Finite Group Databasebeta

← C2×#20246937 #26383999

Subgroups — C2×#20246937 #26383999

Order 12032.

3938 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094008C211yesmaximal, characteristic, complemented
2C22×#13094008C211yesmaximal, characteristic, complemented
3C22×#13093998C211yesmaximal, characteristic
4C22×(C22⋊D47)⋊C4C211yesmaximal, characteristic, complemented
5#20246937C2116yesmaximal, direct product factor
6C2×#15689055C211yesmaximal, characteristic, complemented
7C2×#15689050C211yesmaximal, characteristic, complemented
8C2×#15689045C211yesmaximal, characteristic, complemented
9C2×#15689040C211yesmaximal, characteristic, complemented
10C2×#15689022C211yesmaximal, characteristic, complemented
11C2×#15689015C211yesmaximal, characteristic, complemented
12C2×#15689001C211yesmaximal, characteristic, complemented
13C2×#15689000C211yesmaximal, characteristic, complemented
14C2×#15688980C211yesmaximal, characteristic, complemented
15C22×C47⋊#95C211yesmaximal, characteristic, complemented
16C2×C47×#385C211yesmaximal, characteristic, complemented
17C23×D188C2211yescharacteristic
18C23×C22⋊D47C2211yescharacteristic
19C23×C22⋊D47C2211yescharacteristic
20C24×Dic47C2211yescharacteristic
21C24×Dic47C2211yescharacteristic
22C23×C4×D47C2211yescharacteristic
23C2×#13094008—28no—
24C2×#13094008—28no—
25C2×#13094008C2218yescomplemented
26C2×#13094008C2218yescomplemented
27C2×#13093998—28no—
28C2×#13093998C2218yes—
29C2×(C22⋊D47)⋊C4—28no—
30C2×(C22⋊D47)⋊C4C2218yescomplemented
31C22×C4⋊Dic47C2211yescharacteristic
32C22×C4⋊Dic47C2211yescharacteristic
33C22×C4⋊Dic47C2211yescharacteristic
34C22×C4⋊Dic47C2211yescharacteristic
35C22×C4⋊Dic47C2211yescharacteristic
36C22×Dic47⋊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)⋊C4C2211yescharacteristic
45C22×(C2×D47)⋊C4C2211yescharacteristic
46C22×C4×Dic47C2211yescharacteristic
47#15689055C2218yescomplemented
48#15689050C2218yescomplemented
49#15689045C2218yescomplemented
50#15689040C2218yescomplemented
51#15689022C2218yescomplemented
52#15689015C2218yescomplemented
53#15689001C2218yescomplemented
54#15689000C2218yescomplemented
55#15688980C2218yescomplemented
56C2×C47⋊#95C2211yescharacteristic
57C2×C47⋊#95C2211yescharacteristic
58C2×C47⋊#95C2211yescharacteristic
59C2×C47⋊#95C2211yescharacteristic
60C2×C47⋊#95C2211yescharacteristic
61C2×C47⋊#95C2211yescharacteristic
62C2×C47⋊#95C2218yescomplemented
63C24×C4×C47C2211yescharacteristic
64C22×C4⋊C4×C47C2211yescharacteristic
65C22×C4⋊C4×C47C2211yescharacteristic
66C22×C22⋊C4×C47C2211yescharacteristic
67C22×C22⋊C4×C47C2211yescharacteristic
68C47×#385C2218yescomplemented
69C2×#95×C47C2211yescharacteristic
70C2×#95×C47C2211yescharacteristic
71C24×D47C2311yescharacteristic
72C24×D47C2311yescharacteristic
73C22×D188—24no—
74C22×D188—24no—
75C22×D188—42no—
76C22×D188C2314yes—
