Finite Group Databasebeta

← C2×#20253743 #27085515

Subgroups — C2×#20253743 #27085515

Order 12032.

2262 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689753C211yesmaximal, characteristic, complemented
2C2×#15689686C211yesmaximal, characteristic
3#20253743C2116yesmaximal, direct product factor
4C2×#15689486C211yesmaximal, characteristic, complemented
5C2×#15689483C211yesmaximal, characteristic, complemented
6C2×#15689481C211yesmaximal, characteristic, complemented
7C2×#15689480C211yesmaximal, characteristic, complemented
8C2×#15689476C211yesmaximal, characteristic, complemented
9C2×#15689469C211yesmaximal, characteristic, complemented
10C2×#15689468C211yesmaximal, characteristic, complemented
11C2×#15689121C211yesmaximal, characteristic, complemented
12C2×#15689126C211yesmaximal, characteristic, complemented
13C2×#15689116C211yesmaximal, characteristic, complemented
14C2×#102×D47C211yesmaximal, characteristic, complemented
15C2×#15689080C211yesmaximal, characteristic, complemented
16C2×C47×#490C211yesmaximal, characteristic, complemented
17C22×#10625352C2211yescharacteristic
18C22×D4×D47C2211yescharacteristic
19C22×#10625324C2211yescharacteristic
20C22×C8×D47C2211yescharacteristic
21#15689753—24no—
22#15689753C2218yescomplemented
23#15689686—24no—
24#15689686C2218yes—
25C2×#13094024C2211yescharacteristic, complemented
26C2×#13094023—21no—
27C2×#13094023C2211yescharacteristic, complemented
28C2×#13094020C2211yescharacteristic
29C2×#13094015C2211yescharacteristic, complemented
30C2×#13094014—21no—
31C2×#13094012C2211yescharacteristic
32C2×#13094011C2211yescharacteristic
33C2×#13094004—21no—
34C2×#13094002—21no—
35C2×#13093996—21no—
36C2×#13093996—21no—
37C2×#13093992—21no—
38C2×#13093992—21no—
39C2×#13093982C2211yescharacteristic
40C2×#13093981C2211yescharacteristic
41C2×C4⋊C4×D47C2211yescharacteristic
42#15689486C2218yescomplemented
43#15689483C2218yescomplemented
44#15689481C2218yescomplemented
45#15689480C2218yescomplemented
46#15689476C2218yescomplemented
47#15689469C2218yescomplemented
48#15689468C2218yescomplemented
49#15689126C2218yescomplemented
50#15689121C2218yescomplemented
51#15689116C2218yescomplemented
52C2×#13093949C2211yescharacteristic, complemented
53C2×#13093949C2211yescharacteristic, complemented
54C2×#13093947C2211yescharacteristic, complemented
55C2×#13093947C2211yescharacteristic, complemented
56C2×#13093946C2211yescharacteristic
57C2×#13093946C2211yescharacteristic
58C2×#13093945C2211yescharacteristic
59C2×#13093945C2211yescharacteristic
60C2×#13093945C2211yescharacteristic, complemented
61C2×#13093945C2211yescharacteristic, complemented
62C2×#13093944C2211yescharacteristic
63C2×#13093944C2211yescharacteristic
64#102×D47C2218yescomplemented
65#15689080C2218yescomplemented
66C2×#13093934C2211yescharacteristic, complemented
67C2×C4×C47⋊C8C2211yescharacteristic, complemented
