Finite Group Databasebeta

← C2×#20248305 #26388045

Subgroups — C2×#20248305 #26388045

Order 12032.

3614 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094002C211yesmaximal, characteristic, complemented
2C22×#13094001C211yesmaximal, characteristic, complemented
3C22×#13093989C211yesmaximal, characteristic, complemented
4C22×(C22⋊D47)⋊C4C211yesmaximal, characteristic
5#20248305C2116yesmaximal, direct product factor
6C2×#15689046C211yesmaximal, characteristic, complemented
7C2×#15689045C211yesmaximal, characteristic, complemented
8C2×#15689045C211yesmaximal, characteristic, complemented
9C2×#15689023C211yesmaximal, characteristic
10C2×#15689023C211yesmaximal, characteristic
11C2×#15689020C211yesmaximal, characteristic, complemented
12C2×#15689018C211yesmaximal, characteristic, complemented
13C2×#15688992C211yesmaximal, characteristic, complemented
14C2×#15688982C211yesmaximal, characteristic, complemented
15C2×#15688981C211yesmaximal, characteristic, complemented
16C2×C47×#396C211yesmaximal, characteristic, complemented
17C23×Dic94C2211yescharacteristic
18C23×C22⋊D47C2211yescharacteristic
19C24×Dic47C2211yescharacteristic
20C23×C4×D47C2211yescharacteristic
21C2×#13094002—28no—
22C2×#13094002C2218yescomplemented
23C2×#13094001—28no—
24C2×#13094001C2218yescomplemented
25C2×#13093989—28no—
26C2×#13093989C2218yescomplemented
27C2×(C22⋊D47)⋊C4—28no—
28C2×(C22⋊D47)⋊C4C2218yes—
29C22×C4⋊Dic47C2211yescharacteristic
30C22×C4⋊Dic47C2211yescharacteristic
31C22×Dic47⋊C4C2211yescharacteristic
32C22×Dic47⋊C4C2211yescharacteristic
33C22×Dic47⋊C4C2211yescharacteristic
34C22×Dic47⋊C4C2211yescharacteristic
35C22×Dic47⋊C4C2211yescharacteristic
36C22×Dic47⋊C4C2211yescharacteristic
37C22×Dic47⋊C4C2211yescharacteristic
38C22×Dic47⋊C4C2211yescharacteristic
39C22×Dic47⋊C4C2211yescharacteristic
40C22×C22⋊Dic47C2211yescharacteristic
41C22×C22⋊Dic47C2211yescharacteristic
42C22×(C2×D47)⋊C4C2211yescharacteristic
43C22×(C2×D47)⋊C4C2211yescharacteristic
44C22×(C2×D47)⋊C4C2211yescharacteristic
45C22×(C2×D47)⋊C4C2211yescharacteristic
46C22×(C2×D47)⋊C4C2211yescharacteristic
47C22×C4×Dic47C2211yescharacteristic
48C22×C4×Dic47C2211yescharacteristic
49C22×C4×Dic47C2211yescharacteristic
50#15689046C2218yescomplemented
51#15689045C2218yescomplemented
52#15689045C2218yescomplemented
53#15689023C2218yes—
54#15689023C2218yes—
55#15689020C2218yescomplemented
56#15689018C2218yescomplemented
57#15688992C2218yescomplemented
58#15688982C2218yescomplemented
59#15688981C2218yescomplemented
60C2×C47⋊#95C2211yescharacteristic
61C2×C47⋊#95C2211yescharacteristic
62C2×C47⋊#95C2211yescharacteristic
63C22×C4⋊C4×C47C2211yescharacteristic
64C22×C4⋊C4×C47C2211yescharacteristic
