Finite Group Databasebeta

← #26227377

Subgroups — #26227377

Order 12032.

1156 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689198C211yesmaximal, characteristic, complemented
2C2×#15689087C211yesmaximal, characteristic, complemented
3C4×#13093993C211yesmaximal, characteristic
4#20244184C211yesmaximal, characteristic, complemented
5#20244180C211yesmaximal, characteristic, complemented
6#20243998C211yesmaximal, characteristic, complemented
7#20243997C211yesmaximal, characteristic, complemented
8#20243997C211yesmaximal, characteristic, complemented
9#20243991C211yesmaximal, characteristic, complemented
10#20243683C211yesmaximal, characteristic, complemented
11#20243682C211yesmaximal, characteristic, complemented
12#20243682C211yesmaximal, characteristic, complemented
13#20243570C211yesmaximal, characteristic, complemented
14#20243174C211yesmaximal, characteristic, complemented
15C47×#1779C211yesmaximal, characteristic, complemented
16C22×#10625329C2211yescharacteristic
17C22×#10625329C2211yescharacteristic
18C22×#10625324C2211yescharacteristic, complemented
19C2×#13093993C411yescharacteristic
20C2×C4×C22⋊D47C2211yescharacteristic
21C2×C4×C22⋊D47C2211yescharacteristic
22C2×C4×C22⋊D47C2211yescharacteristic
23#15689198—24no—
24C2×Dic47⋊C8C2211yescharacteristic, complemented
25C2×Dic47⋊C8C2211yescharacteristic, complemented
26C2×Dic47⋊C8C2211yescharacteristic, complemented
27#15689087—24no—
28C2×C22⋊(C47⋊C8)C2211yescharacteristic
29C2×C22⋊(C47⋊C8)C2211yescharacteristic
30C2×C22⋊(C47⋊C8)C2211yescharacteristic
31C2×C22⋊(C47⋊C8)C2211yescharacteristic
32C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
33C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
34C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
35C2×#13093934C2211yescharacteristic, complemented
36C2×C8×Dic47C2211yescharacteristic, complemented
37C2×C8×Dic47C2211yescharacteristic, complemented
38#15689002C411yescharacteristic
39#15689002C411yescharacteristic
40#15689002C411yescharacteristic
41#15688996C411yescharacteristic
42#15688996C411yescharacteristic
43#15688996C411yescharacteristic
44#15688979C411yescharacteristic
45C4×C22⋊Dic47C2211yescharacteristic
46C4×C22⋊Dic47C2211yescharacteristic
47C4×C22⋊Dic47C2211yescharacteristic
48#15688877C2211yescharacteristic, complemented
49#15688877C2211yescharacteristic, complemented
50#15688877C2211yescharacteristic, complemented
51#15688877C2211yescharacteristic, complemented
52#15688877C2211yescharacteristic, complemented
53#15688877C2211yescharacteristic, complemented
54C24×C4×C47C2211yescharacteristic
55C2×C22⋊C8×C47C2211yescharacteristic
56C2×C22⋊C8×C47C2211yescharacteristic
57C2×C22⋊C8×C47C2211yescharacteristic
58C2×C22⋊C8×C47C2211yescharacteristic
