Finite Group Databasebeta

← #26238499

Subgroups — #26238499

Order 12032.

992 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689202C211yesmaximal, characteristic, complemented
2C2×#15689198C211yesmaximal, characteristic, complemented
3C2×#15689191C211yesmaximal, characteristic, complemented
4C2×#15689150C211yesmaximal, characteristic, complemented
5#20246624C211yesmaximal, characteristic
6#20244186C211yesmaximal, characteristic, complemented
7#20244106C211yesmaximal, characteristic, complemented
8#20244002C211yesmaximal, characteristic, complemented
9#20243995C211yesmaximal, characteristic, complemented
10#20243683C211yesmaximal, characteristic, complemented
11#20243678C211yesmaximal, characteristic, complemented
12#20243572C211yesmaximal, characteristic, complemented
13#20243572C211yesmaximal, characteristic, complemented
14#20243260C211yesmaximal, characteristic, complemented
15C47×#1750C211yesmaximal, characteristic, complemented
16C22×#10625329C2211yescharacteristic
17C22×#10625324C2211yescharacteristic
18C22×#10625324C2211yescharacteristic
19C23×C47⋊C8C2211yescharacteristic
20C2×C4×D188C2211yescharacteristic
21C2×C4×C22⋊D47C2211yescharacteristic
22C2×C4×C22⋊D47C2211yescharacteristic
23#15689202—24no—
24#15689198—24no—
25#15689191—24no—
26#15689150—24no—
27C2×C4⋊(C47⋊C8)C2211yescharacteristic
28C2×C4⋊(C47⋊C8)C2211yescharacteristic
29C2×C4⋊(C47⋊C8)C2211yescharacteristic
30C2×C4⋊(C47⋊C8)C2211yescharacteristic
31C2×Dic47⋊C8C2211yescharacteristic
32C2×Dic47⋊C8C2211yescharacteristic
33C2×(C2×D47)⋊C8C2211yescharacteristic
34C2×(C2×D47)⋊C8C2211yescharacteristic
35C2×(C2×D47)⋊C8C2211yescharacteristic
36C2×(C2×D47)⋊C8C2211yescharacteristic
37C2×(C2×D47)⋊C8C2211yescharacteristic
38C2×(C2×D47)⋊C8C2211yescharacteristic
39C2×#13093934C2211yescharacteristic
40C2×C8×Dic47C2211yescharacteristic
41#15689053C411yescharacteristic
42#15689048C411yescharacteristic
43#15689045C411yescharacteristic
44#15689045C411yescharacteristic
45#15689040C411yescharacteristic
46#15689039C411yescharacteristic
47#15689039C411yescharacteristic
48#15689032C411yescharacteristic
49C4×C4⋊Dic47C2211yescharacteristic
50C4×(C2×D47)⋊C4C2211yescharacteristic
51C4×(C2×D47)⋊C4C2211yescharacteristic
52#15688877C2211yescharacteristic
53#15688877C2211yescharacteristic
54#15688877C2211yescharacteristic
55#15688877C2211yescharacteristic
56C2×#117×C47C2211yescharacteristic
57C2×C22⋊C8×C47C2211yescharacteristic
58C2×C22⋊C8×C47C2211yescharacteristic
59C2×#97×C47C2211yescharacteristic
60C2×C4×C8×C47C2211yescharacteristic
61C47×#336C2211yescharacteristic