68C2×C8×Dic47C2211yescharacteristic, complemented
69C2×#127×C47C2211yescharacteristic
70C2×#125×C47C2211yescharacteristic, complemented
71C47×#490C2218yescomplemented
72C2×#102×C47C2211yescharacteristic
73C2×#102×C47C2211yescharacteristic
74C2×#102×C47C2211yescharacteristic, complemented
75C2×#102×C47C2211yescharacteristic, complemented
76C2×#97×C47C2211yescharacteristic, complemented
77C24×D47—21no—
78C2×#10625352—22no—
79C2×#10625352—24no—
80C2×#10625352—24no—
81C2×#10625352C2314yes—
82C22×Dic94—21no—
83C22×Dic94—21no—
84C22×Dic94C2311yescharacteristic
85C22×D188C2311yescharacteristic
86C22×C22⋊D47—21no—
87C22×C22⋊D47—21no—
88C22×C22⋊D47—21no—
89C22×C22⋊D47—21no—
90C2×D4×D47—22no—
91C2×D4×D47—24no—
92C2×D4×D47—24no—
93C2×D4×D47C2314yes—
94C23×Dic47—21no—
95C22×C4×D47—21no—
96C22×C4×D47C2311yescharacteristic
97C2×#10625324—24no—
98C2×#10625324C2314yes—
99C22×C47⋊C8C2311yescharacteristic
100C22×C47⋊C8C2311yescharacteristic
101C2×C8×D47—24no—
102C2×C8×D47C2314yes—
103#13094024—22no—
104#13094024C2314yescomplemented
105#13094023—28no—
106#13094023—22no—
107#13094023C2314yescomplemented
108#13094020—22no—
109#13094020C2314yes—
110#13094015—22no—
111#13094015C2314yescomplemented
112#13094014—28no—
113#13094012—22no—
114#13094012C2314yes—
115#13094011—22no—
116#13094011C2314yes—
117#13094004—28no—
118#13094002—28no—
119#13093996—28no—
120#13093996—28no—
121#13093992—28no—
122#13093992—28no—
123#13093982—22no—
124#13093982C2314yes—
125#13093981D414yes—
126#13093981C2314yes—
127C2×C4⋊Dic47—21no—
128C2×C4⋊Dic47—21no—
129C2×C4⋊Dic47C2311yescharacteristic
130C2×C4⋊Dic47C2311yescharacteristic
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4—21no—
133C2×Dic47⋊C4—21no—
134C2×Dic47⋊C4D411yescharacteristic
135C2×Dic47⋊C4D411yescharacteristic
136C4⋊C4×D47—22no—
137C4⋊C4×D47C2314yes—
138C2×C22⋊Dic47—21no—
139C2×C22⋊Dic47—21no—
140C2×(C2×D47)⋊C4—21no—
141C2×(C2×D47)⋊C4—21no—
142C2×(C2×D47)⋊C4—21no—
143C2×(C2×D47)⋊C4D411yescharacteristic
144C2×(C2×D47)⋊C4D411yescharacteristic
145C2×C4×Dic47—21no—
146C2×C4×Dic47C2311yescharacteristic
147#13093949C2314yescomplemented
148#13093949C2314yescomplemented
149#13093947C2314yescomplemented
150#13093947C2314yescomplemented
151#13093946C2314yes—
152#13093946C2314yes—
153#13093945C2314yes—
154#13093945C2314yes—
155#13093945C2314yescomplemented
156#13093945C2314yescomplemented
157#13093944C2314yes—
158#13093944C2314yes—
159#13093934C2314yescomplemented
160C4×C47⋊C8C2314yescomplemented
161C8×Dic47C2314yescomplemented
162C22×D4×C47—21no—
163C22×D4×C47—21no—
164C22×D4×C47C2311yescharacteristic
165C22×D4×C47C2311yescharacteristic
166C22×C8×C47C2311yescharacteristic
167C22×C8×C47C2311yescharacteristic
168#127×C47—22no—
169#127×C47C2314yes—
170#125×C47—22no—
171#125×C47C2314yescomplemented
172C2×C4⋊C4×C47—21no—
173C2×C4⋊C4×C47—21no—
174C2×C4⋊C4×C47C2311yescharacteristic
175C2×C4⋊C4×C47C2311yescharacteristic
