Finite Group Databasebeta

← #26222365

Subgroups — #26222365

Order 12032.

1096 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689199C211yesmaximal, characteristic, complemented
2C2×#15689196C211yesmaximal, characteristic, complemented
3C2×#15689192C211yesmaximal, characteristic, complemented
4C4×#13093998C211yesmaximal, characteristic
5#20244186C211yesmaximal, characteristic, complemented
6#20244111C211yesmaximal, characteristic, complemented
7#20243994C211yesmaximal, characteristic, complemented
8#20243994C211yesmaximal, characteristic, complemented
9#20243685C211yesmaximal, characteristic, complemented
10#20243685C211yesmaximal, characteristic, complemented
11#20243368C211yesmaximal, characteristic, complemented
12#20243260C211yesmaximal, characteristic, complemented
13#20243171C211yesmaximal, characteristic, complemented
14C8×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
15C2×C4×M16×C47C211yesmaximal, characteristic, complemented
16C22×#10625324C2211yescharacteristic
17C22×C8×D47C2211yescharacteristic
18C2×#13093998C411yescharacteristic
19C2×C4×D188C2211yescharacteristic
20C2×C4×C22⋊D47C2211yescharacteristic
21C2×C4×C22⋊D47C2211yescharacteristic
22#15689199—24no—
23#15689196—24no—
24#15689192—24no—
25C2×C4⋊(C47⋊C8)C2211yescharacteristic
26C2×C4⋊(C47⋊C8)C2211yescharacteristic
27C2×Dic47⋊C8C2211yescharacteristic
28C2×Dic47⋊C8C2211yescharacteristic
29C2×C22⋊(C47⋊C8)C2211yescharacteristic
30C2×C22⋊(C47⋊C8)C2211yescharacteristic
31C2×(C2×D47)⋊C8C2211yescharacteristic
32C2×(C2×D47)⋊C8C2211yescharacteristic
33C2×(C2×D47)⋊C8C2211yescharacteristic
34C2×(C2×D47)⋊C8C2211yescharacteristic
35C2×(C2×D47)⋊C8C2211yescharacteristic
36C2×(C2×D47)⋊C8C2211yescharacteristic
37C2×#13093934C2211yescharacteristic
38C2×C8×Dic47C2211yescharacteristic
39#15689025C411yescharacteristic
40#15689021C411yescharacteristic
41#15689014C411yescharacteristic
42#15689014C411yescharacteristic
43#15689002C411yescharacteristic
44#15689002C411yescharacteristic
45#15688983C411yescharacteristic
46C4×C4⋊Dic47C2211yescharacteristic
47C4×(C2×D47)⋊C4C2211yescharacteristic
48C4×(C2×D47)⋊C4C2211yescharacteristic
49#15688878C2211yescharacteristic
50#15688878C2211yescharacteristic
51#15688877C2211yescharacteristic
52#15688877C2211yescharacteristic
53#15688877C2211yescharacteristic
54#15688877C2211yescharacteristic
55C22×M16×C47C2211yescharacteristic
56C22×M16×C47C2211yescharacteristic
57C22×C42×C47C2211yescharacteristic
58C4×M16×C47—24no—
59C2×#97×C47C2211yescharacteristic
60C2×#97×C47C2211yescharacteristic
61C2×C4×C8×C47C2211yescharacteristic
62C2×C4×C8×C47C2211yescharacteristic
