Finite Group Databasebeta

← C2×#20246236 #26375491

Subgroups — C2×#20246236 #26375491

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
2C22×C22⋊C4×D47C211yesmaximal, characteristic
3C22×C22⋊C4×D47C211yesmaximal, characteristic
4#20246236C2116yesmaximal, direct product factor
5C2×#15689017C211yesmaximal, characteristic, complemented
6C2×#15689016C211yesmaximal, characteristic, complemented
7C2×#15689011C211yesmaximal, characteristic, complemented
8C2×#15688997C211yesmaximal, characteristic, complemented
9C2×#15688994C211yesmaximal, characteristic, complemented
10C2×#15688985C211yesmaximal, characteristic, complemented
11C2×#15688982C211yesmaximal, characteristic, complemented
12C2×#15688978C211yesmaximal, characteristic
13C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
14C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
15C2×#15688970C211yesmaximal, characteristic, complemented
16C2×C47×#388C211yesmaximal, characteristic, complemented
17C25×D47C2211yescharacteristic
18C23×C4×D47C2211yescharacteristic
19C23×C4×D47C2211yescharacteristic
20C23×C4×D47C2211yescharacteristic
21C23×C4×D47C2211yescharacteristic
22C2×#13093982—28no—
23C2×#13093982C2218yescomplemented
24C22×C4⋊Dic47C2211yescharacteristic, complemented
25C22×Dic47⋊C4C2211yescharacteristic, complemented
26C22×Dic47⋊C4C2211yescharacteristic, complemented
27C22×C22⋊Dic47C2211yescharacteristic
28C22×C22⋊Dic47C2211yescharacteristic
29C22×C22⋊Dic47C2211yescharacteristic
30C22×(C2×D47)⋊C4C2211yescharacteristic
31C22×(C2×D47)⋊C4C2211yescharacteristic
32C22×(C2×D47)⋊C4C2211yescharacteristic
33C22×(C2×D47)⋊C4C2211yescharacteristic
34C22×(C2×D47)⋊C4C2211yescharacteristic
35C22×(C2×D47)⋊C4C2211yescharacteristic
36C22×(C2×D47)⋊C4C2211yescharacteristic
37C22×(C2×D47)⋊C4C2211yescharacteristic
38C2×C22⋊C4×D47—28no—
39C2×C22⋊C4×D47C4116yescomplemented
40C2×C22⋊C4×D47C2218yes—
41C2×C22⋊C4×D47C2218yes—
42C22×C4×Dic47C2211yescharacteristic, complemented
43C22×C4×Dic47C2211yescharacteristic, complemented
44C22×C4×Dic47C2211yescharacteristic, complemented
45#15689017C2218yescomplemented
46#15689016C2218yescomplemented
47#15689011C2218yescomplemented
48#15688997C2218yescomplemented
49#15688994C2218yescomplemented
50#15688985C2218yescomplemented
51#15688982C2218yescomplemented
52#15688978C2218yes—
53C4×(C2×D47)⋊C4C2218yescomplemented
54C4×(C2×D47)⋊C4C2218yescomplemented
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
62C22×C4⋊C4×C47C2211yescharacteristic, complemented
63C22×C22⋊C4×C47C2211yescharacteristic
64C22×C22⋊C4×C47C2211yescharacteristic
65C22×C22⋊C4×C47C2211yescharacteristic
66C22×C42×C47C2211yescharacteristic, complemented
67C47×#388C2218yescomplemented
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×D47C2314yes—
78C24×D47C2311yescharacteristic
79C24×D47C2311yescharacteristic
80C23×Dic47C2311yescharacteristic
81C23×Dic47C2311yescharacteristic
82C23×Dic47C2311yescharacteristic
83C23×Dic47C2311yescharacteristic
84C23×Dic47C2311yescharacteristic
85C23×Dic47C2311yescharacteristic
