×D47—24no—
287C22×D47—24no—
288C22×D47—24no—
289C22×D47—24no—
290C22×D47—24no—
291C22×D47—24no—
292C22×D47—24no—
293C22×D47—42no—
294C22×D47—42no—
295C22×D47—41no—
296C22×D47—41no—
297C22×D47—42no—
298C22×D47—42no—
299C22×D47—41no—
300C22×D47—41no—
301C22×D47—416no—
302C22×D47—416no—
303C22×D47C2×M1614yescomplemented
304C22×D47C23×C412yes—
305C22×D47C23×C411yescharacteristic
306C22×D47C23×C412yes—
307C22×D47C23×C411yescharacteristic
308D4×C47—28no—
309C2×C4×C47—22no—
310C2×C4×C47—24no—
311C2×C4×C47—24no—
312C2×C4×C47—22no—
313C2×C4×C47—42no—
314C2×C4×C47—42no—
315C2×C4×C47—41no—
316C2×C4×C47—41no—
317C2×C4×C47—41no—
318C2×C4×C47C23×C412yes—
319C2×C4×C47C23×C412yes—
320C2×C4×C47C23×C411yescharacteristic
321C2×C4×C47C23×C412yes—
322C2×C4×C47C23×C412yes—
323C2×C4×C47C2511yescharacteristic
324C22⋊D47—28no—
325C22⋊D47C2×M16116yescomplemented
326C2×Dic47—22no—
327C2×Dic47—24no—
328C2×Dic47—24no—
329C2×Dic47—42no—
330C2×Dic47—42no—
331C2×Dic47—41no—
332C2×Dic47—41no—
333C2×Dic47—41no—
334C2×Dic47C2×M1614yescomplemented
335C2×Dic47C23×C411yescharacteristic
336C2×Dic47C23×C412yes—
337C2×Dic47C23×C412yes—
338C2×Dic47C23×C412yes—
339C2×Dic47C23×C411yescharacteristic
340C2×Dic47C23×C412yes—
341D188—28no—
342C4×D47—22no—
343C4×D47—24no—
344C4×D47—24no—
345C4×D47—24no—
346C4×D47—24no—
347C4×D47—24no—
348C4×D47—22no—
349C4×D47—22no—
350C4×D47—24no—
351C4×D47—24no—
352C4×D47—24no—
353C4×D47—24no—
354C4×D47—42no—
355C4×D47—42no—
356C4×D47—42no—
357C4×D47—42no—
358C4×D47—42no—
359C4×D47—42no—
360C4×D47—42no—
361C4×D47H(5,𝔽2)14yes—
362C8×C47—28no—
363C47⋊C8—28no—
364#60230—471nomaximal, Sylow
365C22×C47—21no—
366C22×C47—22no—
367C22×C47—21no—
368C22×C47—22no—
369C22×C47—22no—
370C22×C47—22no—
371C22×C47—22no—
372C22×C47—44no—
373C22×C47—44no—
374C22×C47C22×M1612yes—
375C22×C47C22×M1614yes—
376C22×C47C24×C411yescharacteristic
377C2×D47—28no—
378C2×D47—21no—
379C2×D47—22no—
380C2×D47—21no—
381C2×D47—21no—
382C2×D47—21no—
383C2×D47—22no—
384C2×D47—22no—
385C2×D47—22no—
386C2×D47—22no—
387C2×D47—44no—
388C2×D47—48no—
389C2×D47—48no—
390C2×D47—48no—
391C2×D47—48no—
392C2×D47—44no—
393C2×D47#51812yes—
394C2×D47C22×M1614yes—
395C2×D47#56812yes—
396C4×C47—21no—
397C4×C47—22no—
398C4×C47—22no—
399C4×C47—22no—
400C4×C47—22no—
401C4×C47C2×H(5,𝔽2)12yes—
402Dic47—21no—
403Dic47—22no—
404Dic47—22no—
405Dic47—22no—
406Dic47#51812yes—
407Dic47C22×M1614yes—
408C22×C4×D4—471no—
409#2975—472no—
410#2974—478no—
411#2973—472no—
412#2973—471no—
413#2973D4711yescharacteristic, complemented
414#2972—472no—
415D4×M16—478no—
