Finite Group Databasebeta

← C2×#20246856 #26383722

Subgroups — C2×#20246856 #26383722

Order 12032.

5054 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094009C211yesmaximal, characteristic, complemented
2C22×#13093994C211yesmaximal, characteristic
3C22×(C22⋊D47)⋊C4C211yesmaximal, characteristic, complemented
4C23×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
5#20246856C2116yesmaximal, direct product factor
6C2×#15689058C211yesmaximal, characteristic, complemented
7C2×#15689052C211yesmaximal, characteristic, complemented
8C2×#15689041C211yesmaximal, characteristic, complemented
9C2×#15689040C211yesmaximal, characteristic, complemented
10C2×#15689013C211yesmaximal, characteristic, complemented
11C2×#15689012C211yesmaximal, characteristic, complemented
12C2×#15689002C211yesmaximal, characteristic, complemented
13C2×#15689001C211yesmaximal, characteristic, complemented
14C2×#15688995C211yesmaximal, characteristic, complemented
15C2×#15688978C211yesmaximal, characteristic, complemented
16C2×C47×#380C211yesmaximal, characteristic, complemented
17C25×D47C2211yescharacteristic
18C23×D188C2211yescharacteristic
19C23×D188C2211yescharacteristic
20C23×C22⋊D47C2211yescharacteristic
21C24×Dic47C2211yescharacteristic
22C23×C4×D47C2211yescharacteristic, complemented
23C2×#13094009—28no—
24C2×#13094009C2218yescomplemented
25C2×#13093994—28no—
26C2×#13093994C2218yes—
27C2×(C22⋊D47)⋊C4—28no—
28C2×(C22⋊D47)⋊C4C2218yescomplemented
29C22×Dic47⋊C4C2211yescharacteristic, complemented
30C22×Dic47⋊C4C2211yescharacteristic, complemented
31C22×Dic47⋊C4C2211yescharacteristic, complemented
32C22×C22⋊Dic47C2211yescharacteristic
33C22×(C2×D47)⋊C4—28no—
34C22×(C2×D47)⋊C4C2211yescharacteristic
35C22×(C2×D47)⋊C4C2211yescharacteristic
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
44C22×(C2×D47)⋊C4C2218yescomplemented
45C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
46C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
47C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
48C22×C4×Dic47C2211yescharacteristic, complemented
49#15689058C2218yescomplemented
50#15689052C2218yescomplemented
51#15689041C2218yescomplemented
52#15689040C2218yescomplemented
53#15689013C2218yescomplemented
54#15689012C2218yescomplemented
55#15689002C2218yescomplemented
56#15689001C2218yescomplemented
57#15688995C2218yescomplemented
58#15688978C2218yescomplemented
59C2×C47⋊#95C2211yescharacteristic, complemented
60C2×C47⋊#95C2211yescharacteristic, complemented
61C2×C47⋊#95C2211yescharacteristic, complemented
62C2×C47⋊#95C2211yescharacteristic, complemented
63C24×C4×C47C2211yescharacteristic
64C22×C4⋊C4×C47C2211yescharacteristic, complemented
65C22×C4⋊C4×C47C2211yescharacteristic, complemented
66C22×C22⋊C4×C47C2211yescharacteristic
67C22×C22⋊C4×C47C2211yescharacteristic
68C47×#380C2218yescomplemented
69C2×#95×C47C2211yescharacteristic, complemented
70C2×#95×C47C2211yescharacteristic, complemented
