Finite Group Databasebeta

← D3×#4786 #11865456

Subgroups — D3×#4786 #11865456

Order 1152.

1366 conjugacy classes of subgroups.

The subgroup lattice has 973 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#940C211yesmaximal, characteristic, complemented
2C2×D3×#213C211yesmaximal, characteristic, complemented
3C2×D3×D24C211yesmaximal, characteristic, complemented
4D3×#893C211yesmaximal, characteristic, complemented
5#10592485C211yesmaximal, characteristic, complemented
6C3×#4786C211yesmaximal, characteristic, complemented
7C3×D3×#102C211yesmaximal, characteristic, complemented
8#10591433C211yesmaximal, characteristic, complemented
9#10591429C211yesmaximal, characteristic, complemented
10#10590765C211yesmaximal, characteristic, complemented
11#10590749C211yesmaximal, characteristic, complemented
12D3×Dic3⋊C8C211yesmaximal, characteristic, complemented
13D3×#809C211yesmaximal, characteristic, complemented
14#10590551C211yesmaximal, characteristic, complemented
15#10590547C211yesmaximal, characteristic, complemented
16D3×#459—31nomaximal
17C2×#4786—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×D3×#67—21no—
20C2×D3×#67—21no—
21C2×D3×D12C2211yescharacteristic
22C2×D3×D12C2211yescharacteristic
23C2×C4×D32—21no—
24#64149C2211yescharacteristic, complemented
25C2×#3753C2211yescharacteristic, complemented
26C2×#3745C2211yescharacteristic, complemented
27#64102C2211yescharacteristic, complemented
28C3×#940C2211yescharacteristic, complemented
29C2×C3×#213C2211yescharacteristic, complemented
30C2×C3×D24C2211yescharacteristic, complemented
31C2×C3×D3×C8C2211yescharacteristic
32C3×#893C2211yescharacteristic, complemented
33C3×D3×C4⋊C4C2211yescharacteristic
34#63979—21no—
35#63979—21no—
36D3×#213—24no—
37D3×(C2×D3)⋊C4—21no—
38#63914C2211yescharacteristic, complemented
39#63911C2211yescharacteristic, complemented
40#63904—21no—
41#63898C2211yescharacteristic, complemented
42#63894C2211yescharacteristic, complemented
43#63881—21no—
44C4×D3×Dic3C2211yescharacteristic
45C2×#3714C2211yescharacteristic, complemented
46C2×#3714C2211yescharacteristic, complemented
47C2×#3714C2211yescharacteristic, complemented
48C2×#3713C2211yescharacteristic, complemented
49C2×D3×C3⋊C8C2211yescharacteristic
50D3×D24—24no—
51C32×#102C2211yescharacteristic, complemented
52#63641C2211yescharacteristic, complemented
53#63636C2211yescharacteristic, complemented
54C3×#832C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic, complemented
58C3×#809C2211yescharacteristic, complemented
59#63572C2211yescharacteristic, complemented
60Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63C2×#940—31no—
64C22×#213—31no—
65C2×D3×D8—31no—
66C2×D3×D8—31no—
