Finite Group Databasebeta

← C2×#20255590 #27093076

Subgroups — C2×#20255590 #27093076

Order 12032.

2318 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689821C211yesmaximal, characteristic, complemented
2C2×#15689761C211yesmaximal, characteristic, complemented
3#20255590C2116yesmaximal, direct product factor
4C2×#15689479C211yesmaximal, characteristic, complemented
5C2×#15689462C211yesmaximal, characteristic, complemented
6C2×#15689436C211yesmaximal, characteristic, complemented
7C2×#15689425C211yesmaximal, characteristic, complemented
8C2×#15689376C211yesmaximal, characteristic, complemented
9C2×#15689372C211yesmaximal, characteristic, complemented
10C2×#15689341C211yesmaximal, characteristic, complemented
11C2×#15689268C211yesmaximal, characteristic, complemented
12C2×#15689258C211yesmaximal, characteristic, complemented
13C2×#15689203C211yesmaximal, characteristic, complemented
14C2×#15689199C211yesmaximal, characteristic, complemented
15C2×#15689126C211yesmaximal, characteristic, complemented
16C2×C47×#417C211yesmaximal, characteristic, complemented
17C22×D4×D47C2211yescharacteristic
18C22×#10625336C2211yescharacteristic, complemented
19C22×D376C2211yescharacteristic
20C22×#10625334C2211yescharacteristic
21C22×#10625324C2211yescharacteristic
22#15689821—24no—
23#15689821C2218yescomplemented
24#15689761—24no—
25#15689761C2218yescomplemented
26C2×#13094019—21no—
27C2×#13094015C2211yescharacteristic, complemented
28C2×#13094013C2211yescharacteristic
29C2×#13094009—21no—
30C2×#13094007—21no—
31C2×#13094000C2211yescharacteristic
32C2×#13093999C2211yescharacteristic
33C2×#13093998—21no—
34C2×#13093998C2211yescharacteristic
35C2×#13093998C2211yescharacteristic, complemented
36C2×#13093996—21no—
37C2×#13093992—21no—
38C2×D4×Dic47C2211yescharacteristic
39C2×#13093986C2211yescharacteristic, complemented
40C2×C4×C22⋊D47—21no—
41C2×C4×C22⋊D47C2211yescharacteristic
42C2×#13093982C2211yescharacteristic
43C22×(C2×D47)⋊C4—21no—
44#15689479C2218yescomplemented
45#15689462C2218yescomplemented
46#15689436C2218yescomplemented
47#15689425C2218yescomplemented
48#15689376C2218yescomplemented
49#15689372C2218yescomplemented
50#15689341C2218yescomplemented
51#15689268C2218yescomplemented
52#15689258C2218yescomplemented
53#15689203C2218yescomplemented
54#15689199C2218yescomplemented
55C2×#13093957C2211yescharacteristic, complemented
56C2×#13093957C2211yescharacteristic, complemented
57C2×#13093956C2211yescharacteristic, complemented
58C2×Dic47⋊C8C2211yescharacteristic, complemented
59#15689126C2218yescomplemented
60C2×#13093948C2211yescharacteristic, complemented
61C2×#13093946C2211yescharacteristic
62C2×#13093946C2211yescharacteristic, complemented
63C2×#13093945C2211yescharacteristic
64C2×#13093944C2211yescharacteristic
65C2×#13093944C2211yescharacteristic
66C2×C22⋊(C47⋊C8)C2211yescharacteristic, complemented
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic, complemented
69C22×#41×C47C2211yescharacteristic
