Finite Group Databasebeta

← #26139481

Subgroups — #26139481

Order 12032.

2106 conjugacy classes of subgroups.

The subgroup lattice has 1070 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689018C211yesmaximal, characteristic, complemented
2C2×#15688996C211yesmaximal, characteristic
3C2×#15688995C211yesmaximal, characteristic
4C2×#15688995C211yesmaximal, characteristic
5C2×C22⋊C4×Dic47C211yesmaximal, characteristic
6C22×C47⋊#95C211yesmaximal, characteristic
7#20241651C211yesmaximal, characteristic, complemented
8#20241643C211yesmaximal, characteristic, complemented
9#20241639C211yesmaximal, characteristic, complemented
10#20241638C211yesmaximal, characteristic, complemented
11#20241623C211yesmaximal, characteristic, complemented
12#20241620C211yesmaximal, characteristic, complemented
13Dic47⋊#95C211yesmaximal, characteristic, complemented
14#20241610C211yesmaximal, characteristic
15C2×C47×#380C211yesmaximal, characteristic
16C24×Dic47C2211yescharacteristic
17C24×Dic47C2211yescharacteristic
18C22×Dic47⋊C4C2211yescharacteristic
19C22×Dic47⋊C4C2211yescharacteristic
20C22×Dic47⋊C4C2211yescharacteristic
21C22×Dic47⋊C4C2211yescharacteristic
22C22×Dic47⋊C4C2211yescharacteristic
23C22×Dic47⋊C4C2211yescharacteristic
24C22×C22⋊Dic47C2211yescharacteristic
25C22×C22⋊Dic47C2211yescharacteristic
26C22×C4×Dic47C2211yescharacteristic
27C22×C4×Dic47C2211yescharacteristic
28#15689018—24no—
29#15688996C418yescomplemented
30#15688995—24no—
31#15688995—24no—
32C22⋊C4×Dic47—24no—
33C2×C47⋊#95—24no—
34C2×C47⋊#95C2211yescharacteristic
35C2×C47⋊#95C2211yescharacteristic
36C2×C47⋊#95C2211yescharacteristic
37C2×C47⋊#95C2211yescharacteristic
38C2×C47⋊#95C2211yescharacteristic
39C2×C47⋊#95C2211yescharacteristic
40C2×C47⋊#95C2211yescharacteristic
41C2×C47⋊#95C2211yescharacteristic
42C2×C47⋊#95C2211yescharacteristic
43C2×C47⋊#95C2211yescharacteristic
44C2×C47⋊#95C2211yescharacteristic
45C2×C47⋊#95C2211yescharacteristic
46C2×C47⋊#95C2211yescharacteristic
47C2×C47⋊#95C2211yescharacteristic
48C2×C47⋊#95C2211yescharacteristic
49C2×C47⋊#95C2211yescharacteristic
50C24×C4×C47C2211yescharacteristic
51C22×C4⋊C4×C47C2211yescharacteristic
52C22×C4⋊C4×C47C2211yescharacteristic
53C22×C22⋊C4×C47C2211yescharacteristic
54C22×C22⋊C4×C47C2211yescharacteristic
55C47×#380—24no—
56C2×#95×C47C2211yescharacteristic
57C2×#95×C47C2211yescharacteristic
58C23×Dic47—22no—
59C23×Dic47—22no—
60C23×Dic47—22no—
61C23×Dic47—22no—
62C23×Dic47—22no—
63C23×Dic47—22no—
64C23×Dic47—22no—
65C23×Dic47—22no—
66C23×Dic47—22no—
67C23×Dic47—41no—
68C23×Dic47—41no—
69C23×Dic47—41no—
70C23×Dic47—41no—
71C23×Dic47Q814yes—
72C23×Dic47C2311yescharacteristic
73C23×Dic47C2311yescharacteristic
74C23×Dic47C2311yescharacteristic
75C23×Dic47C2311yescharacteristic
76C23×Dic47C2311yescharacteristic
77C23×Dic47C2311yescharacteristic
78C23×Dic47C2311yescharacteristic
79C23×Dic47C2311yescharacteristic