176C2×C42×C47C2311yescharacteristic
177#102×C47C2314yes—
178#102×C47C2314yes—
179#102×C47C2314yescomplemented
180#102×C47C2314yescomplemented
181#97×C47C2314yescomplemented
182C24×C47—21no—
183C24×C47—21no—
184C23×D47—21no—
185C23×D47—24no—
186C23×D47—44no—
187C23×D47—82no—
188C23×D47—82no—
189C23×D47C2×D411yescharacteristic
190C2×D4×C47—21no—
191C2×D4×C47—21no—
192C2×D4×C47—24no—
193C2×D4×C47—24no—
194C2×D4×C47—22no—
195C2×D4×C47—22no—
196C2×D4×C47—22no—
197C2×D4×C47—22no—
198C2×D4×C47—82no—
199C2×D4×C47—82no—
200C2×D4×C47C2412yes—
201C2×D4×C47C2412yes—
202C22×C4×C47—21no—
203C22×C4×C47—21no—
204C22×C4×C47C2×D411yescharacteristic
205C22×C4×C47C2×D411yescharacteristic
206C22×C4×C47C2411yescharacteristic
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—82no—
214C2×C22⋊D47—82no—
215C22×Dic47—21no—
216C22×Dic47—21no—
217C22×Dic47—21no—
218C22×Dic47—24no—
219C22×Dic47—44no—
220C22×Dic47C2×D411yescharacteristic
221C22×Dic47C2×D411yescharacteristic
222C22×Dic47C2×D411yescharacteristic
223#10625352—28no—
224#10625352—28no—
225#10625352—48no—
226D4×D47—28no—
227D4×D47—28no—
228D4×D47—48no—
229C2×D188—22no—
230C2×D188—22no—
231C2×D188—21no—
232C2×D188C2412yes—
233C2×C4×D47—24no—
234C2×C4×D47—82no—
235C2×C4×D47C2×D412yes—
236C2×C4×D47#4114yes—
237C2×C4×D47#4114yes—
238C2×C4×D47C2412yes—
239C2×Dic94—22no—
240C2×Dic94—22no—
241C2×Dic94—21no—
242C2×Dic94—24no—
243C2×Dic94—24no—
244C2×Dic94—82no—
245C2×Dic94—82no—
246C2×Dic94C2412yes—
247C2×C8×C47—22no—
248C2×C8×C47—22no—
249C2×C8×C47C2412yes—
250C2×C8×C47C2412yes—
251C4⋊C4×C47—24no—
252C4⋊C4×C47—24no—
253C4⋊C4×C47—21no—
254C4⋊C4×C47—21no—
255C4⋊C4×C47C2412yes—
256C4⋊C4×C47C2412yes—
257C42×C47C2×D412yes—
258C42×C47C2412yes—
259C22⋊Dic47—24no—
260C22⋊Dic47—24no—
261(C2×D47)⋊C4—24no—
262(C2×D47)⋊C4—24no—
263(C2×D47)⋊C4—24no—
264(C2×D47)⋊C4C2×D414yes—
265(C2×D47)⋊C4C2×D414yes—
266C4⋊Dic47—21no—
267C4⋊Dic47—24no—
268C4⋊Dic47—21no—
269C4⋊Dic47—24no—
270C4⋊Dic47C2412yes—
271C4⋊Dic47C2412yes—
272Dic47⋊C4—24no—
273Dic47⋊C4—24no—
274Dic47⋊C4—24no—
275Dic47⋊C4C2×D414yes—
276Dic47⋊C4C2×D414yes—
277C4×Dic47—24no—
278C4×Dic47C2×D412yes—
279C4×Dic47C2412yes—
280C2×C47⋊C8—22no—
281C2×C47⋊C8—22no—
282C2×C47⋊C8C2412yes—
283C2×C47⋊C8C2412yes—
284#10625324—28no—
285C8×D47—28no—
286C23×C47—22no—
287C23×C47—22no—
288C23×C47—42no—
289C23×C47—42no—
290C23×C47—42no—
291C23×C47—42no—
292C23×C47—42no—
293C23×C47—42no—
294C23×C47C22×D411yescharacteristic
295C22×D47—22no—
296C22×D47—22no—
297C22×D47—22no—
298C22×D47—42no—
299C22×D47—42no—
300C22×D47—42no—
301C22×D47—48no—
302C22×D47—84no—
303C22×D47—84no—
304C22×D47—816no—
305C22×D47#12414yes—
306C22×D47C22×D412yes—
307D4×C47—22no—
308D4×C47—22no—
309D4×C47—22no—
310D4×C47—22no—
311D4×C47—42no—
312D4×C47—42no—
313D4×C47—84no—
314D4×C47—84no—
315C2×C4×C47—22no—
316C2×C4×C47—22no—
317C2×C4×C47—22no—
318C2×C4×C47—22no—
319C2×C4×C47—42no—
