Finite Group Databasebeta

← C2×#20252431 #27081023

Subgroups — C2×#20252431 #27081023

Order 12032.

2306 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689630C211yesmaximal, characteristic
2#20252431C2116yesmaximal, direct product factor
3C2×#15689199C211yesmaximal, characteristic, complemented
4C2×#15689198C211yesmaximal, characteristic, complemented
5C2×#15689197C211yesmaximal, characteristic, complemented
6C2×#15689194C211yesmaximal, characteristic, complemented
7C2×#15689192C211yesmaximal, characteristic, complemented
8C2×#15689191C211yesmaximal, characteristic, complemented
9C2×C8×C22⋊D47C211yesmaximal, characteristic, complemented
10C2×(C22⋊D47)⋊C8C211yesmaximal, characteristic, complemented
11C2×#15689181C211yesmaximal, characteristic, complemented
12C2×#15689181C211yesmaximal, characteristic, complemented
13C2×#15689090C211yesmaximal, characteristic, complemented
14C2×#15689085C211yesmaximal, characteristic, complemented
15C2×C22⋊C8×D47C211yesmaximal, characteristic, complemented
16C2×C47×#408C211yesmaximal, characteristic, complemented
17C23×C4×D47C2211yescharacteristic
18C22×#10625329C2211yescharacteristic, complemented
19C22×#10625324C2211yescharacteristic
20C22×#10625324C2211yescharacteristic
21C23×C47⋊C8C2211yescharacteristic, complemented
22C22×C8×D47C2211yescharacteristic
23C22×C8×D47C2211yescharacteristic
24#15689630C418yes—
25#15689630C2218yes—
26C2×#13094005C411yescharacteristic
27C2×#13094005C411yescharacteristic
28C2×#13094000C411yescharacteristic
29C2×#13094000C411yescharacteristic
30C2×#13093995C411yescharacteristic
31C2×#13093995C411yescharacteristic
32C2×#13093992C411yescharacteristic
33C2×#13093992C411yescharacteristic
34C2×C4×C22⋊D47C2211yescharacteristic
35C2×C4×C22⋊D47C2211yescharacteristic
36C2×C4×C22⋊D47C2211yescharacteristic
37C2×C4×C22⋊D47C2211yescharacteristic
38C2×#13093983C2211yescharacteristic
39#15689199C2218yescomplemented
40#15689198C2218yescomplemented
41#15689197C2218yescomplemented
42#15689194C2218yescomplemented
43#15689192C2218yescomplemented
44#15689191C2218yescomplemented
45C8×C22⋊D47C2218yescomplemented
46(C22⋊D47)⋊C8C2218yescomplemented
47#15689181C2218yescomplemented
48#15689181C2218yescomplemented
49C2×Dic47⋊C8C2211yescharacteristic, complemented
50C2×Dic47⋊C8C2211yescharacteristic, complemented
51C2×Dic47⋊C8C2211yescharacteristic, complemented
52C2×Dic47⋊C8C2211yescharacteristic, complemented
53#15689090C2218yescomplemented
54#15689085C2218yescomplemented
55C2×C22⋊(C47⋊C8)C2211yescharacteristic
56C2×C22⋊(C47⋊C8)C2211yescharacteristic
57C2×C22⋊(C47⋊C8)C2211yescharacteristic, complemented
58C2×C22⋊(C47⋊C8)C2211yescharacteristic, complemented
59C2×(C2×D47)⋊C8C2211yescharacteristic
60C2×(C2×D47)⋊C8C2211yescharacteristic
61C2×(C2×D47)⋊C8C2211yescharacteristic
