Finite Group Databasebeta

← C2×#20255722 #27093219

Subgroups — C2×#20255722 #27093219

Order 12032.

2210 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689828C211yesmaximal, characteristic, complemented
2C2×#15689792C211yesmaximal, characteristic
3#20255722C2116yesmaximal, direct product factor
4C2×#15689468C211yesmaximal, characteristic, complemented
5C2×#15689436C211yesmaximal, characteristic, complemented
6C2×#15689435C211yesmaximal, characteristic, complemented
7C2×#15689416C211yesmaximal, characteristic, complemented
8C2×#15689369C211yesmaximal, characteristic, complemented
9C2×#15689368C211yesmaximal, characteristic, complemented
10C2×#15689322C211yesmaximal, characteristic, complemented
11C2×#15689288C211yesmaximal, characteristic, complemented
12C2×#15689285C211yesmaximal, characteristic, complemented
13C2×#15689215C211yesmaximal, characteristic, complemented
14C2×#15689199C211yesmaximal, characteristic, complemented
15C2×#15689123C211yesmaximal, characteristic, complemented
16C2×C47×#417C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18C22×#10625337C2211yescharacteristic
19C22×#10625325C2211yescharacteristic
20C22×#10625335C2211yescharacteristic
21C22×#10625324C2211yescharacteristic
22#15689828—24no—
23#15689828C2218yescomplemented
24#15689792—24no—
25#15689792C2218yes—
26C2×#13094023C2211yescharacteristic
27C2×#13094020—21no—
28C2×#13094020C2211yescharacteristic
29C2×#13094014—21no—
30C2×#13094004C2211yescharacteristic
31C2×#13094003—21no—
32C2×#13094003C2211yescharacteristic
33C2×#13094002—21no—
34C2×#13093998—21no—
35C2×#13093998C2211yescharacteristic
36C2×#13093995—21no—
37C2×#13093995C2211yescharacteristic
38C2×Q8×Dic47C2211yescharacteristic
39C2×#13093989C2211yescharacteristic
40C2×C4×C22⋊D47—21no—
41C2×C4×C22⋊D47—21no—
42C2×C4×C22⋊D47C2211yescharacteristic
43C2×C4⋊C4×D47C2211yescharacteristic
44#15689468C2218yescomplemented
45#15689436C2218yescomplemented
46#15689435C2218yescomplemented
47#15689416C2218yescomplemented
48#15689369C2218yescomplemented
49#15689368C2218yescomplemented
50#15689322C2218yescomplemented
51#15689288C2218yescomplemented
52#15689285C2218yescomplemented
53#15689215C2218yescomplemented
54#15689199C2218yescomplemented
55C2×#13093958C2211yescharacteristic
56C2×#13093957C2211yescharacteristic
57C2×#13093957C2211yescharacteristic
58C2×Dic47⋊C8C2211yescharacteristic
59#15689123C2218yescomplemented
60C2×#13093949C2211yescharacteristic
61C2×#13093948C2211yescharacteristic
62C2×#13093946C2211yescharacteristic
63C2×#13093945C2211yescharacteristic
64C2×#13093944C2211yescharacteristic
65C2×#13093944C2211yescharacteristic
