Finite Group Databasebeta

← C2×#20254913 #27091275

Subgroups — C2×#20254913 #27091275

Order 12032.

2914 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094048C211yesmaximal, characteristic, complemented
2C2×#15689772C211yesmaximal, characteristic, complemented
3C2×#15689761C211yesmaximal, characteristic, complemented
4#20254913C2116yesmaximal, direct product factor
5C2×#15689516C211yesmaximal, characteristic, complemented
6C2×#15689378C211yesmaximal, characteristic, complemented
7C2×#15689352C211yesmaximal, characteristic, complemented
8C2×#15689340C211yesmaximal, characteristic, complemented
9C2×#15689326C211yesmaximal, characteristic, complemented
10C2×#15689285C211yesmaximal, characteristic, complemented
11C2×#15689282C211yesmaximal, characteristic, complemented
12C2×#15689268C211yesmaximal, characteristic, complemented
13C2×#15689272C211yesmaximal, characteristic, complemented
14C2×#15689235C211yesmaximal, characteristic, complemented
15C2×#15689194C211yesmaximal, characteristic, complemented
16C22×#135×C47C211yesmaximal, characteristic, complemented
17C22×#10625352C2211yescharacteristic
18C22×D4×D47C2211yescharacteristic
19C2×#13094048—28no—
20C2×#13094048C2218yescomplemented
21C22×#10625337C2211yescharacteristic, complemented
22C22×#10625325C2211yescharacteristic
23C22×#10625335C2211yescharacteristic
24C22×#10625336C2211yescharacteristic
25C22×#10625334C2211yescharacteristic
26C22×#10625324C2211yescharacteristic
27#15689772—24no—
28#15689772C2218yescomplemented
29#15689761—24no—
30#15689761C2218yescomplemented
31C2×#13094022C2211yescharacteristic, complemented
32C2×#13094013C2211yescharacteristic
33C2×#13094007—21no—
34C2×#13094007—21no—
35C2×#13094005—21no—
36C2×#13094003C2211yescharacteristic, complemented
37C2×#13094000C2211yescharacteristic
38C2×#13094000C2211yescharacteristic
39C2×#13093998C2211yescharacteristic
40C2×#13093996—21no—
41C2×#13093996—21no—
42C2×#13093992—21no—
43C2×D4×Dic47C2211yescharacteristic
44C2×D4×Dic47C2211yescharacteristic, complemented
45C2×C4×C22⋊D47C2211yescharacteristic
46C22×Dic47⋊C4—21no—
47C22×(C2×D47)⋊C4—21no—
48#15689516C2218yescomplemented
49#15689378C2218yescomplemented
50#15689352C2218yescomplemented
51#15689340C2218yescomplemented
52#15689326C2218yescomplemented
53#15689285C2218yescomplemented
54#15689282C2218yescomplemented
55#15689272C2218yescomplemented
56#15689268C2218yescomplemented
57#15689235C2218yescomplemented
58#15689194C2218yescomplemented
59C2×#13093956C2211yescharacteristic, complemented
60C2×Dic47⋊C8C2211yescharacteristic, complemented
61C2×#13093949C2211yescharacteristic, complemented
62C2×#13093948C2211yescharacteristic, complemented
63C2×#13093948C2211yescharacteristic, complemented
64C2×#13093946C2211yescharacteristic
65C2×#13093945C2211yescharacteristic
66C2×#13093945C2211yescharacteristic, complemented
