Finite Group Databasebeta

← C2×#20246235 #26375490

Subgroups — C2×#20246235 #26375490

Order 12032.

4990 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093982C211yesmaximal, characteristic, complemented
2C23×(C2×D47)⋊C4C211yesmaximal, characteristic
3C22×C22⋊C4×D47C211yesmaximal, characteristic
4#20246235C2116yesmaximal, direct product factor
5C2×#15689015C211yesmaximal, characteristic, complemented
6C2×#15689015C211yesmaximal, characteristic, complemented
7C2×#15689013C211yesmaximal, characteristic, complemented
8C2×#15689013C211yesmaximal, characteristic, complemented
9C2×#15688998C211yesmaximal, characteristic, complemented
10C2×#15688985C211yesmaximal, characteristic, complemented
11C2×#15688980C211yesmaximal, characteristic, complemented
12C2×#15688978C211yesmaximal, characteristic
13C2×C22⋊C4×Dic47C211yesmaximal, characteristic, complemented
14C2×C4×C22⋊Dic47C211yesmaximal, characteristic, complemented
15C2×#15688970C211yesmaximal, characteristic, complemented
16C2×C47×#385C211yesmaximal, characteristic, complemented
17C25×D47C2211yescharacteristic
18C24×Dic47C2211yescharacteristic
19C23×C4×D47C2211yescharacteristic
20C23×C4×D47C2211yescharacteristic
21C2×#13093982—28no—
22C2×#13093982C2218yescomplemented
23C22×C4⋊Dic47C2211yescharacteristic, complemented
24C22×C4⋊Dic47C2211yescharacteristic, complemented
25C22×C22⋊Dic47C2211yescharacteristic
26C22×C22⋊Dic47C2211yescharacteristic
27C22×(C2×D47)⋊C4—28no—
28C22×(C2×D47)⋊C4C2211yescharacteristic
29C22×(C2×D47)⋊C4C2211yescharacteristic
30C22×(C2×D47)⋊C4C2211yescharacteristic
31C22×(C2×D47)⋊C4C2211yescharacteristic
32C22×(C2×D47)⋊C4C2218yes—
33C22×(C2×D47)⋊C4C2211yescharacteristic
34C22×(C2×D47)⋊C4C2211yescharacteristic
35C22×(C2×D47)⋊C4C2211yescharacteristic
36C22×(C2×D47)⋊C4C2211yescharacteristic
37C22×(C2×D47)⋊C4C2211yescharacteristic
38C22×(C2×D47)⋊C4C2211yescharacteristic
39C2×C22⋊C4×D47C4116yescomplemented
40C2×C22⋊C4×D47C2218yes—
41C22×C4×Dic47C2211yescharacteristic, complemented
42C22×C4×Dic47C2211yescharacteristic, complemented
43C22×C4×Dic47C2211yescharacteristic, complemented
44C22×C4×Dic47C2211yescharacteristic, complemented
45#15689015C2218yescomplemented
46#15689015C2218yescomplemented
47#15689013C2218yescomplemented
48#15689013C2218yescomplemented
49#15688998C2218yescomplemented
50#15688985C2218yescomplemented
51#15688980C2218yescomplemented
52#15688978C2218yes—
53C22⋊C4×Dic47C2218yescomplemented
54C4×C22⋊Dic47C2218yescomplemented
55#15688970C2218yescomplemented
56C2×C47⋊#95C2211yescharacteristic, complemented
57C2×C47⋊#95C2211yescharacteristic, complemented
58C2×C47⋊#95C2211yescharacteristic, complemented
59C2×C47⋊#95C2211yescharacteristic, complemented
60C2×C47⋊#95C2211yescharacteristic, complemented
61C2×C47⋊#95C2211yescharacteristic, complemented
62C24×C4×C47C2211yescharacteristic
63C22×C4⋊C4×C47C2211yescharacteristic, complemented