65C22×C4⋊C4×C47C2211yescharacteristic
66C22×C22⋊C4×C47C2211yescharacteristic
67C22×C22⋊C4×C47C2211yescharacteristic
68C22×C22⋊C4×C47C2211yescharacteristic
69C47×#396C2218yescomplemented
70C2×#95×C47C2211yescharacteristic
71C24×D47C2311yescharacteristic
72C22×Dic94—24no—
73C22×Dic94—24no—
74C22×Dic94D418yescomplemented
75C22×Dic94C2314yes—
76C22×C22⋊D47—24no—
77C22×C22⋊D47—24no—
78C22×C22⋊D47Q818yescomplemented
79C22×C22⋊D47C2314yes—
80C23×Dic47—24no—
81C23×Dic47—24no—
82C23×Dic47—24no—
83C23×Dic47C2311yescharacteristic
84C23×Dic47C2311yescharacteristic
85C23×Dic47C2311yescharacteristic
86C23×Dic47C2311yescharacteristic
87C23×Dic47C2314yes—
88C23×Dic47C2311yescharacteristic
89C23×Dic47C2311yescharacteristic
90C23×Dic47C2311yescharacteristic
91C22×C4×D47—24no—
92C22×C4×D47—24no—
93C22×C4×D47—24no—
94C22×C4×D47C2314yes—
95#13094002—232no—
96#13094001—232no—
97#13093989—232no—
98(C22⋊D47)⋊C4—232no—
99C2×C4⋊Dic47—24no—
100C2×C4⋊Dic47—42no—
101C2×C4⋊Dic47C2314yes—
102C2×C4⋊Dic47C2314yes—
103C2×Dic47⋊C4—24no—
104C2×Dic47⋊C4—24no—
105C2×Dic47⋊C4—24no—
106C2×Dic47⋊C4—24no—
107C2×Dic47⋊C4—24no—
108C2×Dic47⋊C4—24no—
109C2×Dic47⋊C4—24no—
110C2×Dic47⋊C4—24no—
111C2×Dic47⋊C4—24no—
112C2×Dic47⋊C4C2314yes—
113C2×Dic47⋊C4C2314yes—
114C2×Dic47⋊C4C2314yes—
115C2×Dic47⋊C4C2314yes—
116C2×Dic47⋊C4C2314yes—
117C2×Dic47⋊C4C2314yes—
118C2×Dic47⋊C4C2314yes—
119C2×Dic47⋊C4C2314yes—
120C2×Dic47⋊C4C2314yes—
121C2×C22⋊Dic47—24no—
122C2×C22⋊Dic47—42no—
123C2×C22⋊Dic47C2314yes—
124C2×C22⋊Dic47C2314yes—
125C2×(C2×D47)⋊C4—24no—
126C2×(C2×D47)⋊C4—24no—
127C2×(C2×D47)⋊C4—24no—
128C2×(C2×D47)⋊C4—42no—
129C2×(C2×D47)⋊C4—42no—
130C2×(C2×D47)⋊C4C2314yes—
131C2×(C2×D47)⋊C4C2314yes—
132C2×(C2×D47)⋊C4C2314yes—
133C2×(C2×D47)⋊C4C2314yes—
134C2×(C2×D47)⋊C4C2314yes—
135C2×C4×Dic47—24no—
136C2×C4×Dic47—24no—
137C2×C4×Dic47D418yes—
138C2×C4×Dic47C2314yes—
139C2×C4×Dic47C2314yes—
140C2×C4×Dic47C2314yes—
141C47⋊#95C2314yes—
142C47⋊#95C2314yes—
143C47⋊#95C2314yes—
144C25×C47C2311yescharacteristic
145C23×C4×C47C2311yescharacteristic
146C23×C4×C47C2311yescharacteristic
147C23×C4×C47C2311yescharacteristic
148C23×C4×C47C2311yescharacteristic
149C23×C4×C47C2311yescharacteristic
150C23×C4×C47C2311yescharacteristic
151C2×C4⋊C4×C47—24no—
152C2×C4⋊C4×C47—24no—
153C2×C4⋊C4×C47—42no—
154C2×C4⋊C4×C47C2314yes—
155C2×C4⋊C4×C47C2314yes—
156C2×C4⋊C4×C47C2314yes—
157C2×C22⋊C4×C47—24no—
158C2×C22⋊C4×C47—24no—
159C2×C22⋊C4×C47—42no—
160C2×C22⋊C4×C47C2314yes—
161C2×C22⋊C4×C47C2314yes—
162C2×C22⋊C4×C47C2314yes—
163#95×C47C2314yes—
164C24×C47—22no—
165C24×C47—22no—
166C24×C47—22no—
167C24×C47—22no—
168C24×C47—22no—
169C24×C47—22no—
170C24×C47C2×Q814yes—
171C24×C47C2412yes—
172C24×C47C2411yescharacteristic
173C23×D47—22no—
