Finite Group Databasebeta

← C2×#20246171 #26375165

Subgroups — C2×#20246171 #26375165

Order 12032.

2982 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094008C211yesmaximal, characteristic
2#20246171C2116yesmaximal, direct product factor
3C2×#15689023C211yesmaximal, characteristic
4C2×#15689021C211yesmaximal, characteristic, complemented
5C2×#15689016C211yesmaximal, characteristic, complemented
6C2×#15689015C211yesmaximal, characteristic, complemented
7C2×#15689012C211yesmaximal, characteristic, complemented
8C2×#15689008C211yesmaximal, characteristic, complemented
9C2×#15689006C211yesmaximal, characteristic, complemented
10C2×#15688999C211yesmaximal, characteristic
11C2×#15688994C211yesmaximal, characteristic, complemented
12C2×#15688981C211yesmaximal, characteristic, complemented
13C2×C4⋊C4×Dic47C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic47C211yesmaximal, characteristic, complemented
15C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
16C2×C47×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D47C2211yescharacteristic
18C24×Dic47C2211yescharacteristic
19C23×C4×D47C2211yescharacteristic
20C2×#13094008C4116yescomplemented
21C2×#13094008C2218yes—
22C22×C4⋊Dic47C2211yescharacteristic
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
37C22×C4×Dic47C2211yescharacteristic
38C22×C4×Dic47C2211yescharacteristic
39#15689023C2218yes—
40#15689021C2218yescomplemented
41#15689016C2218yescomplemented
42#15689015C2218yescomplemented
43#15689012C2218yescomplemented
44#15689008C2218yescomplemented
45#15689006C2218yescomplemented
46#15688999C2218yes—
47#15688994C2218yescomplemented
48#15688981C2218yescomplemented
49C4⋊C4×Dic47C2218yescomplemented
50C22⋊C4×Dic47C2218yescomplemented
51C4×(C2×D47)⋊C4C2218yescomplemented
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×C22⋊D47—42no—
70C22×C22⋊D47—42no—
71C22×C22⋊D47C2×C418yes—
72C22×C22⋊D47C2314yes—
73C23×Dic47—42no—
74C23×Dic47—42no—
75C23×Dic47C2×C418yescomplemented
76C23×Dic47C2311yescharacteristic
77C23×Dic47C2311yescharacteristic
78C23×Dic47C2311yescharacteristic
79C23×Dic47C2311yescharacteristic
80C23×Dic47C2311yescharacteristic
81C23×Dic47C2311yescharacteristic
82C23×Dic47C2311yescharacteristic
83C23×Dic47C2314yes—
84C22×C4×D47—24no—
85C22×C4×D47—42no—
86C22×C4×D47—42no—
87C22×C4×D47C2314yes—
88#13094008C2×C4164yescomplemented
89C2×C4⋊Dic47—42no—
90C2×C4⋊Dic47C2×C418yescomplemented
91C2×C4⋊Dic47C2×C418yescomplemented
92C2×C4⋊Dic47C2314yes—
93C2×C4⋊Dic47C2314yes—
94C2×C4⋊Dic47C2314yes—
95C2×Dic47⋊C4—42no—
96C2×Dic47⋊C4—42no—
97C2×Dic47⋊C4—42no—
98C2×Dic47⋊C4C2314yes—
99C2×Dic47⋊C4C2314yes—
100C2×Dic47⋊C4C2314yes—
101C2×C22⋊Dic47—24no—
102C2×C22⋊Dic47—42no—
103C2×C22⋊Dic47C2314yes—
104C2×C22⋊Dic47C2314yes—
105C2×(C2×D47)⋊C4—24no—
106C2×(C2×D47)⋊C4—42no—
107C2×(C2×D47)⋊C4—42no—
108C2×(C2×D47)⋊C4C2×C418yes—
109C2×(C2×D47)⋊C4C2×C418yes—
110C2×(C2×D47)⋊C4C2314yes—
111C2×(C2×D47)⋊C4C2314yes—
112C2×(C2×D47)⋊C4C2314yes—
113C2×(C2×D47)⋊C4C2314yes—
114C2×(C2×D47)⋊C4C2314yes—
115C2×C4×Dic47—24no—
