Finite Group Databasebeta

← C2×#20246405 #26375808

Subgroups — C2×#20246405 #26375808

Order 12032.

4782 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093996C211yesmaximal, characteristic
2C22×C4×C22⋊D47C211yesmaximal, characteristic, complemented
3C22×(C22⋊D47)⋊C4C211yesmaximal, characteristic, complemented
4C23×Dic47⋊C4C211yesmaximal, characteristic, complemented
5#20246405C2116yesmaximal, direct product factor
6C2×#15689023C211yesmaximal, characteristic, complemented
7C2×#15689018C211yesmaximal, characteristic, complemented
8C2×#15689014C211yesmaximal, characteristic, complemented
9C2×#15689011C211yesmaximal, characteristic, complemented
10C2×#15689003C211yesmaximal, characteristic, complemented
11C2×#15689002C211yesmaximal, characteristic, complemented
12C2×#15688996C211yesmaximal, characteristic, complemented
13C2×#15688994C211yesmaximal, characteristic, complemented
14C2×C4×Dic47⋊C4C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic47C211yesmaximal, characteristic, complemented
16C22×C4×D4×C47C211yesmaximal, characteristic, complemented
17C23×C22⋊D47C2211yescharacteristic
18C23×C22⋊D47C2211yescharacteristic
19C24×Dic47C2211yescharacteristic
20C24×Dic47C2211yescharacteristic
21C23×C4×D47C2211yescharacteristic
22C2×#13093996C4116yescomplemented
23C2×#13093996C2218yes—
24C2×C4×C22⋊D47—28no—
25C2×C4×C22⋊D47C2218yescomplemented
26C2×(C22⋊D47)⋊C4—28no—
27C2×(C22⋊D47)⋊C4C2218yescomplemented
28C22×Dic47⋊C4—28no—
29C22×Dic47⋊C4C2211yescharacteristic
30C22×Dic47⋊C4C2211yescharacteristic
31C22×Dic47⋊C4C2211yescharacteristic
32C22×Dic47⋊C4C2211yescharacteristic
33C22×Dic47⋊C4C2211yescharacteristic
34C22×Dic47⋊C4C2211yescharacteristic
35C22×Dic47⋊C4C2218yescomplemented
36C22×C22⋊Dic47C2211yescharacteristic
37C22×C22⋊Dic47C2211yescharacteristic
38C22×C22⋊Dic47C2211yescharacteristic
39C22×C22⋊Dic47C2211yescharacteristic
40C22×(C2×D47)⋊C4C2211yescharacteristic
41C22×(C2×D47)⋊C4C2211yescharacteristic
42C22×(C2×D47)⋊C4C2211yescharacteristic
43C22×(C2×D47)⋊C4C2211yescharacteristic
44C22×C4×Dic47C2211yescharacteristic
45C22×C4×Dic47C2211yescharacteristic
46C22×C4×Dic47C2211yescharacteristic
47#15689023C2218yescomplemented
48#15689018C2218yescomplemented
49#15689014C2218yescomplemented
50#15689011C2218yescomplemented
51#15689003C2218yescomplemented
52#15689002C2218yescomplemented
53#15688996C2218yescomplemented
54#15688994C2218yescomplemented
55C4×Dic47⋊C4C2218yescomplemented
56C22⋊C4×Dic47C2218yescomplemented
57C2×C47⋊#95C2211yescharacteristic
58C2×C47⋊#95C2211yescharacteristic
59C2×C47⋊#95C2211yescharacteristic
60C2×C47⋊#95C2211yescharacteristic
61C2×C47⋊#95C2211yescharacteristic
62C2×C47⋊#95C2211yescharacteristic
63C23×D4×C47C2211yescharacteristic
64C24×C4×C47C2211yescharacteristic
65C24×C4×C47C2211yescharacteristic
66C2×C4×D4×C47—28no—
