Finite Group Databasebeta

← C2×#20255375 #27092848

Subgroups — C2×#20255375 #27092848

Order 12032.

2374 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689784C211yesmaximal, characteristic, complemented
2C2×#15689774C211yesmaximal, characteristic, complemented
3#20255375C2116yesmaximal, direct product factor
4C2×#15689484C211yesmaximal, characteristic, complemented
5C2×#15689457C211yesmaximal, characteristic, complemented
6C2×#15689436C211yesmaximal, characteristic, complemented
7C2×#15689416C211yesmaximal, characteristic, complemented
8C2×#15689372C211yesmaximal, characteristic, complemented
9C2×#15689359C211yesmaximal, characteristic, complemented
10C2×#15689341C211yesmaximal, characteristic, complemented
11C2×#15689271C211yesmaximal, characteristic, complemented
12C2×#15689262C211yesmaximal, characteristic, complemented
13C2×#15689226C211yesmaximal, characteristic, complemented
14C2×#15689194C211yesmaximal, characteristic, complemented
15C2×#15689123C211yesmaximal, characteristic, complemented
16C22×#103×C47C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18C22×#10625350—21no—
19C22×#10625336C2211yescharacteristic
20C22×#10625336C2211yescharacteristic
21C22×D376C2211yescharacteristic
22C22×#10625324C2211yescharacteristic
23#15689784—24no—
24#15689784C2218yescomplemented
25#15689774—24no—
26#15689774C2218yescomplemented
27C2×#13094023C2211yescharacteristic
28C2×#13094013—21no—
29C2×#13094013C2211yescharacteristic
30C2×#13094009—21no—
31C2×#13094007—21no—
32C2×#13094002—21no—
33C2×#13094000—21no—
34C2×#13094000C2211yescharacteristic
35C2×#13093999C2211yescharacteristic
36C2×#13093998—21no—
37C2×#13093998C2211yescharacteristic
38C2×#13093998C2211yescharacteristic
39C2×Q8×Dic47C2211yescharacteristic
40C2×#13093986C2211yescharacteristic
41C2×C4×C22⋊D47—21no—
42C2×C4×C22⋊D47C2211yescharacteristic
43C2×C4⋊C4×D47C2211yescharacteristic
44#15689484C2218yescomplemented
45#15689457C2218yescomplemented
46#15689436C2218yescomplemented
47#15689416C2218yescomplemented
48#15689372C2218yescomplemented
49#15689359C2218yescomplemented
50#15689341C2218yescomplemented
51#15689271C2218yescomplemented
52#15689262C2218yescomplemented
53#15689226C2218yescomplemented
54#15689194C2218yescomplemented
55C2×#13093958C2211yescharacteristic
56C2×#13093957C2211yescharacteristic
57C2×#13093957C2211yescharacteristic
58C2×Dic47⋊C8C2211yescharacteristic
59#15689123C2218yescomplemented
60C2×#13093948C2211yescharacteristic
61C2×#13093948C2211yescharacteristic
62C2×#13093946C2211yescharacteristic
63C2×#13093946C2211yescharacteristic
64C2×#13093944C2211yescharacteristic
65C2×#13093944C2211yescharacteristic
