Finite Group Databasebeta

← C2×#20246055 #26375004

Subgroups — C2×#20246055 #26375004

Order 12032.

3718 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×#13094006C211yesmaximal, characteristic
2C22×C4×C22⋊D47C211yesmaximal, characteristic
3C22×C4⋊C4×D47C211yesmaximal, characteristic, complemented
4#20246055C2116yesmaximal, direct product factor
5C2×#15689020C211yesmaximal, characteristic, complemented
6C2×#15689019C211yesmaximal, characteristic, complemented
7C2×#15689016C211yesmaximal, characteristic, complemented
8C2×#15689011C211yesmaximal, characteristic, complemented
9C2×#15689008C211yesmaximal, characteristic, complemented
10C2×#15689004C211yesmaximal, characteristic, complemented
11C2×#15688999C211yesmaximal, characteristic
12C2×#15688996C211yesmaximal, characteristic, complemented
13C2×#15688994C211yesmaximal, characteristic, complemented
14C2×#15688985C211yesmaximal, characteristic, complemented
15C2×#15688970C211yesmaximal, characteristic, complemented
16C2×C47×#385C211yesmaximal, characteristic, complemented
17C23×C22⋊D47C2211yescharacteristic
18C23×C4×D47C2211yescharacteristic
19C23×C4×D47C2211yescharacteristic
20C23×C4×D47C2211yescharacteristic
21C2×#13094006C4116yescomplemented
22C2×#13094006C2218yes—
23C2×C4×C22⋊D47—28no—
24C2×C4×C22⋊D47C2218yes—
25C22×C4⋊Dic47C2211yescharacteristic
26C22×C4⋊Dic47C2211yescharacteristic
27C22×Dic47⋊C4C2211yescharacteristic
28C22×Dic47⋊C4C2211yescharacteristic
29C22×Dic47⋊C4C2211yescharacteristic
30C22×Dic47⋊C4C2211yescharacteristic
31C22×Dic47⋊C4C2211yescharacteristic
32C2×C4⋊C4×D47—28no—
33C2×C4⋊C4×D47C2218yescomplemented
34C22×C22⋊Dic47C2211yescharacteristic
35C22×C22⋊Dic47C2211yescharacteristic
36C22×C22⋊Dic47C2211yescharacteristic
37C22×(C2×D47)⋊C4C2211yescharacteristic
38C22×(C2×D47)⋊C4C2211yescharacteristic
39C22×(C2×D47)⋊C4C2211yescharacteristic
40C22×C4×Dic47C2211yescharacteristic
41C22×C4×Dic47C2211yescharacteristic
42C22×C4×Dic47C2211yescharacteristic
43#15689020C2218yescomplemented
44#15689019C2218yescomplemented
45#15689016C2218yescomplemented
46#15689011C2218yescomplemented
47#15689008C2218yescomplemented
48#15689004C2218yescomplemented
49#15688999C2218yes—
50#15688996C2218yescomplemented
51#15688994C2218yescomplemented
52#15688985C2218yescomplemented
53#15688970C2218yescomplemented
54C2×C47⋊#95C2211yescharacteristic
55C2×C47⋊#95C2211yescharacteristic
56C2×C47⋊#95C2211yescharacteristic
57C2×C47⋊#95C2211yescharacteristic
58C2×C47⋊#95C2211yescharacteristic
59C2×C47⋊#95C2211yescharacteristic
60C2×C47⋊#95C2211yescharacteristic
61C2×C47⋊#95C2211yescharacteristic
62C24×C4×C47C2211yescharacteristic
63C22×C4⋊C4×C47C2211yescharacteristic
64C22×C4⋊C4×C47C2211yescharacteristic
65C22×C22⋊C4×C47C2211yescharacteristic
66C22×C22⋊C4×C47C2211yescharacteristic
67C47×#385C2218yescomplemented
68C2×#95×C47C2211yescharacteristic
69C2×#95×C47C2211yescharacteristic
70C24×D47C2311yescharacteristic
71C22×C22⋊D47—24no—
72C22×C22⋊D47—24no—
