Finite Group Databasebeta

← D3×#5185 #11865694

Subgroups — D3×#5185 #11865694

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
1C2×C3×D3×Q16C211yesmaximal, characteristic, complemented
2D3×#947C211yesmaximal, characteristic
3D3×Q8×Dic3C211yesmaximal, characteristic, complemented
4C2×D3×#215C211yesmaximal, characteristic
5#10592884C211yesmaximal, characteristic, complemented
6C3×#5185C211yesmaximal, characteristic, complemented
7#10591612C211yesmaximal, characteristic, complemented
8#10591607C211yesmaximal, characteristic, complemented
9#10591579C211yesmaximal, characteristic, complemented
10#10591578C211yesmaximal, characteristic, complemented
11D3×#835C211yesmaximal, characteristic, complemented
12D3×#821C211yesmaximal, characteristic
13#10590801C211yesmaximal, characteristic, complemented
14#10590797C211yesmaximal, characteristic, complemented
15D3×Dic3⋊C8C211yesmaximal, characteristic, complemented
16C2×#5185—31nomaximal
17D3×#464—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×D3×D12C2211yescharacteristic
21C2×C32×Q16C2211yescharacteristic, complemented
22#64156C2211yescharacteristic
23Q8×C3⋊Dic3C2211yescharacteristic, complemented
24C2×#3755C2211yescharacteristic
25C3×#947C2211yescharacteristic
26C3×Q8×Dic3C2211yescharacteristic, complemented
27C2×C3×#216C2211yescharacteristic, complemented
28C2×C3×#216C2211yescharacteristic, complemented
29C2×C3×#215C2211yescharacteristic
30C3×D3×Q16—24no—
31C2×C3×Dic12C2211yescharacteristic, complemented
32C2×C3×D3×C8C2211yescharacteristic
33D3×#215—24no—
34D3×(C2×D3)⋊C4—21no—
35D3×(C2×D3)⋊C4—21no—
36#63907—21no—
37#63907—21no—
38D3×C4⋊Dic3—21no—
39D3×C4⋊Dic3C2211yescharacteristic
40C4×D3×Dic3—21no—
41C4×D3×Dic3C2211yescharacteristic
42#63864C2211yescharacteristic
43#63863C2211yescharacteristic
44#63843—21no—
45#63843C2211yescharacteristic, complemented
46Dic3×Dic6—21no—
47Dic3×Dic6C2211yescharacteristic, complemented
48C2×#3717C2211yescharacteristic
49C2×#3715C2211yescharacteristic
50C2×D3×C3⋊C8C2211yescharacteristic
51#63662C2211yescharacteristic, complemented
52#63648C2211yescharacteristic
53#63641C2211yescharacteristic, complemented
54C3×#835C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57#63572C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63565C2211yescharacteristic, complemented
61#63564C2211yescharacteristic
62#63563C2211yescharacteristic
63C22×C3×Q16—31no—
64C2×#947—31no—
65C2×Q8×Dic3—31no—
66C22×#215—31no—
67C2×D3×Q16D311yescharacteristic, complemented
68C2×D3×SD16—31no—
