Finite Group Databasebeta

← C2×#20254256 #27086949

Subgroups — C2×#20254256 #27086949

Order 12032.

2314 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689696C211yesmaximal, characteristic, complemented
2C2×#15689689C211yesmaximal, characteristic
3#20254256C2116yesmaximal, direct product factor
4C2×#15689466C211yesmaximal, characteristic, complemented
5C2×#15689463C211yesmaximal, characteristic, complemented
6C2×#15689450C211yesmaximal, characteristic, complemented
7C2×#15689445C211yesmaximal, characteristic, complemented
8C2×#15689369C211yesmaximal, characteristic, complemented
9C2×#15689354C211yesmaximal, characteristic, complemented
10C2×#15689350C211yesmaximal, characteristic, complemented
11C2×#15689263C211yesmaximal, characteristic, complemented
12C2×#15689260C211yesmaximal, characteristic, complemented
13C2×#15689275C211yesmaximal, characteristic, complemented
14C2×#15689272C211yesmaximal, characteristic, complemented
15C2×#15689091C211yesmaximal, characteristic, complemented
16C2×C47×#468C211yesmaximal, characteristic, complemented
17C22×#10625350C2211yescharacteristic
18C22×Q8×D47C2211yescharacteristic, complemented
19C22×D4×D47C2211yescharacteristic
20C22×#10625325C2211yescharacteristic
21C22×#10625335C2211yescharacteristic
22C22×#10625336C2211yescharacteristic
23C23×C47⋊C8C2211yescharacteristic, complemented
24#15689696—24no—
25#15689696C2218yescomplemented
26#15689689—24no—
27#15689689C2218yes—
28C2×#13094023—21no—
29C2×#13094020—21no—
30C2×#13094010—21no—
31C2×#13094010—21no—
32C2×#13094009—21no—
33C2×#13094006—21no—
34C2×#13094004C2211yescharacteristic
35C2×#13094003C2211yescharacteristic, complemented
36C2×#13094000C2211yescharacteristic
37C2×#13093999C2211yescharacteristic
38C2×#13093998C2211yescharacteristic
39C2×#13093995C2211yescharacteristic
40C2×#13093994—21no—
41C2×#13093992—21no—
42C2×#13093982C2211yescharacteristic
43C2×#13093982C2211yescharacteristic, complemented
44#15689466C2218yescomplemented
45#15689463C2218yescomplemented
46#15689450C2218yescomplemented
47#15689445C2218yescomplemented
48#15689369C2218yescomplemented
49#15689354C2218yescomplemented
50#15689350C2218yescomplemented
51#15689275C2218yescomplemented
52#15689272C2218yescomplemented
53#15689263C2218yescomplemented
54#15689260C2218yescomplemented
55C2×#13093958C2211yescharacteristic, complemented
56C2×#13093955C2211yescharacteristic, complemented
57C2×#13093955C2211yescharacteristic, complemented
58C2×#13093949C2211yescharacteristic, complemented
59C2×#13093948C2211yescharacteristic, complemented
60C2×#13093947C2211yescharacteristic, complemented
61C2×#13093946C2211yescharacteristic