73C22×C22⋊D47C2×C418yes—
74C22×C22⋊D47C2314yes—
75C23×Dic47C2311yescharacteristic
76C23×Dic47C2311yescharacteristic
77C23×Dic47C2311yescharacteristic
78C23×Dic47C2311yescharacteristic
79C23×Dic47C2311yescharacteristic
80C23×Dic47C2311yescharacteristic
81C23×Dic47C2311yescharacteristic
82C22×C4×D47—24no—
83C22×C4×D47—24no—
84C22×C4×D47—24no—
85C22×C4×D47—42no—
86C22×C4×D47—42no—
87C22×C4×D47—42no—
88C22×C4×D47—42no—
89C22×C4×D47C2×C418yescomplemented
90C22×C4×D47D418yes—
91C22×C4×D47C2314yes—
92C22×C4×D47C2314yes—
93C22×C4×D47C2314yes—
94#13094006C2×C4164yescomplemented
95C4×C22⋊D47—232no—
96C2×C4⋊Dic47—24no—
97C2×C4⋊Dic47C2×C418yescomplemented
98C2×C4⋊Dic47C2314yes—
99C2×C4⋊Dic47C2314yes—
100C2×Dic47⋊C4—24no—
101C2×Dic47⋊C4—24no—
102C2×Dic47⋊C4—24no—
103C2×Dic47⋊C4—42no—
104C2×Dic47⋊C4C2×C418yescomplemented
105C2×Dic47⋊C4C2314yes—
106C2×Dic47⋊C4C2314yes—
107C2×Dic47⋊C4C2314yes—
108C2×Dic47⋊C4C2314yes—
109C2×Dic47⋊C4C2314yes—
110C4⋊C4×D47—232no—
111C2×C22⋊Dic47—24no—
112C2×C22⋊Dic47—42no—
113C2×C22⋊Dic47C2×C418yescomplemented
114C2×C22⋊Dic47C2314yes—
115C2×C22⋊Dic47C2314yes—
116C2×C22⋊Dic47C2314yes—
117C2×(C2×D47)⋊C4—24no—
118C2×(C2×D47)⋊C4—24no—
119C2×(C2×D47)⋊C4C2×C418yescomplemented
120C2×(C2×D47)⋊C4C2314yes—
121C2×(C2×D47)⋊C4C2314yes—
122C2×(C2×D47)⋊C4C2314yes—
123C2×C4×Dic47—24no—
124C2×C4×Dic47—42no—
125C2×C4×Dic47—42no—
126C2×C4×Dic47C2314yes—
127C2×C4×Dic47C2314yes—
128C2×C4×Dic47C2314yes—
129C47⋊#95C2314yes—
130C47⋊#95C2314yes—
131C47⋊#95C2314yes—
132C47⋊#95C2314yes—
133C47⋊#95C2314yes—
134C47⋊#95C2314yes—
135C47⋊#95C2314yes—
136C47⋊#95C2314yes—
137C25×C47C2311yescharacteristic
138C23×C4×C47—24no—
139C23×C4×C47—42no—
140C23×C4×C47—42no—
141C23×C4×C47C2311yescharacteristic
142C23×C4×C47C2311yescharacteristic
143C23×C4×C47C2311yescharacteristic
144C23×C4×C47C2311yescharacteristic
145C23×C4×C47C2311yescharacteristic
146C23×C4×C47C2311yescharacteristic
147C23×C4×C47C2314yes—
148C2×C4⋊C4×C47—24no—
149C2×C4⋊C4×C47—42no—
150C2×C4⋊C4×C47C2314yes—
151C2×C4⋊C4×C47C2314yes—
152C2×C22⋊C4×C47—42no—
153C2×C22⋊C4×C47C2×C418yescomplemented
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×C47C22×C414yes—
165C24×C47C2412yes—
166C24×C47C2411yescharacteristic
167C23×D47—22no—
168C23×D47—22no—
169C23×D47—22no—
170C23×D47—22no—
171C23×D47C22×C414yes—
172C23×D47C2×D414yes—
173C23×D47#4114yes—
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×C47—28no—
191C22×C4×C47—44no—
192C22×C4×C47—44no—
193C22×C4×C47—416no—
194C22×C4×C47C22×C414yes—
195C22×C4×C47C22×C414yes—
196C22×C4×C47C2×D414yes—
197C22×C4×C47C2412yes—
198C22×C4×C47C2412yes—
199C22×C4×C47C2412yes—
200C22×C4×C47C2412yes—
201C22×C4×C47C2412yes—
202C22×C4×C47C2412yes—
203C2×C22⋊D47—232no—
204C2×C22⋊D47—28no—
205C2×C22⋊D47—28no—
206C2×C22⋊D47C22×C4116yes—
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—22no—
219C22×Dic47—22no—
220C22×Dic47—22no—
221C22×Dic47—22no—
222C22×Dic47—22no—
223C22×Dic47—22no—
224C22×Dic47C22×C414yes—