174C23×D47—22no—
175C23×D47—22no—
176C23×D47—22no—
177C23×D47—22no—
178C23×D47—22no—
179C23×D47C2×Q814yes—
180C23×D47C2412yes—
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×C47—22no—
190C22×C4×C47—22no—
191C22×C4×C47—22no—
192C22×C4×C47—22no—
193C22×C4×C47—22no—
194C22×C4×C47—22no—
195C22×C4×C47—22no—
196C22×C4×C47—22no—
197C22×C4×C47C2×D414yes—
198C22×C4×C47C2×D414yes—
199C22×C4×C47C2412yes—
200C22×C4×C47C2412yes—
201C22×C4×C47C2412yes—
202C22×C4×C47C2412yes—
203C22×C4×C47C2412yes—
204C22×C4×C47C2412yes—
205C2×C22⋊D47—232no—
206C2×C22⋊D47—28no—
207C2×C22⋊D47—28no—
208C2×C22⋊D47C2×Q8116yescomplemented
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—22no—
218C22×Dic47—22no—
219C22×Dic47—22no—
220C22×Dic47—22no—
221C22×Dic47—22no—
222C22×Dic47—22no—
223C22×Dic47—28no—
224C22×Dic47—28no—
225C22×Dic47—28no—
226C22×Dic47—416no—
227C22×Dic47C2×D414yes—
228C22×Dic47C2×D414yes—
229C22×Dic47C2×D414yes—
230C22×Dic47C2×D414yes—
231C22×Dic47C2×Q814yes—
232C22×Dic47#4114yes—
233C22×Dic47#4114yes—
234C22×Dic47C2412yes—
235C22×Dic47C2412yes—
236C22×Dic47C2412yes—
237C22×Dic47C2412yes—
238C22×Dic47C2412yes—
239C22×Dic47C2412yes—
240C22×Dic47C2412yes—
241C2×C4×D47—28no—
242C2×C4×D47—28no—
243C2×C4×D47—28no—
244C2×C4×D47—416no—
245C2×Dic94—232no—
246C2×Dic94—28no—
247C2×Dic94—28no—
248C2×Dic94C2×D4116yescomplemented
249C4⋊C4×C47—28no—
250C4⋊C4×C47—28no—
251C4⋊C4×C47—44no—
252C22⋊C4×C47—28no—
253C22⋊C4×C47—28no—
254C22⋊C4×C47—44no—
255C22⋊Dic47—28no—
256C22⋊Dic47—44no—
257(C2×D47)⋊C4—28no—
258(C2×D47)⋊C4—28no—
259(C2×D47)⋊C4—28no—
260(C2×D47)⋊C4—44no—
261(C2×D47)⋊C4—44no—
262C4⋊Dic47—28no—
263C4⋊Dic47—44no—
264Dic47⋊C4—28no—
265Dic47⋊C4—28no—
266Dic47⋊C4—28no—
267Dic47⋊C4—28no—
268Dic47⋊C4—28no—
269Dic47⋊C4—28no—
270Dic47⋊C4—28no—
271Dic47⋊C4—28no—
272Dic47⋊C4—28no—
273C4×Dic47—28no—
274C4×Dic47—28no—
275C4×Dic47C2×D4116yes—
276C23×C47—28no—
277C23×C47—28no—
278C23×C47—28no—
279C23×C47—22no—
280C23×C47—22no—
281C23×C47—22no—
282C23×C47—22no—
283C23×C47—22no—
284C23×C47—22no—
285C23×C47—44no—
286C23×C47—44no—
287C23×C47—44no—
288C23×C47—44no—
289C23×C47C22×D412yes—
290C23×C47C22×D412yes—
291C23×C47C22×Q814yes—
292C23×C47C22×Q812yes—
293C23×C47C2×#4112yes—
294C23×C47C2×#4112yes—
295C23×C47H(5,𝔽2)12yes—
296C23×C472−1+412yes—
297C23×C47C2511yescharacteristic
298C22×D47—28no—
299C22×D47—28no—
300C22×D47—28no—
301C22×D47—22no—
302C22×D47—22no—
303C22×D47—22no—
304C22×D47—22no—
305C22×D47—22no—
306C22×D47—22no—
307C22×D47—44no—
308C22×D47—44no—
309C22×D47—44no—
310C22×D47—44no—
311C22×D47C22×Q814yes—
312C2×C4×C47—28no—
313C2×C4×C47—28no—
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—22no—
322C2×C4×C47—22no—
323C2×C4×C47—22no—
324C2×C4×C47—22no—
325C2×C4×C47—22no—