70C22×M16×C47C2211yescharacteristic, complemented
71C22×C4⋊C4×C47C2211yescharacteristic, complemented
72C47×#417C2218yescomplemented
73C2×#103×C47C2211yescharacteristic, complemented
74C2×#103×C47C2211yescharacteristic, complemented
75C2×#102×C47C2211yescharacteristic
76C2×#102×C47C2211yescharacteristic
77C24×D47—21no—
78C22×D188—21no—
79C22×D188C2311yescharacteristic
80C22×D188C2311yescharacteristic
81C22×C22⋊D47—21no—
82C22×C22⋊D47—21no—
83C22×C22⋊D47—21no—
84C22×C22⋊D47D411yescharacteristic
85C2×D4×D47—24no—
86C2×D4×D47—22no—
87C2×D4×D47—42no—
88C2×D4×D47C2314yes—
89C23×Dic47—21no—
90C22×C4×D47—21no—
91C22×C4×D47C2311yescharacteristic
92C2×#10625336—42no—
93C2×#10625336C2314yescomplemented
94C2×D376—42no—
95C2×D376C2314yes—
96C2×#10625334—24no—
97C2×#10625334C2314yes—
98C2×#10625324—42no—
99C2×#10625324C2314yes—
100C22×C47⋊C8C2311yescharacteristic
101C22×C47⋊C8C2311yescharacteristic
102#13094019—28no—
103#13094015—22no—
104#13094015C2314yescomplemented
105#13094013—22no—
106#13094013C2314yes—
107#13094009—28no—
108#13094007—28no—
109#13094000—22no—
110#13094000C2314yes—
111#13093999—22no—
112#13093999C2314yes—
113#13093998—22no—
114#13093998—22no—
115#13093998—28no—
116#13093998C2314yes—
117#13093998C2314yescomplemented
118#13093996—28no—
119#13093992—28no—
120D4×Dic47—22no—
121D4×Dic47C2314yes—
122#13093986—22no—
123#13093986C2314yescomplemented
124C4×C22⋊D47—28no—
125C4×C22⋊D47D414yes—
126C4×C22⋊D47C2314yes—
127#13093982—22no—
128#13093982C2314yes—
129C2×C4⋊Dic47—21no—
130C2×C4⋊Dic47C2311yescharacteristic
131C2×C4⋊Dic47C2311yescharacteristic
132C2×Dic47⋊C4—21no—
133C2×Dic47⋊C4—21no—
134C2×Dic47⋊C4D411yescharacteristic
135C2×C22⋊Dic47—21no—
136C2×C22⋊Dic47D411yescharacteristic
137C2×(C2×D47)⋊C4—21no—
138C2×(C2×D47)⋊C4—21no—
139C2×(C2×D47)⋊C4—21no—
140C2×(C2×D47)⋊C4—21no—
141C2×(C2×D47)⋊C4—21no—
142C2×(C2×D47)⋊C4—21no—
143C2×(C2×D47)⋊C4—21no—
144C2×(C2×D47)⋊C4—21no—
145C2×(C2×D47)⋊C4—28no—
146C2×(C2×D47)⋊C4D411yescharacteristic
147C2×C4×Dic47—21no—
148C2×C4×Dic47C2311yescharacteristic
149#13093957C2314yescomplemented
150#13093957C2314yescomplemented
151#13093956C2314yescomplemented
152Dic47⋊C8C2314yescomplemented
153#13093948C2314yescomplemented
154#13093946C2314yes—
155#13093946C2314yescomplemented
156#13093945C2314yes—
157#13093944C2314yes—
158#13093944C2314yes—
159C22⋊(C47⋊C8)C2314yescomplemented
160(C2×D47)⋊C8C2314yes—
161C8×Dic47C2314yescomplemented
162C2×#41×C47—22no—
163C2×#41×C47—24no—
164C2×#41×C47—42no—
165C2×#41×C47C2314yes—
166C22×Q8×C47C2311yescharacteristic
167C22×D4×C47—21no—
168C22×D4×C47C2311yescharacteristic
169C23×C4×C47—21no—
170C23×C4×C47—21no—
171C23×C4×C47C2311yescharacteristic
172C2×M16×C47—42no—
173C2×M16×C47C2314yescomplemented
174C22×C8×C47C2311yescharacteristic
175C22×C8×C47C2311yescharacteristic
176C2×C4⋊C4×C47—22no—
177C2×C4⋊C4×C47—21no—
178C2×C4⋊C4×C47C2311yescharacteristic
179C2×C4⋊C4×C47C2311yescharacteristic
180C2×C4⋊C4×C47C2314yescomplemented
