Finite Group Databasebeta

← C2×#20246557 #26378899

Subgroups — C2×#20246557 #26378899

Order 12032.

2934 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094010C211yesmaximal, characteristic
2#20246557C2116yesmaximal, direct product factor
3C2×#15689029C211yesmaximal, characteristic, complemented
4C2×#15689027C211yesmaximal, characteristic, complemented
5C2×#15689014C211yesmaximal, characteristic, complemented
6C2×#15689013C211yesmaximal, characteristic, complemented
7C2×#15689011C211yesmaximal, characteristic, complemented
8C2×#15689000C211yesmaximal, characteristic
9C2×#15688999C211yesmaximal, characteristic
10C2×#15688998C211yesmaximal, characteristic, complemented
11C2×#15688997C211yesmaximal, characteristic, complemented
12C2×#15688997C211yesmaximal, characteristic, complemented
13C2×#15688995C211yesmaximal, characteristic, complemented
14C2×#15688988C211yesmaximal, characteristic, complemented
15C2×#15688987C211yesmaximal, characteristic, complemented
16C2×C47×#388C211yesmaximal, characteristic, complemented
17C23×Dic94C2211yescharacteristic
18C23×C22⋊D47C2211yescharacteristic
19C24×Dic47C2211yescharacteristic
20C23×C4×D47C2211yescharacteristic
21C2×#13094010C4116yescomplemented
22C2×#13094010C2218yes—
23C22×C4⋊Dic47C2211yescharacteristic
24C22×C4⋊Dic47C2211yescharacteristic
25C22×Dic47⋊C4C2211yescharacteristic
26C22×Dic47⋊C4C2211yescharacteristic
27C22×Dic47⋊C4C2211yescharacteristic
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×C4×Dic47C2211yescharacteristic
36C22×C4×Dic47C2211yescharacteristic
37#15689029C2218yescomplemented
38#15689027C2218yescomplemented
39#15689014C2218yescomplemented
40#15689013C2218yescomplemented
41#15689011C2218yescomplemented
42#15689000C2218yes—
43#15688999C2218yes—
44#15688998C2218yescomplemented
45#15688997C2218yescomplemented
46#15688997C2218yescomplemented
47#15688995C2218yescomplemented
48#15688988C2218yescomplemented
49#15688987C2218yescomplemented
50C2×C47⋊#95C2211yescharacteristic
51C2×C47⋊#95C2211yescharacteristic
52C2×C47⋊#95C2211yescharacteristic
53C2×C47⋊#95C2211yescharacteristic
54C2×C47⋊#95C2211yescharacteristic
55C2×C47⋊#95C2211yescharacteristic
56C2×C47⋊#95C2211yescharacteristic
57C2×C47⋊#95C2211yescharacteristic
58C2×C47⋊#95C2211yescharacteristic
59C2×C47⋊#95C2211yescharacteristic
60C22×C4⋊C4×C47C2211yescharacteristic
61C22×C22⋊C4×C47C2211yescharacteristic
62C22×C22⋊C4×C47C2211yescharacteristic
63C22×C22⋊C4×C47C2211yescharacteristic
64C22×C42×C47C2211yescharacteristic
65C47×#388C2218yescomplemented
66C2×#95×C47C2211yescharacteristic
67C2×#95×C47C2211yescharacteristic
68C24×D47C2311yescharacteristic
