Finite Group Databasebeta

← C2×#20255041 #27091432

Subgroups — C2×#20255041 #27091432

Order 12032.

2762 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094055C211yesmaximal, characteristic, complemented
2C22×#13094054C211yesmaximal, characteristic, complemented
3C2×#15689782C211yesmaximal, characteristic, complemented
4#20255041C2116yesmaximal, direct product factor
5C2×#15689505C211yesmaximal, characteristic, complemented
6C2×#15689371C211yesmaximal, characteristic, complemented
7C2×#15689367C211yesmaximal, characteristic, complemented
8C2×#15689345C211yesmaximal, characteristic, complemented
9C2×#15689342C211yesmaximal, characteristic, complemented
10C2×#15689268C211yesmaximal, characteristic, complemented
11C2×#15689266C211yesmaximal, characteristic, complemented
12C2×#15689279C211yesmaximal, characteristic, complemented
13C2×#15689278C211yesmaximal, characteristic, complemented
14C2×C4×#10625337C211yesmaximal, characteristic, complemented
15C2×#15689201C211yesmaximal, characteristic, complemented
16C2×C47×#548C211yesmaximal, characteristic, complemented
17C22×#10625350C2211yescharacteristic
18C23×Dic94C2211yescharacteristic
19C2×#13094055—28no—
20C2×#13094055C2218yescomplemented
21C2×#13094054—28no—
22C2×#13094054C2218yescomplemented
23C22×#10625337C2211yescharacteristic
24C22×#10625337C2211yescharacteristic
25C22×#10625337C2211yescharacteristic
26C22×#10625337C2211yescharacteristic
27C22×#10625335C2211yescharacteristic
28C22×#10625335C2211yescharacteristic
29C22×#10625336C2211yescharacteristic
30C22×#10625336C2211yescharacteristic
31C22×#10625334C2211yescharacteristic
32C22×#10625329C2211yescharacteristic
33C22×#10625329C2211yescharacteristic
34#15689782—24no—
35#15689782C2218yescomplemented
36C2×#13094012C2211yescharacteristic
37C2×#13094010—21no—
38C2×#13094003C2211yescharacteristic
39C2×#13094002—21no—
40C2×#13093998C2211yescharacteristic
41C2×#13093996—21no—
42C2×C4×Dic94C2211yescharacteristic
43C2×(C22⋊D47)⋊C4—21no—
44#15689505C2218yescomplemented
45#15689371C2218yescomplemented
46#15689367C2218yescomplemented
47#15689345C2218yescomplemented
48#15689342C2218yescomplemented
49#15689279C2218yescomplemented
50#15689278C2218yescomplemented
51#15689268C2218yescomplemented
52#15689266C2218yescomplemented
53C4×#10625337C2218yescomplemented
54#15689201C2218yescomplemented
55C2×#13093957C2211yescharacteristic
56C2×C4⋊(C47⋊C8)C2211yescharacteristic
57C2×#13093948C2211yescharacteristic
58C2×#13093948C2211yescharacteristic
59C2×#13093947C2211yescharacteristic
60C2×#13093947C2211yescharacteristic