116C2×C4×Dic47—42no—
117C2×C4×Dic47—42no—
118C2×C4×Dic47—42no—
119C2×C4×Dic47C2314yes—
120C2×C4×Dic47C2314yes—
121C2×C4×Dic47C2314yes—
122C2×C4×Dic47C2314yes—
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—24no—
139C2×C4⋊C4×C47C2314yes—
140C2×C22⋊C4×C47—24no—
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×C47C22×C414yes—
183C22×C4×C47C22×C414yes—
184C22×C4×C47#4114yes—
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—416no—
213C22×Dic47—44no—
214C22×Dic47—44no—
215C22×Dic47C22×C414yes—
216C22×Dic47C22×C414yes—
217C22×Dic47C22×C414yes—
218C22×Dic47C22×C4116yescomplemented
219C22×Dic47#4114yes—
220C22×Dic47C2412yes—
221C22×Dic47C2412yes—
222C22×Dic47C2412yes—
223C22×Dic47C2412yes—
224C22×Dic47C2412yes—
225C22×Dic47C2412yes—
226C22×Dic47C2412yes—
227C2×C4×D47—28no—
228C2×C4×D47—44no—
229C2×C4×D47—44no—
230C2×C4×D47—416no—
231C4⋊C4×C47—28no—
232C22⋊C4×C47—28no—
233C22⋊C4×C47—44no—
234C22⋊C4×C47C22×C4116yescomplemented
235C42×C47—44no—
236C22⋊Dic47—28no—
237C22⋊Dic47—44no—
238(C2×D47)⋊C4—28no—
239(C2×D47)⋊C4—44no—
240(C2×D47)⋊C4—44no—
241(C2×D47)⋊C4C22×C4116yes—
242(C2×D47)⋊C4C22×C4116yes—
243C4⋊Dic47—44no—
244C4⋊Dic47C22×C4116yescomplemented
245C4⋊Dic47C22×C4116yescomplemented
246Dic47⋊C4—44no—
247Dic47⋊C4—44no—
248Dic47⋊C4—44no—
249C4×Dic47—28no—
250C4×Dic47—44no—
251C4×Dic47—44no—
252C4×Dic47—44no—
253C23×C47—28no—
254C23×C47—28no—
255C23×C47—28no—
256C23×C47—22no—
257C23×C47—22no—
258C23×C47—22no—
259C23×C47—22no—
260C23×C47—22no—
261C23×C47—22no—
262C23×C47—44no—
263C23×C47—44no—
264C23×C47—44no—
265C23×C47—44no—
266C23×C47C23×C414yes—
267C23×C47C23×C412yes—
268C23×C47C2×#4112yes—
269C23×C47C2×#4112yes—
270C23×C47H(5,𝔽2)12yes—
271C23×C47H(5,𝔽2)12yes—
272C23×C47H(5,𝔽2)12yes—
273C23×C472−1+412yes—
274C23×C47C2511yescharacteristic
275C22×D47—28no—
276C22×D47—28no—
277C22×D47—28no—
278C22×D47—22no—
279C22×D47—22no—
280C22×D47—22no—
281C22×D47—22no—
282C22×D47—22no—
283C22×D47—22no—
284C22×D47—44no—
285C22×D47—44no—
286C22×D47—44no—
287C22×D47—44no—
288C22×D47C23×C414yes—
289C2×C4×C47—28no—
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—44no—
308C2×C4×C47—44no—
309C2×C4×C47—44no—
310C2×C4×C47C23×C414yes—
311C2×C4×C47C23×C414yes—
312C2×C4×C47C2×#4114yes—
313C22⋊D47—416no—
314C2×Dic47—28no—
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—416no—
336C2×Dic47—44no—
337C2×Dic47—44no—
338C2×Dic47—44no—
339C2×Dic47C23×C414yes—
340C2×Dic47C23×C414yes—
341C2×Dic47C23×C414yes—
342C2×Dic47C2×#4114yes—
343C4×D47—416no—
344C2×#2335—471nomaximal, Sylow
345C22×C47—24no—
346C22×C47—24no—
347C22×C47—24no—
348C22×C47—416no—
349C22×C47—42no—
350C22×C47—42no—
351C22×C47—42no—
352C22×C47—42no—
353C22×C47C4×#4114yes—
354C22×C47#51814yes—
355C22×C47#52014yes—
356C22×C47#53814yes—
357C22×C47#53914yes—
358C22×C47#54014yes—
359C22×C47#54214yes—
360C22×C47C24×C411yescharacteristic
361C22×C47C22×#4111yescharacteristic
362C22×C47C22×#4111yescharacteristic
363C22×C47C2×H(5,𝔽2)11yescharacteristic
364C22×C47C2×H(5,𝔽2)11yescharacteristic
365C22×C47C2×H(5,𝔽2)11yescharacteristic
