Finite Group Databasebeta

← D3×#5164 #11860056

Subgroups — D3×#5164 #11860056

Order 1152.

1148 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×SD16C211yesmaximal, characteristic
2D3×Q8×Dic3C211yesmaximal, characteristic, complemented
3D3×D4×Dic3C211yesmaximal, characteristic
4#10592863C211yesmaximal, characteristic, complemented
5C3×#5164C211yesmaximal, characteristic, complemented
6#10591572C211yesmaximal, characteristic, complemented
7#10591566C211yesmaximal, characteristic, complemented
8D3×#835C211yesmaximal, characteristic, complemented
9#10591446C211yesmaximal, characteristic, complemented
10#10591440C211yesmaximal, characteristic, complemented
11D3×#832C211yesmaximal, characteristic
12#10590779C211yesmaximal, characteristic, complemented
13#10590766C211yesmaximal, characteristic, complemented
14D3×#818C211yesmaximal, characteristic, complemented
15D3×#815C211yesmaximal, characteristic, complemented
16C2×#5164—31nomaximal
17D3×#440—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C22×D3×Dic3—21no—
21C2×C32×SD16C2211yescharacteristic
22Q8×C3⋊Dic3C2211yescharacteristic, complemented
23D4×C3⋊Dic3C2211yescharacteristic
24C3×Q8×Dic3C2211yescharacteristic, complemented
25C2×C3×#215C2211yescharacteristic
26C3×D4×Dic3C2211yescharacteristic
27C2×C3×#214C2211yescharacteristic
28C3×D3×SD16C418yescomplemented
29C2×C3×#204C2211yescharacteristic
30C2×C3×D3×C8C2211yescharacteristic
31#67⋊Dic3—21no—
32Dic3×#67—21no—
33D3×#217—21no—
34#63898C2211yescharacteristic
35Dic3×D12C2211yescharacteristic
36D3×C4⋊Dic3—21no—
37D3×C4⋊Dic3C2211yescharacteristic
38D3×C4⋊Dic3C2211yescharacteristic
39C4×D3×Dic3—21no—
40C4×D3×Dic3C2211yescharacteristic
41#63843—21no—
42#63843C2211yescharacteristic, complemented
43Dic3×Dic6—21no—
44Dic3×Dic6C2211yescharacteristic, complemented
45C2×D3×C3⋊C8C2211yescharacteristic
46#63662C2211yescharacteristic, complemented
47#63659C2211yescharacteristic
48#63645C2211yescharacteristic, complemented
49#63642C2211yescharacteristic, complemented
50C3×#835C2211yescharacteristic, complemented
51C3×#832C2211yescharacteristic
52C3×#818C2211yescharacteristic, complemented
53C3×#815C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56#63566C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63563C2211yescharacteristic
59#63562C2211yescharacteristic
60#63555C2211yescharacteristic, complemented
61#63554C2211yescharacteristic, complemented
62C22×C3×SD16—31no—
63C2×Q8×Dic3—31no—
64C2×D4×Dic3—31no—
65C2×D3×SD16D311yescharacteristic
66C4×D3×Q8—31no—
67C4×D3×D4—31no—
68C3×#440—31no—
69C2×#835—31no—
70C2×#832—31no—
71#5164—31no—
72#5164—31no—
73#5164—31no—
74#5164—31no—
75#5164—31no—
76#5164—31no—
77#5164—31no—
78#5164—31no—
79#5164—61no—
80#5164D311yescharacteristic, direct product factor
81C2×#818—31no—
82C2×#815—31no—
83#5026—31no—
84#5018—31no—
85#4889—31no—
86D3×#107—31no—
87#4817—31no—
88D3×#103—31no—
89D3×#102—31no—
90#4757—31no—
91#4710—31no—
92D3×#97—31no—
93C23×C3×D3—21no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×D4C2311yescharacteristic
96C22×C3⋊Dic3—21no—
97C2×C3×#67—21no—
98C22×C3×Dic3—21no—
99C3×D3×Q8—22no—
