Finite Group Databasebeta

← D3×#5054 #11865686

Subgroups — D3×#5054 #11865686

Order 1152.

1056 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×#124C211yesmaximal, characteristic
2C2×D3×#216C211yesmaximal, characteristic, complemented
3C2×D3×#214C211yesmaximal, characteristic
4C4×D3×Dic6C211yesmaximal, characteristic, complemented
5#10592753C211yesmaximal, characteristic, complemented
6C3×#5054C211yesmaximal, characteristic, complemented
7#10591578C211yesmaximal, characteristic, complemented
8#10591577C211yesmaximal, characteristic, complemented
9D3×#835C211yesmaximal, characteristic, complemented
10#10591442C211yesmaximal, characteristic, complemented
11#10591441C211yesmaximal, characteristic, complemented
12D3×#832C211yesmaximal, characteristic
13#10590378C211yesmaximal, characteristic, complemented
14D3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
15#10590267C211yesmaximal, characteristic, complemented
16C2×#5054—31nomaximal
17D3×#464—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×D3×Dic6C2211yescharacteristic
21C32×#124C2211yescharacteristic
22C2×#3756C2211yescharacteristic, complemented
23C2×#3754C2211yescharacteristic
24C4×#634C2211yescharacteristic, complemented
25C3×#947C2211yescharacteristic
26C2×C3×#216C2211yescharacteristic, complemented
27C3×#936C2211yescharacteristic
28C2×C3×#214C2211yescharacteristic
29C3×#885—21no—
30C3×#885—21no—
31C3×D3×C22⋊C4—21no—
32C3×D3×C22⋊C4—21no—
33C3×#875C2211yescharacteristic
34C3×C42×D3C2211yescharacteristic
35C3×C4×Dic6C2211yescharacteristic, complemented
36D3×#216—24no—
37D3×#214—24no—
38C4×#627—21no—
39D3×C4⋊Dic3C2211yescharacteristic
40D3×Dic3⋊C4—21no—
41C4×D3×Dic3—21no—
42#63844C2211yescharacteristic, complemented
43Dic3×Dic6C2211yescharacteristic, complemented
44#63837—21no—
45C2×#3719C2211yescharacteristic, complemented
46C2×#3718C2211yescharacteristic, complemented
47C2×#3716C2211yescharacteristic
48C2×#3715C2211yescharacteristic
49C2×D3×C3⋊C8C2211yescharacteristic
50C2×D3×C3⋊C8C2211yescharacteristic
51#63662C2211yescharacteristic, complemented
52#63659C2211yescharacteristic
53C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
54C3×#835C2211yescharacteristic, complemented
55C3×#832C2211yescharacteristic
56C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
57Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63565C2211yescharacteristic, complemented
61#63563C2211yescharacteristic
62#63562C2211yescharacteristic
63C2×C3×#124—31no—
64C22×#216—31no—
65C22×#214—31no—
66C2×D3×Q16—31no—
67C2×D3×SD16—31no—
68D3×#124D311yescharacteristic
69C4×D3×Q8—31no—
70C2×C4×Dic6—31no—
71C3×#464—31no—
72C2×#835—31no—