71C24×D47—24no—
72C24×D47—24no—
73C24×D47—24no—
74C24×D47—24no—
75C24×D47—24no—
76C24×D47—42no—
77C24×D47—42no—
78C24×D47C2311yescharacteristic
79C24×D47C2311yescharacteristic
80C24×D47C2311yescharacteristic
81C24×D47C2314yes—
82C22×D188—24no—
83C22×D188—24no—
84C22×D188—24no—
85C22×D188—24no—
86C22×D188—42no—
87C22×D188—42no—
88C22×D188C2314yes—
89C22×D188C2314yes—
90C22×C22⋊D47—24no—
91C22×C22⋊D47—24no—
92C22×C22⋊D47D418yes—
93C22×C22⋊D47C2314yes—
94C23×Dic47—24no—
95C23×Dic47—24no—
96C23×Dic47—42no—
97C23×Dic47C2311yescharacteristic
98C23×Dic47C2311yescharacteristic
99C23×Dic47C2311yescharacteristic
100C23×Dic47C2314yes—
101C23×Dic47C2311yescharacteristic
102C23×Dic47C2311yescharacteristic
103C22×C4×D47—24no—
104C22×C4×D47—24no—
105C22×C4×D47—42no—
106C22×C4×D47C2314yescomplemented
107#13094009—232no—
108#13093994—232no—
109(C22⋊D47)⋊C4—232no—
110C2×Dic47⋊C4—24no—
111C2×Dic47⋊C4—24no—
112C2×Dic47⋊C4—42no—
113C2×Dic47⋊C4C2314yescomplemented
114C2×Dic47⋊C4C2314yescomplemented
115C2×Dic47⋊C4C2314yescomplemented
116C2×C22⋊Dic47—24no—
117C2×C22⋊Dic47C2314yes—
118C2×(C2×D47)⋊C4—24no—
119C2×(C2×D47)⋊C4—24no—
120C2×(C2×D47)⋊C4—24no—
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)⋊C4—24no—
127C2×(C2×D47)⋊C4—232no—
128C2×(C2×D47)⋊C4—42no—
129C2×(C2×D47)⋊C4—42no—
130C2×(C2×D47)⋊C4—42no—
131C2×(C2×D47)⋊C4D418yescomplemented
132C2×(C2×D47)⋊C4C2314yes—
133C2×(C2×D47)⋊C4C2314yes—
134C2×(C2×D47)⋊C4C2314yes—
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)⋊C4C2314yescomplemented
143C2×(C2×D47)⋊C4C2314yescomplemented
144C2×(C2×D47)⋊C4C2314yescomplemented
145C2×C4×Dic47—24no—
146C2×C4×Dic47C2314yescomplemented
147C47⋊#95C2314yescomplemented
148C47⋊#95C2314yescomplemented
149C47⋊#95C2314yescomplemented
150C47⋊#95C2314yescomplemented
151C25×C47C2311yescharacteristic
152C23×C4×C47—24no—
153C23×C4×C47—24no—
154C23×C4×C47—42no—
155C23×C4×C47C2311yescharacteristic
156C23×C4×C47C2311yescharacteristic
157C23×C4×C47C2311yescharacteristic
158C23×C4×C47C2311yescharacteristic
159C23×C4×C47C2311yescharacteristic
160C23×C4×C47C2314yes—
161C23×C4×C47C2311yescharacteristic
162C2×C4⋊C4×C47—24no—
163C2×C4⋊C4×C47—42no—
164C2×C4⋊C4×C47C2314yescomplemented
165C2×C4⋊C4×C47C2314yescomplemented
166C2×C22⋊C4×C47—24no—
167C2×C22⋊C4×C47—24no—
168C2×C22⋊C4×C47C2314yes—
169C2×C22⋊C4×C47C2314yes—
170#95×C47C2314yescomplemented
171#95×C47C2314yescomplemented
172C24×C47—22no—
173C24×C47—22no—
174C24×C47—22no—
175C24×C47—22no—
176C24×C47C2×D414yes—
177C24×C47#4114yes—
178C24×C47#4114yes—
179C24×C47C2412yes—
180C24×C47C2411yescharacteristic
181C23×D47—232no—
182C23×D47—22no—
183C23×D47—22no—
184C23×D47—22no—
185C23×D47—22no—
186C23×D47—22no—
187C23×D47—22no—
188C23×D47—22no—
189C23×D47—28no—
190C23×D47—22no—
191C23×D47—22no—
192C23×D47—22no—
193C23×D47—22no—
194C23×D47—22no—
195C23×D47—22no—
196C23×D47—22no—
197C23×D47—22no—
198C23×D47—22no—
199C23×D47—22no—
200C23×D47—22no—
