Finite Group Databasebeta

← C2×#20246814 #26384686

Subgroups — C2×#20246814 #26384686

Order 12032.

3526 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×#13094002C211yesmaximal, characteristic, complemented
2C22×#13094001C211yesmaximal, characteristic, complemented
3C22×(C22⋊D47)⋊C4C211yesmaximal, characteristic
4C22×#13093981C211yesmaximal, characteristic, complemented
5#20246814C2116yesmaximal, direct product factor
6C2×#15689052C211yesmaximal, characteristic, complemented
7C2×#15689050C211yesmaximal, characteristic, complemented
8C2×#15689039C211yesmaximal, characteristic
9C2×#15689038C211yesmaximal, characteristic
10C2×#15689027C211yesmaximal, characteristic, complemented
11C2×#15689021C211yesmaximal, characteristic, complemented
12C2×#15689020C211yesmaximal, characteristic, complemented
13C2×#15689018C211yesmaximal, characteristic, complemented
14C2×#15689017C211yesmaximal, characteristic, complemented
15C2×#15688981C211yesmaximal, characteristic, complemented
16C2×C47×#388C211yesmaximal, characteristic, complemented
17C23×Dic94C2211yescharacteristic
18C23×C22⋊D47C2211yescharacteristic
19C24×Dic47C2211yescharacteristic
20C23×C4×D47C2211yescharacteristic
21C2×#13094002—28no—
22C2×#13094002C2218yescomplemented
23C2×#13094001—28no—
24C2×#13094001C2218yescomplemented
25C2×(C22⋊D47)⋊C4—28no—
26C2×(C22⋊D47)⋊C4C2218yes—
27C2×#13093981—28no—
28C2×#13093981C2218yescomplemented
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×C22⋊Dic47C2211yescharacteristic
39C22×C22⋊Dic47C2211yescharacteristic
40C22×(C2×D47)⋊C4C2211yescharacteristic
41C22×(C2×D47)⋊C4C2211yescharacteristic
42C22×(C2×D47)⋊C4C2211yescharacteristic
43C22×(C2×D47)⋊C4C2211yescharacteristic
44C22×(C2×D47)⋊C4C2211yescharacteristic
45C22×C4×Dic47C2211yescharacteristic
46C22×C4×Dic47C2211yescharacteristic
47#15689052C2218yescomplemented
48#15689050C2218yescomplemented
49#15689039C2218yes—
50#15689038C2218yes—
51#15689027C2218yescomplemented
52#15689021C2218yescomplemented
53#15689020C2218yescomplemented
54#15689018C2218yescomplemented
55#15689017C2218yescomplemented
56#15688981C2218yescomplemented
57C2×C47⋊#95C2211yescharacteristic
58C2×C47⋊#95C2211yescharacteristic
59C2×C47⋊#95C2211yescharacteristic
60C2×C47⋊#95C2211yescharacteristic
61C2×C47⋊#95C2211yescharacteristic
62C2×C47⋊#95C2211yescharacteristic
63C22×C4⋊C4×C47C2211yescharacteristic
64C22×C22⋊C4×C47C2211yescharacteristic
65C22×C22⋊C4×C47C2211yescharacteristic
66C22×C22⋊C4×C47C2211yescharacteristic
67C22×C42×C47C2211yescharacteristic
68C47×#388C2218yescomplemented
69C2×#95×C47C2211yescharacteristic
70C2×#95×C47C2211yescharacteristic
71C24×D47C2311yescharacteristic
72C22×Dic94—24no—
73C22×Dic94—24no—
74C22×Dic94—24no—
75C22×Dic94C2314yes—
76C22×C22⋊D47—24no—
77C22×C22⋊D47—24no—
78C22×C22⋊D47—24no—
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×D47D418yes—