366C22×C47C2×2−1+411yescharacteristic
367C2×D47—24no—
368C2×D47—24no—
369C2×D47—24no—
370C2×D47—416no—
371C2×D47—42no—
372C2×D47—42no—
373C2×D47—42no—
374C2×D47—42no—
375C4×C47—24no—
376C4×C47—24no—
377C4×C47—24no—
378C4×C47—42no—
379C4×C47—42no—
380C4×C47—42no—
381Dic47—24no—
382Dic47—24no—
383Dic47—24no—
384Dic47—24no—
385Dic47—42no—
386Dic47—42no—
387Dic47—42no—
388C22×#123—471no—
389#2335—4716no—
390C2×#390—471no—
391C2×#389—471no—
392C2×#388—471no—
393C2×#388—471no—
394C2×#388—471no—
395C2×#388D4711yescharacteristic, complemented
396C2×#387—471no—
397C2×#387—471no—
398C2×#386—471no—
399C2×#385—471no—
400C2×#380—471no—
401C2×C4×C4⋊C4—471no—
402C2×C4×C22⋊C4—471no—
403C2×C4×C22⋊C4—471no—
404C2×C47—44no—
405C2×C47#233518yescomplemented
406C2×C47C2×C4×#4111yescharacteristic
407C2×C47C2×#51811yescharacteristic
408C2×C47C2×#52011yescharacteristic
409C2×C47C2×#53811yescharacteristic
410C2×C47C2×#53911yescharacteristic
411C2×C47C2×#54011yescharacteristic
412C2×C47C2×#54211yescharacteristic
413D47—44no—
414C23×D4—471no—
415C24×C4—471no—
416C24×C4—471no—
417C2×#123—4716no—
418C2×#123—478no—
419C22×C4⋊C4—471no—
420C22×C4⋊C4—471no—
421C22×C4⋊C4—471no—
422C22×C4⋊C4—471no—
423C22×C4⋊C4—471no—
424C22×C4⋊C4—471no—
425C22×C4⋊C4C2×D4711yescharacteristic
426C22×C22⋊C4—471no—
427C22×C22⋊C4—471no—
428C22×C22⋊C4—471no—
429C22×C22⋊C4—471no—
430C22×C22⋊C4—471no—
431C22×C22⋊C4—471no—
432C22×C22⋊C4—471no—
433C22×C22⋊C4C2×D4711yescharacteristic
434C22×C22⋊C4C2×D4711yescharacteristic
435C22×C22⋊C4C2×D4711yescharacteristic
436C22×C42—471no—
437C22×C42—471no—
438C22×C42—471no—
439C22×C42—471no—
440C22×C42C2×D4711yescharacteristic
441#390—478no—
442#389—478no—
443#388—478no—
444#388—478no—
445#388—478no—
446#388C2×D4718yescomplemented
447#387—478no—
448#387—478no—
449#386—478no—
450#385—478no—
451#380—478no—
452C4×C4⋊C4—478no—
453C4×C22⋊C4—478no—
454C4×C22⋊C4—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×#95C2×D4711yescharacteristic
464C2×#95C2×D4711yescharacteristic
465C47C2×#233511yescharacteristic, complemented, Sylow
466C25—471no—
467C25C22×D4711yescharacteristic
468C22×D4—478no—
469C22×D4—474no—
470C22×D4—1882no—
471C22×D4—1882no—
472C23×C4—471no—
473C23×C4—471no—
474C23×C4—471no—
475C23×C4—471no—
476C23×C4—478no—
477C23×C4—474no—
478C23×C4—471no—
479C23×C4—471no—
480C23×C4—471no—
481C23×C4—474no—
482C23×C4—944no—
483C23×C4—1882no—
484C23×C4—1882no—
485C23×C4—1882no—
486C23×C4—1882no—
487C23×C4C22×D4711yescharacteristic
488C23×C4C22×D4711yescharacteristic
489C23×C4C22×D4711yescharacteristic
490C23×C4C22×D4711yescharacteristic
491C23×C4C22×D4711yescharacteristic
492C23×C4C22×D4711yescharacteristic
493#123—4764no—
494C2×C4⋊C4—24no—
495C2×C4⋊C4—478no—
496C2×C4⋊C4—478no—
497C2×C4⋊C4—474no—
498C2×C4⋊C4—474no—
499C2×C4⋊C4—474no—
500C2×C4⋊C4—474no—
501C2×C4⋊C4—474no—
502C2×C4⋊C4—474no—
503C2×C4⋊C4—1882no—
504C2×C4⋊C4—1882no—
505C2×C4⋊C4—1882no—
506C2×C4⋊C4—1882no—
507C2×C4⋊C4C22×D4714yes—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—42no—
510C2×C22⋊C4—478no—
