Finite Group Databasebeta

← C2×#20254068 #27086159

Subgroups — C2×#20254068 #27086159

Order 12032.

2034 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689742C211yesmaximal, characteristic, complemented
2C2×#15689727C211yesmaximal, characteristic, complemented
3#20254068C2116yesmaximal, direct product factor
4C2×#15689532C211yesmaximal, characteristic, complemented
5C2×#15689477C211yesmaximal, characteristic, complemented
6C2×#15689469C211yesmaximal, characteristic, complemented
7C2×#15689373C211yesmaximal, characteristic, complemented
8C2×#15689366C211yesmaximal, characteristic, complemented
9C2×#15689356C211yesmaximal, characteristic, complemented
10C2×#15689349C211yesmaximal, characteristic, complemented
11C2×#15689235C211yesmaximal, characteristic, complemented
12C2×#15689224C211yesmaximal, characteristic, complemented
13C2×SD16×Dic47C211yesmaximal, characteristic, complemented
14C2×D8×Dic47C211yesmaximal, characteristic, complemented
15C2×#15689080C211yesmaximal, characteristic, complemented
16C2×C47×#496C211yesmaximal, characteristic, complemented
17C22×#10625324C2211yescharacteristic
18C22×C8×D47C2211yescharacteristic
19#15689742—24no—
20#15689742C2218yescomplemented
21#15689727—24no—
22#15689727C2218yescomplemented
23C2×#13094024C2211yescharacteristic
24C2×#13094017—21no—
25C2×#13094016C2211yescharacteristic
26C2×#13094010—21no—
27C2×#13094008—21no—
28C2×#13094005—21no—
29C2×#13094005—21no—
30C2×#13094001—21no—
31C2×#13094000C2211yescharacteristic
32C2×#13093996—21no—
33C2×#13093996—21no—
34C2×#13093995C2211yescharacteristic
35C2×#13093995C2211yescharacteristic
36C2×#13093995C2211yescharacteristic
37C2×Q8×Dic47C2211yescharacteristic
38C2×D4×Dic47C2211yescharacteristic
39C2×D4×Dic47C2211yescharacteristic
40C2×D4×Dic47C2211yescharacteristic
41C2×#13093981C2211yescharacteristic
42#15689532C2218yescomplemented
43#15689477C2218yescomplemented
44#15689469C2218yescomplemented
45#15689373C2218yescomplemented
46#15689366C2218yescomplemented
47#15689356C2218yescomplemented
48#15689349C2218yescomplemented
49#15689235C2218yescomplemented
50#15689224C2218yescomplemented
51SD16×Dic47C2218yescomplemented
52D8×Dic47C2218yescomplemented
53C2×#13093958C2211yescharacteristic
54C2×#13093958C2211yescharacteristic
55C2×#13093956C2211yescharacteristic
56C2×#13093956C2211yescharacteristic
57C2×#13093948C2211yescharacteristic
58C2×#13093948C2211yescharacteristic
59C2×#13093945C2211yescharacteristic
60C2×#13093945C2211yescharacteristic
61C2×#13093945C2211yescharacteristic
62C2×#13093945C2211yescharacteristic
63C2×#13093945C2211yescharacteristic