67C22×D24—31no—
68D3×#127—31no—
69C4×D3×D4—31no—
70C2×#893—31no—
71C3×#459—31no—
72C2×C3×#102—31no—
73#5150—31no—
74#5150—31no—
75C2×Dic3⋊C8—31no—
76#5072—31no—
77#5015—31no—
78C2×#809—31no—
79#4843—31no—
80D3×C4⋊C8—31no—
81#4786—31no—
82#4786—31no—
83#4786—31no—
84#4786—31no—
85#4786—31no—
86#4786—31no—
87#4786—31no—
88#4786—31no—
89#4786—31no—
90#4786—61no—
91#4786D311yescharacteristic, direct product factor
92D3×#102—31no—
93D3×#102D311yescharacteristic, complemented
94C23×C3×D3—21no—
95C22×D32—21no—
96C22×D32—21no—
97C2×C32×D4C2311yescharacteristic
98C2×#638—21no—
99C2×#638—21no—
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C4⋊(C3⋊D3)C2311yescharacteristic
102C2×C4×C3⋊D3—21no—
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C2×C3×#67—21no—
106C3×D3×D4—22no—
107C3×D3×D4—22no—
108C2×C3×D12C2311yescharacteristic
109C2×C3×D12C2311yescharacteristic
110C2×C3×D12C2311yescharacteristic
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3C2311yescharacteristic
114D3×#67—44no—
115D3×#67—44no—
116C2×#626—21no—
117C2×#626—21no—
118C2×#626—21no—
119C2×#626—21no—
120C2×#625—21no—
121C2×#625—21no—
122C2×#624—21no—
123C2×D3×Dic3—21no—
124C2×D3×Dic3D411yescharacteristic
125C2×D3×Dic3D411yescharacteristic
126D3×D12—22no—
127D3×D12—22no—
128D3×D12—22no—
129D3×D12D414yescomplemented
130C4×D32—44no—
131C2×C32×C8C2311yescharacteristic
132C32×C4⋊C4C2311yescharacteristic
133#3753—22no—
134#3752—21no—
135C4×C3⋊Dic3C2311yescharacteristic
136C2×C3⋊(C3⋊C8)C2311yescharacteristic
137#3745—22no—
138C3×#213—22no—
139C3×(C2×D3)⋊C4—21no—
140C3×C4⋊Dic3C2311yescharacteristic
141C3×Dic3⋊C4—21no—
142C3×C4×Dic3C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145C3×D24—22no—
146C3×D3×C8—22no—
147#3722—21no—
148(C2×D3)⋊Dic3—21no—
149Dic32D411yescharacteristic
150Dic32D411yescharacteristic
151#3714—22no—
152#3714—22no—
153#3714—22no—
154#3713—22no—
155D3×C3⋊C8—22no—
156C2×#459—91noSylow
157C22×C3×D4—31no—
158C22×#67—61no—
159C22×#67—61no—
160C2×D3×D4—31no—
161C2×D3×D4—31no—
162C2×D3×D4—61no—
163C2×D3×D4—61no—
164C2×D3×D4C2×D311yescharacteristic
165C22×D12—31no—
166C22×D12—31no—
167C22×C4×D3—61no—
168C22×C4×D3—61no—
169C2×C3×D8—31no—
170C2×C3×D8—31no—
171C22×C3×C8—31no—
172C3×#127—31no—
173C3×C4×D4—31no—
174C2×C3×C4⋊C4—31no—
175#940—31no—
176#940—31no—
177#940—31no—
178#940—31no—
179#940—31no—
180#940—61no—
181#940—61no—
182#940—61no—
183#940—61no—
184#940—61no—
185#940C2×D311yescharacteristic, complemented
186D4×Dic3—31no—
187C2×#213—31no—
188C2×#213—31no—
189C2×#213—31no—
190C2×#213—31no—
191C2×#213—31no—
192C2×#213—31no—
193C2×#213—31no—
194C2×#213—61no—
195C2×#213—64no—
196C2×#213C2×D311yescharacteristic, complemented
197C4×#67—61no—