225C22×Dic47C22×C414yes—
226C22×Dic47C22×C414yes—
227C22×Dic47C2×D414yes—
228C22×Dic47C2412yes—
229C22×Dic47C2412yes—
230C22×Dic47C2412yes—
231C22×Dic47C2412yes—
232C22×Dic47C2412yes—
233C22×Dic47C2412yes—
234C22×Dic47C2412yes—
235C2×C4×D47—232no—
236C2×C4×D47—28no—
237C2×C4×D47—28no—
238C2×C4×D47—28no—
239C2×C4×D47—416no—
240C2×C4×D47—44no—
241C2×C4×D47—44no—
242C2×C4×D47—44no—
243C2×C4×D47—44no—
244C2×C4×D47—416no—
245C2×C4×D47C22×C4116yescomplemented
246C2×C4×D47C2×D4116yes—
247C4⋊C4×C47—28no—
248C4⋊C4×C47—44no—
249C22⋊C4×C47—44no—
250C22⋊C4×C47C22×C4116yescomplemented
251C22⋊Dic47—28no—
252C22⋊Dic47—44no—
253C22⋊Dic47C22×C4116yescomplemented
254(C2×D47)⋊C4—28no—
255(C2×D47)⋊C4—28no—
256(C2×D47)⋊C4C22×C4116yescomplemented
257C4⋊Dic47—28no—
258C4⋊Dic47C22×C4116yescomplemented
259Dic47⋊C4—28no—
260Dic47⋊C4—28no—
261Dic47⋊C4—28no—
262Dic47⋊C4—44no—
263Dic47⋊C4C22×C4116yescomplemented
264C4×Dic47—28no—
265C4×Dic47—44no—
266C4×Dic47—44no—
267C23×C47—28no—
268C23×C47—28no—
269C23×C47—28no—
270C23×C47—22no—
271C23×C47—22no—
272C23×C47—22no—
273C23×C47—22no—
274C23×C47—22no—
275C23×C47—22no—
276C23×C47—44no—
277C23×C47—44no—
278C23×C47—44no—
279C23×C47—44no—
280C23×C47C23×C414yes—
281C23×C47C23×C412yes—
282C23×C47C22×D412yes—
283C23×C47C2×#4112yes—
284C23×C47H(5,𝔽2)12yes—
285C23×C47H(5,𝔽2)12yes—
286C23×C472−1+412yes—
287C23×C472−1+412yes—
288C23×C47C2511yescharacteristic
289C22×D47—28no—
290C22×D47—28no—
291C22×D47—28no—
292C22×D47—28no—
293C22×D47—28no—
294C22×D47—28no—
295C22×D47—22no—
296C22×D47—22no—
297C22×D47—22no—
298C22×D47—22no—
299C22×D47C4×D4116yes—
300C22×D47C23×C414yes—
301C22×D47C22×D414yes—
302C22×D47C2×#4114yes—
303C2×C4×C47—28no—
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—22no—
320C2×C4×C47—22no—
321C2×C4×C47—416no—
322C2×C4×C47—44no—
323C2×C4×C47—44no—
324C2×C4×C47—44no—
325C2×C4×C47C23×C414yes—
326C2×C4×C47C23×C414yes—
327C2×C4×C47C22×D414yes—
328C22⋊D47—232no—
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—44no—
351C2×Dic47—44no—
352C2×Dic47—44no—
353C2×Dic47C23×C414yes—
354C2×Dic47C23×C414yes—
355C2×Dic47C23×C414yes—
356C2×Dic47C22×D414yes—
357C4×D47—232no—
358C4×D47—416no—
359C4×D47—416no—
360C2×#2322—471nomaximal, Sylow
361C22×C47—24no—
362C22×C47—24no—
363C22×C47—24no—
364C22×C47—416no—
365C22×C47—42no—
366C22×C47—42no—
367C22×C47—42no—
368C22×C47—42no—
369C22×C47C2×C4×D414yes—
370C22×C47#52014yes—
371C22×C47#52014yes—
372C22×C47#53414yes—
373C22×C47#53614yes—
374C22×C47#53914yes—
375C22×C47#53914yes—
376C22×C47C24×C411yescharacteristic
377C22×C47C23×D411yescharacteristic
378C22×C47C22×#4111yescharacteristic
379C22×C47C2×H(5,𝔽2)11yescharacteristic
380C22×C47C2×H(5,𝔽2)11yescharacteristic
381C22×C47C2×2−1+411yescharacteristic
382C22×C47C2×2−1+411yescharacteristic
383C2×D47—232no—
384C2×D47—24no—
385C2×D47—24no—
386C2×D47—24no—
387C2×D47—24no—
388C2×D47—24no—
389C2×D47—24no—
390C2×D47C2×C4×D418yes—
391C4×C47—24no—
392C4×C47—24no—
393C4×C47—24no—
394C4×C47—42no—
