Finite Group Databasebeta

← C2×#20253535 #27084400

Subgroups — C2×#20253535 #27084400

Order 12032.

2430 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689670C211yesmaximal, characteristic, complemented
2C2×C4×#10625352C211yesmaximal, characteristic, complemented
3#20253535C2116yesmaximal, direct product factor
4C2×#15689449C211yesmaximal, characteristic, complemented
5C2×#15689445C211yesmaximal, characteristic, complemented
6C2×#15689407C211yesmaximal, characteristic, complemented
7C2×#15689401C211yesmaximal, characteristic, complemented
8C2×#15689322C211yesmaximal, characteristic, complemented
9C2×#15689316C211yesmaximal, characteristic, complemented
10C2×#15689269C211yesmaximal, characteristic, complemented
11C2×#15689265C211yesmaximal, characteristic, complemented
12C2×#15689233C211yesmaximal, characteristic, complemented
13C2×#15689225C211yesmaximal, characteristic, complemented
14C2×#15689223C211yesmaximal, characteristic, complemented
15C2×#15689178C211yesmaximal, characteristic, complemented
16C2×C47×#442C211yesmaximal, characteristic, complemented
17C22×#10625350—21no—
18C22×#10625352C2211yescharacteristic
19C22×#10625325C2211yescharacteristic
20C22×#10625335C2211yescharacteristic
21C22×#10625334C2211yescharacteristic
22#15689670—24no—
23#15689670C2218yescomplemented
24C2×#13094023C2211yescharacteristic
25C2×#13094020C2211yescharacteristic
26C2×#13094010—21no—
27C2×#13093999C2211yescharacteristic
28C2×#13093997—21no—
29C2×#13093995C2211yescharacteristic
30C4×#10625352—24no—
31C4×#10625352C2218yescomplemented
32C2×C4×Dic94C2211yescharacteristic
33C2×#13093989C2211yescharacteristic
34C2×C4×D188C2211yescharacteristic
35C2×D4×Dic47C2211yescharacteristic
36C2×C4×C22⋊D47—21no—
37C2×C4×C22⋊D47—21no—
38C2×(C22⋊D47)⋊C4—21no—
39C2×#13093982C2211yescharacteristic
40C2×#13093980—21no—
41C22×C4×Dic47—21no—
42C2×C42×D47C2211yescharacteristic
43#15689449C2218yescomplemented
44#15689445C2218yescomplemented
45#15689407C2218yescomplemented
46#15689401C2218yescomplemented
47#15689322C2218yescomplemented
48#15689316C2218yescomplemented
49#15689269C2218yescomplemented
50#15689265C2218yescomplemented
51#15689233C2218yescomplemented
52#15689225C2218yescomplemented
53#15689223C2218yescomplemented
54#15689178C2218yescomplemented
55C2×#13093958C2211yescharacteristic
56C2×#13093957C2211yescharacteristic
57C2×#13093955C2211yescharacteristic
58C2×Dic47⋊C8C2211yescharacteristic
59C2×Dic47⋊C8C2211yescharacteristic
60C2×#13093949C2211yescharacteristic
61C2×#13093947C2211yescharacteristic
62C2×#13093946C2211yescharacteristic
63C2×#13093945C2211yescharacteristic
64C2×#13093945C2211yescharacteristic
65C2×#13093944C2211yescharacteristic
