Finite Group Databasebeta

← D3×#5169 #11863563

Subgroups — D3×#5169 #11863563

Order 1152.

2086 conjugacy classes of subgroups.

The subgroup lattice has 1099 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D32×D4C211yesmaximal, characteristic
2C2×C3×D3×SD16C211yesmaximal, characteristic, complemented
3D3×#946C211yesmaximal, characteristic, complemented
4C2×D3×#215C211yesmaximal, characteristic, complemented
5#10592868C211yesmaximal, characteristic, complemented
6C3×#5169C211yesmaximal, characteristic, complemented
7#10591652C211yesmaximal, characteristic, complemented
8#10591651C211yesmaximal, characteristic, complemented
9#10591467C211yesmaximal, characteristic, complemented
10#10591458C211yesmaximal, characteristic, complemented
11D3×#832C211yesmaximal, characteristic, complemented
12#10590943C211yesmaximal, characteristic, complemented
13#10590942C211yesmaximal, characteristic, complemented
14D3×#821C211yesmaximal, characteristic, complemented
15D3×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
16C2×#5169—31nomaximal
17D3×#450—31nomaximal
18C23×D32—21no—
19C2×D4×C3⋊D3C2211yescharacteristic
20C2×C3×D3×Q8C2211yescharacteristic, complemented
21C2×C3×D3×D4C2211yescharacteristic
22C2×C3×D3×D4C2211yescharacteristic
23C2×#3811—21no—
24C2×D3×#67—21no—
25C2×D3×#67—21no—
26D32×D4—24no—
27D32×D4—24no—
28C2×#3802C2211yescharacteristic
29C2×D3×D12C2211yescharacteristic
30C2×D3×D12C2211yescharacteristic
31C2×C4×D32C2211yescharacteristic
32C2×C32×SD16C2211yescharacteristic, complemented
33#64155C2211yescharacteristic, complemented
34C2×#3755C2211yescharacteristic, complemented
35C3×#946C2211yescharacteristic, complemented
36C2×C3×#215C2211yescharacteristic, complemented
37C2×C3×#215C2211yescharacteristic, complemented
38C2×C3×#214C2211yescharacteristic, complemented
39C3×D3×SD16—24no—
40C2×C3×#204C2211yescharacteristic, complemented
41C2×C3×D3×C8C2211yescharacteristic, complemented
42D3×#215—24no—
43D3×(C2×D3)⋊C4—21no—
44D3×C4⋊Dic3C2211yescharacteristic, complemented
45#63888—21no—
46#63887—21no—
47D3×Dic3⋊C4—21no—
48#63871C2211yescharacteristic, complemented
49#63856C2211yescharacteristic, complemented
50C2×#3717C2211yescharacteristic, complemented
51C2×#3715C2211yescharacteristic, complemented
52C2×D3×C3⋊C8C2211yescharacteristic, complemented
53#63659C2211yescharacteristic, complemented
54#63648C2211yescharacteristic, complemented
55#63647C2211yescharacteristic, complemented
56C3×#832C2211yescharacteristic, complemented
57C3×#821C2211yescharacteristic, complemented
58C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
59#63564C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61#63563C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63#63557C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C22×D3×D4—31no—
66C22×D3×D4—31no—
67C22×C3×SD16—31no—
68C2×#946—31no—
69C22×#215—31no—
70C2×D3×SD16—31no—
71C2×D3×SD16D311yescharacteristic, complemented
72D3×C22⋊Q8—31no—
73C3×#450—31no—
74#5218—31no—
75C2×#832—31no—
76#5169—31no—
77#5169—31no—
78#5169—31no—
79#5169—31no—
80#5169—31no—
81#5169—31no—
82#5169—31no—