67C2×C4×D4×C47C2218yescomplemented
68C22×C4⋊C4×C47C2211yescharacteristic
69C22×C22⋊C4×C47C2211yescharacteristic
70C22×C22⋊C4×C47C2211yescharacteristic
71C22×C42×C47C2211yescharacteristic
72C24×D47C2311yescharacteristic
73C22×C22⋊D47—24no—
74C22×C22⋊D47—24no—
75C22×C22⋊D47—24no—
76C22×C22⋊D47—24no—
77C22×C22⋊D47C2×C418yescomplemented
78C22×C22⋊D47C2×C418yescomplemented
79C22×C22⋊D47C2314yes—
80C22×C22⋊D47C2314yes—
81C23×Dic47—24no—
82C23×Dic47—24no—
83C23×Dic47—24no—
84C23×Dic47—24no—
85C23×Dic47—42no—
86C23×Dic47C2×C418yescomplemented
87C23×Dic47C2311yescharacteristic
88C23×Dic47C2311yescharacteristic
89C23×Dic47C2311yescharacteristic
90C23×Dic47C2314yes—
91C23×Dic47C2311yescharacteristic
92C23×Dic47C2311yescharacteristic
93C23×Dic47C2314yes—
94C23×Dic47C2311yescharacteristic
95C23×Dic47C2311yescharacteristic
96C22×C4×D47—24no—
97C22×C4×D47—24no—
98C22×C4×D47—42no—
99C22×C4×D47C2314yes—
100#13093996C2×C4164yescomplemented
101C4×C22⋊D47—232no—
102(C22⋊D47)⋊C4—232no—
103C2×Dic47⋊C4—24no—
104C2×Dic47⋊C4—24no—
105C2×Dic47⋊C4—24no—
106C2×Dic47⋊C4—24no—
107C2×Dic47⋊C4—232no—
108C2×Dic47⋊C4C2×C418yescomplemented
109C2×Dic47⋊C4D418yescomplemented
110C2×Dic47⋊C4C2314yes—
111C2×Dic47⋊C4C2314yes—
112C2×Dic47⋊C4C2314yes—
113C2×Dic47⋊C4C2314yes—
114C2×Dic47⋊C4C2314yes—
115C2×Dic47⋊C4C2314yes—
116C2×C22⋊Dic47—24no—
117C2×C22⋊Dic47—24no—
118C2×C22⋊Dic47—42no—
119C2×C22⋊Dic47C2×C418yescomplemented
120C2×C22⋊Dic47C2314yes—
121C2×C22⋊Dic47C2314yes—
122C2×C22⋊Dic47C2314yes—
123C2×C22⋊Dic47C2314yes—
124C2×(C2×D47)⋊C4—24no—
125C2×(C2×D47)⋊C4—24no—
126C2×(C2×D47)⋊C4—42no—
127C2×(C2×D47)⋊C4C2×C418yescomplemented
128C2×(C2×D47)⋊C4C2314yes—
129C2×(C2×D47)⋊C4C2314yes—
130C2×(C2×D47)⋊C4C2314yes—
131C2×(C2×D47)⋊C4C2314yes—
132C2×C4×Dic47—24no—
133C2×C4×Dic47—24no—
134C2×C4×Dic47—24no—
135C2×C4×Dic47C2314yes—
136C2×C4×Dic47C2314yes—
137C2×C4×Dic47C2314yes—
138C47⋊#95C2314yes—
139C47⋊#95C2314yes—
140C47⋊#95C2314yes—
141C47⋊#95C2314yes—
142C47⋊#95C2314yes—
143C47⋊#95C2314yes—
144C25×C47C2311yescharacteristic
145C25×C47C2311yescharacteristic
146C22×D4×C47—24no—
147C22×D4×C47—24no—
148C22×D4×C47C2×C418yescomplemented
149C22×D4×C47C2314yes—
150C23×C4×C47—24no—
151C23×C4×C47—24no—
152C23×C4×C47—24no—
153C23×C4×C47—24no—
154C23×C4×C47—42no—
155C23×C4×C47—42no—
156C23×C4×C47C2311yescharacteristic
157C23×C4×C47C2314yes—
158C23×C4×C47C2314yes—
159C23×C4×C47C2311yescharacteristic
160C23×C4×C47C2311yescharacteristic
161C23×C4×C47C2311yescharacteristic
162C23×C4×C47C2311yescharacteristic
163C4×D4×C47—232no—
164C2×C4⋊C4×C47—24no—
165C2×C4⋊C4×C47C2314yes—
166C2×C22⋊C4×C47—24no—
167C2×C22⋊C4×C47D418yescomplemented
168C2×C22⋊C4×C47C2314yes—
169C2×C22⋊C4×C47C2314yes—
170C2×C42×C47—24no—
171C2×C42×C47C2314yes—
172C24×C47—22no—
173C24×C47—22no—
174C24×C47—22no—
175C24×C47—22no—
176C24×C47—22no—
177C24×C47—22no—