80C2×Dic47⋊C4—22no—
81C2×Dic47⋊C4—22no—
82C2×Dic47⋊C4—22no—
83C2×Dic47⋊C4—22no—
84C2×Dic47⋊C4—22no—
85C2×Dic47⋊C4—22no—
86C2×Dic47⋊C4—22no—
87C2×Dic47⋊C4—22no—
88C2×Dic47⋊C4—22no—
89C2×Dic47⋊C4—22no—
90C2×Dic47⋊C4—41no—
91C2×Dic47⋊C4—41no—
92C2×Dic47⋊C4—41no—
93C2×Dic47⋊C4—41no—
94C2×Dic47⋊C4—41no—
95C2×Dic47⋊C4—41no—
96C2×Dic47⋊C4C2×C414yescomplemented
97C2×Dic47⋊C4C2×C414yescomplemented
98C2×C22⋊Dic47—22no—
99C2×C22⋊Dic47—22no—
100C2×C22⋊Dic47C2×C414yes—
101C2×C22⋊Dic47C2×C414yes—
102C2×C22⋊Dic47D414yes—
103C2×C22⋊Dic47Q814yes—
104C2×C4×Dic47—22no—
105C2×C4×Dic47—22no—
106C2×C4×Dic47—22no—
107C2×C4×Dic47—22no—
108C2×C4×Dic47—41no—
109C2×C4×Dic47—41no—
110C47⋊#95—22no—
111C47⋊#95—22no—
112C47⋊#95—22no—
113C47⋊#95—22no—
114C47⋊#95—22no—
115C47⋊#95—22no—
116C47⋊#95—22no—
117C47⋊#95—22no—
118C47⋊#95—22no—
119C47⋊#95—22no—
120C47⋊#95—22no—
121C47⋊#95—41no—
122C47⋊#95—41no—
123C47⋊#95C2×C414yescomplemented
124C47⋊#95C2×C414yescomplemented
125C47⋊#95D414yes—
126C25×C47C2311yescharacteristic
127C23×C4×C47—22no—
128C23×C4×C47—22no—
129C23×C4×C47—22no—
130C23×C4×C47—22no—
131C23×C4×C47—41no—
132C23×C4×C47—41no—
133C23×C4×C47C2×C414yes—
134C23×C4×C47C2311yescharacteristic
135C23×C4×C47C2311yescharacteristic
136C23×C4×C47C2311yescharacteristic
137C23×C4×C47C2311yescharacteristic
138C23×C4×C47C2311yescharacteristic
139C23×C4×C47C2311yescharacteristic
140C2×C4⋊C4×C47—22no—
141C2×C4⋊C4×C47—22no—
142C2×C4⋊C4×C47—22no—
143C2×C4⋊C4×C47—22no—
144C2×C4⋊C4×C47—41no—
145C2×C4⋊C4×C47—41no—
146C2×C22⋊C4×C47—22no—
147C2×C22⋊C4×C47—22no—
148C2×C22⋊C4×C47—22no—
149C2×C22⋊C4×C47—22no—
150C2×C22⋊C4×C47—22no—
151C2×C22⋊C4×C47D414yes—
152#95×C47—22no—
153#95×C47—22no—
154C24×C47—21no—
155C24×C47—21no—
156C24×C47—21no—
157C24×C47—21no—
158C24×C47—21no—
159C24×C47—21no—
160C24×C47—21no—
161C24×C47—21no—
162C24×C47C22×C412yes—
163C24×C47C2×D412yes—
164C24×C47C2×D412yes—
165C24×C47C2×Q812yes—
166C24×C47C2×Q812yes—
167C24×C47#4112yes—
168C24×C47#4112yes—
169C24×C47C2411yescharacteristic
170C22×C4×C47—21no—
171C22×C4×C47—21no—
172C22×C4×C47—21no—
173C22×C4×C47—21no—
174C22×C4×C47—28no—
175C22×C4×C47—21no—
176C22×C4×C47—21no—
177C22×C4×C47—21no—
178C22×C4×C47—21no—
179C22×C4×C47—21no—
180C22×C4×C47—21no—
181C22×C4×C47—21no—
182C22×C4×C47—21no—
183C22×C4×C47—21no—
184C22×C4×C47—21no—
185C22×C4×C47—21no—
186C22×C4×C47—21no—
187C22×C4×C47—21no—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47—21no—
191C22×C4×C47—21no—
192C22×C4×C47—21no—
193C22×C4×C47—28no—
194C22×C4×C47—21no—
195C22×C4×C47—21no—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47—21no—
200C22×C4×C47—21no—
201C22×C4×C47—21no—
202C22×C4×C47—21no—
203C22×C4×C47—21no—
204C22×C4×C47—21no—
205C22×C4×C47—21no—
206C22×C4×C47—21no—
207C22×C4×C47—21no—
208C22×C4×C47—44no—
209C22×C4×C47—44no—
210C22×C4×C47—44no—
211C22×C4×C47—44no—
212C22×C4×C47—44no—
213C22×C4×C47C22×C412yes—
214C22×C4×C47C22×C412yes—
