Finite Group Databasebeta

← D3×#4776 #11863565

Subgroups — D3×#4776 #11863565

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×D3×#214C211yesmaximal, characteristic, complemented
3C2×D3×#204C211yesmaximal, characteristic, complemented
4D3×#897C211yesmaximal, characteristic, complemented
5#10592475C211yesmaximal, characteristic, complemented
6C3×#4776C211yesmaximal, characteristic, complemented
7C3×D3×#102C211yesmaximal, characteristic, complemented
8#10591467C211yesmaximal, characteristic, complemented
9#10591459C211yesmaximal, characteristic, complemented
10#10590946C211yesmaximal, characteristic, complemented
11#10590943C211yesmaximal, characteristic, complemented
12D3×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
13#10590597C211yesmaximal, characteristic, complemented
14#10590596C211yesmaximal, characteristic, complemented
15D3×#809C211yesmaximal, characteristic, complemented
16D3×#450—31nomaximal
17C2×#4776—31nomaximal
18C23×D32—21no—
19C2×D4×C3⋊D3C2211yescharacteristic
20C2×C3×D3×D4C2211yescharacteristic
21C2×C3×D3×D4C2211yescharacteristic
22C2×#3811—21no—
23C2×D3×#67—21no—
24C2×D3×#67—21no—
25D32×D4—24no—
26D32×D4—24no—
27C2×#3802C2211yescharacteristic
28C2×D3×D12C2211yescharacteristic
29C2×D3×D12C2211yescharacteristic
30C2×C4×D32C2211yescharacteristic
31C2×D3×Dic6C2211yescharacteristic, complemented
32C2×#3754C2211yescharacteristic, complemented
33C2×#3744C2211yescharacteristic, complemented
34#64106C2211yescharacteristic, complemented
35C2×C3×#214C2211yescharacteristic, complemented
36C2×C3×#204C2211yescharacteristic, complemented
37C2×C3×D3×C8C2211yescharacteristic, complemented
38C3×#897C2211yescharacteristic, complemented
39C3×D3×C4⋊C4C2211yescharacteristic, complemented
40D3×#214—24no—
41D3×(C2×D3)⋊C4—21no—
42#63895—21no—
43#63893—21no—
44D3×C4⋊Dic3—21no—
45#63871C2211yescharacteristic, complemented
46#63857C2211yescharacteristic, complemented
47C2×#3717C2211yescharacteristic, complemented
48C2×#3716C2211yescharacteristic, complemented
49C2×#3716C2211yescharacteristic, complemented
50C2×#3715C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52D3×#204—24no—
53C32×#102C2211yescharacteristic, complemented
54#63647C2211yescharacteristic, complemented
55#63636C2211yescharacteristic, complemented
56C3×#832C2211yescharacteristic, complemented
57C3×#821C2211yescharacteristic, complemented
58C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
59C3×#809C2211yescharacteristic, complemented
60C3×#809C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63#63557C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C22×D3×D4—31no—
66C22×D3×D4—31no—
67C22×#214—31no—
68C2×D3×SD16—31no—
69C2×D3×SD16—31no—
70C22×#204—31no—
71D3×C22⋊Q8—31no—
72C2×#897—31no—
73C3×#450—31no—
74C2×C3×#102—31no—
75#5218—31no—
76#5169—31no—
77#5169—31no—
