Finite Group Databasebeta

← C2×#20247637 #26383889

Subgroups — C2×#20247637 #26383889

Order 12032.

4102 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094019C211yesmaximal, characteristic, complemented
2C22×C22⋊C4×D47C211yesmaximal, characteristic
3#20247637C2116yesmaximal, direct product factor
4C2×#15689052C211yesmaximal, characteristic, complemented
5C2×#15689049C211yesmaximal, characteristic, complemented
6C2×#15689048C211yesmaximal, characteristic, complemented
7C2×#15689017C211yesmaximal, characteristic, complemented
8C2×#15689013C211yesmaximal, characteristic, complemented
9C2×#15689011C211yesmaximal, characteristic, complemented
10C2×#15688994C211yesmaximal, characteristic, complemented
11C2×#15688994C211yesmaximal, characteristic, complemented
12C2×#15688980C211yesmaximal, characteristic, complemented
13C2×#15688978C211yesmaximal, characteristic
14C2×#15688978C211yesmaximal, characteristic
15C2×#15688970C211yesmaximal, characteristic, complemented
16C2×C47×#396C211yesmaximal, characteristic, complemented
17C25×D47C2211yescharacteristic
18C23×C4×D47C2211yescharacteristic
19C23×C4×D47C2211yescharacteristic
20C2×#13094019—28no—
21C2×#13094019C2218yescomplemented
22C22×C4⋊Dic47C2211yescharacteristic, complemented
23C22×Dic47⋊C4C2211yescharacteristic, complemented
24C22×Dic47⋊C4C2211yescharacteristic, complemented
25C22×C22⋊Dic47C2211yescharacteristic
26C22×C22⋊Dic47C2211yescharacteristic
27C22×C22⋊Dic47C2211yescharacteristic
28C22×(C2×D47)⋊C4C2211yescharacteristic
29C22×(C2×D47)⋊C4C2211yescharacteristic
30C22×(C2×D47)⋊C4C2211yescharacteristic
31C22×(C2×D47)⋊C4C2211yescharacteristic
32C22×(C2×D47)⋊C4C2211yescharacteristic
33C22×(C2×D47)⋊C4C2211yescharacteristic
34C22×(C2×D47)⋊C4C2211yescharacteristic
35C22×(C2×D47)⋊C4C2211yescharacteristic
36C22×(C2×D47)⋊C4C2211yescharacteristic
37C22×(C2×D47)⋊C4C2211yescharacteristic
38C2×C22⋊C4×D47—28no—
39C2×C22⋊C4×D47C2218yes—
40C22×C4×Dic47C2211yescharacteristic, complemented
41C22×C4×Dic47C2211yescharacteristic, complemented
42#15689052C2218yescomplemented
43#15689049C2218yescomplemented
44#15689048C2218yescomplemented
45#15689017C2218yescomplemented
46#15689013C2218yescomplemented
47#15689011C2218yescomplemented
48#15688994C2218yescomplemented
49#15688994C2218yescomplemented
50#15688980C2218yescomplemented
51#15688978C2218yes—
52#15688978C2218yes—
53#15688970C2218yescomplemented
54C2×C47⋊#95C2211yescharacteristic, complemented
55C2×C47⋊#95C2211yescharacteristic, complemented
56C2×C47⋊#95C2211yescharacteristic, complemented
57C2×C47⋊#95C2211yescharacteristic, complemented
58C2×C47⋊#95C2211yescharacteristic, complemented
59C2×C47⋊#95C2211yescharacteristic, complemented
