Finite Group Databasebeta

← C2×#20247050 #26383702

Subgroups — C2×#20247050 #26383702

Order 12032.

4926 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094004C211yesmaximal, characteristic, complemented
2C22×#13094002C211yesmaximal, characteristic, complemented
3C22×C22⋊C4×D47C211yesmaximal, characteristic
4C22×C22⋊C4×D47C211yesmaximal, characteristic
5#20247050C2116yesmaximal, direct product factor
6C2×#15689059C211yesmaximal, characteristic, complemented
7C2×#15689046C211yesmaximal, characteristic, complemented
8C2×#15689035C211yesmaximal, characteristic, complemented
9C2×#15688997C211yesmaximal, characteristic, complemented
10C2×#15688994C211yesmaximal, characteristic, complemented
11C2×#15688994C211yesmaximal, characteristic, complemented
12C2×#15688994C211yesmaximal, characteristic, complemented
13C2×#15688982C211yesmaximal, characteristic, complemented
14C2×#15688980C211yesmaximal, characteristic, complemented
15C2×#15688978C211yesmaximal, characteristic
16C2×C47×#396C211yesmaximal, characteristic, complemented
17C25×D47C2211yescharacteristic
18C23×Dic94C2211yescharacteristic, complemented
19C23×C4×D47C2211yescharacteristic
20C23×C4×D47C2211yescharacteristic
21C23×C4×D47C2211yescharacteristic
22C23×C4×D47C2211yescharacteristic
23C2×#13094004—28no—
24C2×#13094004C2218yescomplemented
25C2×#13094002—28no—
26C2×#13094002C2218yescomplemented
27C22×C4⋊Dic47C2211yescharacteristic, complemented
28C22×C4⋊Dic47C2211yescharacteristic, complemented
29C22×Dic47⋊C4C2211yescharacteristic, complemented
30C22×Dic47⋊C4C2211yescharacteristic, complemented
31C22×Dic47⋊C4C2211yescharacteristic, complemented
32C22×Dic47⋊C4C2211yescharacteristic, complemented
33C22×C22⋊Dic47C2211yescharacteristic
34C22×C22⋊Dic47C2211yescharacteristic
35C22×C22⋊Dic47C2211yescharacteristic
36C22×(C2×D47)⋊C4C2211yescharacteristic
37C22×(C2×D47)⋊C4C2211yescharacteristic
38C22×(C2×D47)⋊C4C2211yescharacteristic
39C22×(C2×D47)⋊C4C2211yescharacteristic
40C22×(C2×D47)⋊C4C2211yescharacteristic
41C22×(C2×D47)⋊C4C2211yescharacteristic
42C22×(C2×D47)⋊C4C2211yescharacteristic
43C22×(C2×D47)⋊C4C2211yescharacteristic
44C2×C22⋊C4×D47—28no—
45C2×C22⋊C4×D47—28no—
46C2×C22⋊C4×D47C2218yes—
47C2×C22⋊C4×D47C2218yes—
48#15689059C2218yescomplemented
49#15689046C2218yescomplemented
50#15689035C2218yescomplemented
51#15688997C2218yescomplemented
52#15688994C2218yescomplemented
53#15688994C2218yescomplemented
54#15688994C2218yescomplemented
55#15688982C2218yescomplemented
56#15688980C2218yescomplemented
57#15688978C2218yes—
58C2×C47⋊#95C2211yescharacteristic, complemented
59C2×C47⋊#95C2211yescharacteristic, complemented
60C2×C47⋊#95C2211yescharacteristic, complemented
61C2×C47⋊#95C2211yescharacteristic, complemented
62C2×C47⋊#95C2211yescharacteristic, complemented
