Finite Group Databasebeta

← #20257174

Subgroups — #20257174

Order 6016.

1540 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094071C211yesmaximal, characteristic, complemented
2C2×#13094069C211yesmaximal, characteristic, complemented
3#15689783C211yesmaximal, characteristic, complemented
4#15689782C211yesmaximal, characteristic, complemented
5#15689781C211yesmaximal, characteristic, complemented
6#15689779C211yesmaximal, characteristic, complemented
7#15689768C211yesmaximal, characteristic, complemented
8#15689767C211yesmaximal, characteristic, complemented
9#15689765C212yesmaximal, complemented
10#15689763C212yesmaximal, complemented
11#15689762C212yesmaximal, complemented
12#15689761C211yesmaximal, characteristic, complemented
13#15689760C212yesmaximal, complemented
14#15689696C211yesmaximal, characteristic, complemented
15#15689695C212yesmaximal, complemented
16#15689689C211yesmaximal, characteristic, complemented
17#15689688C212yesmaximal, complemented
18#15689670C211yesmaximal, characteristic, complemented
19#15689668C212yesmaximal, complemented
20C2×#13094010C212yesmaximal, complemented
21#124×D47C211yesmaximal, characteristic, complemented
22C4×#10625352C211yesmaximal, characteristic, complemented
23C47×#546C211yesmaximal, characteristic, complemented
24#13094071—28no—
25#13094069—28no—
26C2×#10625350C2211yescharacteristic
27C2×#10625350C2211yescharacteristic
28C2×#10625350C2212yescomplemented
29C2×#10625350C2211yescharacteristic, complemented
30C2×#10625352C2211yescharacteristic
31C2×#10625352C2212yes—
32C2×#10625352C2211yescharacteristic
33C2×#10625352C2212yescomplemented
34C2×#10625352C2211yescharacteristic, complemented
35C2×#10625352C2212yescomplemented
36C22×Dic94C2211yescharacteristic, complemented
37C22×Dic94C2212yescomplemented
38C2×Q8×D47C2211yescharacteristic, complemented
39C2×Q8×D47C2211yescharacteristic, complemented
40C22×C22⋊D47C2212yes—
41C22×C22⋊D47C2212yes—
42C2×D4×D47C2211yescharacteristic
43C2×D4×D47C2212yes—
44C2×D4×D47C2211yescharacteristic
45#13094023C2212yescomplemented
46#13094023C2211yescharacteristic, complemented
47#13094020C2212yescomplemented
48#13094020C2211yescharacteristic, complemented
49#13094013C2211yescharacteristic, complemented
50#13094012C2211yescharacteristic, complemented
51#13094011C2211yescharacteristic, complemented
52#13094010C2212yescomplemented
53#13094010C2212yescomplemented
54#13094010C2212yescomplemented
55#13094010C2212yescomplemented
56#13094010C2212yescomplemented
57#13094010C2212yescomplemented
58#13094010C2211yescharacteristic, complemented
59#13094010C2212yescomplemented
60#13094010C2212yescomplemented
61#13094010C2211yescharacteristic, complemented