69C22×Dic94—42no—
70C22×Dic94—42no—
71C22×Dic94C2×C418yescomplemented
72C22×Dic94C2314yes—
73C22×C22⋊D47—42no—
74C22×C22⋊D47—42no—
75C22×C22⋊D47C2×C418yes—
76C22×C22⋊D47C2314yes—
77C23×Dic47—42no—
78C23×Dic47—42no—
79C23×Dic47—42no—
80C23×Dic47C2311yescharacteristic
81C23×Dic47C2311yescharacteristic
82C23×Dic47C2311yescharacteristic
83C23×Dic47C2311yescharacteristic
84C23×Dic47C2311yescharacteristic
85C23×Dic47C2311yescharacteristic
86C23×Dic47C2311yescharacteristic
87C23×Dic47C2314yes—
88C22×C4×D47—42no—
89C22×C4×D47—42no—
90C22×C4×D47—42no—
91C22×C4×D47C2314yes—
92#13094010C2×C4164yescomplemented
93C2×C4⋊Dic47—42no—
94C2×C4⋊Dic47—42no—
95C2×C4⋊Dic47C2314yes—
96C2×C4⋊Dic47C2314yes—
97C2×Dic47⋊C4—42no—
98C2×Dic47⋊C4—42no—
99C2×Dic47⋊C4—42no—
100C2×Dic47⋊C4C2314yes—
101C2×Dic47⋊C4C2314yes—
102C2×Dic47⋊C4C2314yes—
103C2×C22⋊Dic47—42no—
104C2×C22⋊Dic47C2×C418yescomplemented
105C2×C22⋊Dic47C2314yes—
106C2×C22⋊Dic47C2314yes—
107C2×(C2×D47)⋊C4—42no—
108C2×(C2×D47)⋊C4—42no—
109C2×(C2×D47)⋊C4—42no—
110C2×(C2×D47)⋊C4C2×C418yescomplemented
111C2×(C2×D47)⋊C4C2×C418yescomplemented
112C2×(C2×D47)⋊C4C2314yes—
113C2×(C2×D47)⋊C4C2314yes—
114C2×(C2×D47)⋊C4C2314yes—
115C2×(C2×D47)⋊C4C2314yes—
116C2×(C2×D47)⋊C4C2314yes—
117C2×C4×Dic47—42no—
118C2×C4×Dic47C2×C418yescomplemented
119C2×C4×Dic47C2314yes—
120C2×C4×Dic47C2314yes—
121C47⋊#95C2314yes—
122C47⋊#95C2314yes—
123C47⋊#95C2314yes—
124C47⋊#95C2314yes—
125C47⋊#95C2314yes—
126C47⋊#95C2314yes—
127C47⋊#95C2314yes—
128C47⋊#95C2314yes—
129C47⋊#95C2314yes—
130C47⋊#95C2314yes—
131C25×C47C2311yescharacteristic
132C23×C4×C47C2311yescharacteristic
133C23×C4×C47C2311yescharacteristic
134C23×C4×C47C2311yescharacteristic
135C23×C4×C47C2311yescharacteristic
136C23×C4×C47C2311yescharacteristic
137C23×C4×C47C2311yescharacteristic
138C2×C4⋊C4×C47—42no—
139C2×C4⋊C4×C47C2314yes—
140C2×C22⋊C4×C47—42no—
141C2×C22⋊C4×C47—42no—
142C2×C22⋊C4×C47C2×C418yescomplemented
143C2×C22⋊C4×C47C2314yes—
144C2×C22⋊C4×C47C2314yes—
145C2×C22⋊C4×C47C2314yes—
146C2×C42×C47—42no—
147C2×C42×C47C2314yes—
148#95×C47C2314yes—
149#95×C47C2314yes—
150C24×C47—22no—
151C24×C47—22no—
152C24×C47—22no—
153C24×C47—22no—
154C24×C47—22no—
155C24×C47—22no—
156C24×C47C22×C414yes—
157C24×C47C2412yes—
158C24×C47C2411yescharacteristic
159C23×D47—22no—
160C23×D47—22no—
161C23×D47—22no—
162C23×D47—22no—
163C23×D47—22no—
164C23×D47—22no—
165C23×D47C22×C414yes—
166C23×D47C2412yes—
167C22×C4×C47—22no—
168C22×C4×C47—22no—
169C22×C4×C47—22no—
170C22×C4×C47—22no—
171C22×C4×C47—22no—
172C22×C4×C47—22no—
173C22×C4×C47—22no—
174C22×C4×C47—22no—
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×C47C22×C414yes—