63C22×C4⋊C4×C47C2211yescharacteristic, complemented
64C22×C4⋊C4×C47C2211yescharacteristic, complemented
65C22×C4⋊C4×C47C2211yescharacteristic, complemented
66C22×C22⋊C4×C47C2211yescharacteristic
67C22×C22⋊C4×C47C2211yescharacteristic
68C22×C22⋊C4×C47C2211yescharacteristic
69C47×#396C2218yescomplemented
70C2×#95×C47C2211yescharacteristic, complemented
71C24×D47—24no—
72C24×D47—24no—
73C24×D47—24no—
74C24×D47—24no—
75C24×D47—42no—
76C24×D47—42no—
77C24×D47Q818yescomplemented
78C24×D47C2314yes—
79C24×D47C2311yescharacteristic
80C24×D47C2311yescharacteristic
81C22×Dic94—24no—
82C22×Dic94—24no—
83C22×Dic94—42no—
84C22×Dic94C2314yescomplemented
85C23×Dic47C2311yescharacteristic
86C23×Dic47C2311yescharacteristic
87C23×Dic47C2311yescharacteristic
88C23×Dic47C2311yescharacteristic
89C23×Dic47C2311yescharacteristic
90C23×Dic47C2311yescharacteristic
91C22×C4×D47—24no—
92C22×C4×D47—24no—
93C22×C4×D47—24no—
94C22×C4×D47—24no—
95C22×C4×D47—24no—
96C22×C4×D47—24no—
97C22×C4×D47—24no—
98C22×C4×D47—24no—
99C22×C4×D47—42no—
100C22×C4×D47—42no—
101C22×C4×D47—42no—
102C22×C4×D47—42no—
103C22×C4×D47C2314yes—
104C22×C4×D47C2314yes—
105C22×C4×D47C2314yes—
106C22×C4×D47C2314yes—
107#13094004—232no—
108#13094002—232no—
109C2×C4⋊Dic47—24no—
110C2×C4⋊Dic47—24no—
111C2×C4⋊Dic47C2314yescomplemented
112C2×C4⋊Dic47C2314yescomplemented
113C2×Dic47⋊C4—24no—
114C2×Dic47⋊C4—24no—
115C2×Dic47⋊C4—42no—
116C2×Dic47⋊C4—42no—
117C2×Dic47⋊C4C2314yescomplemented
118C2×Dic47⋊C4C2314yescomplemented
119C2×Dic47⋊C4C2314yescomplemented
120C2×Dic47⋊C4C2314yescomplemented
121C2×C22⋊Dic47—24no—
122C2×C22⋊Dic47—24no—
123C2×C22⋊Dic47—42no—
124C2×C22⋊Dic47C2314yes—
125C2×C22⋊Dic47C2314yes—
126C2×C22⋊Dic47C2314yes—
127C2×(C2×D47)⋊C4—24no—
128C2×(C2×D47)⋊C4—24no—
129C2×(C2×D47)⋊C4—24no—
130C2×(C2×D47)⋊C4—24no—
131C2×(C2×D47)⋊C4—24no—
132C2×(C2×D47)⋊C4—24no—
133C2×(C2×D47)⋊C4D418yes—
134C2×(C2×D47)⋊C4D418yes—
135C2×(C2×D47)⋊C4C2314yes—
136C2×(C2×D47)⋊C4C2314yes—
137C2×(C2×D47)⋊C4C2314yes—
138C2×(C2×D47)⋊C4C2314yes—
139C2×(C2×D47)⋊C4C2314yes—
140C2×(C2×D47)⋊C4C2314yes—
141C2×(C2×D47)⋊C4C2314yes—
142C2×(C2×D47)⋊C4C2314yes—
143C22⋊C4×D47—232no—
144C22⋊C4×D47—232no—
145C47⋊#95C2314yescomplemented
146C47⋊#95C2314yescomplemented
147C47⋊#95C2314yescomplemented
148C47⋊#95C2314yescomplemented
149C47⋊#95C2314yescomplemented
150C25×C47C2311yescharacteristic
151C23×C4×C47C2311yescharacteristic
152C23×C4×C47C2311yescharacteristic
153C23×C4×C47C2311yescharacteristic
154C23×C4×C47C2311yescharacteristic
155C23×C4×C47C2311yescharacteristic
156C23×C4×C47C2311yescharacteristic
157C2×C4⋊C4×C47—24no—
158C2×C4⋊C4×C47—24no—
159C2×C4⋊C4×C47—42no—
160C2×C4⋊C4×C47C2314yescomplemented
161C2×C4⋊C4×C47C2314yescomplemented
162C2×C4⋊C4×C47C2314yescomplemented
163C2×C22⋊C4×C47—24no—
164C2×C22⋊C4×C47—24no—