62#13094009C2212yescomplemented
63#13094008C2212yescomplemented
64#13094007C2212yescomplemented
65#13094006C2212yescomplemented
66#13094005C2212yescomplemented
67#13094004C2211yescharacteristic, complemented
68#13094003C2211yescharacteristic, complemented
69#13094002C2212yescomplemented
70#13094002C2212yescomplemented
71#13094001C2212yescomplemented
72#13094001C2212yescomplemented
73#13094000C2211yescharacteristic, complemented
74#13093999C2211yescharacteristic, complemented
75#13093999C2211yescharacteristic, complemented
76#13093998C2211yescharacteristic, complemented
77#13093998C2212yescomplemented
78#13093997C2211yescharacteristic, complemented
79#13093997C2211yescharacteristic, complemented
80#13093997C2212yescomplemented
81#13093997C2212yescomplemented
82#13093996C2212yescomplemented
83#13093996C2212yescomplemented
84#13093996C2212yescomplemented
85#13093996C2212yescomplemented
86#13093995C2211yescharacteristic, complemented
87#13093995C2211yescharacteristic, complemented
88#13093994C2212yescomplemented
89#13093994C2212yescomplemented
90#13093993C2212yescomplemented
91#13093992C2212yescomplemented
92#13093992C2212yescomplemented
93C4×Dic94C2211yescharacteristic, complemented
94#13093989C2211yescharacteristic, complemented
95C4×D188C2211yescharacteristic, complemented
96D4×Dic47C2212yescomplemented
97D4×Dic47C2211yescharacteristic, complemented
98#13093986C2212yescomplemented
99C4×C22⋊D47C2211yescharacteristic, complemented
100C4×C22⋊D47C2212yescomplemented
101C4×C22⋊D47C2211yescharacteristic, complemented
102(C22⋊D47)⋊C4C2212yescomplemented
103(C22⋊D47)⋊C4C2212yescomplemented
104(C22⋊D47)⋊C4C2212yescomplemented
105#13093982C2211yescharacteristic, complemented
106#13093980C2212yescomplemented
107C2×C22⋊Dic47C2212yescomplemented
108C2×(C2×D47)⋊C4C2212yescomplemented
109C2×(C2×D47)⋊C4C2212yescomplemented
110C22⋊C4×D47C2212yescomplemented
111C22⋊C4×D47C2212yescomplemented
112C2×C4×Dic47C2212yescomplemented
113C42×D47C2211yescharacteristic, complemented
114C2×#41×C47C2211yescharacteristic, complemented
115C22×D4×C47C2211yescharacteristic
116#124×C47C2211yescharacteristic, complemented
117#123×C47C2212yescomplemented
118C22⋊Q8×C47C2211yescharacteristic, complemented
119#121×C47C2212yescomplemented
120#121×C47C2211yescharacteristic, complemented
121#120×C47C2212yescomplemented
122C4×D4×C47C2211yescharacteristic, complemented
123C4×D4×C47C2211yescharacteristic, complemented
124C2×C22⋊C4×C47C2212yescomplemented
125C24×C47C2312yes—
126C23×D47C2312yes—
127C23×D47C2312yes—
128#41×C47—24no—
129C2×Q8×C47C2311yescharacteristic
130C2×D4×C47—24no—
131C2×D4×C47C2312yes—
132C2×D4×C47C2312yes—
133C2×D4×C47C2311yescharacteristic