66C2×C22⋊(C47⋊C8)C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×#13093934C2211yescharacteristic
69C23×Q8×C47C2211yescharacteristic
70C23×C8×C47C2211yescharacteristic
71C22×C4⋊C4×C47C2211yescharacteristic
72C2×#103×C47C2211yescharacteristic
73C2×#103×C47C2211yescharacteristic
74C2×#103×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×#103×C47C2218yescomplemented
77C2×#10625354—22no—
78C2×#10625354—24no—
79C2×#10625354—42no—
80C2×#10625354C2314yes—
81C2×#10625350—28no—
82C2×#10625350—48no—
83C22×Dic94—21no—
84C22×D188—21no—
85C22×D188—21no—
86C22×D188C2311yescharacteristic
87C22×D188C2311yescharacteristic
88C22×C22⋊D47—21no—
89C22×C22⋊D47—21no—
90C22×C22⋊D47D411yescharacteristic
91C22×C4×D47—21no—
92C22×C4×D47—21no—
93C22×C4×D47—21no—
94C22×C4×D47C2311yescharacteristic
95C2×#10625336—24no—
96C2×#10625336—42no—
97C2×#10625336C2314yes—
98C2×#10625336C2314yes—
99C2×D376—42no—
100C2×D376C2314yes—
101C2×#10625324—42no—
102C2×#10625324C2314yes—
103C22×C47⋊C8C2311yescharacteristic
104C22×C47⋊C8C2311yescharacteristic
105#13094023—22no—
106#13094023C2314yes—
107#13094013—28no—
108#13094013—22no—
109#13094013C2314yes—
110#13094009—28no—
111#13094007—28no—
112#13094002—28no—
113#13094000—22no—
114#13094000—28no—
115#13094000C2314yes—
116#13093999—22no—
117#13093999C2314yes—
118#13093998—22no—
119#13093998—22no—
120#13093998—28no—
121#13093998C2314yes—
122#13093998C2314yes—
123Q8×Dic47—22no—
124Q8×Dic47C2314yes—
125#13093986—22no—
126#13093986C2314yes—
127C4×C22⋊D47—28no—
128C4×C22⋊D47D414yes—
129C4×C22⋊D47C2314yes—
130C2×C4⋊Dic47—21no—
131C2×C4⋊Dic47C2311yescharacteristic
132C2×C4⋊Dic47C2311yescharacteristic
133C2×Dic47⋊C4—21no—
134C2×Dic47⋊C4—21no—
135C2×Dic47⋊C4—21no—
136C2×Dic47⋊C4D411yescharacteristic
137C4⋊C4×D47—22no—
138C4⋊C4×D47C2314yes—
139C2×C22⋊Dic47D411yescharacteristic
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—21no—
146C2×(C2×D47)⋊C4—21no—
147C2×(C2×D47)⋊C4D411yescharacteristic
148C2×C4×Dic47—21no—
149C2×C4×Dic47C2311yescharacteristic
150#13093958C2314yes—
151#13093957C2314yes—
152#13093957C2314yes—
153Dic47⋊C8C2314yes—
154#13093948C2314yes—
155#13093948C2314yes—
156#13093946C2314yes—
157#13093946C2314yes—
158#13093944C2314yes—
159#13093944C2314yes—
160C22⋊(C47⋊C8)C2314yes—
161(C2×D47)⋊C8C2314yes—
162#13093934C2314yes—
163C22×Q8×C47—22no—
164C22×Q8×C47—21no—
165C22×Q8×C47—24no—
166C22×Q8×C47—42no—
167C22×Q8×C47C2311yescharacteristic
168C22×Q8×C47C2314yes—
169C22×Q8×C47C2311yescharacteristic
170C23×C4×C47—21no—
171C23×C4×C47—21no—
172C23×C4×C47C2311yescharacteristic
173C22×C8×C47—42no—
174C22×C8×C47C2311yescharacteristic
175C22×C8×C47C2311yescharacteristic
176C22×C8×C47C2314yes—
177C2×C4⋊C4×C47—22no—
178C2×C4⋊C4×C47—21no—
