Finite Group Databasebeta

← C2×#20246097 #26375063

Subgroups — C2×#20246097 #26375063

Order 12032.

3566 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094010C211yesmaximal, characteristic
2C22×C4×Dic94C211yesmaximal, characteristic, complemented
3C22×(C22⋊D47)⋊C4C211yesmaximal, characteristic
4#20246097C2116yesmaximal, direct product factor
5C2×#15689027C211yesmaximal, characteristic, complemented
6C2×#15689023C211yesmaximal, characteristic
7C2×#15689015C211yesmaximal, characteristic, complemented
8C2×#15689014C211yesmaximal, characteristic, complemented
9C2×#15689011C211yesmaximal, characteristic, complemented
10C2×#15688998C211yesmaximal, characteristic, complemented
11C2×#15688997C211yesmaximal, characteristic, complemented
12C2×#15688995C211yesmaximal, characteristic, complemented
13C2×#15688994C211yesmaximal, characteristic, complemented
14C2×#15688992C211yesmaximal, characteristic, complemented
15C2×#15688968C211yesmaximal, characteristic, complemented
16C2×C47×#388C211yesmaximal, characteristic, complemented
17C23×Dic94C2211yescharacteristic
18C23×C22⋊D47C2211yescharacteristic
19C24×Dic47C2211yescharacteristic
20C23×C4×D47C2211yescharacteristic
21C2×#13094010C4116yescomplemented
22C2×#13094010C2218yes—
23C2×C4×Dic94—28no—
24C2×C4×Dic94C2218yescomplemented
25C2×(C22⋊D47)⋊C4—28no—
26C2×(C22⋊D47)⋊C4C2218yes—
27C22×C4⋊Dic47C2211yescharacteristic
28C22×C4⋊Dic47C2211yescharacteristic
29C22×Dic47⋊C4C2211yescharacteristic
30C22×Dic47⋊C4C2211yescharacteristic
31C22×Dic47⋊C4C2211yescharacteristic
32C22×Dic47⋊C4C2211yescharacteristic
33C22×Dic47⋊C4C2211yescharacteristic
34C22×C22⋊Dic47C2211yescharacteristic
35C22×C22⋊Dic47C2211yescharacteristic
36C22×(C2×D47)⋊C4C2211yescharacteristic
37C22×(C2×D47)⋊C4C2211yescharacteristic
38C22×(C2×D47)⋊C4C2211yescharacteristic
39C22×(C2×D47)⋊C4C2211yescharacteristic
40C22×(C2×D47)⋊C4C2211yescharacteristic
41C22×C4×Dic47C2211yescharacteristic
42C22×C4×Dic47C2211yescharacteristic
43C22×C4×Dic47C2211yescharacteristic
44C22×C4×Dic47C2211yescharacteristic
45#15689027C2218yescomplemented
46#15689023C2218yes—
47#15689015C2218yescomplemented
48#15689014C2218yescomplemented
49#15689011C2218yescomplemented
50#15688998C2218yescomplemented
51#15688997C2218yescomplemented
52#15688995C2218yescomplemented
53#15688994C2218yescomplemented
54#15688992C2218yescomplemented
55#15688968C2218yescomplemented
56C2×C47⋊#95C2211yescharacteristic
57C2×C47⋊#95C2211yescharacteristic
58C2×C47⋊#95C2211yescharacteristic
59C2×C47⋊#95C2211yescharacteristic
60C2×C47⋊#95C2211yescharacteristic
61C2×C47⋊#95C2211yescharacteristic
62C22×C4⋊C4×C47C2211yescharacteristic
63C22×C22⋊C4×C47C2211yescharacteristic