326C2×C4×C47—22no—
327C2×C4×C47—22no—
328C2×C4×C47—22no—
329C2×C4×C47—22no—
330C2×C4×C47—44no—
331C2×C4×C47—44no—
332C2×C4×C47—44no—
333C2×C4×C47—44no—
334C2×C4×C47C22×D414yes—
335C2×C4×C47C22×D414yes—
336C22⋊D47—232no—
337C2×Dic47—28no—
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—22no—
347C2×Dic47—22no—
348C2×Dic47—22no—
349C2×Dic47—22no—
350C2×Dic47—22no—
351C2×Dic47—22no—
352C2×Dic47—44no—
353C2×Dic47—44no—
354C2×Dic47—44no—
355C2×Dic47—44no—
356C2×Dic47—416no—
357C2×Dic47#121116yes—
358C2×Dic47C22⋊Q8116yescomplemented
359C2×Dic47C22×D414yes—
360C2×Dic47C22×D414yes—
361C2×Dic47C22×D414yes—
362C2×Dic47C22×D414yes—
363C2×Dic47C22×Q814yes—
364C2×Dic47C2×#4114yes—
365C2×Dic47C2×#4114yes—
366C4×D47—416no—
367Dic94—232no—
368C2×#2538—471nomaximal, Sylow
369C22×C47—24no—
370C22×C47—24no—
371C22×C47—24no—
372C22×C47—42no—
373C22×C47—42no—
374C22×C47—42no—
375C22×C47—42no—
376C22×C47—416no—
377C22×C47C2×#12114yes—
378C22×C47C2×C22⋊Q814yes—
379C22×C47#53714yes—
380C22×C47D4×Q814yes—
381C22×C47#55014yes—
382C22×C47#55414yes—
383C22×C47#55614yes—
384C22×C47C23×D411yescharacteristic
385C22×C47C23×D411yescharacteristic
386C22×C47C23×Q811yescharacteristic
387C22×C47C22×#4111yescharacteristic
388C22×C47C22×#4111yescharacteristic
389C22×C47C2×H(5,𝔽2)11yescharacteristic
390C22×C47C2×2−1+411yescharacteristic
391C2×D47—24no—
392C2×D47—24no—
393C2×D47—24no—
394C2×D47—42no—
395C2×D47—42no—
396C2×D47—42no—
397C2×D47—42no—
398C2×D47—416no—
399C4×C47—24no—
400C4×C47—24no—
401C4×C47—42no—
402C4×C47—42no—
403C4×C47—42no—
404C4×C47—42no—
405Dic47—24no—
406Dic47—42no—
407Dic47—42no—
408Dic47—42no—
409Dic47—42no—
410Dic47C2×#12118yes—
411Dic47C2×C22⋊Q818yescomplemented
412C22×C22⋊Q8—471no—
413C22×C22⋊Q8—471no—
414C22×C4×Q8—471no—
415C22×C4×D4—471no—
416#2538—4716no—
417C2×#396—471no—
418C2×#396—471no—
419C2×#396—471no—
420C2×#396D4711yescharacteristic, complemented
421C2×#390—471no—
422C2×#390—471no—
423C2×#389—471no—
424C2×#389—471no—
425C2×#384—471no—
426C2×#380—471no—
427C2×#380—471no—
428C2×C47—44no—
429C2×C47#253818yescomplemented
430C2×C47C22×#12111yescharacteristic
431C2×C47C22×C22⋊Q811yescharacteristic
432C2×C47C2×#53711yescharacteristic
433C2×C47C2×D4×Q811yescharacteristic
434C2×C47C2×#55011yescharacteristic
435C2×C47C2×#55411yescharacteristic
436C2×C47C2×#55611yescharacteristic
437D47—44no—
438C23×Q8—471no—
439C23×D4—471no—
440C24×C4—471no—
441C24×C4—471no—
442C2×C22⋊Q8—478no—
443C2×C22⋊Q8—478no—
444C2×C22⋊Q8—948no—
445C2×C22⋊Q8—948no—
446C2×C4×Q8—478no—
447C2×C4×Q8—948no—
448C2×C4×D4—478no—
449C2×C4×D4—948no—
450C22×C4⋊C4—471no—
451C22×C4⋊C4—471no—
452C22×C4⋊C4—471no—
453C22×C4⋊C4—471no—
454C22×C4⋊C4—471no—
455C22×C4⋊C4—471no—
456C22×C4⋊C4—471no—