134C2×D4×C47C2311yescharacteristic
135C2×D4×C47C2312yes—
136C2×D4×C47C2311yescharacteristic
137C22×C4×C47C2312yes—
138C22×C4×C47C2311yescharacteristic
139C22×C4×C47C2311yescharacteristic
140C22×C4×C47C2312yes—
141C2×C22⋊D47—28no—
142C2×C22⋊D47—28no—
143C2×C22⋊D47C2311yescharacteristic
144C2×C22⋊D47C2312yes—
145C2×C22⋊D47C2311yescharacteristic
146C2×C22⋊D47C2312yes—
147C2×C22⋊D47C2312yes—
148C2×C22⋊D47C2312yes—
149C2×C22⋊D47C2312yes—
150C2×C22⋊D47C2311yescharacteristic
151C2×C22⋊D47C2311yescharacteristic
152C2×C22⋊D47C2312yes—
153C2×C22⋊D47C2312yes—
154C2×C22⋊D47C2311yescharacteristic
155C2×C22⋊D47C2311yescharacteristic
156C2×C22⋊D47C2312yes—
157C22×Dic47C2312yes—
158C22×Dic47C2312yes—
159C22×Dic47C2312yes—
160C22×Dic47C2312yes—
161C22×Dic47C2312yes—
162Q8×D47—24no—
163Q8×D47—24no—
164#10625352—24no—
165#10625352—28no—
166#10625352—28no—
167#10625352—28no—
168#10625352—24no—
169#10625352D418yescomplemented
170D4×D47—24no—
171D4×D47—28no—
172D4×D47—24no—
173#10625350—28no—
174#10625350—24no—
175#10625350—24no—
176#10625350—24no—
177C2×D188C2311yescharacteristic
178C2×D188C2311yescharacteristic
179C2×D188C2311yescharacteristic
180C2×D188C2312yes—
181C2×D188C2311yescharacteristic
182C2×C4×D47C2312yes—
183C2×C4×D47C2312yes—
184C2×C4×D47C2312yes—
185C2×C4×D47C2311yescharacteristic
186C2×C4×D47C2311yescharacteristic
187C2×C4×D47C2311yescharacteristic
188C2×C4×D47C2311yescharacteristic
189C2×C4×D47C2311yescharacteristic
190C2×Dic94—28no—
191C2×Dic94—24no—
192C2×Dic94C2312yes—
193C2×Dic94C2312yes—
194C2×Dic94C2311yescharacteristic
195C2×Dic94C2312yes—
196C2×Dic94C2311yescharacteristic
197C2×Dic94C2311yescharacteristic
198C2×Dic94C2311yescharacteristic
199C4⋊C4×C47C2311yescharacteristic
200C4⋊C4×C47C2311yescharacteristic
201C4⋊C4×C47C2312yes—
202C22⋊C4×C47C2311yescharacteristic
203C22⋊C4×C47C2312yes—
204C22⋊C4×C47C2312yes—
205C22⋊C4×C47C2312yes—
206C22⋊C4×C47C2312yes—
207C22⋊C4×C47C2311yescharacteristic
208C22⋊C4×C47C2312yes—
209C42×C47C2311yescharacteristic
210C22⋊Dic47C2312yes—
211C22⋊Dic47C2312yes—
212C22⋊Dic47C2311yescharacteristic
213C22⋊Dic47C2312yes—
214C22⋊Dic47C2312yes—
215C22⋊Dic47C2312yes—
216C22⋊Dic47C2311yescharacteristic
217(C2×D47)⋊C4C2312yes—
218(C2×D47)⋊C4C2312yes—
219(C2×D47)⋊C4C2312yes—
220(C2×D47)⋊C4C2312yes—
221(C2×D47)⋊C4C2311yescharacteristic
222(C2×D47)⋊C4C2311yescharacteristic
223(C2×D47)⋊C4C2312yes—
224(C2×D47)⋊C4C2312yes—
225(C2×D47)⋊C4C2312yes—
226(C2×D47)⋊C4C2312yes—
227(C2×D47)⋊C4C2312yes—
228(C2×D47)⋊C4C2311yescharacteristic
229(C2×D47)⋊C4C2311yescharacteristic
230C4⋊Dic47C2311yescharacteristic
231C4⋊Dic47C2312yes—
232C4⋊Dic47C2311yescharacteristic
233Dic47⋊C4C2312yes—
234Dic47⋊C4C2312yes—
