Finite Group Databasebeta

← #26137772

Subgroups — #26137772

Order 12032.

2882 conjugacy classes of subgroups.

The subgroup lattice has 1234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D47)⋊C4C211yesmaximal, characteristic
2C2×#15688999C211yesmaximal, characteristic
3C2×#15688999C211yesmaximal, characteristic
4C2×C22⋊C4×Dic47C211yesmaximal, characteristic, complemented
5C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
6C2×#15688970C211yesmaximal, characteristic, complemented
7C2×#95×D47C211yesmaximal, characteristic, complemented
8#20241625C211yesmaximal, characteristic, complemented
9#20241619C211yesmaximal, characteristic, complemented
10#20241619C211yesmaximal, characteristic, complemented
11#20241612C211yesmaximal, characteristic, complemented
12#20241610C211yesmaximal, characteristic, complemented
13(C2×D47)⋊#95C211yesmaximal, characteristic, complemented
14C4×C47⋊#95C211yesmaximal, characteristic, complemented
15C47×#1437C211yesmaximal, characteristic, complemented
16C23×C22⋊D47C2211yescharacteristic
17C24×Dic47C2211yescharacteristic
18C23×C4×D47C2211yescharacteristic
19C23×C4×D47C2211yescharacteristic
20C23×C4×D47C2211yescharacteristic
21C2×(C22⋊D47)⋊C4—24no—
22C2×(C22⋊D47)⋊C4—24no—
23C2×(C22⋊D47)⋊C4C418yescomplemented
24C22×Dic47⋊C4C2211yescharacteristic
25C22×C22⋊Dic47C2211yescharacteristic
26C22×C22⋊Dic47C2211yescharacteristic
27C22×(C2×D47)⋊C4C2211yescharacteristic
28C22×(C2×D47)⋊C4C2211yescharacteristic
29C22×(C2×D47)⋊C4C2211yescharacteristic
30C22×C4×Dic47C2211yescharacteristic
31C22×C4×Dic47C2211yescharacteristic
32C22×C4×Dic47C2211yescharacteristic
33C22×C4×Dic47C2211yescharacteristic
34#15688999C418yescomplemented
35#15688999C418yescomplemented
36C22⋊C4×Dic47—24no—
37C4×(C2×D47)⋊C4—24no—
38#15688970—24no—
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
50C2×C47⋊#95C2211yescharacteristic
51C2×C47⋊#95C2211yescharacteristic
52#95×D47—24no—
53C22×C22⋊C4×C47C2211yescharacteristic
54C22×C22⋊C4×C47C2211yescharacteristic
55C22×C22⋊C4×C47C2211yescharacteristic
56C22×C42×C47C2211yescharacteristic
57C2×#95×C47C2211yescharacteristic
58C2×#95×C47C2211yescharacteristic
59C2×#95×C47C2211yescharacteristic
60C24×D47C2311yescharacteristic
61C22×C22⋊D47—22no—
62C22×C22⋊D47—22no—
63C22×C22⋊D47—22no—
64C22×C22⋊D47—22no—
65C22×C22⋊D47C2×C414yes—
66C22×C22⋊D47C2×C414yes—
67C22×C22⋊D47C2×C414yes—
68C23×Dic47—22no—
69C23×Dic47—22no—
70C23×Dic47—22no—
71C23×Dic47—22no—
72C23×Dic47—41no—
73C23×Dic47—41no—
74C23×Dic47C2×C414yescomplemented
75C23×Dic47C2311yescharacteristic
76C23×Dic47C2311yescharacteristic
77C23×Dic47C2311yescharacteristic
78C23×Dic47C2311yescharacteristic
79C23×Dic47C2311yescharacteristic
80C23×Dic47C2311yescharacteristic
81C23×Dic47C2311yescharacteristic
82C22×C4×D47—22no—
83C22×C4×D47—22no—
84C22×C4×D47—22no—
85C22×C4×D47—22no—
86C22×C4×D47—22no—
87C22×C4×D47—22no—
88C22×C4×D47—22no—
89C22×C4×D47—22no—
90C22×C4×D47—22no—
91C22×C4×D47—22no—
92C22×C4×D47—22no—
93C22×C4×D47—22no—
94C22×C4×D47—41no—
95C22×C4×D47—41no—
96C22×C4×D47—41no—
97C22×C4×D47—41no—
98C22×C4×D47—41no—
99C22×C4×D47—41no—
100C22×C4×D47C2×C414yes—
101C22×C4×D47C2×C414yescomplemented
102C22×C4×D47C2×C414yescomplemented
103(C22⋊D47)⋊C4—232no—
104C2×Dic47⋊C4—22no—
105C2×Dic47⋊C4—22no—
106C2×Dic47⋊C4C2×C414yescomplemented