165C2×C22⋊C4×C47—42no—
166C2×C22⋊C4×C47C2314yes—
167C2×C22⋊C4×C47C2314yes—
168C2×C22⋊C4×C47C2314yes—
169#95×C47C2314yescomplemented
170C24×C47—22no—
171C24×C47—22no—
172C24×C47—22no—
173C24×C47—22no—
174C24×C47—22no—
175C24×C47—22no—
176C24×C47C2×Q814yes—
177C24×C47C2412yes—
178C24×C47C2411yescharacteristic
179C23×D47—22no—
180C23×D47—22no—
181C23×D47—22no—
182C23×D47—22no—
183C23×D47—22no—
184C23×D47—22no—
185C23×D47—22no—
186C23×D47—22no—
187C23×D47—232no—
188C23×D47—232no—
189C23×D47—28no—
190C23×D47—28no—
191C23×D47—28no—
192C23×D47—28no—
193C23×D47—416no—
194C23×D47—44no—
195C23×D47—44no—
196C23×D47—416no—
197C23×D47—416no—
198C23×D47—416no—
199C23×D47—416no—
200C23×D47C2×D414yes—
201C23×D47C2×D414yes—
202C23×D47C2×Q814yes—
203C23×D47C2×Q814yes—
204C23×D47C2×Q8116yescomplemented
205C23×D47#4114yes—
206C23×D47#4114yes—
207C23×D47C2412yes—
208C23×D47C2412yes—
209C22×C4×C47—22no—
210C22×C4×C47—22no—
211C22×C4×C47—22no—
212C22×C4×C47—22no—
213C22×C4×C47—22no—
214C22×C4×C47—22no—
215C22×C4×C47—22no—
216C22×C4×C47—22no—
217C22×C4×C47—22no—
218C22×C4×C47—22no—
219C22×C4×C47—22no—
220C22×C4×C47—22no—
221C22×C4×C47—22no—
222C22×C4×C47—22no—
223C22×C4×C47—22no—
224C22×C4×C47—22no—
225C22×C4×C47C2×D414yes—
226C22×C4×C47C2×D414yes—
227C22×C4×C47C2412yes—
228C22×C4×C47C2412yes—
229C22×C4×C47C2412yes—
230C22×C4×C47C2412yes—
231C22×C4×C47C2412yes—
232C22×C4×C47C2412yes—
233C22×Dic47—22no—
234C22×Dic47—22no—
235C22×Dic47—22no—
236C22×Dic47—22no—
237C22×Dic47—22no—
238C22×Dic47—22no—
239C22×Dic47—22no—
240C22×Dic47—22no—
241C22×Dic47—22no—
242C22×Dic47—22no—
243C22×Dic47—22no—
244C22×Dic47—22no—
245C22×Dic47—22no—
246C22×Dic47—22no—
247C22×Dic47—22no—
248C22×Dic47—22no—
249C22×Dic47C2×D414yes—
250C22×Dic47C2×D414yes—
251C22×Dic47C2412yes—
252C22×Dic47C2412yes—
253C22×Dic47C2412yes—
254C22×Dic47C2412yes—
255C22×Dic47C2412yes—
256C22×Dic47C2412yes—
257C2×C4×D47—28no—
258C2×C4×D47—28no—
259C2×C4×D47—28no—
260C2×C4×D47—28no—
261C2×C4×D47—28no—
262C2×C4×D47—28no—
263C2×C4×D47—28no—
264C2×C4×D47—28no—
265C2×C4×D47—44no—
266C2×C4×D47—44no—
267C2×C4×D47—44no—
268C2×C4×D47—44no—
269C2×C4×D47—416no—
270C2×C4×D47—416no—
271C2×C4×D47—416no—
272C2×C4×D47—416no—
273C2×Dic94—28no—
274C2×Dic94—28no—
275C2×Dic94—44no—
276C2×Dic94—416no—
277C4⋊C4×C47—28no—
278C4⋊C4×C47—28no—
279C4⋊C4×C47—44no—
280C22⋊C4×C47—28no—
281C22⋊C4×C47—28no—
282C22⋊C4×C47—44no—
283C22⋊Dic47—28no—
284C22⋊Dic47—28no—
285C22⋊Dic47—44no—
286(C2×D47)⋊C4—28no—
287(C2×D47)⋊C4—28no—
288(C2×D47)⋊C4—28no—
289(C2×D47)⋊C4—28no—
290(C2×D47)⋊C4—28no—
291(C2×D47)⋊C4—28no—
292(C2×D47)⋊C4C2×D4116yes—
293(C2×D47)⋊C4C2×D4116yes—
294C4⋊Dic47—28no—
295C4⋊Dic47—28no—
296Dic47⋊C4—28no—
297Dic47⋊C4—28no—
298Dic47⋊C4—44no—
299Dic47⋊C4—44no—
300C23×C47—28no—
301C23×C47—28no—
302C23×C47—28no—
303C23×C47—22no—
