Finite Group Databasebeta

← C2×#20254064 #27086155

Subgroups — C2×#20254064 #27086155

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×#15689746C211yesmaximal, characteristic, complemented
2C2×#15689726C211yesmaximal, characteristic, complemented
3#20254064C2116yesmaximal, direct product factor
4C2×#15689531C211yesmaximal, characteristic, complemented
5C2×#15689509C211yesmaximal, characteristic, complemented
6C2×#15689479C211yesmaximal, characteristic, complemented
7C2×#15689468C211yesmaximal, characteristic, complemented
8C2×#15689376C211yesmaximal, characteristic, complemented
9C2×#15689357C211yesmaximal, characteristic, complemented
10C2×#15689354C211yesmaximal, characteristic, complemented
11C2×#15689232C211yesmaximal, characteristic, complemented
12C2×#15689226C211yesmaximal, characteristic, complemented
13C2×SD16×Dic47C211yesmaximal, characteristic, complemented
14C2×#15689205C211yesmaximal, characteristic, complemented
15C2×#15689081C211yesmaximal, characteristic, complemented
16C2×C47×#468C211yesmaximal, characteristic, complemented
17C22×#10625336C2211yescharacteristic
18C22×D376C2211yescharacteristic
19C22×#10625334C2211yescharacteristic
20C23×C47⋊C8C2211yescharacteristic
21#15689746—24no—
22#15689746C2218yescomplemented
23#15689726—24no—
24#15689726C2218yescomplemented
25C2×#13094023C2211yescharacteristic
26C2×#13094020C2211yescharacteristic
27C2×#13094019—21no—
28C2×#13094015C2211yescharacteristic
29C2×#13094013C2211yescharacteristic
30C2×#13094010—21no—
31C2×#13094008—21no—
32C2×#13094006—21no—
33C2×#13094006—21no—
34C2×#13094004—21no—
35C2×#13093998C2211yescharacteristic
36C2×#13093998C2211yescharacteristic
37C2×#13093996—21no—
38C2×#13093995—21no—
39C2×Q8×Dic47C2211yescharacteristic
40C2×D4×Dic47C2211yescharacteristic
41C2×#13093986C2211yescharacteristic
42C2×#13093986C2211yescharacteristic
43C2×#13093983C2211yescharacteristic
44#15689531C2218yescomplemented
45#15689509C2218yescomplemented
46#15689479C2218yescomplemented
47#15689468C2218yescomplemented
48#15689376C2218yescomplemented
49#15689357C2218yescomplemented
50#15689354C2218yescomplemented
51#15689232C2218yescomplemented
52#15689226C2218yescomplemented
53SD16×Dic47C2218yescomplemented
54#15689205C2218yescomplemented
55C2×#13093957C2211yescharacteristic
56C2×#13093956C2211yescharacteristic
57C2×#13093955C2211yescharacteristic
58C2×#13093948C2211yescharacteristic
59C2×#13093946C2211yescharacteristic
60C2×#13093946C2211yescharacteristic
61C2×#13093945C2211yescharacteristic
62C2×#13093944C2211yescharacteristic
63C2×#13093944C2211yescharacteristic
64#15689081C2218yescomplemented
65C2×#13093934C2211yescharacteristic
66C2×#13093934C2211yescharacteristic
67C2×C8×Dic47C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C22×SD16×C47C2211yescharacteristic
70C22×M16×C47C2211yescharacteristic
71C2×C22⋊Q8×C47C2211yescharacteristic
72C2×#121×C47C2211yescharacteristic