60C2×C47⋊#95C2211yescharacteristic, complemented
61C22×C4⋊C4×C47C2211yescharacteristic, complemented
62C22×C4⋊C4×C47C2211yescharacteristic, complemented
63C22×C4⋊C4×C47C2211yescharacteristic, complemented
64C22×C22⋊C4×C47C2211yescharacteristic
65C22×C22⋊C4×C47C2211yescharacteristic
66C22×C22⋊C4×C47C2211yescharacteristic
67C47×#396C2218yescomplemented
68C2×#95×C47C2211yescharacteristic, complemented
69C24×D47—24no—
70C24×D47—24no—
71C24×D47—24no—
72C24×D47—24no—
73C24×D47—24no—
74C24×D47—42no—
75C24×D47—42no—
76C24×D47C2311yescharacteristic
77C24×D47C2314yes—
78C24×D47C2311yescharacteristic
79C23×Dic47C2311yescharacteristic
80C23×Dic47C2311yescharacteristic
81C23×Dic47C2311yescharacteristic
82C23×Dic47C2311yescharacteristic
83C23×Dic47C2311yescharacteristic
84C23×Dic47C2311yescharacteristic
85C22×C4×D47—24no—
86C22×C4×D47—24no—
87C22×C4×D47—24no—
88C22×C4×D47—24no—
89C22×C4×D47—42no—
90C22×C4×D47—42no—
91C22×C4×D47C2314yes—
92C22×C4×D47C2314yes—
93#13094019—232no—
94C2×C4⋊Dic47—24no—
95C2×C4⋊Dic47C2314yescomplemented
96C2×Dic47⋊C4—24no—
97C2×Dic47⋊C4—42no—
98C2×Dic47⋊C4C2314yescomplemented
99C2×Dic47⋊C4C2314yescomplemented
100C2×C22⋊Dic47—24no—
101C2×C22⋊Dic47—24no—
102C2×C22⋊Dic47—24no—
103C2×C22⋊Dic47C2314yes—
104C2×C22⋊Dic47C2314yes—
105C2×C22⋊Dic47C2314yes—
106C2×(C2×D47)⋊C4—24no—
107C2×(C2×D47)⋊C4—24no—
108C2×(C2×D47)⋊C4—24no—
109C2×(C2×D47)⋊C4—24no—
110C2×(C2×D47)⋊C4—24no—
111C2×(C2×D47)⋊C4—24no—
112C2×(C2×D47)⋊C4—24no—
113C2×(C2×D47)⋊C4—42no—
114C2×(C2×D47)⋊C4—42no—
115C2×(C2×D47)⋊C4D418yes—
116C2×(C2×D47)⋊C4C2314yes—
117C2×(C2×D47)⋊C4C2314yes—
118C2×(C2×D47)⋊C4C2314yes—
119C2×(C2×D47)⋊C4C2314yes—
120C2×(C2×D47)⋊C4C2314yes—
121C2×(C2×D47)⋊C4C2314yes—
122C2×(C2×D47)⋊C4C2314yes—
123C2×(C2×D47)⋊C4C2314yes—
124C2×(C2×D47)⋊C4C2314yes—
125C2×(C2×D47)⋊C4C2314yes—
126C22⋊C4×D47—232no—
127C2×C4×Dic47—24no—
128C2×C4×Dic47—42no—
129C2×C4×Dic47C2314yescomplemented
130C2×C4×Dic47C2314yescomplemented
131C47⋊#95C2314yescomplemented
132C47⋊#95C2314yescomplemented
133C47⋊#95C2314yescomplemented
134C47⋊#95C2314yescomplemented
135C47⋊#95C2314yescomplemented
136C47⋊#95C2314yescomplemented
137C47⋊#95C2314yescomplemented
138C25×C47C2311yescharacteristic
139C23×C4×C47C2311yescharacteristic
140C23×C4×C47C2311yescharacteristic
141C23×C4×C47C2311yescharacteristic
142C23×C4×C47C2311yescharacteristic
143C23×C4×C47C2311yescharacteristic
144C23×C4×C47C2311yescharacteristic
145C2×C4⋊C4×C47—24no—
146C2×C4⋊C4×C47—42no—
147C2×C4⋊C4×C47—42no—
148C2×C4⋊C4×C47C2314yescomplemented
149C2×C4⋊C4×C47C2314yescomplemented
150C2×C4⋊C4×C47C2314yescomplemented
151C2×C22⋊C4×C47—24no—
152C2×C22⋊C4×C47—42no—
153C2×C22⋊C4×C47—42no—
