Finite Group Databasebeta

← C2×#20246777 #26383837

Subgroups — C2×#20246777 #26383837

Order 12032.

5162 conjugacy classes of subgroups.

The subgroup lattice has 1008 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⋊C4×D47C211yesmaximal, characteristic, complemented
4C22×C22⋊C4×D47C211yesmaximal, characteristic, complemented
5#20246777C2116yesmaximal, direct product factor
6C2×#15689051C211yesmaximal, characteristic, complemented
7C2×#15689039C211yesmaximal, characteristic, complemented
8C2×#15689038C211yesmaximal, characteristic, complemented
9C2×#15689001C211yesmaximal, characteristic, complemented
10C2×#15689001C211yesmaximal, characteristic, complemented
11C2×#15689001C211yesmaximal, characteristic, complemented
12C2×#15688997C211yesmaximal, characteristic, complemented
13C2×#15688985C211yesmaximal, characteristic, complemented
14C2×#15688982C211yesmaximal, characteristic, complemented
15C2×#15688980C211yesmaximal, characteristic, complemented
16C2×C47×#397C211yesmaximal, characteristic, complemented
17C25×D47C2211yescharacteristic
18C23×D188C2211yescharacteristic
19C23×D188C2211yescharacteristic
20C23×C22⋊D47C2211yescharacteristic
21C23×C4×D47C2211yescharacteristic
22C23×C4×D47C2211yescharacteristic
23C23×C4×D47C2211yescharacteristic
24C23×C4×D47C2211yescharacteristic
25C2×#13094009—28no—
26C2×#13094009C2218yescomplemented
27C2×#13093994—28no—
28C2×#13093994C2218yes—
29C22×C4⋊Dic47C2211yescharacteristic, complemented
30C22×Dic47⋊C4C2211yescharacteristic, complemented
31C22×Dic47⋊C4C2211yescharacteristic, complemented
32C22×C22⋊Dic47C2211yescharacteristic
33C22×C22⋊Dic47C2211yescharacteristic
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, complemented
41C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
42C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
43C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
44C2×C22⋊C4×D47—28no—
45C2×C22⋊C4×D47—28no—
46C2×C22⋊C4×D47C2218yescomplemented
47C2×C22⋊C4×D47C2218yescomplemented
48#15689051C2218yescomplemented
49#15689039C2218yescomplemented
50#15689038C2218yescomplemented
51#15689001C2218yescomplemented
52#15689001C2218yescomplemented
53#15689001C2218yescomplemented
54#15688997C2218yescomplemented
55#15688985C2218yescomplemented
56#15688982C2218yescomplemented
57#15688980C2218yescomplemented
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×C22⋊C4×C47C2211yescharacteristic
65C22×C22⋊C4×C47C2211yescharacteristic
66C22×C22⋊C4×C47C2211yescharacteristic
67C47×#397C2218yescomplemented
68C2×#95×C47C2211yescharacteristic, complemented
69C2×#95×C47C2211yescharacteristic, complemented
70C2×#95×C47C2211yescharacteristic, complemented
71C24×D47—24no—
72C24×D47—24no—
73C24×D47—24no—
74C24×D47—24no—
75C24×D47—42no—
76C24×D47—42no—
77C24×D47D418yes—
78C24×D47C2311yescharacteristic
79C24×D47C2314yes—
80C24×D47C2311yescharacteristic
81C24×D47C2311yescharacteristic
82C22×D188—24no—
83C22×D188—24no—
84C22×D188—24no—
85C22×D188—24no—
86C22×D188—24no—
87C22×D188—24no—
88C22×D188C2314yes—
