Finite Group Databasebeta

← #26139113

Subgroups — #26139113

Order 12032.

1746 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689020C211yesmaximal, characteristic, complemented
2C2×#15688981C211yesmaximal, characteristic
3C2×#15688981C211yesmaximal, characteristic
4C2×C4×Dic47⋊C4C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×Dic47C211yesmaximal, characteristic
6#20241646C211yesmaximal, characteristic, complemented
7#20241644C211yesmaximal, characteristic, complemented
8#20241633C211yesmaximal, characteristic
9#20241631C211yesmaximal, characteristic
10#20241625C211yesmaximal, characteristic
11Dic47⋊#95C211yesmaximal, characteristic, complemented
12Dic47⋊#95C211yesmaximal, characteristic, complemented
13#20241615C211yesmaximal, characteristic, complemented
14#20241614C211yesmaximal, characteristic, complemented
15C47×#1437C211yesmaximal, characteristic
16C24×Dic47C2211yescharacteristic
17C22×C4⋊Dic47C2211yescharacteristic
18C22×Dic47⋊C4C2211yescharacteristic
19C22×Dic47⋊C4C2211yescharacteristic
20C22×Dic47⋊C4C2211yescharacteristic
21C22×Dic47⋊C4C2211yescharacteristic
22C22×Dic47⋊C4C2211yescharacteristic
23C22×C22⋊Dic47C2211yescharacteristic
24C22×C22⋊Dic47C2211yescharacteristic
25C22×C22⋊Dic47C2211yescharacteristic
26C22×C4×Dic47C2211yescharacteristic
27C22×C4×Dic47C2211yescharacteristic
28C22×C4×Dic47C2211yescharacteristic
29#15689020—24no—
30#15688981—24no—
31#15688981C418yescomplemented
32C4×Dic47⋊C4—24no—
33C22⋊C4×Dic47—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
49C22×C22⋊C4×C47C2211yescharacteristic
50C22×C22⋊C4×C47C2211yescharacteristic
51C22×C22⋊C4×C47C2211yescharacteristic
52C22×C42×C47C2211yescharacteristic
53C2×#95×C47C2211yescharacteristic
54C2×#95×C47C2211yescharacteristic
55C2×#95×C47C2211yescharacteristic
56C23×Dic47—22no—
57C23×Dic47—22no—
58C23×Dic47—22no—
59C23×Dic47—22no—
60C23×Dic47—22no—
61C23×Dic47—22no—
62C23×Dic47C2×C414yes—
63C23×Dic47C2311yescharacteristic
64C23×Dic47C2311yescharacteristic
65C23×Dic47C2311yescharacteristic
66C23×Dic47C2311yescharacteristic
67C23×Dic47C2311yescharacteristic
68C23×Dic47C2311yescharacteristic
69C23×Dic47C2311yescharacteristic
70C23×Dic47C2311yescharacteristic
71C2×C4⋊Dic47—22no—
72C2×C4⋊Dic47—41no—
73C2×C4⋊Dic47—41no—
74C2×Dic47⋊C4—22no—
75C2×Dic47⋊C4—22no—
76C2×Dic47⋊C4—22no—
77C2×Dic47⋊C4—22no—
78C2×Dic47⋊C4—22no—
79C2×Dic47⋊C4—22no—
80C2×Dic47⋊C4—22no—
81C2×Dic47⋊C4—22no—
82C2×Dic47⋊C4—22no—
83C2×Dic47⋊C4—22no—
84C2×Dic47⋊C4—41no—
85C2×Dic47⋊C4—41no—
86C2×Dic47⋊C4C2×C414yes—
87C2×Dic47⋊C4C2×C414yes—