215C22×C4×C47C2×D412yes—
216C22×C4×C47C2×D412yes—
217C22×C4×C47C2×D412yes—
218C22×C4×C47#4112yes—
219C22×Dic47—21no—
220C22×Dic47—21no—
221C22×Dic47—21no—
222C22×Dic47—21no—
223C22×Dic47—21no—
224C22×Dic47—21no—
225C22×Dic47—21no—
226C22×Dic47—21no—
227C22×Dic47—21no—
228C22×Dic47—21no—
229C22×Dic47—21no—
230C22×Dic47—21no—
231C22×Dic47—28no—
232C22×Dic47—28no—
233C22×Dic47—21no—
234C22×Dic47—21no—
235C22×Dic47—21no—
236C22×Dic47—21no—
237C22×Dic47—21no—
238C22×Dic47—21no—
239C22×Dic47—21no—
240C22×Dic47—21no—
241C22×Dic47—21no—
242C22×Dic47—21no—
243C22×Dic47—21no—
244C22×Dic47—21no—
245C22×Dic47—21no—
246C22×Dic47—21no—
247C22×Dic47—21no—
248C22×Dic47—21no—
249C22×Dic47—21no—
250C22×Dic47—21no—
251C22×Dic47—21no—
252C22×Dic47—21no—
253C22×Dic47—21no—
254C22×Dic47—21no—
255C22×Dic47—21no—
256C22×Dic47—21no—
257C22×Dic47—21no—
258C22×Dic47—21no—
259C22×Dic47—21no—
260C22×Dic47—21no—
261C22×Dic47—21no—
262C22×Dic47—21no—
263C22×Dic47—28no—
264C22×Dic47—44no—
265C22×Dic47—44no—
266C22×Dic47—44no—
267C22×Dic47—44no—
268C22×Dic47—44no—
269C22×Dic47—44no—
270C22×Dic47—44no—
271C22×Dic47—44no—
272C22×Dic47—44no—
273C22×Dic47—44no—
274C22×Dic47—44no—
275C22×Dic47C22×C412yes—
276C22×Dic47C22×C412yes—
277C22×Dic47C22×C412yes—
278C22×Dic47C22×C412yes—
279C22×Dic47C2×D412yes—
280C22×Dic47C2×D412yes—
281C22×Dic47C2×D412yes—
282C22×Dic47C2×D412yes—
283C22×Dic47C2×Q812yes—
284C22×Dic47C2×Q812yes—
285C22×Dic47C2×Q812yes—
286C22×Dic47C2×Q812yes—
287C22×Dic47#4112yes—
288C22×Dic47#4112yes—
289C4⋊C4×C47—44no—
290C4⋊C4×C47—44no—
291C22⋊C4×C47—28no—
292C22⋊C4×C47—44no—
293C22⋊Dic47—28no—
294C22⋊Dic47C4⋊C4116yescomplemented
295Dic47⋊C4—28no—
296Dic47⋊C4—44no—
297Dic47⋊C4—44no—
298Dic47⋊C4—44no—
299Dic47⋊C4—44no—
300Dic47⋊C4—44no—
301C4×Dic47—44no—
302C4×Dic47—44no—
303C23×C47—22no—
304C23×C47—22no—
305C23×C47—22no—
306C23×C47—22no—
307C23×C47—22no—
308C23×C47—22no—
309C23×C47—22no—
310C23×C47—22no—
311C23×C47—22no—
312C23×C47—22no—
313C23×C47—22no—
314C23×C47—22no—
315C23×C47—22no—
316C23×C47—22no—
317C23×C47—22no—
318C23×C47—22no—
319C23×C47—22no—
320C23×C47—22no—
321C23×C47—22no—
322C23×C47—22no—
323C23×C47—22no—
324C23×C47—22no—
325C23×C47—22no—
326C23×C47—22no—
327C23×C47—22no—
328C23×C47—22no—
329C23×C47—22no—
330C23×C47—22no—
331C23×C47C2×C4⋊C414yes—
332C23×C47C4×D414yes—
333C23×C47C4×Q814yes—
334C23×C47#12114yes—
335C23×C47C22⋊Q814yes—
336C23×C47#12514yes—
337C23×C47C4⋊Q814yes—
338C23×C47C23×C411yescharacteristic
339C23×C47C22×D411yescharacteristic
340C23×C47C22×D411yescharacteristic
341C23×C47C22×D411yescharacteristic
342C23×C47C22×Q811yescharacteristic
343C23×C47C22×Q811yescharacteristic
344C23×C47C2×#4111yescharacteristic
345C23×C47C2×#4111yescharacteristic
346C23×C47C2×#4111yescharacteristic
347C23×C47C2×#4111yescharacteristic
348C23×C47C2×#4111yescharacteristic
349C23×C47H(5,𝔽2)11yescharacteristic
350C23×C47H(5,𝔽2)11yescharacteristic