154C2×C22⋊C4×C47C2314yes—
155C2×C22⋊C4×C47C2314yes—
156C2×C22⋊C4×C47C2314yes—
157#95×C47C2314yescomplemented
158C24×C47—22no—
159C24×C47—22no—
160C24×C47—22no—
161C24×C47—22no—
162C24×C47—22no—
163C24×C47—22no—
164C24×C47#4114yes—
165C24×C47C2412yes—
166C24×C47C2411yescharacteristic
167C23×D47—22no—
168C23×D47—22no—
169C23×D47—22no—
170C23×D47—22no—
171C23×D47—232no—
172C23×D47—28no—
173C23×D47—22no—
174C23×D47—22no—
175C23×D47—22no—
176C23×D47—22no—
177C23×D47—22no—
178C23×D47—22no—
179C23×D47—28no—
180C23×D47—28no—
181C23×D47—28no—
182C23×D47—28no—
183C23×D47—44no—
184C23×D47—44no—
185C23×D47—416no—
186C23×D47—416no—
187C23×D47—416no—
188C23×D47—416no—
189C23×D47—416no—
190C23×D47—416no—
191C23×D47C2×D414yes—
192C23×D47#4114yes—
193C23×D47#4114yes—
194C23×D47#4114yes—
195C23×D47C2412yes—
196C23×D47C2412yes—
197C22×C4×C47—22no—
198C22×C4×C47—22no—
199C22×C4×C47—22no—
200C22×C4×C47—22no—
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×C47—22no—
208C22×C4×C47—22no—
209C22×C4×C47—22no—
210C22×C4×C47—22no—
211C22×C4×C47—22no—
212C22×C4×C47—22no—
213C22×C4×C47—22no—
214C22×C4×C47C2×D414yes—
215C22×C4×C47C2412yes—
216C22×C4×C47C2412yes—
217C22×C4×C47C2412yes—
218C22×C4×C47C2412yes—
219C22×C4×C47C2412yes—
220C22×C4×C47C2412yes—
221C22×Dic47—22no—
222C22×Dic47—22no—
223C22×Dic47—22no—
224C22×Dic47—22no—
225C22×Dic47—22no—
226C22×Dic47—22no—
227C22×Dic47—22no—
228C22×Dic47—22no—
229C22×Dic47—22no—
230C22×Dic47—22no—
231C22×Dic47—22no—
232C22×Dic47—22no—
233C22×Dic47—22no—
234C22×Dic47—22no—
235C22×Dic47—22no—
236C22×Dic47—22no—
237C22×Dic47—22no—
238C22×Dic47C2×D414yes—
239C22×Dic47C2412yes—
240C22×Dic47C2412yes—
241C22×Dic47C2412yes—
242C22×Dic47C2412yes—
243C22×Dic47C2412yes—
244C22×Dic47C2412yes—
245C2×C4×D47—28no—
246C2×C4×D47—28no—
247C2×C4×D47—28no—
248C2×C4×D47—28no—
249C2×C4×D47—44no—
250C2×C4×D47—44no—
251C2×C4×D47—416no—
252C2×C4×D47—416no—
253C4⋊C4×C47—28no—
254C4⋊C4×C47—44no—
255C4⋊C4×C47—44no—
256C22⋊C4×C47—28no—
257C22⋊C4×C47—44no—
258C22⋊C4×C47—44no—
259C22⋊Dic47—28no—
260C22⋊Dic47—28no—
261C22⋊Dic47—28no—
262(C2×D47)⋊C4—28no—
263(C2×D47)⋊C4—28no—
264(C2×D47)⋊C4—28no—
265(C2×D47)⋊C4—28no—
266(C2×D47)⋊C4—28no—
267(C2×D47)⋊C4—28no—
268(C2×D47)⋊C4—28no—
269(C2×D47)⋊C4—44no—
270(C2×D47)⋊C4—44no—
271(C2×D47)⋊C4C2×D4116yes—
272C4⋊Dic47—28no—
273Dic47⋊C4—28no—
274Dic47⋊C4—44no—
275C4×Dic47—28no—
276C4×Dic47—44no—
277C23×C47—28no—
278C23×C47—28no—
279C23×C47—28no—
280C23×C47—22no—
281C23×C47—22no—
282C23×C47—22no—
283C23×C47—22no—
284C23×C47—22no—
285C23×C47—22no—
286C23×C47—44no—
287C23×C47—44no—
288C23×C47—44no—
289C23×C47—44no—
290C23×C47C22×D412yes—
291C23×C47C2×#4112yes—
292C23×C47C2×#4112yes—