89C22×D188C2314yes—
90C22×C22⋊D47—24no—
91C22×C22⋊D47—42no—
92C22×C22⋊D47—42no—
93C22×C22⋊D47C2314yes—
94C23×Dic47C2311yescharacteristic
95C23×Dic47C2311yescharacteristic
96C23×Dic47C2311yescharacteristic
97C23×Dic47C2311yescharacteristic
98C23×Dic47C2311yescharacteristic
99C22×C4×D47—24no—
100C22×C4×D47—24no—
101C22×C4×D47—24no—
102C22×C4×D47—24no—
103C22×C4×D47—24no—
104C22×C4×D47—24no—
105C22×C4×D47—24no—
106C22×C4×D47—24no—
107C22×C4×D47—42no—
108C22×C4×D47—42no—
109C22×C4×D47—42no—
110C22×C4×D47—42no—
111C22×C4×D47C2314yes—
112C22×C4×D47C2314yes—
113C22×C4×D47C2314yes—
114C22×C4×D47C2314yes—
115#13094009—232no—
116#13093994—232no—
117C2×C4⋊Dic47—42no—
118C2×C4⋊Dic47C2314yescomplemented
119C2×Dic47⋊C4—24no—
120C2×Dic47⋊C4—42no—
121C2×Dic47⋊C4C2314yescomplemented
122C2×Dic47⋊C4C2314yescomplemented
123C2×C22⋊Dic47—24no—
124C2×C22⋊Dic47—24no—
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)⋊C4—24no—
134C2×(C2×D47)⋊C4—42no—
135C2×(C2×D47)⋊C4—42no—
136C2×(C2×D47)⋊C4D418yescomplemented
137C2×(C2×D47)⋊C4C2314yes—
138C2×(C2×D47)⋊C4C2314yes—
139C2×(C2×D47)⋊C4C2314yes—
140C2×(C2×D47)⋊C4C2314yes—
141C2×(C2×D47)⋊C4C2314yes—
142C2×(C2×D47)⋊C4C2314yes—
143C2×(C2×D47)⋊C4C2314yescomplemented
144C2×(C2×D47)⋊C4C2314yescomplemented
145C2×(C2×D47)⋊C4C2314yescomplemented
146C2×(C2×D47)⋊C4C2314yescomplemented
147C22⋊C4×D47—232no—
148C22⋊C4×D47—232no—
149C47⋊#95C2314yescomplemented
150C47⋊#95C2314yescomplemented
151C47⋊#95C2314yescomplemented
152C47⋊#95C2314yescomplemented
153C47⋊#95C2314yescomplemented
154C25×C47C2311yescharacteristic
155C23×C4×C47C2311yescharacteristic
156C23×C4×C47C2311yescharacteristic
157C23×C4×C47C2311yescharacteristic
158C23×C4×C47C2311yescharacteristic
159C23×C4×C47C2311yescharacteristic
160C23×C4×C47C2311yescharacteristic
161C2×C4⋊C4×C47—24no—
162C2×C4⋊C4×C47C2314yescomplemented
163C2×C22⋊C4×C47—24no—
164C2×C22⋊C4×C47—24no—
165C2×C22⋊C4×C47—24no—
166C2×C22⋊C4×C47C2314yes—
167C2×C22⋊C4×C47C2314yes—
168C2×C22⋊C4×C47C2314yes—
169#95×C47C2314yescomplemented
170#95×C47C2314yescomplemented
171#95×C47C2314yescomplemented
172C24×C47—22no—
173C24×C47—22no—
174C24×C47—22no—
175C24×C47—22no—
176C24×C47—22no—
177C24×C47—22no—
178C24×C47C2×D414yes—
179C24×C47C2412yes—
180C24×C47C2411yescharacteristic
181C23×D47—22no—
182C23×D47—22no—
183C23×D47—22no—
184C23×D47—22no—
185C23×D47—22no—
186C23×D47—22no—
187C23×D47—22no—
188C23×D47—22no—
189C23×D47—232no—
190C23×D47—232no—
191C23×D47—28no—
192C23×D47—28no—
193C23×D47—28no—
194C23×D47—28no—
195C23×D47—22no—
196C23×D47—22no—
197C23×D47—22no—
198C23×D47—22no—
199C23×D47—22no—
200C23×D47—22no—
201C23×D47—22no—
202C23×D47—416no—
203C23×D47—44no—
204C23×D47—44no—
205C23×D47—416no—
206C23×D47—416no—
207C23×D47—416no—
208C23×D47—416no—
209C23×D47C2×D4116yes—
210C23×D47C2×D414yes—
211C23×D47C2×D414yes—
212C23×D47C2×D414yes—
213C23×D47#4114yes—
214C23×D47#4114yes—
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—22no—
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×C47C2×D414yes—
237C22×C4×C47C2412yes—