88C2×Dic47⋊C4D414yes—
89C2×C22⋊Dic47—22no—
90C2×C22⋊Dic47—22no—
91C2×C22⋊Dic47—22no—
92C2×C22⋊Dic47—22no—
93C2×C22⋊Dic47—22no—
94C2×C22⋊Dic47—41no—
95C2×C22⋊Dic47—41no—
96C2×C22⋊Dic47—41no—
97C2×C22⋊Dic47C2×C414yes—
98C2×C4×Dic47—22no—
99C2×C4×Dic47—22no—
100C2×C4×Dic47—22no—
101C2×C4×Dic47—22no—
102C2×C4×Dic47—22no—
103C2×C4×Dic47—22no—
104C2×C4×Dic47—22no—
105C2×C4×Dic47—41no—
106C2×C4×Dic47D414yes—
107C47⋊#95—22no—
108C47⋊#95—22no—
109C47⋊#95—22no—
110C47⋊#95—22no—
111C47⋊#95—22no—
112C47⋊#95—22no—
113C47⋊#95—22no—
114C47⋊#95—22no—
115C47⋊#95—22no—
116C47⋊#95—41no—
117C47⋊#95—41no—
118C47⋊#95—41no—
119C47⋊#95—41no—
120C47⋊#95C2×C414yes—
121C47⋊#95C2×C414yes—
122C25×C47C2311yescharacteristic
123C23×C4×C47C2311yescharacteristic
124C23×C4×C47C2311yescharacteristic
125C23×C4×C47C2311yescharacteristic
126C23×C4×C47C2311yescharacteristic
127C23×C4×C47C2311yescharacteristic
128C23×C4×C47C2311yescharacteristic
129C2×C22⋊C4×C47—22no—
130C2×C22⋊C4×C47—22no—
131C2×C22⋊C4×C47—22no—
132C2×C22⋊C4×C47—22no—
133C2×C22⋊C4×C47—41no—
134C2×C22⋊C4×C47—41no—
135C2×C22⋊C4×C47—41no—
136C2×C22⋊C4×C47C2×C414yes—
137C2×C22⋊C4×C47Q814yes—
138C2×C42×C47—22no—
139C2×C42×C47—22no—
140C2×C42×C47—41no—
141#95×C47—22no—
142#95×C47—41no—
143#95×C47—41no—
144C24×C47—21no—
145C24×C47—21no—
146C24×C47—21no—
147C24×C47—21no—
148C24×C47—21no—
149C24×C47—21no—
150C24×C47—21no—
151C24×C47—21no—
152C24×C47—21no—
153C24×C47—21no—
154C24×C47—21no—
155C24×C47—21no—
156C24×C47C22×C412yes—
157C24×C47C2×Q812yes—
158C24×C47#4112yes—
159C24×C47C2411yescharacteristic
160C22×C4×C47—21no—
161C22×C4×C47—21no—
162C22×C4×C47—21no—
163C22×C4×C47—21no—
164C22×C4×C47—21no—
165C22×C4×C47—21no—
166C22×C4×C47—21no—
167C22×C4×C47—21no—
168C22×C4×C47—21no—
169C22×C4×C47—21no—
170C22×C4×C47—21no—
171C22×C4×C47—21no—
172C22×C4×C47—21no—
173C22×C4×C47—21no—
174C22×C4×C47—21no—
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—21no—
194C22×C4×C47—21no—
195C22×C4×C47C22×C412yes—
196C22×C4×C47C22×C412yes—
197C22×C4×C47C2×D412yes—
198C22×C4×C47C2×D412yes—
199C22×C4×C47C2×Q812yes—
200C22×C4×C47C2×Q812yes—
201C22×C4×C47#4112yes—
202C22×Dic47—21no—
203C22×Dic47—21no—
204C22×Dic47—21no—
205C22×Dic47—21no—
206C22×Dic47—21no—
207C22×Dic47—21no—
208C22×Dic47—21no—
209C22×Dic47—21no—
210C22×Dic47—21no—
211C22×Dic47—21no—
212C22×Dic47—21no—
213C22×Dic47—21no—
214C22×Dic47—21no—
215C22×Dic47—21no—
216C22×Dic47—21no—
217C22×Dic47—21no—
218C22×Dic47—21no—
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—21no—
232C22×Dic47—21no—