201C23×D47—28no—
202C23×D47—28no—
203C23×D47—28no—
204C23×D47—28no—
205C23×D47—44no—
206C23×D47—44no—
207C23×D47—416no—
208C23×D47—416no—
209C23×D47—416no—
210C23×D47—416no—
211C23×D47—416no—
212C23×D47—416no—
213C23×D47C2×D414yes—
214C23×D47C2×D414yes—
215C23×D47#4114yes—
216C23×D47C2412yes—
217C23×D47C2412yes—
218C23×D47C2412yes—
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×C47—22no—
226C22×C4×C47—22no—
227C22×C4×C47—22no—
228C22×C4×C47—28no—
229C22×C4×C47—22no—
230C22×C4×C47—22no—
231C22×C4×C47—22no—
232C22×C4×C47—22no—
233C22×C4×C47—22no—
234C22×C4×C47—22no—
235C22×C4×C47—22no—
236C22×C4×C47—22no—
237C22×C4×C47—28no—
238C22×C4×C47—44no—
239C22×C4×C47—416no—
240C22×C4×C47C2×D414yes—
241C22×C4×C47C2412yes—
242C22×C4×C47C2412yes—
243C22×C4×C47C2412yes—
244C22×C4×C47C2412yes—
245C22×C4×C47C2412yes—
246C22×C4×C47C2412yes—
247C2×C22⋊D47—232no—
248C2×C22⋊D47—28no—
249C2×C22⋊D47—28no—
250C2×C22⋊D47C2×D4116yes—
251C22×Dic47—22no—
252C22×Dic47—22no—
253C22×Dic47—22no—
254C22×Dic47—22no—
255C22×Dic47—22no—
256C22×Dic47—22no—
257C22×Dic47—22no—
258C22×Dic47—28no—
259C22×Dic47—22no—
260C22×Dic47—22no—
261C22×Dic47—22no—
262C22×Dic47—22no—
263C22×Dic47—22no—
264C22×Dic47—22no—
265C22×Dic47—28no—
266C22×Dic47—44no—
267C22×Dic47—416no—
268C22×Dic47C2×D414yes—
269C22×Dic47C2×D414yes—
270C22×Dic47C2412yes—
271C22×Dic47C2412yes—
272C22×Dic47C2412yes—
273C22×Dic47C2412yes—
274C22×Dic47C2412yes—
275C2×D188—28no—
276C2×D188—28no—
277C2×D188—28no—
278C2×D188—28no—
279C2×D188—44no—
280C2×D188—44no—
281C2×D188—416no—
282C2×D188—416no—
283C2×C4×D47—28no—
284C2×C4×D47—28no—
285C2×C4×D47—44no—
286C2×C4×D47—416no—
287C4⋊C4×C47—28no—
288C4⋊C4×C47—44no—
289C22⋊C4×C47—28no—
290C22⋊C4×C47—28no—
291C22⋊Dic47—28no—
292(C2×D47)⋊C4—28no—
293(C2×D47)⋊C4—28no—
294(C2×D47)⋊C4—28no—
295(C2×D47)⋊C4—28no—
296(C2×D47)⋊C4—28no—
297(C2×D47)⋊C4—28no—
298(C2×D47)⋊C4—28no—
299(C2×D47)⋊C4—28no—
300(C2×D47)⋊C4—28no—
301(C2×D47)⋊C4—44no—
302(C2×D47)⋊C4—44no—
303(C2×D47)⋊C4—44no—
304(C2×D47)⋊C4C2×D4116yescomplemented
305Dic47⋊C4—28no—
306Dic47⋊C4—28no—
307Dic47⋊C4—44no—
308C4×Dic47—28no—
309C23×C47—28no—
310C23×C47—28no—
311C23×C47—28no—
312C23×C47—28no—
313C23×C47—28no—
314C23×C47—28no—
315C23×C47—22no—
316C23×C47—22no—
317C23×C47—22no—
318C23×C47—22no—
319C23×C47#123116yescomplemented
320C23×C47C22×D414yes—
321C23×C47C22×D412yes—
322C23×C47C22×D412yes—
323C23×C47C2×#4112yes—
324C23×C47C2×#4114yes—
325C23×C47C2×#4112yes—
326C23×C47C2×#4114yes—
327C23×C47C2×#4112yes—
328C23×C47H(5,𝔽2)12yes—
329C23×C47H(5,𝔽2)12yes—
330C23×C47C2511yescharacteristic
331C22×D47—232no—
332C22×D47—28no—
333C22×D47—28no—
334C22×D47—28no—
335C22×D47—28no—
336C22×D47—28no—
337C22×D47—28no—
338C22×D47—28no—
339C22×D47—28no—
340C22×D47—28no—
341C22×D47—22no—
342C22×D47—22no—
343C22×D47—22no—
344C22×D47—22no—
345C22×D47—22no—
346C22×D47—22no—
347C22×D47—22no—
348C22×D47—22no—
349C22×D47—22no—
350C22×D47—22no—
351C22×D47—22no—