62C2×#13093945C2211yescharacteristic
63C2×#13093944C2211yescharacteristic
64#15689091C2218yescomplemented
65C2×(C2×D47)⋊C8C2211yescharacteristic
66C2×(C2×D47)⋊C8C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
68C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
69C22×SD16×C47C2211yescharacteristic
70C22×M16×C47C2211yescharacteristic, complemented
71C2×C22⋊Q8×C47C2211yescharacteristic, complemented
72C2×#121×C47C2211yescharacteristic
73C47×#468C2218yescomplemented
74C2×#107×C47C2211yescharacteristic, complemented
75C2×#103×C47C2211yescharacteristic, complemented
76C2×#102×C47C2211yescharacteristic
77C24×D47—21no—
78C2×#10625350—42no—
79C2×#10625350—42no—
80C2×#10625350D414yes—
81C2×#10625350C2314yes—
82C22×Dic94—21no—
83C22×Dic94D411yescharacteristic
84C22×Dic94C2311yescharacteristic
85C2×Q8×D47—22no—
86C2×Q8×D47—42no—
87C2×Q8×D47—42no—
88C2×Q8×D47C2314yescomplemented
89C22×D188—21no—
90C22×D188D411yescharacteristic
91C22×D188C2311yescharacteristic
92C22×C22⋊D47—21no—
93C22×C22⋊D47—21no—
94C22×C22⋊D47—21no—
95C22×C22⋊D47D411yescharacteristic
96C22×C22⋊D47D411yescharacteristic
97C2×D4×D47—22no—
98C2×D4×D47—42no—
99C2×D4×D47—42no—
100C2×D4×D47C2314yes—
101C22×C4×D47—21no—
102C22×C4×D47C2311yescharacteristic
103C22×C4×D47C2311yescharacteristic
104C2×#10625325—42no—
105C2×#10625325C2314yes—
106C2×#10625335—42no—
107C2×#10625335C2314yes—
108C2×#10625336—42no—
109C2×#10625336C2314yes—
110C22×C47⋊C8—42no—
111C22×C47⋊C8C2311yescharacteristic
112C22×C47⋊C8C2311yescharacteristic
113C22×C47⋊C8C2314yescomplemented
114#13094023—28no—
115#13094020—28no—
116#13094010—28no—
117#13094010—28no—
118#13094009—28no—
119#13094006—28no—
120#13094004—22no—
121#13094004C2314yes—
122#13094003—22no—
123#13094003C2314yescomplemented
124#13094000—22no—
125#13094000C2314yes—
126#13093999—22no—
127#13093999C2314yes—
128#13093998—22no—
129#13093998C2314yes—
130#13093995—22no—
131#13093995C2314yes—
132#13093994—28no—
133#13093992—28no—
134#13093982—22no—
135#13093982—22no—
136#13093982C2314yes—
137#13093982C2314yescomplemented
138C2×C4⋊Dic47—21no—
139C2×C4⋊Dic47C2311yescharacteristic
140C2×C4⋊Dic47C2311yescharacteristic
141C2×Dic47⋊C4—21no—
142C2×Dic47⋊C4—21no—
143C2×C22⋊Dic47—21no—
144C2×C22⋊Dic47—21no—
145C2×(C2×D47)⋊C4—21no—
146C2×(C2×D47)⋊C4—21no—
147C2×(C2×D47)⋊C4—21no—
148C2×(C2×D47)⋊C4—21no—
149C2×(C2×D47)⋊C4—21no—
150C2×(C2×D47)⋊C4—21no—
151C2×C4×Dic47—21no—
152C2×C4×Dic47—21no—
153#13093958C2314yescomplemented
154#13093955C2314yescomplemented
155#13093955C2314yescomplemented
156#13093949C2314yescomplemented
157#13093948C2314yescomplemented
158#13093947C2314yescomplemented
159#13093946C2314yes—
160#13093945C2314yes—
