Finite Group Databasebeta

← C2×#20243927 #26218286

Subgroups — C2×#20243927 #26218286

Order 12032.

2078 conjugacy classes of subgroups.

The subgroup lattice has 1030 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689682C211yesmaximal, characteristic
2C2×#15689596C211yesmaximal, characteristic, complemented
3C22×#13093939C211yesmaximal, characteristic, complemented
4C22×#13093938C211yesmaximal, characteristic, complemented
5#20243927C218yesmaximal, direct product factor
6C2×#15688890C211yesmaximal, characteristic, complemented
7C2×#15688889C211yesmaximal, characteristic, complemented
8C22×#99×C47C211yesmaximal, characteristic, complemented
9C23×C22⋊D47C2211yescharacteristic
10#15689682—22no—
11#15689682—22no—
12#15689682C414yescomplemented
13#15689682C2214yes—
14C2×#13094007C412yescomplemented
15C2×#13094005—21no—
16C2×#13093996—22no—
17C2×#13093993C412yescomplemented
18C2×#13093992—21no—
19#15689596—22no—
20#15689596—22no—
21#15689596—22no—
22#15689596C2214yescomplemented
23C2×C4×C22⋊D47—22no—
24C2×(C22⋊D47)⋊C4—22no—
25C2×#13093980—21no—
26C22×C22⋊Dic47C2211yescharacteristic
27C22×C22⋊Dic47C2211yescharacteristic
28C22×C22⋊Dic47C2211yescharacteristic
29C2×C22⋊C4×D47—21no—
30C2×#13093939—22no—
31C2×#13093939—22no—
32C2×#13093939C2214yescomplemented
33C2×#13093938—22no—
34C2×#13093938—22no—
35C2×#13093938C2214yescomplemented
36#15688890C2214yescomplemented
37#15688889C2214yescomplemented
38C23×D4×C47C2211yescharacteristic
39C22×C22⋊C4×C47C2211yescharacteristic
40C22×C22⋊C4×C47C2211yescharacteristic
41C2×#99×C47—22no—
42C2×#99×C47—22no—
43C2×#99×C47C2214yescomplemented
44C24×D47D411yescharacteristic
45C22×C22⋊D47—21no—
46C22×C22⋊D47—21no—
47C22×C22⋊D47—21no—
48C22×C22⋊D47—21no—
49C22×C22⋊D47—21no—
50C22×C22⋊D47—21no—
51C22×C22⋊D47—21no—
52C22×C22⋊D47—21no—
53C22×C22⋊D47—22no—
54C22×C22⋊D47C2×C412yes—
55C22×C22⋊D47C2×C412yes—
56C22×C22⋊D47D412yes—
57C22×C22⋊D47D412yes—
58C22×C22⋊D47D412yes—
59C22×C22⋊D47C2312yes—
60C23×Dic47—21no—
61C23×Dic47—21no—
62C23×Dic47—21no—
63C23×Dic47D411yescharacteristic
64C22×C4×D47—22no—
65#13094007—24no—
66#13094007C2×C418yescomplemented
67#13094005—24no—
68#13094005—24no—
69#13093996—28no—
70#13093996—28no—
71#13093993—24no—
72#13093993C2×C418yescomplemented
73#13093992—24no—
74#13093992—24no—
75C4×C22⋊D47—28no—
76C4×C22⋊D47—28no—
77(C22⋊D47)⋊C4—28no—
78(C22⋊D47)⋊C4—28no—
79#13093980—24no—
80#13093980—24no—
81C2×Dic47⋊C4—22no—
82C2×Dic47⋊C4—22no—
83C2×C22⋊Dic47—21no—
84C2×C22⋊Dic47—21no—
85C2×C22⋊Dic47—21no—
86C2×C22⋊Dic47—21no—
87C2×C22⋊Dic47—21no—
88C2×C22⋊Dic47—21no—
89C2×C22⋊Dic47—22no—
90C2×C22⋊Dic47—21no—
91C2×C22⋊Dic47—21no—
92C2×C22⋊Dic47—21no—
93C2×C22⋊Dic47—21no—
94C2×C22⋊Dic47—21no—
95C2×C22⋊Dic47C2×C412yescomplemented
96C2×C22⋊Dic47C2×C412yescomplemented
97C2×C22⋊Dic47D412yescomplemented
98C2×C22⋊Dic47D412yescomplemented
99C2×C22⋊Dic47C2312yes—
100C2×C22⋊Dic47C2312yes—