233C22×Dic47—21no—
234C22×Dic47—21no—
235C22×Dic47—21no—
236C22×Dic47—21no—
237C22×Dic47—21no—
238C22×Dic47—28no—
239C22×Dic47—28no—
240C22×Dic47—28no—
241C22×Dic47—21no—
242C22×Dic47—21no—
243C22×Dic47—21no—
244C22×Dic47—21no—
245C22×Dic47—21no—
246C22×Dic47—21no—
247C22×Dic47—21no—
248C22×Dic47—44no—
249C22×Dic47—44no—
250C22×Dic47—44no—
251C22×Dic47—44no—
252C22×Dic47C22×C412yes—
253C22×Dic47C22×C412yes—
254C22×Dic47C22×C412yes—
255C22×Dic47C22×C412yes—
256C22×Dic47C2×D412yes—
257C22×Dic47C2×D412yes—
258C22×Dic47C2×D412yes—
259C22×Dic47C2×D412yes—
260C22×Dic47#4112yes—
261C22×Dic47#4112yes—
262C22×Dic47#4112yes—
263C22×Dic47#4112yes—
264C22×Dic47#4112yes—
265C22⋊C4×C47—28no—
266C22⋊C4×C47—44no—
267C22⋊C4×C47—44no—
268C42×C47—44no—
269C22⋊Dic47—28no—
270C22⋊Dic47—44no—
271C22⋊Dic47—44no—
272C4⋊Dic47—44no—
273Dic47⋊C4—28no—
274Dic47⋊C4—28no—
275Dic47⋊C4—28no—
276Dic47⋊C4—44no—
277Dic47⋊C4—44no—
278C4×Dic47—28no—
279C4×Dic47—44no—
280C4×Dic47—44no—
281C23×C47—22no—
282C23×C47—22no—
283C23×C47—22no—
284C23×C47—22no—
285C23×C47—22no—
286C23×C47—22no—
287C23×C47—22no—
288C23×C47—22no—
289C23×C47—22no—
290C23×C47—22no—
291C23×C47—22no—
292C23×C47—22no—
293C23×C47—22no—
294C23×C47—22no—
295C23×C47—22no—
296C23×C47—22no—
297C23×C47—22no—
298C23×C47—22no—
299C23×C47—41no—
300C23×C47—41no—
301C23×C47—41no—
302C23×C47—41no—
303C23×C47—41no—
304C23×C47—41no—
305C23×C47—41no—
306C23×C47—41no—
307C23×C47—41no—
308C23×C47—41no—
309C23×C47—41no—
310C23×C47—41no—
311C23×C47—41no—
312C23×C47—41no—
313C23×C47—41no—
314C23×C47—41no—
315C23×C47C4×Q814yes—
316C23×C47C23×C411yescharacteristic
317C23×C47C22×D411yescharacteristic
318C23×C47C22×D411yescharacteristic
319C23×C47C22×Q811yescharacteristic
320C23×C47C2×#4111yescharacteristic
321C23×C47C2×#4111yescharacteristic
322C23×C47C2×#4111yescharacteristic
323C23×C47C2×#4111yescharacteristic
324C23×C47C2×#4111yescharacteristic
325C23×C47C2×#4111yescharacteristic
326C23×C47C2×#4111yescharacteristic
327C23×C47H(5,𝔽2)11yescharacteristic
328C23×C47H(5,𝔽2)11yescharacteristic
329C23×C47H(5,𝔽2)11yescharacteristic
330C23×C472−1+411yescharacteristic
331C2×C4×C47—22no—
332C2×C4×C47—22no—
333C2×C4×C47—22no—
334C2×C4×C47—22no—
335C2×C4×C47—22no—
336C2×C4×C47—22no—
337C2×C4×C47—22no—
338C2×C4×C47—22no—
339C2×C4×C47—22no—
340C2×C4×C47—22no—
341C2×C4×C47—22no—
342C2×C4×C47—22no—
343C2×C4×C47—22no—
344C2×C4×C47—22no—
345C2×C4×C47—22no—
346C2×C4×C47—22no—
347C2×C4×C47—22no—
348C2×C4×C47—22no—
349C2×C4×C47—41no—
350C2×C4×C47—41no—
351C2×C4×C47—41no—
352C2×C4×C47—41no—