320C2×C4×C47—42no—
321C2×C4×C47C22×D412yes—
322C2×C4×C47C22×D412yes—
323C2×C4×C47C22×D411yescharacteristic
324C2×C4×C47C2×#4112yes—
325C2×C4×C47C2×#4112yes—
326C2×C4×C47C2511yescharacteristic
327C22⋊D47—48no—
328C22⋊D47—48no—
329C22⋊D47—84no—
330C22⋊D47—84no—
331C2×Dic47—22no—
332C2×Dic47—22no—
333C2×Dic47—22no—
334C2×Dic47—22no—
335C2×Dic47—22no—
336C2×Dic47—42no—
337C2×Dic47—42no—
338C2×Dic47—42no—
339C2×Dic47—48no—
340C2×Dic47#12414yes—
341C2×Dic47C22×D412yes—
342C2×Dic47C22×D412yes—
343C2×Dic47C22×D412yes—
344D188—22no—
345D188—22no—
346D188—42no—
347C4×D47—84no—
348C4×D47#12418yes—
349C4×D47C2×#4114yes—
350C4×D47C2×#4114yes—
351Dic94—22no—
352Dic94—22no—
353Dic94—42no—
354Dic94—84no—
355Dic94—84no—
356C8×C47—22no—
357C8×C47—22no—
358C47⋊C8—22no—
359C47⋊C8—22no—
360C2×#3136—471nomaximal, Sylow
361C22×C47—42no—
362C22×C47—42no—
363C22×C47—42no—
364C22×C47—42no—
365C22×C47—42no—
366C22×C47—42no—
367C22×C47—84no—
368C22×C47—84no—
369C22×C47C2×#12412yes—
370C22×C47#57612yes—
371C22×C47#57712yes—
372C22×C47C23×D411yescharacteristic
373C2×D47—28no—
374C2×D47—22no—
375C2×D47—22no—
376C2×D47—42no—
377C2×D47—42no—
378C2×D47—42no—
379C2×D47—816no—
380C2×D47—84no—
381C2×D47C2×#12414yes—
382C4×C47—22no—
383C4×C47—22no—
384C4×C47—42no—
385C4×C47—42no—
386C4×C47C2×#12412yes—
387C4×C47C22×#4111yescharacteristic
388C4×C47C22×#4111yescharacteristic
389Dic47—22no—
390Dic47—22no—
391Dic47—42no—
392Dic47—42no—
393Dic47—42no—
394Dic47C2×#12414yes—
395C2×#544—471no—
396C2×#535—471no—
397#3136—4716no—
398C2×#490—471no—
399C2×#490D4711yescharacteristic, complemented
400C2×#489—471no—
401C2×#489—471no—
402C2×#488—471no—
403C2×#488—471no—
404C2×#486—471no—
405C2×#486—471no—
406C2×#417—471no—
407C2×#418—471no—
408C2×#416—471no—
409C22×#102—471no—
410C2×#405—471no—
411C2×C47—82no—
412C2×C47—82no—
413C2×C47#313614yescomplemented
414C2×C47C22×#12411yescharacteristic
415C2×C47C2×#57611yescharacteristic
416C2×C47C2×#57711yescharacteristic
417D47—24no—
418D47—82no—
419C22×#41—471no—
420C23×D4—471no—
421C22×M16—471no—
422C23×C8—471no—
423#544—478no—
424#544—944no—
425#535—478no—
426#535—944no—
427C2×C4⋊Q8—471no—
428C2×C4⋊Q8—471no—
429C2×C4⋊Q8—941no—
430C2×#127—471no—
431C2×#127C2×D4711yescharacteristic
432C2×#125—471no—
433C2×#125—941no—
434C2×#125C2×D4711yescharacteristic, complemented
435C2×#124—471no—
436C2×#124—471no—
437C2×C22⋊Q8—941no—
438C2×C22⋊Q8—941no—
439C2×#121—941no—
440C2×#121—941no—
441C2×#120—941no—
442C2×#120—941no—
443C2×#117—471no—
444C2×#117—471no—
445C22×C4⋊C4—471no—
446#490—478no—
447#490C2×D4718yescomplemented
448#489—478no—
449#489—478no—
450#488—478no—
451#488—478no—
452#486—478no—
453#486—478no—
454#418—478no—
455#417—478no—
456#416—478no—
457C2×#103—471no—
458C2×#103—471no—
459C2×#103—471no—
460C2×#103—471no—
461C2×#102—471no—
462C2×#102—471no—
463C2×#102—471no—
464C2×#102—471no—
465C2×#102—471no—
466C2×#102—471no—