293C23×C47C2×#4112yes—
294C23×C47C2×#4114yes—
295C23×C47C2×#4112yes—
296C23×C47H(5,𝔽2)12yes—
297C23×C47H(5,𝔽2)12yes—
298C23×C47C2511yescharacteristic
299C22×D47—28no—
300C22×D47—28no—
301C22×D47—28no—
302C22×D47—28no—
303C22×D47—28no—
304C22×D47—28no—
305C22×D47—22no—
306C22×D47—22no—
307C22×D47—22no—
308C22×D47—22no—
309C22×D47—232no—
310C22×D47—28no—
311C22×D47—28no—
312C22×D47—28no—
313C22×D47—22no—
314C22×D47—22no—
315C22×D47—22no—
316C22×D47—22no—
317C22×D47—22no—
318C22×D47—22no—
319C22×D47—416no—
320C22×D47—416no—
321C22×D47—416no—
322C22×D47—416no—
323C22×D47—416no—
324C22×D47—4128no—
325C22×D47—44no—
326C22×D47—44no—
327C22×D47—44no—
328C22×D47—44no—
329C22×D47—416no—
330C22×D47#126116yescomplemented
331C22×D47C22×D414yes—
332C22×D47C2×#4114yes—
333C22×D47C2×#4114yes—
334C22×D47C2×#4114yes—
335C2×C4×C47—28no—
336C2×C4×C47—22no—
337C2×C4×C47—22no—
338C2×C4×C47—22no—
339C2×C4×C47—22no—
340C2×C4×C47—22no—
341C2×C4×C47—22no—
342C2×C4×C47—22no—
343C2×C4×C47—22no—
344C2×C4×C47—22no—
345C2×C4×C47—22no—
346C2×C4×C47—22no—
347C2×C4×C47—22no—
348C2×C4×C47—22no—
349C2×C4×C47—22no—
350C2×C4×C47—22no—
351C2×C4×C47—22no—
352C2×C4×C47—22no—
353C2×C4×C47—44no—
354C2×C4×C47—44no—
355C2×C4×C47—44no—
356C2×C4×C47—44no—
357C2×C4×C47—44no—
358C2×C4×C47C22×D414yes—
359C2×Dic47—28no—
360C2×Dic47—22no—
361C2×Dic47—22no—
362C2×Dic47—22no—
363C2×Dic47—22no—
364C2×Dic47—22no—
365C2×Dic47—22no—
366C2×Dic47—22no—
367C2×Dic47—22no—
368C2×Dic47—22no—
369C2×Dic47—22no—
370C2×Dic47—22no—
371C2×Dic47—22no—
372C2×Dic47—22no—
373C2×Dic47—22no—
374C2×Dic47—22no—
375C2×Dic47—22no—
376C2×Dic47—22no—
377C2×Dic47—44no—
378C2×Dic47—44no—
379C2×Dic47—44no—
380C2×Dic47—44no—
381C2×Dic47—44no—
382C2×Dic47C22×D414yes—
383C4×D47—416no—
384C4×D47—416no—
385C2×#2480—471nomaximal, Sylow
386C22×C47—24no—
387C22×C47—24no—
388C22×C47—24no—
389C22×C47—42no—
390C22×C47—42no—
391C22×C47—42no—
392C22×C47—42no—
393C22×C47—416no—
394C22×C47#52514yes—
395C22×C47C2×#12614yes—
396C22×C47#53814yes—
397C22×C47#54614yes—
398C22×C47#54614yes—
399C22×C47#55114yes—
400C22×C47#55114yes—
401C22×C47C23×D411yescharacteristic
402C22×C47C22×#4111yescharacteristic
403C22×C47C22×#4111yescharacteristic
404C22×C47C22×#4111yescharacteristic
405C22×C47C22×#4111yescharacteristic
406C22×C47C2×H(5,𝔽2)11yescharacteristic
407C22×C47C2×H(5,𝔽2)11yescharacteristic
408C2×D47—24no—
409C2×D47—24no—
410C2×D47—24no—
411C2×D47—24no—
412C2×D47—24no—
413C2×D47—24no—
414C2×D47—232no—
415C2×D47—24no—
416C2×D47—24no—
417C2×D47—24no—
418C2×D47—464no—
419C2×D47—42no—
420C2×D47—42no—
421C2×D47—42no—
422C2×D47—42no—
423C2×D47—416no—
424C2×D47C2×#12618yescomplemented
425C4×C47—24no—
426C4×C47—42no—