86C22×C4×D47—24no—
87C22×C4×D47—24no—
88C22×C4×D47—24no—
89C22×C4×D47—24no—
90C22×C4×D47—24no—
91C22×C4×D47—24no—
92C22×C4×D47—42no—
93C22×C4×D47—42no—
94C22×C4×D47—42no—
95C22×C4×D47—42no—
96C22×C4×D47C2×C418yescomplemented
97C22×C4×D47C2×C418yescomplemented
98C22×C4×D47C2314yes—
99C22×C4×D47C2314yes—
100C22×C4×D47C2314yes—
101C22×C4×D47C2314yes—
102#13093982—232no—
103C2×C4⋊Dic47—24no—
104C2×C4⋊Dic47C2314yescomplemented
105C2×Dic47⋊C4—42no—
106C2×Dic47⋊C4—42no—
107C2×Dic47⋊C4C2314yescomplemented
108C2×Dic47⋊C4C2314yescomplemented
109C2×C22⋊Dic47—24no—
110C2×C22⋊Dic47—42no—
111C2×C22⋊Dic47C2×C418yescomplemented
112C2×C22⋊Dic47C2314yes—
113C2×C22⋊Dic47C2314yes—
114C2×C22⋊Dic47C2314yes—
115C2×(C2×D47)⋊C4—24no—
116C2×(C2×D47)⋊C4—24no—
117C2×(C2×D47)⋊C4—24no—
118C2×(C2×D47)⋊C4—24no—
119C2×(C2×D47)⋊C4—24no—
120C2×(C2×D47)⋊C4C2×C418yes—
121C2×(C2×D47)⋊C4C2×C418yes—
122C2×(C2×D47)⋊C4D418yes—
123C2×(C2×D47)⋊C4C2314yes—
124C2×(C2×D47)⋊C4C2314yes—
125C2×(C2×D47)⋊C4C2314yes—
126C2×(C2×D47)⋊C4C2314yes—
127C2×(C2×D47)⋊C4C2314yes—
128C2×(C2×D47)⋊C4C2314yes—
129C2×(C2×D47)⋊C4C2314yes—
130C2×(C2×D47)⋊C4C2314yes—
131C22⋊C4×D47—232no—
132C22⋊C4×D47C2×C4164yescomplemented
133C2×C4×Dic47—24no—
134C2×C4×Dic47—24no—
135C2×C4×Dic47—42no—
136C2×C4×Dic47C2314yescomplemented
137C2×C4×Dic47C2314yescomplemented
138C2×C4×Dic47C2314yescomplemented
139C47⋊#95C2314yescomplemented
140C47⋊#95C2314yescomplemented
141C47⋊#95C2314yescomplemented
142C47⋊#95C2314yescomplemented
143C47⋊#95C2314yescomplemented
144C47⋊#95C2314yescomplemented
145C25×C47C2311yescharacteristic
146C23×C4×C47C2311yescharacteristic
147C23×C4×C47C2311yescharacteristic
148C23×C4×C47C2311yescharacteristic
149C23×C4×C47C2311yescharacteristic
150C23×C4×C47C2311yescharacteristic
151C23×C4×C47C2311yescharacteristic
152C2×C4⋊C4×C47—24no—
153C2×C4⋊C4×C47C2314yescomplemented
154C2×C22⋊C4×C47—24no—
155C2×C22⋊C4×C47—42no—
156C2×C22⋊C4×C47C2×C418yescomplemented
157C2×C22⋊C4×C47C2314yes—
158C2×C22⋊C4×C47C2314yes—
159C2×C22⋊C4×C47C2314yes—
160C2×C42×C47—42no—
161C2×C42×C47C2314yescomplemented
162#95×C47C2314yescomplemented
163#95×C47C2314yescomplemented
164C24×C47—22no—
165C24×C47—22no—
166C24×C47—22no—
167C24×C47—22no—
168C24×C47—22no—
169C24×C47—22no—
170C24×C47C22×C414yes—
171C24×C47C2412yes—
172C24×C47C2411yescharacteristic
173C23×D47—22no—
174C23×D47—22no—
175C23×D47—22no—
176C23×D47—22no—
177C23×D47—22no—
178C23×D47—22no—
179C23×D47—22no—
180C23×D47—22no—
181C23×D47—232no—
182C23×D47—232no—
183C23×D47—28no—
184C23×D47—28no—
185C23×D47—28no—
186C23×D47—28no—
187C23×D47—416no—
188C23×D47—44no—
189C23×D47—44no—
190C23×D47—416no—
191C23×D47—416no—
192C23×D47—416no—
193C23×D47—416no—
194C23×D47C22×C4116yes—
195C23×D47C22×C414yes—
196C23×D47C22×C414yes—
197C23×D47C2×D414yes—
198C23×D47#4114yes—
199C23×D47#4114yes—
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—22no—
214C22×C4×C47—22no—
215C22×C4×C47—22no—
216C22×C4×C47—22no—
217C22×C4×C47—22no—
218C22×C4×C47C22×C414yes—
219C22×C4×C47C22×C414yes—