107C2×C22⋊Dic47—22no—
108C2×C22⋊Dic47—22no—
109C2×C22⋊Dic47—41no—
110C2×C22⋊Dic47—41no—
111C2×C22⋊Dic47C2×C414yescomplemented
112C2×C22⋊Dic47C2×C414yescomplemented
113C2×(C2×D47)⋊C4—22no—
114C2×(C2×D47)⋊C4—22no—
115C2×(C2×D47)⋊C4—22no—
116C2×(C2×D47)⋊C4—22no—
117C2×(C2×D47)⋊C4C2×C414yes—
118C2×(C2×D47)⋊C4C2×C414yescomplemented
119C2×(C2×D47)⋊C4C2×C414yescomplemented
120C2×(C2×D47)⋊C4D414yes—
121C2×(C2×D47)⋊C4D414yes—
122C2×C4×Dic47—22no—
123C2×C4×Dic47—22no—
124C2×C4×Dic47—22no—
125C2×C4×Dic47—22no—
126C2×C4×Dic47—22no—
127C2×C4×Dic47—22no—
128C2×C4×Dic47—22no—
129C2×C4×Dic47—22no—
130C2×C4×Dic47—41no—
131C2×C4×Dic47—41no—
132C2×C4×Dic47—41no—
133C2×C4×Dic47C2×C414yescomplemented
134C47⋊#95—22no—
135C47⋊#95—22no—
136C47⋊#95—22no—
137C47⋊#95—22no—
138C47⋊#95—22no—
139C47⋊#95—22no—
140C47⋊#95—22no—
141C47⋊#95—41no—
142C47⋊#95C2×C414yescomplemented
143C47⋊#95C2×C414yescomplemented
144C47⋊#95C2×C414yescomplemented
145C47⋊#95C2×C414yescomplemented
146C47⋊#95D414yescomplemented
147C25×C47C2311yescharacteristic
148C23×C4×C47C2311yescharacteristic
149C23×C4×C47C2311yescharacteristic
150C23×C4×C47C2311yescharacteristic
151C23×C4×C47C2311yescharacteristic
152C23×C4×C47C2311yescharacteristic
153C23×C4×C47C2311yescharacteristic
154C2×C22⋊C4×C47—22no—
155C2×C22⋊C4×C47—22no—
156C2×C22⋊C4×C47—22no—
157C2×C22⋊C4×C47—22no—
158C2×C22⋊C4×C47—41no—
159C2×C22⋊C4×C47—41no—
160C2×C22⋊C4×C47C2×C414yescomplemented
161C2×C22⋊C4×C47C2×C414yescomplemented
162C2×C22⋊C4×C47C2×C414yescomplemented
163C2×C42×C47—22no—
164C2×C42×C47—22no—
165C2×C42×C47—41no—
166#95×C47—22no—
167#95×C47—22no—
168#95×C47—41no—
169C24×C47—21no—
170C24×C47—21no—
171C24×C47—21no—
172C24×C47—21no—
173C24×C47—21no—
174C24×C47—21no—
175C24×C47—21no—
176C24×C47—21no—
177C24×C47—21no—
178C24×C47—21no—
179C24×C47—21no—
180C24×C47—21no—
181C24×C47C22×C412yes—
182C24×C47C22×C412yes—
183C24×C47C22×C412yes—
184C24×C47C2411yescharacteristic
185C23×D47—21no—
186C23×D47—21no—
187C23×D47—21no—
188C23×D47—21no—
189C23×D47—21no—
190C23×D47—21no—
191C23×D47—21no—
192C23×D47—21no—
193C23×D47C22×C412yes—
194C23×D47C22×C412yes—
195C23×D47C22×C412yes—
196C23×D47C2×D412yes—
197C23×D47C2×D412yes—
198C23×D47#4112yes—
199C23×D47#4112yes—
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—21no—
209C22×C4×C47—21no—
210C22×C4×C47—21no—
211C22×C4×C47—21no—
212C22×C4×C47—21no—
213C22×C4×C47—21no—
214C22×C4×C47—21no—
215C22×C4×C47—21no—
216C22×C4×C47—21no—
217C22×C4×C47—21no—
218C22×C4×C47—21no—
219C22×C4×C47—21no—
220C22×C4×C47—21no—
221C22×C4×C47—21no—
222C22×C4×C47—21no—
223C22×C4×C47—21no—
224C22×C4×C47—21no—
225C22×C4×C47—21no—
226C22×C4×C47—21no—
227C22×C4×C47—21no—
228C22×C4×C47—21no—
229C22×C4×C47—21no—
230C22×C4×C47—21no—
231C22×C4×C47—21no—
232C22×C4×C47C22×C412yes—
233C22×C4×C47C22×C412yes—
234C22×C4×C47C22×C412yes—
235C22×C4×C47C22×C412yes—
236C22×C4×C47C22×C412yes—
237C22×C4×C47C22×C412yes—
238C22×C4×C47C2×D412yes—
239C22×C4×C47C2×D412yes—
240C22×C4×C47C2×D412yes—
241C22×C4×C47#4112yes—
242C2×C22⋊D47—28no—
243C2×C22⋊D47—28no—
244C2×C22⋊D47—28no—
245C2×C22⋊D47—28no—
246C2×C22⋊D47—28no—
247C2×C22⋊D47—28no—
248C2×C22⋊D47C42116yescomplemented
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—21no—
264C22×Dic47—21no—
265C22×Dic47—21no—
266C22×Dic47—21no—
267C22×Dic47—21no—
268C22×Dic47—21no—