178C24×C47—22no—
179C24×C47—22no—
180C24×C47—22no—
181C24×C47—22no—
182C24×C47C22×C414yes—
183C24×C47C22×C414yes—
184C24×C47C2×D414yes—
185C24×C47#4114yes—
186C24×C47C2412yes—
187C24×C47C2412yes—
188C24×C47C2411yescharacteristic
189C23×D47—22no—
190C23×D47—22no—
191C23×D47—22no—
192C23×D47—22no—
193C23×D47—22no—
194C23×D47—22no—
195C23×D47C22×C414yes—
196C23×D47C2412yes—
197C2×D4×C47—232no—
198C2×D4×C47—28no—
199C2×D4×C47—28no—
200C2×D4×C47C22×C4116yescomplemented
201C22×C4×C47—22no—
202C22×C4×C47—22no—
203C22×C4×C47—22no—
204C22×C4×C47—22no—
205C22×C4×C47—22no—
206C22×C4×C47—22no—
207C22×C4×C47—22no—
208C22×C4×C47—22no—
209C22×C4×C47—22no—
210C22×C4×C47—28no—
211C22×C4×C47—22no—
212C22×C4×C47—22no—
213C22×C4×C47—28no—
214C22×C4×C47—28no—
215C22×C4×C47—28no—
216C22×C4×C47—44no—
217C22×C4×C47—44no—
218C22×C4×C47—416no—
219C22×C4×C47—416no—
220C22×C4×C47C22×C414yes—
221C22×C4×C47C2×D414yes—
222C22×C4×C47C2×D414yes—
223C22×C4×C47C2×D414yes—
224C22×C4×C47C2412yes—
225C22×C4×C47C2412yes—
226C22×C4×C47C2412yes—
227C22×C4×C47C2412yes—
228C22×C4×C47C2412yes—
229C2×C22⋊D47—232no—
230C2×C22⋊D47—28no—
231C2×C22⋊D47—28no—
232C2×C22⋊D47—232no—
233C2×C22⋊D47—28no—
234C2×C22⋊D47—28no—
235C2×C22⋊D47C22×C4116yescomplemented
236C2×C22⋊D47C22×C4116yescomplemented
237C22×Dic47—22no—
238C22×Dic47—22no—
239C22×Dic47—22no—
240C22×Dic47—22no—
241C22×Dic47—22no—
242C22×Dic47—22no—
243C22×Dic47—232no—
244C22×Dic47—28no—
245C22×Dic47—28no—
246C22×Dic47—22no—
247C22×Dic47—22no—
248C22×Dic47—22no—
249C22×Dic47—28no—
250C22×Dic47—22no—
251C22×Dic47—22no—
252C22×Dic47—22no—
253C22×Dic47—22no—
254C22×Dic47—22no—
255C22×Dic47—22no—
256C22×Dic47—28no—
257C22×Dic47—44no—
258C22×Dic47—416no—
259C22×Dic47C22×C414yes—
260C22×Dic47C22×C414yes—
261C22×Dic47C22×C414yes—
262C22×Dic47C22×C4116yescomplemented
263C22×Dic47C2×D414yes—
264C22×Dic47C2×D414yes—
265C22×Dic47#4114yes—
266C22×Dic47C2412yes—
267C22×Dic47C2412yes—
268C22×Dic47C2412yes—
269C22×Dic47C2412yes—
270C22×Dic47C2412yes—
271C22×Dic47C2412yes—
272C22×Dic47C2412yes—
273C2×C4×D47—28no—
274C2×C4×D47—28no—
275C2×C4×D47—44no—
276C2×C4×D47—416no—
277C4⋊C4×C47—28no—
278C22⋊C4×C47—28no—
279C22⋊C4×C47C2×D4116yescomplemented
280C42×C47—28no—
281C22⋊Dic47—28no—
282C22⋊Dic47—28no—
283C22⋊Dic47—44no—
284C22⋊Dic47C22×C4116yescomplemented
285(C2×D47)⋊C4—28no—
286(C2×D47)⋊C4—28no—
287(C2×D47)⋊C4—44no—
288(C2×D47)⋊C4C22×C4116yescomplemented
289Dic47⋊C4—28no—
290Dic47⋊C4—28no—
291Dic47⋊C4—28no—
292Dic47⋊C4—28no—
293Dic47⋊C4C22×C4116yescomplemented
294Dic47⋊C4C2×D4116yescomplemented
295C4×Dic47—28no—
296C4×Dic47—28no—
297C4×Dic47—28no—
298C23×C47—28no—
299C23×C47—28no—
300C23×C47—28no—
301C23×C47—28no—
302C23×C47—28no—
303C23×C47—28no—
304C23×C47—22no—
305C23×C47—22no—
306C23×C47—22no—
307C23×C47—22no—
308C23×C47—28no—
309C23×C47—28no—
310C23×C47—28no—