101C2×C22⋊Dic47C2312yes—
102C2×(C2×D47)⋊C4—22no—
103C2×(C2×D47)⋊C4—22no—
104C22⋊C4×D47—24no—
105C22⋊C4×D47—24no—
106C2×C4×Dic47—22no—
107#13093939—28no—
108#13093938—28no—
109C25×C47C2×C411yescharacteristic, complemented
110C25×C47C2311yescharacteristic
111C22×D4×C47—21no—
112C22×D4×C47—21no—
113C22×D4×C47—21no—
114C22×D4×C47—21no—
115C22×D4×C47—21no—
116C22×D4×C47—21no—
117C22×D4×C47—21no—
118C22×D4×C47—21no—
119C22×D4×C47—21no—
120C22×D4×C47—21no—
121C22×D4×C47—21no—
122C22×D4×C47—21no—
123C22×D4×C47C2×C412yescomplemented
124C22×D4×C47C2312yes—
125C23×C4×C47—21no—
126C23×C4×C47—21no—
127C23×C4×C47C2×C411yescharacteristic, complemented
128C2×C22⋊C4×C47—21no—
129C2×C22⋊C4×C47—21no—
130C2×C22⋊C4×C47—21no—
131C2×C22⋊C4×C47—21no—
132C2×C22⋊C4×C47—21no—
133C2×C22⋊C4×C47—21no—
134C2×C22⋊C4×C47—21no—
135C2×C22⋊C4×C47—21no—
136C2×C22⋊C4×C47D412yescomplemented
137C2×C22⋊C4×C47D412yescomplemented
138C2×C22⋊C4×C47C2312yes—
139C2×C22⋊C4×C47C2312yes—
140#99×C47—28no—
141C24×C47—21no—
142C24×C47—21no—
143C24×C47—21no—
144C24×C47—21no—
145C24×C47—21no—
146C24×C47—21no—
147C24×C47—82no—
148C24×C47—82no—
149C24×C47C22×C411yescharacteristic
150C24×C47C22×C411yescharacteristic
151C24×C47C22×C412yescomplemented
152C24×C47C2×D411yescharacteristic
153C24×C47C2×D411yescharacteristic
154C24×C47C2×D411yescharacteristic
155C24×C47C2×D411yescharacteristic
156C24×C47C2×D411yescharacteristic
157C24×C47C2×D411yescharacteristic
158C24×C47C2×D411yescharacteristic
159C24×C47C2×D411yescharacteristic
160C24×C47#4111yescharacteristic
161C24×C47#4111yescharacteristic
162C24×C47#4111yescharacteristic
163C24×C47#4111yescharacteristic
164C24×C47C2411yescharacteristic
165C23×D47—21no—
166C23×D47—21no—
167C23×D47—21no—
168C23×D47—21no—
169C23×D47—82no—
170C23×D47C22⋊C412yes—
171C23×D47C22⋊C412yes—
172C23×D47C2×D412yes—
173C2×D4×C47—22no—
174C2×D4×C47—22no—
175C2×D4×C47—22no—
176C2×D4×C47—22no—
177C2×D4×C47—22no—
178C2×D4×C47—22no—
179C2×D4×C47—22no—
180C2×D4×C47—22no—
181C2×D4×C47—22no—
182C2×D4×C47—22no—
183C2×D4×C47—22no—
184C2×D4×C47—22no—
185C2×D4×C47—41no—
186C2×D4×C47—41no—
187C2×D4×C47—41no—
188C2×D4×C47—41no—
189C2×D4×C47—41no—
190C2×D4×C47—41no—
191C2×D4×C47—41no—
192C2×D4×C47—41no—
193C2×D4×C47—41no—
194C2×D4×C47—41no—
195C2×D4×C47—41no—
196C2×D4×C47—41no—
197C2×D4×C47—41no—
198C2×D4×C47—41no—
199C2×D4×C47—41no—
200C2×D4×C47—41no—
201C22×C4×C47—21no—
202C22×C4×C47—21no—
203C22×C4×C47—21no—
204C22×C4×C47—21no—
205C22×C4×C47—21no—
206C22×C4×C47—21no—
207C22×C4×C47—22no—
208C22×C4×C47—22no—
209C22×C4×C47—22no—
210C22×C4×C47—22no—
211C22×C4×C47—41no—
212C22×C4×C47—41no—
213C22×C4×C47—82no—
214C22×C4×C47—82no—
215C22×C4×C47C22×C412yescomplemented
216C2×C22⋊D47—22no—
217C2×C22⋊D47—22no—
218C2×C22⋊D47—22no—
219C2×C22⋊D47—22no—
220C2×C22⋊D47—22no—
221C2×C22⋊D47—22no—
222C2×C22⋊D47—22no—
223C2×C22⋊D47—22no—
224C2×C22⋊D47—22no—
225C2×C22⋊D47—22no—
226C2×C22⋊D47—22no—