64C22×C22⋊C4×C47C2211yescharacteristic
65C22×C22⋊C4×C47C2211yescharacteristic
66C22×C42×C47C2211yescharacteristic
67C47×#388C2218yescomplemented
68C2×#95×C47C2211yescharacteristic
69C2×#95×C47C2211yescharacteristic
70C24×D47C2311yescharacteristic
71C22×Dic94—24no—
72C22×Dic94—24no—
73C22×Dic94C2×C418yescomplemented
74C22×Dic94C2314yes—
75C22×C22⋊D47—24no—
76C22×C22⋊D47—24no—
77C22×C22⋊D47C2×C418yes—
78C22×C22⋊D47C2314yes—
79C23×Dic47—24no—
80C23×Dic47—42no—
81C23×Dic47—42no—
82C23×Dic47C2311yescharacteristic
83C23×Dic47C2311yescharacteristic
84C23×Dic47C2311yescharacteristic
85C23×Dic47C2311yescharacteristic
86C23×Dic47C2311yescharacteristic
87C23×Dic47C2311yescharacteristic
88C23×Dic47C2314yes—
89C23×Dic47C2311yescharacteristic
90C22×C4×D47—24no—
91C22×C4×D47—42no—
92C22×C4×D47—42no—
93C22×C4×D47C2314yes—
94#13094010C2×C4164yescomplemented
95C4×Dic94—232no—
96(C22⋊D47)⋊C4—232no—
97C2×C4⋊Dic47—24no—
98C2×C4⋊Dic47—42no—
99C2×C4⋊Dic47C2314yes—
100C2×C4⋊Dic47C2314yes—
101C2×Dic47⋊C4—24no—
102C2×Dic47⋊C4—24no—
103C2×Dic47⋊C4—24no—
104C2×Dic47⋊C4—42no—
105C2×Dic47⋊C4—42no—
106C2×Dic47⋊C4C2314yes—
107C2×Dic47⋊C4C2314yes—
108C2×Dic47⋊C4C2314yes—
109C2×Dic47⋊C4C2314yes—
110C2×Dic47⋊C4C2314yes—
111C2×C22⋊Dic47—42no—
112C2×C22⋊Dic47C2×C418yescomplemented
113C2×C22⋊Dic47C2314yes—
114C2×C22⋊Dic47C2314yes—
115C2×(C2×D47)⋊C4—24no—
116C2×(C2×D47)⋊C4—42no—
117C2×(C2×D47)⋊C4—42no—
118C2×(C2×D47)⋊C4C2×C418yescomplemented
119C2×(C2×D47)⋊C4C2×C418yescomplemented
120C2×(C2×D47)⋊C4C2314yes—
121C2×(C2×D47)⋊C4C2314yes—
122C2×(C2×D47)⋊C4C2314yes—
123C2×(C2×D47)⋊C4C2314yes—
124C2×(C2×D47)⋊C4C2314yes—
125C2×C4×Dic47—24no—
126C2×C4×Dic47—24no—
127C2×C4×Dic47C2×C418yescomplemented
128C2×C4×Dic47D418yes—
129C2×C4×Dic47C2314yes—
130C2×C4×Dic47C2314yes—
131C2×C4×Dic47C2314yes—
132C2×C4×Dic47C2314yes—
133C47⋊#95C2314yes—
134C47⋊#95C2314yes—
135C47⋊#95C2314yes—
136C47⋊#95C2314yes—
137C47⋊#95C2314yes—
138C47⋊#95C2314yes—
139C25×C47C2311yescharacteristic
140C23×C4×C47C2311yescharacteristic
141C23×C4×C47C2311yescharacteristic
142C23×C4×C47C2311yescharacteristic
143C23×C4×C47C2311yescharacteristic
144C23×C4×C47C2311yescharacteristic
145C23×C4×C47C2311yescharacteristic
146C2×C4⋊C4×C47—42no—
147C2×C4⋊C4×C47C2314yes—
148C2×C22⋊C4×C47—24no—
149C2×C22⋊C4×C47—42no—
150C2×C22⋊C4×C47C2×C418yescomplemented
151C2×C22⋊C4×C47C2314yes—
152C2×C22⋊C4×C47C2314yes—
153C2×C22⋊C4×C47C2314yes—
154C2×C42×C47—24no—
155C2×C42×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×C47C22×C414yes—
165C24×C47C2412yes—
166C24×C47C2411yescharacteristic
167C23×D47—22no—
168C23×D47—22no—
169C23×D47—22no—
170C23×D47—22no—
171C23×D47—22no—
172C23×D47—22no—