220C22×C4×C47C2×D414yes—
221C22×C4×C47C2412yes—
222C22×C4×C47C2412yes—
223C22×C4×C47C2412yes—
224C22×C4×C47C2412yes—
225C22×C4×C47C2412yes—
226C22×C4×C47C2412yes—
227C22×Dic47—22no—
228C22×Dic47—22no—
229C22×Dic47—22no—
230C22×Dic47—22no—
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×Dic47C22×C414yes—
243C22×Dic47C22×C414yes—
244C22×Dic47C2×D414yes—
245C22×Dic47C2412yes—
246C22×Dic47C2412yes—
247C22×Dic47C2412yes—
248C22×Dic47C2412yes—
249C22×Dic47C2412yes—
250C22×Dic47C2412yes—
251C2×C4×D47—232no—
252C2×C4×D47—28no—
253C2×C4×D47—28no—
254C2×C4×D47—28no—
255C2×C4×D47—28no—
256C2×C4×D47—28no—
257C2×C4×D47—28no—
258C2×C4×D47—416no—
259C2×C4×D47—44no—
260C2×C4×D47—44no—
261C2×C4×D47—44no—
262C2×C4×D47—44no—
263C2×C4×D47—416no—
264C2×C4×D47—416no—
265C2×C4×D47C22×C4116yescomplemented
266C2×C4×D47C22×C4116yescomplemented
267C4⋊C4×C47—28no—
268C22⋊C4×C47—28no—
269C22⋊C4×C47—44no—
270C22⋊C4×C47C22×C4116yescomplemented
271C42×C47—44no—
272C22⋊Dic47—28no—
273C22⋊Dic47—44no—
274C22⋊Dic47C22×C4116yescomplemented
275(C2×D47)⋊C4—28no—
276(C2×D47)⋊C4—28no—
277(C2×D47)⋊C4—28no—
278(C2×D47)⋊C4—28no—
279(C2×D47)⋊C4—28no—
280(C2×D47)⋊C4C22×C4116yes—
281(C2×D47)⋊C4C22×C4116yes—
282(C2×D47)⋊C4C2×D4116yes—
283C4⋊Dic47—28no—
284Dic47⋊C4—44no—
285Dic47⋊C4—44no—
286C4×Dic47—28no—
287C4×Dic47—28no—
288C4×Dic47—44no—
289C23×C47—28no—
290C23×C47—28no—
291C23×C47—28no—
292C23×C47—22no—
293C23×C47—22no—
294C23×C47—22no—
295C23×C47—22no—
296C23×C47—22no—
297C23×C47—22no—
298C23×C47—44no—
299C23×C47—44no—
300C23×C47—44no—
301C23×C47—44no—
302C23×C47C23×C414yes—
303C23×C47C23×C412yes—
304C23×C47C22×D412yes—
305C23×C47C2×#4112yes—
306C23×C47C2×#4112yes—
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—28no—
318C22×D47—28no—
319C22×D47—28no—
320C22×D47—28no—
321C22×D47—28no—
322C22×D47—28no—
323C22×D47—22no—
324C22×D47—22no—
325C22×D47—22no—
326C22×D47—22no—
327C22×D47—22no—
328C22×D47—22no—
329C22×D47—22no—
330C22×D47—22no—
331C22×D47—232no—
332C22×D47—232no—
333C22×D47—416no—
334C22×D47—4128no—
335C22×D47—416no—
336C22×D47—416no—
337C22×D47—416no—
338C22×D47—416no—
339C22×D47#117116yescomplemented
340C22×D47C4×D4116yes—
341C22×D47C23×C414yes—
342C22×D47C23×C414yes—
343C22×D47C22×D414yes—
344C22×D47C2×#4114yes—
345C22×D47C2×#4114yes—
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—44no—
366C2×C4×C47—44no—
367C2×C4×C47—44no—
368C2×C4×C47C23×C414yes—
369C2×C4×C47C23×C414yes—
370C2×C4×C47C22×D414yes—
371C2×Dic47—28no—
372C2×Dic47—28no—
373C2×Dic47—28no—
374C2×Dic47—22no—
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—44no—
390C2×Dic47—44no—
391C2×Dic47—44no—
392C2×Dic47C23×C414yes—
393C2×Dic47C23×C414yes—
394C2×Dic47C22×D414yes—
395C4×D47—232no—
396C4×D47—416no—
397C4×D47—416no—
398C4×D47—416no—
399C2×#2342—471nomaximal, Sylow
400C22×C47—24no—
401C22×C47—24no—
402C22×C47—24no—
403C22×C47—416no—
404C22×C47—42no—
405C22×C47—42no—
406C22×C47—42no—
407C22×C47—42no—
408C22×C47C2×#11714yes—
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—232no—