69D3×#124—31no—
70C4×D3×Q8—31no—
71C3×#464—31no—
72C2×#835—31no—
73#5185—31no—
74#5185—31no—
75#5185—31no—
76#5185—31no—
77#5185—31no—
78#5185—31no—
79#5185—31no—
80#5185—31no—
81#5185—61no—
82#5185D311yescharacteristic, direct product factor
83#5166—31no—
84C2×#821—31no—
85C2×Dic3⋊C8—31no—
86#5054—31no—
87#5028—31no—
88#4845—31no—
89D3×C4⋊C8—31no—
90D3×#103—31no—
91#4798—31no—
92D3×#102—31no—
93#4767—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×Q8C2311yescharacteristic
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C3×D3×Q8—22no—
99C3×D3×Q8—22no—
100C3×D3×Q8—22no—
101C3×D3×Q8D414yes—
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6—21no—
107C2×C3×Dic6—21no—
108C2×C3×Dic6C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C2×#626—21no—
111C2×D3×Dic3—21no—
112C2×D3×Dic3D411yescharacteristic
113C2×D3×Dic3D411yescharacteristic
114D3×D12—22no—
115D3×D12—22no—
116C32×Q16—22no—
117C2×C32×C8C2311yescharacteristic
118#3755—22no—
119#3752—21no—
120#3752—21no—
121C4⋊(C3⋊Dic3)—21no—
122C4⋊(C3⋊Dic3)C2311yescharacteristic
123C4×C3⋊Dic3—21no—
124C4×C3⋊Dic3C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C3×#216—22no—
127C3×#216—22no—
128C3×#215—22no—
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4—21no—
131C3×C4⋊Dic3—21no—
132C3×C4⋊Dic3C2311yescharacteristic
133C3×C4×Dic3—21no—
134C3×C4×Dic3C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C3×Dic12—22no—
138C3×D3×C8—22no—
139Dic3⋊Dic3—21no—
140Dic3⋊Dic3—21no—
141Dic3⋊Dic3—21no—
142#3722—21no—
143#3722—21no—
144(C2×D3)⋊Dic3—21no—
145(C2×D3)⋊Dic3—21no—
146Dic32—21no—
147Dic32—21no—
148Dic32D411yescharacteristic
149Dic32D411yescharacteristic
150#3717—22no—
151#3715—22no—
152D3×C3⋊C8—22no—
153C2×#464—91noSylow
154C22×C3×Q8—31no—
155C22×C3×Q8—31no—
156C2×D3×Q8C2×D311yescharacteristic
157C2×D3×Q8C2×D311yescharacteristic
158C2×D3×D4—31no—
159C22×D12—31no—
160C2×C3×Q16—21no—
161C2×C3×Q16—31no—
162C2×C3×Q16—31no—
163C2×C3×Q16—31no—
164C2×C3×Q16—64no—
165C2×C3×Q16C2×D311yescharacteristic, complemented
166C2×C3×Q16C2×D311yescharacteristic, complemented
167C2×C3×SD16—31no—
168C22×C3×C8—31no—
169C3×#124—31no—
170C3×C4×Q8—31no—
171#947—31no—
172#947—31no—
173#947—31no—
174#947—31no—
175#947—61no—
176#947—61no—
177#947—61no—
178#947C2×D311yescharacteristic
179Q8×Dic3—31no—
180Q8×Dic3—31no—
181Q8×Dic3—31no—
182Q8×Dic3—31no—
183Q8×Dic3—61no—
184Q8×Dic3—61no—
185Q8×Dic3—61no—
186Q8×Dic3C2×D311yescharacteristic, complemented
187C2×#216C2×D311yescharacteristic, complemented
188C2×#216C2×D311yescharacteristic, complemented