62C47×#336C2211yescharacteristic
63C22×D188C2×C411yescharacteristic
64C22×C22⋊D47C2×C411yescharacteristic
65C22×C22⋊D47C2×C411yescharacteristic
66C22×C4×D47C2311yescharacteristic
67C22×C4×D47C2311yescharacteristic
68C2×#10625329—22no—
69C2×#10625329—22no—
70C2×#10625329—41no—
71C2×#10625324—22no—
72C2×#10625324—22no—
73C2×#10625324—22no—
74C2×#10625324—22no—
75C2×#10625324—41no—
76C2×#10625324—41no—
77C22×C47⋊C8—22no—
78C22×C47⋊C8—22no—
79C22×C47⋊C8—41no—
80C22×C47⋊C8C2311yescharacteristic
81C22×C47⋊C8C2311yescharacteristic
82C22×C47⋊C8C2311yescharacteristic
83C22×C47⋊C8C2311yescharacteristic
84C4×D188—22no—
85C4×D188—22no—
86C4×C22⋊D47—22no—
87C4×C22⋊D47—22no—
88C4×C22⋊D47—22no—
89C4×C22⋊D47—22no—
90C2×C4⋊Dic47C2×C411yescharacteristic
91C2×C4⋊Dic47C2×C411yescharacteristic
92C2×C4⋊Dic47C2×C411yescharacteristic
93C2×Dic47⋊C4C2×C411yescharacteristic
94C2×Dic47⋊C4C2×C411yescharacteristic
95C2×C22⋊Dic47C2×C411yescharacteristic
96C2×C22⋊Dic47C2×C411yescharacteristic
97C2×(C2×D47)⋊C4C2×C411yescharacteristic
98C2×(C2×D47)⋊C4C2×C411yescharacteristic
99C2×(C2×D47)⋊C4C2×C411yescharacteristic
100C2×(C2×D47)⋊C4C2×C411yescharacteristic
101C2×(C2×D47)⋊C4C2×C411yescharacteristic
102C2×(C2×D47)⋊C4C2×C411yescharacteristic
103C2×(C2×D47)⋊C4C2×C411yescharacteristic
104C2×(C2×D47)⋊C4C2×C411yescharacteristic
105C2×C4×Dic47C2311yescharacteristic
106C2×C4×Dic47C2311yescharacteristic
107C4⋊(C47⋊C8)—22no—
108C4⋊(C47⋊C8)—22no—
109C4⋊(C47⋊C8)—22no—
110C4⋊(C47⋊C8)D414yescomplemented
111Dic47⋊C8—22no—
112Dic47⋊C8—22no—
113(C2×D47)⋊C8—22no—
114(C2×D47)⋊C8—22no—
115(C2×D47)⋊C8—22no—
116(C2×D47)⋊C8—22no—
117(C2×D47)⋊C8—41no—
118(C2×D47)⋊C8—41no—
119#13093934—22no—
120C8×Dic47—22no—
121C47⋊#95C2×C411yescharacteristic
122C47⋊#95C2×C411yescharacteristic
123C47⋊#95C2×C411yescharacteristic
124C47⋊#95C2×C411yescharacteristic
125C47⋊#95C2×C411yescharacteristic
126C47⋊#95C2×C411yescharacteristic
127C23×C4×C47C2311yescharacteristic
128C22×C8×C47C2311yescharacteristic
129C22×C8×C47C2311yescharacteristic
130C22×C8×C47C2311yescharacteristic
131C22×C8×C47C2311yescharacteristic
132#117×C47—22no—
133#117×C47—22no—
134C2×C4⋊C4×C47C2×C411yescharacteristic
135C2×C4⋊C4×C47C2×C411yescharacteristic
136C2×C22⋊C4×C47C2×C411yescharacteristic
137C2×C22⋊C4×C47C2×C411yescharacteristic
138C2×C42×C47C2311yescharacteristic
139C2×C42×C47C2311yescharacteristic
140C22⋊C8×C47—22no—
141C22⋊C8×C47D414yescomplemented
142#97×C47—22no—
143C4×C8×C47—22no—
144C24×C47C22×C411yescharacteristic
145C23×D47C22×C411yescharacteristic
146C23×D47C22×C411yescharacteristic
