Finite Group Databasebeta

← #26139482

Subgroups — #26139482

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×#15688994C211yesmaximal, characteristic
2C2×#15688994C211yesmaximal, characteristic
3C2×#15688994C211yesmaximal, characteristic
4C2×#15688980C211yesmaximal, characteristic
5C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic
6C2×#95×D47C211yesmaximal, characteristic
7#20241651C211yesmaximal, characteristic, complemented
8#20241647C211yesmaximal, characteristic, complemented
9#20241641C211yesmaximal, characteristic, complemented
10#20241638C211yesmaximal, characteristic, complemented
11#20241622C211yesmaximal, characteristic, complemented
12#20241621C211yesmaximal, characteristic, complemented
13Dic47⋊#95C211yesmaximal, characteristic, complemented
14(C2×D47)⋊#95C211yesmaximal, characteristic
15C2×C47×#389C211yesmaximal, characteristic, complemented
16C23×C4×D47C2211yescharacteristic
17C23×C4×D47C2211yescharacteristic
18C23×C4×D47C2211yescharacteristic
19C22×C4⋊Dic47C2211yescharacteristic
20C22×Dic47⋊C4C2211yescharacteristic
21C22×Dic47⋊C4C2211yescharacteristic
22C22×Dic47⋊C4C2211yescharacteristic
23C22×(C2×D47)⋊C4C2211yescharacteristic
24C22×(C2×D47)⋊C4C2211yescharacteristic
25C22×(C2×D47)⋊C4C2211yescharacteristic
26C22×(C2×D47)⋊C4C2211yescharacteristic
27C22×C4×Dic47C2211yescharacteristic
28#15688994—24no—
29#15688994—24no—
30#15688994C418yescomplemented
31#15688980—24no—
32C4×(C2×D47)⋊C4—24no—
33C2×C47⋊#95C2211yescharacteristic
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
49#95×D47—24no—
50C22×C4⋊C4×C47C2211yescharacteristic
51C22×C4⋊C4×C47C2211yescharacteristic
52C22×C4⋊C4×C47C2211yescharacteristic
53C22×C4⋊C4×C47C2211yescharacteristic
54C22×C42×C47C2211yescharacteristic
55C47×#389—24no—
56C2×#95×C47C2211yescharacteristic
57C2×#95×C47C2211yescharacteristic
58C24×D47C2311yescharacteristic
59C23×Dic47C2311yescharacteristic
60C23×Dic47C2311yescharacteristic
61C23×Dic47C2311yescharacteristic
62C23×Dic47C2311yescharacteristic
63C23×Dic47C2311yescharacteristic
64C23×Dic47C2311yescharacteristic
65C23×Dic47C2311yescharacteristic
66C22×C4×D47—22no—
67C22×C4×D47—22no—
68C22×C4×D47—22no—
69C22×C4×D47—22no—
70C22×C4×D47—22no—
71C22×C4×D47—22no—
72C22×C4×D47—22no—
73C22×C4×D47—22no—
74C22×C4×D47—22no—
75C22×C4×D47—22no—
76C22×C4×D47—22no—
77C22×C4×D47—22no—
78C22×C4×D47—22no—
79C22×C4×D47—41no—
80C22×C4×D47—41no—
81C22×C4×D47—41no—
82C22×C4×D47—41no—
83C22×C4×D47—41no—
84C22×C4×D47—41no—
85C22×C4×D47C2×C414yes—
86C22×C4×D47Q814yes—
87C2×C4⋊Dic47—22no—
88C2×C4⋊Dic47—22no—
89C2×C4⋊Dic47—41no—
90C2×Dic47⋊C4—22no—
91C2×Dic47⋊C4—22no—
92C2×Dic47⋊C4—22no—
93C2×Dic47⋊C4—22no—
94C2×Dic47⋊C4—41no—
95C2×Dic47⋊C4—41no—
96C2×Dic47⋊C4—41no—
97C2×Dic47⋊C4—41no—
98C2×Dic47⋊C4C2×C414yescomplemented
99C2×(C2×D47)⋊C4—22no—
100C2×(C2×D47)⋊C4—22no—
101C2×(C2×D47)⋊C4—22no—
102C2×(C2×D47)⋊C4—22no—
103C2×(C2×D47)⋊C4—22no—
104C2×(C2×D47)⋊C4—22no—
105C2×(C2×D47)⋊C4—22no—
106C2×(C2×D47)⋊C4C2×C414yes—
107C2×(C2×D47)⋊C4C2×C414yes—
108C2×(C2×D47)⋊C4D414yes—
109C2×(C2×D47)⋊C4D414yes—
110C2×(C2×D47)⋊C4Q814yes—
111C2×C4×Dic47—22no—
