Finite Group Databasebeta

← C2×#20247105 #26384358

Subgroups — C2×#20247105 #26384358

Order 12032.

2942 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094014C211yesmaximal, characteristic, complemented
2C22×C4⋊C4×D47C211yesmaximal, characteristic
3#20247105C2116yesmaximal, direct product factor
4C2×#15689065C211yesmaximal, characteristic, complemented
5C2×#15689056C211yesmaximal, characteristic, complemented
6C2×#15689055C211yesmaximal, characteristic, complemented
7C2×#15689020C211yesmaximal, characteristic, complemented
8C2×#15689020C211yesmaximal, characteristic, complemented
9C2×#15688997C211yesmaximal, characteristic
10C2×#15688997C211yesmaximal, characteristic
11C2×#15688987C211yesmaximal, characteristic, complemented
12C2×#15688982C211yesmaximal, characteristic
13C2×#15688982C211yesmaximal, characteristic
14C2×#15688980C211yesmaximal, characteristic
15C2×#15688970C211yesmaximal, characteristic
16C2×C47×#400C211yesmaximal, characteristic, complemented
17C23×C4×D47C2211yescharacteristic
18C23×C4×D47C2211yescharacteristic
19C23×C4×D47C2211yescharacteristic
20C2×#13094014—28no—
21C2×#13094014C2218yescomplemented
22C22×C4⋊Dic47C2211yescharacteristic
23C22×C4⋊Dic47C2211yescharacteristic
24C22×C4⋊Dic47C2211yescharacteristic
25C22×C4⋊Dic47C2211yescharacteristic
26C22×Dic47⋊C4C2211yescharacteristic
27C22×Dic47⋊C4C2211yescharacteristic
28C22×Dic47⋊C4C2211yescharacteristic
29C22×Dic47⋊C4C2211yescharacteristic
30C22×Dic47⋊C4C2211yescharacteristic
31C22×Dic47⋊C4C2211yescharacteristic
32C22×Dic47⋊C4C2211yescharacteristic
33C22×Dic47⋊C4C2211yescharacteristic
34C2×C4⋊C4×D47—28no—
35C2×C4⋊C4×D47C2218yes—
36C22×(C2×D47)⋊C4C2211yescharacteristic
37C22×(C2×D47)⋊C4C2211yescharacteristic
38C22×(C2×D47)⋊C4C2211yescharacteristic
39C22×(C2×D47)⋊C4C2211yescharacteristic
40C22×C4×Dic47C2211yescharacteristic
41C22×C4×Dic47C2211yescharacteristic
42#15689065C2218yescomplemented
43#15689056C2218yescomplemented
44#15689055C2218yescomplemented
45#15689020C2218yescomplemented
46#15689020C2218yescomplemented
47#15688997C2218yes—
48#15688997C2218yes—
49#15688987C2218yescomplemented
50#15688982C2218yes—
51#15688982C2218yes—
52#15688980C2218yes—
53#15688970C2218yes—
54C2×C47⋊#95C2211yescharacteristic
55C2×C47⋊#95C2211yescharacteristic
56C2×C47⋊#95C2211yescharacteristic
57C2×C47⋊#95C2211yescharacteristic
58C2×C47⋊#95C2211yescharacteristic
59C2×C47⋊#95C2211yescharacteristic
60C2×C47⋊#95C2211yescharacteristic
61C22×C4⋊C4×C47C2211yescharacteristic
62C22×C4⋊C4×C47C2211yescharacteristic
63C47×#400C2218yescomplemented
64C2×#95×C47C2211yescharacteristic
65C2×#95×C47C2211yescharacteristic
66C2×#95×C47C2211yescharacteristic
67C2×#95×C47C2211yescharacteristic
68C2×#95×C47C2211yescharacteristic
69C24×D47C2311yescharacteristic
70C23×Dic47C2311yescharacteristic