61C2×#13093945C2211yescharacteristic
62C2×#13093944C2211yescharacteristic
63C2×C22⋊(C47⋊C8)C2211yescharacteristic
64C2×C22⋊(C47⋊C8)C2211yescharacteristic
65C2×C4×C47⋊C8C2211yescharacteristic
66C22×#41×C47C2211yescharacteristic
67C23×Q8×C47C2211yescharacteristic
68C47×#548—24no—
69C47×#548C2218yescomplemented
70C2×#124×C47—21no—
71C2×#124×C47C2211yescharacteristic
72C2×C22⋊Q8×C47—21no—
73C2×C22⋊Q8×C47C2211yescharacteristic
74C2×#121×C47—21no—
75C2×#121×C47C2211yescharacteristic
76C2×C4×Q8×C47C2211yescharacteristic
77C2×C4×D4×C47—21no—
78C2×C4×D4×C47C2211yescharacteristic
79C2×#10625350—22no—
80C2×#10625350—24no—
81C2×#10625350—42no—
82C2×#10625350C2314yes—
83C22×Dic94—24no—
84C22×Dic94—22no—
85C22×Dic94—21no—
86C22×Dic94—42no—
87C22×Dic94C2311yescharacteristic
88C22×Dic94C2314yes—
89C22×Dic94C2311yescharacteristic
90C22×D188C2311yescharacteristic
91C22×C22⋊D47—21no—
92C22×C22⋊D47—21no—
93C23×Dic47—21no—
94C22×C4×D47—21no—
95#13094055—232no—
96#13094054—232no—
97C2×#10625337—24no—
98C2×#10625337—24no—
99C2×#10625337—42no—
100C2×#10625337D418yescomplemented
101C2×#10625337C2314yes—
102C2×#10625337C2314yes—
103C2×#10625337C2314yes—
104C2×#10625337C2314yes—
105C2×#10625335—24no—
106C2×#10625335—24no—
107C2×#10625335C2314yes—
108C2×#10625335C2314yes—
109C2×#10625336—24no—
110C2×#10625336—24no—
111C2×#10625336C2314yes—
112C2×#10625336C2314yes—
113C2×#10625334—42no—
114C2×#10625334C2314yes—
115C2×#10625329—24no—
116C2×#10625329—24no—
117C2×#10625329C2314yes—
118C2×#10625329C2314yes—
119C22×C47⋊C8C2311yescharacteristic
120C22×C47⋊C8C2311yescharacteristic
121C22×C47⋊C8C2311yescharacteristic
122C22×C47⋊C8C2311yescharacteristic
123#13094012—22no—
124#13094012C2314yes—
125#13094010—28no—
126#13094003—22no—
127#13094003C2314yes—
128#13094002—28no—
129#13093998—22no—
130#13093998C2314yes—
131#13093996—28no—
132C4×Dic94—22no—
133C4×Dic94C2314yes—
134(C22⋊D47)⋊C4—28no—
135C2×C4⋊Dic47C2311yescharacteristic
136C2×Dic47⋊C4—21no—
137C2×Dic47⋊C4—21no—
138C2×C22⋊Dic47—21no—
139C2×(C2×D47)⋊C4—21no—
140C2×(C2×D47)⋊C4—21no—
141C2×(C2×D47)⋊C4—21no—
142C2×C4×Dic47—21no—
143#13093957C2314yes—
144C4⋊(C47⋊C8)C2314yes—
145#13093948C2314yes—
146#13093948C2314yes—
147#13093947C2314yes—
148#13093947C2314yes—
149#13093945C2314yes—
150#13093944C2314yes—
151C22⋊(C47⋊C8)C2314yes—
152C22⋊(C47⋊C8)C2314yes—
153C4×C47⋊C8C2314yes—
154C2×#41×C47—22no—
155C2×#41×C47—24no—
156C2×#41×C47—42no—
157C2×#41×C47C2314yes—
158C22×Q8×C47—21no—
159C22×Q8×C47—22no—
160C22×Q8×C47—24no—
161C22×Q8×C47—42no—
162C22×Q8×C47C2311yescharacteristic