77C22×C22⋊D47—24no—
78C22×C22⋊D47—24no—
79C22×C22⋊D47—24no—
80C22×C22⋊D47—24no—
81C22×C22⋊D47—24no—
82C22×C22⋊D47D418yes—
83C22×C22⋊D47C2314yes—
84C22×C22⋊D47C2314yes—
85C23×Dic47—24no—
86C23×Dic47—24no—
87C23×Dic47—24no—
88C23×Dic47—24no—
89C23×Dic47—24no—
90C23×Dic47—42no—
91C23×Dic47C2311yescharacteristic
92C23×Dic47C2311yescharacteristic
93C23×Dic47C2311yescharacteristic
94C23×Dic47C2311yescharacteristic
95C23×Dic47C2314yes—
96C23×Dic47C2314yes—
97C23×Dic47C2311yescharacteristic
98C23×Dic47C2311yescharacteristic
99C22×C4×D47—24no—
100C22×C4×D47—24no—
101C22×C4×D47—42no—
102C22×C4×D47C2314yes—
103#13094008—232no—
104#13094008—232no—
105#13093998—232no—
106(C22⋊D47)⋊C4—232no—
107C2×C4⋊Dic47—24no—
108C2×C4⋊Dic47—24no—
109C2×C4⋊Dic47—24no—
110C2×C4⋊Dic47—24no—
111C2×C4⋊Dic47—24no—
112C2×C4⋊Dic47C2314yes—
113C2×C4⋊Dic47C2314yes—
114C2×C4⋊Dic47C2314yes—
115C2×C4⋊Dic47C2314yes—
116C2×C4⋊Dic47C2314yes—
117C2×Dic47⋊C4—24no—
118C2×Dic47⋊C4C2314yes—
119C2×(C2×D47)⋊C4—24no—
120C2×(C2×D47)⋊C4—24no—
121C2×(C2×D47)⋊C4—24no—
122C2×(C2×D47)⋊C4—24no—
123C2×(C2×D47)⋊C4—24no—
124C2×(C2×D47)⋊C4—24no—
125C2×(C2×D47)⋊C4—24no—
126C2×(C2×D47)⋊C4—24no—
127C2×(C2×D47)⋊C4—42no—
128C2×(C2×D47)⋊C4C2314yes—
129C2×(C2×D47)⋊C4C2314yes—
130C2×(C2×D47)⋊C4C2314yes—
131C2×(C2×D47)⋊C4C2314yes—
132C2×(C2×D47)⋊C4C2314yes—
133C2×(C2×D47)⋊C4C2314yes—
134C2×(C2×D47)⋊C4C2314yes—
135C2×(C2×D47)⋊C4C2314yes—
136C2×(C2×D47)⋊C4C2314yes—
137C2×C4×Dic47—24no—
138C2×C4×Dic47C2314yes—
139C47⋊#95C2314yes—
140C47⋊#95C2314yes—
141C47⋊#95C2314yes—
142C47⋊#95C2314yes—
143C47⋊#95C2314yes—
144C47⋊#95C2314yes—
145C25×C47C2311yescharacteristic
146C23×C4×C47—24no—
147C23×C4×C47—24no—
148C23×C4×C47—42no—
149C23×C4×C47C2311yescharacteristic
150C23×C4×C47C2311yescharacteristic
151C23×C4×C47C2311yescharacteristic
152C23×C4×C47C2314yes—
153C23×C4×C47C2311yescharacteristic
154C23×C4×C47C2311yescharacteristic
155C23×C4×C47C2311yescharacteristic
156C2×C4⋊C4×C47—24no—
157C2×C4⋊C4×C47—42no—
158C2×C4⋊C4×C47C2314yes—
159C2×C4⋊C4×C47C2314yes—
160C2×C22⋊C4×C47—24no—
161C2×C22⋊C4×C47D418yescomplemented
162C2×C22⋊C4×C47C2314yes—
163C2×C22⋊C4×C47C2314yes—
164#95×C47C2314yes—
165#95×C47C2314yes—
166C24×C47—22no—
167C24×C47—22no—
168C24×C47—22no—
169C24×C47—22no—
170C24×C47C2×D414yes—
171C24×C47C2×D414yes—
172C24×C47#4114yes—
173C24×C47C2412yes—
174C24×C47C2411yescharacteristic
175C23×D47—22no—
176C23×D47—22no—
177C23×D47—22no—
178C23×D47—22no—
179C23×D47—22no—
180C23×D47—22no—
181C23×D47—22no—
182C23×D47—22no—
183C23×D47—22no—
184C23×D47—22no—
185C23×D47—22no—
186C23×D47—22no—
187C23×D47—22no—
188C23×D47C2×D414yes—
189C23×D47C2412yes—
190C23×D47C2412yes—
191C22×C4×C47—22no—
192C22×C4×C47—22no—
193C22×C4×C47—22no—
194C22×C4×C47—22no—
195C22×C4×C47—22no—
196C22×C4×C47—22no—
197C22×C4×C47—22no—
198C22×C4×C47—22no—
199C22×C4×C47—22no—
200C22×C4×C47—28no—