416#2920—472no—
417C2×#407—472no—
418C2×#407—472no—
419C2×C47—22no—
420C2×C47—24no—
421C2×C47—42no—
422C2×C47C2×#51811yescharacteristic
423C2×C47C23×M1611yescharacteristic
424C2×C47C2×#56811yescharacteristic
425D47—22no—
426D47—22no—
427D47—24no—
428D47—42no—
429C23×D4—471no—
430C24×C4—471no—
431C24×C4—471no—
432C22×M16—474no—
433C22×M16—474no—
434C2×C4×D4—471no—
435C2×C4×D4—471no—
436C2×C4×D4—471no—
437C2×C4×D4—474no—
438C2×C4×D4—474no—
439C2×C4×D4—474no—
440C2×C4×D4—474no—
441C2×C4×D4—471no—
442C2×C4×D4—471no—
443C2×C4×D4—471no—
444C2×C4×D4—471no—
445C2×C4×D4C2×D4711yescharacteristic
446C22×C4⋊C4—471no—
447C22×C22⋊C4—471no—
448C22×C22⋊C4—471no—
449C22×C42—471no—
450#436—478no—
451#436—478no—
452#435—478no—
453#435—478no—
454#435—478no—
455#435C2×D4718yescomplemented
456C8×D4—478no—
457C8×D4—478no—
458#432—472no—
459#432—474no—
460#432C2×D4712yescomplemented
461#431—474no—
462#431—474no—
463#423—474no—
464#407—472no—
465#407—474no—
466#407—474no—
467#407—474no—
468#407—474no—
469#407—474no—
470#407—474no—
471#407C2×D4712yescomplemented
472C2×C22⋊C8—472no—
473C2×C22⋊C8—474no—
474C2×C22⋊C8—474no—
475C2×C22⋊C8—474no—
476C2×C22⋊C8C2×D4712yescomplemented
477C4×M16—474no—
478C47#6023011yescharacteristic, complemented, Sylow
479C25—471no—
480C25—471no—
481C22×D4—471no—
482C22×D4—471no—
483C22×D4—474no—
484C22×D4—474no—
485C22×D4—471no—
486C22×D4—948no—
487C22×D4C4×D4711yescharacteristic
488C23×C4—471no—
489C23×C4—471no—
490C23×C4—471no—
491C23×C4—472no—
492C23×C4—472no—
493C23×C4—471no—
494C23×C4—471no—
495C23×C4—471no—
496C23×C4—471no—
497C23×C4—471no—
498C23×C4—471no—
499C23×C4—472no—
500C23×C4—472no—
501C23×C4—472no—
502C23×C4—472no—
503C23×C4—471no—
504C23×C4—472no—
505C23×C4—472no—
506C23×C4—471no—
507C23×C4—1884no—
508C23×C4—1884no—
509C23×C4C22×D4711yescharacteristic
510C23×C4C22×D4711yescharacteristic
511C2×M16—474no—
512C2×M16—478no—
513C2×M16—478no—
514C2×M16—1888no—
515C2×M16—1888no—
516C2×M16C22×D4714yescomplemented
517C22×C8—474no—
518C22×C8—478no—
519C22×C8C22×D4714yescomplemented
520C4×D4—474no—
521C4×D4—474no—
522C4×D4—474no—
523C4×D4—474no—
524C4×D4—474no—
525C4×D4—474no—
526C4×D4—474no—
527C4×D4—474no—
528C4×D4—474no—
529C4×D4—474no—
530C4×D4—474no—
531C4×D4—474no—
532C4×D4—474no—
533C4×D4—474no—
534C4×D4C4×D4714yes—
535C4×D4C22×D4714yes—
536C2×C4⋊C4—471no—
537C2×C4⋊C4—471no—
538C2×C4⋊C4—471no—
539C2×C4⋊C4—474no—
540C2×C4⋊C4—474no—
541C2×C4⋊C4C4×D4711yescharacteristic
542C2×C22⋊C4—471no—
543C2×C22⋊C4—471no—
544C2×C22⋊C4—471no—
545C2×C22⋊C4—471no—
546C2×C22⋊C4—471no—
547C2×C22⋊C4—471no—