163C22×Q8×C47C2314yes—
164C22×Q8×C47C2311yescharacteristic
165C22×D4×C47—21no—
166C22×D4×C47—21no—
167C22×D4×C47D411yescharacteristic
168C22×D4×C47C2311yescharacteristic
169C23×C4×C47—21no—
170C23×C4×C47—21no—
171C23×C4×C47C2311yescharacteristic
172C23×C4×C47C2311yescharacteristic
173#124×C47—28no—
174#124×C47—22no—
175#124×C47C2314yes—
176C22⋊Q8×C47—22no—
177C22⋊Q8×C47—28no—
178C22⋊Q8×C47C2314yes—
179#121×C47—28no—
180#121×C47—22no—
181#121×C47C2314yes—
182C4×Q8×C47—22no—
183C4×Q8×C47C2314yes—
184C4×D4×C47—28no—
185C4×D4×C47D414yes—
186C4×D4×C47C2314yes—
187C2×C4⋊C4×C47—21no—
188C2×C4⋊C4×C47—21no—
189C2×C4⋊C4×C47D411yescharacteristic
190C2×C4⋊C4×C47C2311yescharacteristic
191C2×C22⋊C4×C47—21no—
192C2×C22⋊C4×C47—21no—
193C2×C22⋊C4×C47—21no—
194C2×C22⋊C4×C47—21no—
195C2×C22⋊C4×C47D411yescharacteristic
196C2×C22⋊C4×C47D411yescharacteristic
197C2×C42×C47—21no—
198C2×C42×C47C2311yescharacteristic
199C24×C47—21no—
200C24×C47C2×D411yescharacteristic
201C24×C47C2×D411yescharacteristic
202C23×D47—21no—
203#41×C47—28no—
204#41×C47—44no—
205#41×C47—48no—
206C2×Q8×C47—21no—
207C2×Q8×C47—24no—
208C2×Q8×C47—21no—
209C2×Q8×C47—22no—
210C2×Q8×C47—28no—
211C2×Q8×C47—22no—
212C2×Q8×C47—22no—
213C2×Q8×C47—44no—
214C2×Q8×C47—44no—
215C2×Q8×C47—48no—
216C2×Q8×C47C2×D414yes—
217C2×Q8×C47C2412yes—
218C2×Q8×C47C2412yes—
219C2×D4×C47—24no—
220C2×D4×C47—24no—
221C2×D4×C47—22no—
222C2×D4×C47—21no—
223C2×D4×C47—22no—
224C2×D4×C47—42no—
225C2×D4×C47—44no—
226C2×D4×C47—44no—
227C2×D4×C47C2×D414yes—
228C2×D4×C47C2412yes—
229C22×C4×C47—21no—
230C22×C4×C47—22no—
231C22×C4×C47—22no—
232C22×C4×C47—22no—
233C22×C4×C47—22no—
234C22×C4×C47—21no—
235C22×C4×C47—21no—
236C22×C4×C47—24no—
237C22×C4×C47—24no—
238C22×C4×C47—44no—
239C22×C4×C47—44no—
240C22×C4×C47C2×D411yescharacteristic
241C22×C4×C47C2×D411yescharacteristic
242C22×C4×C47C2×D411yescharacteristic
243C22×C4×C47C2×D411yescharacteristic
244C22×C4×C47C2×D412yes—
245C22×C4×C47C2×D412yes—
246C22×C4×C47C2412yes—
247C22×C4×C47C2412yes—
248C22×C4×C47C2411yescharacteristic
249C2×C22⋊D47—24no—
250C2×C22⋊D47—24no—
251C2×C22⋊D47—44no—
252C2×C22⋊D47—44no—
253C22×Dic47—21no—
254C22×Dic47—21no—
255C22×Dic47—21no—
256C22×Dic47—24no—
257C22×Dic47—44no—
258#10625350—28no—
259#10625350—44no—
260#10625350—48no—
261C2×D188—22no—
262C2×D188—22no—
263C2×D188—21no—
264C2×D188C2412yes—
265C2×C4×D47—24no—
266C2×C4×D47—44no—
267C2×Dic94—21no—
268C2×Dic94—22no—
269C2×Dic94—22no—
270C2×Dic94—22no—
271C2×Dic94—28no—
272C2×Dic94—24no—
273C2×Dic94—21no—
274C2×Dic94—44no—
275C2×Dic94—48no—
276C2×Dic94—44no—