227C2×C22⋊D47—22no—
228C2×C22⋊D47—22no—
229C2×C22⋊D47—22no—
230C2×C22⋊D47—22no—
231C2×C22⋊D47—22no—
232C2×C22⋊D47—22no—
233C2×C22⋊D47—22no—
234C2×C22⋊D47—22no—
235C2×C22⋊D47—22no—
236C2×C22⋊D47—22no—
237C2×C22⋊D47—22no—
238C2×C22⋊D47—22no—
239C2×C22⋊D47—22no—
240C2×C22⋊D47—28no—
241C2×C22⋊D47—84no—
242C2×C22⋊D47C22⋊C414yes—
243C2×C22⋊D47C22⋊C414yes—
244C2×C22⋊D47C22×C414yes—
245C2×C22⋊D47C2×D414yes—
246C22×Dic47—21no—
247C22×Dic47—21no—
248C22×Dic47—21no—
249C22×Dic47—21no—
250C22×Dic47—22no—
251C22×Dic47—22no—
252C22×Dic47—22no—
253C22×Dic47—22no—
254C22×Dic47—22no—
255C22×Dic47—22no—
256C22×Dic47—22no—
257C22×Dic47—41no—
258C22×Dic47—41no—
259C22×Dic47—82no—
260C22×Dic47—82no—
261C22×Dic47—82no—
262C22×Dic47C22⋊C412yes—
263C22×Dic47C22⋊C412yes—
264C22×Dic47C2×D412yes—
265C2×C4×D47—28no—
266C2×C4×D47—84no—
267C22⋊C4×C47—22no—
268C22⋊C4×C47—22no—
269C22⋊C4×C47—22no—
270C22⋊C4×C47—22no—
271C22⋊C4×C47—22no—
272C22⋊C4×C47—41no—
273C22⋊C4×C47—41no—
274C22⋊C4×C47C2×D414yescomplemented
275C22⋊Dic47—22no—
276C22⋊Dic47—22no—
277C22⋊Dic47—22no—
278C22⋊Dic47—22no—
279C22⋊Dic47—22no—
280C22⋊Dic47—22no—
281C22⋊Dic47—28no—
282C22⋊Dic47—22no—
283C22⋊Dic47—22no—
284C22⋊Dic47—41no—
285C22⋊Dic47—41no—
286C22⋊Dic47C22×C414yescomplemented
287C22⋊Dic47C2×D414yescomplemented
288(C2×D47)⋊C4—28no—
289(C2×D47)⋊C4—28no—
290Dic47⋊C4—28no—
291Dic47⋊C4—28no—
292C4×Dic47—28no—
293C23×C47—22no—
294C23×C47—22no—
295C23×C47—22no—
296C23×C47—42no—
297C23×C47—42no—
298C23×C47—42no—
299C23×C47—42no—
300C23×C47—42no—
301C23×C47—42no—
302C23×C47—42no—
303C23×C47—44no—
304C23×C47—41no—
305C23×C47—41no—
306C23×C47—41no—
307C23×C47—41no—
308C23×C47—82no—
309C23×C47—82no—
310C23×C47—81no—
311C23×C47—81no—
312C23×C47—81no—
313C23×C47—81no—
314C23×C47—81no—
315C23×C47—81no—
316C23×C47—81no—
317C23×C47—81no—
318C23×C47—82no—
319C23×C47—82no—
320C23×C47—82no—
321C23×C47—82no—
322C23×C47C2×C22⋊C411yescharacteristic
323C23×C47C2×C22⋊C411yescharacteristic
324C23×C47C2×C22⋊C411yescharacteristic
325C23×C47C2×C22⋊C411yescharacteristic
326C23×C47C4×D411yescharacteristic
327C23×C47C4×D411yescharacteristic
328C23×C47C4×D411yescharacteristic
329C23×C47C4×D411yescharacteristic
330C23×C47C4×D411yescharacteristic
331C23×C47C4×D411yescharacteristic
332C23×C47C4×D411yescharacteristic
333C23×C47C4×D411yescharacteristic
334C23×C47#12011yescharacteristic
335C23×C47#12011yescharacteristic
336C23×C47#12011yescharacteristic
337C23×C47#12011yescharacteristic
338C23×C47#12111yescharacteristic
339C23×C47#12111yescharacteristic
340C23×C47#12111yescharacteristic
341C23×C47#12111yescharacteristic
342C23×C47#12111yescharacteristic
343C23×C47#12111yescharacteristic
344C23×C47#12111yescharacteristic
345C23×C47#12111yescharacteristic
346C23×C47#12311yescharacteristic
347C23×C47#12311yescharacteristic
348C23×C47#12311yescharacteristic
349C23×C47#12311yescharacteristic
350C23×C47C23×C411yescharacteristic
