Finite Group Databasebeta

← C2×#20246386 #26375787

Subgroups — C2×#20246386 #26375787

Order 12032.

3830 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094005C211yesmaximal, characteristic
2C22×D4×Dic47C211yesmaximal, characteristic
3C22×#13093980C211yesmaximal, characteristic, complemented
4#20246386C2116yesmaximal, direct product factor
5C2×#15689020C211yesmaximal, characteristic, complemented
6C2×#15689017C211yesmaximal, characteristic, complemented
7C2×#15689011C211yesmaximal, characteristic, complemented
8C2×#15689010C211yesmaximal, characteristic, complemented
9C2×#15689005C211yesmaximal, characteristic, complemented
10C2×#15688995C211yesmaximal, characteristic, complemented
11C2×#15688995C211yesmaximal, characteristic, complemented
12C2×#15688974C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×Dic47C211yesmaximal, characteristic, complemented
14C2×C4×C22⋊Dic47C211yesmaximal, characteristic, complemented
15C22×C47⋊#95C211yesmaximal, characteristic, complemented
16C2×C47×#386C211yesmaximal, characteristic
17C24×Dic47C2211yescharacteristic
18C24×Dic47C2211yescharacteristic
19C24×Dic47C2211yescharacteristic
20C2×#13094005C4116yescomplemented
21C2×#13094005C2218yes—
22C2×D4×Dic47—28no—
23C2×D4×Dic47C2218yes—
24C2×#13093980—28no—
25C2×#13093980C2218yescomplemented
26C22×C4⋊Dic47C2211yescharacteristic
27C22×Dic47⋊C4C2211yescharacteristic
28C22×Dic47⋊C4C2211yescharacteristic
29C22×Dic47⋊C4C2211yescharacteristic
30C22×Dic47⋊C4C2211yescharacteristic
31C22×Dic47⋊C4C2211yescharacteristic
32C22×Dic47⋊C4C2211yescharacteristic
33C22×C22⋊Dic47C2211yescharacteristic
34C22×C22⋊Dic47C2211yescharacteristic
35C22×C22⋊Dic47C2211yescharacteristic
36C22×C22⋊Dic47C2211yescharacteristic
37C22×C22⋊Dic47C2211yescharacteristic
38C22×C4×Dic47C2211yescharacteristic
39C22×C4×Dic47C2211yescharacteristic
40C22×C4×Dic47C2211yescharacteristic
41C22×C4×Dic47C2211yescharacteristic
42C22×C4×Dic47C2211yescharacteristic
43#15689020C2218yescomplemented
44#15689017C2218yescomplemented
45#15689011C2218yescomplemented
46#15689010C2218yescomplemented
47#15689005C2218yescomplemented
48#15688995C2218yescomplemented
49#15688995C2218yescomplemented
50#15688974C2218yescomplemented
51C22⋊C4×Dic47C2218yescomplemented
52C4×C22⋊Dic47C2218yescomplemented
53C2×C47⋊#95C2211yescharacteristic
54C2×C47⋊#95C2211yescharacteristic
55C2×C47⋊#95C2211yescharacteristic
56C2×C47⋊#95C2211yescharacteristic
57C2×C47⋊#95C2211yescharacteristic
58C2×C47⋊#95C2211yescharacteristic
59C2×C47⋊#95C2211yescharacteristic
60C2×C47⋊#95C2211yescharacteristic
61C2×C47⋊#95C2218yescomplemented
62C23×D4×C47C2211yescharacteristic
63C24×C4×C47C2211yescharacteristic
64C22×C22⋊C4×C47C2211yescharacteristic
65C22×C22⋊C4×C47C2211yescharacteristic
66C22×C22⋊C4×C47C2211yescharacteristic
67C47×#386C2218yes—