181#103×C47C2314yescomplemented
182#103×C47C2314yescomplemented
183#102×C47C2314yes—
184#102×C47C2314yes—
185C24×C47—21no—
186C24×C47C2×D411yescharacteristic
187C23×D47—21no—
188C23×D47—21no—
189C23×D47—24no—
190C23×D47—44no—
191C23×D47—44no—
192C23×D47—82no—
193C23×D47C2×D411yescharacteristic
194#41×C47—28no—
195#41×C47—44no—
196#41×C47—48no—
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—44no—
205C2×D4×C47#4114yes—
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×C47—24no—
213C22×C4×C47—24no—
214C22×C4×C47—44no—
215C22×C4×C47—82no—
216C22×C4×C47C2×D411yescharacteristic
217C22×C4×C47C2×D412yes—
218C22×C4×C47C2412yes—
219C22×C4×C47C2411yescharacteristic
220C2×C22⋊D47—24no—
221C2×C22⋊D47—24no—
222C2×C22⋊D47—24no—
223C2×C22⋊D47—42no—
224C2×C22⋊D47—44no—
225C2×C22⋊D47—44no—
226C2×C22⋊D47—82no—
227C2×C22⋊D47C2×D414yes—
228C22×Dic47—21no—
229C22×Dic47—21no—
230C22×Dic47—24no—
231C22×Dic47—82no—
232C22×Dic47C2×D411yescharacteristic
233C22×Dic47C2×D411yescharacteristic
234C22×Dic47C2×D411yescharacteristic
235D4×D47—28no—
236D4×D47—44no—
237D4×D47—48no—
238C2×D188—22no—
239C2×D188—22no—
240C2×D188—22no—
241C2×D188—22no—
242C2×D188—21no—
243C2×D188—21no—
244C2×D188—24no—
245C2×D188—82no—
246C2×D188C2412yes—
247C2×D188C2412yes—
248C2×C4×D47—22no—
249C2×C4×D47—22no—
250C2×C4×D47—24no—
251C2×C4×D47—82no—
252C2×C4×D47C2×D412yes—
253C2×C4×D47C2412yes—
254M16×C47—44no—
255C2×C8×C47—22no—
256C2×C8×C47—22no—
257C2×C8×C47C2412yes—
258C2×C8×C47C2412yes—
259C4⋊C4×C47—21no—
260C4⋊C4×C47—21no—
261C4⋊C4×C47—24no—
262C4⋊C4×C47C2412yes—
263C4⋊C4×C47C2412yes—
264C22⋊Dic47—24no—
265C22⋊Dic47C2×D414yes—
266#10625336—44no—
267#10625334—28no—
268(C2×D47)⋊C4—24no—
269(C2×D47)⋊C4—24no—
270(C2×D47)⋊C4—24no—
271(C2×D47)⋊C4—24no—
272(C2×D47)⋊C4—24no—
273(C2×D47)⋊C4—24no—
274(C2×D47)⋊C4—24no—
275(C2×D47)⋊C4—24no—
276(C2×D47)⋊C4C2×D414yes—
277C4⋊Dic47—21no—
278C4⋊Dic47—21no—
279C4⋊Dic47—24no—
280C4⋊Dic47C2412yes—
281C4⋊Dic47C2412yes—
282Dic47⋊C4—24no—
283Dic47⋊C4—24no—
284Dic47⋊C4C2×D414yes—
285C4×Dic47—24no—
286C4×Dic47C2×D412yes—
287C4×Dic47C2412yes—
288C2×C47⋊C8—22no—
289C2×C47⋊C8—22no—
290C2×C47⋊C8C2412yes—
291C2×C47⋊C8C2412yes—
292D376—44no—
293#10625324—44no—
294C23×C47—24no—
295C23×C47—22no—
296C23×C47—22no—
297C23×C47—22no—
298C23×C47—22no—
299C23×C47—42no—
300C23×C47—42no—
301C23×C47C22×D412yes—
302C23×C47C22×D411yescharacteristic
303C22×D47—22no—
304C22×D47—22no—
305C22×D47—22no—
306C22×D47—22no—
307C22×D47—22no—
308C22×D47—48no—
309C22×D47—48no—
310C22×D47—42no—
311C22×D47—42no—
312C22×D47—42no—
313C22×D47—42no—
314C22×D47—42no—
315C22×D47—42no—
316C22×D47—84no—
317C22×D47—816no—
318C22×D47C22×D412yes—
319Q8×C47—22no—
320Q8×C47—22no—
321Q8×C47—42no—
322D4×C47—24no—
323D4×C47—22no—
324D4×C47—48no—
325D4×C47C2×#4114yes—
326C2×C4×C47—22no—
327C2×C4×C47—24no—
328C2×C4×C47—22no—
329C2×C4×C47—22no—
330C2×C4×C47—22no—
331C2×C4×C47—22no—
332C2×C4×C47—22no—
333C2×C4×C47—48no—
334C2×C4×C47—42no—
