Finite Group Databasebeta

← C2×#20245915 #26374719

Subgroups — C2×#20245915 #26374719

Order 12032.

4070 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094006C211yesmaximal, characteristic
2C22×(C22⋊D47)⋊C4C211yesmaximal, characteristic
3C22×C42×D47C211yesmaximal, characteristic, complemented
4#20245915C2116yesmaximal, direct product factor
5C2×#15689011C211yesmaximal, characteristic, complemented
6C2×#15689008C211yesmaximal, characteristic, complemented
7C2×#15689007C211yesmaximal, characteristic, complemented
8C2×#15688999C211yesmaximal, characteristic
9C2×#15688994C211yesmaximal, characteristic, complemented
10C2×#15688985C211yesmaximal, characteristic, complemented
11C2×C4⋊C4×Dic47C211yesmaximal, characteristic, complemented
12C2×#15688974C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×Dic47C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic47C211yesmaximal, characteristic, complemented
15C2×#15688970C211yesmaximal, characteristic, complemented
16C2×C47×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D47C2211yescharacteristic
18C24×Dic47C2211yescharacteristic
19C23×C4×D47C2211yescharacteristic
20C23×C4×D47C2211yescharacteristic
21C23×C4×D47C2211yescharacteristic
22C2×#13094006C4116yescomplemented
23C2×#13094006C2218yes—
24C2×(C22⋊D47)⋊C4—28no—
25C2×(C22⋊D47)⋊C4C2218yes—
26C22×C4⋊Dic47C2211yescharacteristic
27C22×Dic47⋊C4C2211yescharacteristic
28C22×Dic47⋊C4C2211yescharacteristic
29C22×Dic47⋊C4C2211yescharacteristic
30C22×C22⋊Dic47C2211yescharacteristic
31C22×C22⋊Dic47C2211yescharacteristic
32C22×(C2×D47)⋊C4C2211yescharacteristic
33C22×(C2×D47)⋊C4C2211yescharacteristic
34C22×(C2×D47)⋊C4C2211yescharacteristic
35C22×C4×Dic47C2211yescharacteristic
36C22×C4×Dic47C2211yescharacteristic
37C22×C4×Dic47C2211yescharacteristic
38C22×C4×Dic47C2211yescharacteristic
39C22×C4×Dic47C2211yescharacteristic
40C22×C4×Dic47C2211yescharacteristic
41C2×C42×D47—28no—
42C2×C42×D47C2218yescomplemented
43#15689011C2218yescomplemented
44#15689008C2218yescomplemented
45#15689007C2218yescomplemented
46#15688999C2218yes—
47#15688994C2218yescomplemented
48#15688985C2218yescomplemented
49C4⋊C4×Dic47C2218yescomplemented
50#15688974C2218yescomplemented
51C22⋊C4×Dic47C2218yescomplemented
52C22⋊C4×Dic47C2218yescomplemented
53#15688970C2218yescomplemented
54C2×C47⋊#95C2211yescharacteristic
55C2×C47⋊#95C2211yescharacteristic
56C2×C47⋊#95C2211yescharacteristic
57C2×C47⋊#95C2211yescharacteristic
58C2×C47⋊#95C2211yescharacteristic
59C2×C47⋊#95C2211yescharacteristic
60C2×C47⋊#95C2211yescharacteristic
61C2×C47⋊#95C2211yescharacteristic
62C22×C4⋊C4×C47C2211yescharacteristic
63C22×C22⋊C4×C47C2211yescharacteristic
64C22×C22⋊C4×C47C2211yescharacteristic
65C22×C22⋊C4×C47C2211yescharacteristic
66C22×C42×C47C2211yescharacteristic
67C47×#388C2218yescomplemented