352C22×D47—22no—
353C22×D47—22no—
354C22×D47—22no—
355C22×D47—22no—
356C22×D47—22no—
357C22×D47—22no—
358C22×D47—22no—
359C22×D47—416no—
360C22×D47—416no—
361C22×D47—416no—
362C22×D47—416no—
363C22×D47—4128no—
364C22×D47—416no—
365C22×D47—44no—
366C22×D47—44no—
367C22×D47—416no—
368C22×D47—44no—
369C22×D47—44no—
370C22×D47—44no—
371C22×D47—44no—
372C22×D47—44no—
373C22×D47—44no—
374C22×D47—44no—
375C22×D47—44no—
376C22×D47—44no—
377C22×D47—44no—
378C22×D47C22×D414yes—
379C22×D47C22×D414yes—
380C22×D47C2×#4114yes—
381C2×C4×C47—28no—
382C2×C4×C47—22no—
383C2×C4×C47—22no—
384C2×C4×C47—22no—
385C2×C4×C47—22no—
386C2×C4×C47—22no—
387C2×C4×C47—22no—
388C2×C4×C47—22no—
389C2×C4×C47—22no—
390C2×C4×C47—22no—
391C2×C4×C47—22no—
392C2×C4×C47—22no—
393C2×C4×C47—22no—
394C2×C4×C47—22no—
395C2×C4×C47—22no—
396C2×C4×C47—22no—
397C2×C4×C47—22no—
398C2×C4×C47—22no—
399C2×C4×C47—416no—
400C2×C4×C47—44no—
401C2×C4×C47—44no—
402C2×C4×C47—44no—
403C2×C4×C47—44no—
404C2×C4×C47—44no—
405C2×C4×C47C22×D414yes—
406C22⋊D47—232no—
407C2×Dic47—28no—
408C2×Dic47—28no—
409C2×Dic47—22no—
410C2×Dic47—22no—
411C2×Dic47—22no—
412C2×Dic47—22no—
413C2×Dic47—22no—
414C2×Dic47—22no—
415C2×Dic47—22no—
416C2×Dic47—22no—
417C2×Dic47—22no—
418C2×Dic47—22no—
419C2×Dic47—22no—
420C2×Dic47—22no—
421C2×Dic47—22no—
422C2×Dic47—416no—
423C2×Dic47—44no—
424C2×Dic47—44no—
425C2×Dic47—44no—
426C2×Dic47C22×D414yes—
427C2×Dic47C22×D414yes—
428D188—416no—
429D188—416no—
430C4×D47—416no—
431C2×#2418—471nomaximal, Sylow
432C22×C47—24no—
433C22×C47—232no—
434C22×C47—24no—
435C22×C47—24no—
436C22×C47—24no—
437C22×C47—24no—
438C22×C47—24no—
439C22×C47C2×#12314yes—
440C22×C47C2×#12318yescomplemented
441C22×C47#52514yes—
442C22×C47#53814yes—
443C22×C47D4214yes—
444C22×C47#54614yes—
445C22×C47#54614yes—
446C22×C47#55114yes—
447C22×C47C23×D411yescharacteristic
448C22×C47C23×D411yescharacteristic
449C22×C47C22×#4111yescharacteristic
450C22×C47C22×#4111yescharacteristic
451C22×C47C22×#4111yescharacteristic
452C22×C47C2×H(5,𝔽2)11yescharacteristic
453C22×C47C2×H(5,𝔽2)11yescharacteristic
454C2×D47—24no—
455C2×D47—24no—
456C2×D47—24no—
457C2×D47—24no—
458C2×D47—24no—
459C2×D47—24no—
460C2×D47—24no—
461C2×D47—24no—
462C2×D47—24no—
463C2×D47—464no—
464C2×D47—42no—
465C2×D47—42no—
466C2×D47—42no—
467C2×D47—416no—
468C2×D47—416no—
469C2×D47—416no—
470C2×D47—42no—
471C2×D47—42no—
472C2×D47—42no—
473C2×D47—42no—
474C2×D47—42no—
475C2×D47—42no—
476C2×D47—42no—
477C2×D47—42no—
478C2×D47—42no—
479C4×C47—24no—
480C4×C47—42no—
481C4×C47—42no—
482C4×C47—42no—
483C4×C47—42no—
484C4×C47—42no—
485Dic47—24no—
486Dic47—24no—
487Dic47—42no—
488Dic47—42no—
489Dic47—42no—
490C22×#123—471no—
491C22×#120—471no—
492C22×C4×D4—471no—
493C23×C22⋊C4—471no—
494#2418—4716no—
495C2×#399—471no—
496C2×#397—471no—
497C2×#394—471no—
498C2×#394—471no—
499C2×#388—471no—
500C2×#388—471no—
501C2×#386—471no—
502C2×#386—471no—
503C2×#385—471no—