66C2×(C2×D47)⋊C8C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×#13093935C2211yescharacteristic
69C22×D8×C47C2211yescharacteristic
70C2×C4×D4×C47C2211yescharacteristic
71C2×C4×D4×C47C2211yescharacteristic
72C47×#442C2218yescomplemented
73C2×#106×C47C2211yescharacteristic
74C2×#102×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×#97×C47C2211yescharacteristic
77C2×#10625350—28no—
78C2×#10625350—48no—
79C2×#10625352—24no—
80C2×#10625352—22no—
81C2×#10625352—24no—
82C2×#10625352C2314yes—
83C22×Dic94—21no—
84C22×Dic94C2311yescharacteristic
85C22×D188—21no—
86C22×D188C2311yescharacteristic
87C22×C22⋊D47—21no—
88C22×C22⋊D47—21no—
89C22×C22⋊D47—21no—
90C22×C22⋊D47—21no—
91C23×Dic47—21no—
92C23×Dic47—21no—
93C22×C4×D47—21no—
94C22×C4×D47D411yescharacteristic
95C22×C4×D47D411yescharacteristic
96C22×C4×D47C2311yescharacteristic
97C2×#10625325—24no—
98C2×#10625325C2314yes—
99C2×#10625335—24no—
100C2×#10625335C2314yes—
101C2×#10625334—24no—
102C2×#10625334C2314yes—
103C22×C47⋊C8C2311yescharacteristic
104C22×C47⋊C8C2311yescharacteristic
105#13094023—22no—
106#13094023C2314yes—
107#13094020—22no—
108#13094020C2314yes—
109#13094010—28no—
110#13093999—22no—
111#13093999C2314yes—
112#13093997—28no—
113#13093995—22no—
114#13093995C2314yes—
115C4×Dic94—22no—
116C4×Dic94C2314yes—
117#13093989—22no—
118#13093989C2314yes—
119C4×D188—22no—
120C4×D188C2314yes—
121D4×Dic47—22no—
122D4×Dic47C2314yes—
123C4×C22⋊D47—28no—
124C4×C22⋊D47—28no—
125(C22⋊D47)⋊C4—28no—
126#13093982—22no—
127#13093982C2314yes—
128#13093980—28no—
129C2×C4⋊Dic47C2311yescharacteristic
130C2×C4⋊Dic47C2311yescharacteristic
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4—21no—
133C2×Dic47⋊C4—21no—
134C2×C22⋊Dic47—21no—
135C2×C22⋊Dic47—21no—
136C2×(C2×D47)⋊C4—21no—
137C2×(C2×D47)⋊C4—21no—
138C2×(C2×D47)⋊C4—21no—
139C2×C4×Dic47—21no—
140C2×C4×Dic47—21no—
141C2×C4×Dic47—21no—
142C2×C4×Dic47—28no—
143C2×C4×Dic47D411yescharacteristic
144C2×C4×Dic47D411yescharacteristic
145C2×C4×Dic47C2311yescharacteristic
146C42×D47D414yes—
147C42×D47C2314yes—
148#13093958C2314yes—
149#13093957C2314yes—
150#13093955C2314yes—
151Dic47⋊C8C2314yes—
152Dic47⋊C8C2314yes—
153#13093949C2314yes—
154#13093947C2314yes—
155#13093946C2314yes—
156#13093945C2314yes—
157#13093945C2314yes—
158#13093944C2314yes—
159(C2×D47)⋊C8C2314yes—
160(C2×D47)⋊C8C2314yes—
161#13093935C2314yes—
162C22×D4×C47C2311yescharacteristic
163C22×D4×C47C2311yescharacteristic
164C23×C4×C47—21no—
165C23×C4×C47—21no—
166C2×D8×C47—24no—
167C2×D8×C47C2314yes—
168C22×C8×C47C2311yescharacteristic
169C22×C8×C47C2311yescharacteristic
170C4×D4×C47—22no—
171C4×D4×C47—22no—
172C4×D4×C47C2314yes—
173C4×D4×C47C2314yes—
174C2×C4⋊C4×C47C2311yescharacteristic