68C2×#95×C47C2211yescharacteristic
69C2×#95×C47C2211yescharacteristic
70C24×D47C2311yescharacteristic
71C22×C22⋊D47—24no—
72C22×C22⋊D47—24no—
73C22×C22⋊D47C2×C418yes—
74C22×C22⋊D47C2314yes—
75C23×Dic47—24no—
76C23×Dic47—24no—
77C23×Dic47—24no—
78C23×Dic47C2311yescharacteristic
79C23×Dic47C2311yescharacteristic
80C23×Dic47C2314yes—
81C23×Dic47C2311yescharacteristic
82C23×Dic47C2311yescharacteristic
83C23×Dic47C2311yescharacteristic
84C23×Dic47C2311yescharacteristic
85C23×Dic47C2311yescharacteristic
86C22×C4×D47—24no—
87C22×C4×D47—24no—
88C22×C4×D47—24no—
89C22×C4×D47—24no—
90C22×C4×D47—24no—
91C22×C4×D47—24no—
92C22×C4×D47—24no—
93C22×C4×D47C2×C418yescomplemented
94C22×C4×D47D418yes—
95C22×C4×D47C2314yes—
96C22×C4×D47C2314yes—
97C22×C4×D47C2314yes—
98#13094006C2×C4164yescomplemented
99(C22⋊D47)⋊C4—232no—
100C2×C4⋊Dic47C2×C418yescomplemented
101C2×C4⋊Dic47C2314yes—
102C2×Dic47⋊C4—24no—
103C2×Dic47⋊C4—24no—
104C2×Dic47⋊C4C2×C418yescomplemented
105C2×Dic47⋊C4C2314yes—
106C2×Dic47⋊C4C2314yes—
107C2×Dic47⋊C4C2314yes—
108C2×C22⋊Dic47—24no—
109C2×C22⋊Dic47C2×C418yescomplemented
110C2×C22⋊Dic47C2314yes—
111C2×C22⋊Dic47C2314yes—
112C2×(C2×D47)⋊C4—24no—
113C2×(C2×D47)⋊C4—24no—
114C2×(C2×D47)⋊C4C2×C418yescomplemented
115C2×(C2×D47)⋊C4C2314yes—
116C2×(C2×D47)⋊C4C2314yes—
117C2×(C2×D47)⋊C4C2314yes—
118C2×C4×Dic47—24no—
119C2×C4×Dic47—24no—
120C2×C4×Dic47—24no—
121C2×C4×Dic47—24no—
122C2×C4×Dic47—24no—
123C2×C4×Dic47—24no—
124C2×C4×Dic47C2314yes—
125C2×C4×Dic47C2314yes—
126C2×C4×Dic47C2314yes—
127C2×C4×Dic47C2314yes—
128C2×C4×Dic47C2314yes—
129C2×C4×Dic47C2314yes—
130C42×D47—232no—
131C47⋊#95C2314yes—
132C47⋊#95C2314yes—
133C47⋊#95C2314yes—
134C47⋊#95C2314yes—
135C47⋊#95C2314yes—
136C47⋊#95C2314yes—
137C47⋊#95C2314yes—
138C47⋊#95C2314yes—
139C25×C47C2311yescharacteristic
140C23×C4×C47C2311yescharacteristic
141C23×C4×C47C2311yescharacteristic
142C23×C4×C47C2311yescharacteristic
143C23×C4×C47C2311yescharacteristic
144C23×C4×C47C2311yescharacteristic
145C23×C4×C47C2311yescharacteristic
146C2×C4⋊C4×C47—24no—
147C2×C4⋊C4×C47C2314yes—
148C2×C22⋊C4×C47—24no—
149C2×C22⋊C4×C47—24no—
150C2×C22⋊C4×C47C2×C418yescomplemented
151C2×C22⋊C4×C47C2314yes—
152C2×C22⋊C4×C47C2314yes—
153C2×C22⋊C4×C47C2314yes—
154C2×C42×C47—24no—
155C2×C42×C47C2314yes—
156#95×C47C2314yes—
157#95×C47C2314yes—
158C24×C47—22no—
159C24×C47—22no—
160C24×C47—22no—
161C24×C47—22no—
162C24×C47—22no—
163C24×C47—22no—
164C24×C47C22×C414yes—
165C24×C47C2412yes—
166C24×C47C2411yescharacteristic
167C23×D47—22no—
168C23×D47—22no—
169C23×D47—22no—
170C23×D47—22no—
171C23×D47C22×C414yes—
172C23×D47C2×D414yes—
173C23×D47#4114yes—
174C23×D47C2412yes—
175C22×C4×C47—22no—
176C22×C4×C47—22no—
177C22×C4×C47—22no—
178C22×C4×C47—22no—
179C22×C4×C47—22no—
180C22×C4×C47—22no—
181C22×C4×C47—22no—
182C22×C4×C47—22no—
183C22×C4×C47—22no—