511C2×C22⋊C4—478no—
512C2×C22⋊C4—474no—
513C2×C22⋊C4—474no—
514C2×C22⋊C4—474no—
515C2×C22⋊C4—474no—
516C2×C22⋊C4—474no—
517C2×C22⋊C4—474no—
518C2×C22⋊C4—474no—
519C2×C22⋊C4—944no—
520C2×C22⋊C4—944no—
521C2×C22⋊C4—1882no—
522C2×C22⋊C4—1882no—
523C2×C22⋊C4—1882no—
524C2×C22⋊C4C4×D4718yescomplemented
525C2×C22⋊C4C22×D4714yes—
526C2×C22⋊C4C22×D4714yes—
527C2×C22⋊C4C22×D4714yes—
528C2×C42—42no—
529C2×C42—474no—
530C2×C42—474no—
531C2×C42—474no—
532C2×C42—474no—
533C2×C42—944no—
534C2×C42—1882no—
535C2×C42—1882no—
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#95C22×D4714yes—
547#95C22×D4714yes—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—474no—
555C24—472no—
556C24—942no—
557C24—942no—
558C24—942no—
559C24—942no—
560C24—942no—
561C24—942no—
562C24C2×C4×D4714yes—
563C24C23×D4712yes—
564C24C23×D4711yescharacteristic
565C2×D4—4716no—
566C2×D4—18816no—
567C2×D4—1884no—
568C2×D4—1884no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
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—474no—
585C22×C4—474no—
586C22×C4—474no—
587C22×C4—474no—
588C22×C4—472no—
589C22×C4—472no—
590C22×C4—472no—
591C22×C4—472no—
592C22×C4—4716no—
593C22×C4—472no—
594C22×C4—472no—
595C22×C4—472no—
596C22×C4—942no—
597C22×C4—942no—
598C22×C4—942no—
599C22×C4—942no—
600C22×C4—942no—
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—948no—
614C22×C4—1884no—
615C22×C4—1884no—
616C22×C4—18816no—
617C22×C4—18816no—
618C22×C4—1884no—
619C22×C4—1884no—
620C22×C4C2×C4×D4714yes—
621C22×C4C2×C4×D4714yes—
622C22×C4#1062535214yes—
623C22×C4C23×D4712yes—
624C22×C4C23×D4712yes—
625C22×C4C23×D4712yes—
626C22×C4C23×D4712yes—
627C22×C4C23×D4712yes—
628C22×C4C23×D4712yes—
629C4⋊C4—28no—
630C4⋊C4—4716no—
631C4⋊C4—4716no—
632C4⋊C4—1884no—
633C4⋊C4—1884no—
634C4⋊C4—1884no—
635C4⋊C4—1884no—
636C22⋊C4—28no—
637C22⋊C4—44no—
638C22⋊C4—4716no—
639C22⋊C4—4716no—
640C22⋊C4—948no—
641C22⋊C4—948no—
642C22⋊C4—1884no—
643C22⋊C4—1884no—
644C22⋊C4—1884no—
645C22⋊C4C2×C4×D47116yescomplemented
646C42—44no—
647C42—948no—
648C42—1884no—
649C42—1884no—
650C42—1884no—
651C23—28no—
652C23—28no—
653C23—28no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—474no—
665C23—948no—
666C23—948no—
667C23—948no—
668C23—942no—
669C23—942no—
670C23—942no—
671C23—942no—
672C23—942no—
673C23—942no—
674C23—1884no—
675C23—1884no—
676C23—1884no—
677C23—1884no—
678C23C22×C4×D4714yes—
679C23C22×C4×D4712yes—
680C23#41×D4712yes—
681C23C2×#1062535212yes—
682C23#1309406912yes—
683C23#1309407012yes—
684C23#1309407012yes—
685C23#1309407112yes—
686C23C24×D4711yescharacteristic
687D4—18816no—
688C2×C4—28no—
689C2×C4—28no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—28no—
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—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—474no—
710C2×C4—474no—
711C2×C4—474no—
712C2×C4—474no—
713C2×C4—948no—
714C2×C4—948no—
715C2×C4—948no—
716C2×C4—942no—
717C2×C4—942no—
718C2×C4—942no—
719C2×C4—942no—
720C2×C4—942no—
721C2×C4—942no—
722C2×C4—942no—
723C2×C4—942no—
724C2×C4—948no—