64C2×#13093945C2211yescharacteristic
65#15689080C2218yescomplemented
66C2×#13093934C2211yescharacteristic
67C2×C4×C47⋊C8C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C22×SD16×C47C2211yescharacteristic
70C22×SD16×C47C2211yescharacteristic
71C22×D8×C47C2211yescharacteristic
72C22×D8×C47C2211yescharacteristic
73C2×#127×C47C2211yescharacteristic
74C2×#124×C47C2211yescharacteristic
75C47×#496C2218yescomplemented
76C2×#97×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×C22⋊D47—21no—
79C22×C22⋊D47—21no—
80C22×C22⋊D47—21no—
81C23×Dic47—21no—
82C23×Dic47—21no—
83C23×Dic47—21no—
84C22×C4×D47C2311yescharacteristic
85C2×#10625324—24no—
86C2×#10625324C2314yes—
87C22×C47⋊C8C2311yescharacteristic
88C22×C47⋊C8C2311yescharacteristic
89C2×C8×D47—24no—
90C2×C8×D47C2314yes—
91#13094024—22no—
92#13094024C2314yes—
93#13094017—28no—
94#13094016—22no—
95#13094016C2314yes—
96#13094010—28no—
97#13094008—28no—
98#13094005—28no—
99#13094005—28no—
100#13094001—28no—
101#13094000—22no—
102#13094000C2314yes—
103#13093996—28no—
104#13093996—28no—
105#13093995—22no—
106#13093995—22no—
107#13093995—22no—
108#13093995C2314yes—
109#13093995C2314yes—
110#13093995C2314yes—
111Q8×Dic47—22no—
112Q8×Dic47C2314yes—
113D4×Dic47—22no—
114D4×Dic47—22no—
115D4×Dic47—22no—
116D4×Dic47C2314yes—
117D4×Dic47C2314yes—
118D4×Dic47C2314yes—
119#13093981D414yes—
120#13093981C2314yes—
121C2×C4⋊Dic47—21no—
122C2×C4⋊Dic47—21no—
123C2×C4⋊Dic47C2311yescharacteristic
124C2×C4⋊Dic47C2311yescharacteristic
125C2×C4⋊Dic47C2311yescharacteristic
126C2×C4⋊Dic47C2311yescharacteristic
127C2×Dic47⋊C4—21no—
128C2×Dic47⋊C4—21no—
129C2×Dic47⋊C4—21no—
130C2×Dic47⋊C4D411yescharacteristic
131C2×Dic47⋊C4D411yescharacteristic
132C2×C22⋊Dic47—21no—
133C2×C22⋊Dic47—21no—
134C2×C22⋊Dic47—21no—
135C2×C22⋊Dic47—21no—
136C2×C22⋊Dic47—21no—
137C2×C22⋊Dic47—21no—
138C2×(C2×D47)⋊C4—21no—
139C2×(C2×D47)⋊C4D411yescharacteristic
140C2×(C2×D47)⋊C4D411yescharacteristic
141C2×C4×Dic47—21no—
142C2×C4×Dic47C2311yescharacteristic
143#13093958C2314yes—
144#13093958C2314yes—
145#13093956C2314yes—
146#13093956C2314yes—
147#13093948C2314yes—
148#13093948C2314yes—
149#13093945C2314yes—
150#13093945C2314yes—
151#13093945C2314yes—
152#13093945C2314yes—
153#13093945C2314yes—
154#13093945C2314yes—
155#13093934C2314yes—
156C4×C47⋊C8C2314yes—
157C8×Dic47C2314yes—
158C22×Q8×C47C2311yescharacteristic
159C22×D4×C47—21no—
160C22×D4×C47—21no—
161C22×D4×C47C2311yescharacteristic
162C22×D4×C47C2311yescharacteristic
163C22×D4×C47C2311yescharacteristic
164C2×SD16×C47—24no—
165C2×SD16×C47—24no—
166C2×SD16×C47C2314yes—