147C22×C4×C47—21no—
148C22×C4×C47—21no—
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C22×C4×C47C22×C411yescharacteristic
152C22×C4×C47C22×C411yescharacteristic
153C22×C4×C47C22×C411yescharacteristic
154C22×C4×C47C22×C411yescharacteristic
155C22×C4×C47C22×C411yescharacteristic
156C22×C4×C47C2×D412yes—
157C22×C4×C47#4112yes—
158C22×C4×C47C2411yescharacteristic
159C2×C22⋊D47—22no—
160C2×C22⋊D47—22no—
161C2×C22⋊D47—22no—
162C2×C22⋊D47—41no—
163C2×C22⋊D47—41no—
164C2×C22⋊D47—41no—
165C22×Dic47C22×C411yescharacteristic
166C22×Dic47C22×C411yescharacteristic
167C22×Dic47C22×C411yescharacteristic
168C22×Dic47C22×C411yescharacteristic
169C22×Dic47C22×C411yescharacteristic
170C22×Dic47C22×C411yescharacteristic
171C2×D188—22no—
172C2×D188—41no—
173C2×D188—41no—
174C2×C4×D47—21no—
175C2×C4×D47—21no—
176C2×C4×D47—21no—
177C2×C4×D47—21no—
178C2×C4×D47—21no—
179C2×C4×D47—21no—
180C2×C4×D47—21no—
181C2×C4×D47—21no—
182C2×C4×D47—21no—
183C2×C4×D47—21no—
184C2×C4×D47—21no—
185C2×C4×D47—21no—
186C2×C8×C47—21no—
187C2×C8×C47—21no—
188C2×C8×C47—21no—
189C2×C8×C47—21no—
190C2×C8×C47—21no—
191C2×C8×C47—21no—
192C2×C8×C47—21no—
193C2×C8×C47—21no—
194C2×C8×C47—21no—
195C2×C8×C47—21no—
196C2×C8×C47C2×D412yes—
197C2×C8×C47C2×D412yes—
198C4⋊C4×C47—22no—
199C4⋊C4×C47—22no—
200C22⋊C4×C47—22no—
201C22⋊C4×C47—22no—
202C42×C47—21no—
203C42×C47—21no—
204C42×C47C2×D412yes—
205C42×C47#4112yes—
206C22⋊Dic47—22no—
207C22⋊Dic47—22no—
208(C2×D47)⋊C4—22no—
209(C2×D47)⋊C4—22no—
210(C2×D47)⋊C4—22no—
211(C2×D47)⋊C4—22no—
212(C2×D47)⋊C4—22no—
213(C2×D47)⋊C4—41no—
214(C2×D47)⋊C4—41no—
215(C2×D47)⋊C4—41no—
216C4⋊Dic47—22no—
217C4⋊Dic47—22no—
218C4⋊Dic47—41no—
219Dic47⋊C4—22no—
220Dic47⋊C4—22no—
221C4×Dic47—21no—
222C4×Dic47—21no—
223C4×Dic47—21no—
224C4×Dic47—21no—
225#10625329—44no—
226C2×C47⋊C8—21no—
227C2×C47⋊C8—21no—
228C2×C47⋊C8—21no—
229C2×C47⋊C8—21no—
230C2×C47⋊C8—21no—
231C2×C47⋊C8—21no—
232C2×C47⋊C8—21no—
233C2×C47⋊C8—21no—
234C2×C47⋊C8—21no—
235C2×C47⋊C8—21no—
236C2×C47⋊C8—44no—
237C2×C47⋊C8C2×D412yes—
238C2×C47⋊C8C2×D412yes—
239#10625324—44no—
240#10625324—44no—
241C23×C47—21no—
242C23×C47—21no—
243C23×C47—21no—
244C23×C47—21no—
245C23×C47—21no—
246C23×C47—21no—
247C23×C47C4×D412yes—
248C23×C47C23×C411yescharacteristic
249C22×D47—21no—
250C22×D47—21no—
251C22×D47—21no—
252C22×D47—21no—
253C22×D47—21no—
254C22×D47—21no—
255C22×D47—21no—
256C22×D47—21no—
257C22×D47—21no—
258C22×D47—21no—
259C22×D47—21no—
260C22×D47—21no—
261C22×D47—21no—
262C22×D47—21no—
263C2×C4×C47—21no—
264C2×C4×C47—21no—
265C2×C4×C47—21no—
266C2×C4×C47—21no—
