Finite Group Databasebeta

← C2×#20254488 #27087639

Subgroups — C2×#20254488 #27087639

Order 12032.

2278 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689746C211yesmaximal, characteristic, complemented
2C2×#15689687C211yesmaximal, characteristic, complemented
3#20254488C2116yesmaximal, direct product factor
4C2×#15689509C211yesmaximal, characteristic, complemented
5C2×#15689508C211yesmaximal, characteristic, complemented
6C2×#15689484C211yesmaximal, characteristic, complemented
7C2×#15689468C211yesmaximal, characteristic, complemented
8C2×#15689347C211yesmaximal, characteristic, complemented
9C2×#15689321C211yesmaximal, characteristic, complemented
10C2×#15689341C211yesmaximal, characteristic, complemented
11C2×#15689317C211yesmaximal, characteristic, complemented
12C2×#15689268C211yesmaximal, characteristic, complemented
13C2×#15689273C211yesmaximal, characteristic, complemented
14C2×#15689259C211yesmaximal, characteristic, complemented
15C2×#15689181C211yesmaximal, characteristic, complemented
16C2×C47×#452C211yesmaximal, characteristic, complemented
17C23×D188C2211yescharacteristic
18C22×#10625336C2211yescharacteristic
19C22×#10625336C2211yescharacteristic
20C22×#10625336C2211yescharacteristic, complemented
21C22×D376C2211yescharacteristic
22C22×D376C2211yescharacteristic
23C22×#10625334C2211yescharacteristic, complemented
24#15689746—24no—
25#15689746C2218yescomplemented
26#15689687—24no—
27#15689687C2218yescomplemented
28C2×#13094023C2211yescharacteristic, complemented
29C2×#13094020C2211yescharacteristic
30C2×#13094020C2211yescharacteristic
31C2×#13094019—21no—
32C2×#13094013C2211yescharacteristic
33C2×#13094013C2211yescharacteristic
34C2×#13094013C2211yescharacteristic, complemented
35C2×#13094010—21no—
36C2×#13094006—21no—
37C2×#13094004—21no—
38C2×#13093998—21no—
39C2×#13093998—21no—
40C2×#13093998C2211yescharacteristic
41C2×#13093992—21no—
42C2×#13093992—21no—
43C2×Q8×Dic47C2211yescharacteristic, complemented
44C2×#13093986C2211yescharacteristic, complemented
45C2×#13093983C2211yescharacteristic
46#15689509C2218yescomplemented
47#15689508C2218yescomplemented
48#15689484C2218yescomplemented
49#15689468C2218yescomplemented
50#15689347C2218yescomplemented
51#15689341C2218yescomplemented
52#15689321C2218yescomplemented
53#15689317C2218yescomplemented
54#15689273C2218yescomplemented
55#15689268C2218yescomplemented
56#15689259C2218yescomplemented
57#15689181C2218yescomplemented
58C2×Dic47⋊C8C2211yescharacteristic, complemented
59C2×Dic47⋊C8C2211yescharacteristic, complemented
60C2×#13093948C2211yescharacteristic, complemented