78C2×(C2×D3)⋊C8—31no—
79#5046—31no—
80C2×#809—31no—
81#4776—31no—
82#4776—31no—
83#4776—31no—
84#4776—31no—
85#4776—31no—
86#4776—31no—
87#4776—31no—
88#4776—31no—
89#4776—31no—
90#4776—61no—
91#4776D311yescharacteristic, direct product factor
92D3×#102—31no—
93D3×#102D311yescharacteristic, complemented
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×D4C2311yescharacteristic
107C2×#638—21no—
108D4×C3⋊D3—22no—
109D4×C3⋊D3—22no—
110C2×C4⋊(C3⋊D3)C2311yescharacteristic
111C2×C4×C3⋊D3C2311yescharacteristic
112C2×#634C2311yescharacteristic, complemented
113C2×C3×#67—21no—
114C2×C3×#67—21no—
115C3×D3×D4—22no—
116C3×D3×D4—22no—
117C3×D3×D4—22no—
118C3×D3×D4D414yes—
119C2×C3×D12C2311yescharacteristic
120C2×C3×D12C2311yescharacteristic
121C2×C3×C4×D3—21no—
122C2×C3×C4×D3C2311yescharacteristic
123C2×C3×C4×D3C2311yescharacteristic
124C2×C3×Dic6C2311yescharacteristic, complemented
125#3811—28no—
126D3×#67—28no—
127D3×#67—28no—
128C2×#627—21no—
129C2×#626—21no—
130C2×#626—21no—
131C2×#625—21no—
132C2×#624D411yescharacteristic
133C2×D3×Dic3—21no—
134C2×D3×Dic3D411yescharacteristic
135C2×D3×Dic3D411yescharacteristic
136#3802—22no—
137#3802—22no—
138D3×D12—22no—
139D3×D12—22no—
140D3×D12—22no—
141D3×D12D414yes—
142C4×D32—22no—
143C4×D32—22no—
144D3×Dic6—22no—
145D3×Dic6—22no—
146C2×C32×C8C2311yescharacteristic, complemented
147C32×C4⋊C4C2311yescharacteristic, complemented
148#3754—22no—
149#3752—21no—
150C4⋊(C3⋊Dic3)—21no—
151C2×C3⋊(C3⋊C8)C2311yescharacteristic, complemented
152#3744—22no—
153C3×#214—22no—
154C3×(C2×D3)⋊C4—21no—
155C3×C4⋊Dic3—21no—
156C3×C4⋊Dic3C2311yescharacteristic, complemented
157C3×Dic3⋊C4—21no—
158C2×C3×C3⋊C8C2311yescharacteristic, complemented
159C2×C3×C3⋊C8C2311yescharacteristic, complemented
160C3×#204—22no—
161C3×D3×C8—22no—
162Dic3⋊Dic3—21no—
163Dic3⋊Dic3—21no—
164#3722—21no—
165(C2×D3)⋊Dic3—21no—
166#3717—22no—
167#3716—22no—
168#3716—22no—
169#3715—22no—
170D3×C3⋊C8—22no—
171C2×#450—91noSylow
172C24×D3—61no—
173C24×D3—61no—
174C22×C3×D4—31no—
175C22×C3×D4—31no—
176C22×#67—61no—
177C22×#67—61no—
178C2×D3×Q8—31no—
179C2×D3×D4—31no—
180C2×D3×D4—31no—
181C2×D3×D4—31no—
182C2×D3×D4—31no—
183C2×D3×D4—31no—
184C2×D3×D4—31no—
185C2×D3×D4—61no—
186C2×D3×D4—61no—
187C2×D3×D4—61no—
188C2×D3×D4—61no—
189C2×D3×D4—61no—
190C2×D3×D4—64no—
191C2×D3×D4—64no—
192C2×D3×D4—64no—
193C2×D3×D4—64no—
194C2×D3×D4C2×D311yescharacteristic
195C2×D3×D4C2×D311yescharacteristic
196C22×D12—31no—
197C22×D12—31no—
198C22×C4×D3—31no—
199C22×C4×D3—31no—
200C22×Dic6—31no—
201C2×C3×SD16—31no—
202C2×C3×SD16—31no—
203C22×C3×C8—31no—
204C3×C22⋊Q8—31no—
205C2×C3×C4⋊C4—31no—
206#946—31no—
207C2×#215—31no—
208C2×#215—31no—
209C2×#214—31no—
210C2×#214—31no—
211C2×#214—31no—
212C2×#214—31no—
213C2×#214—31no—
214C2×#214—61no—
215C2×#214—64no—
216C2×#214C2×D311yescharacteristic, complemented