73C47×#468C2218yescomplemented
74C2×#107×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×#102×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×D188C2311yescharacteristic
79C22×D188C2311yescharacteristic
80C22×C22⋊D47—21no—
81C22×C22⋊D47—21no—
82C22×C22⋊D47—21no—
83C22×C22⋊D47—21no—
84C23×Dic47—21no—
85C22×C4×D47—21no—
86C22×C4×D47—21no—
87C2×#10625336—24no—
88C2×#10625336C2314yes—
89C2×D376—24no—
90C2×D376C2314yes—
91C2×#10625334—24no—
92C2×#10625334C2314yes—
93C22×C47⋊C8—24no—
94C22×C47⋊C8C2311yescharacteristic
95C22×C47⋊C8C2314yes—
96C22×C47⋊C8C2311yescharacteristic
97#13094023—22no—
98#13094023C2314yes—
99#13094020—22no—
100#13094020C2314yes—
101#13094019—28no—
102#13094015—22no—
103#13094015C2314yes—
104#13094013—22no—
105#13094013C2314yes—
106#13094010—28no—
107#13094008—28no—
108#13094006—28no—
109#13094006—28no—
110#13094004—28no—
111#13093998—22no—
112#13093998—22no—
113#13093998C2314yes—
114#13093998C2314yes—
115#13093996—28no—
116#13093995—28no—
117Q8×Dic47—22no—
118Q8×Dic47C2314yes—
119D4×Dic47—22no—
120D4×Dic47C2314yes—
121#13093986—22no—
122#13093986—22no—
123#13093986C2314yes—
124#13093986C2314yes—
125#13093983D414yes—
126#13093983C2314yes—
127C2×C4⋊Dic47—21no—
128C2×C4⋊Dic47—21no—
129C2×C4⋊Dic47D411yescharacteristic
130C2×C4⋊Dic47D411yescharacteristic
131C2×C4⋊Dic47C2311yescharacteristic
132C2×C4⋊Dic47C2311yescharacteristic
133C2×Dic47⋊C4—21no—
134C2×Dic47⋊C4—21no—
135C2×C22⋊Dic47—21no—
136C2×C22⋊Dic47D411yescharacteristic
137C2×C22⋊Dic47D411yescharacteristic
138C2×(C2×D47)⋊C4—21no—
139C2×(C2×D47)⋊C4—21no—
140C2×(C2×D47)⋊C4—21no—
141C2×(C2×D47)⋊C4—21no—
142C2×(C2×D47)⋊C4—21no—
143C2×(C2×D47)⋊C4—21no—
144C2×C4×Dic47—21no—
145C2×C4×Dic47C2311yescharacteristic
146C2×C4×Dic47C2311yescharacteristic
147#13093957C2314yes—
148#13093956C2314yes—
149#13093955C2314yes—
150#13093948C2314yes—
151#13093946C2314yes—
152#13093946C2314yes—
153#13093945C2314yes—
154#13093944C2314yes—
155#13093944C2314yes—
156#13093934C2314yes—
157#13093934C2314yes—
158C8×Dic47C2314yes—
159C8×Dic47C2314yes—
160C22×Q8×C47C2311yescharacteristic
161C22×D4×C47—21no—
162C22×D4×C47C2311yescharacteristic
163C23×C4×C47C2311yescharacteristic
164C2×SD16×C47—24no—
165C2×SD16×C47C2314yes—
166C2×M16×C47—24no—
167C2×M16×C47C2314yes—
168C22×C8×C47C2311yescharacteristic
169C22×C8×C47C2311yescharacteristic
170C22⋊Q8×C47—22no—
171C22⋊Q8×C47C2314yes—
172#121×C47—22no—
173#121×C47C2314yes—
174C2×C4⋊C4×C47—21no—
175C2×C4⋊C4×C47C2311yescharacteristic
176C2×C4⋊C4×C47C2311yescharacteristic
177C2×C22⋊C4×C47—21no—
178C2×C22⋊C4×C47—21no—
179#107×C47C2314yes—
180#103×C47C2314yes—
181#102×C47C2314yes—
182C24×C47—21no—
183C24×C47C2×D411yescharacteristic
184C23×D47—21no—
185C23×D47—21no—
186C2×Q8×C47—21no—
187C2×Q8×C47—22no—
188C2×Q8×C47—22no—
189C2×Q8×C47C2412yes—
190C2×D4×C47—24no—
191C2×D4×C47—21no—
192C2×D4×C47—22no—
193C2×D4×C47—22no—
194C2×D4×C47—82no—