353C2×C4×C47—41no—
354C2×C4×C47—41no—
355C2×C4×C47—41no—
356C2×C4×C47—41no—
357C2×C4×C47—41no—
358C2×C4×C47—41no—
359C2×C4×C47—41no—
360C2×C4×C47—41no—
361C2×C4×C47—41no—
362C2×C4×C47—41no—
363C2×C4×C47—41no—
364C2×C4×C47—41no—
365C2×C4×C47—41no—
366C2×C4×C47—41no—
367C2×C4×C47—41no—
368C2×C4×C47—41no—
369C2×C4×C47—41no—
370C2×C4×C47—41no—
371C2×C4×C47—41no—
372C2×C4×C47C22⋊Q814yes—
373C2×Dic47—22no—
374C2×Dic47—22no—
375C2×Dic47—22no—
376C2×Dic47—22no—
377C2×Dic47—22no—
378C2×Dic47—22no—
379C2×Dic47—22no—
380C2×Dic47—22no—
381C2×Dic47—22no—
382C2×Dic47—22no—
383C2×Dic47—22no—
384C2×Dic47—22no—
385C2×Dic47—22no—
386C2×Dic47—22no—
387C2×Dic47—22no—
388C2×Dic47—22no—
389C2×Dic47—22no—
390C2×Dic47—22no—
391C2×Dic47—41no—
392C2×Dic47—41no—
393C2×Dic47—41no—
394C2×Dic47—41no—
395C2×Dic47—41no—
396C2×Dic47—41no—
397C2×Dic47—41no—
398C2×Dic47—41no—
399C2×Dic47—41no—
400C2×Dic47—41no—
401C2×Dic47—41no—
402C2×Dic47—41no—
403C2×Dic47—41no—
404C2×Dic47—41no—
405C2×Dic47—41no—
406C2×Dic47—41no—
407C2×Dic47—41no—
408C2×Dic47—41no—
409C2×Dic47—41no—
410C2×Dic47—41no—
411C2×Dic47—41no—
412C2×Dic47—41no—
413C2×Dic47—41no—
414C2×Dic47—41no—
415C2×Dic47—416no—
416C2×Dic47—41no—
417C2×Dic47—41no—
418C2×Dic47—41no—
419C2×Dic47—41no—
420C2×Dic47—41no—
421C2×Dic47—41no—
422C2×Dic47—41no—
423C2×Dic47#11714yes—
424C2×Dic47C4×D414yes—
425C2×Dic47C4×D414yes—
426C2×Dic47#12114yes—
427C2×Dic47#12314yes—
428C2×Dic47#12414yes—
429C2×Dic47#12614yes—
430#13973—471nomaximal, Sylow
431C22×C47—24no—
432C22×C47—24no—
433C22×C47—24no—
434C22×C47—42no—
435C22×C47—42no—
436C22×C47—42no—
437C22×C47—42no—
438C22×C47—42no—
439C22×C47—42no—
440C22×C47—42no—
441C22×C47—42no—
442C22×C47—42no—
443C22×C47—42no—
444C22×C47—42no—
445C22×C47—42no—
446C22×C47C2×#11711yescharacteristic
447C22×C47C2×C4×D411yescharacteristic
448C22×C47C2×C4×D411yescharacteristic
449C22×C47C2×C4×Q811yescharacteristic
450C22×C47C4×#4111yescharacteristic
451C22×C47#51811yescharacteristic
452C22×C47#52011yescharacteristic
453C22×C47C2×#12111yescharacteristic
454C22×C47C2×C22⋊Q811yescharacteristic
455C22×C47C2×#12311yescharacteristic
456C22×C47#52511yescharacteristic
457C22×C47C2×#12411yescharacteristic
458C22×C47C2×#12611yescharacteristic
459C22×C47#52911yescharacteristic
460C22×C47#53311yescharacteristic
461C22×C47#53511yescharacteristic
462C22×C47#53711yescharacteristic
463C22×C47#54011yescharacteristic
464C22×C47#54211yescharacteristic
465C22×C47#54611yescharacteristic
466C22×C47#54611yescharacteristic
467C22×C47D4×Q811yescharacteristic