100C3×D3×Q8C2×C414yescomplemented
101C3×D3×D4—22no—
102C3×D3×D4C2×C414yes—
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6—21no—
107C2×C3×Dic6C2311yescharacteristic
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111C2×D3×Dic3—21no—
112C2×D3×Dic3—44no—
113C2×D3×Dic3D411yescharacteristic
114C2×D3×Dic3D411yescharacteristic
115C32×SD16C2×C414yescomplemented
116C2×C32×C8C2311yescharacteristic
117#3757—21no—
118C4⋊(C3⋊Dic3)—21no—
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121C4×C3⋊Dic3—21no—
122C4×C3⋊Dic3C2311yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124C3×#217—21no—
125C3×#215C2×C414yescomplemented
126C3×#214C2×C414yescomplemented
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4×Dic3—21no—
131C3×C4×Dic3C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C3×#204C2×C414yescomplemented
135C3×D3×C8C2×C414yescomplemented
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142Dic32—21no—
143Dic32—21no—
144Dic32D411yescharacteristic
145Dic32D411yescharacteristic
146D3×C3⋊C8—22no—
147C2×#440—91noSylow
148C22×C3×Q8—31no—
149C22×C3×D4—31no—
150C23×Dic3—61no—
151C2×D3×Q8C2×D311yescharacteristic
152C2×D3×D4C2×D311yescharacteristic
153C22×C4×D3—61no—
154C2×C3×SD16—21no—
155C2×C3×SD16—31no—
156C2×C3×SD16—31no—
157C2×C3×SD16—38no—
158C2×C3×SD16—31no—
159C2×C3×SD16C2×D311yescharacteristic
160C2×C3×SD16C2×D311yescharacteristic
161C22×C3×C8—31no—
162C3×C4×Q8—31no—
163C3×C4×D4—31no—
164C2×#217—61no—
165Q8×Dic3—31no—
166Q8×Dic3—31no—
167Q8×Dic3—31no—
168Q8×Dic3—31no—
169Q8×Dic3—61no—
170Q8×Dic3—61no—
171Q8×Dic3—61no—
172Q8×Dic3C2×D311yescharacteristic, complemented
173C2×#215C2×D311yescharacteristic
174D4×Dic3—31no—
175D4×Dic3—31no—
176D4×Dic3—31no—
177D4×Dic3—31no—
178D4×Dic3—61no—
179D4×Dic3—61no—
180D4×Dic3—61no—
181D4×Dic3C2×D311yescharacteristic
182C2×#214C2×D311yescharacteristic
183C4×#67—61no—
184C2×C4⋊Dic3—31no—
185C2×C4⋊Dic3—31no—
186C2×C4⋊Dic3—61no—
187C2×C4×Dic3—31no—
188C2×C4×Dic3—61no—
189C22×C3⋊C8—31no—
190D3×SD16Dic318yescomplemented
191C2×#204C2×D311yescharacteristic
192C2×D3×C8—31no—
193C2×D3×C8C2×D311yescharacteristic
194#893—31no—
195D3×C4⋊C4—31no—
196D3×C4⋊C4—31no—
197D3×C4⋊C4—61no—
198#887—31no—
199#887—61no—
200#67⋊C4—61no—
201D3×C22⋊C4—61no—
202C4×D12—31no—
203C42×D3—31no—
204C42×D3—61no—
205C4×Dic6—31no—
206C4×Dic6—61no—
207C3×#107—31no—
208C3×#103—31no—
209C3×#102—31no—
210C3×#97—31no—
211#835—31no—
212#835—31no—
213#835—31no—
214#835—31no—
215#835—61no—
216#835C2×D311yescharacteristic, complemented
217#832—31no—
218#832—31no—
219#832—31no—
220#832—31no—
221#832—61no—
222#832C2×D311yescharacteristic
223#821—31no—
224#818—31no—
225#818—31no—
226#818—31no—
227#818—31no—
228#818—61no—
229#818C2×D311yescharacteristic, complemented
230#816—31no—
231#815—31no—
232#815—31no—
233#815—31no—
234#815—31no—
235#815—31no—
236#815—61no—
237#815C2×D311yescharacteristic, complemented
238#810—31no—
239#809—31no—
240#807—31no—
241#807—31no—
242#803—31no—
243C23×C32—21no—
244C22×C3×D3—21no—
245C22×C3×D3—24no—
246C22×C3×D3—42no—
247C22×C3×D3—42no—
248C22×C3×D3C2×D411yescharacteristic
249C32×Q8—21no—