195C2×D4×C47C2412yes—
196C22×C4×C47—22no—
197C22×C4×C47—22no—
198C22×C4×C47—21no—
199C22×C4×C47—21no—
200C22×C4×C47—21no—
201C22×C4×C47C2×D411yescharacteristic
202C22×C4×C47C2×D412yes—
203C22×C4×C47C2412yes—
204C22×C4×C47C2411yescharacteristic
205C2×C22⋊D47—24no—
206C2×C22⋊D47—24no—
207C2×C22⋊D47—24no—
208C2×C22⋊D47—24no—
209C2×C22⋊D47—82no—
210C2×C22⋊D47—82no—
211C2×C22⋊D47—82no—
212C2×C22⋊D47—82no—
213C22×Dic47—21no—
214C22×Dic47—21no—
215C22×Dic47—24no—
216C22×Dic47—82no—
217C22×Dic47C2×D411yescharacteristic
218C22×Dic47C2×D411yescharacteristic
219C22×Dic47C2×D411yescharacteristic
220C22×Dic47C2×D411yescharacteristic
221C2×D188—22no—
222C2×D188—22no—
223C2×D188—22no—
224C2×D188—22no—
225C2×D188—21no—
226C2×D188—21no—
227C2×D188C2412yes—
228C2×D188C2412yes—
229C2×C4×D47—24no—
230C2×C4×D47—24no—
231C2×C4×D47—82no—
232C2×C4×D47—82no—
233C2×Dic94—24no—
234C2×Dic94—82no—
235SD16×C47—28no—
236M16×C47—28no—
237C2×C8×C47—22no—
238C2×C8×C47#4114yes—
239C2×C8×C47C2412yes—
240C2×C8×C47C2412yes—
241C4⋊C4×C47—24no—
242C4⋊C4×C47—21no—
243C4⋊C4×C47—21no—
244C4⋊C4×C47C2412yes—
245C4⋊C4×C47C2412yes—
246C22⋊C4×C47—24no—
247C22⋊C4×C47—24no—
248C22⋊Dic47—24no—
249C22⋊Dic47C2×D414yes—
250C22⋊Dic47C2×D414yes—
251#10625336—28no—
252#10625334—28no—
253(C2×D47)⋊C4—24no—
254(C2×D47)⋊C4—24no—
255(C2×D47)⋊C4—24no—
256(C2×D47)⋊C4—24no—
257(C2×D47)⋊C4—24no—
258(C2×D47)⋊C4—24no—
259C4⋊Dic47—21no—
260C4⋊Dic47—21no—
261C4⋊Dic47—24no—
262C4⋊Dic47—24no—
263C4⋊Dic47C2×D414yes—
264C4⋊Dic47C2×D414yes—
265C4⋊Dic47C2412yes—
266C4⋊Dic47C2412yes—
267Dic47⋊C4—24no—
268Dic47⋊C4—24no—
269C4×Dic47—24no—
270C4×Dic47C2×D412yes—
271C4×Dic47C2×D412yes—
272C4×Dic47C2412yes—
273C4×Dic47C2412yes—
274C2×C47⋊C8—22no—
275C2×C47⋊C8—28no—
276C2×C47⋊C8#4114yes—
277C2×C47⋊C8C2412yes—
278C2×C47⋊C8C2412yes—
279D376—28no—
280C23×C47—22no—
281C23×C47—22no—
282C23×C47—22no—
283C23×C47—22no—
284C23×C47—42no—
285C23×C47—42no—
286C23×C47—42no—
287C23×C47C22×D412yes—
288C23×C47C22×D411yescharacteristic
289C22×D47—22no—
290C22×D47—22no—
291C22×D47—42no—
292C22×D47—42no—
293C22×D47—42no—
294C22×D47—42no—
295C22×D47—42no—
296C22×D47—42no—
297Q8×C47—22no—
298Q8×C47—22no—
299Q8×C47—42no—
300D4×C47—22no—
301D4×C47—22no—
302D4×C47—42no—
303D4×C47—84no—
304C2×C4×C47—22no—
305C2×C4×C47—24no—
306C2×C4×C47—22no—
307C2×C4×C47—22no—
308C2×C4×C47—22no—
309C2×C4×C47—22no—
310C2×C4×C47—22no—
311C2×C4×C47—42no—
312C2×C4×C47—42no—
313C2×C4×C47—42no—
314C2×C4×C47C22×D412yes—
315C2×C4×C47C22×D411yescharacteristic
316C2×C4×C47C2×#4112yes—
317C2×C4×C47C2×#4112yes—
318C2×C4×C47C2511yescharacteristic
319C22⋊D47—84no—
320C22⋊D47—84no—
321C22⋊D47—84no—
322C22⋊D47—84no—
323C2×Dic47—22no—
324C2×Dic47—22no—
325C2×Dic47—22no—
326C2×Dic47—22no—
327C2×Dic47—22no—
328C2×Dic47—22no—
329C2×Dic47—42no—
330C2×Dic47—42no—
331C2×Dic47—84no—
332C2×Dic47C22×D412yes—
333C2×Dic47C22×D412yes—
334C2×Dic47C22×D412yes—
335C2×Dic47C22×D412yes—