184C22×C4×C47—22no—
185C22×C4×C47—22no—
186C22×C4×C47—22no—
187C22×C4×C47—22no—
188C22×C4×C47—22no—
189C22×C4×C47C22×C414yes—
190C22×C4×C47C22×C414yes—
191C22×C4×C47C2×D414yes—
192C22×C4×C47#4114yes—
193C22×C4×C47C2412yes—
194C22×C4×C47C2412yes—
195C22×C4×C47C2412yes—
196C22×C4×C47C2412yes—
197C22×C4×C47C2412yes—
198C22×C4×C47C2412yes—
199C2×C22⋊D47—232no—
200C2×C22⋊D47—28no—
201C2×C22⋊D47—28no—
202C2×C22⋊D47C22×C4116yes—
203C22×Dic47—22no—
204C22×Dic47—22no—
205C22×Dic47—22no—
206C22×Dic47—22no—
207C22×Dic47—22no—
208C22×Dic47—22no—
209C22×Dic47—22no—
210C22×Dic47—22no—
211C22×Dic47—22no—
212C22×Dic47—22no—
213C22×Dic47—22no—
214C22×Dic47—22no—
215C22×Dic47—22no—
216C22×Dic47—22no—
217C22×Dic47—28no—
218C22×Dic47—28no—
219C22×Dic47—28no—
220C22×Dic47—416no—
221C22×Dic47C22×C414yes—
222C22×Dic47C22×C414yes—
223C22×Dic47C22×C414yes—
224C22×Dic47C2×D414yes—
225C22×Dic47#4114yes—
226C22×Dic47#4114yes—
227C22×Dic47#4114yes—
228C22×Dic47C2412yes—
229C22×Dic47C2412yes—
230C22×Dic47C2412yes—
231C22×Dic47C2412yes—
232C22×Dic47C2412yes—
233C22×Dic47C2412yes—
234C22×Dic47C2412yes—
235C2×C4×D47—232no—
236C2×C4×D47—232no—
237C2×C4×D47—28no—
238C2×C4×D47—28no—
239C2×C4×D47—28no—
240C2×C4×D47—28no—
241C2×C4×D47—232no—
242C2×C4×D47—28no—
243C2×C4×D47—28no—
244C2×C4×D47—28no—
245C2×C4×D47C22×C4116yescomplemented
246C2×C4×D47C2×D4116yes—
247C4⋊C4×C47—28no—
248C22⋊C4×C47—28no—
249C22⋊C4×C47—28no—
250C22⋊C4×C47C22×C4116yescomplemented
251C42×C47—28no—
252C22⋊Dic47—28no—
253C22⋊Dic47C22×C4116yescomplemented
254(C2×D47)⋊C4—28no—
255(C2×D47)⋊C4—28no—
256(C2×D47)⋊C4C22×C4116yescomplemented
257C4⋊Dic47C22×C4116yescomplemented
258Dic47⋊C4—28no—
259Dic47⋊C4—28no—
260Dic47⋊C4C22×C4116yescomplemented
261C4×Dic47—28no—
262C4×Dic47—28no—
263C4×Dic47—28no—
264C4×Dic47—28no—
265C4×Dic47—28no—
266C4×Dic47—28no—
267C23×C47—28no—
268C23×C47—28no—
269C23×C47—28no—
270C23×C47—22no—
271C23×C47—22no—
272C23×C47—22no—
273C23×C47—22no—
274C23×C47—22no—
275C23×C47—22no—
276C23×C47—44no—
277C23×C47—44no—
278C23×C47—44no—
279C23×C47—44no—
280C23×C47C23×C414yes—
281C23×C47C23×C412yes—
282C23×C47C22×D412yes—
283C23×C47C2×#4112yes—
284C23×C47C2×#4112yes—
285C23×C47C2×#4112yes—
286C23×C47C2×#4112yes—
287C23×C47C2×#4112yes—
288C23×C47C2511yescharacteristic
289C22×D47—28no—
290C22×D47—28no—
291C22×D47—28no—
292C22×D47—28no—
293C22×D47—28no—
294C22×D47—28no—
295C22×D47—22no—
296C22×D47—22no—
297C22×D47—22no—
298C22×D47—22no—
299C22×D47C4×D4116yes—
300C22×D47C23×C414yes—
301C22×D47C22×D414yes—
302C22×D47C2×#4114yes—
303C2×C4×C47—28no—
304C2×C4×C47—28no—
305C2×C4×C47—28no—
306C2×C4×C47—28no—
307C2×C4×C47—22no—
308C2×C4×C47—22no—
309C2×C4×C47—22no—
310C2×C4×C47—22no—
311C2×C4×C47—22no—
312C2×C4×C47—22no—
313C2×C4×C47—22no—
314C2×C4×C47—22no—
315C2×C4×C47—22no—
316C2×C4×C47—22no—
317C2×C4×C47—22no—