198C2×(C2×D3)⋊C4—61no—
199C2×C4×Dic3—31no—
200C22×C3⋊C8—31no—
201D3×D8—64no—
202D3×D8—64no—
203C2×D24—31no—
204C2×D24—31no—
205C2×D24—31no—
206C2×D24—31no—
207C2×D24—31no—
208C2×D24—61no—
209C2×D24—64no—
210C2×D24C2×D311yescharacteristic, complemented
211C2×D3×C8—31no—
212C2×D3×C8C2×D311yescharacteristic
213#893—31no—
214#893—31no—
215#893—31no—
216#893—31no—
217#893—61no—
218#893—61no—
219#893—61no—
220#893C2×D311yescharacteristic, complemented
221D3×C4⋊C4C2×D311yescharacteristic
222#67⋊C4—61no—
223D3×C22⋊C4—61no—
224#874—31no—
225C4×D12—31no—
226C42×D3—31no—
227C3×C4⋊C8—31no—
228C3×#102—21no—
229C3×#102—31no—
230C3×#102—31no—
231C3×#102—31no—
232C3×#102—31no—
233C3×#102C2×D311yescharacteristic, complemented
234C3×#102C2×D311yescharacteristic, complemented
235#832—31no—
236#832C2×D311yescharacteristic, complemented
237#821—31no—
238#821C2×D311yescharacteristic, complemented
239Dic3⋊C8—31no—
240Dic3⋊C8—31no—
241Dic3⋊C8—31no—
242Dic3⋊C8—31no—
243Dic3⋊C8—31no—
244Dic3⋊C8—61no—
245Dic3⋊C8C2×D311yescharacteristic, complemented
246#809—31no—
247#809—31no—
248#809—31no—
249#809—31no—
250#809—61no—
251#809C2×D311yescharacteristic, complemented
252#809C2×D311yescharacteristic, complemented
253C4⋊(C3⋊C8)—31no—
254C23×C32—21no—
255C22×C3⋊D3—21no—
256C22×C3⋊D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—42no—
261C22×C3×D3—42no—
262C22×C3×D3—42no—
263C22×C3×D3C2×D411yescharacteristic
264C2×D32—24no—
265C2×D32—42no—
266C2×D32—42no—
267C2×D32—42no—
268C2×D32—42no—
269C2×D32—42no—
270C32×D4—21no—
271C32×D4—21no—
272C2×C32×C4—21no—
273C2×C32×C4C2411yescharacteristic
274#638—42no—
275#638—42no—
276C2×C3⋊Dic3C2×D411yescharacteristic
277C2×C3⋊Dic3C2×D411yescharacteristic
278C4⋊(C3⋊D3)—21no—
279C4⋊(C3⋊D3)—21no—
280C4⋊(C3⋊D3)—21no—
281C4⋊(C3⋊D3)C2×D412yescomplemented
282C4×C3⋊D3—42no—
283C3×#67—42no—
284C3×#67—42no—
285C3×#67—42no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3C2×D411yescharacteristic
288C2×C3×Dic3C2×D411yescharacteristic
289C2×C3×Dic3C2×D411yescharacteristic
290C3×D12—21no—
291C3×D12—21no—
292C3×D12—21no—
293C3×D12—21no—
294C3×D12—21no—
295C3×D12C2×D412yescomplemented
296C3×C4×D3—42no—
297C3×C4×D3—42no—
298C3×C4×D3C2×D412yes—
299C3×C4×D3#4112yes—
300#626—24no—
301#626—42no—
302#626—42no—
303#626—42no—
304#625—42no—
305#625—42no—
306#624—42no—
307D3×Dic3—22no—
308D3×Dic3—42no—
309D3×Dic3D814yescomplemented
310C32×C8—21no—
311C3⋊(C3⋊C8)—21no—
312C3×C3⋊C8—21no—
313C3×C3⋊C8—21no—
314C22×D8—91no—
315C22×D8—91no—
316C2×#127—91no—
317C2×C4×D4—91no—
318#459—31no—
319#459—91no—
320#459—91no—
321#459—91no—
322#459—91no—
323#459—91no—
324#459—91no—
325#459—91no—
326C2×C4⋊C8—91no—
327C2×#102—31no—
328C2×#102—91no—