66C2×C22⋊(C47⋊C8)C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C22×#41×C47C2211yescharacteristic
70C22×M16×C47C2211yescharacteristic
71C22×C4⋊C4×C47C2211yescharacteristic
72C47×#417C2218yescomplemented
73C2×#103×C47C2211yescharacteristic
74C2×#103×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×#102×C47C2211yescharacteristic
77C2×#10625354—22no—
78C2×#10625354—24no—
79C2×#10625354—42no—
80C2×#10625354C2314yes—
81C22×Dic94—21no—
82C22×Dic94C2311yescharacteristic
83C22×D188—21no—
84C22×D188C2311yescharacteristic
85C22×C22⋊D47—21no—
86C22×C22⋊D47—21no—
87C22×C22⋊D47—21no—
88C22×C22⋊D47—21no—
89C22×C22⋊D47D411yescharacteristic
90C22×C4×D47—21no—
91C22×C4×D47—21no—
92C22×C4×D47C2311yescharacteristic
93C2×#10625337—24no—
94C2×#10625337C2314yes—
95C2×#10625325—42no—
96C2×#10625325C2314yes—
97C2×#10625335—42no—
98C2×#10625335C2314yes—
99C2×#10625324—42no—
100C2×#10625324C2314yes—
101C22×C47⋊C8C2311yescharacteristic
102C22×C47⋊C8C2311yescharacteristic
103#13094023—22no—
104#13094023C2314yes—
105#13094020—28no—
106#13094020—22no—
107#13094020C2314yes—
108#13094014—28no—
109#13094004—22no—
110#13094004C2314yes—
111#13094003—22no—
112#13094003—28no—
113#13094003C2314yes—
114#13094002—28no—
115#13093998—22no—
116#13093998—28no—
117#13093998C2314yes—
118#13093995—22no—
119#13093995—28no—
120#13093995C2314yes—
121Q8×Dic47—22no—
122Q8×Dic47C2314yes—
123#13093989—22no—
124#13093989C2314yes—
125C4×C22⋊D47—28no—
126C4×C22⋊D47—28no—
127C4×C22⋊D47D414yes—
128C4×C22⋊D47C2314yes—
129C2×C4⋊Dic47—21no—
130C2×C4⋊Dic47—21no—
131C2×C4⋊Dic47C2311yescharacteristic
132C2×C4⋊Dic47C2311yescharacteristic
133C2×Dic47⋊C4—21no—
134C2×Dic47⋊C4—21no—
135C2×Dic47⋊C4—21no—
136C2×Dic47⋊C4—21no—
137C2×Dic47⋊C4D411yescharacteristic
138C4⋊C4×D47—22no—
139C4⋊C4×D47C2314yes—
140C2×C22⋊Dic47—21no—
141C2×C22⋊Dic47—21no—
142C2×C22⋊Dic47D411yescharacteristic
143C2×(C2×D47)⋊C4—21no—
144C2×(C2×D47)⋊C4—21no—
145C2×(C2×D47)⋊C4D411yescharacteristic
146C2×C4×Dic47—21no—
147C2×C4×Dic47—21no—
148C2×C4×Dic47C2311yescharacteristic
149#13093958C2314yes—
150#13093957C2314yes—
151#13093957C2314yes—
152Dic47⋊C8C2314yes—
153#13093949C2314yes—
154#13093948C2314yes—
155#13093946C2314yes—
156#13093945C2314yes—
157#13093944C2314yes—
158#13093944C2314yes—
159C22⋊(C47⋊C8)C2314yes—
160(C2×D47)⋊C8C2314yes—
161C8×Dic47C2314yes—
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×C47C2314yes—
174C22×C8×C47C2311yescharacteristic
175C22×C8×C47C2311yescharacteristic
176C2×C4⋊C4×C47—22no—
177C2×C4⋊C4×C47—21no—
178C2×C4⋊C4×C47C2311yescharacteristic
179C2×C4⋊C4×C47C2314yes—
180C2×C4⋊C4×C47C2311yescharacteristic
181#103×C47C2314yes—
182#103×C47C2314yes—