59C2×C22⋊C8×C47C2211yescharacteristic
60C2×C22⋊C8×C47C2211yescharacteristic
61C22×C22⋊D47C2×C411yescharacteristic
62C22×C22⋊D47C2×C411yescharacteristic
63C22×C22⋊D47C2×C411yescharacteristic
64C22×C4×D47C2311yescharacteristic
65C2×#10625329—22no—
66C2×#10625329—41no—
67C2×#10625329—41no—
68C2×#10625329—41no—
69C2×#10625329—41no—
70C2×#10625329D414yescomplemented
71C2×#10625324—22no—
72C2×#10625324—41no—
73C2×#10625324—41no—
74C22×C47⋊C8C2311yescharacteristic
75C22×C47⋊C8C2311yescharacteristic
76C22×C47⋊C8C2311yescharacteristic
77C22×C47⋊C8C2311yescharacteristic
78#13093993—24no—
79C4×C22⋊D47—22no—
80C4×C22⋊D47—22no—
81C4×C22⋊D47—41no—
82C4×C22⋊D47—41no—
83C4×C22⋊D47—41no—
84C4×C22⋊D47—41no—
85C2×Dic47⋊C4C2×C411yescharacteristic
86C2×Dic47⋊C4C2×C411yescharacteristic
87C2×Dic47⋊C4C2×C411yescharacteristic
88C2×C22⋊Dic47C2×C411yescharacteristic
89C2×C22⋊Dic47C2×C411yescharacteristic
90C2×C22⋊Dic47C2×C411yescharacteristic
91C2×C22⋊Dic47C2×C411yescharacteristic
92C2×C22⋊Dic47C2×C411yescharacteristic
93C2×C22⋊Dic47C2×C411yescharacteristic
94C2×C22⋊Dic47C2×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×C4×Dic47C2311yescharacteristic
101C2×C4×Dic47C2311yescharacteristic
102C2×C4×Dic47C2311yescharacteristic
103Dic47⋊C8—22no—
104Dic47⋊C8—41no—
105Dic47⋊C8—41no—
106C22⋊(C47⋊C8)—22no—
107C22⋊(C47⋊C8)—22no—
108C22⋊(C47⋊C8)—22no—
109C22⋊(C47⋊C8)—22no—
110(C2×D47)⋊C8—22no—
111(C2×D47)⋊C8—41no—
112(C2×D47)⋊C8—41no—
113#13093934—41no—
114C8×Dic47—22no—
115C8×Dic47—41no—
116C47⋊#95C2×C411yescharacteristic
117C47⋊#95C2×C411yescharacteristic
118C47⋊#95C2×C411yescharacteristic
119C47⋊#95C2×C411yescharacteristic
120C47⋊#95C2×C411yescharacteristic
121C47⋊#95C2×C411yescharacteristic
122C25×C47C2×C411yescharacteristic
123C23×C4×C47—22no—
124C23×C4×C47—22no—
125C23×C4×C47—41no—
126C23×C4×C47—41no—
127C23×C4×C47—41no—
128C23×C4×C47—41no—
129C23×C4×C47C2×C411yescharacteristic
130C23×C4×C47C2×C411yescharacteristic
131C23×C4×C47C2×C411yescharacteristic
132C23×C4×C47C2311yescharacteristic
133C23×C4×C47C2311yescharacteristic
134C23×C4×C47C2311yescharacteristic
135C22×C8×C47C2311yescharacteristic
136C22×C8×C47C2311yescharacteristic
137C22×C8×C47C2311yescharacteristic
138C22×C8×C47C2311yescharacteristic
139C22⋊C8×C47—22no—
140C22⋊C8×C47—22no—
141C22⋊C8×C47—41no—
142C22⋊C8×C47—41no—
143C22⋊C8×C47—41no—
144C22⋊C8×C47—41no—
145C24×C47—22no—
146C24×C47—22no—
147C24×C47—22no—
148C24×C47—41no—
149C24×C47—41no—
150C24×C47—41no—
151C24×C47—41no—
152C24×C47C22×C411yescharacteristic
153C24×C47C22×C411yescharacteristic
154C24×C47C22×C411yescharacteristic
155C23×D47C22×C411yescharacteristic
156C22×C4×C47—21no—
157C22×C4×C47—21no—
158C22×C4×C47—21no—
159C22×C4×C47—21no—