161#13093944C2314yes—
162(C2×D47)⋊C8C2314yes—
163(C2×D47)⋊C8C2314yes—
164(C2×D47)⋊C8C2314yescomplemented
165(C2×D47)⋊C8C2314yescomplemented
166C22×Q8×C47C2311yescharacteristic
167C22×D4×C47—21no—
168C22×D4×C47C2311yescharacteristic
169C23×C4×C47C2311yescharacteristic
170C2×SD16×C47—42no—
171C2×SD16×C47C2314yes—
172C2×M16×C47—42no—
173C2×M16×C47C2314yescomplemented
174C22×C8×C47C2311yescharacteristic
175C22×C8×C47C2311yescharacteristic
176C22⋊Q8×C47—22no—
177C22⋊Q8×C47C2314yescomplemented
178#121×C47—22no—
179#121×C47C2314yes—
180C2×C4⋊C4×C47—21no—
181C2×C4⋊C4×C47C2311yescharacteristic
182C2×C4⋊C4×C47C2311yescharacteristic
183C2×C22⋊C4×C47—21no—
184C2×C22⋊C4×C47—21no—
185#107×C47C2314yescomplemented
186#103×C47C2314yescomplemented
187#102×C47C2314yes—
188C24×C47—21no—
189C24×C47C2×D411yescharacteristic
190C23×D47—21no—
191C23×D47—24no—
192C23×D47—44no—
193C23×D47—82no—
194C23×D47—82no—
195C23×D47C2×D411yescharacteristic
196C23×D47C2×D411yescharacteristic
197C2×Q8×C47—21no—
198C2×Q8×C47—22no—
199C2×Q8×C47—22no—
200C2×Q8×C47C2412yes—
201C2×D4×C47—24no—
202C2×D4×C47—21no—
203C2×D4×C47—22no—
204C2×D4×C47—22no—
205C2×D4×C47—82no—
206C2×D4×C47C2412yes—
207C22×C4×C47—22no—
208C22×C4×C47—22no—
209C22×C4×C47—21no—
210C22×C4×C47—21no—
211C22×C4×C47—21no—
212C22×C4×C47C2×D411yescharacteristic
213C22×C4×C47C2×D412yes—
214C22×C4×C47C2412yes—
215C22×C4×C47C2411yescharacteristic
216C2×C22⋊D47—24no—
217C2×C22⋊D47—24no—
218C2×C22⋊D47—24no—
219C2×C22⋊D47—42no—
220C2×C22⋊D47—42no—
221C2×C22⋊D47—44no—
222C2×C22⋊D47—82no—
223C2×C22⋊D47—82no—
224C2×C22⋊D47C2×D414yes—
225C2×C22⋊D47C2×D414yes—
226C22×Dic47—21no—
227C22×Dic47—21no—
228C22×Dic47—21no—
229C22×Dic47C2×D411yescharacteristic
230C22×Dic47C2×D411yescharacteristic
231Q8×D47—44no—
232Q8×D47—44no—
233Q8×D47—48no—
234D4×D47—44no—
235D4×D47—44no—
236D4×D47—48no—
237#10625350—48no—
238#10625350—44no—
239#10625350—44no—
240C2×D188—22no—
241C2×D188—22no—
242C2×D188—21no—
243C2×D188—24no—
244C2×D188—42no—
245C2×D188—82no—
246C2×D188C2×D414yes—
247C2×D188C2412yes—
248C2×C4×D47—22no—
249C2×C4×D47—22no—
250C2×C4×D47—22no—
251C2×C4×D47—22no—
252C2×C4×D47—24no—
253C2×C4×D47—44no—
254C2×C4×D47C2×D412yes—
255C2×C4×D47C2×D412yes—
256C2×C4×D47C2412yes—
257C2×C4×D47C2412yes—
258C2×Dic94—22no—
259C2×Dic94—22no—
260C2×Dic94—21no—
261C2×Dic94—24no—
262C2×Dic94—42no—
263C2×Dic94—44no—
264C2×Dic94C2×D414yes—
265C2×Dic94C2412yes—
266SD16×C47—44no—
267M16×C47—44no—
268C2×C8×C47—22no—
269C2×C8×C47—22no—
270C2×C8×C47C2412yes—
271C2×C8×C47C2412yes—
272C4⋊C4×C47—24no—
273C4⋊C4×C47—21no—
274C4⋊C4×C47—21no—
275C4⋊C4×C47C2412yes—
276C4⋊C4×C47C2412yes—
277C22⋊C4×C47—24no—