173C23×D47C22×C414yes—
174C23×D47C2412yes—
175C22×C4×C47—22no—
176C22×C4×C47—22no—
177C22×C4×C47—22no—
178C22×C4×C47—22no—
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—22no—
187C22×C4×C47—22no—
188C22×C4×C47—22no—
189C22×C4×C47—22no—
190C22×C4×C47C22×C414yes—
191C22×C4×C47C22×C414yes—
192C22×C4×C47C2×D414yes—
193C22×C4×C47C2412yes—
194C22×C4×C47C2412yes—
195C22×C4×C47C2412yes—
196C22×C4×C47C2412yes—
197C22×C4×C47C2412yes—
198C22×C4×C47C2412yes—
199C2×C22⋊D47—232no—
200C2×C22⋊D47—28no—
201C2×C22⋊D47—28no—
202C2×C22⋊D47C22×C4116yes—
203C22×Dic47—22no—
204C22×Dic47—22no—
205C22×Dic47—22no—
206C22×Dic47—22no—
207C22×Dic47—22no—
208C22×Dic47—22no—
209C22×Dic47—22no—
210C22×Dic47—22no—
211C22×Dic47—22no—
212C22×Dic47—22no—
213C22×Dic47—22no—
214C22×Dic47—22no—
215C22×Dic47—22no—
216C22×Dic47—22no—
217C22×Dic47—22no—
218C22×Dic47—28no—
219C22×Dic47—44no—
220C22×Dic47—44no—
221C22×Dic47—416no—
222C22×Dic47C22×C414yes—
223C22×Dic47C22×C414yes—
224C22×Dic47C22×C414yes—
225C22×Dic47C2×D414yes—
226C22×Dic47C2×D414yes—
227C22×Dic47#4114yes—
228C22×Dic47C2412yes—
229C22×Dic47C2412yes—
230C22×Dic47C2412yes—
231C22×Dic47C2412yes—
232C22×Dic47C2412yes—
233C22×Dic47C2412yes—
234C22×Dic47C2412yes—
235C2×C4×D47—28no—
236C2×C4×D47—44no—
237C2×C4×D47—44no—
238C2×C4×D47—416no—
239C2×Dic94—232no—
240C2×Dic94—28no—
241C2×Dic94—28no—
242C2×Dic94C22×C4116yescomplemented
243C4⋊C4×C47—44no—
244C22⋊C4×C47—28no—
245C22⋊C4×C47—44no—
246C22⋊C4×C47C22×C4116yescomplemented
247C42×C47—28no—
248C22⋊Dic47—44no—
249C22⋊Dic47C22×C4116yescomplemented
250(C2×D47)⋊C4—28no—
251(C2×D47)⋊C4—44no—
252(C2×D47)⋊C4—44no—
253(C2×D47)⋊C4C22×C4116yescomplemented
254(C2×D47)⋊C4C22×C4116yescomplemented
255C4⋊Dic47—28no—
256C4⋊Dic47—44no—
257Dic47⋊C4—28no—
258Dic47⋊C4—28no—
259Dic47⋊C4—28no—
260Dic47⋊C4—44no—
261Dic47⋊C4—44no—
262C4×Dic47—28no—
263C4×Dic47—28no—
264C4×Dic47C22×C4116yescomplemented
265C4×Dic47C2×D4116yes—
266C23×C47—28no—
267C23×C47—28no—
268C23×C47—28no—
269C23×C47—22no—
270C23×C47—22no—
271C23×C47—22no—
272C23×C47—22no—
273C23×C47—22no—
274C23×C47—22no—
275C23×C47—44no—
276C23×C47—44no—
277C23×C47—44no—
278C23×C47—44no—
279C23×C47C23×C414yes—
280C23×C47C23×C412yes—
281C23×C47C22×D412yes—
282C23×C47C2×#4112yes—
283C23×C47H(5,𝔽2)12yes—
284C23×C47H(5,𝔽2)12yes—
285C23×C472−1+412yes—
286C23×C472−1+412yes—
287C23×C47C2511yescharacteristic
288C22×D47—28no—
289C22×D47—28no—
290C22×D47—28no—
291C22×D47—22no—
292C22×D47—22no—
293C22×D47—22no—
294C22×D47—22no—
295C22×D47—22no—
296C22×D47—22no—
297C22×D47—44no—
298C22×D47—44no—
299C22×D47—44no—
300C22×D47—44no—
301C22×D47C23×C414yes—
302C2×C4×C47—28no—
303C2×C4×C47—28no—