269C22×Dic47—21no—
270C22×Dic47—21no—
271C22×Dic47—21no—
272C22×Dic47—21no—
273C22×Dic47—21no—
274C22×Dic47—21no—
275C22×Dic47—21no—
276C22×Dic47—21no—
277C22×Dic47—21no—
278C22×Dic47—21no—
279C22×Dic47—21no—
280C22×Dic47—21no—
281C22×Dic47—21no—
282C22×Dic47—21no—
283C22×Dic47—28no—
284C22×Dic47—28no—
285C22×Dic47—44no—
286C22×Dic47—44no—
287C22×Dic47—44no—
288C22×Dic47—44no—
289C22×Dic47—44no—
290C22×Dic47C22×C412yes—
291C22×Dic47C22×C412yes—
292C22×Dic47C22×C412yes—
293C22×Dic47C22×C412yes—
294C22×Dic47C22×C412yes—
295C22×Dic47C22×C412yes—
296C22×Dic47C22×C412yes—
297C22×Dic47C22×C412yes—
298C22×Dic47C22×C412yes—
299C22×Dic47C2×D412yes—
300C22×Dic47C2×D412yes—
301C22×Dic47C2×D412yes—
302C22×Dic47C2×D412yes—
303C22×Dic47#4112yes—
304C22×Dic47#4112yes—
305C2×C4×D47—28no—
306C2×C4×D47—28no—
307C2×C4×D47—28no—
308C2×C4×D47—28no—
309C2×C4×D47—28no—
310C2×C4×D47—28no—
311C2×C4×D47—44no—
312C2×C4×D47—44no—
313C2×C4×D47—44no—
314C2×C4×D47—44no—
315C2×C4×D47—44no—
316C2×C4×D47—44no—
317C2×C4×D47—44no—
318C2×C4×D47—44no—
319C2×C4×D47—44no—
320C2×C4×D47—44no—
321C2×C4×D47—44no—
322C2×C4×D47—44no—
323C2×C4×D47—44no—
324C2×C4×D47—44no—
325C2×C4×D47—44no—
326C22⋊C4×C47—28no—
327C22⋊C4×C47—28no—
328C22⋊C4×C47—44no—
329C42×C47—44no—
330C22⋊Dic47—28no—
331C22⋊Dic47—44no—
332(C2×D47)⋊C4—28no—
333(C2×D47)⋊C4—28no—
334(C2×D47)⋊C4C22⋊C4116yescomplemented
335Dic47⋊C4—28no—
336C4×Dic47—28no—
337C4×Dic47—44no—
338C4×Dic47—44no—
339C4×Dic47—44no—
340C23×C47—22no—
341C23×C47—22no—
342C23×C47—22no—
343C23×C47—22no—
344C23×C47—22no—
345C23×C47—22no—
346C23×C47—22no—
347C23×C47—22no—
348C23×C47—22no—
349C23×C47—22no—
350C23×C47—22no—
351C23×C47—22no—
352C23×C47—22no—
353C23×C47—22no—
354C23×C47—22no—
355C23×C47—22no—
356C23×C47—22no—
357C23×C47—22no—
358C23×C47—41no—
359C23×C47—41no—
360C23×C47—41no—
361C23×C47—41no—
362C23×C47—41no—
363C23×C47—41no—
364C23×C47—41no—
365C23×C47—41no—
366C23×C47—41no—
367C23×C47—41no—
368C23×C47—41no—
369C23×C47—41no—
370C23×C47—41no—
371C23×C47—41no—
372C23×C47—41no—
373C23×C47—41no—
374C23×C47C2×C4214yes—
375C23×C47C23×C411yescharacteristic
376C23×C47C23×C411yescharacteristic
377C23×C47C23×C411yescharacteristic
378C23×C47C22×D411yescharacteristic
379C23×C47C22×D411yescharacteristic
380C23×C47C22×D411yescharacteristic
381C23×C47C2×#4111yescharacteristic
382C23×C47C2×#4111yescharacteristic
383C23×C47C2×#4111yescharacteristic
384C23×C47C2×#4111yescharacteristic
385C23×C47C2×#4111yescharacteristic
386C23×C47H(5,𝔽2)11yescharacteristic
387C23×C47H(5,𝔽2)11yescharacteristic
388C23×C47H(5,𝔽2)11yescharacteristic
389C23×C472−1+411yescharacteristic
390C22×D47—22no—
391C22×D47—22no—
392C22×D47—22no—
393C22×D47—22no—
394C22×D47—22no—
395C22×D47—22no—
396C22×D47—22no—
397C22×D47—22no—
398C22×D47—22no—
399C22×D47—22no—
400C22×D47—22no—
401C22×D47—22no—
402C22×D47—22no—
403C22×D47—22no—
404C22×D47—22no—
405C22×D47—22no—
406C22×D47—22no—
407C22×D47—22no—
408C22×D47—22no—
409C22×D47—22no—
410C22×D47—22no—
411C22×D47—22no—
412C22×D47—22no—
413C22×D47—22no—
414C22×D47—22no—
415C22×D47—22no—
416C22×D47—22no—
417C22×D47—22no—
418C22×D47C2×C4214yes—
419C22×D47C2×C22⋊C414yes—
420C22×D47#11714yes—
421C22×D47C4×D414yes—
422C22×D47C4×D414yes—
423C22×D47C4×D414yes—
424C22×D47C4×D414yes—
425C2×C4×C47—22no—
426C2×C4×C47—22no—
427C2×C4×C47—22no—