238C22×C4×C47C2412yes—
239C22×C4×C47C2412yes—
240C22×C4×C47C2412yes—
241C22×C4×C47C2412yes—
242C22×C4×C47C2412yes—
243C2×C22⋊D47—28no—
244C2×C22⋊D47—44no—
245C2×C22⋊D47—44no—
246C2×C22⋊D47—416no—
247C22×Dic47—22no—
248C22×Dic47—22no—
249C22×Dic47—22no—
250C22×Dic47—22no—
251C22×Dic47—22no—
252C22×Dic47—22no—
253C22×Dic47—22no—
254C22×Dic47—22no—
255C22×Dic47—22no—
256C22×Dic47—22no—
257C22×Dic47—22no—
258C22×Dic47—22no—
259C22×Dic47—22no—
260C22×Dic47—22no—
261C22×Dic47C2×D414yes—
262C22×Dic47C2412yes—
263C22×Dic47C2412yes—
264C22×Dic47C2412yes—
265C22×Dic47C2412yes—
266C22×Dic47C2412yes—
267C2×D188—28no—
268C2×D188—28no—
269C2×D188—28no—
270C2×D188—28no—
271C2×D188—28no—
272C2×D188—28no—
273C2×D188—416no—
274C2×D188—416no—
275C2×C4×D47—28no—
276C2×C4×D47—28no—
277C2×C4×D47—28no—
278C2×C4×D47—28no—
279C2×C4×D47—28no—
280C2×C4×D47—28no—
281C2×C4×D47—28no—
282C2×C4×D47—28no—
283C2×C4×D47—44no—
284C2×C4×D47—44no—
285C2×C4×D47—44no—
286C2×C4×D47—44no—
287C2×C4×D47—416no—
288C2×C4×D47—416no—
289C2×C4×D47—416no—
290C2×C4×D47—416no—
291C4⋊C4×C47—28no—
292C22⋊C4×C47—28no—
293C22⋊C4×C47—28no—
294C22⋊C4×C47—28no—
295C22⋊Dic47—28no—
296C22⋊Dic47—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—28no—
302(C2×D47)⋊C4—28no—
303(C2×D47)⋊C4—28no—
304(C2×D47)⋊C4—44no—
305(C2×D47)⋊C4—44no—
306(C2×D47)⋊C4C2×D4116yescomplemented
307C4⋊Dic47—44no—
308Dic47⋊C4—28no—
309Dic47⋊C4—44no—
310C23×C47—28no—
311C23×C47—28no—
312C23×C47—28no—
313C23×C47—22no—
314C23×C47—22no—
315C23×C47—22no—
316C23×C47—22no—
317C23×C47—22no—
318C23×C47—22no—
319C23×C47—44no—
320C23×C47—44no—
321C23×C47—44no—
322C23×C47—44no—
323C23×C47C22×D414yes—
324C23×C47C22×D412yes—
325C23×C47C22×D412yes—
326C23×C47C2×#4112yes—
327C23×C47C2×#4112yes—
328C23×C47C2×#4112yes—
329C23×C47H(5,𝔽2)12yes—
330C23×C47H(5,𝔽2)12yes—
331C23×C47C2511yescharacteristic
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—28no—
342C22×D47—28no—
343C22×D47—28no—
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—232no—
353C22×D47—232no—
354C22×D47—22no—
355C22×D47—22no—
356C22×D47—22no—
357C22×D47—22no—
358C22×D47—22no—
359C22×D47—22no—
360C22×D47—22no—
361C22×D47—416no—
362C22×D47—4128no—
363C22×D47—416no—
364C22×D47—416no—
365C22×D47—416no—
366C22×D47—416no—
367C22×D47—44no—
368C22×D47—44no—
369C22×D47—44no—
370C22×D47—44no—
371C22×D47—44no—
372C22×D47—44no—
373C22×D47—44no—
374C22×D47#121116yes—
375C22×D47#123116yescomplemented
376C22×D47C22×D414yes—
377C22×D47C22×D414yes—
378C22×D47C22×D414yes—
379C22×D47C2×#4114yes—
380C22×D47C2×#4114yes—
381C22×D47C2×#4114yes—
382C2×C4×C47—28no—
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—22no—
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—416no—
407C2×Dic47—28no—
408C2×Dic47—22no—
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—44no—
423C2×Dic47—44no—
424C2×Dic47—44no—
425C2×Dic47—44no—
426C2×Dic47C22×D414yes—
427D188—416no—
428D188—416no—
429C4×D47—416no—
430C4×D47—416no—
431C4×D47—416no—
432C4×D47—416no—
433C2×#2412—471nomaximal, Sylow
434C22×C47—24no—