189C2×#215—31no—
190C2×#215—31no—
191C2×#215—31no—
192C2×#215—31no—
193C2×#215—61no—
194C2×#215—64no—
195C2×#215C2×D311yescharacteristic
196#936—31no—
197C2×#214—31no—
198C2×(C2×D3)⋊C4—61no—
199C2×(C2×D3)⋊C4—61no—
200C2×C4⋊Dic3—31no—
201C2×C4⋊Dic3—61no—
202C2×C4×Dic3—31no—
203C2×C4×Dic3—61no—
204C22×C3⋊C8—31no—
205D3×Q16—24no—
206D3×SD16—64no—
207C2×Dic12C2×D311yescharacteristic, complemented
208C2×#204—31no—
209C2×D3×C8—31no—
210C2×D3×C8C2×D311yescharacteristic
211D3×C4⋊C4—31no—
212D3×C4⋊C4—61no—
213#887—31no—
214#887—61no—
215#885—61no—
216#885—61no—
217D3×C22⋊C4—61no—
218D3×C22⋊C4—61no—
219#875—31no—
220C42×D3—31no—
221C42×D3—61no—
222C4×Dic6—31no—
223C4×Dic6—61no—
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#821—31no—
235#821—31no—
236#821—31no—
237#821—31no—
238#821—61no—
239#821C2×D311yescharacteristic
240#816—31no—
241Dic3⋊C8—31no—
242Dic3⋊C8—31no—
243Dic3⋊C8—31no—
244Dic3⋊C8—31no—
245Dic3⋊C8—31no—
246Dic3⋊C8—61no—
247Dic3⋊C8C2×D311yescharacteristic, complemented
248#810—31no—
249#809—31no—
250C4⋊(C3⋊C8)—31no—
251C22×C3⋊D3—21no—
252C22×C3×D3—21no—
253C22×C3×D3C2×D411yescharacteristic
254C2×D32—42no—
255C2×D32—42no—
256C2×D32—42no—
257C32×Q8—21no—
258C32×Q8—21no—
259C32×Q8—21no—
260C32×Q8C2×D412yes—
261C2×C32×C4—21no—
262C2×C32×C4—21no—
263C2×C32×C4C2411yescharacteristic
264C2×C3⋊Dic3—21no—
265C2×C3⋊Dic3C2×D411yescharacteristic
266C2×C3⋊Dic3C2×D411yescharacteristic
267C4⋊(C3⋊D3)—21no—
268C4⋊(C3⋊D3)—21no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3C2×D411yescharacteristic
273C2×C3×Dic3C2×D411yescharacteristic
274C2×C3×Dic3C2×D411yescharacteristic
275C3×D12—21no—
276C3×D12—21no—
277C3×C4×D3—24no—
278C3×C4×D3—42no—
279C3×C4×D3C2×D412yes—
280C3×C4×D3#4112yes—
281C3×Dic6—21no—
282C3×Dic6—24no—
283C3×Dic6—21no—
284C3×Dic6—21no—
285C3×Dic6—42no—
286C3×Dic6C2×D412yes—
287#626—42no—
288D3×Dic3—22no—
289D3×Dic3—22no—
290D3×Dic3—42no—
291C32×C8—21no—
292C3⋊(C3⋊C8)—21no—
293C3×C3⋊C8—21no—
294C3×C3⋊C8—21no—
295C22×Q16—31no—
296C22×SD16—91no—
297C2×#124—91no—
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—
310C23×D3—61no—
311C23×D3—61no—
312C2×C3×Q8—21no—
313C2×C3×Q8—21no—
314C2×C3×Q8—34no—
315C2×C3×Q8—31no—
316C2×C3×Q8—31no—
317C2×C3×Q8—61no—
318C2×C3×Q8—61no—
319C2×C3×Q8—62no—
320C2×C3×Q8—62no—
321C2×C3×Q8—62no—
322C2×C3×Q8C22×D311yescharacteristic
323C2×C3×Q8C22×D311yescharacteristic
324C2×C3×Q8C22×D311yescharacteristic
325C2×C3×Q8C22×D311yescharacteristic
326C2×C3×D4—31no—
327C22×C3×C4—31no—
328C22×C3×C4—61no—
