Finite Group Databasebeta

← C2×#20255546 #27092966

Subgroups — C2×#20255546 #27092966

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×#15689838C211yesmaximal, characteristic, complemented
2C2×#15689769C211yesmaximal, characteristic, complemented
3#20255546C2116yesmaximal, direct product factor
4C2×#15689483C211yesmaximal, characteristic, complemented
5C2×#15689465C211yesmaximal, characteristic, complemented
6C2×#15689448C211yesmaximal, characteristic, complemented
7C2×#15689404C211yesmaximal, characteristic, complemented
8C2×#15689369C211yesmaximal, characteristic, complemented
9C2×#15689359C211yesmaximal, characteristic, complemented
10C2×#15689339C211yesmaximal, characteristic, complemented
11C2×#15689270C211yesmaximal, characteristic, complemented
12C2×#15689259C211yesmaximal, characteristic, complemented
13C2×#15689236C211yesmaximal, characteristic, complemented
14C2×#15689129C211yesmaximal, characteristic, complemented
15C2×#15689120C211yesmaximal, characteristic, complemented
16C2×C47×#435C211yesmaximal, characteristic, complemented
17C22×#10625350C2211yescharacteristic
18C23×D188C2211yescharacteristic
19C22×#10625325C2211yescharacteristic, complemented
20C22×D376C2211yescharacteristic
21C22×D376C2211yescharacteristic
22#15689838—24no—
23#15689838C2218yescomplemented
24#15689769—24no—
25#15689769C2218yescomplemented
26C2×#13094024C2211yescharacteristic, complemented
27C2×#13094012C2211yescharacteristic
28C2×#13094010—21no—
29C2×#13094010—21no—
30C2×#13094009—21no—
31C2×#13094003C2211yescharacteristic
32C2×#13093998C2211yescharacteristic
33C2×#13093998C2211yescharacteristic
34C2×#13093998C2211yescharacteristic, complemented
35C2×#13093997—21no—
36C2×#13093995—21no—
37C2×#13093992—21no—
38C2×C4×D188C2211yescharacteristic
39C2×C4×D188C2211yescharacteristic, complemented
40C2×#13093983C2211yescharacteristic
41C2×#13093983C2211yescharacteristic, complemented
42C2×#13093982—21no—
43C2×C22⋊C4×D47—21no—
44#15689483C2218yescomplemented
45#15689465C2218yescomplemented
46#15689448C2218yescomplemented
47#15689404C2218yescomplemented
48#15689369C2218yescomplemented
49#15689359C2218yescomplemented
50#15689339C2218yescomplemented
51#15689270C2218yescomplemented
52#15689259C2218yescomplemented
53#15689236C2218yescomplemented
54C2×#13093958C2211yescharacteristic, complemented
55C2×#13093958C2211yescharacteristic, complemented
56C2×#13093956C2211yescharacteristic, complemented
57#15689129C2218yescomplemented
58#15689120C2218yescomplemented
59C2×#13093949C2211yescharacteristic, complemented
60C2×#13093949C2211yescharacteristic, complemented
61C2×#13093949C2211yescharacteristic, complemented
62C2×#13093946C2211yescharacteristic
63C2×#13093946C2211yescharacteristic
64C2×#13093946C2211yescharacteristic
65C2×#13093946C2211yescharacteristic
66C2×#13093946C2211yescharacteristic
67C2×#13093946C2211yescharacteristic
68C2×#13093946C2211yescharacteristic, complemented