112C2×C4×Dic47—22no—
113C2×C4×Dic47—41no—
114C47⋊#95—22no—
115C47⋊#95—22no—
116C47⋊#95—22no—
117C47⋊#95—22no—
118C47⋊#95—22no—
119C47⋊#95—22no—
120C47⋊#95—22no—
121C47⋊#95—22no—
122C47⋊#95—22no—
123C47⋊#95—22no—
124C47⋊#95—22no—
125C47⋊#95—22no—
126C47⋊#95—41no—
127C47⋊#95—41no—
128C47⋊#95C2×C414yescomplemented
129C47⋊#95C2×C414yescomplemented
130C23×C4×C47C2311yescharacteristic
131C23×C4×C47C2311yescharacteristic
132C23×C4×C47C2311yescharacteristic
133C23×C4×C47C2311yescharacteristic
134C23×C4×C47C2311yescharacteristic
135C23×C4×C47C2311yescharacteristic
136C23×C4×C47C2311yescharacteristic
137C2×C4⋊C4×C47—22no—
138C2×C4⋊C4×C47—22no—
139C2×C4⋊C4×C47—22no—
140C2×C4⋊C4×C47—22no—
141C2×C4⋊C4×C47—22no—
142C2×C4⋊C4×C47—22no—
143C2×C4⋊C4×C47—22no—
144C2×C4⋊C4×C47—22no—
145C2×C4⋊C4×C47—41no—
146C2×C4⋊C4×C47—41no—
147C2×C4⋊C4×C47—41no—
148C2×C4⋊C4×C47C2×C414yescomplemented
149C2×C42×C47—22no—
150C2×C42×C47—22no—
151C2×C42×C47—41no—
152#95×C47—22no—
153#95×C47D414yes—
154C24×C47C2411yescharacteristic
155C23×D47—21no—
156C23×D47—21no—
157C23×D47—21no—
158C23×D47—21no—
159C23×D47—21no—
160C23×D47—21no—
161C23×D47—21no—
162C23×D47—21no—
163C23×D47C22×C412yes—
164C23×D47C2×D412yes—
165C23×D47C2×D412yes—
166C23×D47C2×Q812yes—
167C23×D47C2×Q812yes—
168C23×D47#4112yes—
169C23×D47#4112yes—
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×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×C47C22×C412yes—
208C22×C4×C47C22×C412yes—
209C22×C4×C47C22×C412yes—
210C22×C4×C47C2×D412yes—
211C22×C4×C47C2×D412yes—
212C22×C4×C47C2×D412yes—
213C22×C4×C47C2×D412yes—
214C22×C4×C47C2×D412yes—
215C22×C4×C47C2×Q812yes—
216C22×C4×C47C2×Q812yes—
217C22×C4×C47#4112yes—
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—21no—
232C22×Dic47—21no—
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×Dic47C22×C412yes—
261C22×Dic47C22×C412yes—
262C22×Dic47C22×C412yes—
263C22×Dic47C2×D412yes—
264C22×Dic47C2×D412yes—
265C22×Dic47C2×Q812yes—
266C22×Dic47C2×Q812yes—
267C22×Dic47#4112yes—
268C2×C4×D47—28no—
269C2×C4×D47—28no—
270C2×C4×D47—28no—
271C2×C4×D47—28no—
272C2×C4×D47—28no—
273C2×C4×D47—44no—
274C2×C4×D47—44no—
275C2×C4×D47—44no—
276C2×C4×D47—44no—
277C2×C4×D47—44no—
278C2×C4×D47—44no—
279C2×C4×D47—44no—
280C2×C4×D47—44no—
281C2×C4×D47—44no—
282C2×C4×D47—44no—
283C2×C4×D47—44no—
284C2×C4×D47—44no—
285C2×C4×D47—44no—
286C2×C4×D47—44no—
287C2×C4×D47—44no—
288C2×C4×D47—44no—
289C4⋊C4×C47—28no—
290C4⋊C4×C47—44no—
291C4⋊C4×C47—44no—
292C4⋊C4×C47—44no—
293C42×C47—44no—
294(C2×D47)⋊C4—28no—
295(C2×D47)⋊C4—28no—
296(C2×D47)⋊C4—44no—
297(C2×D47)⋊C4C4⋊C4116yescomplemented
298C4⋊Dic47—44no—
299Dic47⋊C4—44no—
300Dic47⋊C4—44no—
301Dic47⋊C4—44no—
302C4×Dic47—44no—
303C23×C47C23×C411yescharacteristic
304C23×C47C22×D411yescharacteristic
305C23×C47C22×D411yescharacteristic
306C23×C47C22×D411yescharacteristic
307C23×C47C22×Q811yescharacteristic
308C23×C47C22×Q811yescharacteristic
309C23×C47C2×#4111yescharacteristic
310C23×C47C2×#4111yescharacteristic
311C23×C47C2×#4111yescharacteristic
312C23×C47C2×#4111yescharacteristic
313C23×C47C2×#4111yescharacteristic