304C2×C4×C47—28no—
305C2×C4×C47—22no—
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—22no—
320C2×C4×C47—44no—
321C2×C4×C47—44no—
322C2×C4×C47—44no—
323C2×C4×C47C23×C414yes—
324C2×C4×C47C23×C414yes—
325C2×C4×C47C22×D414yes—
326C22⋊D47—232no—
327C2×Dic47—28no—
328C2×Dic47—28no—
329C2×Dic47—28no—
330C2×Dic47—22no—
331C2×Dic47—22no—
332C2×Dic47—22no—
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—416no—
346C2×Dic47—44no—
347C2×Dic47—44no—
348C2×Dic47—44no—
349C2×Dic47C4×D4116yes—
350C2×Dic47C23×C414yes—
351C2×Dic47C23×C414yes—
352C2×Dic47C23×C414yes—
353C2×Dic47C22×D414yes—
354C2×Dic47C22×D414yes—
355C2×Dic47C2×#4114yes—
356C4×D47—416no—
357Dic94—232no—
358C2×#2326—471nomaximal, Sylow
359C22×C47—24no—
360C22×C47—24no—
361C22×C47—24no—
362C22×C47—416no—
363C22×C47—42no—
364C22×C47—42no—
365C22×C47—42no—
366C22×C47—42no—
367C22×C47C2×C4×D414yes—
368C22×C47#52014yes—
369C22×C47#52014yes—
370C22×C47#53514yes—
371C22×C47#53614yes—
372C22×C47#54214yes—
373C22×C47#54214yes—
374C22×C47C24×C411yescharacteristic
375C22×C47C23×D411yescharacteristic
376C22×C47C22×#4111yescharacteristic
377C22×C47C2×H(5,𝔽2)11yescharacteristic
378C22×C47C2×H(5,𝔽2)11yescharacteristic
379C22×C47C2×2−1+411yescharacteristic
380C22×C47C2×2−1+411yescharacteristic
381C2×D47—24no—
382C2×D47—24no—
383C2×D47—24no—
384C2×D47—416no—
385C2×D47—42no—
386C2×D47—42no—
387C2×D47—42no—
388C2×D47—42no—
389C4×C47—24no—
390C4×C47—24no—
391C4×C47—24no—
392C4×C47—42no—
393C4×C47—42no—
394C4×C47—42no—
395Dic47—24no—
396Dic47—24no—
397Dic47—24no—
398Dic47—42no—
399Dic47—42no—
400Dic47—42no—
401Dic47C2×C4×D418yes—
402C22×#124—471no—
403C22×C4×Q8—471no—
404C22×C4×D4—471no—
405#2326—4716no—
406C2×#391—471no—
407C2×#390—471no—
408C2×#388—471no—
409C2×#388—471no—
410C2×#388—471no—
411C2×#388D4711yescharacteristic, complemented
412C2×#385—471no—
413C2×#385—471no—
414C2×#385—471no—
415C2×#385—471no—
416C2×#384—471no—
417C2×#376—471no—
418C2×C47—44no—
419C2×C47#232618yescomplemented
420C2×C47C22×C4×D411yescharacteristic
421C2×C47C2×#52011yescharacteristic
422C2×C47C2×#52011yescharacteristic
423C2×C47C2×#53511yescharacteristic
424C2×C47C2×#53611yescharacteristic
425C2×C47C2×#54211yescharacteristic
426C2×C47C2×#54211yescharacteristic
427D47—44no—
428C23×Q8—471no—
429C23×D4—471no—
430C24×C4—471no—
431C24×C4—471no—
432C2×#124—4716no—
433C2×#124—478no—
434C2×C4×Q8—478no—
435C2×C4×Q8—948no—
436C2×C4×D4—478no—
437C2×C4×D4—948no—
438C22×C4⋊C4—471no—
439C22×C4⋊C4—471no—
440C22×C4⋊C4—471no—
441C22×C4⋊C4—471no—
442C22×C4⋊C4—471no—
443C22×C4⋊C4—471no—
444C22×C4⋊C4—471no—
445C22×C4⋊C4C2×D4711yescharacteristic
446C22×C22⋊C4—471no—