71C23×Dic47C2311yescharacteristic
72C23×Dic47C2311yescharacteristic
73C23×Dic47C2311yescharacteristic
74C23×Dic47C2311yescharacteristic
75C23×Dic47C2311yescharacteristic
76C23×Dic47C2311yescharacteristic
77C22×C4×D47—24no—
78C22×C4×D47—24no—
79C22×C4×D47—24no—
80C22×C4×D47—24no—
81C22×C4×D47—24no—
82C22×C4×D47—24no—
83C22×C4×D47—42no—
84C22×C4×D47—42no—
85C22×C4×D47Q818yes—
86C22×C4×D47C2314yes—
87C22×C4×D47C2314yes—
88C22×C4×D47C2314yes—
89#13094014—232no—
90C2×C4⋊Dic47—24no—
91C2×C4⋊Dic47—24no—
92C2×C4⋊Dic47—42no—
93C2×C4⋊Dic47—42no—
94C2×C4⋊Dic47C2314yes—
95C2×C4⋊Dic47C2314yes—
96C2×C4⋊Dic47C2314yes—
97C2×C4⋊Dic47C2314yes—
98C2×Dic47⋊C4—24no—
99C2×Dic47⋊C4—24no—
100C2×Dic47⋊C4—24no—
101C2×Dic47⋊C4—24no—
102C2×Dic47⋊C4—24no—
103C2×Dic47⋊C4—42no—
104C2×Dic47⋊C4—42no—
105C2×Dic47⋊C4D418yes—
106C2×Dic47⋊C4C2314yes—
107C2×Dic47⋊C4C2314yes—
108C2×Dic47⋊C4C2314yes—
109C2×Dic47⋊C4C2314yes—
110C2×Dic47⋊C4C2314yes—
111C2×Dic47⋊C4C2314yes—
112C2×Dic47⋊C4C2314yes—
113C2×Dic47⋊C4C2314yes—
114C4⋊C4×D47—232no—
115C2×(C2×D47)⋊C4—24no—
116C2×(C2×D47)⋊C4—24no—
117C2×(C2×D47)⋊C4—24no—
118C2×(C2×D47)⋊C4—24no—
119C2×(C2×D47)⋊C4C2314yes—
120C2×(C2×D47)⋊C4C2314yes—
121C2×(C2×D47)⋊C4C2314yes—
122C2×(C2×D47)⋊C4C2314yes—
123C2×C4×Dic47—24no—
124C2×C4×Dic47—24no—
125C2×C4×Dic47C2314yes—
126C2×C4×Dic47C2314yes—
127C47⋊#95C2314yes—
128C47⋊#95C2314yes—
129C47⋊#95C2314yes—
130C47⋊#95C2314yes—
131C47⋊#95C2314yes—
132C47⋊#95C2314yes—
133C47⋊#95C2314yes—
134C23×C4×C47C2311yescharacteristic
135C23×C4×C47C2311yescharacteristic
136C23×C4×C47C2311yescharacteristic
137C23×C4×C47C2311yescharacteristic
138C23×C4×C47C2311yescharacteristic
139C23×C4×C47C2311yescharacteristic
140C23×C4×C47C2311yescharacteristic
141C2×C4⋊C4×C47—24no—
142C2×C4⋊C4×C47—24no—
143C2×C4⋊C4×C47C2314yes—
144C2×C4⋊C4×C47C2314yes—
145#95×C47C2314yes—
146#95×C47C2314yes—
147#95×C47C2314yes—
148#95×C47C2314yes—
149#95×C47C2314yes—
150C24×C47C2411yescharacteristic
151C23×D47—22no—
152C23×D47—22no—
153C23×D47—22no—
154C23×D47—22no—
155C23×D47C2×Q814yes—
156C23×D47#4114yes—
157C23×D47#4114yes—
158C23×D47C2412yes—
159C22×C4×C47—22no—
160C22×C4×C47—22no—
161C22×C4×C47—22no—
162C22×C4×C47—22no—
163C22×C4×C47—22no—
164C22×C4×C47—22no—
165C22×C4×C47—22no—
166C22×C4×C47—22no—
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×C47C2×D414yes—
179C22×C4×C47C2×Q814yes—
180C22×C4×C47C2412yes—
181C22×C4×C47C2412yes—
182C22×C4×C47C2412yes—
183C22×C4×C47C2412yes—
184C22×C4×C47C2412yes—
185C22×C4×C47C2412yes—
186C22×C4×C47C2412yes—
187C22×Dic47—22no—
188C22×Dic47—22no—
189C22×Dic47—22no—
190C22×Dic47—22no—
191C22×Dic47—22no—
192C22×Dic47—22no—
193C22×Dic47—22no—
194C22×Dic47—22no—
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×Dic47C2×D414yes—
205C22×Dic47C2×D414yes—
206C22×Dic47C2×Q814yes—