277C2×Dic94C2×D414yes—
278C2×Dic94C2412yes—
279C2×Dic94C2412yes—
280C4⋊C4×C47—24no—
281C4⋊C4×C47—24no—
282C4⋊C4×C47—21no—
283C4⋊C4×C47C2×D414yes—
284C4⋊C4×C47C2412yes—
285C22⋊C4×C47—24no—
286C22⋊C4×C47—24no—
287C22⋊C4×C47—24no—
288C22⋊C4×C47—24no—
289C22⋊C4×C47C2×D414yes—
290C22⋊C4×C47C2×D414yes—
291C42×C47—24no—
292C42×C47C2×D412yes—
293C42×C47C2412yes—
294C22⋊Dic47—24no—
295#10625337—28no—
296#10625337—28no—
297#10625337—44no—
298#10625337C2×D4116yescomplemented
299#10625336—28no—
300#10625336—28no—
301#10625335—28no—
302#10625335—28no—
303#10625334—44no—
304(C2×D47)⋊C4—24no—
305(C2×D47)⋊C4—24no—
306(C2×D47)⋊C4—24no—
307C4⋊Dic47—21no—
308C4⋊Dic47C2412yes—
309Dic47⋊C4—24no—
310Dic47⋊C4—24no—
311C4×Dic47—24no—
312#10625329—28no—
313#10625329—28no—
314C2×C47⋊C8—22no—
315C2×C47⋊C8—22no—
316C2×C47⋊C8—22no—
317C2×C47⋊C8C2×D414yes—
318C2×C47⋊C8C2412yes—
319C2×C47⋊C8C2412yes—
320C2×C47⋊C8C2412yes—
321C2×C47⋊C8C2412yes—
322C23×C47—22no—
323C23×C47—22no—
324C23×C47—22no—
325C23×C47—22no—
326C23×C47—22no—
327C23×C47—22no—
328C23×C47—22no—
329C23×C47—42no—
330C23×C47—42no—
331C23×C47—42no—
332C23×C47C22×D412yes—
333C23×C47C22×D412yes—
334C23×C47C22×D411yescharacteristic
335C22×D47—22no—
336C22×D47—42no—
337C22×D47—42no—
338C22×D47—42no—
339Q8×C47—24no—
340Q8×C47—22no—
341Q8×C47—22no—
342Q8×C47—22no—
343Q8×C47—48no—
344Q8×C47—42no—
345Q8×C47C22×D414yes—
346D4×C47—22no—
347D4×C47—22no—
348D4×C47—44no—
349D4×C47—48no—
350D4×C47—48no—
351D4×C47—42no—
352C2×C4×C47—22no—
353C2×C4×C47—22no—
354C2×C4×C47—24no—
355C2×C4×C47—22no—
356C2×C4×C47—22no—
357C2×C4×C47—22no—
358C2×C4×C47—24no—
359C2×C4×C47—24no—
360C2×C4×C47—22no—
361C2×C4×C47—22no—
362C2×C4×C47—22no—
363C2×C4×C47—22no—
364C2×C4×C47—22no—
365C2×C4×C47—22no—
366C2×C4×C47—48no—
367C2×C4×C47—48no—
368C2×C4×C47—42no—
369C2×C4×C47—42no—
370C2×C4×C47C22×D412yes—
371C2×C4×C47C22×D412yes—
372C2×C4×C47C22×D412yes—
373C2×C4×C47C22×D412yes—
374C2×C4×C47C22×D412yes—
375C2×C4×C47C22×D411yescharacteristic
376C2×C4×C47H(5,𝔽2)12yes—
377C2×C4×C47C2511yescharacteristic
378C22⋊D47—48no—
379C22⋊D47—48no—
380C2×Dic47—24no—
381C2×Dic47—22no—
382C2×Dic47—22no—
383C2×Dic47—22no—
384C2×Dic47—48no—
385C2×Dic47—42no—
386C2×Dic47—42no—
387D188—22no—
388D188—22no—
389D188—42no—
390C4×D47—48no—
391Dic94—24no—
392Dic94—22no—
393Dic94—22no—
394Dic94—22no—
395Dic94—48no—
396Dic94—42no—
397Dic94C22×D414yes—
398C47⋊C8—22no—
399C47⋊C8—22no—
400C47⋊C8—22no—
401C47⋊C8C22×D414yes—
402C2×#3277—471nomaximal, Sylow
403C22×C47—22no—
404C22×C47—22no—
405C22×C47—22no—
406C22×C47—22no—
407C22×C47—22no—
