Finite Group Databasebeta

← C2×#20253443 #27084334

Subgroups — C2×#20253443 #27084334

Order 12032.

2450 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×#15689668C211yesmaximal, characteristic, complemented
2C2×#15689591C211yesmaximal, characteristic, complemented
3#20253443C2116yesmaximal, direct product factor
4C2×#15689447C211yesmaximal, characteristic, complemented
5C2×#15689417C211yesmaximal, characteristic, complemented
6C2×#15689412C211yesmaximal, characteristic, complemented
7C2×#15689322C211yesmaximal, characteristic, complemented
8C2×#15689317C211yesmaximal, characteristic, complemented
9C2×#15689270C211yesmaximal, characteristic, complemented
10C2×#15689266C211yesmaximal, characteristic, complemented
11C2×#15689214C211yesmaximal, characteristic, complemented
12C2×#15689210C211yesmaximal, characteristic, complemented
13C2×#15689205C211yesmaximal, characteristic, complemented
14C2×#15689203C211yesmaximal, characteristic, complemented
15C2×#15689173C211yesmaximal, characteristic, complemented
16C2×C47×#482C211yesmaximal, characteristic, complemented
17C22×#10625350C2211yescharacteristic
18C22×#10625352—21no—
19C22×#10625325C2211yescharacteristic
20C22×#10625335C2211yescharacteristic
21C22×D376C2211yescharacteristic
22C22×#10625334C2211yescharacteristic
23#15689668—24no—
24#15689668C2218yescomplemented
25C2×#13094023C2211yescharacteristic
26C2×#13094020C2211yescharacteristic
27C2×#13094010—21no—
28C2×#13093998C2211yescharacteristic
29C2×#13093996—21no—
30#15689591—24no—
31#15689591C2218yescomplemented
32C2×#13093989C2211yescharacteristic
33C2×#13093989C2211yescharacteristic
34C2×D4×Dic47C2211yescharacteristic
35C2×#13093986C2211yescharacteristic
36C2×#13093986C2211yescharacteristic
37C2×#13093986C2211yescharacteristic
38C2×(C22⋊D47)⋊C4—21no—
39C2×(C22⋊D47)⋊C4—21no—
40C2×(C22⋊D47)⋊C4—21no—
41C2×#13093981—21no—
42C22×C4×Dic47C2211yescharacteristic
43C2×C42×D47—21no—
44#15689447C2218yescomplemented
45#15689417C2218yescomplemented
46#15689412C2218yescomplemented
47#15689322C2218yescomplemented
48#15689317C2218yescomplemented
49#15689270C2218yescomplemented
50#15689266C2218yescomplemented
51#15689214C2218yescomplemented
52#15689210C2218yescomplemented
53#15689205C2218yescomplemented
54#15689203C2218yescomplemented
55#15689173C2218yescomplemented
56C2×#13093957C2211yescharacteristic
57C2×#13093955C2211yescharacteristic
58C2×Dic47⋊C8C2211yescharacteristic
59C2×Dic47⋊C8C2211yescharacteristic
60C2×#13093949C2211yescharacteristic
61C2×#13093947C2211yescharacteristic
62C2×#13093946C2211yescharacteristic
63C2×#13093944C2211yescharacteristic
64C2×#13093944C2211yescharacteristic
65C2×#13093944C2211yescharacteristic
66C2×C22⋊(C47⋊C8)C2211yescharacteristic
67C2×C8×Dic47C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C2×#121×C47C2211yescharacteristic
70C2×#117×C47C2211yescharacteristic
71C47×#482C2218yescomplemented
72C2×#107×C47C2211yescharacteristic