318C2×C4×C47—22no—
319C2×C4×C47—22no—
320C2×C4×C47—22no—
321C2×C4×C47—44no—
322C2×C4×C47—44no—
323C2×C4×C47C23×C414yes—
324C2×C4×C47C23×C414yes—
325C2×C4×C47C22×D414yes—
326C2×C4×C47C2×#4114yes—
327C22⋊D47—232no—
328C2×Dic47—28no—
329C2×Dic47—28no—
330C2×Dic47—28no—
331C2×Dic47—28no—
332C2×Dic47—22no—
333C2×Dic47—22no—
334C2×Dic47—22no—
335C2×Dic47—22no—
336C2×Dic47—22no—
337C2×Dic47—22no—
338C2×Dic47—22no—
339C2×Dic47—22no—
340C2×Dic47—22no—
341C2×Dic47—22no—
342C2×Dic47—22no—
343C2×Dic47—22no—
344C2×Dic47—22no—
345C2×Dic47—22no—
346C2×Dic47—44no—
347C2×Dic47—44no—
348C2×Dic47—416no—
349C2×Dic47#123116yescomplemented
350C2×Dic47C23×C414yes—
351C2×Dic47C23×C414yes—
352C2×Dic47C23×C414yes—
353C2×Dic47C22×D414yes—
354C2×Dic47C2×#4114yes—
355C2×Dic47C2×#4114yes—
356C2×Dic47C2×#4114yes—
357C4×D47—232no—
358C4×D47—232no—
359C4×D47—232no—
360C2×C4×#123—471nomaximal, Sylow
361C22×C47—24no—
362C22×C47—24no—
363C22×C47—24no—
364C22×C47—42no—
365C22×C47—42no—
366C22×C47—42no—
367C22×C47—42no—
368C22×C47—416no—
369C22×C47C2×C4×D414yes—
370C22×C47C4×#4114yes—
371C22×C47C4×#4114yes—
372C22×C47C2×#12314yes—
373C22×C47#52514yes—
374C22×C47#52914yes—
375C22×C47#52914yes—
376C22×C47C24×C411yescharacteristic
377C22×C47C23×D411yescharacteristic
378C22×C47C22×#4111yescharacteristic
379C22×C47C22×#4111yescharacteristic
380C22×C47C22×#4111yescharacteristic
381C22×C47C22×#4111yescharacteristic
382C22×C47C22×#4111yescharacteristic
383C2×D47—24no—
384C2×D47—24no—
385C2×D47—24no—
386C2×D47—24no—
387C2×D47—24no—
388C2×D47—24no—
389C2×D47—232no—
390C2×D47C2×C4×D418yes—
391C4×C47—24no—
392C4×C47—24no—
393C4×C47—24no—
394C4×C47—24no—
395C4×C47—42no—
396C4×C47—42no—
397Dic47—24no—
398Dic47—24no—
399Dic47—24no—
400Dic47—24no—
401Dic47—42no—
402Dic47—42no—
403Dic47C2×#12318yescomplemented
404C22×#123—471no—
405C22×C4×D4—471no—
406C23×C42—471no—
407C4×#123—4716no—
408C2×#388—471no—
409C2×#388D4711yescharacteristic, complemented
410C2×#387—471no—
411C2×#387—471no—
412C2×#386—471no—
413C2×#385—471no—
414C2×#381—471no—
415C2×C4×C4⋊C4—471no—
416C2×C4×C4⋊C4—471no—
417C2×C4×C22⋊C4—471no—
418C2×C4×C22⋊C4—471no—
419C2×C4×C22⋊C4—471no—
420C2×C47—44no—
421C2×C47C4×#12318yescomplemented
422C2×C47C22×C4×D411yescharacteristic
423C2×C47C2×C4×#4111yescharacteristic
424C2×C47C2×C4×#4111yescharacteristic
425C2×C47C22×#12311yescharacteristic
426C2×C47C2×#52511yescharacteristic
427C2×C47C2×#52911yescharacteristic
428C2×C47C2×#52911yescharacteristic
429D47—28no—
430C23×D4—471no—
431C24×C4—471no—
432C24×C4—471no—
433C24×C4—471no—
434C24×C4—471no—
435C2×#123—4716no—
436C2×#123—478no—
437C2×C4×D4—478no—
438C2×C4×D4—948no—
439C22×C4⋊C4—471no—
440C22×C4⋊C4—471no—
441C22×C4⋊C4—471no—
442C22×C4⋊C4—471no—
443C22×C4⋊C4C2×D4711yescharacteristic
444C22×C22⋊C4—471no—
445C22×C22⋊C4—471no—
446C22×C22⋊C4—471no—