217C2×(C2×D3)⋊C4—61no—
218C2×C4⋊Dic3—61no—
219#924—31no—
220C22×C3⋊C8—31no—
221D3×SD16—64no—
222D3×SD16—64no—
223C2×#204—31no—
224C2×#204—31no—
225C2×#204—31no—
226C2×#204—31no—
227C2×#204—31no—
228C2×#204—61no—
229C2×#204—64no—
230C2×#204C2×D311yescharacteristic, complemented
231C2×D3×C8—31no—
232C2×D3×C8C2×D311yescharacteristic, complemented
233#897—31no—
234#897—31no—
235#897—31no—
236#897—31no—
237#897—61no—
238#897—61no—
239#897—61no—
240#897C2×D311yescharacteristic, complemented
241#896—61no—
242D3×C4⋊C4—61no—
243D3×C4⋊C4C2×D311yescharacteristic, complemented
244D3×C22⋊C4—61no—
245#878—61no—
246C3×#102—21no—
247C3×#102—31no—
248C3×#102—31no—
249C3×#102—31no—
250C3×#102—31no—
251C3×#102C2×D311yescharacteristic, complemented
252C3×#102C2×D311yescharacteristic, complemented
253C3×C22⋊C8—31no—
254#832—31no—
255#832C2×D311yescharacteristic, complemented
256#830—31no—
257#821—31no—
258#821C2×D311yescharacteristic, complemented
259(C2×D3)⋊C8—31no—
260(C2×D3)⋊C8—31no—
261(C2×D3)⋊C8—31no—
262(C2×D3)⋊C8—31no—
263(C2×D3)⋊C8—31no—
264(C2×D3)⋊C8—61no—
265(C2×D3)⋊C8C2×D311yescharacteristic, complemented
266#809—31no—
267#809—31no—
268#809—31no—
269#809—31no—
270#809—61no—
271#809C2×D311yescharacteristic, complemented
272#809C2×D311yescharacteristic, complemented
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×D4—21no—
303C32×D4C2×D412yes—
304C2×C32×C4—21no—
305C2×C32×C4C2411yescharacteristic
306#638—24no—
307C2×C3⋊Dic3—21no—
308C2×C3⋊Dic3C2×D411yescharacteristic
309C4⋊(C3⋊D3)—21no—
310C4⋊(C3⋊D3)C2×D412yes—
311C4×C3⋊D3—21no—
312C4×C3⋊D3—21no—
313#634—21no—
314#634—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—
332#627—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—91no—
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—31no—
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—31no—
381C2×C3×D4—21no—
382C2×C3×D4—34no—
383C2×C3×D4—31no—
384C2×C3×D4—31no—
385C2×C3×D4—62no—
386C2×C3×D4—61no—
387C2×C3×D4—61no—
388C2×C3×D4—62no—
389C2×C3×D4—62no—
390C2×C3×D4C22×D311yescharacteristic
391C2×C3×D4C22×D311yescharacteristic
392C22×C3×C4—31no—
393C22×C3×C4—31no—
394C22×C3×C4—61no—
395C2×#67—21no—
396C2×#67—21no—
397C2×#67—61no—
398C2×#67—61no—
399C2×#67—61no—
400C2×#67—61no—
401C2×#67—68no—
402C2×#67—68no—
403C2×#67—61no—
404C2×#67—61no—
405C2×#67—121no—
406C22×Dic3—31no—
407C22×Dic3—31no—
408C22×Dic3—61no—
409D3×Q8—62no—
410D3×Q8—62no—
411D3×D4—22no—
412D3×D4—22no—
413D3×D4—22no—
414D3×D4—34no—
415D3×D4—62no—
416D3×D4—62no—
417D3×D4—62no—
418D3×D4—62no—
419D3×D4—62no—
420D3×D4—62no—
421D3×D4—68no—
422D3×D4—68no—
423D3×D4—68no—
424D3×D4—68no—
425D3×D4—62no—
426D3×D4—62no—
427D3×D4—62no—
428D3×D4—62no—
429D3×D4—62no—
430D3×D4—122no—
431D3×D4—122no—
432D3×D4D1214yes—
433C2×D12—31no—
434C2×D12—31no—
435C2×D12—34no—