408C22×C47—22no—
409C22×C47—44no—
410C22×C47—44no—
411C22×C47—42no—
412C22×C47—42no—
413C22×C47—42no—
414C22×C47—84no—
415C22×C47D4212yes—
416C22×C47#57512yes—
417C22×C47#57812yes—
418C22×C47C23×D411yescharacteristic
419C2×D47—42no—
420C2×D47—42no—
421C2×D47—42no—
422C2×D47—84no—
423C4×C47—22no—
424C4×C47—22no—
425C4×C47—24no—
426C4×C47—22no—
427C4×C47—22no—
428C4×C47—42no—
429C4×C47—42no—
430C4×C47D4212yes—
431C4×C47C23×D411yescharacteristic
432C4×C47C2×H(5,𝔽2)11yescharacteristic
433Dic47—24no—
434Dic47—42no—
435Dic47—42no—
436C22×#137—471no—
437C22×#137—471no—
438C2×#548—471no—
439C2×#548D4711yescharacteristic, complemented
440#3277—4716no—
441C2×#495—471no—
442C2×#468—471no—
443C2×#468—471no—
444C2×#464—471no—
445C2×#464—471no—
446C2×#449—471no—
447C2×#449—471no—
448C2×#451—471no—
449C2×#451—471no—
450C2×C4×Q16—471no—
451C2×#436—471no—
452C2×C47—42no—
453C2×C47—42no—
454C2×C47—82no—
455C2×C47#327714yescomplemented
456C2×C47C2×D4211yescharacteristic
457C2×C47C2×#57511yescharacteristic
458C2×C47C2×#57811yescharacteristic
459D47—82no—
460C22×#41—471no—
461C22×#41C2×D4711yescharacteristic
462C23×Q8—471no—
463C23×Q8C2×D4711yescharacteristic
464C2×#137—478no—
465C2×#137—478no—
466C2×#137—948no—
467C2×#137—948no—
468C22×Q16—471no—
469C22×Q16—471no—
470C22×Q16—471no—
471C22×Q16—471no—
472C22×SD16—471no—
473C22×SD16—471no—
474C22×SD16—471no—
475C22×SD16—471no—
476C22×D8—471no—
477C22×M16—471no—
478C22×M16—471no—
479#548—24no—
480#548—478no—
481#548—944no—
482#548C2×D4718yescomplemented
483C2×#124—21no—
484C2×#124—471no—
485C2×#124—941no—
486C2×#124C2×D4711yescharacteristic
487C2×C22⋊Q8—21no—
488C2×C22⋊Q8—471no—
489C2×C22⋊Q8—941no—
490C2×C22⋊Q8C2×D4711yescharacteristic
491C2×#121—21no—
492C2×#121—471no—
493C2×#121—941no—
494C2×#121C2×D4711yescharacteristic
495C2×C4×Q8—471no—
496C2×C4×Q8C2×D4711yescharacteristic
497C2×C4×D4—21no—
498C2×C4×D4—941no—
499C2×C4×D4C2×D4711yescharacteristic
500#495—478no—
501#468—478no—
502#468—478no—
503#464—478no—
504#464—478no—
505#451—478no—
506#451—478no—
507#449—478no—
508#449—478no—
509C4×Q16—478no—
510#436—478no—
511C2×#107—471no—
512C2×C4⋊C8—471no—
513C2×#103—471no—
514C2×#103—471no—
515C2×#103—471no—
516C2×#103—471no—
517C2×#102—471no—
518C2×#102—471no—
519C2×C22⋊C8—471no—
520C2×C22⋊C8—471no—
521C2×C4×C8—471no—
522C47C2×#327711yescharacteristic, complemented, Sylow
523C2×#41—22no—
524C2×#41—24no—
525C2×#41—42no—
526C2×#41—474no—
527C2×#41—944no—
528C2×#41—942no—
529C2×#41—1882no—
530C2×#41C22×D4714yes—
531C22×Q8—21no—
532C22×Q8—22no—
533C22×Q8—24no—
534C22×Q8—42no—
535C22×Q8—471no—
