Finite Group Databasebeta

← D3×#5028 #11865692

Subgroups — D3×#5028 #11865692

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×C4×D3×Q8C211yesmaximal, characteristic, complemented
2C2×D3×#216C211yesmaximal, characteristic, complemented
3C2×D3×#215C211yesmaximal, characteristic
4D3×#875C211yesmaximal, characteristic
5#10592727C211yesmaximal, characteristic, complemented
6C3×#5028C211yesmaximal, characteristic, complemented
7#10591607C211yesmaximal, characteristic, complemented
8#10591604C211yesmaximal, characteristic, complemented
9D3×#810C211yesmaximal, characteristic, complemented
10D3×#809C211yesmaximal, characteristic
11#10590536C211yesmaximal, characteristic, complemented
12#10590532C211yesmaximal, characteristic, complemented
13#10590368C211yesmaximal, characteristic, complemented
14D3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
15#10590267C211yesmaximal, characteristic, complemented
16C2×#5028—31nomaximal
17D3×#464—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C2×D3×Dic6C2211yescharacteristic
21C32×C4×Q8C2211yescharacteristic, complemented
22C2×#3756C2211yescharacteristic, complemented
23C2×#3755C2211yescharacteristic
24#64084C2211yescharacteristic
25C3×Q8×Dic3C2211yescharacteristic, complemented
26C2×C3×#216C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic
28C3×D3×C4⋊C4—21no—
29C3×D3×C4⋊C4C2211yescharacteristic
30C3×#887—21no—
31C3×#887C2211yescharacteristic, complemented
32C3×#875C2211yescharacteristic
33C3×C42×D3—21no—
34C3×C42×D3C2211yescharacteristic
35C3×C4×Dic6—21no—
36C3×C4×Dic6C2211yescharacteristic, complemented
37D3×#216—24no—
38D3×#215—24no—
39D3×(C2×D3)⋊C4—21no—
40D3×(C2×D3)⋊C4—21no—
41#63864C2211yescharacteristic
42#63860C2211yescharacteristic
43#63852—21no—
44#63852—21no—
45C2×#3719C2211yescharacteristic, complemented
46C2×#3718C2211yescharacteristic, complemented
47C2×#3717C2211yescharacteristic
48C2×#3715C2211yescharacteristic
49C2×D3×C3⋊C8C2211yescharacteristic
50C2×D3×C3⋊C8C2211yescharacteristic
51#63637C2211yescharacteristic, complemented
52#63636C2211yescharacteristic
53C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
54C3×#810C2211yescharacteristic, complemented
55C3×#809C2211yescharacteristic
56C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
57Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63565C2211yescharacteristic, complemented
61#63564C2211yescharacteristic
62#63562C2211yescharacteristic
63C2×C3×C4×Q8—31no—
64C22×#216—31no—
65C22×#215—31no—
66C2×D3×Q16—31no—
67C2×D3×SD16—31no—
68D3×#124—31no—
69C4×D3×Q8D311yescharacteristic, complemented
70C2×#875—31no—
71C3×#464—31no—
72#5185—31no—
73#5166—31no—
74#5054—31no—
75#5028—31no—
76#5028—31no—
77#5028—31no—
78#5028—31no—
79#5028—31no—
80#5028—31no—
81#5028—31no—
82#5028—31no—
83#5028—61no—
84#5028D311yescharacteristic, direct product factor
85C2×#810—31no—
86C2×#809—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—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×#634C2311yescharacteristic
98C3×D3×Q8—22no—
99C3×D3×Q8D414yes—