69C22×M16×C47C2211yescharacteristic
70C23×C8×C47C2211yescharacteristic, complemented
71C2×C4×D4×C47C2211yescharacteristic
72C47×#435C2218yescomplemented
73C2×C4⋊C8×C47C2211yescharacteristic, complemented
74C2×C22⋊C8×C47C2211yescharacteristic
75C2×C22⋊C8×C47C2211yescharacteristic, complemented
76C2×#97×C47C2211yescharacteristic, complemented
77C24×D47—21no—
78C2×#10625350—22no—
79C2×#10625350—24no—
80C2×#10625350—42no—
81C2×#10625350C2314yes—
82C22×Dic94—21no—
83C22×Dic94C2311yescharacteristic
84C22×D188—24no—
85C22×D188—22no—
86C22×D188—21no—
87C22×D188—42no—
88C22×D188C2311yescharacteristic
89C22×D188C2311yescharacteristic
90C22×D188C2314yes—
91C22×D188C2311yescharacteristic
92C22×C22⋊D47—21no—
93C22×C22⋊D47—21no—
94C22×C22⋊D47—21no—
95C22×C22⋊D47—21no—
96C22×C4×D47—21no—
97C22×C4×D47—21no—
98C22×C4×D47—21no—
99C2×#10625325—42no—
100C2×#10625325C2314yescomplemented
101C2×D376—24no—
102C2×D376—42no—
103C2×D376C2314yes—
104C2×D376C2314yes—
105#13094024—22no—
106#13094024C2314yescomplemented
107#13094012—22no—
108#13094012C2314yes—
109#13094010—28no—
110#13094010—28no—
111#13094009—28no—
112#13094003—22no—
113#13094003C2314yes—
114#13093998—22no—
115#13093998—22no—
116#13093998—22no—
117#13093998C2314yes—
118#13093998C2314yes—
119#13093998C2314yescomplemented
120#13093997—28no—
121#13093995—28no—
122#13093992—28no—
123C4×D188—22no—
124C4×D188—22no—
125C4×D188C2314yes—
126C4×D188C2314yescomplemented
127#13093983—22no—
128#13093983—22no—
129#13093983C2314yes—
130#13093983C2314yescomplemented
131#13093982—28no—
132C2×C4⋊Dic47—21no—
133C2×C4⋊Dic47C2311yescharacteristic
134C2×C4⋊Dic47C2311yescharacteristic
135C2×C4⋊Dic47C2311yescharacteristic
136C2×C4⋊Dic47C2311yescharacteristic
137C2×Dic47⋊C4—21no—
138C2×C22⋊Dic47—21no—
139C2×C22⋊Dic47—21no—
140C2×C22⋊Dic47—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—21no—
146C2×(C2×D47)⋊C4—21no—
147C2×(C2×D47)⋊C4—21no—
148C22⋊C4×D47—28no—
149C2×C4×Dic47—21no—
150C2×C4×Dic47—21no—
151#13093958C2314yescomplemented
152#13093958C2314yescomplemented
153#13093956C2314yescomplemented
154#13093949C2314yescomplemented
155#13093949C2314yescomplemented
156#13093949C2314yescomplemented
157#13093946C2314yes—
158#13093946C2314yes—
159#13093946C2314yes—
160#13093946C2314yes—
161#13093946C2314yes—
162#13093946C2314yes—
163#13093946C2314yescomplemented
164C22×D4×C47D411yescharacteristic
165C23×C4×C47C2311yescharacteristic
166C23×C4×C47C2311yescharacteristic
167C2×M16×C47—42no—
168C2×M16×C47C2314yes—
169C22×C8×C47—42no—
170C22×C8×C47C2311yescharacteristic
171C22×C8×C47C2311yescharacteristic
172C22×C8×C47C2311yescharacteristic
173C22×C8×C47C2311yescharacteristic
174C22×C8×C47C2314yescomplemented
175C4×D4×C47D414yes—
176C4×D4×C47C2314yes—
177C2×C4⋊C4×C47D411yescharacteristic
178C2×C22⋊C4×C47D411yescharacteristic
179C2×C22⋊C4×C47D411yescharacteristic
180C2×C42×C47C2311yescharacteristic
