Finite Group Databasebeta

← C2×#20246768 #26384897

Subgroups — C2×#20246768 #26384897

Order 12032.

4946 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094009C211yesmaximal, characteristic, complemented
2C22×#13093994C211yesmaximal, characteristic
3C22×#13093982C211yesmaximal, characteristic, complemented
4C22×C22⋊C4×D47C211yesmaximal, characteristic, complemented
5#20246768C2116yesmaximal, direct product factor
6C2×#15689045C211yesmaximal, characteristic, complemented
7C2×#15689040C211yesmaximal, characteristic, complemented
8C2×#15689039C211yesmaximal, characteristic, complemented
9C2×#15689024C211yesmaximal, characteristic, complemented
10C2×#15689023C211yesmaximal, characteristic, complemented
11C2×#15689012C211yesmaximal, characteristic, complemented
12C2×#15689011C211yesmaximal, characteristic, complemented
13C2×#15689001C211yesmaximal, characteristic, complemented
14C2×#15688994C211yesmaximal, characteristic, complemented
15C2×#15688978C211yesmaximal, characteristic, complemented
16C2×C47×#396C211yesmaximal, characteristic, complemented
17C25×D47C2211yescharacteristic
18C23×D188C2211yescharacteristic
19C23×D188C2211yescharacteristic
20C23×C22⋊D47C2211yescharacteristic
21C23×C4×D47C2211yescharacteristic
22C23×C4×D47C2211yescharacteristic
23C2×#13094009—28no—
24C2×#13094009C2218yescomplemented
25C2×#13093994—28no—
26C2×#13093994C2218yes—
27C2×#13093982—28no—
28C2×#13093982C2218yescomplemented
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
41C22×(C2×D47)⋊C4C2211yescharacteristic
42C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
43C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
44C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
45C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
46C2×C22⋊C4×D47—28no—
47C2×C22⋊C4×D47C2218yescomplemented
48C22×C4×Dic47C2211yescharacteristic, complemented
49C22×C4×Dic47C2211yescharacteristic, complemented
50#15689045C2218yescomplemented
51#15689040C2218yescomplemented
52#15689039C2218yescomplemented
53#15689024C2218yescomplemented
54#15689023C2218yescomplemented
55#15689012C2218yescomplemented
56#15689011C2218yescomplemented
57#15689001C2218yescomplemented
58#15688994C2218yescomplemented
59#15688978C2218yescomplemented
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—24no—
76C24×D47—42no—
77C24×D47—42no—
78C24×D47C2311yescharacteristic
79C24×D47C2311yescharacteristic
80C24×D47C2314yes—
81C24×D47C2311yescharacteristic
82C22×D188—24no—
83C22×D188—24no—
84C22×D188—24no—
85C22×D188—24no—
86C22×D188—24no—
87C22×D188—42no—
88C22×D188C2314yes—
89C22×D188C2314yes—
90C22×C22⋊D47—24no—
91C22×C22⋊D47—24no—
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—42no—
103C22×C4×D47—42no—
104C22×C4×D47D418yescomplemented
105C22×C4×D47C2314yes—
106C22×C4×D47C2314yes—
107#13094009—232no—
108#13093994—232no—
109#13093982—232no—
110C2×C4⋊Dic47—24no—
111C2×C4⋊Dic47C2314yescomplemented
112C2×Dic47⋊C4—24no—
113C2×Dic47⋊C4—42no—
114C2×Dic47⋊C4C2314yescomplemented
115C2×Dic47⋊C4C2314yescomplemented
116C2×C22⋊Dic47—24no—
117C2×C22⋊Dic47—24no—
118C2×C22⋊Dic47C2314yes—
119C2×C22⋊Dic47C2314yes—
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—24no—