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3D411yescharacteristic
104C2×C3×C4×D3D411yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6—21no—
107C2×C3×Dic6C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×#627—21no—
110C2×#626—21no—
111C2×D3×Dic3—21no—
112D3×D12—22no—
113D3×D12—22no—
114D3×Dic6—22no—
115D3×Dic6—22no—
116C32×C4⋊C4—21no—
117C32×C4⋊C4C2311yescharacteristic
118C32×C42—21no—
119C32×C42C2311yescharacteristic
120#3756—22no—
121#3755—22no—
122#3752—21no—
123#3752—21no—
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C3×#216—22no—
127C3×#215—22no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×C4⋊Dic3—21no—
131C3×C4⋊Dic3C2311yescharacteristic
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C3×C4×Dic3—21no—
136C3×C4×Dic3—21no—
137C3×C4×Dic3—21no—
138C3×C4×Dic3D411yescharacteristic
139C3×C4×Dic3D411yescharacteristic
140C3×C4×Dic3C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143#3722—21no—
144#3722—21no—
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147#3719—22no—
148#3718—22no—
149#3717—22no—
150#3715—22no—
151D3×C3⋊C8—22no—
152D3×C3⋊C8—22no—
153C2×#464—91noSylow
154C22×C3×Q8—31no—
155C2×D3×Q8—31no—
156C2×D3×Q8C2×D311yescharacteristic
157C2×D3×D4—31no—
158C22×D12—31no—
159C22×Dic6—31no—
160C2×C3×Q16—31no—
161C2×C3×SD16—31no—
162C3×#124—31no—
163C3×C4×Q8—21no—
164C3×C4×Q8—31no—
165C3×C4×Q8—31no—
166C3×C4×Q8—31no—
167C3×C4×Q8—61no—
168C3×C4×Q8—61no—
169C3×C4×Q8C2×D311yescharacteristic, complemented
170C3×C4×Q8C2×D311yescharacteristic, complemented
171C2×C3×C4⋊C4—31no—
172C2×C3×C4⋊C4—61no—
173C2×C3×C42—31no—
174C2×C3×C42—61no—
175#947—31no—
176Q8×Dic3C2×D311yescharacteristic, complemented
177C2×#216—31no—
178C2×#216—31no—
179C2×#216—31no—
180C2×#216—31no—
181C2×#216—31no—
182C2×#216—61no—
183C2×#216—64no—
184C2×#216C2×D311yescharacteristic, complemented
185C2×#215—31no—
186C2×#215—31no—
187C2×#215—31no—
188C2×#215—31no—
189C2×#215—61no—
190C2×#215—64no—
191C2×#215C2×D311yescharacteristic
192#936—31no—
193C2×#214—31no—
194C2×(C2×D3)⋊C4—61no—
195C2×(C2×D3)⋊C4—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—21no—
205D3×C4⋊C4C2×D311yescharacteristic
206#887—21no—
207#887C2×D311yescharacteristic, complemented
208#885—61no—
209#885—61no—
210D3×C22⋊C4—61no—
211D3×C22⋊C4—61no—
212#875—31no—
213#875—31no—
214#875—31no—
215#875—31no—
216#875—61no—
217#875—61no—
218#875—61no—
219#875C2×D311yescharacteristic
220C42×D3—21no—
221C42×D3C2×D311yescharacteristic
222C4×Dic6—21no—
223C4×Dic6C2×D311yescharacteristic, complemented
224C3×C4⋊C8—31no—
225C3×#103—31no—
226C3×#102—31no—
227#835—31no—
228#832—31no—
229#821—31no—
230#816—31no—
231Dic3⋊C8—31no—
232Dic3⋊C8—31no—
233#810—31no—
234#810—31no—
235#810—31no—
236#810—31no—
237#810—61no—
238#810C2×D311yescharacteristic, complemented
239#809—31no—
240#809—31no—
241#809—31no—
242#809—31no—
243#809—61no—
244#809C2×D311yescharacteristic
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
