Finite Group Databasebeta

← #26238394

Subgroups — #26238394

Order 12032.

1084 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×#15689197C211yesmaximal, characteristic, complemented
2C2×C8×C22⋊D47C211yesmaximal, characteristic, complemented
3C2×#15689146C211yesmaximal, characteristic, complemented
4C4×#13093996C211yesmaximal, characteristic
5#20244180C211yesmaximal, characteristic, complemented
6#20244103C211yesmaximal, characteristic, complemented
7#20244001C211yesmaximal, characteristic, complemented
8#20243998C211yesmaximal, characteristic, complemented
9#20243686C211yesmaximal, characteristic, complemented
10#20243685C211yesmaximal, characteristic, complemented
11#20243566C211yesmaximal, characteristic, complemented
12#20243564C211yesmaximal, characteristic, complemented
13#20243256C211yesmaximal, characteristic, complemented
14C22⋊C8×Dic47C211yesmaximal, characteristic, complemented
15C2×C47×#435C211yesmaximal, characteristic, complemented
16C22×#10625329C2211yescharacteristic
17C22×C8×D47C2211yescharacteristic
18C2×#13093996C411yescharacteristic
19C2×C4×C22⋊D47C2211yescharacteristic
20C2×C4×C22⋊D47C2211yescharacteristic
21C22×C4×Dic47C2211yescharacteristic
22#15689197—24no—
23C8×C22⋊D47—24no—
24#15689146—24no—
25C2×Dic47⋊C8C2211yescharacteristic
26C2×Dic47⋊C8C2211yescharacteristic
27C2×Dic47⋊C8C2211yescharacteristic
28C2×Dic47⋊C8C2211yescharacteristic
29C2×Dic47⋊C8C2211yescharacteristic
30C2×C22⋊(C47⋊C8)C2211yescharacteristic
31C2×C22⋊(C47⋊C8)C2211yescharacteristic
32C2×C22⋊(C47⋊C8)C2211yescharacteristic
33C2×(C2×D47)⋊C8C2211yescharacteristic
34C2×(C2×D47)⋊C8C2211yescharacteristic
35C2×(C2×D47)⋊C8C2211yescharacteristic
36C2×#13093934C2211yescharacteristic
37C2×C8×Dic47C2211yescharacteristic
38C2×C8×Dic47C2211yescharacteristic
39#15689023C411yescharacteristic
40#15689018C411yescharacteristic
41#15689017C411yescharacteristic
42#15689013C411yescharacteristic
43#15689003C411yescharacteristic
44#15689000C411yescharacteristic
45#15688981C411yescharacteristic
46C4×Dic47⋊C4C2211yescharacteristic
47C4×(C2×D47)⋊C4C2211yescharacteristic
48C4×C22⋊Dic47C2211yescharacteristic
49#15688878C2211yescharacteristic
50#15688878C2211yescharacteristic
51#15688877C2211yescharacteristic
52#15688877C2211yescharacteristic
53#15688877C2211yescharacteristic
54#15688877C2211yescharacteristic
55C22×M16×C47C2211yescharacteristic
56C23×C8×C47C2211yescharacteristic
57C2×C4×D4×C47C2211yescharacteristic
58C47×#435—24no—
59C2×C4⋊C8×C47C2211yescharacteristic
60C2×C22⋊C8×C47C2211yescharacteristic
61C2×C22⋊C8×C47C2211yescharacteristic
62C2×#97×C47C2211yescharacteristic
63C22×C22⋊D47C2×C411yescharacteristic
64C22×C22⋊D47C2×C411yescharacteristic
65C23×Dic47C2×C411yescharacteristic
66C23×Dic47C2×C411yescharacteristic