184C22×C4×C47C22×C414yes—
185C22×C4×C47C2412yes—
186C22×C4×C47C2412yes—
187C22×C4×C47C2412yes—
188C22×C4×C47C2412yes—
189C22×C4×C47C2412yes—
190C22×C4×C47C2412yes—
191C2×C22⋊D47—416no—
192C2×C22⋊D47—44no—
193C2×C22⋊D47—44no—
194C2×C22⋊D47C22×C4116yes—
195C22×Dic47—22no—
196C22×Dic47—22no—
197C22×Dic47—22no—
198C22×Dic47—22no—
199C22×Dic47—22no—
200C22×Dic47—22no—
201C22×Dic47—22no—
202C22×Dic47—22no—
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—44no—
214C22×Dic47—44no—
215C22×Dic47—44no—
216C22×Dic47—416no—
217C22×Dic47C22×C414yes—
218C22×Dic47C22×C414yes—
219C22×Dic47C22×C414yes—
220C22×Dic47C2412yes—
221C22×Dic47C2412yes—
222C22×Dic47C2412yes—
223C22×Dic47C2412yes—
224C22×Dic47C2412yes—
225C22×Dic47C2412yes—
226C22×Dic47C2412yes—
227C2×C4×D47—44no—
228C2×C4×D47—44no—
229C2×C4×D47—44no—
230C2×C4×D47—416no—
231C2×Dic94—416no—
232C2×Dic94—44no—
233C2×Dic94—44no—
234C2×Dic94C22×C4116yescomplemented
235C4⋊C4×C47—44no—
236C22⋊C4×C47—44no—
237C22⋊C4×C47—44no—
238C22⋊C4×C47C22×C4116yescomplemented
239C42×C47—44no—
240C22⋊Dic47—44no—
241C22⋊Dic47C22×C4116yescomplemented
242(C2×D47)⋊C4—44no—
243(C2×D47)⋊C4—44no—
244(C2×D47)⋊C4—44no—
245(C2×D47)⋊C4C22×C4116yescomplemented
246(C2×D47)⋊C4C22×C4116yescomplemented
247C4⋊Dic47—44no—
248C4⋊Dic47—44no—
249Dic47⋊C4—44no—
250Dic47⋊C4—44no—
251Dic47⋊C4—44no—
252C4×Dic47—44no—
253C4×Dic47C22×C4116yescomplemented
254C23×C47—28no—
255C23×C47—28no—
256C23×C47—28no—
257C23×C47—22no—
258C23×C47—22no—
259C23×C47—22no—
260C23×C47—22no—
261C23×C47—22no—
262C23×C47—22no—
263C23×C47—44no—
264C23×C47—44no—
265C23×C47—44no—
266C23×C47—44no—
267C23×C47C23×C414yes—
268C23×C47C23×C412yes—
269C23×C47H(5,𝔽2)12yes—
270C23×C47H(5,𝔽2)12yes—
271C23×C47H(5,𝔽2)12yes—
272C23×C47H(5,𝔽2)12yes—
273C23×C472−1+412yes—
274C23×C472−1+412yes—
275C23×C47C2511yescharacteristic
276C22×D47—28no—
277C22×D47—28no—
278C22×D47—28no—
279C22×D47—22no—
280C22×D47—22no—
281C22×D47—22no—
282C22×D47—22no—
283C22×D47—22no—
284C22×D47—22no—
285C22×D47—44no—
286C22×D47—44no—
287C22×D47—44no—
288C22×D47—44no—
289C22×D47C23×C414yes—
290C2×C4×C47—28no—
291C2×C4×C47—28no—
292C2×C4×C47—22no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—22no—
299C2×C4×C47—22no—
300C2×C4×C47—22no—
301C2×C4×C47—22no—
302C2×C4×C47—22no—
303C2×C4×C47—22no—
304C2×C4×C47—22no—
305C2×C4×C47—22no—
306C2×C4×C47—22no—
307C2×C4×C47—22no—
308C2×C4×C47—44no—
309C2×C4×C47—44no—
310C2×C4×C47—44no—
311C2×C4×C47—44no—
312C2×C4×C47C23×C414yes—
313C2×C4×C47C23×C414yes—
314C22⋊D47—416no—
315C2×Dic47—28no—
316C2×Dic47—28no—
317C2×Dic47—28no—
318C2×Dic47—22no—
319C2×Dic47—22no—
