Finite Group Databasebeta

← C2×#20254489 #27087640

Subgroups — C2×#20254489 #27087640

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×#15689745C211yesmaximal, characteristic, complemented
2C2×#15689691C211yesmaximal, characteristic, complemented
3#20254489C2116yesmaximal, direct product factor
4C2×#15689509C211yesmaximal, characteristic, complemented
5C2×#15689508C211yesmaximal, characteristic, complemented
6C2×#15689484C211yesmaximal, characteristic, complemented
7C2×#15689468C211yesmaximal, characteristic, complemented
8C2×#15689323C211yesmaximal, characteristic, complemented
9C2×#15689335C211yesmaximal, characteristic, complemented
10C2×#15689319C211yesmaximal, characteristic, complemented
11C2×#15689284C211yesmaximal, characteristic, complemented
12C2×#15689271C211yesmaximal, characteristic, complemented
13C2×#15689272C211yesmaximal, characteristic, complemented
14C2×#15689258C211yesmaximal, characteristic, complemented
15C2×#15689183C211yesmaximal, characteristic, complemented
16C2×C47×#464C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18C22×D4×D47C2211yescharacteristic
19C22×#10625336C2211yescharacteristic
20C22×#10625336C2211yescharacteristic, complemented
21C22×#10625336C2211yescharacteristic, complemented
22C22×D376C2211yescharacteristic
23C22×D376C2211yescharacteristic, complemented
24C22×#10625334C2211yescharacteristic
25#15689745—24no—
26#15689745C2218yescomplemented
27#15689691—24no—
28#15689691C2218yescomplemented
29C2×#13094023C2211yescharacteristic, complemented
30C2×#13094021C2211yescharacteristic
31C2×#13094020C2211yescharacteristic
32C2×#13094018—21no—
33C2×#13094013C2211yescharacteristic
34C2×#13094013C2211yescharacteristic, complemented
35C2×#13094012—21no—
36C2×#13094009—21no—
37C2×#13094002—21no—
38C2×#13094000C2211yescharacteristic
39C2×#13093999C2211yescharacteristic
40C2×#13093997—21no—
41C2×#13093997—21no—
42C2×#13093994—21no—
43C2×#13093994—21no—
44C2×C4×D188C2211yescharacteristic, complemented
45C2×#13093981C2211yescharacteristic
46#15689509C2218yescomplemented
47#15689508C2218yescomplemented
48#15689484C2218yescomplemented
49#15689468C2218yescomplemented
50#15689335C2218yescomplemented
51#15689323C2218yescomplemented
52#15689319C2218yescomplemented
53#15689284C2218yescomplemented
54#15689272C2218yescomplemented
55#15689271C2218yescomplemented
56#15689258C2218yescomplemented
57#15689183C2218yescomplemented
58C2×C4⋊(C47⋊C8)C2211yescharacteristic, complemented
59C2×#13093948C2211yescharacteristic, complemented
60C2×#13093946C2211yescharacteristic
61C2×#13093946C2211yescharacteristic, complemented
62C2×#13093945C2211yescharacteristic
63C2×#13093944C2211yescharacteristic
64C2×#13093944C2211yescharacteristic, complemented
65C2×(C2×D47)⋊C8C2211yescharacteristic
66C2×(C2×D47)⋊C8C2211yescharacteristic
67C2×#13093934C2211yescharacteristic, complemented
68C2×C8×Dic47C2211yescharacteristic, complemented
69C22×Q16×C47C2211yescharacteristic, complemented
70C22×SD16×C47C2211yescharacteristic
71C2×#124×C47C2211yescharacteristic
72C2×C4×Q8×C47C2211yescharacteristic, complemented