278C22⋊C4×C47—24no—
279C22⋊Dic47—24no—
280C22⋊Dic47—24no—
281#10625336—44no—
282#10625335—44no—
283(C2×D47)⋊C4—24no—
284(C2×D47)⋊C4—24no—
285(C2×D47)⋊C4—24no—
286(C2×D47)⋊C4—24no—
287(C2×D47)⋊C4—24no—
288(C2×D47)⋊C4—24no—
289C4⋊Dic47—21no—
290C4⋊Dic47—21no—
291C4⋊Dic47—24no—
292C4⋊Dic47C2412yes—
293C4⋊Dic47C2412yes—
294Dic47⋊C4—24no—
295Dic47⋊C4—24no—
296C4×Dic47—24no—
297C4×Dic47—24no—
298C2×C47⋊C8—22no—
299C2×C47⋊C8—22no—
300C2×C47⋊C8—44no—
301C2×C47⋊C8C2412yes—
302C2×C47⋊C8C2412yes—
303#10625325—44no—
304C23×C47—22no—
305C23×C47—22no—
306C23×C47—22no—
307C23×C47—22no—
308C23×C47—42no—
309C23×C47—42no—
310C23×C47—42no—
311C23×C47C22×D412yes—
312C23×C47C22×D411yescharacteristic
313C22×D47—22no—
314C22×D47—22no—
315C22×D47—22no—
316C22×D47—22no—
317C22×D47—22no—
318C22×D47—22no—
319C22×D47—22no—
320C22×D47—48no—
321C22×D47—42no—
322C22×D47—42no—
323C22×D47—42no—
324C22×D47—84no—
325C22×D47—84no—
326C22×D47—816no—
327C22×D47C22×D412yes—
328C22×D47C22×D412yes—
329Q8×C47—22no—
330Q8×C47—22no—
331Q8×C47—42no—
332D4×C47—22no—
333D4×C47—22no—
334D4×C47—42no—
335D4×C47—84no—
336C2×C4×C47—22no—
337C2×C4×C47—24no—
338C2×C4×C47—22no—
339C2×C4×C47—22no—
340C2×C4×C47—22no—
341C2×C4×C47—22no—
342C2×C4×C47—22no—
343C2×C4×C47—42no—
344C2×C4×C47—42no—
345C2×C4×C47—42no—
346C2×C4×C47C22×D412yes—
347C2×C4×C47C22×D411yescharacteristic
348C2×C4×C47H(5,𝔽2)12yes—
349C2×C4×C47H(5,𝔽2)12yes—
350C2×C4×C47C2511yescharacteristic
351C22⋊D47—44no—
352C22⋊D47—44no—
353C22⋊D47—48no—
354C22⋊D47—84no—
355C22⋊D47—84no—
356C2×Dic47—22no—
357C2×Dic47—22no—
358C2×Dic47—22no—
359C2×Dic47—22no—
360C2×Dic47—22no—
361C2×Dic47—42no—
362C2×Dic47—42no—
363C2×Dic47—42no—
364C2×Dic47C22×D412yes—
365C2×Dic47C22×D412yes—
366D188—22no—
367D188—22no—
368D188—44no—
369D188—42no—
370D188—84no—
371C4×D47—24no—
372C4×D47—24no—
373C4×D47—22no—
374C4×D47—22no—
375C4×D47—22no—
376C4×D47—22no—
377C4×D47—48no—
378Dic94—22no—
379Dic94—22no—
380Dic94—44no—
381Dic94—48no—
382Dic94—42no—
383C8×C47—22no—
384C8×C47—22no—
385C47⋊C8—22no—
386C47⋊C8—22no—
387C2×#3200—471nomaximal, Sylow
388C22×C47—22no—
389C22×C47—22no—
390C22×C47—22no—
391C22×C47—44no—
392C22×C47—42no—
393C22×C47—42no—
394C22×C47—42no—
395C22×C47—84no—
396C22×C47#53412yes—
397C22×C47#57712yes—
398C22×C47#57712yes—
399C22×C47C23×D411yescharacteristic
400C2×D47—22no—
401C2×D47—22no—
402C2×D47—22no—
403C2×D47—22no—
404C2×D47—22no—
405C2×D47—22no—
406C2×D47—44no—
407C2×D47—44no—
408C2×D47—42no—
409C2×D47—42no—
410C2×D47—42no—
411C2×D47—816no—
412C2×D47—84no—
413C4×C47—22no—
414C4×C47—42no—
415C4×C47—42no—
416C4×C47—42no—
417C4×C47#53412yes—
418C4×C47C2×H(5,𝔽2)11yescharacteristic
419C4×C47C2×H(5,𝔽2)11yescharacteristic