64C22×C4⋊C4×C47C2211yescharacteristic, complemented
65C22×C22⋊C4×C47C2211yescharacteristic
66C22×C22⋊C4×C47C2211yescharacteristic
67C47×#385C2218yescomplemented
68C2×#95×C47C2211yescharacteristic, complemented
69C2×#95×C47C2211yescharacteristic, complemented
70C24×D47—24no—
71C24×D47—24no—
72C24×D47—24no—
73C24×D47—24no—
74C24×D47—42no—
75C24×D47—42no—
76C24×D47C2×C418yes—
77C24×D47C2311yescharacteristic
78C24×D47C2314yes—
79C24×D47C2311yescharacteristic
80C23×Dic47—24no—
81C23×Dic47—24no—
82C23×Dic47—42no—
83C23×Dic47C2311yescharacteristic
84C23×Dic47C2311yescharacteristic
85C23×Dic47C2311yescharacteristic
86C23×Dic47C2314yes—
87C23×Dic47C2311yescharacteristic
88C23×Dic47C2311yescharacteristic
89C23×Dic47C2311yescharacteristic
90C22×C4×D47—24no—
91C22×C4×D47—24no—
92C22×C4×D47—42no—
93C22×C4×D47—42no—
94C22×C4×D47C2×C418yescomplemented
95C22×C4×D47C2×C418yescomplemented
96C22×C4×D47C2314yes—
97C22×C4×D47C2314yes—
98#13093982—232no—
99C2×C4⋊Dic47—24no—
100C2×C4⋊Dic47—42no—
101C2×C4⋊Dic47C2314yescomplemented
102C2×C4⋊Dic47C2314yescomplemented
103C2×C22⋊Dic47—24no—
104C2×C22⋊Dic47C2×C418yes—
105C2×C22⋊Dic47C2314yes—
106C2×C22⋊Dic47C2314yes—
107C2×(C2×D47)⋊C4—24no—
108C2×(C2×D47)⋊C4—24no—
109C2×(C2×D47)⋊C4—24no—
110C2×(C2×D47)⋊C4—24no—
111C2×(C2×D47)⋊C4—24no—
112C2×(C2×D47)⋊C4—232no—
113C2×(C2×D47)⋊C4—42no—
114C2×(C2×D47)⋊C4—42no—
115C2×(C2×D47)⋊C4C2×C418yescomplemented
116C2×(C2×D47)⋊C4C2×C418yescomplemented
117C2×(C2×D47)⋊C4D418yes—
118C2×(C2×D47)⋊C4C2314yes—
119C2×(C2×D47)⋊C4C2314yes—
120C2×(C2×D47)⋊C4C2314yes—
121C2×(C2×D47)⋊C4C2314yes—
122C2×(C2×D47)⋊C4C2314yes—
123C2×(C2×D47)⋊C4C2314yes—
124C2×(C2×D47)⋊C4C2314yes—
125C2×(C2×D47)⋊C4C2314yes—
126C2×(C2×D47)⋊C4C2314yes—
127C2×(C2×D47)⋊C4C2314yes—
128C22⋊C4×D47C2×C4164yescomplemented
129C2×C4×Dic47—24no—
130C2×C4×Dic47—24no—
131C2×C4×Dic47—42no—
132C2×C4×Dic47—42no—
133C2×C4×Dic47C2314yescomplemented
134C2×C4×Dic47C2314yescomplemented
135C2×C4×Dic47C2314yescomplemented
136C2×C4×Dic47C2314yescomplemented
137C47⋊#95C2314yescomplemented
138C47⋊#95C2314yescomplemented
139C47⋊#95C2314yescomplemented
140C47⋊#95C2314yescomplemented
141C47⋊#95C2314yescomplemented
142C47⋊#95C2314yescomplemented
143C25×C47C2311yescharacteristic
144C23×C4×C47—24no—
145C23×C4×C47—24no—
146C23×C4×C47—42no—
147C23×C4×C47C2311yescharacteristic
148C23×C4×C47C2311yescharacteristic
149C23×C4×C47C2311yescharacteristic
150C23×C4×C47C2314yes—
151C23×C4×C47C2311yescharacteristic
152C23×C4×C47C2311yescharacteristic
153C23×C4×C47C2311yescharacteristic
154C2×C4⋊C4×C47—24no—
155C2×C4⋊C4×C47—42no—
156C2×C4⋊C4×C47C2314yescomplemented
157C2×C4⋊C4×C47C2314yescomplemented
158C2×C22⋊C4×C47—24no—
159C2×C22⋊C4×C47C2×C418yes—
160C2×C22⋊C4×C47C2314yes—
161C2×C22⋊C4×C47C2314yes—
162#95×C47C2314yescomplemented
163#95×C47C2314yescomplemented
164C24×C47—22no—
165C24×C47—22no—
166C24×C47—22no—
167C24×C47—22no—
168C24×C47C22×C414yes—