179C2×C4⋊C4×C47C2314yes—
180C2×C4⋊C4×C47C2311yescharacteristic
181C2×C4⋊C4×C47C2311yescharacteristic
182#103×C47C2314yes—
183#103×C47C2314yes—
184#103×C47C2314yes—
185#103×C47C2314yes—
186C24×C47C2×D411yescharacteristic
187C23×D47—21no—
188C23×D47—21no—
189C23×D47C2×D411yescharacteristic
190C2×Q8×C47—21no—
191C2×Q8×C47—24no—
192C2×Q8×C47—21no—
193C2×Q8×C47—22no—
194C2×Q8×C47—28no—
195C2×Q8×C47—22no—
196C2×Q8×C47—22no—
197C2×Q8×C47—44no—
198C2×Q8×C47—44no—
199C2×Q8×C47—48no—
200C2×Q8×C47#4114yescomplemented
201C2×Q8×C47C2412yes—
202C2×Q8×C47C2412yes—
203C22×C4×C47—21no—
204C22×C4×C47—22no—
205C22×C4×C47—22no—
206C22×C4×C47—21no—
207C22×C4×C47—21no—
208C22×C4×C47—24no—
209C22×C4×C47—21no—
210C22×C4×C47—24no—
211C22×C4×C47—44no—
212C22×C4×C47—44no—
213C22×C4×C47C2×D411yescharacteristic
214C22×C4×C47C2×D412yes—
215C22×C4×C47C2412yes—
216C22×C4×C47C2411yescharacteristic
217C2×C22⋊D47—24no—
218C2×C22⋊D47—24no—
219C2×C22⋊D47—24no—
220C2×C22⋊D47—44no—
221C2×C22⋊D47—44no—
222C2×C22⋊D47C2×D414yes—
223C22×Dic47—21no—
224C22×Dic47—21no—
225C22×Dic47C2×D411yescharacteristic
226C22×Dic47C2×D411yescharacteristic
227C22×Dic47C2×D411yescharacteristic
228#10625354—28no—
229#10625354—44no—
230#10625354—48no—
231#10625350—432no—
232C2×D188—22no—
233C2×D188—22no—
234C2×D188—22no—
235C2×D188—22no—
236C2×D188—24no—
237C2×D188—24no—
238C2×D188—21no—
239C2×D188—21no—
240C2×D188—44no—
241C2×D188—44no—
242C2×D188C2412yes—
243C2×D188C2412yes—
244C2×C4×D47—22no—
245C2×C4×D47—22no—
246C2×C4×D47—24no—
247C2×C4×D47—24no—
248C2×C4×D47—24no—
249C2×C4×D47—44no—
250C2×C4×D47—44no—
251C2×C4×D47—44no—
252C2×C4×D47C2×D412yes—
253C2×C4×D47C2412yes—
254C2×Dic94—24no—
255C2×Dic94—44no—
256C2×C8×C47—22no—
257C2×C8×C47—22no—
258C2×C8×C47—44no—
259C2×C8×C47C2412yes—
260C2×C8×C47C2412yes—
261C4⋊C4×C47—21no—
262C4⋊C4×C47—21no—
263C4⋊C4×C47—24no—
264C4⋊C4×C47C2412yes—
265C4⋊C4×C47C2412yes—
266C22⋊Dic47C2×D414yes—
267#10625336—28no—
268#10625336—44no—
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⋊C4—24no—
285Dic47⋊C4C2×D414yes—
286C4×Dic47—24no—
287C4×Dic47C2×D412yes—
288C4×Dic47C2412yes—
289C2×C47⋊C8—22no—
290C2×C47⋊C8—22no—
291C2×C47⋊C8C2412yes—
292C2×C47⋊C8C2412yes—
293D376—44no—
294#10625324—44no—
295C23×C47—22no—
296C23×C47—22no—
297C23×C47AGL(1,ℤ/8)14yes—
298C23×C47C22×D412yes—
299C23×C47C22×D411yescharacteristic
300C22×D47—22no—
301C22×D47—22no—
302C22×D47—22no—
303C22×D47—22no—
304C22×D47—22no—
305C22×D47—42no—
306C22×D47—42no—
307C22×D47—42no—
308C22×D47—42no—
309C22×D47—42no—
310C22×D47—42no—
311C22×D47C22×D412yes—
312Q8×C47—24no—
313Q8×C47—22no—
314Q8×C47—22no—
315Q8×C47—22no—
316Q8×C47—48no—
317Q8×C47—42no—
318Q8×C47C2×#4114yescomplemented
319C2×C4×C47—24no—