336D188—22no—
337D188—22no—
338D188—22no—
339D188—22no—
340D188—42no—
341D188—42no—
342C4×D47—84no—
343C4×D47—84no—
344Dic94—84no—
345C8×C47—22no—
346C8×C47C2×#4114yes—
347C47⋊C8—22no—
348C47⋊C8C2×#4114yes—
349C2×#3179—471nomaximal, Sylow
350C22×C47—22no—
351C22×C47—22no—
352C22×C47—22no—
353C22×C47—44no—
354C22×C47—42no—
355C22×C47—42no—
356C22×C47—42no—
357C22×C47—84no—
358C22×C47#53212yes—
359C22×C47#57612yes—
360C22×C47#57712yes—
361C22×C47C23×D411yescharacteristic
362C2×D47—42no—
363C2×D47—42no—
364C2×D47—42no—
365C2×D47—42no—
366C2×D47—42no—
367C2×D47—42no—
368C2×D47—84no—
369C2×D47—84no—
370C4×C47—22no—
371C4×C47—42no—
372C4×C47—42no—
373C4×C47—42no—
374C4×C47#53212yes—
375C4×C47C22×#4111yescharacteristic
376C4×C47C22×#4111yescharacteristic
377Dic47—22no—
378Dic47—22no—
379Dic47—22no—
380Dic47—22no—
381Dic47—42no—
382Dic47—42no—
383C2×#542—471no—
384C2×#540—471no—
385#3179—4716no—
386C2×#501—471no—
387C2×#496—471no—
388C2×#488—471no—
389C2×#486—471no—
390C2×#469—471no—
391C2×#468D4711yescharacteristic, complemented
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—42no—
400C2×C47—82no—
401C2×C47#317914yescomplemented
402C2×C47C2×#53211yescharacteristic
403C2×C47C2×#57611yescharacteristic
404C2×C47C2×#57711yescharacteristic
405D47—82no—
406D47—82no—
407C22×SD16—471no—
408C22×SD16C2×D4711yescharacteristic
409C22×D8—471no—
410C22×D8—471no—
411C22×M16C2×D4711yescharacteristic
412C23×C8—471no—
413#542—478no—
414#542—944no—
415#540—478no—
416#540—944no—
417C2×C4⋊Q8—471no—
418C2×#127—471no—
419C2×#126—941no—
420C2×#125—471no—
421C2×#124—471no—
422C2×#124—941no—
423C2×#123—941no—
424C2×#123—941no—
425C2×#123—941no—
426C2×C22⋊Q8—941no—
427C2×C22⋊Q8C2×D4711yescharacteristic
428C2×#121—471no—
429C2×#121—471no—
430C2×#121—941no—
431C2×#121—941no—
432C2×#121C2×D4711yescharacteristic
433C2×C4×Q8—471no—
434C2×C4×D4—471no—
435C2×C4×D4—471no—
436C2×C4×D4—471no—
437C2×#117—471no—
438#501—478no—
439#496—478no—
440#488—478no—
441#486—478no—
442#469—478no—
443#468C2×D4718yescomplemented
444#466—478no—
445#465—478no—
446#442—478no—
447#440—478no—
448C4×SD16—478no—
449C4×D8—478no—
450C2×#107—471no—
451C2×#107C2×D4711yescharacteristic
452C2×#106—471no—
453C2×#106—471no—
454C2×#103—471no—
455C2×#103C2×D4711yescharacteristic
456C2×#102—471no—
457C2×#102—471no—
458C2×#102—471no—
459C2×#102—471no—
460C2×#102—471no—
461C2×#102C2×D4711yescharacteristic
462#405—478no—
463C2×#97—471no—
464C2×#97—471no—
465C2×C4×C8—471no—
466C2×C4×C8—471no—
467C47C2×#317911yescharacteristic, complemented, Sylow
468C22×Q8—941no—
469C22×Q8C22×D4711yescharacteristic
470C22×D4—21no—
471C22×D4—471no—
472C22×D4—471no—
473C22×D4—941no—
474C22×D4—941no—
475C22×D4—941no—
476C22×D4—941no—
477C22×D4C22×D4711yescharacteristic
478C23×C4—941no—
479C23×C4—941no—
480C23×C4—941no—
481C23×C4C22×D4711yescharacteristic
482C2×SD16—24no—
483C2×SD16—474no—
484C2×SD16—944no—