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×Q8C2×D412yes—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4C2×D411yescharacteristic
262C2×C32×C4C2×D411yescharacteristic
263C2×C32×C4C2411yescharacteristic
264C2×C3⋊Dic3—21no—
265C4⋊(C3⋊D3)—21no—
266C4⋊(C3⋊D3)—21no—
267#634—21no—
268#634—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—22no—
279C3×C4×D3—22no—
280C3×C4×D3—42no—
281C3×C4×D3C2×D412yes—
282C3×C4×D3#4112yes—
283C3×Dic6—21no—
284C3×Dic6—24no—
285C3×Dic6—21no—
286C3×Dic6—21no—
287C3×Dic6C2×D412yes—
288#627—42no—
289#626—42no—
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—91no—
298C2×C4×Q8—31no—
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—34no—
314C2×C3×Q8—31no—
315C2×C3×Q8—31no—
316C2×C3×Q8—61no—
317C2×C3×Q8—62no—
318C2×C3×Q8C22×D311yescharacteristic
319C2×C3×Q8C22×D311yescharacteristic
320C2×C3×D4—31no—
321C22×C3×C4—31no—
322C22×C3×C4—31no—
323C22×C3×C4—31no—
324C22×C3×C4—61no—
325C22×C3×C4—61no—
326C2×#67—61no—
327C22×Dic3—61no—
328D3×Q8—22no—
329D3×Q8—62no—
330D3×Q8—62no—
331D3×Q8D1214yes—
332D3×D4—62no—
333D3×D4—62no—
334C2×D12—31no—
335C2×D12—31no—
336C2×D12—61no—
337C2×D12—62no—
338C2×D12—62no—
339C2×D12—61no—
340C2×D12C22×D311yescharacteristic
341C2×C4×D3—21no—
342C2×C4×D3—21no—
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—61no—
351C2×Dic6—62no—
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—21no—
362C3×C4⋊C4—21no—
363C3×C4⋊C4—21no—
364C3×C4⋊C4—31no—
365C3×C4⋊C4—41no—
366C3×C4⋊C4—61no—
367C3×C4⋊C4—61no—
368C3×C4⋊C4—61no—
369C3×C4⋊C4—61no—
370C3×C4⋊C4C22×D311yescharacteristic
371C3×C4⋊C4C22×D311yescharacteristic
372C3×C22⋊C4—61no—
373C3×C22⋊C4—61no—
374C3×C42—21no—
375C3×C42—21no—
376C3×C42—21no—
377C3×C42—31no—
378C3×C42—31no—
379C3×C42—31no—
380C3×C42—41no—
381C3×C42—61no—
382C3×C42—61no—
383C3×C42—61no—
384C3×C42C22×D311yescharacteristic
385C3×C42C22×D311yescharacteristic
386#217—61no—
387#217—61no—
388#216—22no—
389#216—62no—
390#216—62no—
391#216—62no—
392#216—62no—
393#216—62no—
394#216—122no—
395#215—22no—
396#215—62no—
397#215—62no—
398#215—62no—
399#215—62no—
400#215—122no—
401#214—62no—
402(C2×D3)⋊C4—21no—
403(C2×D3)⋊C4—21no—
404(C2×D3)⋊C4—61no—
405(C2×D3)⋊C4—61no—
406(C2×D3)⋊C4—61no—
407(C2×D3)⋊C4—61no—
408(C2×D3)⋊C4—61no—
409(C2×D3)⋊C4—61no—
410(C2×D3)⋊C4—61no—
411(C2×D3)⋊C4—61no—
412(C2×D3)⋊C4—61no—
413(C2×D3)⋊C4—61no—
414(C2×D3)⋊C4—121no—
415(C2×D3)⋊C4—121no—
416C4⋊Dic3—21no—
417C4⋊Dic3C22×D311yescharacteristic
418Dic3⋊C4—21no—
419Dic3⋊C4—21no—
420Dic3⋊C4—21no—
421C4×Dic3—21no—
422C4×Dic3—21no—
423C4×Dic3—21no—
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×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—21no—
454C32×C4—21no—
455C32×C4—41no—
456C32×C4C22×D411yescharacteristic
457C32×C4C2×#4111yescharacteristic
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—91no—
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—91no—
482#124—91no—
483#124—91no—
484#124—181no—
485#124—181no—
486C4×Q8—31no—
487C4×Q8—31no—
488C4×Q8—31no—
489C4×Q8—61no—
490C4×Q8—61no—
491C4×Q8D3211yescharacteristic, complemented
492C2×C4⋊C4—31no—
