Finite Group Databasebeta

← C2×#20246370 #26375770

Subgroups — C2×#20246370 #26375770

Order 12032.

5942 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093994C211yesmaximal, characteristic
2C22×C4×D188C211yesmaximal, characteristic, complemented
3C22×(C22⋊D47)⋊C4C211yesmaximal, characteristic, complemented
4C23×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
5C22×C22⋊C4×D47C211yesmaximal, characteristic, complemented
6#20246370C2116yesmaximal, direct product factor
7C2×#15689025C211yesmaximal, characteristic, complemented
8C2×#15689015C211yesmaximal, characteristic, complemented
9C2×#15689014C211yesmaximal, characteristic, complemented
10C2×#15689002C211yesmaximal, characteristic, complemented
11C2×#15689001C211yesmaximal, characteristic, complemented
12C2×#15689001C211yesmaximal, characteristic, complemented
13C2×#15688998C211yesmaximal, characteristic, complemented
14C2×#15688997C211yesmaximal, characteristic, complemented
15C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
16C2×C4×C22⋊C4×C47C211yesmaximal, characteristic, complemented
17C25×D47C2211yescharacteristic
18C23×D188C2211yescharacteristic
19C23×D188C2211yescharacteristic
20C23×C22⋊D47C2211yescharacteristic
21C24×Dic47C2211yescharacteristic
22C23×C4×D47C2211yescharacteristic
23C23×C4×D47C2211yescharacteristic
24C23×C4×D47C2211yescharacteristic, complemented
25C2×#13093994C4116yescomplemented
26C2×#13093994C2218yes—
27C2×C4×D188—28no—
28C2×C4×D188C2218yescomplemented
29C2×(C22⋊D47)⋊C4—28no—
30C2×(C22⋊D47)⋊C4C2218yescomplemented
31C22×C4⋊Dic47C2211yescharacteristic, complemented
32C22×C4⋊Dic47C2211yescharacteristic, complemented
33C22×Dic47⋊C4C2211yescharacteristic, complemented
34C22×C22⋊Dic47C2211yescharacteristic
35C22×(C2×D47)⋊C4—28no—
36C22×(C2×D47)⋊C4C2211yescharacteristic
37C22×(C2×D47)⋊C4C2211yescharacteristic
38C22×(C2×D47)⋊C4C2211yescharacteristic
39C22×(C2×D47)⋊C4C2211yescharacteristic
40C22×(C2×D47)⋊C4C2211yescharacteristic
41C22×(C2×D47)⋊C4C2211yescharacteristic
42C22×(C2×D47)⋊C4C2211yescharacteristic
43C22×(C2×D47)⋊C4C2211yescharacteristic
44C22×(C2×D47)⋊C4C2218yescomplemented
45C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
46C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
47C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
48C2×C22⋊C4×D47—28no—
49C2×C22⋊C4×D47C2218yescomplemented
50C22×C4×Dic47C2211yescharacteristic, complemented
51#15689025C2218yescomplemented
52#15689015C2218yescomplemented
53#15689014C2218yescomplemented
54#15689002C2218yescomplemented
55#15689001C2218yescomplemented
56#15689001C2218yescomplemented
57#15688998C2218yescomplemented
58#15688997C2218yescomplemented
59C4×(C2×D47)⋊C4C2218yescomplemented
60C2×C47⋊#95C2211yescharacteristic, complemented
61C2×C47⋊#95C2211yescharacteristic, complemented
62C2×C47⋊#95C2211yescharacteristic, complemented
63C2×C47⋊#95C2211yescharacteristic, complemented
64C24×C4×C47C2211yescharacteristic
65C22×C22⋊C4×C47C2211yescharacteristic
66C22×C22⋊C4×C47C2211yescharacteristic
67C22×C42×C47C2211yescharacteristic, complemented
68C22×C42×C47C2211yescharacteristic, complemented
69C4×C22⋊C4×C47C2218yescomplemented
70C2×#95×C47C2211yescharacteristic, complemented
71C2×#95×C47C2211yescharacteristic, complemented