320C2×C4×C47—22no—
321C2×C4×C47—22no—
322C2×C4×C47—24no—
323C2×C4×C47—22no—
324C2×C4×C47—22no—
325C2×C4×C47—22no—
326C2×C4×C47—22no—
327C2×C4×C47—22no—
328C2×C4×C47—48no—
329C2×C4×C47—42no—
330C2×C4×C47—42no—
331C2×C4×C47—42no—
332C2×C4×C47—48no—
333C2×C4×C47C22×D412yes—
334C2×C4×C47C22×D411yescharacteristic
335C2×C4×C47C2×#4112yes—
336C2×C4×C47H(5,𝔽2)12yes—
337C2×C4×C47C2511yescharacteristic
338C22⋊D47—28no—
339C22⋊D47—48no—
340C22⋊D47—48no—
341C2×Dic47—22no—
342C2×Dic47—22no—
343C2×Dic47—22no—
344C2×Dic47—22no—
345C2×Dic47—22no—
346C2×Dic47—42no—
347C2×Dic47—42no—
348C2×Dic47C22×D412yes—
349C2×Dic47C22×D412yes—
350C2×Dic47C22×D412yes—
351D188—22no—
352D188—22no—
353D188—22no—
354D188—22no—
355D188—48no—
356D188—48no—
357D188—42no—
358D188—42no—
359C4×D47—24no—
360C4×D47—22no—
361C4×D47—22no—
362C4×D47—48no—
363C4×D47—48no—
364C4×D47—48no—
365Dic94—48no—
366C8×C47—22no—
367C8×C47—22no—
368C47⋊C8—22no—
369C47⋊C8—22no—
370C2×#3308—471nomaximal, Sylow
371C22×C47—22no—
372C22×C47—28no—
373C22×C47—22no—
374C22×C47#54612yes—
375C22×C47C2×AGL(1,ℤ/8)14yes—
376C22×C47C2×AGL(1,ℤ/8)12yes—
377C22×C47#57812yes—
378C22×C47C23×D411yescharacteristic
379C2×D47—22no—
380C2×D47—22no—
381C2×D47—22no—
382C2×D47—44no—
383C2×D47—42no—
384C2×D47—42no—
385C2×D47—42no—
386C2×D47—42no—
387C2×D47—42no—
388C2×D47—42no—
389C2×D47—84no—
390C2×D47—84no—
391C4×C47—24no—
392C4×C47—22no—
393C4×C47—42no—
394C4×C47—42no—
395C4×C47—42no—
396C4×C47#54612yes—
397C4×C47C22×#4111yescharacteristic
398C4×C47C2×H(5,𝔽2)11yescharacteristic
399Dic47—22no—
400Dic47—22no—
401Dic47—22no—
402Dic47—42no—
403Dic47—42no—
404C2×#548—471no—
405C2×#547—471no—
406#3308—4716no—
407C2×#489—471no—
408C2×#484—471no—
409C2×#480—471no—
410C2×#477—471no—
411C2×#468—471no—
412C2×#466—471no—
413C2×#463—471no—
414C2×#449—471no—
415C2×#448—471no—
416C2×#440—471no—
417C2×#435—471no—
418C2×#417—471no—
419C22×#103D4711yescharacteristic, complemented
420C2×C47—24no—
421C2×C47#330814yescomplemented
422C2×C47C2×#54611yescharacteristic
423C2×C47C22×AGL(1,ℤ/8)11yescharacteristic
424C2×C47C2×#57811yescharacteristic
425D47—42no—
426D47—82no—
427D47—82no—
428C22×#41—471no—
429C22×#41—941no—
430C23×Q8C2×D4711yescharacteristic
431C22×SD16—471no—
432C22×SD16—471no—
433C22×D8—471no—
434C22×M16—471no—
435C23×C8C2×D4711yescharacteristic
436#548—478no—
437#548—944no—
438#547—478no—
439#547—944no—
440C2×C4⋊Q8—471no—
441C2×#124—471no—
442C2×#124—941no—
443C2×#123—941no—
444C2×#123—941no—
445C2×C22⋊Q8—471no—
446C2×C22⋊Q8—941no—
447C2×C22⋊Q8—941no—
448C2×#121—471no—
449C2×#121—471no—
450C2×#121—471no—
451C2×#121—941no—
452C2×C4×Q8—471no—
453C2×C4×D4—471no—
454C2×C4×D4—471no—
455C2×C4×D4—941no—