250C32×Q8C22×C412yescomplemented
251C32×D4—21no—
252C32×D4C22×C412yes—
253C2×C32×C4—21no—
254C2×C32×C4C2411yescharacteristic
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3—21no—
257C2×C3⋊Dic3—42no—
258C2×C3⋊Dic3C2×D411yescharacteristic
259C2×C3⋊Dic3C2×D411yescharacteristic
260C3×#67—24no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—42no—
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C3×D12—21no—
269C3×D12C22×C412yes—
270C3×C4×D3—24no—
271C3×C4×D3C22×C412yes—
272C3×C4×D3#4112yes—
273C3×Dic6—21no—
274C3×Dic6—24no—
275C3×Dic6C22×C412yescomplemented
276D3×Dic3—22no—
277D3×Dic3—22no—
278D3×Dic3—42no—
279D3×Dic3—42no—
280D3×Dic3—42no—
281D3×Dic3—42no—
282C32×C8C22×C412yescomplemented
283C3⋊(C3⋊C8)—21no—
284C3×C3⋊C8—21no—
285C3×C3⋊C8C22×C412yescomplemented
286C22×SD16—31no—
287C2×C4×Q8—91no—
288C2×C4×D4—91no—
289#440—31no—
290#440—91no—
291#440—91no—
292#440—91no—
293#440—91no—
294#440—91no—
295#440—91no—
296#440—91no—
297C2×#107—91no—
298C2×#103—91no—
299C2×#102—91no—
300C2×#97—91no—
301C24×C3—61no—
302C23×D3—21no—
303C2×C3×Q8—21no—
304C2×C3×Q8—34no—
305C2×C3×Q8—31no—
306C2×C3×Q8—61no—
307C2×C3×Q8—62no—
308C2×C3×Q8C22×D311yescharacteristic
309C2×C3×Q8C22×D311yescharacteristic
310C2×C3×D4—21no—
311C2×C3×D4—34no—
312C2×C3×D4—31no—
313C2×C3×D4—62no—
314C2×C3×D4—61no—
315C2×C3×D4C22×D311yescharacteristic
316C2×C3×D4C22×D311yescharacteristic
317C22×C3×C4—31no—
318C22×C3×C4—61no—
319C22×C3×C4—61no—
320C2×#67—21no—
321C22×Dic3—21no—
322C22×Dic3—31no—
323C22×Dic3—31no—
324C22×Dic3—61no—
325C22×Dic3—61no—
326C22×Dic3—61no—
327C22×Dic3—61no—
328C22×Dic3—61no—
329C22×Dic3—61no—
330C22×Dic3—121no—
331C22×Dic3—124no—
332D3×Q8—22no—
333D3×Q8C2×Dic314yescomplemented
334D3×D4—22no—
335D3×D4C2×Dic314yes—
336C2×D12C22×D311yescharacteristic
337C2×C4×D3—21no—
338C2×C4×D3—31no—
339C2×C4×D3—31no—
340C2×C4×D3—61no—
341C2×C4×D3—61no—
342C2×C4×D3—61no—
343C2×C4×D3—61no—
344C2×C4×D3—124no—
345C2×C4×D3C22×D311yescharacteristic
346C2×Dic6—21no—
347C2×Dic6C22×D311yescharacteristic
348C3×SD16—24no—
349C3×SD16—34no—
350C3×SD16—34no—
351C3×SD16—34no—
352C3×SD16C4×D314yescomplemented
353C3×SD16C2×Dic314yescomplemented
354C2×C3×C8—21no—
355C2×C3×C8—31no—
356C2×C3×C8—34no—
357C2×C3×C8—31no—
358C2×C3×C8C22×D311yescharacteristic
359C2×C3×C8C22×D311yescharacteristic
360C3×C4⋊C4—31no—
361C3×C4⋊C4—31no—
362C3×C4⋊C4—61no—
363C3×C22⋊C4—61no—
364C3×C42—31no—
365C3×C42—61no—
366#217—21no—
367#217—61no—
368#217—61no—
369#217—61no—
370#217—61no—
371#217—121no—
372#215C2×Dic314yescomplemented
373#214C2×Dic314yescomplemented
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376C4⋊Dic3—21no—
377C4⋊Dic3—31no—
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—31no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3—121no—
390C4⋊Dic3C22×D311yescharacteristic
391C4⋊Dic3C22×D311yescharacteristic
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396C4×Dic3—21no—
397C4×Dic3—31no—
398C4×Dic3—31no—
399C4×Dic3—31no—
400C4×Dic3—31no—
401C4×Dic3—31no—
402C4×Dic3—31no—
403C4×Dic3—61no—
404C4×Dic3—61no—
405C4×Dic3—61no—
406C4×Dic3—61no—
407C4×Dic3—61no—
408C4×Dic3—61no—