83#5169—31no—
84#5169—31no—
85#5169—61no—
86#5169D311yescharacteristic, direct product factor
87C2×#821—31no—
88C2×(C2×D3)⋊C8—31no—
89#5046—31no—
90#4776—31no—
91#4776—31no—
92D3×#102—31no—
93D3×#102—31no—
94#4731—31no—
95D3×C22⋊C8—31no—
96C23×C3⋊D3—21no—
97C23×C3×D3—21no—
98C23×C3×D3—21no—
99C22×D32—28no—
100C22×D32—21no—
101C22×D32—21no—
102C22×D32—21no—
103C22×D32—44no—
104C22×D32—44no—
105C22×D32D411yescharacteristic
106C2×C32×Q8C2311yescharacteristic, complemented
107C2×C32×D4C2311yescharacteristic
108C2×#638—21no—
109D4×C3⋊D3—22no—
110D4×C3⋊D3—22no—
111C2×C4⋊(C3⋊D3)C2311yescharacteristic
112C2×C4×C3⋊D3C2311yescharacteristic
113C2×C3×#67—21no—
114C2×C3×#67—21no—
115C3×D3×Q8—22no—
116C3×D3×Q8—22no—
117C3×D3×D4—22no—
118C3×D3×D4—22no—
119C3×D3×D4—22no—
120C3×D3×D4D414yes—
121C2×C3×D12C2311yescharacteristic
122C2×C3×D12C2311yescharacteristic
123C2×C3×C4×D3—21no—
124C2×C3×C4×D3C2311yescharacteristic
125C2×C3×C4×D3C2311yescharacteristic
126C2×C3×Dic6—21no—
127C2×C3×Dic6C2311yescharacteristic, complemented
128#3811—28no—
129D3×#67—28no—
130D3×#67—28no—
131C2×#626—21no—
132C2×#626—21no—
133C2×#625—21no—
134C2×#624D411yescharacteristic
135C2×D3×Dic3—21no—
136C2×D3×Dic3D411yescharacteristic
137C2×D3×Dic3D411yescharacteristic
138#3802—22no—
139#3802—22no—
140D3×D12—22no—
141D3×D12—22no—
142D3×D12—22no—
143D3×D12D414yes—
144C4×D32—22no—
145C4×D32—22no—
146C32×SD16—22no—
147C2×C32×C8C2311yescharacteristic, complemented
148#3755—22no—
149#3752—21no—
150C4⋊(C3⋊Dic3)C2311yescharacteristic, complemented
151#3750—21no—
152C2×C3⋊(C3⋊C8)C2311yescharacteristic, complemented
153C3×#215—22no—
154C3×#215—22no—
155C3×#214—22no—
156C3×(C2×D3)⋊C4—21no—
157C3×C4⋊Dic3C2311yescharacteristic, complemented
158C3×Dic3⋊C4—21no—
159C2×C3×C3⋊C8C2311yescharacteristic, complemented
160C2×C3×C3⋊C8C2311yescharacteristic, complemented
161C3×#204—22no—
162C3×D3×C8—22no—
163#3724—21no—
164Dic3⋊Dic3—21no—
165Dic3⋊Dic3—21no—
166#3722—21no—
167(C2×D3)⋊Dic3—21no—
168#3717—22no—
169#3715—22no—
170D3×C3⋊C8—22no—
171C2×#450—91noSylow
172C24×D3—61no—
173C24×D3—61no—
174C22×C3×Q8—31no—
175C22×C3×D4—31no—
176C22×C3×D4—31no—
177C22×#67—61no—
178C22×#67—61no—
179C2×D3×Q8C2×D311yescharacteristic, complemented
180C2×D3×D4—31no—
181C2×D3×D4—31no—
182C2×D3×D4—31no—
183C2×D3×D4—31no—
184C2×D3×D4—31no—
185C2×D3×D4—31no—
186C2×D3×D4—61no—
187C2×D3×D4—61no—
188C2×D3×D4—61no—
189C2×D3×D4—61no—
190C2×D3×D4—61no—
191C2×D3×D4—64no—
192C2×D3×D4—64no—
193C2×D3×D4—64no—
194C2×D3×D4—64no—
195C2×D3×D4C2×D311yescharacteristic
196C2×D3×D4C2×D311yescharacteristic
197C22×D12—31no—
198C22×D12—31no—
199C22×C4×D3—31no—
200C22×C4×D3—31no—
201C2×C3×SD16—21no—
202C2×C3×SD16—31no—
203C2×C3×SD16—31no—
204C2×C3×SD16—31no—
205C2×C3×SD16—31no—
206C2×C3×SD16—64no—
207C2×C3×SD16C2×D311yescharacteristic, complemented
208C2×C3×SD16C2×D311yescharacteristic, complemented
209C22×C3×C8—31no—
210C3×C22⋊Q8—31no—
211#946—31no—
212#946—31no—
213#946—31no—
214#946—31no—
215#946—61no—
216#946—61no—
217#946—61no—
218#946C2×D311yescharacteristic, complemented
219C2×#215—31no—
220C2×#215—31no—
221C2×#215—31no—
222C2×#215—31no—