304C23×C47—22no—
305C23×C47—22no—
306C23×C47—22no—
307C23×C47—22no—
308C23×C47—22no—
309C23×C47—44no—
310C23×C47—44no—
311C23×C47—44no—
312C23×C47—44no—
313C23×C47C22×D412yes—
314C23×C47C22×D412yes—
315C23×C47C22×Q814yes—
316C23×C47C22×Q812yes—
317C23×C47C2×#4112yes—
318C23×C47C2×#4112yes—
319C23×C47H(5,𝔽2)12yes—
320C23×C47H(5,𝔽2)12yes—
321C23×C47C2511yescharacteristic
322C22×D47—28no—
323C22×D47—28no—
324C22×D47—28no—
325C22×D47—28no—
326C22×D47—28no—
327C22×D47—28no—
328C22×D47—28no—
329C22×D47—28no—
330C22×D47—28no—
331C22×D47—28no—
332C22×D47—28no—
333C22×D47—28no—
334C22×D47—22no—
335C22×D47—22no—
336C22×D47—22no—
337C22×D47—22no—
338C22×D47—22no—
339C22×D47—22no—
340C22×D47—22no—
341C22×D47—22no—
342C22×D47—232no—
343C22×D47—232no—
344C22×D47—416no—
345C22×D47—4128no—
346C22×D47—416no—
347C22×D47—416no—
348C22×D47—416no—
349C22×D47—416no—
350C22×D47C22⋊Q8116yescomplemented
351C22×D47C22⋊Q8116yescomplemented
352C22×D47C22×D414yes—
353C22×D47C22×D414yes—
354C22×D47C22×Q814yes—
355C22×D47C22×Q814yes—
356C22×D47C2×#4114yes—
357C22×D47C2×#4114yes—
358C2×C4×C47—28no—
359C2×C4×C47—28no—
360C2×C4×C47—22no—
361C2×C4×C47—22no—
362C2×C4×C47—22no—
363C2×C4×C47—22no—
364C2×C4×C47—22no—
365C2×C4×C47—22no—
366C2×C4×C47—22no—
367C2×C4×C47—22no—
368C2×C4×C47—22no—
369C2×C4×C47—22no—
370C2×C4×C47—22no—
371C2×C4×C47—22no—
372C2×C4×C47—22no—
373C2×C4×C47—22no—
374C2×C4×C47—22no—
375C2×C4×C47—22no—
376C2×C4×C47—44no—
377C2×C4×C47—44no—
378C2×C4×C47—44no—
379C2×C4×C47—44no—
380C2×C4×C47C22×D414yes—
381C2×C4×C47C22×D414yes—
382C2×Dic47—28no—
383C2×Dic47—28no—
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—22no—
393C2×Dic47—22no—
394C2×Dic47—22no—
395C2×Dic47—22no—
396C2×Dic47—22no—
397C2×Dic47—22no—
398C2×Dic47—22no—
399C2×Dic47—22no—
400C2×Dic47—44no—
401C2×Dic47—44no—
402C2×Dic47—44no—
403C2×Dic47—44no—
404C2×Dic47C22×D414yes—
405C2×Dic47C22×D414yes—
406C4×D47—416no—
407C4×D47—416no—
408C4×D47—416no—
409C4×D47—416no—
410Dic94—416no—
411C2×#2437—471nomaximal, Sylow
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×C22⋊Q814yes—
421C22×C47C2×C22⋊Q814yes—
422C22×C47#54314yes—
423C22×C47D4214yes—
424C22×C47#54614yes—
425C22×C47#54614yes—
426C22×C47#55114yes—
427C22×C47C23×D411yescharacteristic
428C22×C47C23×D411yescharacteristic
429C22×C47C23×Q811yescharacteristic
430C22×C47C22×#4111yescharacteristic
431C22×C47C22×#4111yescharacteristic
432C22×C47C2×H(5,𝔽2)11yescharacteristic
433C22×C47C2×H(5,𝔽2)11yescharacteristic
434C2×D47—24no—
435C2×D47—24no—
436C2×D47—24no—
437C2×D47—24no—
438C2×D47—232no—
439C2×D47—232no—
440C2×D47—24no—
441C2×D47—24no—
442C2×D47—24no—
443C2×D47—24no—
444C2×D47—24no—
445C2×D47—24no—
446C2×D47—24no—
447C2×D47—24no—
448C2×D47—464no—
449C2×D47C2×C22⋊Q818yescomplemented
450C2×D47C2×C22⋊Q818yescomplemented