311C23×C47—22no—
312C23×C47—22no—
313C23×C47—22no—
314C23×C47—22no—
315C23×C47—22no—
316C23×C47—22no—
317C23×C47—44no—
318C23×C47—44no—
319C23×C47—44no—
320C23×C47—44no—
321C23×C47C4×D4116yescomplemented
322C23×C47C23×C414yes—
323C23×C47C23×C414yes—
324C23×C47C23×C412yes—
325C23×C47C22×D412yes—
326C23×C47C22×D414yes—
327C23×C47C22×D412yes—
328C23×C47C2×#4112yes—
329C23×C47C2×#4114yes—
330C23×C47C2×#4112yes—
331C23×C47H(5,𝔽2)12yes—
332C23×C472−1+412yes—
333C23×C47C2511yescharacteristic
334C22×D47—28no—
335C22×D47—28no—
336C22×D47—28no—
337C22×D47—22no—
338C22×D47—22no—
339C22×D47—22no—
340C22×D47—22no—
341C22×D47—22no—
342C22×D47—22no—
343C22×D47—44no—
344C22×D47—44no—
345C22×D47—44no—
346C22×D47—44no—
347C22×D47C23×C414yes—
348D4×C47—232no—
349C2×C4×C47—28no—
350C2×C4×C47—28no—
351C2×C4×C47—28no—
352C2×C4×C47—28no—
353C2×C4×C47—22no—
354C2×C4×C47—22no—
355C2×C4×C47—22no—
356C2×C4×C47—22no—
357C2×C4×C47—22no—
358C2×C4×C47—22no—
359C2×C4×C47—22no—
360C2×C4×C47—22no—
361C2×C4×C47—22no—
362C2×C4×C47—22no—
363C2×C4×C47—22no—
364C2×C4×C47—416no—
365C2×C4×C47—416no—
366C2×C4×C47—44no—
367C2×C4×C47C23×C414yes—
368C2×C4×C47C22×D414yes—
369C2×C4×C47C22×D414yes—
370C2×C4×C47C22×D414yes—
371C22⋊D47—232no—
372C22⋊D47—232no—
373C2×Dic47—28no—
374C2×Dic47—28no—
375C2×Dic47—28no—
376C2×Dic47—22no—
377C2×Dic47—22no—
378C2×Dic47—22no—
379C2×Dic47—22no—
380C2×Dic47—22no—
381C2×Dic47—22no—
382C2×Dic47—232no—
383C2×Dic47—22no—
384C2×Dic47—22no—
385C2×Dic47—22no—
386C2×Dic47—22no—
387C2×Dic47—22no—
388C2×Dic47—22no—
389C2×Dic47—22no—
390C2×Dic47—22no—
391C2×Dic47—22no—
392C2×Dic47—416no—
393C2×Dic47—44no—
394C2×Dic47—44no—
395C2×Dic47—44no—
396C2×Dic47C4×D4116yescomplemented
397C2×Dic47C23×C414yes—
398C2×Dic47C23×C414yes—
399C2×Dic47C23×C414yes—
400C2×Dic47C22×D414yes—
401C2×Dic47C22×D414yes—
402C2×Dic47C2×#4114yes—
403C4×D47—416no—
404C2×#2361—471nomaximal, Sylow
405C22×C47—232no—
406C22×C47—24no—
407C22×C47—24no—
408C22×C47—24no—
409C22×C47—24no—
410C22×C47—24no—
411C22×C47—24no—
412C22×C47—24no—
413C22×C47—24no—
414C22×C47—24no—
415C22×C47—416no—
416C22×C47—42no—
417C22×C47—42no—
418C22×C47—42no—
419C22×C47—42no—
420C22×C47C2×C4×D414yes—
421C22×C47C2×C4×D414yes—
422C22×C47C2×C4×D418yescomplemented
423C22×C47#52014yes—
424C22×C47D4214yes—
425C22×C47#54714yes—
426C22×C47#54814yes—
427C22×C47#55314yes—
428C22×C47C24×C411yescharacteristic
429C22×C47C23×D411yescharacteristic
430C22×C47C23×D411yescharacteristic
431C22×C47C22×#4111yescharacteristic
432C22×C47C22×#4111yescharacteristic
433C22×C47C2×H(5,𝔽2)11yescharacteristic
434C22×C47C2×2−1+411yescharacteristic
435C2×D47—24no—
436C2×D47—24no—
437C2×D47—24no—
438C2×D47—416no—
439C2×D47—42no—
440C2×D47—42no—
441C2×D47—42no—
442C2×D47—42no—
443C4×C47—24no—
444C4×C47—24no—
445C4×C47—24no—
446C4×C47—24no—
447C4×C47—42no—