67C2×C22⋊(C47⋊C8)C2211yescharacteristic, complemented
68C2×(C2×D47)⋊C8C2211yescharacteristic
69C2×#13093934C2211yescharacteristic, complemented
70C22×#41×C47C2211yescharacteristic
71C22×#41×C47C2211yescharacteristic, complemented
72C2×#135×C47—28no—
73C2×#135×C47C2218yescomplemented
74C22×Q16×C47C2211yescharacteristic, complemented
75C22×SD16×C47C2211yescharacteristic
76C22×SD16×C47C2211yescharacteristic, complemented
77C22×D8×C47C2211yescharacteristic
78C23×C8×C47C2211yescharacteristic, complemented
79C24×D47—21no—
80C2×#10625352—24no—
81C2×#10625352—22no—
82C2×#10625352—42no—
83C2×#10625352C2314yes—
84C22×Dic94C2311yescharacteristic
85C22×D188C2311yescharacteristic
86C22×C22⋊D47—21no—
87C22×C22⋊D47—21no—
88C22×C22⋊D47—21no—
89C22×C22⋊D47D411yescharacteristic
90C2×D4×D47—24no—
91C2×D4×D47—22no—
92C2×D4×D47—42no—
93C2×D4×D47C2314yes—
94C23×Dic47—21no—
95C23×Dic47—21no—
96C23×Dic47—21no—
97C22×C4×D47C2311yescharacteristic
98#13094048—232no—
99C2×#10625337—42no—
100C2×#10625337C2314yescomplemented
101C2×#10625325—24no—
102C2×#10625325C2314yes—
103C2×#10625335—24no—
104C2×#10625335C2314yes—
105C2×#10625336—42no—
106C2×#10625336C2314yes—
107C2×#10625334—24no—
108C2×#10625334C2314yes—
109C2×#10625324—24no—
110C2×#10625324C2314yes—
111C22×C47⋊C8C2311yescharacteristic
112C22×C47⋊C8C2311yescharacteristic
113#13094022—22no—
114#13094022C2314yescomplemented
115#13094013—22no—
116#13094013C2314yes—
117#13094007—28no—
118#13094007—28no—
119#13094005—28no—
120#13094003—22no—
121#13094003C2314yescomplemented
122#13094000—22no—
123#13094000—22no—
124#13094000C2314yes—
125#13094000C2314yes—
126#13093998—22no—
127#13093998C2314yes—
128#13093996—28no—
129#13093996—28no—
130#13093992—28no—
131D4×Dic47—22no—
132D4×Dic47—22no—
133D4×Dic47C2314yes—
134D4×Dic47C2314yescomplemented
135C4×C22⋊D47D414yes—
136C4×C22⋊D47C2314yes—
137C2×C4⋊Dic47C2311yescharacteristic
138C2×C4⋊Dic47C2311yescharacteristic
139C2×Dic47⋊C4—21no—
140C2×Dic47⋊C4—21no—
141C2×Dic47⋊C4—21no—
142C2×Dic47⋊C4—21no—
143C2×Dic47⋊C4—21no—
144C2×Dic47⋊C4—28no—
145C2×Dic47⋊C4D411yescharacteristic
146C2×C22⋊Dic47—21no—
147C2×C22⋊Dic47—21no—
148C2×C22⋊Dic47—21no—
149C2×C22⋊Dic47D411yescharacteristic
150C2×(C2×D47)⋊C4—21no—
151C2×(C2×D47)⋊C4—21no—
152C2×(C2×D47)⋊C4—21no—
153C2×(C2×D47)⋊C4—21no—
154C2×(C2×D47)⋊C4—21no—
155C2×(C2×D47)⋊C4—28no—
156C2×(C2×D47)⋊C4D411yescharacteristic
157C2×C4×Dic47C2311yescharacteristic
158#13093956C2314yescomplemented
159Dic47⋊C8C2314yescomplemented
160#13093949C2314yescomplemented
161#13093948C2314yescomplemented
162#13093948C2314yescomplemented
163#13093946C2314yes—
164#13093945C2314yes—
165#13093945C2314yescomplemented
166C22⋊(C47⋊C8)C2314yescomplemented
167(C2×D47)⋊C8C2314yes—
168#13093934C2314yescomplemented
169C2×#41×C47—22no—
170C2×#41×C47—22no—
171C2×#41×C47—24no—
