Finite Group Databasebeta

← C2×#20246195 #26375191

Subgroups — C2×#20246195 #26375191

Order 12032.

3046 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#20246195C2116yesmaximal, direct product factor
3C2×#15689029C211yesmaximal, characteristic, complemented
4C2×#15689027C211yesmaximal, characteristic, complemented
5C2×#15689017C211yesmaximal, characteristic, complemented
6C2×#15689015C211yesmaximal, characteristic, complemented
7C2×#15689015C211yesmaximal, characteristic, complemented
8C2×#15689000C211yesmaximal, characteristic
9C2×#15688999C211yesmaximal, characteristic
10C2×#15688998C211yesmaximal, characteristic, complemented
11C2×#15688994C211yesmaximal, characteristic, complemented
12C2×#15688990C211yesmaximal, 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×Dic94C2211yescharacteristic
18C23×C22⋊D47C2211yescharacteristic
19C24×Dic47C2211yescharacteristic
20C23×C4×D47C2211yescharacteristic
21C2×#13094010C4116yescomplemented
22C2×#13094010C2218yes—
23C22×C4⋊Dic47C2211yescharacteristic
24C22×C4⋊Dic47C2211yescharacteristic
25C22×Dic47⋊C4C2211yescharacteristic
26C22×C22⋊Dic47C2211yescharacteristic
27C22×C22⋊Dic47C2211yescharacteristic
28C22×(C2×D47)⋊C4C2211yescharacteristic
29C22×(C2×D47)⋊C4C2211yescharacteristic
30C22×(C2×D47)⋊C4C2211yescharacteristic
31C22×(C2×D47)⋊C4C2211yescharacteristic
32C22×(C2×D47)⋊C4C2211yescharacteristic
33C22×C4×Dic47C2211yescharacteristic
34C22×C4×Dic47C2211yescharacteristic
35C22×C4×Dic47C2211yescharacteristic
36C22×C4×Dic47C2211yescharacteristic
37#15689029C2218yescomplemented
38#15689027C2218yescomplemented
39#15689017C2218yescomplemented
40#15689015C2218yescomplemented
41#15689015C2218yescomplemented
42#15689000C2218yes—
43#15688999C2218yes—
44#15688998C2218yescomplemented
45#15688994C2218yescomplemented
46#15688990C2218yescomplemented
47C4⋊C4×Dic47C2218yescomplemented
48C22⋊C4×Dic47C2218yescomplemented
49C4×(C2×D47)⋊C4C2218yescomplemented
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—24no—
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—24no—
89C22×C4×D47—42no—
90C22×C4×D47—42no—
91C22×C4×D47C2314yes—
92#13094010C2×C4164yescomplemented
93C2×C4⋊Dic47—24no—
94C2×C4⋊Dic47—42no—
95C2×C4⋊Dic47C2314yes—
96C2×C4⋊Dic47C2314yes—
97C2×Dic47⋊C4—42no—
98C2×Dic47⋊C4C2314yes—
99C2×C22⋊Dic47—42no—
100C2×C22⋊Dic47C2×C418yescomplemented
101C2×C22⋊Dic47C2314yes—
102C2×C22⋊Dic47C2314yes—
103C2×(C2×D47)⋊C4—24no—
104C2×(C2×D47)⋊C4—42no—
105C2×(C2×D47)⋊C4—42no—
106C2×(C2×D47)⋊C4C2×C418yescomplemented
107C2×(C2×D47)⋊C4C2×C418yescomplemented
108C2×(C2×D47)⋊C4C2314yes—
109C2×(C2×D47)⋊C4C2314yes—
110C2×(C2×D47)⋊C4C2314yes—
111C2×(C2×D47)⋊C4C2314yes—
112C2×(C2×D47)⋊C4C2314yes—
113C2×C4×Dic47—42no—
114C2×C4×Dic47—42no—
115C2×C4×Dic47—42no—
116C2×C4×Dic47C2×C418yescomplemented
117C2×C4×Dic47C2314yes—
118C2×C4×Dic47C2314yes—
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—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—28no—
213C22×Dic47—44no—
214C22×Dic47—44no—
215C22×Dic47—416no—
216C22×Dic47C22×C414yes—
217C22×Dic47C22×C414yes—
218C22×Dic47C22×C414yes—
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—
231C2×Dic94—416no—
232C2×Dic94—44no—
233C2×Dic94—44no—
234C2×Dic94C22×C4116yescomplemented
235C4⋊C4×C47—28no—
236C22⋊C4×C47—28no—
237C22⋊C4×C47—44no—
238C22⋊C4×C47C22×C4116yescomplemented
239C42×C47—44no—
240C22⋊Dic47—44no—
241C22⋊Dic47C22×C4116yescomplemented
242(C2×D47)⋊C4—28no—
