Finite Group Databasebeta

← D3×#5238 #11863712

Subgroups — D3×#5238 #11863712

Order 1152.

1705 conjugacy classes of subgroups.

The subgroup lattice has 1057 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×#41C211yesmaximal, characteristic, complemented
2C2×D3×#215C211yesmaximal, characteristic, complemented
3C2×D3×#213C211yesmaximal, characteristic, complemented
4D3×#930C211yesmaximal, characteristic, complemented
5#10592937C211yesmaximal, characteristic, complemented
6C3×#5238C211yesmaximal, characteristic, complemented
7#10591588C211yesmaximal, characteristic, complemented
8#10591586C211yesmaximal, characteristic, complemented
9D3×#835C211yesmaximal, characteristic, complemented
10#10591452C211yesmaximal, characteristic, complemented
11#10591450C211yesmaximal, characteristic, complemented
12D3×#832C211yesmaximal, characteristic, complemented
13#10591163C211yesmaximal, characteristic, complemented
14#10591161C211yesmaximal, characteristic, complemented
15D3×#830C211yesmaximal, characteristic, complemented
16C2×#5238—31nomaximal
17D3×#449—31nomaximal
18C2×C32×#41C2211yescharacteristic, complemented
19C3×D3×#41—24no—
20C3×D3×#41—24no—
21C2×C3×#239C2211yescharacteristic, complemented
22C2×C3×D3×Q8C2211yescharacteristic
23C2×C3×#237—21no—
24C2×C3×#237C2211yescharacteristic, complemented
25C2×C3×D3×D4—21no—
26C2×C3×D3×D4C2211yescharacteristic
27C2×C3×#235—21no—
28C2×C3×#235C2211yescharacteristic, complemented
29C22×C3×C4×D3—21no—
30C22×C3×C4×D3C2211yescharacteristic
31C2×D3×#67—21no—
32C2×D3×D12C2211yescharacteristic
33C2×#3755C2211yescharacteristic, complemented
34C2×#3753C2211yescharacteristic, complemented
35#64139C2211yescharacteristic, complemented
36C2×C3×#215C2211yescharacteristic, complemented
37C2×C3×#213C2211yescharacteristic, complemented
38C3×#930C2211yescharacteristic, complemented
39#63978—21no—
40D3×#215—24no—
41D3×#213—24no—
42D3×(C2×D3)⋊C4—21no—
43#63909C2211yescharacteristic, complemented
44#63908C2211yescharacteristic, complemented
45#63906—21no—
46D3×C4⋊Dic3C2211yescharacteristic
47C2×#3717C2211yescharacteristic, complemented
48C2×#3715C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50C2×#3713C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic
52C2×D3×C3⋊C8C2211yescharacteristic
53#63662C2211yescharacteristic, complemented
54#63659C2211yescharacteristic, complemented
55#63657C2211yescharacteristic, complemented
56C3×#835C2211yescharacteristic, complemented
57C3×#832C2211yescharacteristic, complemented
58C3×#830C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63565C2211yescharacteristic, complemented
61#63563C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C22×C3×#41—31no—
66C2×D3×#41D311yescharacteristic, complemented
67C22×#215—31no—
68C22×#213—31no—
69C2×#930—31no—
70C2×D3×SD16—31no—
71C2×D3×D8—31no—
72D3×#121—31no—
73C3×#449—31no—
74#5238—31no—
75#5238—31no—
76#5238—31no—
77#5238—31no—
78#5238—31no—
79#5238—31no—
80#5238—31no—