457C22×C4⋊C4—471no—
458C22×C4⋊C4—471no—
459C22×C4⋊C4—471no—
460C22×C4⋊C4—471no—
461C22×C4⋊C4C2×D4711yescharacteristic
462C22×C4⋊C4C2×D4711yescharacteristic
463C22×C4⋊C4C2×D4711yescharacteristic
464C22×C22⋊C4—471no—
465C22×C22⋊C4—471no—
466C22×C22⋊C4—471no—
467C22×C22⋊C4—471no—
468C22×C22⋊C4—471no—
469C22×C22⋊C4—471no—
470C22×C22⋊C4—471no—
471C22×C22⋊C4C2×D4711yescharacteristic
472C22×C22⋊C4C2×D4711yescharacteristic
473C22×C22⋊C4C2×D4711yescharacteristic
474C22×C42—471no—
475C22×C42—471no—
476C22×C42—471no—
477#396—478no—
478#396—478no—
479#396—478no—
480#396C2×D4718yescomplemented
481#390—478no—
482#390—478no—
483#389—478no—
484#389—478no—
485#384—478no—
486#380—478no—
487#380—478no—
488C2×#95—471no—
489C2×#95—471no—
490C2×#95—471no—
491C2×#95C2×D4711yescharacteristic
492C47C2×#253811yescharacteristic, complemented, Sylow
493C25—471no—
494C25C22×D4711yescharacteristic
495C22×Q8—478no—
496C22×Q8—474no—
497C22×Q8—944no—
498C22×Q8—944no—
499C22×D4—478no—
500C22×D4—474no—
501C22×D4—944no—
502C22×D4—944no—
503C23×C4—471no—
504C23×C4—471no—
505C23×C4—471no—
506C23×C4—474no—
507C23×C4—471no—
508C23×C4—471no—
509C23×C4—471no—
510C23×C4—471no—
511C23×C4—474no—
512C23×C4—944no—
513C23×C4—944no—
514C23×C4—944no—
515C23×C4—944no—
516C23×C4—944no—
517C23×C4—944no—
518C23×C4C22×D4711yescharacteristic
519C23×C4C22×D4711yescharacteristic
520C23×C4C22×D4711yescharacteristic
521C23×C4C22×D4711yescharacteristic
522C23×C4C22×D4711yescharacteristic
523C23×C4C22×D4711yescharacteristic
524C22⋊Q8—9432no—
525C22⋊Q8—9432no—
526C4×Q8—9432no—
527C4×D4—9432no—
528C2×C4⋊C4—24no—
529C2×C4⋊C4—24no—
530C2×C4⋊C4—42no—
531C2×C4⋊C4—474no—
532C2×C4⋊C4—474no—
533C2×C4⋊C4—474no—
534C2×C4⋊C4—474no—
535C2×C4⋊C4—474no—
536C2×C4⋊C4—474no—
537C2×C4⋊C4—474no—
538C2×C4⋊C4—474no—
539C2×C4⋊C4—474no—
540C2×C4⋊C4—474no—
541C2×C4⋊C4—474no—
542C2×C4⋊C4—944no—
543C2×C4⋊C4—944no—
544C2×C4⋊C4—944no—
545C2×C4⋊C4—944no—
546C2×C4⋊C4—944no—
547C2×C4⋊C4—944no—
548C2×C4⋊C4—944no—
549C2×C4⋊C4—944no—
550C2×C4⋊C4—944no—
551C2×C4⋊C4—944no—
552C2×C4⋊C4—1882no—
553C2×C4⋊C4C22×D4714yes—
554C2×C4⋊C4C22×D4714yes—
555C2×C4⋊C4C22×D4714yes—
556C2×C22⋊C4—24no—
557C2×C22⋊C4—24no—
558C2×C22⋊C4—42no—
559C2×C22⋊C4—474no—
560C2×C22⋊C4—474no—
561C2×C22⋊C4—474no—
562C2×C22⋊C4—474no—
563C2×C22⋊C4—474no—
564C2×C22⋊C4—474no—
565C2×C22⋊C4—474no—
566C2×C22⋊C4—944no—
567C2×C22⋊C4—944no—
568C2×C22⋊C4—944no—
569C2×C22⋊C4—944no—
570C2×C22⋊C4—1882no—
571C2×C22⋊C4—1882no—
572C2×C22⋊C4—1882no—
573C2×C22⋊C4C22×D4714yes—
574C2×C22⋊C4C22×D4714yes—
575C2×C22⋊C4C22×D4714yes—
576C2×C42—478no—
577C2×C42—474no—
578C2×C42—474no—
579C2×C42—474no—
580C2×C42—944no—
581C2×C42—944no—
582#95—474no—
583#95—474no—
584#95—474no—