485C2×SD16C22×D4714yes—
486C2×D8—474no—
487C2×D8—474no—
488C2×D8—944no—
489C2×D8—944no—
490C2×M16—24no—
491C2×M16C22×D4714yes—
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—474no—
501#127—942no—
502#126—948no—
503#125—474no—
504#125—942no—
505#124—474no—
506#124—942no—
507#124—948no—
508#123—948no—
509#123—948no—
510#123—948no—
511C22⋊Q8—22no—
512C22⋊Q8—948no—
513C22⋊Q8C22×D4714yes—
514#121—22no—
515#121—474no—
516#121—474no—
517#121—948no—
518#121—948no—
519#121—942no—
520#121—942no—
521#121C22×D4714yes—
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—21no—
533C2×C4⋊C4—471no—
534C2×C4⋊C4—471no—
535C2×C4⋊C4—471no—
536C2×C4⋊C4—471no—
537C2×C4⋊C4—941no—
538C2×C4⋊C4—941no—
539C2×C4⋊C4—941no—
540C2×C4⋊C4—941no—
541C2×C4⋊C4C22×D4711yescharacteristic
542C2×C4⋊C4C22×D4711yescharacteristic
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—471no—
556C2×C42—941no—
557#107—474no—
558#107C22×D4714yes—
559#106—474no—
560#106—474no—
561#103—474no—
562#103C22×D4714yes—
563#102—474no—
564#102—474no—
565#102—474no—
566#102—474no—
567#102—474no—
568#102C22×D4714yes—
569#97—474no—
570#97—474no—
571C4×C8—474no—
572C4×C8—474no—
573C24—21no—
574C24—941no—
575C24—941no—
576C24D4×D4711yescharacteristic
577C2×Q8—21no—
578C2×Q8—22no—
579C2×Q8—22no—
580C2×Q8—944no—
581C2×Q8—3762no—
582C2×Q8C23×D4712yes—
583C2×D4—24no—
584C2×D4—21no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—82no—
588C2×D4—472no—
589C2×D4—472no—
590C2×D4—944no—
591C2×D4—944no—
592C2×D4—944no—
593C2×D4—944no—
594C2×D4—941no—
595C2×D4—941no—
596C2×D4—942no—
597C2×D4—942no—
598C2×D4—942no—
599C2×D4—942no—
600C2×D4—3762no—
601C2×D4—3762no—
602C2×D4—3762no—
603C2×D4—3762no—
604C2×D4C23×D4712yes—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—471no—
611C22×C4—471no—
612C22×C4—471no—
613C22×C4—471no—
614C22×C4—944no—
615C22×C4—944no—
616C22×C4—944no—
617C22×C4—941no—
618C22×C4—941no—
619C22×C4—3762no—
620C22×C4—3762no—
621C22×C4—3762no—
622C22×C4D4×D4712yes—
623C22×C4D4×D4711yescharacteristic
624C22×C4C23×D4712yes—
625C22×C4C23×D4711yescharacteristic
626SD16—28no—
627SD16—948no—
628D8—948no—
629D8—948no—
630M16—28no—
631C2×C8—22no—
632C2×C8—474no—
633C2×C8—472no—
634C2×C8—472no—
635C2×C8—948no—
636C2×C8—942no—
637C2×C8#1062535214yes—
638C2×C8C23×D4712yes—
639C2×C8C23×D4712yes—
640C4⋊C4—24no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—474no—
644C4⋊C4—474no—
645C4⋊C4—472no—
646C4⋊C4—472no—
647C4⋊C4—944no—
648C4⋊C4—944no—
649C4⋊C4—944no—
650C4⋊C4—944no—
651C4⋊C4—941no—
652C4⋊C4—941no—
653C4⋊C4C23×D4712yes—
654C4⋊C4C23×D4712yes—
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—472no—
669C42—472no—
670C42—944no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—942no—
679C23—942no—
680C23—1882no—
681C23—1882no—
682C23—1882no—
683C23—1882no—
684C23—1882no—
685C23—1882no—
686C23C2×D4×D4712yes—
687C23C2×D4×D4711yescharacteristic
688Q8—22no—
689Q8—22no—
690Q8—42no—