72C24×D47—24no—
73C24×D47—24no—
74C24×D47—24no—
75C24×D47—24no—
76C24×D47—42no—
77C24×D47—42no—
78C24×D47C2×C418yescomplemented
79C24×D47C2311yescharacteristic
80C24×D47C2311yescharacteristic
81C24×D47C2314yes—
82C24×D47C2311yescharacteristic
83C22×D188—24no—
84C22×D188—24no—
85C22×D188—42no—
86C22×D188—42no—
87C22×D188C2×C418yescomplemented
88C22×D188C2×C418yescomplemented
89C22×D188C2314yes—
90C22×D188C2314yes—
91C22×C22⋊D47—24no—
92C22×C22⋊D47—24no—
93C22×C22⋊D47C2×C418yescomplemented
94C22×C22⋊D47C2314yes—
95C23×Dic47—24no—
96C23×Dic47—24no—
97C23×Dic47—42no—
98C23×Dic47C2311yescharacteristic
99C23×Dic47C2311yescharacteristic
100C23×Dic47C2311yescharacteristic
101C23×Dic47C2314yes—
102C23×Dic47C2311yescharacteristic
103C23×Dic47C2311yescharacteristic
104C22×C4×D47—24no—
105C22×C4×D47—24no—
106C22×C4×D47—24no—
107C22×C4×D47—24no—
108C22×C4×D47—24no—
109C22×C4×D47—24no—
110C22×C4×D47—42no—
111C22×C4×D47—42no—
112C22×C4×D47—42no—
113C22×C4×D47C2314yes—
114C22×C4×D47C2314yes—
115C22×C4×D47C2314yescomplemented
116#13093994C2×C4164yescomplemented
117C4×D188—232no—
118(C22⋊D47)⋊C4—232no—
119C2×C4⋊Dic47—24no—
120C2×C4⋊Dic47—42no—
121C2×C4⋊Dic47C2314yescomplemented
122C2×C4⋊Dic47C2314yescomplemented
123C2×Dic47⋊C4—24no—
124C2×Dic47⋊C4C2314yescomplemented
125C2×C22⋊Dic47—24no—
126C2×C22⋊Dic47C2314yes—
127C2×(C2×D47)⋊C4—24no—
128C2×(C2×D47)⋊C4—24no—
129C2×(C2×D47)⋊C4—24no—
130C2×(C2×D47)⋊C4—24no—
131C2×(C2×D47)⋊C4—24no—
132C2×(C2×D47)⋊C4—24no—
133C2×(C2×D47)⋊C4—24no—
134C2×(C2×D47)⋊C4—232no—
135C2×(C2×D47)⋊C4—42no—
136C2×(C2×D47)⋊C4C2×C418yescomplemented
137C2×(C2×D47)⋊C4C2×C418yescomplemented
138C2×(C2×D47)⋊C4D418yescomplemented
139C2×(C2×D47)⋊C4C2314yes—
140C2×(C2×D47)⋊C4C2314yes—
141C2×(C2×D47)⋊C4C2314yes—
142C2×(C2×D47)⋊C4C2314yes—
143C2×(C2×D47)⋊C4C2314yes—
144C2×(C2×D47)⋊C4C2314yes—
145C2×(C2×D47)⋊C4C2314yes—
146C2×(C2×D47)⋊C4C2314yes—
147C2×(C2×D47)⋊C4C2314yescomplemented
148C2×(C2×D47)⋊C4C2314yescomplemented
149C2×(C2×D47)⋊C4C2314yescomplemented
150C22⋊C4×D47—232no—
151C2×C4×Dic47—24no—
152C2×C4×Dic47C2314yescomplemented
153C47⋊#95C2314yescomplemented
154C47⋊#95C2314yescomplemented
155C47⋊#95C2314yescomplemented
156C47⋊#95C2314yescomplemented
157C25×C47C2311yescharacteristic
158C23×C4×C47—24no—
159C23×C4×C47—24no—
160C23×C4×C47—42no—
161C23×C4×C47C2311yescharacteristic
162C23×C4×C47C2314yes—
163C23×C4×C47C2311yescharacteristic
164C23×C4×C47C2311yescharacteristic
165C23×C4×C47C2311yescharacteristic
166C23×C4×C47C2311yescharacteristic
167C23×C4×C47C2311yescharacteristic
168C2×C22⋊C4×C47C2×C418yescomplemented
169C2×C22⋊C4×C47D418yescomplemented
170C2×C22⋊C4×C47C2314yes—
171C2×C22⋊C4×C47C2314yes—
172C2×C42×C47—24no—
173C2×C42×C47—42no—
174C2×C42×C47C2314yescomplemented
175C2×C42×C47C2314yescomplemented
176#95×C47C2314yescomplemented
177#95×C47C2314yescomplemented
178C24×C47—22no—
179C24×C47—22no—
180C24×C47—22no—
181C24×C47—22no—
182C24×C47C22×C414yes—
183C24×C47C2×D414yes—
184C24×C47#4114yes—
185C24×C47C2412yes—
186C24×C47C2411yescharacteristic
187C23×D47—22no—
188C23×D47—22no—
189C23×D47—22no—
190C23×D47—22no—
191C23×D47—232no—
192C23×D47—28no—
193C23×D47—22no—
194C23×D47—22no—
195C23×D47—22no—
196C23×D47—22no—
197C23×D47—22no—
198C23×D47—22no—
199C23×D47—28no—