436C2×D12—61no—
437C2×D12—62no—
438C2×D12—62no—
439C2×D12—61no—
440C2×D12—61no—
441C2×D12—62no—
442C2×D12C22×D311yescharacteristic
443C2×D12C22×D311yescharacteristic
444C2×C4×D3—21no—
445C2×C4×D3—31no—
446C2×C4×D3—31no—
447C2×C4×D3—31no—
448C2×C4×D3—31no—
449C2×C4×D3—31no—
450C2×C4×D3—31no—
451C2×C4×D3—61no—
452C2×C4×D3—62no—
453C2×C4×D3—62no—
454C2×C4×D3—62no—
455C2×C4×D3—62no—
456C2×C4×D3—61no—
457C2×C4×D3C22×D311yescharacteristic
458C2×C4×D3C22×D311yescharacteristic
459C2×Dic6—31no—
460C2×Dic6—31no—
461C2×Dic6—61no—
462C2×Dic6—62no—
463C2×Dic6—62no—
464C2×Dic6—61no—
465C2×Dic6—61no—
466C2×Dic6C22×D311yescharacteristic, complemented
467C3×SD16—62no—
468C3×SD16—62no—
469C2×C3×C8—21no—
470C2×C3×C8—31no—
471C2×C3×C8—31no—
472C2×C3×C8—62no—
473C2×C3×C8C22×D311yescharacteristic, complemented
474C2×C3×C8C22×D311yescharacteristic, complemented
475C3×C4⋊C4—21no—
476C3×C4⋊C4—31no—
477C3×C4⋊C4—61no—
478C3×C4⋊C4—61no—
479C3×C4⋊C4C22×D311yescharacteristic, complemented
480C3×C4⋊C4C22×D311yescharacteristic, complemented
481C3×C22⋊C4—61no—
482#217—61no—
483#215—62no—
484#215—62no—
485#214—22no—
486#214—62no—
487#214—62no—
488#214—62no—
489#214—62no—
490#214—62no—
491#214—122no—
492(C2×D3)⋊C4—21no—
493(C2×D3)⋊C4—61no—
494(C2×D3)⋊C4—61no—
495(C2×D3)⋊C4—61no—
496(C2×D3)⋊C4—61no—
497(C2×D3)⋊C4—61no—
498(C2×D3)⋊C4—121no—
499C4⋊Dic3—21no—
500C4⋊Dic3—61no—
501C4⋊Dic3—61no—
502C4⋊Dic3—61no—
503C4⋊Dic3—61no—
504C4⋊Dic3—121no—
505C4⋊Dic3C22×D311yescharacteristic, complemented
506Dic3⋊C4—21no—
507Dic3⋊C4—61no—
508Dic3⋊C4—61no—
509C2×C3⋊C8—31no—
510C2×C3⋊C8—31no—
511C2×C3⋊C8—61no—
512C2×C3⋊C8—62no—
513C2×C3⋊C8C22×D311yescharacteristic, complemented
514C2×C3⋊C8C22×D311yescharacteristic, complemented
515#204—22no—
516#204—62no—
517#204—62no—
518#204—62no—
519#204—62no—
520#204—62no—
521#204—122no—
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—91no—
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—91no—
579C2×SD16—91no—
580C2×SD16—91no—
581C2×SD16—91no—
582C2×SD16—91no—
583C2×SD16—91no—
584C2×SD16—184no—
585C2×SD16—184no—
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—31no—
595C2×C4⋊C4—181no—
596C2×C22⋊C4—181no—
597#102—31no—
598#102—31no—
599#102—31no—
600#102—31no—
601#102—91no—
602#102—91no—
603#102—91no—
604#102D3211yescharacteristic, complemented
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—61no—
674C3×Q8—61no—
675C3×D4—21no—
676C3×D4—21no—
677C3×D4—22no—
678C3×D4—32no—
679C3×D4—32no—
680C3×D4—41no—
681C3×D4—64no—
682C3×D4—64no—
683C3×D4—61no—
684C3×D4—61no—
685C3×D4C2×D1212yes—
686C3×D4D3×D412yes—
687C2×C3×C4—21no—
688C2×C3×C4—21no—
689C2×C3×C4—21no—
690C2×C3×C4—31no—
691C2×C3×C4—32no—
692C2×C3×C4—32no—
693C2×C3×C4—31no—
694C2×C3×C4—41no—
695C2×C3×C4—61no—
696C2×C3×C4—61no—
697C2×C3×C4—61no—
698C2×C3×C4—61no—
699C2×C3×C4—122no—