223C2×#215—61no—
224C2×#215—64no—
225C2×#215C2×D311yescharacteristic, complemented
226C2×#215C2×D311yescharacteristic, complemented
227C2×#214—31no—
228C2×#214C2×D311yescharacteristic, complemented
229C2×(C2×D3)⋊C4—61no—
230C2×C4⋊Dic3—31no—
231#924—31no—
232C2×Dic3⋊C4—61no—
233C22×C3⋊C8—31no—
234D3×SD16—24no—
235D3×SD16—64no—
236C2×#204—31no—
237C2×#204C2×D311yescharacteristic, complemented
238C2×D3×C8—31no—
239C2×D3×C8C2×D311yescharacteristic, complemented
240#897—31no—
241#896—61no—
242D3×C4⋊C4—31no—
243D3×C4⋊C4—61no—
244D3×C22⋊C4—61no—
245#878—61no—
246C3×#102—31no—
247C3×#102—31no—
248C3×C22⋊C8—31no—
249#832—31no—
250#832—31no—
251#832—31no—
252#832—31no—
253#832—31no—
254#832—61no—
255#832C2×D311yescharacteristic, complemented
256#830—31no—
257#821—31no—
258#821—31no—
259#821—31no—
260#821—31no—
261#821—31no—
262#821—61no—
263#821C2×D311yescharacteristic, complemented
264(C2×D3)⋊C8—31no—
265(C2×D3)⋊C8—31no—
266(C2×D3)⋊C8—31no—
267(C2×D3)⋊C8—31no—
268(C2×D3)⋊C8—31no—
269(C2×D3)⋊C8—61no—
270(C2×D3)⋊C8C2×D311yescharacteristic, complemented
271#809—31no—
272#809—31no—
273C23×C32—21no—
274C22×C3⋊D3—24no—
275C22×C3⋊D3—21no—
276C22×C3⋊D3—42no—
277C22×C3⋊D3—42no—
278C22×C3⋊D3C2×D411yescharacteristic
279C22×C3×D3—24no—
280C22×C3×D3—21no—
281C22×C3×D3—21no—
282C22×C3×D3—24no—
283C22×C3×D3—42no—
284C22×C3×D3—42no—
285C22×C3×D3—42no—
286C22×C3×D3—42no—
287C22×C3×D3C2×D411yescharacteristic
288C22×C3×D3C2×D411yescharacteristic
289C2×D32—22no—
290C2×D32—22no—
291C2×D32—24no—
292C2×D32—24no—
293C2×D32—24no—
294C2×D32—432no—
295C2×D32—42no—
296C2×D32—42no—
297C2×D32—42no—
298C2×D32—42no—
299C2×D32—42no—
300C2×D32—42no—
301C2×D32SD1614yescomplemented
302C32×Q8—21no—
303C32×Q8—21no—
304C32×D4—21no—
305C32×D4C2×D412yes—
306C2×C32×C4—21no—
307C2×C32×C4C2411yescharacteristic
308#638—24no—
309C2×C3⋊Dic3—21no—
310C2×C3⋊Dic3C2×D411yescharacteristic
311C4⋊(C3⋊D3)—21no—
312C4⋊(C3⋊D3)C2×D412yes—
313C4×C3⋊D3—21no—
314C4×C3⋊D3—21no—
315C3×#67—24no—
316C3×#67—24no—
317C2×C3×Dic3—21no—
318C2×C3×Dic3—21no—
319C2×C3×Dic3C2×D411yescharacteristic
320C2×C3×Dic3C2×D411yescharacteristic
321C3×D12—21no—
322C3×D12—21no—
323C3×D12C2×D412yes—
324C3×D12C2×D412yes—
325C3×C4×D3—21no—
326C3×C4×D3—21no—
327C3×C4×D3—42no—
328C3×C4×D3C2×D412yes—
329C3×C4×D3C2×D412yes—
330C3×Dic6—21no—
331C3×Dic6—21no—
332C3×Dic6—42no—
333#626—24no—
334#626—24no—
335#625—24no—
336#624—22no—
337D3×Dic3—22no—
338D3×Dic3—22no—
339D3×Dic3—42no—
340C32×C8—21no—
341C3⋊(C3⋊C8)—21no—
342C3×C3⋊C8—21no—
343C3×C3⋊C8—21no—
344C23×D4—91no—
345C22×SD16—31no—
346C22×SD16—91no—
347C2×C22⋊Q8—91no—
348#450—31no—
349#450—91no—
350#450—91no—
351#450—91no—
352#450—91no—
353#450—91no—
354#450—91no—
355#450—91no—
356C2×#102—91no—
357C2×#102—91no—
358C2×C22⋊C8—91no—
359C24×C3—61no—
360C24×C3—61no—
361C23×D3—21no—
362C23×D3—21no—
363C23×D3—31no—
364C23×D3—31no—
365C23×D3—61no—
366C23×D3—61no—
367C23×D3—61no—
368C23×D3—61no—
369C23×D3—68no—
370C23×D3—68no—
371C23×D3—61no—
372C23×D3—61no—
373C23×D3—61no—
374C23×D3—61no—
375C23×D3—121no—
376C23×D3—124no—
377C23×D3—124no—
378C23×D3—124no—
379C23×D3—124no—
380C2×C3×Q8—21no—
