Finite Group Databasebeta

← C2×#20247127 #26383730

Subgroups — C2×#20247127 #26383730

Order 12032.

4002 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×#13094009C211yesmaximal, characteristic, complemented
2C22×#13093998C211yesmaximal, characteristic
3C22×(C22⋊D47)⋊C4C211yesmaximal, characteristic, complemented
4C23×Dic47⋊C4C211yesmaximal, characteristic, complemented
5#20247127C2116yesmaximal, direct product factor
6C2×#15689058C211yesmaximal, characteristic, complemented
7C2×#15689056C211yesmaximal, characteristic, complemented
8C2×#15689052C211yesmaximal, characteristic, complemented
9C2×#15689041C211yesmaximal, characteristic, complemented
10C2×#15689012C211yesmaximal, characteristic, complemented
11C2×#15689010C211yesmaximal, characteristic, complemented
12C2×#15689000C211yesmaximal, characteristic, complemented
13C2×#15689000C211yesmaximal, characteristic, complemented
14C2×#15689000C211yesmaximal, characteristic, complemented
15C2×#15688994C211yesmaximal, characteristic, complemented
16C2×C47×#385C211yesmaximal, characteristic, complemented
17C23×D188C2211yescharacteristic
18C23×C22⋊D47C2211yescharacteristic
19C23×C22⋊D47C2211yescharacteristic
20C24×Dic47C2211yescharacteristic
21C24×Dic47C2211yescharacteristic
22C23×C4×D47C2211yescharacteristic
23C2×#13094009—28no—
24C2×#13094009C2218yescomplemented
25C2×#13093998—28no—
26C2×#13093998C2218yes—
27C2×(C22⋊D47)⋊C4—28no—
28C2×(C22⋊D47)⋊C4C2218yescomplemented
29C22×C4⋊Dic47C2211yescharacteristic
30C22×Dic47⋊C4—28no—
31C22×Dic47⋊C4C2211yescharacteristic
32C22×Dic47⋊C4C2211yescharacteristic
33C22×Dic47⋊C4C2211yescharacteristic
34C22×Dic47⋊C4C2211yescharacteristic
35C22×Dic47⋊C4C2211yescharacteristic
36C22×Dic47⋊C4C2218yescomplemented
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#15689058C2218yescomplemented
48#15689056C2218yescomplemented
49#15689052C2218yescomplemented
50#15689041C2218yescomplemented
51#15689012C2218yescomplemented
52#15689010C2218yescomplemented
53#15689000C2218yescomplemented
54#15689000C2218yescomplemented
55#15689000C2218yescomplemented
56#15688994C2218yescomplemented
57C2×C47⋊#95C2211yescharacteristic
58C2×C47⋊#95C2211yescharacteristic
59C2×C47⋊#95C2211yescharacteristic
60C2×C47⋊#95C2211yescharacteristic
61C2×C47⋊#95C2211yescharacteristic
62C2×C47⋊#95C2211yescharacteristic
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×Dic47C2314yes—
94C23×Dic47C2314yes—
95C23×Dic47C2311yescharacteristic
96C23×Dic47C2311yescharacteristic
97C23×Dic47C2311yescharacteristic
98C23×Dic47C2311yescharacteristic
99C22×C4×D47—24no—
100C22×C4×D47—24no—
101C22×C4×D47—42no—
102C22×C4×D47C2314yes—
103#13094009—232no—
104#13093998—232no—
105(C22⋊D47)⋊C4—232no—
106C2×C4⋊Dic47—24no—
107C2×C4⋊Dic47C2314yes—
108C2×Dic47⋊C4—24no—
109C2×Dic47⋊C4—24no—
110C2×Dic47⋊C4—24no—
111C2×Dic47⋊C4—24no—
112C2×Dic47⋊C4—232no—
113C2×Dic47⋊C4D418yescomplemented
114C2×Dic47⋊C4C2314yes—
115C2×Dic47⋊C4C2314yes—
116C2×Dic47⋊C4C2314yes—
117C2×Dic47⋊C4C2314yes—
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×C47C2311yescharacteristic
153C23×C4×C47C2311yescharacteristic
154C23×C4×C47C2314yes—