585#95C22×D4714yes—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—474no—
593C24—472no—
594C24—942no—
595C24—942no—
596C24—942no—
597C24—942no—
598C24—942no—
599C24—942no—
600C24Q8×D4714yes—
601C24C23×D4712yes—
602C24C23×D4711yescharacteristic
603C2×Q8—4716no—
604C2×Q8—948no—
605C2×Q8—9432no—
606C2×Q8—948no—
607C2×D4—4716no—
608C2×D4—948no—
609C2×D4—9432no—
610C2×D4—948no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—474no—
628C22×C4—474no—
629C22×C4—474no—
630C22×C4—474no—
631C22×C4—474no—
632C22×C4—474no—
633C22×C4—472no—
634C22×C4—472no—
635C22×C4—474no—
636C22×C4—472no—
637C22×C4—472no—
638C22×C4—472no—
639C22×C4—472no—
640C22×C4—472no—
641C22×C4—948no—
642C22×C4—948no—
643C22×C4—948no—
644C22×C4—948no—
645C22×C4—948no—
646C22×C4—948no—
647C22×C4—942no—
648C22×C4—942no—
649C22×C4—942no—
650C22×C4—942no—
651C22×C4—942no—
652C22×C4—942no—
653C22×C4—942no—
654C22×C4—942no—
655C22×C4—942no—
656C22×C4—942no—
657C22×C4—942no—
658C22×C4—942no—
659C22×C4—942no—
660C22×C4—942no—
661C22×C4—18816no—
662C22×C4—18816no—
663C22×C4D4×D4714yes—
664C22×C4D4×D4714yes—
665C22×C4C23×D4712yes—
666C22×C4C23×D4712yes—
667C22×C4C23×D4712yes—
668C22×C4C23×D4712yes—
669C22×C4C23×D4712yes—
670C22×C4C23×D4712yes—
671C4⋊C4—28no—
672C4⋊C4—28no—
673C4⋊C4—44no—
674C4⋊C4—948no—
675C4⋊C4—948no—
676C4⋊C4—948no—
677C4⋊C4—948no—
678C4⋊C4—948no—
679C4⋊C4—948no—
680C4⋊C4—948no—
681C4⋊C4—948no—
682C4⋊C4—948no—
683C4⋊C4—948no—
684C4⋊C4—1884no—
685C22⋊C4—28no—
686C22⋊C4—28no—
687C22⋊C4—44no—
688C22⋊C4—948no—
689C22⋊C4—948no—
690C22⋊C4—948no—
691C22⋊C4—948no—
692C22⋊C4—1884no—
693C22⋊C4—1884no—
694C22⋊C4—1884no—
695C42—4716no—
696C42—948no—
697C42—948no—
698C23—28no—
699C23—28no—
700C23—28no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—44no—
711C23—474no—
712C23—948no—
713C23—948no—
714C23—948no—
715C23—942no—
716C23—942no—
717C23—942no—
718C23—942no—
719C23—942no—
720C23—942no—
721C23—1884no—
722C23—1884no—
723C23—1884no—
724C23—1884no—
725C23C2×D4×D4712yes—
726C23C2×D4×D4712yes—
727C23C2×Q8×D4714yes—
728C23C2×Q8×D4712yes—
729C23#41×D4712yes—
730C23#41×D4712yes—
731C23#1309406912yes—
732C23#1309407112yes—
733C23C24×D4711yescharacteristic
734Q8—9432no—
735D4—9432no—
736C2×C4—28no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—28no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—4716no—
759C2×C4—4716no—
760C2×C4—474no—
761C2×C4—474no—
762C2×C4—474no—
763C2×C4—474no—
764C2×C4—474no—
765C2×C4—474no—
766C2×C4—474no—
767C2×C4—948no—
768C2×C4—942no—
769C2×C4—942no—
770C2×C4—942no—
771C2×C4—942no—
772C2×C4—942no—
773C2×C4—942no—
774C2×C4—942no—
775C2×C4—942no—
776C2×C4—942no—
777C2×C4—942no—
778C2×C4—942no—
779C2×C4—942no—
780C2×C4—942no—
781C2×C4—942no—
782C2×C4—18816no—
