Finite Group Databasebeta

← #26137770

Subgroups — #26137770

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×#13093986C211yesmaximal, characteristic
2C2×#15689001C211yesmaximal, characteristic
3C2×#15689001C211yesmaximal, characteristic
4C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
5C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
6C2×#15688970C211yesmaximal, characteristic, complemented
7C2×#95×D47C211yesmaximal, characteristic, complemented
8#20241624C211yesmaximal, characteristic, complemented
9#20241624C211yesmaximal, characteristic, complemented
10#20241620C211yesmaximal, characteristic, complemented
11#20241613C211yesmaximal, characteristic, complemented
12(C2×D47)⋊#95C211yesmaximal, characteristic, complemented
13(C2×D47)⋊#95C211yesmaximal, characteristic, complemented
14#95×Dic47C211yesmaximal, characteristic, complemented
15C47×#1436C211yesmaximal, characteristic, complemented
16C23×D188C2211yescharacteristic
17C23×C4×D47C2211yescharacteristic
18C23×C4×D47C2211yescharacteristic
19C23×C4×D47C2211yescharacteristic
20C23×C4×D47C2211yescharacteristic
21C2×#13093986—24no—
22C2×#13093986—24no—
23C2×#13093986C418yescomplemented
24C22×(C2×D47)⋊C4C2211yescharacteristic
25C22×(C2×D47)⋊C4C2211yescharacteristic
26C22×(C2×D47)⋊C4C2211yescharacteristic
27C22×(C2×D47)⋊C4C2211yescharacteristic
28C22×(C2×D47)⋊C4C2211yescharacteristic
29C22×(C2×D47)⋊C4C2211yescharacteristic
30C22×(C2×D47)⋊C4C2211yescharacteristic
31C22×(C2×D47)⋊C4C2211yescharacteristic
32C22×C4×Dic47C2211yescharacteristic
33C22×C4×Dic47C2211yescharacteristic
34C22×C4×Dic47C2211yescharacteristic
35C22×C4×Dic47C2211yescharacteristic
36#15689001C418yescomplemented
37#15689001C418yescomplemented
38C4×(C2×D47)⋊C4—24no—
39C4×(C2×D47)⋊C4—24no—
40#15688970—24no—
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×C4⋊C4×C47C2211yescharacteristic
54C22×C42×C47C2211yescharacteristic
55C2×#95×C47C2211yescharacteristic
56C2×#95×C47C2211yescharacteristic
57C2×#95×C47C2211yescharacteristic
58C2×#95×C47C2211yescharacteristic
59C2×#95×C47C2211yescharacteristic
60C24×D47C2311yescharacteristic
61C24×D47C2311yescharacteristic
62C22×D188—22no—
63C22×D188—22no—
64C22×D188—22no—
65C22×D188—22no—
66C22×D188C2×C414yes—
67C22×D188C2×C414yes—
68C22×D188C2×C414yes—
69C23×Dic47C2311yescharacteristic
70C23×Dic47C2311yescharacteristic
71C23×Dic47C2311yescharacteristic
72C23×Dic47C2311yescharacteristic
73C23×Dic47C2311yescharacteristic
74C23×Dic47C2311yescharacteristic
75C22×C4×D47—22no—
76C22×C4×D47—22no—
77C22×C4×D47—22no—
78C22×C4×D47—22no—
79C22×C4×D47—22no—
80C22×C4×D47—22no—
81C22×C4×D47—22no—
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—41no—
92C22×C4×D47—41no—
93C22×C4×D47—41no—
94C22×C4×D47—41no—
95C22×C4×D47—41no—
96C22×C4×D47—41no—
97C22×C4×D47—41no—
98C22×C4×D47—41no—
99C22×C4×D47C2×C414yes—
100C22×C4×D47C2×C414yescomplemented