456C22×C4⋊C4—471no—
457C22×C4⋊C4C2×D4711yescharacteristic
458#489—478no—
459#484—478no—
460#480—478no—
461#477—478no—
462#468—478no—
463#466—478no—
464#463—478no—
465#449—478no—
466#448—478no—
467#440—478no—
468#435—478no—
469C2×#107—471no—
470C2×#107—471no—
471C2×#107—471no—
472C2×C4⋊C8—471no—
473#417—478no—
474C2×#103—471no—
475C2×#103—471no—
476C2×#103C2×D4711yescharacteristic
477C2×#103C2×D4711yescharacteristic
478C2×#103C2×D4711yescharacteristic
479C2×#103C2×D4711yescharacteristic
480C2×#103C2×D4718yescomplemented
481C2×#102—471no—
482C2×#102—471no—
483C2×#102—471no—
484C2×#102—471no—
485C2×C22⋊C8—471no—
486C2×C22⋊C8—471no—
487C2×#97—471no—
488C47C2×#330811yescharacteristic, complemented, Sylow
489C2×#41—474no—
490C2×#41—948no—
491C2×#41—942no—
492C2×#41—944no—
493C2×#41—1888no—
494C2×#41—1882no—
495C22×Q8—21no—
496C22×Q8—22no—
497C22×Q8—24no—
498C22×Q8—42no—
499C22×Q8—941no—
500C22×Q8C22×D4711yescharacteristic
501C22×Q8C22×D4714yes—
502C22×Q8C22×D4711yescharacteristic
503C22×D4—471no—
504C22×D4—471no—
505C22×D4—471no—
506C22×D4—941no—
507C22×D4—941no—
508C22×D4—941no—
509C22×D4—941no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—471no—
513C23×C4—941no—
514C23×C4—941no—
515C23×C4—941no—
516C23×C4C22×D4711yescharacteristic
517C2×SD16—474no—
518C2×SD16—474no—
519C2×SD16—944no—
520C2×SD16—1882no—
521C2×D8—474no—
522C2×D8—1882no—
523C2×M16—474no—
524C2×M16—1882no—
525C22×C8—42no—
526C22×C8—471no—
527C22×C8—471no—
528C22×C8C22×D4711yescharacteristic
529C22×C8C22×D4711yescharacteristic
530C22×C8C22×D4714yes—
531C4⋊Q8—474no—
532C4⋊Q8—942no—
533#124—474no—
534#124—942no—
535#124—948no—
536#123—948no—
537#123—948no—
538C22⋊Q8—474no—
539C22⋊Q8—948no—
540C22⋊Q8—948no—
541C22⋊Q8—942no—
542#121—474no—
543#121—474no—
544#121—474no—
545#121—942no—
546#121—948no—
547#121—942no—
548#121—942no—
549C4×Q8—474no—
550C4×Q8—942no—
551C4×D4—474no—
552C4×D4—474no—
553C4×D4—474no—
554C4×D4—942no—
555C4×D4—948no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—471no—
559C2×C4⋊C4—471no—
560C2×C4⋊C4—471no—
561C2×C4⋊C4—474no—
562C2×C4⋊C4—942no—
563C2×C4⋊C4—941no—
564C2×C4⋊C4—941no—
565C2×C4⋊C4—941no—
566C2×C4⋊C4—941no—
567C2×C4⋊C4C22×D4711yescharacteristic
568C2×C4⋊C4C22×D4711yescharacteristic
569C2×C4⋊C4C22×D4714yes—
570C2×C22⋊C4—471no—
571C2×C22⋊C4—471no—
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×C42—471no—
580C2×C42—941no—
581#107—474no—
582#107—474no—
583#107—474no—
584C4⋊C8—474no—
585#103—474no—
586#103—474no—
587#103C22×D4714yes—
588#103C22×D4714yes—
589#103C22×D4714yes—
590#103C22×D4714yes—
591#102—474no—
592#102—474no—
593#102—474no—
594#102—474no—
595C22⋊C8—474no—
596C22⋊C8—474no—
597#97—474no—
598C24—471no—