320C2×Dic47—22no—
321C2×Dic47—22no—
322C2×Dic47—22no—
323C2×Dic47—22no—
324C2×Dic47—22no—
325C2×Dic47—22no—
326C2×Dic47—22no—
327C2×Dic47—22no—
328C2×Dic47—22no—
329C2×Dic47—22no—
330C2×Dic47—22no—
331C2×Dic47—22no—
332C2×Dic47—22no—
333C2×Dic47—22no—
334C2×Dic47—22no—
335C2×Dic47—22no—
336C2×Dic47—416no—
337C2×Dic47—44no—
338C2×Dic47—44no—
339C2×Dic47—44no—
340C2×Dic47—44no—
341C2×Dic47C23×C414yes—
342C2×Dic47C23×C414yes—
343C2×Dic47C23×C414yes—
344C4×D47—416no—
345Dic94—416no—
346C2×#2379—471nomaximal, Sylow
347C22×C47—24no—
348C22×C47—24no—
349C22×C47—24no—
350C22×C47—416no—
351C22×C47—42no—
352C22×C47—42no—
353C22×C47—42no—
354C22×C47—42no—
355C22×C47#51814yes—
356C22×C47#52014yes—
357C22×C47#52014yes—
358C22×C47H(3,𝔽4)14yes—
359C22×C47#56214yes—
360C22×C47#56214yes—
361C22×C47#56314yes—
362C22×C47C24×C411yescharacteristic
363C22×C47C2×H(5,𝔽2)11yescharacteristic
364C22×C47C2×H(5,𝔽2)11yescharacteristic
365C22×C47C2×H(5,𝔽2)11yescharacteristic
366C22×C47C2×H(5,𝔽2)11yescharacteristic
367C22×C47C2×2−1+411yescharacteristic
368C22×C47C2×2−1+411yescharacteristic
369C2×D47—24no—
370C2×D47—24no—
371C2×D47—24no—
372C2×D47—416no—
373C2×D47—42no—
374C2×D47—42no—
375C2×D47—42no—
376C2×D47—42no—
377C4×C47—24no—
378C4×C47—24no—
379C4×C47—42no—
380C4×C47—42no—
381C4×C47—42no—
382C4×C47—42no—
383Dic47—24no—
384Dic47—24no—
385Dic47—24no—
386Dic47—42no—
387Dic47—42no—
388Dic47—42no—
389Dic47—42no—
390C22×#124—471no—
391#2379—4716no—
392C2×#391—471no—
393C2×#391—471no—
394C2×#388—471no—
395C2×#388—471no—
396C2×#388—471no—
397C2×#388D4711yescharacteristic, complemented
398C2×#386—471no—
399C2×#386—471no—
400C2×#385—471no—
401C2×#385—471no—
402C2×#385—471no—
403C2×#385—471no—
404C2×#382—471no—
405C2×#382—471no—
406C2×C47—44no—
407C2×C47#237918yescomplemented
408C2×C47C2×#51811yescharacteristic
409C2×C47C2×#52011yescharacteristic
410C2×C47C2×#52011yescharacteristic
411C2×C47C2×H(3,𝔽4)11yescharacteristic
412C2×C47C2×#56211yescharacteristic
413C2×C47C2×#56211yescharacteristic
414C2×C47C2×#56311yescharacteristic
415D47—44no—
416C23×Q8—471no—
417C23×D4—471no—
418C24×C4—471no—
419C24×C4—471no—
420C2×#124—4716no—
421C2×#124—478no—
422C22×C4⋊C4—471no—
423C22×C4⋊C4—471no—
424C22×C4⋊C4—471no—
425C22×C4⋊C4—471no—
426C22×C4⋊C4—471no—
427C22×C4⋊C4C2×D4711yescharacteristic
428C22×C22⋊C4—471no—
429C22×C22⋊C4—471no—
430C22×C22⋊C4—471no—
431C22×C22⋊C4—471no—
432C22×C22⋊C4—471no—
433C22×C22⋊C4—471no—
434C22×C22⋊C4—471no—
435C22×C22⋊C4C2×D4711yescharacteristic
436C22×C22⋊C4C2×D4711yescharacteristic
437C22×C22⋊C4C2×D4711yescharacteristic
438C22×C42—471no—
439C22×C42—471no—
440C22×C42C2×D4711yescharacteristic