73C2×#832—31no—
74#5185—31no—
75#5166—31no—
76#5054—31no—
77#5054—31no—
78#5054—31no—
79#5054—31no—
80#5054—31no—
81#5054—31no—
82#5054—31no—
83#5054—31no—
84#5054—61no—
85#5054D311yescharacteristic, direct product factor
86#5028—31no—
87C2×C4⋊(C3⋊C8)—31no—
88#4845—31no—
89D3×C4⋊C8—31no—
90D3×#103—31no—
91#4798—31no—
92D3×#102—31no—
93#4767—31no—
94C23×C3×D3—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×D4C2311yescharacteristic
97C2×#634C2311yescharacteristic
98C2×C3×#67—21no—
99C3×D3×Q8—22no—
100C3×D3×Q8—22no—
101C3×D3×D4—22no—
102C3×D3×D4—22no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3D411yescharacteristic
106C2×C3×C4×D3D411yescharacteristic
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6—21no—
109C2×C3×Dic6C2311yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111C2×#627—21no—
112C2×D3×Dic3—21no—
113C2×D3×Dic3—21no—
114D3×Dic6—22no—
115D3×Dic6D414yes—
116C32×C22⋊C4—21no—
117C32×C22⋊C4—21no—
118C32×C42C2311yescharacteristic
119#3756—22no—
120#3754—22no—
121C4⋊(C3⋊Dic3)C2311yescharacteristic
122#3750—21no—
123C4×C3⋊Dic3—21no—
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C3×#217—21no—
127C3×#217—21no—
128C3×#216—22no—
129C3×#214—22no—
130C3×(C2×D3)⋊C4—21no—
131C3×(C2×D3)⋊C4—21no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×C4⋊Dic3C2311yescharacteristic
135C3×Dic3⋊C4—21no—
136C3×C4×Dic3—21no—
137C3×C4×Dic3D411yescharacteristic
138C3×C4×Dic3D411yescharacteristic
139C3×C4×Dic3C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142#3724—21no—
143Dic3⋊Dic3—21no—
144Dic3⋊Dic3—21no—
145Dic32—21no—
146Dic32—21no—
147#3719—22no—
148#3718—22no—
149#3716—22no—
150#3715—22no—
151D3×C3⋊C8—22no—
152D3×C3⋊C8—22no—
153C2×#464—91noSylow
154C22×C3×Q8—31no—
155C22×C3×D4—31no—
156C2×D3×Q8—31no—
157C2×D3×Q8C2×D311yescharacteristic
158C2×D3×D4C2×D311yescharacteristic
159C22×Dic6—31no—
160C2×C3×Q16—31no—
161C2×C3×SD16—31no—
162C3×#124—21no—
163C3×#124—31no—
164C3×#124—31no—
165C3×#124—31no—
166C3×#124—61no—
167C3×#124—61no—
168C3×#124C2×D311yescharacteristic
169C3×#124C2×D311yescharacteristic
170C3×C4×Q8—31no—
171C2×C3×C22⋊C4—61no—
172C2×C3×C22⋊C4—61no—
173C2×C3×C42—31no—
174#947C2×D311yescharacteristic
175Q8×Dic3—31no—
176C2×#216—31no—
177C2×#216—31no—
178C2×#216—31no—
179C2×#216—31no—
180C2×#216—31no—
181C2×#216—61no—
182C2×#216—64no—
183C2×#216C2×D311yescharacteristic, complemented
184C2×#215—31no—
185#936C2×D311yescharacteristic
186C2×#214—31no—
187C2×#214—31no—
188C2×#214—31no—
189C2×#214—31no—
190C2×#214—61no—
191C2×#214—64no—
192C2×#214C2×D311yescharacteristic
193C2×C4⋊Dic3—31no—
194C2×Dic3⋊C4—61no—
195C2×C4×Dic3—61no—
196C22×C3⋊C8—31no—