207C22×Dic47#4114yes—
208C22×Dic47C2412yes—
209C22×Dic47C2412yes—
210C22×Dic47C2412yes—
211C22×Dic47C2412yes—
212C22×Dic47C2412yes—
213C22×Dic47C2412yes—
214C22×Dic47C2412yes—
215C2×C4×D47—232no—
216C2×C4×D47—28no—
217C2×C4×D47—28no—
218C2×C4×D47—28no—
219C2×C4×D47—28no—
220C2×C4×D47—28no—
221C2×C4×D47—28no—
222C2×C4×D47—44no—
223C2×C4×D47—44no—
224C2×C4×D47—416no—
225C2×C4×D47—416no—
226C2×C4×D47C2×Q8116yes—
227C4⋊C4×C47—28no—
228C4⋊C4×C47—28no—
229(C2×D47)⋊C4—28no—
230(C2×D47)⋊C4—28no—
231(C2×D47)⋊C4—28no—
232(C2×D47)⋊C4—28no—
233C4⋊Dic47—28no—
234C4⋊Dic47—28no—
235C4⋊Dic47—44no—
236C4⋊Dic47—44no—
237Dic47⋊C4—28no—
238Dic47⋊C4—28no—
239Dic47⋊C4—28no—
240Dic47⋊C4—28no—
241Dic47⋊C4—28no—
242Dic47⋊C4—44no—
243Dic47⋊C4—44no—
244Dic47⋊C4C2×D4116yes—
245C4×Dic47—28no—
246C4×Dic47—28no—
247C23×C47C22×D412yes—
248C23×C47C22×Q812yes—
249C23×C47C2×#4112yes—
250C23×C47C2×#4112yes—
251C23×C47C2×#4112yes—
252C23×C47H(5,𝔽2)12yes—
253C23×C472−1+412yes—
254C23×C47C2511yescharacteristic
255C22×D47—28no—
256C22×D47—28no—
257C22×D47—28no—
258C22×D47—28no—
259C22×D47—28no—
260C22×D47—28no—
261C22×D47—22no—
262C22×D47—22no—
263C22×D47—22no—
264C22×D47—22no—
265C22×D47#125116yescomplemented
266C22×D47C22×Q814yes—
267C22×D47C2×#4114yes—
268C22×D47C2×#4114yes—
269C2×C4×C47—28no—
270C2×C4×C47—28no—
271C2×C4×C47—22no—
272C2×C4×C47—22no—
273C2×C4×C47—22no—
274C2×C4×C47—22no—
275C2×C4×C47—22no—
276C2×C4×C47—22no—
277C2×C4×C47—22no—
278C2×C4×C47—22no—
279C2×C4×C47—22no—
280C2×C4×C47—22no—
281C2×C4×C47—22no—
282C2×C4×C47—22no—
283C2×C4×C47—22no—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
290C2×C4×C47—44no—
291C2×C4×C47—44no—
292C2×C4×C47—44no—
293C2×C4×C47—44no—
294C2×C4×C47—44no—
295C2×C4×C47C22×D414yes—
296C2×C4×C47C22×Q814yes—
297C2×Dic47—28no—
298C2×Dic47—22no—
299C2×Dic47—22no—
300C2×Dic47—22no—
301C2×Dic47—22no—
302C2×Dic47—22no—
303C2×Dic47—22no—
304C2×Dic47—22no—
305C2×Dic47—22no—
306C2×Dic47—22no—
307C2×Dic47—22no—
308C2×Dic47—22no—
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—22no—
313C2×Dic47—22no—
314C2×Dic47—22no—
315C2×Dic47—44no—
316C2×Dic47—44no—
317C2×Dic47—44no—
318C2×Dic47—44no—
319C2×Dic47—44no—
320C2×Dic47C22⋊Q8116yes—
321C2×Dic47C22×D414yes—
322C2×Dic47C22×D414yes—
323C2×Dic47C22×Q814yes—
324C2×Dic47C2×#4114yes—
325C4×D47—232no—
326C4×D47—416no—
327C4×D47—416no—
328C2×#2442—471nomaximal, Sylow
329C22×C47C2×C22⋊Q814yes—
330C22×C47C2×#12514yes—
331C22×C47#54414yes—
332C22×C47#54614yes—
333C22×C47#54814yes—
334C22×C47#55214yes—
335C22×C47#55314yes—
336C22×C47C23×D411yescharacteristic
337C22×C47C23×Q811yescharacteristic
338C22×C47C22×#4111yescharacteristic
339C22×C47C22×#4111yescharacteristic
340C22×C47C22×#4111yescharacteristic
341C22×C47C2×H(5,𝔽2)11yescharacteristic
342C22×C47C2×2−1+411yescharacteristic