167C2×SD16×C47C2314yes—
168C2×D8×C47—24no—
169C2×D8×C47—24no—
170C2×D8×C47C2314yes—
171C2×D8×C47C2314yes—
172C22×C8×C47C2311yescharacteristic
173C22×C8×C47C2311yescharacteristic
174#127×C47—22no—
175#127×C47C2314yes—
176#124×C47—22no—
177#124×C47C2314yes—
178C2×C22⋊C4×C47—21no—
179C2×C22⋊C4×C47—21no—
180C2×C42×C47C2311yescharacteristic
181#97×C47C2314yes—
182C24×C47—21no—
183C24×C47—21no—
184C24×C47—21no—
185C23×D47C2×D411yescharacteristic
186C2×Q8×C47—21no—
187C2×Q8×C47—22no—
188C2×Q8×C47—22no—
189C2×Q8×C47C2412yes—
190C2×D4×C47—21no—
191C2×D4×C47—21no—
192C2×D4×C47—21no—
193C2×D4×C47—24no—
194C2×D4×C47—24no—
195C2×D4×C47—22no—
196C2×D4×C47—22no—
197C2×D4×C47—22no—
198C2×D4×C47—22no—
199C2×D4×C47—22no—
200C2×D4×C47—22no—
201C2×D4×C47—82no—
202C2×D4×C47—82no—
203C2×D4×C47C2412yes—
204C2×D4×C47C2412yes—
205C2×D4×C47C2412yes—
206C22×C4×C47—21no—
207C22×C4×C47C2×D411yescharacteristic
208C22×C4×C47C2×D411yescharacteristic
209C22×C4×C47C2411yescharacteristic
210C2×C22⋊D47—24no—
211C2×C22⋊D47—24no—
212C2×C22⋊D47—24no—
213C2×C22⋊D47—82no—
214C2×C22⋊D47—82no—
215C2×C22⋊D47—82no—
216C22×Dic47—21no—
217C22×Dic47—21no—
218C22×Dic47—21no—
219C22×Dic47—21no—
220C22×Dic47—24no—
221C22×Dic47—24no—
222C22×Dic47—24no—
223C22×Dic47—82no—
224C22×Dic47—82no—
225C22×Dic47—82no—
226C22×Dic47C2×D411yescharacteristic
227C22×Dic47C2×D411yescharacteristic
228C22×Dic47C2×D411yescharacteristic
229C2×C4×D47—22no—
230C2×C4×D47—22no—
231C2×C4×D47C2×D412yes—
232C2×C4×D47C2412yes—
233C2×Dic94—24no—
234C2×Dic94—82no—
235SD16×C47—28no—
236SD16×C47—28no—
237D8×C47—28no—
238D8×C47—28no—
239C2×C8×C47#4114yes—
240C2×C8×C47#4114yes—
241C2×C8×C47C2412yes—
242C2×C8×C47C2412yes—
243C22⋊C4×C47—24no—
244C22⋊C4×C47—24no—
245C42×C47C2×D412yes—
246C42×C47C2412yes—
247C22⋊Dic47—24no—
248C22⋊Dic47—24no—
249C22⋊Dic47—24no—
250C22⋊Dic47—24no—
251C22⋊Dic47—24no—
252C22⋊Dic47—24no—
253(C2×D47)⋊C4—24no—
254(C2×D47)⋊C4C2×D414yes—
255(C2×D47)⋊C4C2×D414yes—
256C4⋊Dic47—24no—
257C4⋊Dic47—21no—
258C4⋊Dic47—21no—
259C4⋊Dic47—21no—
260C4⋊Dic47—21no—
261C4⋊Dic47—24no—
262C4⋊Dic47C2412yes—
263C4⋊Dic47C2412yes—
264C4⋊Dic47C2412yes—
265C4⋊Dic47C2412yes—
266Dic47⋊C4—24no—
267Dic47⋊C4—24no—
268Dic47⋊C4—24no—
269Dic47⋊C4C2×D414yes—
270Dic47⋊C4C2×D414yes—
271C4×Dic47—24no—
272C4×Dic47C2×D412yes—
273C4×Dic47C2412yes—
274C2×C47⋊C8—22no—
275C2×C47⋊C8—22no—
276C2×C47⋊C8C2412yes—
277C2×C47⋊C8C2412yes—
278#10625324—28no—
279C8×D47—28no—
280C23×C47—22no—
281C23×C47—22no—
282C23×C47—22no—
283C23×C47—42no—
284C23×C47—42no—
285C23×C47—42no—
286C23×C47—42no—
287C23×C47—42no—
288C23×C47—42no—
289C23×C47—42no—