700C2×C3×C4C23×D311yescharacteristic
701C2×C3×C4C23×D311yescharacteristic
702#67—24no—
703#67—24no—
704#67—64no—
705#67—64no—
706#67—64no—
707#67—64no—
708#67—64no—
709#67—64no—
710#67—124no—
711C2×Dic3—21no—
712C2×Dic3—21no—
713C2×Dic3—31no—
714C2×Dic3—31no—
715C2×Dic3—61no—
716C2×Dic3—62no—
717C2×Dic3—62no—
718C2×Dic3—61no—
719C2×Dic3—61no—
720C2×Dic3—121no—
721C2×Dic3—122no—
722C2×Dic3D3×D411yescharacteristic
723C2×Dic3D3×D411yescharacteristic
724D12—21no—
725D12—21no—
726D12—32no—
727D12—32no—
728D12—62no—
729D12—64no—
730D12—64no—
731D12—61no—
732D12—61no—
733D12—121no—
734D12C2×D1212yes—
735D12D3×D412yes—
736C4×D3—21no—
737C4×D3—21no—
738C4×D3—42no—
739C4×D3—62no—
740C4×D3—62no—
741C4×D3—62no—
742C4×D3—61no—
743C4×D3—61no—
744C4×D3—61no—
745C4×D3—61no—
746C4×D3—62no—
747C4×D3—121no—
748C4×D3—121no—
749C4×D3—122no—
750C4×D3C2×D1212yes—
751C4×D3D3×D412yes—
752Dic6—21no—
753Dic6—21no—
754Dic6—61no—
755Dic6—61no—
756Dic6—61no—
757Dic6—61no—
758Dic6—121no—
759Dic6—121no—
760Dic6—122no—
761Dic6—122no—
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—91no—
794C2×Q8—181no—
795C2×Q8—182no—
796C2×Q8—182no—
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—62no—
833SD16—62no—
834SD16—182no—
835SD16—182no—
836SD16—182no—
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—61no—
849C4⋊C4—181no—
850C4⋊C4—181no—
851C4⋊C4—181no—
852C4⋊C4C2×D3211yescharacteristic, complemented
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×D3#88212yes—
923C2×D3#91112yes—
924C2×D3D3×SD1612yes—
925C2×D3D3×SD1612yescomplemented
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×C4C22×D1211yescharacteristic
936C3×C4C2×D3×D411yescharacteristic
937C3×C4C2×D3×D411yescharacteristic
938C3×C4C2×D3×D411yescharacteristic
939Dic3—21no—
940Dic3—41no—
941Dic3—41no—
942Dic3—61no—
943Dic3—61no—
944Dic3—121no—
945Dic3—121no—
946Dic3—121no—
947Dic3—241no—
948Dic3#88212yes—
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—61no—
980Q8—61no—
981Q8—181no—
982Q8—181no—
983Q8—362no—
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×D1212yes—
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×C3C2×#88211yescharacteristic
1032C2×C3D3×#12011yescharacteristic
1033C2×C3C2×#91111yescharacteristic
1034C2×C3C2×D3×SD1611yescharacteristic
1035C2×C3C2×D3×SD1611yescharacteristic
1036C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
1037D3—22no—
1038D3—42no—
1039D3—42no—
1040D3—62no—
1041D3—62no—
1042D3—122no—
1043D3—122no—
1044D3—122no—
1045D3—242no—
1046D3#477614yesdirect 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—
1083C4C2×D3×D1211yescharacteristic
1084C4D32×D411yescharacteristic
1085C3—21no—
1086C3C2×#477611yescharacteristic, complemented
1087C3D3×#45011yescharacteristic, complemented
1088C2—34no—
1089C2—42no—
1090C2—62no—
1091C2—122no—
1092C2—122no—
1093C2—182no—