343C2×D47—24no—
344C2×D47—24no—
345C2×D47—24no—
346C2×D47—24no—
347C2×D47—232no—
348C2×D47—24no—
349C2×D47—24no—
350C2×D47C2×#12518yescomplemented
351C4×C47—24no—
352C4×C47—24no—
353C4×C47—42no—
354C4×C47—42no—
355C4×C47—42no—
356C4×C47—42no—
357C4×C47—42no—
358Dic47—24no—
359Dic47—42no—
360Dic47—42no—
361Dic47—42no—
362Dic47—42no—
363Dic47—42no—
364Dic47C2×C22⋊Q818yes—
365C22×#125—471no—
366C23×C4⋊C4—471no—
367#2442—4716no—
368C2×#400—471no—
369C2×#400D4711yescharacteristic, complemented
370C2×#398—471no—
371C2×#398—471no—
372C2×#389—471no—
373C2×#389—471no—
374C2×#385—471no—
375C2×#385—471no—
376C2×#382—471no—
377C2×#380—471no—
378C2×#380—471no—
379C2×#380—471no—
380C2×C4×C22⋊C4—471no—
381C2×C47#244218yescomplemented
382C2×C47C22×C22⋊Q811yescharacteristic
383C2×C47C22×#12511yescharacteristic
384C2×C47C2×#54411yescharacteristic
385C2×C47C2×#54611yescharacteristic
386C2×C47C2×#54811yescharacteristic
387C2×C47C2×#55211yescharacteristic
388C2×C47C2×#55311yescharacteristic
389D47—28no—
390C24×C4—471no—
391C24×C4—471no—
392C24×C4—471no—
393C2×#125—478no—
394C2×#125—948no—
395C22×C4⋊C4—471no—
396C22×C4⋊C4—471no—
397C22×C4⋊C4—471no—
398C22×C4⋊C4—471no—
399C22×C4⋊C4—471no—
400C22×C4⋊C4—471no—
401C22×C4⋊C4—471no—
402C22×C4⋊C4—471no—
403C22×C4⋊C4—471no—
404C22×C4⋊C4—471no—
405C22×C4⋊C4—471no—
406C22×C4⋊C4—471no—
407C22×C4⋊C4—478no—
408C22×C4⋊C4—948no—
409C22×C4⋊C4C2×D4711yescharacteristic
410C22×C4⋊C4C2×D4711yescharacteristic
411C22×C22⋊C4—471no—
412C22×C22⋊C4—471no—
413C22×C22⋊C4—471no—
414C22×C22⋊C4—471no—
415C22×C42—471no—
416C22×C42—471no—
417#400—478no—
418#400C2×D4718yescomplemented
419#398—478no—
420#398—478no—
421#389—478no—
422#389—478no—
423#385—478no—
424#385—478no—
425#382—478no—
426#380—478no—
427#380—478no—
428#380—478no—
429C4×C22⋊C4—478no—
430C2×#95—471no—
431C2×#95—471no—
432C2×#95—471no—
433C2×#95—471no—
434C2×#95—471no—
435C2×#95—471no—
436C2×#95—471no—
437C2×#95C2×D4711yescharacteristic
438C2×#95C2×D4711yescharacteristic
439C2×#95C2×D4711yescharacteristic
440C2×#95C2×D4711yescharacteristic
441C2×#95C2×D4711yescharacteristic
442C47C2×#244211yescharacteristic, complemented, Sylow
443C25—471no—
444C23×C4—471no—
445C23×C4—471no—
446C23×C4—478no—
447C23×C4—474no—
448C23×C4—471no—
449C23×C4—471no—
450C23×C4—471no—
451C23×C4—471no—
452C23×C4—471no—
453C23×C4—474no—
454C23×C4—474no—
455C23×C4—944no—
456C23×C4—944no—
457C23×C4—944no—
458C23×C4—944no—
459C23×C4—944no—
460C23×C4—944no—
461C23×C4—1882no—
462C23×C4—1882no—
463C23×C4C22×D4711yescharacteristic
464C23×C4C22×D4711yescharacteristic
465C23×C4C22×D4711yescharacteristic
466C23×C4C22×D4711yescharacteristic
467C23×C4C22×D4711yescharacteristic
468C23×C4C22×D4711yescharacteristic
469C23×C4C22×D4711yescharacteristic
470#125—9432no—
471C2×C4⋊C4—24no—
472C2×C4⋊C4—24no—