67C22×C4×D47C2311yescharacteristic
68C2×#10625329—22no—
69C2×#10625329—22no—
70C2×#10625329—41no—
71C22×C47⋊C8C2311yescharacteristic
72C22×C47⋊C8C2311yescharacteristic
73C22×C47⋊C8C2311yescharacteristic
74C22×C47⋊C8C2311yescharacteristic
75C2×C8×D47—22no—
76C2×C8×D47—22no—
77C2×C8×D47—41no—
78#13093996—24no—
79C4×C22⋊D47—22no—
80C4×C22⋊D47—22no—
81C4×C22⋊D47—22no—
82C4×C22⋊D47—22no—
83C2×Dic47⋊C4C2×C411yescharacteristic
84C2×Dic47⋊C4C2×C411yescharacteristic
85C2×Dic47⋊C4C2×C411yescharacteristic
86C2×Dic47⋊C4C2×C411yescharacteristic
87C2×C22⋊Dic47C2×C411yescharacteristic
88C2×C22⋊Dic47C2×C411yescharacteristic
89C2×C22⋊Dic47C2×C411yescharacteristic
90C2×C22⋊Dic47C2×C411yescharacteristic
91C2×(C2×D47)⋊C4C2×C411yescharacteristic
92C2×(C2×D47)⋊C4C2×C411yescharacteristic
93C2×(C2×D47)⋊C4C2×C411yescharacteristic
94C2×(C2×D47)⋊C4C2×C411yescharacteristic
95C2×C4×Dic47—22no—
96C2×C4×Dic47—22no—
97C2×C4×Dic47C2×C411yescharacteristic
98C2×C4×Dic47C2×C411yescharacteristic
99C2×C4×Dic47C2311yescharacteristic
100C2×C4×Dic47C2311yescharacteristic
101C2×C4×Dic47C2311yescharacteristic
102Dic47⋊C8—22no—
103Dic47⋊C8—22no—
104Dic47⋊C8—22no—
105Dic47⋊C8—22no—
106Dic47⋊C8D414yescomplemented
107C22⋊(C47⋊C8)—22no—
108C22⋊(C47⋊C8)—22no—
109C22⋊(C47⋊C8)—41no—
110(C2×D47)⋊C8—22no—
111(C2×D47)⋊C8—22no—
112(C2×D47)⋊C8—41no—
113#13093934—22no—
114C8×Dic47—22no—
115C8×Dic47—22no—
116C47⋊#95C2×C411yescharacteristic
117C47⋊#95C2×C411yescharacteristic
118C47⋊#95C2×C411yescharacteristic
119C47⋊#95C2×C411yescharacteristic
120C47⋊#95C2×C411yescharacteristic
121C47⋊#95C2×C411yescharacteristic
122C22×D4×C47C2×C411yescharacteristic
123C23×C4×C47C2311yescharacteristic
124C23×C4×C47C2311yescharacteristic
125C2×M16×C47—22no—
126C2×M16×C47—22no—
127C2×M16×C47—41no—
128C22×C8×C47—22no—
129C22×C8×C47—22no—
130C22×C8×C47—41no—
131C22×C8×C47C2311yescharacteristic
132C22×C8×C47C2311yescharacteristic
133C22×C8×C47C2311yescharacteristic
134C22×C8×C47C2311yescharacteristic
135C4×D4×C47—22no—
136C4×D4×C47—22no—
137C2×C4⋊C4×C47C2×C411yescharacteristic
138C2×C22⋊C4×C47C2×C411yescharacteristic
139C2×C22⋊C4×C47C2×C411yescharacteristic
140C2×C42×C47C2311yescharacteristic
141C4⋊C8×C47—22no—
142C22⋊C8×C47—22no—
143C22⋊C8×C47D414yescomplemented
144#97×C47—22no—
145C24×C47C22×C411yescharacteristic
146C24×C47C22×C411yescharacteristic
147C23×D47C22×C411yescharacteristic
148C2×D4×C47—22no—
149C2×D4×C47—22no—
150C2×D4×C47—41no—
151C22×C4×C47—21no—
152C22×C4×C47—21no—
153C22×C4×C47—21no—
154C22×C4×C47—21no—
155C22×C4×C47—21no—
156C22×C4×C47—21no—
157C22×C4×C47—21no—
158C22×C4×C47—21no—
159C22×C4×C47—21no—
160C22×C4×C47—21no—
161C22×C4×C47C22×C411yescharacteristic
162C22×C4×C47C22×C411yescharacteristic
163C22×C4×C47C22×C411yescharacteristic