536C22×Q8—471no—
537C22×Q8—474no—
538C22×Q8—944no—
539C22×Q8—941no—
540C22×Q8—942no—
541C22×Q8—1882no—
542C22×Q8C22×D4711yescharacteristic
543C22×Q8C22×D4714yes—
544C22×Q8C22×D4711yescharacteristic
545C22×D4—21no—
546C22×D4—21no—
547C22×D4—471no—
548C22×D4—941no—
549C22×D4—941no—
550C22×D4C22⋊D4711yescharacteristic
551C22×D4C22×D4711yescharacteristic
552C23×C4—21no—
553C23×C4—21no—
554C23×C4—941no—
555C23×C4—941no—
556C23×C4C22×D4711yescharacteristic
557C23×C4C22×D4711yescharacteristic
558#137—9432no—
559#137—9432no—
560C2×Q16—478no—
561C2×Q16—474no—
562C2×Q16—474no—
563C2×Q16—474no—
564C2×Q16—474no—
565C2×Q16—944no—
566C2×Q16—944no—
567C2×Q16—1882no—
568C2×SD16—474no—
569C2×SD16—474no—
570C2×SD16—474no—
571C2×SD16—474no—
572C2×SD16—944no—
573C2×SD16—944no—
574C2×SD16—944no—
575C2×SD16—944no—
576C2×D8—474no—
577C2×D8—1882no—
578C2×M16—474no—
579C2×M16—474no—
580C2×M16—944no—
581C2×M16—944no—
582C22×C8—471no—
583C22×C8—471no—
584C22×C8—471no—
585C22×C8—471no—
586#124—28no—
587#124—22no—
588#124—474no—
589#124—948no—
590#124—942no—
591#124C22×D4714yes—
592C22⋊Q8—22no—
593C22⋊Q8—28no—
594C22⋊Q8—474no—
595C22⋊Q8—942no—
596C22⋊Q8—948no—
597C22⋊Q8C22×D4714yes—
598#121—28no—
599#121—22no—
600#121—474no—
601#121—948no—
602#121—942no—
603#121C22×D4714yes—
604C4×Q8—22no—
605C4×Q8—474no—
606C4×Q8—942no—
607C4×Q8C22×D4714yes—
608C4×D4—28no—
609C4×D4—948no—
610C4×D4C22⋊D4714yes—
611C4×D4C22×D4714yes—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—471no—
615C2×C4⋊C4—941no—
616C2×C4⋊C4—941no—
617C2×C4⋊C4C22⋊D4711yescharacteristic
618C2×C4⋊C4C22×D4711yescharacteristic
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—941no—
624C2×C22⋊C4—941no—
625C2×C22⋊C4—941no—
626C2×C22⋊C4—941no—
627C2×C22⋊C4C22⋊D4711yescharacteristic
628C2×C22⋊C4C22⋊D4711yescharacteristic
629C2×C42—21no—
630C2×C42—941no—
631C2×C42C22×D4711yescharacteristic
632#107—474no—
633C4⋊C8—474no—
634#103—474no—
635#103—474no—
636#103—474no—
637#103—474no—
638#102—474no—
639#102—474no—
640C22⋊C8—474no—
641C22⋊C8—474no—
642C4×C8—474no—
643C24—21no—
644C24—941no—
645C24C2×C22⋊D4711yescharacteristic
646C24C2×C22⋊D4711yescharacteristic
647#41—28no—
648#41—44no—
649#41—48no—
650#41—948no—
651#41—1884no—
652#41—1888no—
653C2×Q8—21no—
654C2×Q8—24no—
655C2×Q8—21no—
656C2×Q8—22no—
657C2×Q8—28no—
658C2×Q8—22no—
659C2×Q8—22no—
660C2×Q8—44no—
661C2×Q8—44no—
662C2×Q8—48no—
663C2×Q8—474no—
664C2×Q8—472no—
665C2×Q8—472no—
666C2×Q8—948no—
667C2×Q8—941no—
668C2×Q8—944no—
669C2×Q8—941no—
670C2×Q8—942no—
671C2×Q8—942no—
672C2×Q8—942no—
673C2×Q8—1884no—