691Q8—3764no—
692D4—22no—
693D4—22no—
694D4—42no—
695D4—84no—
696D4—942no—
697D4—942no—
698D4—942no—
699D4—942no—
700D4—3764no—
701D4—3764no—
702D4—3764no—
703D4—3764no—
704D4—1882no—
705D4—1882no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—472no—
717C2×C4—472no—
718C2×C4—472no—
719C2×C4—472no—
720C2×C4—942no—
721C2×C4—942no—
722C2×C4—942no—
723C2×C4—942no—
724C2×C4—942no—
725C2×C4—942no—
726C2×C4—3764no—
727C2×C4—3764no—
728C2×C4—3764no—
729C2×C4—1882no—
730C2×C4—1882no—
731C2×C4C2×D4×D4712yes—
732C2×C4C2×D4×D4711yescharacteristic
733C2×C4#41×D4712yes—
734C2×C4C2×#1062535212yes—
735C2×C4C24×D4711yescharacteristic
736C8—22no—
737C8—474no—
738C8—942no—
739C8C2×#1062535214yes—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—44no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—84no—
748C22—3764no—
749C22—3764no—
750C22—1882no—
751C22—1882no—
752C22—1882no—
753C22—1882no—
754C22—1882no—
755C22—1882no—
756C22#1568966812yes—
757C22#1568992712yes—
758C22#1568993212yes—
759C22C22×D4×D4711yescharacteristic
760C4—22no—
761C4—42no—
762C4—42no—
763C4—42no—
764C4—942no—
765C4—942no—
766C4—942no—
767C4—942no—
768C4—1882no—
769C4—1882no—
770C4#1568966812yes—
771C4C2×#41×D4711yescharacteristic
772C4C22×#1062535211yescharacteristic
773C2—42no—
774C2—82no—
775C2—3762no—
776C2—3762no—
777C2#2025406414yesdirect product factor
778C2C2×#1568966811yescharacteristic
779C2C2×#1568992711yescharacteristic
780C2C2×#1568993211yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#468C2
socleC23×C47C22×D4
hypercenterC2×#468D47
hypocenterC47C2×#3179
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#15689746C2semidirect
2. C2×#15689726C2semidirect
3. #20254064C2direct (N × H)
4. C2×#15689531C2semidirect
5. C2×#15689509C2semidirect
6. C2×#15689479C2semidirect
7. C2×#15689468C2semidirect
8. C2×#15689376C2semidirect
9. C2×#15689357C2semidirect
10. C2×#15689354C2semidirect
11. C2×#15689232C2semidirect
12. C2×#15689226C2semidirect
13. C2×SD16×Dic47C2semidirect
14. C2×#15689205C2semidirect
15. C2×#15689081C2semidirect
16. C2×C47×#468C2semidirect
22. #15689746C22semidirect
24. #15689726C22semidirect
44. #15689531C22semidirect
45. #15689509C22semidirect
46. #15689479C22semidirect
47. #15689468C22semidirect
48. #15689376C22semidirect
49. #15689357C22semidirect
50. #15689354C22semidirect
51. #15689232C22semidirect
52. #15689226C22semidirect
53. SD16×Dic47C22semidirect
54. #15689205C22semidirect
64. #15689081C22semidirect
73. C47×#468C22semidirect
391. C2×#468D47semidirect
401. C2×C47#3179semidirect
443. #468C2×D47semidirect
467. C47C2×#3179semidirect
777. C2#20254064direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897462
C2×#156897262
#202540642
C2×#156895312
C2×#156895092
C2×#156894792
C2×#156894682
C2×#156893762
C2×#156893572
C2×#156893542
C2×#156892322
C2×#156892262
C2×SD16×Dic472
C2×#156892052
C2×#156890812
C2×C47×#4682
C2×#317947