160C22×C4×C47—22no—
161C22×C4×C47—22no—
162C22×C4×C47—22no—
163C22×C4×C47—21no—
164C22×C4×C47—21no—
165C22×C4×C47—21no—
166C22×C4×C47—21no—
167C22×C4×C47—21no—
168C22×C4×C47—21no—
169C22×C4×C47—21no—
170C22×C4×C47—21no—
171C22×C4×C47—21no—
172C22×C4×C47—21no—
173C22×C4×C47—21no—
174C22×C4×C47—21no—
175C22×C4×C47—41no—
176C22×C4×C47—41no—
177C22×C4×C47—41no—
178C22×C4×C47—41no—
179C22×C4×C47—41no—
180C22×C4×C47—41no—
181C22×C4×C47—44no—
182C22×C4×C47—44no—
183C22×C4×C47—44no—
184C22×C4×C47—44no—
185C22×C4×C47C22×C411yescharacteristic
186C22×C4×C47C22×C411yescharacteristic
187C22×C4×C47C22×C411yescharacteristic
188C22×C4×C47C2×D412yes—
189C22×C4×C47#4112yes—
190C22×C4×C47C2411yescharacteristic
191C2×C22⋊D47—22no—
192C2×C22⋊D47—22no—
193C2×C22⋊D47—22no—
194C2×C22⋊D47—22no—
195C2×C22⋊D47—22no—
196C2×C22⋊D47—41no—
197C2×C22⋊D47—41no—
198C2×C22⋊D47—41no—
199C2×C22⋊D47—41no—
200C22×Dic47C22×C411yescharacteristic
201C22×Dic47C22×C411yescharacteristic
202C22×Dic47C22×C411yescharacteristic
203C22×Dic47C22×C411yescharacteristic
204C22×Dic47C22×C411yescharacteristic
205C22×Dic47C22×C411yescharacteristic
206C22×Dic47C22×C411yescharacteristic
207C2×C4×D47—21no—
208C2×C4×D47—21no—
209C2×C4×D47—21no—
210C2×C4×D47—21no—
211C2×C4×D47—21no—
212C2×C4×D47—21no—
213C2×C8×C47—21no—
214C2×C8×C47—21no—
215C2×C8×C47—21no—
216C2×C8×C47—21no—
217C2×C8×C47—21no—
218C2×C8×C47—21no—
219C2×C8×C47—21no—
220C2×C8×C47—21no—
221C2×C8×C47—21no—
222C2×C8×C47—21no—
223C2×C8×C47—21no—
224C2×C8×C47—21no—
225C22⋊Dic47—22no—
226C22⋊Dic47—22no—
227C22⋊Dic47—22no—
228C22⋊Dic47—22no—
229C22⋊Dic47—41no—
230C22⋊Dic47—41no—
231C22⋊Dic47—41no—
232C22⋊Dic47—41no—
233C22⋊Dic47M1614yescomplemented
234(C2×D47)⋊C4—22no—
235(C2×D47)⋊C4—41no—
236(C2×D47)⋊C4—41no—
237Dic47⋊C4—22no—
238Dic47⋊C4—41no—
239Dic47⋊C4—41no—
240C4×Dic47—21no—
241C4×Dic47—21no—
242C4×Dic47—21no—
243C4×Dic47—21no—
244C4×Dic47—21no—
245C4×Dic47—21no—
246#10625329—44no—
247#10625329—44no—
248C2×C47⋊C8—21no—
249C2×C47⋊C8—21no—
250C2×C47⋊C8—21no—
251C2×C47⋊C8—21no—
252C2×C47⋊C8—21no—
253C2×C47⋊C8—21no—
254C2×C47⋊C8—21no—
255C2×C47⋊C8—21no—
256C2×C47⋊C8—21no—
257C2×C47⋊C8—21no—
258C2×C47⋊C8C2×D412yes—
259C2×C47⋊C8C2×D412yes—
260#10625324—44no—
261C23×C47—21no—
262C23×C47—21no—
263C23×C47—21no—
264C23×C47—21no—
265C23×C47—21no—
266C23×C47—21no—
267C23×C47—21no—
268C23×C47—21no—
269C23×C47—21no—
270C23×C47—21no—
271C23×C47—21no—
272C23×C47—21no—
273C23×C47—21no—
274C23×C47—21no—
275C23×C47—21no—
276C23×C47—21no—
277C23×C47—21no—
278C23×C47—21no—
279C23×C47—44no—
280C23×C47—44no—
281C23×C47—44no—
282C23×C47—44no—
283C23×C47—44no—
284C23×C47—44no—
285C23×C47—44no—
286C23×C47C4×D412yes—
287C23×C47C2×M1612yes—
288C23×C47#13112yes—
289C23×C47C23×C411yescharacteristic