329C22×C3×C4—61no—
330C2×#67—61no—
331C22×Dic3—31no—
332C22×Dic3—31no—
333C22×Dic3—61no—
334D3×Q8—22no—
335D3×Q8—22no—
336D3×Q8—22no—
337D3×Q8#6714yes—
338D3×D4—62no—
339D3×D4—62no—
340C2×D12—31no—
341C2×D12—31no—
342C2×D12—61no—
343C2×D12—62no—
344C2×D12—62no—
345C2×D12—61no—
346C2×D12C22×D311yescharacteristic
347C2×C4×D3—21no—
348C2×C4×D3—21no—
349C2×C4×D3—31no—
350C2×C4×D3—31no—
351C2×C4×D3—61no—
352C2×C4×D3C22×D311yescharacteristic
353C2×Dic6—21no—
354C2×Dic6—21no—
355C2×Dic6C22×D311yescharacteristic
356C2×Dic6C22×D311yescharacteristic
357C3×Q16—22no—
358C3×Q16—22no—
359C3×Q16—42no—
360C3×Q16—62no—
361C3×Q16—62no—
362C3×Q16—62no—
363C3×SD16—62no—
364C2×C3×C8—21no—
365C2×C3×C8—31no—
366C2×C3×C8—31no—
367C2×C3×C8—62no—
368C2×C3×C8C22×D311yescharacteristic
369C2×C3×C8C22×D311yescharacteristic
370C3×C4⋊C4—31no—
371C3×C4⋊C4—61no—
372C3×C22⋊C4—61no—
373C3×C22⋊C4—61no—
374C3×C42—31no—
375C3×C42—61no—
376#217—61no—
377#217—61no—
378#216—22no—
379#216—22no—
380#215—22no—
381#215—62no—
382#215—62no—
383#215—62no—
384#215—62no—
385#215—122no—
386#214—62no—
387(C2×D3)⋊C4—21no—
388(C2×D3)⋊C4—21no—
389(C2×D3)⋊C4—61no—
390(C2×D3)⋊C4—61no—
391(C2×D3)⋊C4—61no—
392(C2×D3)⋊C4—61no—
393(C2×D3)⋊C4—61no—
394(C2×D3)⋊C4—61no—
395(C2×D3)⋊C4—61no—
396(C2×D3)⋊C4—61no—
397(C2×D3)⋊C4—61no—
398(C2×D3)⋊C4—61no—
399(C2×D3)⋊C4—121no—
400(C2×D3)⋊C4—121no—
401C4⋊Dic3—21no—
402C4⋊Dic3—31no—
403C4⋊Dic3—31no—
404C4⋊Dic3—61no—
405C4⋊Dic3—61no—
406C4⋊Dic3—61no—
407C4⋊Dic3—61no—
408C4⋊Dic3—61no—
409C4⋊Dic3—61no—
410C4⋊Dic3—121no—
411C4⋊Dic3C22×D311yescharacteristic
412Dic3⋊C4—61no—
413Dic3⋊C4—61no—
414Dic3⋊C4—61no—
415C4×Dic3—21no—
416C4×Dic3—31no—
417C4×Dic3—31no—
418C4×Dic3—31no—
419C4×Dic3—31no—
420C4×Dic3—31no—
421C4×Dic3—31no—
422C4×Dic3—61no—
423C4×Dic3—61no—
424C4×Dic3—61no—
425C4×Dic3—61no—
426C4×Dic3—61no—
427C4×Dic3—61no—
428C4×Dic3—61no—
429C4×Dic3—121no—
430C4×Dic3C22×D311yescharacteristic
431C2×C3⋊C8—31no—
432C2×C3⋊C8—31no—
433C2×C3⋊C8—61no—
434C2×C3⋊C8—62no—
435C2×C3⋊C8C22×D311yescharacteristic
436C2×C3⋊C8C22×D311yescharacteristic
437Dic12—22no—
438#204—62no—
439D3×C8—22no—
440D3×C8—62no—
441C22×C32C22×D411yescharacteristic
442C2×C3⋊D3—41no—
443C2×C3⋊D3—41no—
444C2×C3⋊D3—41no—
445C2×C3×D3—41no—
446C2×C3×D3—41no—
447C2×C3×D3—41no—
448C2×C3×D3#12112yes—
449C2×C3×D3#13512yes—
450C2×C3×D3#13712yes—
451D32—84no—
452C32×C4—22no—
453C32×C4—41no—
454C32×C4C22×D411yescharacteristic
455C32×C4C2×#4111yescharacteristic
456C3⋊Dic3—21no—
457C3⋊Dic3—21no—
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—31no—