62C2×(C2×D47)⋊C8C2211yescharacteristic
63C22⋊C8×D47C2218yescomplemented
64C2×#13093934C2211yescharacteristic, complemented
65C2×#13093934C2211yescharacteristic, complemented
66C2×C8×Dic47C2211yescharacteristic, complemented
67C2×C8×Dic47C2211yescharacteristic, complemented
68C22×#41×C47C2211yescharacteristic
69C22×M16×C47C2211yescharacteristic, complemented
70C23×C8×C47C2211yescharacteristic, complemented
71C47×#408C2218yescomplemented
72C2×C22⋊C8×C47C2211yescharacteristic
73C2×C22⋊C8×C47C2211yescharacteristic
74C2×C22⋊C8×C47C2211yescharacteristic, complemented
75C2×C22⋊C8×C47C2211yescharacteristic, complemented
76C24×D47C2×C411yescharacteristic
77C22×C22⋊D47C2×C411yescharacteristic
78C22×C22⋊D47C2×C411yescharacteristic
79C22×C22⋊D47C2×C411yescharacteristic
80C22×C22⋊D47C2×C411yescharacteristic
81C23×Dic47C2×C411yescharacteristic
82C22×C4×D47—42no—
83C22×C4×D47—42no—
84C22×C4×D47C2×C411yescharacteristic
85C22×C4×D47C2×C411yescharacteristic
86C22×C4×D47C2×C414yes—
87C22×C4×D47C2311yescharacteristic
88C22×C4×D47C2311yescharacteristic
89C22×C4×D47C2314yes—
90C2×#10625329—42no—
91C2×#10625329C2314yescomplemented
92C2×#10625324—42no—
93C2×#10625324—42no—
94C2×#10625324C2314yes—
95C2×#10625324C2314yes—
96C22×C47⋊C8—42no—
97C22×C47⋊C8C2311yescharacteristic
98C22×C47⋊C8C2311yescharacteristic
99C22×C47⋊C8C2311yescharacteristic
100C22×C47⋊C8C2311yescharacteristic
101C22×C47⋊C8C2314yescomplemented
102C2×C8×D47—42no—
103C2×C8×D47—42no—
104C2×C8×D47C2314yes—
105C2×C8×D47C2314yes—
106#13094005C2×C418yes—
107#13094005C2×C418yes—
108#13094000C2×C418yes—
109#13094000C2×C418yes—
110#13093995C2×C418yes—
111#13093995C2×C418yes—
112#13093992C2×C418yes—
113#13093992C2×C418yes—
114C4×C22⋊D47C2×C414yes—
115C4×C22⋊D47C2×C414yes—
116C4×C22⋊D47C2×C414yes—
117C4×C22⋊D47C2×C414yes—
118C4×C22⋊D47C2314yes—
119C4×C22⋊D47C2314yes—
120C4×C22⋊D47C2314yes—
121C4×C22⋊D47C2314yes—
122#13093983C2×C414yes—
123#13093983C2314yes—
124C2×C4⋊Dic47C2×C411yescharacteristic
125C2×C4⋊Dic47C2×C411yescharacteristic
126C2×Dic47⋊C4C2×C411yescharacteristic
127C2×Dic47⋊C4C2×C411yescharacteristic
128C2×Dic47⋊C4C2×C411yescharacteristic
129C2×Dic47⋊C4C2×C411yescharacteristic
130C2×C22⋊Dic47C2×C411yescharacteristic
131C2×C22⋊Dic47C2×C411yescharacteristic
132C2×C22⋊Dic47C2×C411yescharacteristic
133C2×C22⋊Dic47C2×C411yescharacteristic
134C2×C22⋊Dic47C2×C411yescharacteristic
135C2×C22⋊Dic47C2×C411yescharacteristic
136C2×(C2×D47)⋊C4C2×C411yescharacteristic
137C2×(C2×D47)⋊C4C2×C411yescharacteristic
138C2×(C2×D47)⋊C4C2×C411yescharacteristic
139C2×(C2×D47)⋊C4C2×C411yescharacteristic
140C2×C4×Dic47C2311yescharacteristic
141C2×C4×Dic47C2311yescharacteristic
142Dic47⋊C8C2314yescomplemented
143Dic47⋊C8C2314yescomplemented
144Dic47⋊C8C2314yescomplemented