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—28no—
208C22×C4×C47—44no—
209C22×C4×C47—416no—
210C22×C4×C47C2×D414yes—
211C22×C4×C47C2×D414yes—
212C22×C4×C47#4114yes—
213C22×C4×C47C2412yes—
214C22×C4×C47C2412yes—
215C22×C4×C47C2412yes—
216C22×C4×C47C2412yes—
217C22×C4×C47C2412yes—
218C22×C4×C47C2412yes—
219C2×C22⋊D47—232no—
220C2×C22⋊D47—28no—
221C2×C22⋊D47—28no—
222C2×C22⋊D47—28no—
223C2×C22⋊D47—28no—
224C2×C22⋊D47—28no—
225C2×C22⋊D47—416no—
226C2×C22⋊D47C2×D4116yes—
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×Dic47—28no—
239C22×Dic47—28no—
240C22×Dic47—28no—
241C22×Dic47—28no—
242C22×Dic47—22no—
243C22×Dic47—22no—
244C22×Dic47—22no—
245C22×Dic47—22no—
246C22×Dic47—22no—
247C22×Dic47—28no—
248C22×Dic47—44no—
249C22×Dic47—416no—
250C22×Dic47—416no—
251C22×Dic47C2×D414yes—
252C22×Dic47#4114yes—
253C22×Dic47C2412yes—
254C22×Dic47C2412yes—
255C22×Dic47C2412yes—
256C22×Dic47C2412yes—
257C22×Dic47C2412yes—
258C22×Dic47C2412yes—
259C2×D188—28no—
260C2×D188—28no—
261C2×D188—44no—
262C2×D188—416no—
263C2×C4×D47—28no—
264C2×C4×D47—28no—
265C2×C4×D47—44no—
266C2×C4×D47—416no—
267C4⋊C4×C47—28no—
268C4⋊C4×C47—44no—
269C22⋊C4×C47—28no—
270C22⋊C4×C47C2×D4116yescomplemented
271(C2×D47)⋊C4—28no—
272(C2×D47)⋊C4—28no—
273(C2×D47)⋊C4—28no—
274(C2×D47)⋊C4—28no—
275(C2×D47)⋊C4—28no—
276(C2×D47)⋊C4—28no—
277(C2×D47)⋊C4—28no—
278(C2×D47)⋊C4—28no—
279(C2×D47)⋊C4—44no—
280C4⋊Dic47—28no—
281C4⋊Dic47—28no—
282C4⋊Dic47—28no—
283C4⋊Dic47—28no—
284C4⋊Dic47—28no—
285Dic47⋊C4—28no—
286C4×Dic47—28no—
287C23×C47—28no—
288C23×C47—28no—
289C23×C47—28no—
290C23×C47—28no—
291C23×C47—28no—
292C23×C47—28no—
293C23×C47—22no—
294C23×C47—22no—
295C23×C47—22no—
296C23×C47—22no—
297C23×C47#121116yes—
298C23×C47C22×D414yes—
299C23×C47C22×D412yes—
300C23×C47C22×D414yes—
301C23×C47C22×D412yes—
302C23×C47C2×#4112yes—
303C23×C47C2×#4112yes—
304C23×C47C2×#4114yes—
305C23×C47C2×#4112yes—
306C23×C47H(5,𝔽2)12yes—
307C23×C472−1+412yes—
308C23×C47C2511yescharacteristic
309C22×D47—28no—
310C22×D47—28no—
311C22×D47—28no—
312C22×D47—22no—
313C22×D47—22no—
314C22×D47—22no—
315C22×D47—22no—
316C22×D47—22no—
317C22×D47—22no—
318C22×D47—22no—
319C22×D47—22no—
320C22×D47—22no—
321C22×D47—22no—
322C22×D47—22no—
323C22×D47—22no—
324C22×D47—22no—
325C22×D47—44no—
326C22×D47—44no—
327C22×D47—44no—
328C22×D47—44no—
329C22×D47—44no—
330C22×D47—44no—
331C22×D47—44no—
332C22×D47—44no—
333C22×D47—44no—
334C22×D47—44no—
335C22×D47—44no—
336C22×D47C22×D414yes—
337C2×C4×C47—28no—
338C2×C4×C47—28no—
339C2×C4×C47—28no—
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—22no—
354C2×C4×C47—22no—
355C2×C4×C47—416no—
356C2×C4×C47—44no—
357C2×C4×C47—44no—
358C2×C4×C47—44no—
359C2×C4×C47C22×D414yes—
360C2×C4×C47C22×D414yes—
361C2×C4×C47C2×#4114yes—
362C22⋊D47—232no—
363C22⋊D47—416no—
364C2×Dic47—28no—
365C2×Dic47—28no—