181C4⋊C8×C47C2314yescomplemented
182C22⋊C8×C47C2314yes—
183C22⋊C8×C47C2314yescomplemented
184#97×C47C2314yescomplemented
185C24×C47C2×D411yescharacteristic
186C24×C47C2×D411yescharacteristic
187C23×D47—21no—
188C23×D47—21no—
189C23×D47—21no—
190C23×D47—24no—
191C23×D47—44no—
192C23×D47—44no—
193C23×D47—82no—
194C2×D4×C47—42no—
195C2×D4×C47C2×D414yes—
196C22×C4×C47—22no—
197C22×C4×C47—22no—
198C22×C4×C47—22no—
199C22×C4×C47—22no—
200C22×C4×C47C2×D411yescharacteristic
201C22×C4×C47C2×D411yescharacteristic
202C22×C4×C47C2×D411yescharacteristic
203C22×C4×C47C2×D411yescharacteristic
204C22×C4×C47C2×D412yes—
205C22×C4×C47C2×D412yes—
206C22×C4×C47C2412yes—
207C22×C4×C47C2412yes—
208C22×C4×C47C2411yescharacteristic
209C2×C22⋊D47—24no—
210C2×C22⋊D47—24no—
211C2×C22⋊D47—24no—
212C2×C22⋊D47—24no—
213C2×C22⋊D47—44no—
214C2×C22⋊D47—82no—
215C2×C22⋊D47—82no—
216C2×C22⋊D47—82no—
217C22×Dic47—21no—
218C22×Dic47—21no—
219C22×Dic47—21no—
220C22×Dic47—21no—
221C22×Dic47—21no—
222#10625350—28no—
223#10625350—44no—
224#10625350—48no—
225C2×D188—21no—
226C2×D188—22no—
227C2×D188—22no—
228C2×D188—22no—
229C2×D188—22no—
230C2×D188—22no—
231C2×D188—28no—
232C2×D188—21no—
233C2×D188—24no—
234C2×D188—21no—
235C2×D188—44no—
236C2×D188—48no—
237C2×D188—44no—
238C2×D188#4114yes—
239C2×D188C2412yes—
240C2×D188C2412yes—
241C2×D188C2412yes—
242C2×C4×D47—24no—
243C2×C4×D47—24no—
244C2×C4×D47—24no—
245C2×C4×D47—44no—
246C2×C4×D47—44no—
247C2×C4×D47—82no—
248C2×Dic94—22no—
249C2×Dic94—22no—
250C2×Dic94—21no—
251C2×Dic94—24no—
252C2×Dic94—82no—
253C2×Dic94C2412yes—
254M16×C47—44no—
255C2×C8×C47—22no—
256C2×C8×C47—22no—
257C2×C8×C47—22no—
258C2×C8×C47—22no—
259C2×C8×C47—44no—
260C2×C8×C47C2412yes—
261C2×C8×C47C2412yes—
262C2×C8×C47C2412yes—
263C2×C8×C47C2412yes—
264C4⋊C4×C47C2×D414yes—
265C22⋊C4×C47C2×D414yes—
266C22⋊C4×C47C2×D414yes—
267C42×C47C2×D412yes—
268C42×C47C2412yes—
269C22⋊Dic47—24no—
270C22⋊Dic47—24no—
271C22⋊Dic47—24no—
272(C2×D47)⋊C4—24no—
273(C2×D47)⋊C4—24no—
274(C2×D47)⋊C4—24no—
275(C2×D47)⋊C4—24no—
276(C2×D47)⋊C4—24no—
277(C2×D47)⋊C4—24no—
278(C2×D47)⋊C4—24no—
279C4⋊Dic47—24no—
280C4⋊Dic47—21no—
281C4⋊Dic47—21no—
282C4⋊Dic47—21no—
283C4⋊Dic47—21no—
284C4⋊Dic47C2412yes—
285C4⋊Dic47C2412yes—
286C4⋊Dic47C2412yes—
287C4⋊Dic47C2412yes—
288Dic47⋊C4—24no—
289C4×Dic47—24no—
290C4×Dic47—24no—
291D376—28no—
292D376—44no—
293#10625325—44no—
294C23×C47—22no—
295C23×C47—22no—
296C23×C47—22no—
297C23×C47—22no—
298C23×C47—22no—
299C23×C47—22no—
300C23×C47C22×D412yes—
301C23×C47C22×D412yes—
302C23×C47C22×D411yescharacteristic
303C22×D47—24no—
304C22×D47—22no—
305C22×D47—22no—
306C22×D47—22no—
307C22×D47—48no—
308C22×D47—42no—
309C22×D47—42no—
310C22×D47—48no—
311C22×D47—42no—
312C22×D47—42no—
313C22×D47—42no—
314C22×D47—42no—
315C22×D47—42no—
316C22×D47—42no—
317C22×D47—84no—
318C22×D47—816no—
319D4×C47—44no—
320C2×C4×C47—22no—
321C2×C4×C47—22no—
322C2×C4×C47—22no—
323C2×C4×C47—22no—