61C2×#13093946C2211yescharacteristic
62C2×#13093946C2211yescharacteristic
63C2×#13093945C2211yescharacteristic, complemented
64C2×#13093944C2211yescharacteristic
65C2×#13093944C2211yescharacteristic
66C2×C22⋊(C47⋊C8)C2211yescharacteristic
67C2×#13093934C2211yescharacteristic, complemented
68C2×C8×Dic47C2211yescharacteristic, complemented
69C22×#41×C47C2211yescharacteristic
70C22×Q16×C47C2211yescharacteristic, complemented
71C22×SD16×C47C2211yescharacteristic, complemented
72C2×C22⋊Q8×C47C2211yescharacteristic
73C47×#452C2218yescomplemented
74C2×#103×C47C2211yescharacteristic, complemented
75C2×#102×C47C2211yescharacteristic, complemented
76C2×C22⋊C8×C47C2211yescharacteristic
77C24×D47—21no—
78C22×Dic94—21no—
79C22×D188—21no—
80C22×D188—22no—
81C22×D188—42no—
82C22×D188—42no—
83C22×D188C2311yescharacteristic
84C22×D188C2311yescharacteristic
85C22×D188C2311yescharacteristic
86C22×D188C2314yes—
87C22×C22⋊D47—21no—
88C22×C22⋊D47—21no—
89C22×C22⋊D47—21no—
90C22×C22⋊D47—21no—
91C22×C22⋊D47—21no—
92C22×C4×D47—21no—
93C2×#10625336—42no—
94C2×#10625336—42no—
95C2×#10625336—42no—
96C2×#10625336C2314yes—
97C2×#10625336C2314yes—
98C2×#10625336C2314yescomplemented
99C2×D376—42no—
100C2×D376—42no—
101C2×D376C2314yes—
102C2×D376C2314yes—
103C2×#10625334—42no—
104C2×#10625334C2314yescomplemented
105C22×C47⋊C8C2311yescharacteristic
106C22×C47⋊C8C2311yescharacteristic
107#13094023—22no—
108#13094023C2314yescomplemented
109#13094020—22no—
110#13094020—22no—
111#13094020C2314yes—
112#13094020C2314yes—
113#13094019—28no—
114#13094013—22no—
115#13094013—22no—
116#13094013—22no—
117#13094013C2314yes—
118#13094013C2314yes—
119#13094013C2314yescomplemented
120#13094010—28no—
121#13094006—28no—
122#13094004—28no—
123#13093998—22no—
124#13093998—28no—
125#13093998—28no—
126#13093998C2314yes—
127#13093992—28no—
128#13093992—28no—
129Q8×Dic47—22no—
130Q8×Dic47C2314yescomplemented
131#13093986—22no—
132#13093986C2314yescomplemented
133#13093983D414yes—
134#13093983C2314yes—
135C2×C4⋊Dic47—21no—
136C2×C4⋊Dic47D411yescharacteristic
137C2×C4⋊Dic47D411yescharacteristic
138C2×C4⋊Dic47C2311yescharacteristic
139C2×Dic47⋊C4—21no—
140C2×C22⋊Dic47D411yescharacteristic
141C2×C22⋊Dic47D411yescharacteristic
142C2×(C2×D47)⋊C4—21no—
143C2×(C2×D47)⋊C4—21no—
144C2×(C2×D47)⋊C4—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×C4×Dic47—21no—
151C2×C4×Dic47C2311yescharacteristic
152C2×C4×Dic47C2311yescharacteristic
153Dic47⋊C8C2314yescomplemented
154Dic47⋊C8C2314yescomplemented
155#13093948C2314yescomplemented
156#13093946C2314yes—
157#13093946C2314yes—
158#13093945C2314yescomplemented
159#13093944C2314yes—