164C22×C4×C47C22×C411yescharacteristic
165C22×C4×C47C2×D412yes—
166C22×C4×C47#4112yes—
167C22×C4×C47C2411yescharacteristic
168C2×C22⋊D47—22no—
169C2×C22⋊D47—22no—
170C2×C22⋊D47—22no—
171C2×C22⋊D47—22no—
172C2×C22⋊D47—41no—
173C2×C22⋊D47M1614yescomplemented
174C22×Dic47—22no—
175C22×Dic47—22no—
176C22×Dic47—22no—
177C22×Dic47—22no—
178C22×Dic47—22no—
179C22×Dic47—41no—
180C22×Dic47C22×C411yescharacteristic
181C22×Dic47C22×C411yescharacteristic
182C22×Dic47C22×C411yescharacteristic
183C22×Dic47C22×C411yescharacteristic
184C22×Dic47C22×C411yescharacteristic
185C22×Dic47C22×C411yescharacteristic
186C22×Dic47C22×C411yescharacteristic
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—44no—
194C2×C8×C47—21no—
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×C47—21no—
202C2×C8×C47—21no—
203C2×C8×C47—44no—
204C2×C8×C47C2×D412yes—
205C2×C8×C47C2×D412yes—
206C2×C8×C47C2×D412yes—
207C4⋊C4×C47—22no—
208C22⋊C4×C47—22no—
209C22⋊C4×C47—22no—
210C42×C47—21no—
211C42×C47—21no—
212C22⋊Dic47—22no—
213C22⋊Dic47—22no—
214C22⋊Dic47—22no—
215C22⋊Dic47—22no—
216(C2×D47)⋊C4—22no—
217(C2×D47)⋊C4—22no—
218(C2×D47)⋊C4—22no—
219(C2×D47)⋊C4—22no—
220Dic47⋊C4—22no—
221Dic47⋊C4—22no—
222Dic47⋊C4—22no—
223Dic47⋊C4—22no—
224C4×Dic47—21no—
225C4×Dic47—21no—
226C4×Dic47—21no—
227C4×Dic47—21no—
228C4×Dic47—22no—
229C4×Dic47—22no—
230C4×Dic47C2×D412yes—
231C4×Dic47#4112yes—
232#10625329—44no—
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—
244C2×C47⋊C8C2×D412yes—
245C8×D47—44no—
246C23×C47—21no—
247C23×C47—21no—
248C23×C47—21no—
249C23×C47—21no—
250C23×C47—21no—
251C23×C47—21no—
252C23×C47—21no—
253C23×C47—21no—
254C23×C47—21no—
255C23×C47—21no—
256C23×C47—21no—
257C23×C47—21no—
258C23×C47C4×D412yes—
259C23×C47C2×M1612yes—
260C23×C47C23×C411yescharacteristic
261C22×D47—21no—
262C22×D47—21no—
263C22×D47—21no—
264C22×D47—21no—
265C22×D47—21no—
266C22×D47—21no—
267C22×D47C2×M1612yes—
268D4×C47—44no—
269C2×C4×C47—21no—
270C2×C4×C47—21no—
271C2×C4×C47—22no—
272C2×C4×C47—22no—
273C2×C4×C47—22no—
274C2×C4×C47—22no—
275C2×C4×C47—21no—
276C2×C4×C47—21no—
277C2×C4×C47—21no—
278C2×C4×C47—21no—
279C2×C4×C47—21no—
280C2×C4×C47—21no—
281C2×C4×C47—21no—
282C2×C4×C47—21no—
283C2×C4×C47—21no—
284C2×C4×C47—41no—
285C2×C4×C47—41no—
286C2×C4×C47—41no—
287C2×C4×C47—41no—
288C2×C4×C47C4×D412yes—
289C2×C4×C47C22×D411yescharacteristic
290C2×C4×C47C22×D411yescharacteristic
291C2×C4×C47C2×#4111yescharacteristic
292C2×C4×C47C2×#4111yescharacteristic
293C2×C4×C47H(5,𝔽2)11yescharacteristic
294C2×C4×C472−1+411yescharacteristic
295C22⋊D47—28no—
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—44no—
314C2×Dic47—44no—
315C2×Dic47C4×D412yes—
316C2×Dic47C4×D412yes—
317C2×Dic47C2×M1612yes—
318C2×Dic47#13112yes—
319C2×Dic47#13112yes—
320C4×D47—41no—