324C2×C4×C47—24no—
325C2×C4×C47—24no—
326C2×C4×C47—22no—
327C2×C4×C47—22no—
328C2×C4×C47—22no—
329C2×C4×C47—22no—
330C2×C4×C47C22×D412yes—
331C2×C4×C47C22×D412yes—
332C2×C4×C47C22×D412yes—
333C2×C4×C47C22×D412yes—
334C2×C4×C47C22×D411yescharacteristic
335C2×C4×C47C2×#4112yes—
336C2×C4×C47H(5,𝔽2)12yes—
337C2×C4×C47C2511yescharacteristic
338C22⋊D47—48no—
339C22⋊D47—84no—
340C22⋊D47—84no—
341C22⋊D47—84no—
342C2×Dic47—22no—
343C2×Dic47—22no—
344C2×Dic47—22no—
345C2×Dic47—22no—
346C2×Dic47—22no—
347C2×Dic47—42no—
348C2×Dic47—42no—
349C2×Dic47—42no—
350C2×Dic47—42no—
351C2×Dic47—42no—
352D188—24no—
353D188—22no—
354D188—22no—
355D188—22no—
356D188—22no—
357D188—22no—
358D188—48no—
359D188—42no—
360D188—42no—
361D188C2×#4114yes—
362C4×D47—48no—
363C4×D47—48no—
364C4×D47—84no—
365Dic94—22no—
366Dic94—22no—
367Dic94—42no—
368Dic94—84no—
369C8×C47—22no—
370C8×C47—22no—
371C8×C47—22no—
372C8×C47—22no—
373C2×#3319—471nomaximal, Sylow
374C22×C47—22no—
375C22×C47—22no—
376C22×C47—22no—
377C22×C47—22no—
378C22×C47—22no—
379C22×C47—22no—
380C22×C47—44no—
381C22×C47—44no—
382C22×C47#54612yes—
383C22×C47#57512yes—
384C22×C47#57612yes—
385C22×C47C23×D411yescharacteristic
386C2×D47—24no—
387C2×D47—48no—
388C2×D47—42no—
389C2×D47—42no—
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—22no—
401C4×C47—22no—
402C4×C47—22no—
403C4×C47#54612yes—
404C4×C47C22×#4111yescharacteristic
405C4×C47C2×H(5,𝔽2)11yescharacteristic
406Dic47—42no—
407Dic47—42no—
408Dic47—42no—
409Dic47—42no—
410Dic47—42no—
411C2×#555—471no—
412C2×#546—471no—
413#3319—4716no—
414C2×#489—471no—
415C2×#485—471no—
416C2×#482—471no—
417C2×#474—471no—
418C2×#468—471no—
419C2×#466—471no—
420C2×#463—471no—
421C2×#449—471no—
422C2×#447—471no—
423C2×#442—471no—
424C2×#435D4711yescharacteristic, complemented
425C2×#418—471no—
426C2×#416—471no—
427C2×C47—42no—
428C2×C47—42no—
429C2×C47#331914yescomplemented
430C2×C47C2×#54611yescharacteristic
431C2×C47C2×#57511yescharacteristic
432C2×C47C2×#57611yescharacteristic
433D47—44no—
434D47—82no—
435D47—82no—
436C22×#41—471no—
437C23×D4—471no—
438C22×SD16—471no—
439C22×D8—471no—
440C22×D8—471no—
441C22×M16C2×D4711yescharacteristic
442C23×C8C2×D4711yescharacteristic, complemented
443#555—478no—
444#555—944no—
445#546—478no—
446#546—944no—
447C2×C4⋊Q8—471no—
448C2×#124—471no—
449C2×#124—941no—
450C2×#124—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×D4C2×D4711yescharacteristic
462C2×#117—471no—
463C2×#117—471no—
464C2×#117—941no—
465C22×C22⋊C4—941no—
466#489—478no—
467#485—478no—
468#482—478no—
469#474—478no—
470#468—478no—
471#466—478no—
472#463—478no—
473#449—478no—
474#447—478no—
475#442—478no—
476#435C2×D4718yescomplemented
477C2×#107—471no—
478C2×#107—471no—
479C2×#106—471no—
480C2×C4⋊C8C2×D4711yescharacteristic, complemented
481#418—478no—
482#416—478no—
483C2×#103—471no—
484C2×#103—471no—
485C2×#103—471no—
486C2×#102—471no—
487C2×#102—471no—