68C2×#95×C47C2211yescharacteristic
69C2×#95×C47C2211yescharacteristic
70C23×Dic47—24no—
71C23×Dic47—24no—
72C23×Dic47—24no—
73C23×Dic47—24no—
74C23×Dic47—24no—
75C23×Dic47—24no—
76C23×Dic47—42no—
77C23×Dic47—42no—
78C23×Dic47C2×C418yescomplemented
79C23×Dic47C2311yescharacteristic
80C23×Dic47C2314yes—
81C23×Dic47C2314yes—
82C23×Dic47C2311yescharacteristic
83C23×Dic47C2311yescharacteristic
84C23×Dic47C2311yescharacteristic
85C23×Dic47C2311yescharacteristic
86C23×Dic47C2314yes—
87C23×Dic47C2311yescharacteristic
88C23×Dic47C2311yescharacteristic
89C23×Dic47C2311yescharacteristic
90#13094005C2×C4164yescomplemented
91D4×Dic47—232no—
92#13093980—232no—
93C2×C4⋊Dic47—24no—
94C2×C4⋊Dic47C2314yes—
95C2×Dic47⋊C4—24no—
96C2×Dic47⋊C4—24no—
97C2×Dic47⋊C4—24no—
98C2×Dic47⋊C4—42no—
99C2×Dic47⋊C4C2×C418yescomplemented
100C2×Dic47⋊C4C2×C418yescomplemented
101C2×Dic47⋊C4C2314yes—
102C2×Dic47⋊C4C2314yes—
103C2×Dic47⋊C4C2314yes—
104C2×Dic47⋊C4C2314yes—
105C2×Dic47⋊C4C2314yes—
106C2×Dic47⋊C4C2314yes—
107C2×C22⋊Dic47—24no—
108C2×C22⋊Dic47C2×C418yescomplemented
109C2×C22⋊Dic47C2×C418yescomplemented
110C2×C22⋊Dic47C2×C418yescomplemented
111C2×C22⋊Dic47D418yes—
112C2×C22⋊Dic47C2314yes—
113C2×C22⋊Dic47C2314yes—
114C2×C22⋊Dic47C2314yes—
115C2×C22⋊Dic47C2314yes—
116C2×C22⋊Dic47C2314yes—
117C2×C4×Dic47—24no—
118C2×C4×Dic47—24no—
119C2×C4×Dic47—24no—
120C2×C4×Dic47—24no—
121C2×C4×Dic47—42no—
122C2×C4×Dic47C2314yes—
123C2×C4×Dic47C2314yes—
124C2×C4×Dic47C2314yes—
125C2×C4×Dic47C2314yes—
126C2×C4×Dic47C2314yes—
127C47⋊#95C2314yes—
128C47⋊#95C2314yes—
129C47⋊#95C2314yes—
130C47⋊#95C2314yes—
131C47⋊#95C2314yes—
132C47⋊#95C2314yes—
133C47⋊#95C2314yes—
134C47⋊#95C2314yes—
135C25×C47C2311yescharacteristic
136C25×C47C2311yescharacteristic
137C22×D4×C47—24no—
138C22×D4×C47—24no—
139C22×D4×C47C2×C418yes—
140C22×D4×C47C2314yes—
141C23×C4×C47—24no—
142C23×C4×C47—24no—
143C23×C4×C47—42no—
144C23×C4×C47C2311yescharacteristic
145C23×C4×C47C2311yescharacteristic
146C23×C4×C47C2311yescharacteristic
147C23×C4×C47C2314yes—
148C23×C4×C47C2311yescharacteristic
149C23×C4×C47C2311yescharacteristic
150C2×C22⋊C4×C47—24no—
151C2×C22⋊C4×C47—24no—
152C2×C22⋊C4×C47—42no—
153C2×C22⋊C4×C47C2314yes—
154C2×C22⋊C4×C47C2314yes—
155C2×C22⋊C4×C47C2314yes—
156#95×C47C2314yes—
157#95×C47C2314yes—
158C24×C47—22no—
159C24×C47—22no—
160C24×C47—22no—
161C24×C47—22no—
162C24×C47—22no—
163C24×C47—22no—
164C24×C47—22no—
165C24×C47—22no—
166C24×C47—22no—
167C24×C47—22no—
168C24×C47C22×C414yes—
169C24×C47C22×C414yes—
170C24×C47C2×D414yes—
171C24×C47#4114yes—
172C24×C47C2412yes—
173C24×C47C2412yes—
174C24×C47C2411yescharacteristic
175C2×D4×C47—232no—
176C2×D4×C47—28no—
177C2×D4×C47—28no—
178C2×D4×C47C22×C4116yes—
179C22×C4×C47—22no—
180C22×C4×C47—22no—
181C22×C4×C47—22no—
182C22×C4×C47—22no—
183C22×C4×C47—22no—