395C4×C47—42no—
396C4×C47—42no—
397Dic47—24no—
398Dic47—24no—
399Dic47—24no—
400Dic47—24no—
401Dic47—42no—
402Dic47—42no—
403Dic47—42no—
404C22×#123—471no—
405C22×C4×D4—471no—
406C23×C4⋊C4—471no—
407#2322—4716no—
408C2×#389—471no—
409C2×#389—471no—
410C2×#388—471no—
411C2×#388—471no—
412C2×#387—471no—
413C2×#387—471no—
414C2×#386—471no—
415C2×#385—471no—
416C2×#385—471no—
417C2×#385D4711yescharacteristic, complemented
418C2×#381—471no—
419C2×C4×C22⋊C4—471no—
420C2×C47—44no—
421C2×C47#232218yescomplemented
422C2×C47C22×C4×D411yescharacteristic
423C2×C47C2×#52011yescharacteristic
424C2×C47C2×#52011yescharacteristic
425C2×C47C2×#53411yescharacteristic
426C2×C47C2×#53611yescharacteristic
427C2×C47C2×#53911yescharacteristic
428C2×C47C2×#53911yescharacteristic
429D47—28no—
430C23×D4—471no—
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—
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⋊C4—471no—
446C22×C4⋊C4—478no—
447C22×C4⋊C4—948no—
448C22×C4⋊C4C2×D4711yescharacteristic
449C22×C4⋊C4C2×D4711yescharacteristic
450C22×C22⋊C4—471no—
451C22×C22⋊C4—471no—
452C22×C22⋊C4—471no—
453C22×C22⋊C4—471no—
454C22×C22⋊C4—471no—
455C22×C22⋊C4—471no—
456C22×C22⋊C4C2×D4711yescharacteristic
457C22×C22⋊C4C2×D4711yescharacteristic
458C22×C42—471no—
459C22×C42—471no—
460C22×C42—471no—
461#389—478no—
462#389—478no—
463#388—478no—
464#388—478no—
465#387—478no—
466#387—478no—
467#386—478no—
468#385—478no—
469#385—478no—
470#385C2×D4718yescomplemented
471#381—478no—
472C4×C22⋊C4—478no—
473C2×#95—471no—
474C2×#95—471no—
475C2×#95—471no—
476C2×#95—471no—
477C2×#95—471no—
478C2×#95—471no—
479C2×#95—471no—
480C2×#95—471no—
481C2×#95C2×D4711yescharacteristic
482C2×#95C2×D4711yescharacteristic
483C47C2×#232211yescharacteristic, complemented, Sylow
484C25—471no—
485C25C22×D4711yescharacteristic
486C22×D4—478no—
487C22×D4—474no—
488C22×D4—944no—
489C22×D4—944no—
490C23×C4—24no—
491C23×C4—42no—
492C23×C4—42no—
493C23×C4—471no—
494C23×C4—471no—
495C23×C4—471no—
496C23×C4—471no—
497C23×C4—478no—
498C23×C4—474no—
499C23×C4—478no—
500C23×C4—474no—
501C23×C4—471no—
502C23×C4—471no—
503C23×C4—471no—
504C23×C4—474no—
505C23×C4—944no—
506C23×C4—944no—
507C23×C4—944no—
508C23×C4—1882no—
509C23×C4—1882no—
510C23×C4—1882no—
511C23×C4—1882no—
512C23×C4C22×D4711yescharacteristic
513C23×C4C22×D4711yescharacteristic
514C23×C4C22×D4711yescharacteristic
515C23×C4C22×D4711yescharacteristic
516C23×C4C22×D4711yescharacteristic
517C23×C4C22×D4711yescharacteristic
518C23×C4C22×D4714yes—
519#123—4764no—
520C4×D4—9432no—
521C2×C4⋊C4—24no—
522C2×C4⋊C4—42no—
523C2×C4⋊C4—478no—
524C2×C4⋊C4—478no—
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—474no—
532C2×C4⋊C4—9432no—
533C2×C4⋊C4—944no—
534C2×C4⋊C4—944no—
535C2×C4⋊C4—944no—
536C2×C4⋊C4—944no—
537C2×C4⋊C4—1882no—
538C2×C4⋊C4C22×D4714yes—
539C2×C4⋊C4C22×D4714yes—
540C2×C22⋊C4—42no—
541C2×C22⋊C4—478no—
542C2×C22⋊C4—474no—
543C2×C22⋊C4—478no—
544C2×C22⋊C4—474no—
545C2×C22⋊C4—474no—
546C2×C22⋊C4—474no—