488C2×#102—471no—
489C2×#102—471no—
490C2×#102—471no—
491C2×#102—471no—
492C2×#102—471no—
493C2×C22⋊C8C2×D4711yescharacteristic
494C2×C22⋊C8C2×D4711yescharacteristic, complemented
495C2×#97C2×D4711yescharacteristic, complemented
496C47C2×#331911yescharacteristic, complemented, Sylow
497C25—941no—
498C2×#41—474no—
499C2×#41—944no—
500C2×#41—942no—
501C2×#41—1882no—
502C22×Q8—471no—
503C22×Q8—941no—
504C22×D4—471no—
505C22×D4—471no—
506C22×D4—471no—
507C22×D4—474no—
508C22×D4—944no—
509C22×D4—941no—
510C22×D4—941no—
511C22×D4—941no—
512C22×D4—941no—
513C22×D4—941no—
514C22×D4—942no—
515C22×D4—1882no—
516C22×D4D18811yescharacteristic
517C23×C4—941no—
518C23×C4—941no—
519C23×C4—941no—
520C23×C4C22×D4711yescharacteristic
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×M16C22×D4714yes—
530C22×C8—42no—
531C22×C8C22×D4711yescharacteristic
532C22×C8C22×D4711yescharacteristic
533C22×C8C22×D4711yescharacteristic
534C22×C8C22×D4711yescharacteristic
535C22×C8C22×D4714yescomplemented
536C4⋊Q8—474no—
537C4⋊Q8—942no—
538#124—474no—
539#124—948no—
540#124—948no—
541#124—942no—
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—942no—
551#121—942no—
552#121—948no—
553#120—948no—
554C4×D4—474no—
555C4×D4—474no—
556C4×D4—942no—
557C4×D4—942no—
558C4×D4D18814yes—
559C4×D4C22×D4714yes—
560#117—474no—
561#117—474no—
562#117—942no—
563#117—942no—
564#117—948no—
565C2×C4⋊C4—471no—
566C2×C4⋊C4—471no—
567C2×C4⋊C4—471no—
568C2×C4⋊C4—471no—
569C2×C4⋊C4—941no—
570C2×C4⋊C4—941no—
571C2×C4⋊C4D18811yescharacteristic
572C2×C22⋊C4—941no—
573C2×C22⋊C4—941no—
574C2×C22⋊C4—941no—
575C2×C22⋊C4—941no—
576C2×C22⋊C4—941no—
577C2×C22⋊C4—941no—
578C2×C22⋊C4—941no—
579C2×C22⋊C4—941no—
580C2×C22⋊C4—941no—
581C2×C22⋊C4—941no—
582C2×C22⋊C4—948no—
583C2×C22⋊C4D18811yescharacteristic
584C2×C22⋊C4D18811yescharacteristic
585C2×C42—941no—
586C2×C42—941no—
587C2×C42C22×D4711yescharacteristic
588#107—474no—
589#107—474no—
590#106—474no—
591C4⋊C8C22×D4714yescomplemented
592#103—474no—
593#103—474no—
594#103—474no—
595#102—474no—
596#102—474no—
597#102—474no—
598#102—474no—
599#102—474no—
600#102—474no—
601#102—474no—
602C22⋊C8C22×D4714yes—
603C22⋊C8C22×D4714yescomplemented
604#97C22×D4714yescomplemented
605C24—941no—
606C24—944no—
607C24—941no—
608C24—941no—
609C24—3762no—
610C24—1884no—
611C24—1884no—
612C24C2×D18811yescharacteristic
613C24C2×D18811yescharacteristic
614#41—948no—
615#41—1884no—
616#41—1888no—
617C2×Q8—472no—
618C2×Q8—944no—
619C2×Q8—941no—
620C2×Q8—942no—
621C2×Q8—942no—
622C2×Q8—3762no—
623C2×D4—42no—
624C2×D4—474no—
625C2×D4—472no—
626C2×D4—472no—
627C2×D4—472no—
628C2×D4—948no—
629C2×D4—944no—
630C2×D4—944no—
631C2×D4—944no—
632C2×D4—944no—
633C2×D4—941no—
634C2×D4—941no—
635C2×D4—944no—
636C2×D4—941no—
637C2×D4—942no—
638C2×D4—942no—
639C2×D4—942no—
640C2×D4—942no—
641C2×D4—942no—
642C2×D4—3762no—
643C2×D4—3762no—
644C2×D4—3762no—
645C2×D4—1884no—
646C2×D4—1888no—