235Dic47⋊C4C2312yes—
236Dic47⋊C4C2312yes—
237Dic47⋊C4C2311yescharacteristic
238Dic47⋊C4C2311yescharacteristic
239C4×Dic47C2311yescharacteristic
240C4×Dic47C2311yescharacteristic
241C4×Dic47C2311yescharacteristic
242C4×Dic47C2312yes—
243C4×Dic47C2312yes—
244C4×Dic47C2312yes—
245C23×C47—24no—
246C23×C47—42no—
247C23×C47—42no—
248C23×C47C2412yes—
249C23×C47C2411yescharacteristic
250C23×C47C2411yescharacteristic
251C23×C47C2412yes—
252C22×D47—24no—
253C22×D47—24no—
254C22×D47—42no—
255C22×D47—42no—
256C22×D47—42no—
257C22×D47—42no—
258C22×D47C2412yes—
259C22×D47C2411yescharacteristic
260C22×D47C2411yescharacteristic
261C22×D47C2411yescharacteristic
262Q8×C47—22no—
263D4×C47—24no—
264D4×C47—24no—
265D4×C47—22no—
266D4×C47—41no—
267D4×C47—42no—
268D4×C47C2×D414yes—
269C2×C4×C47—24no—
270C2×C4×C47—22no—
271C2×C4×C47—22no—
272C2×C4×C47—42no—
273C2×C4×C47C2411yescharacteristic
274C2×C4×C47C2412yes—
275C2×C4×C47C2411yescharacteristic
276C2×C4×C47C2411yescharacteristic
277C2×C4×C47C2411yescharacteristic
278C2×C4×C47C2412yes—
279C2×C4×C47C2411yescharacteristic
280C22⋊D47—24no—
281C22⋊D47—24no—
282C22⋊D47—22no—
283C22⋊D47—22no—
284C22⋊D47—22no—
285C22⋊D47—22no—
286C22⋊D47—24no—
287C22⋊D47—24no—
288C22⋊D47—24no—
289C22⋊D47—41no—
290C22⋊D47—41no—
291C22⋊D47—42no—
292C22⋊D47—42no—
293C22⋊D47C2×D418yes—
294C2×Dic47—24no—
295C2×Dic47—24no—
296C2×Dic47—24no—
297C2×Dic47—42no—
298C2×Dic47C2×D418yes—
299C2×Dic47C2411yescharacteristic
300C2×Dic47C2411yescharacteristic
301C2×Dic47C2412yes—
302C2×Dic47C2411yescharacteristic
303C2×Dic47C2412yes—
304C2×Dic47C2411yescharacteristic
305C2×Dic47C2411yescharacteristic
306C2×Dic47C2412yes—
307D188—22no—
308D188—22no—
309D188—22no—
310D188—41no—
311D188—42no—
312C4×D47—24no—
313C4×D47—22no—
314C4×D47—22no—
315C4×D47—24no—
316C4×D47—24no—
317C4×D47—41no—
318C4×D47—41no—
319C4×D47C2×D414yes—
320Dic94—22no—
321Dic94—22no—
322Dic94—24no—
323Dic94—24no—
324Dic94—24no—
325Dic94—22no—
326Dic94C2×D414yes—
327C22×C47—22no—
328C22×C47—22no—
329C22×C47—21no—
330C22×C47—22no—
331C22×C47—21no—
332C22×C47—21no—
333C22×C47—21no—
334C22×C47—22no—
335C22×C47—21no—
336C22×C47—22no—
337C22×C47—21no—
338C22×C47—84no—
339C22×C47C22×D414yes—
340C22×C47C2511yescharacteristic
341C2×D47—21no—
342C2×D47—21no—
343C2×D47—21no—
344C2×D47—21no—
345C2×D47—22no—
346C2×D47—21no—
347C2×D47—21no—
348C2×D47—22no—
349C2×D47—21no—
350C2×D47—21no—
351C2×D47—22no—
352C2×D47—84no—
353C2×D47—84no—
354C2×D47C22×D412yes—
355C4×C47—21no—
356C4×C47—22no—
357C4×C47—21no—
358C4×C47—21no—
359C4×C47—21no—
360C4×C47—22no—
361C4×C47C22×D412yes—
362Dic47—22no—
363Dic47—21no—
364Dic47—21no—
365Dic47—21no—
366Dic47—21no—
367Dic47—22no—