441#391—478no—
442#391—478no—
443#388—478no—
444#388—478no—
445#388—478no—
446#388C2×D4718yescomplemented
447#386—478no—
448#386—478no—
449#385—478no—
450#385—478no—
451#385—478no—
452#385—478no—
453#382—478no—
454#382—478no—
455C2×#95—471no—
456C2×#95—471no—
457C2×#95—471no—
458C2×#95—471no—
459C2×#95—471no—
460C2×#95—471no—
461C2×#95—471no—
462C2×#95—471no—
463C2×#95—471no—
464C2×#95—471no—
465C2×#95C2×D4711yescharacteristic
466C2×#95C2×D4711yescharacteristic
467C47C2×#237911yescharacteristic, complemented, Sylow
468C25—471no—
469C25C22×D4711yescharacteristic
470C22×Q8—478no—
471C22×Q8—474no—
472C22×Q8—1882no—
473C22×Q8—1882no—
474C22×D4—478no—
475C22×D4—474no—
476C22×D4—1882no—
477C22×D4—1882no—
478C23×C4—471no—
479C23×C4—471no—
480C23×C4—471no—
481C23×C4—471no—
482C23×C4—471no—
483C23×C4—471no—
484C23×C4—471no—
485C23×C4—474no—
486C23×C4—474no—
487C23×C4—1882no—
488C23×C4—1882no—
489C23×C4—1882no—
490C23×C4—1882no—
491C23×C4—1882no—
492C23×C4—1882no—
493C23×C4C22×D4711yescharacteristic
494C23×C4C22×D4711yescharacteristic
495C23×C4C22×D4711yescharacteristic
496C23×C4C22×D4711yescharacteristic
497C23×C4C22×D4711yescharacteristic
498C23×C4C22×D4711yescharacteristic
499#124—4764no—
500C2×C4⋊C4—42no—
501C2×C4⋊C4—474no—
502C2×C4⋊C4—474no—
503C2×C4⋊C4—474no—
504C2×C4⋊C4—474no—
505C2×C4⋊C4—474no—
506C2×C4⋊C4—1882no—
507C2×C4⋊C4—1882no—
508C2×C4⋊C4—1882no—
509C2×C4⋊C4—1882no—
510C2×C4⋊C4—1882no—
511C2×C4⋊C4C22×D4714yes—
512C2×C22⋊C4—42no—
513C2×C22⋊C4—42no—
514C2×C22⋊C4—478no—
515C2×C22⋊C4—474no—
516C2×C22⋊C4—478no—
517C2×C22⋊C4—478no—
518C2×C22⋊C4—474no—
519C2×C22⋊C4—474no—
520C2×C22⋊C4—474no—
521C2×C22⋊C4—474no—
522C2×C22⋊C4—474no—
523C2×C22⋊C4—474no—
524C2×C22⋊C4—1882no—
525C2×C22⋊C4—1882no—
526C2×C22⋊C4—1882no—
527C2×C22⋊C4—1882no—
528C2×C22⋊C4C4×D4718yescomplemented
529C2×C22⋊C4C22×D4714yes—
530C2×C22⋊C4C22×D4714yes—
531C2×C22⋊C4C22×D4714yes—
532C2×C42—42no—
533C2×C42—478no—
534C2×C42—474no—
535C2×C42—474no—
536C2×C42—1882no—
537C2×C42C22×D4714yes—
538#95—474no—
539#95—474no—
540#95—474no—
541#95—474no—
542#95—474no—
543#95—474no—
544#95—474no—
545#95—474no—
546#95—474no—
547#95—474no—
548#95C22×D4714yes—
549#95C22×D4714yes—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—474no—
557C24—472no—
558C24—942no—
559C24—942no—
560C24—942no—
561C24—942no—
562C24—942no—
563C24—942no—
564C24C2×C4×D4714yes—
565C24C23×D4712yes—
566C24C23×D4711yescharacteristic
567C2×Q8—4716no—
568C2×Q8—18816no—
569C2×Q8—1884no—
570C2×Q8—1884no—
571C2×D4—4716no—
572C2×D4—18816no—
573C2×D4—1884no—
574C2×D4—1884no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—474no—