73C2×#106×C47C2211yescharacteristic
74C2×#102×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×C22⋊C8×C47C2211yescharacteristic
77C2×#10625350—22no—
78C2×#10625350—24no—
79C2×#10625350—24no—
80C2×#10625350C2314yes—
81C2×#10625352—28no—
82C2×#10625352—48no—
83C22×Dic94—21no—
84C22×Dic94C2311yescharacteristic
85C22×D188C2311yescharacteristic
86C22×D188C2311yescharacteristic
87C22×C22⋊D47—21no—
88C22×C22⋊D47—21no—
89C22×C22⋊D47—21no—
90C22×C22⋊D47—21no—
91C23×Dic47—21no—
92C23×Dic47D411yescharacteristic
93C23×Dic47D411yescharacteristic
94C22×C4×D47—21no—
95C22×C4×D47—21no—
96C22×C4×D47—21no—
97C22×C4×D47—21no—
98C2×#10625325—24no—
99C2×#10625325C2314yes—
100C2×#10625335—24no—
101C2×#10625335C2314yes—
102C2×D376—24no—
103C2×D376C2314yes—
104C2×#10625334—24no—
105C2×#10625334C2314yes—
106C22×C47⋊C8C2311yescharacteristic
107C22×C47⋊C8C2311yescharacteristic
108#13094023—22no—
109#13094023C2314yes—
110#13094020—22no—
111#13094020C2314yes—
112#13094010—28no—
113#13093998—22no—
114#13093998C2314yes—
115#13093996—28no—
116#13093989—22no—
117#13093989—22no—
118#13093989C2314yes—
119#13093989C2314yes—
120D4×Dic47—22no—
121D4×Dic47C2314yes—
122#13093986—22no—
123#13093986—22no—
124#13093986—22no—
125#13093986C2314yes—
126#13093986C2314yes—
127#13093986C2314yes—
128(C22⋊D47)⋊C4—28no—
129(C22⋊D47)⋊C4—28no—
130(C22⋊D47)⋊C4—28no—
131#13093981—28no—
132C2×C4⋊Dic47C2311yescharacteristic
133C2×Dic47⋊C4—21no—
134C2×Dic47⋊C4—21no—
135C2×Dic47⋊C4—21no—
136C2×C22⋊Dic47—21no—
137C2×(C2×D47)⋊C4—21no—
138C2×(C2×D47)⋊C4—21no—
139C2×(C2×D47)⋊C4—21no—
140C2×(C2×D47)⋊C4—21no—
141C2×C4×Dic47—21no—
142C2×C4×Dic47—21no—
143C2×C4×Dic47D411yescharacteristic
144C2×C4×Dic47D411yescharacteristic
145C2×C4×Dic47D414yes—
146C2×C4×Dic47C2311yescharacteristic
147C2×C4×Dic47C2311yescharacteristic
148C2×C4×Dic47C2314yes—
149C42×D47—28no—
150#13093957C2314yes—
151#13093955C2314yes—
152Dic47⋊C8C2314yes—
153Dic47⋊C8C2314yes—
154#13093949C2314yes—
155#13093947C2314yes—
156#13093946C2314yes—
157#13093944C2314yes—
158#13093944C2314yes—
159#13093944C2314yes—
160C22⋊(C47⋊C8)C2314yes—
161C8×Dic47C2314yes—
162C8×Dic47C2314yes—
163C22×D4×C47—21no—
164C22×D4×C47C2311yescharacteristic
165C23×C4×C47C2311yescharacteristic
166C22×C8×C47C2311yescharacteristic
167C22×C8×C47C2311yescharacteristic
168#121×C47—22no—
169#121×C47C2314yes—
170#117×C47—22no—
171#117×C47C2314yes—
172C2×C4⋊C4×C47C2311yescharacteristic
173C2×C4⋊C4×C47C2311yescharacteristic
174C2×C4⋊C4×C47C2311yescharacteristic
175C2×C22⋊C4×C47—21no—
176C2×C22⋊C4×C47—21no—
177C2×C42×C47—21no—
178#107×C47C2314yes—
179#106×C47C2314yes—
180#102×C47C2314yes—
181#102×C47C2314yes—
182C22⋊C8×C47C2314yes—
183C24×C47—21no—
184C24×C47C2×D411yescharacteristic
185C23×D47—21no—
186C23×D47—21no—
187C2×D4×C47—24no—
188C2×D4×C47—21no—
189C2×D4×C47—22no—
190C2×D4×C47—22no—
191C2×D4×C47—44no—
192C2×D4×C47C2412yes—
193C22×C4×C47—22no—
194C22×C4×C47—22no—