368Dic47C22×D412yes—
369Dic47C22×D414yes—
370#3500—471nomaximal, Sylow
371C2×C47—24no—
372C2×C47—42no—
373C2×C47—41no—
374C2×C47—41no—
375C2×C47C23×D411yescharacteristic
376C2×C47#58511yescharacteristic
377C2×C47#58511yescharacteristic
378D47—22no—
379D47—41no—
380D47—42no—
381D47—41no—
382C2×2−1+4—471no—
383C2×H(5,𝔽2)—471no—
384#548—471no—
385#548—471no—
386#548—471no—
387#548—471no—
388#546—471no—
389#546—471no—
390#546—472no—
391#546—472no—
392#546—472no—
393#546—471no—
394#546—472no—
395#546D4711yescharacteristic, complemented
396#536—472no—
397#536—471no—
398#535—471no—
399#535—472no—
400#532—472no—
401#532—471no—
402C2×#124—471no—
403C2×#124—472no—
404C4×#41—471no—
405C47#350011yescharacteristic, complemented, Sylow
4062−1+4—948no—
407H(5,𝔽2)—948no—
408C2×#41—471no—
409C2×#41—472no—
410C2×#41—472no—
411C2×#41—471no—
412C2×#41—472no—
413C2×#41—471no—
414C2×#41—471no—
415C2×#41—471no—
416C2×#41—472no—
417C2×#41—471no—
418C2×#41C2×D4711yescharacteristic, complemented
419C22×Q8—471no—
420C22×Q8—471no—
421C22×Q8—472no—
422C22×Q8—471no—
423C22×D4—472no—
424C22×D4—472no—
425C22×D4—471no—
426C22×D4—472no—
427C22×D4—471no—
428C22×D4C2×D4711yescharacteristic
429C4⋊Q8—472no—
430C4⋊Q8—471no—
431#127—472no—
432#127—471no—
433#124—471no—
434#124—471no—
435#124—472no—
436#124—471no—
437#124—472no—
438#124—472no—
439#124—472no—
440#124—472no—
441#124—472no—
442#124—472no—
443#124—472no—
444#124—471no—
445#124—471no—
446#124C2×D4711yescharacteristic, complemented
447#123—472no—
448#123—472no—
449#123—472no—
450#123—472no—
451#123—472no—
452#123C2×D4712yescomplemented
453C22⋊Q8—471no—
454C22⋊Q8—471no—
455C22⋊Q8—472no—
456C22⋊Q8—472no—
457C22⋊Q8—471no—
458C22⋊Q8—472no—
459C22⋊Q8—472no—
460C22⋊Q8C2×D4711yescharacteristic, complemented
461#121—471no—
462#121—472no—
463#121—472no—
464#121—471no—
465#121—472no—
466#121—472no—
467#121—472no—
468#121—471no—
469#121—471no—
470#121—471no—
471#121—471no—
472#121—471no—
473#121—472no—
474#121—472no—
475#121C2×D4712yescomplemented
476#121C2×D4711yescharacteristic, complemented
477#120—472no—
478#120—472no—
479#120—472no—
480#120—472no—
481#120—472no—
482#120C2×D4712yescomplemented
483C4×Q8—471no—
484C4×Q8—471no—
485C4×D4—471no—
486C4×D4—472no—
487C4×D4—472no—
488C4×D4—471no—
489C4×D4—471no—
490C4×D4—472no—
491C4×D4—472no—
492C4×D4—472no—
493C4×D4—472no—
494C4×D4—471no—
495C4×D4C2×D4711yescharacteristic, complemented
496C4×D4C2×D4711yescharacteristic, complemented
497#117—471no—
498#117—472no—
499C2×C22⋊C4—472no—
500C2×C22⋊C4—472no—
501C2×C22⋊C4—472no—
502C2×C22⋊C4—472no—
503C2×C22⋊C4—472no—
504C2×C22⋊C4C2×D4712yescomplemented
505C2×C42—472no—
506C2×C42—471no—
507C24—472no—
508C24—472no—