200C23×D47—22no—
201C23×D47—22no—
202C23×D47—22no—
203C23×D47—22no—
204C23×D47—22no—
205C23×D47—22no—
206C23×D47—232no—
207C23×D47—28no—
208C23×D47—28no—
209C23×D47—416no—
210C23×D47—44no—
211C23×D47—44no—
212C23×D47—416no—
213C23×D47—416no—
214C23×D47—416no—
215C23×D47—416no—
216C23×D47C22×C414yes—
217C23×D47C22×C414yes—
218C23×D47C22×C414yes—
219C23×D47C22×C4116yescomplemented
220C23×D47C2×D414yes—
221C23×D47#4114yes—
222C23×D47C2412yes—
223C23×D47C2412yes—
224C23×D47C2412yes—
225C22×C4×C47—22no—
226C22×C4×C47—22no—
227C22×C4×C47—22no—
228C22×C4×C47—22no—
229C22×C4×C47—22no—
230C22×C4×C47—22no—
231C22×C4×C47—22no—
232C22×C4×C47—22no—
233C22×C4×C47—22no—
234C22×C4×C47—22no—
235C22×C4×C47—22no—
236C22×C4×C47—28no—
237C22×C4×C47—22no—
238C22×C4×C47—22no—
239C22×C4×C47—28no—
240C22×C4×C47—44no—
241C22×C4×C47—416no—
242C22×C4×C47C22×C414yes—
243C22×C4×C47C22×C414yes—
244C22×C4×C47C2×D414yes—
245C22×C4×C47C2×D414yes—
246C22×C4×C47C2×D414yes—
247C22×C4×C47C2412yes—
248C22×C4×C47C2412yes—
249C22×C4×C47C2412yes—
250C22×C4×C47C2412yes—
251C22×C4×C47C2412yes—
252C22×C4×C47C2412yes—
253C2×C22⋊D47—232no—
254C2×C22⋊D47—28no—
255C2×C22⋊D47—28no—
256C2×C22⋊D47C22×C4116yescomplemented
257C22×Dic47—22no—
258C22×Dic47—22no—
259C22×Dic47—22no—
260C22×Dic47—22no—
261C22×Dic47—22no—
262C22×Dic47—22no—
263C22×Dic47—22no—
264C22×Dic47—22no—
265C22×Dic47—22no—
266C22×Dic47—28no—
267C22×Dic47—22no—
268C22×Dic47—22no—
269C22×Dic47—22no—
270C22×Dic47—22no—
271C22×Dic47—28no—
272C22×Dic47—44no—
273C22×Dic47—416no—
274C22×Dic47C22×C414yes—
275C22×Dic47C2×D414yes—
276C22×Dic47C2412yes—
277C22×Dic47C2412yes—
278C22×Dic47C2412yes—
279C22×Dic47C2412yes—
280C22×Dic47C2412yes—
281C2×D188—232no—
282C2×D188—28no—
283C2×D188—28no—
284C2×D188—416no—
285C2×D188—44no—
286C2×D188—44no—
287C2×D188C22×C4116yescomplemented
288C2×D188C22×C4116yescomplemented
289C2×C4×D47—28no—
290C2×C4×D47—28no—
291C2×C4×D47—28no—
292C2×C4×D47—28no—
293C2×C4×D47—28no—
294C2×C4×D47—28no—
295C2×C4×D47—44no—
296C2×C4×D47—44no—
297C2×C4×D47—44no—
298C2×C4×D47—416no—
299C2×C4×D47—416no—
300C2×C4×D47—416no—
301C22⋊C4×C47C22×C4116yescomplemented
302C22⋊C4×C47C2×D4116yescomplemented
303C42×C47—28no—
304C42×C47—44no—
305C22⋊Dic47—28no—
306(C2×D47)⋊C4—28no—
307(C2×D47)⋊C4—28no—
308(C2×D47)⋊C4—28no—
309(C2×D47)⋊C4—28no—
310(C2×D47)⋊C4—28no—
311(C2×D47)⋊C4—28no—
312(C2×D47)⋊C4—28no—
313(C2×D47)⋊C4—44no—
314(C2×D47)⋊C4C22×C4116yescomplemented
315(C2×D47)⋊C4C22×C4116yescomplemented
316(C2×D47)⋊C4C2×D4116yescomplemented
317C4⋊Dic47—28no—
318C4⋊Dic47—44no—
319Dic47⋊C4—28no—
320C4×Dic47—28no—
321C23×C47—28no—
322C23×C47—28no—
323C23×C47—28no—
324C23×C47—28no—
325C23×C47—28no—
326C23×C47—28no—
327C23×C47—22no—
328C23×C47—22no—
329C23×C47—22no—
330C23×C47—22no—
331C23×C47C4×D4116yescomplemented
332C23×C47C23×C414yes—
333C23×C47C23×C412yes—
334C23×C47C22×D412yes—
335C23×C47C22×D414yes—
336C23×C47C22×D412yes—
337C23×C47C2×#4112yes—
338C23×C47C2×#4114yes—
339C23×C47C2×#4112yes—
340C23×C47H(5,𝔽2)12yes—
341C23×C47H(5,𝔽2)12yes—
342C23×C47C2511yescharacteristic
343C22×D47—28no—
344C22×D47—28no—
345C22×D47—28no—
346C22×D47—28no—
347C22×D47—28no—
348C22×D47—28no—
349C22×D47—22no—
350C22×D47—22no—
351C22×D47—22no—
352C22×D47—22no—
353C22×D47—28no—