504C2×#380D4711yescharacteristic, complemented
505C2×#379—471no—
506C2×C47—28no—
507C2×C47#241818yescomplemented
508C2×C47C22×#12311yescharacteristic
509C2×C47C2×#52511yescharacteristic
510C2×C47C2×#53811yescharacteristic
511C2×C47C2×D4211yescharacteristic
512C2×C47C2×#54611yescharacteristic
513C2×C47C2×#54611yescharacteristic
514C2×C47C2×#55111yescharacteristic
515D47—44no—
516D47—44no—
517D47—44no—
518C26—471no—
519C23×D4—471no—
520C23×D4—471no—
521C23×D4—471no—
522C24×C4—471no—
523C24×C4—471no—
524C24×C4C2×D4711yescharacteristic
525C2×#123—478no—
526C2×#123—948no—
527C2×#120—478no—
528C2×#120—948no—
529C2×C4×D4—478no—
530C2×C4×D4—948no—
531C22×C4⋊C4—471no—
532C22×C4⋊C4—471no—
533C22×C4⋊C4—471no—
534C22×C4⋊C4C2×D4711yescharacteristic, complemented
535C22×C4⋊C4C2×D4711yescharacteristic, complemented
536C22×C22⋊C4—471no—
537C22×C22⋊C4—471no—
538C22×C22⋊C4—471no—
539C22×C22⋊C4—471no—
540C22×C22⋊C4—471no—
541C22×C22⋊C4—471no—
542C22×C22⋊C4—471no—
543C22×C22⋊C4—471no—
544C22×C22⋊C4—471no—
545C22×C22⋊C4—471no—
546C22×C22⋊C4—471no—
547C22×C22⋊C4—478no—
548C22×C22⋊C4—471no—
549C22×C22⋊C4—471no—
550C22×C22⋊C4—471no—
551C22×C22⋊C4—948no—
552C22×C22⋊C4C2×D4711yescharacteristic
553C22×C22⋊C4C2×D4711yescharacteristic
554C22×C42—471no—
555#399—478no—
556#397—478no—
557#394—478no—
558#394—478no—
559#388—478no—
560#388—478no—
561#386—478no—
562#386—478no—
563#385—478no—
564#380C2×D4718yescomplemented
565#379—478no—
566C2×#95—471no—
567C2×#95—471no—
568C2×#95—471no—
569C2×#95—471no—
570C2×#95C2×D4711yescharacteristic, complemented
571C2×#95C2×D4711yescharacteristic, complemented
572C47C2×#241811yescharacteristic, complemented, Sylow
573C25—471no—
574C25—471no—
575C25—471no—
576C25—474no—
577C25—944no—
578C25—944no—
579C25—944no—
580C25—944no—
581C25—944no—
582C25—1882no—
583C25—1882no—
584C25C22×D4711yescharacteristic
585C22×D4—478no—
586C22×D4—474no—
587C22×D4—474no—
588C22×D4—474no—
589C22×D4—944no—
590C22×D4—944no—
591C22×D4—944no—
592C22×D4—944no—
593C22×D4—944no—
594C22×D4—944no—
595C22×D4—1882no—
596C22×D4—1882no—
597C23×C4—24no—
598C23×C4—24no—
599C23×C4—42no—
600C23×C4—471no—
601C23×C4—471no—
602C23×C4—471no—
603C23×C4—471no—
604C23×C4—471no—
605C23×C4—474no—
606C23×C4—474no—
607C23×C4—944no—
608C23×C4—944no—
609C23×C4—944no—
610C23×C4—944no—
611C23×C4—1882no—
612C23×C4—1882no—
613C23×C4C22×D4711yescharacteristic
614C23×C4C22×D4711yescharacteristic
615C23×C4C22×D4711yescharacteristic
616C23×C4C22×D4711yescharacteristic
617C23×C4C22×D4711yescharacteristic
618C23×C4C22×D4714yes—
619C23×C4C22×D4711yescharacteristic
620#123—9432no—
621#120—9432no—
622C4×D4—9432no—
623C2×C4⋊C4—24no—
624C2×C4⋊C4—42no—
625C2×C4⋊C4—474no—
626C2×C4⋊C4—474no—
627C2×C4⋊C4—474no—
628C2×C4⋊C4—944no—
629C2×C4⋊C4—944no—
630C2×C4⋊C4—1882no—
631C2×C4⋊C4C22×D4714yescomplemented
632C2×C4⋊C4C22×D4714yescomplemented
633C2×C22⋊C4—24no—
634C2×C22⋊C4—24no—
635C2×C22⋊C4—478no—
636C2×C22⋊C4—474no—
637C2×C22⋊C4—474no—