548C2×C22⋊C4—474no—
549C2×C22⋊C4—474no—
550C2×C22⋊C4—474no—
551C2×C22⋊C4—474no—
552C2×C22⋊C4C4×D4711yescharacteristic
553C2×C22⋊C4C4×D4711yescharacteristic
554C2×C42—471no—
555C2×C42—471no—
556C2×C42—471no—
557C2×C42—472no—
558C2×C42—472no—
559C2×C42—472no—
560C2×C42—472no—
561C2×C42C22×D4711yescharacteristic
562C4⋊C8—478no—
563C4⋊C8—474no—
564C4⋊C8C22×D4714yescomplemented
565C22⋊C8—474no—
566C22⋊C8—474no—
567C22⋊C8—474no—
568C22⋊C8—478no—
569C22⋊C8—478no—
570C22⋊C8—478no—
571C22⋊C8C22×D4714yes—
572C22⋊C8C22×D4714yescomplemented
573C22⋊C8C22×D4714yescomplemented
574#97—474no—
575#97C22×D4714yescomplemented
576C4×C8—478no—
577C24—471no—
578C24—471no—
579C24—472no—
580C24—472no—
581C24—472no—
582C24—472no—
583C24—471no—
584C24—944no—
585C24—944no—
586C24—1882no—
587C24—1882no—
588C24—1882no—
589C24—1882no—
590C24C2×C4×D4711yescharacteristic
591C24C2×C4×D4711yescharacteristic
592C2×D4—24no—
593C2×D4—478no—
594C2×D4—474no—
595C2×D4—474no—
596C2×D4—474no—
597C2×D4—944no—
598C2×D4—944no—
599C2×D4—9416no—
600C2×D4—9416no—
601C2×D4C2×C4×D4714yes—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—471no—
605C22×C4—471no—
606C22×C4—471no—
607C22×C4—472no—
608C22×C4—472no—
609C22×C4—471no—
610C22×C4—471no—
611C22×C4—471no—
612C22×C4—472no—
613C22×C4—472no—
614C22×C4—472no—
615C22×C4—472no—
616C22×C4—472no—
617C22×C4—471no—
618C22×C4—471no—
619C22×C4—472no—
620C22×C4—472no—
621C22×C4—472no—
622C22×C4—472no—
623C22×C4—471no—
624C22×C4—472no—
625C22×C4—472no—
626C22×C4—472no—
627C22×C4—472no—
628C22×C4—472no—
629C22×C4—472no—
630C22×C4—472no—
631C22×C4—472no—
632C22×C4—472no—
633C22×C4—948no—
634C22×C4—948no—
635C22×C4—944no—
636C22×C4—944no—
637C22×C4—1884no—
638C22×C4—1884no—
639C22×C4—1882no—
640C22×C4—1882no—
641C22×C4—1882no—
642C22×C4—1882no—
643C22×C4—1884no—
644C22×C4—1884no—
645C22×C4—1882no—
646C22×C4—1882no—
647C22×C4—1882no—
648C22×C4—1884no—
649C22×C4—1884no—
650C22×C4—1882no—
651C22×C4—1882no—
652C22×C4C2×C4×D4711yescharacteristic
653C22×C4C2×C4×D4711yescharacteristic
654C22×C4C2×C4×D4711yescharacteristic
655C22×C4C2×C4×D4711yescharacteristic
656C22×C4C2×C4×D4712yes—
657C22×C4C2×C4×D4712yes—
658C22×C4C23×D4711yescharacteristic
659C22×C4C23×D4712yes—
660C22×C4C23×D4712yes—
661M16—44no—
662M16—9416no—
663M16—1888no—
664M16—1884no—
665C2×C8—44no—
666C2×C8—478no—
667C2×C8—1888no—
668C2×C8—1884no—
669C2×C8C23×D4718yes—
670C4⋊C4—474no—
671C4⋊C4—474no—
672C4⋊C4—474no—
673C4⋊C4C2×C4×D4714yes—
674C22⋊C4—474no—
675C22⋊C4—474no—
676C22⋊C4—474no—
677C22⋊C4—474no—
678C22⋊C4—474no—
679C22⋊C4—474no—