175C2×C4⋊C4×C47C2311yescharacteristic
176C2×C22⋊C4×C47—21no—
177C2×C22⋊C4×C47—21no—
178C2×C42×C47C2311yescharacteristic
179#106×C47C2314yes—
180#102×C47C2314yes—
181#102×C47C2314yes—
182#97×C47C2314yes—
183C24×C47—21no—
184C24×C47—21no—
185C23×D47—21no—
186C23×D47C2×D411yescharacteristic
187C2×D4×C47—21no—
188C2×D4×C47—21no—
189C2×D4×C47—22no—
190C2×D4×C47—22no—
191C2×D4×C47—22no—
192C2×D4×C47#4114yescomplemented
193C2×D4×C47C2412yes—
194C2×D4×C47C2412yes—
195C22×C4×C47—21no—
196C22×C4×C47—21no—
197C22×C4×C47—24no—
198C22×C4×C47—24no—
199C22×C4×C47—44no—
200C22×C4×C47—44no—
201C22×C4×C47C2×D411yescharacteristic
202C22×C4×C47C2×D411yescharacteristic
203C22×C4×C47C2411yescharacteristic
204C2×C22⋊D47—28no—
205C2×C22⋊D47—24no—
206C2×C22⋊D47—24no—
207C2×C22⋊D47—24no—
208C2×C22⋊D47—24no—
209C2×C22⋊D47—44no—
210C2×C22⋊D47—44no—
211C2×C22⋊D47—44no—
212C22×Dic47—28no—
213C22×Dic47—21no—
214C22×Dic47—24no—
215C22×Dic47—21no—
216C22×Dic47—21no—
217C22×Dic47—24no—
218C22×Dic47—44no—
219C22×Dic47C2×D411yescharacteristic
220C22×Dic47C2×D411yescharacteristic
221C22×Dic47C2×D411yescharacteristic
222#10625352—216no—
223#10625352—28no—
224#10625352—28no—
225#10625350—432no—
226C2×D188—22no—
227C2×D188—22no—
228C2×D188—24no—
229C2×D188—21no—
230C2×D188—44no—
231C2×D188C2412yes—
232C2×C4×D47—22no—
233C2×C4×D47—22no—
234C2×C4×D47—24no—
235C2×C4×D47—24no—
236C2×C4×D47—42no—
237C2×C4×D47—44no—
238C2×C4×D47C2×D412yes—
239C2×C4×D47C2×D414yes—
240C2×C4×D47C2×D414yes—
241C2×C4×D47C2412yes—
242C2×Dic94—21no—
243C2×Dic94—22no—
244C2×Dic94—24no—
245C2×Dic94—44no—
246C2×Dic94#4114yescomplemented
247C2×Dic94C2412yes—
248D8×C47—28no—
249C2×C8×C47—22no—
250C2×C8×C47—22no—
251C2×C8×C47C2412yes—
252C2×C8×C47C2412yes—
253C4⋊C4×C47—21no—
254C4⋊C4×C47—21no—
255C4⋊C4×C47C2412yes—
256C4⋊C4×C47C2412yes—
257C22⋊C4×C47—24no—
258C22⋊C4×C47—24no—
259C42×C47C2×D412yes—
260C42×C47C2412yes—
261C22⋊Dic47—24no—
262C22⋊Dic47—24no—
263#10625335—28no—
264#10625334—28no—
265(C2×D47)⋊C4—24no—
266(C2×D47)⋊C4—24no—
267(C2×D47)⋊C4—24no—
268C4⋊Dic47—21no—
269C4⋊Dic47—21no—
270C4⋊Dic47C2412yes—
271C4⋊Dic47C2412yes—
272Dic47⋊C4—24no—
273Dic47⋊C4—24no—
274Dic47⋊C4—24no—
275C4×Dic47—24no—
276C4×Dic47—24no—
277C4×Dic47—24no—
278C4×Dic47C2×D412yes—
279C4×Dic47C2×D414yes—
280C4×Dic47C2×D414yes—
281C4×Dic47C2412yes—
282C2×C47⋊C8—22no—
283C2×C47⋊C8—22no—
284C2×C47⋊C8C2412yes—
285C2×C47⋊C8C2412yes—
286#10625325—28no—
287C23×C47—24no—
288C23×C47—22no—
289C23×C47—22no—
290C23×C47—42no—
291C23×C47—42no—
292C23×C47—42no—
293C23×C47—42no—
294C23×C47—42no—
295C23×C47C22×D411yescharacteristic
296C22×D47—22no—
297C22×D47—22no—
298C22×D47—22no—
299C22×D47—22no—
300C22×D47—42no—
301C22×D47—42no—
302C22×D47—42no—
303C22×D47C22×D412yes—