172C2×#41×C47—24no—
173C2×#41×C47—42no—
174C2×#41×C47—42no—
175C2×#41×C47C2314yes—
176C2×#41×C47C2314yescomplemented
177C22×Q8×C47C2311yescharacteristic
178C22×Q8×C47C2311yescharacteristic
179C22×D4×C47—21no—
180C22×D4×C47—21no—
181C22×D4×C47C2311yescharacteristic
182C22×D4×C47C2311yescharacteristic
183C23×C4×C47—21no—
184C23×C4×C47—21no—
185C23×C4×C47C2311yescharacteristic
186#135×C47—232no—
187C2×Q16×C47—24no—
188C2×Q16×C47C2314yescomplemented
189C2×SD16×C47—24no—
190C2×SD16×C47—24no—
191C2×SD16×C47C2314yes—
192C2×SD16×C47C2314yescomplemented
193C2×D8×C47D418yescomplemented
194C2×D8×C47C2314yes—
195C22×C8×C47—24no—
196C22×C8×C47C2311yescharacteristic
197C22×C8×C47C2311yescharacteristic
198C22×C8×C47C2314yescomplemented
199C24×C47—21no—
200C24×C47—21no—
201C24×C47C2×D411yescharacteristic
202C23×D47—21no—
203C23×D47—24no—
204C23×D47—44no—
205C23×D47—44no—
206C23×D47—82no—
207C23×D47C2×D411yescharacteristic
208#41×C47—28no—
209#41×C47—28no—
210#41×C47—44no—
211#41×C47—44no—
212#41×C47—48no—
213#41×C47—48no—
214C2×Q8×C47—21no—
215C2×Q8×C47—21no—
216C2×Q8×C47—22no—
217C2×Q8×C47—22no—
218C2×Q8×C47—22no—
219C2×Q8×C47—22no—
220C2×Q8×C47C2412yes—
221C2×Q8×C47C2412yes—
222C2×D4×C47—24no—
223C2×D4×C47—24no—
224C2×D4×C47—21no—
225C2×D4×C47—21no—
226C2×D4×C47—22no—
227C2×D4×C47—22no—
228C2×D4×C47—44no—
229C2×D4×C47—44no—
230C2×D4×C47C2×D414yes—
231C2×D4×C47C2×D414yes—
232C2×D4×C47C2412yes—
233C2×D4×C47C2412yes—
234C22×C4×C47—22no—
235C22×C4×C47—22no—
236C22×C4×C47—21no—
237C22×C4×C47—21no—
238C22×C4×C47—24no—
239C22×C4×C47—24no—
240C22×C4×C47—44no—
241C22×C4×C47—44no—
242C22×C4×C47C2×D411yescharacteristic
243C22×C4×C47C2×D412yes—
244C22×C4×C47C2412yes—
245C22×C4×C47C2411yescharacteristic
246C2×C22⋊D47—24no—
247C2×C22⋊D47—24no—
248C2×C22⋊D47—24no—
249C2×C22⋊D47—42no—
250C2×C22⋊D47—44no—
251C2×C22⋊D47—44no—
252C2×C22⋊D47—82no—
253C2×C22⋊D47C2×D414yes—
254C22×Dic47—21no—
255C22×Dic47—21no—
256C22×Dic47—21no—
257C22×Dic47—24no—
258C22×Dic47—24no—
259C22×Dic47—24no—
260C22×Dic47—44no—
261C22×Dic47—44no—
262C22×Dic47—82no—
263C22×Dic47C2×D411yescharacteristic
264C22×Dic47C2×D411yescharacteristic
265C22×Dic47C2×D411yescharacteristic
266#10625352—28no—
267#10625352—44no—
268#10625352—48no—
269D4×D47—28no—
270D4×D47—44no—
271D4×D47—48no—
272C2×D188—22no—
273C2×D188—22no—
274C2×D188—21no—
275C2×D188C2412yes—
276C2×C4×D47—22no—
277C2×C4×D47—22no—
278C2×C4×D47C2×D412yes—
279C2×C4×D47C2412yes—
280C2×Dic94—22no—
281C2×Dic94—22no—
282C2×Dic94—21no—
283C2×Dic94C2412yes—
284Q16×C47—28no—
285SD16×C47—28no—
286SD16×C47—28no—
287D8×C47C2×D4116yescomplemented
288C2×C8×C47—22no—
289C2×C8×C47—28no—
290C2×C8×C47C2×D414yes—
291C2×C8×C47C2412yes—
292C2×C8×C47C2412yes—
293C22⋊Dic47—24no—
294C22⋊Dic47—24no—
295C22⋊Dic47—24no—
296C22⋊Dic47C2×D414yes—
297#10625337—44no—
298#10625336—44no—
299#10625335—28no—