73C47×#464C2218yescomplemented
74C2×C4⋊C8×C47C2211yescharacteristic, complemented
75C2×#103×C47C2211yescharacteristic, complemented
76C2×#102×C47C2211yescharacteristic
77C24×D47—21no—
78C2×#10625354—22no—
79C2×#10625354—42no—
80C2×#10625354—42no—
81C2×#10625354C2314yes—
82C22×Dic94—21no—
83C22×D188—21no—
84C22×D188—21no—
85C22×D188—21no—
86C22×D188—21no—
87C22×D188C2311yescharacteristic
88C22×D188C2311yescharacteristic
89C22×D188C2311yescharacteristic
90C22×C22⋊D47—21no—
91C22×C22⋊D47—21no—
92C22×C22⋊D47—21no—
93C2×D4×D47—22no—
94C2×D4×D47—42no—
95C2×D4×D47—42no—
96C2×D4×D47C2314yes—
97C22×C4×D47—21no—
98C22×C4×D47—21no—
99C22×C4×D47C2311yescharacteristic
100C2×#10625336—42no—
101C2×#10625336—42no—
102C2×#10625336—42no—
103C2×#10625336C2314yes—
104C2×#10625336C2314yescomplemented
105C2×#10625336C2314yescomplemented
106C2×D376—42no—
107C2×D376—42no—
108C2×D376C2314yes—
109C2×D376C2314yescomplemented
110C2×#10625334—42no—
111C2×#10625334C2314yes—
112C22×C47⋊C8C2311yescharacteristic
113C22×C47⋊C8C2311yescharacteristic
114#13094023—22no—
115#13094023C2314yescomplemented
116#13094021—22no—
117#13094021C2314yes—
118#13094020—22no—
119#13094020C2314yes—
120#13094018—28no—
121#13094013—22no—
122#13094013—22no—
123#13094013C2314yes—
124#13094013C2314yescomplemented
125#13094012—28no—
126#13094009—28no—
127#13094002—28no—
128#13094000—22no—
129#13094000C2314yes—
130#13093999—22no—
131#13093999C2314yes—
132#13093997—28no—
133#13093997—28no—
134#13093994—28no—
135#13093994—28no—
136C4×D188—22no—
137C4×D188C2314yescomplemented
138#13093981D414yes—
139#13093981C2314yes—
140C2×C4⋊Dic47C2311yescharacteristic
141C2×Dic47⋊C4—21no—
142C2×Dic47⋊C4—21no—
143C2×Dic47⋊C4D411yescharacteristic
144C2×Dic47⋊C4D411yescharacteristic
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×(C2×D47)⋊C4—21no—
152C2×(C2×D47)⋊C4D411yescharacteristic
153C2×(C2×D47)⋊C4D411yescharacteristic
154C2×C4×Dic47C2311yescharacteristic
155C4⋊(C47⋊C8)C2314yescomplemented
156#13093948C2314yescomplemented
157#13093946C2314yes—
158#13093946C2314yescomplemented
159#13093945C2314yes—
160#13093944C2314yes—
161#13093944C2314yescomplemented
162(C2×D47)⋊C8C2314yes—
163(C2×D47)⋊C8C2314yes—
164#13093934C2314yescomplemented
165C8×Dic47C2314yescomplemented
166C22×Q8×C47C2311yescharacteristic
167C22×Q8×C47C2311yescharacteristic
168C22×D4×C47C2311yescharacteristic
169C2×Q16×C47—42no—
170C2×Q16×C47C2314yescomplemented
171C2×SD16×C47—42no—
172C2×SD16×C47C2314yes—
173C22×C8×C47C2311yescharacteristic
174C22×C8×C47C2311yescharacteristic
175#124×C47—22no—
176#124×C47C2314yes—
177C4×Q8×C47—22no—
178C4×Q8×C47C2314yescomplemented
179C2×C4⋊C4×C47—21no—
180C2×C4⋊C4×C47C2311yescharacteristic
181C2×C22⋊C4×C47—21no—
182C2×C22⋊C4×C47—21no—
183C2×C42×C47—21no—
184C2×C42×C47C2311yescharacteristic
185C4⋊C8×C47C2314yescomplemented
186#103×C47C2314yescomplemented
187#102×C47C2314yes—
188C24×C47—21no—
189C23×D47—21no—
190C23×D47—21no—
191C23×D47—21no—
192C23×D47—24no—
193C23×D47—44no—
194C23×D47—82no—
195C23×D47—82no—
196C23×D47C2×D411yescharacteristic
197C2×Q8×C47—21no—
198C2×Q8×C47—21no—
199C2×Q8×C47—22no—