160#13093944C2314yes—
161C22⋊(C47⋊C8)C2314yes—
162#13093934C2314yescomplemented
163C8×Dic47C2314yescomplemented
164C2×#41×C47—22no—
165C2×#41×C47—42no—
166C2×#41×C47—42no—
167C2×#41×C47C2314yes—
168C22×Q8×C47C2311yescharacteristic
169C22×Q8×C47C2311yescharacteristic
170C22×D4×C47—21no—
171C22×D4×C47C2311yescharacteristic
172C23×C4×C47—21no—
173C23×C4×C47C2311yescharacteristic
174C2×Q16×C47—42no—
175C2×Q16×C47C2314yescomplemented
176C2×SD16×C47—42no—
177C2×SD16×C47C2314yescomplemented
178C22×C8×C47C2311yescharacteristic
179C22×C8×C47C2311yescharacteristic
180C22⋊Q8×C47—22no—
181C22⋊Q8×C47C2314yes—
182C2×C4⋊C4×C47—21no—
183C2×C4⋊C4×C47C2311yescharacteristic
184C2×C22⋊C4×C47—21no—
185#103×C47C2314yescomplemented
186#102×C47C2314yescomplemented
187C22⋊C8×C47C2314yes—
188C24×C47—21no—
189C24×C47C2×D411yescharacteristic
190C23×D47—21no—
191C23×D47—21no—
192C23×D47—21no—
193C23×D47—24no—
194C23×D47—44no—
195C23×D47—82no—
196C23×D47—82no—
197#41×C47—44no—
198#41×C47—44no—
199#41×C47—48no—
200C2×Q8×C47—21no—
201C2×Q8×C47—21no—
202C2×Q8×C47—22no—
203C2×Q8×C47—22no—
204C2×Q8×C47—22no—
205C2×Q8×C47—22no—
206C2×Q8×C47C2412yes—
207C2×Q8×C47C2412yes—
208C2×D4×C47—24no—
209C2×D4×C47—21no—
210C2×D4×C47—22no—
211C2×D4×C47—22no—
212C2×D4×C47—44no—
213C2×D4×C47C2412yes—
214C22×C4×C47—22no—
215C22×C4×C47—22no—
216C22×C4×C47—21no—
217C22×C4×C47—21no—
218C22×C4×C47—21no—
219C22×C4×C47—24no—
220C22×C4×C47—44no—
221C22×C4×C47C2×D411yescharacteristic
222C22×C4×C47C2×D412yes—
223C22×C4×C47C2412yes—
224C22×C4×C47C2411yescharacteristic
225C2×C22⋊D47—24no—
226C2×C22⋊D47—24no—
227C2×C22⋊D47—24no—
228C2×C22⋊D47—24no—
229C2×C22⋊D47—24no—
230C2×C22⋊D47—82no—
231C2×C22⋊D47—82no—
232C2×C22⋊D47—82no—
233C2×C22⋊D47—82no—
234C2×C22⋊D47—82no—
235C22×Dic47—21no—
236C22×Dic47C2×D411yescharacteristic
237C22×Dic47C2×D411yescharacteristic
238C22×Dic47C2×D411yescharacteristic
239C22×Dic47C2×D411yescharacteristic
240C2×D188—22no—
241C2×D188—22no—
242C2×D188—22no—
243C2×D188—22no—
244C2×D188—22no—
245C2×D188—22no—
246C2×D188—21no—
247C2×D188—24no—
248C2×D188—21no—
249C2×D188—21no—
250C2×D188—44no—
251C2×D188—44no—
252C2×D188—44no—
253C2×D188—48no—
254C2×D188C2412yes—
255C2×D188C2412yes—
256C2×D188C2412yes—
257C2×C4×D47—24no—
258C2×C4×D47—82no—
259C2×Dic94—24no—
260C2×Dic94—82no—
261Q16×C47—44no—
262SD16×C47—44no—
263C2×C8×C47—22no—
264C2×C8×C47—22no—
265C2×C8×C47C2412yes—
266C2×C8×C47C2412yes—
267C4⋊C4×C47—24no—
268C4⋊C4×C47—21no—
269C4⋊C4×C47C2412yes—
270C22⋊C4×C47—24no—
271C22⋊Dic47C2×D414yes—
272C22⋊Dic47C2×D414yes—
273#10625336—44no—
274#10625336—44no—
275#10625336—44no—
276#10625334—44no—
277(C2×D47)⋊C4—24no—