63C22×D188C2×C411yescharacteristic
64C22×C22⋊D47C2×C411yescharacteristic
65C22×C22⋊D47C2×C411yescharacteristic
66C22×C4×D47C2311yescharacteristic
67C22×C4×D47C2311yescharacteristic
68C2×#10625324—22no—
69C2×#10625324—22no—
70C2×#10625324—22no—
71C22×C47⋊C8C2311yescharacteristic
72C22×C47⋊C8C2311yescharacteristic
73C22×C47⋊C8C2311yescharacteristic
74C22×C47⋊C8C2311yescharacteristic
75C2×C8×D47—22no—
76C2×C8×D47—22no—
77C2×C8×D47—22no—
78#13093998—24no—
79C4×D188—22no—
80C4×D188—22no—
81C4×C22⋊D47—22no—
82C4×C22⋊D47—22no—
83C4×C22⋊D47—22no—
84C4×C22⋊D47—22no—
85C2×C4⋊Dic47C2×C411yescharacteristic
86C2×C4⋊Dic47C2×C411yescharacteristic
87C2×C4⋊Dic47C2×C411yescharacteristic
88C2×Dic47⋊C4C2×C411yescharacteristic
89C2×Dic47⋊C4C2×C411yescharacteristic
90C2×C22⋊Dic47C2×C411yescharacteristic
91C2×C22⋊Dic47C2×C411yescharacteristic
92C2×(C2×D47)⋊C4C2×C411yescharacteristic
93C2×(C2×D47)⋊C4C2×C411yescharacteristic
94C2×(C2×D47)⋊C4C2×C411yescharacteristic
95C2×(C2×D47)⋊C4C2×C411yescharacteristic
96C2×(C2×D47)⋊C4C2×C411yescharacteristic
97C2×(C2×D47)⋊C4C2×C411yescharacteristic
98C2×(C2×D47)⋊C4C2×C411yescharacteristic
99C2×(C2×D47)⋊C4C2×C411yescharacteristic
100C2×C4×Dic47C2311yescharacteristic
101C2×C4×Dic47C2311yescharacteristic
102C4⋊(C47⋊C8)—22no—
103C4⋊(C47⋊C8)—22no—
104Dic47⋊C8—22no—
105Dic47⋊C8—22no—
106C22⋊(C47⋊C8)—22no—
107C22⋊(C47⋊C8)—22no—
108(C2×D47)⋊C8—22no—
109(C2×D47)⋊C8—22no—
110(C2×D47)⋊C8—22no—
111(C2×D47)⋊C8—22no—
112(C2×D47)⋊C8—22no—
113(C2×D47)⋊C8—22no—
114#13093934—22no—
115C8×Dic47—22no—
116C47⋊#95C2×C411yescharacteristic
117C47⋊#95C2×C411yescharacteristic
118C47⋊#95C2×C411yescharacteristic
119C47⋊#95C2×C411yescharacteristic
120C47⋊#95C2×C411yescharacteristic
121C47⋊#95C2×C411yescharacteristic
122C23×C4×C47C2×C411yescharacteristic
123C23×C4×C47C2×C411yescharacteristic
124C23×C4×C47C2311yescharacteristic
125C2×M16×C47—22no—
126C2×M16×C47—22no—
127C2×M16×C47—22no—
128C2×M16×C47—22no—
129C2×M16×C47—22no—
130C2×M16×C47D414yescomplemented
131C22×C8×C47C2311yescharacteristic
132C22×C8×C47C2311yescharacteristic
133C22×C8×C47C2311yescharacteristic
134C22×C8×C47C2311yescharacteristic
135C2×C42×C47—22no—
136C2×C42×C47—22no—
137C2×C42×C47C2×C411yescharacteristic
138C2×C42×C47C2×C411yescharacteristic
139C2×C42×C47C2311yescharacteristic
140C2×C42×C47C2311yescharacteristic
141#97×C47—22no—
142#97×C47D414yescomplemented
143C4×C8×C47—22no—
144C4×C8×C47—22no—
145C24×C47C22×C411yescharacteristic
146C23×D47C22×C411yescharacteristic
147C23×D47C22×C411yescharacteristic
148C22×C4×C47—21no—
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C22×C4×C47—21no—