592C22×C4—474no—
593C22×C4—474no—
594C22×C4—472no—
595C22×C4—472no—
596C22×C4—472no—
597C22×C4—472no—
598C22×C4—472no—
599C22×C4—472no—
600C22×C4—472no—
601C22×C4—942no—
602C22×C4—942no—
603C22×C4—942no—
604C22×C4—942no—
605C22×C4—942no—
606C22×C4—942no—
607C22×C4—942no—
608C22×C4—942no—
609C22×C4—942no—
610C22×C4—942no—
611C22×C4—942no—
612C22×C4—942no—
613C22×C4—942no—
614C22×C4—942no—
615C22×C4—942no—
616C22×C4—942no—
617C22×C4—942no—
618C22×C4—942no—
619C22×C4—1884no—
620C22×C4—1884no—
621C22×C4—1884no—
622C22×C4—18816no—
623C22×C4—1884no—
624C22×C4—1884no—
625C22×C4—1884no—
626C22×C4—18816no—
627C22×C4C2×C4×D4714yes—
628C22×C4C2×C4×D4714yes—
629C22×C4C23×D4712yes—
630C22×C4C23×D4712yes—
631C22×C4C23×D4712yes—
632C22×C4C23×D4712yes—
633C22×C4C23×D4712yes—
634C22×C4C23×D4712yes—
635C4⋊C4—44no—
636C4⋊C4—1884no—
637C4⋊C4—1884no—
638C4⋊C4—1884no—
639C4⋊C4—1884no—
640C4⋊C4—1884no—
641C22⋊C4—44no—
642C22⋊C4—44no—
643C22⋊C4—4716no—
644C22⋊C4—4716no—
645C22⋊C4—4716no—
646C22⋊C4—1884no—
647C22⋊C4—1884no—
648C22⋊C4—1884no—
649C22⋊C4—1884no—
650C22⋊C4C2×C4×D47116yescomplemented
651C42—44no—
652C42—4716no—
653C42—1884no—
654C23—28no—
655C23—28no—
656C23—28no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—474no—
668C23—948no—
669C23—948no—
670C23—948no—
671C23—942no—
672C23—942no—
673C23—942no—
674C23—942no—
675C23—942no—
676C23—942no—
677C23—1884no—
678C23—1884no—
679C23—1884no—
680C23—1884no—
681C23C22×C4×D4714yes—
682C23C22×C4×D4712yes—
683C23#1309406912yes—
684C23#1309406912yes—
685C23#1309407012yes—
686C23#1309407012yes—
687C23#1309407112yes—
688C23#1309407112yes—
689C23C24×D4711yescharacteristic
690Q8—18816no—
691D4—18816no—
692C2×C4—28no—
693C2×C4—28no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—474no—
715C2×C4—474no—
716C2×C4—474no—
717C2×C4—948no—
718C2×C4—948no—
719C2×C4—948no—
720C2×C4—942no—
721C2×C4—942no—
722C2×C4—942no—
723C2×C4—942no—
724C2×C4—942no—
725C2×C4—942no—
726C2×C4—942no—
727C2×C4—942no—
728C2×C4—942no—
729C2×C4—942no—
730C2×C4—942no—
731C2×C4—942no—
732C2×C4—942no—
733C2×C4—942no—
734C2×C4—942no—
735C2×C4—942no—
736C2×C4—942no—
737C2×C4—942no—
738C2×C4—18816no—
739C2×C4—18816no—
740C2×C4—1884no—
741C2×C4—1884no—
742C2×C4—1884no—
743C2×C4—1884no—
744C2×C4C22×C4×D4714yes—
745C2×C4C22×C4×D4714yes—
746C22—24no—
747C22—24no—
748C22—24no—
749C22—416no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—944no—
755C22—944no—
756C22—944no—
757C22—18816no—
758C22—1882no—
759C22—1882no—
760C22—1882no—
761C22—1882no—
762C22#1568959514yes—
763C22#1568960214yes—
764C22#1568960314yes—
765C22#1568986514yes—
766C22#1568986814yes—
767C22#1568987014yes—
