Finite Group Databasebeta

← C2×#20255396 #27092982

Subgroups — C2×#20255396 #27092982

Order 12032.

2242 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689819C211yesmaximal, characteristic, complemented
2C2×#15689794C211yesmaximal, characteristic, complemented
3#20255396C2116yesmaximal, direct product factor
4C2×#15689488C211yesmaximal, characteristic, complemented
5C2×#15689448C211yesmaximal, characteristic, complemented
6C2×#15689437C211yesmaximal, characteristic, complemented
7C2×#15689431C211yesmaximal, characteristic, complemented
8C2×#15689376C211yesmaximal, characteristic, complemented
9C2×#15689359C211yesmaximal, characteristic, complemented
10C2×#15689319C211yesmaximal, characteristic, complemented
11C2×#15689270C211yesmaximal, characteristic, complemented
12C2×#15689270C211yesmaximal, characteristic, complemented
13C2×#15689225C211yesmaximal, characteristic, complemented
14C2×#15689125C211yesmaximal, characteristic, complemented
15C2×#15689120C211yesmaximal, characteristic, complemented
16C2×C47×#435C211yesmaximal, characteristic, complemented
17C22×#10625350C2211yescharacteristic
18C22×#10625350C2211yescharacteristic
19C22×#10625325C2211yescharacteristic
20C22×D376C2211yescharacteristic
21C22×D376C2211yescharacteristic
22#15689819—24no—
23#15689819C2218yescomplemented
24#15689794—24no—
25#15689794C2218yescomplemented
26C2×#13094021C2211yescharacteristic
27C2×#13094020—21no—
28C2×#13094019—21no—
29C2×#13094016C2211yescharacteristic
30C2×#13094006—21no—
31C2×#13093998C2211yescharacteristic
32C2×#13093998C2211yescharacteristic
33C2×#13093998C2211yescharacteristic
34C2×#13093998C2211yescharacteristic
35C2×#13093997—21no—
36C2×#13093997—21no—
37C2×#13093996—21no—
38C2×C4×Dic94C2211yescharacteristic
39C2×C4×D188C2211yescharacteristic
40C2×#13093986—21no—
41C2×(C22⋊D47)⋊C4—21no—
42C2×#13093983C2211yescharacteristic
43C22×C4⋊Dic47C2211yescharacteristic
44#15689488C2218yescomplemented
45#15689448C2218yescomplemented
46#15689437C2218yescomplemented
47#15689431C2218yescomplemented
48#15689376C2218yescomplemented
49#15689359C2218yescomplemented
50#15689319C2218yescomplemented
51#15689270C2218yescomplemented
52#15689270C2218yescomplemented
53#15689225C2218yescomplemented
54C2×#13093958C2211yescharacteristic
55C2×#13093958C2211yescharacteristic
56C2×#13093956C2211yescharacteristic
57#15689125C2218yescomplemented
58#15689120C2218yescomplemented
59C2×#13093949C2211yescharacteristic
60C2×#13093949C2211yescharacteristic
61C2×#13093949C2211yescharacteristic
62C2×#13093946C2211yescharacteristic
63C2×#13093946C2211yescharacteristic
64C2×#13093946C2211yescharacteristic
65C2×#13093946C2211yescharacteristic
66C2×#13093946C2211yescharacteristic
67C2×#13093946C2211yescharacteristic
68C2×#13093946C2211yescharacteristic
69C22×M16×C47C2211yescharacteristic
70C23×C8×C47C2211yescharacteristic
71C2×C4×D4×C47C2211yescharacteristic
72C47×#435C2218yescomplemented
73C2×C4⋊C8×C47C2211yescharacteristic