473C2×C4⋊C4—478no—
474C2×C4⋊C4—474no—
475C2×C4⋊C4—474no—
476C2×C4⋊C4—474no—
477C2×C4⋊C4—474no—
478C2×C4⋊C4—474no—
479C2×C4⋊C4—474no—
480C2×C4⋊C4—474no—
481C2×C4⋊C4—474no—
482C2×C4⋊C4—474no—
483C2×C4⋊C4—474no—
484C2×C4⋊C4—474no—
485C2×C4⋊C4—474no—
486C2×C4⋊C4—9432no—
487C2×C4⋊C4—944no—
488C2×C4⋊C4—944no—
489C2×C4⋊C4—944no—
490C2×C4⋊C4—944no—
491C2×C4⋊C4—944no—
492C2×C4⋊C4—944no—
493C2×C4⋊C4—944no—
494C2×C4⋊C4—1882no—
495C2×C4⋊C4—1882no—
496C2×C4⋊C4—1882no—
497C2×C4⋊C4—1882no—
498C2×C4⋊C4C22×D4714yes—
499C2×C4⋊C4C22×D4714yes—
500C2×C22⋊C4—474no—
501C2×C22⋊C4—474no—
502C2×C22⋊C4—474no—
503C2×C22⋊C4—474no—
504C2×C22⋊C4—944no—
505C2×C22⋊C4—944no—
506C2×C22⋊C4—944no—
507C2×C22⋊C4—944no—
508C2×C42—474no—
509C2×C42—474no—
510C2×C42—944no—
511C2×C42—944no—
512#95—474no—
513#95—474no—
514#95—474no—
515#95—474no—
516#95—474no—
517#95—474no—
518#95—474no—
519#95C22×D4714yes—
520#95C22×D4714yes—
521#95C22×D4714yes—
522#95C22×D4714yes—
523#95C22×D4714yes—
524C24—474no—
525C24—474no—
526C24—474no—
527C24—472no—
528C24—942no—
529C24—942no—
530C24—942no—
531C24—942no—
532C24C23×D4711yescharacteristic
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—474no—
553C22×C4—474no—
554C22×C4—474no—
555C22×C4—472no—
556C22×C4—474no—
557C22×C4—472no—
558C22×C4—4716no—
559C22×C4—472no—
560C22×C4—472no—
561C22×C4—472no—
562C22×C4—472no—
563C22×C4—472no—
564C22×C4—948no—
565C22×C4—9432no—
566C22×C4—948no—
567C22×C4—948no—
568C22×C4—948no—
569C22×C4—948no—
570C22×C4—942no—
571C22×C4—942no—
572C22×C4—942no—
573C22×C4—942no—
574C22×C4—942no—
575C22×C4—942no—
576C22×C4—942no—
577C22×C4—942no—
578C22×C4—942no—
579C22×C4—942no—
580C22×C4—942no—
581C22×C4—942no—
582C22×C4—942no—
583C22×C4—942no—
584C22×C4—942no—
585C22×C4—942no—
586C22×C4—942no—
587C22×C4—948no—
588C22×C4—1884no—
589C22×C4—1884no—
590C22×C4—18816no—
591C22×C4—18816no—
592C22×C4D4×D4714yes—
593C22×C4Q8×D4714yes—
594C22×C4C23×D4712yes—
595C22×C4C23×D4712yes—
596C22×C4C23×D4712yes—
597C22×C4C23×D4712yes—
598C22×C4C23×D4712yes—
599C22×C4C23×D4712yes—
600C22×C4C23×D4712yes—
601C4⋊C4—28no—
602C4⋊C4—28no—
603C4⋊C4—4716no—
604C4⋊C4—948no—
605C4⋊C4—948no—
606C4⋊C4—948no—
607C4⋊C4—948no—
608C4⋊C4—948no—
609C4⋊C4—948no—
610C4⋊C4—948no—
611C4⋊C4—1884no—
612C4⋊C4—1884no—
613C4⋊C4—1884no—
614C4⋊C4—1884no—
615C22⋊C4—948no—
616C22⋊C4—948no—
617C22⋊C4—948no—
618C22⋊C4—948no—
619C42—948no—
620C42—948no—
621C23—4716no—
622C23—474no—
623C23—474no—
624C23—474no—
625C23—948no—
626C23—948no—
627C23—948no—
628C23—948no—
629C23—948no—
630C23—948no—
631C23—942no—
632C23—942no—
633C23—942no—
634C23—942no—
635C23C2×D4×D4712yes—
636C23C2×Q8×D4712yes—
637C23#41×D4712yes—
638C23#41×D4712yes—
639C23#41×D4712yes—
640C23#1309407012yes—
641C23#1309407112yes—
642C23C24×D4711yescharacteristic
643C2×C4—28no—