768C22#1568987514yes—
769C22C23×C4×D4711yescharacteristic
770C22C2×#1309406911yescharacteristic
771C22C2×#1309406911yescharacteristic
772C22C2×#1309407011yescharacteristic
773C22C2×#1309407011yescharacteristic
774C22C2×#1309407111yescharacteristic
775C22C2×#1309407111yescharacteristic
776C4—24no—
777C4—24no—
778C4—42no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—944no—
783C4—944no—
784C4—944no—
785C4—1882no—
786C4—1882no—
787C4—1882no—
788C4—1882no—
789C2—44no—
790C2—1884no—
791C2#2024655718yesdirect product factor
792C2C2×#1568959511yescharacteristic
793C2C2×#1568960211yescharacteristic
794C2C2×#1568960311yescharacteristic
795C2C2×#1568986511yescharacteristic
796C2C2×#1568986811yescharacteristic
797C2C2×#1568987011yescharacteristic
798C2C2×#1568987511yescharacteristic
subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C47×#388C2
socleC24×C47C24
prime radicalC23×C22⋊D47C22
cosocleC23×C47C25
hypercenterC2×#388D47
hypocenterC47C2×#2379
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. #20246557C2direct (N × H)
3. C2×#15689029C2semidirect
4. C2×#15689027C2semidirect
5. C2×#15689014C2semidirect
6. C2×#15689013C2semidirect
7. C2×#15689011C2semidirect
10. C2×#15688998C2semidirect
11. C2×#15688997C2semidirect
12. C2×#15688997C2semidirect
13. C2×#15688995C2semidirect
14. C2×#15688988C2semidirect
15. C2×#15688987C2semidirect
16. C2×C47×#388C2semidirect
21. C2×#13094010C4semidirect
37. #15689029C22semidirect
38. #15689027C22semidirect
39. #15689014C22semidirect
40. #15689013C22semidirect
41. #15689011C22semidirect
44. #15688998C22semidirect
45. #15688997C22semidirect
46. #15688997C22semidirect
47. #15688995C22semidirect
48. #15688988C22semidirect
49. #15688987C22semidirect
65. C47×#388C22semidirect
71. C22×Dic94C2×C4semidirect
92. #13094010C2×C4semidirect
104. C2×C22⋊Dic47C2×C4semidirect
110. C2×(C2×D47)⋊C4C2×C4semidirect
111. C2×(C2×D47)⋊C4C2×C4semidirect
118. C2×C4×Dic47C2×C4semidirect
142. C2×C22⋊C4×C47C2×C4semidirect
234. C2×Dic94C22×C4semidirect
238. C22⋊C4×C47C22×C4semidirect
241. C22⋊Dic47C22×C4semidirect
245. (C2×D47)⋊C4C22×C4semidirect
246. (C2×D47)⋊C4C22×C4semidirect
253. C4×Dic47C22×C4semidirect
397. C2×#388D47semidirect
407. C2×C47#2379semidirect
446. #388C2×D47semidirect
467. C47C2×#2379semidirect
528. C2×C22⋊C4C4×D47semidirect
650. C22⋊C4C2×C4×D47semidirect
791. C2#20246557direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940102
#202465572
C2×#156890292
C2×#156890272
C2×#156890142
C2×#156890132
C2×#156890112
C2×#156890002
C2×#156889992
C2×#156889982
C2×#156889972
C2×#156889952
C2×#156889882
C2×#156889872
C2×C47×#3882
C2×#237947