290C23×C47—42no—
291C23×C47—42no—
292C23×C47C22×D411yescharacteristic
293C22×D47—22no—
294C22×D47—22no—
295C22×D47—22no—
296C22×D47C22×D412yes—
297Q8×C47—22no—
298Q8×C47—22no—
299Q8×C47—42no—
300D4×C47—22no—
301D4×C47—22no—
302D4×C47—22no—
303D4×C47—22no—
304D4×C47—22no—
305D4×C47—22no—
306D4×C47—42no—
307D4×C47—42no—
308D4×C47—42no—
309D4×C47—84no—
310D4×C47—84no—
311C2×C4×C47—22no—
312C2×C4×C47—22no—
313C2×C4×C47—22no—
314C2×C4×C47—42no—
315C2×C4×C47C22×D412yes—
316C2×C4×C47C22×D412yes—
317C2×C4×C47C22×D411yescharacteristic
318C2×C4×C47C2×#4112yes—
319C2×C4×C47C2×#4112yes—
320C2×C4×C47C2511yescharacteristic
321C22⋊D47—84no—
322C22⋊D47—84no—
323C22⋊D47—84no—
324C2×Dic47—22no—
325C2×Dic47—22no—
326C2×Dic47—22no—
327C2×Dic47—22no—
328C2×Dic47—22no—
329C2×Dic47—22no—
330C2×Dic47—22no—
331C2×Dic47—42no—
332C2×Dic47—42no—
333C2×Dic47—42no—
334C2×Dic47—42no—
335C2×Dic47—84no—
336C2×Dic47—84no—
337C2×Dic47—84no—
338C2×Dic47C22×D412yes—
339C2×Dic47C22×D412yes—
340C2×Dic47C22×D412yes—
341C4×D47—24no—
342C4×D47—22no—
343C4×D47—22no—
344Dic94—84no—
345C8×C47C2×#4114yes—
346C8×C47C2×#4114yes—
347C47⋊C8—22no—
348C47⋊C8—22no—
349C2×#3179—471nomaximal, Sylow
350C22×C47—42no—
351C22×C47—42no—
352C22×C47—42no—
353C22×C47—42no—
354C22×C47—42no—
355C22×C47—42no—
356C22×C47—42no—
357C22×C47—42no—
358C22×C47—42no—
359C22×C47—84no—
360C22×C47—84no—
361C22×C47—84no—
362C22×C47#53212yes—
363C22×C47#57612yes—
364C22×C47#57712yes—
365C22×C47C23×D411yescharacteristic
366C2×D47—22no—
367C2×D47—22no—
368C2×D47—22no—
369C2×D47—44no—
370C4×C47—22no—
371C4×C47—22no—
372C4×C47—42no—
373C4×C47#53212yes—
374C4×C47C22×#4111yescharacteristic
375C4×C47C22×#4111yescharacteristic
376Dic47—22no—
377Dic47—22no—
378Dic47—22no—
379Dic47—42no—
380Dic47—42no—
381Dic47—42no—
382Dic47—42no—
383C2×#542—471no—
384C2×#540—471no—
385#3179—4716no—
386C2×#501—471no—
387C2×#496D4711yescharacteristic, complemented
388C2×#488—471no—
389C2×#486—471no—
390C2×#469—471no—
391C2×#468—471no—
392C2×#466—471no—
393C2×#465—471no—
394C2×#442—471no—
395C2×#440—471no—
396C2×C4×SD16—471no—
397C2×C4×D8—471no—
398C2×#405—471no—
399C2×C47—82no—
400C2×C47—82no—
401C2×C47—82no—
402C2×C47#317914yescomplemented
403C2×C47C2×#53211yescharacteristic
404C2×C47C2×#57611yescharacteristic
405C2×C47C2×#57711yescharacteristic
406D47—42no—
407C22×SD16C2×D4711yescharacteristic
408C22×SD16C2×D4711yescharacteristic
409C22×D8C2×D4711yescharacteristic
410C22×D8C2×D4711yescharacteristic
411C22×M16—471no—
412C23×C8—471no—
413#542—478no—
414#542—944no—
415#540—478no—
416#540—944no—
417C2×C4⋊Q8—471no—