509C24C22×D4712yes—
510#41—24no—
511#41—478no—
512#41—944no—
513#41—944no—
514#41—948no—
515#41—944no—
516#41—948no—
517#41—948no—
518#41—948no—
519#41—944no—
520#41—944no—
521C2×Q8—471no—
522C2×Q8—472no—
523C2×Q8—472no—
524C2×Q8—471no—
525C2×Q8—472no—
526C2×Q8—471no—
527C2×Q8—471no—
528C2×Q8—948no—
529C2×Q8—944no—
530C2×Q8—944no—
531C2×Q8—944no—
532C2×Q8C22×D4711yescharacteristic
533C2×D4—24no—
534C2×D4—472no—
535C2×D4—471no—
536C2×D4—472no—
537C2×D4—471no—
538C2×D4—472no—
539C2×D4—472no—
540C2×D4—472no—
541C2×D4—472no—
542C2×D4—471no—
543C2×D4—471no—
544C2×D4—472no—
545C2×D4—471no—
546C2×D4—472no—
547C2×D4—471no—
548C2×D4—471no—
549C2×D4—471no—
550C2×D4—471no—
551C2×D4—472no—
552C2×D4—471no—
553C2×D4—944no—
554C2×D4—948no—
555C2×D4—948no—
556C2×D4—948no—
557C2×D4—944no—
558C2×D4C22×D4712yes—
559C2×D4C22×D4712yes—
560C2×D4C22×D4711yescharacteristic
561C2×D4C22×D4712yes—
562C2×D4C22×D4711yescharacteristic
563C2×D4C22×D4711yescharacteristic
564C22×C4—472no—
565C22×C4—471no—
566C22×C4—472no—
567C22×C4—472no—
568C22×C4—472no—
569C22×C4—472no—
570C22×C4—472no—
571C22×C4—472no—
572C22×C4—471no—
573C22×C4—472no—
574C22×C4—471no—
575C22×C4—471no—
576C22×C4—471no—
577C22×C4C22×D4712yes—
578C22×C4C22×D4711yescharacteristic
579C22×C4C22×D4711yescharacteristic
580C22×C4C22×D4712yes—
581C4⋊C4—472no—
582C4⋊C4—472no—
583C4⋊C4—472no—
584C4⋊C4—471no—
585C4⋊C4—472no—
586C4⋊C4—471no—
587C4⋊C4—471no—
588C4⋊C4—472no—
589C4⋊C4—471no—
590C4⋊C4C22×D4711yescharacteristic
591C4⋊C4C22×D4712yes—
592C4⋊C4C22×D4711yescharacteristic
593C22⋊C4—472no—
594C22⋊C4—471no—
595C22⋊C4—472no—
596C22⋊C4—472no—
597C22⋊C4—472no—
598C22⋊C4—472no—
599C22⋊C4—471no—
600C22⋊C4—472no—
601C22⋊C4—471no—
602C22⋊C4—472no—
603C22⋊C4—471no—
604C22⋊C4—472no—
605C22⋊C4—472no—
606C22⋊C4—472no—
607C22⋊C4—472no—
608C22⋊C4—472no—
609C22⋊C4—472no—
610C22⋊C4—472no—
611C22⋊C4—471no—
612C22⋊C4—471no—
613C22⋊C4C22×D4712yes—
614C22⋊C4C22×D4712yes—
615C22⋊C4C22×D4711yescharacteristic
616C22⋊C4C22×D4712yes—
617C22⋊C4C22×D4712yes—
618C22⋊C4C22×D4712yes—
619C22⋊C4C22×D4711yescharacteristic
620C42—471no—
621C42—472no—
622C42—471no—
623C42—472no—
624C42—472no—
625C42—471no—
626C42C22×D4711yescharacteristic
627C23—24no—
628C23—42no—
629C23—42no—
630C23—471no—
631C23—472no—
632C23—471no—
633C23—471no—
634C23—944no—
635C23—944no—
636C23—1882no—
637C23—1882no—
638C23—1882no—
639C23—1882no—
640C23C23×D4712yes—
641C23C23×D4711yescharacteristic
642C23C23×D4711yescharacteristic
643C23C23×D4712yes—
644Q8—22no—
645Q8—474no—
646Q8—942no—
647Q8—944no—
648Q8—944no—
649Q8—944no—
650Q8—942no—
651Q8—942no—
652D4—24no—
653D4—24no—
654D4—22no—
655D4—42no—
656D4—41no—
657D4—478no—
658D4—942no—
659D4—942no—