468C22×C47#55011yescharacteristic
469C22×C47#55211yescharacteristic
470C22×C47#55211yescharacteristic
471C22×C47#55211yescharacteristic
472C22×C47#55311yescharacteristic
473C22×C47#55311yescharacteristic
474C22×C47#55311yescharacteristic
475C22×C47#55411yescharacteristic
476C22×C47#55411yescharacteristic
477C22×C47#55411yescharacteristic
478C22×C47#55511yescharacteristic
479C22×C47#55511yescharacteristic
480C22×C47#55511yescharacteristic
481C4×C47—24no—
482C4×C47—42no—
483C4×C47—42no—
484C4×C47—42no—
485C4×C47—42no—
486C4×C47—81no—
487Dic47—42no—
488Dic47—42no—
489Dic47—42no—
490Dic47—42no—
491Dic47—42no—
492Dic47—42no—
493Dic47—81no—
494Dic47#38818yes—
495C2×#389—471no—
496C2×#380—471no—
497C2×#380—471no—
498C2×C4×C4⋊C4—471no—
499C2×C4×C22⋊C4—471no—
500#1442—471no—
501#1442—471no—
502#1439—471no—
503#1439—471no—
504#1437—471no—
505#1437D4711yescharacteristic
506C4⋊#95—471no—
507C4⋊#95—471no—
508#1434—471no—
509#1434—471no—
510C2×C47—44no—
511C2×C47C2×#38811yescharacteristic
512C2×C47C4×C22⋊Q811yescharacteristic
513C2×C47#232411yescharacteristic
514C2×C47#234511yescharacteristic
515C2×C47#234611yescharacteristic
516C2×C47#236011yescharacteristic
517C2×C47#236311yescharacteristic
518C2×C47#241411yescharacteristic
519C2×C47#241711yescharacteristic
520C2×C47#242011yescharacteristic
521C2×C47#242311yescharacteristic
522C2×C47#249511yescharacteristic
523C2×C47#249711yescharacteristic
524C2×C47#256211yescharacteristic
525C2×C47#256311yescharacteristic
526C24×C4—471no—
527C22×C4⋊C4—471no—
528C22×C4⋊C4—471no—
529C22×C4⋊C4—471no—
530C22×C4⋊C4—471no—
531C22×C4⋊C4—471no—
532C22×C4⋊C4—471no—
533C22×C22⋊C4—471no—
534C22×C22⋊C4—471no—
535C22×C22⋊C4—471no—
536C22×C22⋊C4C2×D4711yescharacteristic
537C22×C22⋊C4C2×D4711yescharacteristic
538C22×C22⋊C4C2×D4711yescharacteristic
539C22×C42—471no—
540C22×C42—471no—
541C22×C42—471no—
542C22×C42C2×D4711yescharacteristic
543#389—944no—
544#380—478no—
545#380—944no—
546C4×C4⋊C4—944no—
547C4×C22⋊C4—944no—
548C2×#95—471no—
549C2×#95—471no—
550C2×#95—471no—
551C2×#95—471no—
552C2×#95—471no—
553C2×#95—471no—
554C2×#95—471no—
555C2×#95—471no—
556C2×#95—471no—
557C2×#95—471no—
558C2×#95—471no—
559C2×#95—471no—
560C2×#95—471no—
561C2×#95—471no—
562C2×#95—471no—
563C2×#95C2×D4711yescharacteristic
564C2×#95C2×D4711yescharacteristic
565C2×#95C2×D4711yescharacteristic
566C47#1397311yescharacteristic, complemented, Sylow
567C25C22×D4711yescharacteristic
568C23×C4—471no—
569C23×C4—474no—
570C23×C4—471no—
571C23×C4—471no—
572C23×C4—471no—
573C23×C4—471no—
574C23×C4—471no—