451C4×C47—24no—
452C4×C47—24no—
453C4×C47—42no—
454C4×C47—42no—
455C4×C47—42no—
456C4×C47—42no—
457Dic47—24no—
458Dic47—24no—
459Dic47—42no—
460Dic47—42no—
461Dic47—42no—
462Dic47—42no—
463C22×C22⋊Q8—471no—
464C22×C22⋊Q8—471no—
465C23×C22⋊C4—471no—
466C23×C22⋊C4—471no—
467#2437—4716no—
468C2×#399—471no—
469C2×#396—471no—
470C2×#396D4711yescharacteristic, complemented
471C2×#393—471no—
472C2×#385—471no—
473C2×#385—471no—
474C2×#385—471no—
475C2×#385—471no—
476C2×#380—471no—
477C2×#380—471no—
478C2×#379—471no—
479C2×C47—44no—
480C2×C47#243718yescomplemented
481C2×C47C22×C22⋊Q811yescharacteristic
482C2×C47C22×C22⋊Q811yescharacteristic
483C2×C47C2×#54311yescharacteristic
484C2×C47C2×D4211yescharacteristic
485C2×C47C2×#54611yescharacteristic
486C2×C47C2×#54611yescharacteristic
487C2×C47C2×#55111yescharacteristic
488D47—28no—
489D47—28no—
490C26—471no—
491C23×Q8—471no—
492C24×C4—471no—
493C24×C4—471no—
494C24×C4—471no—
495C24×C4—471no—
496C2×C22⋊Q8—478no—
497C2×C22⋊Q8—478no—
498C2×C22⋊Q8—948no—
499C2×C22⋊Q8—948no—
500C22×C4⋊C4—471no—
501C22×C4⋊C4—471no—
502C22×C4⋊C4—471no—
503C22×C4⋊C4—471no—
504C22×C4⋊C4—471no—
505C22×C4⋊C4—471no—
506C22×C4⋊C4C2×D4711yescharacteristic, complemented
507C22×C4⋊C4C2×D4711yescharacteristic, complemented
508C22×C4⋊C4C2×D4711yescharacteristic, complemented
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⋊C4—471no—
516C22×C22⋊C4—471no—
517C22×C22⋊C4—471no—
518C22×C22⋊C4—471no—
519C22×C22⋊C4—471no—
520C22×C22⋊C4—478no—
521C22×C22⋊C4—478no—
522C22×C22⋊C4—948no—
523C22×C22⋊C4—948no—
524C22×C22⋊C4C2×D4711yescharacteristic
525C22×C22⋊C4C2×D4711yescharacteristic
526C22×C22⋊C4C2×D4711yescharacteristic
527#399—478no—
528#396—478no—
529#396C2×D4718yescomplemented
530#393—478no—
531#385—478no—
532#385—478no—
533#385—478no—
534#385—478no—
535#380—478no—
536#380—478no—
537#379—478no—
538C2×#95—471no—
539C2×#95—471no—
540C2×#95—471no—
541C2×#95—471no—
542C2×#95—471no—
543C2×#95C2×D4711yescharacteristic, complemented
544C47C2×#243711yescharacteristic, complemented, Sylow
545C25—471no—
546C25—471no—
547C25—478no—
548C25—474no—
549C25—944no—
550C25—944no—
551C25—944no—
552C25—944no—
553C25—1882no—
554C25—1882no—
555C25C22×D4711yescharacteristic
556C22×Q8—474no—
557C22×Q8—944no—
558C22×Q8—944no—
559C22×Q8—1882no—
560C23×C4—471no—
561C23×C4—471no—
562C23×C4—471no—
563C23×C4—471no—
564C23×C4—471no—
565C23×C4—471no—
566C23×C4—474no—
567C23×C4—474no—
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—944no—
577C23×C4—944no—
578C23×C4—1882no—
579C23×C4—1882no—
580C23×C4—1882no—
581C23×C4—1882no—
582C23×C4C22×D4711yescharacteristic
583C23×C4C22×D4711yescharacteristic
584C23×C4C22×D4711yescharacteristic
585C23×C4C22×D4711yescharacteristic
586C23×C4C22×D4711yescharacteristic
587C23×C4C22×D4711yescharacteristic