183#102×C47C2314yes—
184#102×C47C2314yes—
185C24×C47—21no—
186C24×C47C2×D411yescharacteristic
187C23×D47—21no—
188C23×D47C2×D411yescharacteristic
189#41×C47—28no—
190#41×C47—44no—
191#41×C47—48no—
192C2×Q8×C47—21no—
193C2×Q8×C47—22no—
194C2×Q8×C47#4114yes—
195C2×Q8×C47C2412yes—
196C2×D4×C47—24no—
197C2×D4×C47—21no—
198C2×D4×C47—22no—
199C2×D4×C47—22no—
200C2×D4×C47—44no—
201C2×D4×C47C2412yes—
202C22×C4×C47—21no—
203C22×C4×C47—22no—
204C22×C4×C47—22no—
205C22×C4×C47—21no—
206C22×C4×C47—21no—
207C22×C4×C47—24no—
208C22×C4×C47—24no—
209C22×C4×C47—44no—
210C22×C4×C47—82no—
211C22×C4×C47C2×D411yescharacteristic
212C22×C4×C47C2×D412yes—
213C22×C4×C47C2412yes—
214C22×C4×C47C2411yescharacteristic
215C2×C22⋊D47—24no—
216C2×C22⋊D47—24no—
217C2×C22⋊D47—24no—
218C2×C22⋊D47—24no—
219C2×C22⋊D47—24no—
220C2×C22⋊D47—44no—
221C2×C22⋊D47—82no—
222C2×C22⋊D47—82no—
223C2×C22⋊D47—82no—
224C2×C22⋊D47C2×D414yes—
225C22×Dic47—21no—
226C22×Dic47—21no—
227C22×Dic47—21no—
228C22×Dic47C2×D411yescharacteristic
229C22×Dic47C2×D411yescharacteristic
230C22×Dic47C2×D411yescharacteristic
231#10625354—28no—
232#10625354—44no—
233#10625354—48no—
234C2×D188—22no—
235C2×D188—22no—
236C2×D188—24no—
237C2×D188—21no—
238C2×D188—44no—
239C2×D188C2412yes—
240C2×C4×D47—22no—
241C2×C4×D47—22no—
242C2×C4×D47—24no—
243C2×C4×D47—24no—
244C2×C4×D47—44no—
245C2×C4×D47—82no—
246C2×C4×D47C2×D412yes—
247C2×C4×D47C2412yes—
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×C47C2412yes—
258C2×C8×C47C2412yes—
259C4⋊C4×C47—21no—
260C4⋊C4×C47—24no—
261C4⋊C4×C47—21no—
262C4⋊C4×C47C2412yes—
263C4⋊C4×C47C2412yes—
264C22⋊Dic47—24no—
265C22⋊Dic47—24no—
266C22⋊Dic47C2×D414yes—
267#10625337—28no—
268#10625335—44no—
269(C2×D47)⋊C4—24no—
270(C2×D47)⋊C4—24no—
271(C2×D47)⋊C4C2×D414yes—
272C4⋊Dic47—21no—
273C4⋊Dic47—21no—
274C4⋊Dic47—24no—
275C4⋊Dic47—24no—
276C4⋊Dic47C2412yes—
277C4⋊Dic47C2412yes—
278Dic47⋊C4—24no—
279Dic47⋊C4—24no—
280Dic47⋊C4—24no—
281Dic47⋊C4—24no—
282Dic47⋊C4C2×D414yes—
283C4×Dic47—24no—
284C4×Dic47—24no—
285C4×Dic47C2×D412yes—
286C4×Dic47C2412yes—
287C2×C47⋊C8—22no—
288C2×C47⋊C8—22no—
289C2×C47⋊C8C2412yes—
290C2×C47⋊C8C2412yes—
291#10625325—44no—
292#10625324—44no—
293C23×C47—22no—
294C23×C47—22no—
295C23×C47—22no—
296C23×C47—22no—
297C23×C47—42no—
298C23×C47—42no—
299C23×C47—42no—
300C23×C47C22×D412yes—
301C23×C47C22×D411yescharacteristic
302C22×D47—22no—
303C22×D47—22no—
304C22×D47—22no—
305C22×D47—22no—
306C22×D47—42no—
307C22×D47—42no—
308C22×D47—42no—
309C22×D47C22×D412yes—
310Q8×C47—24no—
311Q8×C47—22no—
312Q8×C47C2×#4114yes—
313D4×C47—22no—
314D4×C47—22no—
315D4×C47—48no—
316D4×C47—42no—
317C2×C4×C47—24no—