575C23×C4—471no—
576C23×C4—471no—
577C23×C4—942no—
578C23×C4—942no—
579C23×C4—942no—
580C23×C4—942no—
581C23×C4—942no—
582C23×C4—942no—
583C23×C4C22×D4711yescharacteristic
584C23×C4C22×D4711yescharacteristic
585C23×C4C22×D4711yescharacteristic
586C23×C4C22×D4711yescharacteristic
587C23×C4C22×D4711yescharacteristic
588C23×C4C22×D4711yescharacteristic
589C2×C4⋊C4—474no—
590C2×C4⋊C4—474no—
591C2×C4⋊C4—474no—
592C2×C4⋊C4—942no—
593C2×C4⋊C4—942no—
594C2×C4⋊C4—942no—
595C2×C4⋊C4—942no—
596C2×C4⋊C4—942no—
597C2×C4⋊C4—942no—
598C2×C4⋊C4—942no—
599C2×C4⋊C4—942no—
600C2×C4⋊C4—942no—
601C2×C4⋊C4—942no—
602C2×C4⋊C4—942no—
603C2×C4⋊C4—1881no—
604C2×C4⋊C4—1881no—
605C2×C4⋊C4—1881no—
606C2×C4⋊C4—1881no—
607C2×C22⋊C4—22no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—22no—
610C2×C22⋊C4—22no—
611C2×C22⋊C4—41no—
612C2×C22⋊C4—41no—
613C2×C22⋊C4—41no—
614C2×C22⋊C4—474no—
615C2×C22⋊C4—942no—
616C2×C22⋊C4—942no—
617C2×C22⋊C4—942no—
618C2×C22⋊C4—942no—
619C2×C22⋊C4—942no—
620C2×C22⋊C4—1881no—
621C2×C22⋊C4—1881no—
622C2×C22⋊C4—1881no—
623C2×C22⋊C4Dic9414yes—
624C2×C22⋊C4C4×D4714yes—
625C2×C42—22no—
626C2×C42—22no—
627C2×C42—41no—
628C2×C42—474no—
629C2×C42—942no—
630C2×C42—942no—
631C2×C42—942no—
632C2×C42—942no—
633C2×C42—942no—
634C2×C42—942no—
635C2×C42—942no—
636C2×C42—1881no—
637#95—22no—
638#95—41no—
639#95—41no—
640#95—474no—
641#95—474no—
642#95—942no—
643#95—942no—
644#95—942no—
645#95—942no—
646#95—942no—
647#95—942no—
648#95—942no—
649#95—942no—
650#95—942no—
651#95—1881no—
652#95—1881no—
653#95—1881no—
654#95—1881no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24C2×Dic9412yes—
668C24C2×C4×D4712yes—
669C24#1062535012yes—
670C24C23×D4711yescharacteristic
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—472no—
707C22×C4—472no—
708C22×C4—472no—
709C22×C4—472no—
710C22×C4—472no—
711C22×C4—472no—
712C22×C4—472no—
713C22×C4—472no—
714C22×C4—472no—
715C22×C4—472no—
716C22×C4—472no—
717C22×C4—472no—
718C22×C4—472no—
719C22×C4—948no—
720C22×C4—948no—
721C22×C4—948no—
722C22×C4—941no—
723C22×C4—941no—
724C22×C4—941no—
725C22×C4—941no—
726C22×C4—941no—
727C22×C4—941no—
728C22×C4—941no—
729C22×C4—941no—
730C22×C4—941no—
731C22×C4—941no—
732C22×C4—941no—
733C22×C4—941no—
734C22×C4—941no—
735C22×C4—941no—
736C22×C4—941no—
737C22×C4—941no—
738C22×C4—941no—
739C22×C4—941no—
740C22×C4—941no—
741C22×C4—941no—
742C22×C4—941no—
743C22×C4—941no—
744C22×C4—941no—
745C22×C4—941no—
746C22×C4—941no—
747C22×C4—941no—
748C22×C4—941no—
749C22×C4—941no—
750C22×C4—941no—
751C22×C4—941no—