448Dic47—24no—
449Dic47—24no—
450Dic47—24no—
451Dic47—42no—
452Dic47—42no—
453Dic47—42no—
454Dic47C2×C4×D418yescomplemented
455C22×#121—471no—
456C22×C4×D4—471no—
457C22×C4×D4—471no—
458C22×C4×D4D4711yescharacteristic, complemented
459C23×C4⋊C4—471no—
460#2361—4716no—
461C2×#390—471no—
462C2×#389—471no—
463C2×#388—471no—
464C2×#388—471no—
465C2×#386—471no—
466C2×#386—471no—
467C2×#385—471no—
468C2×#385—471no—
469C2×C4×C4⋊C4—471no—
470C2×C4×C22⋊C4—471no—
471C2×C47—28no—
472C2×C47—44no—
473C2×C47#236118yescomplemented
474C2×C47C22×C4×D411yescharacteristic
475C2×C47C22×C4×D411yescharacteristic
476C2×C47C2×#52011yescharacteristic
477C2×C47C2×D4211yescharacteristic
478C2×C47C2×#54711yescharacteristic
479C2×C47C2×#54811yescharacteristic
480C2×C47C2×#55311yescharacteristic
481D47—44no—
482C23×D4—471no—
483C23×D4—471no—
484C23×D4C2×D4711yescharacteristic
485C24×C4—471no—
486C24×C4—471no—
487C24×C4—471no—
488C24×C4C2×D4711yescharacteristic
489C24×C4C2×D4711yescharacteristic
490C2×#121—4716no—
491C2×#121—478no—
492C2×C4×D4—28no—
493C2×C4×D4—478no—
494C2×C4×D4—478no—
495C2×C4×D4—948no—
496C2×C4×D4—948no—
497C2×C4×D4C2×D4718yescomplemented
498C22×C4⋊C4—471no—
499C22×C4⋊C4—471no—
500C22×C4⋊C4—478no—
501C22×C4⋊C4—471no—
502C22×C4⋊C4—471no—
503C22×C4⋊C4—471no—
504C22×C4⋊C4—471no—
505C22×C4⋊C4—948no—
506C22×C4⋊C4C2×D4711yescharacteristic
507C22×C22⋊C4—471no—
508C22×C22⋊C4—471no—
509C22×C22⋊C4—471no—
510C22×C22⋊C4—471no—
511C22×C22⋊C4—471no—
512C22×C22⋊C4—471no—
513C22×C22⋊C4—471no—
514C22×C22⋊C4—471no—
515C22×C22⋊C4C2×D4711yescharacteristic
516C22×C22⋊C4C2×D4711yescharacteristic
517C22×C42—471no—
518C22×C42—471no—
519C22×C42—471no—
520C22×C42C2×D4711yescharacteristic
521#390—478no—
522#389—478no—
523#388—478no—
524#388—478no—
525#386—478no—
526#386—478no—
527#385—478no—
528#385—478no—
529C4×C4⋊C4—478no—
530C4×C22⋊C4—478no—
531C2×#95—471no—
532C2×#95—471no—
533C2×#95—471no—
534C2×#95—471no—
535C2×#95—471no—
536C2×#95—471no—
537C47C2×#236111yescharacteristic, complemented, Sylow
538C25—471no—
539C25C22×D4711yescharacteristic
540C25C22×D4711yescharacteristic
541C22×D4—24no—
542C22×D4—24no—
543C22×D4—478no—
544C22×D4—478no—
545C22×D4—474no—
546C22×D4—474no—
547C22×D4—944no—
548C22×D4—944no—
549C22×D4—944no—
550C22×D4—944no—
551C22×D4C4×D4718yescomplemented
552C22×D4C22×D4714yes—
553C23×C4—24no—
554C23×C4—24no—
555C23×C4—24no—
556C23×C4—24no—
557C23×C4—42no—
558C23×C4—42no—
559C23×C4—471no—
560C23×C4—478no—
561C23×C4—474no—
562C23×C4—471no—
563C23×C4—471no—
564C23×C4—471no—
565C23×C4—471no—
566C23×C4—471no—
567C23×C4—471no—
568C23×C4—474no—
569C23×C4—474no—
570C23×C4—944no—
571C23×C4—944no—
572C23×C4—944no—
573C23×C4—944no—
574C23×C4—944no—
575C23×C4—944no—
576C23×C4—1882no—
577C23×C4—1882no—
578C23×C4C22×D4711yescharacteristic
579C23×C4C22×D4714yes—
580C23×C4C22×D4714yes—