381C2×C3×Q8—31no—
382C2×C3×Q8—61no—
383C2×C3×Q8—62no—
384C2×C3×Q8—62no—
385C2×C3×Q8C22×D311yescharacteristic, complemented
386C2×C3×Q8C22×D311yescharacteristic, complemented
387C2×C3×D4—21no—
388C2×C3×D4—34no—
389C2×C3×D4—31no—
390C2×C3×D4—31no—
391C2×C3×D4—62no—
392C2×C3×D4—61no—
393C2×C3×D4—61no—
394C2×C3×D4—62no—
395C2×C3×D4—62no—
396C2×C3×D4C22×D311yescharacteristic
397C2×C3×D4C22×D311yescharacteristic
398C22×C3×C4—31no—
399C22×C3×C4—31no—
400C22×C3×C4—61no—
401C2×#67—21no—
402C2×#67—21no—
403C2×#67—61no—
404C2×#67—61no—
405C2×#67—61no—
406C2×#67—61no—
407C2×#67—68no—
408C2×#67—68no—
409C2×#67—61no—
410C2×#67—61no—
411C2×#67—121no—
412C22×Dic3—31no—
413C22×Dic3—31no—
414C22×Dic3—61no—
415D3×Q8—22no—
416D3×Q8—22no—
417D3×D4—22no—
418D3×D4—22no—
419D3×D4—22no—
420D3×D4—34no—
421D3×D4—62no—
422D3×D4—62no—
423D3×D4—62no—
424D3×D4—62no—
425D3×D4—62no—
426D3×D4—62no—
427D3×D4—68no—
428D3×D4—68no—
429D3×D4—68no—
430D3×D4—68no—
431D3×D4—62no—
432D3×D4—62no—
433D3×D4—62no—
434D3×D4—62no—
435D3×D4—62no—
436D3×D4—122no—
437D3×D4—122no—
438D3×D4#6714yes—
439C2×D12—31no—
440C2×D12—31no—
441C2×D12—34no—
442C2×D12—61no—
443C2×D12—62no—
444C2×D12—62no—
445C2×D12—61no—
446C2×D12—61no—
447C2×D12—62no—
448C2×D12C22×D311yescharacteristic
449C2×D12C22×D311yescharacteristic
450C2×C4×D3—21no—
451C2×C4×D3—31no—
452C2×C4×D3—31no—
453C2×C4×D3—31no—
454C2×C4×D3—31no—
455C2×C4×D3—31no—
456C2×C4×D3—31no—
457C2×C4×D3—61no—
458C2×C4×D3—62no—
459C2×C4×D3—62no—
460C2×C4×D3—62no—
461C2×C4×D3—62no—
462C2×C4×D3—61no—
463C2×C4×D3C22×D311yescharacteristic
464C2×C4×D3C22×D311yescharacteristic
465C2×Dic6—21no—
466C2×Dic6C22×D311yescharacteristic, complemented
467C3×SD16—22no—
468C3×SD16—22no—
469C3×SD16—42no—
470C3×SD16—62no—
471C3×SD16—62no—
472C3×SD16—62no—
473C3×SD16—62no—
474C2×C3×C8—21no—
475C2×C3×C8—31no—
476C2×C3×C8—31no—
477C2×C3×C8—62no—
478C2×C3×C8C22×D311yescharacteristic, complemented
479C2×C3×C8C22×D311yescharacteristic, complemented
480C3×C4⋊C4—31no—
481C3×C4⋊C4—61no—
482C3×C22⋊C4—61no—
483#217—61no—
484#215—22no—
485#215—22no—
486#215—62no—
487#215—62no—
488#215—62no—
489#215—62no—
490#215—122no—
491#214—22no—
492#214—62no—
493(C2×D3)⋊C4—21no—
494(C2×D3)⋊C4—61no—
495(C2×D3)⋊C4—61no—
496(C2×D3)⋊C4—61no—
497(C2×D3)⋊C4—61no—
498(C2×D3)⋊C4—61no—
499(C2×D3)⋊C4—121no—
500C4⋊Dic3—31no—
501C4⋊Dic3—31no—
502C4⋊Dic3—61no—
503C4⋊Dic3—61no—
504C4⋊Dic3—61no—
505C4⋊Dic3C22×D311yescharacteristic, complemented
506Dic3⋊C4—21no—
507Dic3⋊C4—61no—
508Dic3⋊C4—61no—
509Dic3⋊C4—61no—
510Dic3⋊C4—61no—
511Dic3⋊C4—61no—
512Dic3⋊C4—61no—
513Dic3⋊C4—121no—
514C2×C3⋊C8—31no—
515C2×C3⋊C8—31no—
516C2×C3⋊C8—61no—
517C2×C3⋊C8—62no—
518C2×C3⋊C8C22×D311yescharacteristic, complemented
519C2×C3⋊C8C22×D311yescharacteristic, complemented
520#204—22no—
521#204—62no—
522D3×C8—22no—
523D3×C8—62no—
524C22×C32—22no—
525C22×C32—41no—
526C22×C32—41no—
527C22×C32C22×D411yescharacteristic
528C2×C3⋊D3—21no—
529C2×C3⋊D3—21no—
530C2×C3⋊D3—22no—
531C2×C3⋊D3—48no—
532C2×C3⋊D3—41no—
533C2×C3⋊D3—41no—
534C2×C3⋊D3C2×SD1612yescomplemented
535C2×C3×D3—21no—
536C2×C3×D3—21no—
537C2×C3×D3—22no—