74C2×C22⋊C8×C47C2211yescharacteristic
75C2×C22⋊C8×C47C2211yescharacteristic
76C2×#97×C47C2211yescharacteristic
77C2×#10625350—22no—
78C2×#10625350—22no—
79C2×#10625350—24no—
80C2×#10625350—24no—
81C2×#10625350—42no—
82C2×#10625350—42no—
83C2×#10625350C2314yes—
84C2×#10625350C2314yes—
85C22×Dic94C2311yescharacteristic
86C22×D188—21no—
87C22×D188—21no—
88C22×D188C2311yescharacteristic
89C22×D188C2311yescharacteristic
90C22×D188C2311yescharacteristic
91C22×C22⋊D47—21no—
92C22×C22⋊D47—21no—
93C22×C22⋊D47—21no—
94C22×C22⋊D47—21no—
95C22×C22⋊D47—21no—
96C22×C22⋊D47—21no—
97C23×Dic47—21no—
98C22×C4×D47—21no—
99C22×C4×D47—21no—
100C22×C4×D47—21no—
101C2×#10625325—24no—
102C2×#10625325C2314yes—
103C2×D376—42no—
104C2×D376—42no—
105C2×D376C2314yes—
106C2×D376C2314yes—
107#13094021—22no—
108#13094021C2314yes—
109#13094020—28no—
110#13094019—28no—
111#13094016—22no—
112#13094016C2314yes—
113#13094006—28no—
114#13093998—22no—
115#13093998—22no—
116#13093998—22no—
117#13093998—22no—
118#13093998C2314yes—
119#13093998C2314yes—
120#13093998C2314yes—
121#13093998C2314yes—
122#13093997—28no—
123#13093997—28no—
124#13093996—28no—
125C4×Dic94—22no—
126C4×Dic94C2314yes—
127C4×D188—22no—
128C4×D188C2314yes—
129#13093986—28no—
130(C22⋊D47)⋊C4—28no—
131#13093983—22no—
132#13093983C2314yes—
133C2×C4⋊Dic47—22no—
134C2×C4⋊Dic47—21no—
135C2×C4⋊Dic47C2314yes—
136C2×C4⋊Dic47C2311yescharacteristic
137C2×C4⋊Dic47C2311yescharacteristic
138C2×C4⋊Dic47C2311yescharacteristic
139C2×C4⋊Dic47C2311yescharacteristic
140C2×Dic47⋊C4—21no—
141C2×Dic47⋊C4—21no—
142C2×Dic47⋊C4—21no—
143C2×C22⋊Dic47—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×C4×Dic47—21no—
150C2×C4×Dic47—21no—
151#13093958C2314yes—
152#13093958C2314yes—
153#13093956C2314yes—
154#13093949C2314yes—
155#13093949C2314yes—
156#13093949C2314yes—
157#13093946C2314yes—
158#13093946C2314yes—
159#13093946C2314yes—
160#13093946C2314yes—
161#13093946C2314yes—
162#13093946C2314yes—
163#13093946C2314yes—
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×C47C2314yes—
175C4×D4×C47D414yes—
176C4×D4×C47C2314yes—
177C2×C4⋊C4×C47D411yescharacteristic
178C2×C22⋊C4×C47D411yescharacteristic
179C2×C22⋊C4×C47D411yescharacteristic
180C2×C42×C47C2311yescharacteristic
181C4⋊C8×C47C2314yes—
182C22⋊C8×C47C2314yes—
183C22⋊C8×C47C2314yes—
184#97×C47C2314yes—
185C24×C47C2×D411yescharacteristic
186C24×C47C2×D411yescharacteristic
187C23×D47—21no—
188C23×D47—21no—
189C23×D47—21no—
190C2×D4×C47—42no—
191C2×D4×C47C2×D414yes—
192C22×C4×C47—22no—
193C22×C4×C47—22no—
194C22×C4×C47—22no—
195C22×C4×C47—22no—
196C22×C4×C47C2×D411yescharacteristic
197C22×C4×C47C2×D411yescharacteristic
198C22×C4×C47C2×D411yescharacteristic
199C22×C4×C47C2×D411yescharacteristic
200C22×C4×C47C2×D412yes—
201C22×C4×C47C2×D412yes—
202C22×C4×C47C2412yes—
203C22×C4×C47C2412yes—
204C22×C4×C47C2411yescharacteristic
205C2×C22⋊D47—24no—
206C2×C22⋊D47—24no—
207C2×C22⋊D47—24no—
208C2×C22⋊D47—24no—
209C2×C22⋊D47—24no—