278(C2×D47)⋊C4—24no—
279(C2×D47)⋊C4—24no—
280(C2×D47)⋊C4—24no—
281(C2×D47)⋊C4—24no—
282(C2×D47)⋊C4—24no—
283(C2×D47)⋊C4—24no—
284(C2×D47)⋊C4—24no—
285C4⋊Dic47—21no—
286C4⋊Dic47—24no—
287C4⋊Dic47C2×D414yes—
288C4⋊Dic47C2×D414yes—
289C4⋊Dic47C2412yes—
290Dic47⋊C4—24no—
291C4×Dic47—24no—
292C4×Dic47C2×D412yes—
293C4×Dic47C2×D412yes—
294C4×Dic47C2412yes—
295C4×Dic47C2412yes—
296C2×C47⋊C8—22no—
297C2×C47⋊C8—22no—
298C2×C47⋊C8C2412yes—
299C2×C47⋊C8C2412yes—
300D376—44no—
301D376—44no—
302C23×C47—22no—
303C23×C47—22no—
304C23×C47—22no—
305C23×C47—22no—
306C23×C47—42no—
307C23×C47—42no—
308C23×C47—42no—
309C23×C47C22×D412yes—
310C23×C47C22×D411yescharacteristic
311C22×D47—22no—
312C22×D47—22no—
313C22×D47—22no—
314C22×D47—48no—
315C22×D47—42no—
316C22×D47—42no—
317C22×D47—42no—
318C22×D47—42no—
319C22×D47—42no—
320C22×D47—42no—
321C22×D47—42no—
322C22×D47—42no—
323C22×D47—42no—
324C22×D47—84no—
325C22×D47—84no—
326C22×D47—816no—
327Q8×C47—22no—
328Q8×C47—22no—
329Q8×C47—22no—
330Q8×C47—22no—
331Q8×C47—42no—
332Q8×C47—42no—
333D4×C47—22no—
334D4×C47—22no—
335D4×C47—48no—
336D4×C47—42no—
337C2×C4×C47—22no—
338C2×C4×C47—24no—
339C2×C4×C47—22no—
340C2×C4×C47—22no—
341C2×C4×C47—22no—
342C2×C4×C47—22no—
343C2×C4×C47—22no—
344C2×C4×C47—48no—
345C2×C4×C47—42no—
346C2×C4×C47—42no—
347C2×C4×C47—42no—
348C2×C4×C47C22×D412yes—
349C2×C4×C47C22×D411yescharacteristic
350C2×C4×C47H(5,𝔽2)12yes—
351C2×C4×C47H(5,𝔽2)12yes—
352C2×C4×C47C2511yescharacteristic
353C22⋊D47—84no—
354C22⋊D47—84no—
355C22⋊D47—84no—
356C22⋊D47—84no—
357C22⋊D47—84no—
358C2×Dic47—22no—
359C2×Dic47—22no—
360C2×Dic47—22no—
361C2×Dic47—22no—
362C2×Dic47—22no—
363C2×Dic47—42no—
364C2×Dic47C22×D412yes—
365C2×Dic47C22×D412yes—
366C2×Dic47C22×D412yes—
367C2×Dic47C22×D412yes—
368D188—22no—
369D188—22no—
370D188—22no—
371D188—22no—
372D188—22no—
373D188—22no—
374D188—48no—
375D188—42no—
376D188—42no—
377D188—42no—
378C4×D47—84no—
379Dic94—84no—
380C8×C47—22no—
381C8×C47—22no—
382C47⋊C8—22no—
383C47⋊C8—22no—
384C2×#3224—471nomaximal, Sylow
385C22×C47—22no—
386C22×C47—22no—
387C22×C47—22no—
388C22×C47—44no—
389C22×C47—42no—
390C22×C47—42no—
391C22×C47—42no—
392C22×C47—84no—
393C22×C47#53512yes—
394C22×C47#57612yes—
395C22×C47#57712yes—
396C22×C47C23×D411yescharacteristic
397C2×D47—42no—
398C2×D47—42no—
399C2×D47—42no—
400C2×D47—42no—
401C2×D47—42no—
402C2×D47—42no—
403C2×D47—42no—
404C2×D47—42no—
405C2×D47—42no—
406C2×D47—816no—
407C2×D47—84no—
408C2×D47—84no—
409C2×D47—84no—
410C4×C47—22no—
411C4×C47—42no—
412C4×C47—42no—
413C4×C47—42no—
414C4×C47#53512yes—
415C4×C47C2×H(5,𝔽2)11yescharacteristic