200C2×Q8×C47—22no—
201C2×Q8×C47—22no—
202C2×Q8×C47—22no—
203C2×Q8×C47C2412yes—
204C2×Q8×C47C2412yes—
205C2×D4×C47—21no—
206C2×D4×C47—22no—
207C2×D4×C47—22no—
208C2×D4×C47C2412yes—
209C22×C4×C47—21no—
210C22×C4×C47—21no—
211C22×C4×C47—21no—
212C22×C4×C47C2×D411yescharacteristic
213C22×C4×C47C2×D411yescharacteristic
214C22×C4×C47C2411yescharacteristic
215C2×C22⋊D47—24no—
216C2×C22⋊D47—24no—
217C2×C22⋊D47—24no—
218C2×C22⋊D47—44no—
219C2×C22⋊D47—82no—
220C2×C22⋊D47—82no—
221C22×Dic47—21no—
222C22×Dic47C2×D411yescharacteristic
223C22×Dic47C2×D411yescharacteristic
224C22×Dic47C2×D411yescharacteristic
225#10625354—44no—
226#10625354—44no—
227#10625354—48no—
228D4×D47—44no—
229D4×D47—44no—
230D4×D47—48no—
231C2×D188—22no—
232C2×D188—22no—
233C2×D188—22no—
234C2×D188—22no—
235C2×D188—22no—
236C2×D188—22no—
237C2×D188—24no—
238C2×D188—21no—
239C2×D188—21no—
240C2×D188—21no—
241C2×D188—24no—
242C2×D188—24no—
243C2×D188—24no—
244C2×D188—44no—
245C2×D188—82no—
246C2×D188—82no—
247C2×D188—82no—
248C2×D188C2412yes—
249C2×D188C2412yes—
250C2×D188C2412yes—
251C2×C4×D47—22no—
252C2×C4×D47—22no—
253C2×C4×D47—24no—
254C2×C4×D47—24no—
255C2×C4×D47—44no—
256C2×C4×D47—82no—
257C2×C4×D47C2×D412yes—
258C2×C4×D47C2412yes—
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⋊C4×C47—24no—
272C42×C47—24no—
273C42×C47C2×D412yes—
274C42×C47C2412yes—
275#10625336—44no—
276#10625336—44no—
277#10625336—44no—
278#10625334—44no—
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—
285(C2×D47)⋊C4—24no—
286(C2×D47)⋊C4C2×D414yes—
287(C2×D47)⋊C4C2×D414yes—
288C4⋊Dic47—21no—
289C4⋊Dic47C2412yes—
290Dic47⋊C4—24no—
291Dic47⋊C4—24no—
292Dic47⋊C4C2×D414yes—
293Dic47⋊C4C2×D414yes—
294C4×Dic47C2×D412yes—
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—42no—
304C23×C47—42no—
305C23×C47—42no—
306C23×C47C22×D411yescharacteristic
307C22×D47—22no—
308C22×D47—22no—
309C22×D47—22no—
310C22×D47—22no—
311C22×D47—22no—
312C22×D47—22no—
313C22×D47—48no—
314C22×D47—42no—
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—84no—
324C22×D47—84no—
325C22×D47—816no—
326C22×D47C22×D412yes—
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—42no—
336C2×C4×C47—22no—
337C2×C4×C47—22no—
338C2×C4×C47—22no—
339C2×C4×C47—22no—
340C2×C4×C47—22no—
341C2×C4×C47—42no—
342C2×C4×C47—42no—
343C2×C4×C47—42no—
344C2×C4×C47C22×D412yes—
345C2×C4×C47C22×D412yes—
346C2×C4×C47C22×D411yescharacteristic
347C2×C4×C47H(5,𝔽2)12yes—
348C2×C4×C47H(5,𝔽2)12yes—
349C2×C4×C47C2511yescharacteristic
350C22⋊D47—48no—
351C22⋊D47—84no—
352C22⋊D47—84no—
353C2×Dic47—22no—
354C2×Dic47—22no—
355C2×Dic47—22no—
356C2×Dic47—22no—
357C2×Dic47—42no—
358C2×Dic47C22×D412yes—
359C2×Dic47C22×D412yes—
360C2×Dic47C22×D412yes—
361D188—22no—
362D188—22no—
363D188—22no—
364D188—22no—
365D188—22no—
366D188—22no—
367D188—48no—
368D188—42no—
369D188—42no—
370D188—42no—
371D188—84no—
372D188—84no—
373D188—84no—
374C4×D47—24no—
375C4×D47—22no—
376C4×D47—22no—
377C4×D47—48no—
378C4×D47—84no—
379Dic94—84no—
380C8×C47—22no—
381C8×C47—22no—
382C47⋊C8—22no—
383C47⋊C8—22no—
384C2×#3224—471nomaximal, Sylow
385C22×C47—42no—