210C2×C22⋊D47—24no—
211C2×C22⋊D47—44no—
212C2×C22⋊D47—44no—
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—
222C22×Dic47—24no—
223C22×Dic47—82no—
224#10625350—28no—
225#10625350—28no—
226#10625350—44no—
227#10625350—44no—
228#10625350—48no—
229#10625350—48no—
230C2×D188—22no—
231C2×D188—22no—
232C2×D188—22no—
233C2×D188—22no—
234C2×D188—22no—
235C2×D188—22no—
236C2×D188—24no—
237C2×D188—21no—
238C2×D188—21no—
239C2×D188—21no—
240C2×D188—24no—
241C2×D188—44no—
242C2×D188—82no—
243C2×D188C2412yes—
244C2×D188C2412yes—
245C2×D188C2412yes—
246C2×C4×D47—24no—
247C2×C4×D47—24no—
248C2×C4×D47—24no—
249C2×C4×D47—44no—
250C2×C4×D47—44no—
251C2×C4×D47—82no—
252C2×Dic94—21no—
253C2×Dic94—22no—
254C2×Dic94#4114yes—
255C2×Dic94C2412yes—
256M16×C47—44no—
257C2×C8×C47—22no—
258C2×C8×C47—22no—
259C2×C8×C47—22no—
260C2×C8×C47—22no—
261C2×C8×C47—44no—
262C2×C8×C47C2412yes—
263C2×C8×C47C2412yes—
264C2×C8×C47C2412yes—
265C2×C8×C47C2412yes—
266C4⋊C4×C47C2×D414yes—
267C22⋊C4×C47C2×D414yes—
268C22⋊C4×C47C2×D414yes—
269C42×C47C2×D412yes—
270C42×C47C2412yes—
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—
277C4⋊Dic47—21no—
278C4⋊Dic47—21no—
279C4⋊Dic47—24no—
280C4⋊Dic47—21no—
281C4⋊Dic47—21no—
282C4⋊Dic47C2412yes—
283C4⋊Dic47C2412yes—
284C4⋊Dic47C2412yes—
285C4⋊Dic47C2412yes—
286Dic47⋊C4—24no—
287Dic47⋊C4—24no—
288Dic47⋊C4—24no—
289C4×Dic47—24no—
290C4×Dic47—24no—
291D376—44no—
292D376—44no—
293#10625325—28no—
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—22no—
304C22×D47—22no—
305C22×D47—22no—
306C22×D47—42no—
307C22×D47—42no—
308C22×D47—42no—
309C22×D47—42no—
310C22×D47—42no—
311C22×D47—42no—
312C22×D47—42no—
313C22×D47—42no—
314C22×D47—42no—
315D4×C47—44no—
316C2×C4×C47—22no—
317C2×C4×C47—22no—
318C2×C4×C47—22no—
319C2×C4×C47—22no—
320C2×C4×C47—24no—
321C2×C4×C47—24no—
322C2×C4×C47—22no—
323C2×C4×C47—22no—
324C2×C4×C47—22no—
325C2×C4×C47—22no—
326C2×C4×C47C22×D412yes—
327C2×C4×C47C22×D412yes—
328C2×C4×C47C22×D412yes—
329C2×C4×C47C22×D412yes—
330C2×C4×C47C22×D411yescharacteristic
331C2×C4×C47C2×#4112yes—
332C2×C4×C47H(5,𝔽2)12yes—
333C2×C4×C47C2511yescharacteristic
334C22⋊D47—48no—
335C22⋊D47—48no—
336C22⋊D47—48no—
337C22⋊D47—84no—
338C22⋊D47—84no—
339C22⋊D47—84no—
340C2×Dic47—24no—
341C2×Dic47—22no—
342C2×Dic47—22no—
343C2×Dic47—22no—
344C2×Dic47—22no—
345C2×Dic47—22no—
346C2×Dic47—42no—
347C2×Dic47—42no—
348C2×Dic47—42no—
349C2×Dic47—42no—
350C2×Dic47—84no—
351D188—22no—
352D188—22no—
353D188—22no—
354D188—22no—
355D188—22no—
356D188—22no—
357D188—48no—
358D188—42no—
359D188—42no—
360D188—42no—
361D188—84no—
362C4×D47—48no—
363C4×D47—48no—
364C4×D47—84no—
365Dic94—24no—
366Dic94—22no—
367Dic94C2×#4114yes—
368C8×C47—22no—
369C8×C47—22no—
370C8×C47—22no—
371C8×C47—22no—
372C2×#3309—471nomaximal, Sylow
373C22×C47—22no—
374C22×C47—22no—
375C22×C47—22no—
376C22×C47—22no—
377C22×C47—22no—
378C22×C47—22no—
379C22×C47—44no—
380C22×C47—44no—
381C22×C47#54612yes—
382C22×C47#57512yes—