547C2×C22⋊C4—474no—
548C2×C22⋊C4—474no—
549C2×C22⋊C4—944no—
550C2×C22⋊C4—944no—
551C2×C22⋊C4—944no—
552C2×C22⋊C4—1882no—
553C2×C22⋊C4C4×D4718yescomplemented
554C2×C22⋊C4C22×D4714yes—
555C2×C22⋊C4C22×D4714yes—
556C2×C42—474no—
557C2×C42—474no—
558C2×C42—474no—
559C2×C42—944no—
560C2×C42—1882no—
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—474no—
579C24—474no—
580C24—474no—
581C24—472no—
582C24—942no—
583C24—942no—
584C24—942no—
585C24—942no—
586C24C2×C4×D4714yes—
587C24C23×D4712yes—
588C24C23×D4711yescharacteristic
589C2×D4—4716no—
590C2×D4—948no—
591C2×D4—9432no—
592C2×D4—948no—
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—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—28no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—416no—
612C22×C4—474no—
613C22×C4—474no—
614C22×C4—474no—
615C22×C4—474no—
616C22×C4—472no—
617C22×C4—472no—
618C22×C4—472no—
619C22×C4—472no—
620C22×C4—4716no—
621C22×C4—4716no—
622C22×C4—472no—
623C22×C4—472no—
624C22×C4—472no—
625C22×C4—948no—
626C22×C4—9432no—
627C22×C4—948no—
628C22×C4—948no—
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—942no—
641C22×C4—942no—
642C22×C4—942no—
643C22×C4—942no—
644C22×C4—942no—
645C22×C4—942no—
646C22×C4—18816no—
647C22×C4—1884no—
648C22×C4—1884no—
649C22×C4—1884no—
650C22×C4—1884no—
651C22×C4—18816no—
652C22×C4C2×C4×D4714yes—
653C22×C4C2×C4×D4714yes—
654C22×C4D4×D4714yes—
655C22×C4C23×D4712yes—
656C22×C4C23×D4712yes—
657C22×C4C23×D4712yes—
658C22×C4C23×D4712yes—
659C22×C4C23×D4712yes—
660C22×C4C23×D4712yes—
661C4⋊C4—28no—
662C4⋊C4—44no—
663C4⋊C4—4716no—
664C4⋊C4—4716no—
665C4⋊C4—948no—
666C4⋊C4—948no—
667C4⋊C4—948no—
668C4⋊C4—948no—
669C4⋊C4—1884no—
670C22⋊C4—44no—
671C22⋊C4—4716no—
672C22⋊C4—4716no—
673C22⋊C4—948no—
674C22⋊C4—948no—
675C22⋊C4—948no—
676C22⋊C4—1884no—
677C22⋊C4C2×C4×D47116yescomplemented
678C42—948no—
679C42—1884no—
680C42—1884no—
681C23—28no—
682C23—28no—
683C23—28no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—4716no—
695C23—474no—
696C23—474no—
697C23—474no—
698C23—948no—
699C23—948no—
700C23—948no—
701C23—948no—
702C23—942no—
703C23—942no—
704C23—942no—
705C23—942no—
706C23—948no—
707C23—948no—
708C23C22×C4×D4714yes—
709C23C22×C4×D4712yes—
710C23C2×D4×D4712yes—
711C23#41×D4712yes—
712C23#1309406912yes—
713C23#1309406912yes—
714C23#1309407112yes—
715C23#1309407212yes—
716C23C24×D4711yescharacteristic
717D4—9432no—
718C2×C4—28no—
719C2×C4—28no—
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—22no—
735C2×C4—22no—
736C2×C4—416no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—474no—
741C2×C4—474no—
742C2×C4—474no—
743C2×C4—474no—
744C2×C4—9432no—
745C2×C4—948no—
746C2×C4—948no—
747C2×C4—948no—
748C2×C4—948no—
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—942no—
763C2×C4—942no—
764C2×C4—942no—
765C2×C4—942no—
766C2×C4—18816no—
767C2×C4—18816no—
768C2×C4—1884no—
769C2×C4—1884no—
770C2×C4—1884no—
771C2×C4C22×C4×D4714yes—
772C2×C4C22×C4×D4714yes—