145Dic47⋊C8C2314yescomplemented
146C22⋊(C47⋊C8)C2314yes—
147C22⋊(C47⋊C8)C2314yes—
148C22⋊(C47⋊C8)C2314yescomplemented
149C22⋊(C47⋊C8)C2314yescomplemented
150(C2×D47)⋊C8C2314yes—
151(C2×D47)⋊C8C2314yes—
152(C2×D47)⋊C8C2314yes—
153(C2×D47)⋊C8C2314yes—
154#13093934C2314yescomplemented
155#13093934C2314yescomplemented
156C8×Dic47C2314yescomplemented
157C8×Dic47C2314yescomplemented
158C2×#41×C47—42no—
159C2×#41×C47—42no—
160C2×#41×C47C2×C414yes—
161C2×#41×C47C2314yes—
162C22×Q8×C47C2×C411yescharacteristic
163C22×D4×C47C2×C411yescharacteristic
164C22×D4×C47C2×C411yescharacteristic
165C22×D4×C47C2×C411yescharacteristic
166C23×C4×C47C2311yescharacteristic
167C23×C4×C47C2311yescharacteristic
168C23×C4×C47C2311yescharacteristic
169C2×M16×C47—42no—
170C2×M16×C47C2314yescomplemented
171C22×C8×C47—42no—
172C22×C8×C47C2311yescharacteristic
173C22×C8×C47C2311yescharacteristic
174C22×C8×C47C2311yescharacteristic
175C22×C8×C47C2311yescharacteristic
176C22×C8×C47C2314yescomplemented
177C22⋊C8×C47C2314yes—
178C22⋊C8×C47C2314yes—
179C22⋊C8×C47C2314yescomplemented
180C22⋊C8×C47C2314yescomplemented
181C24×C47C22×C411yescharacteristic
182C24×C47C22×C411yescharacteristic
183C24×C47C22×C411yescharacteristic
184C23×D47—24no—
185C23×D47—42no—
186C23×D47—42no—
187C23×D47C22×C411yescharacteristic
188C23×D47C22×C411yescharacteristic
189C23×D47C22×C414yes—
190#41×C47—48no—
191#41×C47—44no—
192#41×C47—44no—
193C2×Q8×C47—42no—
194C2×Q8×C47C22×C414yes—
195C2×D4×C47—42no—
196C2×D4×C47—42no—
197C2×D4×C47—42no—
198C2×D4×C47C22×C414yes—
199C2×D4×C47C22×C414yes—
200C2×D4×C47C22×C414yes—
201C22×C4×C47—22no—
202C22×C4×C47—22no—
203C22×C4×C47—22no—
204C22×C4×C47—22no—
205C22×C4×C47—22no—
206C22×C4×C47—22no—
207C22×C4×C47C22×C411yescharacteristic
208C22×C4×C47C22×C411yescharacteristic
209C22×C4×C47C22×C411yescharacteristic
210C22×C4×C47C22×C412yes—
211C22×C4×C47C22×C412yes—
212C22×C4×C47C22×C412yes—
213C22×C4×C47C2412yes—
214C22×C4×C47C2412yes—
215C22×C4×C47C2412yes—
216C22×C4×C47C2411yescharacteristic
217C2×C22⋊D47—24no—
218C2×C22⋊D47—24no—
219C2×C22⋊D47—42no—
220C2×C22⋊D47—42no—
221C2×C22⋊D47C22×C414yes—
222C2×C22⋊D47C22×C414yes—
223C2×C22⋊D47C22×C414yes—
224C2×C22⋊D47C22×C414yes—
225C22×Dic47—42no—
226C22×Dic47C22×C411yescharacteristic
227C22×Dic47C22×C411yescharacteristic
228C22×Dic47C22×C411yescharacteristic
229C22×Dic47C22×C411yescharacteristic
230C22×Dic47C22×C411yescharacteristic
231C22×Dic47C22×C411yescharacteristic
232C22×Dic47C22×C414yes—
233C2×C4×D47—22no—
234C2×C4×D47—22no—
235C2×C4×D47—22no—
236C2×C4×D47—22no—
237C2×C4×D47—48no—
238C2×C4×D47—44no—
239C2×C4×D47—44no—
240C2×C4×D47—42no—
241C2×C4×D47—42no—
242C2×C4×D47C22×C412yes—
243C2×C4×D47C22×C412yes—
244C2×C4×D47C22×C414yes—
245C2×C4×D47C22×C414yes—
246C2×C4×D47C2412yes—