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—22no—
378C2×Dic47—22no—
379C2×Dic47—22no—
380C2×Dic47—22no—
381C2×Dic47—22no—
382C2×Dic47—416no—
383C2×Dic47—416no—
384C2×Dic47—44no—
385C2×Dic47—44no—
386C2×Dic47—44no—
387C2×Dic47—44no—
388C2×Dic47C22×D414yes—
389C2×Dic47C2×#4114yes—
390D188—416no—
391C4×D47—416no—
392C2×#2425—471nomaximal, Sylow
393C22×C47—24no—
394C22×C47—232no—
395C22×C47—24no—
396C22×C47—24no—
397C22×C47—24no—
398C22×C47—24no—
399C22×C47—24no—
400C22×C47C2×#12118yes—
401C22×C47C2×#12114yes—
402C22×C47#52914yes—
403C22×C47#53914yes—
404C22×C47#54614yes—
405C22×C47#54614yes—
406C22×C47#54714yes—
407C22×C47#54714yes—
408C22×C47C23×D411yescharacteristic
409C22×C47C23×D411yescharacteristic
410C22×C47C22×#4111yescharacteristic
411C22×C47C22×#4111yescharacteristic
412C22×C47C22×#4111yescharacteristic
413C22×C47C2×H(5,𝔽2)11yescharacteristic
414C22×C47C2×2−1+411yescharacteristic
415C2×D47—24no—
416C2×D47—24no—
417C2×D47—24no—
418C2×D47—42no—
419C2×D47—416no—
420C2×D47—42no—
421C2×D47—42no—
422C2×D47—42no—
423C2×D47—42no—
424C2×D47—42no—
425C2×D47—42no—
426C2×D47—42no—
427C2×D47—42no—
428C2×D47—42no—
429C2×D47—42no—
430C2×D47—88no—
431C4×C47—24no—
432C4×C47—24no—
433C4×C47—24no—
434C4×C47—42no—
435C4×C47—42no—
436C4×C47—42no—
437Dic47—24no—
438Dic47—24no—
439Dic47—42no—
440Dic47—42no—
441Dic47—42no—
442Dic47—42no—
443C22×#123—471no—
444C22×#123—471no—
445C22×#121—471no—
446C22×C4×D4—471no—
447#2425—4716no—
448C2×#398—471no—
449C2×#397—471no—
450C2×#396—471no—
451C2×#394—471no—
452C2×#389—471no—
453C2×#388—471no—
454C2×#386—471no—
455C2×#386—471no—
456C2×#385D4711yescharacteristic, complemented
457C2×#380—471no—
458C22×#95—471no—
459C2×C47—28no—
460C2×C47#242518yescomplemented
461C2×C47C22×#12111yescharacteristic
462C2×C47C2×#52911yescharacteristic
463C2×C47C2×#53911yescharacteristic
464C2×C47C2×#54611yescharacteristic
465C2×C47C2×#54611yescharacteristic
466C2×C47C2×#54711yescharacteristic
467C2×C47C2×#54711yescharacteristic
468D47—44no—
469D47—82no—
470C23×D4—471no—
471C23×D4—471no—
472C23×D4—471no—
473C24×C4—471no—
474C24×C4—471no—
475C24×C4—471no—
476C24×C4C2×D4711yescharacteristic
477C2×#123—478no—
478C2×#123—478no—
479C2×#123—948no—
480C2×#123—948no—
481C2×#121—478no—
482C2×#121—948no—
483C2×C4×D4—478no—
484C2×C4×D4—948no—
485C22×C4⋊C4—471no—
486C22×C4⋊C4—471no—
487C22×C4⋊C4—471no—
488C22×C4⋊C4—471no—
489C22×C4⋊C4—471no—
490C22×C4⋊C4—471no—
491C22×C4⋊C4C2×D4711yescharacteristic
492C22×C4⋊C4C2×D4711yescharacteristic
493C22×C22⋊C4—471no—
494C22×C22⋊C4—471no—
495C22×C22⋊C4—471no—
496C22×C22⋊C4—471no—
497C22×C22⋊C4—471no—
498C22×C22⋊C4—471no—
499C22×C22⋊C4—471no—
500C22×C22⋊C4—471no—
501C22×C22⋊C4—471no—
502C22×C22⋊C4C2×D4711yescharacteristic
503C22×C22⋊C4C2×D4711yescharacteristic
504C22×C42—471no—
505#398—478no—
506#397—478no—
507#396—478no—