184C22×C4×C47—22no—
185C22×C4×C47—22no—
186C22×C4×C47—28no—
187C22×C4×C47—22no—
188C22×C4×C47—22no—
189C22×C4×C47—22no—
190C22×C4×C47—22no—
191C22×C4×C47—22no—
192C22×C4×C47—22no—
193C22×C4×C47—28no—
194C22×C4×C47—44no—
195C22×C4×C47—416no—
196C22×C4×C47C22×C414yes—
197C22×C4×C47#4114yes—
198C22×C4×C47C2412yes—
199C22×C4×C47C2412yes—
200C22×C4×C47C2412yes—
201C22×C4×C47C2412yes—
202C22×C4×C47C2412yes—
203C22×Dic47—232no—
204C22×Dic47—22no—
205C22×Dic47—22no—
206C22×Dic47—22no—
207C22×Dic47—28no—
208C22×Dic47—22no—
209C22×Dic47—22no—
210C22×Dic47—22no—
211C22×Dic47—22no—
212C22×Dic47—22no—
213C22×Dic47—28no—
214C22×Dic47—22no—
215C22×Dic47—22no—
216C22×Dic47—22no—
217C22×Dic47—22no—
218C22×Dic47—22no—
219C22×Dic47—22no—
220C22×Dic47—22no—
221C22×Dic47—28no—
222C22×Dic47—22no—
223C22×Dic47—22no—
224C22×Dic47—28no—
225C22×Dic47—28no—
226C22×Dic47—28no—
227C22×Dic47—44no—
228C22×Dic47—44no—
229C22×Dic47—416no—
230C22×Dic47—416no—
231C22×Dic47C22×C414yes—
232C22×Dic47C22×C414yes—
233C22×Dic47C22×C414yes—
234C22×Dic47C22×C414yes—
235C22×Dic47C22×C4116yescomplemented
236C22×Dic47C2×D414yes—
237C22×Dic47C2×D414yes—
238C22×Dic47#4114yes—
239C22×Dic47C2412yes—
240C22×Dic47C2412yes—
241C22×Dic47C2412yes—
242C22×Dic47C2412yes—
243C22×Dic47C2412yes—
244C22×Dic47C2412yes—
245C22×Dic47C2412yes—
246C22×Dic47C2412yes—
247C22⋊C4×C47—28no—
248C22⋊C4×C47—28no—
249C22⋊C4×C47—44no—
250C22⋊Dic47—28no—
251C22⋊Dic47C22×C4116yescomplemented
252C22⋊Dic47C22×C4116yescomplemented
253C22⋊Dic47C22×C4116yescomplemented
254C22⋊Dic47C2×D4116yes—
255C4⋊Dic47—28no—
256Dic47⋊C4—28no—
257Dic47⋊C4—28no—
258Dic47⋊C4—28no—
259Dic47⋊C4—44no—
260Dic47⋊C4C22×C4116yescomplemented
261Dic47⋊C4C22×C4116yescomplemented
262C4×Dic47—28no—
263C4×Dic47—28no—
264C4×Dic47—28no—
265C4×Dic47—28no—
266C4×Dic47—44no—
267C23×C47—28no—
268C23×C47—28no—
269C23×C47—28no—
270C23×C47—28no—
271C23×C47—28no—
272C23×C47—28no—
273C23×C47—22no—
274C23×C47—22no—
275C23×C47—22no—
276C23×C47—22no—
277C23×C47—28no—
278C23×C47—28no—
279C23×C47—28no—
280C23×C47—22no—
281C23×C47—22no—
282C23×C47—22no—
283C23×C47—22no—
284C23×C47—22no—
285C23×C47—22no—
286C23×C47—44no—
287C23×C47—44no—
288C23×C47—44no—
289C23×C47—44no—
290C23×C47C4×D4116yes—
291C23×C47C23×C414yes—
292C23×C47C23×C414yes—
293C23×C47C23×C412yes—
294C23×C47C22×D414yes—
295C23×C47C22×D412yes—
296C23×C47C2×#4112yes—
297C23×C47C2×#4114yes—
298C23×C47C2×#4112yes—
299C23×C47C2×#4112yes—
300C23×C47H(5,𝔽2)12yes—
301C23×C472−1+412yes—
302C23×C47C2511yescharacteristic
303D4×C47—232no—
304C2×C4×C47—28no—
305C2×C4×C47—28no—
306C2×C4×C47—22no—
307C2×C4×C47—22no—
308C2×C4×C47—22no—
309C2×C4×C47—22no—
310C2×C4×C47—22no—
311C2×C4×C47—22no—
312C2×C4×C47—22no—
313C2×C4×C47—22no—
314C2×C4×C47—22no—
315C2×C4×C47—22no—
316C2×C4×C47—22no—
317C2×C4×C47—22no—
318C2×C4×C47—22no—