94C22×C4×D47C2314yes—
95#13094002—232no—
96#13094001—232no—
97(C22⋊D47)⋊C4—232no—
98#13093981—232no—
99C2×C4⋊Dic47—24no—
100C2×C4⋊Dic47—24no—
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⋊C4D418yescomplemented
110C2×Dic47⋊C4C2314yes—
111C2×Dic47⋊C4C2314yes—
112C2×Dic47⋊C4C2314yes—
113C2×Dic47⋊C4C2314yes—
114C2×Dic47⋊C4C2314yes—
115C2×Dic47⋊C4C2314yes—
116C2×Dic47⋊C4C2314yes—
117C2×C22⋊Dic47—24no—
118C2×C22⋊Dic47—24no—
119C2×C22⋊Dic47C2314yes—
120C2×C22⋊Dic47C2314yes—
121C2×(C2×D47)⋊C4—24no—
122C2×(C2×D47)⋊C4—24no—
123C2×(C2×D47)⋊C4—24no—
124C2×(C2×D47)⋊C4—24no—
125C2×(C2×D47)⋊C4—24no—
126C2×(C2×D47)⋊C4C2314yes—
127C2×(C2×D47)⋊C4C2314yes—
128C2×(C2×D47)⋊C4C2314yes—
129C2×(C2×D47)⋊C4C2314yes—
130C2×(C2×D47)⋊C4C2314yes—
131C2×C4×Dic47—24no—
132C2×C4×Dic47—24no—
133C2×C4×Dic47C2314yes—
134C2×C4×Dic47C2314yes—
135C47⋊#95C2314yes—
136C47⋊#95C2314yes—
137C47⋊#95C2314yes—
138C47⋊#95C2314yes—
139C47⋊#95C2314yes—
140C47⋊#95C2314yes—
141C25×C47C2311yescharacteristic
142C23×C4×C47C2311yescharacteristic
143C23×C4×C47C2311yescharacteristic
144C23×C4×C47C2311yescharacteristic
145C23×C4×C47C2311yescharacteristic
146C23×C4×C47C2311yescharacteristic
147C23×C4×C47C2311yescharacteristic
148C2×C4⋊C4×C47—24no—
149C2×C4⋊C4×C47C2314yes—
150C2×C22⋊C4×C47—24no—
151C2×C22⋊C4×C47—24no—
152C2×C22⋊C4×C47—24no—
153C2×C22⋊C4×C47C2314yes—
154C2×C22⋊C4×C47C2314yes—
155C2×C22⋊C4×C47C2314yes—
156C2×C42×C47—24no—
157C2×C42×C47C2314yes—
158#95×C47C2314yes—
159#95×C47C2314yes—
160C24×C47—22no—
161C24×C47—22no—
162C24×C47—22no—
163C24×C47—22no—
164C24×C47—22no—
165C24×C47—22no—
166C24×C47#4114yes—
167C24×C47C2412yes—
168C24×C47C2411yescharacteristic
169C23×D47—22no—
170C23×D47—22no—
171C23×D47—22no—
172C23×D47—22no—
173C23×D47—22no—
174C23×D47—22no—
175C23×D47C2×D414yes—
176C23×D47C2412yes—
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×C47—22no—
190C22×C4×C47—22no—
191C22×C4×C47—22no—
192C22×C4×C47—22no—
193C22×C4×C47C2×D414yes—
194C22×C4×C47C2×D414yes—
195C22×C4×C47C2412yes—
196C22×C4×C47C2412yes—
197C22×C4×C47C2412yes—
198C22×C4×C47C2412yes—
199C22×C4×C47C2412yes—
200C22×C4×C47C2412yes—
201C2×C22⋊D47—232no—
202C2×C22⋊D47—28no—
203C2×C22⋊D47—28no—
204C2×C22⋊D47—28no—
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—22no—
218C22×Dic47—22no—
219C22×Dic47—22no—
220C22×Dic47—22no—
221C22×Dic47—28no—
222C22×Dic47—28no—
223C22×Dic47—28no—
224C22×Dic47—416no—
225C22×Dic47C2×D414yes—
226C22×Dic47C2×D414yes—
227C22×Dic47C2×D414yes—
228C22×Dic47#4114yes—
229C22×Dic47#4114yes—
230C22×Dic47C2412yes—
231C22×Dic47C2412yes—
232C22×Dic47C2412yes—
233C22×Dic47C2412yes—
234C22×Dic47C2412yes—
235C22×Dic47C2412yes—
236C22×Dic47C2412yes—
237C2×C4×D47—232no—
238C2×C4×D47—28no—
239C2×C4×D47—28no—
240C2×C4×D47C2×D4116yes—
241C2×Dic94—28no—
242C2×Dic94—28no—
243C2×Dic94—28no—
244C2×Dic94—416no—