435C22×C47—24no—
436C22×C47—24no—
437C22×C47—416no—
438C22×C47—42no—
439C22×C47—42no—
440C22×C47—42no—
441C22×C47—42no—
442C22×C47C2×#12114yes—
443C22×C47C2×#12314yes—
444C22×C47#53414yes—
445C22×C47#54614yes—
446C22×C47#54614yes—
447C22×C47#55114yes—
448C22×C47#55114yes—
449C22×C47C23×D411yescharacteristic
450C22×C47C23×D411yescharacteristic
451C22×C47C22×#4111yescharacteristic
452C22×C47C22×#4111yescharacteristic
453C22×C47C22×#4111yescharacteristic
454C22×C47C2×H(5,𝔽2)11yescharacteristic
455C22×C47C2×H(5,𝔽2)11yescharacteristic
456C2×D47—24no—
457C2×D47—24no—
458C2×D47—232no—
459C2×D47—232no—
460C2×D47—24no—
461C2×D47—24no—
462C2×D47—24no—
463C2×D47—24no—
464C2×D47—24no—
465C2×D47—24no—
466C2×D47—24no—
467C2×D47—24no—
468C2×D47—24no—
469C2×D47—24no—
470C2×D47—464no—
471C2×D47—42no—
472C2×D47—42no—
473C2×D47—42no—
474C2×D47—42no—
475C2×D47—42no—
476C2×D47—42no—
477C2×D47—42no—
478C2×D47—88no—
479C2×D47C2×#12118yes—
480C2×D47C2×#12318yescomplemented
481C4×C47—24no—
482C4×C47—42no—
483C4×C47—42no—
484C4×C47—42no—
485C4×C47—42no—
486C4×C47—42no—
487Dic47—24no—
488Dic47—42no—
489Dic47—42no—
490Dic47—42no—
491Dic47—42no—
492C22×#123—471no—
493C22×#120—471no—
494C23×C22⋊C4—471no—
495C23×C22⋊C4—471no—
496#2412—4716no—
497C2×#397—471no—
498C2×#397D4711yescharacteristic, complemented
499C2×#394—471no—
500C2×#394—471no—
501C2×#386—471no—
502C2×#386—471no—
503C2×#386—471no—
504C2×#385—471no—
505C2×#381—471no—
506C2×#380—471no—
507C2×#380—471no—
508C2×C47—44no—
509C2×C47#241218yescomplemented
510C2×C47C22×#12111yescharacteristic
511C2×C47C22×#12311yescharacteristic
512C2×C47C2×#53411yescharacteristic
513C2×C47C2×#54611yescharacteristic
514C2×C47C2×#54611yescharacteristic
515C2×C47C2×#55111yescharacteristic
516C2×C47C2×#55111yescharacteristic
517D47—28no—
518D47—28no—
519D47—82no—
520C26—471no—
521C23×D4—471no—
522C23×D4—471no—
523C23×D4—471no—
524C24×C4—471no—
525C24×C4—471no—
526C24×C4—471no—
527C24×C4—471no—
528C2×#123—478no—
529C2×#123—948no—
530C2×#120—478no—
531C2×#120—948no—
532C22×C4⋊C4—471no—
533C22×C4⋊C4—471no—
534C22×C4⋊C4—471no—
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—471no—
548C22×C22⋊C4—478no—
549C22×C22⋊C4—478no—
550C22×C22⋊C4—948no—
551C22×C22⋊C4—948no—
552C22×C22⋊C4C2×D4711yescharacteristic
553C22×C22⋊C4C2×D4711yescharacteristic
554C22×C22⋊C4C2×D4711yescharacteristic
555#397—478no—
556#397C2×D4718yescomplemented
557#394—478no—
558#394—478no—
559#386—478no—
560#386—478no—
561#386—478no—
562#385—478no—
563#381—478no—
564#380—478no—
565#380—478no—
566C2×#95—471no—
567C2×#95—471no—
568C2×#95—471no—
569C2×#95—471no—
570C2×#95—471no—
571C2×#95C2×D4711yescharacteristic, complemented
572C2×#95C2×D4711yescharacteristic, complemented
573C2×#95C2×D4711yescharacteristic, complemented
574C47C2×#241211yescharacteristic, complemented, Sylow
575C25—471no—
576C25—471no—
577C25—478no—
578C25—474no—
579C25—471no—
580C25—944no—
581C25—944no—
582C25—944no—
583C25—944no—
584C25—1882no—
585C25—1882no—
586C25C22×D4711yescharacteristic
587C22×D4—474no—
588C22×D4—474no—