152C22×C4×C47—22no—
153C22×C4×C47—22no—
154C22×C4×C47—22no—
155C22×C4×C47—22no—
156C22×C4×C47—41no—
157C22×C4×C47—41no—
158C22×C4×C47C22×C411yescharacteristic
159C22×C4×C47C22×C411yescharacteristic
160C22×C4×C47C22×C411yescharacteristic
161C22×C4×C47C22×C411yescharacteristic
162C22×C4×C47C22×C411yescharacteristic
163C22×C4×C47C2×D412yes—
164C22×C4×C47#4112yes—
165C22×C4×C47C2411yescharacteristic
166C2×C22⋊D47—22no—
167C2×C22⋊D47—22no—
168C2×C22⋊D47—22no—
169C2×C22⋊D47—22no—
170C2×C22⋊D47—41no—
171C2×C22⋊D47—41no—
172C22×Dic47C22×C411yescharacteristic
173C22×Dic47C22×C411yescharacteristic
174C22×Dic47C22×C411yescharacteristic
175C22×Dic47C22×C411yescharacteristic
176C22×Dic47C22×C411yescharacteristic
177C22×Dic47C22×C411yescharacteristic
178C2×D188—22no—
179C2×D188—22no—
180C2×D188—41no—
181C2×C4×D47—21no—
182C2×C4×D47—21no—
183C2×C4×D47—21no—
184C2×C4×D47—21no—
185C2×C4×D47—21no—
186C2×C4×D47—21no—
187C2×C4×D47—21no—
188C2×C4×D47—21no—
189C2×C4×D47—21no—
190C2×C4×D47—21no—
191C2×C4×D47—21no—
192C2×C4×D47—21no—
193M16×C47—28no—
194M16×C47—28no—
195C2×C8×C47—21no—
196C2×C8×C47—21no—
197C2×C8×C47—21no—
198C2×C8×C47—21no—
199C2×C8×C47—21no—
200C2×C8×C47—21no—
201C2×C8×C47C2×D412yes—
202C2×C8×C47C2×D412yes—
203C2×C8×C47C2×D412yes—
204C2×C8×C47C2×D412yes—
205C2×C8×C47#4112yes—
206C2×C8×C47#4112yes—
207C42×C47—22no—
208C42×C47—22no—
209C42×C47—21no—
210C42×C47—21no—
211C42×C47C2×D412yes—
212C42×C47#4112yes—
213C22⋊Dic47—22no—
214C22⋊Dic47—22no—
215(C2×D47)⋊C4—22no—
216(C2×D47)⋊C4—22no—
217(C2×D47)⋊C4—22no—
218(C2×D47)⋊C4—22no—
219(C2×D47)⋊C4—22no—
220(C2×D47)⋊C4—22no—
221(C2×D47)⋊C4—22no—
222(C2×D47)⋊C4M1614yescomplemented
223C4⋊Dic47—22no—
224C4⋊Dic47—22no—
225C4⋊Dic47—41no—
226Dic47⋊C4—22no—
227Dic47⋊C4—22no—
228C4×Dic47—21no—
229C4×Dic47—21no—
230C4×Dic47—21no—
231C4×Dic47—21no—
232C2×C47⋊C8—21no—
233C2×C47⋊C8—21no—
234C2×C47⋊C8—21no—
235C2×C47⋊C8—21no—
236C2×C47⋊C8—21no—
237C2×C47⋊C8—21no—
238C2×C47⋊C8—21no—
239C2×C47⋊C8—21no—
240C2×C47⋊C8—21no—
241C2×C47⋊C8—21no—
242C2×C47⋊C8—21no—
243C2×C47⋊C8—21no—
244#10625324—44no—
245C8×D47—44no—
246C23×C47—21no—
247C23×C47—21no—
248C23×C47—21no—
249C23×C47—21no—
250C23×C47—21no—
251C23×C47—21no—
252C23×C47C4×D412yes—
253C23×C47C23×C411yescharacteristic
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—
263C22×D47—21no—
264C22×D47—21no—
265C22×D47—21no—
266C22×D47—21no—
267C22×D47C2×M1612yes—
268C2×C4×C47—21no—
269C2×C4×C47—21no—
270C2×C4×C47—21no—
271C2×C4×C47—21no—
272C2×C4×C47—21no—
273C2×C4×C47—21no—
274C2×C4×C47—21no—
275C2×C4×C47—21no—
276C2×C4×C47—21no—
277C2×C4×C47—21no—