101C22×C4×D47C2×C414yescomplemented
102C22×C4×D47C2×C414yescomplemented
103#13093986—232no—
104C2×(C2×D47)⋊C4—22no—
105C2×(C2×D47)⋊C4—22no—
106C2×(C2×D47)⋊C4—22no—
107C2×(C2×D47)⋊C4—22no—
108C2×(C2×D47)⋊C4—22no—
109C2×(C2×D47)⋊C4—22no—
110C2×(C2×D47)⋊C4—22no—
111C2×(C2×D47)⋊C4—22no—
112C2×(C2×D47)⋊C4—22no—
113C2×(C2×D47)⋊C4—22no—
114C2×(C2×D47)⋊C4—41no—
115C2×(C2×D47)⋊C4—41no—
116C2×(C2×D47)⋊C4—41no—
117C2×(C2×D47)⋊C4—41no—
118C2×(C2×D47)⋊C4C2×C414yes—
119C2×(C2×D47)⋊C4C2×C414yescomplemented
120C2×(C2×D47)⋊C4C2×C414yescomplemented
121C2×(C2×D47)⋊C4C2×C414yescomplemented
122C2×(C2×D47)⋊C4C2×C414yescomplemented
123C2×(C2×D47)⋊C4C2×C414yescomplemented
124C2×(C2×D47)⋊C4C2×C414yescomplemented
125C2×(C2×D47)⋊C4C2×C414yescomplemented
126C2×(C2×D47)⋊C4D414yes—
127C2×(C2×D47)⋊C4D414yes—
128C2×C4×Dic47—22no—
129C2×C4×Dic47—22no—
130C2×C4×Dic47—22no—
131C2×C4×Dic47—22no—
132C2×C4×Dic47—22no—
133C2×C4×Dic47—22no—
134C2×C4×Dic47—22no—
135C2×C4×Dic47—22no—
136C2×C4×Dic47—41no—
137C2×C4×Dic47—41no—
138C2×C4×Dic47—41no—
139C2×C4×Dic47C2×C414yescomplemented
140C47⋊#95—22no—
141C47⋊#95—22no—
142C47⋊#95—22no—
143C47⋊#95—22no—
144C47⋊#95—22no—
145C47⋊#95—22no—
146C47⋊#95—22no—
147C47⋊#95—41no—
148C47⋊#95C2×C414yescomplemented
149C47⋊#95C2×C414yescomplemented
150C47⋊#95D414yescomplemented
151C23×C4×C47C2311yescharacteristic
152C23×C4×C47C2311yescharacteristic
153C23×C4×C47C2311yescharacteristic
154C23×C4×C47C2311yescharacteristic
155C23×C4×C47C2311yescharacteristic
156C23×C4×C47C2311yescharacteristic
157C23×C4×C47C2311yescharacteristic
158C2×C4⋊C4×C47—22no—
159C2×C4⋊C4×C47—22no—
160C2×C4⋊C4×C47C2×C414yescomplemented
161C2×C42×C47—22no—
162C2×C42×C47—22no—
163C2×C42×C47—41no—
164#95×C47—22no—
165#95×C47—22no—
166#95×C47—41no—
167#95×C47C2×C414yescomplemented
168#95×C47C2×C414yescomplemented
169C24×C47C2411yescharacteristic
170C23×D47—21no—
171C23×D47—21no—
172C23×D47—21no—
173C23×D47—21no—
174C23×D47—21no—
175C23×D47—21no—
176C23×D47—21no—
177C23×D47—21no—
178C23×D47—21no—
179C23×D47—21no—
180C23×D47—21no—
181C23×D47—21no—
182C23×D47—21no—
183C23×D47—21no—
184C23×D47—21no—
185C23×D47—21no—
186C23×D47—21no—
187C23×D47—21no—
188C23×D47—21no—
189C23×D47—21no—
190C23×D47C22×C412yes—
191C23×D47C22×C412yes—
192C23×D47C22×C412yes—
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×C47—21no—
233C22×C4×C47—21no—
234C22×C4×C47—21no—
235C22×C4×C47—21no—
236C22×C4×C47C22×C412yes—
237C22×C4×C47C22×C412yes—
238C22×C4×C47C22×C412yes—
239C22×C4×C47C22×C412yes—
240C22×C4×C47C22×C412yes—
241C22×C4×C47C22×C412yes—
242C22×C4×C47C22×C412yes—
243C22×C4×C47C22×C412yes—
244C22×C4×C47C22×C412yes—
245C22×C4×C47C2×D412yes—
246C22×C4×C47C2×D412yes—
247C22×C4×C47C2×D412yes—
248C22×C4×C47#4112yes—
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×Dic47C22×C412yes—
280C22×Dic47C22×C412yes—
281C22×Dic47C22×C412yes—
282C22×Dic47C22×C412yes—