245C4⋊C4×C47—28no—
246C22⋊C4×C47—28no—
247C22⋊C4×C47—28no—
248C22⋊C4×C47—28no—
249C42×C47—28no—
250C22⋊Dic47—28no—
251C22⋊Dic47—28no—
252(C2×D47)⋊C4—28no—
253(C2×D47)⋊C4—28no—
254(C2×D47)⋊C4—28no—
255(C2×D47)⋊C4—28no—
256(C2×D47)⋊C4—28no—
257C4⋊Dic47—28no—
258C4⋊Dic47—28no—
259Dic47⋊C4—28no—
260Dic47⋊C4—28no—
261Dic47⋊C4—28no—
262Dic47⋊C4—28no—
263Dic47⋊C4—28no—
264Dic47⋊C4—28no—
265Dic47⋊C4C2×D4116yescomplemented
266C4×Dic47—28no—
267C4×Dic47—28no—
268C23×C47—28no—
269C23×C47—28no—
270C23×C47—28no—
271C23×C47—22no—
272C23×C47—22no—
273C23×C47—22no—
274C23×C47—22no—
275C23×C47—22no—
276C23×C47—22no—
277C23×C47—44no—
278C23×C47—44no—
279C23×C47—44no—
280C23×C47—44no—
281C23×C47C22×D412yes—
282C23×C47C22×D412yes—
283C23×C47C2×#4112yes—
284C23×C47C2×#4112yes—
285C23×C47C2×#4114yes—
286C23×C47C2×#4112yes—
287C23×C472−1+412yes—
288C23×C472−1+412yes—
289C23×C47C2511yescharacteristic
290C22×D47—28no—
291C22×D47—28no—
292C22×D47—28no—
293C22×D47—22no—
294C22×D47—22no—
295C22×D47—22no—
296C22×D47—22no—
297C22×D47—22no—
298C22×D47—22no—
299C22×D47—44no—
300C22×D47—44no—
301C22×D47—44no—
302C22×D47—44no—
303C22×D47C22×D414yes—
304C2×C4×C47—28no—
305C2×C4×C47—28no—
306C2×C4×C47—22no—
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—22no—
322C2×C4×C47—44no—
323C2×C4×C47—44no—
324C2×C4×C47—44no—
325C2×C4×C47—44no—
326C2×C4×C47C22×D414yes—
327C2×C4×C47C22×D414yes—
328C22⋊D47—232no—
329C2×Dic47—28no—
330C2×Dic47—28no—
331C2×Dic47—22no—
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—22no—
347C2×Dic47—44no—
348C2×Dic47—44no—
349C2×Dic47—44no—
350C2×Dic47—44no—
351C2×Dic47—416no—
352C2×Dic47#121116yes—
353C2×Dic47C22×D414yes—
354C2×Dic47C22×D414yes—
355C2×Dic47C22×D414yes—
356C2×Dic47C2×#4114yes—
357C2×Dic47C2×#4114yes—
358C4×D47—232no—
359Dic94—416no—
360C2×#2415—471nomaximal, Sylow
361C22×C47—24no—
362C22×C47—24no—
363C22×C47—24no—
364C22×C47—42no—
365C22×C47—416no—
366C22×C47—42no—
367C22×C47—42no—
368C22×C47—42no—
369C22×C47C2×#12114yes—
370C22×C47#52514yes—
371C22×C47#53614yes—
372C22×C47#54714yes—
373C22×C47#54814yes—
374C22×C47#55214yes—
375C22×C47#55614yes—
376C22×C47C23×D411yescharacteristic
377C22×C47C23×D411yescharacteristic
378C22×C47C22×#4111yescharacteristic
379C22×C47C22×#4111yescharacteristic
380C22×C47C22×#4111yescharacteristic
381C22×C47C2×2−1+411yescharacteristic
382C22×C47C2×2−1+411yescharacteristic
383C2×D47—24no—
384C2×D47—24no—
385C2×D47—24no—
386C2×D47—416no—
387C2×D47—42no—
388C2×D47—42no—
389C2×D47—42no—
390C2×D47—42no—
391C4×C47—24no—
392C4×C47—24no—
393C4×C47—42no—
394C4×C47—42no—
395C4×C47—42no—
396C4×C47—42no—
397Dic47—24no—
398Dic47—24no—
399Dic47—42no—
400Dic47—42no—
401Dic47—42no—
402Dic47—42no—
403Dic47C2×#12118yes—
404C22×C22⋊Q8—471no—
405C22×C22⋊Q8—471no—
406C22×C4×D4—471no—
407C22×#117—471no—
408#2415—4716no—
409C2×#397—471no—