383C22×C47#57612yes—
384C22×C47C23×D411yescharacteristic
385C2×D47—42no—
386C2×D47—42no—
387C2×D47—42no—
388C2×D47—42no—
389C2×D47—42no—
390C2×D47—42no—
391C2×D47—42no—
392C2×D47—42no—
393C2×D47—42no—
394C2×D47—84no—
395C2×D47—84no—
396C2×D47—84no—
397C4×C47—22no—
398C4×C47—22no—
399C4×C47—22no—
400C4×C47—22no—
401C4×C47#54612yes—
402C4×C47C22×#4111yescharacteristic
403C4×C47C2×H(5,𝔽2)11yescharacteristic
404Dic47—24no—
405Dic47—42no—
406Dic47—42no—
407Dic47—42no—
408Dic47—42no—
409C2×#553—471no—
410C2×#550—471no—
411#3309—4716no—
412C2×#490—471no—
413C2×#482—471no—
414C2×#480—471no—
415C2×#479—471no—
416C2×#469—471no—
417C2×#466—471no—
418C2×#459—471no—
419C2×#449—471no—
420C2×#449—471no—
421C2×#440—471no—
422C2×#435D4711yescharacteristic, complemented
423C2×#417—471no—
424C2×#416—471no—
425C2×C47—42no—
426C2×C47—42no—
427C2×C47#330914yescomplemented
428C2×C47C2×#54611yescharacteristic
429C2×C47C2×#57511yescharacteristic
430C2×C47C2×#57611yescharacteristic
431D47—82no—
432D47—82no—
433D47—82no—
434C22×#41—471no—
435C22×#41—471no—
436C22×SD16—471no—
437C22×D8—471no—
438C22×D8—471no—
439C22×M16C2×D4711yescharacteristic
440C23×C8C2×D4711yescharacteristic
441#553—478no—
442#553—944no—
443#550—478no—
444#550—944no—
445C2×#127—471no—
446C2×#127—941no—
447C2×#126—941no—
448C2×#125—471no—
449C2×#123—941no—
450C2×#121—471no—
451C2×#121—471no—
452C2×#121—471no—
453C2×#121—471no—
454C2×#121—941no—
455C2×#121—941no—
456C2×#121—941no—
457C2×C4×Q8—471no—
458C2×C4×D4—471no—
459C2×C4×D4—941no—
460C2×C4×D4—941no—
461C2×C4×D4C2×D4711yescharacteristic
462C2×#117—471no—
463C22×C4⋊C4—471no—
464#490—478no—
465#482—478no—
466#480—478no—
467#479—478no—
468#469—478no—
469#466—478no—
470#459—478no—
471#449—478no—
472#449—478no—
473#440—478no—
474#435C2×D4718yescomplemented
475C2×#107—471no—
476C2×#107—471no—
477C2×#106—471no—
478C2×C4⋊C8C2×D4711yescharacteristic
479#417—478no—
480#416—478no—
481C2×#103—471no—
482C2×#103—471no—
483C2×#103—471no—
484C2×#102—471no—
485C2×#102—471no—
486C2×#102—471no—
487C2×#102—471no—
488C2×#102—471no—
489C2×#102—471no—
490C2×#102—471no—
491C2×C22⋊C8C2×D4711yescharacteristic
492C2×C22⋊C8C2×D4711yescharacteristic
493C2×#97C2×D4711yescharacteristic
494C47C2×#330911yescharacteristic, complemented, Sylow
495C2×#41—474no—
496C2×#41—474no—
497C2×#41—944no—
498C2×#41—944no—
499C2×#41—942no—
500C2×#41—942no—
501C2×#41—1882no—
502C2×#41—1882no—
503C22×Q8—471no—
504C22×D4—471no—
505C22×D4—471no—
506C22×D4—471no—
507C22×D4—941no—
508C22×D4—941no—
509C22×D4—941no—
510C22×D4—941no—
511C22×D4—941no—
512C22×D4—941no—
513C22×D4—941no—
514C22×D4—941no—
515C22×D4D18811yescharacteristic
516C23×C4—941no—
517C23×C4—941no—
518C23×C4—941no—
519C23×C4—941no—
520C23×C4C22×D4711yescharacteristic
521C23×C4C22×D4711yescharacteristic
522C2×SD16—474no—
523C2×SD16—944no—
524C2×D8—474no—
525C2×D8—474no—
526C2×D8—1882no—
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×D4714yes—
536#127—474no—
537#127—948no—