304D4×C47—24no—
305D4×C47—22no—
306D4×C47—22no—
307D4×C47—22no—
308D4×C47—42no—
309D4×C47C2×#4114yescomplemented
310C2×C4×C47—22no—
311C2×C4×C47—22no—
312C2×C4×C47—22no—
313C2×C4×C47—22no—
314C2×C4×C47—48no—
315C2×C4×C47—48no—
316C2×C4×C47—42no—
317C2×C4×C47—42no—
318C2×C4×C47C22×D412yes—
319C2×C4×C47C22×D412yes—
320C2×C4×C47C22×D411yescharacteristic
321C2×C4×C47C2×#4112yes—
322C2×C4×C47C2×#4112yes—
323C2×C4×C47C2511yescharacteristic
324C22⋊D47—216no—
325C22⋊D47—48no—
326C22⋊D47—48no—
327C22⋊D47—48no—
328C2×Dic47—216no—
329C2×Dic47—24no—
330C2×Dic47—22no—
331C2×Dic47—22no—
332C2×Dic47—22no—
333C2×Dic47—22no—
334C2×Dic47—22no—
335C2×Dic47—42no—
336C2×Dic47—42no—
337C2×Dic47—48no—
338C2×Dic47AGL(1,ℤ/8)14yes—
339C2×Dic47C22×D412yes—
340C2×Dic47C22×D412yes—
341C2×Dic47C22×D412yes—
342D188—22no—
343D188—22no—
344D188—48no—
345D188—42no—
346C4×D47—24no—
347C4×D47—22no—
348C4×D47—22no—
349C4×D47—28no—
350C4×D47—44no—
351C4×D47—48no—
352Dic94—24no—
353Dic94—22no—
354Dic94—48no—
355Dic94C2×#4114yescomplemented
356C8×C47—22no—
357C8×C47—22no—
358C47⋊C8—22no—
359C47⋊C8—22no—
360C2×#3115—471nomaximal, Sylow
361C22×C47—24no—
362C22×C47—48no—
363C22×C47—42no—
364C22×C47—42no—
365C22×C47—42no—
366C22×C47—42no—
367C22×C47—42no—
368C22×C47—84no—
369C22×C47#52512yes—
370C22×C47C2×AGL(1,ℤ/8)12yes—
371C22×C47#57512yes—
372C22×C47C23×D411yescharacteristic
373C2×D47—22no—
374C2×D47—22no—
375C2×D47—22no—
376C2×D47—44no—
377C2×D47—42no—
378C2×D47—42no—
379C2×D47—42no—
380C2×D47—84no—
381C4×C47—22no—
382C4×C47—22no—
383C4×C47—42no—
384C4×C47—42no—
385C4×C47#52512yes—
386C4×C47C22×#4111yescharacteristic
387C4×C47C22×#4111yescharacteristic
388Dic47—24no—
389Dic47—22no—
390Dic47—22no—
391Dic47—42no—
392Dic47—42no—
393Dic47C2×AGL(1,ℤ/8)14yes—
394C2×#532—471no—
395C2×C4×#41—471no—
396#3115—4716no—
397C2×#482—471no—
398C2×#482—471no—
399C2×#475—471no—
400C2×#474—471no—
401C2×#460—471no—
402C2×#459—471no—
403C2×#449—471no—
404C2×#449—471no—
405C2×#442—471no—
406C2×#442D4711yescharacteristic, complemented
407C2×#440—471no—
408C2×#440—471no—
409C2×#432—471no—
410C2×C47—44no—
411C2×C47—82no—
412C2×C47#311514yescomplemented
413C2×C47C2×#52511yescharacteristic
414C2×C47C22×AGL(1,ℤ/8)11yescharacteristic
415C2×C47C2×#57511yescharacteristic
416D47—42no—
417D47—82no—
418C22×#41—471no—
419C22×#41—941no—
420C22×SD16—471no—
421C22×SD16—471no—
422C22×D8—471no—
423C22×D8C2×D4711yescharacteristic
424#532—478no—
425#532—944no—
426C2×C4⋊Q8—471no—
427C2×#127—471no—
428C2×#124—941no—
429C2×#121—471no—
430C2×#121—471no—
431C2×#121—941no—
432C4×#41—478no—
433C4×#41—944no—
434C2×C4×Q8—471no—
435C2×C4×Q8—471no—
436C2×C4×D4—471no—
437C2×C4×D4—471no—
438C2×C4×D4—941no—
439C2×C4×D4—941no—