247C2×C4×D47C2412yes—
248M16×C47—44no—
249C2×C8×C47—22no—
250C2×C8×C47—22no—
251C2×C8×C47—22no—
252C2×C8×C47—22no—
253C2×C8×C47—44no—
254C2×C8×C47C2412yes—
255C2×C8×C47C2412yes—
256C2×C8×C47C2412yes—
257C2×C8×C47C2412yes—
258C22⋊Dic47C22×C414yes—
259C22⋊Dic47C22×C414yes—
260C22⋊Dic47C22×C414yes—
261C22⋊Dic47C22×C414yes—
262C22⋊Dic47C22×C414yes—
263C22⋊Dic47C22×C414yes—
264(C2×D47)⋊C4C22×C414yes—
265(C2×D47)⋊C4C22×C414yes—
266(C2×D47)⋊C4C22×C414yes—
267(C2×D47)⋊C4C22×C414yes—
268C4⋊Dic47C22×C414yes—
269C4⋊Dic47C22×C414yes—
270Dic47⋊C4C22×C414yes—
271Dic47⋊C4C22×C414yes—
272Dic47⋊C4C22×C414yes—
273Dic47⋊C4C22×C414yes—
274C4×Dic47C22×C412yes—
275C4×Dic47C22×C412yes—
276C4×Dic47C2412yes—
277C4×Dic47C2412yes—
278#10625329—44no—
279C2×C47⋊C8—22no—
280C2×C47⋊C8—22no—
281C2×C47⋊C8—22no—
282C2×C47⋊C8—22no—
283C2×C47⋊C8—44no—
284C2×C47⋊C8C2412yes—
285C2×C47⋊C8C2412yes—
286C2×C47⋊C8C2412yes—
287C2×C47⋊C8C2412yes—
288#10625324—44no—
289#10625324—44no—
290C8×D47—44no—
291C8×D47—44no—
292C23×C47—22no—
293C23×C47—22no—
294C23×C47—22no—
295C23×C47—22no—
296C23×C47—22no—
297C23×C47—22no—
298C23×C47—22no—
299C23×C47—22no—
300C23×C47—22no—
301C23×C47C23×C412yes—
302C23×C47C23×C412yes—
303C23×C47C23×C412yes—
304C23×C47C23×C411yescharacteristic
305C22×D47—22no—
306C22×D47—22no—
307C22×D47—22no—
308C22×D47—22no—
309C22×D47—22no—
310C22×D47—28no—
311C22×D47—44no—
312C22×D47—44no—
313C22×D47—416no—
314C22×D47#13114yes—
315C22×D47C23×C412yes—
316C22×D47C23×C412yes—
317Q8×C47—44no—
318D4×C47—44no—
319D4×C47—44no—
320D4×C47—44no—
321C2×C4×C47—22no—
322C2×C4×C47—22no—
323C2×C4×C47—22no—
324C2×C4×C47—24no—
325C2×C4×C47—24no—
326C2×C4×C47—24no—
327C2×C4×C47—22no—
328C2×C4×C47—22no—
329C2×C4×C47—22no—
330C2×C4×C47—22no—
331C2×C4×C47—22no—
332C2×C4×C47—22no—
333C2×C4×C47C23×C412yes—
334C2×C4×C47C23×C412yes—
335C2×C4×C47C23×C412yes—
336C2×C4×C47C23×C411yescharacteristic
337C2×C4×C47H(5,𝔽2)12yes—
338C2×C4×C47H(5,𝔽2)12yes—
339C2×C4×C47C2511yescharacteristic
340C22⋊D47—28no—
341C22⋊D47—28no—
342C22⋊D47—44no—
343C22⋊D47—44no—
344C2×Dic47—22no—
345C2×Dic47—22no—
346C2×Dic47—22no—
347C2×Dic47—22no—
348C2×Dic47—22no—
349C2×Dic47—22no—
350C2×Dic47—44no—
351C2×Dic47C23×C412yes—
352C2×Dic47C23×C412yes—
353C2×Dic47C23×C412yes—
354C2×Dic47C23×C412yes—
355C2×Dic47C23×C412yes—
356C2×Dic47C23×C412yes—
357C4×D47—24no—
358C4×D47—24no—
359C4×D47—22no—
360C4×D47—22no—
361C4×D47—22no—
362C4×D47—22no—
363C4×D47—44no—
364C4×D47—44no—
365C8×C47—22no—
366C8×C47—22no—
367C8×C47—22no—
368C8×C47—22no—
369C47⋊C8—22no—
370C47⋊C8—22no—
371C47⋊C8—22no—
372C47⋊C8—22no—
373C2×#2976—471nomaximal, Sylow
374C22×C47—22no—
375C22×C47—22no—
376C22×C47—22no—
377C22×C47—22no—
378C22×C47—22no—
379C22×C47—22no—
380C22×C47—22no—
381C22×C47—22no—
382C22×C47—22no—
383C22×C47—44no—