321C4×D47—41no—
322C4×D47—41no—
323C4×D47—41no—
324C8×C47—22no—
325C8×C47—22no—
326C8×C47—22no—
327C8×C47—41no—
328C47⋊C8—22no—
329C47⋊C8—41no—
330C47⋊C8—41no—
331C47⋊C8—41no—
332#22986—471nomaximal, Sylow
333C22×C47—22no—
334C22×C47—22no—
335C22×C47—22no—
336C22×C47—22no—
337C22×C47—22no—
338C22×C47—22no—
339C22×C47—41no—
340C22×C47—41no—
341C22×C47—41no—
342C22×C47—41no—
343C22×C47—41no—
344C22×C47—41no—
345C22×C47—41no—
346C22×C47—41no—
347C22×C47C2×C4×D411yescharacteristic
348C22×C47C2×C4×D411yescharacteristic
349C22×C47#52011yescharacteristic
350C22×C47C22×M1611yescharacteristic
351C22×C47C2×#13111yescharacteristic
352C22×C47C2×#13111yescharacteristic
353C22×C47#56811yescharacteristic
354C2×D47—22no—
355C2×D47—22no—
356C2×D47—22no—
357C2×D47—41no—
358C2×D47—41no—
359C2×D47—41no—
360C2×D47—41no—
361C4×C47—22no—
362C4×C47—41no—
363C4×C47—41no—
364C4×C47—41no—
365C4×C47D4211yescharacteristic
366C4×C47#54711yescharacteristic
367C4×C47#54811yescharacteristic
368C4×C47#55311yescharacteristic
369Dic47—22no—
370Dic47—22no—
371Dic47—41no—
372Dic47—41no—
373Dic47—41no—
374Dic47—41no—
375Dic47#43514yescomplemented
376C2×#435—471no—
377C2×#435D4711yescharacteristic, complemented
378C2×C8×D4—471no—
379C2×#423—471no—
380C4×#121—471no—
381#1954—471no—
382#1939—471no—
383#1924—471no—
384#1924—471no—
385#1870—471no—
386#1870—471no—
387#1850—471no—
388#1850—471no—
389#1770—471no—
390C4×C22⋊C8—471no—
391C2×C47—42no—
392C2×C47—42no—
393C2×C47#236111yescharacteristic
394C2×C47C2×#43511yescharacteristic
395C2×C47#293111yescharacteristic
396C2×C47#293311yescharacteristic
397C2×C47D4×M1611yescharacteristic
398C2×C47#299011yescharacteristic
399C2×C47#299311yescharacteristic
400D47—42no—
401C22×M16—471no—
402C22×M16C2×D4711yescharacteristic
403C23×C8—471no—
404C23×C8C2×D4711yescharacteristic
405C2×#121—471no—
406C2×C4×D4—471no—
407C2×C4×D4—471no—
408C2×C4×D4C2×D4711yescharacteristic
409C22×C42—471no—
410#435—24no—
411#435—944no—
412C8×D4—944no—
413#423—944no—
414C2×C4⋊C8—471no—
415C2×C4⋊C8—471no—
416C2×C4⋊C8—471no—
417C2×C4⋊C8—471no—
418C2×C4⋊C8—471no—
419C2×C4⋊C8C2×D4711yescharacteristic
420C2×C22⋊C8—471no—
421C2×C22⋊C8—471no—
422C2×C22⋊C8—471no—
423C2×C22⋊C8—471no—
424C2×C22⋊C8—471no—
425C2×C22⋊C8—471no—
426C2×C22⋊C8C2×D4711yescharacteristic
427C2×C22⋊C8C2×D4711yescharacteristic
428C2×#97—471no—
429C2×#97C2×D4711yescharacteristic
430C2×C4×C8—471no—
431C2×C4×C8—471no—
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#2298611yescharacteristic, complemented, Sylow
449C22×D4—471no—
450C22×D4—471no—
451C22×D4C4×D4711yescharacteristic
452C23×C4—471no—
453C23×C4—471no—
454C23×C4—471no—
455C23×C4C22×D4711yescharacteristic
456C23×C4C22×D4711yescharacteristic
457C2×M16—22no—
458C2×M16—22no—
459C2×M16—41no—
460C2×M16—942no—