752C22×C4—941no—
753C22×C4—941no—
754C22×C4—941no—
755C22×C4—941no—
756C22×C4—941no—
757C22×C4—941no—
758C22×C4—941no—
759C22×C4—941no—
760C22×C4—941no—
761C22×C4—941no—
762C22×C4—941no—
763C22×C4—941no—
764C22×C4—941no—
765C22×C4—1884no—
766C22×C4—1884no—
767C22×C4—1884no—
768C22×C4—1884no—
769C22×C4C2×Dic9412yes—
770C22×C4C2×Dic9412yes—
771C22×C4C2×C4×D4712yes—
772C22×C4C2×C4×D4712yes—
773C22×C4D4×D4712yes—
774C22×C4D4×D4712yes—
775C22×C4#1062535212yes—
776C4⋊C4—948no—
777C4⋊C4—948no—
778C4⋊C4—948no—
779C4⋊C4—1884no—
780C4⋊C4—1884no—
781C4⋊C4—1884no—
782C22⋊C4—28no—
783C22⋊C4—44no—
784C22⋊C4—44no—
785C22⋊C4—948no—
786C22⋊C4—1884no—
787C22⋊C4—1884no—
788C42—44no—
789C42—948no—
790C42—1884no—
791C42—1884no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23C4×Dic9414yes—
827C23C22×C4×D4711yescharacteristic
828C23C2×D4×D4711yescharacteristic
829C23C2×D4×D4711yescharacteristic
830C23C22×Dic9411yescharacteristic
831C23#41×D4711yescharacteristic
832C23#41×D4711yescharacteristic
833C23#41×D4711yescharacteristic
834C23#41×D4711yescharacteristic
835C23#41×D4711yescharacteristic
836C23C2×#1062535211yescharacteristic
837C23C2×#1062535011yescharacteristic
838C23#1309406911yescharacteristic
839C23#1309406911yescharacteristic
840C23#1309406911yescharacteristic
841C23#1309407111yescharacteristic
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—474no—
884C2×C4—474no—
885C2×C4—474no—
886C2×C4—474no—
887C2×C4—474no—
888C2×C4—474no—
889C2×C4—474no—
890C2×C4—942no—
891C2×C4—942no—
892C2×C4—942no—
893C2×C4—942no—
894C2×C4—942no—
895C2×C4—942no—
896C2×C4—942no—
897C2×C4—942no—
898C2×C4—942no—
899C2×C4—942no—
900C2×C4—942no—
901C2×C4—942no—
902C2×C4—942no—
903C2×C4—942no—
904C2×C4—942no—
905C2×C4—942no—
906C2×C4—942no—
907C2×C4—942no—
908C2×C4—18816no—
909C2×C4—1881no—
910C2×C4—1881no—
911C2×C4—1881no—
912C2×C4—1881no—
913C2×C4—1881no—
914C2×C4—1881no—
915C2×C4—1881no—
916C2×C4—1881no—
917C2×C4—1881no—
918C2×C4—1881no—
919C2×C4—1881no—
920C2×C4—1881no—
921C2×C4—1881no—
922C2×C4—1881no—
923C2×C4—1881no—
924C2×C4—1881no—
925C2×C4—1881no—
926C2×C4—1881no—
927C2×C4—1881no—
928C2×C4—1881no—
929C2×C4—1881no—
930C2×C4—1881no—
931C2×C4—1881no—
932C2×C4—1881no—
933C2×C4—1881no—
934C2×C4—1881no—
935C2×C4—1881no—
936C2×C4—1881no—
937C2×C4—1881no—
938C2×C4—1881no—
939C2×C4—1881no—
940C2×C4#1309400114yes—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22#117×D4711yescharacteristic
957C22C4×D4×D4711yescharacteristic
958C22C4×D4×D4711yescharacteristic
959C22C2×C4×Dic9411yescharacteristic