599C24—941no—
600C24—941no—
601C24D4×D4711yescharacteristic
602#41—948no—
603#41—18832no—
604#41—1884no—
605#41—1888no—
606C2×Q8—21no—
607C2×Q8—24no—
608C2×Q8—21no—
609C2×Q8—22no—
610C2×Q8—28no—
611C2×Q8—22no—
612C2×Q8—22no—
613C2×Q8—44no—
614C2×Q8—44no—
615C2×Q8—48no—
616C2×Q8—944no—
617C2×Q8—1884no—
618C2×Q8#1062535014yescomplemented
619C2×Q8C23×D4712yes—
620C2×Q8C23×D4712yes—
621C2×D4—474no—
622C2×D4—472no—
623C2×D4—472no—
624C2×D4—944no—
625C2×D4—944no—
626C2×D4—944no—
627C2×D4—944no—
628C2×D4—944no—
629C2×D4—941no—
630C2×D4—941no—
631C2×D4—942no—
632C2×D4—942no—
633C2×D4—942no—
634C2×D4—942no—
635C2×D4—1884no—
636C2×D4—1884no—
637C2×D4—1884no—
638C2×D4—1884no—
639C22×C4—21no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—24no—
643C22×C4—24no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—44no—
648C22×C4—44no—
649C22×C4—471no—
650C22×C4—471no—
651C22×C4—471no—
652C22×C4—472no—
653C22×C4—472no—
654C22×C4—944no—
655C22×C4—944no—
656C22×C4—944no—
657C22×C4—942no—
658C22×C4—942no—
659C22×C4—941no—
660C22×C4—941no—
661C22×C4—1884no—
662C22×C4—1884no—
663C22×C4—1884no—
664C22×C4D4×D4712yes—
665C22×C4D4×D4711yescharacteristic
666C22×C4C23×D4712yes—
667C22×C4C23×D4711yescharacteristic
668SD16—948no—
669SD16—1884no—
670D8—1884no—
671M16—1884no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—44no—
675C2×C8—472no—
676C2×C8—472no—
677C2×C8—942no—
678C2×C8—942no—
679C2×C8C23×D4712yes—
680C2×C8C23×D4712yes—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—24no—
684C4⋊C4—474no—
685C4⋊C4—472no—
686C4⋊C4—472no—
687C4⋊C4—944no—
688C4⋊C4—944no—
689C4⋊C4—944no—
690C4⋊C4—944no—
691C4⋊C4—941no—
692C4⋊C4—941no—
693C4⋊C4C23×D4712yes—
694C4⋊C4C23×D4712yes—
695C22⋊C4—474no—
696C22⋊C4—474no—
697C22⋊C4—944no—
698C22⋊C4—944no—
699C22⋊C4—944no—
700C22⋊C4—944no—
701C22⋊C4—944no—
702C22⋊C4—944no—
703C22⋊C4—944no—
704C42—472no—
705C42—472no—
706C42—944no—
707C23—22no—
708C23—22no—
709C23—472no—
710C23—942no—
711C23—942no—
712C23—942no—
713C23—942no—
714C23—942no—
715C23—1882no—
716C23—1882no—
717C23—1882no—
718C23—1882no—
719C23—1882no—
720C23—1882no—
721C23#1309405114yes—
722C23C2×D4×D4712yes—
723C23C2×D4×D4711yescharacteristic
724Q8—24no—
725Q8—22no—
726Q8—22no—
727Q8—22no—
728Q8—48no—
729Q8—42no—
730Q8—1888no—
731Q8C2×#1062535014yescomplemented
732D4—948no—
733D4—942no—
734D4—942no—
735D4—942no—
736D4—942no—
737D4—1888no—
738D4—1888no—
739D4—1888no—
740D4—1888no—
741D4—1882no—
742D4—1882no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—48no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—48no—
757C2×C4—472no—
758C2×C4—472no—
759C2×C4—472no—
760C2×C4—942no—
761C2×C4—942no—
762C2×C4—942no—
763C2×C4—944no—
764C2×C4—942no—