195C22×C4×C47—21no—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47C2×D411yescharacteristic
199C22×C4×C47C2×D412yes—
200C22×C4×C47C2412yes—
201C22×C4×C47C2411yescharacteristic
202C2×C22⋊D47—28no—
203C2×C22⋊D47—24no—
204C2×C22⋊D47—24no—
205C2×C22⋊D47—24no—
206C2×C22⋊D47—24no—
207C2×C22⋊D47—44no—
208C2×C22⋊D47—44no—
209C2×C22⋊D47—44no—
210C22×Dic47—21no—
211C22×Dic47—24no—
212C22×Dic47—24no—
213C22×Dic47—21no—
214C22×Dic47—24no—
215C22×Dic47—44no—
216C22×Dic47C2×D411yescharacteristic
217C22×Dic47C2×D411yescharacteristic
218C22×Dic47C2×D414yes—
219C22×Dic47C2×D414yes—
220C22×Dic47C2×D411yescharacteristic
221C22×Dic47C2×D411yescharacteristic
222#10625352—432no—
223#10625350—216no—
224#10625350—28no—
225#10625350—28no—
226C2×D188—21no—
227C2×D188—22no—
228C2×D188—22no—
229C2×D188—22no—
230C2×D188—21no—
231C2×D188#4114yescomplemented
232C2×D188C2412yes—
233C2×D188C2412yes—
234C2×C4×D47—28no—
235C2×C4×D47—24no—
236C2×C4×D47—24no—
237C2×C4×D47—24no—
238C2×C4×D47—24no—
239C2×C4×D47—44no—
240C2×C4×D47—44no—
241C2×C4×D47—44no—
242C2×Dic94—21no—
243C2×Dic94—22no—
244C2×Dic94—24no—
245C2×Dic94—44no—
246C2×Dic94#4114yescomplemented
247C2×Dic94C2412yes—
248C2×C8×C47—22no—
249C2×C8×C47—22no—
250C2×C8×C47C2412yes—
251C2×C8×C47C2412yes—
252C4⋊C4×C47—21no—
253C4⋊C4×C47—21no—
254C4⋊C4×C47—21no—
255C4⋊C4×C47C2412yes—
256C4⋊C4×C47C2412yes—
257C4⋊C4×C47C2412yes—
258C22⋊C4×C47—24no—
259C22⋊C4×C47—24no—
260C42×C47—24no—
261C22⋊Dic47—24no—
262#10625335—28no—
263#10625334—28no—
264(C2×D47)⋊C4—24no—
265(C2×D47)⋊C4—24no—
266(C2×D47)⋊C4—24no—
267(C2×D47)⋊C4—24no—
268C4⋊Dic47—21no—
269C4⋊Dic47C2412yes—
270Dic47⋊C4—24no—
271Dic47⋊C4—24no—
272Dic47⋊C4—24no—
273C4×Dic47—24no—
274C4×Dic47—24no—
275C4×Dic47C2×D414yes—
276C4×Dic47C2×D414yes—
277C4×Dic47C2×D412yes—
278C4×Dic47C2×D412yes—
279C4×Dic47C2412yes—
280C4×Dic47C2412yes—
281C2×C47⋊C8—22no—
282C2×C47⋊C8—22no—
283C2×C47⋊C8C2412yes—
284C2×C47⋊C8C2412yes—
285D376—28no—
286#10625325—28no—
287C23×C47—22no—
288C23×C47—22no—
289C23×C47—22no—
290C23×C47—22no—
291C23×C47—42no—
292C23×C47—42no—
293C23×C47—42no—
294C23×C47C22×D412yes—
295C23×C47C22×D411yescharacteristic
296C22×D47—24no—
297C22×D47—22no—
298C22×D47—22no—
299C22×D47—42no—
300C22×D47—42no—
301C22×D47—42no—
302C22×D47—42no—
303C22×D47—42no—
304D4×C47—22no—
305D4×C47—22no—
306D4×C47—48no—
307D4×C47—42no—
308C2×C4×C47—22no—
309C2×C4×C47—24no—
310C2×C4×C47—22no—
311C2×C4×C47—22no—
312C2×C4×C47—22no—
313C2×C4×C47—22no—
314C2×C4×C47—22no—
315C2×C4×C47—42no—
316C2×C4×C47—42no—
317C2×C4×C47—42no—
318C2×C4×C47C22×D412yes—
319C2×C4×C47C22×D411yescharacteristic
320C2×C4×C47C2×#4112yes—
321C2×C4×C47C2×#4112yes—
322C2×C4×C47C2511yescharacteristic
323C22⋊D47—216no—
324C22⋊D47—48no—
325C22⋊D47—48no—
326C22⋊D47—48no—
327C2×Dic47—24no—
328C2×Dic47—22no—
329C2×Dic47—22no—
330C2×Dic47—22no—
331C2×Dic47—28no—
332C2×Dic47—28no—
333C2×Dic47—22no—
334C2×Dic47—42no—
335C2×Dic47—48no—
336C2×Dic47#13514yes—
337C2×Dic47AGL(1,ℤ/8)14yes—
338C2×Dic47C22×D412yes—