267C2×C4×C47—21no—
268C2×C4×C47—21no—
269C2×C4×C47—22no—
270C2×C4×C47—22no—
271C2×C4×C47—22no—
272C2×C4×C47—22no—
273C2×C4×C47—21no—
274C2×C4×C47—21no—
275C2×C4×C47—21no—
276C2×C4×C47—21no—
277C2×C4×C47—21no—
278C2×C4×C47—21no—
279C2×C4×C47C4×D412yes—
280C2×C4×C47C4×D412yes—
281C2×C4×C47C4×D412yes—
282C2×C4×C47C22×D411yescharacteristic
283C2×C4×C47C22×D411yescharacteristic
284C2×C4×C47C2×#4111yescharacteristic
285C2×C4×C47C2×#4111yescharacteristic
286C2×C4×C47H(5,𝔽2)11yescharacteristic
287C2×C4×C472−1+411yescharacteristic
288C22⋊D47—44no—
289C22⋊D47—44no—
290C2×Dic47—21no—
291C2×Dic47—21no—
292C2×Dic47—21no—
293C2×Dic47—21no—
294C2×Dic47—21no—
295C2×Dic47—21no—
296C2×Dic47—21no—
297C2×Dic47—21no—
298C2×Dic47—21no—
299C2×Dic47—21no—
300C2×Dic47—21no—
301C2×Dic47—21no—
302C2×Dic47—21no—
303C2×Dic47—21no—
304C2×Dic47—21no—
305C2×Dic47—21no—
306C2×Dic47—21no—
307C2×Dic47#13112yes—
308D188—44no—
309C4×D47—41no—
310C4×D47—41no—
311C4×D47—41no—
312C4×D47—41no—
313C4×D47—41no—
314C4×D47—41no—
315C4×D47—41no—
316C4×D47—41no—
317C8×C47—22no—
318C8×C47—22no—
319C8×C47—41no—
320C8×C47—41no—
321C47⋊C8—22no—
322C47⋊C8—22no—
323C47⋊C8—41no—
324C47⋊C8—41no—
325#22994—471nomaximal, Sylow
326C22×C47—22no—
327C22×C47—22no—
328C22×C47—22no—
329C22×C47—41no—
330C22×C47—41no—
331C22×C47—41no—
332C22×C47—41no—
333C22×C47C2×C4×D411yescharacteristic
334C22×C47C2×C4×D411yescharacteristic
335C22×C47#52011yescharacteristic
336C22×C47C2×#13111yescharacteristic
337C22×C47#56811yescharacteristic
338C22×C47#56811yescharacteristic
339C22×C47#56811yescharacteristic
340C2×D47—41no—
341C2×D47—41no—
342C2×D47—41no—
343C2×D47—41no—
344C2×D47—41no—
345C2×D47—41no—
346C2×D47—41no—
347C2×D47—41no—
348C2×D47—41no—
349C2×D47—41no—
350C2×D47—41no—
351C2×D47—41no—
352C2×D47—41no—
353C2×D47—41no—
354C4×C47—22no—
355C4×C47—22no—
356C4×C47—22no—
357C4×C47—41no—
358C4×C47—41no—
359C4×C47D4211yescharacteristic
360C4×C47#54711yescharacteristic
361C4×C47#54811yescharacteristic
362C4×C47#55311yescharacteristic
363Dic47—22no—
364Dic47—41no—
365Dic47—41no—
366Dic47—41no—
367Dic47—41no—
368Dic47—41no—
369C2×#436—471no—
370C2×#436—471no—
371C2×#435—471no—
372C2×#424—471no—
373#2392—471no—
374#1955—471no—
375#1939—471no—
376#1924—471no—
377#1923—471no—
378#1870—471no—
379#1869—471no—
380#1851—471no—
381#1851—471no—
382#1771—471no—
383#1750D4711yescharacteristic, complemented
384C2×C47—42no—
385C2×C47#236111yescharacteristic
386C2×C47#293011yescharacteristic
387C2×C47#293011yescharacteristic
388C2×C47#293311yescharacteristic
389C2×C47#293511yescharacteristic