300#10625334—28no—
301(C2×D47)⋊C4—24no—
302(C2×D47)⋊C4—24no—
303(C2×D47)⋊C4—24no—
304(C2×D47)⋊C4—24no—
305(C2×D47)⋊C4—24no—
306(C2×D47)⋊C4C2×D414yes—
307C4⋊Dic47—21no—
308C4⋊Dic47—21no—
309C4⋊Dic47C2412yes—
310C4⋊Dic47C2412yes—
311Dic47⋊C4—24no—
312Dic47⋊C4—24no—
313Dic47⋊C4—24no—
314Dic47⋊C4—24no—
315Dic47⋊C4—24no—
316Dic47⋊C4C2×D414yes—
317C4×Dic47C2×D412yes—
318C4×Dic47C2412yes—
319C2×C47⋊C8—22no—
320C2×C47⋊C8—22no—
321C2×C47⋊C8C2412yes—
322C2×C47⋊C8C2412yes—
323#10625325—28no—
324#10625324—28no—
325C23×C47—24no—
326C23×C47—24no—
327C23×C47—22no—
328C23×C47—22no—
329C23×C47—22no—
330C23×C47—22no—
331C23×C47—22no—
332C23×C47—42no—
333C23×C47—42no—
334C23×C47—42no—
335C23×C47—42no—
336C23×C47C22×D412yes—
337C23×C47C22×D411yescharacteristic
338C22×D47—22no—
339C22×D47—22no—
340C22×D47—22no—
341C22×D47—22no—
342C22×D47—48no—
343C22×D47—48no—
344C22×D47—42no—
345C22×D47—42no—
346C22×D47—42no—
347C22×D47—84no—
348C22×D47—816no—
349C22×D47C22×D412yes—
350Q8×C47—22no—
351Q8×C47—22no—
352Q8×C47—22no—
353Q8×C47—22no—
354Q8×C47—42no—
355Q8×C47—42no—
356D4×C47—24no—
357D4×C47—24no—
358D4×C47—22no—
359D4×C47—22no—
360D4×C47—48no—
361D4×C47—48no—
362D4×C47C22×D414yes—
363D4×C47C22×D414yes—
364C2×C4×C47—22no—
365C2×C4×C47—24no—
366C2×C4×C47—22no—
367C2×C4×C47—22no—
368C2×C4×C47—22no—
369C2×C4×C47—22no—
370C2×C4×C47—48no—
371C2×C4×C47—48no—
372C2×C4×C47—42no—
373C2×C4×C47—42no—
374C2×C4×C47C22×D412yes—
375C2×C4×C47C22×D411yescharacteristic
376C2×C4×C47C22×D412yes—
377C2×C4×C47H(5,𝔽2)12yes—
378C2×C4×C47C2511yescharacteristic
379C22⋊D47—44no—
380C22⋊D47—48no—
381C22⋊D47—48no—
382C22⋊D47—84no—
383C2×Dic47—22no—
384C2×Dic47—22no—
385C2×Dic47—22no—
386C2×Dic47—22no—
387C2×Dic47—22no—
388C2×Dic47—22no—
389C2×Dic47—48no—
390C2×Dic47—48no—
391C2×Dic47—42no—
392C2×Dic47—42no—
393C2×Dic47—42no—
394C2×Dic47—84no—
395C2×Dic47C22×D412yes—
396C2×Dic47C22×D412yes—
397C2×Dic47C22×D412yes—
398D188—22no—
399D188—22no—
400D188—42no—
401C4×D47—24no—
402C4×D47—22no—
403C4×D47—22no—
404Dic94—22no—
405Dic94—22no—
406Dic94—42no—
407C8×C47—22no—
408C8×C47C22×D414yes—
409C47⋊C8—22no—
410C47⋊C8—22no—
411C2×#3267—471nomaximal, Sylow
412C22×C47—24no—
413C22×C47—24no—
414C22×C47—22no—
415C22×C47—22no—
416C22×C47—22no—
417C22×C47—48no—
418C22×C47—44no—
419C22×C47—48no—
420C22×C47—42no—
421C22×C47—42no—
422C22×C47—42no—
423C22×C47—42no—
424C22×C47D4212yes—
425C22×C47#57512yes—
426C22×C47#57712yes—
427C22×C47C23×D411yescharacteristic
428C2×D47—22no—
429C2×D47—22no—
430C2×D47—22no—
431C2×D47—44no—
432C2×D47—42no—
433C2×D47—42no—
434C2×D47—42no—
435C2×D47—816no—
436C2×D47—84no—
437C4×C47—22no—
438C4×C47—42no—
439C4×C47—42no—
440C4×C47D4212yes—
441C4×C47C23×D411yescharacteristic
442C4×C47C2×H(5,𝔽2)11yescharacteristic
443Dic47—22no—
444Dic47—22no—
445Dic47—22no—
446Dic47—42no—
447Dic47—42no—
448Dic47—42no—