588C22⋊Q8—9432no—
589C22⋊Q8—9432no—
590C2×C4⋊C4—24no—
591C2×C4⋊C4—24no—
592C2×C4⋊C4—42no—
593C2×C4⋊C4—474no—
594C2×C4⋊C4—474no—
595C2×C4⋊C4—474no—
596C2×C4⋊C4—474no—
597C2×C4⋊C4—474no—
598C2×C4⋊C4—474no—
599C2×C4⋊C4—944no—
600C2×C4⋊C4—944no—
601C2×C4⋊C4—944no—
602C2×C4⋊C4—944no—
603C2×C4⋊C4—1882no—
604C2×C4⋊C4—1882no—
605C2×C4⋊C4C22×D4714yescomplemented
606C2×C4⋊C4C22×D4714yescomplemented
607C2×C4⋊C4C22×D4714yescomplemented
608C2×C22⋊C4—24no—
609C2×C22⋊C4—24no—
610C2×C22⋊C4—42no—
611C2×C22⋊C4—478no—
612C2×C22⋊C4—478no—
613C2×C22⋊C4—474no—
614C2×C22⋊C4—474no—
615C2×C22⋊C4—474no—
616C2×C22⋊C4—474no—
617C2×C22⋊C4—474no—
618C2×C22⋊C4—474no—
619C2×C22⋊C4—474no—
620C2×C22⋊C4—474no—
621C2×C22⋊C4—474no—
622C2×C22⋊C4—474no—
623C2×C22⋊C4—474no—
624C2×C22⋊C4—9432no—
625C2×C22⋊C4—9432no—
626C2×C22⋊C4—944no—
627C2×C22⋊C4—944no—
628C2×C22⋊C4—944no—
629C2×C22⋊C4—944no—
630C2×C22⋊C4—944no—
631C2×C22⋊C4—944no—
632C2×C22⋊C4—944no—
633C2×C22⋊C4—944no—
634C2×C22⋊C4—1882no—
635C2×C22⋊C4C22×D4714yes—
636C2×C22⋊C4C22×D4714yes—
637C2×C22⋊C4C22×D4714yes—
638#95—474no—
639#95—474no—
640#95—474no—
641#95—474no—
642#95—474no—
643#95C22×D4714yescomplemented
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—474no—
651C24—474no—
652C24—474no—
653C24—474no—
654C24—474no—
655C24—474no—
656C24—472no—
657C24—472no—
658C24—4716no—
659C24—948no—
660C24—948no—
661C24—9432no—
662C24—9432no—
663C24—948no—
664C24—948no—
665C24—942no—
666C24—942no—
667C24—942no—
668C24—942no—
669C24—942no—
670C24—942no—
671C24—942no—
672C24—942no—
673C24—18816no—
674C24—1884no—
675C24—1884no—
676C24—18816no—
677C24—18816no—
678C24—18816no—
679C24—18816no—
680C24Q8×D4714yes—
681C24C23×D4712yes—
682C24C23×D4711yescharacteristic
683C2×Q8—948no—
684C2×Q8—948no—
685C2×Q8—1884no—
686C2×Q8—18816no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—474no—
704C22×C4—474no—
705C22×C4—472no—
706C22×C4—472no—
707C22×C4—472no—
708C22×C4—472no—
709C22×C4—472no—
710C22×C4—472no—
711C22×C4—948no—
712C22×C4—948no—
713C22×C4—948no—
714C22×C4—948no—
715C22×C4—948no—
716C22×C4—948no—
717C22×C4—942no—
718C22×C4—942no—
719C22×C4—942no—
720C22×C4—942no—
721C22×C4—942no—
722C22×C4—942no—
723C22×C4—942no—
724C22×C4—942no—
725C22×C4—942no—
726C22×C4—942no—
727C22×C4—942no—
728C22×C4—942no—
729C22×C4—942no—
730C22×C4—942no—
731C22×C4—942no—
732C22×C4—942no—
733C22×C4—948no—
734C22×C4—948no—
735C22×C4—1884no—
736C22×C4—1884no—
737C22×C4—1884no—
738C22×C4—1884no—
739C22×C4—18816no—
740C22×C4—18816no—
741C22×C4—18816no—
742C22×C4—18816no—
743C22×C4D4×D4714yes—
744C22×C4D4×D4714yes—
745C22×C4C23×D4712yes—
746C22×C4C23×D4712yes—
747C22×C4C23×D4712yes—
748C22×C4C23×D4712yes—
749C22×C4C23×D4712yes—
750C22×C4C23×D4712yes—
751C4⋊C4—28no—
752C4⋊C4—28no—
753C4⋊C4—44no—
754C4⋊C4—948no—
755C4⋊C4—948no—
756C4⋊C4—948no—