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—18816no—
735C2×C4—18816no—
736C2×C4—1884no—
737C2×C4—1884no—
738C2×C4—1884no—
739C2×C4C22×C4×D4714yes—
740C2×C4C22×C4×D4714yes—
741C2×C4C2×#1062535214yes—
742C22—24no—
743C22—24no—
744C22—24no—
745C22—416no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—944no—
751C22—944no—
752C22—944no—
753C22—18816no—
754C22—1882no—
755C22—1882no—
756C22—1882no—
757C22—1882no—
758C22C4×#1062535214yes—
759C22#1568959714yes—
760C22#1568960214yes—
761C22#1568971014yes—
762C22#1568971414yes—
763C22#1568972514yes—
764C22#1568974214yes—
765C22C23×C4×D4711yescharacteristic
766C22C2×#41×D4711yescharacteristic
767C22C22×#1062535211yescharacteristic
768C22C2×#1309406911yescharacteristic
769C22C2×#1309407011yescharacteristic
770C22C2×#1309407011yescharacteristic
771C22C2×#1309407111yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—944no—
779C4—944no—
780C4—944no—
781C4—944no—
782C4—1882no—
783C4—1882no—
784C4—1882no—
785C2—44no—
786C2—1884no—
787C2#2024617118yesdirect product factor
788C2C2×C4×#1062535211yescharacteristic
789C2C2×#1568959711yescharacteristic
790C2C2×#1568960211yescharacteristic
791C2C2×#1568971011yescharacteristic
792C2C2×#1568971411yescharacteristic
793C2C2×#1568972511yescharacteristic
794C2C2×#1568974211yescharacteristic
subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C47×#388C2
socleC24×C47C24
prime radicalC23×C22⋊D47C22
cosocleC23×C47C25
hypercenterC2×#388D47
hypocenterC47C2×#2335
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. #20246171C2direct (N × H)
4. C2×#15689021C2semidirect
5. C2×#15689016C2semidirect
6. C2×#15689015C2semidirect
7. C2×#15689012C2semidirect
8. C2×#15689008C2semidirect
9. C2×#15689006C2semidirect
11. C2×#15688994C2semidirect
12. C2×#15688981C2semidirect
13. C2×C4⋊C4×Dic47C2semidirect
14. C2×C22⋊C4×Dic47C2semidirect
15. C2×C4×(C2×D47)⋊C4C2semidirect
16. C2×C47×#388C2semidirect
20. C2×#13094008C4semidirect
40. #15689021C22semidirect
41. #15689016C22semidirect
42. #15689015C22semidirect
43. #15689012C22semidirect
44. #15689008C22semidirect
45. #15689006C22semidirect
47. #15688994C22semidirect
48. #15688981C22semidirect
49. C4⋊C4×Dic47C22semidirect
50. C22⋊C4×Dic47C22semidirect
51. C4×(C2×D47)⋊C4C22semidirect
65. C47×#388C22semidirect
75. C23×Dic47C2×C4semidirect
88. #13094008C2×C4semidirect
90. C2×C4⋊Dic47C2×C4semidirect
91. C2×C4⋊Dic47C2×C4semidirect
142. C2×C22⋊C4×C47C2×C4semidirect
218. C22×Dic47C22×C4semidirect
234. C22⋊C4×C47C22×C4semidirect
244. C4⋊Dic47C22×C4semidirect
245. C4⋊Dic47C22×C4semidirect
395. C2×#388D47semidirect
405. C2×C47#2335semidirect
446. #388C2×D47semidirect
465. C47C2×#2335semidirect
524. C2×C22⋊C4C4×D47semidirect
645. C22⋊C4C2×C4×D47semidirect
787. C2#20246171direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940082
#202461712
C2×#156890232
C2×#156890212
C2×#156890162
C2×#156890152
C2×#156890122
C2×#156890082
C2×#156890062
C2×#156889992
C2×#156889942
C2×#156889812
C2×C4⋊C4×Dic472
C2×C22⋊C4×Dic472
C2×C4×(C2×D47)⋊C42
C2×C47×#3882
C2×#233547