339C2×Dic47C22×D412yes—
340C2×Dic47C22×D412yes—
341C2×Dic47C22×D412yes—
342D188—24no—
343D188—22no—
344D188—22no—
345D188—22no—
346D188—42no—
347D188C2×#4114yescomplemented
348C4×D47—216no—
349C4×D47—48no—
350C4×D47—48no—
351C4×D47—48no—
352Dic94—24no—
353Dic94—22no—
354Dic94—48no—
355Dic94C2×#4114yescomplemented
356C8×C47—22no—
357C8×C47—22no—
358C47⋊C8—22no—
359C47⋊C8—22no—
360C2×#3106—471nomaximal, Sylow
361C22×C47—22no—
362C22×C47—22no—
363C22×C47—22no—
364C22×C47—44no—
365C22×C47—42no—
366C22×C47—42no—
367C22×C47—42no—
368C22×C47—84no—
369C22×C47#52512yes—
370C22×C47C2×#13512yes—
371C22×C47C2×AGL(1,ℤ/8)12yes—
372C22×C47C23×D411yescharacteristic
373C2×D47—24no—
374C2×D47—48no—
375C2×D47—42no—
376C2×D47—42no—
377C2×D47—42no—
378C2×D47—42no—
379C2×D47—42no—
380C2×D47—84no—
381C4×C47—22no—
382C4×C47—42no—
383C4×C47—42no—
384C4×C47—42no—
385C4×C47#52512yes—
386C4×C47C22×#4111yescharacteristic
387C4×C47C22×#4111yescharacteristic
388Dic47—24no—
389Dic47—22no—
390Dic47—22no—
391Dic47—42no—
392Dic47C2×#13514yes—
393Dic47C2×AGL(1,ℤ/8)14yes—
394C2×#532—471no—
395C2×C4×#41—471no—
396#3106—4716no—
397C2×#482—471no—
398C2×#482D4711yescharacteristic, complemented
399C2×#477—471no—
400C2×#476—471no—
401C2×#460—471no—
402C2×#459—471no—
403C2×#449—471no—
404C2×#449—471no—
405C2×C4×SD16—471no—
406C2×C4×SD16—471no—
407C2×C4×D8—471no—
408C2×C4×D8—471no—
409C2×#431—471no—
410C2×C47—42no—
411C2×C47—82no—
412C2×C47#310614yescomplemented
413C2×C47C2×#52511yescharacteristic
414C2×C47C22×#13511yescharacteristic
415C2×C47C22×AGL(1,ℤ/8)11yescharacteristic
416D47—44no—
417D47—82no—
418C22×#41—471no—
419C22×#41—941no—
420C22×SD16—471no—
421C22×SD16—471no—
422C22×D8—471no—
423C22×D8—471no—
424#532—478no—
425#532—944no—
426C2×C4⋊Q8—471no—
427C2×#127—471no—
428C2×#124—941no—
429C2×#121—471no—
430C2×#121—941no—
431C2×#121C2×D4711yescharacteristic
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—471no—
439C2×C4×D4—471no—
440C2×C4×D4—941no—
441C2×C4×D4—941no—
442C2×C4×D4—941no—
443C2×#117—941no—
444C2×#117C2×D4711yescharacteristic
445C22×C42—471no—
446C22×C42—941no—
447#482—478no—
448#482C2×D4718yescomplemented
449#477—478no—
450#476—478no—
451#460—478no—
452#459—478no—
453#449—478no—
454#449—478no—
455C4×SD16—478no—
456C4×SD16—478no—
457C4×D8—478no—
458C4×D8—478no—
459#431—478no—
460C2×#107—471no—
461C2×#107C2×D4711yescharacteristic
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⋊C8C2×D4711yescharacteristic
476C2×C4×C8—471no—
477C2×C4×C8—471no—
478C47C2×#310611yescharacteristic, complemented, Sylow
479C2×#41—474no—
480C2×#41—944no—
481C2×#41—944no—
482C2×#41—948no—
483C2×#41—942no—
484C2×#41—1888no—
485C22×Q8—471no—
486C22×Q8—941no—
487C22×D4—21no—
488C22×D4—471no—
489C22×D4—471no—
490C22×D4—941no—
491C22×D4—941no—
492C22×D4—941no—
493C22×D4—941no—
494C22×D4C22×D4711yescharacteristic
495C23×C4—471no—
496C23×C4—471no—
497C23×C4—941no—
498C23×C4—941no—
499C23×C4—941no—
500C23×C4—941no—