581C23×C4C22×D4711yescharacteristic
582C23×C4C22×D4711yescharacteristic
583C23×C4C22×D4711yescharacteristic
584C23×C4C22×D4711yescharacteristic
585#121—4764no—
586C4×D4—232no—
587C4×D4—9432no—
588C4×D4—9432no—
589C2×C4⋊C4—24no—
590C2×C4⋊C4—478no—
591C2×C4⋊C4—478no—
592C2×C4⋊C4—474no—
593C2×C4⋊C4—474no—
594C2×C4⋊C4—474no—
595C2×C4⋊C4—474no—
596C2×C4⋊C4—474no—
597C2×C4⋊C4—474no—
598C2×C4⋊C4—9432no—
599C2×C4⋊C4—944no—
600C2×C4⋊C4—944no—
601C2×C4⋊C4—944no—
602C2×C4⋊C4—944no—
603C2×C4⋊C4C22×D4714yes—
604C2×C22⋊C4—24no—
605C2×C22⋊C4—478no—
606C2×C22⋊C4—474no—
607C2×C22⋊C4—478no—
608C2×C22⋊C4—474no—
609C2×C22⋊C4—474no—
610C2×C22⋊C4—474no—
611C2×C22⋊C4—474no—
612C2×C22⋊C4—474no—
613C2×C22⋊C4—474no—
614C2×C22⋊C4—474no—
615C2×C22⋊C4—944no—
616C2×C22⋊C4—944no—
617C2×C22⋊C4—944no—
618C2×C22⋊C4—944no—
619C2×C22⋊C4—1882no—
620C2×C22⋊C4—1882no—
621C2×C22⋊C4C22⋊D4718yescomplemented
622C2×C22⋊C4C22×D4714yes—
623C2×C22⋊C4C22×D4714yes—
624C2×C42—24no—
625C2×C42—474no—
626C2×C42—474no—
627C2×C42—474no—
628C2×C42—944no—
629C2×C42—944no—
630C2×C42—944no—
631C2×C42C22×D4714yes—
632#95—474no—
633#95—474no—
634#95—474no—
635#95—474no—
636#95—474no—
637#95—474no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—474no—
649C24—472no—
650C24—942no—
651C24—942no—
652C24—942no—
653C24—942no—
654C24—942no—
655C24—942no—
656C24C2×C4×D4714yes—
657C24C2×C4×D4714yes—
658C24#1062535014yes—
659C24C2×C22⋊D4714yes—
660C24C23×D4712yes—
661C24C23×D4712yes—
662C24C23×D4711yescharacteristic
663C2×D4—232no—
664C2×D4—28no—
665C2×D4—28no—
666C2×D4—4716no—
667C2×D4—4716no—
668C2×D4—948no—
669C2×D4—9432no—
670C2×D4—948no—
671C2×D4—9432no—
672C2×D4—948no—
673C2×D4—948no—
674C2×D4C2×C4×D47116yescomplemented
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—28no—
686C22×C4—22no—
687C22×C4—28no—
688C22×C4—28no—
689C22×C4—28no—
690C22×C4—44no—
691C22×C4—44no—
692C22×C4—416no—
693C22×C4—416no—
694C22×C4—474no—
695C22×C4—474no—
696C22×C4—474no—
697C22×C4—472no—
698C22×C4—474no—
699C22×C4—474no—
700C22×C4—4716no—
701C22×C4—474no—
702C22×C4—472no—
703C22×C4—472no—
704C22×C4—472no—
705C22×C4—472no—
706C22×C4—472no—
707C22×C4—472no—
708C22×C4—948no—
709C22×C4—948no—
710C22×C4—9432no—
711C22×C4—948no—
712C22×C4—948no—
713C22×C4—942no—
714C22×C4—942no—
715C22×C4—942no—
716C22×C4—942no—
717C22×C4—942no—
718C22×C4—942no—
719C22×C4—942no—
720C22×C4—942no—
721C22×C4—942no—
722C22×C4—948no—
723C22×C4—942no—
724C22×C4—942no—
725C22×C4—942no—
726C22×C4—942no—
727C22×C4—942no—
728C22×C4—942no—
729C22×C4—948no—
730C22×C4—1884no—
731C22×C4—18816no—
732C22×C4—1884no—
733C22×C4—18816no—
734C22×C4C2×C4×D4714yes—
735C22×C4D4×D4714yes—
736C22×C4C2×C22⋊D4714yes—
737C22×C4C2×C22⋊D4714yes—
738C22×C4C23×D4712yes—
739C22×C4C23×D4712yes—
740C22×C4C23×D4712yes—
741C22×C4C23×D4712yes—
742C22×C4C23×D4712yes—
743C4⋊C4—28no—