354C22×D47—28no—
355C22×D47—28no—
356C22×D47—28no—
357C22×D47—232no—
358C22×D47—28no—
359C22×D47—28no—
360C22×D47—22no—
361C22×D47—22no—
362C22×D47—22no—
363C22×D47—22no—
364C22×D47—22no—
365C22×D47—22no—
366C22×D47—22no—
367C22×D47—22no—
368C22×D47—22no—
369C22×D47—22no—
370C22×D47—22no—
371C22×D47—22no—
372C22×D47—232no—
373C22×D47—416no—
374C22×D47—4128no—
375C22×D47—416no—
376C22×D47—416no—
377C22×D47—416no—
378C22×D47—416no—
379C22×D47—44no—
380C22×D47—44no—
381C22×D47—44no—
382C22×D47—44no—
383C22×D47—44no—
384C22×D47—44no—
385C22×D47—44no—
386C22×D47—44no—
387C22×D47C4×D4116yescomplemented
388C22×D47C23×C414yes—
389C22×D47C23×C414yes—
390C22×D47C23×C414yes—
391C22×D47C22×D414yes—
392C22×D47C2×#4114yes—
393C2×C4×C47—28no—
394C2×C4×C47—28no—
395C2×C4×C47—28no—
396C2×C4×C47—28no—
397C2×C4×C47—28no—
398C2×C4×C47—22no—
399C2×C4×C47—22no—
400C2×C4×C47—22no—
401C2×C4×C47—22no—
402C2×C4×C47—22no—
403C2×C4×C47—22no—
404C2×C4×C47—22no—
405C2×C4×C47—22no—
406C2×C4×C47—22no—
407C2×C4×C47—22no—
408C2×C4×C47—22no—
409C2×C4×C47—22no—
410C2×C4×C47—22no—
411C2×C4×C47—416no—
412C2×C4×C47—44no—
413C2×C4×C47C23×C414yes—
414C2×C4×C47C23×C414yes—
415C2×C4×C47C22×D414yes—
416C2×C4×C47C22×D414yes—
417C2×C4×C47C22×D414yes—
418C22⋊D47—232no—
419C2×Dic47—28no—
420C2×Dic47—28no—
421C2×Dic47—22no—
422C2×Dic47—22no—
423C2×Dic47—22no—
424C2×Dic47—22no—
425C2×Dic47—22no—
426C2×Dic47—22no—
427C2×Dic47—22no—
428C2×Dic47—22no—
429C2×Dic47—22no—
430C2×Dic47—22no—
431C2×Dic47—22no—
432C2×Dic47—22no—
433C2×Dic47—22no—
434C2×Dic47—416no—
435C2×Dic47—44no—
436C2×Dic47—44no—
437C2×Dic47—44no—
438C2×Dic47C23×C414yes—
439C2×Dic47C22×D414yes—
440D188—232no—
441D188—416no—
442C4×D47—416no—
443C4×D47—416no—
444C4×D47—416no—
445C2×#2358—471nomaximal, Sylow
446C22×C47—232no—
447C22×C47—24no—
448C22×C47—24no—
449C22×C47—24no—
450C22×C47—24no—
451C22×C47—24no—
452C22×C47—24no—
453C22×C47C2×C4×D414yes—
454C22×C47C2×C4×D414yes—
455C22×C47C2×C4×D418yescomplemented
456C22×C47#51814yes—
457C22×C47D4214yes—
458C22×C47#54614yes—
459C22×C47#54614yes—
460C22×C47#55114yes—
461C22×C47C24×C411yescharacteristic
462C22×C47C23×D411yescharacteristic
463C22×C47C23×D411yescharacteristic
464C22×C47C22×#4111yescharacteristic
465C22×C47C22×#4111yescharacteristic
466C22×C47C2×H(5,𝔽2)11yescharacteristic
467C22×C47C2×H(5,𝔽2)11yescharacteristic
468C2×D47—232no—
469C2×D47—24no—
470C2×D47—24no—
471C2×D47—24no—
472C2×D47—24no—
473C2×D47—24no—
474C2×D47—24no—
475C2×D47—24no—
476C2×D47—24no—
477C2×D47—24no—
478C2×D47—24no—
479C2×D47—24no—
480C2×D47—24no—
481C2×D47—464no—
482C2×D47—416no—
483C2×D47—416no—
484C2×D47—42no—
485C2×D47—42no—
486C2×D47—42no—
487C2×D47—42no—
488C2×D47—42no—
489C2×D47—42no—
490C2×D47—42no—
491C2×D47—42no—
492C2×D47C2×C4×D418yescomplemented
493C4×C47—24no—
494C4×C47—24no—
495C4×C47—24no—
496C4×C47—24no—
497C4×C47—24no—
498C4×C47—42no—
499Dic47—24no—
500Dic47—24no—
501Dic47—42no—
502Dic47—42no—
503Dic47—42no—
504C22×#120—471no—
505C22×C4×D4—471no—
506C22×C4×D4—471no—
507C23×C22⋊C4—471no—
508C23×C22⋊C4—471no—
509#2358—4716no—
510C2×#390—471no—
511C2×#388—471no—
512C2×#388—471no—
513C2×#386—471no—
514C2×#386—471no—
515C2×#386—471no—
516C2×#385—471no—
517C2×#385—471no—
518C2×C4×C22⋊C4—471no—
519C2×C4×C22⋊C4D4711yescharacteristic, complemented