314C23×C47H(5,𝔽2)11yescharacteristic
315C23×C47H(5,𝔽2)11yescharacteristic
316C23×C47H(5,𝔽2)11yescharacteristic
317C23×C472−1+411yescharacteristic
318C22×D47—22no—
319C22×D47—22no—
320C22×D47—22no—
321C22×D47—22no—
322C22×D47—22no—
323C22×D47—22no—
324C22×D47—22no—
325C22×D47—22no—
326C22×D47—22no—
327C22×D47—22no—
328C22×D47—22no—
329C22×D47—22no—
330C22×D47—22no—
331C22×D47—22no—
332C22×D47—22no—
333C22×D47—22no—
334C22×D47—22no—
335C22×D47—22no—
336C22×D47—22no—
337C22×D47—22no—
338C22×D47—22no—
339C22×D47—22no—
340C22×D47—22no—
341C22×D47—22no—
342C22×D47—22no—
343C22×D47—22no—
344C22×D47—22no—
345C22×D47—22no—
346C22×D47C2×C4⋊C414yes—
347C22×D47C4×D414yes—
348C22×D47C4×Q814yes—
349C22×D47#12114yes—
350C22×D47C22⋊Q814yes—
351C22×D47#12514yes—
352C22×D47C4⋊Q814yes—
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—22no—
369C2×C4×C47—22no—
370C2×C4×C47—22no—
371C2×C4×C47—22no—
372C2×C4×C47—22no—
373C2×C4×C47—22no—
374C2×C4×C47—22no—
375C2×C4×C47—22no—
376C2×C4×C47—22no—
377C2×C4×C47—22no—
378C2×C4×C47—22no—
379C2×C4×C47—22no—
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×C47—41no—
396C2×C4×C47—41no—
397C2×C4×C47—41no—
398C2×C4×C47—41no—
399C2×C4×C47C2×C4⋊C414yes—
400C2×C4×C47C4×D414yes—
401C2×C4×C47C22⋊Q814yes—
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—41no—
424C2×Dic47—41no—
425C2×Dic47—41no—
426C2×Dic47—41no—
427C2×Dic47—41no—
428C2×Dic47—41no—
429C2×Dic47—41no—
430C2×Dic47—41no—
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×Dic47C2×C4⋊C414yes—
451C4×D47—416no—
452C4×D47—416no—
453C4×D47—416no—
454#14004—471nomaximal, Sylow
455C22×C47C22×C4⋊C411yescharacteristic
456C22×C47C2×C4×D411yescharacteristic
457C22×C47C2×C4×D411yescharacteristic
458C22×C47C2×C4×Q811yescharacteristic
459C22×C47C4×#4111yescharacteristic
460C22×C47#51811yescharacteristic
461C22×C47#52011yescharacteristic
462C22×C47C2×#12111yescharacteristic
463C22×C47C2×C22⋊Q811yescharacteristic
464C22×C47C2×C22⋊Q811yescharacteristic
465C22×C47#52511yescharacteristic
466C22×C47C2×#12511yescharacteristic
467C22×C47#52911yescharacteristic
468C22×C47C2×C4⋊Q811yescharacteristic
469C22×C47#53311yescharacteristic
470C22×C47#53811yescharacteristic
471C22×C47#53911yescharacteristic
472C22×C47#54311yescharacteristic
473C22×C47#54411yescharacteristic
474C22×C47D4211yescharacteristic
475C22×C47D4211yescharacteristic
476C22×C47#54611yescharacteristic
477C22×C47#54611yescharacteristic
478C22×C47#54611yescharacteristic
479C22×C47#54611yescharacteristic
480C22×C47#54611yescharacteristic
481C22×C47#54711yescharacteristic
482C22×C47#54711yescharacteristic
483C22×C47D4×Q811yescharacteristic
484C22×C47#55111yescharacteristic
485C22×C47#55111yescharacteristic
486C22×C47#55211yescharacteristic
487C22×C47#55411yescharacteristic
488C22×C47#55411yescharacteristic
489C22×C47#55411yescharacteristic
490C2×D47—24no—
491C2×D47—24no—
492C2×D47—24no—
493C2×D47—24no—
494C2×D47—24no—
495C2×D47—24no—
496C2×D47—24no—
497C2×D47—24no—
498C2×D47—24no—
499C2×D47—24no—
500C2×D47—24no—
501C2×D47—24no—
502C2×D47—24no—
503C2×D47—24no—
504C2×D47#38918yescomplemented