589C22×D4—474no—
590C22×D4—944no—
591C22×D4—944no—
592C22×D4—944no—
593C22×D4—944no—
594C22×D4—944no—
595C22×D4—944no—
596C22×D4—944no—
597C22×D4—1882no—
598C22×D4—1882no—
599C23×C4—471no—
600C23×C4—471no—
601C23×C4—471no—
602C23×C4—471no—
603C23×C4—471no—
604C23×C4—474no—
605C23×C4—474no—
606C23×C4—474no—
607C23×C4—474no—
608C23×C4—944no—
609C23×C4—944no—
610C23×C4—944no—
611C23×C4—944no—
612C23×C4—944no—
613C23×C4—944no—
614C23×C4—944no—
615C23×C4—944no—
616C23×C4—1882no—
617C23×C4—1882no—
618C23×C4—1882no—
619C23×C4—1882no—
620C23×C4C22×D4711yescharacteristic
621C23×C4C22×D4711yescharacteristic
622C23×C4C22×D4711yescharacteristic
623C23×C4C22×D4711yescharacteristic
624C23×C4C22×D4711yescharacteristic
625C23×C4C22×D4711yescharacteristic
626#123—9432no—
627#120—9432no—
628C2×C4⋊C4—24no—
629C2×C4⋊C4—474no—
630C2×C4⋊C4—474no—
631C2×C4⋊C4—474no—
632C2×C4⋊C4—944no—
633C2×C4⋊C4—1882no—
634C2×C4⋊C4—1882no—
635C2×C4⋊C4C22×D4714yescomplemented
636C2×C22⋊C4—24no—
637C2×C22⋊C4—24no—
638C2×C22⋊C4—24no—
639C2×C22⋊C4—478no—
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—474no—
651C2×C22⋊C4—474no—
652C2×C22⋊C4—9432no—
653C2×C22⋊C4—9432no—
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—944no—
662C2×C22⋊C4—944no—
663C2×C22⋊C4—1882no—
664C2×C22⋊C4—1882no—
665C2×C22⋊C4C22×D4714yes—
666C2×C22⋊C4C22×D4714yes—
667C2×C22⋊C4C22×D4714yes—
668#95—474no—
669#95—474no—
670#95—474no—
671#95—474no—
672#95—474no—
673#95C22×D4714yescomplemented
674#95C22×D4714yescomplemented
675#95C22×D4714yescomplemented
676C24—22no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—22no—
681C24—22no—
682C24—474no—
683C24—474no—
684C24—474no—
685C24—474no—
686C24—474no—
687C24—474no—
688C24—472no—
689C24—472no—
690C24—4716no—
691C24—472no—
692C24—948no—
693C24—9432no—
694C24—9432no—
695C24—948no—
696C24—948no—
697C24—948no—
698C24—942no—
699C24—942no—
700C24—942no—
701C24—942no—
702C24—942no—
703C24—942no—
704C24—942no—
705C24—942no—
706C24—942no—
707C24—942no—
708C24—942no—
709C24—942no—
710C24—942no—
711C24—942no—
712C24—942no—
713C24—18816no—
714C24—1884no—
715C24—1884no—
716C24—18816no—
717C24—18816no—
718C24—18816no—
719C24—18816no—
720C24D4×D4714yes—
721C24C23×D4712yes—
722C24C23×D4711yescharacteristic
723C2×D4—948no—
724C2×D4—948no—
725C2×D4—948no—
726C2×D4—948no—
727C2×D4—948no—
728C2×D4—948no—
729C2×D4—948no—
730C2×D4—18816no—
731C2×D4—18816no—
732C2×D4—1884no—
733C2×D4—1884no—
734C2×D4—18816no—
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—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—474no—
753C22×C4—472no—
754C22×C4—472no—
755C22×C4—472no—
756C22×C4—472no—
757C22×C4—472no—
758C22×C4—948no—
759C22×C4—948no—
760C22×C4—948no—
761C22×C4—948no—
762C22×C4—948no—
763C22×C4—948no—
764C22×C4—948no—
765C22×C4—942no—
766C22×C4—942no—
767C22×C4—942no—
768C22×C4—942no—
769C22×C4—942no—
770C22×C4—942no—
771C22×C4—942no—
772C22×C4—942no—
773C22×C4—942no—
774C22×C4—942no—
775C22×C4—942no—
776C22×C4—942no—
777C22×C4—942no—
778C22×C4—942no—
779C22×C4—948no—