508#394—478no—
509#389—478no—
510#388—478no—
511#386—478no—
512#386—478no—
513#385C2×D4718yescomplemented
514#380—478no—
515C2×#95—471no—
516C2×#95—471no—
517C2×#95—471no—
518C2×#95—471no—
519C2×#95—471no—
520C2×#95—471no—
521C2×#95—478no—
522C2×#95C2×D4711yescharacteristic
523C2×#95C2×D4711yescharacteristic
524C47C2×#242511yescharacteristic, complemented, Sylow
525C25—471no—
526C25—471no—
527C25C22×D4711yescharacteristic
528C22×D4—478no—
529C22×D4—474no—
530C22×D4—474no—
531C22×D4—474no—
532C22×D4—944no—
533C22×D4—944no—
534C22×D4—944no—
535C22×D4—944no—
536C22×D4—944no—
537C22×D4—944no—
538C22×D4—944no—
539C22×D4—1882no—
540C23×C4—24no—
541C23×C4—24no—
542C23×C4—42no—
543C23×C4—471no—
544C23×C4—471no—
545C23×C4—474no—
546C23×C4—471no—
547C23×C4—471no—
548C23×C4—471no—
549C23×C4—471no—
550C23×C4—474no—
551C23×C4—474no—
552C23×C4—944no—
553C23×C4—944no—
554C23×C4—944no—
555C23×C4—944no—
556C23×C4—944no—
557C23×C4—944no—
558C23×C4—944no—
559C23×C4—1882no—
560C23×C4—1882no—
561C23×C4C22×D4711yescharacteristic
562C23×C4C22×D4711yescharacteristic
563C23×C4C22×D4711yescharacteristic
564C23×C4C22×D4714yes—
565C23×C4C22×D4711yescharacteristic
566C23×C4C22×D4711yescharacteristic
567C23×C4C22×D4711yescharacteristic
568#123—9432no—
569#123—9432no—
570#121—9432no—
571C4×D4—9432no—
572C2×C4⋊C4—24no—
573C2×C4⋊C4—42no—
574C2×C4⋊C4—474no—
575C2×C4⋊C4—474no—
576C2×C4⋊C4—474no—
577C2×C4⋊C4—474no—
578C2×C4⋊C4—474no—
579C2×C4⋊C4—474no—
580C2×C4⋊C4—944no—
581C2×C4⋊C4—944no—
582C2×C4⋊C4—944no—
583C2×C4⋊C4—944no—
584C2×C4⋊C4—944no—
585C2×C4⋊C4—944no—
586C2×C4⋊C4C22×D4714yes—
587C2×C4⋊C4C22×D4714yes—
588C2×C22⋊C4—24no—
589C2×C22⋊C4—474no—
590C2×C22⋊C4—474no—
591C2×C22⋊C4—474no—
592C2×C22⋊C4—474no—
593C2×C22⋊C4—474no—
594C2×C22⋊C4—474no—
595C2×C22⋊C4—474no—
596C2×C22⋊C4—474no—
597C2×C22⋊C4—474no—
598C2×C22⋊C4—944no—
599C2×C22⋊C4—944no—
600C2×C22⋊C4—944no—
601C2×C22⋊C4—944no—
602C2×C22⋊C4—944no—
603C2×C22⋊C4—944no—
604C2×C22⋊C4—944no—
605C2×C22⋊C4—944no—
606C2×C22⋊C4—1882no—
607C2×C22⋊C4D18818yescomplemented
608C2×C22⋊C4C22×D4714yes—
609C2×C22⋊C4C22×D4714yes—
610C2×C42—474no—
611C2×C42—944no—
612#95—474no—
613#95—474no—
614#95—474no—
615#95—474no—
616#95—474no—
617#95—474no—
618#95C22×D4714yes—
619#95C22×D4714yes—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—474no—
625C24—472no—
626C24—472no—
627C24—942no—
628C24—942no—
629C24—942no—
630C24—942no—
631C24—942no—
632C24—942no—
633C24—942no—
634C24—942no—
635C24—942no—
636C24—942no—
637C24—942no—
638C24—942no—
639C24—942no—
640C24C2×D18814yes—
641C24D4×D4714yes—
642C24#1062535414yes—
643C24C23×D4712yes—
644C24C23×D4711yescharacteristic
645C2×D4—4716no—
646C2×D4—948no—
647C2×D4—9432no—
648C2×D4—948no—
649C2×D4—948no—
650C2×D4—948no—
651C2×D4—948no—
652C2×D4—948no—
653C2×D4—948no—
654C2×D4—1884no—
655C2×D4—18816no—