538C2×C3×D3—22no—
539C2×C3×D3—48no—
540C2×C3×D3—41no—
541C2×C3×D3—41no—
542C2×C3×D3—41no—
543C2×C3×D3—41no—
544C2×C3×D3—48no—
545C2×C3×D3#12012yes—
546C2×C3×D3C2×SD1612yes—
547C2×C3×D3C2×SD1612yescomplemented
548C2×C3×D3AGL(1,ℤ/8)12yes—
549D32—28no—
550D32—48no—
551D32—48no—
552D32—48no—
553C32×C4—41no—
554C32×C4C22×D411yescharacteristic
555C32×C4C22×D411yescharacteristic
556C3⋊Dic3—21no—
557C3⋊Dic3—41no—
558C3×Dic3—21no—
559C3×Dic3—41no—
560C3×Dic3—41no—
561C3×Dic3#12012yes—
562C25—181no—
563C22×Q8—31no—
564C22×D4—31no—
565C22×D4—31no—
566C22×D4—91no—
567C22×D4—91no—
568C22×D4—91no—
569C22×D4—91no—
570C22×D4—181no—
571C22×D4—181no—
572C22×D4—181no—
573C22×D4—184no—
574C22×D4—184no—
575C23×C4—91no—
576C2×SD16—31no—
577C2×SD16—31no—
578C2×SD16—31no—
579C2×SD16—31no—
580C2×SD16—64no—
581C2×SD16—91no—
582C2×SD16—91no—
583C2×SD16—91no—
584C2×SD16—184no—
585C2×SD16D3211yescharacteristic, complemented
586C22×C8—31no—
587C22×C8—91no—
588C22⋊Q8—31no—
589C22⋊Q8—91no—
590C22⋊Q8—91no—
591C22⋊Q8—91no—
592C22⋊Q8—181no—
593C22⋊Q8—181no—
594C2×C4⋊C4—91no—
595C2×C4⋊C4—181no—
596C2×C22⋊C4—181no—
597#102—31no—
598#102—31no—
599#102—91no—
600#102—91no—
601#102—91no—
602#102—91no—
603#102—91no—
604#102—91no—
605C22⋊C8—31no—
606C22⋊C8—91no—
607C22⋊C8—91no—
608C22⋊C8—91no—
609C23×C3—21no—
610C23×C3—21no—
611C23×C3—31no—
612C23×C3—31no—
613C23×C3—41no—
614C23×C3—64no—
615C23×C3—64no—
616C23×C3—61no—
617C23×C3—61no—
618C23×C3—122no—
619C23×C3—122no—
620C23×C3—122no—
621C23×C3—122no—
622C22×D3—24no—
623C22×D3—21no—
624C22×D3—21no—
625C22×D3—24no—
626C22×D3—31no—
627C22×D3—31no—
628C22×D3—34no—
629C22×D3—34no—
630C22×D3—42no—
631C22×D3—42no—
632C22×D3—42no—
633C22×D3—42no—
634C22×D3—61no—
635C22×D3—62no—
636C22×D3—62no—
637C22×D3—64no—
638C22×D3—64no—
639C22×D3—64no—
640C22×D3—64no—
641C22×D3—64no—
642C22×D3—62no—
643C22×D3—62no—
644C22×D3—64no—
645C22×D3—64no—
646C22×D3—61no—
647C22×D3—61no—
648C22×D3—64no—
649C22×D3—121no—
650C22×D3—124no—
651C22×D3—122no—
652C22×D3—122no—
653C22×D3—122no—
654C22×D3—122no—
655C22×D3—122no—
656C22×D3—1232no—
657C22×D3—122no—
658C22×D3—122no—
659C22×D3—1232no—
660C22×D3—122no—
661C22×D3—122no—
662C22×D3—122no—
663C22×D3—122no—
664C22×D3—122no—
665C22×D3—122no—
666C22×D3—122no—
667C22×D3—122no—
668C22×D3—122no—
669C22×D3—242no—
670C22×D3—242no—
671C22×D3D3×D411yescharacteristic
672C22×D3D3×D411yescharacteristic
673C3×Q8—21no—
674C3×Q8—21no—
675C3×Q8—21no—
676C3×Q8—21no—
677C3×Q8—41no—
678C3×Q8—41no—
679C3×Q8—61no—
680C3×Q8—61no—
681C3×Q8—122no—
682C3×D4—21no—
683C3×D4—21no—
684C3×D4—22no—
685C3×D4—32no—
686C3×D4—32no—
687C3×D4—41no—
688C3×D4—64no—
689C3×D4—64no—
690C3×D4—61no—
691C3×D4—61no—
692C3×D4D3×D412yes—
693C3×D4C2×#6712yes—
694C2×C3×C4—21no—
695C2×C3×C4—21no—
696C2×C3×C4—21no—
697C2×C3×C4—31no—
698C2×C3×C4—32no—
699C2×C3×C4—32no—
700C2×C3×C4—31no—
701C2×C3×C4—41no—
702C2×C3×C4—61no—
703C2×C3×C4—61no—
704C2×C3×C4—61no—
705C2×C3×C4—61no—
706C2×C3×C4—122no—
707C2×C3×C4C23×D311yescharacteristic
708C2×C3×C4C23×D311yescharacteristic
709#67—24no—
710#67—24no—
711#67—64no—
712#67—64no—
713#67—64no—
714#67—64no—
715#67—64no—