493C2×C4⋊C4—61no—
494C2×C22⋊C4—181no—
495C2×C22⋊C4—181no—
496C2×C42—31no—
497C2×C42—61no—
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×D3C2×#6711yescharacteristic
523C3×Q8—21no—
524C3×Q8—21no—
525C3×Q8—22no—
526C3×Q8—32no—
527C3×Q8—41no—
528C3×Q8—64no—
529C3×Q8—61no—
530C3×Q8—61no—
531C3×Q8—61no—
532C3×Q8C2×D1212yes—
533C3×Q8D3×D412yes—
534C3×D4—61no—
535C3×D4—61no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—31no—
544C2×C3×C4—32no—
545C2×C3×C4—32no—
546C2×C3×C4—31no—
547C2×C3×C4—31no—
548C2×C3×C4—41no—
549C2×C3×C4—41no—
550C2×C3×C4—62no—
551C2×C3×C4—62no—
552C2×C3×C4—64no—
553C2×C3×C4—61no—
554C2×C3×C4—61no—
555C2×C3×C4—61no—
556C2×C3×C4—122no—
557C2×C3×C4D3×D411yescharacteristic
558C2×C3×C4D3×D411yescharacteristic
559C2×C3×C4C2×#6711yescharacteristic
560C2×C3×C4C2×#6711yescharacteristic
561C2×C3×C4C23×D311yescharacteristic
562C2×C3×C4C23×D311yescharacteristic
563#67—122no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—21no—
567C2×Dic3—61no—
568C2×Dic3—61no—
569C2×Dic3—121no—
570C2×Dic3—122no—
571C2×Dic3C2×#6711yescharacteristic
572C2×Dic3C2×#6711yescharacteristic
573C2×Dic3C2×#6711yescharacteristic
574D12—21no—
575D12—21no—
576D12—61no—
577D12—61no—
578D12—61no—
579D12—61no—
580D12—121no—
581D12—121no—
582D12—122no—
583C4×D3—24no—
584C4×D3—22no—
585C4×D3—22no—
586C4×D3—42no—
587C4×D3—122no—
588C4×D3C2×D1212yes—
589C4×D3#23512yes—
590Dic6—21no—
591Dic6—24no—
592Dic6—21no—
593Dic6—21no—
594Dic6—61no—
595Dic6—61no—
596Dic6—61no—
597Dic6—61no—
598Dic6—121no—
599Dic6—121no—
600Dic6—122no—
601Dic6—122no—
602Dic6C2×D1212yes—
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×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—62no—
625C2×Q8—91no—
626C2×Q8—181no—
627C2×Q8—182no—
628C2×Q8—182no—
629C2×Q8C2×D3211yescharacteristic
630C2×D4—31no—
631C2×D4—91no—
632C2×D4—182no—
633C2×D4—182no—
634C2×D4—181no—
635C22×C4—31no—
636C22×C4—31no—
637C22×C4—31no—
638C22×C4—61no—
639C22×C4—61no—
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—21no—
656C4⋊C4—31no—
657C4⋊C4—61no—
658C4⋊C4—61no—
659C4⋊C4—61no—
660C4⋊C4—61no—
661C4⋊C4C2×D3211yescharacteristic
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—21no—
671C42—31no—
672C42—31no—
673C42—31no—
674C42—61no—
675C42—61no—
676C42—61no—
677C42C2×D3211yescharacteristic
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×C3C22×#6711yescharacteristic
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#93012yes—
702C2×D3#94212yes—
703C2×D3#95012yes—
704C3×C4—21no—
705C3×C4—21no—
706C3×C4—22no—
707C3×C4—21no—
708C3×C4—21no—
709C3×C4—22no—
710C3×C4—21no—
711C3×C4—21no—
712C3×C4—32no—
713C3×C4—41no—
714C3×C4—41no—
715C3×C4—42no—
716C3×C4—41no—
717C3×C4—41no—
718C3×C4—61no—
719C3×C4—61no—
720C3×C4—62no—
721C3×C4—81no—
722C3×C4—121no—
723C3×C4—121no—
724C3×C4C22×D1211yescharacteristic
725C3×C4C2×#23511yescharacteristic
726C3×C4C2×D3×D411yescharacteristic
727C3×C4D3×#4111yescharacteristic
728Dic3—22no—
729Dic3—21no—
730Dic3—21no—
731Dic3—41no—
732Dic3—41no—
733Dic3—121no—
734Dic3—121no—