81#5238—31no—
82#5238—61no—
83#5238D311yescharacteristic, direct product factor
84C2×#835—31no—
85C2×#832—31no—
86C2×#830—31no—
87#5172—31no—
88#5158—31no—
89#5037—31no—
90#4810—31no—
91D3×#103—31no—
92#4781—31no—
93D3×#102—31no—
94#4734—31no—
95D3×C22⋊C8—31no—
96C23×C3×D3—21no—
97C23×C3×D3D411yescharacteristic
98C22×D32—21no—
99C32×#41—22no—
100C32×#41—22no—
101C2×C32×Q8C2311yescharacteristic
102C2×C32×D4—21no—
103C2×C32×D4C2311yescharacteristic
104C22×C32×C4—21no—
105C22×C32×C4C2311yescharacteristic
106C2×#638—21no—
107C2×C4⋊(C3⋊D3)C2311yescharacteristic
108C2×C3×#67—21no—
109C2×C3×#67—21no—
110C2×C3×#67—21no—
111C2×C3×#67—21no—
112C22×C3×Dic3—21no—
113C22×C3×Dic3D411yescharacteristic
114C3×#239—22no—
115C3×#239—22no—
116C3×D3×Q8—22no—
117C3×D3×Q8D414yescomplemented
118C3×#237—28no—
119C3×#237—22no—
120C3×#237—22no—
121C3×D3×D4—28no—
122C3×D3×D4—22no—
123C3×D3×D4D414yescomplemented
124C3×#235—28no—
125C3×#235—22no—
126C3×#235—22no—
127C2×C3×D12—21no—
128C2×C3×D12C2311yescharacteristic
129C2×C3×D12C2311yescharacteristic
130C2×C3×C4×D3—28no—
131C2×C3×C4×D3—21no—
132C2×C3×C4×D3—21no—
133C2×C3×C4×D3—21no—
134C2×C3×C4×D3—22no—
135C2×C3×C4×D3—22no—
136C2×C3×C4×D3D411yescharacteristic
137C2×C3×C4×D3D411yescharacteristic
138C2×C3×C4×D3C2311yescharacteristic
139C2×C3×C4×D3C2311yescharacteristic
140C2×C3×Dic6—21no—
141C2×C3×Dic6C2311yescharacteristic
142D3×#67—44no—
143C2×#626—21no—
144C2×#626—21no—
145C2×#625—21no—
146C2×D3×Dic3—21no—
147D3×D12—22no—
148D3×D12—22no—
149#3755—22no—
150#3753—22no—
151#3752—21no—
152C4⋊(C3⋊Dic3)C2311yescharacteristic
153C2×C3⋊(C3⋊C8)C2311yescharacteristic
154C2×C3⋊(C3⋊C8)C2311yescharacteristic
155C3×#215—22no—
156C3×#213—22no—
157C3×(C2×D3)⋊C4—21no—
158C3×C4⋊Dic3C2311yescharacteristic
159C2×C3×C3⋊C8C2311yescharacteristic
160C2×C3×C3⋊C8C2311yescharacteristic
161Dic3⋊Dic3—21no—
162#3722—21no—
163(C2×D3)⋊Dic3—21no—
164#3717—22no—
165#3715—22no—
166#3714—22no—
167#3713—22no—
168D3×C3⋊C8—22no—
169D3×C3⋊C8—22no—
170C2×#449—91noSylow
171C2×C3×#41—21no—
172C2×C3×#41—31no—
173C2×C3×#41—31no—
174C2×C3×#41—31no—
175C2×C3×#41—61no—
176C2×C3×#41—61no—
177C2×C3×#41—64no—
178C2×C3×#41—64no—
179C2×C3×#41C2×D311yescharacteristic, complemented
180C2×C3×#41C2×D311yescharacteristic, complemented
181C22×C3×Q8—31no—
182C22×C3×D4—31no—
183C22×C3×D4—61no—
184C23×C3×C4—31no—
185C23×C3×C4—61no—
186C22×#67—61no—
187D3×#41—24no—
188D3×#41—24no—
189C2×#239C2×D311yescharacteristic, complemented
190C2×D3×Q8C2×D311yescharacteristic
191C2×#237—21no—
192C2×#237C2×D311yescharacteristic, complemented
193C2×D3×D4—21no—
194C2×D3×D4—31no—
195C2×D3×D4—61no—
196C2×D3×D4C2×D311yescharacteristic
197C2×#235—21no—
198C2×#235C2×D311yescharacteristic, complemented
199C22×D12—31no—
200C22×C4×D3—21no—
201C22×C4×D3C2×D311yescharacteristic
202C2×C3×SD16—31no—
203C2×C3×D8—31no—
204C3×#121—31no—
205C2×#215—31no—
206C2×#215—31no—
207C2×#215—31no—
208C2×#215—31no—
209C2×#215—61no—
210C2×#215—64no—