427C4×C47—42no—
428C4×C47—42no—
429C4×C47—42no—
430C4×C47—42no—
431Dic47—24no—
432Dic47—42no—
433Dic47—42no—
434Dic47—42no—
435Dic47—42no—
436Dic47—42no—
437C22×#126—471no—
438C23×C22⋊C4—471no—
439#2480—4716no—
440C2×#397—471no—
441C2×#397—471no—
442C2×#397—471no—
443C2×#396D4711yescharacteristic, complemented
444C2×#388—471no—
445C2×#388—471no—
446C2×#388—471no—
447C2×#385—471no—
448C2×#385—471no—
449C2×#380—471no—
450C2×#379—471no—
451C2×#379—471no—
452C2×C4×C22⋊C4—471no—
453C2×C47—44no—
454C2×C47#248018yescomplemented
455C2×C47C2×#52511yescharacteristic
456C2×C47C22×#12611yescharacteristic
457C2×C47C2×#53811yescharacteristic
458C2×C47C2×#54611yescharacteristic
459C2×C47C2×#54611yescharacteristic
460C2×C47C2×#55111yescharacteristic
461C2×C47C2×#55111yescharacteristic
462D47—28no—
463D47—44no—
464C26—471no—
465C24×C4—471no—
466C24×C4—471no—
467C2×#126—478no—
468C2×#126—948no—
469C22×C4⋊C4—471no—
470C22×C4⋊C4—471no—
471C22×C4⋊C4—471no—
472C22×C4⋊C4C2×D4711yescharacteristic, complemented
473C22×C4⋊C4C2×D4711yescharacteristic, complemented
474C22×C4⋊C4C2×D4711yescharacteristic, complemented
475C22×C22⋊C4—471no—
476C22×C22⋊C4—471no—
477C22×C22⋊C4—471no—
478C22×C22⋊C4—471no—
479C22×C22⋊C4—471no—
480C22×C22⋊C4—471no—
481C22×C22⋊C4—471no—
482C22×C22⋊C4—471no—
483C22×C22⋊C4—471no—
484C22×C22⋊C4—471no—
485C22×C22⋊C4—471no—
486C22×C22⋊C4—471no—
487C22×C22⋊C4—471no—
488C22×C22⋊C4—478no—
489C22×C22⋊C4—948no—
490C22×C22⋊C4C2×D4711yescharacteristic
491C22×C22⋊C4C2×D4711yescharacteristic
492C22×C22⋊C4C2×D4711yescharacteristic
493C22×C42—471no—
494C22×C42—471no—
495#397—478no—
496#397—478no—
497#397—478no—
498#396C2×D4718yescomplemented
499#388—478no—
500#388—478no—
501#388—478no—
502#385—478no—
503#385—478no—
504#380—478no—
505#379—478no—
506#379—478no—
507C4×C22⋊C4—478no—
508C2×#95—471no—
509C2×#95—471no—
510C2×#95—471no—
511C2×#95—471no—
512C2×#95—471no—
513C2×#95—471no—
514C2×#95—471no—
515C2×#95C2×D4711yescharacteristic, complemented
516C47C2×#248011yescharacteristic, complemented, Sylow
517C25—471no—
518C25—471no—
519C25—474no—
520C25—944no—
521C25—944no—
522C25—944no—
523C25—944no—
524C25—944no—
525C25—1882no—
526C25—1882no—
527C25C22×D4711yescharacteristic
528C23×C4—471no—
529C23×C4—471no—
530C23×C4—471no—
531C23×C4—471no—
532C23×C4—471no—
533C23×C4—471no—
534C23×C4—474no—
535C23×C4—474no—
536C23×C4—944no—
537C23×C4—944no—
538C23×C4—944no—
539C23×C4—944no—
540C23×C4—1882no—
541C23×C4—1882no—
542C23×C4C22×D4711yescharacteristic
543C23×C4C22×D4711yescharacteristic
544C23×C4C22×D4711yescharacteristic
545C23×C4C22×D4711yescharacteristic
546C23×C4C22×D4711yescharacteristic
547C23×C4C22×D4711yescharacteristic
548#126—9432no—