128C2×(C2×D47)⋊C4—42no—
129C2×(C2×D47)⋊C4—42no—
130C2×(C2×D47)⋊C4—42no—
131C2×(C2×D47)⋊C4D418yes—
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)⋊C4C2314yescomplemented
141C2×(C2×D47)⋊C4C2314yescomplemented
142C2×(C2×D47)⋊C4C2314yescomplemented
143C2×(C2×D47)⋊C4C2314yescomplemented
144C22⋊C4×D47—232no—
145C2×C4×Dic47—24no—
146C2×C4×Dic47—24no—
147C2×C4×Dic47C2314yescomplemented
148C2×C4×Dic47C2314yescomplemented
149C47⋊#95C2314yescomplemented
150C47⋊#95C2314yescomplemented
151C47⋊#95C2314yescomplemented
152C25×C47C2311yescharacteristic
153C23×C4×C47C2311yescharacteristic
154C23×C4×C47C2311yescharacteristic
155C23×C4×C47C2311yescharacteristic
156C23×C4×C47C2311yescharacteristic
157C23×C4×C47C2311yescharacteristic
158C23×C4×C47C2311yescharacteristic
159C2×C4⋊C4×C47—24no—
160C2×C4⋊C4×C47—24no—
161C2×C4⋊C4×C47—42no—
162C2×C4⋊C4×C47C2314yescomplemented
163C2×C4⋊C4×C47C2314yescomplemented
164C2×C4⋊C4×C47C2314yescomplemented
165C2×C22⋊C4×C47—24no—
166C2×C22⋊C4×C47—24no—
167C2×C22⋊C4×C47—42no—
168C2×C22⋊C4×C47C2314yes—
169C2×C22⋊C4×C47C2314yes—
170C2×C22⋊C4×C47C2314yes—
171#95×C47C2314yescomplemented
172C24×C47—22no—
173C24×C47—22no—
174C24×C47—22no—
175C24×C47—22no—
176C24×C47—22no—
177C24×C47—22no—
178C24×C47#4114yes—
179C24×C47C2412yes—
180C24×C47C2411yescharacteristic
181C23×D47—22no—
182C23×D47—22no—
183C23×D47—22no—
184C23×D47—22no—
185C23×D47—232no—
186C23×D47—22no—
187C23×D47—22no—
188C23×D47—28no—
189C23×D47—22no—
190C23×D47—22no—
191C23×D47—22no—
192C23×D47—22no—
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—28no—
203C23×D47—28no—
204C23×D47—44no—
205C23×D47—44no—
206C23×D47—416no—
207C23×D47—416no—
208C23×D47—416no—
209C23×D47—416no—
210C23×D47—416no—
211C23×D47—416no—
212C23×D47C2×D414yes—
213C23×D47C2×D414yes—
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×C47C2×D414yes—
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—28no—
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×Dic47C2×D414yes—
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—44no—
273C2×D188—416no—
274C2×D188—416no—
275C2×C4×D47—232no—
276C2×C4×D47—28no—
277C2×C4×D47—28no—
278C2×C4×D47—28no—
279C2×C4×D47—44no—
280C2×C4×D47—44no—
281C2×C4×D47—416no—
282C2×C4×D47C2×D4116yescomplemented
283C4⋊C4×C47—28no—
284C4⋊C4×C47—28no—
285C4⋊C4×C47—44no—
286C22⋊C4×C47—28no—
287C22⋊C4×C47—28no—
288C22⋊C4×C47—44no—
289C22⋊Dic47—28no—
290C22⋊Dic47—28no—
291(C2×D47)⋊C4—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—44no—
300(C2×D47)⋊C4—44no—
301(C2×D47)⋊C4—44no—
302(C2×D47)⋊C4C2×D4116yes—
303C4⋊Dic47—28no—
304Dic47⋊C4—28no—
305Dic47⋊C4—44no—
306C4×Dic47—28no—
307C4×Dic47—28no—
308C23×C47—28no—
309C23×C47—28no—
310C23×C47—28no—
311C23×C47—22no—
312C23×C47—22no—
313C23×C47—22no—
314C23×C47—22no—
315C23×C47—22no—
316C23×C47—22no—
317C23×C47—44no—
318C23×C47—44no—
319C23×C47—44no—
320C23×C47—44no—
321C23×C47C22×D412yes—
322C23×C47C22×D412yes—
323C23×C47C2×#4112yes—
324C23×C47C2×#4112yes—
325C23×C47C2×#4114yes—
326C23×C47C2×#4112yes—
327C23×C47H(5,𝔽2)12yes—
328C23×C47H(5,𝔽2)12yes—
329C23×C47C2511yescharacteristic
330C22×D47—28no—
331C22×D47—28no—
332C22×D47—28no—
333C22×D47—28no—
334C22×D47—28no—
335C22×D47—28no—
336C22×D47—22no—