461C2×M16—942no—
462C2×M16—1881no—
463C22×C8—22no—
464C22×C8—22no—
465C22×C8—41no—
466C22×C8—471no—
467C22×C8—471no—
468C22×C8—471no—
469C22×C8—471no—
470C22×C8—942no—
471C22×C8—942no—
472C22×C8—1881no—
473C22×C8C22×D4711yescharacteristic
474C22×C8C22×D4711yescharacteristic
475C22×C8C22×D4711yescharacteristic
476C22×C8C22×D4711yescharacteristic
477#121—944no—
478C4×D4—22no—
479C4×D4—22no—
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⋊C4C4×D4711yescharacteristic
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⋊C4C4×D4711yescharacteristic
498C2×C22⋊C4C4×D4711yescharacteristic
499C2×C42—471no—
500C2×C42—471no—
501C2×C42—471no—
502C2×C42—471no—
503C2×C42—471no—
504C2×C42—942no—
505C2×C42—942no—
506C2×C42C22×D4711yescharacteristic
507C4⋊C8—22no—
508C4⋊C8—474no—
509C4⋊C8—942no—
510C4⋊C8—942no—
511C4⋊C8—942no—
512C4⋊C8—942no—
513C22⋊C8—22no—
514C22⋊C8—942no—
515C22⋊C8—942no—
516C22⋊C8—942no—
517C22⋊C8—942no—
518C22⋊C8—1881no—
519C22⋊C8—1881no—
520C22⋊C8C22⋊D4714yescomplemented
521#97—22no—
522#97—942no—
523C4×C8—942no—
524C4×C8—942no—
525#95—471no—
526#95—471no—
527#95—471no—
528#95—471no—
529#95—471no—
530#95—471no—
531C24—471no—
532C24C2×C4×D4711yescharacteristic
533C24C2×C4×D4711yescharacteristic
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—41no—
537C2×D4—474no—
538C2×D4—942no—
539C2×D4—942no—
540C2×D4—942no—
541C2×D4—942no—
542C2×D4—1881no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—471no—
554C22×C4—471no—
555C22×C4—471no—
556C22×C4—471no—
557C22×C4—471no—
558C22×C4—471no—
559C22×C4—471no—
560C22×C4—942no—
561C22×C4—942no—
562C22×C4—942no—
563C22×C4—942no—
564C22×C4—942no—
565C22×C4—941no—
566C22×C4—941no—
567C22×C4—941no—
568C22×C4—941no—
569C22×C4—941no—
570C22×C4—941no—
571C22×C4—1881no—
572C22×C4C2×C4×D4711yescharacteristic
573C22×C4C2×C4×D4711yescharacteristic
574C22×C4C2×C4×D4711yescharacteristic
575C22×C4C2×C4×D4711yescharacteristic
576C22×C4#1062535012yes—
577C22×C4C2×C22⋊D4712yes—
578C22×C4C23×D4711yescharacteristic
579M16—44no—
580M16—1884no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—44no—
591C2×C8—472no—
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—941no—
601C2×C8—941no—
602C2×C8—941no—
603C2×C8—1884no—
604C2×C8D4×D4712yes—
605C2×C8C2×C22⋊D4712yes—
606C2×C8C2×C22⋊D4712yes—
607C4⋊C4—22no—
608C4⋊C4—942no—
609C4⋊C4—942no—
610C4⋊C4—942no—
611C4⋊C4—942no—
612C22⋊C4—22no—
613C22⋊C4—22no—
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—21no—
623C42—21no—
624C42—472no—
625C42—472no—
626C42—942no—
627C42—942no—
628C42—941no—
629C42—941no—
630C42—941no—
631C42—941no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—472no—
645C23—941no—
646C23—941no—
647C23—941no—
648C23—941no—
649C23—941no—
650C23—941no—
651C23C4×C22⋊D4712yes—