329C24×C3—61no—
330C23×D3—21no—
331C23×D3—61no—
332C23×D3—61no—
333C23×D3—61no—
334C23×D3—61no—
335C2×C3×D4—21no—
336C2×C3×D4—31no—
337C2×C3×D4—31no—
338C2×C3×D4—31no—
339C2×C3×D4—62no—
340C2×C3×D4—62no—
341C2×C3×D4—61no—
342C2×C3×D4—61no—
343C2×C3×D4—61no—
344C2×C3×D4C22×D311yescharacteristic
345C2×C3×D4C22×D311yescharacteristic
346C22×C3×C4—31no—
347C22×C3×C4—61no—
348C22×C3×C4—61no—
349C2×#67—21no—
350C2×#67—21no—
351C2×#67—21no—
352C2×#67—61no—
353C2×#67—61no—
354C2×#67—61no—
355C2×#67—61no—
356C2×#67—61no—
357C2×#67—61no—
358C2×#67—61no—
359C2×#67—61no—
360C2×#67—61no—
361C2×#67—61no—
362C2×#67—61no—
363C2×#67—61no—
364C2×#67—121no—
365C2×#67—121no—
366C2×#67—124no—
367C2×#67—124no—
368C22×Dic3—31no—
369C22×Dic3—31no—
370C22×Dic3—61no—
371D3×D4—22no—
372D3×D4—22no—
373D3×D4—34no—
374D3×D4—62no—
375D3×D4—62no—
376D3×D4—62no—
377D3×D4—124no—
378D3×D4—124no—
379C2×D12—31no—
380C2×D12—31no—
381C2×D12—34no—
382C2×D12—31no—
383C2×D12—31no—
384C2×D12—61no—
385C2×D12—61no—
386C2×D12—62no—
387C2×D12—62no—
388C2×D12—62no—
389C2×D12—61no—
390C2×D12—61no—
391C2×D12—61no—
392C2×D12—61no—
393C2×D12C22×D311yescharacteristic
394C2×D12C22×D311yescharacteristic
395C2×D12C22×D311yescharacteristic
396C2×C4×D3—21no—
397C2×C4×D3—21no—
398C2×C4×D3—31no—
399C2×C4×D3—31no—
400C2×C4×D3—61no—
401C2×C4×D3—61no—
402C2×C4×D3—61no—
403C2×C4×D3—61no—
404C2×C4×D3—61no—
405C2×C4×D3—121no—
406C2×C4×D3—124no—
407C2×C4×D3—124no—
408C2×C4×D3C22×D311yescharacteristic
409C3×D8—62no—
410C3×D8—62no—
411C2×C3×C8—21no—
412C2×C3×C8—31no—
413C2×C3×C8—31no—
414C2×C3×C8—62no—
415C2×C3×C8C22×D311yescharacteristic
416C2×C3×C8C22×D311yescharacteristic
417C3×C4⋊C4—21no—
418C3×C4⋊C4—31no—
419C3×C4⋊C4—61no—
420C3×C4⋊C4C22×D311yescharacteristic
421C3×C4⋊C4C22×D311yescharacteristic
422C3×C22⋊C4—61no—
423C3×C42—31no—
424#217—61no—
425#213—22no—
426#213—62no—
427#213—62no—
428#213—62no—
429#213—62no—
430#213—62no—
431#213—62no—
432#213—62no—
433#213—122no—
434(C2×D3)⋊C4—21no—
435(C2×D3)⋊C4—61no—
436(C2×D3)⋊C4—61no—
437(C2×D3)⋊C4—61no—
438(C2×D3)⋊C4—61no—
439(C2×D3)⋊C4—61no—
440(C2×D3)⋊C4—121no—
441C4⋊Dic3C22×D311yescharacteristic
442Dic3⋊C4—21no—
443C4×Dic3—31no—
444C4×Dic3—31no—
445C4×Dic3—31no—
446C4×Dic3—31no—
447C4×Dic3—31no—
448C4×Dic3—31no—
449C4×Dic3—61no—
450C4×Dic3C22×D311yescharacteristic
451C2×C3⋊C8—31no—
452C2×C3⋊C8—31no—
453C2×C3⋊C8—61no—
454C2×C3⋊C8—62no—
455C2×C3⋊C8C22×D311yescharacteristic
456C2×C3⋊C8C22×D311yescharacteristic
457D24—22no—
458D24—62no—
459D24—62no—
460D24—62no—
461D24—62no—
462D24—62no—
463D24—122no—
464D3×C8—22no—
465D3×C8—62no—
466C22×C32—41no—
467C22×C32—41no—
468C22×C32—41no—
469C22×C32C22×D411yescharacteristic
470C2×C3⋊D3—22no—
