Finite Group Databasebeta

← C2×#20246202 #26375198

Subgroups — C2×#20246202 #26375198

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#20246202C2116yesmaximal, direct product factor
3C2×#15689028C211yesmaximal, characteristic, complemented
4C2×#15689027C211yesmaximal, characteristic, complemented
5C2×#15689016C211yesmaximal, characteristic, complemented
6C2×#15689013C211yesmaximal, characteristic, complemented
7C2×#15689013C211yesmaximal, characteristic, complemented
8C2×#15689011C211yesmaximal, characteristic, complemented
9C2×#15689002C211yesmaximal, characteristic
10C2×#15688999C211yesmaximal, characteristic
11C2×#15688997C211yesmaximal, characteristic, complemented
12C2×#15688990C211yesmaximal, characteristic, complemented
13C2×C4⋊C4×Dic47C211yesmaximal, characteristic, complemented
14C2×C4×C22⋊Dic47C211yesmaximal, characteristic, complemented
15C2×#15688970C211yesmaximal, characteristic, complemented
16C2×C47×#385C211yesmaximal, characteristic, complemented
17C23×Dic94C2211yescharacteristic
18C23×C22⋊D47C2211yescharacteristic
19C23×C4×D47C2211yescharacteristic
20C2×#13094010C4116yescomplemented
21C2×#13094010C2218yes—
22C22×C4⋊Dic47C2211yescharacteristic
23C22×Dic47⋊C4C2211yescharacteristic
24C22×C22⋊Dic47C2211yescharacteristic
25C22×C22⋊Dic47C2211yescharacteristic
26C22×C22⋊Dic47C2211yescharacteristic
27C22×(C2×D47)⋊C4C2211yescharacteristic
28C22×(C2×D47)⋊C4C2211yescharacteristic
29C22×(C2×D47)⋊C4C2211yescharacteristic
30C22×(C2×D47)⋊C4C2211yescharacteristic
31C22×(C2×D47)⋊C4C2211yescharacteristic
32C22×C4×Dic47C2211yescharacteristic
33C22×C4×Dic47C2211yescharacteristic
34C22×C4×Dic47C2211yescharacteristic
35C22×C4×Dic47C2211yescharacteristic
36C22×C4×Dic47C2211yescharacteristic
37#15689028C2218yescomplemented
38#15689027C2218yescomplemented
39#15689016C2218yescomplemented
40#15689013C2218yescomplemented
41#15689013C2218yescomplemented
42#15689011C2218yescomplemented
43#15689002C2218yes—
44#15688999C2218yes—
45#15688997C2218yescomplemented
46#15688990C2218yescomplemented
47C4⋊C4×Dic47C2218yescomplemented
48C4×C22⋊Dic47C2218yescomplemented
49#15688970C2218yescomplemented
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
60C24×C4×C47C2211yescharacteristic
61C22×C4⋊C4×C47C2211yescharacteristic
62C22×C4⋊C4×C47C2211yescharacteristic
63C22×C22⋊C4×C47C2211yescharacteristic
64C22×C22⋊C4×C47C2211yescharacteristic
65C47×#385C2218yescomplemented
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×Dic47C2311yescharacteristic
78C23×Dic47C2311yescharacteristic
79C23×Dic47C2311yescharacteristic
80C23×Dic47C2311yescharacteristic
81C23×Dic47C2311yescharacteristic
82C23×Dic47C2311yescharacteristic
83C23×Dic47C2311yescharacteristic
84C22×C4×D47—24no—
85C22×C4×D47—42no—
86C22×C4×D47—42no—
87C22×C4×D47C2314yes—
88#13094010C2×C4164yescomplemented
89C2×C4⋊Dic47—24no—
90C2×C4⋊Dic47C2314yes—
91C2×Dic47⋊C4—42no—
92C2×Dic47⋊C4C2314yes—
93C2×C22⋊Dic47—24no—
94C2×C22⋊Dic47—42no—
95C2×C22⋊Dic47C2×C418yescomplemented
96C2×C22⋊Dic47C2314yes—
97C2×C22⋊Dic47C2314yes—
98C2×C22⋊Dic47C2314yes—
99C2×(C2×D47)⋊C4—24no—
100C2×(C2×D47)⋊C4—42no—
101C2×(C2×D47)⋊C4—42no—
102C2×(C2×D47)⋊C4C2×C418yescomplemented
103C2×(C2×D47)⋊C4C2×C418yescomplemented
104C2×(C2×D47)⋊C4C2314yes—
105C2×(C2×D47)⋊C4C2314yes—
106C2×(C2×D47)⋊C4C2314yes—
107C2×(C2×D47)⋊C4C2314yes—
108C2×(C2×D47)⋊C4C2314yes—
109C2×C4×Dic47—42no—
110C2×C4×Dic47—42no—
111C2×C4×Dic47—42no—
112C2×C4×Dic47—42no—
113C2×C4×Dic47C2×C418yescomplemented
114C2×C4×Dic47C2314yes—
115C2×C4×Dic47C2314yes—
116C2×C4×Dic47C2314yes—
117C2×C4×Dic47C2314yes—
118C2×C4×Dic47C2314yes—
119C47⋊#95C2314yes—
120C47⋊#95C2314yes—
121C47⋊#95C2314yes—
122C47⋊#95C2314yes—
123C47⋊#95C2314yes—
124C47⋊#95C2314yes—
125C47⋊#95C2314yes—
126C47⋊#95C2314yes—
127C47⋊#95C2314yes—