1094C2—362no—
1095C2D3×#88211yescharacteristic
1096C2D3×#91111yescharacteristic
1097C2D32×SD1611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC2×D32×D4C2
hypercenter#102D32
hypocenterC32C2×#450
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. C2×D3×#214C2semidirect
3. C2×D3×#204C2semidirect
4. D3×#897C2semidirect
5. #10592475C2semidirect
6. C3×#4776C2semidirect
7. C3×D3×#102C2semidirect
8. #10591467C2semidirect
9. #10591459C2semidirect
10. #10590946C2semidirect
11. #10590943C2semidirect
12. D3×(C2×D3)⋊C8C2semidirect
13. #10590597C2semidirect
14. #10590596C2semidirect
15. D3×#809C2semidirect
31. C2×D3×Dic6C22semidirect
32. C2×#3754C22semidirect
33. C2×#3744C22semidirect
34. #64106C22semidirect
35. C2×C3×#214C22semidirect
36. C2×C3×#204C22semidirect
37. C2×C3×D3×C8C22semidirect
38. C3×#897C22semidirect
39. C3×D3×C4⋊C4C22semidirect
45. #63871C22semidirect
46. #63857C22semidirect
47. C2×#3717C22semidirect
48. C2×#3716C22semidirect
49. C2×#3716C22semidirect
50. C2×#3715C22semidirect
51. C2×D3×C3⋊C8C22semidirect
53. C32×#102C22semidirect
54. #63647C22semidirect
55. #63636C22semidirect
56. C3×#832C22semidirect
57. C3×#821C22semidirect
58. C3×(C2×D3)⋊C8C22semidirect
59. C3×#809C22semidirect
60. C3×#809C22semidirect
61. #63564C22semidirect
62. #63562C22semidirect
63. #63557C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
91. #4776D3direct (N × H)
93. D3×#102D3semidirect
112. C2×#634C23semidirect
124. C2×C3×Dic6C23semidirect
146. C2×C32×C8C23semidirect
147. C32×C4⋊C4C23semidirect
151. C2×C3⋊(C3⋊C8)C23semidirect
156. C3×C4⋊Dic3C23semidirect
158. C2×C3×C3⋊C8C23semidirect
159. C2×C3×C3⋊C8C23semidirect
216. C2×#214C2×D3semidirect
230. C2×#204C2×D3semidirect
232. C2×D3×C8C2×D3semidirect
240. #897C2×D3semidirect
243. D3×C4⋊C4C2×D3semidirect
251. C3×#102C2×D3semidirect
252. C3×#102C2×D3semidirect
255. #832C2×D3semidirect
258. #821C2×D3semidirect
265. (C2×D3)⋊C8C2×D3semidirect
271. #809C2×D3semidirect
272. #809C2×D3semidirect
301. C2×D32SD16semidirect
466. C2×Dic6C22×D3semidirect
473. C2×C3×C8C22×D3semidirect
474. C2×C3×C8C22×D3semidirect
479. C3×C4⋊C4C22×D3semidirect
480. C3×C4⋊C4C22×D3semidirect
505. C4⋊Dic3C22×D3semidirect
513. C2×C3⋊C8C22×D3semidirect
514. C2×C3⋊C8C22×D3semidirect
534. C2×C3⋊D3C2×SD16semidirect
547. C2×C3×D3C2×SD16semidirect
604. #102D32semidirect
781. C3×D3#450semidirect
845. C2×C8C2×D32semidirect
852. C4⋊C4C2×D32semidirect
925. C2×D3D3×SD16semidirect
949. C32C2×#450semidirect
1046. D3#4776direct (N × H)
1086. C3C2×#4776semidirect
1087. C3D3×#450semidirect

Maximal subgroups

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

subgroupindex
C2×D32×D42
C2×D3×#2142
C2×D3×#2042
D3×#8972
#105924752
C3×#47762
C3×D3×#1022
#105914672
#105914592
#105909462
#105909432
D3×(C2×D3)⋊C82
#105905972
#105905962
D3×#8092
D3×#4503
C2×#47763