505C4×C47—24no—
506C4×C47—24no—
507C4×C47—24no—
508C4×C47—42no—
509C4×C47—42no—
510C4×C47—42no—
511C4×C47—81no—
512Dic47—24no—
513Dic47—42no—
514Dic47—42no—
515Dic47—42no—
516Dic47—42no—
517Dic47—42no—
518Dic47—81no—
519C2×#389D4711yescharacteristic, complemented
520C2×#385—471no—
521C2×#385—471no—
522C2×#385—471no—
523C2×#380—471no—
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×C47C2×#38911yescharacteristic
535C2×C47C4×C22⋊Q811yescharacteristic
536C2×C47#232911yescharacteristic
537C2×C47D4×C4⋊C411yescharacteristic
538C2×C47#234911yescharacteristic
539C2×C47#235811yescharacteristic
540C2×C47#235911yescharacteristic
541C2×C47#242411yescharacteristic
542C2×C47#242511yescharacteristic
543C2×C47#243711yescharacteristic
544C2×C47#243811yescharacteristic
545C2×C47#244011yescharacteristic
546C2×C47#247311yescharacteristic
547C2×C47#250511yescharacteristic
548C2×C47#254911yescharacteristic
549D47—28no—
550C24×C4—471no—
551C24×C4—471no—
552C24×C4—471no—
553C22×C4⋊C4—471no—
554C22×C4⋊C4—471no—
555C22×C4⋊C4—471no—
556C22×C4⋊C4—471no—
557C22×C4⋊C4C2×D4711yescharacteristic
558C22×C4⋊C4C2×D4711yescharacteristic
559C22×C4⋊C4C2×D4711yescharacteristic
560C22×C4⋊C4C2×D4711yescharacteristic
561C22×C22⋊C4—471no—
562C22×C22⋊C4—471no—
563C22×C22⋊C4—471no—
564C22×C22⋊C4—471no—
565C22×C42—471no—
566C22×C42C2×D4711yescharacteristic
567#389—24no—
568#385—478no—
569#385—944no—
570#385—944no—
571#380—944no—
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
593C25—471no—
594C23×C4—471no—
595C23×C4—471no—
596C23×C4—471no—
597C23×C4—471no—
598C23×C4—471no—
599C23×C4—471no—
600C23×C4—474no—
601C23×C4—474no—
602C23×C4—471no—
603C23×C4—942no—
604C23×C4—942no—
605C23×C4—942no—
606C23×C4—942no—
607C23×C4—942no—
608C23×C4—942no—
609C23×C4—942no—
610C23×C4—942no—
611C23×C4—942no—
612C23×C4—942no—
613C23×C4—942no—
614C23×C4—942no—
615C23×C4—942no—
616C23×C4—1881no—
617C23×C4—1881no—
618C23×C4—1881no—
619C23×C4—1881no—
620C23×C4—1881no—
621C23×C4—1881no—
622C23×C4C22×D4711yescharacteristic
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—22no—
634C2×C4⋊C4—22no—
635C2×C4⋊C4—22no—
636C2×C4⋊C4—22no—
637C2×C4⋊C4—41no—
638C2×C4⋊C4—41no—
639C2×C4⋊C4—41no—
640C2×C4⋊C4—474no—
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⋊C4C4×D4714yescomplemented
653C2×C22⋊C4—474no—
654C2×C22⋊C4—474no—
655C2×C22⋊C4—474no—
656C2×C22⋊C4—474no—
657C2×C22⋊C4—474no—
658C2×C22⋊C4—942no—
659C2×C22⋊C4—942no—
660C2×C22⋊C4—942no—
661C2×C22⋊C4—942no—
662C2×C22⋊C4—942no—
663C2×C22⋊C4—942no—
664C2×C22⋊C4—942no—
665C2×C42—22no—
666C2×C42—22no—
667C2×C42—41no—
668C2×C42—942no—
669C2×C42—942no—
670C2×C42—1881no—
671#95—22no—
672#95—474no—
673#95—474no—
674#95—942no—
675#95—942no—
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—1881no—
687#95—1881no—
688#95C22⋊D4714yes—
689C24—472no—
690C24—472no—
691C24—472no—
692C24—472no—
693C24—472no—
694C24—472no—
695C24—472no—
696C24—941no—
697C24—941no—
698C24—941no—
699C24—941no—
700C24—941no—
701C24—941no—
702C24—941no—
703C24—941no—
704C24C23×D4711yescharacteristic
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