283C22×Dic47C22×C412yes—
284C22×Dic47C22×C412yes—
285C22×Dic47C2×D412yes—
286C22×Dic47C2×D412yes—
287C22×Dic47C2×D412yes—
288C22×Dic47C2×D412yes—
289C22×Dic47#4112yes—
290C22×Dic47#4112yes—
291C2×D188—28no—
292C2×D188—28no—
293C2×D188—28no—
294C2×D188—28no—
295C2×D188—28no—
296C2×D188—28no—
297C2×D188C42116yescomplemented
298C2×C4×D47—28no—
299C2×C4×D47—28no—
300C2×C4×D47—28no—
301C2×C4×D47—28no—
302C2×C4×D47—28no—
303C2×C4×D47—28no—
304C2×C4×D47—28no—
305C2×C4×D47—28no—
306C2×C4×D47—44no—
307C2×C4×D47—44no—
308C2×C4×D47—44no—
309C2×C4×D47—44no—
310C2×C4×D47—44no—
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—
326C4⋊C4×C47—28no—
327C42×C47—44no—
328(C2×D47)⋊C4—28no—
329(C2×D47)⋊C4—28no—
330(C2×D47)⋊C4—28no—
331(C2×D47)⋊C4—28no—
332(C2×D47)⋊C4—28no—
333(C2×D47)⋊C4—44no—
334(C2×D47)⋊C4—44no—
335(C2×D47)⋊C4C22⋊C4116yescomplemented
336C4×Dic47—28no—
337C4×Dic47—44no—
338C4×Dic47—44no—
339C4×Dic47—44no—
340C23×C47C23×C411yescharacteristic
341C23×C47C23×C411yescharacteristic
342C23×C47C23×C411yescharacteristic
343C23×C47C22×D411yescharacteristic
344C23×C47C22×D411yescharacteristic
345C23×C47C22×D411yescharacteristic
346C23×C47C2×#4111yescharacteristic
347C23×C47C2×#4111yescharacteristic
348C23×C47C2×#4111yescharacteristic
349C23×C47C2×#4111yescharacteristic
350C23×C47C2×#4111yescharacteristic
351C23×C47H(5,𝔽2)11yescharacteristic
352C23×C47H(5,𝔽2)11yescharacteristic
353C23×C47H(5,𝔽2)11yescharacteristic
354C23×C472−1+411yescharacteristic
355C22×D47—22no—
356C22×D47—22no—
357C22×D47—22no—
358C22×D47—22no—
359C22×D47—22no—
360C22×D47—22no—
361C22×D47—22no—
362C22×D47—22no—
363C22×D47—22no—
364C22×D47—22no—
365C22×D47—22no—
366C22×D47—22no—
367C22×D47—22no—
368C22×D47—22no—
369C22×D47—22no—
370C22×D47—22no—
371C22×D47—22no—
372C22×D47—22no—
373C22×D47—22no—
374C22×D47—22no—
375C22×D47—22no—
376C22×D47—22no—
377C22×D47—22no—
378C22×D47—22no—
379C22×D47—22no—
380C22×D47—22no—
381C22×D47—22no—
382C22×D47—22no—
383C22×D47—22no—
384C22×D47—22no—
385C22×D47—22no—
386C22×D47—22no—
387C22×D47—22no—
388C22×D47—22no—
389C22×D47—22no—
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—41no—
402C22×D47—41no—
403C22×D47—41no—
404C22×D47—41no—
405C22×D47—41no—
406C22×D47—41no—
407C22×D47—41no—
408C22×D47—41no—
409C22×D47—41no—
410C22×D47—41no—
411C22×D47—41no—
412C22×D47—41no—
413C22×D47—41no—
414C22×D47—41no—
415C22×D47—41no—
416C22×D47—41no—
417C22×D47C2×C4214yes—
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—22no—
450C2×C4×C47—22no—
451C2×C4×C47—22no—
452C2×C4×C47—22no—
453C2×C4×C47—22no—
454C2×C4×C47—22no—
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×C47—41no—
466C2×C4×C47—41no—
467C2×C4×C47—41no—
468C2×C4×C47—41no—
469C2×C4×C47—41no—
470C2×C4×C47—41no—
471C2×C4×C47C2×C4214yes—
472C2×C4×C47C2×C22⋊C414yes—
473C2×C4×C47C4×D414yescomplemented
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—41no—