471C2×C3⋊D3—41no—
472C2×C3⋊D3—41no—
473C2×C3⋊D3—41no—
474C2×C3⋊D3—41no—
475C2×C3⋊D3—41no—
476C2×C3×D3—22no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3—41no—
482C2×C3×D3—41no—
483C2×C3×D3—41no—
484C2×C3×D3—41no—
485C2×C3×D3—84no—
486C2×C3×D3#12112yes—
487C2×C3×D3C2×D812yes—
488C2×C3×D3AGL(1,ℤ/8)12yes—
489D32—48no—
490D32—84no—
491C32×C4—41no—
492C32×C4C22×D411yescharacteristic
493C32×C4C2×#4111yescharacteristic
494C3⋊Dic3—21no—
495C3⋊Dic3C2×D812yescomplemented
496C3×Dic3—21no—
497C3×Dic3—41no—
498C3×Dic3#12112yes—
499C3×Dic3C2×D812yescomplemented
500C22×D4—31no—
501C22×D4—91no—
502C22×D4—91no—
503C22×D4—181no—
504C22×D4—181no—
505C23×C4—181no—
506C2×D8—31no—
507C2×D8—31no—
508C2×D8—91no—
509C2×D8—91no—
510C2×D8—91no—
511C2×D8—91no—
512C2×D8—91no—
513C2×D8—91no—
514C2×D8—184no—
515C2×D8—184no—
516C22×C8—31no—
517C22×C8—91no—
518#127—31no—
519#127—91no—
520#127—91no—
521#127—91no—
522#127—181no—
523#127—181no—
524C4×D4—31no—
525C4×D4—91no—
526C4×D4—91no—
527C4×D4—91no—
528C4×D4—181no—
529C4×D4—181no—
530C2×C4⋊C4—31no—
531C2×C22⋊C4—181no—
532C2×C42—91no—
533C4⋊C8—31no—
534C4⋊C8—91no—
535C4⋊C8—91no—
536C4⋊C8—91no—
537#102—31no—
538#102—31no—
539#102—31no—
540#102—31no—
541#102—91no—
542#102—91no—
543#102—91no—
544#102D3211yescharacteristic, complemented
545C23×C3—21no—
546C23×C3—21no—
547C23×C3—31no—
548C23×C3—41no—
549C23×C3—61no—
550C23×C3—61no—
551C23×C3—61no—
552C23×C3—122no—
553C23×C3—122no—
554C23×C3—122no—
555C22×D3—21no—
556C22×D3—21no—
557C22×D3—21no—
558C22×D3—42no—
559C22×D3—42no—
560C22×D3—42no—
561C22×D3—64no—
562C22×D3—61no—
563C22×D3—61no—
564C22×D3—64no—
565C22×D3—61no—
566C22×D3—61no—
567C22×D3—121no—
568C22×D3—121no—
569C22×D3—122no—
570C22×D3—122no—
571C22×D3—122no—
572C22×D3—122no—
573C22×D3—122no—
574C22×D3—122no—
575C22×D3—122no—
576C22×D3—122no—
577C22×D3—122no—
578C22×D3—122no—
579C22×D3D3×D411yescharacteristic
580C3×D4—21no—
581C3×D4—21no—
582C3×D4—21no—
583C3×D4—21no—
584C3×D4—32no—
585C3×D4—41no—
586C3×D4—41no—
587C3×D4—61no—
588C3×D4—61no—
589C3×D4—61no—
590C3×D4—61no—
591C3×D4—61no—
592C3×D4—122no—
593C3×D4—122no—
594C3×D4—122no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—21no—
598C2×C3×C4—31no—
599C2×C3×C4—31no—
600C2×C3×C4—32no—
601C2×C3×C4—32no—
602C2×C3×C4—31no—
603C2×C3×C4—41no—
604C2×C3×C4—61no—
605C2×C3×C4—122no—
606C2×C3×C4—122no—
607C2×C3×C4C23×D311yescharacteristic
608C2×C3×C4C23×D311yescharacteristic
609#67—42no—
610#67—42no—
611#67—42no—
612#67—64no—
613#67—122no—
614#67—122no—
615#67—122no—
616#67—122no—
617#67—122no—
618#67—122no—
619#67—122no—
620#67—122no—
621#67—122no—
622#67—122no—
623#67—122no—
624#67—242no—
625#67—242no—
626C2×Dic3—21no—
627C2×Dic3—31no—