128C47⋊#95C2314yes—
129C25×C47C2311yescharacteristic
130C23×C4×C47—24no—
131C23×C4×C47—42no—
132C23×C4×C47—42no—
133C23×C4×C47C2311yescharacteristic
134C23×C4×C47C2311yescharacteristic
135C23×C4×C47C2311yescharacteristic
136C23×C4×C47C2311yescharacteristic
137C23×C4×C47C2311yescharacteristic
138C23×C4×C47C2311yescharacteristic
139C23×C4×C47C2314yes—
140C2×C4⋊C4×C47—24no—
141C2×C4⋊C4×C47—42no—
142C2×C4⋊C4×C47C2314yes—
143C2×C4⋊C4×C47C2314yes—
144C2×C22⋊C4×C47—42no—
145C2×C22⋊C4×C47C2×C418yescomplemented
146C2×C22⋊C4×C47C2314yes—
147C2×C22⋊C4×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—28no—
183C22×C4×C47—44no—
184C22×C4×C47—44no—
185C22×C4×C47—416no—
186C22×C4×C47C22×C414yes—
187C22×C4×C47C22×C414yes—
188C22×C4×C47#4114yes—
189C22×C4×C47C2412yes—
190C22×C4×C47C2412yes—
191C22×C4×C47C2412yes—
192C22×C4×C47C2412yes—
193C22×C4×C47C2412yes—
194C22×C4×C47C2412yes—
195C2×C22⋊D47—416no—
196C2×C22⋊D47—44no—
197C2×C22⋊D47—44no—
198C2×C22⋊D47C22×C4116yes—
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—22no—
214C22×Dic47—22no—
215C22×Dic47—22no—
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—
236C4⋊C4×C47—44no—
237C22⋊C4×C47—44no—
238C22⋊C4×C47C22×C4116yescomplemented
239C22⋊Dic47—28no—
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—
248Dic47⋊C4—44no—
249C4×Dic47—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—416no—
309C2×C4×C47—44no—
310C2×C4×C47—44no—
311C2×C4×C47—44no—
312C2×C4×C47C23×C414yes—
313C2×C4×C47C23×C414yes—
314C2×C4×C47C2×#4114yes—
315C22⋊D47—416no—
316C2×Dic47—28no—
317C2×Dic47—28no—
318C2×Dic47—28no—
319C2×Dic47—28no—
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—22no—
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×#388—471no—
398C2×#386—471no—
399C2×#386—471no—
400C2×#385—471no—
401C2×#385D4711yescharacteristic, complemented
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×C4C2×D4711yescharacteristic
420C2×#124—4716no—
421C2×#124—478no—
422C22×C4⋊C4—471no—
423C22×C4⋊C4—471no—
424C22×C4⋊C4C2×D4711yescharacteristic
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⋊C4—471no—
434C22×C22⋊C4C2×D4711yescharacteristic
435C22×C22⋊C4C2×D4711yescharacteristic
436C22×C42—471no—
437C22×C42—471no—
438C22×C42—471no—
439C22×C42—471no—
440C22×C42—471no—
441#391—478no—
442#391—478no—
443#388—478no—
444#388—478no—
445#388—478no—
446#388—478no—
447#386—478no—
448#386—478no—
449#385—478no—
450#385C2×D4718yescomplemented
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—24no—
479C23×C4—42no—
480C23×C4—42no—
481C23×C4—471no—
482C23×C4—471no—
483C23×C4—471no—
484C23×C4—471no—
485C23×C4—471no—
486C23×C4—471no—
487C23×C4—471no—
488C23×C4—474no—
489C23×C4—944no—
490C23×C4—1882no—
491C23×C4—1882no—
492C23×C4C22×D4711yescharacteristic
493C23×C4C22×D4711yescharacteristic
494C23×C4C22×D4711yescharacteristic
495C23×C4C22×D4711yescharacteristic
496C23×C4C22×D4711yescharacteristic
497C23×C4C22×D4711yescharacteristic
498C23×C4C22×D4714yes—
499#124—4764no—
500C2×C4⋊C4—24no—
501C2×C4⋊C4—42no—
502C2×C4⋊C4—474no—
503C2×C4⋊C4—474no—
504C2×C4⋊C4—944no—
505C2×C4⋊C4—1882no—
506C2×C4⋊C4C22×D4714yes—
507C2×C4⋊C4C22×D4714yes—
508C2×C22⋊C4—42no—
509C2×C22⋊C4—478no—
510C2×C22⋊C4—474no—
511C2×C22⋊C4—478no—
512C2×C22⋊C4—478no—
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—474no—
520C2×C22⋊C4—944no—
521C2×C22⋊C4—944no—
522C2×C22⋊C4—1882no—
523C2×C22⋊C4—1882no—
524C2×C22⋊C4—1882no—
525C2×C22⋊C4C4×D4718yescomplemented
526C2×C22⋊C4C22×D4714yes—
527C2×C22⋊C4C22×D4714yes—
528C2×C42—478no—
529C2×C42—474no—
530C2×C42—474no—
531C2×C42—474no—
532C2×C42—474no—
533C2×C42—474no—
534C2×C42—1882no—
535C2×C42—1882no—
536C2×C42—1882no—
537C2×C42—1882no—
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—28no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—416no—