656C2×D4—18816no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—28no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—28no—
674C22×C4—44no—
675C22×C4—416no—
676C22×C4—474no—
677C22×C4—474no—
678C22×C4—472no—
679C22×C4—472no—
680C22×C4—472no—
681C22×C4—472no—
682C22×C4—472no—
683C22×C4—472no—
684C22×C4—948no—
685C22×C4—948no—
686C22×C4—942no—
687C22×C4—942no—
688C22×C4—942no—
689C22×C4—942no—
690C22×C4—942no—
691C22×C4—942no—
692C22×C4—942no—
693C22×C4—948no—
694C22×C4—942no—
695C22×C4—942no—
696C22×C4—942no—
697C22×C4—942no—
698C22×C4—948no—
699C22×C4—948no—
700C22×C4—942no—
701C22×C4—948no—
702C22×C4—942no—
703C22×C4—942no—
704C22×C4—942no—
705C22×C4—942no—
706C22×C4—948no—
707C22×C4—1884no—
708C22×C4—18816no—
709C22×C4—1884no—
710C22×C4—18816no—
711C22×C4—18816no—
712C22×C4C2×D18814yes—
713C22×C4C2×D18814yes—
714C22×C4#1062535214yes—
715C22×C4C23×D4712yes—
716C22×C4C23×D4712yes—
717C22×C4C23×D4712yes—
718C22×C4C23×D4712yes—
719C22×C4C23×D4712yes—
720C22×C4C23×D4712yes—
721C4⋊C4—28no—
722C4⋊C4—44no—
723C4⋊C4—948no—
724C4⋊C4—948no—
725C4⋊C4—948no—
726C4⋊C4—948no—
727C4⋊C4—948no—
728C4⋊C4—948no—
729C22⋊C4—28no—
730C22⋊C4—948no—
731C22⋊C4—948no—
732C22⋊C4—948no—
733C22⋊C4—948no—
734C22⋊C4—948no—
735C22⋊C4—948no—
736C22⋊C4—948no—
737C22⋊C4—948no—
738C22⋊C4—1884no—
739C22⋊C4C2×D188116yescomplemented
740C42—948no—
741C23—28no—
742C23—28no—
743C23—28no—
744C23—28no—
745C23—28no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—28no—
751C23—474no—
752C23—948no—
753C23—948no—
754C23—948no—
755C23—942no—
756C23—942no—
757C23—942no—
758C23—942no—
759C23—942no—
760C23—942no—
761C23—942no—
762C23—942no—
763C23—942no—
764C23—942no—
765C23—942no—
766C23—942no—
767C23—942no—
768C23—1884no—
769C23—1884no—
770C23—1884no—
771C23—1884no—
772C23—1884no—
773C23—1884no—
774C23—1884no—
775C23—1884no—
776C23—1884no—
777C23—1884no—
778C23—1884no—
779C23#13093999116yes—
780C23C2×D4×D4714yes—
781C23C2×D4×D4712yes—
782C23C22×D18814yes—
783C23C22×D18812yes—
784C23#41×D4712yes—
785C23C2×#1062535212yes—
786C23C2×#1062535414yes—
787C23C2×#1062535412yes—
788C23#1309406912yes—
789C23#1309407112yes—
790C23C24×D4711yescharacteristic
791D4—9432no—
792D4—18816no—
793D4—18816no—
794C2×C4—28no—
795C2×C4—28no—
796C2×C4—28no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—416no—
813C2×C4—44no—
814C2×C4—44no—
815C2×C4—44no—
816C2×C4—474no—
817C2×C4—474no—
818C2×C4—948no—
819C2×C4—948no—
820C2×C4—942no—
821C2×C4—942no—
822C2×C4—942no—
823C2×C4—942no—
824C2×C4—942no—
825C2×C4—942no—
826C2×C4—942no—
827C2×C4—942no—
828C2×C4—942no—
829C2×C4—942no—
830C2×C4—942no—
831C2×C4—942no—
832C2×C4—942no—
833C2×C4—942no—
834C2×C4—942no—
835C2×C4—942no—
836C2×C4—18816no—
837C2×C4—18816no—
838C2×C4—1884no—
839C2×C4—18816no—
840C2×C4—1884no—
841C2×C4—1884no—
842C2×C4—1884no—
843C2×C4C22×D18814yes—
844C2×C4C22×D18814yes—