169C24×C47#4114yes—
170C24×C47#4114yes—
171C24×C47C2412yes—
172C24×C47C2411yescharacteristic
173C23×D47—22no—
174C23×D47—22no—
175C23×D47—22no—
176C23×D47—22no—
177C23×D47—232no—
178C23×D47—22no—
179C23×D47—28no—
180C23×D47—28no—
181C23×D47—22no—
182C23×D47—22no—
183C23×D47—22no—
184C23×D47—22no—
185C23×D47—22no—
186C23×D47—232no—
187C23×D47—28no—
188C23×D47—28no—
189C23×D47—416no—
190C23×D47—44no—
191C23×D47—44no—
192C23×D47—416no—
193C23×D47—416no—
194C23×D47—416no—
195C23×D47—416no—
196C23×D47C22×C414yes—
197C23×D47C22×C4116yes—
198C23×D47C22×C414yes—
199C23×D47C2×D414yes—
200C23×D47#4114yes—
201C23×D47C2412yes—
202C23×D47C2412yes—
203C22×C4×C47—22no—
204C22×C4×C47—22no—
205C22×C4×C47—22no—
206C22×C4×C47—22no—
207C22×C4×C47—22no—
208C22×C4×C47—22no—
209C22×C4×C47—22no—
210C22×C4×C47—22no—
211C22×C4×C47—22no—
212C22×C4×C47—22no—
213C22×C4×C47—28no—
214C22×C4×C47—22no—
215C22×C4×C47—22no—
216C22×C4×C47—22no—
217C22×C4×C47—22no—
218C22×C4×C47—22no—
219C22×C4×C47—28no—
220C22×C4×C47—44no—
221C22×C4×C47—416no—
222C22×C4×C47C22×C414yes—
223C22×C4×C47C22×C414yes—
224C22×C4×C47C2×D414yes—
225C22×C4×C47C2412yes—
226C22×C4×C47C2412yes—
227C22×C4×C47C2412yes—
228C22×C4×C47C2412yes—
229C22×C4×C47C2412yes—
230C22×C4×C47C2412yes—
231C22×Dic47—22no—
232C22×Dic47—22no—
233C22×Dic47—22no—
234C22×Dic47—22no—
235C22×Dic47—22no—
236C22×Dic47—22no—
237C22×Dic47—22no—
238C22×Dic47—22no—
239C22×Dic47—22no—
240C22×Dic47—22no—
241C22×Dic47—22no—
242C22×Dic47—28no—
243C22×Dic47—22no—
244C22×Dic47—22no—
245C22×Dic47—22no—
246C22×Dic47—22no—
247C22×Dic47—28no—
248C22×Dic47—44no—
249C22×Dic47—416no—
250C22×Dic47C22×C414yes—
251C22×Dic47C22×C414yes—
252C22×Dic47C2×D414yes—
253C22×Dic47C2412yes—
254C22×Dic47C2412yes—
255C22×Dic47C2412yes—
256C22×Dic47C2412yes—
257C22×Dic47C2412yes—
258C22×Dic47C2412yes—
259C2×C4×D47—232no—
260C2×C4×D47—28no—
261C2×C4×D47—28no—
262C2×C4×D47—416no—
263C2×C4×D47—44no—
264C2×C4×D47—44no—
265C2×C4×D47C22×C4116yescomplemented
266C2×C4×D47C22×C4116yescomplemented
267C4⋊C4×C47—28no—
268C4⋊C4×C47—44no—
269C22⋊C4×C47—28no—
270C22⋊C4×C47C22×C4116yes—
271C22⋊Dic47—28no—
272C22⋊Dic47C22×C4116yes—
273(C2×D47)⋊C4—28no—
274(C2×D47)⋊C4—28no—
275(C2×D47)⋊C4—28no—
276(C2×D47)⋊C4—28no—
277(C2×D47)⋊C4—28no—
278(C2×D47)⋊C4—44no—
279(C2×D47)⋊C4—44no—
280(C2×D47)⋊C4C22×C4116yescomplemented
281(C2×D47)⋊C4C22×C4116yescomplemented
282(C2×D47)⋊C4C2×D4116yes—
283C4⋊Dic47—28no—
284C4⋊Dic47—44no—
285C4×Dic47—28no—
286C4×Dic47—28no—
287C4×Dic47—44no—
288C4×Dic47—44no—
289C23×C47—28no—
290C23×C47—28no—
291C23×C47—28no—
292C23×C47—28no—
293C23×C47—28no—
294C23×C47—28no—
295C23×C47—22no—
296C23×C47—22no—
297C23×C47—22no—
298C23×C47—22no—
299C23×C47#117116yescomplemented
300C23×C47C23×C414yes—
301C23×C47C23×C412yes—
302C23×C47C22×D412yes—
303C23×C47C2×#4112yes—
304C23×C47C2×#4114yes—
305C23×C47C2×#4112yes—
306C23×C47C2×#4114yes—
307C23×C47C2×#4112yes—