420Dic47—22no—
421Dic47—22no—
422Dic47—42no—
423Dic47—42no—
424Dic47—42no—
425C2×#536—471no—
426C2×#535—471no—
427#3200—4716no—
428C2×#485—471no—
429C2×#485—471no—
430C2×#482—471no—
431C2×#482—471no—
432C2×#468—471no—
433C2×#468D4711yescharacteristic, complemented
434C2×#465—471no—
435C2×#465—471no—
436C2×#448—471no—
437C2×#448—471no—
438C2×#450—471no—
439C2×#450—471no—
440C2×#408—471no—
441C2×C47—42no—
442C2×C47—82no—
443C2×C47#320014yescomplemented
444C2×C47C2×#53411yescharacteristic
445C2×C47C2×#57711yescharacteristic
446C2×C47C2×#57711yescharacteristic
447D47—42no—
448D47—42no—
449D47—82no—
450C22×#41—471no—
451C23×Q8—471no—
452C23×D4—471no—
453C22×SD16—471no—
454C22×SD16—471no—
455C22×SD16—471no—
456C22×SD16C2×D4711yescharacteristic
457C22×M16C2×D4711yescharacteristic, complemented
458C23×C8—471no—
459#536—478no—
460#536—944no—
461#535—478no—
462#535—944no—
463C2×C4⋊Q8—941no—
464C2×#127—941no—
465C2×#124—941no—
466C2×#124—941no—
467C2×#123—941no—
468C2×#123—941no—
469C2×C22⋊Q8—471no—
470C2×C22⋊Q8—471no—
471C2×C22⋊Q8—471no—
472C2×C22⋊Q8C2×D4711yescharacteristic, complemented
473C2×#121—471no—
474C2×#121—471no—
475C2×#121—471no—
476C2×#121C2×D4711yescharacteristic
477C2×#120—941no—
478C2×#120—941no—
479C2×#117—471no—
480C2×#117—471no—
481#485—478no—
482#485—478no—
483#482—478no—
484#482—478no—
485#468—478no—
486#468C2×D4718yescomplemented
487#465—478no—
488#465—478no—
489#450—478no—
490#450—478no—
491#448—478no—
492#448—478no—
493C2×#107—471no—
494C2×#107C2×D4711yescharacteristic, complemented
495C2×#106—471no—
496C2×#106—471no—
497C2×#103—471no—
498C2×#103—471no—
499C2×#103—471no—
500C2×#103C2×D4711yescharacteristic, complemented
501C2×#102—471no—
502C2×#102—471no—
503C2×#102—471no—
504C2×#102C2×D4711yescharacteristic
505#408—478no—
506C2×C22⋊C8—471no—
507C2×C22⋊C8—471no—
508C2×C22⋊C8—471no—
509C2×C22⋊C8—471no—
510C47C2×#320011yescharacteristic, complemented, Sylow
511C25—941no—
512C2×#41—474no—
513C2×#41—474no—
514C2×#41—1882no—
515C2×#41—1882no—
516C22×Q8—471no—
517C22×Q8—474no—
518C22×Q8—471no—
519C22×Q8—941no—
520C22×Q8—942no—
521C22×Q8—1882no—
522C22×Q8—1882no—
523C22×Q8C22×D4711yescharacteristic
524C22×D4—21no—
525C22×D4—471no—
526C22×D4—471no—
527C22×D4—474no—
528C22×D4—471no—
529C22×D4—471no—
530C22×D4—941no—
531C22×D4—942no—
532C22×D4—941no—
533C22×D4—941no—
534C22×D4—941no—
535C22×D4—1882no—
536C22×D4—1882no—
537C22×D4C22×D4711yescharacteristic
538C23×C4—471no—
539C23×C4—471no—
540C23×C4—941no—
541C23×C4C22×D4711yescharacteristic
542C2×SD16—42no—
543C2×SD16—474no—
544C2×SD16—474no—
545C2×SD16—474no—
546C2×SD16—1882no—
547C2×SD16—1882no—
548C2×SD16—1882no—