428C2×C4×C47—22no—
429C2×C4×C47—22no—
430C2×C4×C47—22no—
431C2×C4×C47—22no—
432C2×C4×C47—22no—
433C2×C4×C47—22no—
434C2×C4×C47—22no—
435C2×C4×C47—22no—
436C2×C4×C47—22no—
437C2×C4×C47—22no—
438C2×C4×C47—22no—
439C2×C4×C47—22no—
440C2×C4×C47—22no—
441C2×C4×C47—22no—
442C2×C4×C47—22no—
443C2×C4×C47—22no—
444C2×C4×C47—22no—
445C2×C4×C47—22no—
446C2×C4×C47—22no—
447C2×C4×C47—22no—
448C2×C4×C47—22no—
449C2×C4×C47—41no—
450C2×C4×C47—41no—
451C2×C4×C47—41no—
452C2×C4×C47—41no—
453C2×C4×C47—41no—
454C2×C4×C47—41no—
455C2×C4×C47—41no—
456C2×C4×C47—41no—
457C2×C4×C47—41no—
458C2×C4×C47—41no—
459C2×C4×C47—41no—
460C2×C4×C47—41no—
461C2×C4×C47—41no—
462C2×C4×C47—41no—
463C2×C4×C47—41no—
464C2×C4×C47—41no—
465C2×C4×C47C2×C22⋊C414yes—
466C2×C4×C47C4×D414yescomplemented
467C22⋊D47—232no—
468C2×Dic47—22no—
469C2×Dic47—22no—
470C2×Dic47—22no—
471C2×Dic47—22no—
472C2×Dic47—22no—
473C2×Dic47—22no—
474C2×Dic47—22no—
475C2×Dic47—22no—
476C2×Dic47—22no—
477C2×Dic47—22no—
478C2×Dic47—22no—
479C2×Dic47—22no—
480C2×Dic47—22no—
481C2×Dic47—22no—
482C2×Dic47—22no—
483C2×Dic47—22no—
484C2×Dic47—22no—
485C2×Dic47—22no—
486C2×Dic47—22no—
487C2×Dic47—22no—
488C2×Dic47—22no—
489C2×Dic47—22no—
490C2×Dic47—22no—
491C2×Dic47—22no—
492C2×Dic47—22no—
493C2×Dic47—22no—
494C2×Dic47—22no—
495C2×Dic47—22no—
496C2×Dic47—22no—
497C2×Dic47—22no—
498C2×Dic47—22no—
499C2×Dic47—22no—
500C2×Dic47—22no—
501C2×Dic47—416no—
502C2×Dic47—41no—
503C2×Dic47—41no—
504C2×Dic47—41no—
505C2×Dic47—41no—
506C2×Dic47—41no—
507C2×Dic47—41no—
508C2×Dic47—41no—
509C2×Dic47—41no—
510C2×Dic47—41no—
511C2×Dic47—41no—
512C2×Dic47—41no—
513C2×Dic47—41no—
514C2×Dic47C2×C4214yes—
515C2×Dic47C2×C22⋊C414yes—
516C2×Dic47C4×D414yes—
517C2×Dic47C4×D414yescomplemented
518C4×D47—416no—
519C4×D47—416no—
520C4×D47—416no—
521#13813—471nomaximal, Sylow
522C22×C47—24no—
523C22×C47—24no—
524C22×C47—24no—
525C22×C47—42no—
526C22×C47—42no—
527C22×C47—42no—
528C22×C47—42no—
529C22×C47—42no—
530C22×C47—42no—
531C22×C47—42no—
532C22×C47—42no—
533C22×C47—42no—
534C22×C47—42no—
535C22×C47—42no—
536C22×C47—42no—
537C22×C47C22×C4211yescharacteristic
538C22×C47C22×C22⋊C411yescharacteristic
539C22×C47C2×#11711yescharacteristic
540C22×C47C2×C4×D411yescharacteristic
541C22×C47C2×C4×D411yescharacteristic
542C22×C47C2×C4×D411yescharacteristic
543C22×C47C2×C4×D411yescharacteristic
544C22×C47C2×C4×D411yescharacteristic
545C22×C47C2×C4×D411yescharacteristic
546C22×C47C2×C4×D411yescharacteristic
547C22×C47C4×#4111yescharacteristic
548C22×C47C4×#4111yescharacteristic
549C22×C47C4×#4111yescharacteristic
550C22×C47#51811yescharacteristic
551C22×C47#51811yescharacteristic
552C22×C47#51811yescharacteristic
553C22×C47#52011yescharacteristic
554C22×C47#52011yescharacteristic
555C22×C47#52011yescharacteristic
556C22×C47D4211yescharacteristic
557C22×C47D4211yescharacteristic
558C22×C47#54611yescharacteristic
559C22×C47#54611yescharacteristic
560C22×C47#54611yescharacteristic
561C22×C47#54611yescharacteristic
562C22×C47#54611yescharacteristic
563C22×C47#54711yescharacteristic
564C22×C47#54711yescharacteristic
565C22×C47#54811yescharacteristic
566C22×C47#55111yescharacteristic
567C22×C47#55111yescharacteristic
568C22×C47#55211yescharacteristic
569C22×C47#55311yescharacteristic
570C22×C47#55311yescharacteristic