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×C47—24no—
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×C47#4114yes—
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—28no—
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—28no—
210C22×C4×C47—44no—
211C22×C4×C47—416no—
212C22×C4×C47C2×D414yes—
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—232no—
228C22×Dic47—22no—
229C22×Dic47—22no—
230C22×Dic47—28no—
231C22×Dic47—22no—
232C22×Dic47—22no—
233C22×Dic47—22no—
234C22×Dic47—22no—
235C22×Dic47—22no—
236C22×Dic47—22no—
237C22×Dic47—28no—
238C22×Dic47—28no—
239C22×Dic47—22no—
240C22×Dic47—22no—
241C22×Dic47—22no—
242C22×Dic47—28no—
243C22×Dic47—22no—
244C22×Dic47—22no—
245C22×Dic47—22no—
246C22×Dic47—28no—
247C22×Dic47—44no—
248C22×Dic47—416no—
249C22×Dic47C2×D414yes—
250C22×Dic47C2×D414yes—
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×C47—28no—
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—
281Dic47⋊C4—28no—
282Dic47⋊C4—28no—
283Dic47⋊C4—28no—
284Dic47⋊C4—28no—
285Dic47⋊C4C2×D4116yescomplemented
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#123116yescomplemented
298C23×C47C22×D414yes—
299C23×C47C22×D412yes—
300C23×C47C22×D412yes—
301C23×C47C2×#4112yes—
302C23×C47C2×#4114yes—
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—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—22no—
354C2×C4×C47—22no—
355C2×C4×C47—416no—
356C2×C4×C47—44no—
357C2×C4×C47—44no—
358C2×C4×C47—44no—
359C2×C4×C47—44no—
360C2×C4×C47—44no—
361C2×C4×C47C22×D414yes—
362C22⋊D47—232no—
363C22⋊D47—416no—
364C2×Dic47—232no—
365C2×Dic47—28no—
366C2×Dic47—28no—
367C2×Dic47—28no—
368C2×Dic47—28no—
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—22no—
383C2×Dic47—416no—
384C2×Dic47—44no—
385C2×Dic47—44no—
386C2×Dic47C22×D414yes—
387C2×Dic47C22×D414yes—
388C2×Dic47C22×D414yes—
389C2×Dic47C2×#4114yes—
390D188—416no—
391C4×D47—416no—
392C2×#2443—471nomaximal, Sylow
393C22×C47—24no—
394C22×C47—24no—
395C22×C47—24no—
396C22×C47—24no—
397C22×C47—24no—
398C22×C47—232no—
399C22×C47—24no—
400C22×C47C2×#12314yes—
401C22×C47C2×#12318yescomplemented
402C22×C47#52514yes—
403C22×C47#53914yes—
404C22×C47D4214yes—
405C22×C47#54714yes—
406C22×C47#54814yes—
407C22×C47#55314yes—
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—42no—
420C2×D47—42no—
421C2×D47—416no—
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—42no—
433C4×C47—42no—
434C4×C47—42no—
435C4×C47—42no—
436C4×C47—42no—
437Dic47—24no—
438Dic47—24no—
439Dic47—24no—
440Dic47—24no—
441Dic47—42no—
442Dic47—42no—
443C22×#123—471no—
444C22×#121—471no—
445C22×C4×D4—471no—
446C23×C4⋊C4—471no—
447#2443—4716no—
448C2×#399—471no—
449C2×#398—471no—
450C2×#397—471no—
451C2×#394—471no—
452C2×#388—471no—
453C2×#387—471no—
454C2×#386—471no—
455C2×#386—471no—
456C2×#386—471no—
457C2×#385—471no—
458C2×#385D4711yescharacteristic, complemented
459C2×C47—28no—
460C2×C47#244318yescomplemented
461C2×C47C22×#12311yescharacteristic
462C2×C47C2×#52511yescharacteristic
463C2×C47C2×#53911yescharacteristic
464C2×C47C2×D4211yescharacteristic
465C2×C47C2×#54711yescharacteristic