447C22×C22⋊C4—471no—
448C22×C22⋊C4—471no—
449C22×C22⋊C4C2×D4711yescharacteristic
450C22×C22⋊C4C2×D4711yescharacteristic
451C22×C22⋊C4C2×D4711yescharacteristic
452C22×C42—471no—
453C22×C42—471no—
454C22×C42—471no—
455C22×C42—471no—
456C22×C42—471no—
457C22×C42—471no—
458C22×C42—478no—
459C22×C42—948no—
460C22×C42C2×D4711yescharacteristic
461#388—478no—
462#388C2×D4718yescomplemented
463#387—478no—
464#387—478no—
465#386—478no—
466#385—478no—
467#381—478no—
468C4×C4⋊C4—478no—
469C4×C4⋊C4—478no—
470C4×C22⋊C4—478no—
471C4×C22⋊C4—478no—
472C4×C22⋊C4—478no—
473C2×#95—471no—
474C2×#95—471no—
475C2×#95—471no—
476C2×#95—471no—
477C2×#95—471no—
478C2×#95—471no—
479C2×#95—471no—
480C2×#95—471no—
481C2×#95C2×D4711yescharacteristic
482C2×#95C2×D4711yescharacteristic
483C47C2×C4×#12311yescharacteristic, complemented, Sylow
484C25—471no—
485C25C22×D4711yescharacteristic
486C22×D4—478no—
487C22×D4—474no—
488C22×D4—944no—
489C22×D4—944no—
490C23×C4—471no—
491C23×C4—471no—
492C23×C4—471no—
493C23×C4—471no—
494C23×C4—471no—
495C23×C4—478no—
496C23×C4—478no—
497C23×C4—474no—
498C23×C4—474no—
499C23×C4—474no—
500C23×C4—471no—
501C23×C4—471no—
502C23×C4—474no—
503C23×C4—944no—
504C23×C4—944no—
505C23×C4—944no—
506C23×C4—944no—
507C23×C4—944no—
508C23×C4—944no—
509C23×C4—944no—
510C23×C4—944no—
511C23×C4—944no—
512C23×C4—944no—
513C23×C4C22×D4711yescharacteristic
514C23×C4C22×D4711yescharacteristic
515C23×C4C22×D4711yescharacteristic
516C23×C4C22×D4711yescharacteristic
517C23×C4C22×D4711yescharacteristic
518C23×C4C22×D4711yescharacteristic
519#123—4764no—
520C4×D4—9432no—
521C2×C4⋊C4—24no—
522C2×C4⋊C4—478no—
523C2×C4⋊C4—478no—
524C2×C4⋊C4—474no—
525C2×C4⋊C4—474no—
526C2×C4⋊C4—474no—
527C2×C4⋊C4—474no—
528C2×C4⋊C4—944no—
529C2×C4⋊C4—944no—
530C2×C4⋊C4C22×D4714yes—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—478no—
534C2×C22⋊C4—474no—
535C2×C22⋊C4—478no—
536C2×C22⋊C4—474no—
537C2×C22⋊C4—474no—
538C2×C22⋊C4—474no—
539C2×C22⋊C4—474no—
540C2×C22⋊C4—944no—
541C2×C22⋊C4—944no—
542C2×C22⋊C4—944no—
543C2×C22⋊C4C4×D4718yescomplemented
544C2×C22⋊C4C22×D4714yes—
545C2×C22⋊C4C22×D4714yes—
546C2×C22⋊C4C22×D4714yes—
547C2×C42—24no—
548C2×C42—474no—
549C2×C42—474no—
550C2×C42—474no—
551C2×C42—474no—
552C2×C42—474no—
553C2×C42—474no—
554C2×C42—9432no—
555C2×C42—944no—
556C2×C42—944no—
557C2×C42—944no—
558C2×C42—944no—
559C2×C42—944no—
560C2×C42—944no—
561C2×C42C22×D4714yes—
562#95—474no—
563#95—474no—
564#95—474no—
565#95—474no—
566#95—474no—
567#95—474no—
568#95—474no—
569#95—474no—
570#95C22×D4714yes—
571#95C22×D4714yes—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—474no—
579C24—474no—
580C24—474no—
581C24—472no—
582C24—942no—
583C24—942no—
584C24—942no—
585C24—942no—
586C24C2×C4×D4714yes—
587C24C23×D4712yes—
588C24C23×D4711yescharacteristic
589C2×D4—4716no—
590C2×D4—948no—