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—24no—
433C2×D47—24no—
434C2×D47—24no—
435C2×D47—24no—
436C2×D47—464no—
437C2×D47C2×#11718yescomplemented
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×#388D4711yescharacteristic, complemented
459C2×#385—471no—
460C2×#385—471no—
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—44no—
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—28no—
478C26—471no—
479C24×C4—471no—
480C24×C4—471no—
481C24×C4—471no—
482C24×C4—471no—
483C2×#117—478no—
484C2×#117—948no—
485C22×C4⋊C4—471no—
486C22×C4⋊C4—471no—
487C22×C4⋊C4—471no—
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—471no—
497C22×C22⋊C4—471no—
498C22×C22⋊C4—471no—
499C22×C22⋊C4—471no—
500C22×C22⋊C4—471no—
501C22×C22⋊C4—471no—
502C22×C22⋊C4—478no—
503C22×C22⋊C4—948no—
504C22×C22⋊C4C2×D4711yescharacteristic
505C22×C22⋊C4C2×D4711yescharacteristic
506C22×C22⋊C4C2×D4711yescharacteristic
507C22×C42—471no—
508C22×C42—471no—
509C22×C42—471no—
510C22×C42C2×D4711yescharacteristic, complemented
511#388—478no—
512#388—478no—
513#388—478no—
514#388C2×D4718yescomplemented
515#385—478no—
516#385—478no—
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—471no—
544C23×C4—471no—
545C23×C4—471no—
546C23×C4—478no—
547C23×C4—474no—
548C23×C4—478no—
549C23×C4—474no—
550C23×C4—471no—
551C23×C4—471no—
552C23×C4—471no—
553C23×C4—474no—
554C23×C4—474no—
555C23×C4—944no—
556C23×C4—944no—
557C23×C4—944no—
558C23×C4—944no—
559C23×C4—944no—
560C23×C4—944no—
561C23×C4—1882no—
562C23×C4—1882no—
563C23×C4—1882no—
564C23×C4—1882no—
565C23×C4C22×D4711yescharacteristic
566C23×C4C22×D4711yescharacteristic
567C23×C4C22×D4711yescharacteristic
568C23×C4C22×D4711yescharacteristic
569C23×C4C22×D4711yescharacteristic
570C23×C4C22×D4711yescharacteristic
571#117—9432no—
572C2×C4⋊C4—24no—
573C2×C4⋊C4—474no—
574C2×C4⋊C4—474no—
575C2×C4⋊C4—474no—
576C2×C4⋊C4—944no—
577C2×C4⋊C4—1882no—
578C2×C4⋊C4—1882no—
579C2×C4⋊C4C22×D4714yescomplemented
580C2×C22⋊C4—24no—
581C2×C22⋊C4—42no—
582C2×C22⋊C4—478no—
583C2×C22⋊C4—474no—
584C2×C22⋊C4—478no—
585C2×C22⋊C4—478no—
586C2×C22⋊C4—478no—
587C2×C22⋊C4—474no—
588C2×C22⋊C4—474no—
589C2×C22⋊C4—474no—
590C2×C22⋊C4—4764no—
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⋊C4C4×D4718yescomplemented
607C2×C22⋊C4C22×D4714yes—
608C2×C22⋊C4C22×D4714yes—
609C2×C22⋊C4C22×D4714yes—
610C2×C42—42no—
611C2×C42—474no—
612C2×C42—474no—
613C2×C42—474no—
614C2×C42—944no—
615C2×C42—944no—
616C2×C42—1882no—
617C2×C42C22×D4714yescomplemented
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—22no—
631C24—22no—
632C24—474no—
633C24—474no—
634C24—474no—
635C24—474no—
636C24—474no—
637C24—474no—
638C24—472no—
639C24—472no—
640C24—4716no—
641C24—948no—
642C24—9432no—
643C24—9432no—
644C24—948no—
645C24—948no—
646C24—948no—
647C24—942no—
648C24—942no—
649C24—942no—
650C24—942no—
651C24—942no—
652C24—942no—
653C24—942no—
654C24—942no—
655C24—18816no—
656C24—1884no—
657C24—1884no—
658C24—18816no—
659C24—18816no—
660C24—18816no—