416C4×C47C2×H(5,𝔽2)11yescharacteristic
417Dic47—22no—
418Dic47—22no—
419Dic47—22no—
420Dic47—22no—
421Dic47—42no—
422C2×#542—471no—
423C2×#535—471no—
424#3224—4716no—
425C2×#496—471no—
426C2×#495—471no—
427C2×#489—471no—
428C2×#486—471no—
429C2×#464—471no—
430C2×#460—471no—
431C2×#463—471no—
432C2×#459—471no—
433C2×#452D4711yescharacteristic, complemented
434C2×#449—471no—
435C2×#450—471no—
436C2×#447—471no—
437C2×#433—471no—
438C2×C47—42no—
439C2×C47—82no—
440C2×C47#322414yescomplemented
441C2×C47C2×#53511yescharacteristic
442C2×C47C2×#57611yescharacteristic
443C2×C47C2×#57711yescharacteristic
444D47—82no—
445D47—82no—
446D47—82no—
447C22×#41C2×D4711yescharacteristic
448C23×D4—471no—
449C22×Q16C2×D4711yescharacteristic, complemented
450C22×SD16—471no—
451C22×SD16—471no—
452C22×SD16—471no—
453C22×SD16C2×D4711yescharacteristic, complemented
454C22×D8—471no—
455C22×D8—471no—
456C22×D8—471no—
457#542—478no—
458#542—944no—
459#535—478no—
460#535—944no—
461C2×C4⋊Q8—471no—
462C2×#127—471no—
463C2×#127—471no—
464C2×#126—941no—
465C2×#124—471no—
466C2×#124—471no—
467C2×#124—471no—
468C2×#124—941no—
469C2×#123—941no—
470C2×C22⋊Q8—941no—
471C2×C22⋊Q8C2×D4711yescharacteristic
472C2×#121—471no—
473C2×#121—941no—
474C2×#121—941no—
475C2×#120—941no—
476C2×#120—941no—
477C2×C4×Q8—471no—
478C2×C4×D4—471no—
479C2×#117—471no—
480#496—478no—
481#495—478no—
482#489—478no—
483#486—478no—
484#464—478no—
485#463—478no—
486#460—478no—
487#459—478no—
488#452C2×D4718yescomplemented
489#450—478no—
490#449—478no—
491#447—478no—
492#433—478no—
493C2×C4⋊C8—471no—
494C2×C4⋊C8—471no—
495C2×#103—471no—
496C2×#103C2×D4711yescharacteristic, complemented
497C2×#102—471no—
498C2×#102—471no—
499C2×#102—471no—
500C2×#102—471no—
501C2×#102—471no—
502C2×#102C2×D4711yescharacteristic, complemented
503C2×C22⋊C8—471no—
504C2×C22⋊C8C2×D4711yescharacteristic
505C2×#97—471no—
506C2×C4×C8—471no—
507C47C2×#322411yescharacteristic, complemented, Sylow
508C25—941no—
509C2×#41—22no—
510C2×#41—42no—
511C2×#41—42no—
512C2×#41C22×D4714yes—
513C22×Q8—941no—
514C22×Q8C22×D4711yescharacteristic
515C22×Q8C22×D4711yescharacteristic
516C22×D4—21no—
517C22×D4—471no—
518C22×D4—471no—
519C22×D4—471no—
520C22×D4—474no—
521C22×D4—941no—
522C22×D4—941no—
523C22×D4—941no—
524C22×D4—941no—
525C22×D4—941no—
526C22×D4—941no—
527C22×D4—942no—
528C22×D4—1882no—
529C22×D4—1882no—
530C22×D4C22×D4711yescharacteristic
531C23×C4—21no—
532C23×C4—941no—
533C23×C4C22×D4711yescharacteristic
534C2×Q16—42no—
535C2×Q16C22×D4714yescomplemented
536C2×SD16—42no—
537C2×SD16—474no—
538C2×SD16—474no—
539C2×SD16—474no—
540C2×SD16—1882no—
541C2×SD16—1882no—