773C2×C4C2×D4×D4714yes—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—416no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—478no—
783C22—9432no—
784C22—944no—
785C22—944no—
786C22—944no—
787C22—944no—
788C22—944no—
789C22—944no—
790C22C4×D4×D4714yes—
791C22#1568960214yes—
792C22#1568960414yes—
793C22#1568968314yes—
794C22#1568969614yes—
795C22#1568971614yes—
796C22#1568971914yes—
797C22C23×C4×D4711yescharacteristic
798C22C22×D4×D4711yescharacteristic
799C22C2×#41×D4711yescharacteristic
800C22C2×#1309406911yescharacteristic
801C22C2×#1309406911yescharacteristic
802C22C2×#1309407111yescharacteristic
803C22C2×#1309407211yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—944no—
811C4—944no—
812C4—944no—
813C4—944no—
814C4—1882no—
815C4—1882no—
816C4—1882no—
817C2—44no—
818C2—948no—
819C2#2024605518yesdirect product factor
820C2C2×C4×D4×D4711yescharacteristic
821C2C2×#1568960211yescharacteristic
822C2C2×#1568960411yescharacteristic
823C2C2×#1568968311yescharacteristic
824C2C2×#1568969611yescharacteristic
825C2C2×#1568971611yescharacteristic
826C2C2×#1568971911yescharacteristic
subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C47×#385C2
socleC24×C47C24
prime radicalC23×C22⋊D47C22
cosocleC23×C47C25
hypercenterC2×#385D47
hypocenterC47C2×#2322
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
3. C22×C4⋊C4×D47C2semidirect
4. #20246055C2direct (N × H)
5. C2×#15689020C2semidirect
6. C2×#15689019C2semidirect
7. C2×#15689016C2semidirect
8. C2×#15689011C2semidirect
9. C2×#15689008C2semidirect
10. C2×#15689004C2semidirect
12. C2×#15688996C2semidirect
13. C2×#15688994C2semidirect
14. C2×#15688985C2semidirect
15. C2×#15688970C2semidirect
16. C2×C47×#385C2semidirect
21. C2×#13094006C4semidirect
33. C2×C4⋊C4×D47C22semidirect
43. #15689020C22semidirect
44. #15689019C22semidirect
45. #15689016C22semidirect
46. #15689011C22semidirect
47. #15689008C22semidirect
48. #15689004C22semidirect
50. #15688996C22semidirect
51. #15688994C22semidirect
52. #15688985C22semidirect
53. #15688970C22semidirect
67. C47×#385C22semidirect
89. C22×C4×D47C2×C4semidirect
94. #13094006C2×C4semidirect
97. C2×C4⋊Dic47C2×C4semidirect
104. C2×Dic47⋊C4C2×C4semidirect
113. C2×C22⋊Dic47C2×C4semidirect
119. C2×(C2×D47)⋊C4C2×C4semidirect
153. C2×C22⋊C4×C47C2×C4semidirect
245. C2×C4×D47C22×C4semidirect
250. C22⋊C4×C47C22×C4semidirect
253. C22⋊Dic47C22×C4semidirect
256. (C2×D47)⋊C4C22×C4semidirect
258. C4⋊Dic47C22×C4semidirect
263. Dic47⋊C4C22×C4semidirect
417. C2×#385D47semidirect
421. C2×C47#2322semidirect
470. #385C2×D47semidirect
483. C47C2×#2322semidirect
553. C2×C22⋊C4C4×D47semidirect
677. C22⋊C4C2×C4×D47semidirect
819. C2#20246055direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940062
C22×C4×C22⋊D472
C22×C4⋊C4×D472
#202460552
C2×#156890202
C2×#156890192
C2×#156890162
C2×#156890112
C2×#156890082
C2×#156890042
C2×#156889992
C2×#156889962
C2×#156889942
C2×#156889852
C2×#156889702
C2×C47×#3852
C2×#232247