638C2×C22⋊C4—474no—
639C2×C22⋊C4—474no—
640C2×C22⋊C4—474no—
641C2×C22⋊C4—474no—
642C2×C22⋊C4—474no—
643C2×C22⋊C4—474no—
644C2×C22⋊C4—474no—
645C2×C22⋊C4—474no—
646C2×C22⋊C4—474no—
647C2×C22⋊C4—474no—
648C2×C22⋊C4—474no—
649C2×C22⋊C4—474no—
650C2×C22⋊C4—9432no—
651C2×C22⋊C4—944no—
652C2×C22⋊C4—944no—
653C2×C22⋊C4—944no—
654C2×C22⋊C4—944no—
655C2×C22⋊C4—944no—
656C2×C22⋊C4—944no—
657C2×C22⋊C4—944no—
658C2×C22⋊C4—944no—
659C2×C22⋊C4—944no—
660C2×C22⋊C4—944no—
661C2×C22⋊C4—1882no—
662C2×C22⋊C4—1882no—
663C2×C22⋊C4—1882no—
664C2×C22⋊C4C22×D4714yes—
665C2×C22⋊C4C22×D4714yes—
666C2×C42—474no—
667C2×C42—944no—
668#95—474no—
669#95—474no—
670#95—474no—
671#95—474no—
672#95C22×D4714yescomplemented
673#95C22×D4714yescomplemented
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—474no—
679C24—474no—
680C24—474no—
681C24—472no—
682C24—472no—
683C24—472no—
684C24—948no—
685C24—948no—
686C24—9432no—
687C24—942no—
688C24—942no—
689C24—942no—
690C24—942no—
691C24—942no—
692C24—942no—
693C24—942no—
694C24—942no—
695C24—942no—
696C24—942no—
697C24—948no—
698C24—942no—
699C24—942no—
700C24—942no—
701C24—942no—
702C24—942no—
703C24—942no—
704C24—942no—
705C24—942no—
706C24—948no—
707C24—948no—
708C24—1884no—
709C24—1884no—
710C24—18816no—
711C24—18816no—
712C24—18816no—
713C24—18816no—
714C24—18816no—
715C24—18816no—
716C24#1062535014yes—
717C24D4×D4714yes—
718C24#1062535414yes—
719C24C23×D4712yes—
720C24C23×D4711yescharacteristic
721C2×D4—4716no—
722C2×D4—948no—
723C2×D4—948no—
724C2×D4—948no—
725C2×D4—948no—
726C2×D4—9432no—
727C2×D4—948no—
728C2×D4—948no—
729C2×D4—1884no—
730C2×D4—1884no—
731C2×D4—18816no—
732C2×D4—18816no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—28no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—28no—
752C22×C4—44no—
753C22×C4—416no—
754C22×C4—474no—
755C22×C4—474no—
756C22×C4—472no—
757C22×C4—472no—
758C22×C4—472no—
759C22×C4—472no—
760C22×C4—472no—
761C22×C4—948no—
762C22×C4—948no—
763C22×C4—948no—
764C22×C4—942no—
765C22×C4—942no—
766C22×C4—942no—
767C22×C4—942no—
768C22×C4—942no—
769C22×C4—942no—
770C22×C4—942no—
771C22×C4—948no—
772C22×C4—942no—
773C22×C4—942no—
774C22×C4—942no—
775C22×C4—942no—
776C22×C4—942no—
777C22×C4—942no—
778C22×C4—1884no—
779C22×C4—18816no—
780C22×C4—1884no—
781C22×C4—18816no—
782C22×C4D4×D4714yes—
783C22×C4C23×D4712yes—
784C22×C4C23×D4712yes—
785C22×C4C23×D4712yes—
786C22×C4C23×D4712yes—
787C22×C4C23×D4712yes—
788C22×C4C23×D4712yes—
789C4⋊C4—28no—
790C4⋊C4—44no—
791C4⋊C4—948no—
792C4⋊C4—948no—
793C4⋊C4—1884no—
794C22⋊C4—28no—
795C22⋊C4—28no—
796C22⋊C4—4716no—
797C22⋊C4—948no—
798C22⋊C4—948no—
799C22⋊C4—948no—
800C22⋊C4—948no—
801C22⋊C4—948no—
802C22⋊C4—948no—
803C22⋊C4—948no—
804C22⋊C4—948no—
805C22⋊C4—948no—
806C22⋊C4—948no—
807C22⋊C4—1884no—
808C22⋊C4—1884no—
809C22⋊C4—1884no—
810C42—948no—
811C23—28no—
812C23—28no—
813C23—28no—
814C23—28no—
815C23—28no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—28no—