520C2×C47—28no—
521C2×C47#235818yescomplemented
522C2×C47C22×C4×D411yescharacteristic
523C2×C47C22×C4×D411yescharacteristic
524C2×C47C2×#51811yescharacteristic
525C2×C47C2×D4211yescharacteristic
526C2×C47C2×#54611yescharacteristic
527C2×C47C2×#54611yescharacteristic
528C2×C47C2×#55111yescharacteristic
529D47—28no—
530D47—44no—
531D47—44no—
532C26—471no—
533C23×D4—471no—
534C23×D4—471no—
535C23×D4—471no—
536C24×C4—471no—
537C24×C4—471no—
538C24×C4—471no—
539C24×C4—471no—
540C24×C4C2×D4711yescharacteristic
541C2×#120—4716no—
542C2×#120—478no—
543C2×C4×D4—478no—
544C2×C4×D4—478no—
545C2×C4×D4—948no—
546C2×C4×D4—948no—
547C22×C4⋊C4—471no—
548C22×C4⋊C4—471no—
549C22×C4⋊C4—471no—
550C22×C22⋊C4—471no—
551C22×C22⋊C4—471no—
552C22×C22⋊C4—471no—
553C22×C22⋊C4—471no—
554C22×C22⋊C4—478no—
555C22×C22⋊C4—471no—
556C22×C22⋊C4—471no—
557C22×C22⋊C4—471no—
558C22×C22⋊C4—471no—
559C22×C22⋊C4—471no—
560C22×C22⋊C4—471no—
561C22×C22⋊C4—471no—
562C22×C22⋊C4—471no—
563C22×C22⋊C4—478no—
564C22×C22⋊C4—948no—
565C22×C22⋊C4—948no—
566C22×C22⋊C4C2×D4711yescharacteristic
567C22×C22⋊C4C2×D4711yescharacteristic
568C22×C42—471no—
569C22×C42C2×D4711yescharacteristic, complemented
570C22×C42C2×D4711yescharacteristic, complemented
571#390—478no—
572#388—478no—
573#388—478no—
574#386—478no—
575#386—478no—
576#386—478no—
577#385—478no—
578#385—478no—
579C4×C22⋊C4—478no—
580C4×C22⋊C4C2×D4718yescomplemented
581C2×#95—471no—
582C2×#95—471no—
583C2×#95—471no—
584C2×#95—471no—
585C2×#95C2×D4711yescharacteristic, complemented
586C2×#95C2×D4711yescharacteristic, complemented
587C47C2×#235811yescharacteristic, complemented, Sylow
588C25—471no—
589C25—471no—
590C25—471no—
591C25—478no—
592C25—474no—
593C25—944no—
594C25—944no—
595C25—944no—
596C25—944no—
597C25—1882no—
598C25—1882no—
599C25C22×D4711yescharacteristic
600C22×D4—478no—
601C22×D4—474no—
602C22×D4—478no—
603C22×D4—478no—
604C22×D4—474no—
605C22×D4—474no—
606C22×D4—944no—
607C22×D4—944no—
608C22×D4—944no—
609C22×D4—944no—
610C22×D4—1882no—
611C22×D4—1882no—
612C23×C4—24no—
613C23×C4—24no—
614C23×C4—42no—
615C23×C4—471no—
616C23×C4—471no—
617C23×C4—471no—
618C23×C4—471no—
619C23×C4—471no—
620C23×C4—474no—
621C23×C4—474no—
622C23×C4—474no—
623C23×C4—474no—
624C23×C4—944no—
625C23×C4—944no—
626C23×C4—944no—
627C23×C4—944no—
628C23×C4—944no—
629C23×C4—944no—
630C23×C4—944no—
631C23×C4—944no—
632C23×C4—1882no—
633C23×C4—1882no—
634C23×C4—1882no—
635C23×C4—1882no—
636C23×C4C22×D4711yescharacteristic
637C23×C4C22×D4714yes—
638C23×C4C22×D4711yescharacteristic
639C23×C4C22×D4711yescharacteristic
640C23×C4C22×D4711yescharacteristic
641C23×C4C22×D4711yescharacteristic
642C23×C4C22×D4711yescharacteristic
643#120—4764no—
644C4×D4—9432no—
645C4×D4—9432no—
646C2×C4⋊C4—474no—
647C2×C4⋊C4—474no—
648C2×C4⋊C4—474no—
649C2×C4⋊C4—944no—
650C2×C4⋊C4—944no—
651C2×C4⋊C4—1882no—
652C2×C22⋊C4—478no—
653C2×C22⋊C4—478no—
654C2×C22⋊C4—478no—
655C2×C22⋊C4—474no—
656C2×C22⋊C4—474no—
657C2×C22⋊C4—474no—
658C2×C22⋊C4—474no—
659C2×C22⋊C4—474no—
660C2×C22⋊C4—474no—
661C2×C22⋊C4—474no—
662C2×C22⋊C4—474no—
663C2×C22⋊C4—474no—
664C2×C22⋊C4—474no—
665C2×C22⋊C4—474no—
666C2×C22⋊C4—474no—
667C2×C22⋊C4—9432no—
668C2×C22⋊C4—944no—
669C2×C22⋊C4—944no—
670C2×C22⋊C4—944no—