744C4⋊C4—4716no—
745C4⋊C4—4716no—
746C4⋊C4—948no—
747C4⋊C4—948no—
748C4⋊C4—948no—
749C4⋊C4—948no—
750C22⋊C4—28no—
751C22⋊C4—4716no—
752C22⋊C4—4716no—
753C22⋊C4—948no—
754C22⋊C4—948no—
755C22⋊C4—948no—
756C22⋊C4—948no—
757C22⋊C4—1884no—
758C22⋊C4—1884no—
759C22⋊C4C2×C22⋊D47116yescomplemented
760C42—28no—
761C42—948no—
762C42—948no—
763C42—948no—
764C23—28no—
765C23—28no—
766C23—28no—
767C23—28no—
768C23—28no—
769C23—28no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—28no—
775C23—28no—
776C23—28no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—44no—
784C23—44no—
785C23—44no—
786C23—44no—
787C23—474no—
788C23—948no—
789C23—948no—
790C23—948no—
791C23—942no—
792C23—942no—
793C23—942no—
794C23—942no—
795C23—942no—
796C23—942no—
797C23—1884no—
798C23—1884no—
799C23—1884no—
800C23—1884no—
801C23C4×C22⋊D47116yescomplemented
802C23C22×C4×D4714yes—
803C23C22×C4×D4714yes—
804C23C22×C4×D4712yes—
805C23C2×D4×D4712yes—
806C23C22×C22⋊D4714yes—
807C23C22×C22⋊D4712yes—
808C23#41×D4712yes—
809C23C2×#1062535014yes—
810C23C2×#1062535012yes—
811C23#1309406912yes—
812C23#1309407112yes—
813C23C24×D4711yescharacteristic
814D4—232no—
815D4—9432no—
816D4—9432no—
817C2×C4—28no—
818C2×C4—28no—
819C2×C4—28no—
820C2×C4—28no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—416no—
833C2×C4—416no—
834C2×C4—44no—
835C2×C4—4716no—
836C2×C4—474no—
837C2×C4—474no—
838C2×C4—474no—
839C2×C4—474no—
840C2×C4—474no—
841C2×C4—474no—
842C2×C4—9432no—
843C2×C4—948no—
844C2×C4—948no—
845C2×C4—948no—
846C2×C4—942no—
847C2×C4—942no—
848C2×C4—942no—
849C2×C4—942no—
850C2×C4—942no—
851C2×C4—942no—
852C2×C4—942no—
853C2×C4—942no—
854C2×C4—942no—
855C2×C4—942no—
856C2×C4—942no—
857C2×C4—942no—
858C2×C4—942no—
859C2×C4—942no—
860C2×C4—942no—
861C2×C4—18816no—
862C2×C4—18816no—
863C2×C4—1884no—
864C2×C4—1884no—
865C2×C4—1884no—
866C2×C4C22×C4×D4714yes—
867C2×C4C2×D4×D4714yes—
868C2×C4C22×C22⋊D4714yes—
869C2×C4C22×C22⋊D4714yes—
870C22—24no—
871C22—24no—
872C22—24no—
873C22—24no—
874C22—24no—
875C22—232no—
876C22—24no—
877C22—24no—
878C22—24no—
879C22—24no—
880C22—42no—
881C22—42no—
882C22—42no—
883C22—416no—
884C22—42no—
885C22—944no—
886C22—944no—
887C22—944no—
888C22—1882no—
889C22—1882no—
890C22—1882no—
891C22—18816no—
892C22—1882no—
893C22C4×D4×D4714yes—
894C22C2×C4×C22⋊D4714yes—
895C22C2×C4×C22⋊D4718yescomplemented
896C22#1568960214yes—
897C22D4×C22⋊D4714yes—
898C22#1568977214yes—
899C22#1568978214yes—
900C22#1568982214yes—
901C22C23×C4×D4711yescharacteristic
902C22C22×D4×D4711yescharacteristic
903C22C23×C22⋊D4711yescharacteristic
904C22C2×#41×D4711yescharacteristic
905C22C22×#1062535011yescharacteristic
906C22C2×#1309406911yescharacteristic
907C22C2×#1309407111yescharacteristic
908C4—24no—
909C4—24no—
910C4—24no—
911C4—24no—
912C4—42no—
913C4—478no—
914C4—944no—
915C4—944no—
916C4—944no—