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—21no—
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—472no—
743C22×C4—472no—
744C22×C4—472no—
745C22×C4—472no—
746C22×C4—472no—
747C22×C4—472no—
748C22×C4—472no—
749C22×C4—472no—
750C22×C4—948no—
751C22×C4—948no—
752C22×C4—948no—
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—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—941no—
776C22×C4—941no—
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—948no—
788C22×C4—948no—
789C22×C4—941no—
790C22×C4—941no—
791C22×C4—941no—
792C22×C4—941no—
793C22×C4—941no—
794C22×C4—941no—
795C22×C4—941no—
796C22×C4—1884no—
797C22×C4—1884no—
798C22×C4—1884no—
799C22×C4—1884no—
800C22×C4—1884no—
801C22×C4—1884no—
802C22×C4—1884no—
803C22×C4—1884no—
804C22×C4—1884no—
805C22×C4—1884no—
806C22×C4—1884no—
807C22×C4—1884no—
808C22×C4—1884no—
809C22×C4—1884no—
810C22×C4—1884no—
811C22×C4—1884no—
812C22×C4C2×C4×D4712yes—
813C22×C4C2×C4×D4712yes—
814C22×C4C2×C4×D4712yes—
815C22×C4#1062535012yes—
816C22×C4D4×D4712yes—
817C22×C4D4×D4712yes—
818C22×C4Q8×D4712yes—
819C22×C4Q8×D4712yes—
820C22×C4#1062535412yes—
821C22×C4C2×C22⋊D4712yes—
822C22×C4C2×C22⋊D4712yes—
823C22×C4C2×C22⋊D4712yes—
824C4⋊C4—28no—
825C4⋊C4—44no—
826C4⋊C4—44no—
827C4⋊C4—44no—
828C4⋊C4—1884no—
829C4⋊C4—1884no—
830C4⋊C4—1884no—
831C4⋊C4—1884no—
832C22⋊C4—4716no—
833C22⋊C4—948no—
834C22⋊C4—948no—
835C22⋊C4—1884no—
836C42—44no—
837C42—1884no—
838C23—474no—
839C23—474no—
840C23—474no—
841C23—474no—
842C23—474no—
843C23—474no—
844C23—474no—
845C23—942no—
846C23—942no—
847C23—942no—
848C23—942no—
849C23—942no—
850C23—942no—
851C23—942no—
852C23—942no—
853C23—942no—
854C23—942no—
855C23—942no—
856C23—942no—
857C23—942no—
858C23—942no—
859C23—942no—
860C23—942no—
861C23—942no—
862C23—942no—
863C23—942no—
864C23—942no—
865C23—942no—
866C23—942no—
867C23—942no—
868C23—942no—
869C23—942no—
870C23—942no—
871C23—942no—
872C23—942no—
873C23C22×C4×D4711yescharacteristic
874C23C2×D4×D4711yescharacteristic
875C23C2×D4×D4711yescharacteristic
876C23C22×C22⋊D4711yescharacteristic
877C23C2×Q8×D4711yescharacteristic
878C23C2×Q8×D4711yescharacteristic
879C23#41×D4711yescharacteristic
880C23#41×D4711yescharacteristic
881C23#41×D4711yescharacteristic
882C23C2×#1062535011yescharacteristic
883C23C2×#1062535411yescharacteristic
884C23#1309406911yescharacteristic
885C23#1309406911yescharacteristic
886C23#1309407011yescharacteristic
887C23#1309407211yescharacteristic
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—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
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—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—474no—
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—18816no—
957C2×C4—18816no—
958C2×C4—18816no—
959C2×C4—1881no—
960C2×C4—1881no—
961C2×C4—1881no—
962C2×C4—1881no—
963C2×C4—1881no—
964C2×C4—1881no—
965C2×C4—1881no—
966C2×C4—1881no—
967C2×C4—1881no—
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×C4C4⋊C4×D4714yes—
987C2×C4C4×C22⋊D4714yes—
988C2×C4#1309400014yes—
989C22—478no—
990C22—944no—
991C22—944no—