467C22×D4—91no—
468C2×Q16—31no—
469C2×Q16—31no—
470C2×Q16—31no—
471C2×Q16—64no—
472C2×Q16D3211yescharacteristic, complemented
473C2×SD16—31no—
474C2×SD16—91no—
475C2×SD16—91no—
476C2×SD16—91no—
477C2×SD16—184no—
478C22×C8—31no—
479C22×C8—91no—
480#124—31no—
481#124—91no—
482#124—91no—
483#124—91no—
484#124—181no—
485#124—181no—
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—181no—
495C2×C22⋊C4—181no—
496C2×C42—91no—
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—31no—
511C23×C3—61no—
512C22×D3—21no—
513C22×D3—61no—
514C22×D3—61no—
515C22×D3—121no—
516C22×D3—122no—
517C22×D3—122no—
518C22×D3—122no—
519C22×D3—122no—
520C22×D3—122no—
521C22×D3—122no—
522C22×D3D3×D411yescharacteristic
523C3×Q8—21no—
524C3×Q8—21no—
525C3×Q8—21no—
526C3×Q8—21no—
527C3×Q8—21no—
528C3×Q8—21no—
529C3×Q8—22no—
530C3×Q8—32no—
531C3×Q8—41no—
532C3×Q8—41no—
533C3×Q8—41no—
534C3×Q8—64no—
535C3×Q8—61no—
536C3×Q8—61no—
537C3×Q8—61no—
538C3×Q8—122no—
539C3×Q8D3×D412yes—
540C3×Q8C2×#6712yes—
541C3×D4—61no—
542C3×D4—61no—
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—41no—
555C2×C3×C4—64no—
556C2×C3×C4—61no—
557C2×C3×C4—61no—
558C2×C3×C4—61no—
559C2×C3×C4—122no—
560C2×C3×C4C23×D311yescharacteristic
561C2×C3×C4C23×D311yescharacteristic
562#67—122no—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—31no—
567C2×Dic3—31no—
568C2×Dic3—31no—
569C2×Dic3—31no—
570C2×Dic3—61no—
571C2×Dic3—61no—
572C2×Dic3—62no—
573C2×Dic3—62no—
574C2×Dic3—61no—
575C2×Dic3—61no—
576C2×Dic3—121no—
577C2×Dic3—122no—
578C2×Dic3D3×D411yescharacteristic
579C2×Dic3D3×D411yescharacteristic
580C2×Dic3D3×D411yescharacteristic
581D12—21no—
582D12—21no—
583D12—61no—
584D12—61no—
585D12—61no—
586D12—61no—
587D12—121no—
588D12—121no—
589D12—122no—
590C4×D3—24no—
591C4×D3—42no—
592C4×D3—62no—
593C4×D3—62no—
594C4×D3—122no—
595C4×D3#23712yes—
596C4×D3C2×#6712yes—
597Dic6—21no—
598Dic6—24no—
599Dic6—21no—
600Dic6—21no—
601Dic6—42no—
602Dic6C2×#6712yes—
603C3×C8—21no—
604C3×C8—21no—
605C3×C8—41no—
606C3×C8—61no—
607C3×C8—61no—
608C3⋊C8—21no—
609C3⋊C8—21no—
610C3⋊C8—61no—
611C3⋊C8—61no—
612C3⋊C8—121no—
613C2×C32C2×#12111yescharacteristic
614C2×C32C2×#13511yescharacteristic
615C2×C32C2×#13711yescharacteristic
616C3⋊D3—81no—
617C3×D3—81no—
618C3×D3#46414yescomplemented
619C24—181no—
620C2×Q8—34no—
621C2×Q8—31no—
622C2×Q8—31no—
623C2×Q8—61no—
624C2×Q8—61no—
625C2×Q8—62no—
626C2×Q8—62no—
627C2×Q8—62no—
628C2×Q8C2×D3211yescharacteristic
629C2×Q8C2×D3211yescharacteristic
630C2×D4—31no—
631C2×D4—91no—