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×Dic47C2×C22⋊C414yes—
514C2×Dic47C4×D414yes—
515C2×Dic47C4×D414yescomplemented
516D188—232no—
517C4×D47—416no—
518C4×D47—416no—
519C4×D47—416no—
520C4×D47—416no—
521#13813—471nomaximal, Sylow
522C22×C47C22×C4211yescharacteristic
523C22×C47C22×C22⋊C411yescharacteristic
524C22×C47C2×#11711yescharacteristic
525C22×C47C2×C4×D411yescharacteristic
526C22×C47C2×C4×D411yescharacteristic
527C22×C47C2×C4×D411yescharacteristic
528C22×C47C2×C4×D411yescharacteristic
529C22×C47C2×C4×D411yescharacteristic
530C22×C47C2×C4×D411yescharacteristic
531C22×C47C2×C4×D411yescharacteristic
532C22×C47C4×#4111yescharacteristic
533C22×C47C4×#4111yescharacteristic
534C22×C47C4×#4111yescharacteristic
535C22×C47#51811yescharacteristic
536C22×C47#51811yescharacteristic
537C22×C47#51811yescharacteristic
538C22×C47#52011yescharacteristic
539C22×C47#52011yescharacteristic
540C22×C47#52011yescharacteristic
541C22×C47D4211yescharacteristic
542C22×C47D4211yescharacteristic
543C22×C47#54611yescharacteristic
544C22×C47#54611yescharacteristic
545C22×C47#54611yescharacteristic
546C22×C47#54611yescharacteristic
547C22×C47#54611yescharacteristic
548C22×C47#54711yescharacteristic
549C22×C47#54711yescharacteristic
550C22×C47#54811yescharacteristic
551C22×C47#55111yescharacteristic
552C22×C47#55111yescharacteristic
553C22×C47#55211yescharacteristic
554C22×C47#55311yescharacteristic
555C22×C47#55311yescharacteristic
556C22×C47#55311yescharacteristic
557C2×D47—24no—
558C2×D47—24no—
559C2×D47—24no—
560C2×D47—24no—
561C2×D47—24no—
562C2×D47—24no—
563C2×D47—24no—
564C2×D47—24no—
565C2×D47—24no—
566C2×D47—24no—
567C2×D47—24no—
568C2×D47—24no—
569C2×D47—24no—
570C2×D47—24no—
571C2×D47—24no—
572C2×D47—24no—
573C2×D47—24no—
574C2×D47—42no—
575C2×D47—42no—
576C2×D47—42no—
577C2×D47—42no—
578C2×D47—42no—
579C2×D47—42no—
580C2×D47—42no—
581C2×D47—42no—
582C2×D47—42no—
583C2×D47—42no—
584C2×D47—42no—
585C2×D47—42no—
586C2×D47C4×C22⋊C418yescomplemented
587C4×C47—24no—
588C4×C47—24no—
589C4×C47—24no—
590C4×C47—42no—
591C4×C47—42no—
592C4×C47—42no—
593C4×C47—42no—
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#1437—471no—
609#1436—471no—
610#1436D4711yescharacteristic, complemented
611#1434—471no—
612C22⋊#95—471no—
613C22⋊#95—471no—
614C4×#95—471no—
615C2×C47C2×C4×C22⋊C411yescharacteristic
616C2×C47C42×D411yescharacteristic
617C2×C47#227511yescharacteristic
618C2×C47D4×C22⋊C411yescharacteristic
619C2×C47#233911yescharacteristic
620C2×C47#235211yescharacteristic
621C2×C47#235311yescharacteristic
622C2×C47#235811yescharacteristic
623C2×C47#235811yescharacteristic
624C2×C47#235911yescharacteristic
625C2×C47#235911yescharacteristic
626C2×C47#236111yescharacteristic
627C2×C47#236111yescharacteristic
628C2×C47#236411yescharacteristic
629C2×C47#236411yescharacteristic
630D47—28no—