197C22×C3⋊C8—31no—
198D3×Q16—64no—
199D3×SD16—64no—
200C2×Dic12—31no—
201C2×#204—31no—
202C2×D3×C8—31no—
203C2×D3×C8—31no—
204D3×C4⋊C4—31no—
205D3×C4⋊C4—61no—
206#887—31no—
207#887—61no—
208#885—21no—
209#885—21no—
210D3×C22⋊C4—21no—
211D3×C22⋊C4—21no—
212#875C2×D311yescharacteristic
213C42×D3—61no—
214C42×D3C2×D311yescharacteristic
215C4×Dic6—31no—
216C4×Dic6—31no—
217C4×Dic6—31no—
218C4×Dic6—31no—
219C4×Dic6—61no—
220C4×Dic6—61no—
221C4×Dic6—61no—
222C4×Dic6—61no—
223C4×Dic6C2×D311yescharacteristic, complemented
224C3×C4⋊C8—31no—
225C3×#103—31no—
226C3×#102—31no—
227#835—31no—
228#835—31no—
229#835—31no—
230#835—31no—
231#835—61no—
232#835C2×D311yescharacteristic, complemented
233#832—31no—
234#832—31no—
235#832—31no—
236#832—31no—
237#832—61no—
238#832C2×D311yescharacteristic
239#821—31no—
240#816—31no—
241Dic3⋊C8—31no—
242Dic3⋊C8—31no—
243#810—31no—
244#809—31no—
245C4⋊(C3⋊C8)—31no—
246C4⋊(C3⋊C8)—31no—
247C4⋊(C3⋊C8)—31no—
248C4⋊(C3⋊C8)—31no—
249C4⋊(C3⋊C8)—61no—
250C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
251C23×C32—21no—
252C22×C3×D3—21no—
253C22×C3×D3—42no—
254C22×C3×D3—42no—
255C22×C3×D3—42no—
256C22×C3×D3C2×D411yescharacteristic
257C32×Q8—21no—
258C32×Q8—21no—
259C32×D4—21no—
260C32×D4—21no—
261C2×C32×C4—21no—
262C2×C32×C4C2×D411yescharacteristic
263C2×C32×C4C2×D411yescharacteristic
264C2×C32×C4C2411yescharacteristic
265C2×C3⋊Dic3—21no—
266C2×C3⋊Dic3—21no—
267#634—21no—
268#634C2×D412yes—
269C3×#67—42no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3C2×D411yescharacteristic
274C2×C3×Dic3C2×D411yescharacteristic
275C2×C3×Dic3C2×D411yescharacteristic
276C3×D12—21no—
277C3×D12—21no—
278C3×C4×D3—22no—
279C3×C4×D3—22no—
280C3×C4×D3—42no—
281C3×C4×D3C2×D412yes—
282C3×C4×D3#4112yes—
283C3×Dic6—21no—
284C3×Dic6—21no—
285C3×Dic6—21no—
286C3×Dic6—42no—
287C3×Dic6C2×D412yes—
288#627—24no—
289D3×Dic3—24no—
290D3×Dic3—42no—
291C3⋊(C3⋊C8)—21no—
292C3⋊(C3⋊C8)—21no—
293C3×C3⋊C8—21no—
294C3×C3⋊C8—21no—
295C22×Q16—91no—
296C22×SD16—91no—
297C2×#124—31no—
298C2×C4×Q8—91no—
299#464—31no—
300#464—91no—
301#464—91no—
302#464—91no—
303#464—91no—
304#464—91no—
305#464—91no—
306#464—91no—
307C2×C4⋊C8—91no—
308C2×#103—91no—
309C2×#102—91no—
310C24×C3—61no—
311C23×D3—21no—
312C2×C3×Q8—21no—
313C2×C3×Q8—31no—
314C2×C3×Q8—31no—
315C2×C3×Q8—61no—
316C2×C3×Q8—62no—
317C2×C3×Q8—62no—
318C2×C3×Q8C22×D311yescharacteristic
319C2×C3×Q8C22×D311yescharacteristic
320C2×C3×D4—21no—
321C2×C3×D4—31no—
322C2×C3×D4—62no—
323C2×C3×D4—62no—
324C2×C3×D4—61no—
325C2×C3×D4C22×D311yescharacteristic
326C2×C3×D4C22×D311yescharacteristic
327C22×C3×C4—31no—
328C22×C3×C4—31no—
329C22×C3×C4—31no—
330C22×C3×C4—61no—