632C2×D4—182no—
633C2×D4—182no—
634C2×D4—181no—
635C22×C4—31no—
636C22×C4—61no—
637C22×C4—61no—
638C22×C4—91no—
639C22×C4—91no—
640C22×C4—181no—
641Q16—22no—
642Q16—62no—
643Q16—62no—
644Q16—62no—
645SD16—62no—
646SD16—182no—
647SD16—182no—
648SD16—182no—
649C2×C8—31no—
650C2×C8—31no—
651C2×C8—62no—
652C2×C8—91no—
653C2×C8—182no—
654C2×C8C2×D3211yescharacteristic
655C4⋊C4—31no—
656C4⋊C4—61no—
657C4⋊C4—91no—
658C4⋊C4—181no—
659C4⋊C4—181no—
660C4⋊C4—181no—
661C4⋊C4—181no—
662C22⋊C4—61no—
663C22⋊C4—61no—
664C22⋊C4—181no—
665C22⋊C4—181no—
666C22⋊C4—181no—
667C22⋊C4—181no—
668C22⋊C4—181no—
669C22⋊C4—181no—
670C42—31no—
671C42—61no—
672C42—91no—
673C42—91no—
674C42—91no—
675C42—181no—
676C42—181no—
677C42—181no—
678C22×C3—21no—
679C22×C3—32no—
680C22×C3—32no—
681C22×C3—32no—
682C22×C3—121no—
683C22×C3—121no—
684C22×C3—121no—
685C22×C3C2×D3×D411yescharacteristic
686C22×C3C2×D3×D411yescharacteristic
687C2×D3—41no—
688C2×D3—41no—
689C2×D3—41no—
690C2×D3—121no—
691C2×D3—121no—
692C2×D3—121no—
693C2×D3—121no—
694C2×D3—121no—
695C2×D3—121no—
696C2×D3—241no—
697C2×D3—241no—
698C2×D3—241no—
699C2×D3—244no—
700C2×D3—244no—
701C2×D3#91812yes—
702C2×D3#91912yes—
703C2×D3#93912yes—
704C3×C4—22no—
705C3×C4—22no—
706C3×C4—21no—
707C3×C4—21no—
708C3×C4—32no—
709C3×C4—42no—
710C3×C4—41no—
711C3×C4—41no—
712C3×C4—61no—
713C3×C4—61no—
714C3×C4—62no—
715C3×C4—81no—
716C3×C4—121no—
717C3×C4—121no—
718C3×C4C2×D3×D411yescharacteristic
719C3×C4C2×#23711yescharacteristic
720C3×C4D3×#4111yescharacteristic
721C3×C4C22×#6711yescharacteristic
722Dic3—21no—
723Dic3—21no—
724Dic3—22no—
725Dic3—41no—
726Dic3—41no—
727Dic3—61no—
728Dic3—61no—
729Dic3—61no—
730Dic3—61no—
731Dic3—121no—
732Dic3—121no—
733Dic3—121no—
734Dic3—121no—
735Dic3—241no—
736Dic3#93912yes—
737C32C2×#46411yescharacteristic, complemented, Sylow
738C23—31no—
739C23—61no—
740C23—181no—
741C23—362no—
742C23—362no—
743C23—362no—
744Q8—21no—
745Q8—21no—
746Q8—21no—
747Q8—32no—
748Q8—64no—
749Q8—61no—
750Q8—61no—
751Q8—61no—
752Q8—122no—
753Q8D3×#6712yes—
754D4—61no—
755D4—61no—
756D4—181no—
757D4—181no—
758D4—362no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—31no—
762C2×C4—32no—
763C2×C4—32no—
764C2×C4—31no—
765C2×C4—31no—
766C2×C4—64no—
767C2×C4—61no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—91no—
771C2×C4—91no—
772C2×C4—122no—
773C2×C4—182no—
774C2×C4—182no—
775C2×C4—181no—
776C2×C4—362no—
777C2×C4C22×D3211yescharacteristic
778C8—21no—
779C8—61no—
780C8—61no—
781C8—181no—
782C2×C3—21no—
783C2×C3—21no—