384C22×C47—44no—
385C22×C47—44no—
386C22×C47#51812yes—
387C22×C47C2×#13112yes—
388C22×C47#56812yes—
389C22×C47C24×C411yescharacteristic
390C2×D47—22no—
391C2×D47—28no—
392C2×D47—22no—
393C2×D47—22no—
394C2×D47—22no—
395C2×D47—22no—
396C2×D47—416no—
397C2×D47—44no—
398C2×D47C2×#13114yes—
399C4×C47—22no—
400C4×C47—22no—
401C4×C47—22no—
402C4×C47#51812yes—
403C4×C47C2×H(5,𝔽2)11yescharacteristic
404C4×C47C2×H(5,𝔽2)11yescharacteristic
405Dic47—22no—
406Dic47—22no—
407Dic47—22no—
408Dic47—22no—
409Dic47—22no—
410Dic47—22no—
411C2×#525—471no—
412#2976—4716no—
413C2×#436—471no—
414C2×#436—471no—
415C2×#435—471no—
416C2×#435—471no—
417C2×#435—471no—
418C2×#435—471no—
419C2×C8×D4—471no—
420C2×C8×D4—471no—
421C2×#433—471no—
422C2×#433—471no—
423C2×#408—471no—
424C2×#408D4711yescharacteristic, complemented
425C2×#407—471no—
426C22×C22⋊C8—471no—
427C2×C47—42no—
428C2×C47—42no—
429C2×C47—42no—
430C2×C47#297614yescomplemented
431C2×C47C2×#51811yescharacteristic
432C2×C47C22×#13111yescharacteristic
433C2×C47C2×#56811yescharacteristic
434D47—24no—
435D47—42no—
436C22×#41C2×D4711yescharacteristic
437C24×C4—471no—
438C22×M16—471no—
439C22×M16—471no—
440C22×M16—471no—
441C22×M16C2×D4711yescharacteristic, complemented
442C23×C8—471no—
443C23×C8—471no—
444C23×C8—471no—
445C23×C8C2×D4711yescharacteristic, complemented
446#525—478no—
447#525—478no—
448C2×#123—471no—
449C2×#123—471no—
450C2×C22⋊Q8—471no—
451C2×C22⋊Q8—471no—
452C2×#121—471no—
453C2×#121—471no—
454C2×#120—471no—
455C2×#120—471no—
456C2×C4×D4—471no—
457C2×C4×D4—471no—
458C2×C4×D4—471no—
459C2×C4×D4—471no—
460C2×#117—471no—
461#436—478no—
462#436—478no—
463#435—478no—
464#435—478no—
465#435—478no—
466#435—478no—
467C8×D4—478no—
468C8×D4—478no—
469#433—478no—
470#433—478no—
471C2×C4⋊C8—471no—
472C2×C4⋊C8—471no—
473C2×C4⋊C8—471no—
474C2×C4⋊C8—471no—
475#408—478no—
476#408C2×D4718yescomplemented
477#407—478no—
478C2×C22⋊C8—471no—
479C2×C22⋊C8—471no—
480C2×C22⋊C8—471no—
481C2×C22⋊C8—471no—
482C2×C22⋊C8—471no—
483C2×C22⋊C8—471no—
484C2×C22⋊C8—471no—
485C2×C22⋊C8—471no—
486C2×C22⋊C8—478no—
487C2×C22⋊C8C2×D4711yescharacteristic
488C2×C22⋊C8C2×D4711yescharacteristic
489C2×C22⋊C8C2×D4711yescharacteristic, complemented
490C2×C22⋊C8C2×D4711yescharacteristic, complemented
491C2×#97—471no—
492C2×#97—471no—
493C2×C4×C8—471no—
494C2×C4×C8—471no—
495C47C2×#297611yescharacteristic, complemented, Sylow
496C25—471no—
497C2×#41—42no—
498C2×#41—42no—
499C2×#41C4×D4714yes—
500C2×#41C22×D4714yes—
501C22×Q8C4×D4711yescharacteristic
502C22×D4—471no—
503C22×D4—471no—
504C22×D4—471no—
505C22×D4—471no—
506C22×D4C4×D4711yescharacteristic
507C22×D4C4×D4711yescharacteristic
508C22×D4C4×D4711yescharacteristic
509C23×C4—471no—
510C23×C4—471no—
511C23×C4—471no—
512C23×C4—471no—
513C23×C4—471no—