538#127—942no—
539#126—948no—
540#125—474no—
541#125—942no—
542#123—948no—
543#121—474no—
544#121—474no—
545#121—474no—
546#121—474no—
547#121—948no—
548#121—942no—
549#121—942no—
550#121—942no—
551#121—942no—
552#121—948no—
553#121—948no—
554C4×Q8—474no—
555C4×Q8—942no—
556C4×D4—474no—
557C4×D4—948no—
558C4×D4—948no—
559C4×D4—942no—
560C4×D4D18814yes—
561C4×D4C22×D4714yes—
562#117—474no—
563#117—942no—
564C2×C4⋊C4—471no—
565C2×C4⋊C4—471no—
566C2×C4⋊C4—474no—
567C2×C4⋊C4—471no—
568C2×C4⋊C4—471no—
569C2×C4⋊C4—941no—
570C2×C4⋊C4—942no—
571C2×C4⋊C4—941no—
572C2×C4⋊C4—941no—
573C2×C4⋊C4—941no—
574C2×C4⋊C4D18811yescharacteristic
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⋊C4D18811yescharacteristic
582C2×C22⋊C4D18811yescharacteristic
583C2×C42—941no—
584C2×C42—941no—
585C2×C42C22×D4711yescharacteristic
586#107—474no—
587#107—474no—
588#106—474no—
589C4⋊C8C22×D4714yes—
590#103—474no—
591#103—474no—
592#103—474no—
593#102—474no—
594#102—474no—
595#102—474no—
596#102—474no—
597#102—474no—
598#102—474no—
599#102—474no—
600C22⋊C8C22×D4714yes—
601C22⋊C8C22×D4714yes—
602#97C22×D4714yes—
603C24—941no—
604C24—941no—
605C24—941no—
606C24C2×D18811yescharacteristic
607C24C2×D18811yescharacteristic
608#41—948no—
609#41—948no—
610#41—1884no—
611#41—1884no—
612#41—1888no—
613#41—1888no—
614C2×Q8—474no—
615C2×Q8—472no—
616C2×Q8—941no—
617C2×Q8—942no—
618C2×D4—42no—
619C2×D4—472no—
620C2×D4—472no—
621C2×D4—472no—
622C2×D4—944no—
623C2×D4—944no—
624C2×D4—944no—
625C2×D4—944no—
626C2×D4—944no—
627C2×D4—944no—
628C2×D4—944no—
629C2×D4—941no—
630C2×D4—944no—
631C2×D4—941no—
632C2×D4—941no—
633C2×D4—942no—
634C2×D4—942no—
635C2×D4—942no—
636C2×D4—942no—
637C2×D4—942no—
638C2×D4—942no—
639C2×D4—3762no—
640C2×D4—3762no—
641C2×D4—3762no—
642C2×D4—3762no—
643C2×D4—1884no—
644C2×D4—1884no—
645C2×D4—1884no—
646C2×D4—1884no—
647C2×D4C2×D18814yes—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—941no—
653C22×C4—944no—
654C22×C4—941no—
655C22×C4—941no—
656C22×C4—941no—
657C22×C4—941no—
658C22×C4—944no—
659C22×C4—944no—
660C22×C4—944no—
661C22×C4—3762no—
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—948no—
675D8—1884no—
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—944no—
693C4⋊C4—944no—
694C4⋊C4—941no—
695C4⋊C4—941no—
696C4⋊C4—944no—
697C4⋊C4—941no—
698C4⋊C4—941no—
699C4⋊C4C2×D18814yes—
700C22⋊C4—944no—
701C22⋊C4—944no—
702C22⋊C4—944no—
703C22⋊C4—944no—
704C22⋊C4—944no—
705C22⋊C4—944no—
706C22⋊C4C2×D18814yes—
707C22⋊C4C2×D18814yes—
708C42—944no—
709C42—944no—
710C42C2×D18812yes—
711C42C23×D4712yes—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—942no—
719C23—942no—
720C23—942no—
721C23—1882no—
722C23—1882no—
723C23—1882no—
724C23—1882no—
725C23—1882no—
726C23—1882no—
727C23—1882no—
728C23—1882no—
729C23—1882no—
730C23C22×D18812yes—
731C23C22×D18812yes—
732C23C22×D18811yescharacteristic
733Q8—474no—
734Q8—944no—
735Q8—942no—
736D4—44no—
737D4—942no—
738D4—942no—
739D4—942no—
740D4—942no—