319C2×C4×C47—416no—
320C2×C4×C47—44no—
321C2×C4×C47—44no—
322C2×C4×C47—44no—
323C2×C4×C47C23×C414yes—
324C2×C4×C47C2×#4114yes—
325C2×Dic47—28no—
326C2×Dic47—28no—
327C2×Dic47—232no—
328C2×Dic47—28no—
329C2×Dic47—28no—
330C2×Dic47—28no—
331C2×Dic47—28no—
332C2×Dic47—28no—
333C2×Dic47—22no—
334C2×Dic47—22no—
335C2×Dic47—22no—
336C2×Dic47—22no—
337C2×Dic47—22no—
338C2×Dic47—22no—
339C2×Dic47—22no—
340C2×Dic47—22no—
341C2×Dic47—22no—
342C2×Dic47—22no—
343C2×Dic47—22no—
344C2×Dic47—22no—
345C2×Dic47—22no—
346C2×Dic47—22no—
347C2×Dic47—22no—
348C2×Dic47—22no—
349C2×Dic47—22no—
350C2×Dic47—416no—
351C2×Dic47—416no—
352C2×Dic47—44no—
353C2×Dic47C23×C414yes—
354C2×Dic47C23×C414yes—
355C2×Dic47C23×C414yes—
356C2×Dic47C23×C414yes—
357C2×Dic47C22×D414yes—
358C2×Dic47C22×D414yes—
359C2×Dic47C2×#4114yes—
360C2×#2359—471nomaximal, Sylow
361C22×C47—232no—
362C22×C47—24no—
363C22×C47—24no—
364C22×C47—24no—
365C22×C47—24no—
366C22×C47—24no—
367C22×C47—24no—
368C22×C47—24no—
369C22×C47—24no—
370C22×C47—24no—
371C22×C47—416no—
372C22×C47—42no—
373C22×C47—42no—
374C22×C47—42no—
375C22×C47—42no—
376C22×C47C2×C4×D418yes—
377C22×C47C2×C4×D414yes—
378C22×C47C4×#4114yes—
379C22×C47#52014yes—
380C22×C47#54614yes—
381C22×C47#54714yes—
382C22×C47#55114yes—
383C22×C47#55214yes—
384C22×C47C24×C411yescharacteristic
385C22×C47C23×D411yescharacteristic
386C22×C47C22×#4111yescharacteristic
387C22×C47C22×#4111yescharacteristic
388C22×C47C22×#4111yescharacteristic
389C22×C47C2×H(5,𝔽2)11yescharacteristic
390C22×C47C2×2−1+411yescharacteristic
391C4×C47—24no—
392C4×C47—24no—
393C4×C47—42no—
394C4×C47—42no—
395C4×C47—42no—
396Dic47—24no—
397Dic47—24no—
398Dic47—24no—
399Dic47—24no—
400Dic47—24no—
401Dic47—24no—
402Dic47—24no—
403Dic47—42no—
404C22×#123—471no—
405C22×C4×D4—471no—
406C22×#117—471no—
407#2359—4716no—
408C2×#389—471no—
409C2×#388—471no—
410C2×#388—471no—
411C2×#387—471no—
412C2×#387—471no—
413C2×#386D4711yescharacteristic
414C2×#385—471no—
415C2×#385—471no—
416C2×C4×C4⋊C4—471no—
417C2×C4×C22⋊C4—471no—
418C2×C4×C22⋊C4—471no—
419C22×#95—471no—
420C2×C47—28no—
421C2×C47—44no—
422C2×C47#235918yescomplemented
423C2×C47C22×C4×D411yescharacteristic
424C2×C47C2×C4×#4111yescharacteristic
425C2×C47C2×#52011yescharacteristic
426C2×C47C2×#54611yescharacteristic
427C2×C47C2×#54711yescharacteristic
428C2×C47C2×#55111yescharacteristic
429C2×C47C2×#55211yescharacteristic
430C23×D4C2×D4711yescharacteristic
431C24×C4—471no—
432C24×C4—471no—
433C24×C4—471no—
434C24×C4C2×D4711yescharacteristic
435C2×#123—4716no—
436C2×#123—478no—
437C2×C4×D4—478no—
438C2×C4×D4—948no—
439C2×#117—478no—
440C2×#117—948no—
441C22×C4⋊C4—471no—
442C22×C4⋊C4—471no—
443C22×C4⋊C4—471no—
444C22×C4⋊C4—471no—
445C22×C4⋊C4—471no—
446C22×C4⋊C4—471no—
447C22×C4⋊C4—471no—
448C22×C22⋊C4—471no—
449C22×C22⋊C4—471no—