331C2×#67—21no—
332C22×Dic3—61no—
333C22×Dic3—61no—
334D3×Q8—22no—
335D3×Q8—22no—
336D3×Q8—34no—
337D3×Q8—62no—
338D3×D4—22no—
339D3×D4—22no—
340C2×D12C22×D311yescharacteristic
341C2×C4×D3—21no—
342C2×C4×D3—61no—
343C2×C4×D3—61no—
344C2×C4×D3#6711yescharacteristic
345C2×C4×D3#6711yescharacteristic
346C2×C4×D3C22×D311yescharacteristic
347C2×Dic6—21no—
348C2×Dic6—31no—
349C2×Dic6—31no—
350C2×Dic6—34no—
351C2×Dic6—61no—
352C2×Dic6—62no—
353C2×Dic6—61no—
354C2×Dic6—61no—
355C2×Dic6C22×D311yescharacteristic
356C2×Dic6C22×D311yescharacteristic
357C3×Q16—62no—
358C3×SD16—62no—
359C2×C3×C8—31no—
360C2×C3×C8—31no—
361C3×C4⋊C4—31no—
362C3×C4⋊C4—61no—
363C3×C22⋊C4—21no—
364C3×C22⋊C4—21no—
365C3×C22⋊C4—21no—
366C3×C22⋊C4—21no—
367C3×C22⋊C4—41no—
368C3×C22⋊C4—41no—
369C3×C22⋊C4—61no—
370C3×C22⋊C4—61no—
371C3×C22⋊C4—61no—
372C3×C22⋊C4—61no—
373C3×C22⋊C4—61no—
374C3×C22⋊C4—61no—
375C3×C42—21no—
376C3×C42—31no—
377C3×C42—31no—
378C3×C42—31no—
379C3×C42—61no—
380C3×C42C22×D311yescharacteristic
381C3×C42C22×D311yescharacteristic
382#217—21no—
383#217—21no—
384#216—22no—
385#216—62no—
386#216—62no—
387#216—62no—
388#216—62no—
389#216—62no—
390#216—122no—
391#215—62no—
392#214—22no—
393#214—62no—
394#214—62no—
395#214—62no—
396#214—62no—
397#214—122no—
398(C2×D3)⋊C4—21no—
399(C2×D3)⋊C4—21no—
400(C2×D3)⋊C4—21no—
401(C2×D3)⋊C4—21no—
402C4⋊Dic3—31no—
403C4⋊Dic3—31no—
404C4⋊Dic3—61no—
405C4⋊Dic3—61no—
406C4⋊Dic3—61no—
407C4⋊Dic3C22×D311yescharacteristic
408Dic3⋊C4—21no—
409Dic3⋊C4—61no—
410Dic3⋊C4—61no—
411Dic3⋊C4—61no—
412Dic3⋊C4—61no—
413Dic3⋊C4—61no—
414Dic3⋊C4—61no—
415Dic3⋊C4—121no—
416C4×Dic3—21no—
417C4×Dic3—61no—
418C4×Dic3—61no—
419C4×Dic3—61no—
420C4×Dic3—61no—
421C4×Dic3—61no—
422C4×Dic3—61no—
423C4×Dic3—121no—
424C4×Dic3#6711yescharacteristic
425C4×Dic3#6711yescharacteristic
426C4×Dic3C22×D311yescharacteristic
427C2×C3⋊C8—31no—
428C2×C3⋊C8—31no—
429C2×C3⋊C8—31no—
430C2×C3⋊C8—31no—
431C2×C3⋊C8—61no—
432C2×C3⋊C8—61no—
433C2×C3⋊C8—62no—
434C2×C3⋊C8—62no—
435C2×C3⋊C8C22×D311yescharacteristic
436C2×C3⋊C8C22×D311yescharacteristic
437Dic12—62no—
438#204—62no—
439D3×C8—62no—
440D3×C8—62no—
441C22×C32—41no—
442C22×C32—41no—
443C22×C32—41no—
444C22×C32C22×D411yescharacteristic
445C2×C3×D3—41no—
446C2×C3×D3—41no—
447C2×C3×D3—41no—
448C2×C3×D3—84no—
449C2×C3×D3#12112yes—
450C2×C3×D3#13512yes—
451C2×C3×D3#13712yes—
452C32×C4—21no—
453C32×C4—21no—
454C32×C4—41no—
455C32×C4C22×D411yescharacteristic
456C32×C4C2×#4111yescharacteristic
457C3⋊Dic3—22no—
458C3⋊Dic3—41no—
459C3×Dic3—22no—
460C3×Dic3—21no—
461C3×Dic3—21no—
462C3×Dic3—41no—
463C3×Dic3—41no—
464C3×Dic3#12112yes—
465C22×Q8—31no—
466C22×Q8—91no—