351C23×C47C22×D411yescharacteristic
352C23×C47C22×D411yescharacteristic
353C23×C47C22×D411yescharacteristic
354C23×C47C22×D411yescharacteristic
355C23×C47C2×#4111yescharacteristic
356C23×C47C2×#4111yescharacteristic
357C22×D47—22no—
358C22×D47—22no—
359C22×D47—22no—
360C22×D47—22no—
361C22×D47—22no—
362C22×D47—22no—
363C22×D47—44no—
364C22×D47—44no—
365C22×D47—82no—
366C22×D47—82no—
367C22×D47—82no—
368C22×D47—82no—
369C22×D47—82no—
370C22×D47C2×C22⋊C414yes—
371D4×C47—42no—
372D4×C47—42no—
373D4×C47—42no—
374D4×C47—42no—
375D4×C47—42no—
376D4×C47—42no—
377D4×C47—42no—
378D4×C47—42no—
379C2×C4×C47—22no—
380C2×C4×C47—22no—
381C2×C4×C47—22no—
382C2×C4×C47—24no—
383C2×C4×C47—44no—
384C2×C4×C47—41no—
385C2×C4×C47—41no—
386C2×C4×C47—41no—
387C2×C4×C47—41no—
388C2×C4×C47—42no—
389C2×C4×C47—82no—
390C2×C4×C47—82no—
391C2×C4×C47—82no—
392C2×C4×C47—82no—
393C2×C4×C47—82no—
394C22⋊D47—24no—
395C22⋊D47—24no—
396C22⋊D47—24no—
397C22⋊D47—24no—
398C22⋊D47—24no—
399C22⋊D47—24no—
400C22⋊D47—24no—
401C22⋊D47—24no—
402C22⋊D47—88no—
403C2×Dic47—22no—
404C2×Dic47—22no—
405C2×Dic47—22no—
406C2×Dic47—22no—
407C2×Dic47—22no—
408C2×Dic47—22no—
409C2×Dic47—24no—
410C2×Dic47—24no—
411C2×Dic47—44no—
412C2×Dic47—44no—
413C2×Dic47—42no—
414C2×Dic47—82no—
415C2×Dic47—82no—
416C2×Dic47—82no—
417C2×Dic47—82no—
418C2×Dic47—82no—
419C2×Dic47—82no—
420C2×Dic47—82no—
421C2×Dic47C2×C22⋊C414yes—
422C4×D47—88no—
423C2×#1913—471nomaximal, Sylow
424C22×C47—22no—
425C22×C47—22no—
426C22×C47—22no—
427C22×C47—22no—
428C22×C47—22no—
429C22×C47—22no—
430C22×C47—22no—
431C22×C47—41no—
432C22×C47—41no—
433C22×C47—41no—
434C22×C47—41no—
435C22×C47—41no—
436C22×C47—41no—
437C22×C47—41no—
438C22×C47—41no—
439C22×C47—41no—
440C22×C47—41no—
441C22×C47—41no—
442C22×C47—41no—
443C22×C47—41no—
444C22×C47—41no—
445C22×C47—41no—
446C22×C47—41no—
447C22×C47—41no—
448C22×C47—41no—
449C22×C47—41no—
450C22×C47—41no—
451C22×C47—41no—
452C22×C47—41no—
453C22×C47—41no—
454C22×C47—41no—
455C22×C47—41no—
456C22×C47—41no—
457C22×C47—41no—
458C22×C47—41no—
459C22×C47—44no—
460C22×C47—42no—
461C22×C47—82no—
462C22×C47—82no—
463C22×C47—82no—
464C22×C47—82no—
465C22×C47—82no—
466C22×C47—82no—
467C22×C47#38611yescharacteristic
468C22×C47#38611yescharacteristic
469C22×C47#38611yescharacteristic
470C22×C47#38611yescharacteristic
471C22×C47#38611yescharacteristic
472C22×C47#38611yescharacteristic
473C22×C47#38611yescharacteristic
474C22×C47#38611yescharacteristic
475C22×C47C22×C22⋊C411yescharacteristic
476C22×C47C2×C4×D411yescharacteristic
477C22×C47C2×C4×D411yescharacteristic
478C22×C47C2×#12011yescharacteristic
479C22×C47C2×#12111yescharacteristic
480C22×C47C2×#12111yescharacteristic
481C22×C47C2×#12311yescharacteristic
482C2×D47—24no—
483C2×D47—44no—
484C2×D47—44no—
485C2×D47—44no—
486C2×D47—44no—
487C2×D47—82no—
488C2×D47—82no—
489C2×D47—82no—
490C4×C47—44no—
491C4×C47—42no—
492C4×C47—82no—
493Dic47—24no—