501C23×C4—941no—
502C23×C4C22×D4711yescharacteristic
503C2×SD16—474no—
504C2×SD16—474no—
505C2×SD16—944no—
506C2×SD16—944no—
507C2×D8—474no—
508C2×D8—474no—
509C2×D8—944no—
510C2×D8—944no—
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—22no—
521#121—474no—
522#121—948no—
523#121—942no—
524#121C22×D4714yes—
525C4×Q8—474no—
526C4×Q8—474no—
527C4×Q8—942no—
528C4×Q8—942no—
529C4×D4—474no—
530C4×D4—474no—
531C4×D4—474no—
532C4×D4—474no—
533C4×D4—948no—
534C4×D4—942no—
535C4×D4—942no—
536C4×D4—942no—
537C4×D4—942no—
538C4×D4—948no—
539C4×D4—948no—
540#117—22no—
541#117—948no—
542#117C22×D4714yes—
543C2×C4⋊C4—471no—
544C2×C4⋊C4—941no—
545C2×C4⋊C4—941no—
546C2×C4⋊C4—941no—
547C2×C4⋊C4C22×D4711yescharacteristic
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—21no—
558C2×C42—471no—
559C2×C42—471no—
560C2×C42—474no—
561C2×C42—471no—
562C2×C42—471no—
563C2×C42—474no—
564C2×C42—948no—
565C2×C42—941no—
566C2×C42—941no—
567#107—474no—
568#107C22×D4714yes—
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⋊C8C22×D4714yes—
583C4×C8—474no—
584C4×C8—474no—
585C24—21no—
586C24—941no—
587C24—941no—
588C24D4×D4711yescharacteristic
589#41—948no—
590#41—948no—
591#41—9416no—
592#41—18832no—
593C2×Q8—474no—
594C2×Q8—472no—
595C2×Q8—944no—
596C2×Q8—941no—
597C2×Q8—942no—
598C2×Q8—1884no—
599C2×D4—24no—
600C2×D4—21no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—44no—
604C2×D4—474no—
605C2×D4—472no—
606C2×D4—472no—
607C2×D4—944no—
608C2×D4—944no—
609C2×D4—948no—
610C2×D4—944no—
611C2×D4—944no—
612C2×D4—941no—
613C2×D4—941no—
614C2×D4—942no—
615C2×D4—942no—
616C2×D4—942no—
617C2×D4—1884no—
618C2×D4—1884no—
619C2×D4—1884no—
620C2×D4C23×D4712yes—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—471no—
627C22×C4—471no—
628C22×C4—474no—
629C22×C4—474no—
630C22×C4—471no—
631C22×C4—471no—
632C22×C4—944no—
633C22×C4—944no—
634C22×C4—944no—
635C22×C4—948no—
636C22×C4—944no—
637C22×C4—944no—
638C22×C4—944no—
639C22×C4—941no—
640C22×C4—944no—
641C22×C4—941no—
642C22×C4—1884no—
643C22×C4—1884no—
644C22×C4—1884no—
645C22×C4—1884no—
646C22×C4D4×D4712yes—
647C22×C4D4×D4711yescharacteristic
648C22×C4C23×D4712yes—
649C22×C4C23×D4711yescharacteristic
650SD16—948no—
651SD16—948no—
652D8—948no—
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—21no—
665C4⋊C4—472no—
666C4⋊C4—944no—
667C4⋊C4—944no—
668C4⋊C4—944no—
669C4⋊C4—941no—
670C4⋊C4C23×D4712yes—
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—24no—
681C42—474no—
682C42—474no—
683C42—472no—
684C42—472no—
685C42—472no—
686C42—472no—
687C42—944no—
688C42—944no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—944no—
697C23—942no—
698C23—942no—
699C23—1882no—
700C23—1882no—
701C23—1882no—
702C23—1882no—
703C23—1882no—
704C23C2×D4×D4712yes—
705C23C2×D4×D4711yescharacteristic
706Q8—474no—
707Q8—944no—
708Q8—942no—
709Q8—1888no—
710D4—22no—
711D4—22no—
712D4—48no—
713D4—42no—
714D4—474no—
715D4—9416no—
716D4—944no—
717D4—942no—