571C22×C47#55311yescharacteristic
572C2×D47—24no—
573C2×D47—24no—
574C2×D47—24no—
575C2×D47—24no—
576C2×D47—24no—
577C2×D47—24no—
578C2×D47—24no—
579C2×D47—24no—
580C2×D47—24no—
581C2×D47—24no—
582C2×D47—24no—
583C2×D47—24no—
584C2×D47—24no—
585C2×D47—24no—
586C2×D47C4×C22⋊C418yescomplemented
587C4×C47—24no—
588C4×C47—24no—
589C4×C47—42no—
590C4×C47—42no—
591C4×C47—42no—
592C4×C47—42no—
593Dic47—24no—
594Dic47—24no—
595Dic47—24no—
596Dic47—24no—
597Dic47—42no—
598Dic47—42no—
599Dic47—42no—
600C22×C4×D4—471no—
601C2×#386—471no—
602C2×#386—471no—
603C2×C4×C22⋊C4—471no—
604C2×C4×C22⋊C4—471no—
605C2×C4×C22⋊C4—471no—
606C22×#95—471no—
607#1437—471no—
608#1437D4711yescharacteristic, complemented
609#1436—471no—
610#1436—471no—
611#1434—471no—
612C22⋊#95—471no—
613C22⋊#95—471no—
614C4×#95—471no—
615C2×C47—44no—
616C2×C47C2×C4×C22⋊C411yescharacteristic
617C2×C47C42×D411yescharacteristic
618C2×C47#227511yescharacteristic
619C2×C47D4×C22⋊C411yescharacteristic
620C2×C47#233911yescharacteristic
621C2×C47#235211yescharacteristic
622C2×C47#235311yescharacteristic
623C2×C47#235811yescharacteristic
624C2×C47#235811yescharacteristic
625C2×C47#235911yescharacteristic
626C2×C47#235911yescharacteristic
627C2×C47#236111yescharacteristic
628C2×C47#236111yescharacteristic
629C2×C47#236411yescharacteristic
630C2×C47#236411yescharacteristic
631D47—28no—
632C23×D4—471no—
633C24×C4—471no—
634C24×C4—471no—
635C24×C4—471no—
636C24×C4—471no—
637C2×C4×D4—478no—
638C2×C4×D4—944no—
639C2×C4×D4—944no—
640C22×C4⋊C4—471no—
641C22×C22⋊C4—471no—
642C22×C22⋊C4—471no—
643C22×C22⋊C4—471no—
644C22×C22⋊C4—471no—
645C22×C22⋊C4—471no—
646C22×C22⋊C4C2×D4711yescharacteristic
647C22×C22⋊C4C2×D4711yescharacteristic
648C22×C22⋊C4C2×D4711yescharacteristic
649C22×C42—471no—
650C22×C42—471no—
651C22×C42—471no—
652C22×C42—471no—
653C22×C42C2×D4711yescharacteristic
654#386—478no—
655#386—478no—
656C4×C22⋊C4—944no—
657C4×C22⋊C4—944no—
658C4×C22⋊C4—944no—
659C2×#95—471no—
660C2×#95—471no—
661C2×#95—471no—
662C2×#95—471no—
663C2×#95—471no—
664C2×#95—471no—
665C2×#95—471no—
666C2×#95—471no—
667C2×#95—471no—
668C2×#95—471no—
669C2×#95—471no—
670C2×#95—471no—
671C2×#95—471no—
672C2×#95—944no—
673C2×#95C2×D4711yescharacteristic
674C2×#95C2×D4711yescharacteristic
675C2×#95C2×D4711yescharacteristic
676C47#1381311yescharacteristic, complemented, Sylow
677C25—471no—
678C25C22×D4711yescharacteristic
679C22×D4—474no—
680C22×D4—474no—
681C22×D4—474no—
682C22×D4—942no—
683C22×D4—942no—
684C22×D4—942no—
685C22×D4—942no—
686C23×C4—471no—
687C23×C4—471no—
688C23×C4—471no—
689C23×C4—471no—
690C23×C4—471no—
691C23×C4—471no—
692C23×C4—471no—
693C23×C4—474no—
694C23×C4—474no—
695C23×C4—474no—
696C23×C4—474no—
697C23×C4—942no—
698C23×C4—942no—
699C23×C4—942no—
700C23×C4—942no—
701C23×C4—942no—
702C23×C4—942no—
703C23×C4—942no—
704C23×C4—942no—
705C23×C4—942no—
706C23×C4—942no—
707C23×C4—942no—
708C23×C4—942no—
709C23×C4—942no—
710C23×C4—942no—
711C23×C4—942no—
712C23×C4—942no—
713C23×C4—1881no—
714C23×C4—1881no—
715C23×C4—1881no—
716C23×C4—1881no—
717C23×C4—1881no—
718C23×C4—1881no—
719C23×C4—1881no—
720C23×C4—1881no—
721C23×C4C22×D4711yescharacteristic
722C23×C4C22×D4711yescharacteristic
723C23×C4C22×D4711yescharacteristic
724C23×C4C22×D4711yescharacteristic
725C23×C4C22×D4711yescharacteristic