671C2×C22⋊C4—944no—
672C2×C22⋊C4—944no—
673C2×C22⋊C4—944no—
674C2×C22⋊C4—944no—
675C2×C22⋊C4—944no—
676C2×C22⋊C4—9432no—
677C2×C22⋊C4—1882no—
678C2×C22⋊C4C4×D4718yescomplemented
679C2×C22⋊C4D18818yescomplemented
680C2×C22⋊C4C22×D4714yes—
681C2×C22⋊C4C22×D4714yes—
682C2×C42—24no—
683C2×C42—42no—
684C2×C42—474no—
685C2×C42—944no—
686C2×C42C22×D4714yescomplemented
687C2×C42C22×D4714yescomplemented
688#95—474no—
689#95—474no—
690#95—474no—
691#95—474no—
692#95C22×D4714yescomplemented
693#95C22×D4714yescomplemented
694C24—22no—
695C24—22no—
696C24—22no—
697C24—22no—
698C24—474no—
699C24—474no—
700C24—474no—
701C24—472no—
702C24—474no—
703C24—474no—
704C24—472no—
705C24—472no—
706C24—4716no—
707C24—948no—
708C24—9432no—
709C24—948no—
710C24—942no—
711C24—942no—
712C24—942no—
713C24—942no—
714C24—9432no—
715C24—942no—
716C24—942no—
717C24—948no—
718C24—942no—
719C24—942no—
720C24—942no—
721C24—942no—
722C24—942no—
723C24—948no—
724C24—942no—
725C24—942no—
726C24—942no—
727C24—942no—
728C24—942no—
729C24—18816no—
730C24—1884no—
731C24—1884no—
732C24—18816no—
733C24—18816no—
734C24—18816no—
735C24—18816no—
736C24C2×C4×D4714yes—
737C24C2×D18814yes—
738C24#1062535014yes—
739C24C23×D4712yes—
740C24C23×D4711yescharacteristic
741C2×D4—4716no—
742C2×D4—4716no—
743C2×D4—4716no—
744C2×D4—948no—
745C2×D4—9432no—
746C2×D4—948no—
747C2×D4—9432no—
748C2×D4—948no—
749C2×D4—948no—
750C2×D4—18816no—
751C2×D4—1884no—
752C2×D4—1884no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—28no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—28no—
768C22×C4—44no—
769C22×C4—416no—
770C22×C4—474no—
771C22×C4—474no—
772C22×C4—472no—
773C22×C4—472no—
774C22×C4—472no—
775C22×C4—472no—
776C22×C4—472no—
777C22×C4—948no—
778C22×C4—948no—
779C22×C4—948no—
780C22×C4—948no—
781C22×C4—942no—
782C22×C4—942no—
783C22×C4—942no—
784C22×C4—942no—
785C22×C4—942no—
786C22×C4—942no—
787C22×C4—942no—
788C22×C4—942no—
789C22×C4—942no—
790C22×C4—948no—
791C22×C4—942no—
792C22×C4—942no—
793C22×C4—942no—
794C22×C4—942no—
795C22×C4—948no—
796C22×C4—948no—
797C22×C4—948no—
798C22×C4—1884no—
799C22×C4—1884no—
800C22×C4—1884no—
801C22×C4—18816no—
802C22×C4—18816no—
803C22×C4—18816no—
804C22×C4—1884no—
805C22×C4—18816no—
806C22×C4C2×C4×D4714yes—
807C22×C4C2×C4×D4714yes—
808C22×C4C2×D18814yes—
809C22×C4C2×D18814yes—
810C22×C4D4×D4714yes—
811C22×C4C23×D4712yes—
812C22×C4C23×D4712yes—
813C22×C4C23×D4712yes—
814C22×C4C23×D4712yes—
815C22×C4C23×D4712yes—
816C22×C4C23×D4712yes—
817C4⋊C4—948no—
818C4⋊C4—948no—
819C4⋊C4—1884no—
820C22⋊C4—4716no—
821C22⋊C4—4716no—
822C22⋊C4—4716no—
823C22⋊C4—948no—
824C22⋊C4—948no—
825C22⋊C4—948no—
826C22⋊C4—948no—
827C22⋊C4—948no—
828C22⋊C4—948no—
829C22⋊C4—948no—
830C22⋊C4—948no—
831C22⋊C4—1884no—
832C22⋊C4C2×C4×D47116yescomplemented
833C22⋊C4C2×D188116yescomplemented
834C42—28no—
835C42—44no—
836C42—948no—
837C23—28no—
838C23—28no—
839C23—28no—
840C23—28no—
841C23—28no—
842C23—28no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—4716no—
848C23—474no—
849C23—474no—
850C23—474no—
851C23—474no—
852C23—474no—
853C23—9432no—
854C23—948no—
855C23—948no—
856C23—948no—
857C23—948no—
858C23—948no—
859C23—948no—
860C23—942no—
861C23—942no—
862C23—942no—
863C23—942no—
864C23—948no—
865C23—948no—