335C2×C4×C47—42no—
336C2×C4×C47—42no—
337C2×C4×C47—84no—
338C2×C4×C47C22×D412yes—
339C2×C4×C47C22×D411yescharacteristic
340C2×C4×C47C2×#4112yes—
341C2×C4×C47H(5,𝔽2)12yes—
342C2×C4×C47C2511yescharacteristic
343C22⋊D47—44no—
344C22⋊D47—48no—
345C22⋊D47—48no—
346C22⋊D47—84no—
347C2×Dic47—22no—
348C2×Dic47—22no—
349C2×Dic47—22no—
350C2×Dic47—22no—
351C2×Dic47—22no—
352C2×Dic47—42no—
353C2×Dic47—42no—
354C2×Dic47—84no—
355C2×Dic47C22×D412yes—
356C2×Dic47C22×D412yes—
357C2×Dic47C22×D412yes—
358D188—22no—
359D188—22no—
360D188—22no—
361D188—22no—
362D188—42no—
363D188—42no—
364D188—84no—
365C4×D47—24no—
366C4×D47—22no—
367C4×D47—22no—
368C4×D47—84no—
369C8×C47—22no—
370C8×C47—22no—
371C47⋊C8—22no—
372C47⋊C8—22no—
373C2×#3322—471nomaximal, Sylow
374C22×C47—24no—
375C22×C47—22no—
376C22×C47—22no—
377C22×C47—22no—
378C22×C47—48no—
379C22×C47—44no—
380C22×C47—42no—
381C22×C47—42no—
382C22×C47#54612yes—
383C22×C47#57512yes—
384C22×C47#57612yes—
385C22×C47C23×D411yescharacteristic
386C2×D47—22no—
387C2×D47—22no—
388C2×D47—22no—
389C2×D47—44no—
390C2×D47—42no—
391C2×D47—42no—
392C2×D47—42no—
393C2×D47—42no—
394C2×D47—42no—
395C2×D47—42no—
396C2×D47—816no—
397C2×D47—84no—
398C2×D47—84no—
399C4×C47—22no—
400C4×C47—42no—
401C4×C47—42no—
402C4×C47—42no—
403C4×C47#54612yes—
404C4×C47C22×#4111yescharacteristic
405C4×C47C2×H(5,𝔽2)11yescharacteristic
406Dic47—22no—
407Dic47—22no—
408Dic47—22no—
409Dic47—42no—
410Dic47—42no—
411C2×#553—471no—
412C2×#546—471no—
413#3322—4716no—
414C2×#488—471no—
415C2×#485—471no—
416C2×#480—471no—
417C2×#478—471no—
418C2×#469—471no—
419C2×#468—471no—
420C2×#463—471no—
421C2×#449—471no—
422C2×#447—471no—
423C2×C4×D8—471no—
424C2×#436—471no—
425C2×#417D4711yescharacteristic, complemented
426C2×#418—471no—
427C2×C47—44no—
428C2×C47—42no—
429C2×C47#332214yescomplemented
430C2×C47C2×#54611yescharacteristic
431C2×C47C2×#57511yescharacteristic
432C2×C47C2×#57611yescharacteristic
433D47—42no—
434D47—82no—
435D47—82no—
436C22×#41C2×D4711yescharacteristic
437C23×D4—471no—
438C22×SD16—471no—
439C22×D8—471no—
440C22×D8—471no—
441C22×M16—471no—
442C22×M16C2×D4711yescharacteristic, complemented
443#553—478no—
444#553—944no—
445#546—478no—
446#546—944no—
447C2×#126—941no—
448C2×#125—471no—
449C2×#124—471no—
450C2×#123—941no—
451C2×#123—941no—
452C2×C22⋊Q8—471no—
453C2×#121—471no—
454C2×#121—471no—
455C2×#121—471no—
456C2×#121—941no—
457C2×#121—941no—
458C2×#120—941no—
459C2×C4×D4—471no—
460C2×C4×D4—471no—
461C2×C4×D4—471no—
462C2×C4×D4—941no—
463C2×#117—471no—
464C22×C4⋊C4C2×D4711yescharacteristic, complemented
465C22×C22⋊C4—941no—
466#488—478no—
467#485—478no—
468#480—478no—
469#478—478no—
470#469—478no—
471#468—478no—
472#463—478no—
473#449—478no—
474#447—478no—
475C4×D8—478no—
476#436—478no—
477C2×#107—471no—
478C2×#107—471no—
479C2×#106—471no—
480C2×C4⋊C8—471no—
481#418—478no—
482#417C2×D4718yescomplemented
483C2×#103—471no—
484C2×#103C2×D4711yescharacteristic, complemented