845C2×C4C2×#1062535214yes—
846C22—24no—
847C22—24no—
848C22—24no—
849C22—24no—
850C22—24no—
851C22—232no—
852C22—24no—
853C22—944no—
854C22—944no—
855C22—944no—
856C22—3768no—
857C22—1882no—
858C22—1882no—
859C22—1882no—
860C22—1882no—
861C22—1882no—
862C22—1882no—
863C22—1882no—
864C22—1882no—
865C22—1882no—
866C22—1882no—
867C22—18816no—
868C22—1882no—
869C22C2×#1309399918yes—
870C22C2×#1309399914yes—
871C22#1568965914yes—
872C22#1568972214yes—
873C22#1568976014yes—
874C22#1568976814yes—
875C22#1568977114yes—
876C22#1568977714yes—
877C22C22×D4×D4711yescharacteristic
878C22C23×D18811yescharacteristic
879C22C2×#41×D4711yescharacteristic
880C22C22×#1062535211yescharacteristic
881C22C22×#1062535411yescharacteristic
882C22C2×#1309406911yescharacteristic
883C22C2×#1309407111yescharacteristic
884C4—24no—
885C4—24no—
886C4—24no—
887C4—42no—
888C4—42no—
889C4—42no—
890C4—944no—
891C4—944no—
892C4—1882no—
893C4—1882no—
894C4—1882no—
895C4—1882no—
896C2—28no—
897C2—3762no—
898C2—1884no—
899C2#2024693718yesdirect product factor
900C2C22×#1309399911yescharacteristic
901C2C2×#1568965911yescharacteristic
902C2C2×#1568972211yescharacteristic
903C2C2×#1568976011yescharacteristic
904C2C2×#1568976811yescharacteristic
905C2C2×#1568977111yescharacteristic
906C2C2×#1568977711yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#385C2
socleC24×C47C24
prime radicalC22×#13093998C2
hypercenterC2×#385D47
hypocenterC47C2×#2425
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C22×#13094008C2semidirect
2. C22×#13094008C2semidirect
4. C22×(C22⋊D47)⋊C4C2semidirect
5. #20246937C2direct (N × H)
6. C2×#15689055C2semidirect
7. C2×#15689050C2semidirect
8. C2×#15689045C2semidirect
9. C2×#15689040C2semidirect
10. C2×#15689022C2semidirect
11. C2×#15689015C2semidirect
12. C2×#15689001C2semidirect
13. C2×#15689000C2semidirect
14. C2×#15688980C2semidirect
15. C22×C47⋊#95C2semidirect
16. C2×C47×#385C2semidirect
25. C2×#13094008C22semidirect
26. C2×#13094008C22semidirect
30. C2×(C22⋊D47)⋊C4C22semidirect
47. #15689055C22semidirect
48. #15689050C22semidirect
49. #15689045C22semidirect
50. #15689040C22semidirect
51. #15689022C22semidirect
52. #15689015C22semidirect
53. #15689001C22semidirect
54. #15689000C22semidirect
55. #15688980C22semidirect
62. C2×C47⋊#95C22semidirect
68. C47×#385C22semidirect
161. C2×C22⋊C4×C47D4semidirect
270. C22⋊C4×C47C2×D4semidirect
456. C2×#385D47semidirect
460. C2×C47#2425semidirect
513. #385C2×D47semidirect
524. C47C2×#2425semidirect
607. C2×C22⋊C4D188semidirect
739. C22⋊C4C2×D188semidirect
899. C2#20246937direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940082
C22×#130939982
C22×(C22⋊D47)⋊C42
#202469372
C2×#156890552
C2×#156890502
C2×#156890452
C2×#156890402
C2×#156890222
C2×#156890152
C2×#156890012
C2×#156890002
C2×#156889802
C22×C47⋊#952
C2×C47×#3852
C2×#242547