449C22×AGL(1,ℤ/8)—471no—
450C22×#135D4711yescharacteristic, complemented
451C2×#547—471no—
452C2×#546—471no—
453#3267—4716no—
454C2×#497—471no—
455C2×#470—471no—
456C2×#465—471no—
457C2×#463—471no—
458C2×#461—471no—
459C2×#452—471no—
460C2×#452—471no—
461C2×#449—471no—
462C2×#450—471no—
463C2×#442—471no—
464C2×#435—471no—
465C2×C47—44no—
466C2×C47—42no—
467C2×C47—44no—
468C2×C47#326714yescomplemented
469C2×C47C2×D4211yescharacteristic
470C2×C47C2×#57511yescharacteristic
471C2×C47C2×#57711yescharacteristic
472D47—42no—
473D47—82no—
474C22×#41—471no—
475C22×#41C2×D4711yescharacteristic
476C22×#41C2×D4711yescharacteristic, complemented
477C23×D4—471no—
478C2×AGL(1,ℤ/8)—478no—
479C2×AGL(1,ℤ/8)—948no—
480C2×#135—28no—
481C2×#135C2×D4718yescomplemented
482C22×Q16—471no—
483C22×Q16C2×D4711yescharacteristic, complemented
484C22×SD16—471no—
485C22×SD16—471no—
486C22×SD16—471no—
487C22×SD16C2×D4711yescharacteristic
488C22×SD16C2×D4711yescharacteristic, complemented
489C22×D8—471no—
490C22×D8C2×D4711yescharacteristic
491C22×M16—471no—
492C23×C8C2×D4711yescharacteristic, complemented
493#547—478no—
494#547—944no—
495#546—478no—
496#546—944no—
497C2×C4⋊Q8—471no—
498C2×#124—471no—
499C2×#123—941no—
500C2×#123—941no—
501C2×#123—941no—
502C2×C22⋊Q8—471no—
503C2×C22⋊Q8—471no—
504C2×C22⋊Q8—471no—
505C2×#121—471no—
506C2×#121—941no—
507C2×#121—941no—
508C2×#120—941no—
509C2×C4×D4—471no—
510C2×C4×D4—471no—
511C2×C4×D4—471no—
512C22×C4⋊C4—941no—
513C22×C22⋊C4—941no—
514#497—478no—
515#470—478no—
516#465—478no—
517#463—478no—
518#461—478no—
519#452—478no—
520#452—478no—
521#450—478no—
522#449—478no—
523#442—478no—
524#435—478no—
525C2×#106—471no—
526C2×C4⋊C8—471no—
527C2×#103—471no—
528C2×#103—471no—
529C2×#103—471no—
530C2×#102—471no—
531C2×#102—471no—
532C2×#102—471no—
533C2×C22⋊C8—471no—
534C2×C22⋊C8—471no—
535C2×#97—471no—
536C47C2×#326711yescharacteristic, complemented, Sylow
537C25—941no—
538C2×#41—22no—
539C2×#41—22no—
540C2×#41—24no—
541C2×#41—24no—
542C2×#41—42no—
543C2×#41—42no—
544C2×#41—474no—
545C2×#41—942no—
546C2×#41—944no—
547C2×#41—1882no—
548C2×#41C22×D4714yes—
549C2×#41C22×D4714yescomplemented
550C22×Q8—471no—
551C22×Q8C22×D4711yescharacteristic
552C22×Q8C22×D4711yescharacteristic
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—471no—
556C22×D4—474no—
557C22×D4—471no—
558C22×D4—942no—
559C22×D4—941no—
560C22×D4—944no—
561C22×D4—941no—
562C22×D4—941no—
563C22×D4—1882no—
564C22×D4C22×D4711yescharacteristic
565C22×D4C22×D4711yescharacteristic
566C23×C4—21no—
567C23×C4—21no—
568C23×C4—471no—
569C23×C4—941no—
570C23×C4—941no—
571C23×C4—941no—
572C23×C4C22×D4711yescharacteristic
573AGL(1,ℤ/8)—9432no—
574#135—232no—
575C2×Q16—24no—
576C2×Q16—474no—
577C2×Q16—1882no—
578C2×Q16C22×D4714yescomplemented
579C2×SD16—24no—
580C2×SD16—24no—
581C2×SD16—474no—
582C2×SD16—474no—