211C2×#215C2×D311yescharacteristic, complemented
212#939—61no—
213#938—31no—
214C2×#214—31no—
215C2×#213—31no—
216C2×#213—31no—
217C2×#213—31no—
218C2×#213—31no—
219C2×#213—31no—
220C2×#213—61no—
221C2×#213—64no—
222C2×#213C2×D311yescharacteristic, complemented
223#930—31no—
224#930—31no—
225#930—31no—
226#930—31no—
227#930—61no—
228#930—61no—
229#930—61no—
230#930C2×D311yescharacteristic, complemented
231C2×(C2×D3)⋊C4—61no—
232C2×C4⋊Dic3—31no—
233C22×C3⋊C8—31no—
234C22×C3⋊C8—31no—
235D3×SD16—64no—
236D3×D8—64no—
237C2×D24—31no—
238C2×#204—31no—
239C2×D3×C8—31no—
240C2×D3×C8—31no—
241#895—31no—
242D3×C4⋊C4—31no—
243#884—61no—
244D3×C22⋊C4—61no—
245C3×#103—31no—
246C3×#102—31no—
247C3×C22⋊C8—31no—
248#835—31no—
249#835—31no—
250#835—31no—
251#835—31no—
252#835—61no—
253#835C2×D311yescharacteristic, complemented
254#832—31no—
255#832—31no—
256#832—31no—
257#832—31no—
258#832—61no—
259#832C2×D311yescharacteristic, complemented
260#830—31no—
261#830—31no—
262#830—31no—
263#830—31no—
264#830—61no—
265#830C2×D311yescharacteristic, complemented
266#821—31no—
267(C2×D3)⋊C8—31no—
268(C2×D3)⋊C8—31no—
269#816—31no—
270#810—31no—
271#809—31no—
272C23×C32—21no—
273C23×C32C2×D411yescharacteristic
274C22×C3⋊D3—21no—
275C22×C3×D3—21no—
276C22×C3×D3—24no—
277C22×C3×D3—22no—
278C22×C3×D3—22no—
279C22×C3×D3—22no—
280C22×C3×D3—21no—
281C22×C3×D3—42no—
282C22×C3×D3—42no—
283C22×C3×D3C2×D411yescharacteristic
284C22×C3×D3C2×D411yescharacteristic
285C2×D32—42no—
286C2×D32—42no—
287C2×D32—42no—
288C32×Q8—21no—
289C32×Q8C2×D412yescomplemented
290C32×D4—24no—
291C32×D4—21no—
292C32×D4C2×D412yescomplemented
293C2×C32×C4—24no—
294C2×C32×C4—21no—
295C2×C32×C4—21no—
296C2×C32×C4—21no—
297C2×C32×C4C2×D411yescharacteristic
298C2×C32×C4C2411yescharacteristic
299#638—42no—
300C2×C3⋊Dic3—21no—
301C4⋊(C3⋊D3)—21no—
302C4⋊(C3⋊D3)—21no—
303C3×#67—24no—
304C3×#67—24no—
305C3×#67—24no—
306C3×#67—42no—
307C2×C3×Dic3—24no—
308C2×C3×Dic3—21no—
309C2×C3×Dic3—22no—
310C2×C3×Dic3—21no—
311C2×C3×Dic3C2×D411yescharacteristic
312C2×C3×Dic3C2×D411yescharacteristic
313C3×D12—24no—
314C3×D12—21no—
315C3×D12—21no—
316C3×D12—21no—
317C3×D12C2×D412yescomplemented
318C3×C4×D3—24no—
319C3×C4×D3—24no—
320C3×C4×D3—22no—
321C3×C4×D3—24no—
322C3×C4×D3—21no—
323C3×C4×D3—21no—
324C3×C4×D3—22no—
325C3×C4×D3C2×D412yes—
326C3×C4×D3C2×D412yes—
327C3×Dic6—21no—
328C3×Dic6—24no—
329C3×Dic6C2×D412yescomplemented
330#626—42no—
331#626—42no—
332#625—42no—
333D3×Dic3—42no—
334C3⋊(C3⋊C8)—21no—
335C3⋊(C3⋊C8)—21no—
336C3×C3⋊C8—21no—
337C3×C3⋊C8—21no—
338C22×#41—31no—
339C22×SD16—91no—
340C22×D8—91no—
341C2×#121—91no—
342#449—31no—
343#449—91no—
344#449—91no—
345#449—91no—
346#449—91no—
347#449—91no—
348#449—91no—
349#449—91no—
350C2×#103—91no—
351C2×#102—91no—
352C2×C22⋊C8—91no—
353C24×C3—31no—
354C24×C3—61no—
355C23×D3—21no—
356C23×D3—61no—
357C23×D3—61no—
358C23×D3#6711yescharacteristic
359C3×#41—22no—
360C3×#41—22no—
361C3×#41—22no—
362C3×#41—22no—
363C3×#41—42no—
364C3×#41—42no—