243(C2×D47)⋊C4—44no—
244(C2×D47)⋊C4—44no—
245(C2×D47)⋊C4C22×C4116yescomplemented
246(C2×D47)⋊C4C22×C4116yescomplemented
247C4⋊Dic47—28no—
248C4⋊Dic47—44no—
249Dic47⋊C4—44no—
250C4×Dic47—44no—
251C4×Dic47—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×C47C2×#4112yes—
270C23×C47C2×#4112yes—
271C23×C47H(5,𝔽2)12yes—
272C23×C47H(5,𝔽2)12yes—
273C23×C47H(5,𝔽2)12yes—
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—28no—
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×C47C23×C414yes—
312C2×C4×C47C23×C414yes—
313C2×C4×C47C2×#4114yes—
314C22⋊D47—416no—
315C2×Dic47—28no—
316C2×Dic47—28no—
317C2×Dic47—28no—
318C2×Dic47—28no—
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×Dic47C23×C414yes—
341C2×Dic47C23×C414yes—
342C2×Dic47C23×C414yes—
343C2×Dic47C2×#4114yes—
344C4×D47—416no—
345Dic94—416no—
346C2×#2337—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×C47C4×#4114yes—
356C22×C47#51814yes—
357C22×C47#52014yes—
358C22×C47#53814yes—
359C22×C47#53814yes—
360C22×C47#54214yes—
361C22×C47#54214yes—
362C22×C47C24×C411yescharacteristic
363C22×C47C22×#4111yescharacteristic
364C22×C47C22×#4111yescharacteristic
365C22×C47C2×H(5,𝔽2)11yescharacteristic
366C22×C47C2×H(5,𝔽2)11yescharacteristic
367C22×C47C2×H(5,𝔽2)11yescharacteristic
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—24no—
380C4×C47—42no—
381C4×C47—42no—
382C4×C47—42no—
383Dic47—24no—
384Dic47—24no—
385Dic47—24no—
386Dic47—24no—
387Dic47—42no—
388Dic47—42no—
389Dic47—42no—
390C22×#124—471no—
391#2337—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×#383—471no—
403C2×C4×C4⋊C4—471no—
404C2×C4×C22⋊C4—471no—
405C2×C4×C22⋊C4—471no—
406C2×C47—44no—
407C2×C47#233718yescomplemented
408C2×C47C2×C4×#4111yescharacteristic
409C2×C47C2×#51811yescharacteristic
410C2×C47C2×#52011yescharacteristic
411C2×C47C2×#53811yescharacteristic
412C2×C47C2×#53811yescharacteristic
413C2×C47C2×#54211yescharacteristic
414C2×C47C2×#54211yescharacteristic
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⋊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#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#383—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×#95—471no—
464C2×#95—471no—
465C2×#95C2×D4711yescharacteristic
466C2×#95C2×D4711yescharacteristic
467C47C2×#233711yescharacteristic, 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—944no—
488C23×C4—944no—
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—24no—
501C2×C4⋊C4—474no—
502C2×C4⋊C4—474no—
503C2×C4⋊C4—474no—
504C2×C4⋊C4—944no—
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—474no—
512C2×C22⋊C4—478no—
513C2×C22⋊C4—478no—
514C2×C22⋊C4—474no—
515C2×C22⋊C4—474no—
516C2×C22⋊C4—474no—
517C2×C22⋊C4—474no—
518C2×C22⋊C4—474no—
519C2×C22⋊C4—474no—
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—478no—
530C2×C42—474no—
531C2×C42—474no—
532C2×C42—474no—
533C2×C42—474no—
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#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—474no—
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—948no—
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—948no—
620C22×C4—1884no—
621C22×C4—1884no—
622C22×C4—18816no—
623C22×C4—1884no—
624C22×C4—1884no—
625C22×C4—18816no—
626C22×C4C2×C4×D4714yes—
627C22×C4C2×C4×D4714yes—
628C22×C4#1062535214yes—
629C22×C4C23×D4712yes—
630C22×C4C23×D4712yes—
631C22×C4C23×D4712yes—
632C22×C4C23×D4712yes—
633C22×C4C23×D4712yes—