466C2×C47C2×#54811yescharacteristic
467C2×C47C2×#55311yescharacteristic
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—948no—
479C2×#121—478no—
480C2×#121—948no—
481C2×C4×D4—478no—
482C2×C4×D4—948no—
483C22×C4⋊C4—471no—
484C22×C4⋊C4—471no—
485C22×C4⋊C4—471no—
486C22×C4⋊C4—471no—
487C22×C4⋊C4—471no—
488C22×C4⋊C4—471no—
489C22×C4⋊C4—478no—
490C22×C4⋊C4—948no—
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#399—478no—
506#398—478no—
507#397—478no—
508#394—478no—
509#388—478no—
510#387—478no—
511#386—478no—
512#386—478no—
513#386—478no—
514#385—478no—
515#385C2×D4718yescomplemented
516C2×#95—471no—
517C2×#95—471no—
518C2×#95—471no—
519C2×#95—471no—
520C2×#95—471no—
521C2×#95—471no—
522C2×#95C2×D4711yescharacteristic
523C2×#95C2×D4711yescharacteristic
524C47C2×#244311yescharacteristic, 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—471no—
546C23×C4—471no—
547C23×C4—474no—
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×D4711yescharacteristic
565C23×C4C22×D4711yescharacteristic
566C23×C4C22×D4714yes—
567C23×C4C22×D4711yescharacteristic
568#123—9432no—
569#121—9432no—
570C4×D4—9432no—
571C2×C4⋊C4—24no—
572C2×C4⋊C4—42no—
573C2×C4⋊C4—478no—
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—9432no—
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—24no—
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—474no—
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—944no—
607C2×C22⋊C4—1882no—
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—
640C24#1062535014yes—
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—28no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—28no—
676C22×C4—44no—
677C22×C4—416no—
678C22×C4—474no—
679C22×C4—474no—
680C22×C4—474no—
681C22×C4—474no—
682C22×C4—472no—
683C22×C4—472no—
684C22×C4—472no—
685C22×C4—472no—
686C22×C4—472no—
687C22×C4—472no—
688C22×C4—948no—
689C22×C4—948no—
690C22×C4—948no—
691C22×C4—948no—
692C22×C4—948no—
693C22×C4—9432no—
694C22×C4—942no—
695C22×C4—942no—
696C22×C4—942no—
697C22×C4—942no—
698C22×C4—948no—
699C22×C4—942no—
700C22×C4—942no—
701C22×C4—942no—
702C22×C4—942no—
703C22×C4—942no—
704C22×C4—942no—
705C22×C4—942no—
706C22×C4—948no—
707C22×C4—942no—
708C22×C4—942no—
709C22×C4—942no—
710C22×C4—1884no—
711C22×C4—18816no—
712C22×C4—1884no—
713C22×C4—18816no—
714C22×C4D4×D4714yes—
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—4716no—
724C4⋊C4—948no—
725C4⋊C4—948no—
726C4⋊C4—948no—
727C4⋊C4—948no—
728C4⋊C4—948no—
729C22⋊C4—28no—
730C22⋊C4—28no—
731C22⋊C4—948no—
732C22⋊C4—948no—
733C22⋊C4—948no—
734C22⋊C4—948no—
735C22⋊C4—948no—
736C22⋊C4—948no—
737C22⋊C4—948no—
738C22⋊C4—948no—
739C22⋊C4—1884no—
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#13094009116yescomplemented
780C23C2×D4×D4714yes—
781C23C2×D4×D4712yes—
782C23C2×D4×D4712yes—
783C23#41×D4712yes—
784C23C2×#1062535014yes—
785C23C2×#1062535012yes—
786C23C2×#1062535414yes—
787C23C2×#1062535412yes—
788C23#1309406912yes—
789C23#1309407112yes—
790C23C24×D4711yescharacteristic
791D4—9432no—
792D4—18816no—
793D4—18816no—
794C2×C4—28no—
795C2×C4—22no—
796C2×C4—22no—
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—44no—