365C3×#41—62no—
366C3×#41—62no—
367C3×#41—68no—
368C3×#41—62no—
369C3×#41—68no—
370C3×#41—62no—
371C3×#41—62no—
372C3×#41—62no—
373C2×C3×Q8—21no—
374C2×C3×Q8—34no—
375C2×C3×Q8—31no—
376C2×C3×Q8—61no—
377C2×C3×Q8—62no—
378C2×C3×Q8C22×D311yescharacteristic
379C2×C3×Q8C22×D311yescharacteristic
380C2×C3×D4—21no—
381C2×C3×D4—21no—
382C2×C3×D4—21no—
383C2×C3×D4—34no—
384C2×C3×D4—31no—
385C2×C3×D4—31no—
386C2×C3×D4—41no—
387C2×C3×D4—61no—
388C2×C3×D4—62no—
389C2×C3×D4—61no—
390C2×C3×D4—68no—
391C2×C3×D4—61no—
392C2×C3×D4—61no—
393C2×C3×D4—61no—
394C2×C3×D4C22×D311yescharacteristic
395C2×C3×D4C22×D311yescharacteristic
396C22×C3×C4—21no—
397C22×C3×C4—21no—
398C22×C3×C4—21no—
399C22×C3×C4—31no—
400C22×C3×C4—31no—
401C22×C3×C4—31no—
402C22×C3×C4—31no—
403C22×C3×C4—31no—
404C22×C3×C4—41no—
405C22×C3×C4—62no—
406C22×C3×C4—62no—
407C22×C3×C4—61no—
408C22×C3×C4—61no—
409C22×C3×C4—68no—
410C22×C3×C4—61no—
411C22×C3×C4—61no—
412C22×C3×C4C22×D311yescharacteristic
413C22×C3×C4C22×D311yescharacteristic
414C2×#67—21no—
415C2×#67—21no—
416C2×#67—21no—
417C2×#67—21no—
418C2×#67—61no—
419C2×#67—61no—
420C2×#67—61no—
421C2×#67—61no—
422C2×#67—61no—
423C2×#67—61no—
424C2×#67—121no—
425C2×#67—124no—
426C22×Dic3—21no—
427C22×Dic3—61no—
428C22×Dic3#6711yescharacteristic
429#239—22no—
430#239—22no—
431D3×Q8—22no—
432D3×Q8#6714yescomplemented
433#237—28no—
434#237—22no—
435#237—22no—
436D3×D4—28no—
437D3×D4—22no—
438D3×D4—62no—
439D3×D4—62no—
440D3×D4—124no—
441D3×D4#6714yescomplemented
442#235—28no—
443#235—22no—
444#235—22no—
445C2×D12—21no—
446C2×D12—31no—
447C2×D12—31no—
448C2×D12—61no—
449C2×D12—62no—
450C2×D12—62no—
451C2×D12—61no—
452C2×D12—61no—
453C2×D12C22×D311yescharacteristic
454C2×D12C22×D311yescharacteristic
455C2×C4×D3—28no—
456C2×C4×D3—21no—
457C2×C4×D3—21no—
458C2×C4×D3—21no—
459C2×C4×D3—22no—
460C2×C4×D3—22no—
461C2×C4×D3—61no—
462C2×C4×D3#6711yescharacteristic
463C2×C4×D3#6711yescharacteristic
464C2×C4×D3C22×D311yescharacteristic
465C2×C4×D3C22×D311yescharacteristic
466C2×Dic6—21no—
467C2×Dic6C22×D311yescharacteristic
468C3×SD16—62no—
469C3×D8—62no—
470C2×C3×C8—31no—
471C2×C3×C8—31no—
472C3×C4⋊C4—31no—
473C3×C22⋊C4—61no—
474#217—61no—
475#215—22no—
476#215—62no—
477#215—62no—
478#215—62no—
479#215—62no—
480#215—122no—
481#214—62no—
482#213—22no—
483#213—62no—
484#213—62no—
485#213—62no—
486#213—62no—
487#213—62no—
488#213—122no—
489(C2×D3)⋊C4—21no—
490(C2×D3)⋊C4—61no—
491(C2×D3)⋊C4—61no—
492(C2×D3)⋊C4—61no—
493(C2×D3)⋊C4—61no—
494(C2×D3)⋊C4—61no—
495(C2×D3)⋊C4—121no—
496C4⋊Dic3—31no—
497C4⋊Dic3—31no—
498C4⋊Dic3—61no—
499C4⋊Dic3—61no—
500C4⋊Dic3C22×D311yescharacteristic
501Dic3⋊C4—61no—
502C2×C3⋊C8—31no—
503C2×C3⋊C8—31no—
504C2×C3⋊C8—31no—
505C2×C3⋊C8—31no—
506C2×C3⋊C8—61no—
507C2×C3⋊C8—61no—
508C2×C3⋊C8—62no—
509C2×C3⋊C8—62no—
510C2×C3⋊C8C22×D311yescharacteristic
511C2×C3⋊C8C22×D311yescharacteristic
512D24—62no—
513#204—62no—
514D3×C8—62no—
515D3×C8—62no—
516C22×C32—21no—
517C22×C32—22no—