450C22×C22⋊C4—471no—
451C22×C22⋊C4—471no—
452C22×C22⋊C4—471no—
453C22×C22⋊C4C2×D4711yescharacteristic
454C22×C22⋊C4C2×D4711yescharacteristic
455C22×C22⋊C4C2×D4711yescharacteristic
456C22×C42—471no—
457C22×C42—471no—
458C22×C42—471no—
459C22×C42—471no—
460C22×C42—471no—
461#389—478no—
462#388—478no—
463#388—478no—
464#387—478no—
465#387—478no—
466#386C2×D4718yes—
467#385—478no—
468#385—478no—
469C4×C4⋊C4—478no—
470C4×C22⋊C4—478no—
471C4×C22⋊C4—478no—
472C2×#95—471no—
473C2×#95—471no—
474C2×#95—471no—
475C2×#95—471no—
476C2×#95—471no—
477C2×#95—471no—
478C2×#95—471no—
479C2×#95—471no—
480C2×#95—478no—
481C2×#95C2×D4711yescharacteristic
482C2×#95C2×D4711yescharacteristic
483C47C2×#235911yescharacteristic, complemented, Sylow
484C25C22×D4711yescharacteristic
485C25C22×D4711yescharacteristic
486C22×D4—24no—
487C22×D4—24no—
488C22×D4C4×D4718yes—
489C22×D4C22×D4714yes—
490C23×C4—24no—
491C23×C4—24no—
492C23×C4—42no—
493C23×C4—478no—
494C23×C4—474no—
495C23×C4—471no—
496C23×C4—471no—
497C23×C4—471no—
498C23×C4—471no—
499C23×C4—471no—
500C23×C4—471no—
501C23×C4—471no—
502C23×C4—471no—
503C23×C4—474no—
504C23×C4—474no—
505C23×C4—944no—
506C23×C4—944no—
507C23×C4—944no—
508C23×C4—944no—
509C23×C4—944no—
510C23×C4—944no—
511C23×C4—1882no—
512C23×C4—1882no—
513C23×C4C22×D4711yescharacteristic
514C23×C4C22×D4711yescharacteristic
515C23×C4C22×D4711yescharacteristic
516C23×C4C22×D4714yes—
517C23×C4C22×D4711yescharacteristic
518C23×C4C22×D4711yescharacteristic
519#123—4764no—
520C4×D4—9432no—
521#117—9432no—
522C2×C4⋊C4—478no—
523C2×C4⋊C4—478no—
524C2×C4⋊C4—474no—
525C2×C4⋊C4—474no—
526C2×C4⋊C4—474no—
527C2×C4⋊C4—474no—
528C2×C4⋊C4—474no—
529C2×C4⋊C4—474no—
530C2×C4⋊C4—474no—
531C2×C4⋊C4—944no—
532C2×C4⋊C4—944no—
533C2×C4⋊C4—944no—
534C2×C4⋊C4—944no—
535C2×C4⋊C4—1882no—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—24no—
538C2×C22⋊C4—42no—
539C2×C22⋊C4—478no—
540C2×C22⋊C4—478no—
541C2×C22⋊C4—478no—
542C2×C22⋊C4—478no—
543C2×C22⋊C4—474no—
544C2×C22⋊C4—474no—
545C2×C22⋊C4—474no—
546C2×C22⋊C4—474no—
547C2×C22⋊C4—474no—
548C2×C22⋊C4—944no—
549C2×C22⋊C4C22×D4714yes—
550C2×C22⋊C4C22×D4714yes—
551C2×C22⋊C4C22×D4714yes—
552C2×C42—474no—
553C2×C42—474no—
554C2×C42—474no—
555C2×C42—474no—
556C2×C42—474no—
557C2×C42—944no—
558C2×C42—944no—
559C2×C42—944no—
560C2×C42—944no—
561C2×C42—1882no—
562#95—474no—
563#95—474no—
564#95—474no—
565#95—474no—
566#95—474no—
567#95—474no—
568#95—474no—
569#95—474no—
570#95C22×D4714yes—
571#95C22×D4714yes—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—22no—
580C24—22no—
581C24—22no—
582C24C2×C4×D4714yes—
583C24C2×C4×D4714yes—
584C24D4×D4714yes—
585C24#1062535214yes—
586C24C23×D4712yes—
587C24C23×D4712yes—
588C24C23×D4711yescharacteristic
589C2×D4—232no—
590C2×D4—28no—
591C2×D4—28no—