308C23×C47H(5,𝔽2)12yes—
309C23×C47H(5,𝔽2)12yes—
310C23×C47C2511yescharacteristic
311C22×D47—28no—
312C22×D47—28no—
313C22×D47—28no—
314C22×D47—28no—
315C22×D47—28no—
316C22×D47—28no—
317C22×D47—22no—
318C22×D47—22no—
319C22×D47—22no—
320C22×D47—22no—
321C22×D47—28no—
322C22×D47—232no—
323C22×D47—28no—
324C22×D47—28no—
325C22×D47—22no—
326C22×D47—22no—
327C22×D47—22no—
328C22×D47—22no—
329C22×D47—22no—
330C22×D47—22no—
331C22×D47—232no—
332C22×D47—416no—
333C22×D47—4128no—
334C22×D47—416no—
335C22×D47—416no—
336C22×D47—416no—
337C22×D47—416no—
338C22×D47—44no—
339C22×D47—44no—
340C22×D47—44no—
341C22×D47—44no—
342C22×D47C4×D4116yes—
343C22×D47C23×C414yes—
344C22×D47C23×C414yes—
345C22×D47C22×D414yes—
346C22×D47C2×#4114yes—
347C2×C4×C47—28no—
348C2×C4×C47—28no—
349C2×C4×C47—28no—
350C2×C4×C47—22no—
351C2×C4×C47—22no—
352C2×C4×C47—22no—
353C2×C4×C47—22no—
354C2×C4×C47—22no—
355C2×C4×C47—22no—
356C2×C4×C47—22no—
357C2×C4×C47—22no—
358C2×C4×C47—22no—
359C2×C4×C47—22no—
360C2×C4×C47—22no—
361C2×C4×C47—22no—
362C2×C4×C47—22no—
363C2×C4×C47—22no—
364C2×C4×C47—22no—
365C2×C4×C47—416no—
366C2×C4×C47—44no—
367C2×C4×C47—44no—
368C2×C4×C47—44no—
369C2×C4×C47C23×C414yes—
370C2×C4×C47C23×C414yes—
371C2×C4×C47C22×D414yes—
372C2×Dic47—28no—
373C2×Dic47—28no—
374C2×Dic47—28no—
375C2×Dic47—22no—
376C2×Dic47—22no—
377C2×Dic47—22no—
378C2×Dic47—22no—
379C2×Dic47—22no—
380C2×Dic47—22no—
381C2×Dic47—22no—
382C2×Dic47—22no—
383C2×Dic47—22no—
384C2×Dic47—22no—
385C2×Dic47—22no—
386C2×Dic47—22no—
387C2×Dic47—22no—
388C2×Dic47—22no—
389C2×Dic47—22no—
390C2×Dic47—416no—
391C2×Dic47—44no—
392C2×Dic47—44no—
393C2×Dic47—44no—
394C2×Dic47C23×C414yes—
395C2×Dic47C23×C414yes—
396C2×Dic47C22×D414yes—
397C4×D47—232no—
398C4×D47—416no—
399C2×#2342—471nomaximal, Sylow
400C22×C47—232no—
401C22×C47—24no—
402C22×C47—24no—
403C22×C47—24no—
404C22×C47—24no—
405C22×C47—24no—
406C22×C47—24no—
407C22×C47C2×#11714yes—
408C22×C47C2×#11718yescomplemented
409C22×C47C2×C4×D414yes—
410C22×C47#51814yes—
411C22×C47#54614yes—
412C22×C47#54614yes—
413C22×C47#55114yes—
414C22×C47#55114yes—
415C22×C47C24×C411yescharacteristic
416C22×C47C23×D411yescharacteristic
417C22×C47C22×#4111yescharacteristic
418C22×C47C22×#4111yescharacteristic
419C22×C47C22×#4111yescharacteristic
420C22×C47C2×H(5,𝔽2)11yescharacteristic
421C22×C47C2×H(5,𝔽2)11yescharacteristic
422C2×D47—232no—
423C2×D47—24no—
424C2×D47—24no—
425C2×D47—24no—
426C2×D47—24no—
427C2×D47—24no—
428C2×D47—24no—
429C2×D47—24no—
430C2×D47—24no—
431C2×D47—24no—
432C2×D47—464no—
433C2×D47—416no—
434C2×D47—42no—
435C2×D47—42no—
436C2×D47—42no—
437C2×D47—42no—
438C2×D47C2×C4×D418yes—
439C4×C47—24no—
440C4×C47—24no—
441C4×C47—24no—
442C4×C47—42no—
443C4×C47—42no—
444C4×C47—42no—
445Dic47—24no—
446Dic47—24no—
447Dic47—24no—
448Dic47—42no—
449Dic47—42no—
450Dic47—42no—
451C22×#117—471no—
452C23×C22⋊C4—471no—
453C23×C22⋊C4—471no—