518C22×C32—21no—
519C22×C32—21no—
520C22×C32—41no—
521C22×C32—41no—
522C22×C32C22×D411yescharacteristic
523C2×C3⋊D3—41no—
524C2×C3⋊D3—41no—
525C2×C3⋊D3—41no—
526C2×C3×D3—21no—
527C2×C3×D3—22no—
528C2×C3×D3—21no—
529C2×C3×D3—21no—
530C2×C3×D3—41no—
531C2×C3×D3—41no—
532C2×C3×D3—44no—
533C2×C3×D3—48no—
534C2×C3×D3—41no—
535C2×C3×D3—41no—
536C2×C3×D3—41no—
537C2×C3×D3#12012yes—
538C2×C3×D3#13512yes—
539C2×C3×D3AGL(1,ℤ/8)12yes—
540D32—84no—
541C32×C4—22no—
542C32×C4—21no—
543C32×C4C22×D411yescharacteristic
544C32×C4C22×D411yescharacteristic
545C3⋊Dic3—41no—
546C3×Dic3—22no—
547C3×Dic3—21no—
548C3×Dic3—41no—
549C3×Dic3#12012yes—
550C2×#41—31no—
551C2×#41—31no—
552C2×#41—31no—
553C2×#41—61no—
554C2×#41—61no—
555C2×#41—64no—
556C2×#41—64no—
557C2×#41D3211yescharacteristic, complemented
558C22×Q8—31no—
559C22×D4—31no—
560C22×D4—61no—
561C22×D4—91no—
562C22×D4—181no—
563C23×C4—31no—
564C23×C4—61no—
565C2×SD16—31no—
566C2×SD16—91no—
567C2×SD16—91no—
568C2×SD16—91no—
569C2×SD16—184no—
570C2×D8—31no—
571C2×D8—91no—
572C2×D8—91no—
573C2×D8—91no—
574C2×D8—184no—
575C22×C8—91no—
576C22×C8—91no—
577#121—31no—
578#121—91no—
579#121—91no—
580#121—91no—
581#121—181no—
582#121—181no—
583C2×C4⋊C4—91no—
584C2×C22⋊C4—181no—
585#103—31no—
586#103—91no—
587#103—91no—
588#103—91no—
589#102—31no—
590#102—91no—
591#102—91no—
592#102—91no—
593C22⋊C8—31no—
594C22⋊C8—91no—
595C22⋊C8—91no—
596C22⋊C8—91no—
597C23×C3—21no—
598C23×C3—21no—
599C23×C3—21no—
600C23×C3—31no—
601C23×C3—31no—
602C23×C3—41no—
603C23×C3—62no—
604C23×C3—64no—
605C23×C3—62no—
606C23×C3—62no—
607C23×C3—61no—
608C23×C3—61no—
609C23×C3—122no—
610C23×C3—122no—
611C23×C3D3×D411yescharacteristic
612C23×C3C2×#6711yescharacteristic
613C22×D3—21no—
614C22×D3—22no—
615C22×D3—22no—
616C22×D3—22no—
617C22×D3—24no—
618C22×D3—21no—
619C22×D3—42no—
620C22×D3—42no—
621C22×D3—61no—
622C22×D3—61no—
623C22×D3—121no—
624C22×D3—122no—
625C22×D3—122no—
626C22×D3—122no—
627C22×D3—122no—
628C22×D3—122no—
629C22×D3—122no—
630C22×D3C2×#6711yescharacteristic
631C22×D3C2×#6711yescharacteristic
632C3×Q8—21no—
633C3×Q8—21no—
634C3×Q8—22no—
635C3×Q8—32no—
636C3×Q8—41no—
637C3×Q8—64no—
638C3×Q8—61no—
639C3×Q8D3×D412yescomplemented
640C3×Q8C2×#6712yescomplemented
641C3×D4—24no—
642C3×D4—24no—
643C3×D4—21no—
644C3×D4—21no—
645C3×D4—22no—
646C3×D4—32no—
647C3×D4—41no—
648C3×D4—44no—
649C3×D4—64no—
650C3×D4—64no—
651C3×D4—64no—
652C3×D4—64no—
653C3×D4—61no—
654C3×D4—61no—
655C3×D4—61no—
656C3×D4—122no—
657C3×D4D3×D412yescomplemented
658C3×D4C2×#6712yescomplemented
659C2×C3×C4—24no—
660C2×C3×C4—24no—
661C2×C3×C4—21no—
662C2×C3×C4—21no—
663C2×C3×C4—21no—
664C2×C3×C4—21no—
665C2×C3×C4—21no—
666C2×C3×C4—21no—
667C2×C3×C4—21no—
668C2×C3×C4—21no—
669C2×C3×C4—31no—
670C2×C3×C4—32no—
671C2×C3×C4—32no—
672C2×C3×C4—31no—
673C2×C3×C4—41no—
674C2×C3×C4—41no—
675C2×C3×C4—41no—
676C2×C3×C4—44no—
677C2×C3×C4—62no—
678C2×C3×C4—62no—
679C2×C3×C4—64no—
680C2×C3×C4—64no—
681C2×C3×C4—64no—