680C22⋊C4C2×C4×D4714yes—
681C22⋊C4C2×C4×D4714yes—
682C42—472no—
683C42—472no—
684C42—472no—
685C42—472no—
686C42—472no—
687C42—472no—
688C42C2×C4×D4712yes—
689C42C23×D4712yes—
690C23—22no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—472no—
696C23—471no—
697C23—471no—
698C23—474no—
699C23—472no—
700C23—942no—
701C23—942no—
702C23—944no—
703C23—944no—
704C23—944no—
705C23—944no—
706C23—944no—
707C23—944no—
708C23—942no—
709C23—944no—
710C23—944no—
711C23—942no—
712C23—1881no—
713C23—1881no—
714C23—1882no—
715C23—1882no—
716C23—1881no—
717C23—1881no—
718C23—1882no—
719C23—1882no—
720C23—18816no—
721C23—18816no—
722C23M16×D4714yescomplemented
723C23C22×C4×D4712yes—
724C23C22×C4×D4712yes—
725C23C22×C4×D4711yescharacteristic
726D4—28no—
727D4—4716no—
728D4—948no—
729D4—948no—
730C2×C4—22no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—22no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—474no—
740C2×C4—472no—
741C2×C4—471no—
742C2×C4—474no—
743C2×C4—472no—
744C2×C4—471no—
745C2×C4—472no—
746C2×C4—472no—
747C2×C4—944no—
748C2×C4—944no—
749C2×C4—942no—
750C2×C4—944no—
751C2×C4—944no—
752C2×C4—944no—
753C2×C4—944no—
754C2×C4—942no—
755C2×C4—944no—
756C2×C4—944no—
757C2×C4—944no—
758C2×C4—942no—
759C2×C4—944no—
760C2×C4—944no—
761C2×C4—942no—
762C2×C4—1882no—
763C2×C4—1882no—
764C2×C4—1882no—
765C2×C4—1882no—
766C2×C4—1882no—
767C2×C4—1882no—
768C2×C4—1882no—
769C2×C4—1881no—
770C2×C4—1882no—
771C2×C4—1882no—
772C2×C4—1881no—
773C2×C4—1881no—
774C2×C4C22×C4×D4711yescharacteristic
775C2×C4C22×C4×D4712yes—
776C2×C4C22×C4×D4712yes—
777C2×C4C22×C4×D4712yes—
778C2×C4C22×C4×D4712yes—
779C2×C4C24×D4711yescharacteristic
780C8—28no—
781C8—948no—
782C22—21no—
783C22—22no—
784C22—21no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—44no—
790C22—44no—
791C22—474no—
792C22—472no—
793C22—472no—
794C22—948no—
795C22—941no—
796C22—941no—
797C22—941no—
798C22—942no—
799C22—941no—
800C22—942no—
801C22—942no—
802C22—942no—
803C22—942no—
804C22—1884no—
805C22—1888no—
806C22—1888no—
807C22—1884no—
808C22—1888no—
809C22—1888no—
810C22C2×M16×D4712yes—
811C22C2×M16×D4714yes—
812C22C23×C4×D4711yescharacteristic
813C4—22no—
814C4—22no—
815C4—21no—
816C4—22no—
817C4—22no—
818C4—474no—
819C4—472no—
820C4—942no—
821C4—941no—
822C4—942no—
823C4—942no—
824C4H(5,𝔽2)×D4712yes—
825C2—22no—
826C2—24no—
827C2—42no—
828C2—942no—
829C2—942no—
830C2—944no—
831C2—1882no—
832C2#518×D4711yescharacteristic
833C2C22×M16×D4711yescharacteristic
834C2#568×D4711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D47