549C2×C4⋊C4—24no—
550C2×C4⋊C4—42no—
551C2×C4⋊C4—42no—
552C2×C4⋊C4—474no—
553C2×C4⋊C4—474no—
554C2×C4⋊C4—474no—
555C2×C4⋊C4—944no—
556C2×C4⋊C4—944no—
557C2×C4⋊C4—1882no—
558C2×C4⋊C4C22×D4714yescomplemented
559C2×C4⋊C4C22×D4714yescomplemented
560C2×C4⋊C4C22×D4714yescomplemented
561C2×C22⋊C4—24no—
562C2×C22⋊C4—42no—
563C2×C22⋊C4—42no—
564C2×C22⋊C4—478no—
565C2×C22⋊C4—474no—
566C2×C22⋊C4—474no—
567C2×C22⋊C4—474no—
568C2×C22⋊C4—474no—
569C2×C22⋊C4—474no—
570C2×C22⋊C4—474no—
571C2×C22⋊C4—474no—
572C2×C22⋊C4—474no—
573C2×C22⋊C4—474no—
574C2×C22⋊C4—474no—
575C2×C22⋊C4—474no—
576C2×C22⋊C4—474no—
577C2×C22⋊C4—474no—
578C2×C22⋊C4—9432no—
579C2×C22⋊C4—944no—
580C2×C22⋊C4—944no—
581C2×C22⋊C4—944no—
582C2×C22⋊C4—944no—
583C2×C22⋊C4—944no—
584C2×C22⋊C4—944no—
585C2×C22⋊C4—944no—
586C2×C22⋊C4—944no—
587C2×C22⋊C4—944no—
588C2×C22⋊C4—944no—
589C2×C22⋊C4—1882no—
590C2×C22⋊C4—1882no—
591C2×C22⋊C4C22×D4714yes—
592C2×C22⋊C4C22×D4714yes—
593C2×C22⋊C4C22×D4714yes—
594C2×C42—474no—
595C2×C42—474no—
596C2×C42—944no—
597C2×C42—1882no—
598#95—474no—
599#95—474no—
600#95—474no—
601#95—474no—
602#95—474no—
603#95—474no—
604#95—474no—
605#95C22×D4714yescomplemented
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—474no—
613C24—474no—
614C24—474no—
615C24—472no—
616C24—474no—
617C24—472no—
618C24—948no—
619C24—948no—
620C24—948no—
621C24—948no—
622C24—9432no—
623C24—942no—
624C24—942no—
625C24—942no—
626C24—942no—
627C24—942no—
628C24—942no—
629C24—942no—
630C24—948no—
631C24—942no—
632C24—942no—
633C24—942no—
634C24—1884no—
635C24—1884no—
636C24—18816no—
637C24—18816no—
638C24—18816no—
639C24—18816no—
640C24—18816no—
641C24—18816no—
642C24#1062535414yes—
643C24C23×D4712yes—
644C24C23×D4711yescharacteristic
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—474no—
663C22×C4—472no—
664C22×C4—472no—
665C22×C4—472no—
666C22×C4—472no—
667C22×C4—472no—
668C22×C4—472no—
669C22×C4—948no—
670C22×C4—948no—
671C22×C4—948no—
672C22×C4—942no—
673C22×C4—942no—
674C22×C4—942no—
675C22×C4—942no—
676C22×C4—942no—
677C22×C4—942no—
678C22×C4—942no—
679C22×C4—942no—
680C22×C4—942no—
681C22×C4—942no—
682C22×C4—942no—
683C22×C4—942no—
684C22×C4—942no—
685C22×C4—942no—
686C22×C4—942no—
687C22×C4—942no—
688C22×C4—942no—
689C22×C4—948no—
690C22×C4—1884no—
691C22×C4—1884no—
692C22×C4—18816no—
693C22×C4—18816no—
694C22×C4D4×D4714yes—
695C22×C4C23×D4712yes—
696C22×C4C23×D4712yes—
697C22×C4C23×D4712yes—
698C22×C4C23×D4712yes—
699C22×C4C23×D4712yes—
700C22×C4C23×D4712yes—
701C4⋊C4—28no—
702C4⋊C4—44no—
703C4⋊C4—44no—
704C4⋊C4—948no—
705C4⋊C4—948no—
706C4⋊C4—1884no—
707C22⋊C4—28no—
708C22⋊C4—44no—
709C22⋊C4—44no—
710C22⋊C4—4716no—
711C22⋊C4—948no—