780C22×C4—1884no—
781C22×C4—1884no—
782C22×C4—1884no—
783C22×C4—1884no—
784C22×C4—18816no—
785C22×C4—18816no—
786C22×C4—18816no—
787C22×C4—18816no—
788C22×C4D4×D4714yes—
789C22×C4C23×D4712yes—
790C22×C4C23×D4712yes—
791C22×C4C23×D4712yes—
792C22×C4C23×D4712yes—
793C22×C4C23×D4712yes—
794C22×C4C23×D4712yes—
795C4⋊C4—28no—
796C4⋊C4—948no—
797C4⋊C4—1884no—
798C4⋊C4—1884no—
799C22⋊C4—28no—
800C22⋊C4—28no—
801C22⋊C4—28no—
802C22⋊C4—4716no—
803C22⋊C4—948no—
804C22⋊C4—948no—
805C22⋊C4—948no—
806C22⋊C4—948no—
807C22⋊C4—948no—
808C22⋊C4—948no—
809C22⋊C4—948no—
810C22⋊C4—948no—
811C22⋊C4—948no—
812C22⋊C4—1884no—
813C22⋊C4—1884no—
814C23—28no—
815C23—28no—
816C23—28no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—44no—
824C23—44no—
825C23—44no—
826C23—44no—
827C23—4716no—
828C23—4716no—
829C23—474no—
830C23—474no—
831C23—474no—
832C23—474no—
833C23—474no—
834C23—474no—
835C23—9432no—
836C23—9432no—
837C23—948no—
838C23—948no—
839C23—948no—
840C23—948no—
841C23—948no—
842C23—948no—
843C23—948no—
844C23—948no—
845C23—948no—
846C23—948no—
847C23—948no—
848C23—948no—
849C23—942no—
850C23—942no—
851C23—942no—
852C23—942no—
853C23—942no—
854C23—942no—
855C23—942no—
856C23—942no—
857C23—942no—
858C23—942no—
859C23—942no—
860C23—942no—
861C23—942no—
862C23—942no—
863C23—942no—
864C23—18816no—
865C23—18816no—
866C23—18816no—
867C23—18816no—
868C23—18816no—
869C23—188128no—
870C23—1884no—
871C23—1884no—
872C23—1884no—
873C23—1884no—
874C23—1884no—
875C23—1884no—
876C23—1884no—
877C23C2×D4×D4714yes—
878C23C2×D4×D4712yes—
879C23C2×D4×D4712yes—
880C23#41×D4712yes—
881C23#41×D4712yes—
882C23#41×D4712yes—
883C23#1309407012yes—
884C23#1309407012yes—
885C23C24×D4711yescharacteristic
886D4—18816no—
887D4—18816no—
888D4—18816no—
889C2×C4—28no—
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—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—44no—
908C2×C4—44no—
909C2×C4—44no—
910C2×C4—44no—
911C2×C4—44no—
912C2×C4—474no—
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—942no—
928C2×C4—18816no—
929C2×C4—18816no—
930C2×C4—18816no—
931C2×C4—18816no—
932C2×C4—1884no—
933C2×C4—1884no—
934C2×C4—1884no—
935C2×C4—1884no—
936C2×C4C2×D4×D4714yes—
937C22—24no—
938C22—24no—
939C22—24no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—416no—
945C22—478no—
946C22—478no—
947C22—944no—
948C22—944no—
949C22—944no—
950C22—944no—
951C22—944no—
952C22—944no—
953C22—944no—
954C22—944no—
955C22—944no—
956C22—944no—
957C22—944no—
958C22—944no—
959C22—9432no—
960C22—9432no—
961C22—3768no—
962C22—18864no—
963C22—1882no—
964C22—1882no—
965C22—1882no—
966C22—1882no—
967C22—1882no—
968C22—1882no—
969C22—1882no—
970C22#121×D4714yes—
971C22#123×D4714yes—
972C22#1568968414yes—
973C22#1568976514yes—
974C22#1568976614yes—
975C22#1568979814yes—
976C22#1568979814yes—
977C22C22×D4×D4711yescharacteristic
978C22C22×D4×D4711yescharacteristic
979C22C2×#41×D4711yescharacteristic
980C22C2×#41×D4711yescharacteristic
981C22C2×#41×D4711yescharacteristic
982C22C2×#1309407011yescharacteristic