418C2×#127C2×D4711yescharacteristic
419C2×#126—941no—
420C2×#125—471no—
421C2×#124—941no—
422C2×#124C2×D4711yescharacteristic
423C2×#123—941no—
424C2×#123—941no—
425C2×#123—941no—
426C2×C22⋊Q8—471no—
427C2×C22⋊Q8—941no—
428C2×#121—471no—
429C2×#121—471no—
430C2×#121—471no—
431C2×#121—941no—
432C2×#121—941no—
433C2×C4×Q8—471no—
434C2×C4×D4—471no—
435C2×C4×D4—471no—
436C2×C4×D4—471no—
437C2×#117—471no—
438#501—478no—
439#496C2×D4718yescomplemented
440#488—478no—
441#486—478no—
442#469—478no—
443#468—478no—
444#466—478no—
445#465—478no—
446#442—478no—
447#440—478no—
448C4×SD16—478no—
449C4×D8—478no—
450C2×#107—471no—
451C2×#107—471no—
452C2×#106—471no—
453C2×#106—471no—
454C2×#103—471no—
455C2×#103—471no—
456C2×#102—471no—
457C2×#102—471no—
458C2×#102—471no—
459C2×#102—471no—
460C2×#102—471no—
461C2×#102—471no—
462#405—478no—
463C2×#97—471no—
464C2×#97C2×D4711yescharacteristic
465C2×C4×C8—471no—
466C2×C4×C8—471no—
467C47C2×#317911yescharacteristic, complemented, Sylow
468C22×Q8—941no—
469C22×Q8C22×D4711yescharacteristic
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—941no—
473C22×D4—941no—
474C22×D4—941no—
475C22×D4C22×D4711yescharacteristic
476C22×D4C22×D4711yescharacteristic
477C22×D4C22×D4711yescharacteristic
478C23×C4—471no—
479C23×C4—941no—
480C23×C4—941no—
481C23×C4—941no—
482C2×SD16—24no—
483C2×SD16—24no—
484C2×SD16C22×D4714yes—
485C2×SD16C22×D4714yes—
486C2×D8—24no—
487C2×D8—24no—
488C2×D8C22×D4714yes—
489C2×D8C22×D4714yes—
490C2×M16—474no—
491C2×M16—944no—
492C22×C8—471no—
493C22×C8—471no—
494C22×C8—474no—
495C22×C8—944no—
496C22×C8C22×D4711yescharacteristic
497C22×C8C22×D4711yescharacteristic
498C4⋊Q8—474no—
499C4⋊Q8—942no—
500#127—22no—
501#127C22×D4714yes—
502#126—948no—
503#125—474no—
504#125—942no—
505#124—22no—
506#124—948no—
507#124C22×D4714yes—
508#123—948no—
509#123—948no—
510#123—948no—
511C22⋊Q8—474no—
512C22⋊Q8—948no—
513C22⋊Q8—942no—
514#121—474no—
515#121—474no—
516#121—474no—
517#121—948no—
518#121—948no—
519#121—942no—
520#121—942no—
521#121—942no—
522C4×Q8—474no—
523C4×Q8—942no—
524C4×D4—474no—
525C4×D4—474no—
526C4×D4—474no—
527C4×D4—942no—
528C4×D4—942no—
529C4×D4—942no—
530#117—474no—
531#117—474no—
532C2×C4⋊C4—471no—
533C2×C4⋊C4—471no—
534C2×C4⋊C4—471no—
535C2×C4⋊C4—471no—
536C2×C4⋊C4—471no—
537C2×C4⋊C4—471no—
538C2×C4⋊C4—941no—
539C2×C4⋊C4—941no—
540C2×C4⋊C4—941no—
541C2×C4⋊C4—941no—
542C2×C4⋊C4—941no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—471no—
546C2×C22⋊C4—471no—
547C2×C22⋊C4—941no—
548C2×C22⋊C4—941no—
549C2×C22⋊C4—941no—
550C2×C22⋊C4—941no—
551C2×C22⋊C4—941no—
552C2×C22⋊C4—941no—
553C2×C22⋊C4—941no—