583C2×SD16—474no—
584C2×SD16—944no—
585C2×SD16—944no—
586C2×SD16—1882no—
587C2×SD16C22×D4714yes—
588C2×SD16C22×D4714yescomplemented
589C2×D8—474no—
590C2×D8—944no—
591C2×D8C22⋊D4718yescomplemented
592C2×D8C22×D4714yes—
593C2×M16—474no—
594C2×M16—944no—
595C22×C8—24no—
596C22×C8—471no—
597C22×C8—471no—
598C22×C8C22×D4711yescharacteristic
599C22×C8C22×D4711yescharacteristic
600C22×C8C22×D4714yescomplemented
601C4⋊Q8—474no—
602C4⋊Q8—942no—
603#124—474no—
604#124—942no—
605#123—948no—
606#123—948no—
607#123—948no—
608C22⋊Q8—474no—
609C22⋊Q8—474no—
610C22⋊Q8—474no—
611C22⋊Q8—942no—
612C22⋊Q8—942no—
613C22⋊Q8—942no—
614#121—474no—
615#121—948no—
616#121—948no—
617#121—942no—
618#120—948no—
619C4×D4—474no—
620C4×D4—474no—
621C4×D4—474no—
622C4×D4—474no—
623C4×D4—942no—
624C4×D4—942no—
625C2×C4⋊C4—471no—
626C2×C4⋊C4—471no—
627C2×C4⋊C4—471no—
628C2×C4⋊C4—948no—
629C2×C4⋊C4—941no—
630C2×C4⋊C4—941no—
631C2×C4⋊C4—941no—
632C2×C4⋊C4—941no—
633C2×C4⋊C4—941no—
634C2×C22⋊C4—471no—
635C2×C22⋊C4—471no—
636C2×C22⋊C4—948no—
637C2×C22⋊C4—941no—
638C2×C22⋊C4—941no—
639C2×C22⋊C4—941no—
640C2×C22⋊C4—941no—
641C2×C22⋊C4—941no—
642C2×C22⋊C4—941no—
643C2×C22⋊C4—941no—
644C2×C22⋊C4—941no—
645C2×C42—471no—
646#106—474no—
647C4⋊C8—474no—
648#103—474no—
649#103—474no—
650#103—474no—
651#102—474no—
652#102—474no—
653#102—474no—
654C22⋊C8—474no—
655C22⋊C8—474no—
656#97—474no—
657C24—21no—
658C24—21no—
659C24—471no—
660C24—944no—
661C24—941no—
662C24—3762no—
663C24—1884no—
664C24—1884no—
665C24D4×D4711yescharacteristic
666#41—28no—
667#41—28no—
668#41—44no—
669#41—44no—
670#41—48no—
671#41—48no—
672#41—948no—
673#41—1884no—
674#41—1888no—
675C2×Q8—21no—
676C2×Q8—21no—
677C2×Q8—22no—
678C2×Q8—22no—
679C2×Q8—22no—
680C2×Q8—22no—
681C2×Q8—472no—
682C2×Q8—941no—
683C2×Q8—942no—
684C2×Q8—942no—
685C2×Q8C23×D4712yes—
686C2×Q8C23×D4712yes—
687C2×D4—24no—
688C2×D4—24no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—44no—
694C2×D4—44no—
695C2×D4—474no—
696C2×D4—472no—
697C2×D4—944no—
698C2×D4—948no—
699C2×D4—944no—
700C2×D4—944no—
701C2×D4—941no—
702C2×D4—942no—
703C2×D4—942no—
704C2×D4—3762no—
705C2×D4—1884no—
706C2×D4—1888no—
707C2×D4—1882no—
708C2×D4—1884no—
709C2×D4—1884no—
710C2×D4C2×C22⋊D4714yes—
711C2×D4C2×C22⋊D4714yes—
712C2×D4C23×D4712yes—
713C2×D4C23×D4712yes—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—24no—
719C22×C4—24no—
720C22×C4—44no—
721C22×C4—44no—
722C22×C4—471no—
723C22×C4—471no—
724C22×C4—471no—
725C22×C4—472no—
726C22×C4—472no—
727C22×C4—944no—
728C22×C4—944no—
729C22×C4—944no—
730C22×C4—942no—
731C22×C4—942no—
732C22×C4—941no—
733C22×C4—941no—
734C22×C4—941no—
735C22×C4—3762no—
736C22×C4—1884no—
737C22×C4—1884no—
738C22×C4D4×D4712yes—
739C22×C4D4×D4711yescharacteristic
740C22×C4C23×D4712yes—
741C22×C4C23×D4711yescharacteristic
742Q16—28no—
743Q16—1884no—