784C2×C3—21no—
785C2×C3—34no—
786C2×C3—241no—
787C2×C3D3×#12111yescharacteristic
788C2×C3C2×#91811yescharacteristic
789C2×C3C2×#91911yescharacteristic
790C2×C3D3×#13511yescharacteristic
791C2×C3D3×#13711yescharacteristic
792C2×C3C2×#93911yescharacteristic
793D3—81no—
794D3—241no—
795D3—241no—
796D3—481no—
797D3#518514yesdirect product factor
798C22—32no—
799C22—32no—
800C22—32no—
801C22—121no—
802C22—121no—
803C22—121no—
804C22—361no—
805C22—361no—
806C22—361no—
807C22—724no—
808C22D32×D411yescharacteristic
809C4—22no—
810C4—32no—
811C4—41no—
812C4—61no—
813C4—61no—
814C4—62no—
815C4—121no—
816C4—121no—
817C4—181no—
818C4—181no—
819C4—361no—
820C4D3×#23711yescharacteristic
821C4C2×D3×#6711yescharacteristic
822C3—21no—
823C3D3×#46411yescharacteristic, complemented
824C3C2×#518511yescharacteristic, complemented
825C2—34no—
826C2—241no—
827C2—721no—
828C2D3×#91811yescharacteristic
829C2D3×#91911yescharacteristic
830C2D3×#93911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radicalC2×D3×D12C22
hypercenterC2×Q16D32
hypocenterC32C2×#464
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×Q16C2semidirect
3. D3×Q8×Dic3C2semidirect
5. #10592884C2semidirect
6. C3×#5185C2semidirect
7. #10591612C2semidirect
8. #10591607C2semidirect
9. #10591579C2semidirect
10. #10591578C2semidirect
11. D3×#835C2semidirect
13. #10590801C2semidirect
14. #10590797C2semidirect
15. D3×Dic3⋊C8C2semidirect
21. C2×C32×Q16C22semidirect
23. Q8×C3⋊Dic3C22semidirect
26. C3×Q8×Dic3C22semidirect
27. C2×C3×#216C22semidirect
28. C2×C3×#216C22semidirect
31. C2×C3×Dic12C22semidirect
45. #63843C22semidirect
47. Dic3×Dic6C22semidirect
51. #63662C22semidirect
53. #63641C22semidirect
54. C3×#835C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. #63572C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
59. #63566C22semidirect
60. #63565C22semidirect
67. C2×D3×Q16D3semidirect
82. #5185D3direct (N × H)
165. C2×C3×Q16C2×D3semidirect
166. C2×C3×Q16C2×D3semidirect
186. Q8×Dic3C2×D3semidirect
187. C2×#216C2×D3semidirect
188. C2×#216C2×D3semidirect
207. C2×Dic12C2×D3semidirect
232. #835C2×D3semidirect
247. Dic3⋊C8C2×D3semidirect
472. C2×Q16D32semidirect
618. C3×D3#464semidirect
737. C32C2×#464semidirect
797. D3#5185direct (N × H)
823. C3D3×#464semidirect
824. C3C2×#5185semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×Q162
D3×#9472
D3×Q8×Dic32
C2×D3×#2152
#105928842
C3×#51852
#105916122
#105916072
#105915792
#105915782
D3×#8352
D3×#8212
#105908012
#105907972
D3×Dic3⋊C82
C2×#51853
D3×#4643