351C23×C47H(5,𝔽2)11yescharacteristic
352C23×C472−1+411yescharacteristic
353C2×C4×C47—22no—
354C2×C4×C47—22no—
355C2×C4×C47—22no—
356C2×C4×C47—22no—
357C2×C4×C47—22no—
358C2×C4×C47—22no—
359C2×C4×C47—22no—
360C2×C4×C47—22no—
361C2×C4×C47—22no—
362C2×C4×C47—22no—
363C2×C4×C47—22no—
364C2×C4×C47—22no—
365C2×C4×C47—22no—
366C2×C4×C47—22no—
367C2×C4×C47—22no—
368C2×C4×C47—416no—
369C2×C4×C47—41no—
370C2×C4×C47—41no—
371C2×C4×C47—41no—
372C2×C4×C47—41no—
373C2×C4×C47—41no—
374C2×C4×C47—41no—
375C2×C4×C47—41no—
376C2×C4×C47—41no—
377C2×C4×C47—41no—
378C2×C4×C47—41no—
379C2×C4×C47—41no—
380C2×C4×C47—41no—
381C2×C4×C47—41no—
382C2×C4×C47—41no—
383C2×C4×C47—41no—
384C2×C4×C47—41no—
385C2×C4×C47—41no—
386C2×C4×C47—41no—
387C2×C4×C47—41no—
388C2×C4×C47—41no—
389C2×C4×C47—41no—
390C2×C4×C47—41no—
391C2×C4×C47—41no—
392C2×C4×C47—41no—
393C2×C4×C47—41no—
394C2×C4×C47—41no—
395C2×C4×C47C4×D414yes—
396C2×Dic47—22no—
397C2×Dic47—22no—
398C2×Dic47—22no—
399C2×Dic47—22no—
400C2×Dic47—22no—
401C2×Dic47—22no—
402C2×Dic47—22no—
403C2×Dic47—22no—
404C2×Dic47—22no—
405C2×Dic47—22no—
406C2×Dic47—22no—
407C2×Dic47—22no—
408C2×Dic47—22no—
409C2×Dic47—22no—
410C2×Dic47—22no—
411C2×Dic47—22no—
412C2×Dic47—22no—
413C2×Dic47—22no—
414C2×Dic47—22no—
415C2×Dic47—22no—
416C2×Dic47—22no—
417C2×Dic47—22no—
418C2×Dic47—22no—
419C2×Dic47—22no—
420C2×Dic47—22no—
421C2×Dic47—22no—
422C2×Dic47—22no—
423C2×Dic47—22no—
424C2×Dic47—22no—
425C2×Dic47—22no—
426C2×Dic47—22no—
427C2×Dic47—22no—
428C2×Dic47—22no—
429C2×Dic47—416no—
430C2×Dic47—416no—
431C2×Dic47—41no—
432C2×Dic47—41no—
433C2×Dic47—41no—
434C2×Dic47—41no—
435C2×Dic47—41no—
436C2×Dic47—41no—
437C2×Dic47—41no—
438C2×Dic47—41no—
439C2×Dic47—41no—
440C2×Dic47—41no—
441C2×Dic47—41no—
442C2×Dic47—41no—
443C2×Dic47—41no—
444C2×Dic47—41no—
445C2×Dic47—41no—
446C2×Dic47—41no—
447C2×Dic47—41no—
448C2×Dic47—41no—
449C2×Dic47—41no—
450C2×Dic47—41no—
451C2×Dic47C2×C4⋊C414yes—
452C2×Dic47C2×C4⋊C414yes—
453C2×Dic47C22⋊Q814yes—
454#14004—471nomaximal, Sylow
455C22×C47—24no—
456C22×C47—24no—
457C22×C47—24no—
458C22×C47—24no—
459C22×C47—24no—
460C22×C47—24no—
461C22×C47—24no—
462C22×C47—24no—
463C22×C47—24no—
464C22×C47—24no—
465C22×C47—24no—
466C22×C47—24no—
467C22×C47—24no—
468C22×C47—24no—
469C22×C47#38918yescomplemented
470C22×C47C22×C4⋊C411yescharacteristic
471C22×C47C2×C4×D411yescharacteristic
472C22×C47C2×C4×D411yescharacteristic
473C22×C47C2×C4×Q811yescharacteristic
474C22×C47C4×#4111yescharacteristic
475C22×C47#51811yescharacteristic
476C22×C47#52011yescharacteristic
477C22×C47C2×#12111yescharacteristic
478C22×C47C2×C22⋊Q811yescharacteristic
479C22×C47C2×C22⋊Q811yescharacteristic
480C22×C47#52511yescharacteristic
481C22×C47C2×#12511yescharacteristic
482C22×C47#52911yescharacteristic
483C22×C47C2×C4⋊Q811yescharacteristic
484C22×C47#53311yescharacteristic
485C22×C47#53811yescharacteristic
486C22×C47#53911yescharacteristic