628C2×Dic3—31no—
629C2×Dic3—34no—
630C2×Dic3—31no—
631C2×Dic3—31no—
632C2×Dic3—61no—
633C2×Dic3—61no—
634C2×Dic3—62no—
635C2×Dic3—122no—
636C2×Dic3D3×D411yescharacteristic
637C2×Dic3D3×D411yescharacteristic
638C2×Dic3D3×D411yescharacteristic
639D12—21no—
640D12—21no—
641D12—21no—
642D12—21no—
643D12—21no—
644D12—32no—
645D12—32no—
646D12—62no—
647D12—64no—
648D12—61no—
649D12—61no—
650D12—61no—
651D12—61no—
652D12—61no—
653D12—61no—
654D12—121no—
655D12—121no—
656D12—121no—
657D12—122no—
658D12—122no—
659D12—122no—
660D12D3×D412yescomplemented
661C4×D3—34no—
662C4×D3—42no—
663C4×D3—42no—
664C4×D3—62no—
665C4×D3—122no—
666C4×D3—122no—
667C4×D3—122no—
668C4×D3—122no—
669C4×D3—122no—
670C4×D3—242no—
671C4×D3#23512yes—
672C4×D3D3×D412yes—
673C3×C8—21no—
674C3×C8—21no—
675C3×C8—41no—
676C3×C8—61no—
677C3×C8—61no—
678C3⋊C8—21no—
679C3⋊C8—21no—
680C3⋊C8—61no—
681C3⋊C8—61no—
682C3⋊C8—121no—
683C2×C32—81no—
684C2×C32C2×#12111yescharacteristic
685C2×C32C22×D811yescharacteristic
686C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
687C3⋊D3—42no—
688C3⋊D3—81no—
689C3×D3—42no—
690C3×D3—81no—
691C3×D3—81no—
692C3×D3#45914yescomplemented
693C24—61no—
694C24—181no—
695C24—181no—
696C2×D4—31no—
697C2×D4—31no—
698C2×D4—31no—
699C2×D4—62no—
700C2×D4—62no—
701C2×D4—61no—
702C2×D4—61no—
703C2×D4—61no—
704C2×D4—94no—
705C2×D4—91no—
706C2×D4—91no—
707C2×D4—182no—
708C2×D4—182no—
709C2×D4—182no—
710C2×D4—181no—
711C2×D4—181no—
712C2×D4—181no—
713C2×D4—181no—
714C2×D4—181no—
715C2×D4—181no—
716C2×D4—181no—
717C2×D4—181no—
718C2×D4—364no—
719C2×D4—364no—
720C2×D4C2×D3211yescharacteristic
721C22×C4—31no—
722C22×C4—61no—
723C22×C4—61no—
724C22×C4—91no—
725C22×C4—91no—
726C22×C4—181no—
727C22×C4—181no—
728C22×C4—181no—
729C22×C4—364no—
730D8—62no—
731D8—62no—
732D8—182no—
733D8—182no—
734D8—182no—
735D8—182no—
736D8—182no—
737D8—182no—
738C2×C8—31no—
739C2×C8—31no—
740C2×C8—62no—
741C2×C8—91no—
742C2×C8—182no—
743C2×C8C2×D3211yescharacteristic
744C4⋊C4—31no—
745C4⋊C4—61no—
746C4⋊C4C2×D3211yescharacteristic
747C22⋊C4—61no—
748C22⋊C4—181no—
749C22⋊C4—181no—
750C22⋊C4—181no—
751C42—31no—
752C42—91no—
753C42—91no—
754C42—91no—
755C22×C3—21no—
756C22×C3—32no—
757C22×C3—32no—
758C22×C3—32no—
759C22×C3—41no—
760C22×C3—41no—
761C22×C3—41no—
762C22×C3—41no—
763C22×C3—41no—
764C22×C3—41no—
765C22×C3—62no—
766C22×C3—81no—
767C22×C3—81no—
768C22×C3—81no—
769C22×C3—121no—
770C22×C3—121no—
771C22×C3—121no—
772C22×C3—121no—
773C22×C3—121no—
774C22×C3—121no—
775C22×C3—121no—
776C22×C3—121no—
777C22×C3—244no—
778C22×C3C2×D3×D411yescharacteristic
779C22×C3C2×D3×D411yescharacteristic
780C2×D3—22no—
781C2×D3—41no—
782C2×D3—41no—
783C2×D3—41no—
784C2×D3—41no—