278C2×C4×C47—22no—
279C2×C4×C47—22no—
280C2×C4×C47—22no—
281C2×C4×C47—22no—
282C2×C4×C47—44no—
283C2×C4×C47—44no—
284C2×C4×C47C4×D412yes—
285C2×C4×C47C4×D412yes—
286C2×C4×C47C4×D412yes—
287C2×C4×C47C2×M1612yes—
288C2×C4×C47#13112yes—
289C2×C4×C47C22×D411yescharacteristic
290C2×C4×C47C22×D411yescharacteristic
291C2×C4×C47C2×#4111yescharacteristic
292C2×C4×C47C2×#4111yescharacteristic
293C2×C4×C47C2×#4111yescharacteristic
294C2×C4×C47C2×#4111yescharacteristic
295C22⋊D47—44no—
296C22⋊D47—44no—
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—21no—
308C2×Dic47—21no—
309C2×Dic47—21no—
310C2×Dic47—21no—
311C2×Dic47—21no—
312C2×Dic47—21no—
313C2×Dic47—21no—
314C2×Dic47C2×M1612yes—
315D188—44no—
316C4×D47—41no—
317C4×D47—41no—
318C4×D47—41no—
319C4×D47—41no—
320C4×D47—41no—
321C4×D47—41no—
322C4×D47—41no—
323C4×D47—41no—
324C8×C47—22no—
325C8×C47—22no—
326C8×C47—22no—
327C8×C47#12114yescomplemented
328C47⋊C8—41no—
329C47⋊C8—41no—
330C47⋊C8—41no—
331C47⋊C8—41no—
332#21490—471nomaximal, Sylow
333C22×C47—22no—
334C22×C47—22no—
335C22×C47—22no—
336C22×C47—41no—
337C22×C47—41no—
338C22×C47—41no—
339C22×C47—41no—
340C22×C47C2×C4×D411yescharacteristic
341C22×C47C2×C4×D411yescharacteristic
342C22×C47C4×#4111yescharacteristic
343C22×C47C22×M1611yescharacteristic
344C22×C47C2×#13111yescharacteristic
345C22×C47#56811yescharacteristic
346C22×C47#56811yescharacteristic
347C2×D47—22no—
348C2×D47—22no—
349C2×D47—22no—
350C2×D47—41no—
351C2×D47—41no—
352C2×D47—41no—
353C2×D47—41no—
354C2×D47—41no—
355C2×D47—41no—
356C2×D47—41no—
357C2×D47—41no—
358C2×D47—41no—
359C2×D47—41no—
360C2×D47—41no—
361C4×C47—22no—
362C4×C47—22no—
363C4×C47—22no—
364C4×C47—22no—
365C4×C47—22no—
366C4×C47C2×#12111yescharacteristic
367C4×C47#52511yescharacteristic
368C4×C47#52911yescharacteristic
369C4×C47#53211yescharacteristic
370Dic47—22no—
371Dic47—41no—
372Dic47—41no—
373Dic47—41no—
374Dic47—41no—
375Dic47—41no—
376C2×#436—471no—
377C2×#435—471no—
378C2×#435—471no—
379C2×C4×M16D4711yescharacteristic, complemented
380C4×#121—471no—
381#1955—471no—
382#1940—471no—
383#1923—471no—
384#1923—471no—
385#1870—471no—
386#1870—471no—
387#1797—471no—
388#1771—471no—
389#1753—471no—
390C8×C22⋊C4—471no—
391C2×C47—42no—
392C2×C47C4×#12111yescharacteristic
393C2×C47#293311yescharacteristic
394C2×C47D4×M1611yescharacteristic
395C2×C47D4×M1611yescharacteristic
396C2×C47#293511yescharacteristic
397C2×C47#296511yescharacteristic
398C2×C47#296711yescharacteristic
399D47—42no—
400D47—81no—
401C22×M16—471no—
402C22×M16C2×D4711yescharacteristic
403C22×M16C2×D4711yescharacteristic
404C23×C8—471no—