712C22⋊C4—948no—
713C22⋊C4—948no—
714C22⋊C4—948no—
715C22⋊C4—948no—
716C22⋊C4—948no—
717C22⋊C4—948no—
718C22⋊C4—948no—
719C22⋊C4—948no—
720C22⋊C4—948no—
721C22⋊C4—1884no—
722C22⋊C4—1884no—
723C42—948no—
724C42—1884no—
725C23—28no—
726C23—28no—
727C23—28no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—4716no—
739C23—474no—
740C23—474no—
741C23—474no—
742C23—474no—
743C23—9432no—
744C23—948no—
745C23—948no—
746C23—948no—
747C23—948no—
748C23—948no—
749C23—942no—
750C23—942no—
751C23—942no—
752C23—942no—
753C23—948no—
754C23—948no—
755C23—948no—
756C23—948no—
757C23—942no—
758C23—942no—
759C23—942no—
760C23—942no—
761C23—942no—
762C23—942no—
763C23—18816no—
764C23—18816no—
765C23—18816no—
766C23—18816no—
767C23—18816no—
768C23—188128no—
769C23—18816no—
770C23—1884no—
771C23—1884no—
772C23—1884no—
773C23—1884no—
774C23C2×D4×D4712yes—
775C23#41×D4712yes—
776C23#41×D4712yes—
777C23#41×D4712yes—
778C23C2×#1062535414yes—
779C23C2×#1062535412yes—
780C23#1309406912yes—
781C23#1309406912yes—
782C23C24×D4711yescharacteristic
783C2×C4—28no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—44no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—474no—
807C2×C4—948no—
808C2×C4—942no—
809C2×C4—942no—
810C2×C4—942no—
811C2×C4—942no—
812C2×C4—942no—
813C2×C4—942no—
814C2×C4—942no—
815C2×C4—942no—
816C2×C4—942no—
817C2×C4—942no—
818C2×C4—942no—
819C2×C4—942no—
820C2×C4—942no—
821C2×C4—942no—
822C2×C4—942no—
823C2×C4—942no—
824C2×C4—942no—
825C2×C4—18816no—
826C2×C4—18816no—
827C2×C4—1884no—
828C2×C4—1884no—
829C2×C4—1884no—
830C2×C4—1884no—
831C2×C4—1884no—
832C2×C4C2×D4×D4714yes—
833C22—24no—
834C22—24no—
835C22—24no—
836C22—42no—
837C22—42no—
838C22—416no—
839C22—42no—
840C22—42no—
841C22—478no—
842C22—944no—
843C22—944no—
844C22—9432no—
845C22—944no—
846C22—944no—
847C22—944no—
848C22—944no—
849C22—944no—
850C22—944no—
851C22—944no—
852C22—18864no—
853C22—18816no—
854C22—1882no—
855C22—1882no—
856C22—1882no—
857C22—1882no—
858C22#1568963614yes—
859C22#126×D4714yes—
860C22#1568970514yes—
861C22#1568976214yes—
862C22#1568977014yes—
863C22#1568980014yes—
864C22#1568980014yes—
865C22C22×D4×D4711yescharacteristic
866C22C2×#41×D4711yescharacteristic
867C22C2×#41×D4711yescharacteristic
868C22C2×#41×D4711yescharacteristic
869C22C22×#1062535411yescharacteristic
870C22C2×#1309406911yescharacteristic
871C22C2×#1309406911yescharacteristic
872C4—24no—
873C4—42no—
874C4—42no—
875C4—42no—
876C4—42no—
877C4—42no—
878C4—944no—
879C4—1882no—
880C4—1882no—
881C4—1882no—
882C4—1882no—
883C4—1882no—
884C2—44no—
885C2—948no—
886C2—1884no—
887C2#2024763718yesdirect product factor
888C2C2×#1568963611yescharacteristic
889C2C2×#126×D4711yescharacteristic