485C2×#103C2×D4711yescharacteristic, complemented
486C2×#102—471no—
487C2×#102—471no—
488C2×#102—471no—
489C2×#102—471no—
490C2×#102—471no—
491C2×#102C2×D4711yescharacteristic
492C2×#102C2×D4711yescharacteristic
493C2×C22⋊C8—471no—
494C2×C22⋊C8—471no—
495C2×C4×C8—471no—
496C47C2×#332211yescharacteristic, complemented, Sylow
497C25—941no—
498C2×#41—22no—
499C2×#41—24no—
500C2×#41—42no—
501C2×#41C22×D4714yes—
502C22×Q8C22×D4711yescharacteristic
503C22×D4—21no—
504C22×D4—471no—
505C22×D4—474no—
506C22×D4—471no—
507C22×D4—471no—
508C22×D4—941no—
509C22×D4—942no—
510C22×D4—941no—
511C22×D4—944no—
512C22×D4—941no—
513C22×D4—941no—
514C22×D4—1882no—
515C22×D4C22×D4711yescharacteristic
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—471no—
519C23×C4—941no—
520C23×C4—941no—
521C23×C4C22×D4711yescharacteristic
522C2×SD16—474no—
523C2×SD16—1882no—
524C2×D8—474no—
525C2×D8—474no—
526C2×D8—944no—
527C2×D8—1882no—
528C2×M16—42no—
529C2×M16—474no—
530C2×M16—1882no—
531C2×M16C22×D4714yescomplemented
532C22×C8—471no—
533C22×C8—471no—
534C22×C8C22×D4711yescharacteristic
535C22×C8C22×D4711yescharacteristic
536#126—948no—
537#125—474no—
538#125—942no—
539#124—474no—
540#124—942no—
541#123—948no—
542#123—948no—
543C22⋊Q8—474no—
544C22⋊Q8—942no—
545#121—474no—
546#121—474no—
547#121—474no—
548#121—948no—
549#121—942no—
550#121—948no—
551#121—942no—
552#121—942no—
553#120—948no—
554C4×D4—474no—
555C4×D4—474no—
556C4×D4—474no—
557C4×D4—474no—
558C4×D4—942no—
559C4×D4—942no—
560C4×D4—948no—
561#117—474no—
562#117—942no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—22no—
565C2×C4⋊C4—471no—
566C2×C4⋊C4—471no—
567C2×C4⋊C4—471no—
568C2×C4⋊C4—941no—
569C2×C4⋊C4—941no—
570C2×C4⋊C4—941no—
571C2×C4⋊C4C22×D4711yescharacteristic
572C2×C4⋊C4C22×D4711yescharacteristic
573C2×C4⋊C4C22×D4714yescomplemented
574C2×C22⋊C4—471no—
575C2×C22⋊C4—471no—
576C2×C22⋊C4—948no—
577C2×C22⋊C4—941no—
578C2×C22⋊C4—941no—
579C2×C22⋊C4—941no—
580C2×C22⋊C4—941no—
581C2×C22⋊C4—941no—
582C2×C22⋊C4—941no—
583C2×C22⋊C4—941no—
584C2×C22⋊C4—941no—
585C2×C22⋊C4—941no—
586C2×C42—471no—
587C2×C42—941no—
588#107—474no—
589#107—474no—
590#106—474no—
591C4⋊C8—474no—
592#103—474no—
593#103C22×D4714yescomplemented
594#103C22×D4714yescomplemented
595#102—474no—
596#102—474no—
597#102—474no—
598#102—474no—
599#102—474no—
600#102C22×D4714yes—
601#102C22×D4714yes—
602C22⋊C8—474no—
603C22⋊C8—474no—
604C4×C8—474no—
605C24—21no—
606C24—471no—
607C24—944no—
608C24—941no—
609C24—941no—
610C24—3762no—
611C24—1884no—
612C24—1884no—
613C24D4×D4711yescharacteristic
614#41—28no—
615#41—44no—
616#41—48no—
617C2×Q8—21no—
618C2×Q8—22no—
619C2×Q8—22no—
620C2×Q8C23×D4712yes—
621C2×D4—24no—
622C2×D4—21no—
623C2×D4—22no—
624C2×D4—44no—
625C2×D4—474no—
626C2×D4—472no—
627C2×D4—472no—
628C2×D4—944no—
629C2×D4—944no—
630C2×D4—948no—
631C2×D4—944no—
632C2×D4—944no—
633C2×D4—941no—
634C2×D4—941no—
635C2×D4—942no—
636C2×D4—942no—
637C2×D4—942no—
638C2×D4—942no—
639C2×D4—3762no—
640C2×D4—3762no—