487C22×C47#54311yescharacteristic
488C22×C47#54411yescharacteristic
489C22×C47D4211yescharacteristic
490C22×C47D4211yescharacteristic
491C22×C47#54611yescharacteristic
492C22×C47#54611yescharacteristic
493C22×C47#54611yescharacteristic
494C22×C47#54611yescharacteristic
495C22×C47#54611yescharacteristic
496C22×C47#54711yescharacteristic
497C22×C47#54711yescharacteristic
498C22×C47D4×Q811yescharacteristic
499C22×C47#55111yescharacteristic
500C22×C47#55111yescharacteristic
501C22×C47#55211yescharacteristic
502C22×C47#55411yescharacteristic
503C22×C47#55411yescharacteristic
504C22×C47#55411yescharacteristic
505C4×C47—24no—
506C4×C47—42no—
507C4×C47—42no—
508C4×C47—42no—
509C4×C47—81no—
510C4×C47—81no—
511Dic47—24no—
512Dic47—24no—
513Dic47—24no—
514Dic47—42no—
515Dic47—42no—
516Dic47—42no—
517Dic47—42no—
518Dic47—42no—
519C2×#389—471no—
520C2×#385—471no—
521C2×#385—471no—
522C2×#385—471no—
523C2×#380D4711yescharacteristic
524C2×C4×C22⋊C4—471no—
525C22×#95—471no—
526#1444—471no—
527#1442—471no—
528#1441—471no—
529#1441—471no—
530#1436—471no—
531#1436—471no—
532C4⋊#95—471no—
533C22⋊#95—471no—
534C2×C47—28no—
535C2×C47C2×#38911yescharacteristic
536C2×C47C4×C22⋊Q811yescharacteristic
537C2×C47#232911yescharacteristic
538C2×C47D4×C4⋊C411yescharacteristic
539C2×C47#234911yescharacteristic
540C2×C47#235811yescharacteristic
541C2×C47#235911yescharacteristic
542C2×C47#242411yescharacteristic
543C2×C47#242511yescharacteristic
544C2×C47#243711yescharacteristic
545C2×C47#243811yescharacteristic
546C2×C47#244011yescharacteristic
547C2×C47#247311yescharacteristic
548C2×C47#250511yescharacteristic
549C2×C47#254911yescharacteristic
550C24×C4—471no—
551C24×C4—471no—
552C24×C4C2×D4711yescharacteristic
553C22×C4⋊C4—471no—
554C22×C4⋊C4—471no—
555C22×C4⋊C4—471no—
556C22×C4⋊C4—471no—
557C22×C4⋊C4—471no—
558C22×C4⋊C4—471no—
559C22×C4⋊C4C2×D4711yescharacteristic
560C22×C4⋊C4C2×D4711yescharacteristic
561C22×C22⋊C4—471no—
562C22×C22⋊C4—471no—
563C22×C22⋊C4C2×D4711yescharacteristic
564C22×C22⋊C4C2×D4711yescharacteristic
565C22×C42—471no—
566C22×C42—471no—
567#389—944no—
568#385—478no—
569#385—944no—
570#385—944no—
571#380—24no—
572C4×C22⋊C4—944no—
573C2×#95—471no—
574C2×#95—471no—
575C2×#95—471no—
576C2×#95—471no—
577C2×#95—471no—
578C2×#95—471no—
579C2×#95—471no—
580C2×#95—471no—
581C2×#95—471no—
582C2×#95—471no—
583C2×#95—471no—
584C2×#95—471no—
585C2×#95—471no—
586C2×#95—471no—
587C2×#95—471no—
588C2×#95—471no—
589C2×#95—944no—
590C2×#95C2×D4711yescharacteristic
591C2×#95C2×D4711yescharacteristic
592C47#1400411yescharacteristic, complemented, Sylow
593C25C22×D4711yescharacteristic
594C23×C4—22no—
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—22no—
598C23×C4—41no—
599C23×C4—41no—
600C23×C4—471no—
601C23×C4—471no—
602C23×C4—471no—
603C23×C4—471no—
604C23×C4—471no—
605C23×C4—471no—
606C23×C4—471no—
607C23×C4—471no—
608C23×C4—474no—