554C2×C42—471no—
555C2×C42—941no—
556C2×C42C22×D4711yescharacteristic
557#107—474no—
558#107—474no—
559#106—474no—
560#106—474no—
561#103—474no—
562#103—474no—
563#102—474no—
564#102—474no—
565#102—474no—
566#102—474no—
567#102—474no—
568#102—474no—
569#97—474no—
570#97C22×D4714yes—
571C4×C8—474no—
572C4×C8—474no—
573C24—21no—
574C24—21no—
575C24—21no—
576C24—471no—
577C2×Q8—21no—
578C2×Q8—22no—
579C2×Q8—22no—
580C2×Q8—944no—
581C2×Q8—3762no—
582C2×Q8C23×D4712yes—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—24no—
587C2×D4—24no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—82no—
595C2×D4—82no—
596C2×D4—944no—
597C2×D4—944no—
598C2×D4—944no—
599C2×D4—3762no—
600C2×D4—3762no—
601C2×D4—3762no—
602C2×D4C23×D4712yes—
603C2×D4C23×D4712yes—
604C2×D4C23×D4712yes—
605C22×C4—21no—
606C22×C4—471no—
607C22×C4—471no—
608C22×C4—471no—
609C22×C4—472no—
610C22×C4—472no—
611C22×C4—944no—
612C22×C4—944no—
613C22×C4—944no—
614C22×C4—942no—
615C22×C4—942no—
616C22×C4—941no—
617C22×C4—941no—
618C22×C4—941no—
619C22×C4—941no—
620C22×C4—3762no—
621C22×C4—3762no—
622C22×C4—3762no—
623C22×C4D4×D4711yescharacteristic
624C22×C4D4×D4711yescharacteristic
625C22×C4C23×D4711yescharacteristic
626SD16—28no—
627SD16—28no—
628D8—28no—
629D8—28no—
630M16—948no—
631C2×C8—472no—
632C2×C8—472no—
633C2×C8—942no—
634C2×C8—942no—
635C2×C8—948no—
636C2×C8#1062535214yes—
637C2×C8#1062535214yes—
638C2×C8C23×D4712yes—
639C2×C8C23×D4712yes—
640C4⋊C4—474no—
641C4⋊C4—474no—
642C4⋊C4—472no—
643C4⋊C4—472no—
644C4⋊C4—472no—
645C4⋊C4—472no—
646C4⋊C4—944no—
647C4⋊C4—944no—
648C4⋊C4—944no—
649C4⋊C4—944no—
650C4⋊C4—941no—
651C4⋊C4—941no—
652C4⋊C4—941no—
653C4⋊C4—941no—
654C4⋊C4—944no—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—474no—
658C22⋊C4—474no—
659C22⋊C4—944no—
660C22⋊C4—944no—
661C22⋊C4—944no—
662C22⋊C4—944no—
663C22⋊C4—944no—
664C22⋊C4—944no—
665C22⋊C4—944no—
666C42—472no—
667C42—472no—
668C42—944no—
669C42D4×D4712yes—
670C42C23×D4712yes—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—472no—
684C23—942no—
685C23—942no—
686C23—942no—
687C23C2×D4×D4711yescharacteristic
688Q8—22no—
689Q8—22no—
690Q8—42no—
691Q8—3764no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—22no—
696D4—22no—
697D4—22no—
698D4—42no—
699D4—42no—
700D4—42no—
701D4—84no—
702D4—84no—
703D4—3764no—
704D4—3764no—
705D4—3764no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—42no—
710C2×C4—472no—
711C2×C4—472no—
712C2×C4—472no—
713C2×C4—942no—
714C2×C4—942no—
715C2×C4—942no—
716C2×C4—944no—
717C2×C4—942no—
718C2×C4—942no—
719C2×C4—942no—
720C2×C4—942no—