549C2×SD16C22×D4714yes—
550C2×M16—42no—
551C2×M16C22×D4714yescomplemented
552C22×C8—471no—
553C22×C8—471no—
554C22×C8—474no—
555C22×C8—1882no—
556C22×C8C22×D4711yescharacteristic
557C22×C8C22×D4711yescharacteristic
558C4⋊Q8—948no—
559#127—948no—
560#124—948no—
561#124—948no—
562#123—948no—
563#123—948no—
564C22⋊Q8—22no—
565C22⋊Q8—474no—
566C22⋊Q8—474no—
567C22⋊Q8—474no—
568C22⋊Q8—942no—
569C22⋊Q8—942no—
570C22⋊Q8—942no—
571C22⋊Q8C22×D4714yescomplemented
572#121—22no—
573#121—474no—
574#121—474no—
575#121—474no—
576#121—942no—
577#121—942no—
578#121—942no—
579#121C22×D4714yes—
580#120—948no—
581#120—948no—
582#117—474no—
583#117—474no—
584#117—942no—
585#117—942no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—471no—
588C2×C4⋊C4—471no—
589C2×C4⋊C4—941no—
590C2×C4⋊C4—941no—
591C2×C4⋊C4—941no—
592C2×C4⋊C4C22×D4711yescharacteristic
593C2×C4⋊C4C22×D4711yescharacteristic
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—941no—
597C2×C22⋊C4—941no—
598C2×C22⋊C4—941no—
599C2×C22⋊C4—941no—
600C2×C22⋊C4—941no—
601C2×C22⋊C4—941no—
602C2×C22⋊C4—941no—
603C2×C22⋊C4—941no—
604C2×C42—941no—
605C2×C42—941no—
606#107—474no—
607#107C22×D4714yescomplemented
608#106—474no—
609#106—474no—
610#103—474no—
611#103—474no—
612#103—474no—
613#103C22×D4714yescomplemented
614#102—474no—
615#102—474no—
616#102—474no—
617#102C22×D4714yes—
618C22⋊C8—474no—
619C22⋊C8—474no—
620C22⋊C8—474no—
621C22⋊C8—474no—
622C24—21no—
623C24—471no—
624C24—471no—
625C24—944no—
626C24—941no—
627C24—3762no—
628C24—3762no—
629C24—1884no—
630C24D4×D4711yescharacteristic
631#41—1888no—
632#41—1884no—
633#41—1884no—
634C2×Q8—21no—
635C2×Q8—22no—
636C2×Q8—22no—
637C2×Q8—474no—
638C2×Q8—472no—
639C2×Q8—944no—
640C2×Q8—941no—
641C2×Q8—942no—
642C2×Q8—942no—
643C2×Q8—1882no—
644C2×Q8—1884no—
645C2×Q8—1884no—
646C2×Q8—1884no—
647C2×Q8—1888no—
648C2×Q8C23×D4712yes—
649C2×D4—24no—
650C2×D4—21no—
651C2×D4—22no—
652C2×D4—22no—
653C2×D4—82no—
654C2×D4—474no—
655C2×D4—474no—
656C2×D4—474no—
657C2×D4—472no—
658C2×D4—944no—
659C2×D4—944no—
660C2×D4—944no—
661C2×D4—944no—
662C2×D4—941no—
663C2×D4—942no—
664C2×D4—942no—
665C2×D4—3762no—
666C2×D4—3762no—
667C2×D4—3762no—
668C2×D4—1882no—
669C2×D4—1884no—
670C2×D4—1884no—
671C2×D4—1888no—
672C2×D4—1882no—
673C2×D4—1882no—
674C2×D4—1884no—
675C2×D4C23×D4712yes—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—471no—
682C22×C4—471no—
683C22×C4—472no—
684C22×C4—472no—
685C22×C4—472no—
686C22×C4—472no—
687C22×C4—944no—
688C22×C4—942no—
689C22×C4—942no—
690C22×C4—942no—
691C22×C4—942no—
692C22×C4—941no—
693C22×C4—941no—
694C22×C4—941no—
695C22×C4—1884no—
696C22×C4D4×D4712yes—
697C22×C4D4×D4711yescharacteristic