726C23×C4C22×D4711yescharacteristic
727C4×D4—9432no—
728C2×C4⋊C4—474no—
729C2×C4⋊C4—942no—
730C2×C4⋊C4—942no—
731C2×C22⋊C4—22no—
732C2×C22⋊C4—22no—
733C2×C22⋊C4—22no—
734C2×C22⋊C4—22no—
735C2×C22⋊C4—41no—
736C2×C22⋊C4—41no—
737C2×C22⋊C4—474no—
738C2×C22⋊C4—474no—
739C2×C22⋊C4—474no—
740C2×C22⋊C4—474no—
741C2×C22⋊C4—474no—
742C2×C22⋊C4—474no—
743C2×C22⋊C4—474no—
744C2×C22⋊C4—942no—
745C2×C22⋊C4—942no—
746C2×C22⋊C4—942no—
747C2×C22⋊C4—942no—
748C2×C22⋊C4—942no—
749C2×C22⋊C4—942no—
750C2×C22⋊C4—1881no—
751C2×C22⋊C4—1881no—
752C2×C22⋊C4C4×D4714yescomplemented
753C2×C22⋊C4C4×D4714yescomplemented
754C2×C22⋊C4C4×D4714yescomplemented
755C2×C42—22no—
756C2×C42—22no—
757C2×C42—41no—
758C2×C42—474no—
759C2×C42—942no—
760C2×C42—942no—
761C2×C42—942no—
762C2×C42—942no—
763C2×C42—942no—
764C2×C42—942no—
765C2×C42—942no—
766C2×C42—942no—
767C2×C42—1881no—
768C2×C42—1881no—
769C2×C42—1881no—
770#95—22no—
771#95—22no—
772#95—41no—
773#95—474no—
774#95—474no—
775#95—474no—
776#95—474no—
777#95—474no—
778#95—942no—
779#95—942no—
780#95—942no—
781#95—942no—
782#95—942no—
783#95—942no—
784#95—942no—
785#95—1881no—
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24—21no—
791C24—21no—
792C24—21no—
793C24—21no—
794C24—21no—
795C24—21no—
796C24—21no—
797C24—21no—
798C24—472no—
799C24—472no—
800C24—472no—
801C24—472no—
802C24—472no—
803C24—472no—
804C24—472no—
805C24—941no—
806C24—941no—
807C24—941no—
808C24—941no—
809C24—941no—
810C24—941no—
811C24—941no—
812C24—941no—
813C24C2×C4×D4712yes—
814C24C2×C4×D4712yes—
815C24C2×C4×D4712yes—
816C24C23×D4711yescharacteristic
817C2×D4—4716no—
818C2×D4—948no—
819C2×D4—948no—
820C2×D4—948no—
821C2×D4—948no—
822C2×D4—948no—
823C2×D4—948no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—472no—
857C22×C4—472no—
858C22×C4—472no—
859C22×C4—472no—
860C22×C4—472no—
861C22×C4—472no—
862C22×C4—472no—
863C22×C4—472no—
864C22×C4—472no—
865C22×C4—472no—
866C22×C4—472no—
867C22×C4—472no—
868C22×C4—472no—
869C22×C4—472no—
870C22×C4—472no—
871C22×C4—948no—
872C22×C4—948no—
873C22×C4—948no—
874C22×C4—948no—
875C22×C4—948no—
876C22×C4—948no—
877C22×C4—948no—
878C22×C4—941no—
879C22×C4—941no—
880C22×C4—941no—
881C22×C4—941no—
882C22×C4—941no—
883C22×C4—941no—
884C22×C4—941no—
885C22×C4—941no—
886C22×C4—941no—
887C22×C4—941no—
888C22×C4—941no—
889C22×C4—941no—
890C22×C4—941no—
891C22×C4—941no—
892C22×C4—941no—
893C22×C4—941no—
894C22×C4—941no—
895C22×C4—941no—
896C22×C4—941no—
897C22×C4—941no—
898C22×C4—941no—
899C22×C4—941no—
900C22×C4—941no—
901C22×C4—941no—
902C22×C4—941no—
903C22×C4—941no—
904C22×C4—941no—
905C22×C4—941no—
906C22×C4—941no—
907C22×C4—941no—
908C22×C4—941no—
909C22×C4—941no—
910C22×C4—941no—
911C22×C4—941no—
912C22×C4—948no—
913C22×C4—1884no—
914C22×C4—1884no—
915C22×C4—1884no—
916C22×C4—1884no—
917C22×C4—1884no—
918C22×C4—1884no—
919C22×C4—1884no—
920C22×C4—1884no—
921C22×C4—1884no—
922C22×C4—1884no—
923C22×C4—1884no—
924C22×C4—1884no—
925C22×C4—1884no—
926C22×C4—1884no—
927C22×C4—1884no—
928C22×C4—1884no—
929C22×C4—1884no—
930C22×C4—1884no—
931C22×C4—1884no—
932C22×C4—1884no—
933C22×C4C2×C4×D4712yes—
934C22×C4C2×C4×D4712yes—
935C22×C4C2×C4×D4712yes—
936C22×C4C2×C4×D4712yes—
937C22×C4C2×C4×D4712yes—
938C22×C4C2×C4×D4712yes—
939C22×C4D4×D4712yes—
940C22×C4D4×D4712yes—
941C22×C4D4×D4712yes—
942C22×C4#1062535212yes—