494Dic47—44no—
495Dic47—44no—
496Dic47—82no—
497C2×#534—471no—
498C2×#518—471no—
499C22×#99—471no—
500C22×#99—471no—
501C22×#99D4711yescharacteristic, complemented
502#1913—478no—
503C2×#342—471no—
504C2×#342—471no—
505C2×C47—21no—
506C2×C47—21no—
507C2×C47—21no—
508C2×C47—21no—
509C2×C47—21no—
510C2×C47—21no—
511C2×C47—21no—
512C2×C47—21no—
513C2×C47—21no—
514C2×C47—21no—
515C2×C47—21no—
516C2×C47—21no—
517C2×C47—21no—
518C2×C47—21no—
519C2×C47—82no—
520C2×C47#191312yescomplemented
521C2×C47C2×#38611yescharacteristic
522D47—44no—
523C23×D4—471no—
524C23×D4C2×D4711yescharacteristic
525#534—474no—
526#534—474no—
527#534—942no—
528#534—942no—
529C2×#123—472no—
530C2×#123—941no—
531C2×#121—942no—
532C2×#120—472no—
533C2×#120—941no—
534#518—474no—
535#518—942no—
536#518—942no—
537#518—942no—
538C2×C4×D4—942no—
539C2×C4×D4—942no—
540C2×#117—941no—
541C22×C22⋊C4—471no—
542C22×C22⋊C4—471no—
543C22×C22⋊C4—471no—
544C22×C22⋊C4—941no—
545C22×C22⋊C4C2×D4711yescharacteristic
546C22×C22⋊C4C2×D4711yescharacteristic
547C2×#99—22no—
548C2×#99—22no—
549C2×#99—474no—
550C2×#99—474no—
551C2×#99—942no—
552C2×#99—942no—
553C2×#99—942no—
554C2×#99—942no—
555C2×#99C2×D4714yescomplemented
556#342—474no—
557#342—474no—
558C47C2×#191311yescharacteristic, complemented, Sylow
559C25—471no—
560C25C4×D4711yescharacteristic, complemented
561C25C22×D4711yescharacteristic
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—21no—
565C22×D4—21no—
566C22×D4—21no—
567C22×D4—21no—
568C22×D4—21no—
569C22×D4—21no—
570C22×D4—21no—
571C22×D4—21no—
572C22×D4—21no—
573C22×D4—21no—
574C22×D4—472no—
575C22×D4—472no—
576C22×D4—472no—
577C22×D4—472no—
578C22×D4—472no—
579C22×D4—472no—
580C22×D4—941no—
581C22×D4—941no—
582C22×D4—941no—
583C22×D4—941no—
584C22×D4—941no—
585C22×D4—941no—
586C22×D4—941no—
587C22×D4—941no—
588C22×D4—942no—
589C22×D4C4×D4712yescomplemented
590C22×D4C22×D4712yes—
591C23×C4—21no—
592C23×C4—21no—
593C23×C4—471no—
594C23×C4—942no—
595C23×C4—941no—
596C23×C4—941no—
597C23×C4—941no—
598C23×C4C4×D4711yescharacteristic, complemented
599#123—478no—
600#123—944no—
601#123—944no—
602#123—944no—
603#121—948no—
604#121—948no—
605#120—478no—
606#120—944no—
607#120—944no—
608#120—944no—
609C4×D4—948no—
610C4×D4—948no—
611C4×D4—948no—
612C4×D4—948no—
613#117—944no—
614#117—944no—
615C2×C4⋊C4—942no—
616C2×C4⋊C4—942no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—472no—
626C2×C22⋊C4—472no—
627C2×C22⋊C4—472no—
628C2×C22⋊C4—472no—
629C2×C22⋊C4—472no—
630C2×C22⋊C4—472no—
631C2×C22⋊C4—472no—
632C2×C22⋊C4—944no—
633C2×C22⋊C4—944no—
634C2×C22⋊C4—942no—
635C2×C22⋊C4—942no—
636C2×C22⋊C4—942no—
637C2×C22⋊C4—941no—
638C2×C22⋊C4—941no—
639C2×C22⋊C4—941no—
640C2×C22⋊C4—941no—
641C2×C22⋊C4—941no—
642C2×C22⋊C4—941no—
643C2×C22⋊C4—941no—
644C2×C22⋊C4—941no—
645C2×C22⋊C4—941no—
646C2×C22⋊C4—941no—
647C2×C22⋊C4—941no—
648C2×C22⋊C4C22⋊D4712yescomplemented