592C2×D4C2×C4×D47116yes—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—28no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—28no—
608C22×C4—44no—
609C22×C4—416no—
610C22×C4—474no—
611C22×C4—474no—
612C22×C4—474no—
613C22×C4—474no—
614C22×C4—4716no—
615C22×C4—474no—
616C22×C4—474no—
617C22×C4—474no—
618C22×C4—472no—
619C22×C4—472no—
620C22×C4—472no—
621C22×C4—472no—
622C22×C4—472no—
623C22×C4—472no—
624C22×C4—472no—
625C22×C4—472no—
626C22×C4—948no—
627C22×C4—948no—
628C22×C4—948no—
629C22×C4—9432no—
630C22×C4—942no—
631C22×C4—942no—
632C22×C4—942no—
633C22×C4—948no—
634C22×C4—942no—
635C22×C4—942no—
636C22×C4—942no—
637C22×C4—942no—
638C22×C4—948no—
639C22×C4—942no—
640C22×C4—942no—
641C22×C4—942no—
642C22×C4—942no—
643C22×C4—942no—
644C22×C4—942no—
645C22×C4—942no—
646C22×C4—942no—
647C22×C4—948no—
648C22×C4—942no—
649C22×C4—942no—
650C22×C4—1884no—
651C22×C4—1884no—
652C22×C4—18816no—
653C22×C4—18816no—
654C22×C4C2×C4×D4714yes—
655C22×C4#1062535214yes—
656C22×C4C23×D4712yes—
657C22×C4C23×D4712yes—
658C22×C4C23×D4712yes—
659C22×C4C23×D4712yes—
660C22×C4C23×D4712yes—
661C4⋊C4—4716no—
662C4⋊C4—4716no—
663C4⋊C4—948no—
664C4⋊C4—948no—
665C4⋊C4—948no—
666C4⋊C4—948no—
667C4⋊C4—1884no—
668C22⋊C4—28no—
669C22⋊C4—28no—
670C22⋊C4—44no—
671C22⋊C4—4716no—
672C22⋊C4—4716no—
673C22⋊C4—4716no—
674C22⋊C4—4716no—
675C22⋊C4—948no—
676C42—948no—
677C42—948no—
678C42—948no—
679C42—948no—
680C42—1884no—
681C23—28no—
682C23—28no—
683C23—28no—
684C23—28no—
685C23—28no—
686C23—28no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—28no—
692C23—28no—
693C23—28no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—44no—
701C23—44no—
702C23—44no—
703C23—44no—
704C23(C22⋊D47)⋊C4116yes—
705C23C22×C4×D4714yes—
706C23C22×C4×D4714yes—
707C23C22×C4×D4712yes—
708C23C2×D4×D4714yes—
709C23C2×D4×D4712yes—
710C23#41×D4712yes—
711C23C2×#1062535214yes—
712C23C2×#1062535212yes—
713C23C2×#1062535212yes—
714C23#1309406912yes—
715C23#1309407112yes—
716C23C24×D4711yescharacteristic
717D4—232no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—416no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—474no—
738C2×C4—474no—
739C2×C4—474no—
740C2×C4—474no—
741C2×C4—474no—
742C2×C4—474no—
743C2×C4—474no—
744C2×C4—948no—
745C2×C4—948no—
746C2×C4—948no—
747C2×C4—9432no—
748C2×C4—948no—
749C2×C4—948no—
750C2×C4—948no—
751C2×C4—948no—
752C2×C4—942no—
753C2×C4—942no—
754C2×C4—942no—
755C2×C4—942no—
756C2×C4—942no—
757C2×C4—942no—
758C2×C4—942no—
759C2×C4—942no—
760C2×C4—942no—
761C2×C4—942no—
762C2×C4—942no—
763C2×C4—942no—
764C2×C4—942no—
765C2×C4—942no—
766C2×C4—942no—
767C2×C4—942no—
768C2×C4—942no—
769C2×C4—18816no—
770C2×C4—18816no—
771C2×C4—1884no—
772C2×C4C22×C4×D4714yes—
773C2×C4C2×#1062535214yes—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—24no—
778C22—232no—
779C22—24no—