454#2342—4716no—
455C2×#388—471no—
456C2×#388—471no—
457C2×#388—471no—
458C2×#388—471no—
459C2×#385—471no—
460C2×#385D4711yescharacteristic, complemented
461C2×#381—471no—
462C2×#380—471no—
463C2×#379—471no—
464C2×C4×C22⋊C4—471no—
465C2×C4×C22⋊C4—471no—
466C2×C4×C22⋊C4—471no—
467C2×C47—28no—
468C2×C47#234218yescomplemented
469C2×C47C22×#11711yescharacteristic
470C2×C47C22×C4×D411yescharacteristic
471C2×C47C2×#51811yescharacteristic
472C2×C47C2×#54611yescharacteristic
473C2×C47C2×#54611yescharacteristic
474C2×C47C2×#55111yescharacteristic
475C2×C47C2×#55111yescharacteristic
476D47—28no—
477D47—44no—
478C26—471no—
479C24×C4—471no—
480C24×C4—471no—
481C24×C4—471no—
482C24×C4C2×D4711yescharacteristic
483C2×#117—478no—
484C2×#117—948no—
485C22×C4⋊C4—471no—
486C22×C4⋊C4—471no—
487C22×C4⋊C4C2×D4711yescharacteristic, complemented
488C22×C4⋊C4C2×D4711yescharacteristic, complemented
489C22×C22⋊C4—471no—
490C22×C22⋊C4—471no—
491C22×C22⋊C4—471no—
492C22×C22⋊C4—471no—
493C22×C22⋊C4—4716no—
494C22×C22⋊C4—478no—
495C22×C22⋊C4—471no—
496C22×C22⋊C4—478no—
497C22×C22⋊C4—471no—
498C22×C22⋊C4—471no—
499C22×C22⋊C4—471no—
500C22×C22⋊C4—471no—
501C22×C22⋊C4—471no—
502C22×C22⋊C4—471no—
503C22×C22⋊C4—471no—
504C22×C22⋊C4—948no—
505C22×C22⋊C4C2×D4711yescharacteristic
506C22×C22⋊C4C2×D4711yescharacteristic
507C22×C42—471no—
508C22×C42—471no—
509C22×C42—471no—
510C22×C42—471no—
511#388—478no—
512#388—478no—
513#388—478no—
514#388—478no—
515#385—478no—
516#385C2×D4718yescomplemented
517#381—478no—
518#380—478no—
519#379—478no—
520C4×C22⋊C4—478no—
521C4×C22⋊C4—478no—
522C4×C22⋊C4—478no—
523C2×#95—471no—
524C2×#95—471no—
525C2×#95—471no—
526C2×#95—471no—
527C2×#95—471no—
528C2×#95—471no—
529C2×#95C2×D4711yescharacteristic, complemented
530C2×#95C2×D4711yescharacteristic, complemented
531C47C2×#234211yescharacteristic, complemented, Sylow
532C25—471no—
533C25—471no—
534C25—478no—
535C25—474no—
536C25—944no—
537C25—944no—
538C25—944no—
539C25—944no—
540C25—1882no—
541C25—1882no—
542C25C22×D4711yescharacteristic
543C23×C4—24no—
544C23×C4—24no—
545C23×C4—42no—
546C23×C4—471no—
547C23×C4—471no—
548C23×C4—471no—
549C23×C4—478no—
550C23×C4—474no—
551C23×C4—478no—
552C23×C4—474no—
553C23×C4—471no—
554C23×C4—471no—
555C23×C4—471no—
556C23×C4—474no—
557C23×C4—944no—
558C23×C4—944no—
559C23×C4—944no—
560C23×C4—944no—
561C23×C4—1882no—
562C23×C4—1882no—
563C23×C4—1882no—
564C23×C4C22×D4711yescharacteristic
565C23×C4C22×D4711yescharacteristic
566C23×C4C22×D4711yescharacteristic
567C23×C4C22×D4714yes—
568C23×C4C22×D4711yescharacteristic
569C23×C4C22×D4711yescharacteristic
570C23×C4C22×D4711yescharacteristic
571#117—9432no—
572C2×C4⋊C4—24no—
573C2×C4⋊C4—42no—
574C2×C4⋊C4—474no—
575C2×C4⋊C4—474no—
576C2×C4⋊C4—944no—
577C2×C4⋊C4—1882no—
578C2×C4⋊C4C22×D4714yescomplemented
579C2×C4⋊C4C22×D4714yescomplemented
580C2×C22⋊C4—24no—
581C2×C22⋊C4—478no—
582C2×C22⋊C4—474no—