682C2×C3×C4—62no—
683C2×C3×C4—64no—
684C2×C3×C4—61no—
685C2×C3×C4—61no—
686C2×C3×C4—61no—
687C2×C3×C4—61no—
688C2×C3×C4D3×D411yescharacteristic
689C2×C3×C4C2×#6711yescharacteristic
690C2×C3×C4C23×D311yescharacteristic
691C2×C3×C4C23×D311yescharacteristic
692#67—24no—
693#67—24no—
694#67—24no—
695#67—42no—
696#67—122no—
697#67—122no—
698#67—122no—
699#67—122no—
700#67—122no—
701#67—122no—
702#67—242no—
703C2×Dic3—24no—
704C2×Dic3—21no—
705C2×Dic3—22no—
706C2×Dic3—21no—
707C2×Dic3—61no—
708C2×Dic3—61no—
709C2×Dic3—121no—
710C2×Dic3—122no—
711C2×Dic3C2×#6711yescharacteristic
712C2×Dic3C2×#6711yescharacteristic
713D12—24no—
714D12—21no—
715D12—21no—
716D12—21no—
717D12—61no—
718D12—61no—
719D12—61no—
720D12—61no—
721D12—121no—
722D12—121no—
723D12—122no—
724D12—122no—
725D12C2×#6712yescomplemented
726C4×D3—24no—
727C4×D3—24no—
728C4×D3—22no—
729C4×D3—24no—
730C4×D3—21no—
731C4×D3—21no—
732C4×D3—22no—
733C4×D3—122no—
734C4×D3C2×#6712yes—
735C4×D3C2×#6712yes—
736Dic6—21no—
737Dic6—24no—
738Dic6C2×#6712yescomplemented
739C3×C8—61no—
740C3×C8—61no—
741C3⋊C8—21no—
742C3⋊C8—21no—
743C3⋊C8—61no—
744C3⋊C8—61no—
745C3⋊C8—61no—
746C3⋊C8—61no—
747C3⋊C8—121no—
748C3⋊C8—121no—
749C2×C32—41no—
750C2×C32—42no—
751C2×C32C2×#12011yescharacteristic
752C2×C32C2×#13511yescharacteristic
753C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
754C3⋊D3—81no—
755C3×D3—41no—
756C3×D3—42no—
757C3×D3—81no—
758C3×D3#44914yescomplemented
759C24—31no—
760C24—61no—
761C24—181no—
762#41—22no—
763#41—22no—
764#41—62no—
765#41—62no—
766#41—68no—
767#41—62no—
768#41—68no—
769#41—62no—
770#41—62no—
771#41—62no—
772C2×Q8—34no—
773C2×Q8—31no—
774C2×Q8—61no—
775C2×Q8—62no—
776C2×Q8C2×D3211yescharacteristic
777C2×D4—21no—
778C2×D4—34no—
779C2×D4—31no—
780C2×D4—31no—
781C2×D4—61no—
782C2×D4—62no—
783C2×D4—61no—
784C2×D4—68no—
785C2×D4—61no—
786C2×D4—61no—
787C2×D4—61no—
788C2×D4—91no—
789C2×D4—182no—
790C2×D4—182no—
791C2×D4—181no—
792C2×D4—181no—
793C2×D4—181no—
794C2×D4—181no—
795C2×D4—364no—
796C2×D4C2×D3211yescharacteristic
797C22×C4—21no—
798C22×C4—31no—
799C22×C4—31no—
800C22×C4—31no—
801C22×C4—31no—
802C22×C4—31no—
803C22×C4—62no—
804C22×C4—62no—
805C22×C4—61no—
806C22×C4—61no—
807C22×C4—68no—
808C22×C4—61no—
809C22×C4—61no—
810C22×C4—181no—
811C22×C4C2×D3211yescharacteristic
812SD16—62no—
813SD16—182no—
814SD16—182no—
815SD16—182no—
816D8—62no—
817D8—182no—
818D8—182no—
819D8—182no—
820C2×C8—31no—
821C2×C8—31no—
822C2×C8—91no—
823C2×C8—91no—
824C2×C8—182no—
825C2×C8—182no—
826C4⋊C4—31no—
827C4⋊C4—91no—
828C4⋊C4—181no—
829C22⋊C4—61no—
830C22⋊C4—181no—
831C22⋊C4—181no—
832C22⋊C4—181no—
833C22×C3—21no—
834C22×C3—21no—
835C22×C3—21no—
836C22×C3—21no—
837C22×C3—21no—
838C22×C3—22no—
839C22×C3—21no—
840C22×C3—22no—
841C22×C3—21no—
842C22×C3—32no—
843C22×C3—32no—
844C22×C3—32no—
845C22×C3—41no—
846C22×C3—42no—
847C22×C3—41no—
848C22×C3—41no—
849C22×C3—41no—
850C22×C3—41no—
851C22×C3—41no—
852C22×C3—41no—
853C22×C3—61no—
854C22×C3—61no—