649C2×C22⋊C4C22⋊D4712yescomplemented
650C2×C22⋊C4C22×D4712yes—
651C2×C22⋊C4C22×D4712yes—
652C2×C42—942no—
653#99—28no—
654#99—948no—
655#99—948no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—82no—
663C24—82no—
664C24—472no—
665C24—472no—
666C24—472no—
667C24—941no—
668C24—941no—
669C24—941no—
670C24—941no—
671C24—3762no—
672C24C2×C4×D4711yescharacteristic
673C24C2×C4×D4711yescharacteristic
674C24C2×C4×D4712yescomplemented
675C24#1062535011yescharacteristic
676C24#1062535011yescharacteristic
677C24D4×D4711yescharacteristic
678C24D4×D4711yescharacteristic
679C24D4×D4711yescharacteristic
680C24D4×D4711yescharacteristic
681C24D4×D4711yescharacteristic
682C24D4×D4711yescharacteristic
683C24#1062535211yescharacteristic
684C24#1062535211yescharacteristic
685C24C2×C22⋊D4711yescharacteristic
686C24C2×C22⋊D4711yescharacteristic
687C24C23×D4711yescharacteristic
688C2×D4—22no—
689C2×D4—22no—
690C2×D4—22no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—22no—
694C2×D4—22no—
695C2×D4—22no—
696C2×D4—22no—
697C2×D4—22no—
698C2×D4—22no—
699C2×D4—22no—
700C2×D4—41no—
701C2×D4—41no—
702C2×D4—41no—
703C2×D4—41no—
704C2×D4—41no—
705C2×D4—41no—
706C2×D4—41no—
707C2×D4—41no—
708C2×D4—41no—
709C2×D4—41no—
710C2×D4—41no—
711C2×D4—41no—
712C2×D4—41no—
713C2×D4—41no—
714C2×D4—41no—
715C2×D4—41no—
716C2×D4—474no—
717C2×D4—474no—
718C2×D4—474no—
719C2×D4—474no—
720C2×D4—942no—
721C2×D4—942no—
722C2×D4—942no—
723C2×D4—942no—
724C2×D4—942no—
725C2×D4—942no—
726C2×D4—942no—
727C2×D4—942no—
728C2×D4—942no—
729C2×D4—942no—
730C2×D4—942no—
731C2×D4—942no—
732C2×D4—942no—
733C2×D4—942no—
734C2×D4—942no—
735C2×D4—942no—
736C2×D4—942no—
737C2×D4—942no—
738C2×D4—942no—
739C2×D4—942no—
740C2×D4—942no—
741C2×D4—942no—
742C2×D4—942no—
743C2×D4—942no—
744C2×D4—948no—
745C2×D4—3764no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—41no—
757C22×C4—41no—
758C22×C4—82no—
759C22×C4—82no—
760C22×C4—472no—
761C22×C4—472no—
762C22×C4—472no—
763C22×C4—948no—
764C22×C4—941no—
765C22×C4—941no—
766C22×C4—941no—
767C22×C4—941no—
768C22×C4—942no—
769C22×C4—942no—
770C22×C4—942no—
771C22×C4—942no—
772C22×C4—942no—
773C22×C4—942no—
774C22×C4—942no—
775C22×C4—3764no—
776C22×C4—3762no—
777C22×C4—3762no—
778C22×C4—3762no—
779C22×C4—1881no—
780C22×C4—1881no—
781C22×C4C2×C4×D4712yescomplemented
782C4⋊C4—948no—
783C4⋊C4—948no—
784C22⋊C4—22no—
785C22⋊C4—22no—
786C22⋊C4—22no—
787C22⋊C4—22no—
788C22⋊C4—22no—
789C22⋊C4—41no—
790C22⋊C4—41no—
791C22⋊C4—474no—
792C22⋊C4—474no—
793C22⋊C4—948no—
794C22⋊C4—948no—
795C22⋊C4—948no—
796C22⋊C4—942no—
797C22⋊C4—942no—
798C22⋊C4—942no—
799C22⋊C4—942no—
800C22⋊C4—942no—
801C22⋊C4—942no—
802C22⋊C4—942no—
803C22⋊C4—942no—
804C22⋊C4—1881no—
805C22⋊C4—1881no—
806C22⋊C4C2×C22⋊D4714yescomplemented
807C42—948no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—42no—
816C23—42no—
817C23—42no—
818C23—44no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—82no—