866C23—948no—
867C23—948no—
868C23—9432no—
869C23—948no—
870C23—948no—
871C23—942no—
872C23—942no—
873C23—942no—
874C23—942no—
875C23—942no—
876C23—942no—
877C23—942no—
878C23—942no—
879C23—942no—
880C23—942no—
881C23—942no—
882C23—942no—
883C23—18816no—
884C23—18816no—
885C23—18816no—
886C23—18816no—
887C23—188128no—
888C23—18816no—
889C23—1884no—
890C23—1884no—
891C23—1884no—
892C23—1884no—
893C23—1884no—
894C23—1884no—
895C23—1884no—
896C23—1884no—
897C23C4×D188116yescomplemented
898C23C22×C4×D4714yes—
899C23C22×C4×D4712yes—
900C23C2×D4×D4712yes—
901C23C22×D18814yes—
902C23C22×D18812yes—
903C23#41×D4712yes—
904C23C2×#1062535014yes—
905C23C2×#1062535012yes—
906C23#1309406912yes—
907C23#1309407012yes—
908C23C24×D4711yescharacteristic
909D4—9432no—
910D4—9432no—
911D4—18816no—
912C2×C4—28no—
913C2×C4—28no—
914C2×C4—28no—
915C2×C4—28no—
916C2×C4—28no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—416no—
931C2×C4—44no—
932C2×C4—474no—
933C2×C4—474no—
934C2×C4—948no—
935C2×C4—948no—
936C2×C4—942no—
937C2×C4—942no—
938C2×C4—942no—
939C2×C4—942no—
940C2×C4—942no—
941C2×C4—942no—
942C2×C4—942no—
943C2×C4—942no—
944C2×C4—942no—
945C2×C4—942no—
946C2×C4—942no—
947C2×C4—942no—
948C2×C4—942no—
949C2×C4—18816no—
950C2×C4—18816no—
951C2×C4—18816no—
952C2×C4—18816no—
953C2×C4—1884no—
954C2×C4—1884no—
955C2×C4—1884no—
956C2×C4C22×C4×D4714yes—
957C2×C4C22×C4×D4714yes—
958C2×C4C2×D4×D4714yes—
959C2×C4C22×D18814yes—
960C2×C4C22×D18814yes—
961C22—24no—
962C22—24no—
963C22—24no—
964C22—24no—
965C22—24no—
966C22—232no—
967C22—24no—
968C22—478no—
969C22—944no—
970C22—944no—
971C22—944no—
972C22—944no—
973C22—944no—
974C22—9432no—
975C22—944no—
976C22—944no—
977C22—944no—
978C22—944no—
979C22—944no—
980C22—944no—
981C22—944no—
982C22—18864no—
983C22—1882no—
984C22—1882no—
985C22—1882no—
986C22—1882no—
987C22—1882no—
988C22—1882no—
989C22—18816no—
990C22—18816no—
991C22—1882no—
992C22—1882no—
993C22C4×D4×D4714yes—
994C22C2×C4×D18814yes—
995C22C2×C4×D18818yescomplemented
996C22#1568959514yes—
997C22D4×D18814yes—
998C22#1568976314yes—
999C22#1568976814yes—
1000C22#1568979714yes—
1001C22C23×C4×D4711yescharacteristic
1002C22C22×D4×D4711yescharacteristic
1003C22C23×D18811yescharacteristic
1004C22C2×#41×D4711yescharacteristic
1005C22C22×#1062535011yescharacteristic
1006C22C2×#1309406911yescharacteristic
1007C22C2×#1309407011yescharacteristic
1008C4—24no—
1009C4—24no—
1010C4—24no—
1011C4—24no—
1012C4—24no—
1013C4—42no—
1014C4—944no—
1015C4—944no—
1016C4—1882no—
1017C4—1882no—
1018C4—1882no—
1019C2—28no—
1020C2—948no—
1021C2—1884no—
1022C2—1884no—
1023C2#2024637018yesdirect product factor
1024C2C2×C4×D4×D4711yescharacteristic
1025C2C22×C4×D18811yescharacteristic
1026C2C2×#1568959511yescharacteristic
1027C2C2×D4×D18811yescharacteristic
1028C2C2×#1568976311yescharacteristic
1029C2C2×#1568976811yescharacteristic
1030C2C2×#1568979711yescharacteristic
subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C4×C22⋊C4×C47C2
socleC24×C47C24
prime radicalC22×#13093994C2
cosocleC23×C47C25
hypercenterC2×C4×C22⋊C4D47
hypocenterC47C2×#2358
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C4×D188C2semidirect
3. C22×(C22⋊D47)⋊C4C2semidirect
4. C23×(C2×D47)⋊C4C2semidirect
5. C22×C22⋊C4×D47C2semidirect