716#67—64no—
717#67—124no—
718C2×Dic3—21no—
719C2×Dic3—21no—
720C2×Dic3—31no—
721C2×Dic3—31no—
722C2×Dic3—61no—
723C2×Dic3—62no—
724C2×Dic3—62no—
725C2×Dic3—61no—
726C2×Dic3—61no—
727C2×Dic3—121no—
728C2×Dic3—122no—
729C2×Dic3D3×D411yescharacteristic
730C2×Dic3D3×D411yescharacteristic
731D12—21no—
732D12—21no—
733D12—32no—
734D12—32no—
735D12—62no—
736D12—64no—
737D12—64no—
738D12—61no—
739D12—61no—
740D12—121no—
741D12D3×D412yes—
742D12C2×#6712yes—
743C4×D3—21no—
744C4×D3—21no—
745C4×D3—42no—
746C4×D3—62no—
747C4×D3—62no—
748C4×D3—62no—
749C4×D3—61no—
750C4×D3—61no—
751C4×D3—61no—
752C4×D3—61no—
753C4×D3—62no—
754C4×D3—121no—
755C4×D3—121no—
756C4×D3—122no—
757C4×D3D3×D412yes—
758C4×D3C2×#6712yes—
759Dic6—21no—
760Dic6—21no—
761Dic6—42no—
762C3×C8—21no—
763C3×C8—21no—
764C3×C8—41no—
765C3×C8—61no—
766C3×C8—61no—
767C3⋊C8—21no—
768C3⋊C8—21no—
769C3⋊C8—61no—
770C3⋊C8—61no—
771C3⋊C8—121no—
772C2×C32—42no—
773C2×C32C2×#12011yescharacteristic
774C2×C32C22×SD1611yescharacteristic
775C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
776C3⋊D3—22no—
777C3⋊D3—42no—
778C3×D3—22no—
779C3×D3—42no—
780C3×D3—42no—
781C3×D3#45014yescomplemented
782C24—61no—
783C24—61no—
784C24—91no—
785C24—181no—
786C24—181no—
787C24—181no—
788C24—181no—
789C24—188no—
790C24—364no—
791C24—364no—
792C2×Q8—31no—
793C2×Q8—61no—
794C2×Q8—62no—
795C2×Q8—62no—
796C2×Q8C2×D3211yescharacteristic, complemented
797C2×D4—34no—
798C2×D4—31no—
799C2×D4—31no—
800C2×D4—62no—
801C2×D4—61no—
802C2×D4—61no—
803C2×D4—62no—
804C2×D4—62no—
805C2×D4—94no—
806C2×D4—91no—
807C2×D4—182no—
808C2×D4—181no—
809C2×D4—181no—
810C2×D4—182no—
811C2×D4—182no—
812C2×D4—181no—
813C2×D4—181no—
814C2×D4—182no—
815C2×D4—182no—
816C2×D4—182no—
817C2×D4—188no—
818C2×D4—188no—
819C2×D4—188no—
820C2×D4—182no—
821C2×D4C2×D3211yescharacteristic
822C22×C4—31no—
823C22×C4—31no—
824C22×C4—61no—
825C22×C4—91no—
826C22×C4—91no—
827C22×C4—91no—
828C22×C4—91no—
829C22×C4—182no—
830C22×C4—182no—
831C22×C4—181no—
832SD16—22no—
833SD16—62no—
834SD16—62no—
835SD16—62no—
836SD16—62no—
837SD16—182no—
838SD16—182no—
839SD16—182no—
840C2×C8—31no—
841C2×C8—31no—
842C2×C8—62no—
843C2×C8—91no—
844C2×C8—182no—
845C2×C8C2×D3211yescharacteristic, complemented
846C4⋊C4—31no—
847C4⋊C4—61no—
848C4⋊C4—91no—
849C4⋊C4—181no—
850C4⋊C4—181no—
851C4⋊C4—181no—
852C4⋊C4—181no—
853C22⋊C4—61no—
854C22⋊C4—181no—
855C22⋊C4—181no—
856C22⋊C4—181no—
857C22×C3—22no—
858C22×C3—22no—
859C22×C3—21no—
860C22×C3—32no—
861C22×C3—32no—
862C22×C3—32no—
863C22×C3—32no—
864C22×C3—42no—
865C22×C3—41no—
866C22×C3—41no—
867C22×C3—41no—
868C22×C3—41no—
869C22×C3—61no—
870C22×C3—61no—
871C22×C3—62no—
872C22×C3—62no—
873C22×C3—81no—
874C22×C3—81no—
875C22×C3—128no—
876C22×C3—128no—
877C22×C3—121no—
878C22×C3—121no—
879C22×C3—121no—
880C22×C3—121no—
881C22×C3C2×D3×D411yescharacteristic
882C22×C3C2×D3×D411yescharacteristic
883C2×D3—21no—
884C2×D3—21no—
885C2×D3—22no—
886C2×D3—22no—
887C2×D3—32no—
888C2×D3—32no—
889C2×D3—48no—
890C2×D3—41no—
891C2×D3—41no—
892C2×D3—41no—
893C2×D3—41no—
894C2×D3—48no—
895C2×D3—62no—
896C2×D3—68no—
897C2×D3—61no—