390C2×C47#299311yescharacteristic
391C2×C47#299511yescharacteristic
392D47—81no—
393D47—81no—
394C22×M16—471no—
395C22×M16—471no—
396C22×M16—471no—
397C23×C8—471no—
398C2×C4×D4—471no—
399C2×C4×D4—471no—
400C2×C4×D4—471no—
401C2×#117C2×D4711yescharacteristic
402#436—944no—
403#436—944no—
404#435—944no—
405#424—944no—
406C2×C4⋊C8—471no—
407C2×C4⋊C8—471no—
408C2×C4⋊C8—471no—
409C2×C4⋊C8—471no—
410C2×C4⋊C8—471no—
411C2×C4⋊C8—471no—
412C2×C22⋊C8—471no—
413C2×C22⋊C8—471no—
414C2×C22⋊C8—471no—
415C2×C22⋊C8—471no—
416C2×C22⋊C8—471no—
417C2×C22⋊C8—471no—
418C2×C22⋊C8C2×D4711yescharacteristic
419C2×C22⋊C8C2×D4711yescharacteristic
420C2×#97—471no—
421C2×#97C2×D4711yescharacteristic
422C2×C4×C8—471no—
423C2×C4×C8C2×D4711yescharacteristic
424#398—471no—
425#397—471no—
426#396—471no—
427#396—471no—
428#394—471no—
429#394—471no—
430#394—471no—
431#392—471no—
432C4×C4⋊C4—471no—
433C4×C22⋊C4—471no—
434C4×C22⋊C4—471no—
435#336—471no—
436#336—471no—
437#336—471no—
438#336—471no—
439#336C2×D4711yescharacteristic
440#336C2×D4711yescharacteristic
441C47#2299411yescharacteristic, complemented, Sylow
442C22×D4—471no—
443C22×D4—471no—
444C22×D4—471no—
445C23×C4—471no—
446C23×C4—471no—
447C23×C4C22×D4711yescharacteristic
448C2×M16—942no—
449C2×M16—942no—
450C2×M16—942no—
451C2×M16—942no—
452C2×M16—942no—
453C2×M16—942no—
454C2×M16—1881no—
455C2×M16—1881no—
456C2×M16—1881no—
457C22×C8—471no—
458C22×C8—471no—
459C22×C8—471no—
460C22×C8—471no—
461C22×C8—942no—
462C22×C8—942no—
463C22×C8—1881no—
464C22×C8C22×D4711yescharacteristic
465C22×C8C22×D4711yescharacteristic
466C22×C8C22×D4711yescharacteristic
467C22×C8C22×D4711yescharacteristic
468C4×D4—942no—
469C4×D4—942no—
470C4×D4—942no—
471C4×D4—942no—
472C4×D4—942no—
473C4×D4—942no—
474#117—22no—
475#117—22no—
476C2×C4⋊C4—471no—
477C2×C4⋊C4—471no—
478C2×C4⋊C4—471no—
479C2×C4⋊C4—471no—
480C2×C4⋊C4—471no—
481C2×C4⋊C4C4×D4711yescharacteristic
482C2×C4⋊C4C4×D4711yescharacteristic
483C2×C22⋊C4—471no—
484C2×C22⋊C4—471no—
485C2×C22⋊C4—471no—
486C2×C22⋊C4—471no—
487C2×C22⋊C4—471no—
488C2×C22⋊C4—471no—
489C2×C22⋊C4—471no—
490C2×C22⋊C4—471no—
491C2×C22⋊C4—471no—
492C2×C22⋊C4—471no—
493C2×C22⋊C4C4×D4711yescharacteristic
494C2×C22⋊C4C4×D4711yescharacteristic
495C2×C42—471no—
496C2×C42—471no—
497C2×C42C22×D4711yescharacteristic
498C2×C42C22×D4711yescharacteristic
499C4⋊C8—474no—
500C4⋊C8—942no—
501C4⋊C8—942no—
502C4⋊C8—942no—
503C4⋊C8—942no—
504C4⋊C8—942no—
505C22⋊C8—22no—
506C22⋊C8—942no—
507C22⋊C8—942no—
508C22⋊C8—942no—
509C22⋊C8—942no—
510C22⋊C8—1881no—
511C22⋊C8—1881no—
512C22⋊C8D18814yescomplemented