290C22×D47—21no—
291C22×D47—21no—
292C22×D47—21no—
293C22×D47—21no—
294C22×D47—21no—
295C22×D47—21no—
296C22×D47—21no—
297C2×C4×C47—21no—
298C2×C4×C47—21no—
299C2×C4×C47—22no—
300C2×C4×C47—22no—
301C2×C4×C47—22no—
302C2×C4×C47—22no—
303C2×C4×C47—21no—
304C2×C4×C47—21no—
305C2×C4×C47—21no—
306C2×C4×C47—21no—
307C2×C4×C47—21no—
308C2×C4×C47—21no—
309C2×C4×C47—44no—
310C2×C4×C47—44no—
311C2×C4×C47—44no—
312C2×C4×C47—41no—
313C2×C4×C47—41no—
314C2×C4×C47—41no—
315C2×C4×C47—41no—
316C2×C4×C47—41no—
317C2×C4×C47—41no—
318C2×C4×C47—41no—
319C2×C4×C47—41no—
320C2×C4×C47C4×D412yes—
321C2×C4×C47C22×D411yescharacteristic
322C2×C4×C47C2×#4111yescharacteristic
323C2×C4×C47H(5,𝔽2)11yescharacteristic
324C2×C4×C47H(5,𝔽2)11yescharacteristic
325C2×C4×C47H(5,𝔽2)11yescharacteristic
326C2×C4×C47H(5,𝔽2)11yescharacteristic
327C22⋊D47—44no—
328C22⋊D47—44no—
329C22⋊D47—44no—
330C2×Dic47—21no—
331C2×Dic47—21no—
332C2×Dic47—21no—
333C2×Dic47—21no—
334C2×Dic47—21no—
335C2×Dic47—21no—
336C2×Dic47—21no—
337C2×Dic47—21no—
338C2×Dic47—21no—
339C2×Dic47—21no—
340C2×Dic47—21no—
341C2×Dic47—21no—
342C2×Dic47—21no—
343C2×Dic47—21no—
344C2×Dic47—21no—
345C2×Dic47—21no—
346C2×Dic47—21no—
347C2×Dic47—21no—
348C2×Dic47—21no—
349C2×Dic47C2×M1612yes—
350C2×Dic47C2×M1612yes—
351C4×D47—41no—
352C4×D47—41no—
353C4×D47—41no—
354C4×D47—41no—
355C8×C47—41no—
356C8×C47—41no—
357C8×C47—41no—
358C8×C47—41no—
359C47⋊C8—22no—
360C47⋊C8—22no—
361C47⋊C8—41no—
362C47⋊C8—41no—
363#22038—471nomaximal, Sylow
364C22×C47—22no—
365C22×C47—22no—
366C22×C47—22no—
367C22×C47—22no—
368C22×C47—22no—
369C22×C47—22no—
370C22×C47—22no—
371C22×C47—22no—
372C22×C47—22no—
373C22×C47—416no—
374C22×C47—41no—
375C22×C47—41no—
376C22×C47—41no—
377C22×C47—41no—
378C22×C47—41no—
379C22×C47—41no—
380C22×C47—41no—
381C22×C47—41no—
382C22×C47—41no—
383C22×C47—41no—
384C22×C47—41no—
385C22×C47—41no—
386C22×C47C2×C4×D411yescharacteristic
387C22×C47#51811yescharacteristic
388C22×C47#51811yescharacteristic
389C22×C47C22×M1611yescharacteristic
390C22×C47C2×#13111yescharacteristic
391C22×C47#56811yescharacteristic
392C22×C47#56811yescharacteristic
393C2×D47—41no—
394C2×D47—41no—
395C2×D47—41no—
396C2×D47—41no—
397C2×D47—41no—
398C2×D47—41no—
399C2×D47—41no—
400C4×C47—22no—
401C4×C47—41no—
402C4×C47—41no—
403C4×C47#53411yescharacteristic
404C4×C47#53511yescharacteristic
405C4×C47#53811yescharacteristic
406C4×C47#53811yescharacteristic
407Dic47—22no—
408Dic47—22no—
409Dic47—41no—
410Dic47—41no—
411Dic47—41no—
412Dic47—41no—
413Dic47—41no—
414C2×#436—471no—
415C2×#407—471no—
416C4×#120—471no—
417#1955—471no—
418#1954—471no—
419#1924—471no—
420#1923—471no—
421#1923—471no—
422#1923—471no—
423#1870—471no—
424#1870—471no—
425#1870—471no—