661C24—18816no—
662C24C2×C4×D4714yes—
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—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—474no—
681C22×C4—474no—
682C22×C4—474no—
683C22×C4—472no—
684C22×C4—472no—
685C22×C4—472no—
686C22×C4—4716no—
687C22×C4—4716no—
688C22×C4—472no—
689C22×C4—472no—
690C22×C4—472no—
691C22×C4—948no—
692C22×C4—948no—
693C22×C4—9432no—
694C22×C4—948no—
695C22×C4—948no—
696C22×C4—948no—
697C22×C4—942no—
698C22×C4—942no—
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—942no—
711C22×C4—942no—
712C22×C4—948no—
713C22×C4—18816no—
714C22×C4—1884no—
715C22×C4—1884no—
716C22×C4—1884no—
717C22×C4—1884no—
718C22×C4—18816no—
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—948no—
731C4⋊C4—1884no—
732C4⋊C4—1884no—
733C22⋊C4—28no—
734C22⋊C4—44no—
735C22⋊C4—4716no—
736C22⋊C4—4716no—
737C22⋊C4—4716no—
738C22⋊C4—4716no—
739C22⋊C4—948no—
740C22⋊C4—948no—
741C22⋊C4—948no—
742C22⋊C4—948no—
743C22⋊C4—948no—
744C22⋊C4—948no—
745C22⋊C4—1884no—
746C22⋊C4C2×C4×D47116yescomplemented
747C42—44no—
748C42—948no—
749C42—948no—
750C42—1884no—
751C23—28no—
752C23—28no—
753C23—28no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—44no—
761C23—44no—
762C23—44no—
763C23—44no—
764C23—4716no—
765C23—4716no—
766C23—474no—
767C23—474no—
768C23—474no—
769C23—474no—
770C23—474no—
771C23—474no—
772C23—9432no—
773C23—9432no—
774C23—948no—
775C23—948no—
776C23—948no—
777C23—948no—
778C23—948no—
779C23—948no—
780C23—948no—
781C23—948no—
782C23—948no—
783C23—948no—
784C23—948no—
785C23—948no—
786C23—942no—
787C23—942no—
788C23—942no—
789C23—942no—
790C23—942no—
791C23—942no—
792C23—942no—
793C23—942no—
794C23—18816no—
795C23—18816no—
796C23—18816no—
797C23—18816no—
798C23—18816no—
799C23—188128no—
800C23C22×C4×D4714yes—
801C23C22×C4×D4712yes—
802C23C2×D4×D4712yes—
803C23#41×D4712yes—
804C23#41×D4712yes—
805C23#41×D4712yes—
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—44no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—474no—
831C2×C4—474no—
832C2×C4—474no—
833C2×C4—9432no—
834C2×C4—948no—
835C2×C4—948no—
836C2×C4—948no—
837C2×C4—942no—
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—18816no—
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—42no—
865C22—42no—
866C22—42no—
867C22—42no—
868C22—416no—
869C22—478no—
870C22—478no—
871C22—944no—
872C22—944no—
873C22—944no—
874C22—944no—
875C22—944no—
876C22—944no—
877C22—944no—
878C22—944no—
879C22—944no—
880C22—944no—
881C22—944no—
882C22—944no—
883C22—9432no—
884C22—9432no—
885C22—18864no—
886C22#117×D4714yes—
887C22C4×D4×D4714yes—
888C22#1568959514yes—
889C22#1568976214yes—
890C22#1568976614yes—
891C22#1568979814yes—
892C22#1568980114yes—
893C22C23×C4×D4711yescharacteristic
894C22C22×D4×D4711yescharacteristic
895C22C2×#41×D4711yescharacteristic
896C22C2×#41×D4711yescharacteristic
897C22C2×#41×D4711yescharacteristic
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—44no—
913C2—948no—
914C2—948no—
915C2#2024623618yesdirect product factor