514C23×C4—474no—
515C23×C4—474no—
516C23×C4—1882no—
517C23×C4—1882no—
518C23×C4C22×D4711yescharacteristic
519C23×C4C22×D4711yescharacteristic
520C23×C4C22×D4711yescharacteristic
521C2×M16—42no—
522C2×M16—474no—
523C2×M16—474no—
524C2×M16—474no—
525C2×M16—1882no—
526C2×M16—1882no—
527C2×M16—1882no—
528C2×M16C22×D4714yescomplemented
529C22×C8—42no—
530C22×C8—471no—
531C22×C8—471no—
532C22×C8—471no—
533C22×C8—471no—
534C22×C8—474no—
535C22×C8—474no—
536C22×C8—474no—
537C22×C8—1882no—
538C22×C8—1882no—
539C22×C8—1882no—
540C22×C8C22×D4711yescharacteristic
541C22×C8C22×D4711yescharacteristic
542C22×C8C22×D4711yescharacteristic
543C22×C8C22×D4711yescharacteristic
544C22×C8C22×D4714yescomplemented
545#123—478no—
546#123—478no—
547C22⋊Q8—478no—
548C22⋊Q8—478no—
549#121—478no—
550#121—478no—
551#120—478no—
552#120—478no—
553C4×D4—474no—
554C4×D4—474no—
555C4×D4—474no—
556C4×D4—474no—
557C4×D4—474no—
558C4×D4—474no—
559C4×D4—474no—
560C4×D4—474no—
561#117—474no—
562#117—474no—
563C2×C4⋊C4—471no—
564C2×C4⋊C4—471no—
565C2×C4⋊C4—471no—
566C2×C4⋊C4—471no—
567C2×C4⋊C4—471no—
568C2×C4⋊C4—471no—
569C2×C22⋊C4—471no—
570C2×C22⋊C4—471no—
571C2×C22⋊C4—471no—
572C2×C22⋊C4—471no—
573C2×C22⋊C4—471no—
574C2×C22⋊C4—471no—
575C2×C22⋊C4—471no—
576C2×C22⋊C4—471no—
577C2×C22⋊C4—471no—
578C2×C22⋊C4—471no—
579C2×C42—471no—
580C2×C42—471no—
581C4⋊C8—474no—
582C4⋊C8—474no—
583C4⋊C8—474no—
584C4⋊C8—474no—
585C22⋊C8—474no—
586C22⋊C8—474no—
587C22⋊C8—474no—
588C22⋊C8—474no—
589C22⋊C8—474no—
590C22⋊C8—474no—
591C22⋊C8—474no—
592C22⋊C8—474no—
593C22⋊C8C22×D4714yes—
594C22⋊C8C22×D4714yes—
595C22⋊C8C22×D4714yescomplemented
596C22⋊C8C22×D4714yescomplemented
597#97—474no—
598#97—474no—
599C4×C8—474no—
600C4×C8—474no—
601C24—471no—
602C24—471no—
603C24—474no—
604C24—944no—
605C24—1882no—
606C24—1882no—
607C24C2×C4×D4711yescharacteristic
608C24C2×C4×D4711yescharacteristic
609C24C2×C4×D4711yescharacteristic
610#41—48no—
611#41—44no—
612#41—44no—
613C2×Q8—42no—
614C2×Q8C2×C4×D4714yes—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—474no—
619C2×D4—474no—
620C2×D4—474no—
621C2×D4—474no—
622C2×D4—944no—
623C2×D4—944no—
624C2×D4—1882no—
625C2×D4—1882no—
626C2×D4C2×C4×D4714yes—
627C2×D4C2×C4×D4714yes—
628C2×D4C2×C4×D4714yes—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—471no—
636C22×C4—471no—
637C22×C4—471no—
638C22×C4—471no—
639C22×C4—471no—
640C22×C4—471no—
641C22×C4—474no—
642C22×C4—472no—
643C22×C4—472no—
644C22×C4—472no—
645C22×C4—472no—
646C22×C4—474no—
647C22×C4—474no—
648C22×C4—942no—
649C22×C4—942no—
650C22×C4—942no—
651C22×C4—942no—
652C22×C4—1888no—
653C22×C4—1884no—
654C22×C4—1884no—
655C22×C4—1882no—
656C22×C4—1882no—
657C22×C4—1882no—
658C22×C4C2×C4×D4711yescharacteristic
659C22×C4C2×C4×D4711yescharacteristic