718D4—942no—
719D4—942no—
720D4—1888no—
721D4—1888no—
722D4—1888no—
723D4—1882no—
724C2×C4—22no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—474no—
735C2×C4—474no—
736C2×C4—472no—
737C2×C4—472no—
738C2×C4—472no—
739C2×C4—472no—
740C2×C4—9416no—
741C2×C4—948no—
742C2×C4—948no—
743C2×C4—944no—
744C2×C4—942no—
745C2×C4—942no—
746C2×C4—942no—
747C2×C4—942no—
748C2×C4—1888no—
749C2×C4—1888no—
750C2×C4—1888no—
751C2×C4—1888no—
752C2×C4—1882no—
753C2×C4C2×D4×D4712yes—
754C2×C4C2×D4×D4711yescharacteristic
755C2×C4#41×D4712yes—
756C2×C4#41×D4712yes—
757C2×C4C24×D4711yescharacteristic
758C8—22no—
759C8—22no—
760C8—942no—
761C8—942no—
762C22—22no—
763C22—22no—
764C22—22no—
765C22—44no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—84no—
770C22—944no—
771C22—3764no—
772C22—1882no—
773C22—1882no—
774C22—1882no—
775C22—1888no—
776C22—1882no—
777C22—1882no—
778C22#1568963112yes—
779C22#135×D4712yes—
780C22AGL(1,ℤ/8)×D4712yes—
781C22C22×D4×D4711yescharacteristic
782C4—22no—
783C4—42no—
784C4—42no—
785C4—42no—
786C4—474no—
787C4—474no—
788C4—942no—
789C4—942no—
790C4—944no—
791C4—1882no—
792C4#1568963112yes—
793C4C2×#41×D4711yescharacteristic
794C4C2×#41×D4711yescharacteristic
795C2—42no—
796C2—82no—
797C2—3762no—
798C2—1884no—
799C2#2025344314yesdirect product factor
800C2C2×#1568963111yescharacteristic
801C2C2×#135×D4711yescharacteristic
802C2C2×AGL(1,ℤ/8)×D4711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#482C2
socleC23×C47C22×D4
hypercenterC2×#482D47
hypocenterC47C2×#3106
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
1. C2×#15689668C2semidirect
2. C2×#15689591C2semidirect
3. #20253443C2direct (N × H)
4. C2×#15689447C2semidirect
5. C2×#15689417C2semidirect
6. C2×#15689412C2semidirect
7. C2×#15689322C2semidirect
8. C2×#15689317C2semidirect
9. C2×#15689270C2semidirect
10. C2×#15689266C2semidirect
11. C2×#15689214C2semidirect
12. C2×#15689210C2semidirect
13. C2×#15689205C2semidirect
14. C2×#15689203C2semidirect
15. C2×#15689173C2semidirect
16. C2×C47×#482C2semidirect
24. #15689668C22semidirect
31. #15689591C22semidirect
44. #15689447C22semidirect
45. #15689417C22semidirect
46. #15689412C22semidirect
47. #15689322C22semidirect
48. #15689317C22semidirect
49. #15689270C22semidirect
50. #15689266C22semidirect
51. #15689214C22semidirect
52. #15689210C22semidirect
53. #15689205C22semidirect
54. #15689203C22semidirect
55. #15689173C22semidirect
71. C47×#482C22semidirect
231. C2×D188#41semidirect
246. C2×Dic94#41semidirect
347. D188C2×#41semidirect
355. Dic94C2×#41semidirect
398. C2×#482D47semidirect
412. C2×C47#3106semidirect
448. #482C2×D47semidirect
478. C47C2×#3106semidirect
799. C2#20253443direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896682
C2×#156895912
#202534432
C2×#156894472
C2×#156894172
C2×#156894122
C2×#156893222
C2×#156893172
C2×#156892702
C2×#156892662
C2×#156892142
C2×#156892102
C2×#156892052
C2×#156892032
C2×#156891732
C2×C47×#4822
C2×#310647