594C22×C4—474no—
595C22×C4—474no—
596C22×C4—474no—
597C22×C4—474no—
598C22×C4—472no—
599C22×C4—472no—
600C22×C4—472no—
601C22×C4—472no—
602C22×C4—472no—
603C22×C4—472no—
604C22×C4—472no—
605C22×C4—948no—
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—942no—
620C22×C4—942no—
621C22×C4—942no—
622C22×C4—942no—
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—44no—
637C4⋊C4—948no—
638C4⋊C4—1884no—
639C22⋊C4—44no—
640C22⋊C4—4716no—
641C22⋊C4—4716no—
642C22⋊C4—4716no—
643C22⋊C4—948no—
644C22⋊C4—948no—
645C22⋊C4—1884no—
646C22⋊C4—1884no—
647C22⋊C4—1884no—
648C22⋊C4C2×C4×D47116yescomplemented
649C42—4716no—
650C42—1884no—
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#1309406912yes—
687C23#1309407012yes—
688C23#1309407212yes—
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—416no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—474no—
715C2×C4—474no—
716C2×C4—474no—
717C2×C4—474no—
718C2×C4—948no—
719C2×C4—948no—
720C2×C4—948no—
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—948no—
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—942no—
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—42no—
750C22—416no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—944no—
755C22—944no—
756C22—944no—
757C22—1882no—
758C22—18816no—
759C22—1882no—
760C22—1882no—
761C22—1882no—
762C22C4×#1062535214yes—
763C22#1568959514yes—
764C22#1568960414yes—
765C22#1568970814yes—
766C22#1568970914yes—
767C22#1568974314yes—
768C22#1568974614yes—
769C22C23×C4×D4711yescharacteristic
770C22C2×#41×D4711yescharacteristic
771C22C22×#1062535211yescharacteristic
772C22C2×#1309406911yescharacteristic
773C22C2×#1309406911yescharacteristic
774C22C2×#1309407011yescharacteristic
775C22C2×#1309407211yescharacteristic
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#2024620218yesdirect product factor
792C2C2×C4×#1062535211yescharacteristic
793C2C2×#1568959511yescharacteristic
794C2C2×#1568960411yescharacteristic
795C2C2×#1568970811yescharacteristic
796C2C2×#1568970911yescharacteristic
797C2C2×#1568974311yescharacteristic
798C2C2×#1568974611yescharacteristic
subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C47×#385C2
socleC24×C47C24
prime radicalC23×C22⋊D47C22
cosocleC23×C47C25
hypercenterC2×#385D47
hypocenterC47C2×#2337
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. #20246202C2direct (N × H)
3. C2×#15689028C2semidirect
4. C2×#15689027C2semidirect
5. C2×#15689016C2semidirect
6. C2×#15689013C2semidirect
7. C2×#15689013C2semidirect
8. C2×#15689011C2semidirect
11. C2×#15688997C2semidirect
12. C2×#15688990C2semidirect
13. C2×C4⋊C4×Dic47C2semidirect
14. C2×C4×C22⋊Dic47C2semidirect
15. C2×#15688970C2semidirect
16. C2×C47×#385C2semidirect
20. C2×#13094010C4semidirect
37. #15689028C22semidirect
38. #15689027C22semidirect
39. #15689016C22semidirect
40. #15689013C22semidirect
41. #15689013C22semidirect
42. #15689011C22semidirect
45. #15688997C22semidirect
46. #15688990C22semidirect
47. C4⋊C4×Dic47C22semidirect
48. C4×C22⋊Dic47C22semidirect
49. #15688970C22semidirect
65. C47×#385C22semidirect
71. C22×Dic94C2×C4semidirect
88. #13094010C2×C4semidirect
95. C2×C22⋊Dic47C2×C4semidirect
102. C2×(C2×D47)⋊C4C2×C4semidirect
103. C2×(C2×D47)⋊C4C2×C4semidirect
113. C2×C4×Dic47C2×C4semidirect
145. 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
401. C2×#385D47semidirect
407. C2×C47#2337semidirect
450. #385C2×D47semidirect
467. C47C2×#2337semidirect
525. C2×C22⋊C4C4×D47semidirect
648. C22⋊C4C2×C4×D47semidirect
791. C2#20246202direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940102
#202462022
C2×#156890282
C2×#156890272
C2×#156890162
C2×#156890132
C2×#156890112
C2×#156890022
C2×#156889992
C2×#156889972
C2×#156889902
C2×C4⋊C4×Dic472
C2×C4×C22⋊Dic472
C2×#156889702
C2×C47×#3852
C2×#233747