6. #20246370C2direct (N × H)
7. C2×#15689025C2semidirect
8. C2×#15689015C2semidirect
9. C2×#15689014C2semidirect
10. C2×#15689002C2semidirect
11. C2×#15689001C2semidirect
12. C2×#15689001C2semidirect
13. C2×#15688998C2semidirect
14. C2×#15688997C2semidirect
15. C2×C4×(C2×D47)⋊C4C2semidirect
16. C2×C4×C22⋊C4×C47C2semidirect
24. C23×C4×D47C22semidirect
25. C2×#13093994C4semidirect
28. C2×C4×D188C22semidirect
30. C2×(C22⋊D47)⋊C4C22semidirect
31. C22×C4⋊Dic47C22semidirect
32. C22×C4⋊Dic47C22semidirect
33. C22×Dic47⋊C4C22semidirect
44. C22×(C2×D47)⋊C4C22semidirect
45. C22×(C2×D47)⋊C4C22semidirect
46. C22×(C2×D47)⋊C4C22semidirect
47. C22×(C2×D47)⋊C4C22semidirect
49. C2×C22⋊C4×D47C22semidirect
50. C22×C4×Dic47C22semidirect
51. #15689025C22semidirect
52. #15689015C22semidirect
53. #15689014C22semidirect
54. #15689002C22semidirect
55. #15689001C22semidirect
56. #15689001C22semidirect
57. #15688998C22semidirect
58. #15688997C22semidirect
59. C4×(C2×D47)⋊C4C22semidirect
60. C2×C47⋊#95C22semidirect
61. C2×C47⋊#95C22semidirect
62. C2×C47⋊#95C22semidirect
63. C2×C47⋊#95C22semidirect
67. C22×C42×C47C22semidirect
68. C22×C42×C47C22semidirect
69. C4×C22⋊C4×C47C22semidirect
70. C2×#95×C47C22semidirect
71. C2×#95×C47C22semidirect
78. C24×D47C2×C4semidirect
87. C22×D188C2×C4semidirect
88. C22×D188C2×C4semidirect
93. C22×C22⋊D47C2×C4semidirect
115. C22×C4×D47C23semidirect
116. #13093994C2×C4semidirect
121. C2×C4⋊Dic47C23semidirect
122. C2×C4⋊Dic47C23semidirect
124. C2×Dic47⋊C4C23semidirect
136. C2×(C2×D47)⋊C4C2×C4semidirect
137. C2×(C2×D47)⋊C4C2×C4semidirect
138. C2×(C2×D47)⋊C4D4semidirect
147. C2×(C2×D47)⋊C4C23semidirect
148. C2×(C2×D47)⋊C4C23semidirect
149. C2×(C2×D47)⋊C4C23semidirect
152. C2×C4×Dic47C23semidirect
153. C47⋊#95C23semidirect
154. C47⋊#95C23semidirect
155. C47⋊#95C23semidirect
156. C47⋊#95C23semidirect
168. C2×C22⋊C4×C47C2×C4semidirect
169. C2×C22⋊C4×C47D4semidirect
174. C2×C42×C47C23semidirect
175. C2×C42×C47C23semidirect
176. #95×C47C23semidirect
177. #95×C47C23semidirect
219. C23×D47C22×C4semidirect
256. C2×C22⋊D47C22×C4semidirect
287. C2×D188C22×C4semidirect
288. C2×D188C22×C4semidirect
301. C22⋊C4×C47C22×C4semidirect
302. C22⋊C4×C47C2×D4semidirect
314. (C2×D47)⋊C4C22×C4semidirect
315. (C2×D47)⋊C4C22×C4semidirect
316. (C2×D47)⋊C4C2×D4semidirect
331. C23×C47C4×D4semidirect
387. C22×D47C4×D4semidirect
455. C22×C47C2×C4×D4semidirect
492. C2×D47C2×C4×D4semidirect
519. C2×C4×C22⋊C4D47semidirect
521. C2×C47#2358semidirect
569. C22×C42C2×D47semidirect
570. C22×C42C2×D47semidirect
580. C4×C22⋊C4C2×D47semidirect
585. C2×#95C2×D47semidirect
586. C2×#95C2×D47semidirect
587. C47C2×#2358semidirect
678. C2×C22⋊C4C4×D47semidirect
679. C2×C22⋊C4D188semidirect
686. C2×C42C22×D47semidirect
687. C2×C42C22×D47semidirect
692. #95C22×D47semidirect
693. #95C22×D47semidirect
832. C22⋊C4C2×C4×D47semidirect
833. C22⋊C4C2×D188semidirect
897. C23C4×D188semidirect
995. C22C2×C4×D188semidirect
1023. C2#20246370direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130939942
C22×C4×D1882
C22×(C22⋊D47)⋊C42
C23×(C2×D47)⋊C42
C22×C22⋊C4×D472
#202463702
C2×#156890252
C2×#156890152
C2×#156890142
C2×#156890022
C2×#156890012
C2×#156889982
C2×#156889972
C2×C4×(C2×D47)⋊C42
C2×C4×C22⋊C4×C472
C2×#235847