757C4⋊C4—948no—
758C4⋊C4—1884no—
759C4⋊C4—1884no—
760C22⋊C4—28no—
761C22⋊C4—28no—
762C22⋊C4—44no—
763C22⋊C4—4716no—
764C22⋊C4—4716no—
765C22⋊C4—948no—
766C22⋊C4—948no—
767C22⋊C4—948no—
768C22⋊C4—948no—
769C22⋊C4—948no—
770C22⋊C4—948no—
771C22⋊C4—948no—
772C22⋊C4—948no—
773C22⋊C4—1884no—
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—4716no—
788C23—4716no—
789C23—474no—
790C23—474no—
791C23—474no—
792C23—474no—
793C23—474no—
794C23—474no—
795C23—9432no—
796C23—9432no—
797C23—948no—
798C23—948no—
799C23—948no—
800C23—948no—
801C23—948no—
802C23—948no—
803C23—948no—
804C23—948no—
805C23—948no—
806C23—948no—
807C23—948no—
808C23—948no—
809C23—942no—
810C23—942no—
811C23—942no—
812C23—942no—
813C23—942no—
814C23—942no—
815C23—942no—
816C23—942no—
817C23—18816no—
818C23—188128no—
819C23—18816no—
820C23—18816no—
821C23—18816no—
822C23—18816no—
823C23C2×D4×D4712yes—
824C23C2×D4×D4712yes—
825C23C2×Q8×D4714yes—
826C23C2×Q8×D4712yes—
827C23#41×D4712yes—
828C23#41×D4712yes—
829C23#1309406912yes—
830C23#1309407012yes—
831C23C24×D4711yescharacteristic
832Q8—18816no—
833C2×C4—28no—
834C2×C4—28no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—44no—
852C2×C4—44no—
853C2×C4—44no—
854C2×C4—44no—
855C2×C4—474no—
856C2×C4—474no—
857C2×C4—948no—
858C2×C4—948no—
859C2×C4—942no—
860C2×C4—942no—
861C2×C4—942no—
862C2×C4—942no—
863C2×C4—942no—
864C2×C4—942no—
865C2×C4—942no—
866C2×C4—942no—
867C2×C4—942no—
868C2×C4—942no—
869C2×C4—942no—
870C2×C4—942no—
871C2×C4—942no—
872C2×C4—942no—
873C2×C4—942no—
874C2×C4—942no—
875C2×C4—18816no—
876C2×C4—18816no—
877C2×C4—18816no—
878C2×C4—18816no—
879C2×C4—1884no—
880C2×C4—1884no—
881C2×C4—1884no—
882C2×C4—1884no—
883C2×C4C2×D4×D4714yes—
884C2×C4C2×D4×D4714yes—
885C22—24no—
886C22—24no—
887C22—24no—
888C22—416no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—478no—
894C22—478no—
895C22—9432no—
896C22—9432no—
897C22—944no—
898C22—944no—
899C22—944no—
900C22—944no—
901C22—944no—
902C22—944no—
903C22—944no—
904C22—944no—
905C22—944no—
906C22—944no—
907C22—944no—
908C22—944no—
909C22—18864no—
910C22C22⋊Q8×D4714yes—
911C22C22⋊Q8×D4714yes—
912C22#1568974814yes—
913C22#1568975714yes—
914C22#1568976214yes—
915C22#1568977014yes—
916C22#1568979814yes—
917C22C22×D4×D4711yescharacteristic
918C22C22×D4×D4711yescharacteristic
919C22C22×Q8×D4711yescharacteristic
920C22C2×#41×D4711yescharacteristic
921C22C2×#41×D4711yescharacteristic
922C22C2×#1309406911yescharacteristic
923C22C2×#1309407011yescharacteristic
924C4—24no—
925C4—24no—
926C4—42no—
927C4—42no—
928C4—42no—
929C4—42no—
930C4—944no—
931C4—944no—
932C4—1882no—
933C4—1882no—
934C4—1882no—
935C4—1882no—
936C2—44no—
937C2—948no—
938C2—948no—
939C2#2024705018yesdirect product factor
940C2C2×C22⋊Q8×D4711yescharacteristic
941C2C2×C22⋊Q8×D4711yescharacteristic