318C2×C4×C47—22no—
319C2×C4×C47—22no—
320C2×C4×C47—24no—
321C2×C4×C47—22no—
322C2×C4×C47—22no—
323C2×C4×C47—22no—
324C2×C4×C47—22no—
325C2×C4×C47—48no—
326C2×C4×C47—42no—
327C2×C4×C47—42no—
328C2×C4×C47—84no—
329C2×C4×C47C22×D412yes—
330C2×C4×C47C22×D411yescharacteristic
331C2×C4×C47C2×#4112yes—
332C2×C4×C47H(5,𝔽2)12yes—
333C2×C4×C47C2511yescharacteristic
334C22⋊D47—28no—
335C22⋊D47—48no—
336C22⋊D47—84no—
337C22⋊D47—84no—
338C22⋊D47—84no—
339C2×Dic47—22no—
340C2×Dic47—22no—
341C2×Dic47—22no—
342C2×Dic47—22no—
343C2×Dic47—22no—
344C2×Dic47—42no—
345C2×Dic47—42no—
346C2×Dic47—42no—
347C2×Dic47#13714yes—
348C2×Dic47C22×D412yes—
349C2×Dic47C22×D412yes—
350C2×Dic47C22×D412yes—
351D188—22no—
352D188—22no—
353D188—48no—
354D188—42no—
355C4×D47—24no—
356C4×D47—22no—
357C4×D47—22no—
358C4×D47—48no—
359C4×D47—84no—
360Dic94—22no—
361Dic94—22no—
362Dic94—42no—
363Dic94—84no—
364C8×C47—22no—
365C8×C47—22no—
366C47⋊C8—22no—
367C47⋊C8—22no—
368C2×#3333—471nomaximal, Sylow
369C22×C47—22no—
370C22×C47—22no—
371C22×C47—22no—
372C22×C47—44no—
373C22×C47—42no—
374C22×C47—42no—
375C22×C47—42no—
376C22×C47—84no—
377C22×C47#54612yes—
378C22×C47C2×#13712yes—
379C22×C47#57612yes—
380C22×C47C23×D411yescharacteristic
381C2×D47—22no—
382C2×D47—22no—
383C2×D47—22no—
384C2×D47—44no—
385C2×D47—42no—
386C2×D47—42no—
387C2×D47—42no—
388C2×D47—84no—
389C4×C47—24no—
390C4×C47—22no—
391C4×C47—42no—
392C4×C47—42no—
393C4×C47#54612yes—
394C4×C47C22×#4111yescharacteristic
395C4×C47C2×H(5,𝔽2)11yescharacteristic
396Dic47—22no—
397Dic47—22no—
398Dic47—42no—
399Dic47—42no—
400Dic47—42no—
401Dic47C2×#13714yes—
402C2×#554—471no—
403C2×#550—471no—
404#3333—4716no—
405C2×#486—471no—
406C2×#480—471no—
407C2×#480—471no—
408C2×#477—471no—
409C2×#468—471no—
410C2×#468—471no—
411C2×#460—471no—
412C2×#452—471no—
413C2×#452—471no—
414C2×C4×Q16—471no—
415C2×#436—471no—
416C2×#417—471no—
417C2×#417D4711yescharacteristic, complemented
418C2×C47—42no—
419C2×C47—82no—
420C2×C47#333314yescomplemented
421C2×C47C2×#54611yescharacteristic
422C2×C47C22×#13711yescharacteristic
423C2×C47C2×#57611yescharacteristic
424D47—42no—
425D47—82no—
426C22×#41—471no—
427C22×#41C2×D4711yescharacteristic
428C22×Q16—471no—
429C22×SD16—471no—
430C22×SD16—471no—
431C22×M16—471no—
432C22×M16C2×D4711yescharacteristic
433#554—478no—
434#554—944no—
435#550—478no—
436#550—944no—
437C2×C4⋊Q8—471no—
438C2×#127—471no—
439C2×#127—941no—
440C2×#125—941no—
441C2×C22⋊Q8—471no—
442C2×C22⋊Q8—471no—
443C2×C22⋊Q8—941no—
444C2×C22⋊Q8—941no—
445C2×#121—471no—
446C2×#121—471no—
447C2×#121—941no—
448C2×#121—941no—
449C2×C4×Q8—471no—
450C2×C4×Q8—471no—
451C2×C4×D4—471no—