641C2×D4—1884no—
642C2×D4—1888no—
643C2×D4—1882no—
644C2×D4—1884no—
645C2×D4—1884no—
646C2×D4#1062535014yes—
647C2×D4C23×D4712yes—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—24no—
654C22×C4—24no—
655C22×C4—44no—
656C22×C4—82no—
657C22×C4—471no—
658C22×C4—471no—
659C22×C4—471no—
660C22×C4—472no—
661C22×C4—472no—
662C22×C4—944no—
663C22×C4—944no—
664C22×C4—942no—
665C22×C4—942no—
666C22×C4—941no—
667C22×C4—941no—
668C22×C4—3762no—
669C22×C4—3762no—
670C22×C4D4×D4712yes—
671C22×C4D4×D4711yescharacteristic
672C22×C4C23×D4712yes—
673C22×C4C23×D4711yescharacteristic
674SD16—1884no—
675D8—948no—
676D8—1884no—
677M16—44no—
678M16—1884no—
679C2×C8—22no—
680C2×C8—22no—
681C2×C8—472no—
682C2×C8—472no—
683C2×C8—942no—
684C2×C8—942no—
685C2×C8C23×D4712yes—
686C2×C8C23×D4712yes—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—24no—
690C4⋊C4—474no—
691C4⋊C4—472no—
692C4⋊C4—472no—
693C4⋊C4—944no—
694C4⋊C4—944no—
695C4⋊C4—944no—
696C4⋊C4—941no—
697C4⋊C4—941no—
698C4⋊C4C23×D4712yes—
699C4⋊C4C23×D4712yes—
700C22⋊C4—474no—
701C22⋊C4—474no—
702C22⋊C4—944no—
703C22⋊C4—944no—
704C22⋊C4—944no—
705C22⋊C4—944no—
706C22⋊C4—944no—
707C22⋊C4—944no—
708C22⋊C4—944no—
709C22⋊C4—944no—
710C22⋊C4—944no—
711C42—472no—
712C42—472no—
713C42—944no—
714C23—22no—
715C23—24no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—42no—
720C23—42no—
721C23—472no—
722C23—942no—
723C23—942no—
724C23—942no—
725C23—942no—
726C23—942no—
727C23—3764no—
728C23—37616no—
729C23—1888no—
730C23—1888no—
731C23—1882no—
732C23—1882no—
733C23—1882no—
734C23—1882no—
735C23—1882no—
736C23—1882no—
737C23C2×D4×D4712yes—
738C23C2×D4×D4711yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—42no—
742D4—24no—
743D4—22no—
744D4—48no—
745D4—942no—
746D4—942no—
747D4—942no—
748D4—942no—
749D4—3764no—
750D4—3764no—
751D4—1884no—
752D4—1888no—
753D4—1888no—
754D4—1882no—
755D4—1882no—
756D4C2×#1062535014yes—
757C2×C4—22no—
758C2×C4—24no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—48no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—84no—
769C2×C4—472no—
770C2×C4—472no—
771C2×C4—472no—
772C2×C4—942no—
773C2×C4—942no—
774C2×C4—942no—
775C2×C4—944no—
776C2×C4—942no—
777C2×C4—942no—
778C2×C4—942no—
779C2×C4—942no—
780C2×C4—3764no—
781C2×C4—3764no—
782C2×C4—1882no—
783C2×C4—1882no—
784C2×C4C2×D4×D4712yes—
785C2×C4C2×D4×D4711yescharacteristic
786C2×C4C2×#1062535012yes—
787C2×C4#1309406912yes—
788C2×C4C24×D4711yescharacteristic
789C8—22no—
790C8—22no—
791C8—942no—
792C8—942no—
793C22—22no—
794C22—24no—
795C22—22no—
796C22—22no—
797C22—42no—
798C22—42no—
799C22—44no—
800C22—48no—
801C22—942no—
802C22—942no—
803C22—942no—
804C22—37616no—
805C22—3764no—
806C22—3764no—
807C22—1882no—
808C22—1882no—
809C22—1882no—
810C22—1882no—
811C22—1882no—
812C22—1882no—
813C22—1884no—
814C22#1568976312yes—
815C22#1568992212yes—
816C22#1568992712yes—
817C22C22×D4×D4711yescharacteristic
818C4—22no—
819C4—42no—
820C4—42no—
821C4—42no—
822C4—942no—
823C4—942no—