commutator, socleC22×C47C24×C4
FittingC47×#2973C2
prime radicalC22×D4×D47C4
cosocleC2×C4×C47C25
hypercenter#2973D47
hypocenterC47#60230
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ #2973

Complements

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

NH ≅ G/Ntype
2. #20252427C2semidirect
3. #20252418C2semidirect
4. #20252417C2semidirect
5. #20252416C2semidirect
6. #20252410C2semidirect
7. #20252121C2semidirect
8. #20252018C2semidirect
9. C2×#15689085C2semidirect
10. #407×D47C2semidirect
11. C47×#2973C2semidirect
15. C22×#10625324C22semidirect
16. C2×M16×D47C22semidirect
32. #15689199C22semidirect
33. #15689198C22semidirect
34. #15689196C22semidirect
35. #15689195C22semidirect
36. #15689193C22semidirect
37. C8×C22⋊D47C22semidirect
38. (C22⋊D47)⋊C8C22semidirect
39. #15689180C22semidirect
40. #15689178C22semidirect
41. #15689175C22semidirect
42. #15689173C22semidirect
43. #15689145C22semidirect
44. #15689087C22semidirect
45. #15689086C22semidirect
47. #15689085C22semidirect
48. #15689085C22semidirect
49. #15689085C22semidirect
50. #15689085C22semidirect
51. C2×C22⋊(C47⋊C8)C22semidirect
52. C2×(C2×D47)⋊C8C22semidirect
53. C22⋊C8×D47C22semidirect
54. C22⋊C8×D47C22semidirect
55. #15689075C22semidirect
57. C47×#435C22semidirect
58. C47×#432C22semidirect
59. C47×#407C22semidirect
60. C2×C22⋊C8×C47C22semidirect
90. C2×#10625329C23semidirect
93. C2×#10625324C23semidirect
95. C22×C47⋊C8C23semidirect
96. C2×C8×D47C23semidirect
133. C4⋊(C47⋊C8)C23semidirect
134. Dic47⋊C8C23semidirect
136. C22⋊(C47⋊C8)C23semidirect
137. C22⋊(C47⋊C8)C23semidirect
139. (C2×D47)⋊C8C23semidirect
140. (C2×D47)⋊C8C23semidirect
141. #13093935C23semidirect
142. C8×Dic47C23semidirect
146. C2×M16×C47C23semidirect
147. C22×C8×C47C23semidirect
154. C4⋊C8×C47C23semidirect
156. C22⋊C8×C47C23semidirect
157. C22⋊C8×C47C23semidirect
158. #97×C47C23semidirect
188. C2×C22⋊D47M16semidirect
277. C23×C47C2×M16semidirect
303. C22×D47C2×M16semidirect
325. C22⋊D47C2×M16semidirect
334. C2×Dic47C2×M16semidirect
413. #2973D47semidirect
455. #435C2×D47semidirect
460. #432C2×D47semidirect
471. #407C2×D47semidirect
476. C2×C22⋊C8C2×D47semidirect
478. C47#60230semidirect
516. C2×M16C22×D47semidirect
519. C22×C8C22×D47semidirect
564. C4⋊C8C22×D47semidirect
572. C22⋊C8C22×D47semidirect
573. C22⋊C8C22×D47semidirect
575. #97C22×D47semidirect
722. C23M16×D47semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D472
#202524272
#202524182
#202524172
#202524162
#202524102
#202521212
#202520182
C2×#156890852
#407×D472
C47×#29732
#6023047