452C2×C4×D4—941no—
453C2×C4×D4—941no—
454C22×C4⋊C4—471no—
455C22×C4⋊C4C2×D4711yescharacteristic
456#486—478no—
457#480—478no—
458#480—478no—
459#477—478no—
460#468—478no—
461#468—478no—
462#460—478no—
463#452—478no—
464#452—478no—
465C4×Q16—478no—
466#436—478no—
467C2×#107—471no—
468C2×#107—471no—
469C2×#107—471no—
470C2×C4⋊C8—471no—
471#417—478no—
472#417C2×D4718yescomplemented
473C2×#103—471no—
474C2×#103—471no—
475C2×#103C2×D4711yescharacteristic
476C2×#103C2×D4711yescharacteristic
477C2×#102—471no—
478C2×#102—471no—
479C2×#102—471no—
480C2×#102—471no—
481C2×#102C2×D4711yescharacteristic
482C2×#102C2×D4711yescharacteristic
483C2×C22⋊C8—471no—
484C2×C22⋊C8—471no—
485C2×C4×C8—471no—
486C47C2×#333311yescharacteristic, complemented, Sylow
487C2×#41—22no—
488C2×#41—24no—
489C2×#41—42no—
490C2×#41—474no—
491C2×#41—942no—
492C2×#41—944no—
493C2×#41—1882no—
494C2×#41C22×D4714yes—
495C22×Q8—471no—
496C22×Q8—941no—
497C22×Q8C22×D4711yescharacteristic
498C22×D4—21no—
499C22×D4—471no—
500C22×D4—471no—
501C22×D4—941no—
502C22×D4—941no—
503C22×D4—941no—
504C22×D4—941no—
505C22×D4—941no—
506C22×D4C22×D4711yescharacteristic
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—471no—
510C23×C4—941no—
511C23×C4—941no—
512C23×C4C22×D4711yescharacteristic
513C2×Q16—474no—
514C2×Q16—944no—
515C2×SD16—474no—
516C2×SD16—474no—
517C2×SD16—1882no—
518C2×SD16—1882no—
519C2×M16—42no—
520C2×M16—474no—
521C2×M16—1882no—
522C2×M16C22×D4714yes—
523C22×C8—471no—
524C22×C8—471no—
525C22×C8C22×D4711yescharacteristic
526C22×C8C22×D4711yescharacteristic
527C4⋊Q8—474no—
528C4⋊Q8—942no—
529#127—474no—
530#127—942no—
531#127—948no—
532#125—948no—
533C22⋊Q8—474no—
534C22⋊Q8—474no—
535C22⋊Q8—948no—
536C22⋊Q8—948no—
537C22⋊Q8—942no—
538C22⋊Q8—942no—
539#121—474no—
540#121—474no—
541#121—948no—
542#121—948no—
543#121—942no—
544#121—942no—
545C4×Q8—474no—
546C4×Q8—474no—
547C4×Q8—942no—
548C4×Q8—942no—
549C4×D4—474no—
550C4×D4—474no—
551C4×D4—948no—
552C4×D4—948no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—22no—
555C2×C4⋊C4—471no—
556C2×C4⋊C4—471no—
557C2×C4⋊C4—471no—
558C2×C4⋊C4—474no—
559C2×C4⋊C4—942no—
560C2×C4⋊C4—941no—
561C2×C4⋊C4—941no—
562C2×C4⋊C4—941no—
563C2×C4⋊C4—941no—
564C2×C4⋊C4—941no—
565C2×C4⋊C4—941no—
566C2×C4⋊C4C22×D4711yescharacteristic
567C2×C4⋊C4C22×D4711yescharacteristic
568C2×C4⋊C4C22×D4714yes—
569C2×C22⋊C4—471no—
570C2×C22⋊C4—471no—
571C2×C22⋊C4—941no—
572C2×C22⋊C4—941no—
573C2×C22⋊C4—941no—
574C2×C22⋊C4—941no—
575C2×C42—471no—
576C2×C42—941no—
577C2×C42—941no—
578#107—474no—
579#107—474no—
580#107—474no—
581C4⋊C8—474no—
582#103—474no—
583#103—474no—
584#103C22×D4714yes—
585#103C22×D4714yes—