785C2×D3—41no—
786C2×D3—41no—
787C2×D3—41no—
788C2×D3—41no—
789C2×D3—62no—
790C2×D3—62no—
791C2×D3—84no—
792C2×D3—122no—
793C2×D3—128no—
794C2×D3—121no—
795C2×D3—121no—
796C2×D3—121no—
797C2×D3—121no—
798C2×D3—128no—
799C2×D3—121no—
800C2×D3—121no—
801C2×D3—121no—
802C2×D3—121no—
803C2×D3—121no—
804C2×D3—121no—
805C2×D3—241no—
806C2×D3—241no—
807C2×D3—241no—
808C2×D3—241no—
809C2×D3—241no—
810C2×D3—244no—
811C2×D3—244no—
812C2×D3#88412yes—
813C2×D3D3×D812yes—
814C2×D3#91412yes—
815C3×C4—21no—
816C3×C4—21no—
817C3×C4—32no—
818C3×C4—32no—
819C3×C4—41no—
820C3×C4—41no—
821C3×C4—61no—
822C3×C4—81no—
823C3×C4—121no—
824C3×C4C2×#23511yescharacteristic
825C3×C4C2×D3×D411yescharacteristic
826C3×C4C2×D3×D411yescharacteristic
827C3×C4D3×#4111yescharacteristic
828Dic3—21no—
829Dic3—32no—
830Dic3—32no—
831Dic3—41no—
832Dic3—62no—
833Dic3—61no—
834Dic3—61no—
835Dic3—121no—
836Dic3#88412yes—
837Dic3D3×D812yescomplemented
838C32C2×#45911yescharacteristic, complemented, Sylow
839C23—21no—
840C23—31no—
841C23—61no—
842C23—61no—
843C23—61no—
844C23—122no—
845C23—122no—
846C23—122no—
847C23—184no—
848C23—181no—
849C23—181no—
850C23—362no—
851C23—362no—
852C23—362no—
853C23—362no—
854C23—362no—
855D4—21no—
856D4—21no—
857D4—32no—
858D4—61no—
859D4—61no—
860D4—61no—
861D4—61no—
862D4—61no—
863D4—92no—
864D4—122no—
865D4—122no—
866D4—122no—
867D4—184no—
868D4—181no—
869D4—181no—
870D4—181no—
871D4—362no—
872D4—362no—
873D4—362no—
874D4—362no—
875D4—362no—
876D4—362no—
877D4—362no—
878C2×C4—21no—
879C2×C4—31no—
880C2×C4—31no—
881C2×C4—32no—
882C2×C4—32no—
883C2×C4—31no—
884C2×C4—61no—
885C2×C4—94no—
886C2×C4—91no—
887C2×C4—91no—
888C2×C4—122no—
889C2×C4—122no—
890C2×C4—182no—
891C2×C4—362no—
892C2×C4—362no—
893C2×C4—362no—
894C2×C4C22×D3211yescharacteristic
895C8—21no—
896C8—61no—
897C8—61no—
898C8—181no—
899C2×C3—21no—
900C2×C3—21no—
901C2×C3—21no—
902C2×C3—34no—
903C2×C3—81no—
904C2×C3—81no—
905C2×C3—122no—
906C2×C3—161no—
907C2×C3—241no—
908C2×C3—241no—
909C2×C3C2×#88411yescharacteristic
910C2×C3D3×#12111yescharacteristic
911C2×C3C2×D3×D811yescharacteristic
912C2×C3C2×D3×D811yescharacteristic
913C2×C3C2×#91411yescharacteristic
914C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
915D3—42no—
916D3—81no—
917D3—81no—
918D3—122no—
919D3—122no—
920D3—242no—
921D3—241no—
922D3—241no—
923D3—481no—
924D3#478614yesdirect product factor
925C22—32no—
926C22—32no—
927C22—32no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22—62no—
932C22—121no—
933C22—121no—
934C22—121no—
935C22—121no—
936C22—121no—
937C22—121no—
938C22—121no—
939C22—121no—
940C22—182no—
941C22—244no—
942C22—368no—
943C22—361no—
944C22—361no—
945C22—361no—
946C22—361no—