426#1851—471no—
427#1779D4711yescharacteristic, complemented
428#1753—471no—
429C2×C47—42no—
430C2×C47—42no—
431C2×C47—42no—
432C2×C47#232111yescharacteristic
433C2×C47#293311yescharacteristic
434C2×C47D4×M1611yescharacteristic
435C2×C47#297411yescharacteristic
436C2×C47#297511yescharacteristic
437C2×C47#297611yescharacteristic
438C2×C47#297811yescharacteristic
439D47—81no—
440C24×C4C2×D4711yescharacteristic
441C22×M16—471no—
442C22×M16—471no—
443C22×M16—471no—
444C2×#120—471no—
445C2×C4×D4—471no—
446C2×C4×D4—471no—
447C2×C4×D4—471no—
448#436—944no—
449C2×C4⋊C8—471no—
450C2×C4⋊C8—471no—
451C2×C4⋊C8—471no—
452#407—944no—
453C2×C22⋊C8—471no—
454C2×C22⋊C8—471no—
455C2×C22⋊C8—471no—
456C2×C22⋊C8—471no—
457C2×C22⋊C8—471no—
458C2×C22⋊C8—471no—
459C2×C22⋊C8—471no—
460C2×C22⋊C8C2×D4711yescharacteristic
461C2×C22⋊C8C2×D4711yescharacteristic
462C2×C22⋊C8C2×D4711yescharacteristic
463C2×C22⋊C8C2×D4711yescharacteristic
464C2×C22⋊C8C2×D4711yescharacteristic
465C2×C22⋊C8C2×D4711yescharacteristic
466C2×#97—471no—
467C2×C4×C8—471no—
468C2×C4×C8—471no—
469#386—471no—
470#386—471no—
471#386—471no—
472#385—471no—
473#385—471no—
474#385—471no—
475#379—471no—
476C4×C22⋊C4—471no—
477C4×C22⋊C4—471no—
478C4×C22⋊C4—471no—
479#336—471no—
480#336—471no—
481#336—471no—
482#336—471no—
483#336—471no—
484#336—471no—
485C47#2203811yescharacteristic, complemented, Sylow
486C25C4×D4711yescharacteristic
487C22×D4—471no—
488C22×D4—471no—
489C22×D4—471no—
490C23×C4—22no—
491C23×C4—22no—
492C23×C4—41no—
493C23×C4—41no—
494C23×C4—41no—
495C23×C4—41no—
496C23×C4—471no—
497C23×C4C4×D4711yescharacteristic
498C23×C4C4×D4711yescharacteristic
499C23×C4C4×D4711yescharacteristic
500C23×C4C22×D4711yescharacteristic
501C23×C4C22×D4711yescharacteristic
502C23×C4C22×D4711yescharacteristic
503C2×M16—474no—
504C2×M16—942no—
505C2×M16—942no—
506C2×M16—1881no—
507C2×M16—1881no—
508C2×M16—1881no—
509C2×M16—1881no—
510C2×M16—1881no—
511C2×M16—1881no—
512C22×C8—471no—
513C22×C8—471no—
514C22×C8—471no—
515C22×C8—471no—
516C22×C8C22×D4711yescharacteristic
517C22×C8C22×D4711yescharacteristic
518C22×C8C22×D4711yescharacteristic
519C22×C8C22×D4711yescharacteristic
520#120—944no—
521C4×D4—942no—
522C4×D4—942no—
523C4×D4—1881no—
524C4×D4—1881no—
525C4×D4—1881no—
526C4×D4—1881no—
527C2×C4⋊C4—471no—
528C2×C4⋊C4—471no—
529C2×C4⋊C4—471no—
530C2×C22⋊C4—471no—
531C2×C22⋊C4—471no—
532C2×C22⋊C4—471no—
533C2×C22⋊C4—471no—
534C2×C22⋊C4—471no—
535C2×C22⋊C4—471no—
536C2×C22⋊C4—471no—
537C2×C22⋊C4—471no—
538C2×C22⋊C4—471no—
539C2×C22⋊C4—471no—
540C2×C22⋊C4—471no—
541C2×C22⋊C4—471no—
542C2×C42—471no—
543C2×C42—471no—
544C2×C42—471no—
545C4⋊C8—942no—
546C4⋊C8—1881no—
547C4⋊C8—1881no—
548C22⋊C8—22no—
549C22⋊C8—22no—
550C22⋊C8—41no—