647C2×D4—1884no—
648C2×D4—1884no—
649C2×D4C2×D18814yes—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—941no—
655C22×C4—941no—
656C22×C4—941no—
657C22×C4—941no—
658C22×C4—941no—
659C22×C4—944no—
660C22×C4—944no—
661C22×C4—944no—
662C22×C4—3762no—
663C22×C4—1884no—
664C22×C4—1884no—
665C22×C4C2×D18812yes—
666C22×C4C2×D18812yes—
667C22×C4C2×D18811yescharacteristic
668C22×C4C2×D18811yescharacteristic
669C22×C4C2×D18811yescharacteristic
670C22×C4C2×D18811yescharacteristic
671C22×C4C23×D4712yes—
672C22×C4C23×D4712yes—
673C22×C4C23×D4711yescharacteristic
674SD16—1884no—
675D8—948no—
676D8—1884no—
677M16—44no—
678C2×C8—22no—
679C2×C8—22no—
680C2×C8—22no—
681C2×C8—22no—
682C2×C8—44no—
683C2×C8C23×D4712yes—
684C2×C8C23×D4712yes—
685C2×C8C23×D4712yes—
686C2×C8C23×D4712yes—
687C4⋊C4—472no—
688C4⋊C4—472no—
689C4⋊C4—472no—
690C4⋊C4—472no—
691C4⋊C4—944no—
692C4⋊C4—941no—
693C4⋊C4—941no—
694C4⋊C4—941no—
695C4⋊C4—941no—
696C4⋊C4—944no—
697C4⋊C4C2×D18814yes—
698C22⋊C4—944no—
699C22⋊C4—944no—
700C22⋊C4—944no—
701C22⋊C4—944no—
702C22⋊C4—944no—
703C22⋊C4—944no—
704C22⋊C4—944no—
705C22⋊C4—944no—
706C22⋊C4—944no—
707C22⋊C4—944no—
708C22⋊C4C2×D18814yes—
709C22⋊C4C2×D18814yes—
710C42—944no—
711C42—944no—
712C42C2×D18812yes—
713C42C23×D4712yes—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—944no—
721C23—942no—
722C23—942no—
723C23—942no—
724C23—3764no—
725C23—37616no—
726C23—1888no—
727C23—1888no—
728C23—1882no—
729C23—1882no—
730C23—1882no—
731C23—1882no—
732C23—1882no—
733C23—1882no—
734C23—1882no—
735C23—1882no—
736C23C22×D18812yes—
737C23C22×D18812yes—
738C23C22×D18811yescharacteristic
739Q8—942no—
740Q8—942no—
741Q8—3764no—
742Q8—1882no—
743D4—44no—
744D4—474no—
745D4—944no—
746D4—942no—
747D4—942no—
748D4—942no—
749D4—942no—
750D4—942no—
751D4—3764no—
752D4—3764no—
753D4—3764no—
754D4—1888no—
755D4—1888no—
756D4—1882no—
757D4—1882no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—942no—
769C2×C4—942no—
770C2×C4—942no—
771C2×C4—942no—
772C2×C4—942no—
773C2×C4—3764no—
774C2×C4—1888no—
775C2×C4—1888no—
776C2×C4—1882no—
777C2×C4—1882no—
778C2×C4—1882no—
779C2×C4—1882no—
780C2×C4—1882no—
781C2×C4C22×D18812yes—
782C2×C4C22×D18812yes—
783C2×C4C22×D18812yes—
784C2×C4C22×D18812yes—
785C2×C4C22×D18811yescharacteristic
786C2×C4#41×D4712yes—
787C2×C4#1309406912yes—
788C2×C4C24×D4711yescharacteristic
789C8—22no—
790C8—22no—
791C8—22no—
792C8—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—44no—
800C22—44no—
801C22—944no—
802C22—37616no—
803C22—3764no—
804C22—3764no—
805C22—1882no—
806C22—1882no—
807C22—1882no—
808C22—1882no—
809C22—1882no—
810C22—1882no—
811C22—1888no—
812C22—1882no—
813C22—1882no—
814C22#1568976812yes—
815C22#1568992312yes—
816C22#1568992812yes—
817C22C23×D18811yescharacteristic
818C4—22no—
819C4—22no—
820C4—22no—
821C4—22no—
822C4—1882no—
823C4—1882no—
824C4—1882no—
825C4—1882no—
826C4—1882no—
827C4#1568976812yes—