542C2×SD16—1882no—
543C2×SD16C22×D4714yescomplemented
544C2×D8—474no—
545C2×D8—474no—
546C2×D8—474no—
547C2×D8—1882no—
548C2×D8—1882no—
549C2×D8—1882no—
550C22×C8—471no—
551C22×C8—471no—
552C22×C8C22×D4711yescharacteristic
553C22×C8C22×D4711yescharacteristic
554C4⋊Q8—474no—
555C4⋊Q8—942no—
556#127—474no—
557#127—474no—
558#127—942no—
559#127—942no—
560#126—948no—
561#124—474no—
562#124—474no—
563#124—474no—
564#124—942no—
565#124—942no—
566#124—942no—
567#124—948no—
568#123—948no—
569C22⋊Q8—22no—
570C22⋊Q8—948no—
571C22⋊Q8C22×D4714yes—
572#121—474no—
573#121—948no—
574#121—948no—
575#121—942no—
576#120—948no—
577#120—948no—
578C4×Q8—474no—
579C4×Q8—942no—
580C4×D4—474no—
581C4×D4—942no—
582#117—474no—
583#117—474no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—471no—
586C2×C4⋊C4—471no—
587C2×C4⋊C4—471no—
588C2×C4⋊C4—941no—
589C2×C4⋊C4—941no—
590C2×C4⋊C4C22×D4711yescharacteristic
591C2×C22⋊C4—21no—
592C2×C22⋊C4—471no—
593C2×C22⋊C4—471no—
594C2×C22⋊C4—941no—
595C2×C22⋊C4—941no—
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×C42—471no—
603C2×C42—471no—
604C2×C42—941no—
605C4⋊C8—474no—
606C4⋊C8—474no—
607#103—474no—
608#103C22×D4714yescomplemented
609#102—474no—
610#102—474no—
611#102—474no—
612#102—474no—
613#102—474no—
614#102C22×D4714yescomplemented
615C22⋊C8—474no—
616C22⋊C8C22×D4714yes—
617#97—474no—
618C4×C8—474no—
619C24—21no—
620C24—944no—
621C24—941no—
622C24—941no—
623C24—941no—
624C24—3762no—
625C24—3762no—
626C24—1884no—
627C24D4×D4711yescharacteristic
628#41—44no—
629#41—44no—
630#41—48no—
631C2×Q8—21no—
632C2×Q8—21no—
633C2×Q8—22no—
634C2×Q8—22no—
635C2×Q8—22no—
636C2×Q8—22no—
637C2×Q8—944no—
638C2×Q8—3762no—
639C2×Q8C23×D4712yes—
640C2×Q8C23×D4712yes—
641C2×D4—24no—
642C2×D4—21no—
643C2×D4—22no—
644C2×D4—22no—
645C2×D4—44no—
646C2×D4—472no—
647C2×D4—472no—
648C2×D4—472no—
649C2×D4—944no—
650C2×D4—944no—
651C2×D4—944no—
652C2×D4—944no—
653C2×D4—944no—
654C2×D4—941no—
655C2×D4—944no—
656C2×D4—941no—
657C2×D4—941no—
658C2×D4—942no—
659C2×D4—942no—
660C2×D4—942no—
661C2×D4—942no—
662C2×D4—942no—
663C2×D4—942no—
664C2×D4—3762no—
665C2×D4—3762no—
666C2×D4—3762no—
667C2×D4—3762no—
668C2×D4—3762no—
669C2×D4—1884no—
670C2×D4—1884no—
671C2×D4—1884no—
672C2×D4—1888no—
673C2×D4C23×D4712yes—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—24no—
680C22×C4—44no—
681C22×C4—471no—
682C22×C4—471no—
683C22×C4—471no—
684C22×C4—471no—
685C22×C4—944no—
686C22×C4—941no—
687C22×C4—3762no—
688C22×C4D4×D4712yes—
689C22×C4D4×D4711yescharacteristic
690C22×C4C23×D4712yes—
691C22×C4C23×D4711yescharacteristic
692Q16—44no—
693SD16—44no—
694SD16—1884no—