467C2×#102—471no—
468C2×#102—471no—
469C2×#102—478no—
470C2×#102C2×D4711yescharacteristic
471C2×#102C2×D4711yescharacteristic
472C2×#102C2×D4711yescharacteristic, complemented
473C2×#102C2×D4711yescharacteristic, complemented
474#405—478no—
475C2×#97—471no—
476C2×#97C2×D4711yescharacteristic, complemented
477C2×C4×C8—471no—
478C2×C4×C8—471no—
479C47C2×#313611yescharacteristic, complemented, Sylow
480C25—941no—
481C2×#41—474no—
482C2×#41—942no—
483C2×#41—944no—
484C2×#41—944no—
485C22×Q8—471no—
486C22×Q8—941no—
487C22×Q8—941no—
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—474no—
491C22×D4—471no—
492C22×D4—944no—
493C22×D4—944no—
494C22×D4—942no—
495C22×D4—941no—
496C22×D4—941no—
497C22×D4—941no—
498C22×D4—941no—
499C22×D4C22×D4711yescharacteristic
500C22×D4C22×D4711yescharacteristic
501C23×C4—471no—
502C23×C4—941no—
503C23×C4—941no—
504C2×M16—474no—
505C2×M16—944no—
506C22×C8—471no—
507C22×C8—471no—
508C22×C8—474no—
509C22×C8—944no—
510C22×C8C22×D4711yescharacteristic
511C22×C8C22×D4711yescharacteristic
512C4⋊Q8—474no—
513C4⋊Q8—474no—
514C4⋊Q8—942no—
515C4⋊Q8—948no—
516C4⋊Q8—942no—
517#127—22no—
518#127—474no—
519#127—942no—
520#127C22×D4714yes—
521#125—22no—
522#125—474no—
523#125—942no—
524#125—948no—
525#125C22×D4714yescomplemented
526#124—474no—
527#124—474no—
528#124—942no—
529#124—942no—
530C22⋊Q8—948no—
531C22⋊Q8—948no—
532#121—948no—
533#121—948no—
534#120—948no—
535#120—948no—
536#117—474no—
537#117—474no—
538#117—474no—
539#117—942no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—471no—
543C2×C4⋊C4—471no—
544C2×C4⋊C4—471no—
545C2×C4⋊C4—471no—
546C2×C4⋊C4—474no—
547C2×C4⋊C4—942no—
548C2×C4⋊C4—941no—
549C2×C4⋊C4—941no—
550C2×C4⋊C4—941no—
551C2×C4⋊C4—941no—
552C2×C4⋊C4—941no—
553C2×C4⋊C4C22×D4711yescharacteristic
554C2×C4⋊C4C22×D4711yescharacteristic
555C2×C22⋊C4—471no—
556C2×C22⋊C4—471no—
557C2×C22⋊C4—941no—
558C2×C22⋊C4—941no—
559C2×C22⋊C4—941no—
560C2×C22⋊C4—941no—
561C2×C22⋊C4—941no—
562C2×C42—471no—
563C2×C42—941no—
564C2×C42C22×D4711yescharacteristic
565#103—474no—
566#103—474no—
567#103—474no—
568#103—474no—
569#102—474no—
570#102—474no—
571#102—474no—
572#102—474no—
573#102—474no—
574#102—474no—
575#102—474no—
576#102—474no—
577#102C22×D4714yes—
578#102C22×D4714yes—
579#102C22×D4714yescomplemented
580#102C22×D4714yescomplemented
581#97—474no—
582#97C22×D4714yescomplemented
583C4×C8—474no—
584C4×C8—474no—
585C24—21no—
586C24—21no—
587C24—471no—
588C24—944no—
589C24—941no—
590C24—3762no—
591C24—3762no—
592C24—1884no—
593#41—948no—
594#41—948no—
595#41—1888no—
596C2×Q8—472no—
597C2×Q8—944no—
598C2×Q8—944no—
599C2×Q8—941no—
600C2×Q8—942no—
601C2×Q8—942no—
602C2×Q8—3762no—
603C2×Q8—3762no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—24no—
607C2×D4—24no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—82no—
613C2×D4—82no—
614C2×D4—472no—
615C2×D4—948no—
616C2×D4—948no—