960C22C4×#1062535211yescharacteristic
961C22#1568959611yescharacteristic
962C22#1568960211yescharacteristic
963C22#121×D4711yescharacteristic
964C22C2×#1309400111yescharacteristic
965C22#123×D4711yescharacteristic
966C22#1568963211yescharacteristic
967C22#124×D4711yescharacteristic
968C22#126×D4711yescharacteristic
969C22#1568965311yescharacteristic
970C22#1568967611yescharacteristic
971C22#1568968611yescharacteristic
972C22#1568970011yescharacteristic
973C22#1568972311yescharacteristic
974C22#1568973711yescharacteristic
975C22#1568976011yescharacteristic
976C22#1568976311yescharacteristic
977C22D4×Dic9411yescharacteristic
978C22#1568979111yescharacteristic
979C22#1568980611yescharacteristic
980C22#1568980911yescharacteristic
981C22#1568981011yescharacteristic
982C22#1568981811yescharacteristic
983C22#1568982211yescharacteristic
984C22#1568982211yescharacteristic
985C22#1568983211yescharacteristic
986C22#1568983211yescharacteristic
987C22#1568983211yescharacteristic
988C22#1568983511yescharacteristic
989C22#1568983711yescharacteristic
990C22#1568983711yescharacteristic
991C4—24no—
992C4—42no—
993C4—42no—
994C4—42no—
995C4—42no—
996C4—81no—
997C4—478no—
998C4—3761no—
999C4—1882no—
1000C4—1882no—
1001C4—1882no—
1002C4—1882no—
1003C4—1882no—
1004C4—1882no—
1005C2—44no—
1006C2#388×D4711yescharacteristic
1007C2C4×#1309400111yescharacteristic
1008C2#2024607411yescharacteristic
1009C2#2024626611yescharacteristic
1010C2#2024627011yescharacteristic
1011C2#2024639411yescharacteristic
1012C2#2024642911yescharacteristic
1013C2#2024680311yescharacteristic
1014C2#2024683611yescharacteristic
1015C2#2024687711yescharacteristic
1016C2#2024691011yescharacteristic
1017C2#2024779611yescharacteristic
1018C2#2024781811yescharacteristic
1019C2#2024855211yescharacteristic
1020C2#2024855911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC47×#1437C2
socle, cosocleC24×C47C24
prime radicalC25×C47C23
hypercenter#1437D47
hypocenterC47#13973
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
1. C2×#15689020C2semidirect
4. C2×C4×Dic47⋊C4C2semidirect
6. #20241646C2semidirect
7. #20241644C2semidirect
11. Dic47⋊#95C2semidirect
12. Dic47⋊#95C2semidirect
13. #20241615C2semidirect
14. #20241614C2semidirect
31. #15688981C4semidirect
566. C47#13973semidirect

Maximal subgroups

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

subgroupindex
C2×#156890202
C2×#156889812
C2×C4×Dic47⋊C42
C2×C22⋊C4×Dic472
#202416462
#202416442
#202416332
#202416312
#202416252
Dic47⋊#952
#202416152
#202416142
C47×#14372
#1397347