591C2×D4—9432no—
592C2×D4—948no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—474no—
608C22×C4—474no—
609C22×C4—474no—
610C22×C4—472no—
611C22×C4—474no—
612C22×C4—474no—
613C22×C4—474no—
614C22×C4—474no—
615C22×C4—472no—
616C22×C4—472no—
617C22×C4—472no—
618C22×C4—472no—
619C22×C4—4716no—
620C22×C4—4716no—
621C22×C4—472no—
622C22×C4—472no—
623C22×C4—9432no—
624C22×C4—948no—
625C22×C4—948no—
626C22×C4—948no—
627C22×C4—948no—
628C22×C4—948no—
629C22×C4—9432no—
630C22×C4—948no—
631C22×C4—9432no—
632C22×C4—948no—
633C22×C4—948no—
634C22×C4—948no—
635C22×C4—942no—
636C22×C4—942no—
637C22×C4—942no—
638C22×C4—942no—
639C22×C4—942no—
640C22×C4—942no—
641C22×C4—942no—
642C22×C4—942no—
643C22×C4—948no—
644C22×C4—942no—
645C22×C4—942no—
646C22×C4—942no—
647C22×C4—942no—
648C22×C4—942no—
649C22×C4—942no—
650C22×C4—18816no—
651C22×C4C2×C4×D4714yes—
652C22×C4C2×C4×D4714yes—
653C22×C4D4×D4714yes—
654C22×C4#1062535214yes—
655C22×C4C23×D4712yes—
656C22×C4C23×D4712yes—
657C22×C4C23×D4712yes—
658C22×C4C23×D4712yes—
659C22×C4C23×D4712yes—
660C22×C4C23×D4712yes—
661C4⋊C4—28no—
662C4⋊C4—4716no—
663C4⋊C4—4716no—
664C4⋊C4—948no—
665C4⋊C4—948no—
666C22⋊C4—28no—
667C22⋊C4—28no—
668C22⋊C4—4716no—
669C22⋊C4—4716no—
670C22⋊C4—948no—
671C22⋊C4—948no—
672C22⋊C4—948no—
673C22⋊C4C2×C4×D47116yescomplemented
674C42—28no—
675C42—948no—
676C42—948no—
677C42—948no—
678C42—948no—
679C42—948no—
680C42—948no—
681C23—28no—
682C23—28no—
683C23—28no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—4716no—
695C23—474no—
696C23—474no—
697C23—474no—
698C23—948no—
699C23—948no—
700C23—948no—
701C23—948no—
702C23—948no—
703C23—948no—
704C23—942no—
705C23—942no—
706C23—942no—
707C23—942no—
708C23C22×C4×D4714yes—
709C23C22×C4×D4712yes—
710C23C2×D4×D4712yes—
711C23#41×D4712yes—
712C23#41×D4712yes—
713C23#41×D4712yes—
714C23#41×D4712yes—
715C23C2×#1062535212yes—
716C23C24×D4711yescharacteristic
717D4—9432no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—28no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—4716no—
739C2×C4—474no—
740C2×C4—474no—
741C2×C4—474no—
742C2×C4—474no—
743C2×C4—474no—
744C2×C4—474no—
745C2×C4—474no—
746C2×C4—9432no—
747C2×C4—9432no—
748C2×C4—9432no—
749C2×C4—948no—
750C2×C4—948no—
751C2×C4—948no—
752C2×C4—948no—
753C2×C4—942no—
754C2×C4—942no—
755C2×C4—942no—
756C2×C4—942no—
757C2×C4—942no—
758C2×C4—942no—
759C2×C4—942no—
760C2×C4—942no—
761C2×C4—942no—
762C2×C4—942no—
763C2×C4—942no—
764C2×C4—942no—
765C2×C4—942no—
766C2×C4—942no—
767C2×C4—18816no—
768C2×C4—1884no—
769C2×C4—1884no—
770C2×C4C22×C4×D4714yes—
771C2×C4C22×C4×D4714yes—
772C2×C4C2×D4×D4714yes—
773C2×C4C2×#1062535214yes—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—416no—
782C22—478no—
783C22—944no—
784C22—944no—
785C22—944no—
786C22—944no—
787C22—944no—
788C22—944no—
789C22—9432no—