337C22×D47—22no—
338C22×D47—22no—
339C22×D47—22no—
340C22×D47—232no—
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—22no—
353C22×D47—22no—
354C22×D47—22no—
355C22×D47—22no—
356C22×D47—22no—
357C22×D47—416no—
358C22×D47—416no—
359C22×D47—416no—
360C22×D47—416no—
361C22×D47—4128no—
362C22×D47—416no—
363C22×D47—44no—
364C22×D47—44no—
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#121116yes—
376C22×D47C22×D414yes—
377C22×D47C22×D414yes—
378C22×D47C2×#4114yes—
379C22×D47C2×#4114yes—
380C2×C4×C47—28no—
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—44no—
399C2×C4×C47—44no—
400C2×C4×C47—44no—
401C2×C4×C47—44no—
402C2×C4×C47C22×D414yes—
403C2×C4×C47C22×D414yes—
404C22⋊D47—416no—
405C2×Dic47—28no—
406C2×Dic47—28no—
407C2×Dic47—22no—
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—44no—
421C2×Dic47—44no—
422C2×Dic47—44no—
423C2×Dic47C22×D414yes—
424C2×Dic47C22×D414yes—
425D188—416no—
426D188—416no—
427C4×D47—232no—
428C4×D47—416no—
429C2×#2411—471nomaximal, Sylow
430C22×C47—24no—
431C22×C47—24no—
432C22×C47—24no—
433C22×C47—42no—
434C22×C47—416no—
435C22×C47—42no—
436C22×C47—42no—
437C22×C47—42no—
438C22×C47C2×#12114yes—
439C22×C47#52514yes—
440C22×C47#53514yes—
441C22×C47#54614yes—
442C22×C47#54614yes—
443C22×C47#55114yes—
444C22×C47#55114yes—
445C22×C47C23×D411yescharacteristic
446C22×C47C23×D411yescharacteristic
447C22×C47C22×#4111yescharacteristic
448C22×C47C22×#4111yescharacteristic
449C22×C47C22×#4111yescharacteristic
450C22×C47C2×H(5,𝔽2)11yescharacteristic
451C22×C47C2×H(5,𝔽2)11yescharacteristic
452C2×D47—232no—
453C2×D47—24no—
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—464no—
463C2×D47—42no—
464C2×D47—416no—
465C2×D47—42no—
466C2×D47—42no—
467C2×D47—42no—
468C2×D47—42no—
469C2×D47—42no—
470C2×D47—42no—
471C2×D47—42no—
472C2×D47—42no—
473C2×D47—42no—
474C2×D47—42no—
475C2×D47—88no—
476C2×D47C2×#12118yes—
477C4×C47—24no—
478C4×C47—24no—
479C4×C47—42no—
480C4×C47—42no—
481C4×C47—42no—
482C4×C47—42no—
483Dic47—24no—
484Dic47—24no—
485Dic47—42no—
486Dic47—42no—
487Dic47—42no—
488C22×#123—471no—
489C22×#120—471no—
490C22×#117—471no—
491C23×C22⋊C4—471no—
492#2411—4716no—
493C2×#396—471no—
494C2×#396D4711yescharacteristic, complemented
495C2×#394—471no—
496C2×#394—471no—
497C2×#390—471no—
498C2×#390—471no—
499C2×#388—471no—
500C2×#388—471no—
501C2×#386—471no—
502C2×#385—471no—
503C2×#379—471no—
504C2×C47—44no—
505C2×C47#241118yescomplemented
506C2×C47C22×#12111yescharacteristic
507C2×C47C2×#52511yescharacteristic
508C2×C47C2×#53511yescharacteristic
509C2×C47C2×#54611yescharacteristic
510C2×C47C2×#54611yescharacteristic
511C2×C47C2×#55111yescharacteristic
512C2×C47C2×#55111yescharacteristic
513D47—28no—
514D47—44no—
515D47—82no—
516C26—471no—
517C23×D4—471no—
518C23×D4—471no—
519C23×D4—471no—
520C24×C4—471no—
521C24×C4—471no—
522C2×#123—478no—
523C2×#123—948no—
524C2×#120—478no—
525C2×#120—948no—
526C2×#117—478no—
527C2×#117—948no—
528C22×C4⋊C4—471no—
529C22×C4⋊C4—471no—
530C22×C4⋊C4—471no—
531C22×C4⋊C4C2×D4711yescharacteristic, complemented
532C22×C4⋊C4C2×D4711yescharacteristic, complemented
533C22×C4⋊C4C2×D4711yescharacteristic, complemented
534C22×C22⋊C4—471no—
535C22×C22⋊C4—471no—