467C22×D4—31no—
468C2×Q16—31no—
469C2×Q16—91no—
470C2×Q16—91no—
471C2×Q16—91no—
472C2×Q16—184no—
473C2×SD16—31no—
474C2×SD16—91no—
475C2×SD16—91no—
476C2×SD16—91no—
477C2×SD16—184no—
478C22×C8—91no—
479C22×C8—91no—
480#124—31no—
481#124—31no—
482#124—31no—
483#124—61no—
484#124—61no—
485#124D3211yescharacteristic
486C4×Q8—31no—
487C4×Q8—91no—
488C4×Q8—91no—
489C4×Q8—91no—
490C4×Q8—181no—
491C4×Q8—181no—
492C2×C4⋊C4—91no—
493C2×C4⋊C4—181no—
494C2×C22⋊C4—61no—
495C2×C22⋊C4—61no—
496C2×C42—31no—
497C2×C42—181no—
498C4⋊C8—31no—
499C4⋊C8—91no—
500C4⋊C8—91no—
501C4⋊C8—91no—
502#103—31no—
503#103—91no—
504#103—91no—
505#103—91no—
506#102—31no—
507#102—91no—
508#102—91no—
509#102—91no—
510C23×C3—21no—
511C23×C3—21no—
512C23×C3—31no—
513C23×C3—41no—
514C23×C3—61no—
515C23×C3—122no—
516C23×C3—122no—
517C23×C3—122no—
518C22×D3—21no—
519C22×D3—42no—
520C22×D3—42no—
521C22×D3—42no—
522C22×D3C2×#6711yescharacteristic
523C3×Q8—21no—
524C3×Q8—21no—
525C3×Q8—21no—
526C3×Q8—21no—
527C3×Q8—32no—
528C3×Q8—41no—
529C3×Q8—41no—
530C3×Q8—61no—
531C3×Q8—61no—
532C3×Q8—61no—
533C3×Q8—122no—
534C3×D4—21no—
535C3×D4—21no—
536C3×D4—21no—
537C3×D4—21no—
538C3×D4—41no—
539C3×D4—41no—
540C3×D4—61no—
541C3×D4—61no—
542C3×D4—122no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—31no—
549C2×C3×C4—32no—
550C2×C3×C4—32no—
551C2×C3×C4—31no—
552C2×C3×C4—31no—
553C2×C3×C4—41no—
554C2×C3×C4—62no—
555C2×C3×C4—62no—
556C2×C3×C4—61no—
557C2×C3×C4—61no—
558C2×C3×C4—61no—
559C2×C3×C4—122no—
560C2×C3×C4D3×D411yescharacteristic
561C2×C3×C4D3×D411yescharacteristic
562C2×C3×C4C2×#6711yescharacteristic
563C2×C3×C4C2×#6711yescharacteristic
564C2×C3×C4C23×D311yescharacteristic
565C2×C3×C4C23×D311yescharacteristic
566#67—42no—
567C2×Dic3—21no—
568C2×Dic3—21no—
569C2×Dic3—21no—
570C2×Dic3—64no—
571C2×Dic3—61no—
572C2×Dic3—61no—
573C2×Dic3—61no—
574C2×Dic3—61no—
575C2×Dic3—121no—
576C2×Dic3—121no—
577C2×Dic3—122no—
578C2×Dic3C2×#6711yescharacteristic
579C2×Dic3C2×#6711yescharacteristic
580C2×Dic3C2×#6711yescharacteristic
581D12—21no—
582D12—21no—
583C4×D3—22no—
584C4×D3—22no—
585C4×D3—42no—
586C4×D3—64no—
587C4×D3—122no—
588C4×D3D3×D412yes—
589C4×D3#23712yes—
590Dic6—21no—
591Dic6—21no—
592Dic6—21no—
593Dic6—32no—
594Dic6—32no—
595Dic6—42no—
596Dic6—62no—
597Dic6—64no—
598Dic6—61no—
599Dic6—61no—
600Dic6—64no—
601Dic6—121no—
602Dic6D3×D412yes—
603C3×C8—61no—
604C3×C8—61no—
605C3⋊C8—21no—
606C3⋊C8—21no—
607C3⋊C8—61no—
608C3⋊C8—61no—
609C3⋊C8—61no—
610C3⋊C8—61no—
611C3⋊C8—121no—
612C3⋊C8—121no—
613C2×C32—81no—
614C2×C32C2×#12111yescharacteristic
615C2×C32C2×#13511yescharacteristic
616C2×C32C2×#13711yescharacteristic