698C22×C4C23×D4712yes—
699C22×C4C23×D4711yescharacteristic
700SD16—44no—
701SD16—1884no—
702SD16—1884no—
703SD16—1884no—
704M16—44no—
705C2×C8—22no—
706C2×C8—22no—
707C2×C8—472no—
708C2×C8—472no—
709C2×C8—942no—
710C2×C8—942no—
711C2×C8—1884no—
712C2×C8C23×D4712yes—
713C2×C8C23×D4712yes—
714C4⋊C4—24no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—472no—
718C4⋊C4—472no—
719C4⋊C4—944no—
720C4⋊C4—944no—
721C4⋊C4—944no—
722C4⋊C4—941no—
723C4⋊C4—941no—
724C4⋊C4C23×D4712yes—
725C4⋊C4C23×D4712yes—
726C22⋊C4—24no—
727C22⋊C4—24no—
728C22⋊C4—944no—
729C22⋊C4—944no—
730C22⋊C4—944no—
731C22⋊C4—944no—
732C22⋊C4—944no—
733C22⋊C4—944no—
734C22⋊C4—944no—
735C22⋊C4—944no—
736C42—944no—
737C42—944no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—472no—
746C23—472no—
747C23—942no—
748C23—942no—
749C23—942no—
750C23—942no—
751C23—942no—
752C23—942no—
753C23—942no—
754C23—3764no—
755C23—3764no—
756C23—37616no—
757C23—1888no—
758C23—1882no—
759C23—1882no—
760C23—1882no—
761C23C2×D4×D4712yes—
762C23C2×D4×D4711yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—42no—
766Q8—942no—
767Q8—942no—
768Q8—1884no—
769Q8—1888no—
770Q8—1882no—
771D4—22no—
772D4—22no—
773D4—42no—
774D4—84no—
775D4—942no—
776D4—942no—
777D4—3764no—
778D4—3764no—
779D4—3764no—
780D4—1884no—
781D4—1884no—
782D4—1884no—
783D4—1888no—
784D4—1882no—
785C2×C4—22no—
786C2×C4—24no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—472no—
796C2×C4—472no—
797C2×C4—942no—
798C2×C4—942no—
799C2×C4—944no—
800C2×C4—944no—
801C2×C4—942no—
802C2×C4—942no—
803C2×C4—942no—
804C2×C4—942no—
805C2×C4—942no—
806C2×C4—942no—
807C2×C4—942no—
808C2×C4—1888no—
809C2×C4—1882no—
810C2×C4—1882no—
811C2×C4—1882no—
812C2×C4C2×D4×D4712yes—
813C2×C4C2×D4×D4711yescharacteristic
814C2×C4#1309406912yes—
815C2×C4#1309407012yes—
816C2×C4C24×D4711yescharacteristic
817C8—22no—
818C8—22no—
819C8—942no—
820C8—942no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—44no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—84no—
829C22—942no—
830C22—942no—
831C22—942no—
832C22—942no—
833C22—942no—
834C22—942no—
835C22—37616no—
836C22—3764no—
837C22—1882no—
838C22—1882no—
839C22—1882no—
840C22—1884no—
841C22—1884no—
842C22#1568968112yes—
843C22#1568993212yes—
844C22#1568993312yes—
845C22C22×D4×D4711yescharacteristic
846C4—22no—
847C4—42no—
848C4—42no—
849C4—42no—
850C4—942no—
851C4—942no—
852C4—1882no—
853C4—1882no—
854C4—1882no—
855C4#1568968112yes—
856C4C2×#1309406911yescharacteristic
857C4C2×#1309407011yescharacteristic
858C2—42no—
859C2—82no—
860C2—3762no—
861C2—1882no—
862C2—1882no—
863C2#2025425614yesdirect product factor
864C2C2×#1568968111yescharacteristic