386C22×C47—42no—
387C22×C47—42no—
388C22×C47—84no—
389C22×C47#53512yes—
390C22×C47#57612yes—
391C22×C47#57712yes—
392C22×C47C23×D411yescharacteristic
393C2×D47—22no—
394C2×D47—22no—
395C2×D47—22no—
396C2×D47—44no—
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—22no—
412C4×C47—42no—
413C4×C47—42no—
414C4×C47—42no—
415C4×C47#53512yes—
416C4×C47C2×H(5,𝔽2)11yescharacteristic
417C4×C47C2×H(5,𝔽2)11yescharacteristic
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×#464D4711yescharacteristic, complemented
430C2×#460—471no—
431C2×#463—471no—
432C2×#459—471no—
433C2×#452—471no—
434C2×#449—471no—
435C2×#450—471no—
436C2×#447—471no—
437C2×#433—471no—
438C2×C47—82no—
439C2×C47#322414yescomplemented
440C2×C47C2×#53511yescharacteristic
441C2×C47C2×#57611yescharacteristic
442C2×C47C2×#57711yescharacteristic
443D47—42no—
444D47—82no—
445D47—82no—
446D47—82no—
447C22×#41—471no—
448C23×D4—471no—
449C22×Q16C2×D4711yescharacteristic, complemented
450C22×SD16—471no—
451C22×SD16—471no—
452C22×SD16—471no—
453C22×SD16C2×D4711yescharacteristic
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—941no—
468C2×#124C2×D4711yescharacteristic
469C2×#123—941no—
470C2×C22⋊Q8—471no—
471C2×C22⋊Q8—941no—
472C2×#121—471no—
473C2×#121—941no—
474C2×#121—941no—
475C2×#120—941no—
476C2×#120—941no—
477C2×C4×Q8C2×D4711yescharacteristic, complemented
478C2×C4×D4—471no—
479C2×#117—471no—
480#496—478no—
481#495—478no—
482#489—478no—
483#486—478no—
484#464C2×D4718yescomplemented
485#463—478no—
486#460—478no—
487#459—478no—
488#452—478no—
489#450—478no—
490#449—478no—
491#447—478no—
492#433—478no—
493C2×C4⋊C8—471no—
494C2×C4⋊C8C2×D4711yescharacteristic, complemented
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
503C2×C22⋊C8—471no—
504C2×C22⋊C8—471no—
505C2×#97—471no—
506C2×C4×C8—471no—
507C47C2×#322411yescharacteristic, complemented, Sylow
508C25—941no—
509C2×#41—474no—
510C2×#41—942no—
511C2×#41—1882no—
512C2×#41—1882no—
513C22×Q8—941no—
514C22×Q8C22×D4711yescharacteristic
515C22×Q8C22×D4711yescharacteristic
516C22×D4—474no—
517C22×D4—471no—
518C22×D4—471no—
519C22×D4—471no—
520C22×D4—941no—
521C22×D4—941no—
522C22×D4—942no—
523C22×D4—941no—
524C22×D4—941no—
525C22×D4—941no—
526C22×D4—941no—
527C22×D4—941no—
528C22×D4—1882no—
529C22×D4—1882no—
530C22×D4C22×D4711yescharacteristic
531C23×C4—471no—
532C23×C4—941no—
533C23×C4—941no—
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×D4714yes—
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—22no—
562#124—474no—
563#124—474no—
564#124—948no—
565#124—942no—
566#124—942no—
567#124C22×D4714yes—
568#123—948no—
569C22⋊Q8—474no—
570C22⋊Q8—948no—
571C22⋊Q8—942no—
572#121—474no—
573#121—948no—
574#121—948no—
575#121—942no—
576#120—948no—
577#120—948no—
578C4×Q8—22no—
579C4×Q8C22×D4714yescomplemented
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—21no—
593C2×C22⋊C4—471no—
594C2×C22⋊C4—471no—
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—21no—
603C2×C42—471no—
604C2×C42C22×D4711yescharacteristic
605C4⋊C8—474no—
606C4⋊C8C22×D4714yescomplemented
607#103—474no—
608#103C22×D4714yescomplemented