405C2×#121—471no—
406C2×C4×D4—471no—
407C2×C4×D4—471no—
408C2×C4×D4—471no—
409C22×C42C2×D4711yescharacteristic
410#436—944no—
411#435—944no—
412#435—944no—
413C2×C4⋊C8—471no—
414C2×C4⋊C8—471no—
415C2×C4⋊C8—471no—
416C2×C4⋊C8—471no—
417C2×C22⋊C8—471no—
418C2×C22⋊C8—471no—
419C2×C22⋊C8—471no—
420C2×C22⋊C8—471no—
421C2×C22⋊C8—471no—
422C2×C22⋊C8—471no—
423C2×C22⋊C8—471no—
424C2×C22⋊C8—471no—
425C4×M16—24no—
426C2×#97—471no—
427C2×#97C2×D4711yescharacteristic
428C2×#97C2×D4711yescharacteristic
429C2×C4×C8—471no—
430C2×C4×C8C2×D4711yescharacteristic
431C2×C4×C8C2×D4711yescharacteristic
432#390—471no—
433#389—471no—
434#388—471no—
435#388—471no—
436#386—471no—
437#386—471no—
438#380—471no—
439C4×C4⋊C4—471no—
440C4×C22⋊C4—471no—
441C4×C22⋊C4—471no—
442#336—471no—
443#336—471no—
444#336—471no—
445#336—471no—
446#336—471no—
447#336—471no—
448C47#2149011yescharacteristic, complemented, Sylow
449C22×D4—471no—
450C22×D4—471no—
451C22×D4—471no—
452C23×C4—471no—
453C23×C4—471no—
454C23×C4C4×D4711yescharacteristic
455C23×C4C4×D4711yescharacteristic
456C23×C4C22×D4711yescharacteristic
457C2×M16—22no—
458C2×M16—22no—
459C2×M16—22no—
460C2×M16—22no—
461C2×M16—22no—
462C2×M16—942no—
463C2×M16—942no—
464C2×M16—942no—
465C2×M16D18814yescomplemented
466C22×C8—471no—
467C22×C8—471no—
468C22×C8—471no—
469C22×C8—471no—
470C22×C8—942no—
471C22×C8—942no—
472C22×C8—942no—
473C22×C8C22×D4711yescharacteristic
474C22×C8C22×D4711yescharacteristic
475C22×C8C22×D4711yescharacteristic
476C22×C8C22×D4711yescharacteristic
477#121—944no—
478C4×D4—942no—
479C4×D4—942no—
480C4×D4—942no—
481C4×D4—942no—
482C4×D4—942no—
483C4×D4—942no—
484C2×C4⋊C4—471no—
485C2×C4⋊C4—471no—
486C2×C4⋊C4—471no—
487C2×C4⋊C4—471no—
488C2×C4⋊C4—471no—
489C2×C22⋊C4—471no—
490C2×C22⋊C4—471no—
491C2×C22⋊C4—471no—
492C2×C22⋊C4—471no—
493C2×C22⋊C4—471no—
494C2×C22⋊C4—471no—
495C2×C22⋊C4—471no—
496C2×C22⋊C4—471no—
497C2×C22⋊C4—471no—
498C2×C22⋊C4—471no—
499C2×C42—22no—
500C2×C42—22no—
501C2×C42—471no—
502C2×C42—471no—
503C2×C42C4×D4711yescharacteristic
504C2×C42C4×D4711yescharacteristic
505C2×C42C22×D4711yescharacteristic
506C2×C42C22×D4711yescharacteristic
507C4⋊C8—942no—
508C4⋊C8—942no—
509C4⋊C8—942no—
510C4⋊C8—942no—
511C22⋊C8—942no—
512C22⋊C8—942no—
513C22⋊C8—942no—
514C22⋊C8—942no—
515C22⋊C8—942no—
516C22⋊C8—942no—
517C22⋊C8—942no—
518C22⋊C8—942no—
519#97—22no—
520#97—942no—
521#97C22⋊D4714yescomplemented
522C4×C8—22no—
523C4×C8—22no—
524C4×C8—942no—
525#95—471no—
526#95—471no—
527#95—471no—
528#95—471no—
529#95—471no—
530#95—471no—
531C24—471no—
532C24—471no—
533C24C2×C4×D4711yescharacteristic
534C2×D4—942no—