410C2×#397—471no—
411C2×#394—471no—
412C2×#394—471no—
413C2×#391—471no—
414C2×#389—471no—
415C2×#389—471no—
416C2×#389—471no—
417C2×#388—471no—
418C2×#388D4711yescharacteristic, complemented
419C2×#380—471no—
420C2×C47—44no—
421C2×C47#241518yescomplemented
422C2×C47C22×#12111yescharacteristic
423C2×C47C2×#52511yescharacteristic
424C2×C47C2×#53611yescharacteristic
425C2×C47C2×#54711yescharacteristic
426C2×C47C2×#54811yescharacteristic
427C2×C47C2×#55211yescharacteristic
428C2×C47C2×#55611yescharacteristic
429D47—44no—
430C23×Q8—471no—
431C23×D4—471no—
432C24×C4—471no—
433C24×C4—471no—
434C2×C22⋊Q8—478no—
435C2×C22⋊Q8—478no—
436C2×C22⋊Q8—948no—
437C2×C22⋊Q8—948no—
438C2×C4×D4—478no—
439C2×C4×D4—948no—
440C2×#117—478no—
441C2×#117—948no—
442C22×C4⋊C4—471no—
443C22×C4⋊C4—471no—
444C22×C4⋊C4—471no—
445C22×C4⋊C4—471no—
446C22×C4⋊C4—471no—
447C22×C4⋊C4—471no—
448C22×C4⋊C4—471no—
449C22×C4⋊C4—471no—
450C22×C4⋊C4—471no—
451C22×C4⋊C4C2×D4711yescharacteristic
452C22×C22⋊C4—471no—
453C22×C22⋊C4—471no—
454C22×C22⋊C4—471no—
455C22×C22⋊C4—471no—
456C22×C22⋊C4—471no—
457C22×C22⋊C4—471no—
458C22×C22⋊C4—471no—
459C22×C22⋊C4C2×D4711yescharacteristic
460C22×C22⋊C4C2×D4711yescharacteristic
461C22×C22⋊C4C2×D4711yescharacteristic
462C22×C42—471no—
463C22×C42—471no—
464C22×C42C2×D4711yescharacteristic
465#397—478no—
466#397—478no—
467#394—478no—
468#394—478no—
469#391—478no—
470#389—478no—
471#389—478no—
472#389—478no—
473#388—478no—
474#388C2×D4718yescomplemented
475#380—478no—
476C2×#95—471no—
477C2×#95—471no—
478C2×#95—471no—
479C2×#95—471no—
480C2×#95—471no—
481C2×#95—471no—
482C2×#95C2×D4711yescharacteristic
483C2×#95C2×D4711yescharacteristic
484C47C2×#241511yescharacteristic, complemented, Sylow
485C25—471no—
486C25C22×D4711yescharacteristic
487C22×Q8—474no—
488C22×Q8—944no—
489C22×Q8—944no—
490C22×Q8—944no—
491C22×D4—474no—
492C22×D4—944no—
493C22×D4—944no—
494C22×D4—944no—
495C23×C4—471no—
496C23×C4—471no—
497C23×C4—471no—
498C23×C4—478no—
499C23×C4—474no—
500C23×C4—474no—
501C23×C4—471no—
502C23×C4—471no—
503C23×C4—471no—
504C23×C4—471no—
505C23×C4—944no—
506C23×C4—944no—
507C23×C4—944no—
508C23×C4—944no—
509C23×C4—944no—
510C23×C4C22×D4711yescharacteristic
511C23×C4C22×D4711yescharacteristic
512C23×C4C22×D4711yescharacteristic
513C23×C4C22×D4711yescharacteristic
514C23×C4C22×D4711yescharacteristic
515C23×C4C22×D4711yescharacteristic
516C22⋊Q8—9432no—
517C22⋊Q8—9432no—
518C4×D4—9432no—
519#117—9432no—
520C2×C4⋊C4—24no—
521C2×C4⋊C4—478no—
522C2×C4⋊C4—474no—
523C2×C4⋊C4—474no—
524C2×C4⋊C4—474no—
525C2×C4⋊C4—474no—
526C2×C4⋊C4—474no—
527C2×C4⋊C4—474no—
528C2×C4⋊C4—474no—
529C2×C4⋊C4—474no—
530C2×C4⋊C4—474no—
531C2×C4⋊C4—944no—
532C2×C4⋊C4—944no—
533C2×C4⋊C4—944no—
534C2×C4⋊C4—944no—
535C2×C4⋊C4—944no—
536C2×C4⋊C4—944no—
537C2×C4⋊C4—944no—
538C2×C4⋊C4—944no—