855C22×C3—62no—
856C22×C3—61no—
857C22×C3—81no—
858C22×C3—81no—
859C22×C3—124no—
860C22×C3—128no—
861C22×C3—121no—
862C22×C3—121no—
863C22×C3—121no—
864C22×C3—121no—
865C22×C3—121no—
866C22×C3C2×D3×D411yescharacteristic
867C22×C3C22×#6711yescharacteristic
868C2×D3—21no—
869C2×D3—21no—
870C2×D3—21no—
871C2×D3—22no—
872C2×D3—41no—
873C2×D3—41no—
874C2×D3—44no—
875C2×D3—48no—
876C2×D3—41no—
877C2×D3—41no—
878C2×D3—41no—
879C2×D3—121no—
880C2×D3—121no—
881C2×D3—121no—
882C2×D3—121no—
883C2×D3—121no—
884C2×D3—121no—
885C2×D3—241no—
886C2×D3—241no—
887C2×D3—241no—
888C2×D3—244no—
889C2×D3—244no—
890C2×D3#94912yes—
891C2×D3#95012yes—
892C2×D3#95312yes—
893C3×C4—22no—
894C3×C4—21no—
895C3×C4—21no—
896C3×C4—22no—
897C3×C4—21no—
898C3×C4—21no—
899C3×C4—32no—
900C3×C4—41no—
901C3×C4—42no—
902C3×C4—61no—
903C3×C4—62no—
904C3×C4—121no—
905C3×C4C2×D3×D411yescharacteristic
906C3×C4C2×D3×D411yescharacteristic
907C3×C4C22×#6711yescharacteristic
908C3×C4C22×#6711yescharacteristic
909Dic3—22no—
910Dic3—21no—
911Dic3—41no—
912Dic3—121no—
913Dic3—121no—
914Dic3—241no—
915Dic3#95312yes—
916C32C2×#44911yescharacteristic, complemented, Sylow
917C23—21no—
918C23—31no—
919C23—31no—
920C23—64no—
921C23—62no—
922C23—62no—
923C23—62no—
924C23—61no—
925C23—61no—
926C23—122no—
927C23—122no—
928C23—181no—
929C23—362no—
930C23—362no—
931C23—362no—
932C23D3×#6711yescharacteristic
933Q8—21no—
934Q8—32no—
935Q8—64no—
936Q8—61no—
937Q8D3×#6712yescomplemented
938D4—24no—
939D4—21no—
940D4—32no—
941D4—64no—
942D4—64no—
943D4—64no—
944D4—64no—
945D4—61no—
946D4—61no—
947D4—61no—
948D4—122no—
949D4—181no—
950D4—181no—
951D4—362no—
952D4—362no—
953D4—362no—
954D4—362no—
955D4D3×#6712yescomplemented
956C2×C4—24no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—31no—
961C2×C4—32no—
962C2×C4—32no—
963C2×C4—31no—
964C2×C4—62no—
965C2×C4—62no—
966C2×C4—64no—
967C2×C4—64no—
968C2×C4—64no—
969C2×C4—62no—
970C2×C4—64no—
971C2×C4—61no—
972C2×C4—61no—
973C2×C4—61no—
974C2×C4—61no—
975C2×C4—181no—
976C2×C4—362no—
977C2×C4D3×#6711yescharacteristic
978C2×C4C22×D3211yescharacteristic
979C8—61no—
980C8—61no—
981C8—181no—
982C8—181no—
983C2×C3—21no—
984C2×C3—21no—
985C2×C3—21no—
986C2×C3—34no—
987C2×C3—41no—
988C2×C3—42no—
989C2×C3—41no—
990C2×C3—42no—
991C2×C3—81no—
992C2×C3—82no—
993C2×C3—121no—
994C2×C3—122no—
995C2×C3—241no—
996C2×C3D3×#12011yescharacteristic
997C2×C3D3×#13511yescharacteristic
998C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
999C2×C3C2×#94911yescharacteristic
1000C2×C3C2×#95011yescharacteristic
1001C2×C3C2×#95311yescharacteristic
1002D3—41no—
1003D3—42no—
1004D3—81no—
1005D3—241no—
1006D3—241no—
1007D3—481no—
1008D3#523814yesdirect product factor
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—22no—
1013C22—32no—
1014C22—32no—
1015C22—32no—
1016C22—41no—
1017C22—41no—
1018C22—61no—
1019C22—61no—
1020C22—62no—
1021C22—61no—
1022C22—124no—
1023C22—128no—
1024C22—121no—
1025C22—121no—
1026C22—121no—