617C3×D3—81no—
618C3×D3#46414yescomplemented
619C24—61no—
620C2×Q8—31no—
621C2×Q8—31no—
622C2×Q8—61no—
623C2×Q8—62no—
624C2×Q8—62no—
625C2×Q8—94no—
626C2×Q8—91no—
627C2×Q8—181no—
628C2×Q8—182no—
629C2×Q8C2×D3211yescharacteristic
630C2×D4—31no—
631C2×D4—62no—
632C2×D4—62no—
633C2×D4—61no—
634C2×D4C2×D3211yescharacteristic
635C22×C4—31no—
636C22×C4—31no—
637C22×C4—31no—
638C22×C4—61no—
639C22×C4—181no—
640C22×C4—181no—
641Q16—62no—
642Q16—182no—
643Q16—182no—
644Q16—182no—
645SD16—62no—
646SD16—182no—
647SD16—182no—
648SD16—182no—
649C2×C8—31no—
650C2×C8—31no—
651C2×C8—91no—
652C2×C8—91no—
653C2×C8—182no—
654C2×C8—182no—
655C4⋊C4—31no—
656C4⋊C4—61no—
657C4⋊C4—91no—
658C4⋊C4—181no—
659C4⋊C4—181no—
660C4⋊C4—181no—
661C4⋊C4—181no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—61no—
665C22⋊C4—61no—
666C22⋊C4—61no—
667C22⋊C4—61no—
668C22⋊C4—61no—
669C22⋊C4—61no—
670C42—31no—
671C42—31no—
672C42—31no—
673C42—61no—
674C42—181no—
675C42—181no—
676C42—181no—
677C42C2×D3211yescharacteristic
678C22×C3—21no—
679C22×C3—32no—
680C22×C3—32no—
681C22×C3—32no—
682C22×C3—41no—
683C22×C3—41no—
684C22×C3—41no—
685C22×C3—41no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—81no—
689C22×C3—81no—
690C22×C3—81no—
691C22×C3—121no—
692C22×C3—121no—
693C22×C3—121no—
694C22×C3—244no—
695C22×C3C2×D3×D411yescharacteristic
696C22×C3C22×#6711yescharacteristic
697C2×D3—41no—
698C2×D3—41no—
699C2×D3—41no—
700C2×D3—84no—
701C2×D3#93812yes—
702C2×D3#95012yes—
703C2×D3#95112yes—
704C3×C4—21no—
705C3×C4—21no—
706C3×C4—21no—
707C3×C4—21no—
708C3×C4—21no—
709C3×C4—21no—
710C3×C4—32no—
711C3×C4—41no—
712C3×C4—41no—
713C3×C4—41no—
714C3×C4—41no—
715C3×C4—61no—
716C3×C4—61no—
717C3×C4—62no—
718C3×C4—81no—
719C3×C4—121no—
720C3×C4—121no—
721C3×C4C2×D3×D411yescharacteristic
722C3×C4C2×D3×D411yescharacteristic
723C3×C4C2×#23711yescharacteristic
724C3×C4D3×#4111yescharacteristic
725Dic3—21no—
726Dic3—21no—
727Dic3—22no—
728Dic3—41no—
729Dic3—41no—
730Dic3—62no—
731Dic3—62no—
732Dic3—122no—
733Dic3—121no—
734Dic3—121no—
735Dic3—241no—
736Dic3#93812yes—
737C32C2×#46411yescharacteristic, complemented, Sylow
738C23—21no—
739C23—31no—
740C23—61no—
741C23—122no—
742C23—122no—
743C23—122no—
744Q8—21no—
745Q8—21no—
746Q8—32no—
747Q8—61no—
748Q8—61no—
749Q8—61no—
750Q8—92no—
751Q8—122no—
752Q8—184no—
753Q8—181no—
754D4—21no—
755D4—21no—
756D4—61no—
757D4—61no—
758D4—122no—
759C2×C4—21no—
760C2×C4—31no—
761C2×C4—32no—
762C2×C4—32no—
763C2×C4—31no—
764C2×C4—31no—
765C2×C4—62no—
766C2×C4—62no—
767C2×C4—61no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—122no—
771C2×C4—184no—
772C2×C4—181no—
773C2×C4—181no—
774C2×C4—362no—