824C4—942no—
825C4—1882no—
826C4—1882no—
827C4#1568976312yes—
828C4C22×#1062535011yescharacteristic
829C4C2×#1309406911yescharacteristic
830C2—42no—
831C2—44no—
832C2—3762no—
833C2—3762no—
834C2—1882no—
835C2#2025559014yesdirect product factor
836C2C2×#1568976311yescharacteristic
837C2C2×#1568992211yescharacteristic
838C2C2×#1568992711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#417C2
socleC23×C47C22×D4
hypercenterC2×#417D47
hypocenterC47C2×#3322
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. C2×#15689821C2semidirect
2. C2×#15689761C2semidirect
3. #20255590C2direct (N × H)
4. C2×#15689479C2semidirect
5. C2×#15689462C2semidirect
6. C2×#15689436C2semidirect
7. C2×#15689425C2semidirect
8. C2×#15689376C2semidirect
9. C2×#15689372C2semidirect
10. C2×#15689341C2semidirect
11. C2×#15689268C2semidirect
12. C2×#15689258C2semidirect
13. C2×#15689203C2semidirect
14. C2×#15689199C2semidirect
15. C2×#15689126C2semidirect
16. C2×C47×#417C2semidirect
18. C22×#10625336C22semidirect
23. #15689821C22semidirect
25. #15689761C22semidirect
27. C2×#13094015C22semidirect
35. C2×#13093998C22semidirect
39. C2×#13093986C22semidirect
44. #15689479C22semidirect
45. #15689462C22semidirect
46. #15689436C22semidirect
47. #15689425C22semidirect
48. #15689376C22semidirect
49. #15689372C22semidirect
50. #15689341C22semidirect
51. #15689268C22semidirect
52. #15689258C22semidirect
53. #15689203C22semidirect
54. #15689199C22semidirect
55. C2×#13093957C22semidirect
56. C2×#13093957C22semidirect
57. C2×#13093956C22semidirect
58. C2×Dic47⋊C8C22semidirect
59. #15689126C22semidirect
60. C2×#13093948C22semidirect
62. C2×#13093946C22semidirect
66. C2×C22⋊(C47⋊C8)C22semidirect
68. C2×C8×Dic47C22semidirect
70. C22×M16×C47C22semidirect
71. C22×C4⋊C4×C47C22semidirect
72. C47×#417C22semidirect
73. C2×#103×C47C22semidirect
74. C2×#103×C47C22semidirect
93. C2×#10625336C23semidirect
104. #13094015C23semidirect
117. #13093998C23semidirect
123. #13093986C23semidirect
149. #13093957C23semidirect
150. #13093957C23semidirect
151. #13093956C23semidirect
152. Dic47⋊C8C23semidirect
153. #13093948C23semidirect
155. #13093946C23semidirect
159. C22⋊(C47⋊C8)C23semidirect
161. C8×Dic47C23semidirect
173. C2×M16×C47C23semidirect
180. C2×C4⋊C4×C47C23semidirect
181. #103×C47C23semidirect
182. #103×C47C23semidirect
425. C2×#417D47semidirect
429. C2×C47#3322semidirect
442. C22×M16C2×D47semidirect
464. C22×C4⋊C4C2×D47semidirect
482. #417C2×D47semidirect
484. C2×#103C2×D47semidirect
485. C2×#103C2×D47semidirect
496. C47C2×#3322semidirect
531. C2×M16C22×D47semidirect
573. C2×C4⋊C4C22×D47semidirect
593. #103C22×D47semidirect
594. #103C22×D47semidirect
835. C2#20255590direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898212
C2×#156897612
#202555902
C2×#156894792
C2×#156894622
C2×#156894362
C2×#156894252
C2×#156893762
C2×#156893722
C2×#156893412
C2×#156892682
C2×#156892582
C2×#156892032
C2×#156891992
C2×#156891262
C2×C47×#4172
C2×#332247