898C2×D3—61no—
899C2×D3—61no—
900C2×D3—61no—
901C2×D3—68no—
902C2×D3—62no—
903C2×D3—62no—
904C2×D3—121no—
905C2×D3—121no—
906C2×D3—122no—
907C2×D3—128no—
908C2×D3—128no—
909C2×D3—128no—
910C2×D3—128no—
911C2×D3—128no—
912C2×D3—128no—
913C2×D3—128no—
914C2×D3—121no—
915C2×D3—121no—
916C2×D3—121no—
917C2×D3—121no—
918C2×D3—128no—
919C2×D3—248no—
920C2×D3—241no—
921C2×D3—241no—
922C2×D3D3×SD1612yes—
923C2×D3D3×SD1612yescomplemented
924C2×D3#91412yes—
925C2×D3#93712yes—
926C3×C4—21no—
927C3×C4—21no—
928C3×C4—32no—
929C3×C4—41no—
930C3×C4—41no—
931C3×C4—61no—
932C3×C4—81no—
933C3×C4—121no—
934C3×C4—121no—
935C3×C4C2×D3×D411yescharacteristic
936C3×C4C2×D3×D411yescharacteristic
937C3×C4C2×D3×D411yescharacteristic
938C3×C4C22×#6711yescharacteristic
939Dic3—21no—
940Dic3—41no—
941Dic3—41no—
942Dic3—61no—
943Dic3—61no—
944Dic3—121no—
945Dic3—121no—
946Dic3—121no—
947Dic3—241no—
948Dic3#93712yes—
949C32C2×#45011yescharacteristic, complemented, Sylow
950C23—21no—
951C23—31no—
952C23—31no—
953C23—64no—
954C23—64no—
955C23—61no—
956C23—61no—
957C23—94no—
958C23—91no—
959C23—122no—
960C23—122no—
961C23—122no—
962C23—122no—
963C23—184no—
964C23—182no—
965C23—182no—
966C23—184no—
967C23—184no—
968C23—184no—
969C23—181no—
970C23—362no—
971C23—362no—
972C23—362no—
973C23—362no—
974C23—362no—
975C23—362no—
976C23—362no—
977C23—3632no—
978C23—362no—
979Q8—21no—
980Q8—21no—
981Q8—61no—
982Q8—61no—
983Q8—122no—
984D4—21no—
985D4—32no—
986D4—32no—
987D4—64no—
988D4—64no—
989D4—61no—
990D4—61no—
991D4—92no—
992D4—184no—
993D4—184no—
994D4—184no—
995D4—184no—
996D4—181no—
997D4D3×#6712yes—
998C2×C4—21no—
999C2×C4—31no—
1000C2×C4—32no—
1001C2×C4—32no—
1002C2×C4—31no—
1003C2×C4—61no—
1004C2×C4—61no—
1005C2×C4—61no—
1006C2×C4—61no—
1007C2×C4—91no—
1008C2×C4—122no—
1009C2×C4—182no—
1010C2×C4—182no—
1011C2×C4—182no—
1012C2×C4—181no—
1013C2×C4—181no—
1014C2×C4—181no—
1015C2×C4—362no—
1016C2×C4C22×D3211yescharacteristic
1017C8—21no—
1018C8—61no—
1019C8—61no—
1020C8—181no—
1021C2×C3—21no—
1022C2×C3—21no—
1023C2×C3—21no—
1024C2×C3—34no—
1025C2×C3—42no—
1026C2×C3—42no—
1027C2×C3—62no—
1028C2×C3—82no—
1029C2×C3—122no—
1030C2×C3—122no—
1031C2×C3D3×#12011yescharacteristic
1032C2×C3C2×D3×SD1611yescharacteristic
1033C2×C3C2×D3×SD1611yescharacteristic
1034C2×C3C2×#91411yescharacteristic
1035C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
1036C2×C3C2×#93711yescharacteristic
1037D3—22no—
1038D3—42no—
1039D3—42no—
1040D3—62no—
1041D3—62no—
1042D3—122no—
1043D3—122no—
1044D3—122no—
1045D3—242no—
1046D3#516914yesdirect product factor
1047C22—22no—
1048C22—32no—
1049C22—32no—
1050C22—32no—
1051C22—32no—
1052C22—41no—
1053C22—41no—
1054C22—61no—
1055C22—61no—
1056C22—62no—
1057C22—62no—
1058C22—92no—
1059C22—128no—
1060C22—128no—
1061C22—121no—
1062C22—121no—
1063C22—121no—
1064C22—121no—
1065C22—188no—
1066C22—181no—
1067C22—181no—
1068C22—182no—
1069C22—368no—
1070C22—368no—
1071C22—368no—
1072C22—368no—
1073C22—361no—
1074C22—361no—
1075C22D32×D411yescharacteristic
1076C4—32no—
1077C4—41no—
1078C4—61no—
1079C4—121no—
1080C4—121no—
1081C4—181no—
1082C4—361no—