644C2×C4—28no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—44no—
665C2×C4—44no—
666C2×C4—44no—
667C2×C4—44no—
668C2×C4—44no—
669C2×C4—4716no—
670C2×C4—474no—
671C2×C4—474no—
672C2×C4—474no—
673C2×C4—474no—
674C2×C4—9432no—
675C2×C4—948no—
676C2×C4—942no—
677C2×C4—942no—
678C2×C4—942no—
679C2×C4—942no—
680C2×C4—942no—
681C2×C4—942no—
682C2×C4—942no—
683C2×C4—942no—
684C2×C4—942no—
685C2×C4—942no—
686C2×C4—942no—
687C2×C4—942no—
688C2×C4—942no—
689C2×C4—942no—
690C2×C4—942no—
691C2×C4—942no—
692C2×C4—942no—
693C2×C4—18816no—
694C2×C4—18816no—
695C2×C4—1884no—
696C2×C4—1884no—
697C2×C4—1884no—
698C2×C4—1884no—
699C2×C4—1884no—
700C2×C4C2×D4×D4714yes—
701C2×C4C2×Q8×D4714yes—
702C22—478no—
703C22—944no—
704C22—9432no—
705C22—944no—
706C22—944no—
707C22—944no—
708C22—944no—
709C22—944no—
710C22C22⋊Q8×D4714yes—
711C22#125×D4714yes—
712C22#1568975314yes—
713C22#1568976514yes—
714C22#1568978114yes—
715C22#1568980914yes—
716C22#1568982414yes—
717C22C22×D4×D4711yescharacteristic
718C22C22×Q8×D4711yescharacteristic
719C22C2×#41×D4711yescharacteristic
720C22C2×#41×D4711yescharacteristic
721C22C2×#41×D4711yescharacteristic
722C22C2×#1309407011yescharacteristic
723C22C2×#1309407111yescharacteristic
724C4—24no—
725C4—24no—
726C4—42no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—478no—
732C4—944no—
733C4—1882no—
734C4—1882no—
735C4—1882no—
736C4—1882no—
737C4—1882no—
738C2—948no—
739C2#2024710518yesdirect product factor
740C2C2×C22⋊Q8×D4711yescharacteristic
741C2C2×#125×D4711yescharacteristic
742C2C2×#1568975311yescharacteristic
743C2C2×#1568976511yescharacteristic
744C2C2×#1568978111yescharacteristic
745C2C2×#1568980911yescharacteristic
746C2C2×#1568982411yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#400C2
socleC24×C47C24
prime radicalC24×D47C23
hypercenterC2×#400D47
hypocenterC47C2×#2442
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
1. C22×#13094014C2semidirect
3. #20247105C2direct (N × H)
4. C2×#15689065C2semidirect
5. C2×#15689056C2semidirect
6. C2×#15689055C2semidirect
7. C2×#15689020C2semidirect
8. C2×#15689020C2semidirect
11. C2×#15688987C2semidirect
16. C2×C47×#400C2semidirect
21. C2×#13094014C22semidirect
42. #15689065C22semidirect
43. #15689056C22semidirect
44. #15689055C22semidirect
45. #15689020C22semidirect
46. #15689020C22semidirect
49. #15688987C22semidirect
63. C47×#400C22semidirect
265. C22×D47#125semidirect
350. C2×D47C2×#125semidirect
369. C2×#400D47semidirect
381. C2×C47#2442semidirect
418. #400C2×D47semidirect
442. C47C2×#2442semidirect
739. C2#20247105direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940142
C22×C4⋊C4×D472
#202471052
C2×#156890652
C2×#156890562
C2×#156890552
C2×#156890202
C2×#156889972
C2×#156889872
C2×#156889822
C2×#156889802
C2×#156889702
C2×C47×#4002
C2×#244247