631D47—44no—
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⋊C4C2×D4711yescharacteristic
641C22×C22⋊C4—471no—
642C22×C22⋊C4—471no—
643C22×C22⋊C4—471no—
644C22×C22⋊C4—471no—
645C22×C22⋊C4—471no—
646C22×C22⋊C4—471no—
647C22×C22⋊C4—471no—
648C22×C22⋊C4—471no—
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—944no—
671C2×#95C2×D4711yescharacteristic
672C2×#95C2×D4711yescharacteristic
673C2×#95C2×D4711yescharacteristic
674C2×#95C2×D4711yescharacteristic
675C2×#95C2×D4711yescharacteristic
676C47#1381311yescharacteristic, complemented, Sylow
677C25—471no—
678C25—471no—
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—474no—
693C23×C4—474no—
694C23×C4—474no—
695C23×C4—474no—
696C23×C4—942no—
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—1881no—
713C23×C4—1881no—
714C23×C4—1881no—
715C23×C4—1881no—
716C23×C4—1881no—
717C23×C4—1881no—
718C23×C4—1881no—
719C23×C4—1881no—
720C23×C4C22×D4711yescharacteristic
721C23×C4C22×D4711yescharacteristic
722C23×C4C22×D4711yescharacteristic
723C23×C4C22×D4711yescharacteristic
724C23×C4C22×D4711yescharacteristic
725C23×C4C22×D4711yescharacteristic
726C23×C4C22×D4711yescharacteristic
727C4×D4—9432no—
728C2×C4⋊C4—22no—
729C2×C4⋊C4—22no—
730C2×C4⋊C4C4×D4714yescomplemented
731C2×C22⋊C4—474no—
732C2×C22⋊C4—474no—
733C2×C22⋊C4—474no—
734C2×C22⋊C4—474no—
735C2×C22⋊C4—474no—
736C2×C22⋊C4—474no—
737C2×C22⋊C4—474no—
738C2×C22⋊C4—474no—
739C2×C22⋊C4—474no—
740C2×C22⋊C4—474no—
741C2×C22⋊C4—942no—
742C2×C22⋊C4—942no—
743C2×C22⋊C4—942no—
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—942no—
751C2×C22⋊C4—1881no—
752C2×C22⋊C4—1881no—
753C2×C22⋊C4—1881no—
754C2×C22⋊C4—1881no—
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—942no—
777#95—942no—
778#95—942no—
779#95—942no—
780#95—942no—
781#95—942no—
782#95—942no—
783#95—1881no—
784#95C4×D4714yescomplemented
785#95C4×D4714yescomplemented
786C24—472no—
787C24—472no—
788C24—472no—
789C24—472no—
790C24—472no—
791C24—472no—
792C24—472no—
793C24—472no—
794C24—472no—
795C24—472no—
796C24—941no—
797C24—941no—
798C24—941no—
799C24—941no—
800C24—941no—
801C24—941no—
802C24—941no—
803C24—941no—
804C24—941no—
805C24—941no—
806C24—941no—
807C24—941no—
808C24—941no—
809C24—941no—
810C24—941no—
811C24—941no—
812C24—941no—
813C24—941no—
814C24—941no—
815C24—941no—
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—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
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—472no—
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—948no—
909C22×C4—948no—
910C22×C4—1884no—
911C22×C4—1884no—
912C22×C4—1884no—
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×C4C2×C4×D4712yes—
931C22×C4C2×C4×D4712yes—
932C22×C4C2×C4×D4712yes—
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#1062535412yes—
943C4⋊C4—28no—
944C22⋊C4—4716no—
945C22⋊C4—948no—
946C22⋊C4—948no—