992C22—944no—
993C22—944no—
994C22—944no—
995C22—944no—
996C22—944no—
997C22—944no—
998C22—944no—
999C22—944no—
1000C22—944no—
1001C22—944no—
1002C22—944no—
1003C22—944no—
1004C22C2×C4⋊C4×D4711yescharacteristic
1005C22C4×D4×D4711yescharacteristic
1006C22C2×C4×C22⋊D4711yescharacteristic
1007C22C4×Q8×D4711yescharacteristic
1008C22C4×#1062535411yescharacteristic
1009C22#1568959511yescharacteristic
1010C22#1568960411yescharacteristic
1011C22#121×D4711yescharacteristic
1012C22C22⋊Q8×D4711yescharacteristic
1013C22C2×#1309400011yescharacteristic
1014C22#1568963011yescharacteristic
1015C22#125×D4711yescharacteristic
1016C22#1568966011yescharacteristic
1017C22C4⋊Q8×D4711yescharacteristic
1018C22#1568967711yescharacteristic
1019C22#1568970511yescharacteristic
1020C22#1568972111yescharacteristic
1021C22#1568974811yescharacteristic
1022C22#1568975011yescharacteristic
1023C22D4×C22⋊D4711yescharacteristic
1024C22D4×C22⋊D4711yescharacteristic
1025C22#1568976111yescharacteristic
1026C22#1568976211yescharacteristic
1027C22#1568976411yescharacteristic
1028C22#1568976911yescharacteristic
1029C22#1568977011yescharacteristic
1030C22#1568977411yescharacteristic
1031C22#1568977611yescharacteristic
1032C22Q8×C22⋊D4711yescharacteristic
1033C22#1568980011yescharacteristic
1034C22#1568980211yescharacteristic
1035C22#1568980511yescharacteristic
1036C22#1568982811yescharacteristic
1037C22#1568982911yescharacteristic
1038C22#1568983411yescharacteristic
1039C4—24no—
1040C4—24no—
1041C4—24no—
1042C4—42no—
1043C4—42no—
1044C4—42no—
1045C4—81no—
1046C4—944no—
1047C4—3761no—
1048C4—1882no—
1049C4—1882no—
1050C4—1882no—
1051C4—1882no—
1052C4—1882no—
1053C2—948no—
1054C2#389×D4711yescharacteristic
1055C2C4×#1309400011yescharacteristic
1056C2#2024612211yescharacteristic
1057C2C4⋊C4×C22⋊D4711yescharacteristic
1058C2#2024629711yescharacteristic
1059C2#2024636511yescharacteristic
1060C2#2024637511yescharacteristic
1061C2#2024692111yescharacteristic
1062C2#2024694611yescharacteristic
1063C2#2024705111yescharacteristic
1064C2#2024707111yescharacteristic
1065C2#2024708611yescharacteristic
1066C2#2024752511yescharacteristic
1067C2#2024789411yescharacteristic
1068C2#2024839811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C47×#389C2
socle, cosocleC24×C47C24
prime radicalC24×D47C23
hypercenterC2×#389D47
hypocenterC47#14004
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
7. #20241651C2semidirect
8. #20241647C2semidirect
9. #20241641C2semidirect
10. #20241638C2semidirect
11. #20241622C2semidirect
12. #20241621C2semidirect
13. Dic47⋊#95C2semidirect
15. C2×C47×#389C2semidirect
30. #15688994C4semidirect
98. C2×Dic47⋊C4C2×C4semidirect
128. C47⋊#95C2×C4semidirect
129. C47⋊#95C2×C4semidirect
148. C2×C4⋊C4×C47C2×C4semidirect
297. (C2×D47)⋊C4C4⋊C4semidirect
504. C2×D47#389semidirect
519. C2×#389D47semidirect
592. C47#14004semidirect
652. C2×C4⋊C4C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156889942
C2×#156889802
C2×C4×(C2×D47)⋊C42
C2×#95×D472
#202416512
#202416472
#202416412
#202416382
#202416222
#202416212
Dic47⋊#952
(C2×D47)⋊#952
C2×C47×#3892
#1400447