660C22×C4C2×C4×D4711yescharacteristic
661C22×C4C2×C4×D4712yes—
662C22×C4C2×C4×D4712yes—
663C22×C4C2×C4×D4712yes—
664C22×C4C23×D4712yes—
665C22×C4C23×D4712yes—
666C22×C4C23×D4712yes—
667C22×C4C23×D4711yescharacteristic
668M16—44no—
669M16—1884no—
670M16—1884no—
671M16—1884no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—22no—
675C2×C8—22no—
676C2×C8—44no—
677C2×C8—472no—
678C2×C8—472no—
679C2×C8—472no—
680C2×C8—472no—
681C2×C8—942no—
682C2×C8—942no—
683C2×C8—942no—
684C2×C8—942no—
685C2×C8—1884no—
686C2×C8—1884no—
687C2×C8—1884no—
688C2×C8C23×D4712yes—
689C2×C8C23×D4712yes—
690C2×C8C23×D4712yes—
691C2×C8C23×D4712yes—
692C4⋊C4—474no—
693C4⋊C4—474no—
694C4⋊C4—474no—
695C4⋊C4—474no—
696C4⋊C4—474no—
697C4⋊C4—474no—
698C22⋊C4—474no—
699C22⋊C4—474no—
700C22⋊C4—474no—
701C22⋊C4—474no—
702C22⋊C4—474no—
703C22⋊C4—474no—
704C22⋊C4—474no—
705C22⋊C4—474no—
706C22⋊C4—474no—
707C22⋊C4—474no—
708C42—472no—
709C42—472no—
710C42—472no—
711C42—472no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—474no—
722C23—472no—
723C23—472no—
724C23—948no—
725C23—942no—
726C23—942no—
727C23—942no—
728C23—942no—
729C23—942no—
730C23—1884no—
731C23—1884no—
732C23—18816no—
733C23C22×C4×D4712yes—
734C23C22×C4×D4712yes—
735C23C22×C4×D4712yes—
736C23C22×C4×D4711yescharacteristic
737Q8—44no—
738D4—44no—
739D4—44no—
740D4—44no—
741D4—948no—
742D4—948no—
743D4—1884no—
744D4—1884no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—472no—
758C2×C4—472no—
759C2×C4—472no—
760C2×C4—472no—
761C2×C4—472no—
762C2×C4—472no—
763C2×C4—942no—
764C2×C4—942no—
765C2×C4—942no—
766C2×C4—942no—
767C2×C4—942no—
768C2×C4—942no—
769C2×C4—944no—
770C2×C4—944no—
771C2×C4—942no—
772C2×C4—942no—
773C2×C4—942no—
774C2×C4—942no—
775C2×C4—1884no—
776C2×C4—1884no—
777C2×C4—1884no—
778C2×C4C22×C4×D4712yes—
779C2×C4C22×C4×D4712yes—
780C2×C4C22×C4×D4712yes—
781C2×C4C22×C4×D4711yescharacteristic
782C2×C4#1309406912yes—
783C2×C4#1309406912yes—
784C2×C4C24×D4711yescharacteristic
785C8—22no—
786C8—22no—
787C8—22no—
788C8—22no—
789C8—942no—
790C8—942no—
791C8—942no—
792C8—942no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—44no—
803C22—44no—
804C22—44no—
805C22—474no—
806C22—948no—
807C22—942no—
808C22—942no—
809C22—942no—
810C22—942no—
811C22—942no—
812C22—18816no—
813C22—1884no—
814C22#1568959612yes—
815C22#131×D4712yes—
816C22#1568988812yes—
817C22C23×C4×D4711yescharacteristic
818C4—22no—
819C4—22no—
820C4—22no—
821C4—942no—
822C4—942no—
823C4—942no—
824C4—942no—
825C4—942no—
826C4—942no—
827C4#1568959612yes—
828C4C2×#1309406911yescharacteristic
829C4C2×#1309406911yescharacteristic
830C2—42no—
831C2—42no—
832C2—42no—
833C2—944no—
834C2—1882no—
835C2#2025243114yesdirect product factor
836C2C2×#1568959611yescharacteristic
837C2C2×#131×D4711yescharacteristic