609C23×C4—942no—
610C23×C4—942no—
611C23×C4—942no—
612C23×C4—942no—
613C23×C4—942no—
614C23×C4—942no—
615C23×C4—942no—
616C23×C4—942no—
617C23×C4—942no—
618C23×C4—1881no—
619C23×C4—1881no—
620C23×C4—1881no—
621C23×C4—1881no—
622C23×C4C4×D4714yes—
623C23×C4C22×D4711yescharacteristic
624C23×C4C22×D4711yescharacteristic
625C23×C4C22×D4711yescharacteristic
626C23×C4C22×D4711yescharacteristic
627C23×C4C22×D4711yescharacteristic
628C23×C4C22×D4711yescharacteristic
629C2×C4⋊C4—22no—
630C2×C4⋊C4—22no—
631C2×C4⋊C4—22no—
632C2×C4⋊C4—22no—
633C2×C4⋊C4—41no—
634C2×C4⋊C4—41no—
635C2×C4⋊C4—474no—
636C2×C4⋊C4—474no—
637C2×C4⋊C4—942no—
638C2×C4⋊C4—942no—
639C2×C4⋊C4—942no—
640C2×C4⋊C4—942no—
641C2×C4⋊C4—942no—
642C2×C4⋊C4—942no—
643C2×C4⋊C4—942no—
644C2×C4⋊C4—942no—
645C2×C4⋊C4—942no—
646C2×C4⋊C4—942no—
647C2×C4⋊C4—1881no—
648C2×C4⋊C4—1881no—
649C2×C4⋊C4—1881no—
650C2×C4⋊C4—1881no—
651C2×C4⋊C4—1881no—
652C2×C4⋊C4—1881no—
653C2×C22⋊C4—22no—
654C2×C22⋊C4—22no—
655C2×C22⋊C4—22no—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—22no—
658C2×C22⋊C4—474no—
659C2×C22⋊C4—474no—
660C2×C22⋊C4—474no—
661C2×C22⋊C4—474no—
662C2×C22⋊C4—942no—
663C2×C22⋊C4—942no—
664C2×C22⋊C4C22⋊D4714yes—
665C2×C42—942no—
666C2×C42—942no—
667C2×C42—942no—
668C2×C42—942no—
669C2×C42—1881no—
670C2×C42—1881no—
671#95—22no—
672#95—22no—
673#95—474no—
674#95—474no—
675#95—474no—
676#95—942no—
677#95—942no—
678#95—942no—
679#95—942no—
680#95—942no—
681#95—942no—
682#95—942no—
683#95—942no—
684#95—942no—
685#95—942no—
686#95—942no—
687#95—1881no—
688#95—1881no—
689C24—21no—
690C24—21no—
691C24—21no—
692C24—21no—
693C24—21no—
694C24—21no—
695C24—21no—
696C24—21no—
697C24C2×C4×D4712yes—
698C24#1062535012yes—
699C24D4×D4712yes—
700C24#1062535212yes—
701C24Q8×D4712yes—
702C24Q8×D4712yes—
703C24C2×C22⋊D4712yes—
704C24C23×D4711yescharacteristic
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—28no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—28no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—44no—
744C22×C4—44no—
745C22×C4—44no—
746C22×C4—44no—
747C22×C4—44no—
748C22×C4—472no—
749C22×C4—472no—
750C22×C4—472no—
751C22×C4—472no—
752C22×C4—472no—
753C22×C4—472no—
754C22×C4—472no—
755C22×C4—472no—
756C22×C4—472no—
757C22×C4—472no—
758C22×C4—472no—
759C22×C4—472no—
760C22×C4—472no—
761C22×C4—472no—
762C22×C4—948no—
763C22×C4—941no—
764C22×C4—941no—
765C22×C4—941no—
766C22×C4—941no—
767C22×C4—941no—
768C22×C4—941no—
769C22×C4—941no—
770C22×C4—941no—
771C22×C4—941no—
772C22×C4—941no—
773C22×C4—941no—
774C22×C4—941no—
775C22×C4—948no—
776C22×C4—948no—
777C22×C4—941no—
778C22×C4—941no—
779C22×C4—941no—
780C22×C4—941no—
781C22×C4—941no—
782C22×C4—941no—
783C22×C4—941no—
784C22×C4—941no—
785C22×C4—941no—
786C22×C4—941no—
787C22×C4—941no—
788C22×C4—941no—
789C22×C4—941no—
790C22×C4—941no—
791C22×C4—941no—
792C22×C4—941no—
793C22×C4—941no—
794C22×C4—941no—
795C22×C4—941no—