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—948no—
550C22×C22⋊C4C2×D4711yescharacteristic
551C22×C22⋊C4C2×D4711yescharacteristic
552C22×C22⋊C4C2×D4711yescharacteristic
553C22×C42—471no—
554C22×C42—471no—
555#396—478no—
556#396C2×D4718yescomplemented
557#394—478no—
558#394—478no—
559#390—478no—
560#390—478no—
561#388—478no—
562#388—478no—
563#386—478no—
564#385—478no—
565#379—478no—
566C2×#95—471no—
567C2×#95—471no—
568C2×#95—471no—
569C2×#95C2×D4711yescharacteristic, complemented
570C47C2×#241111yescharacteristic, complemented, Sylow
571C25—471no—
572C25—471no—
573C25—471no—
574C25—474no—
575C25—944no—
576C25—944no—
577C25—944no—
578C25—944no—
579C25—944no—
580C25—1882no—
581C25—1882no—
582C25C22×D4711yescharacteristic
583C22×D4—474no—
584C22×D4—474no—
585C22×D4—474no—
586C22×D4—944no—
587C22×D4—944no—
588C22×D4—944no—
589C22×D4—944no—
590C22×D4—944no—
591C22×D4—944no—
592C22×D4—944no—
593C22×D4—1882no—
594C22×D4—1882no—
595C23×C4—471no—
596C23×C4—471no—
597C23×C4—478no—
598C23×C4—474no—
599C23×C4—471no—
600C23×C4—471no—
601C23×C4—471no—
602C23×C4—474no—
603C23×C4—944no—
604C23×C4—944no—
605C23×C4—944no—
606C23×C4—1882no—
607C23×C4—1882no—
608C23×C4C22×D4711yescharacteristic
609C23×C4C22×D4711yescharacteristic
610C23×C4C22×D4711yescharacteristic
611C23×C4C22×D4711yescharacteristic
612C23×C4C22×D4711yescharacteristic
613C23×C4C22×D4711yescharacteristic
614#123—9432no—
615#120—9432no—
616#117—9432no—
617C2×C4⋊C4—24no—
618C2×C4⋊C4—24no—
619C2×C4⋊C4—42no—
620C2×C4⋊C4—474no—
621C2×C4⋊C4—474no—
622C2×C4⋊C4—474no—
623C2×C4⋊C4—944no—
624C2×C4⋊C4—944no—
625C2×C4⋊C4—1882no—
626C2×C4⋊C4C22×D4714yescomplemented
627C2×C4⋊C4C22×D4714yescomplemented
628C2×C4⋊C4C22×D4714yescomplemented
629C2×C22⋊C4—24no—
630C2×C22⋊C4—24no—
631C2×C22⋊C4—42no—
632C2×C22⋊C4—478no—
633C2×C22⋊C4—474no—
634C2×C22⋊C4—474no—
635C2×C22⋊C4—474no—
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—9432no—
648C2×C22⋊C4—944no—
649C2×C22⋊C4—944no—
650C2×C22⋊C4—944no—
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—1882no—
659C2×C22⋊C4—1882no—
660C2×C22⋊C4—1882no—
661C2×C22⋊C4C22×D4714yes—
662C2×C22⋊C4C22×D4714yes—
663C2×C22⋊C4C22×D4714yes—
664C2×C42—474no—
665C2×C42—474no—
666C2×C42—944no—
667C2×C42—944no—
668#95—474no—
669#95—474no—
670#95—474no—
671#95C22×D4714yescomplemented
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—474no—
679C24—474no—
680C24—474no—
681C24—472no—
682C24—474no—
683C24—472no—
684C24—472no—
685C24—948no—
686C24—948no—
687C24—948no—
688C24—948no—
689C24—9432no—
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—942no—
707C24—942no—
708C24—1884no—
709C24—1884no—
710C24—18816no—
711C24—18816no—
712C24—18816no—
713C24—18816no—
714C24—18816no—
715C24—18816no—
716C24#1062535414yes—
717C24C23×D4712yes—
718C24C23×D4711yescharacteristic
719C2×D4—948no—
720C2×D4—948no—
721C2×D4—948no—
722C2×D4—948no—
723C2×D4—948no—
724C2×D4—948no—
725C2×D4—948no—
726C2×D4—1884no—
727C2×D4—18816no—
728C2×D4—18816no—
729C2×D4—1884no—
730C2×D4—18816no—
731C22×C4—22no—
732C22×C4—22no—
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—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—474no—
748C22×C4—474no—
749C22×C4—472no—