660D4—942no—
661D4—944no—
662D4—944no—
663D4—944no—
664D4—942no—
665D4—942no—
666D4—942no—
667D4—944no—
668D4—944no—
669D4—942no—
670D4—1882no—
671D4—1881no—
672D4—1881no—
673D4—1881no—
674D4—1882no—
675D4—1882no—
676D4D4×D4714yes—
677C2×C4—24no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—42no—
681C2×C4—478no—
682C2×C4—471no—
683C2×C4—472no—
684C2×C4—474no—
685C2×C4—471no—
686C2×C4—471no—
687C2×C4—472no—
688C2×C4—471no—
689C2×C4—472no—
690C2×C4—471no—
691C2×C4—944no—
692C2×C4—944no—
693C2×C4—944no—
694C2×C4—944no—
695C2×C4—944no—
696C2×C4—944no—
697C2×C4—942no—
698C2×C4—942no—
699C2×C4—1881no—
700C2×C4—1881no—
701C2×C4—1882no—
702C2×C4C23×D4711yescharacteristic
703C2×C4C23×D4712yes—
704C2×C4C23×D4711yescharacteristic
705C2×C4C23×D4712yes—
706C2×C4C23×D4711yescharacteristic
707C2×C4C23×D4711yescharacteristic
708C2×C4C23×D4711yescharacteristic
709C22—22no—
710C22—22no—
711C22—21no—
712C22—21no—
713C22—22no—
714C22—21no—
715C22—22no—
716C22—21no—
717C22—21no—
718C22—21no—
719C22—22no—
720C22—84no—
721C22—472no—
722C22—941no—
723C22—941no—
724C22—941no—
725C22—942no—
726C22—941no—
727C22—941no—
728C22—942no—
729C22—941no—
730C22—941no—
731C22—941no—
732C22—942no—
733C22—3764no—
734C22—3764no—
735C22C2×D4×D4714yes—
736C22C24×D4711yescharacteristic
737C4—21no—
738C4—21no—
739C4—22no—
740C4—21no—
741C4—22no—
742C4—21no—
743C4—472no—
744C4—474no—
745C4—941no—
746C4—942no—
747C4—941no—
748C4—941no—
749C4—941no—
750C4—942no—
751C4C2×D4×D4712yes—
752C2—24no—
753C2—41no—
754C2—42no—
755C2—41no—
756C2—942no—
757C2—1881no—
758C2—1882no—
759C2—1881no—
760C2C22×D4×D4711yescharacteristic
761C2#1568995811yescharacteristic
762C2#1568995911yescharacteristic
subgroupG/H
center, FrattiniC22C24×D47
commutator, socleC22×C47C25
FittingC47×#546C2
hypercenter#546D47
hypocenterC47#3500
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #546

Complements

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

NH ≅ G/Ntype
1. C2×#13094071C2semidirect
2. C2×#13094069C2semidirect
3. #15689783C2semidirect
4. #15689782C2semidirect
5. #15689781C2semidirect
6. #15689779C2semidirect
7. #15689768C2semidirect
8. #15689767C2semidirect
9. #15689765C2semidirect
10. #15689763C2semidirect
11. #15689762C2semidirect
12. #15689761C2semidirect
13. #15689760C2semidirect
14. #15689696C2semidirect
15. #15689695C2semidirect
16. #15689689C2semidirect
17. #15689688C2semidirect
18. #15689670C2semidirect
19. #15689668C2semidirect
20. C2×#13094010C2semidirect
21. #124×D47C2semidirect
22. C4×#10625352C2semidirect
23. C47×#546C2semidirect
28. C2×#10625350C22semidirect
29. C2×#10625350C22semidirect
33. C2×#10625352C22semidirect
34. C2×#10625352C22semidirect