838C2C2×#1568988811yescharacteristic
subgroupG/H
centerC22×C4C23×D47
commutatorC22×C47C24×C4
FrattiniC2×C4C24×D47
FittingC2×C47×#408C2
socleC23×C47C23×C4
prime radicalC2×#15689630C2
cosocleC2×C4×C47C25
hypercenterC2×#408D47
hypocenterC47C2×#2976
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×#408

Complements

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

NH ≅ G/Ntype
2. #20252431C2direct (N × H)
3. C2×#15689199C2semidirect
4. C2×#15689198C2semidirect
5. C2×#15689197C2semidirect
6. C2×#15689194C2semidirect
7. C2×#15689192C2semidirect
8. C2×#15689191C2semidirect
9. C2×C8×C22⋊D47C2semidirect
10. C2×(C22⋊D47)⋊C8C2semidirect
11. C2×#15689181C2semidirect
12. C2×#15689181C2semidirect
13. C2×#15689090C2semidirect
14. C2×#15689085C2semidirect
15. C2×C22⋊C8×D47C2semidirect
16. C2×C47×#408C2semidirect
18. C22×#10625329C22semidirect
21. C23×C47⋊C8C22semidirect
39. #15689199C22semidirect
40. #15689198C22semidirect
41. #15689197C22semidirect
42. #15689194C22semidirect
43. #15689192C22semidirect
44. #15689191C22semidirect
45. C8×C22⋊D47C22semidirect
46. (C22⋊D47)⋊C8C22semidirect
47. #15689181C22semidirect
48. #15689181C22semidirect
49. C2×Dic47⋊C8C22semidirect
50. C2×Dic47⋊C8C22semidirect
51. C2×Dic47⋊C8C22semidirect
52. C2×Dic47⋊C8C22semidirect
53. #15689090C22semidirect
54. #15689085C22semidirect
57. C2×C22⋊(C47⋊C8)C22semidirect
58. C2×C22⋊(C47⋊C8)C22semidirect
63. C22⋊C8×D47C22semidirect
64. C2×#13093934C22semidirect
65. C2×#13093934C22semidirect
66. C2×C8×Dic47C22semidirect
67. C2×C8×Dic47C22semidirect
69. C22×M16×C47C22semidirect
70. C23×C8×C47C22semidirect
71. C47×#408C22semidirect
74. C2×C22⋊C8×C47C22semidirect
75. C2×C22⋊C8×C47C22semidirect
91. C2×#10625329C23semidirect
101. C22×C47⋊C8C23semidirect
142. Dic47⋊C8C23semidirect
143. Dic47⋊C8C23semidirect
144. Dic47⋊C8C23semidirect
145. Dic47⋊C8C23semidirect
148. C22⋊(C47⋊C8)C23semidirect
149. C22⋊(C47⋊C8)C23semidirect
154. #13093934C23semidirect
155. #13093934C23semidirect
156. C8×Dic47C23semidirect
157. C8×Dic47C23semidirect
170. C2×M16×C47C23semidirect
176. C22×C8×C47C23semidirect
179. C22⋊C8×C47C23semidirect
180. C22⋊C8×C47C23semidirect
424. C2×#408D47semidirect
430. C2×C47#2976semidirect
441. C22×M16C2×D47semidirect
445. C23×C8C2×D47semidirect
476. #408C2×D47semidirect
489. C2×C22⋊C8C2×D47semidirect
490. C2×C22⋊C8C2×D47semidirect
495. C47C2×#2976semidirect
528. C2×M16C22×D47semidirect
544. C22×C8C22×D47semidirect
595. C22⋊C8C22×D47semidirect
596. C22⋊C8C22×D47semidirect
835. C2#20252431direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896302
#202524312
C2×#156891992
C2×#156891982
C2×#156891972
C2×#156891942
C2×#156891922
C2×#156891912
C2×C8×C22⋊D472
C2×(C22⋊D47)⋊C82
C2×#156891812
C2×#156890902
C2×#156890852
C2×C22⋊C8×D472
C2×C47×#4082
C2×#297647