750C22×C4—472no—
751C22×C4—4716no—
752C22×C4—472no—
753C22×C4—472no—
754C22×C4—472no—
755C22×C4—948no—
756C22×C4—9432no—
757C22×C4—948no—
758C22×C4—948no—
759C22×C4—942no—
760C22×C4—942no—
761C22×C4—942no—
762C22×C4—942no—
763C22×C4—942no—
764C22×C4—942no—
765C22×C4—942no—
766C22×C4—942no—
767C22×C4—942no—
768C22×C4—942no—
769C22×C4—942no—
770C22×C4—942no—
771C22×C4—942no—
772C22×C4—1884no—
773C22×C4—1884no—
774C22×C4—18816no—
775C22×C4D4×D4714yes—
776C22×C4D4×D4714yes—
777C22×C4C23×D4712yes—
778C22×C4C23×D4712yes—
779C22×C4C23×D4712yes—
780C22×C4C23×D4712yes—
781C22×C4C23×D4712yes—
782C22×C4C23×D4712yes—
783C4⋊C4—28no—
784C4⋊C4—28no—
785C4⋊C4—44no—
786C4⋊C4—948no—
787C4⋊C4—948no—
788C4⋊C4—1884no—
789C22⋊C4—28no—
790C22⋊C4—28no—
791C22⋊C4—44no—
792C22⋊C4—4716no—
793C22⋊C4—948no—
794C22⋊C4—948no—
795C22⋊C4—948no—
796C22⋊C4—948no—
797C22⋊C4—948no—
798C22⋊C4—948no—
799C22⋊C4—948no—
800C22⋊C4—948no—
801C22⋊C4—948no—
802C22⋊C4—948no—
803C22⋊C4—1884no—
804C22⋊C4—1884no—
805C22⋊C4—1884no—
806C42—948no—
807C42—948no—
808C23—28no—
809C23—28no—
810C23—28no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—44no—
818C23—44no—
819C23—44no—
820C23—44no—
821C23—4716no—
822C23—474no—
823C23—474no—
824C23—474no—
825C23—474no—
826C23—9432no—
827C23—948no—
828C23—948no—
829C23—948no—
830C23—948no—
831C23—948no—
832C23—948no—
833C23—942no—
834C23—942no—
835C23—942no—
836C23—942no—
837C23—948no—
838C23—948no—
839C23—948no—
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—942no—
853C23—18816no—
854C23—18816no—
855C23—18816no—
856C23—18816no—
857C23—18816no—
858C23—18816no—
859C23—188128no—
860C23—1884no—
861C23—1884no—
862C23—1884no—
863C23—1884no—
864C23—1884no—
865C23—1884no—
866C23—1884no—
867C23—1884no—
868C23—1884no—
869C23—1884no—
870C23—1884no—
871C23C2×D4×D4712yes—
872C23C2×D4×D4712yes—
873C23#41×D4712yes—
874C23#41×D4712yes—
875C23C2×#1062535414yes—
876C23C2×#1062535412yes—
877C23#1309406912yes—
878C23#1309407012yes—
879C23C24×D4711yescharacteristic
880D4—18816no—
881D4—18816no—
882D4—18816no—
883C2×C4—28no—
884C2×C4—28no—
885C2×C4—22no—
886C2×C4—22no—
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—44no—
902C2×C4—44no—
903C2×C4—44no—
904C2×C4—44no—
905C2×C4—474no—
906C2×C4—474no—
907C2×C4—9432no—
908C2×C4—948no—
909C2×C4—948no—
910C2×C4—942no—
911C2×C4—942no—
912C2×C4—942no—
913C2×C4—942no—
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—18816no—
924C2×C4—1884no—
925C2×C4—1884no—
926C2×C4—1884no—
927C2×C4C2×D4×D4714yes—
928C2×C4C2×D4×D4714yes—
929C22—24no—
930C22—24no—
931C22—24no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—416no—
937C22—478no—
938C22—944no—
939C22—944no—
940C22—944no—
941C22—944no—
942C22—944no—
943C22—944no—
944C22—9432no—
945C22—944no—
946C22—944no—
947C22—944no—
948C22—3768no—
949C22—18864no—
950C22—1882no—
951C22—1882no—
952C22—1882no—
953C22—1882no—
954C22—1882no—
955C22—1882no—
956C22—1882no—
957C22—1882no—
958C22—1882no—
959C22—1882no—
960C22—1882no—
961C22—18816no—
962C22#121×D4714yes—
963C22#1568963614yes—
964C22#1568968914yes—
965C22#1568976214yes—
966C22#1568976414yes—
967C22#1568979814yes—
968C22#1568980014yes—
969C22C22×D4×D4711yescharacteristic
970C22C22×D4×D4711yescharacteristic