539C2×C4⋊C4C22×D4714yes—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—24no—
542C2×C22⋊C4—24no—
543C2×C22⋊C4—474no—
544C2×C22⋊C4—474no—
545C2×C22⋊C4—474no—
546C2×C22⋊C4—474no—
547C2×C22⋊C4—474no—
548C2×C22⋊C4—474no—
549C2×C22⋊C4—474no—
550C2×C22⋊C4—944no—
551C2×C22⋊C4—944no—
552C2×C22⋊C4—944no—
553C2×C22⋊C4—944no—
554C2×C22⋊C4—944no—
555C2×C22⋊C4—944no—
556C2×C22⋊C4—944no—
557C2×C22⋊C4C22×D4714yes—
558C2×C22⋊C4C22×D4714yes—
559C2×C22⋊C4C22×D4714yes—
560C2×C42—24no—
561C2×C42—474no—
562C2×C42—474no—
563C2×C42—944no—
564C2×C42—944no—
565C2×C42C22×D4714yes—
566#95—474no—
567#95—474no—
568#95—474no—
569#95—474no—
570#95—474no—
571#95—474no—
572#95C22×D4714yes—
573#95C22×D4714yes—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—22no—
580C24—474no—
581C24—472no—
582C24—942no—
583C24—942no—
584C24—942no—
585C24—942no—
586C24—942no—
587C24—942no—
588C24#1062535014yes—
589C24C23×D4712yes—
590C24C23×D4711yescharacteristic
591C2×Q8—948no—
592C2×Q8—948no—
593C2×Q8—948no—
594C2×Q8—18816no—
595C2×D4—948no—
596C2×D4—948no—
597C2×D4—9432no—
598C2×D4—948no—
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—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—474no—
616C22×C4—474no—
617C22×C4—474no—
618C22×C4—472no—
619C22×C4—474no—
620C22×C4—474no—
621C22×C4—472no—
622C22×C4—472no—
623C22×C4—4716no—
624C22×C4—472no—
625C22×C4—472no—
626C22×C4—472no—
627C22×C4—472no—
628C22×C4—948no—
629C22×C4—9432no—
630C22×C4—948no—
631C22×C4—948no—
632C22×C4—948no—
633C22×C4—948no—
634C22×C4—942no—
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—942no—
644C22×C4—942no—
645C22×C4—942no—
646C22×C4—942no—
647C22×C4—942no—
648C22×C4—942no—
649C22×C4—942no—
650C22×C4—18816no—
651C22×C4D4×D4714yes—
652C22×C4D4×D4714yes—
653C22×C4C23×D4712yes—
654C22×C4C23×D4712yes—
655C22×C4C23×D4712yes—
656C22×C4C23×D4712yes—
657C22×C4C23×D4712yes—
658C22×C4C23×D4712yes—
659C4⋊C4—28no—
660C4⋊C4—4716no—
661C4⋊C4—948no—
662C4⋊C4—948no—
663C4⋊C4—948no—
664C4⋊C4—948no—
665C4⋊C4—948no—
666C4⋊C4—948no—
667C4⋊C4—948no—
668C4⋊C4—948no—
669C22⋊C4—28no—
670C22⋊C4—28no—
671C22⋊C4—28no—
672C22⋊C4—948no—
673C22⋊C4—948no—
674C22⋊C4—948no—
675C22⋊C4—948no—
676C22⋊C4—948no—
677C22⋊C4—948no—
678C22⋊C4—948no—
679C42—28no—
680C42—948no—
681C42—948no—
682C23—28no—
683C23—28no—
684C23—28no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23—474no—
696C23—948no—
697C23—948no—
698C23—942no—
699C23—942no—
700C23—942no—
701C23—948no—
702C23—942no—
703C23—942no—
704C23—942no—
705C23—1884no—
706C23—1884no—
707C23—1884no—
708C23—1884no—
709C23C2×D4×D4712yes—
710C23C2×D4×D4712yes—
711C23#41×D4712yes—
712C23#41×D4712yes—
713C23C2×#1062535014yes—
714C23C2×#1062535012yes—
715C23#1309407112yes—
716C23#1309407112yes—
717C23C24×D4711yescharacteristic
718Q8—18816no—
719D4—9432no—
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—22no—