513#97—22no—
514#97—942no—
515C4×C8—22no—
516C4×C8—942no—
517#95—471no—
518#95—471no—
519#95—471no—
520#95—471no—
521#95—471no—
522#95—471no—
523C24—471no—
524C24—471no—
525C24C2×C4×D4711yescharacteristic
526C2×D4—942no—
527C2×D4—942no—
528C2×D4—942no—
529C2×D4—942no—
530C2×D4—1881no—
531C2×D4—1881no—
532C2×D4—1881no—
533C2×D4—1881no—
534C2×D4—1881no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—471no—
540C22×C4—471no—
541C22×C4—471no—
542C22×C4—471no—
543C22×C4—471no—
544C22×C4—471no—
545C22×C4—941no—
546C22×C4—941no—
547C22×C4—941no—
548C22×C4—941no—
549C22×C4—941no—
550C22×C4—941no—
551C22×C4—941no—
552C22×C4—941no—
553C22×C4—941no—
554C22×C4—941no—
555C22×C4—941no—
556C22×C4—941no—
557C22×C4C2×C4×D4711yescharacteristic
558C22×C4C2×C4×D4711yescharacteristic
559C22×C4C2×C4×D4711yescharacteristic
560C22×C4C2×C4×D4711yescharacteristic
561C22×C4C2×C4×D4711yescharacteristic
562C22×C4C2×D18812yes—
563C22×C4#1062535012yes—
564C22×C4C23×D4711yescharacteristic
565M16—1884no—
566M16—1884no—
567M16—1884no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—472no—
579C2×C8—472no—
580C2×C8—941no—
581C2×C8—941no—
582C2×C8—941no—
583C2×C8—941no—
584C2×C8—941no—
585C2×C8—941no—
586C2×C8—941no—
587C2×C8—941no—
588C2×C8—941no—
589C2×C8—941no—
590C2×C8—1884no—
591C2×C8C2×D18812yes—
592C2×C8C2×D18812yes—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—942no—
596C4⋊C4—942no—
597C4⋊C4—942no—
598C4⋊C4—942no—
599C4⋊C4—1881no—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—942no—
603C22⋊C4—942no—
604C22⋊C4—942no—
605C22⋊C4—942no—
606C22⋊C4—942no—
607C22⋊C4—942no—
608C22⋊C4—942no—
609C22⋊C4—1881no—
610C22⋊C4—1881no—
611C22⋊C4—1881no—
612C42—21no—
613C42—21no—
614C42—941no—
615C42—941no—
616C42—941no—
617C42—941no—
618C42D4×D4712yes—
619C42#1062535212yes—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—941no—
627C23—941no—
628C23—941no—
629C23—941no—
630C23—941no—
631C23—941no—
632C23—941no—
633C23—941no—
634C23—941no—
635C23—941no—
636C23—941no—
637C23—941no—
638C23—941no—
639C23—941no—
640C23C4×D18812yes—
641C23C22×C4×D4711yescharacteristic
642D4—1884no—
643D4—1884no—
644D4—1884no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—472no—
662C2×C4—941no—
663C2×C4—941no—
664C2×C4—941no—
665C2×C4—941no—
666C2×C4—941no—
667C2×C4—941no—
668C2×C4—941no—
669C2×C4—941no—
670C2×C4—941no—
671C2×C4—941no—
672C2×C4—941no—
673C2×C4—941no—
674C2×C4—941no—
675C2×C4—941no—
676C2×C4—941no—
677C2×C4—941no—
678C2×C4—941no—
679C2×C4—1881no—
680C2×C4—1881no—
681C2×C4—1881no—
682C2×C4—1881no—
683C2×C4—1881no—