652C23M16×D4712yes—
653C23C22×C4×D4711yescharacteristic
654D4—44no—
655D4—948no—
656D4—1884no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—472no—
677C2×C4—472no—
678C2×C4—472no—
679C2×C4—472no—
680C2×C4—472no—
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—941no—
692C2×C4—941no—
693C2×C4—941no—
694C2×C4—941no—
695C2×C4—941no—
696C2×C4—941no—
697C2×C4—1884no—
698C2×C4—1884no—
699C2×C4—1881no—
700C2×C4—1881no—
701C2×C4—1881no—
702C2×C4—1881no—
703C2×C4C4×C22⋊D4712yes—
704C2×C4C2×D4×D4711yescharacteristic
705C2×C4C22×C22⋊D4711yescharacteristic
706C2×C4#41×D4711yescharacteristic
707C2×C4C2×#1062535011yescharacteristic
708C2×C4#1309406911yescharacteristic
709C2×C4#1309407111yescharacteristic
710C8—22no—
711C8—22no—
712C8—22no—
713C8—41no—
714C8—942no—
715C8—1881no—
716C8—1881no—
717C8—1881no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—942no—
733C22—942no—
734C22—942no—
735C22—1881no—
736C22—1881no—
737C22—1881no—
738C22—1881no—
739C22C4×D4×D4711yescharacteristic
740C22C2×C4×C22⋊D4711yescharacteristic
741C22#1568960211yescharacteristic
742C22C2×M16×D4711yescharacteristic
743C22#131×D4711yescharacteristic
744C22#131×D4711yescharacteristic
745C22#1568988911yescharacteristic
746C4—22no—
747C4—41no—
748C4—41no—
749C4—41no—
750C4—474no—
751C4—942no—
752C4—942no—
753C4—1881no—
754C4—1881no—
755C4—1881no—
756C4—1881no—
757C4D4×C22⋊D4711yescharacteristic
758C4#1568977211yescharacteristic
759C4#1568978211yescharacteristic
760C4#1568982211yescharacteristic
761C2—42no—
762C2—42no—
763C2—1882no—
764C2#2024640511yescharacteristic
765C2#435×D4711yescharacteristic
766C2#2025209811yescharacteristic
767C2#2025211111yescharacteristic
768C2M16×C22⋊D4711yescharacteristic
769C2#2025250811yescharacteristic
770C2#2025253011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC2×C47×#435C2
prime radicalC2×#13093996C4
cosocleC22×C4×C47C24
hypercenterC2×#435D47
hypocenterC47#22986
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#15689197C2semidirect
2. C2×C8×C22⋊D47C2semidirect
3. C2×#15689146C2semidirect
5. #20244180C2semidirect
6. #20244103C2semidirect
7. #20244001C2semidirect
8. #20243998C2semidirect
9. #20243686C2semidirect
10. #20243685C2semidirect
11. #20243566C2semidirect
12. #20243564C2semidirect
13. #20243256C2semidirect
14. C22⋊C8×Dic47C2semidirect
15. C2×C47×#435C2semidirect
106. Dic47⋊C8D4semidirect
143. C22⋊C8×C47D4semidirect
173. C2×C22⋊D47M16semidirect
375. Dic47#435semidirect
377. C2×#435D47semidirect
448. C47#22986semidirect
520. C22⋊C8C22⋊D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156891972
C2×C8×C22⋊D472
C2×#156891462
C4×#130939962
#202441802
#202441032
#202440012
#202439982
#202436862
#202436852
#202435662
#202435642
#202432562
C22⋊C8×Dic472
C2×C47×#4352
#2298647