551C22⋊C8—41no—
552C22⋊C8—41no—
553C22⋊C8—41no—
554C22⋊C8—942no—
555C22⋊C8—942no—
556C22⋊C8—942no—
557C22⋊C8—942no—
558C22⋊C8—942no—
559C22⋊C8—1881no—
560C22⋊C8—1881no—
561#97—1881no—
562C4×C8—942no—
563C4×C8—1881no—
564#95—471no—
565#95—471no—
566#95—471no—
567#95—471no—
568#95—471no—
569#95—471no—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—41no—
574C24—41no—
575C24—41no—
576C24—41no—
577C24—471no—
578C24C2×C4×D4711yescharacteristic
579C24C2×C4×D4711yescharacteristic
580C24C2×C4×D4711yescharacteristic
581C2×D4—942no—
582C2×D4—942no—
583C2×D4—942no—
584C2×D4—942no—
585C2×D4—942no—
586C2×D4—1881no—
587C2×D4—1881no—
588C2×D4—1881no—
589C2×D4—1881no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—44no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4—44no—
619C22×C4—471no—
620C22×C4—471no—
621C22×C4—471no—
622C22×C4—471no—
623C22×C4—471no—
624C22×C4—471no—
625C22×C4—471no—
626C22×C4—941no—
627C22×C4—941no—
628C22×C4—941no—
629C22×C4—941no—
630C22×C4—941no—
631C22×C4—941no—
632C22×C4C2×C4×D4711yescharacteristic
633C22×C4C2×C4×D4711yescharacteristic
634C22×C4C2×C4×D4711yescharacteristic
635C22×C4D4×D4712yes—
636C22×C4#1062535212yes—
637C22×C4C23×D4711yescharacteristic
638M16—1884no—
639M16—1884no—
640M16—1884no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—472no—
654C2×C8—472no—
655C2×C8—941no—
656C2×C8—941no—
657C2×C8—941no—
658C2×C8—941no—
659C2×C8—941no—
660C2×C8—941no—
661C2×C8—941no—
662C2×C8—941no—
663C2×C8—941no—
664C2×C8—941no—
665C4⋊C4—942no—
666C4⋊C4—1881no—
667C4⋊C4—1881no—
668C22⋊C4—474no—
669C22⋊C4—942no—
670C22⋊C4—942no—
671C22⋊C4—942no—
672C22⋊C4—942no—
673C22⋊C4—942no—
674C22⋊C4—1881no—
675C22⋊C4—1881no—
676C22⋊C4—1881no—
677C22⋊C4—1881no—
678C22⋊C4—1881no—
679C22⋊C4—1881no—
680C42—941no—
681C42—941no—
682C42—941no—
683C42—941no—
684C42—941no—
685C42—941no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—44no—
711C23—941no—
712C23—941no—
713C23—941no—
714C23—941no—
715C23—941no—
716C23—941no—
717C23—941no—
718C23(C22⋊D47)⋊C412yes—
719C23M16×D4712yes—
720C23#1309403012yes—
721C23C22×C4×D4711yescharacteristic
722D4—1884no—
723D4—1884no—
724D4—1884no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—472no—
749C2×C4—472no—
750C2×C4—941no—
751C2×C4—941no—
752C2×C4—941no—
753C2×C4—941no—
754C2×C4—941no—
755C2×C4—941no—
756C2×C4—941no—
757C2×C4—941no—
758C2×C4—941no—
759C2×C4—941no—
760C2×C4—941no—
761C2×C4—941no—
762C2×C4—941no—
763C2×C4—941no—
764C2×C4—941no—
765C2×C4—941no—
766C2×C4—941no—
767C2×C4—941no—
768C2×C4—941no—
769C2×C4—1881no—
770C2×C4—1881no—
771C2×C4—1881no—
772C2×C4—1881no—
773C2×C4(C22⋊D47)⋊C412yes—
774C2×C4C2×D4×D4711yescharacteristic
775C2×C4C2×#1062535211yescharacteristic
776C2×C4#1309406911yescharacteristic