737C2×C4—22no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—4716no—
743C2×C4—474no—
744C2×C4—474no—
745C2×C4—474no—
746C2×C4—474no—
747C2×C4—474no—
748C2×C4—9432no—
749C2×C4—948no—
750C2×C4—948no—
751C2×C4—942no—
752C2×C4—942no—
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×C4—1884no—
771C2×C4—1884no—
772C2×C4C2×D4×D4714yes—
773C2×C4C2×D4×D4714yes—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—416no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—944no—
783C22—944no—
784C22—944no—
785C22—18816no—
786C22—1882no—
787C22—1882no—
788C22—1882no—
789C22—1882no—
790C22#121×D4714yes—
791C22#1568963214yes—
792C22#1568969314yes—
793C22#1568977114yes—
794C22#1568978214yes—
795C22#1568980614yes—
796C22#1568984014yes—
797C22C22×D4×D4711yescharacteristic
798C22C22×D4×D4711yescharacteristic
799C22C2×#41×D4711yescharacteristic
800C22C2×#41×D4711yescharacteristic
801C22C22×#1062535011yescharacteristic
802C22C2×#1309407111yescharacteristic
803C22C2×#1309407111yescharacteristic
804C4—24no—
805C4—24no—
806C4—42no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—478no—
811C4—944no—
812C4—944no—
813C4—1882no—
814C4—1882no—
815C4—1882no—
816C4—1882no—
817C2—44no—
818C2—1884no—
819C2#2024681418yesdirect product factor
820C2C2×#121×D4711yescharacteristic
821C2C2×#1568963211yescharacteristic
822C2C2×#1568969311yescharacteristic
823C2C2×#1568977111yescharacteristic
824C2C2×#1568978211yescharacteristic
825C2C2×#1568980611yescharacteristic
826C2C2×#1568984011yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#388C2
socleC24×C47C24
prime radicalC23×C22⋊D47C22
hypercenterC2×#388D47
hypocenterC47C2×#2415
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#13094002C2semidirect
2. C22×#13094001C2semidirect
4. C22×#13093981C2semidirect
5. #20246814C2direct (N × H)
6. C2×#15689052C2semidirect
7. C2×#15689050C2semidirect
10. C2×#15689027C2semidirect
11. C2×#15689021C2semidirect
12. C2×#15689020C2semidirect
13. C2×#15689018C2semidirect
14. C2×#15689017C2semidirect
15. C2×#15688981C2semidirect
16. C2×C47×#388C2semidirect
22. C2×#13094002C22semidirect
24. C2×#13094001C22semidirect
28. C2×#13093981C22semidirect
47. #15689052C22semidirect
48. #15689050C22semidirect
51. #15689027C22semidirect
52. #15689021C22semidirect
53. #15689020C22semidirect
54. #15689018C22semidirect
55. #15689017C22semidirect
56. #15688981C22semidirect
68. C47×#388C22semidirect
109. C2×Dic47⋊C4D4semidirect
265. Dic47⋊C4C2×D4semidirect
418. C2×#388D47semidirect
421. C2×C47#2415semidirect
474. #388C2×D47semidirect
484. C47C2×#2415semidirect
819. C2#20246814direct (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×(C22⋊D47)⋊C42
C22×#130939812
#202468142
C2×#156890522
C2×#156890502
C2×#156890392
C2×#156890382
C2×#156890272
C2×#156890212
C2×#156890202
C2×#156890182
C2×#156890172
C2×#156889812
C2×C47×#3882
C2×#241547