821C23—474no—
822C23—474no—
823C23—474no—
824C23—9432no—
825C23—948no—
826C23—948no—
827C23—948no—
828C23—948no—
829C23—948no—
830C23—948no—
831C23—948no—
832C23—948no—
833C23—948no—
834C23—942no—
835C23—942no—
836C23—942no—
837C23—942no—
838C23—942no—
839C23—942no—
840C23—942no—
841C23—942no—
842C23—942no—
843C23—942no—
844C23—942no—
845C23—942no—
846C23—942no—
847C23—942no—
848C23—942no—
849C23—942no—
850C23—942no—
851C23—942no—
852C23—18816no—
853C23—18816no—
854C23—18816no—
855C23—18816no—
856C23—188128no—
857C23—18816no—
858C23—1884no—
859C23—1884no—
860C23—1884no—
861C23—1884no—
862C23—1884no—
863C23—1884no—
864C23—1884no—
865C23—1884no—
866C23—18816no—
867C23—1884no—
868C23—1884no—
869C23—1884no—
870C23—1884no—
871C23#13094009116yescomplemented
872C23C2×D4×D4714yes—
873C23C2×D4×D4712yes—
874C23C2×D4×D4712yes—
875C23#41×D4712yes—
876C23C2×#1062535014yes—
877C23C2×#1062535012yes—
878C23C2×#1062535414yes—
879C23C2×#1062535412yes—
880C23#1309406912yes—
881C23#1309407012yes—
882C23C24×D4711yescharacteristic
883D4—9432no—
884D4—18816no—
885D4—18816no—
886C2×C4—28no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—416no—
905C2×C4—44no—
906C2×C4—44no—
907C2×C4—44no—
908C2×C4—44no—
909C2×C4—44no—
910C2×C4—474no—
911C2×C4—474no—
912C2×C4—948no—
913C2×C4—948no—
914C2×C4—942no—
915C2×C4—942no—
916C2×C4—942no—
917C2×C4—942no—
918C2×C4—942no—
919C2×C4—942no—
920C2×C4—942no—
921C2×C4—942no—
922C2×C4—942no—
923C2×C4—942no—
924C2×C4—942no—
925C2×C4—942no—
926C2×C4—942no—
927C2×C4—18816no—
928C2×C4—18816no—
929C2×C4—1884no—
930C2×C4—1884no—
931C2×C4—1884no—
932C2×C4C2×D4×D4714yes—
933C22—24no—
934C22—24no—
935C22—24no—
936C22—232no—
937C22—24no—
938C22—24no—
939C22—24no—
940C22—944no—
941C22—944no—
942C22—944no—
943C22—944no—
944C22—944no—
945C22—944no—
946C22—944no—
947C22—944no—
948C22—944no—
949C22—18864no—
950C22—1882no—
951C22—1882no—
952C22—1882no—
953C22—1882no—
954C22—18816no—
955C22—18816no—
956C22—18816no—
957C22—1882no—
958C22—1882no—
959C22—1882no—
960C22—1882no—
961C22—1882no—
962C22—1882no—
963C22—1882no—
964C22—1882no—
965C22C2×#1309400914yes—
966C22C2×#1309400918yescomplemented
967C22#1568963614yes—
968C22#1568971314yes—
969C22#1568975714yes—
970C22#1568976214yes—
971C22#1568976314yes—
972C22#1568979714yes—
973C22C22×D4×D4711yescharacteristic
974C22C22×D4×D4711yescharacteristic
975C22C2×#41×D4711yescharacteristic
976C22C22×#1062535011yescharacteristic
977C22C22×#1062535411yescharacteristic
978C22C2×#1309406911yescharacteristic
979C22C2×#1309407011yescharacteristic
980C4—24no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—42no—
986C4—944no—
987C4—944no—
988C4—1882no—
989C4—1882no—
990C4—1882no—
991C2—28no—
992C2—1884no—
993C2—1884no—
994C2—1884no—
995C2#2024685618yesdirect product factor
996C2C22×#1309400911yescharacteristic
997C2C2×#1568963611yescharacteristic
998C2C2×#1568971311yescharacteristic
999C2C2×#1568975711yescharacteristic