583C2×C22⋊C4—478no—
584C2×C22⋊C4—478no—
585C2×C22⋊C4—478no—
586C2×C22⋊C4—474no—
587C2×C22⋊C4—474no—
588C2×C22⋊C4—474no—
589C2×C22⋊C4—4764no—
590C2×C22⋊C4—474no—
591C2×C22⋊C4—474no—
592C2×C22⋊C4—474no—
593C2×C22⋊C4—474no—
594C2×C22⋊C4—474no—
595C2×C22⋊C4—474no—
596C2×C22⋊C4—474no—
597C2×C22⋊C4—474no—
598C2×C22⋊C4—9432no—
599C2×C22⋊C4—944no—
600C2×C22⋊C4—944no—
601C2×C22⋊C4—944no—
602C2×C22⋊C4—944no—
603C2×C22⋊C4—944no—
604C2×C22⋊C4—944no—
605C2×C22⋊C4—1882no—
606C2×C22⋊C4—1882no—
607C2×C22⋊C4C4×D4718yes—
608C2×C22⋊C4C22×D4714yes—
609C2×C22⋊C4C22×D4714yes—
610C2×C42—474no—
611C2×C42—474no—
612C2×C42—474no—
613C2×C42—474no—
614C2×C42—944no—
615C2×C42—944no—
616C2×C42—1882no—
617C2×C42—1882no—
618#95—474no—
619#95—474no—
620#95—474no—
621#95—474no—
622#95—474no—
623#95—474no—
624#95C22×D4714yescomplemented
625#95C22×D4714yescomplemented
626C24—22no—
627C24—22no—
628C24—22no—
629C24—22no—
630C24—474no—
631C24—474no—
632C24—474no—
633C24—472no—
634C24—474no—
635C24—472no—
636C24—4716no—
637C24—948no—
638C24—9432no—
639C24—948no—
640C24—942no—
641C24—942no—
642C24—942no—
643C24—942no—
644C24—9432no—
645C24—942no—
646C24—942no—
647C24—948no—
648C24—942no—
649C24—948no—
650C24—942no—
651C24—942no—
652C24—942no—
653C24—18816no—
654C24—1884no—
655C24—1884no—
656C24—18816no—
657C24—18816no—
658C24—18816no—
659C24—18816no—
660C24C2×C4×D4714yes—
661C24#1062535214yes—
662C24#1062535414yes—
663C24C23×D4712yes—
664C24C23×D4711yescharacteristic
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—28no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—28no—
682C22×C4—44no—
683C22×C4—416no—
684C22×C4—474no—
685C22×C4—474no—
686C22×C4—474no—
687C22×C4—472no—
688C22×C4—472no—
689C22×C4—472no—
690C22×C4—4716no—
691C22×C4—4716no—
692C22×C4—472no—
693C22×C4—472no—
694C22×C4—472no—
695C22×C4—948no—
696C22×C4—9432no—
697C22×C4—948no—
698C22×C4—948no—
699C22×C4—942no—
700C22×C4—942no—
701C22×C4—942no—
702C22×C4—942no—
703C22×C4—942no—
704C22×C4—942no—
705C22×C4—942no—
706C22×C4—942no—
707C22×C4—942no—
708C22×C4—942no—
709C22×C4—942no—
710C22×C4—948no—
711C22×C4—942no—
712C22×C4—942no—
713C22×C4—942no—
714C22×C4—942no—
715C22×C4—18816no—
716C22×C4—1884no—
717C22×C4—1884no—
718C22×C4—1884no—
719C22×C4—18816no—
720C22×C4C2×C4×D4714yes—
721C22×C4C2×C4×D4714yes—
722C22×C4D4×D4714yes—
723C22×C4C23×D4712yes—
724C22×C4C23×D4712yes—
725C22×C4C23×D4712yes—
726C22×C4C23×D4712yes—
727C22×C4C23×D4712yes—
728C22×C4C23×D4712yes—
729C4⋊C4—28no—
730C4⋊C4—44no—
731C4⋊C4—948no—
732C4⋊C4—1884no—
733C22⋊C4—28no—
734C22⋊C4—4716no—
735C22⋊C4—4716no—
736C22⋊C4—4716no—
737C22⋊C4—4716no—
738C22⋊C4—948no—
739C22⋊C4—948no—
740C22⋊C4—948no—
741C22⋊C4—948no—
742C22⋊C4—948no—
743C22⋊C4—948no—
744C22⋊C4—1884no—
745C22⋊C4—1884no—
746C22⋊C4C2×C4×D47116yes—
747C42—948no—
748C42—948no—
749C42—1884no—
750C42—1884no—
751C23—28no—
752C23—28no—
753C23—28no—
754C23—28no—
755C23—28no—