674C2×Q8—1884no—
675C2×Q8—1888no—
676C2×Q8D4×D4714yes—
677C2×Q8C23×D4712yes—
678C2×Q8C23×D4712yes—
679C2×D4—24no—
680C2×D4—24no—
681C2×D4—22no—
682C2×D4—21no—
683C2×D4—22no—
684C2×D4—42no—
685C2×D4—44no—
686C2×D4—44no—
687C2×D4—472no—
688C2×D4—944no—
689C2×D4—944no—
690C2×D4—942no—
691C2×D4—941no—
692C2×D4—942no—
693C2×D4—1884no—
694C2×D4—1884no—
695C2×D4C2×C22⋊D4714yes—
696C2×D4C23×D4712yes—
697C22×C4—21no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—24no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—24no—
706C22×C4—44no—
707C22×C4—44no—
708C22×C4—941no—
709C22×C4—944no—
710C22×C4—941no—
711C22×C4—941no—
712C22×C4—944no—
713C22×C4—1884no—
714C22×C4—1884no—
715C22×C4C2×C22⋊D4712yes—
716C22×C4C2×C22⋊D4712yes—
717C22×C4C2×C22⋊D4711yescharacteristic
718C22×C4C2×C22⋊D4711yescharacteristic
719C22×C4C2×C22⋊D4711yescharacteristic
720C22×C4C2×C22⋊D4711yescharacteristic
721C22×C4C23×D4712yes—
722C22×C4C23×D4712yes—
723C22×C4C23×D4711yescharacteristic
724Q16—4716no—
725Q16—948no—
726Q16—948no—
727Q16—1884no—
728SD16—948no—
729SD16—948no—
730SD16—948no—
731SD16—948no—
732D8—1884no—
733M16—948no—
734M16—948no—
735C2×C8—474no—
736C2×C8—472no—
737C2×C8—472no—
738C2×C8—472no—
739C2×C8—472no—
740C2×C8—942no—
741C2×C8—942no—
742C2×C8—942no—
743C4⋊C4—24no—
744C4⋊C4—24no—
745C4⋊C4—21no—
746C4⋊C4—472no—
747C4⋊C4—944no—
748C4⋊C4—944no—
749C4⋊C4—941no—
750C4⋊C4C2×C22⋊D4714yes—
751C4⋊C4C23×D4712yes—
752C22⋊C4—24no—
753C22⋊C4—24no—
754C22⋊C4—24no—
755C22⋊C4—24no—
756C22⋊C4—944no—
757C22⋊C4—944no—
758C22⋊C4—944no—
759C22⋊C4—944no—
760C22⋊C4C2×C22⋊D4714yes—
761C22⋊C4C2×C22⋊D4714yes—
762C42—24no—
763C42—944no—
764C42C2×C22⋊D4712yes—
765C42C23×D4712yes—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—42no—
774C23—42no—
775C23—42no—
776C23—942no—
777C23—1882no—
778C23—1882no—
779C23—1882no—
780C23C22×C22⋊D4712yes—
781C23C22×C22⋊D4712yes—
782C23C22×C22⋊D4711yescharacteristic
783Q8—24no—
784Q8—22no—
785Q8—22no—
786Q8—22no—
787Q8—48no—
788Q8—42no—
789Q8—474no—
790Q8—944no—
791Q8—942no—
792Q8—942no—
793Q8—942no—
794Q8—1888no—
795Q8—1882no—
796Q8C2×D4×D4714yes—
797D4—22no—
798D4—22no—
799D4—44no—
800D4—48no—
801D4—48no—
802D4—42no—
803D4—942no—
804D4—942no—
805D4—1888no—
806D4—1888no—
807D4—1882no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—24no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—24no—
815C2×C4—24no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—48no—
823C2×C4—48no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—944no—
827C2×C4—942no—
828C2×C4—942no—
829C2×C4—942no—
830C2×C4—1888no—