1083C4D32×D411yescharacteristic
1084C4C2×D3×#6711yescharacteristic
1085C3—21no—
1086C3D3×#45011yescharacteristic, complemented
1087C3C2×#516911yescharacteristic, complemented
1088C2—34no—
1089C2—42no—
1090C2—62no—
1091C2—122no—
1092C2—122no—
1093C2—182no—
1094C2—362no—
1095C2D32×SD1611yescharacteristic
1096C2D3×#91411yescharacteristic
1097C2D3×#93711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radicalC2×D32×D4C2
hypercenterC2×SD16D32
hypocenterC32C2×#450
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
2. C2×C3×D3×SD16C2semidirect
3. D3×#946C2semidirect
4. C2×D3×#215C2semidirect
5. #10592868C2semidirect
6. C3×#5169C2semidirect
7. #10591652C2semidirect
8. #10591651C2semidirect
9. #10591467C2semidirect
10. #10591458C2semidirect
11. D3×#832C2semidirect
12. #10590943C2semidirect
13. #10590942C2semidirect
14. D3×#821C2semidirect
15. D3×(C2×D3)⋊C8C2semidirect
20. C2×C3×D3×Q8C22semidirect
32. C2×C32×SD16C22semidirect
33. #64155C22semidirect
34. C2×#3755C22semidirect
35. C3×#946C22semidirect
36. C2×C3×#215C22semidirect
37. C2×C3×#215C22semidirect
38. C2×C3×#214C22semidirect
40. C2×C3×#204C22semidirect
41. C2×C3×D3×C8C22semidirect
44. D3×C4⋊Dic3C22semidirect
48. #63871C22semidirect
49. #63856C22semidirect
50. C2×#3717C22semidirect
51. C2×#3715C22semidirect
52. C2×D3×C3⋊C8C22semidirect
53. #63659C22semidirect
54. #63648C22semidirect
55. #63647C22semidirect
56. C3×#832C22semidirect
57. C3×#821C22semidirect
58. C3×(C2×D3)⋊C8C22semidirect
59. #63564C22semidirect
60. #63563C22semidirect
61. #63563C22semidirect
62. #63562C22semidirect
63. #63557C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
71. C2×D3×SD16D3semidirect
86. #5169D3direct (N × H)
106. C2×C32×Q8C23semidirect
127. C2×C3×Dic6C23semidirect
147. C2×C32×C8C23semidirect
150. C4⋊(C3⋊Dic3)C23semidirect
152. C2×C3⋊(C3⋊C8)C23semidirect
157. C3×C4⋊Dic3C23semidirect
159. C2×C3×C3⋊C8C23semidirect
160. C2×C3×C3⋊C8C23semidirect
179. C2×D3×Q8C2×D3semidirect
207. C2×C3×SD16C2×D3semidirect
208. C2×C3×SD16C2×D3semidirect
218. #946C2×D3semidirect
225. C2×#215C2×D3semidirect
226. C2×#215C2×D3semidirect
228. C2×#214C2×D3semidirect
237. C2×#204C2×D3semidirect
239. C2×D3×C8C2×D3semidirect
255. #832C2×D3semidirect
263. #821C2×D3semidirect
270. (C2×D3)⋊C8C2×D3semidirect
301. C2×D32SD16semidirect
385. C2×C3×Q8C22×D3semidirect
386. C2×C3×Q8C22×D3semidirect
466. C2×Dic6C22×D3semidirect
478. C2×C3×C8C22×D3semidirect
479. C2×C3×C8C22×D3semidirect
505. C4⋊Dic3C22×D3semidirect
518. C2×C3⋊C8C22×D3semidirect
519. C2×C3⋊C8C22×D3semidirect
534. C2×C3⋊D3C2×SD16semidirect
547. C2×C3×D3C2×SD16semidirect
585. C2×SD16D32semidirect
781. C3×D3#450semidirect
796. C2×Q8C2×D32semidirect
845. C2×C8C2×D32semidirect
923. C2×D3D3×SD16semidirect
949. C32C2×#450semidirect
1046. D3#5169direct (N × H)
1086. C3D3×#450semidirect
1087. C3C2×#5169semidirect

Maximal subgroups

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

subgroupindex
C2×D32×D42
C2×C3×D3×SD162
D3×#9462
C2×D3×#2152
#105928682
C3×#51692
#105916522
#105916512
#105914672
#105914582
D3×#8322
#105909432
#105909422
D3×#8212
D3×(C2×D3)⋊C82
C2×#51693
D3×#4503