828C4C2×#41×D4711yescharacteristic
829C4C2×#1309406911yescharacteristic
830C2—42no—
831C2—42no—
832C2—3762no—
833C2—3762no—
834C2—1884no—
835C2#2025554614yesdirect product factor
836C2C2×#1568976811yescharacteristic
837C2C2×#1568992311yescharacteristic
838C2C2×#1568992811yescharacteristic
subgroupG/H
centerC23C22×D188
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#435C2
socleC23×C47C22×D4
hypercenterC2×#435D47
hypocenterC47C2×#3319
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#15689838C2semidirect
2. C2×#15689769C2semidirect
3. #20255546C2direct (N × H)
4. C2×#15689483C2semidirect
5. C2×#15689465C2semidirect
6. C2×#15689448C2semidirect
7. C2×#15689404C2semidirect
8. C2×#15689369C2semidirect
9. C2×#15689359C2semidirect
10. C2×#15689339C2semidirect
11. C2×#15689270C2semidirect
12. C2×#15689259C2semidirect
13. C2×#15689236C2semidirect
14. C2×#15689129C2semidirect
15. C2×#15689120C2semidirect
16. C2×C47×#435C2semidirect
19. C22×#10625325C22semidirect
23. #15689838C22semidirect
25. #15689769C22semidirect
26. C2×#13094024C22semidirect
34. C2×#13093998C22semidirect
39. C2×C4×D188C22semidirect
41. C2×#13093983C22semidirect
44. #15689483C22semidirect
45. #15689465C22semidirect
46. #15689448C22semidirect
47. #15689404C22semidirect
48. #15689369C22semidirect
49. #15689359C22semidirect
50. #15689339C22semidirect
51. #15689270C22semidirect
52. #15689259C22semidirect
53. #15689236C22semidirect
54. C2×#13093958C22semidirect
55. C2×#13093958C22semidirect
56. C2×#13093956C22semidirect
57. #15689129C22semidirect
58. #15689120C22semidirect
59. C2×#13093949C22semidirect
60. C2×#13093949C22semidirect
61. C2×#13093949C22semidirect
68. C2×#13093946C22semidirect
70. C23×C8×C47C22semidirect
72. C47×#435C22semidirect
73. C2×C4⋊C8×C47C22semidirect
75. C2×C22⋊C8×C47C22semidirect
76. C2×#97×C47C22semidirect
100. C2×#10625325C23semidirect
106. #13094024C23semidirect
119. #13093998C23semidirect
126. C4×D188C23semidirect
130. #13093983C23semidirect
151. #13093958C23semidirect
152. #13093958C23semidirect
153. #13093956C23semidirect
154. #13093949C23semidirect
155. #13093949C23semidirect
156. #13093949C23semidirect
163. #13093946C23semidirect
174. C22×C8×C47C23semidirect
181. C4⋊C8×C47C23semidirect
183. C22⋊C8×C47C23semidirect
184. #97×C47C23semidirect
424. C2×#435D47semidirect
429. C2×C47#3319semidirect
442. C23×C8C2×D47semidirect
476. #435C2×D47semidirect
480. C2×C4⋊C8C2×D47semidirect
494. C2×C22⋊C8C2×D47semidirect
495. C2×#97C2×D47semidirect
496. C47C2×#3319semidirect
535. C22×C8C22×D47semidirect
591. C4⋊C8C22×D47semidirect
603. C22⋊C8C22×D47semidirect
604. #97C22×D47semidirect
835. C2#20255546direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898382
C2×#156897692
#202555462
C2×#156894832
C2×#156894652
C2×#156894482
C2×#156894042
C2×#156893692
C2×#156893592
C2×#156893392
C2×#156892702
C2×#156892592
C2×#156892362
C2×#156891292
C2×#156891202
C2×C47×#4352
C2×#331947