609#102—474no—
610#102—474no—
611#102—474no—
612#102—474no—
613#102—474no—
614#102C22×D4714yes—
615C22⋊C8—474no—
616C22⋊C8—474no—
617#97—474no—
618C4×C8—474no—
619C24—21no—
620C24—471no—
621C24—944no—
622C24—941no—
623C24—941no—
624C24—941no—
625C24—3762no—
626C24—3762no—
627C24—1884no—
628#41—1884no—
629#41—1884no—
630#41—1888no—
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—21no—
642C2×D4—22no—
643C2×D4—22no—
644C2×D4—472no—
645C2×D4—472no—
646C2×D4—472no—
647C2×D4—944no—
648C2×D4—944no—
649C2×D4—944no—
650C2×D4—944no—
651C2×D4—944no—
652C2×D4—944no—
653C2×D4—944no—
654C2×D4—941no—
655C2×D4—941no—
656C2×D4—941no—
657C2×D4—942no—
658C2×D4—942no—
659C2×D4—942no—
660C2×D4—942no—
661C2×D4—942no—
662C2×D4—942no—
663C2×D4—3762no—
664C2×D4—3762no—
665C2×D4—3762no—
666C2×D4—3762no—
667C2×D4—3762no—
668C2×D4—1884no—
669C2×D4—1884no—
670C2×D4—1884no—
671C2×D4—1888no—
672C2×D4—1884no—
673C2×D4C23×D4712yes—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—471no—
678C22×C4—471no—
679C22×C4—471no—
680C22×C4—472no—
681C22×C4—472no—
682C22×C4—944no—
683C22×C4—942no—
684C22×C4—942no—
685C22×C4—941no—
686C22×C4—944no—
687C22×C4—3762no—
688C22×C4—1884no—
689C22×C4D4×D4711yescharacteristic
690C22×C4D4×D4711yescharacteristic
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—24no—
719C22⋊C4—474no—
720C22⋊C4—474no—
721C22⋊C4—944no—
722C22⋊C4—944no—
723C22⋊C4—944no—
724C22⋊C4—944no—
725C22⋊C4—944no—
726C22⋊C4—944no—
727C22⋊C4—944no—
728C42—24no—
729C42—472no—
730C42—472no—
731C42D4×D4712yes—
732C42C23×D4712yes—
733C23—22no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—472no—
738C23—942no—
739C23—942no—
740C23—942no—
741C23—942no—
742C23—942no—
743C23—942no—
744C23—3764no—
745C23—3764no—
746C23—37616no—
747C23—1888no—
748C23—1882no—
749C23—1882no—
750C23—1882no—
751C23—1882no—
752C23—1882no—
753C23—1882no—
754C23—1882no—
755C23—1882no—
756C23—1882no—
757C23C2×D4×D4711yescharacteristic
758Q8—22no—
759Q8—22no—
760Q8—22no—
761Q8—22no—
762Q8—42no—
763Q8—42no—
764Q8—3764no—
765D4—22no—
766D4—22no—
767D4—42no—
768D4—942no—
769D4—942no—
770D4—942no—
771D4—942no—
772D4—942no—
773D4—942no—
774D4—3764no—
775D4—3764no—
776D4—3764no—
777D4—3764no—
778D4—3764no—
779D4—1888no—
780D4—1888no—
781D4—1882no—
782D4—1882no—
783D4—1882no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—472no—
793C2×C4—472no—
794C2×C4—472no—
795C2×C4—942no—
796C2×C4—942no—
797C2×C4—942no—
798C2×C4—944no—
799C2×C4—942no—
800C2×C4—942no—
801C2×C4—942no—
802C2×C4—3764no—
803C2×C4—1888no—
804C2×C4—1882no—
805C2×C4C2×D4×D4712yes—
806C2×C4C2×D4×D4712yes—
807C2×C4C2×D4×D4711yescharacteristic
808C2×C4#1309406912yes—
809C2×C4#1309407012yes—
810C2×C4C24×D4711yescharacteristic
811C8—22no—
812C8—22no—
813C8—942no—
814C8—942no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—84no—
819C22—942no—
820C22—942no—
821C22—942no—
822C22—37616no—
823C22—3764no—
824C22—3764no—
825C22—3764no—
826C22—1882no—
827C22—1882no—
828C22—1882no—
829C22—1882no—
830C22—1882no—
831C22—1882no—
832C22—1882no—
833C22—1882no—
834C22—1882no—
835C22—1884no—
836C22#1568968912yes—