695SD16—1884no—
696SD16—1884no—
697D8—1884no—
698D8—1884no—
699D8—1884no—
700C2×C8—22no—
701C2×C8—22no—
702C2×C8—472no—
703C2×C8—472no—
704C2×C8—942no—
705C2×C8—942no—
706C2×C8C23×D4712yes—
707C2×C8C23×D4712yes—
708C4⋊C4—24no—
709C4⋊C4—21no—
710C4⋊C4—474no—
711C4⋊C4—474no—
712C4⋊C4—472no—
713C4⋊C4—944no—
714C4⋊C4—944no—
715C4⋊C4—941no—
716C4⋊C4C23×D4712yes—
717C22⋊C4—24no—
718C22⋊C4—474no—
719C22⋊C4—474no—
720C22⋊C4—944no—
721C22⋊C4—944no—
722C22⋊C4—944no—
723C22⋊C4—944no—
724C22⋊C4—944no—
725C22⋊C4—944no—
726C22⋊C4—944no—
727C22⋊C4—944no—
728C42—472no—
729C42—472no—
730C42—472no—
731C42—472no—
732C42—944no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—942no—
741C23—942no—
742C23—942no—
743C23—3764no—
744C23—3764no—
745C23—37616no—
746C23—1888no—
747C23—1882no—
748C23—1882no—
749C23—1882no—
750C23—1882no—
751C23—1882no—
752C23—1882no—
753C23—1882no—
754C23—1882no—
755C23—1882no—
756C23C2×D4×D4712yes—
757C23C2×D4×D4711yescharacteristic
758Q8—22no—
759Q8—22no—
760Q8—22no—
761Q8—22no—
762Q8—42no—
763Q8—42no—
764Q8—3764no—
765D4—22no—
766D4—22no—
767D4—48no—
768D4—42no—
769D4—942no—
770D4—942no—
771D4—942no—
772D4—942no—
773D4—942no—
774D4—942no—
775D4—3764no—
776D4—3764no—
777D4—3764no—
778D4—3764no—
779D4—3764no—
780D4—1888no—
781D4—1882no—
782D4—1882no—
783D4—1882no—
784C2×C4—22no—
785C2×C4—24no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—48no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—472no—
796C2×C4—472no—
797C2×C4—472no—
798C2×C4—472no—
799C2×C4—942no—
800C2×C4—942no—
801C2×C4—942no—
802C2×C4—942no—
803C2×C4—942no—
804C2×C4—3764no—
805C2×C4—1882no—
806C2×C4C2×D4×D4712yes—
807C2×C4C2×D4×D4711yescharacteristic
808C2×C4#1309406912yes—
809C2×C4#1309406912yes—
810C2×C4C24×D4711yescharacteristic
811C8—22no—
812C8—22no—
813C8—942no—
814C8—942no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—44no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—84no—
823C22—37616no—
824C22—3764no—
825C22—3764no—
826C22—3764no—
827C22—1882no—
828C22—1882no—
829C22—1882no—
830C22—1882no—
831C22—1882no—
832C22—1882no—
833C22—1882no—
834C22—1882no—
835C22—1882no—
836C22#1568968812yes—
837C22#1568992512yes—
838C22#1568993212yes—
839C22C22×D4×D4711yescharacteristic
840C4—22no—
841C4—42no—
842C4—42no—
843C4—42no—
844C4—942no—
845C4—942no—
846C4—942no—
847C4—942no—
848C4—1882no—
849C4#1568968812yes—
850C4C2×#1309406911yescharacteristic
851C4C2×#1309406911yescharacteristic
852C2—42no—
853C2—82no—
854C2—3762no—
855C2—3762no—
856C2—3762no—
857C2#2025448814yesdirect product factor
858C2C2×#1568968811yescharacteristic
859C2C2×#1568992511yescharacteristic