783C2×C4—18816no—
784C2×C4—1884no—
785C2×C4—1884no—
786C2×C4—1884no—
787C2×C4—1884no—
788C2×C4C2×D4×D4714yes—
789C2×C4C2×D4×D4714yes—
790C22—24no—
791C22—24no—
792C22—24no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—416no—
798C22—944no—
799C22—944no—
800C22—944no—
801C22—1882no—
802C22—1882no—
803C22—1882no—
804C22—1882no—
805C22—18816no—
806C22#121×D4714yes—
807C22C22⋊Q8×D4714yes—
808C22#1568970014yes—
809C22#1568978614yes—
810C22#1568979114yes—
811C22#1568982714yes—
812C22#1568984014yes—
813C22C22×D4×D4711yescharacteristic
814C22C22×D4×D4711yescharacteristic
815C22C22×Q8×D4711yescharacteristic
816C22C2×#41×D4711yescharacteristic
817C22C2×#41×D4711yescharacteristic
818C22C2×#1309406911yescharacteristic
819C22C2×#1309407111yescharacteristic
820C4—24no—
821C4—24no—
822C4—42no—
823C4—42no—
824C4—42no—
825C4—42no—
826C4—478no—
827C4—478no—
828C4—944no—
829C4—1882no—
830C4—1882no—
831C4—1882no—
832C4—1882no—
833C2—44no—
834C2—1884no—
835C2#2024830518yesdirect product factor
836C2C2×#121×D4711yescharacteristic
837C2C2×C22⋊Q8×D4711yescharacteristic
838C2C2×#1568970011yescharacteristic
839C2C2×#1568978611yescharacteristic
840C2C2×#1568979111yescharacteristic
841C2C2×#1568982711yescharacteristic
842C2C2×#1568984011yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#396C2
socleC24×C47C24
prime radicalC23×C22⋊D47C22
hypercenterC2×#396D47
hypocenterC47C2×#2538
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#13094002C2semidirect
2. C22×#13094001C2semidirect
3. C22×#13093989C2semidirect
5. #20248305C2direct (N × H)
6. C2×#15689046C2semidirect
7. C2×#15689045C2semidirect
8. C2×#15689045C2semidirect
11. C2×#15689020C2semidirect
12. C2×#15689018C2semidirect
13. C2×#15688992C2semidirect
14. C2×#15688982C2semidirect
15. C2×#15688981C2semidirect
16. C2×C47×#396C2semidirect
22. C2×#13094002C22semidirect
24. C2×#13094001C22semidirect
26. C2×#13093989C22semidirect
50. #15689046C22semidirect
51. #15689045C22semidirect
52. #15689045C22semidirect
55. #15689020C22semidirect
56. #15689018C22semidirect
57. #15688992C22semidirect
58. #15688982C22semidirect
59. #15688981C22semidirect
69. C47×#396C22semidirect
74. C22×Dic94D4semidirect
78. C22×C22⋊D47Q8semidirect
208. C2×C22⋊D47C2×Q8semidirect
248. C2×Dic94C2×D4semidirect
358. C2×Dic47C22⋊Q8semidirect
411. Dic47C2×C22⋊Q8semidirect
420. C2×#396D47semidirect
429. C2×C47#2538semidirect
480. #396C2×D47semidirect
492. C47C2×#2538semidirect
835. C2#20248305direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940022
C22×#130940012
C22×#130939892
C22×(C22⋊D47)⋊C42
#202483052
C2×#156890462
C2×#156890452
C2×#156890232
C2×#156890202
C2×#156890182
C2×#156889922
C2×#156889822
C2×#156889812
C2×C47×#3962
C2×#253847