775C2×C4D3×#6711yescharacteristic
776C2×C4D3×#6711yescharacteristic
777C2×C4C22×D3211yescharacteristic
778C8—61no—
779C8—61no—
780C8—181no—
781C8—181no—
782C2×C3—21no—
783C2×C3—21no—
784C2×C3—21no—
785C2×C3—34no—
786C2×C3—81no—
787C2×C3—81no—
788C2×C3—161no—
789C2×C3—241no—
790C2×C3D3×#12111yescharacteristic
791C2×C3D3×#13511yescharacteristic
792C2×C3D3×#13711yescharacteristic
793C2×C3C2×#93811yescharacteristic
794C2×C3C2×#95011yescharacteristic
795C2×C3C2×#95111yescharacteristic
796D3—81no—
797D3#505414yesdirect product factor
798C22—32no—
799C22—32no—
800C22—32no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—121no—
805C22—121no—
806C22—121no—
807C22—244no—
808C22C2×D3×#6711yescharacteristic
809C4—21no—
810C4—21no—
811C4—32no—
812C4—41no—
813C4—61no—
814C4—61no—
815C4—62no—
816C4—121no—
817C4—121no—
818C4—182no—
819C4—361no—
820C4D32×D411yescharacteristic
821C4D3×#23711yescharacteristic
822C3—21no—
823C3D3×#46411yescharacteristic, complemented
824C3C2×#505411yescharacteristic, complemented
825C2—34no—
826C2—81no—
827C2—241no—
828C2D3×#93811yescharacteristic
829C2D3×#95011yescharacteristic
830C2D3×#95111yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#124C22
socleC22×C32C22×D4
prime radicalC2×C3×D3×D4C22
hypercenter#124D32
hypocenterC32C2×#464
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. C2×D3×#216C2semidirect
4. C4×D3×Dic6C2semidirect
5. #10592753C2semidirect
6. C3×#5054C2semidirect
7. #10591578C2semidirect
8. #10591577C2semidirect
9. D3×#835C2semidirect
10. #10591442C2semidirect
11. #10591441C2semidirect
13. #10590378C2semidirect
14. D3×C4⋊(C3⋊C8)C2semidirect
15. #10590267C2semidirect
22. C2×#3756C22semidirect
24. C4×#634C22semidirect
26. C2×C3×#216C22semidirect
35. C3×C4×Dic6C22semidirect
42. #63844C22semidirect
43. Dic3×Dic6C22semidirect
45. C2×#3719C22semidirect
46. C2×#3718C22semidirect
51. #63662C22semidirect
53. C4⋊(C3⋊(C3⋊C8))C22semidirect
54. C3×#835C22semidirect
56. C3×C4⋊(C3⋊C8)C22semidirect
57. Dic3⋊(C3⋊C8)C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
59. #63566C22semidirect
60. #63565C22semidirect
85. #5054D3direct (N × H)
183. C2×#216C2×D3semidirect
223. C4×Dic6C2×D3semidirect
232. #835C2×D3semidirect
250. C4⋊(C3⋊C8)C2×D3semidirect
618. C3×D3#464semidirect
737. C32C2×#464semidirect
797. D3#5054direct (N × H)
823. C3D3×#464semidirect
824. C3C2×#5054semidirect

Maximal subgroups

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

subgroupindex
C3×D3×#1242
C2×D3×#2162
C2×D3×#2142
C4×D3×Dic62
#105927532
C3×#50542
#105915782
#105915772
D3×#8352
#105914422
#105914412
D3×#8322
#105903782
D3×C4⋊(C3⋊C8)2
#105902672
C2×#50543
D3×#4643