917C4—1882no—
918C4—1882no—
919C4—1882no—
920C2—28no—
921C2—44no—
922C2—1884no—
923C2#2024640518yesdirect product factor
924C2C2×C4×D4×D4711yescharacteristic
925C2C22×C4×C22⋊D4711yescharacteristic
926C2C2×#1568960211yescharacteristic
927C2C2×D4×C22⋊D4711yescharacteristic
928C2C2×#1568977211yescharacteristic
929C2C2×#1568978211yescharacteristic
930C2C2×#1568982211yescharacteristic
subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC22×C4×D4×C47C2
socleC24×C47C24
prime radicalC22×#13093996C2
cosocleC23×C47C25
hypercenterC22×C4×D4D47
hypocenterC47C2×#2361
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
2. C22×C4×C22⋊D47C2semidirect
3. C22×(C22⋊D47)⋊C4C2semidirect
4. C23×Dic47⋊C4C2semidirect
5. #20246405C2direct (N × H)
6. C2×#15689023C2semidirect
7. C2×#15689018C2semidirect
8. C2×#15689014C2semidirect
9. C2×#15689011C2semidirect
10. C2×#15689003C2semidirect
11. C2×#15689002C2semidirect
12. C2×#15688996C2semidirect
13. C2×#15688994C2semidirect
14. C2×C4×Dic47⋊C4C2semidirect
15. C2×C22⋊C4×Dic47C2semidirect
16. C22×C4×D4×C47C2semidirect
22. C2×#13093996C4semidirect
25. C2×C4×C22⋊D47C22semidirect
27. C2×(C22⋊D47)⋊C4C22semidirect
35. C22×Dic47⋊C4C22semidirect
47. #15689023C22semidirect
48. #15689018C22semidirect
49. #15689014C22semidirect
50. #15689011C22semidirect
51. #15689003C22semidirect
52. #15689002C22semidirect
53. #15688996C22semidirect
54. #15688994C22semidirect
55. C4×Dic47⋊C4C22semidirect
56. C22⋊C4×Dic47C22semidirect
67. C2×C4×D4×C47C22semidirect
77. C22×C22⋊D47C2×C4semidirect
78. C22×C22⋊D47C2×C4semidirect
86. C23×Dic47C2×C4semidirect
100. #13093996C2×C4semidirect
108. C2×Dic47⋊C4C2×C4semidirect
109. C2×Dic47⋊C4D4semidirect
119. C2×C22⋊Dic47C2×C4semidirect
127. C2×(C2×D47)⋊C4C2×C4semidirect
148. C22×D4×C47C2×C4semidirect
167. C2×C22⋊C4×C47D4semidirect
200. C2×D4×C47C22×C4semidirect
235. C2×C22⋊D47C22×C4semidirect
236. C2×C22⋊D47C22×C4semidirect
262. C22×Dic47C22×C4semidirect
279. C22⋊C4×C47C2×D4semidirect
284. C22⋊Dic47C22×C4semidirect
288. (C2×D47)⋊C4C22×C4semidirect
293. Dic47⋊C4C22×C4semidirect
294. Dic47⋊C4C2×D4semidirect
321. C23×C47C4×D4semidirect
396. C2×Dic47C4×D4semidirect
422. C22×C47C2×C4×D4semidirect
454. Dic47C2×C4×D4semidirect
458. C22×C4×D4D47semidirect
473. C2×C47#2361semidirect
497. C2×C4×D4C2×D47semidirect
537. C47C2×#2361semidirect
551. C22×D4C4×D47semidirect
621. C2×C22⋊C4C22⋊D47semidirect
674. C2×D4C2×C4×D47semidirect
759. C22⋊C4C2×C22⋊D47semidirect
801. C23C4×C22⋊D47semidirect
895. C22C2×C4×C22⋊D47semidirect
923. C2#20246405direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130939962
C22×C4×C22⋊D472
C22×(C22⋊D47)⋊C42
C23×Dic47⋊C42
#202464052
C2×#156890232
C2×#156890182
C2×#156890142
C2×#156890112
C2×#156890032
C2×#156890022
C2×#156889962
C2×#156889942
C2×C4×Dic47⋊C42
C2×C22⋊C4×Dic472
C22×C4×D4×C472
C2×#236147