684C2×C4—1881no—
685C2×C4—1881no—
686C2×C4—1881no—
687C2×C4(C22⋊D47)⋊C412yes—
688C2×C4(C22⋊D47)⋊C412yes—
689C2×C4C4×D18812yes—
690C2×C4C2×D4×D4711yescharacteristic
691C2×C4C22×D18811yescharacteristic
692C2×C4C2×#1062535211yescharacteristic
693C2×C4C2×#1062535011yescharacteristic
694C2×C4#1309407011yescharacteristic
695C2×C4#1309407111yescharacteristic
696C8—22no—
697C8—22no—
698C8—41no—
699C8—41no—
700C8—942no—
701C8—942no—
702C8—1881no—
703C8—1881no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—1881no—
712C22—1881no—
713C22—1881no—
714C22—1881no—
715C22—1881no—
716C22—1881no—
717C22—1881no—
718C22—1881no—
719C22—1881no—
720C22—1881no—
721C22—1881no—
722C22—1881no—
723C22—1881no—
724C22—1881no—
725C22C2×(C22⋊D47)⋊C411yescharacteristic
726C22C2×C4×D18811yescharacteristic
727C22#1568960311yescharacteristic
728C22#131×D4711yescharacteristic
729C22#1568988811yescharacteristic
730C22#1568988811yescharacteristic
731C22#1568988811yescharacteristic
732C4—22no—
733C4—22no—
734C4—22no—
735C4—41no—
736C4—41no—
737C4—942no—
738C4—1881no—
739C4—1881no—
740C4—1881no—
741C4—1881no—
742C4—1881no—
743C4D4×D18811yescharacteristic
744C4#1568977711yescharacteristic
745C4#1568978211yescharacteristic
746C4#1568981911yescharacteristic
747C2—42no—
748C2—3761no—
749C2—3761no—
750C2#2024640211yescharacteristic
751C2#2025209311yescharacteristic
752C2#2025209411yescharacteristic
753C2#2025211611yescharacteristic
754C2#2025212811yescharacteristic
755C2#2025253111yescharacteristic
756C2#2025255311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC47×#1750C2
prime radical#15689032C4
cosocleC22×C4×C47C24
hypercenter#1750D47
hypocenterC47#22994
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #1750

Complements

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

NH ≅ G/Ntype
1. C2×#15689202C2semidirect
2. C2×#15689198C2semidirect
3. C2×#15689191C2semidirect
4. C2×#15689150C2semidirect
6. #20244186C2semidirect
7. #20244106C2semidirect
8. #20244002C2semidirect
9. #20243995C2semidirect
10. #20243683C2semidirect
11. #20243678C2semidirect
12. #20243572C2semidirect
13. #20243572C2semidirect
14. #20243260C2semidirect
15. C47×#1750C2semidirect
110. C4⋊(C47⋊C8)D4semidirect
141. C22⋊C8×C47D4semidirect
383. #1750D47semidirect
441. C47#22994semidirect
512. C22⋊C8D188semidirect

Maximal subgroups

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

subgroupindex
C2×#156892022
C2×#156891982
C2×#156891912
C2×#156891502
#202466242
#202441862
#202441062
#202440022
#202439952
#202436832
#202436782
#202435722
#202432602
C47×#17502
#2299447