535C2×D4—942no—
536C2×D4—942no—
537C2×D4—942no—
538C2×D4—942no—
539C2×D4—942no—
540C2×D4—1881no—
541C2×D4—1881no—
542C2×D4—1881no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—471no—
554C22×C4—471no—
555C22×C4—471no—
556C22×C4—471no—
557C22×C4—471no—
558C22×C4—471no—
559C22×C4—941no—
560C22×C4—941no—
561C22×C4—941no—
562C22×C4—941no—
563C22×C4—941no—
564C22×C4—941no—
565C22×C4—941no—
566C22×C4—941no—
567C22×C4—941no—
568C22×C4—941no—
569C22×C4—941no—
570C22×C4—941no—
571C22×C4C2×C4×D4711yescharacteristic
572C22×C4C2×C4×D4711yescharacteristic
573C22×C4C2×C4×D4711yescharacteristic
574C22×C4C2×C4×D4711yescharacteristic
575C22×C4C2×C4×D4711yescharacteristic
576C22×C4C2×D18812yes—
577C22×C4#1062535012yes—
578C22×C4C23×D4711yescharacteristic
579M16—28no—
580M16—28no—
581M16—1884no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—941no—
589C2×C8—941no—
590C2×C8—941no—
591C2×C8—941no—
592C2×C8—941no—
593C2×C8—941no—
594C2×C8—941no—
595C2×C8—941no—
596C2×C8—941no—
597C2×C8—941no—
598C2×C8—941no—
599C2×C8—941no—
600C2×C8—1884no—
601C2×C8C2×D18812yes—
602C2×C8C2×D18812yes—
603C2×C8#1062535012yes—
604C2×C8#1062535012yes—
605C2×C8C2×C22⋊D4712yes—
606C2×C8C2×C22⋊D4712yes—
607C4⋊C4—942no—
608C4⋊C4—942no—
609C4⋊C4—942no—
610C4⋊C4—942no—
611C4⋊C4—1881no—
612C22⋊C4—474no—
613C22⋊C4—942no—
614C22⋊C4—942no—
615C22⋊C4—942no—
616C22⋊C4—942no—
617C22⋊C4—942no—
618C22⋊C4—942no—
619C22⋊C4—942no—
620C22⋊C4—942no—
621C22⋊C4—942no—
622C42—22no—
623C42—22no—
624C42—21no—
625C42—21no—
626C42—941no—
627C42—941no—
628C42—941no—
629C42—941no—
630C42#1062535012yes—
631C42C2×C22⋊D4712yes—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—472no—
639C23—941no—
640C23—941no—
641C23—941no—
642C23—941no—
643C23—941no—
644C23—941no—
645C23—941no—
646C23—941no—
647C23—941no—
648C23—941no—
649C23—941no—
650C23—941no—
651C23—941no—
652C23C4×D18812yes—
653C23C22×C4×D4711yescharacteristic
654D4—1884no—
655D4—1884no—
656D4—1884no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—44no—
672C2×C4—44no—
673C2×C4—472no—
674C2×C4—941no—
675C2×C4—941no—
676C2×C4—941no—
677C2×C4—941no—
678C2×C4—941no—
679C2×C4—941no—
680C2×C4—941no—
681C2×C4—941no—
682C2×C4—941no—
683C2×C4—941no—
684C2×C4—941no—
685C2×C4—941no—
686C2×C4—941no—
687C2×C4—941no—
688C2×C4—941no—
689C2×C4—941no—
690C2×C4—941no—
691C2×C4—1881no—
692C2×C4—1881no—
693C2×C4—1881no—
694C2×C4—1881no—
695C2×C4—1881no—
696C2×C4—1881no—
697C2×C4—1881no—
698C2×C4—1881no—
699C2×C4C4×C22⋊D4712yes—
700C2×C4C4×C22⋊D4712yes—
701C2×C4C4×D18812yes—
702C2×C4M16×D4712yes—
703C2×C4#1309403212yes—
704C2×C4C22×C22⋊D4711yescharacteristic