586#102—474no—
587#102—474no—
588#102—474no—
589#102—474no—
590#102C22×D4714yes—
591#102C22×D4714yes—
592C22⋊C8—474no—
593C22⋊C8—474no—
594C4×C8—474no—
595C24—21no—
596C24—471no—
597C24—941no—
598C24D4×D4711yescharacteristic
599#41—28no—
600#41—44no—
601#41—48no—
602#41—948no—
603#41—1884no—
604#41—1888no—
605C2×Q8—21no—
606C2×Q8—22no—
607C2×Q8—472no—
608C2×Q8—944no—
609C2×Q8—941no—
610C2×Q8—942no—
611C2×Q8—942no—
612C2×Q8—3762no—
613C2×Q8#1062535014yes—
614C2×Q8C23×D4712yes—
615C2×D4—24no—
616C2×D4—21no—
617C2×D4—22no—
618C2×D4—22no—
619C2×D4—44no—
620C2×D4—474no—
621C2×D4—472no—
622C2×D4—944no—
623C2×D4—944no—
624C2×D4—944no—
625C2×D4—944no—
626C2×D4—944no—
627C2×D4—944no—
628C2×D4—941no—
629C2×D4—942no—
630C2×D4—942no—
631C2×D4—3762no—
632C2×D4—3762no—
633C2×D4—3762no—
634C2×D4—1884no—
635C2×D4—1884no—
636C2×D4C23×D4712yes—
637C22×C4—21no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—24no—
643C22×C4—24no—
644C22×C4—44no—
645C22×C4—82no—
646C22×C4—471no—
647C22×C4—471no—
648C22×C4—471no—
649C22×C4—472no—
650C22×C4—472no—
651C22×C4—944no—
652C22×C4—944no—
653C22×C4—942no—
654C22×C4—942no—
655C22×C4—941no—
656C22×C4—941no—
657C22×C4—941no—
658C22×C4—3762no—
659C22×C4—1884no—
660C22×C4D4×D4712yes—
661C22×C4D4×D4711yescharacteristic
662C22×C4C23×D4712yes—
663C22×C4C23×D4711yescharacteristic
664Q16—948no—
665SD16—1884no—
666SD16—1884no—
667M16—44no—
668M16—1884no—
669C2×C8—22no—
670C2×C8—22no—
671C2×C8—472no—
672C2×C8—472no—
673C2×C8—942no—
674C2×C8—942no—
675C2×C8C23×D4712yes—
676C2×C8C23×D4712yes—
677C4⋊C4—21no—
678C4⋊C4—24no—
679C4⋊C4—21no—
680C4⋊C4—474no—
681C4⋊C4—472no—
682C4⋊C4—472no—
683C4⋊C4—944no—
684C4⋊C4—944no—
685C4⋊C4—944no—
686C4⋊C4—944no—
687C4⋊C4—944no—
688C4⋊C4—944no—
689C4⋊C4—941no—
690C4⋊C4—941no—
691C4⋊C4C23×D4712yes—
692C4⋊C4C23×D4712yes—
693C22⋊C4—474no—
694C22⋊C4—474no—
695C22⋊C4—944no—
696C22⋊C4—944no—
697C22⋊C4—944no—
698C22⋊C4—944no—
699C42—472no—
700C42—472no—
701C42—944no—
702C42—944no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—472no—
711C23—942no—
712C23—942no—
713C23—942no—
714C23—942no—
715C23—1882no—
716C23—1882no—
717C23—1882no—
718C23C2×D4×D4712yes—
719C23C2×D4×D4711yescharacteristic
720Q8—24no—
721Q8—22no—
722Q8—942no—
723Q8—942no—
724Q8—3764no—
725Q8—1882no—
726Q8C2×#1062535014yes—
727D4—22no—
728D4—22no—
729D4—48no—
730D4—42no—
731D4—948no—
732D4—942no—
733D4—942no—
734D4—3764no—
735D4—3764no—
736D4—3764no—
737D4—1888no—
738D4—1888no—
739D4—1882no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—24no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—48no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—84no—