447C22×C22⋊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×C42C2×D4711yescharacteristic
461#391—478no—
462#390—478no—
463#388—478no—
464#388—478no—
465#388—478no—
466#388C2×D4718yescomplemented
467#385—478no—
468#385—478no—
469#385—478no—
470#385—478no—
471#384—478no—
472#376—478no—
473C2×#95—471no—
474C2×#95—471no—
475C2×#95—471no—
476C2×#95—471no—
477C2×#95—471no—
478C2×#95—471no—
479C2×#95C2×D4711yescharacteristic
480C2×#95C2×D4711yescharacteristic
481C47C2×#232611yescharacteristic, complemented, Sylow
482C25—471no—
483C25C22×D4711yescharacteristic
484C22×Q8—478no—
485C22×Q8—474no—
486C22×Q8—944no—
487C22×Q8—944no—
488C22×D4—478no—
489C22×D4—474no—
490C22×D4—944no—
491C22×D4—944no—
492C23×C4—471no—
493C23×C4—471no—
494C23×C4—471no—
495C23×C4—471no—
496C23×C4—471no—
497C23×C4—471no—
498C23×C4—471no—
499C23×C4—474no—
500C23×C4—474no—
501C23×C4—944no—
502C23×C4—944no—
503C23×C4—1882no—
504C23×C4—1882no—
505C23×C4—1882no—
506C23×C4—1882no—
507C23×C4C22×D4711yescharacteristic
508C23×C4C22×D4711yescharacteristic
509C23×C4C22×D4711yescharacteristic
510C23×C4C22×D4711yescharacteristic
511C23×C4C22×D4711yescharacteristic
512C23×C4C22×D4711yescharacteristic
513#124—4764no—
514C4×Q8—9432no—
515C4×D4—9432no—
516C2×C4⋊C4—42no—
517C2×C4⋊C4—474no—
518C2×C4⋊C4—474no—
519C2×C4⋊C4—474no—
520C2×C4⋊C4—474no—
521C2×C4⋊C4—474no—
522C2×C4⋊C4—474no—
523C2×C4⋊C4—474no—
524C2×C4⋊C4—944no—
525C2×C4⋊C4—944no—
526C2×C4⋊C4—944no—
527C2×C4⋊C4—944no—
528C2×C4⋊C4—1882no—
529C2×C4⋊C4—1882no—
530C2×C4⋊C4—1882no—
531C2×C4⋊C4C22×D4714yes—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—42no—
534C2×C22⋊C4—478no—
535C2×C22⋊C4—474no—
536C2×C22⋊C4—478no—
537C2×C22⋊C4—478no—
538C2×C22⋊C4—474no—
539C2×C22⋊C4—474no—
540C2×C22⋊C4—474no—
541C2×C22⋊C4—474no—
542C2×C22⋊C4—474no—
543C2×C22⋊C4—474no—
544C2×C22⋊C4—944no—
545C2×C22⋊C4—1882no—
546C2×C22⋊C4—1882no—
547C2×C22⋊C4—1882no—
548C2×C22⋊C4C4×D4718yescomplemented
549C2×C22⋊C4C22×D4714yes—
550C2×C22⋊C4C22×D4714yes—
551C2×C22⋊C4C22×D4714yes—
552C2×C42—24no—
553C2×C42—478no—
554C2×C42—478no—
555C2×C42—474no—
556C2×C42—474no—
557C2×C42—474no—
558C2×C42—474no—
559C2×C42—944no—
560C2×C42—944no—
561C2×C42C22×D4714yes—
562#95—474no—
563#95—474no—
564#95—474no—
565#95—474no—
566#95—474no—
567#95—474no—
568#95C22×D4714yes—
569#95C22×D4714yes—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—474no—
577C24—472no—
578C24—942no—
579C24—942no—
580C24—942no—
581C24—942no—
582C24—942no—
583C24—942no—
584C24C2×C4×D4714yes—
585C24C23×D4712yes—
586C24C23×D4711yescharacteristic
587C2×Q8—4716no—
588C2×Q8—948no—
589C2×Q8—9432no—
590C2×Q8—948no—
591C2×D4—4716no—
592C2×D4—948no—
593C2×D4—9432no—