943C4⋊C4—948no—
944C22⋊C4—28no—
945C22⋊C4—28no—
946C22⋊C4—44no—
947C22⋊C4—4716no—
948C22⋊C4—948no—
949C22⋊C4—948no—
950C22⋊C4—948no—
951C22⋊C4—1884no—
952C42—44no—
953C42—948no—
954C42—1884no—
955C42—1884no—
956C42—1884no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—474no—
992C23—474no—
993C23—474no—
994C23—474no—
995C23—474no—
996C23—474no—
997C23—474no—
998C23—942no—
999C23—942no—
1000C23—942no—
1001C23—942no—
1002C23—942no—
1003C23—942no—
1004C23—942no—
1005C23—942no—
1006C23—942no—
1007C23—942no—
1008C23—942no—
1009C23—942no—
1010C23—942no—
1011C23—942no—
1012C23—942no—
1013C23—942no—
1014C23—942no—
1015C23—942no—
1016C23—942no—
1017C23—942no—
1018C23—942no—
1019C23—942no—
1020C23—942no—
1021C23—942no—
1022C23—942no—
1023C23—942no—
1024C23—942no—
1025C23—942no—
1026C23C42×D4714yes—
1027C23C22×C4×D4711yescharacteristic
1028C23C22×C4×D4711yescharacteristic
1029C23C22×C4×D4711yescharacteristic
1030C23C2×D4×D4711yescharacteristic
1031C23C2×D4×D4711yescharacteristic
1032C23C2×D4×D4711yescharacteristic
1033C23#41×D4711yescharacteristic
1034C23#41×D4711yescharacteristic
1035C23#41×D4711yescharacteristic
1036C23#41×D4711yescharacteristic
1037C23C2×#1062535211yescharacteristic
1038C23#1309406911yescharacteristic
1039C23#1309406911yescharacteristic
1040C23#1309407011yescharacteristic
1041C23#1309407111yescharacteristic
1042D4—9432no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—474no—
1084C2×C4—474no—
1085C2×C4—474no—
1086C2×C4—474no—
1087C2×C4—942no—
1088C2×C4—942no—
1089C2×C4—942no—
1090C2×C4—942no—
1091C2×C4—942no—
1092C2×C4—942no—
1093C2×C4—942no—
1094C2×C4—942no—
1095C2×C4—942no—
1096C2×C4—942no—
1097C2×C4—942no—
1098C2×C4—942no—
1099C2×C4—942no—
1100C2×C4—942no—
1101C2×C4—942no—
1102C2×C4—942no—
1103C2×C4—942no—
1104C2×C4—942no—
1105C2×C4—942no—
1106C2×C4—942no—
1107C2×C4—942no—
1108C2×C4—942no—
1109C2×C4—942no—
1110C2×C4—942no—
1111C2×C4—942no—
1112C2×C4—942no—
1113C2×C4—942no—
1114C2×C4—942no—
1115C2×C4—942no—
1116C2×C4—942no—
1117C2×C4—942no—
1118C2×C4—942no—
1119C2×C4—942no—
1120C2×C4—18816no—
1121C2×C4—18816no—
1122C2×C4—18816no—
1123C2×C4—18816no—
1124C2×C4—1881no—
1125C2×C4—1881no—
1126C2×C4—1881no—
1127C2×C4—1881no—
1128C2×C4—1881no—
1129C2×C4—1881no—
1130C2×C4—1881no—
1131C2×C4—1881no—
1132C2×C4—1881no—
1133C2×C4—1881no—
1134C2×C4—1881no—
1135C2×C4—1881no—
1136C2×C4C22⋊C4×D4714yes—
1137C2×C4(C22⋊D47)⋊C414yescomplemented
1138C22—24no—
1139C22—24no—
1140C22—24no—
1141C22—42no—
1142C22—42no—
1143C22—42no—
1144C22—42no—
1145C22—42no—
1146C22—42no—
1147C22—42no—
1148C22—42no—
1149C22—42no—
1150C22—42no—
1151C22—42no—
1152C22—42no—
1153C22—478no—
1154C22—944no—
1155C22—944no—
1156C22—944no—
1157C22—944no—
1158C22—944no—
1159C22—944no—
1160C22—944no—
1161C22—944no—
1162C22—944no—
1163C22—944no—
1164C22—944no—
1165C22—944no—
1166C22—944no—
1167C22—944no—
1168C22C2×C42×D4711yescharacteristic
1169C22C2×C22⋊C4×D4711yescharacteristic
1170C22#117×D4711yescharacteristic
1171C22C4×D4×D4711yescharacteristic
1172C22C4×D4×D4711yescharacteristic
1173C22C4×D4×D4711yescharacteristic
1174C22C4×D4×D4711yescharacteristic
1175C22C4×D4×D4711yescharacteristic
1176C22C4×D4×D4711yescharacteristic
1177C22C2×(C22⋊D47)⋊C411yescharacteristic
1178C22C4×#1062535211yescharacteristic
1179C22C4×#1062535211yescharacteristic