824C23—82no—
825C23—81no—
826C23—81no—
827C23—81no—
828C23—81no—
829C23—81no—
830C23—81no—
831C23—81no—
832C23—81no—
833C23—82no—
834C23—82no—
835C23—82no—
836C23—82no—
837C23—474no—
838C23—942no—
839C23—942no—
840C23—942no—
841C23—942no—
842C23—942no—
843C23—942no—
844C23—3762no—
845C23—3762no—
846C23—3762no—
847C23—3762no—
848C23—3762no—
849C23—1884no—
850C23—1884no—
851C23C22⋊C4×D4711yescharacteristic
852C23C22⋊C4×D4711yescharacteristic
853C23C22⋊C4×D4711yescharacteristic
854C23C22⋊C4×D4711yescharacteristic
855C23(C22⋊D47)⋊C411yescharacteristic
856C23(C22⋊D47)⋊C411yescharacteristic
857C23(C22⋊D47)⋊C411yescharacteristic
858C23(C22⋊D47)⋊C411yescharacteristic
859C23C4×C22⋊D4711yescharacteristic
860C23C4×C22⋊D4711yescharacteristic
861C23C4×C22⋊D4711yescharacteristic
862C23C4×C22⋊D4711yescharacteristic
863C23#1309399211yescharacteristic
864C23#1309399211yescharacteristic
865C23#1309399211yescharacteristic
866C23#1309399211yescharacteristic
867C23#1309399511yescharacteristic
868C23#1309399511yescharacteristic
869C23#1309399511yescharacteristic
870C23#1309399511yescharacteristic
871C23#1309399711yescharacteristic
872C23#1309399711yescharacteristic
873C23#1309399711yescharacteristic
874C23#1309399711yescharacteristic
875C23#1309400611yescharacteristic
876C23#1309400611yescharacteristic
877C23#1309400611yescharacteristic
878C23#1309400611yescharacteristic
879C23C22×C4×D4711yescharacteristic
880C23C2×D4×D4711yescharacteristic
881C23C2×D4×D4711yescharacteristic
882C23C2×D4×D4711yescharacteristic
883C23C22×C22⋊D4711yescharacteristic
884C23C2×#1062535211yescharacteristic
885C23C2×#1062535011yescharacteristic
886D4—42no—
887D4—42no—
888D4—42no—
889D4—42no—
890D4—42no—
891D4—42no—
892D4—42no—
893D4—42no—
894D4—944no—
895D4—944no—
896D4—944no—
897D4—944no—
898D4—944no—
899D4—944no—
900D4—944no—
901D4—944no—
902D4—3768no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—24no—
907C2×C4—44no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—42no—
913C2×C4—82no—
914C2×C4—82no—
915C2×C4—82no—
916C2×C4—82no—
917C2×C4—82no—
918C2×C4—474no—
919C2×C4—942no—
920C2×C4—942no—
921C2×C4—942no—
922C2×C4—942no—
923C2×C4—942no—
924C2×C4—942no—
925C2×C4—944no—
926C2×C4—944no—
927C2×C4—3768no—
928C2×C4—3762no—
929C2×C4—3762no—
930C2×C4—3762no—
931C2×C4—3762no—
932C2×C4—3762no—
933C2×C4—3762no—
934C2×C4—3762no—
935C2×C4—1882no—
936C2×C4—1884no—
937C2×C4—1884no—
938C22—22no—
939C22—22no—
940C22—22no—
941C22—22no—
942C22—22no—
943C22—22no—
944C22—22no—
945C22—41no—
946C22—41no—
947C22—41no—
948C22—41no—
949C22—41no—
950C22—41no—
951C22—41no—
952C22—41no—
953C22—41no—
954C22—41no—
955C22—41no—
956C22—41no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—41no—
967C22—41no—
968C22—41no—
969C22—41no—
970C22—41no—
971C22—41no—
972C22—41no—
973C22—44no—
974C22—42no—
975C22—82no—
976C22—82no—
977C22—82no—
978C22—82no—
979C22—82no—
980C22—82no—