634C22×C4C23×D4712yes—
635C4⋊C4—28no—
636C4⋊C4—948no—
637C4⋊C4—1884no—
638C4⋊C4—1884no—
639C22⋊C4—28no—
640C22⋊C4—44no—
641C22⋊C4—4716no—
642C22⋊C4—4716no—
643C22⋊C4—4716no—
644C22⋊C4—948no—
645C22⋊C4—1884no—
646C22⋊C4—1884no—
647C22⋊C4—1884no—
648C22⋊C4C2×C4×D47116yescomplemented
649C42—44no—
650C42—4716no—
651C42—1884no—
652C42—1884no—
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#41×D4712yes—
684C23C2×#1062535212yes—
685C23#1309406912yes—
686C23#1309407012yes—
687C23#1309407012yes—
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—28no—
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—474no—
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—948no—
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×C4C22×C4×D4714yes—
744C2×C4C22×C4×D4714yes—
745C2×C4C2×#1062535214yes—
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—
762C22C4×#1062535214yes—
763C22#1568959514yes—
764C22#1568960314yes—
765C22#1568971014yes—
766C22#1568971214yes—
767C22#1568974114yes—
768C22#1568974214yes—
769C22C23×C4×D4711yescharacteristic
770C22C2×#41×D4711yescharacteristic
771C22C22×#1062535211yescharacteristic
772C22C2×#1309406911yescharacteristic
773C22C2×#1309407011yescharacteristic
774C22C2×#1309407011yescharacteristic
775C22C2×#1309407111yescharacteristic
776C4—24no—
777C4—24no—
778C4—24no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—944no—
783C4—944no—
784C4—944no—
785C4—944no—
786C4—1882no—
787C4—1882no—
788C4—1882no—
789C2—44no—
790C2—1884no—
791C2#2024619518yesdirect product factor
792C2C2×C4×#1062535211yescharacteristic
793C2C2×#1568959511yescharacteristic
794C2C2×#1568960311yescharacteristic
795C2C2×#1568971011yescharacteristic
796C2C2×#1568971211yescharacteristic
797C2C2×#1568974111yescharacteristic
798C2C2×#1568974211yescharacteristic
subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C47×#388C2
socleC24×C47C24
prime radicalC23×C22⋊D47C22
cosocleC23×C47C25
hypercenterC2×#388D47
hypocenterC47C2×#2337
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. #20246195C2direct (N × H)
3. C2×#15689029C2semidirect
4. C2×#15689027C2semidirect
5. C2×#15689017C2semidirect
6. C2×#15689015C2semidirect
7. C2×#15689015C2semidirect
10. C2×#15688998C2semidirect
11. C2×#15688994C2semidirect
12. C2×#15688990C2semidirect
13. C2×C4⋊C4×Dic47C2semidirect
14. C2×C22⋊C4×Dic47C2semidirect
15. C2×C4×(C2×D47)⋊C4C2semidirect
16. C2×C47×#388C2semidirect
21. C2×#13094010C4semidirect
37. #15689029C22semidirect
38. #15689027C22semidirect
39. #15689017C22semidirect
40. #15689015C22semidirect
41. #15689015C22semidirect
44. #15688998C22semidirect
45. #15688994C22semidirect
46. #15688990C22semidirect
47. C4⋊C4×Dic47C22semidirect
48. C22⋊C4×Dic47C22semidirect
49. C4×(C2×D47)⋊C4C22semidirect
65. C47×#388C22semidirect
71. C22×Dic94C2×C4semidirect
92. #13094010C2×C4semidirect
100. C2×C22⋊Dic47C2×C4semidirect
106. C2×(C2×D47)⋊C4C2×C4semidirect
107. C2×(C2×D47)⋊C4C2×C4semidirect
116. 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#2337semidirect
446. #388C2×D47semidirect
467. C47C2×#2337semidirect
524. C2×C22⋊C4C4×D47semidirect
648. C22⋊C4C2×C4×D47semidirect
791. C2#20246195direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940102
#202461952
C2×#156890292
C2×#156890272
C2×#156890172
C2×#156890152
C2×#156890002
C2×#156889992
C2×#156889982
C2×#156889942
C2×#156889902
C2×C4⋊C4×Dic472
C2×C22⋊C4×Dic472
C2×C4×(C2×D47)⋊C42
C2×C47×#3882
C2×#233747