1000C2C2×#1568976211yescharacteristic
1001C2C2×#1568976311yescharacteristic
1002C2C2×#1568979711yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#380C2
socleC24×C47C24
prime radicalC22×#13093994C2
hypercenterC2×#380D47
hypocenterC47C2×#2418
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
1. C22×#13094009C2semidirect
3. C22×(C22⋊D47)⋊C4C2semidirect
4. C23×(C2×D47)⋊C4C2semidirect
5. #20246856C2direct (N × H)
6. C2×#15689058C2semidirect
7. C2×#15689052C2semidirect
8. C2×#15689041C2semidirect
9. C2×#15689040C2semidirect
10. C2×#15689013C2semidirect
11. C2×#15689012C2semidirect
12. C2×#15689002C2semidirect
13. C2×#15689001C2semidirect
14. C2×#15688995C2semidirect
15. C2×#15688978C2semidirect
16. C2×C47×#380C2semidirect
22. C23×C4×D47C22semidirect
24. C2×#13094009C22semidirect
28. C2×(C22⋊D47)⋊C4C22semidirect
29. C22×Dic47⋊C4C22semidirect
30. C22×Dic47⋊C4C22semidirect
31. C22×Dic47⋊C4C22semidirect
44. C22×(C2×D47)⋊C4C22semidirect
45. C22×(C2×D47)⋊C4C22semidirect
46. C22×(C2×D47)⋊C4C22semidirect
47. C22×(C2×D47)⋊C4C22semidirect
48. C22×C4×Dic47C22semidirect
49. #15689058C22semidirect
50. #15689052C22semidirect
51. #15689041C22semidirect
52. #15689040C22semidirect
53. #15689013C22semidirect
54. #15689012C22semidirect
55. #15689002C22semidirect
56. #15689001C22semidirect
57. #15688995C22semidirect
58. #15688978C22semidirect
59. C2×C47⋊#95C22semidirect
60. C2×C47⋊#95C22semidirect
61. C2×C47⋊#95C22semidirect
62. C2×C47⋊#95C22semidirect
64. C22×C4⋊C4×C47C22semidirect
65. C22×C4⋊C4×C47C22semidirect
68. C47×#380C22semidirect
69. C2×#95×C47C22semidirect
70. C2×#95×C47C22semidirect
106. C22×C4×D47C23semidirect
113. C2×Dic47⋊C4C23semidirect
114. C2×Dic47⋊C4C23semidirect
115. C2×Dic47⋊C4C23semidirect
131. C2×(C2×D47)⋊C4D4semidirect
142. C2×(C2×D47)⋊C4C23semidirect
143. C2×(C2×D47)⋊C4C23semidirect
144. C2×(C2×D47)⋊C4C23semidirect
146. C2×C4×Dic47C23semidirect
147. C47⋊#95C23semidirect
148. C47⋊#95C23semidirect
149. C47⋊#95C23semidirect
150. C47⋊#95C23semidirect
164. C2×C4⋊C4×C47C23semidirect
165. C2×C4⋊C4×C47C23semidirect
170. #95×C47C23semidirect
171. #95×C47C23semidirect
304. (C2×D47)⋊C4C2×D4semidirect
319. C23×C47#123semidirect
440. C22×C47C2×#123semidirect
504. C2×#380D47semidirect
507. C2×C47#2418semidirect
534. C22×C4⋊C4C2×D47semidirect
535. C22×C4⋊C4C2×D47semidirect
564. #380C2×D47semidirect
570. C2×#95C2×D47semidirect
571. C2×#95C2×D47semidirect
572. C47C2×#2418semidirect
631. C2×C4⋊C4C22×D47semidirect
632. C2×C4⋊C4C22×D47semidirect
672. #95C22×D47semidirect
673. #95C22×D47semidirect
871. C23#13094009semidirect
966. C22C2×#13094009semidirect
995. C2#20246856direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940092
C22×#130939942
C22×(C22⋊D47)⋊C42
C23×(C2×D47)⋊C42
#202468562
C2×#156890582
C2×#156890522
C2×#156890412
C2×#156890402
C2×#156890132
C2×#156890122
C2×#156890022
C2×#156890012
C2×#156889952
C2×#156889782
C2×C47×#3802
C2×#241847