440C2×C4×D4—941no—
441C2×C4×D4C2×D4711yescharacteristic
442C2×C4×D4C2×D4711yescharacteristic
443C2×#117—471no—
444C2×#117—941no—
445C22×C42—471no—
446C22×C42—941no—
447#482—478no—
448#482—478no—
449#475—478no—
450#474—478no—
451#460—478no—
452#459—478no—
453#449—478no—
454#449—478no—
455#442—478no—
456#442C2×D4718yescomplemented
457#440—478no—
458#440—478no—
459#432—478no—
460C2×#107—471no—
461C2×#107—471no—
462C2×#106—471no—
463C2×#106C2×D4711yescharacteristic
464C2×C4⋊C8—471no—
465C2×C4⋊C8—471no—
466C2×#103—471no—
467C2×#103—471no—
468C2×#102—471no—
469C2×#102—471no—
470C2×#102—471no—
471C2×#102—471no—
472C2×#102C2×D4711yescharacteristic
473C2×#102C2×D4711yescharacteristic
474C2×C22⋊C8—471no—
475C2×C22⋊C8—471no—
476C2×#97—471no—
477C2×#97C2×D4711yescharacteristic
478C47C2×#311511yescharacteristic, complemented, Sylow
479C2×#41—474no—
480C2×#41—948no—
481C2×#41—942no—
482C2×#41—944no—
483C2×#41—944no—
484C2×#41—1888no—
485C22×Q8—471no—
486C22×Q8—941no—
487C22×D4—471no—
488C22×D4—941no—
489C22×D4—941no—
490C22×D4—941no—
491C22×D4—941no—
492C22×D4—941no—
493C22×D4C22×D4711yescharacteristic
494C22×D4C22×D4711yescharacteristic
495C23×C4—21no—
496C23×C4—21no—
497C23×C4—471no—
498C23×C4—471no—
499C23×C4—471no—
500C23×C4—941no—
501C23×C4—941no—
502C23×C4—941no—
503C2×SD16—474no—
504C2×SD16—474no—
505C2×SD16—944no—
506C2×SD16—944no—
507C2×D8—24no—
508C2×D8—474no—
509C2×D8—944no—
510C2×D8C22×D4714yes—
511C22×C8—471no—
512C22×C8—471no—
513C22×C8C22×D4711yescharacteristic
514C22×C8C22×D4711yescharacteristic
515C4⋊Q8—474no—
516C4⋊Q8—942no—
517#127—474no—
518#127—942no—
519#124—948no—
520#121—474no—
521#121—474no—
522#121—948no—
523#121—942no—
524#121—942no—
525C4×Q8—474no—
526C4×Q8—474no—
527C4×Q8—942no—
528C4×Q8—942no—
529C4×D4—22no—
530C4×D4—22no—
531C4×D4—474no—
532C4×D4—474no—
533C4×D4—948no—
534C4×D4—942no—
535C4×D4—948no—
536C4×D4—948no—
537C4×D4—942no—
538C4×D4C22×D4714yes—
539C4×D4C22×D4714yes—
540#117—474no—
541#117—948no—
542#117—942no—
543C2×C4⋊C4—471no—
544C2×C4⋊C4—471no—
545C2×C4⋊C4—941no—
546C2×C4⋊C4—941no—
547C2×C4⋊C4—941no—
548C2×C4⋊C4C22×D4711yescharacteristic
549C2×C4⋊C4C22×D4711yescharacteristic
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—941no—
553C2×C22⋊C4—941no—
554C2×C22⋊C4—941no—
555C2×C22⋊C4—941no—
556C2×C22⋊C4—941no—
557C2×C42—471no—
558C2×C42—471no—
559C2×C42—471no—
560C2×C42—474no—
561C2×C42—474no—
562C2×C42—948no—
563C2×C42—941no—
564C2×C42—941no—
565C2×C42—941no—
566C2×C42C22×D4711yescharacteristic
567#107—474no—
568#107—474no—
569#106—474no—
570#106C22×D4714yes—
571C4⋊C8—474no—
572C4⋊C8—474no—
573#103—474no—
574#103—474no—
575#102—474no—
576#102—474no—
577#102—474no—
578#102—474no—
579#102C22×D4714yes—