947C22⋊C4—948no—
948C22⋊C4—948no—
949C22⋊C4—948no—
950C22⋊C4—1884no—
951C22⋊C4—1884no—
952C42—44no—
953C42—948no—
954C42—1884no—
955C42—1884no—
956C42—1884no—
957C23—474no—
958C23—474no—
959C23—474no—
960C23—474no—
961C23—474no—
962C23—474no—
963C23—474no—
964C23—474no—
965C23—942no—
966C23—942no—
967C23—942no—
968C23—942no—
969C23—942no—
970C23—942no—
971C23—942no—
972C23—942no—
973C23—942no—
974C23—942no—
975C23—942no—
976C23—942no—
977C23—942no—
978C23—942no—
979C23—942no—
980C23—942no—
981C23—942no—
982C23—942no—
983C23—942no—
984C23—942no—
985C23—942no—
986C23—942no—
987C23—942no—
988C23—942no—
989C23—942no—
990C23—942no—
991C23—942no—
992C23—942no—
993C23—942no—
994C23—942no—
995C23—942no—
996C23—942no—
997C23—942no—
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—1881no—
1012C23—1881no—
1013C23—1881no—
1014C23—1881no—
1015C23—1881no—
1016C23—1881no—
1017C23—1881no—
1018C23—1881no—
1019C23—1881no—
1020C23—1881no—
1021C23—1881no—
1022C23—1881no—
1023C23—1881no—
1024C23—1881no—
1025C23—1881no—
1026C23—1881no—
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×#1062535411yescharacteristic
1038C23#1309406911yescharacteristic
1039C23#1309407011yescharacteristic
1040C23#1309407011yescharacteristic
1041C23#1309407211yescharacteristic
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—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
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—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—474no—
1090C2×C4—474no—
1091C2×C4—474no—
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—18816no—
1120C2×C4—18816no—
1121C2×C4—18816no—
1122C2×C4—18816no—
1123C2×C4—1881no—
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×C4C42×D4714yes—
1136C2×C4C22⋊C4×D4714yes—
1137C2×C4#1309398614yescomplemented
1138C22—478no—
1139C22—944no—
1140C22—944no—
1141C22—944no—
1142C22—944no—
1143C22—944no—
1144C22—944no—
1145C22—944no—
1146C22—944no—
1147C22—944no—
1148C22—944no—
1149C22—944no—
1150C22—944no—
1151C22—944no—
1152C22—944no—
1153C22—944no—
1154C22—944no—
1155C22—944no—
1156C22—1882no—
1157C22—1882no—
1158C22—1882no—
1159C22—1882no—
1160C22—1882no—
1161C22—1882no—
1162C22—1882no—
1163C22—1882no—
1164C22—1882no—
1165C22—1882no—
1166C22—1882no—
1167C22—1882no—
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×#1309398611yescharacteristic
1178C22#1568959111yescharacteristic
1179C22C4×#1062535411yescharacteristic
1180C22C4×#1062535411yescharacteristic
1181C22#1568959511yescharacteristic
1182C22#1568959511yescharacteristic
1183C22#1568959711yescharacteristic
1184C22#1568960411yescharacteristic
1185C22#1568960511yescharacteristic
1186C22#1568960511yescharacteristic
1187C22#1568975511yescharacteristic
1188C22#1568975711yescharacteristic
1189C22#1568976211yescharacteristic
1190C22#1568976411yescharacteristic
1191C22#1568976511yescharacteristic