865C2C2×#1568993211yescharacteristic
866C2C2×#1568993311yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#468C2
socleC23×C47C22×D4
prime radicalC2×#15689689C2
hypercenterC2×#468D47
hypocenterC47C2×#3200
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#15689696C2semidirect
3. #20254256C2direct (N × H)
4. C2×#15689466C2semidirect
5. C2×#15689463C2semidirect
6. C2×#15689450C2semidirect
7. C2×#15689445C2semidirect
8. C2×#15689369C2semidirect
9. C2×#15689354C2semidirect
10. C2×#15689350C2semidirect
11. C2×#15689263C2semidirect
12. C2×#15689260C2semidirect
13. C2×#15689275C2semidirect
14. C2×#15689272C2semidirect
15. C2×#15689091C2semidirect
16. C2×C47×#468C2semidirect
18. C22×Q8×D47C22semidirect
23. C23×C47⋊C8C22semidirect
25. #15689696C22semidirect
35. C2×#13094003C22semidirect
43. C2×#13093982C22semidirect
44. #15689466C22semidirect
45. #15689463C22semidirect
46. #15689450C22semidirect
47. #15689445C22semidirect
48. #15689369C22semidirect
49. #15689354C22semidirect
50. #15689350C22semidirect
51. #15689275C22semidirect
52. #15689272C22semidirect
53. #15689263C22semidirect
54. #15689260C22semidirect
55. C2×#13093958C22semidirect
56. C2×#13093955C22semidirect
57. C2×#13093955C22semidirect
58. C2×#13093949C22semidirect
59. C2×#13093948C22semidirect
60. C2×#13093947C22semidirect
64. #15689091C22semidirect
67. C2×(C2×D47)⋊C8C22semidirect
68. C2×(C2×D47)⋊C8C22semidirect
70. C22×M16×C47C22semidirect
71. C2×C22⋊Q8×C47C22semidirect
73. C47×#468C22semidirect
74. C2×#107×C47C22semidirect
75. C2×#103×C47C22semidirect
88. C2×Q8×D47C23semidirect
113. C22×C47⋊C8C23semidirect
123. #13094003C23semidirect
137. #13093982C23semidirect
153. #13093958C23semidirect
154. #13093955C23semidirect
155. #13093955C23semidirect
156. #13093949C23semidirect
157. #13093948C23semidirect
158. #13093947C23semidirect
164. (C2×D47)⋊C8C23semidirect
165. (C2×D47)⋊C8C23semidirect
173. C2×M16×C47C23semidirect
177. C22⋊Q8×C47C23semidirect
185. #107×C47C23semidirect
186. #103×C47C23semidirect
433. C2×#468D47semidirect
443. C2×C47#3200semidirect
457. C22×M16C2×D47semidirect
472. C2×C22⋊Q8C2×D47semidirect
486. #468C2×D47semidirect
494. C2×#107C2×D47semidirect
500. C2×#103C2×D47semidirect
510. C47C2×#3200semidirect
551. C2×M16C22×D47semidirect
571. C22⋊Q8C22×D47semidirect
607. #107C22×D47semidirect
613. #103C22×D47semidirect
863. C2#20254256direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896962
C2×#156896892
#202542562
C2×#156894662
C2×#156894632
C2×#156894502
C2×#156894452
C2×#156893692
C2×#156893542
C2×#156893502
C2×#156892632
C2×#156892602
C2×#156892752
C2×#156892722
C2×#156890912
C2×C47×#4682
C2×#320047