744SD16—28no—
745SD16—28no—
746SD16—948no—
747SD16—948no—
748SD16—1884no—
749D8—948no—
750D8C2×C22⋊D47116yescomplemented
751M16—948no—
752C2×C8—22no—
753C2×C8—28no—
754C2×C8—472no—
755C2×C8—472no—
756C2×C8—942no—
757C2×C8—942no—
758C2×C8C2×C22⋊D4714yes—
759C2×C8C23×D4712yes—
760C2×C8C23×D4712yes—
761C4⋊C4—474no—
762C4⋊C4—472no—
763C4⋊C4—472no—
764C4⋊C4—944no—
765C4⋊C4—944no—
766C4⋊C4—944no—
767C4⋊C4—944no—
768C4⋊C4—944no—
769C4⋊C4—941no—
770C4⋊C4—941no—
771C22⋊C4—474no—
772C22⋊C4—474no—
773C22⋊C4—944no—
774C22⋊C4—944no—
775C22⋊C4—944no—
776C22⋊C4—944no—
777C22⋊C4—944no—
778C22⋊C4—944no—
779C22⋊C4—944no—
780C22⋊C4—944no—
781C42—472no—
782C42—472no—
783C23—22no—
784C23—24no—
785C23—24no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—42no—
791C23—42no—
792C23—42no—
793C23—42no—
794C23—472no—
795C23—942no—
796C23—942no—
797C23—942no—
798C23—942no—
799C23—3764no—
800C23—37616no—
801C23—1888no—
802C23—1888no—
803C23—1882no—
804C23—1882no—
805C23—1882no—
806C23C2×D4×D4712yes—
807C23C2×D4×D4711yescharacteristic
808Q8—22no—
809Q8—22no—
810Q8—22no—
811Q8—22no—
812Q8—42no—
813Q8—42no—
814Q8—942no—
815Q8—942no—
816Q8—1882no—
817D4—24no—
818D4—24no—
819D4—22no—
820D4—22no—
821D4—48no—
822D4—48no—
823D4—942no—
824D4—942no—
825D4—3764no—
826D4—1884no—
827D4—1888no—
828D4—1888no—
829D4—1882no—
830D4C22×C22⋊D4714yes—
831D4C22×C22⋊D4714yes—
832C2×C4—22no—
833C2×C4—24no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—48no—
839C2×C4—48no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—472no—
843C2×C4—472no—
844C2×C4—472no—
845C2×C4—942no—
846C2×C4—942no—
847C2×C4—942no—
848C2×C4—944no—
849C2×C4—942no—
850C2×C4—942no—
851C2×C4—942no—
852C2×C4—942no—
853C2×C4—942no—
854C2×C4—3764no—
855C2×C4—1888no—
856C2×C4—1888no—
857C2×C4—1882no—
858C2×C4—1882no—
859C2×C4—1882no—
860C2×C4C2×D4×D4712yes—
861C2×C4C2×D4×D4711yescharacteristic
862C2×C4C22×C22⋊D4712yes—
863C2×C4#1309406912yes—
864C2×C4C24×D4711yescharacteristic
865C8—22no—
866C8—942no—
867C8—942no—
868C8C22×C22⋊D4714yes—
869C22—22no—
870C22—24no—
871C22—24no—
872C22—22no—
873C22—22no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—44no—
879C22—48no—
880C22—48no—
881C22—942no—
882C22—942no—
883C22—942no—
884C22—37616no—
885C22—3764no—
886C22—1882no—
887C22—1882no—
888C22—1882no—
889C22—1884no—
890C22D4×C22⋊D4712yes—
891C22#1568992012yes—
892C22#1568993012yes—
893C22C22×D4×D4711yescharacteristic
894C4—22no—
895C4—42no—
896C4—42no—
897C4—942no—
898C4—942no—
899C4—942no—
900C4—1882no—
901C4—1882no—
902C4—1882no—
903C4D4×C22⋊D4712yes—
904C4C23×C22⋊D4711yescharacteristic
905C4C2×#1309406911yescharacteristic
906C2—42no—
907C2—44no—
908C2—44no—
909C2—3762no—
910C2—1882no—
911C2#2025491314yesdirect product factor
912C2C2×D4×C22⋊D4711yescharacteristic
913C2C2×#1568992011yescharacteristic