780C22—24no—
781C22—24no—
782C22—24no—
783C22—24no—
784C22—42no—
785C22—42no—
786C22—416no—
787C22—42no—
788C22—42no—
789C22C2×(C22⋊D47)⋊C418yes—
790C22C2×(C22⋊D47)⋊C414yes—
791C22C4×#1062535214yes—
792C22#1568960214yes—
793C22#1568976214yes—
794C22#1568977314yes—
795C22#1568980414yes—
796C22#1568981014yes—
797C22C23×C4×D4711yescharacteristic
798C22C22×D4×D4711yescharacteristic
799C22C2×#41×D4711yescharacteristic
800C22C22×#1062535211yescharacteristic
801C22C22×#1062535211yescharacteristic
802C22C2×#1309406911yescharacteristic
803C22C2×#1309407111yescharacteristic
804C4—24no—
805C4—24no—
806C4—42no—
807C4—42no—
808C4—42no—
809C4—944no—
810C4—944no—
811C4—944no—
812C4—944no—
813C4—944no—
814C4—944no—
815C4—944no—
816C4—1882no—
817C2—28no—
818C2—44no—
819C2#2024638618yesdirect product factor
820C2C22×(C22⋊D47)⋊C411yescharacteristic
821C2C2×C4×#1062535211yescharacteristic
822C2C2×#1568960211yescharacteristic
823C2C2×#1568976211yescharacteristic
824C2C2×#1568977311yescharacteristic
825C2C2×#1568980411yescharacteristic
826C2C2×#1568981011yescharacteristic
subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C47×#386C2
socleC24×C47C24
prime radicalC23×D4×C47C22
cosocleC23×C47C25
hypercenterC2×#386D47
hypocenterC47C2×#2359
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
3. C22×#13093980C2semidirect
4. #20246386C2direct (N × H)
5. C2×#15689020C2semidirect
6. C2×#15689017C2semidirect
7. C2×#15689011C2semidirect
8. C2×#15689010C2semidirect
9. C2×#15689005C2semidirect
10. C2×#15688995C2semidirect
11. C2×#15688995C2semidirect
12. C2×#15688974C2semidirect
13. C2×C22⋊C4×Dic47C2semidirect
14. C2×C4×C22⋊Dic47C2semidirect
15. C22×C47⋊#95C2semidirect
20. C2×#13094005C4semidirect
25. C2×#13093980C22semidirect
43. #15689020C22semidirect
44. #15689017C22semidirect
45. #15689011C22semidirect
46. #15689010C22semidirect
47. #15689005C22semidirect
48. #15688995C22semidirect
49. #15688995C22semidirect
50. #15688974C22semidirect
51. C22⋊C4×Dic47C22semidirect
52. C4×C22⋊Dic47C22semidirect
61. C2×C47⋊#95C22semidirect
78. C23×Dic47C2×C4semidirect
90. #13094005C2×C4semidirect
99. C2×Dic47⋊C4C2×C4semidirect
100. C2×Dic47⋊C4C2×C4semidirect
108. C2×C22⋊Dic47C2×C4semidirect
109. C2×C22⋊Dic47C2×C4semidirect
110. C2×C22⋊Dic47C2×C4semidirect
235. C22×Dic47C22×C4semidirect
251. C22⋊Dic47C22×C4semidirect
252. C22⋊Dic47C22×C4semidirect
253. C22⋊Dic47C22×C4semidirect
260. Dic47⋊C4C22×C4semidirect
261. Dic47⋊C4C22×C4semidirect
422. C2×C47#2359semidirect
483. C47C2×#2359semidirect
819. C2#20246386direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940052
C22×D4×Dic472
C22×#130939802
#202463862
C2×#156890202
C2×#156890172
C2×#156890112
C2×#156890102
C2×#156890052
C2×#156889952
C2×#156889742
C2×C22⋊C4×Dic472
C2×C4×C22⋊Dic472
C22×C47⋊#952
C2×C47×#3862
C2×#235947