35. C2×#10625352C22semidirect
36. C22×Dic94C22semidirect
37. C22×Dic94C22semidirect
38. C2×Q8×D47C22semidirect
39. C2×Q8×D47C22semidirect
45. #13094023C22semidirect
46. #13094023C22semidirect
47. #13094020C22semidirect
48. #13094020C22semidirect
49. #13094013C22semidirect
50. #13094012C22semidirect
51. #13094011C22semidirect
52. #13094010C22semidirect
53. #13094010C22semidirect
54. #13094010C22semidirect
55. #13094010C22semidirect
56. #13094010C22semidirect
57. #13094010C22semidirect
58. #13094010C22semidirect
59. #13094010C22semidirect
60. #13094010C22semidirect
61. #13094010C22semidirect
62. #13094009C22semidirect
63. #13094008C22semidirect
64. #13094007C22semidirect
65. #13094006C22semidirect
66. #13094005C22semidirect
67. #13094004C22semidirect
68. #13094003C22semidirect
69. #13094002C22semidirect
70. #13094002C22semidirect
71. #13094001C22semidirect
72. #13094001C22semidirect
73. #13094000C22semidirect
74. #13093999C22semidirect
75. #13093999C22semidirect
76. #13093998C22semidirect
77. #13093998C22semidirect
78. #13093997C22semidirect
79. #13093997C22semidirect
80. #13093997C22semidirect
81. #13093997C22semidirect
82. #13093996C22semidirect
83. #13093996C22semidirect
84. #13093996C22semidirect
85. #13093996C22semidirect
86. #13093995C22semidirect
87. #13093995C22semidirect
88. #13093994C22semidirect
89. #13093994C22semidirect
90. #13093993C22semidirect
91. #13093992C22semidirect
92. #13093992C22semidirect
93. C4×Dic94C22semidirect
94. #13093989C22semidirect
95. C4×D188C22semidirect
96. D4×Dic47C22semidirect
97. D4×Dic47C22semidirect
98. #13093986C22semidirect
99. C4×C22⋊D47C22semidirect
100. C4×C22⋊D47C22semidirect
101. C4×C22⋊D47C22semidirect
102. (C22⋊D47)⋊C4C22semidirect
103. (C22⋊D47)⋊C4C22semidirect
104. (C22⋊D47)⋊C4C22semidirect
105. #13093982C22semidirect
106. #13093980C22semidirect
107. C2×C22⋊Dic47C22semidirect
108. C2×(C2×D47)⋊C4C22semidirect
109. C2×(C2×D47)⋊C4C22semidirect
110. C22⋊C4×D47C22semidirect
111. C22⋊C4×D47C22semidirect
112. C2×C4×Dic47C22semidirect
113. C42×D47C22semidirect
114. C2×#41×C47C22semidirect
116. #124×C47C22semidirect
117. #123×C47C22semidirect
118. C22⋊Q8×C47C22semidirect
119. #121×C47C22semidirect
120. #121×C47C22semidirect
121. #120×C47C22semidirect
122. C4×D4×C47C22semidirect
123. C4×D4×C47C22semidirect
124. C2×C22⋊C4×C47C22semidirect
169. #10625352D4semidirect
395. #546D47semidirect
405. C47#3500semidirect
418. C2×#41C2×D47semidirect
446. #124C2×D47semidirect
452. #123C2×D47semidirect
460. C22⋊Q8C2×D47semidirect
475. #121C2×D47semidirect
476. #121C2×D47semidirect
482. #120C2×D47semidirect
495. C4×D4C2×D47semidirect
496. C4×D4C2×D47semidirect
504. C2×C22⋊C4C2×D47semidirect