617C2×D4—944no—
618C2×D4—944no—
619C2×D4—944no—
620C2×D4—944no—
621C2×D4—941no—
622C2×D4—942no—
623C2×D4—942no—
624C2×D4—3762no—
625C2×D4—3762no—
626C2×D4—1888no—
627C2×D4—1884no—
628C2×D4—1884no—
629C2×D4C23×D4712yes—
630C2×D4C23×D4712yes—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—471no—
634C22×C4—472no—
635C22×C4—474no—
636C22×C4—474no—
637C22×C4—472no—
638C22×C4—471no—
639C22×C4—471no—
640C22×C4—944no—
641C22×C4—944no—
642C22×C4—941no—
643C22×C4—941no—
644C22×C4—941no—
645C22×C4—3762no—
646C22×C4—1884no—
647C22×C4D4×D4711yescharacteristic
648C22×C4D4×D4711yescharacteristic
649C22×C4C23×D4711yescharacteristic
650M16—948no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—472no—
654C2×C8—472no—
655C2×C8—948no—
656C2×C8—942no—
657C2×C8—942no—
658C2×C8C23×D4712yes—
659C2×C8C23×D4712yes—
660C4⋊C4—24no—
661C4⋊C4—24no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—474no—
665C4⋊C4—474no—
666C4⋊C4—472no—
667C4⋊C4—472no—
668C4⋊C4—944no—
669C4⋊C4—944no—
670C4⋊C4—944no—
671C4⋊C4—944no—
672C4⋊C4—941no—
673C4⋊C4—941no—
674C4⋊C4—944no—
675C4⋊C4C23×D4712yes—
676C4⋊C4C23×D4712yes—
677C22⋊C4—474no—
678C22⋊C4—474no—
679C22⋊C4—944no—
680C22⋊C4—944no—
681C22⋊C4—944no—
682C22⋊C4—944no—
683C22⋊C4—944no—
684C42—472no—
685C42—472no—
686C42—944no—
687C42D4×D4712yes—
688C42C23×D4712yes—
689C23—22no—
690C23—22no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—474no—
698C23—472no—
699C23—942no—
700C23—942no—
701C23—942no—
702C23—3764no—
703C23—3764no—
704C23—37616no—
705C23—1888no—
706C23—1882no—
707C23—1882no—
708C23—1882no—
709C23C2×D4×D4711yescharacteristic
710Q8—942no—
711Q8—942no—
712Q8—3764no—
713Q8—3764no—
714Q8—1882no—
715D4—22no—
716D4—22no—
717D4—22no—
718D4—22no—
719D4—42no—
720D4—42no—
721D4—84no—
722D4—84no—
723D4—942no—
724D4—942no—
725D4—3764no—
726D4—3764no—
727D4—1888no—
728D4—1888no—
729D4—1882no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—474no—
737C2×C4—472no—
738C2×C4—478no—
739C2×C4—474no—
740C2×C4—474no—
741C2×C4—472no—
742C2×C4—472no—
743C2×C4—942no—
744C2×C4—942no—
745C2×C4—942no—
746C2×C4—942no—
747C2×C4—942no—
748C2×C4—3764no—
749C2×C4—1888no—
750C2×C4—1882no—
751C2×C4—1882no—
752C2×C4—1882no—
753C2×C4C2×D4×D4712yes—
754C2×C4C2×D4×D4712yes—
755C2×C4C2×D4×D4711yescharacteristic
756C2×C4#41×D4712yes—
757C2×C4#41×D4712yes—
758C2×C4C24×D4711yescharacteristic
759C8—22no—
760C8—22no—
761C8—942no—
762C8—942no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—84no—
770C22—84no—
771C22—474no—
772C22—948no—
773C22—942no—
774C22—942no—
775C22—37616no—
776C22—3764no—
777C22—1882no—
778C22—1882no—
779C22—1882no—
780C22#124×D4712yes—
781C22#1568992712yes—
782C22#1568993312yes—
783C22C22×D4×D4711yescharacteristic
784C4—22no—
785C4—22no—
786C4—42no—
787C4—42no—
788C4—474no—
789C4—942no—
790C4—942no—
791C4—1882no—
792C4—1882no—
793C4—1882no—
794C4#124×D4712yes—
795C4C2×#41×D4711yescharacteristic