765C2×C4—942no—
766C2×C4—942no—
767C2×C4—942no—
768C2×C4—1888no—
769C2×C4—1888no—
770C2×C4—1888no—
771C2×C4—1882no—
772C2×C4—1882no—
773C2×C4C2×D4×D4712yes—
774C2×C4C2×D4×D4711yescharacteristic
775C2×C4C2×#1062535012yes—
776C2×C4#1309406912yes—
777C2×C4C24×D4711yescharacteristic
778C8—22no—
779C8—22no—
780C8—942no—
781C8—942no—
782C22—22no—
783C22—22no—
784C22—28no—
785C22—942no—
786C22—942no—
787C22—942no—
788C22—3764no—
789C22—3764no—
790C22—1882no—
791C22—1882no—
792C22—1882no—
793C22—1882no—
794C22—1882no—
795C22—1882no—
796C22—1884no—
797C22#1568976312yes—
798C22C2×#1309405114yes—
799C22C2×#1309405112yes—
800C22#1568993612yes—
801C22C22×D4×D4711yescharacteristic
802C4—22no—
803C4—24no—
804C4—42no—
805C4—42no—
806C4—42no—
807C4—942no—
808C4—942no—
809C4—942no—
810C4—1882no—
811C4—1882no—
812C4#1568976312yes—
813C4C22×#1062535011yescharacteristic
814C4C2×#1309406911yescharacteristic
815C2—24no—
816C2—3762no—
817C2—3762no—
818C2—1882no—
819C2#2025537514yesdirect product factor
820C2C2×#1568976311yescharacteristic
821C2C22×#1309405111yescharacteristic
822C2C2×#1568993611yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC22×#103×C47C2
socleC23×C47C22×D4
hypercenterC22×#103D47
hypocenterC47C2×#3308
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
1. C2×#15689784C2semidirect
2. C2×#15689774C2semidirect
3. #20255375C2direct (N × H)
4. C2×#15689484C2semidirect
5. C2×#15689457C2semidirect
6. C2×#15689436C2semidirect
7. C2×#15689416C2semidirect
8. C2×#15689372C2semidirect
9. C2×#15689359C2semidirect
10. C2×#15689341C2semidirect
11. C2×#15689271C2semidirect
12. C2×#15689262C2semidirect
13. C2×#15689226C2semidirect
14. C2×#15689194C2semidirect
15. C2×#15689123C2semidirect
16. C22×#103×C47C2semidirect
24. #15689784C22semidirect
26. #15689774C22semidirect
44. #15689484C22semidirect
45. #15689457C22semidirect
46. #15689436C22semidirect
47. #15689416C22semidirect
48. #15689372C22semidirect
49. #15689359C22semidirect
50. #15689341C22semidirect
51. #15689271C22semidirect
52. #15689262C22semidirect
53. #15689226C22semidirect
54. #15689194C22semidirect
59. #15689123C22semidirect
76. C2×#103×C47C22semidirect
200. C2×Q8×C47#41semidirect
318. Q8×C47C2×#41semidirect
419. C22×#103D47semidirect
421. C2×C47#3308semidirect
480. C2×#103C2×D47semidirect
488. C47C2×#3308semidirect
618. C2×Q8#10625350semidirect
731. Q8C2×#10625350semidirect
819. C2#20255375direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897842
C2×#156897742
#202553752
C2×#156894842
C2×#156894572
C2×#156894362
C2×#156894162
C2×#156893722
C2×#156893592
C2×#156893412
C2×#156892712
C2×#156892622
C2×#156892262
C2×#156891942
C2×#156891232
C22×#103×C472
C2×#330847