777C2×C4#1309406911yescharacteristic
778C2×C4#1309406911yescharacteristic
779C2×C4#1309406911yescharacteristic
780C8—41no—
781C8—41no—
782C8—41no—
783C8—41no—
784C8—942no—
785C8—942no—
786C8—1881no—
787C8—1881no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—416no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—1881no—
811C22—1881no—
812C22—1881no—
813C22—1881no—
814C22—1881no—
815C22—1881no—
816C22—1881no—
817C22C2×(C22⋊D47)⋊C411yescharacteristic
818C22#1568959611yescharacteristic
819C22#1568959611yescharacteristic
820C22C2×M16×D4711yescharacteristic
821C22C2×#1309403011yescharacteristic
822C22#1568988911yescharacteristic
823C22#1568988911yescharacteristic
824C4—22no—
825C4—41no—
826C4—41no—
827C4—942no—
828C4—942no—
829C4—1881no—
830C4—1881no—
831C4—1881no—
832C4—1881no—
833C4—1881no—
834C4#1568968311yescharacteristic
835C4#1568968811yescharacteristic
836C4#1568970811yescharacteristic
837C4#1568970811yescharacteristic
838C2—42no—
839C2—42no—
840C2—42no—
841C2—3761no—
842C2#2024604311yescharacteristic
843C2#2025210911yescharacteristic
844C2#2025212011yescharacteristic
845C2#2025241911yescharacteristic
846C2#2025242711yescharacteristic
847C2#2025243311yescharacteristic
848C2#2025244811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC47×#1779C2
prime radicalC2×#13093993C4
cosocleC22×C4×C47C24
hypercenter#1779D47
hypocenterC47#22038
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #1779

Complements

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

NH ≅ G/Ntype
1. C2×#15689198C2semidirect
2. C2×#15689087C2semidirect
4. #20244184C2semidirect
5. #20244180C2semidirect
6. #20243998C2semidirect
7. #20243997C2semidirect
8. #20243997C2semidirect
9. #20243991C2semidirect
10. #20243683C2semidirect
11. #20243682C2semidirect
12. #20243682C2semidirect
13. #20243570C2semidirect
14. #20243174C2semidirect
15. C47×#1779C2semidirect
18. C22×#10625324C22semidirect
24. C2×Dic47⋊C8C22semidirect
25. C2×Dic47⋊C8C22semidirect
26. C2×Dic47⋊C8C22semidirect
32. C2×(C2×D47)⋊C8C22semidirect
33. C2×(C2×D47)⋊C8C22semidirect
34. C2×(C2×D47)⋊C8C22semidirect
35. C2×#13093934C22semidirect
36. C2×C8×Dic47C22semidirect
37. C2×C8×Dic47C22semidirect
48. #15688877C22semidirect
49. #15688877C22semidirect
50. #15688877C22semidirect
51. #15688877C22semidirect
52. #15688877C22semidirect
53. #15688877C22semidirect
70. C2×#10625329D4semidirect
233. C22⋊Dic47M16semidirect
427. #1779D47semidirect
485. C47#22038semidirect

Maximal subgroups

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

subgroupindex
C2×#156891982
C2×#156890872
C4×#130939932
#202441842
#202441802
#202439982
#202439972
#202439912
#202436832
#202436822
#202435702
#202431742
C47×#17792
#2203847