890C2C2×#1568970511yescharacteristic
891C2C2×#1568976211yescharacteristic
892C2C2×#1568977011yescharacteristic
893C2C2×#1568980011yescharacteristic
894C2C2×#1568980011yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#396C2
socleC24×C47C24
prime radicalC25×D47C22
hypercenterC2×#396D47
hypocenterC47C2×#2480
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#13094019C2semidirect
3. #20247637C2direct (N × H)
4. C2×#15689052C2semidirect
5. C2×#15689049C2semidirect
6. C2×#15689048C2semidirect
7. C2×#15689017C2semidirect
8. C2×#15689013C2semidirect
9. C2×#15689011C2semidirect
10. C2×#15688994C2semidirect
11. C2×#15688994C2semidirect
12. C2×#15688980C2semidirect
15. C2×#15688970C2semidirect
16. C2×C47×#396C2semidirect
21. C2×#13094019C22semidirect
22. C22×C4⋊Dic47C22semidirect
23. C22×Dic47⋊C4C22semidirect
24. C22×Dic47⋊C4C22semidirect
40. C22×C4×Dic47C22semidirect
41. C22×C4×Dic47C22semidirect
42. #15689052C22semidirect
43. #15689049C22semidirect
44. #15689048C22semidirect
45. #15689017C22semidirect
46. #15689013C22semidirect
47. #15689011C22semidirect
48. #15688994C22semidirect
49. #15688994C22semidirect
50. #15688980C22semidirect
53. #15688970C22semidirect
54. C2×C47⋊#95C22semidirect
55. C2×C47⋊#95C22semidirect
56. C2×C47⋊#95C22semidirect
57. C2×C47⋊#95C22semidirect
58. C2×C47⋊#95C22semidirect
59. C2×C47⋊#95C22semidirect
60. C2×C47⋊#95C22semidirect
61. C22×C4⋊C4×C47C22semidirect
62. C22×C4⋊C4×C47C22semidirect
63. C22×C4⋊C4×C47C22semidirect
67. C47×#396C22semidirect
68. C2×#95×C47C22semidirect
95. C2×C4⋊Dic47C23semidirect
98. C2×Dic47⋊C4C23semidirect
99. C2×Dic47⋊C4C23semidirect
129. C2×C4×Dic47C23semidirect
130. C2×C4×Dic47C23semidirect
131. C47⋊#95C23semidirect
132. C47⋊#95C23semidirect
133. C47⋊#95C23semidirect
134. C47⋊#95C23semidirect
135. C47⋊#95C23semidirect
136. C47⋊#95C23semidirect
137. C47⋊#95C23semidirect
148. C2×C4⋊C4×C47C23semidirect
149. C2×C4⋊C4×C47C23semidirect
150. C2×C4⋊C4×C47C23semidirect
157. #95×C47C23semidirect
330. C22×D47#126semidirect
424. C2×D47C2×#126semidirect
443. C2×#396D47semidirect
454. C2×C47#2480semidirect
472. C22×C4⋊C4C2×D47semidirect
473. C22×C4⋊C4C2×D47semidirect
474. C22×C4⋊C4C2×D47semidirect
498. #396C2×D47semidirect
515. C2×#95C2×D47semidirect
516. C47C2×#2480semidirect
558. C2×C4⋊C4C22×D47semidirect
559. C2×C4⋊C4C22×D47semidirect
560. C2×C4⋊C4C22×D47semidirect
605. #95C22×D47semidirect
887. C2#20247637direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940192
C22×C22⋊C4×D472
#202476372
C2×#156890522
C2×#156890492
C2×#156890482
C2×#156890172
C2×#156890132
C2×#156890112
C2×#156889942
C2×#156889802
C2×#156889782
C2×#156889702
C2×C47×#3962
C2×#248047