1192C22#1568976511yescharacteristic
1193C22#1568976611yescharacteristic
1194C22#1568977511yescharacteristic
1195C22#1568977611yescharacteristic
1196C22#1568978311yescharacteristic
1197C22#1568979811yescharacteristic
1198C22#1568980011yescharacteristic
1199C22#1568980511yescharacteristic
1200C22#1568981811yescharacteristic
1201C22#1568982411yescharacteristic
1202C22#1568982611yescharacteristic
1203C4—24no—
1204C4—24no—
1205C4—24no—
1206C4—42no—
1207C4—42no—
1208C4—42no—
1209C4—42no—
1210C4—944no—
1211C4—944no—
1212C4—944no—
1213C4—1882no—
1214C4—1882no—
1215C4—1882no—
1216C2—948no—
1217C2—1884no—
1218C2C4×C22⋊C4×D4711yescharacteristic
1219C2C4×#1309398611yescharacteristic
1220C2#2024574811yescharacteristic
1221C2#2024620611yescharacteristic
1222C2#2024621711yescharacteristic
1223C2#2024631211yescharacteristic
1224C2#2024632711yescharacteristic
1225C2#2024636411yescharacteristic
1226C2#2024636611yescharacteristic
1227C2#2024637311yescharacteristic
1228C2#2024637511yescharacteristic
1229C2#2024640311yescharacteristic
1230C2#2024640711yescharacteristic
1231C2#2024643211yescharacteristic
1232C2#2024643411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC22×C47C22×C42
FittingC47×#1436C2
socle, cosocleC24×C47C24
prime radicalC23×D188C22
hypercenter#1436D47
hypocenterC47#13813
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
4. C2×C4×(C2×D47)⋊C4C2semidirect
5. C2×C4×(C2×D47)⋊C4C2semidirect
6. C2×#15688970C2semidirect
7. C2×#95×D47C2semidirect
8. #20241624C2semidirect
9. #20241624C2semidirect
10. #20241620C2semidirect
11. #20241613C2semidirect
12. (C2×D47)⋊#95C2semidirect
13. (C2×D47)⋊#95C2semidirect
14. #95×Dic47C2semidirect
15. C47×#1436C2semidirect
23. C2×#13093986C4semidirect
36. #15689001C4semidirect
37. #15689001C4semidirect
100. C22×C4×D47C2×C4semidirect
101. C22×C4×D47C2×C4semidirect
102. C22×C4×D47C2×C4semidirect
119. C2×(C2×D47)⋊C4C2×C4semidirect
120. C2×(C2×D47)⋊C4C2×C4semidirect
121. C2×(C2×D47)⋊C4C2×C4semidirect
122. C2×(C2×D47)⋊C4C2×C4semidirect
123. C2×(C2×D47)⋊C4C2×C4semidirect
124. C2×(C2×D47)⋊C4C2×C4semidirect
125. C2×(C2×D47)⋊C4C2×C4semidirect
139. C2×C4×Dic47C2×C4semidirect
148. C47⋊#95C2×C4semidirect
149. C47⋊#95C2×C4semidirect
150. C47⋊#95D4semidirect
160. C2×C4⋊C4×C47C2×C4semidirect
167. #95×C47C2×C4semidirect
168. #95×C47C2×C4semidirect
297. C2×D188C42semidirect
335. (C2×D47)⋊C4C22⋊C4semidirect
473. C2×C4×C47C4×D4semidirect
515. C2×Dic47C4×D4semidirect
586. C2×D47C4×C22⋊C4semidirect
610. #1436D47semidirect
676. C47#13813semidirect
730. C2×C4⋊C4C4×D47semidirect
784. #95C4×D47semidirect
785. #95C4×D47semidirect
1137. C2×C4#13093986semidirect

Maximal subgroups

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

subgroupindex
C22×#130939862
C2×#156890012
C2×C4×(C2×D47)⋊C42
C2×#156889702
C2×#95×D472
#202416242
#202416202
#202416132
(C2×D47)⋊#952
#95×Dic472
C47×#14362
#1381347