860C2C2×#1568993211yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#452C2
socleC23×C47C22×D4
hypercenterC2×#452D47
hypocenterC47C2×#3224
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#15689746C2semidirect
2. C2×#15689687C2semidirect
3. #20254488C2direct (N × H)
4. C2×#15689509C2semidirect
5. C2×#15689508C2semidirect
6. C2×#15689484C2semidirect
7. C2×#15689468C2semidirect
8. C2×#15689347C2semidirect
9. C2×#15689321C2semidirect
10. C2×#15689341C2semidirect
11. C2×#15689317C2semidirect
12. C2×#15689268C2semidirect
13. C2×#15689273C2semidirect
14. C2×#15689259C2semidirect
15. C2×#15689181C2semidirect
16. C2×C47×#452C2semidirect
20. C22×#10625336C22semidirect
23. C22×#10625334C22semidirect
25. #15689746C22semidirect
27. #15689687C22semidirect
28. C2×#13094023C22semidirect
34. C2×#13094013C22semidirect
43. C2×Q8×Dic47C22semidirect
44. C2×#13093986C22semidirect
46. #15689509C22semidirect
47. #15689508C22semidirect
48. #15689484C22semidirect
49. #15689468C22semidirect
50. #15689347C22semidirect
51. #15689341C22semidirect
52. #15689321C22semidirect
53. #15689317C22semidirect
54. #15689273C22semidirect
55. #15689268C22semidirect
56. #15689259C22semidirect
57. #15689181C22semidirect
58. C2×Dic47⋊C8C22semidirect
59. C2×Dic47⋊C8C22semidirect
60. C2×#13093948C22semidirect
63. C2×#13093945C22semidirect
67. C2×#13093934C22semidirect
68. C2×C8×Dic47C22semidirect
70. C22×Q16×C47C22semidirect
71. C22×SD16×C47C22semidirect
73. C47×#452C22semidirect
74. C2×#103×C47C22semidirect
75. C2×#102×C47C22semidirect
98. C2×#10625336C23semidirect
104. C2×#10625334C23semidirect
108. #13094023C23semidirect
119. #13094013C23semidirect
130. Q8×Dic47C23semidirect
132. #13093986C23semidirect
153. Dic47⋊C8C23semidirect
154. Dic47⋊C8C23semidirect
155. #13093948C23semidirect
158. #13093945C23semidirect
162. #13093934C23semidirect
163. C8×Dic47C23semidirect
175. C2×Q16×C47C23semidirect
177. C2×SD16×C47C23semidirect
185. #103×C47C23semidirect
186. #102×C47C23semidirect
433. C2×#452D47semidirect
440. C2×C47#3224semidirect
449. C22×Q16C2×D47semidirect
453. C22×SD16C2×D47semidirect
488. #452C2×D47semidirect
496. C2×#103C2×D47semidirect
502. C2×#102C2×D47semidirect
507. C47C2×#3224semidirect
535. C2×Q16C22×D47semidirect
543. C2×SD16C22×D47semidirect
608. #103C22×D47semidirect
614. #102C22×D47semidirect
857. C2#20254488direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897462
C2×#156896872
#202544882
C2×#156895092
C2×#156895082
C2×#156894842
C2×#156894682
C2×#156893472
C2×#156893212
C2×#156893412
C2×#156893172
C2×#156892682
C2×#156892732
C2×#156892592
C2×#156891812
C2×C47×#4522
C2×#322447