735Dic3—241no—
736Dic3#93012yes—
737C32C2×#46411yescharacteristic, complemented, Sylow
738C23—31no—
739C23—61no—
740C23—181no—
741C23—362no—
742C23—362no—
743C23—362no—
744Q8—21no—
745Q8—32no—
746Q8—64no—
747Q8—61no—
748Q8—61no—
749Q8—61no—
750Q8—181no—
751Q8—181no—
752Q8—362no—
753Q8D3×D1212yes—
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—62no—
767C2×C4—62no—
768C2×C4—64no—
769C2×C4—61no—
770C2×C4—61no—
771C2×C4—61no—
772C2×C4—122no—
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—241no—
787C2×C3D3×#12111yescharacteristic
788C2×C3D3×#13511yescharacteristic
789C2×C3D3×#13711yescharacteristic
790C2×C3C2×#93011yescharacteristic
791C2×C3C2×#94211yescharacteristic
792C2×C3C2×#95011yescharacteristic
793D3—81no—
794D3—241no—
795D3—241no—
796D3—481no—
797D3#502814yesdirect product factor
798C22—32no—
799C22—32no—
800C22—32no—
801C22—121no—
802C22—121no—
803C22—121no—
804C22—361no—
805C22—361no—
806C22—361no—
807C22—724no—
808C22C2×D3×#6711yescharacteristic
809C4—21no—
810C4—21no—
811C4—22no—
812C4—32no—
813C4—41no—
814C4—61no—
815C4—61no—
816C4—62no—
817C4—121no—
818C4—121no—
819C4—361no—
820C4C2×D3×D1211yescharacteristic
821C4D3×#23511yescharacteristic
822C3—21no—
823C3D3×#46411yescharacteristic, complemented
824C3C2×#502811yescharacteristic, complemented
825C2—34no—
826C2—241no—
827C2—721no—
828C2D3×#93011yescharacteristic
829C2D3×#94211yescharacteristic
830C2D3×#95011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×D3×D12C22
hypercenterC4×Q8D32
hypocenterC32C2×#464
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C3×C4×D3×Q8C2semidirect
2. C2×D3×#216C2semidirect
5. #10592727C2semidirect
6. C3×#5028C2semidirect
7. #10591607C2semidirect
8. #10591604C2semidirect
9. D3×#810C2semidirect
11. #10590536C2semidirect
12. #10590532C2semidirect
13. #10590368C2semidirect
14. D3×C4⋊(C3⋊C8)C2semidirect
15. #10590267C2semidirect
21. C32×C4×Q8C22semidirect
22. C2×#3756C22semidirect
25. C3×Q8×Dic3C22semidirect
26. C2×C3×#216C22semidirect
31. C3×#887C22semidirect
36. C3×C4×Dic6C22semidirect
45. C2×#3719C22semidirect
46. C2×#3718C22semidirect
51. #63637C22semidirect
53. C4⋊(C3⋊(C3⋊C8))C22semidirect
54. C3×#810C22semidirect
56. C3×C4⋊(C3⋊C8)C22semidirect
57. Dic3⋊(C3⋊C8)C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
59. #63567C22semidirect
60. #63565C22semidirect
69. C4×D3×Q8D3semidirect
84. #5028D3direct (N × H)
169. C3×C4×Q8C2×D3semidirect
170. C3×C4×Q8C2×D3semidirect
176. Q8×Dic3C2×D3semidirect
184. C2×#216C2×D3semidirect
207. #887C2×D3semidirect
223. C4×Dic6C2×D3semidirect
238. #810C2×D3semidirect
250. C4⋊(C3⋊C8)C2×D3semidirect
491. C4×Q8D32semidirect
618. C3×D3#464semidirect
737. C32C2×#464semidirect
797. D3#5028direct (N × H)
823. C3D3×#464semidirect
824. C3C2×#5028semidirect

Maximal subgroups

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

subgroupindex
C3×C4×D3×Q82
C2×D3×#2162
C2×D3×#2152
D3×#8752
#105927272
C3×#50282
#105916072
#105916042
D3×#8102
D3×#8092
#105905362
#105905322
#105903682
D3×C4⋊(C3⋊C8)2
#105902672
C2×#50283
D3×#4643