817C2×C4—44no—
818C2×C4—474no—
819C2×C4—474no—
820C2×C4—474no—
821C2×C4—474no—
822C2×C4—9432no—
823C2×C4—948no—
824C2×C4—948no—
825C2×C4—948no—
826C2×C4—948no—
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—942no—
837C2×C4—942no—
838C2×C4—942no—
839C2×C4—942no—
840C2×C4—942no—
841C2×C4—18816no—
842C2×C4—18816no—
843C2×C4—1884no—
844C2×C4—1884no—
845C2×C4C2×D4×D4714yes—
846C22—24no—
847C22—24no—
848C22—24no—
849C22—232no—
850C22—24no—
851C22—24no—
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—18816no—
866C22—1882no—
867C22—1882no—
868C22—1882no—
869C22C2×#1309400914yes—
870C22C2×#1309400918yescomplemented
871C22#1568963614yes—
872C22#1568972214yes—
873C22#1568975514yes—
874C22#1568977114yes—
875C22#1568978214yes—
876C22#1568982214yes—
877C22C22×D4×D4711yescharacteristic
878C22C22×D4×D4711yescharacteristic
879C22C2×#41×D4711yescharacteristic
880C22C22×#1062535011yescharacteristic
881C22C22×#1062535411yescharacteristic
882C22C2×#1309406911yescharacteristic
883C22C2×#1309407111yescharacteristic
884C4—24no—
885C4—42no—
886C4—42no—
887C4—42no—
888C4—42no—
889C4—42no—
890C4—944no—
891C4—944no—
892C4—944no—
893C4—944no—
894C4—1882no—
895C4—1882no—
896C2—28no—
897C2—3762no—
898C2—1884no—
899C2#2024712718yesdirect product factor
900C2C22×#1309400911yescharacteristic
901C2C2×#1568963611yescharacteristic
902C2C2×#1568972211yescharacteristic
903C2C2×#1568975511yescharacteristic
904C2C2×#1568977111yescharacteristic
905C2C2×#1568978211yescharacteristic
906C2C2×#1568982211yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#385C2
socleC24×C47C24
prime radicalC22×#13093998C2
hypercenterC2×#385D47
hypocenterC47C2×#2443
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C22×#13094009C2semidirect
3. C22×(C22⋊D47)⋊C4C2semidirect
4. C23×Dic47⋊C4C2semidirect
5. #20247127C2direct (N × H)
6. C2×#15689058C2semidirect
7. C2×#15689056C2semidirect
8. C2×#15689052C2semidirect
9. C2×#15689041C2semidirect
10. C2×#15689012C2semidirect
11. C2×#15689010C2semidirect
12. C2×#15689000C2semidirect
13. C2×#15689000C2semidirect
14. C2×#15689000C2semidirect
15. C2×#15688994C2semidirect
16. C2×C47×#385C2semidirect
24. C2×#13094009C22semidirect
28. C2×(C22⋊D47)⋊C4C22semidirect
36. C22×Dic47⋊C4C22semidirect
47. #15689058C22semidirect
48. #15689056C22semidirect
49. #15689052C22semidirect
50. #15689041C22semidirect
51. #15689012C22semidirect
52. #15689010C22semidirect
53. #15689000C22semidirect
54. #15689000C22semidirect
55. #15689000C22semidirect
56. #15688994C22semidirect
68. C47×#385C22semidirect
113. C2×Dic47⋊C4D4semidirect
285. Dic47⋊C4C2×D4semidirect
297. C23×C47#123semidirect
401. C22×C47C2×#123semidirect
458. C2×#385D47semidirect
460. C2×C47#2443semidirect
515. #385C2×D47semidirect
524. C47C2×#2443semidirect
779. C23#13094009semidirect
870. C22C2×#13094009semidirect
899. C2#20247127direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940092
C22×#130939982
C22×(C22⋊D47)⋊C42
C23×Dic47⋊C42
#202471272
C2×#156890582
C2×#156890562
C2×#156890522
C2×#156890412
C2×#156890122
C2×#156890102
C2×#156890002
C2×#156889942
C2×C47×#3852
C2×#244347