756C23—28no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—4716no—
762C23—474no—
763C23—474no—
764C23—474no—
765C23—474no—
766C23—9432no—
767C23—948no—
768C23—948no—
769C23—948no—
770C23—948no—
771C23—948no—
772C23—948no—
773C23—942no—
774C23—942no—
775C23—942no—
776C23—942no—
777C23—948no—
778C23—9432no—
779C23—948no—
780C23—948no—
781C23—942no—
782C23—942no—
783C23—942no—
784C23—942no—
785C23—942no—
786C23—942no—
787C23—18816no—
788C23—18816no—
789C23—18816no—
790C23—18816no—
791C23—18816no—
792C23—188128no—
793C23—1884no—
794C23—1884no—
795C23—1884no—
796C23—1884no—
797C23#13093982116yescomplemented
798C23C22×C4×D4714yes—
799C23C22×C4×D4712yes—
800C23C2×D4×D4712yes—
801C23#41×D4712yes—
802C23C2×#1062535214yes—
803C23C2×#1062535212yes—
804C23C2×#1062535414yes—
805C23C2×#1062535412yes—
806C23#1309406912yes—
807C23#1309407012yes—
808C23C24×D4711yescharacteristic
809C2×C4—28no—
810C2×C4—28no—
811C2×C4—28no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—416no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—44no—
831C2×C4—474no—
832C2×C4—474no—
833C2×C4—474no—
834C2×C4—9432no—
835C2×C4—948no—
836C2×C4—948no—
837C2×C4—948no—
838C2×C4—942no—
839C2×C4—942no—
840C2×C4—942no—
841C2×C4—942no—
842C2×C4—942no—
843C2×C4—942no—
844C2×C4—942no—
845C2×C4—942no—
846C2×C4—942no—
847C2×C4—942no—
848C2×C4—942no—
849C2×C4—942no—
850C2×C4—942no—
851C2×C4—942no—
852C2×C4—942no—
853C2×C4—18816no—
854C2×C4—18816no—
855C2×C4—1884no—
856C2×C4—1884no—
857C2×C4—1884no—
858C2×C4C22×C4×D4714yes—
859C2×C4C22×C4×D4714yes—
860C2×C4C2×D4×D4714yes—
861C22—24no—
862C22—24no—
863C22—24no—
864C22—24no—
865C22—24no—
866C22—24no—
867C22—232no—
868C22—478no—
869C22—944no—
870C22—944no—
871C22—944no—
872C22—944no—
873C22—944no—
874C22—944no—
875C22—9432no—
876C22—944no—
877C22—944no—
878C22—944no—
879C22—18864no—
880C22—1882no—
881C22—1882no—
882C22—1882no—
883C22—1882no—
884C22—18816no—
885C22C2×#1309398214yes—
886C22C2×#1309398218yescomplemented
887C22C4×D4×D4714yes—
888C22#1568959514yes—
889C22#1568976014yes—
890C22#1568976414yes—
891C22#1568979614yes—
892C22#1568980014yes—
893C22C23×C4×D4711yescharacteristic
894C22C22×D4×D4711yescharacteristic
895C22C2×#41×D4711yescharacteristic
896C22C22×#1062535211yescharacteristic
897C22C22×#1062535411yescharacteristic
898C22C2×#1309406911yescharacteristic
899C22C2×#1309407011yescharacteristic
900C4—24no—
901C4—24no—
902C4—24no—
903C4—42no—
904C4—42no—
905C4—42no—
906C4—944no—
907C4—944no—
908C4—944no—
909C4—1882no—
910C4—1882no—
911C4—1882no—
912C2—28no—
913C2—948no—
914C2—1884no—
915C2#2024623518yesdirect product factor
916C2C22×#1309398211yescharacteristic
917C2C2×C4×D4×D4711yescharacteristic
918C2C2×#1568959511yescharacteristic
919C2C2×#1568976011yescharacteristic
920C2C2×#1568976411yescharacteristic
921C2C2×#1568979611yescharacteristic
922C2C2×#1568980011yescharacteristic
subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C47×#385C2
socleC24×C47C24
prime radicalC25×D47C22
cosocleC23×C47C25
hypercenterC2×#385D47
hypocenterC47C2×#2342
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C22×#13093982C2semidirect
4. #20246235C2direct (N × H)
5. C2×#15689015C2semidirect
6. C2×#15689015C2semidirect
7. C2×#15689013C2semidirect
8. C2×#15689013C2semidirect
9. C2×#15688998C2semidirect
10. C2×#15688985C2semidirect
11. C2×#15688980C2semidirect
13. C2×C22⋊C4×Dic47C2semidirect
14. C2×C4×C22⋊Dic47C2semidirect
15. C2×#15688970C2semidirect
16. C2×C47×#385C2semidirect
22. C2×#13093982C22semidirect
23. C22×C4⋊Dic47C22semidirect
24. C22×C4⋊Dic47C22semidirect
39. C2×C22⋊C4×D47C4semidirect
41. C22×C4×Dic47C22semidirect
42. C22×C4×Dic47C22semidirect
43. C22×C4×Dic47C22semidirect
44. C22×C4×Dic47C22semidirect
45. #15689015C22semidirect
46. #15689015C22semidirect
47. #15689013C22semidirect
48. #15689013C22semidirect
49. #15688998C22semidirect
50. #15688985C22semidirect
51. #15688980C22semidirect
53. C22⋊C4×Dic47C22semidirect
54. C4×C22⋊Dic47C22semidirect
55. #15688970C22semidirect
56. C2×C47⋊#95C22semidirect
57. C2×C47⋊#95C22semidirect
58. C2×C47⋊#95C22semidirect
59. C2×C47⋊#95C22semidirect
60. C2×C47⋊#95C22semidirect
61. C2×C47⋊#95C22semidirect
63. C22×C4⋊C4×C47C22semidirect
64. C22×C4⋊C4×C47C22semidirect
67. C47×#385C22semidirect
68. C2×#95×C47C22semidirect
69. C2×#95×C47C22semidirect
94. C22×C4×D47C2×C4semidirect
95. C22×C4×D47C2×C4semidirect
101. C2×C4⋊Dic47C23semidirect
102. C2×C4⋊Dic47C23semidirect
115. C2×(C2×D47)⋊C4C2×C4semidirect
116. C2×(C2×D47)⋊C4C2×C4semidirect
128. C22⋊C4×D47C2×C4semidirect
133. C2×C4×Dic47C23semidirect
134. C2×C4×Dic47C23semidirect
135. C2×C4×Dic47C23semidirect
136. C2×C4×Dic47C23semidirect
137. C47⋊#95C23semidirect
138. C47⋊#95C23semidirect
139. C47⋊#95C23semidirect
140. C47⋊#95C23semidirect
141. C47⋊#95C23semidirect
142. C47⋊#95C23semidirect
156. C2×C4⋊C4×C47C23semidirect
157. C2×C4⋊C4×C47C23semidirect
162. #95×C47C23semidirect
163. #95×C47C23semidirect
265. C2×C4×D47C22×C4semidirect
266. C2×C4×D47C22×C4semidirect
280. (C2×D47)⋊C4C22×C4semidirect
281. (C2×D47)⋊C4C22×C4semidirect
299. C23×C47#117semidirect
408. C22×C47C2×#117semidirect
460. C2×#385D47semidirect
468. C2×C47#2342semidirect
487. C22×C4⋊C4C2×D47semidirect
488. C22×C4⋊C4C2×D47semidirect
516. #385C2×D47semidirect
529. C2×#95C2×D47semidirect
530. C2×#95C2×D47semidirect
531. C47C2×#2342semidirect
578. C2×C4⋊C4C22×D47semidirect
579. C2×C4⋊C4C22×D47semidirect
624. #95C22×D47semidirect
625. #95C22×D47semidirect
797. C23#13093982semidirect
886. C22C2×#13093982semidirect
915. C2#20246235direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130939822
C23×(C2×D47)⋊C42
C22×C22⋊C4×D472
#202462352
C2×#156890152
C2×#156890132
C2×#156889982
C2×#156889852
C2×#156889802
C2×#156889782
C2×C22⋊C4×Dic472
C2×C4×C22⋊Dic472
C2×#156889702
C2×C47×#3852
C2×#234247