914C2C2×#1568993011yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC22×#135×C47C2
socleC23×C47C22×D4
hypercenterC22×#135D47
hypocenterC47C2×#3267
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#135

Complements

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

NH ≅ G/Ntype
1. C22×#13094048C2semidirect
2. C2×#15689772C2semidirect
3. C2×#15689761C2semidirect
4. #20254913C2direct (N × H)
5. C2×#15689516C2semidirect
6. C2×#15689378C2semidirect
7. C2×#15689352C2semidirect
8. C2×#15689340C2semidirect
9. C2×#15689326C2semidirect
10. C2×#15689285C2semidirect
11. C2×#15689282C2semidirect
12. C2×#15689268C2semidirect
13. C2×#15689272C2semidirect
14. C2×#15689235C2semidirect
15. C2×#15689194C2semidirect
16. C22×#135×C47C2semidirect
20. C2×#13094048C22semidirect
21. C22×#10625337C22semidirect
28. #15689772C22semidirect
30. #15689761C22semidirect
31. C2×#13094022C22semidirect
36. C2×#13094003C22semidirect
44. C2×D4×Dic47C22semidirect
48. #15689516C22semidirect
49. #15689378C22semidirect
50. #15689352C22semidirect
51. #15689340C22semidirect
52. #15689326C22semidirect
53. #15689285C22semidirect
54. #15689282C22semidirect
55. #15689272C22semidirect
56. #15689268C22semidirect
57. #15689235C22semidirect
58. #15689194C22semidirect
59. C2×#13093956C22semidirect
60. C2×Dic47⋊C8C22semidirect
61. C2×#13093949C22semidirect
62. C2×#13093948C22semidirect
63. C2×#13093948C22semidirect
66. C2×#13093945C22semidirect
67. C2×C22⋊(C47⋊C8)C22semidirect
69. C2×#13093934C22semidirect
71. C22×#41×C47C22semidirect
73. C2×#135×C47C22semidirect
74. C22×Q16×C47C22semidirect
76. C22×SD16×C47C22semidirect
78. C23×C8×C47C22semidirect
100. C2×#10625337C23semidirect
114. #13094022C23semidirect
121. #13094003C23semidirect
134. D4×Dic47C23semidirect
158. #13093956C23semidirect
159. Dic47⋊C8C23semidirect
160. #13093949C23semidirect
161. #13093948C23semidirect
162. #13093948C23semidirect
165. #13093945C23semidirect
166. C22⋊(C47⋊C8)C23semidirect
168. #13093934C23semidirect
176. C2×#41×C47C23semidirect
188. C2×Q16×C47C23semidirect
192. C2×SD16×C47C23semidirect
193. C2×D8×C47D4semidirect
198. C22×C8×C47C23semidirect
287. D8×C47C2×D4semidirect
450. C22×#135D47semidirect
468. C2×C47#3267semidirect
476. C22×#41C2×D47semidirect
481. C2×#135C2×D47semidirect
483. C22×Q16C2×D47semidirect
488. C22×SD16C2×D47semidirect
492. C23×C8C2×D47semidirect
536. C47C2×#3267semidirect
549. C2×#41C22×D47semidirect
578. C2×Q16C22×D47semidirect
588. C2×SD16C22×D47semidirect
591. C2×D8C22⋊D47semidirect
600. C22×C8C22×D47semidirect
750. D8C2×C22⋊D47semidirect
911. C2#20254913direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940482
C2×#156897722
C2×#156897612
#202549132
C2×#156895162
C2×#156893782
C2×#156893522
C2×#156893402
C2×#156893262
C2×#156892852
C2×#156892822
C2×#156892682
C2×#156892722
C2×#156892352
C2×#156891942
C22×#135×C472
C2×#326747