837C22#1568992512yes—
838C22#1568993212yes—
839C22C22×D4×D4711yescharacteristic
840C4—22no—
841C4—22no—
842C4—42no—
843C4—42no—
844C4—42no—
845C4—942no—
846C4—942no—
847C4—942no—
848C4—1882no—
849C4#1568968912yes—
850C4C2×#1309406911yescharacteristic
851C4C2×#1309407011yescharacteristic
852C2—82no—
853C2—3762no—
854C2—3762no—
855C2—3762no—
856C2—1882no—
857C2#2025448914yesdirect product factor
858C2C2×#1568968911yescharacteristic
859C2C2×#1568992511yescharacteristic
860C2C2×#1568993211yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#464C2
socleC23×C47C22×D4
hypercenterC2×#464D47
hypocenterC47C2×#3224
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C2×#15689745C2semidirect
2. C2×#15689691C2semidirect
3. #20254489C2direct (N × H)
4. C2×#15689509C2semidirect
5. C2×#15689508C2semidirect
6. C2×#15689484C2semidirect
7. C2×#15689468C2semidirect
8. C2×#15689323C2semidirect
9. C2×#15689335C2semidirect
10. C2×#15689319C2semidirect
11. C2×#15689284C2semidirect
12. C2×#15689271C2semidirect
13. C2×#15689272C2semidirect
14. C2×#15689258C2semidirect
15. C2×#15689183C2semidirect
16. C2×C47×#464C2semidirect
20. C22×#10625336C22semidirect
21. C22×#10625336C22semidirect
23. C22×D376C22semidirect
26. #15689745C22semidirect
28. #15689691C22semidirect
29. C2×#13094023C22semidirect
34. C2×#13094013C22semidirect
44. C2×C4×D188C22semidirect
46. #15689509C22semidirect
47. #15689508C22semidirect
48. #15689484C22semidirect
49. #15689468C22semidirect
50. #15689335C22semidirect
51. #15689323C22semidirect
52. #15689319C22semidirect
53. #15689284C22semidirect
54. #15689272C22semidirect
55. #15689271C22semidirect
56. #15689258C22semidirect
57. #15689183C22semidirect
58. C2×C4⋊(C47⋊C8)C22semidirect
59. C2×#13093948C22semidirect
61. C2×#13093946C22semidirect
64. C2×#13093944C22semidirect
67. C2×#13093934C22semidirect
68. C2×C8×Dic47C22semidirect
69. C22×Q16×C47C22semidirect
72. C2×C4×Q8×C47C22semidirect
73. C47×#464C22semidirect
74. C2×C4⋊C8×C47C22semidirect
75. C2×#103×C47C22semidirect
104. C2×#10625336C23semidirect
105. C2×#10625336C23semidirect
109. C2×D376C23semidirect
115. #13094023C23semidirect
124. #13094013C23semidirect
137. C4×D188C23semidirect
155. C4⋊(C47⋊C8)C23semidirect
156. #13093948C23semidirect
158. #13093946C23semidirect
161. #13093944C23semidirect
164. #13093934C23semidirect
165. C8×Dic47C23semidirect
170. C2×Q16×C47C23semidirect
178. C4×Q8×C47C23semidirect
185. C4⋊C8×C47C23semidirect
186. #103×C47C23semidirect
429. C2×#464D47semidirect
439. C2×C47#3224semidirect
449. C22×Q16C2×D47semidirect
477. C2×C4×Q8C2×D47semidirect
484. #464C2×D47semidirect
494. C2×C4⋊C8C2×D47semidirect
496. C2×#103C2×D47semidirect
507. C47C2×#3224semidirect
535. C2×Q16C22×D47semidirect
579. C4×Q8C22×D47semidirect
606. C4⋊C8C22×D47semidirect
608. #103C22×D47semidirect
857. C2#20254489direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897452
C2×#156896912
#202544892
C2×#156895092
C2×#156895082
C2×#156894842
C2×#156894682
C2×#156893232
C2×#156893352
C2×#156893192
C2×#156892842
C2×#156892712
C2×#156892722
C2×#156892582
C2×#156891832
C2×C47×#4642
C2×#322447