1180C22#1568959111yescharacteristic
1181C22#1568959511yescharacteristic
1182C22#1568959511yescharacteristic
1183C22#1568959611yescharacteristic
1184C22#1568960211yescharacteristic
1185C22#1568960211yescharacteristic
1186C22#1568960311yescharacteristic
1187C22#1568975711yescharacteristic
1188C22#1568975811yescharacteristic
1189C22#1568976011yescharacteristic
1190C22#1568976211yescharacteristic
1191C22#1568976211yescharacteristic
1192C22#1568976611yescharacteristic
1193C22#1568977011yescharacteristic
1194C22#1568977111yescharacteristic
1195C22#1568977311yescharacteristic
1196C22#1568978111yescharacteristic
1197C22#1568979611yescharacteristic
1198C22#1568980311yescharacteristic
1199C22#1568980911yescharacteristic
1200C22#1568981811yescharacteristic
1201C22#1568982011yescharacteristic
1202C22#1568982411yescharacteristic
1203C4—24no—
1204C4—24no—
1205C4—42no—
1206C4—42no—
1207C4—42no—
1208C4—42no—
1209C4—944no—
1210C4—944no—
1211C4—944no—
1212C4—944no—
1213C4—1882no—
1214C4—1882no—
1215C4—1882no—
1216C2—44no—
1217C2—948no—
1218C2C4×C22⋊C4×D4711yescharacteristic
1219C2C4×(C22⋊D47)⋊C411yescharacteristic
1220C2#2024574711yescharacteristic
1221C2#2024620911yescharacteristic
1222C2#2024621411yescharacteristic
1223C2#2024631611yescharacteristic
1224C2#2024632311yescharacteristic
1225C2#2024636811yescharacteristic
1226C2#2024636911yescharacteristic
1227C2#2024637711yescharacteristic
1228C2#2024637911yescharacteristic
1229C2#2024640111yescharacteristic
1230C2#2024640911yescharacteristic
1231C2#2024643211yescharacteristic
1232C2#2024643711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC22×C47C22×C42
FittingC47×#1437C2
socle, cosocleC24×C47C24
prime radicalC23×C22⋊D47C22
hypercenter#1437D47
hypocenterC47#13813
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
4. C2×C22⋊C4×Dic47C2semidirect
5. C2×C4×(C2×D47)⋊C4C2semidirect
6. C2×#15688970C2semidirect
7. C2×#95×D47C2semidirect
8. #20241625C2semidirect
9. #20241619C2semidirect
10. #20241619C2semidirect
11. #20241612C2semidirect
12. #20241610C2semidirect
13. (C2×D47)⋊#95C2semidirect
14. C4×C47⋊#95C2semidirect
15. C47×#1437C2semidirect
23. C2×(C22⋊D47)⋊C4C4semidirect
34. #15688999C4semidirect
35. #15688999C4semidirect
74. C23×Dic47C2×C4semidirect
101. C22×C4×D47C2×C4semidirect
102. C22×C4×D47C2×C4semidirect
106. C2×Dic47⋊C4C2×C4semidirect
111. C2×C22⋊Dic47C2×C4semidirect
112. C2×C22⋊Dic47C2×C4semidirect
118. C2×(C2×D47)⋊C4C2×C4semidirect
119. C2×(C2×D47)⋊C4C2×C4semidirect
133. C2×C4×Dic47C2×C4semidirect
142. C47⋊#95C2×C4semidirect
143. C47⋊#95C2×C4semidirect
144. C47⋊#95C2×C4semidirect
145. C47⋊#95C2×C4semidirect
146. C47⋊#95D4semidirect
160. C2×C22⋊C4×C47C2×C4semidirect
161. C2×C22⋊C4×C47C2×C4semidirect
162. C2×C22⋊C4×C47C2×C4semidirect
248. C2×C22⋊D47C42semidirect
334. (C2×D47)⋊C4C22⋊C4semidirect
466. C2×C4×C47C4×D4semidirect
517. C2×Dic47C4×D4semidirect
586. C2×D47C4×C22⋊C4semidirect
608. #1437D47semidirect
676. C47#13813semidirect
752. C2×C22⋊C4C4×D47semidirect
753. C2×C22⋊C4C4×D47semidirect
754. C2×C22⋊C4C4×D47semidirect
1137. C2×C4(C22⋊D47)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×(C22⋊D47)⋊C42
C2×#156889992
C2×C22⋊C4×Dic472
C2×C4×(C2×D47)⋊C42
C2×#156889702
C2×#95×D472
#202416252
#202416192
#202416122
#202416102
(C2×D47)⋊#952
C4×C47⋊#952
C47×#14372
#1381347