594C2×D4—948no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—474no—
611C22×C4—474no—
612C22×C4—474no—
613C22×C4—472no—
614C22×C4—474no—
615C22×C4—474no—
616C22×C4—474no—
617C22×C4—472no—
618C22×C4—472no—
619C22×C4—472no—
620C22×C4—472no—
621C22×C4—472no—
622C22×C4—472no—
623C22×C4—948no—
624C22×C4—948no—
625C22×C4—942no—
626C22×C4—942no—
627C22×C4—942no—
628C22×C4—942no—
629C22×C4—942no—
630C22×C4—942no—
631C22×C4—942no—
632C22×C4—942no—
633C22×C4—942no—
634C22×C4—942no—
635C22×C4—942no—
636C22×C4—942no—
637C22×C4—942no—
638C22×C4—942no—
639C22×C4—942no—
640C22×C4—1884no—
641C22×C4—1884no—
642C22×C4—18816no—
643C22×C4—1884no—
644C22×C4—1884no—
645C22×C4—18816no—
646C22×C4C2×C4×D4714yes—
647C22×C4C2×C4×D4714yes—
648C22×C4D4×D4714yes—
649C22×C4C23×D4712yes—
650C22×C4C23×D4712yes—
651C22×C4C23×D4712yes—
652C22×C4C23×D4712yes—
653C22×C4C23×D4712yes—
654C22×C4C23×D4712yes—
655C4⋊C4—44no—
656C4⋊C4—948no—
657C4⋊C4—948no—
658C4⋊C4—948no—
659C4⋊C4—948no—
660C4⋊C4—1884no—
661C4⋊C4—1884no—
662C4⋊C4—1884no—
663C22⋊C4—28no—
664C22⋊C4—44no—
665C22⋊C4—4716no—
666C22⋊C4—4716no—
667C22⋊C4—4716no—
668C22⋊C4—948no—
669C22⋊C4—1884no—
670C22⋊C4—1884no—
671C22⋊C4—1884no—
672C22⋊C4C2×C4×D47116yescomplemented
673C42—28no—
674C42—4716no—
675C42—4716no—
676C42—948no—
677C42—948no—
678C23—28no—
679C23—28no—
680C23—28no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—474no—
692C23—948no—
693C23—948no—
694C23—948no—
695C23—942no—
696C23—942no—
697C23—942no—
698C23—942no—
699C23—942no—
700C23—942no—
701C23—1884no—
702C23—1884no—
703C23—1884no—
704C23—1884no—
705C23C22×C4×D4714yes—
706C23C22×C4×D4712yes—
707C23C2×D4×D4712yes—
708C23#41×D4712yes—
709C23#1309406912yes—
710C23#1309407012yes—
711C23#1309407112yes—
712C23#1309407112yes—
713C23C24×D4711yescharacteristic
714Q8—9432no—
715D4—9432no—
716C2×C4—28no—
717C2×C4—28no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—28no—
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—22no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—4716no—
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—942no—
747C2×C4—948no—
748C2×C4—942no—
749C2×C4—942no—
750C2×C4—942no—
751C2×C4—942no—
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—18816no—
763C2×C4—18816no—
764C2×C4—1884no—
765C2×C4—1884no—
766C2×C4—1884no—
767C2×C4C22×C4×D4714yes—
768C2×C4C22×C4×D4714yes—
769C2×C4C2×D4×D4714yes—
770C22—24no—
771C22—24no—
772C22—24no—
773C22—416no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—944no—
779C22—944no—
780C22—944no—
781C22—18816no—
782C22—1882no—
783C22—1882no—
784C22—1882no—
785C22—1882no—
786C22C4×D4×D4714yes—
787C22#1568960214yes—
788C22#1568960314yes—
789C22#1568968914yes—
790C22#1568969514yes—