721C2×C4—942no—
722C2×C4—942no—
723C2×C4—3764no—
724C2×C4—3764no—
725C2×C4—3764no—
726C2×C4—1882no—
727C2×C4—1882no—
728C2×C4—1882no—
729C2×C4—1882no—
730C2×C4C2×D4×D4712yes—
731C2×C4C2×D4×D4712yes—
732C2×C4C2×D4×D4711yescharacteristic
733C2×C4C2×#1062535212yes—
734C2×C4C2×#1062535212yes—
735C2×C4C24×D4711yescharacteristic
736C8—942no—
737C8—942no—
738C8C2×#1062535214yes—
739C8C2×#1062535214yes—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—84no—
750C22—84no—
751C22—84no—
752C22—942no—
753C22—942no—
754C22—942no—
755C22—1884no—
756C22#1568967112yes—
757C22#1568992712yes—
758C22#1568993312yes—
759C22C22×D4×D4711yescharacteristic
760C4—22no—
761C4—22no—
762C4—42no—
763C4—942no—
764C4—942no—
765C4—942no—
766C4—1882no—
767C4—1882no—
768C4—1882no—
769C4—1882no—
770C4#1568967112yes—
771C4C22×#1062535211yescharacteristic
772C4C22×#1062535211yescharacteristic
773C2—82no—
774C2—82no—
775C2—82no—
776C2—1882no—
777C2#2025406814yesdirect product factor
778C2C2×#1568967111yescharacteristic
779C2C2×#1568992711yescharacteristic
780C2C2×#1568993311yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#496C2
socleC23×C47C22×D4
hypercenterC2×#496D47
hypocenterC47C2×#3179
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#496

Complements

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

NH ≅ G/Ntype
1. C2×#15689742C2semidirect
2. C2×#15689727C2semidirect
3. #20254068C2direct (N × H)
4. C2×#15689532C2semidirect
5. C2×#15689477C2semidirect
6. C2×#15689469C2semidirect
7. C2×#15689373C2semidirect
8. C2×#15689366C2semidirect
9. C2×#15689356C2semidirect
10. C2×#15689349C2semidirect
11. C2×#15689235C2semidirect
12. C2×#15689224C2semidirect
13. C2×SD16×Dic47C2semidirect
14. C2×D8×Dic47C2semidirect
15. C2×#15689080C2semidirect
16. C2×C47×#496C2semidirect
20. #15689742C22semidirect
22. #15689727C22semidirect
42. #15689532C22semidirect
43. #15689477C22semidirect
44. #15689469C22semidirect
45. #15689373C22semidirect
46. #15689366C22semidirect
47. #15689356C22semidirect
48. #15689349C22semidirect
49. #15689235C22semidirect
50. #15689224C22semidirect
51. SD16×Dic47C22semidirect
52. D8×Dic47C22semidirect
65. #15689080C22semidirect
75. C47×#496C22semidirect
387. C2×#496D47semidirect
402. C2×C47#3179semidirect
439. #496C2×D47semidirect
467. C47C2×#3179semidirect
777. C2#20254068direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897422
C2×#156897272
#202540682
C2×#156895322
C2×#156894772
C2×#156894692
C2×#156893732
C2×#156893662
C2×#156893562
C2×#156893492
C2×#156892352
C2×#156892242
C2×SD16×Dic472
C2×D8×Dic472
C2×#156890802
C2×C47×#4962
C2×#317947