1027C22—121no—
1028C22—121no—
1029C22—361no—
1030C22—361no—
1031C22—361no—
1032C22—724no—
1033C22C2×D3×#6711yescharacteristic
1034C4—21no—
1035C4—22no—
1036C4—32no—
1037C4—61no—
1038C4—62no—
1039C4—121no—
1040C4—361no—
1041C4C2×D3×#6711yescharacteristic
1042C4C2×D3×#6711yescharacteristic
1043C3—21no—
1044C3D3×#44911yescharacteristic, complemented
1045C3C2×#523811yescharacteristic, complemented
1046C2—34no—
1047C2—41no—
1048C2—42no—
1049C2—121no—
1050C2—122no—
1051C2—241no—
1052C2—721no—
1053C2D3×#94911yescharacteristic
1054C2D3×#95011yescharacteristic
1055C2D3×#95311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32C2×#449
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×#41C2semidirect
2. C2×D3×#215C2semidirect
3. C2×D3×#213C2semidirect
4. D3×#930C2semidirect
5. #10592937C2semidirect
6. C3×#5238C2semidirect
7. #10591588C2semidirect
8. #10591586C2semidirect
9. D3×#835C2semidirect
10. #10591452C2semidirect
11. #10591450C2semidirect
12. D3×#832C2semidirect
13. #10591163C2semidirect
14. #10591161C2semidirect
15. D3×#830C2semidirect
18. C2×C32×#41C22semidirect
21. C2×C3×#239C22semidirect
24. C2×C3×#237C22semidirect
28. C2×C3×#235C22semidirect
33. C2×#3755C22semidirect
34. C2×#3753C22semidirect
35. #64139C22semidirect
36. C2×C3×#215C22semidirect
37. C2×C3×#213C22semidirect
38. C3×#930C22semidirect
43. #63909C22semidirect
44. #63908C22semidirect
47. C2×#3717C22semidirect
48. C2×#3715C22semidirect
49. C2×#3714C22semidirect
50. C2×#3713C22semidirect
53. #63662C22semidirect
54. #63659C22semidirect
55. #63657C22semidirect
56. C3×#835C22semidirect
57. C3×#832C22semidirect
58. C3×#830C22semidirect
59. #63566C22semidirect
60. #63565C22semidirect
61. #63563C22semidirect
62. #63562C22semidirect
63. (C2×D3)⋊(C3⋊C8)C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
66. C2×D3×#41D3semidirect
83. #5238D3direct (N × H)
117. C3×D3×Q8D4semidirect
123. C3×D3×D4D4semidirect
179. C2×C3×#41C2×D3semidirect
180. C2×C3×#41C2×D3semidirect
189. C2×#239C2×D3semidirect
192. C2×#237C2×D3semidirect
198. C2×#235C2×D3semidirect
211. C2×#215C2×D3semidirect
222. C2×#213C2×D3semidirect
230. #930C2×D3semidirect
253. #835C2×D3semidirect
259. #832C2×D3semidirect
265. #830C2×D3semidirect
289. C32×Q8C2×D4semidirect
292. C32×D4C2×D4semidirect
317. C3×D12C2×D4semidirect
329. C3×Dic6C2×D4semidirect
432. D3×Q8#67semidirect
441. D3×D4#67semidirect
557. C2×#41D32semidirect
639. C3×Q8D3×D4semidirect
640. C3×Q8C2×#67semidirect
657. C3×D4D3×D4semidirect
658. C3×D4C2×#67semidirect
725. D12C2×#67semidirect
738. Dic6C2×#67semidirect
758. C3×D3#449semidirect
916. C32C2×#449semidirect
937. Q8D3×#67semidirect
955. D4D3×#67semidirect
1008. D3#5238direct (N × H)
1044. C3D3×#449semidirect
1045. C3C2×#5238semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×#412
C2×D3×#2152
C2×D3×#2132
D3×#9302
#105929372
C3×#52382
#105915882
#105915862
D3×#8352
#105914522
#105914502
D3×#8322
#105911632
#105911612
D3×#8302
C2×#52383
D3×#4493