916C2C2×#117×D4711yescharacteristic
917C2C2×C4×D4×D4711yescharacteristic
918C2C2×#1568959511yescharacteristic
919C2C2×#1568976211yescharacteristic
920C2C2×#1568976611yescharacteristic
921C2C2×#1568979811yescharacteristic
922C2C2×#1568980111yescharacteristic
subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C47×#388C2
socleC24×C47C24
prime radicalC25×D47C22
cosocleC23×C47C25
hypercenterC2×#388D47
hypocenterC47C2×#2342
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#13093982C2semidirect
4. #20246236C2direct (N × H)
5. C2×#15689017C2semidirect
6. C2×#15689016C2semidirect
7. C2×#15689011C2semidirect
8. C2×#15688997C2semidirect
9. C2×#15688994C2semidirect
10. C2×#15688985C2semidirect
11. C2×#15688982C2semidirect
13. C2×C4×(C2×D47)⋊C4C2semidirect
14. C2×C4×(C2×D47)⋊C4C2semidirect
15. C2×#15688970C2semidirect
16. C2×C47×#388C2semidirect
23. C2×#13093982C22semidirect
24. C22×C4⋊Dic47C22semidirect
25. C22×Dic47⋊C4C22semidirect
26. C22×Dic47⋊C4C22semidirect
39. C2×C22⋊C4×D47C4semidirect
42. C22×C4×Dic47C22semidirect
43. C22×C4×Dic47C22semidirect
44. C22×C4×Dic47C22semidirect
45. #15689017C22semidirect
46. #15689016C22semidirect
47. #15689011C22semidirect
48. #15688997C22semidirect
49. #15688994C22semidirect
50. #15688985C22semidirect
51. #15688982C22semidirect
53. C4×(C2×D47)⋊C4C22semidirect
54. C4×(C2×D47)⋊C4C22semidirect
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
62. C22×C4⋊C4×C47C22semidirect
66. C22×C42×C47C22semidirect
67. C47×#388C22semidirect
68. C2×#95×C47C22semidirect
69. C2×#95×C47C22semidirect
96. C22×C4×D47C2×C4semidirect
97. C22×C4×D47C2×C4semidirect
104. C2×C4⋊Dic47C23semidirect
107. C2×Dic47⋊C4C23semidirect
108. C2×Dic47⋊C4C23semidirect
111. C2×C22⋊Dic47C2×C4semidirect
132. C22⋊C4×D47C2×C4semidirect
136. C2×C4×Dic47C23semidirect
137. C2×C4×Dic47C23semidirect
138. C2×C4×Dic47C23semidirect
139. C47⋊#95C23semidirect
140. C47⋊#95C23semidirect
141. C47⋊#95C23semidirect
142. C47⋊#95C23semidirect
143. C47⋊#95C23semidirect
144. C47⋊#95C23semidirect
153. C2×C4⋊C4×C47C23semidirect
156. C2×C22⋊C4×C47C2×C4semidirect
161. C2×C42×C47C23semidirect
162. #95×C47C23semidirect
163. #95×C47C23semidirect
265. C2×C4×D47C22×C4semidirect
266. C2×C4×D47C22×C4semidirect
270. C22⋊C4×C47C22×C4semidirect
274. C22⋊Dic47C22×C4semidirect
339. C22×D47#117semidirect
437. C2×D47C2×#117semidirect
458. C2×#388D47semidirect
468. C2×C47#2342semidirect
488. C22×C4⋊C4C2×D47semidirect
510. C22×C42C2×D47semidirect
514. #388C2×D47semidirect
529. C2×#95C2×D47semidirect
530. C2×#95C2×D47semidirect
531. C47C2×#2342semidirect
579. C2×C4⋊C4C22×D47semidirect
606. C2×C22⋊C4C4×D47semidirect
617. C2×C42C22×D47semidirect
624. #95C22×D47semidirect
625. #95C22×D47semidirect
746. C22⋊C4C2×C4×D47semidirect
915. C2#20246236direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130939822
C22×C22⋊C4×D472
#202462362
C2×#156890172
C2×#156890162
C2×#156890112
C2×#156889972
C2×#156889942
C2×#156889852
C2×#156889822
C2×#156889782
C2×C4×(C2×D47)⋊C42
C2×#156889702
C2×C47×#3882
C2×#234247