741D4—942no—
742D4—942no—
743D4—3764no—
744D4—3764no—
745D4—3764no—
746D4—3764no—
747D4—1888no—
748D4—1888no—
749D4—1888no—
750D4—1888no—
751D4—1882no—
752D4—1882no—
753D4—1882no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—944no—
765C2×C4—942no—
766C2×C4—942no—
767C2×C4—942no—
768C2×C4—942no—
769C2×C4—942no—
770C2×C4—3764no—
771C2×C4—3764no—
772C2×C4—1888no—
773C2×C4—1888no—
774C2×C4—1882no—
775C2×C4—1882no—
776C2×C4—1882no—
777C2×C4—1882no—
778C2×C4C22×D18812yes—
779C2×C4C22×D18812yes—
780C2×C4C22×D18812yes—
781C2×C4C22×D18812yes—
782C2×C4C22×D18811yescharacteristic
783C2×C4#41×D4712yes—
784C2×C4#1309406912yes—
785C2×C4C24×D4711yescharacteristic
786C8—22no—
787C8—22no—
788C8—22no—
789C8—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—44no—
797C22—44no—
798C22—3764no—
799C22—3764no—
800C22—3764no—
801C22—1882no—
802C22—1882no—
803C22—1882no—
804C22—1882no—
805C22—1882no—
806C22—1882no—
807C22—1882no—
808C22—1882no—
809C22—1882no—
810C22#1568976812yes—
811C22#1568992312yes—
812C22#1568992812yes—
813C22C23×D18811yescharacteristic
814C4—22no—
815C4—22no—
816C4—22no—
817C4—22no—
818C4—944no—
819C4—1882no—
820C4—1882no—
821C4—1882no—
822C4—1882no—
823C4#1568976812yes—
824C4C2×#41×D4711yescharacteristic
825C4C2×#1309406911yescharacteristic
826C2—42no—
827C2—42no—
828C2—3762no—
829C2—3762no—
830C2—3762no—
831C2#2025539614yesdirect product factor
832C2C2×#1568976811yescharacteristic
833C2C2×#1568992311yescharacteristic
834C2C2×#1568992811yescharacteristic
subgroupG/H
centerC23C22×D188
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#435C2
socleC23×C47C22×D4
hypercenterC2×#435D47
hypocenterC47C2×#3309
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×#15689819C2semidirect
2. C2×#15689794C2semidirect
3. #20255396C2direct (N × H)
4. C2×#15689488C2semidirect
5. C2×#15689448C2semidirect
6. C2×#15689437C2semidirect
7. C2×#15689431C2semidirect
8. C2×#15689376C2semidirect
9. C2×#15689359C2semidirect
10. C2×#15689319C2semidirect
11. C2×#15689270C2semidirect
12. C2×#15689270C2semidirect
13. C2×#15689225C2semidirect
14. C2×#15689125C2semidirect
15. C2×#15689120C2semidirect
16. C2×C47×#435C2semidirect
23. #15689819C22semidirect
25. #15689794C22semidirect
44. #15689488C22semidirect
45. #15689448C22semidirect
46. #15689437C22semidirect
47. #15689431C22semidirect
48. #15689376C22semidirect
49. #15689359C22semidirect
50. #15689319C22semidirect
51. #15689270C22semidirect
52. #15689270C22semidirect
53. #15689225C22semidirect
57. #15689125C22semidirect
58. #15689120C22semidirect
72. C47×#435C22semidirect
422. C2×#435D47semidirect
427. C2×C47#3309semidirect
474. #435C2×D47semidirect
494. C47C2×#3309semidirect
831. C2#20255396direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898192
C2×#156897942
#202553962
C2×#156894882
C2×#156894482
C2×#156894372
C2×#156894312
C2×#156893762
C2×#156893592
C2×#156893192
C2×#156892702
C2×#156892252
C2×#156891252
C2×#156891202
C2×C47×#4352
C2×#330947