981C22—944no—
982C22—3762no—
983C22—3762no—
984C22—3762no—
985C22—1884no—
986C22—1884no—
987C22—1884no—
988C22—1884no—
989C22#1568899911yescharacteristic
990C22#1568899911yescharacteristic
991C22#1568899911yescharacteristic
992C22#1568899911yescharacteristic
993C22#1568899911yescharacteristic
994C22#1568899911yescharacteristic
995C22#1568899911yescharacteristic
996C22#1568899911yescharacteristic
997C22C2×C22⋊C4×D4711yescharacteristic
998C22C2×(C22⋊D47)⋊C411yescharacteristic
999C22C2×C4×C22⋊D4711yescharacteristic
1000C22C2×#1309399211yescharacteristic
1001C22C2×#1309399511yescharacteristic
1002C22C2×#1309399711yescharacteristic
1003C22C2×#1309400611yescharacteristic
1004C4—44no—
1005C4—42no—
1006C4—82no—
1007C4—944no—
1008C4—3762no—
1009C4—1884no—
1010C4—1884no—
1011C2—21no—
1012C2—21no—
1013C2—21no—
1014C2—21no—
1015C2—21no—
1016C2—21no—
1017C2—21no—
1018C2—21no—
1019C2—21no—
1020C2—21no—
1021C2—21no—
1022C2—21no—
1023C2—21no—
1024C2—21no—
1025C2—82no—
1026C2—1884no—
1027C2#2024392712yesdirect product factor
1028C2C2×#1568899911yescharacteristic
subgroupG/H
centerC22#15688999
commutatorC23×C47C23×C4
FrattiniC24C23×D47
FittingC22×#99×C47C2
socleC22×C47#386
prime radicalC2×#15689682C2
cosocleC24×C47C24
hypercenterC22×#99D47
hypocenterC47C2×#1913
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C25 ◁ C22×#99

Complements

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

NH ≅ G/Ntype
2. C2×#15689596C2semidirect
3. C22×#13093939C2semidirect
4. C22×#13093938C2semidirect
5. #20243927C2direct (N × H)
6. C2×#15688890C2semidirect
7. C2×#15688889C2semidirect
8. C22×#99×C47C2semidirect
12. #15689682C4semidirect
14. C2×#13094007C4semidirect
17. C2×#13093993C4semidirect
22. #15689596C22semidirect
32. C2×#13093939C22semidirect
35. C2×#13093938C22semidirect
36. #15688890C22semidirect
37. #15688889C22semidirect
43. C2×#99×C47C22semidirect
66. #13094007C2×C4semidirect
72. #13093993C2×C4semidirect
95. C2×C22⋊Dic47C2×C4semidirect
96. C2×C22⋊Dic47C2×C4semidirect
97. C2×C22⋊Dic47D4semidirect
98. C2×C22⋊Dic47D4semidirect
109. C25×C47C2×C4semidirect
123. C22×D4×C47C2×C4semidirect
127. C23×C4×C47C2×C4semidirect
136. C2×C22⋊C4×C47D4semidirect
137. C2×C22⋊C4×C47D4semidirect
151. C24×C47C22×C4semidirect
215. C22×C4×C47C22×C4semidirect
274. C22⋊C4×C47C2×D4semidirect
286. C22⋊Dic47C22×C4semidirect
287. C22⋊Dic47C2×D4semidirect
501. C22×#99D47semidirect
520. C2×C47#1913semidirect
555. C2×#99C2×D47semidirect
558. C47C2×#1913semidirect
560. C25C4×D47semidirect
589. C22×D4C4×D47semidirect
598. C23×C4C4×D47semidirect
648. C2×C22⋊C4C22⋊D47semidirect
649. C2×C22⋊C4C22⋊D47semidirect
674. C24C2×C4×D47semidirect
781. C22×C4C2×C4×D47semidirect
806. C22⋊C4C2×C22⋊D47semidirect
1027. C2#20243927direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896822
C2×#156895962
C22×#130939392
C22×#130939382
#202439272
C2×#156888902
C2×#156888892
C22×#99×C472
C2×#191347