983C22C2×#1309407011yescharacteristic
984C4—24no—
985C4—42no—
986C4—42no—
987C4—42no—
988C4—42no—
989C4—42no—
990C4—944no—
991C4—1882no—
992C4—1882no—
993C4—1882no—
994C4—1882no—
995C2—44no—
996C2—948no—
997C2—948no—
998C2—3762no—
999C2#2024677718yesdirect product factor
1000C2C2×#121×D4711yescharacteristic
1001C2C2×#123×D4711yescharacteristic
1002C2C2×#1568968411yescharacteristic
1003C2C2×#1568976511yescharacteristic
1004C2C2×#1568976611yescharacteristic
1005C2C2×#1568979811yescharacteristic
1006C2C2×#1568979811yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#397C2
socleC24×C47C24
prime radicalC22×#13093994C2
hypercenterC2×#397D47
hypocenterC47C2×#2412
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
1. C22×#13094009C2semidirect
3. C22×C22⋊C4×D47C2semidirect
4. C22×C22⋊C4×D47C2semidirect
5. #20246777C2direct (N × H)
6. C2×#15689051C2semidirect
7. C2×#15689039C2semidirect
8. C2×#15689038C2semidirect
9. C2×#15689001C2semidirect
10. C2×#15689001C2semidirect
11. C2×#15689001C2semidirect
12. C2×#15688997C2semidirect
13. C2×#15688985C2semidirect
14. C2×#15688982C2semidirect
15. C2×#15688980C2semidirect
16. C2×C47×#397C2semidirect
26. C2×#13094009C22semidirect
29. C22×C4⋊Dic47C22semidirect
30. C22×Dic47⋊C4C22semidirect
31. C22×Dic47⋊C4C22semidirect
40. C22×(C2×D47)⋊C4C22semidirect
41. C22×(C2×D47)⋊C4C22semidirect
42. C22×(C2×D47)⋊C4C22semidirect
43. C22×(C2×D47)⋊C4C22semidirect
46. C2×C22⋊C4×D47C22semidirect
47. C2×C22⋊C4×D47C22semidirect
48. #15689051C22semidirect
49. #15689039C22semidirect
50. #15689038C22semidirect
51. #15689001C22semidirect
52. #15689001C22semidirect
53. #15689001C22semidirect
54. #15688997C22semidirect
55. #15688985C22semidirect
56. #15688982C22semidirect
57. #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
67. C47×#397C22semidirect
68. C2×#95×C47C22semidirect
69. C2×#95×C47C22semidirect
70. C2×#95×C47C22semidirect
118. C2×C4⋊Dic47C23semidirect
121. C2×Dic47⋊C4C23semidirect
122. C2×Dic47⋊C4C23semidirect
136. C2×(C2×D47)⋊C4D4semidirect
143. C2×(C2×D47)⋊C4C23semidirect
144. C2×(C2×D47)⋊C4C23semidirect
145. C2×(C2×D47)⋊C4C23semidirect
146. C2×(C2×D47)⋊C4C23semidirect
149. C47⋊#95C23semidirect
150. C47⋊#95C23semidirect
151. C47⋊#95C23semidirect
152. C47⋊#95C23semidirect
153. C47⋊#95C23semidirect
162. C2×C4⋊C4×C47C23semidirect
169. #95×C47C23semidirect
170. #95×C47C23semidirect
171. #95×C47C23semidirect
306. (C2×D47)⋊C4C2×D4semidirect
375. C22×D47#123semidirect
480. C2×D47C2×#123semidirect
498. C2×#397D47semidirect
509. C2×C47#2412semidirect
535. C22×C4⋊C4C2×D47semidirect
556. #397C2×D47semidirect
571. C2×#95C2×D47semidirect
572. C2×#95C2×D47semidirect
573. C2×#95C2×D47semidirect
574. C47C2×#2412semidirect
635. C2×C4⋊C4C22×D47semidirect
673. #95C22×D47semidirect
674. #95C22×D47semidirect
675. #95C22×D47semidirect
999. C2#20246777direct (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⋊C4×D472
#202467772
C2×#156890512
C2×#156890392
C2×#156890382
C2×#156890012
C2×#156889972
C2×#156889852
C2×#156889822
C2×#156889802
C2×C47×#3972
C2×#241247