796C22×C4—941no—
797C22×C4—941no—
798C22×C4—941no—
799C22×C4—941no—
800C22×C4—941no—
801C22×C4—941no—
802C22×C4—941no—
803C22×C4—941no—
804C22×C4—941no—
805C22×C4—941no—
806C22×C4—941no—
807C22×C4—1884no—
808C22×C4—1884no—
809C22×C4—1884no—
810C22×C4—1884no—
811C22×C4—1884no—
812C22×C4—1884no—
813C22×C4—1884no—
814C22×C4—1884no—
815C22×C4—1884no—
816C22×C4—1884no—
817C22×C4—1884no—
818C22×C4C2×C4×D4712yes—
819C22×C4C2×C4×D4712yes—
820C22×C4D4×D4712yes—
821C22×C4#1062535212yes—
822C22×C4C2×C22⋊D4712yes—
823C22×C4C2×C22⋊D4712yes—
824C4⋊C4—44no—
825C4⋊C4—44no—
826C4⋊C4—948no—
827C4⋊C4—1884no—
828C4⋊C4—1884no—
829C4⋊C4—1884no—
830C4⋊C4—1884no—
831C4⋊C4—1884no—
832C22⋊C4—28no—
833C22⋊C4—44no—
834C22⋊C4—4716no—
835C22⋊C4—948no—
836C42—1884no—
837C42—1884no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23C4⋊C4×D4714yes—
867C23C4×C22⋊D4714yes—
868C23#1309398914yes—
869C23#1309399614yes—
870C23#1309400214yes—
871C23#1309401414yes—
872C23#1309402214yes—
873C23C22×C4×D4711yescharacteristic
874C23C2×D4×D4711yescharacteristic
875C23C2×D4×D4711yescharacteristic
876C23C22×C22⋊D4711yescharacteristic
877C23C2×Q8×D4711yescharacteristic
878C23C2×Q8×D4711yescharacteristic
879C23#41×D4711yescharacteristic
880C23#41×D4711yescharacteristic
881C23C2×#1062535211yescharacteristic
882C23C2×#1062535211yescharacteristic
883C23C2×#1062535011yescharacteristic
884C23#1309406911yescharacteristic
885C23#1309406911yescharacteristic
886C23#1309407011yescharacteristic
887C23#1309407111yescharacteristic
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—416no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—474no—
931C2×C4—474no—
932C2×C4—474no—
933C2×C4—942no—
934C2×C4—942no—
935C2×C4—942no—
936C2×C4—942no—
937C2×C4—942no—
938C2×C4—942no—
939C2×C4—942no—
940C2×C4—942no—
941C2×C4—942no—
942C2×C4—942no—
943C2×C4—942no—
944C2×C4—942no—
945C2×C4—942no—
946C2×C4—942no—
947C2×C4—942no—
948C2×C4—942no—
949C2×C4—942no—
950C2×C4—942no—
951C2×C4—942no—
952C2×C4—942no—
953C2×C4—942no—
954C2×C4—942no—
955C2×C4—942no—
956C2×C4—942no—
957C2×C4—942no—
958C2×C4—942no—
959C2×C4—942no—
960C2×C4—942no—
961C2×C4—942no—
962C2×C4—942no—
963C2×C4—942no—
964C2×C4—942no—
965C2×C4—942no—
966C2×C4—18816no—
967C2×C4—18816no—
968C2×C4—1881no—
969C2×C4—1881no—
970C2×C4—1881no—
971C2×C4—1881no—
972C2×C4—1881no—
973C2×C4—1881no—
974C2×C4—1881no—
975C2×C4—1881no—
976C2×C4—1881no—
977C2×C4—1881no—
978C2×C4—1881no—
979C2×C4—1881no—
980C2×C4—1881no—
981C2×C4—1881no—
982C2×C4—1881no—
983C2×C4—1881no—
984C2×C4—1881no—
985C2×C4—1881no—
986C2×C4—1881no—
987C2×C4—1881no—
988C2×C4(C22⋊D47)⋊C414yes—
989C22—24no—
990C22—24no—
991C22—24no—
992C22—24no—
993C22—24no—
994C22—24no—
995C22—24no—
996C22—24no—
997C22—24no—
998C22—24no—
999C22—24no—
1000C22—24no—
1001C22—24no—
1002C22—24no—
1003C22#1568901818yescomplemented
1004C22C2×C4⋊C4×D4711yescharacteristic
1005C22C2×(C22⋊D47)⋊C411yescharacteristic