947C22—361no—
948C22—724no—
949C22D32×D411yescharacteristic
950C4—32no—
951C4—32no—
952C4—41no—
953C4—61no—
954C4—92no—
955C4—121no—
956C4—181no—
957C4D3×#23511yescharacteristic
958C4D32×D411yescharacteristic
959C3—21no—
960C3C2×#478611yescharacteristic, complemented
961C3D3×#45911yescharacteristic, complemented
962C2—34no—
963C2—81no—
964C2—122no—
965C2—241no—
966C2—241no—
967C2—362no—
968C2—721no—
969C2D3×#88411yescharacteristic
970C2D32×D811yescharacteristic
971C2D3×#91411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32C2×#459
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
1. D3×#940C2semidirect
2. C2×D3×#213C2semidirect
3. C2×D3×D24C2semidirect
4. D3×#893C2semidirect
5. #10592485C2semidirect
6. C3×#4786C2semidirect
7. C3×D3×#102C2semidirect
8. #10591433C2semidirect
9. #10591429C2semidirect
10. #10590765C2semidirect
11. #10590749C2semidirect
12. D3×Dic3⋊C8C2semidirect
13. D3×#809C2semidirect
14. #10590551C2semidirect
15. #10590547C2semidirect
24. #64149C22semidirect
25. C2×#3753C22semidirect
26. C2×#3745C22semidirect
27. #64102C22semidirect
28. C3×#940C22semidirect
29. C2×C3×#213C22semidirect
30. C2×C3×D24C22semidirect
32. C3×#893C22semidirect
38. #63914C22semidirect
39. #63911C22semidirect
41. #63898C22semidirect
42. #63894C22semidirect
45. C2×#3714C22semidirect
46. C2×#3714C22semidirect
47. C2×#3714C22semidirect
48. C2×#3713C22semidirect
51. C32×#102C22semidirect
52. #63641C22semidirect
53. #63636C22semidirect
54. C3×#832C22semidirect
55. C3×#821C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. C3×#809C22semidirect
58. C3×#809C22semidirect
59. #63572C22semidirect
60. Dic3⋊(C3⋊C8)C22semidirect
61. #63564C22semidirect
62. #63562C22semidirect
91. #4786D3direct (N × H)
93. D3×#102D3semidirect
129. D3×D12D4semidirect
185. #940C2×D3semidirect
196. C2×#213C2×D3semidirect
210. C2×D24C2×D3semidirect
220. #893C2×D3semidirect
233. C3×#102C2×D3semidirect
234. C3×#102C2×D3semidirect
236. #832C2×D3semidirect
238. #821C2×D3semidirect
245. Dic3⋊C8C2×D3semidirect
251. #809C2×D3semidirect
252. #809C2×D3semidirect
281. C4⋊(C3⋊D3)C2×D4semidirect
295. C3×D12C2×D4semidirect
309. D3×Dic3D8semidirect
495. C3⋊Dic3C2×D8semidirect
499. C3×Dic3C2×D8semidirect
544. #102D32semidirect
660. D12D3×D4semidirect
692. C3×D3#459semidirect
837. Dic3D3×D8semidirect
838. C32C2×#459semidirect
924. D3#4786direct (N × H)
960. C3C2×#4786semidirect
961. C3D3×#459semidirect

Maximal subgroups

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

subgroupindex
D3×#9402
C2×D3×#2132
C2×D3×D242
D3×#8932
#105924852
C3×#47862
C3×D3×#1022
#105914332
#105914292
#105907652
#105907492
D3×Dic3⋊C82
D3×#8092
#105905512
#105905472
D3×#4593
C2×#47863