831C2×C4—1888no—
832C2×C4—1882no—
833C2×C4—1882no—
834C2×C4C2×D4×D4712yes—
835C2×C4C22×C22⋊D4712yes—
836C2×C4C22×C22⋊D4712yes—
837C2×C4C22×C22⋊D4712yes—
838C2×C4C22×C22⋊D4712yes—
839C2×C4C22×C22⋊D4711yescharacteristic
840C2×C4#1309406912yes—
841C2×C4C24×D4711yescharacteristic
842C8—474no—
843C8—942no—
844C8—942no—
845C8—942no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—44no—
853C22—44no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—84no—
858C22—3764no—
859C22—1882no—
860C22—1882no—
861C22—1882no—
862C22D4×C22⋊D4712yes—
863C22#1568992112yes—
864C22#1568993812yes—
865C22C23×C22⋊D4711yescharacteristic
866C4—22no—
867C4—22no—
868C4—24no—
869C4—22no—
870C4—22no—
871C4—42no—
872C4—42no—
873C4—944no—
874C4—1882no—
875C4—1882no—
876C4D4×C22⋊D4712yes—
877C4C22×D4×D4711yescharacteristic
878C4C2×#1309406911yescharacteristic
879C2—42no—
880C2—42no—
881C2—82no—
882C2—3762no—
883C2#2025504114yesdirect product factor
884C2C2×D4×C22⋊D4711yescharacteristic
885C2C2×#1568992111yescharacteristic
886C2C2×#1568993811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#548C2
socleC23×C47C22×D4
hypercenterC2×#548D47
hypocenterC47C2×#3277
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#13094055C2semidirect
2. C22×#13094054C2semidirect
3. C2×#15689782C2semidirect
4. #20255041C2direct (N × H)
5. C2×#15689505C2semidirect
6. C2×#15689371C2semidirect
7. C2×#15689367C2semidirect
8. C2×#15689345C2semidirect
9. C2×#15689342C2semidirect
10. C2×#15689268C2semidirect
11. C2×#15689266C2semidirect
12. C2×#15689279C2semidirect
13. C2×#15689278C2semidirect
14. C2×C4×#10625337C2semidirect
15. C2×#15689201C2semidirect
16. C2×C47×#548C2semidirect
20. C2×#13094055C22semidirect
22. C2×#13094054C22semidirect
35. #15689782C22semidirect
44. #15689505C22semidirect
45. #15689371C22semidirect
46. #15689367C22semidirect
47. #15689345C22semidirect
48. #15689342C22semidirect
49. #15689279C22semidirect
50. #15689278C22semidirect
51. #15689268C22semidirect
52. #15689266C22semidirect
53. C4×#10625337C22semidirect
54. #15689201C22semidirect
69. C47×#548C22semidirect
100. C2×#10625337D4semidirect
298. #10625337C2×D4semidirect
439. C2×#548D47semidirect
455. C2×C47#3277semidirect
482. #548C2×D47semidirect
522. C47C2×#3277semidirect
883. C2#20255041direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940552
C22×#130940542
C2×#156897822
#202550412
C2×#156895052
C2×#156893712
C2×#156893672
C2×#156893452
C2×#156893422
C2×#156892682
C2×#156892662
C2×#156892792
C2×#156892782
C2×C4×#106253372
C2×#156892012
C2×C47×#5482
C2×#327747