942C2C2×#1568974811yescharacteristic
943C2C2×#1568975711yescharacteristic
944C2C2×#1568976211yescharacteristic
945C2C2×#1568977011yescharacteristic
946C2C2×#1568979811yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#396C2
socleC24×C47C24
prime radicalC25×D47C22
hypercenterC2×#396D47
hypocenterC47C2×#2437
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#13094004C2semidirect
2. C22×#13094002C2semidirect
5. #20247050C2direct (N × H)
6. C2×#15689059C2semidirect
7. C2×#15689046C2semidirect
8. C2×#15689035C2semidirect
9. C2×#15688997C2semidirect
10. C2×#15688994C2semidirect
11. C2×#15688994C2semidirect
12. C2×#15688994C2semidirect
13. C2×#15688982C2semidirect
14. C2×#15688980C2semidirect
16. C2×C47×#396C2semidirect
18. C23×Dic94C22semidirect
24. C2×#13094004C22semidirect
26. C2×#13094002C22semidirect
27. C22×C4⋊Dic47C22semidirect
28. C22×C4⋊Dic47C22semidirect
29. C22×Dic47⋊C4C22semidirect
30. C22×Dic47⋊C4C22semidirect
31. C22×Dic47⋊C4C22semidirect
32. C22×Dic47⋊C4C22semidirect
48. #15689059C22semidirect
49. #15689046C22semidirect
50. #15689035C22semidirect
51. #15688997C22semidirect
52. #15688994C22semidirect
53. #15688994C22semidirect
54. #15688994C22semidirect
55. #15688982C22semidirect
56. #15688980C22semidirect
58. C2×C47⋊#95C22semidirect
59. C2×C47⋊#95C22semidirect
60. C2×C47⋊#95C22semidirect
61. C2×C47⋊#95C22semidirect
62. C2×C47⋊#95C22semidirect
63. C22×C4⋊C4×C47C22semidirect
64. C22×C4⋊C4×C47C22semidirect
65. C22×C4⋊C4×C47C22semidirect
69. C47×#396C22semidirect
70. C2×#95×C47C22semidirect
77. C24×D47Q8semidirect
84. C22×Dic94C23semidirect
111. C2×C4⋊Dic47C23semidirect
112. C2×C4⋊Dic47C23semidirect
117. C2×Dic47⋊C4C23semidirect
118. C2×Dic47⋊C4C23semidirect
119. C2×Dic47⋊C4C23semidirect
120. C2×Dic47⋊C4C23semidirect
145. C47⋊#95C23semidirect
146. C47⋊#95C23semidirect
147. C47⋊#95C23semidirect
148. C47⋊#95C23semidirect
149. C47⋊#95C23semidirect
160. C2×C4⋊C4×C47C23semidirect
161. C2×C4⋊C4×C47C23semidirect
162. C2×C4⋊C4×C47C23semidirect
169. #95×C47C23semidirect
204. C23×D47C2×Q8semidirect
350. C22×D47C22⋊Q8semidirect
351. C22×D47C22⋊Q8semidirect
449. C2×D47C2×C22⋊Q8semidirect
450. C2×D47C2×C22⋊Q8semidirect
470. C2×#396D47semidirect
480. C2×C47#2437semidirect
506. C22×C4⋊C4C2×D47semidirect
507. C22×C4⋊C4C2×D47semidirect
508. C22×C4⋊C4C2×D47semidirect
529. #396C2×D47semidirect
543. C2×#95C2×D47semidirect
544. C47C2×#2437semidirect
605. C2×C4⋊C4C22×D47semidirect
606. C2×C4⋊C4C22×D47semidirect
607. C2×C4⋊C4C22×D47semidirect
643. #95C22×D47semidirect
939. C2#20247050direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940042
C22×#130940022
C22×C22⋊C4×D472
#202470502
C2×#156890592
C2×#156890462
C2×#156890352
C2×#156889972
C2×#156889942
C2×#156889822
C2×#156889802
C2×#156889782
C2×C47×#3962
C2×#243747