580#102C22×D4714yes—
581C22⋊C8—474no—
582C22⋊C8—474no—
583#97—474no—
584#97C22×D4714yes—
585C24—21no—
586C24—21no—
587C24—471no—
588C24—941no—
589#41—948no—
590#41—9416no—
591#41—948no—
592#41—18832no—
593C2×Q8—474no—
594C2×Q8—472no—
595C2×Q8—944no—
596C2×Q8—941no—
597C2×Q8—942no—
598C2×Q8—1884no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—22no—
604C2×D4—472no—
605C2×D4—944no—
606C2×D4—944no—
607C2×D4—944no—
608C2×D4—944no—
609C2×D4—948no—
610C2×D4—944no—
611C2×D4—941no—
612C2×D4—942no—
613C2×D4—942no—
614C2×D4—1884no—
615C2×D4—1884no—
616C2×D4—1884no—
617C2×D4—1884no—
618C2×D4#1062535014yescomplemented
619C2×D4C23×D4712yes—
620C2×D4C23×D4712yes—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—24no—
624C22×C4—24no—
625C22×C4—44no—
626C22×C4—44no—
627C22×C4—471no—
628C22×C4—471no—
629C22×C4—471no—
630C22×C4—472no—
631C22×C4—474no—
632C22×C4—472no—
633C22×C4—474no—
634C22×C4—944no—
635C22×C4—944no—
636C22×C4—944no—
637C22×C4—948no—
638C22×C4—941no—
639C22×C4—942no—
640C22×C4—942no—
641C22×C4—941no—
642C22×C4—941no—
643C22×C4—944no—
644C22×C4—1882no—
645C22×C4—1884no—
646C22×C4—1884no—
647C22×C4D4×D4711yescharacteristic
648C22×C4D4×D4711yescharacteristic
649C22×C4C23×D4711yescharacteristic
650SD16—948no—
651SD16—948no—
652D8—28no—
653D8—948no—
654C2×C8—22no—
655C2×C8—22no—
656C2×C8—472no—
657C2×C8—472no—
658C2×C8—942no—
659C2×C8—942no—
660C2×C8C23×D4712yes—
661C2×C8C23×D4712yes—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—472no—
665C4⋊C4—472no—
666C4⋊C4—944no—
667C4⋊C4—944no—
668C4⋊C4—944no—
669C4⋊C4—941no—
670C4⋊C4—941no—
671C4⋊C4C23×D4712yes—
672C4⋊C4C23×D4712yes—
673C22⋊C4—24no—
674C22⋊C4—24no—
675C22⋊C4—944no—
676C22⋊C4—944no—
677C22⋊C4—944no—
678C22⋊C4—944no—
679C22⋊C4—944no—
680C42—474no—
681C42—474no—
682C42—472no—
683C42—472no—
684C42—944no—
685C42—944no—
686C42—944no—
687C42D4×D4712yes—
688C42C23×D4712yes—
689C23—24no—
690C23—22no—
691C23—22no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—472no—
698C23—942no—
699C23—942no—
700C23—942no—
701C23—942no—
702C23—1882no—
703C23—1882no—
704C23—1882no—
705C23C2×D4×D4711yescharacteristic
706Q8—474no—
707Q8—944no—
708Q8—942no—
709Q8—1888no—
710D4—24no—
711D4—22no—
712D4—22no—
713D4—22no—
714D4—42no—
715D4—9416no—
716D4—942no—
717D4—942no—
718D4—1888no—
719D4—1888no—
720D4—1888no—
721D4—1888no—
722D4—1882no—
723D4C2×#1062535014yescomplemented
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—48no—
729C2×C4—48no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—474no—
733C2×C4—472no—
734C2×C4—472no—
735C2×C4—472no—
736C2×C4—948no—
737C2×C4—9416no—
738C2×C4—942no—
739C2×C4—944no—
740C2×C4—942no—
741C2×C4—942no—
742C2×C4—944no—
743C2×C4—942no—
744C2×C4—942no—