790C22C4×D4×D4714yes—
791C22C4×#1062535214yes—
792C22#1568959114yes—
793C22#123×D4714yes—
794C22#1568963314yes—
795C22#1568965214yes—
796C22#1568965614yes—
797C22C23×C4×D4711yescharacteristic
798C22C22×D4×D4711yescharacteristic
799C22C2×#41×D4711yescharacteristic
800C22C2×#41×D4711yescharacteristic
801C22C2×#41×D4711yescharacteristic
802C22C2×#41×D4711yescharacteristic
803C22C22×#1062535211yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—24no—
808C4—42no—
809C4—42no—
810C4—478no—
811C4—944no—
812C4—944no—
813C4—944no—
814C4—944no—
815C4—1882no—
816C4—1882no—
817C2—44no—
818C2—948no—
819C2#2024591518yesdirect product factor
820C2C2×C4×D4×D4711yescharacteristic
821C2C2×C4×#1062535211yescharacteristic
822C2C2×#1568959111yescharacteristic
823C2C2×#123×D4711yescharacteristic
824C2C2×#1568963311yescharacteristic
825C2C2×#1568965211yescharacteristic
826C2C2×#1568965611yescharacteristic
subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C47×#388C2
socleC24×C47C24
prime radicalC23×C22⋊D47C22
cosocleC23×C47C25
hypercenterC2×#388D47
hypocenterC47C2×C4×#123
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
3. C22×C42×D47C2semidirect
4. #20245915C2direct (N × H)
5. C2×#15689011C2semidirect
6. C2×#15689008C2semidirect
7. C2×#15689007C2semidirect
9. C2×#15688994C2semidirect
10. C2×#15688985C2semidirect
11. C2×C4⋊C4×Dic47C2semidirect
12. C2×#15688974C2semidirect
13. C2×C22⋊C4×Dic47C2semidirect
14. C2×C22⋊C4×Dic47C2semidirect
15. C2×#15688970C2semidirect
16. C2×C47×#388C2semidirect
22. C2×#13094006C4semidirect
42. C2×C42×D47C22semidirect
43. #15689011C22semidirect
44. #15689008C22semidirect
45. #15689007C22semidirect
47. #15688994C22semidirect
48. #15688985C22semidirect
49. C4⋊C4×Dic47C22semidirect
50. #15688974C22semidirect
51. C22⋊C4×Dic47C22semidirect
52. C22⋊C4×Dic47C22semidirect
53. #15688970C22semidirect
67. C47×#388C22semidirect
93. C22×C4×D47C2×C4semidirect
98. #13094006C2×C4semidirect
100. C2×C4⋊Dic47C2×C4semidirect
104. C2×Dic47⋊C4C2×C4semidirect
109. C2×C22⋊Dic47C2×C4semidirect
114. C2×(C2×D47)⋊C4C2×C4semidirect
150. C2×C22⋊C4×C47C2×C4semidirect
245. C2×C4×D47C22×C4semidirect
250. C22⋊C4×C47C22×C4semidirect
253. C22⋊Dic47C22×C4semidirect
256. (C2×D47)⋊C4C22×C4semidirect
257. C4⋊Dic47C22×C4semidirect
260. Dic47⋊C4C22×C4semidirect
349. C2×Dic47#123semidirect
403. Dic47C2×#123semidirect
409. C2×#388D47semidirect
421. C2×C47C4×#123semidirect
462. #388C2×D47semidirect
483. C47C2×C4×#123semidirect
543. C2×C22⋊C4C4×D47semidirect
673. C22⋊C4C2×C4×D47semidirect
819. C2#20245915direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940062
C22×(C22⋊D47)⋊C42
C22×C42×D472
#202459152
C2×#156890112
C2×#156890082
C2×#156890072
C2×#156889992
C2×#156889942
C2×#156889852
C2×C4⋊C4×Dic472
C2×#156889742
C2×C22⋊C4×Dic472
C2×#156889702
C2×C47×#3882
C2×C4×#12347