705C2×C4C22×D18811yescharacteristic
706C2×C4C2×#1062535011yescharacteristic
707C2×C4C2×#1062535011yescharacteristic
708C2×C4C2×#1062535011yescharacteristic
709C2×C4C2×#1062535011yescharacteristic
710C8—22no—
711C8—22no—
712C8—22no—
713C8—1881no—
714C8—1881no—
715C8—1881no—
716C8—1881no—
717C8#1309399814yescomplemented
718C22—22no—
719C22—22no—
720C22—22no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—942no—
726C22—942no—
727C22—942no—
728C22—1881no—
729C22—1881no—
730C22—1881no—
731C22—1881no—
732C22—1881no—
733C22—1881no—
734C22—1881no—
735C22—1881no—
736C22—1881no—
737C22—1881no—
738C22—1881no—
739C22C2×C4×C22⋊D4711yescharacteristic
740C22C2×C4×D18811yescharacteristic
741C22C4×#1062535011yescharacteristic
742C22C2×M16×D4711yescharacteristic
743C22C2×#1309403211yescharacteristic
744C22#1568988911yescharacteristic
745C22#1568988911yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—22no—
751C4—942no—
752C4—1881no—
753C4—1881no—
754C4—1881no—
755C4—1881no—
756C4—1881no—
757C4C2×#1309399811yescharacteristic
758C4#1568963411yescharacteristic
759C4#1568965711yescharacteristic
760C4#1568967311yescharacteristic
761C2—42no—
762C2—3761no—
763C2—1882no—
764C2C4×#1309399811yescharacteristic
765C2#2025211311yescharacteristic
766C2M16×C22⋊D4711yescharacteristic
767C2M16×D18811yescharacteristic
768C2#2025213411yescharacteristic
769C2#2025235011yescharacteristic
770C2#2025237311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC2×C4×M16×C47C2
prime radicalC2×#13093998C4
cosocleC22×C4×C47C24
hypercenterC2×C4×M16D47
hypocenterC47#21490
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C4×M16

Complements

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

NH ≅ G/Ntype
1. C2×#15689199C2semidirect
2. C2×#15689196C2semidirect
3. C2×#15689192C2semidirect
5. #20244186C2semidirect
6. #20244111C2semidirect
7. #20243994C2semidirect
8. #20243994C2semidirect
9. #20243685C2semidirect
10. #20243685C2semidirect
11. #20243368C2semidirect
12. #20243260C2semidirect
13. #20243171C2semidirect
14. C8×(C2×D47)⋊C4C2semidirect
15. C2×C4×M16×C47C2semidirect
130. C2×M16×C47D4semidirect
142. #97×C47D4semidirect
222. (C2×D47)⋊C4M16semidirect
327. C8×C47#121semidirect
379. C2×C4×M16D47semidirect
448. C47#21490semidirect
465. C2×M16D188semidirect
521. #97C22⋊D47semidirect
717. C8#13093998semidirect

Maximal subgroups

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

subgroupindex
C2×#156891992
C2×#156891962
C2×#156891922
C4×#130939982
#202441862
#202441112
#202439942
#202436852
#202433682
#202432602
#202431712
C8×(C2×D47)⋊C42
C2×C4×M16×C472
#2149047