971C22C2×#41×D4711yescharacteristic
972C22C2×#41×D4711yescharacteristic
973C22C22×#1062535411yescharacteristic
974C22C2×#1309406911yescharacteristic
975C22C2×#1309407011yescharacteristic
976C4—24no—
977C4—24no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—42no—
982C4—944no—
983C4—944no—
984C4—1882no—
985C4—1882no—
986C4—1882no—
987C2—44no—
988C2—948no—
989C2—3762no—
990C2—1884no—
991C2#2024676818yesdirect product factor
992C2C2×#121×D4711yescharacteristic
993C2C2×#1568963611yescharacteristic
994C2C2×#1568968911yescharacteristic
995C2C2×#1568976211yescharacteristic
996C2C2×#1568976411yescharacteristic
997C2C2×#1568979811yescharacteristic
998C2C2×#1568980011yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#396C2
socleC24×C47C24
prime radicalC22×#13093994C2
hypercenterC2×#396D47
hypocenterC47C2×#2411
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#13094009C2semidirect
3. C22×#13093982C2semidirect
4. C22×C22⋊C4×D47C2semidirect
5. #20246768C2direct (N × H)
6. C2×#15689045C2semidirect
7. C2×#15689040C2semidirect
8. C2×#15689039C2semidirect
9. C2×#15689024C2semidirect
10. C2×#15689023C2semidirect
11. C2×#15689012C2semidirect
12. C2×#15689011C2semidirect
13. C2×#15689001C2semidirect
14. C2×#15688994C2semidirect
15. C2×#15688978C2semidirect
16. C2×C47×#396C2semidirect
24. C2×#13094009C22semidirect
28. C2×#13093982C22semidirect
29. C22×C4⋊Dic47C22semidirect
30. C22×Dic47⋊C4C22semidirect
31. C22×Dic47⋊C4C22semidirect
42. C22×(C2×D47)⋊C4C22semidirect
43. C22×(C2×D47)⋊C4C22semidirect
44. C22×(C2×D47)⋊C4C22semidirect
45. C22×(C2×D47)⋊C4C22semidirect
47. C2×C22⋊C4×D47C22semidirect
48. C22×C4×Dic47C22semidirect
49. C22×C4×Dic47C22semidirect
50. #15689045C22semidirect
51. #15689040C22semidirect
52. #15689039C22semidirect
53. #15689024C22semidirect
54. #15689023C22semidirect
55. #15689012C22semidirect
56. #15689011C22semidirect
57. #15689001C22semidirect
58. #15688994C22semidirect
59. #15688978C22semidirect
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
104. C22×C4×D47D4semidirect
111. C2×C4⋊Dic47C23semidirect
114. C2×Dic47⋊C4C23semidirect
115. C2×Dic47⋊C4C23semidirect
140. C2×(C2×D47)⋊C4C23semidirect
141. C2×(C2×D47)⋊C4C23semidirect
142. C2×(C2×D47)⋊C4C23semidirect
143. C2×(C2×D47)⋊C4C23semidirect
147. C2×C4×Dic47C23semidirect
148. C2×C4×Dic47C23semidirect
149. C47⋊#95C23semidirect
150. C47⋊#95C23semidirect
151. C47⋊#95C23semidirect
162. C2×C4⋊C4×C47C23semidirect
163. C2×C4⋊C4×C47C23semidirect
164. C2×C4⋊C4×C47C23semidirect
171. #95×C47C23semidirect
282. C2×C4×D47C2×D4semidirect
494. C2×#396D47semidirect
505. C2×C47#2411semidirect
531. C22×C4⋊C4C2×D47semidirect
532. C22×C4⋊C4C2×D47semidirect
533. C22×C4⋊C4C2×D47semidirect
556. #396C2×D47semidirect
569. C2×#95C2×D47semidirect
570. C47C2×#2411semidirect
626. C2×C4⋊C4C22×D47semidirect
627. C2×C4⋊C4C22×D47semidirect
628. C2×C4⋊C4C22×D47semidirect
671. #95C22×D47semidirect
991. C2#20246768direct (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×#130939822
C22×C22⋊C4×D472
#202467682
C2×#156890452
C2×#156890402
C2×#156890392
C2×#156890242
C2×#156890232
C2×#156890122
C2×#156890112
C2×#156890012
C2×#156889942
C2×#156889782
C2×C47×#3962
C2×#241147