791C22#1568973714yes—
792C22#1568973914yes—
793C22C23×C4×D4711yescharacteristic
794C22C22×D4×D4711yescharacteristic
795C22C2×#41×D4711yescharacteristic
796C22C2×#1309406911yescharacteristic
797C22C2×#1309407011yescharacteristic
798C22C2×#1309407111yescharacteristic
799C22C2×#1309407111yescharacteristic
800C4—24no—
801C4—24no—
802C4—24no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—478no—
807C4—944no—
808C4—944no—
809C4—944no—
810C4—1882no—
811C4—1882no—
812C4—1882no—
813C2—44no—
814C2—1884no—
815C2#2024609718yesdirect product factor
816C2C2×C4×D4×D4711yescharacteristic
817C2C2×#1568960211yescharacteristic
818C2C2×#1568960311yescharacteristic
819C2C2×#1568968911yescharacteristic
820C2C2×#1568969511yescharacteristic
821C2C2×#1568973711yescharacteristic
822C2C2×#1568973911yescharacteristic
subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C47×#388C2
socleC24×C47C24
prime radicalC23×C22⋊D47C22
cosocleC23×C47C25
hypercenterC2×#388D47
hypocenterC47C2×#2326
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic94C2semidirect
4. #20246097C2direct (N × H)
5. C2×#15689027C2semidirect
7. C2×#15689015C2semidirect
8. C2×#15689014C2semidirect
9. C2×#15689011C2semidirect
10. C2×#15688998C2semidirect
11. C2×#15688997C2semidirect
12. C2×#15688995C2semidirect
13. C2×#15688994C2semidirect
14. C2×#15688992C2semidirect
15. C2×#15688968C2semidirect
16. C2×C47×#388C2semidirect
21. C2×#13094010C4semidirect
24. C2×C4×Dic94C22semidirect
45. #15689027C22semidirect
47. #15689015C22semidirect
48. #15689014C22semidirect
49. #15689011C22semidirect
50. #15688998C22semidirect
51. #15688997C22semidirect
52. #15688995C22semidirect
53. #15688994C22semidirect
54. #15688992C22semidirect
55. #15688968C22semidirect
67. C47×#388C22semidirect
73. C22×Dic94C2×C4semidirect
94. #13094010C2×C4semidirect
112. C2×C22⋊Dic47C2×C4semidirect
118. C2×(C2×D47)⋊C4C2×C4semidirect
119. C2×(C2×D47)⋊C4C2×C4semidirect
127. C2×C4×Dic47C2×C4semidirect
150. C2×C22⋊C4×C47C2×C4semidirect
242. C2×Dic94C22×C4semidirect
246. C22⋊C4×C47C22×C4semidirect
249. C22⋊Dic47C22×C4semidirect
253. (C2×D47)⋊C4C22×C4semidirect
254. (C2×D47)⋊C4C22×C4semidirect
264. C4×Dic47C22×C4semidirect
411. C2×#388D47semidirect
419. C2×C47#2326semidirect
466. #388C2×D47semidirect
481. C47C2×#2326semidirect
548. C2×C22⋊C4C4×D47semidirect
672. C22⋊C4C2×C4×D47semidirect
815. C2#20246097direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940102
C22×C4×Dic942
C22×(C22⋊D47)⋊C42
#202460972
C2×#156890272
C2×#156890232
C2×#156890152
C2×#156890142
C2×#156890112
C2×#156889982
C2×#156889972
C2×#156889952
C2×#156889942
C2×#156889922
C2×#156889682
C2×C47×#3882
C2×#232647