1006C22C2×C4×C22⋊D4711yescharacteristic
1007C22C2×#1309398911yescharacteristic
1008C22#1568959111yescharacteristic
1009C22#1568959611yescharacteristic
1010C22#1568960311yescharacteristic
1011C22C2×#1309399611yescharacteristic
1012C22C22⋊Q8×D4711yescharacteristic
1013C22C2×#1309400211yescharacteristic
1014C22#1568963311yescharacteristic
1015C22C2×#1309401411yescharacteristic
1016C22#1568965411yescharacteristic
1017C22C2×#1309402211yescharacteristic
1018C22#1568967511yescharacteristic
1019C22#1568971011yescharacteristic
1020C22#1568971811yescharacteristic
1021C22#1568974811yescharacteristic
1022C22#1568975211yescharacteristic
1023C22D4×C22⋊D4711yescharacteristic
1024C22#1568975711yescharacteristic
1025C22#1568976111yescharacteristic
1026C22#1568976211yescharacteristic
1027C22#1568976211yescharacteristic
1028C22#1568976311yescharacteristic
1029C22#1568976711yescharacteristic
1030C22#1568977211yescharacteristic
1031C22#1568977311yescharacteristic
1032C22#1568978611yescharacteristic
1033C22#1568979711yescharacteristic
1034C22#1568979911yescharacteristic
1035C22#1568980611yescharacteristic
1036C22#1568982711yescharacteristic
1037C22#1568982711yescharacteristic
1038C22#1568983111yescharacteristic
1039C4—24no—
1040C4—42no—
1041C4—42no—
1042C4—42no—
1043C4—81no—
1044C4—81no—
1045C4—944no—
1046C4—944no—
1047C4—944no—
1048C4—1882no—
1049C4—1882no—
1050C4—1882no—
1051C4—1882no—
1052C4—1882no—
1053C2—28no—
1054C2C2×#1568901811yescharacteristic
1055C2#2024591611yescharacteristic
1056C2#2024611811yescharacteristic
1057C2#2024628411yescharacteristic
1058C2#2024629211yescharacteristic
1059C2#2024636711yescharacteristic
1060C2#2024638011yescharacteristic
1061C2#2024693011yescharacteristic
1062C2#2024694511yescharacteristic
1063C2#2024705611yescharacteristic
1064C2#2024707011yescharacteristic
1065C2#2024708711yescharacteristic
1066C2#2024753411yescharacteristic
1067C2#2024788511yescharacteristic
1068C2#2024839611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C47×#380C2
socle, cosocleC24×C47C24
prime radicalC25×C47C23
hypercenterC2×#380D47
hypocenterC47#14004
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
1. C2×#15689018C2semidirect
7. #20241651C2semidirect
8. #20241643C2semidirect
9. #20241639C2semidirect
10. #20241638C2semidirect
11. #20241623C2semidirect
12. #20241620C2semidirect
13. Dic47⋊#95C2semidirect
29. #15688996C4semidirect
96. C2×Dic47⋊C4C2×C4semidirect
97. C2×Dic47⋊C4C2×C4semidirect
123. C47⋊#95C2×C4semidirect
124. C47⋊#95C2×C4semidirect
294. C22⋊Dic47C4⋊C4semidirect
469. C22×C47#389semidirect
592. C47#14004semidirect
1003. C22#15689018semidirect

Maximal subgroups

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

subgroupindex
C2×#156890182
C2×#156889962
C2×#156889952
C2×C22⋊C4×Dic472
C22×C47⋊#952
#202416512
#202416432
#202416392
#202416382
#202416232
#202416202
Dic47⋊#952
#202416102
C2×C47×#3802
#1400447