745C2×C4—942no—
746C2×C4—942no—
747C2×C4—1884no—
748C2×C4—1888no—
749C2×C4—1888no—
750C2×C4—1882no—
751C2×C4—1882no—
752C2×C4C2×D4×D4712yes—
753C2×C4C2×D4×D4712yes—
754C2×C4C2×D4×D4711yescharacteristic
755C2×C4#41×D4712yes—
756C2×C4C2×#1062535012yes—
757C2×C4C24×D4711yescharacteristic
758C8—22no—
759C8—22no—
760C8—942no—
761C8—942no—
762C22—24no—
763C22—42no—
764C22—42no—
765C22—48no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—84no—
770C22—942no—
771C22—942no—
772C22—942no—
773C22—3764no—
774C22—1882no—
775C22—1882no—
776C22—1882no—
777C22—1884no—
778C22#1568963212yes—
779C22AGL(1,ℤ/8)×D4712yes—
780C22#1568991912yes—
781C22C22×D4×D4711yescharacteristic
782C4—22no—
783C4—22no—
784C4—42no—
785C4—42no—
786C4—474no—
787C4—942no—
788C4—942no—
789C4—944no—
790C4—1882no—
791C4—1882no—
792C4#1568963212yes—
793C4C2×#41×D4711yescharacteristic
794C4C22×#1062535011yescharacteristic
795C2—44no—
796C2—82no—
797C2—3762no—
798C2—1882no—
799C2#2025353514yesdirect product factor
800C2C2×#1568963211yescharacteristic
801C2C2×AGL(1,ℤ/8)×D4711yescharacteristic
802C2C2×#1568991911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#442C2
socleC23×C47C22×D4
hypercenterC2×#442D47
hypocenterC47C2×#3115
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×#15689670C2semidirect
2. C2×C4×#10625352C2semidirect
3. #20253535C2direct (N × H)
4. C2×#15689449C2semidirect
5. C2×#15689445C2semidirect
6. C2×#15689407C2semidirect
7. C2×#15689401C2semidirect
8. C2×#15689322C2semidirect
9. C2×#15689316C2semidirect
10. C2×#15689269C2semidirect
11. C2×#15689265C2semidirect
12. C2×#15689233C2semidirect
13. C2×#15689225C2semidirect
14. C2×#15689223C2semidirect
15. C2×#15689178C2semidirect
16. C2×C47×#442C2semidirect
23. #15689670C22semidirect
31. C4×#10625352C22semidirect
43. #15689449C22semidirect
44. #15689445C22semidirect
45. #15689407C22semidirect
46. #15689401C22semidirect
47. #15689322C22semidirect
48. #15689316C22semidirect
49. #15689269C22semidirect
50. #15689265C22semidirect
51. #15689233C22semidirect
52. #15689225C22semidirect
53. #15689223C22semidirect
54. #15689178C22semidirect
72. C47×#442C22semidirect
192. C2×D4×C47#41semidirect
246. C2×Dic94#41semidirect
309. D4×C47C2×#41semidirect
355. Dic94C2×#41semidirect
406. C2×#442D47semidirect
412. C2×C47#3115semidirect
456. #442C2×D47semidirect
478. C47C2×#3115semidirect
618. C2×D4#10625350semidirect
723. D4C2×#10625350semidirect
799. C2#20253535direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896702
C2×C4×#106253522
#202535352
C2×#156894492
C2×#156894452
C2×#156894072
C2×#156894012
C2×#156893222
C2×#156893162
C2×#156892692
C2×#156892652
C2×#156892332
C2×#156892252
C2×#156892232
C2×#156891782
C2×C47×#4422
C2×#311547