752C2×C4—474no—
753C2×C4—472no—
754C2×C4—472no—
755C2×C4—472no—
756C2×C4—942no—
757C2×C4—942no—
758C2×C4—944no—
759C2×C4—942no—
760C2×C4—942no—
761C2×C4—942no—
762C2×C4—942no—
763C2×C4—942no—
764C2×C4—3764no—
765C2×C4—1888no—
766C2×C4—1882no—
767C2×C4—1882no—
768C2×C4—1882no—
769C2×C4C2×D4×D4712yes—
770C2×C4C2×D4×D4711yescharacteristic
771C2×C4C2×#1062535012yes—
772C2×C4#1309406912yes—
773C2×C4C24×D4711yescharacteristic
774C8—22no—
775C8—22no—
776C8—942no—
777C8—942no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—44no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—84no—
786C22—942no—
787C22—942no—
788C22—942no—
789C22—3764no—
790C22—1882no—
791C22—1882no—
792C22—1882no—
793C22—1884no—
794C22#1568976312yes—
795C22#137×D4712yes—
796C22#1568992712yes—
797C22C22×D4×D4711yescharacteristic
798C4—22no—
799C4—24no—
800C4—42no—
801C4—42no—
802C4—474no—
803C4—942no—
804C4—942no—
805C4—1882no—
806C4—1882no—
807C4—1882no—
808C4#1568976312yes—
809C4C22×#1062535011yescharacteristic
810C4C2×#1309406911yescharacteristic
811C2—42no—
812C2—82no—
813C2—3762no—
814C2—1882no—
815C2#2025572214yesdirect product factor
816C2C2×#1568976311yescharacteristic
817C2C2×#137×D4711yescharacteristic
818C2C2×#1568992711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#417C2
socleC23×C47C22×D4
prime radicalC2×#15689792C2
hypercenterC2×#417D47
hypocenterC47C2×#3333
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×#15689828C2semidirect
3. #20255722C2direct (N × H)
4. C2×#15689468C2semidirect
5. C2×#15689436C2semidirect
6. C2×#15689435C2semidirect
7. C2×#15689416C2semidirect
8. C2×#15689369C2semidirect
9. C2×#15689368C2semidirect
10. C2×#15689322C2semidirect
11. C2×#15689288C2semidirect
12. C2×#15689285C2semidirect
13. C2×#15689215C2semidirect
14. C2×#15689199C2semidirect
15. C2×#15689123C2semidirect
16. C2×C47×#417C2semidirect
23. #15689828C22semidirect
44. #15689468C22semidirect
45. #15689436C22semidirect
46. #15689435C22semidirect
47. #15689416C22semidirect
48. #15689369C22semidirect
49. #15689368C22semidirect
50. #15689322C22semidirect
51. #15689288C22semidirect
52. #15689285C22semidirect
53. #15689215C22semidirect
54. #15689199C22semidirect
59. #15689123C22semidirect
72. C47×#417C22semidirect
417. C2×#417D47semidirect
420. C2×C47#3333semidirect
472. #417C2×D47semidirect
486. C47C2×#3333semidirect
815. C2#20255722direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898282
C2×#156897922
#202557222
C2×#156894682
C2×#156894362
C2×#156894352
C2×#156894162
C2×#156893692
C2×#156893682
C2×#156893222
C2×#156892882
C2×#156892852
C2×#156892152
C2×#156891992
C2×#156891232
C2×C47×#4172
C2×#333347