796C4C2×#41×D4711yescharacteristic
797C2—82no—
798C2—82no—
799C2—944no—
800C2—3762no—
801C2#2025374314yesdirect product factor
802C2C2×#124×D4711yescharacteristic
803C2C2×#1568992711yescharacteristic
804C2C2×#1568993311yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#490C2
socleC23×C47C22×D4
prime radicalC2×#15689686C2
hypercenterC2×#490D47
hypocenterC47C2×#3136
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#490

Complements

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

NH ≅ G/Ntype
1. C2×#15689753C2semidirect
3. #20253743C2direct (N × H)
4. C2×#15689486C2semidirect
5. C2×#15689483C2semidirect
6. C2×#15689481C2semidirect
7. C2×#15689480C2semidirect
8. C2×#15689476C2semidirect
9. C2×#15689469C2semidirect
10. C2×#15689468C2semidirect
11. C2×#15689121C2semidirect
12. C2×#15689126C2semidirect
13. C2×#15689116C2semidirect
14. C2×#102×D47C2semidirect
15. C2×#15689080C2semidirect
16. C2×C47×#490C2semidirect
22. #15689753C22semidirect
25. C2×#13094024C22semidirect
27. C2×#13094023C22semidirect
29. C2×#13094015C22semidirect
42. #15689486C22semidirect
43. #15689483C22semidirect
44. #15689481C22semidirect
45. #15689480C22semidirect
46. #15689476C22semidirect
47. #15689469C22semidirect
48. #15689468C22semidirect
49. #15689126C22semidirect
50. #15689121C22semidirect
51. #15689116C22semidirect
52. C2×#13093949C22semidirect
53. C2×#13093949C22semidirect
54. C2×#13093947C22semidirect
55. C2×#13093947C22semidirect
60. C2×#13093945C22semidirect
61. C2×#13093945C22semidirect
64. #102×D47C22semidirect
65. #15689080C22semidirect
66. C2×#13093934C22semidirect
67. C2×C4×C47⋊C8C22semidirect
68. C2×C8×Dic47C22semidirect
70. C2×#125×C47C22semidirect
71. C47×#490C22semidirect
74. C2×#102×C47C22semidirect
75. C2×#102×C47C22semidirect
76. C2×#97×C47C22semidirect
104. #13094024C23semidirect
107. #13094023C23semidirect
111. #13094015C23semidirect
147. #13093949C23semidirect
148. #13093949C23semidirect
149. #13093947C23semidirect
150. #13093947C23semidirect
155. #13093945C23semidirect
156. #13093945C23semidirect
159. #13093934C23semidirect
160. C4×C47⋊C8C23semidirect
161. C8×Dic47C23semidirect
171. #125×C47C23semidirect
179. #102×C47C23semidirect
180. #102×C47C23semidirect
181. #97×C47C23semidirect
399. C2×#490D47semidirect
413. C2×C47#3136semidirect
434. C2×#125C2×D47semidirect
447. #490C2×D47semidirect
472. C2×#102C2×D47semidirect
473. C2×#102C2×D47semidirect
476. C2×#97C2×D47semidirect
479. C47C2×#3136semidirect
525. #125C22×D47semidirect
579. #102C22×D47semidirect
580. #102C22×D47semidirect
582. #97C22×D47semidirect
801. C2#20253743direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897532
C2×#156896862
#202537432
C2×#156894862
C2×#156894832
C2×#156894812
C2×#156894802
C2×#156894762
C2×#156894692
C2×#156894682
C2×#156891212
C2×#156891262
C2×#156891162
C2×#102×D472
C2×#156890802
C2×C47×#4902
C2×#313647