409C4×Dic3—61no—
410C4×Dic3—121no—
411C4×Dic3C22×D311yescharacteristic
412C2×C3⋊C8—31no—
413C2×C3⋊C8—31no—
414C2×C3⋊C8—61no—
415C2×C3⋊C8—62no—
416C2×C3⋊C8C22×D311yescharacteristic
417C2×C3⋊C8C22×D311yescharacteristic
418#204C2×Dic314yescomplemented
419D3×C8—62no—
420D3×C8C2×Dic314yescomplemented
421C22×C32—22no—
422C22×C32—41no—
423C22×C32—41no—
424C22×C32C22×D411yescharacteristic
425C2×C3×D3—22no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C2×C3×D3—48no—
429C2×C3×D3C4×D412yes—
430C2×C3×D3AGL(1,ℤ/8)12yes—
431C2×C3×D3#13712yes—
432C32×C4—22no—
433C32×C4C23×C411yescharacteristic
434C32×C4C2×#4111yescharacteristic
435C3⋊Dic3—21no—
436C3⋊Dic3—21no—
437C3⋊Dic3—41no—
438C3⋊Dic3—41no—
439C3×Dic3—22no—
440C3×Dic3—21no—
441C3×Dic3—21no—
442C3×Dic3—41no—
443C3×Dic3—41no—
444C3×Dic3C4×D412yes—
445C22×Q8—31no—
446C22×D4—31no—
447C23×C4—181no—
448C2×SD16—31no—
449C2×SD16—31no—
450C2×SD16—38no—
451C2×SD16—31no—
452C2×SD16D3211yescharacteristic
453C22×C8—31no—
454C22×C8—91no—
455C4×Q8—31no—
456C4×Q8—91no—
457C4×Q8—91no—
458C4×Q8—91no—
459C4×Q8—181no—
460C4×Q8—181no—
461C4×D4—31no—
462C4×D4—91no—
463C4×D4—91no—
464C4×D4—91no—
465C4×D4—181no—
466C4×D4—181no—
467C2×C4⋊C4—91no—
468C2×C4⋊C4—91no—
469C2×C4⋊C4—181no—
470C2×C22⋊C4—181no—
471C2×C42—91no—
472C2×C42—181no—
473#107—31no—
474#107—91no—
475#107—91no—
476#107—91no—
477#103—31no—
478#103—91no—
479#103—91no—
480#103—91no—
481#102—31no—
482#102—91no—
483#102—91no—
484#102—91no—
485#97—31no—
486#97—91no—
487#97—91no—
488#97—91no—
489C23×C3—21no—
490C23×C3—21no—
491C23×C3—31no—
492C23×C3—41no—
493C23×C3—64no—
494C23×C3—61no—
495C23×C3—122no—
496C23×C3—122no—
497C22×D3—21no—
498C22×D3—24no—
499C22×D3—42no—
500C22×D3—42no—
501C22×D3D3×D411yescharacteristic
502C3×Q8—21no—
503C3×Q8—21no—
504C3×Q8—22no—
505C3×Q8—32no—
506C3×Q8—41no—
507C3×Q8—64no—
508C3×Q8—61no—
509C3×Q8C2×C4×D312yescomplemented
510C3×Q8C22×Dic312yescomplemented
511C3×D4—21no—
512C3×D4—21no—
513C3×D4—22no—
514C3×D4—32no—
515C3×D4—41no—
516C3×D4—64no—
517C3×D4—61no—
518C3×D4C2×C4×D312yes—
519C3×D4C22×Dic312yes—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—31no—
524C2×C3×C4—32no—
525C2×C3×C4—32no—
526C2×C3×C4—31no—
527C2×C3×C4—31no—
528C2×C3×C4—41no—
529C2×C3×C4—64no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—122no—
534C2×C3×C4C23×D311yescharacteristic
535C2×C3×C4C23×D311yescharacteristic
536#67—24no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—31no—
541C2×Dic3—31no—
542C2×Dic3—31no—
543C2×Dic3—31no—
544C2×Dic3—42no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—62no—
548C2×Dic3—62no—
549C2×Dic3—61no—
550C2×Dic3—61no—
551C2×Dic3—61no—
552C2×Dic3—61no—
553C2×Dic3—121no—
554C2×Dic3—121no—
555C2×Dic3—122no—
556C2×Dic3—122no—
557C2×Dic3—122no—
558C2×Dic3—122no—
559C2×Dic3—122no—
560C2×Dic3—122no—
561C2×Dic3—242no—
562C2×Dic3D3×D411yescharacteristic
563C2×Dic3D3×D411yescharacteristic
564C2×Dic3D3×D411yescharacteristic
565D12—21no—
566D12C22×Dic312yes—
567C4×D3—24no—
568C4×D3—62no—
569C4×D3—62no—
570C4×D3—122no—
571C4×D3—122no—
572C4×D3—122no—
573C4×D3—122no—
574C4×D3#23712yes—
575C4×D3C22×Dic312yes—
576Dic6—21no—
577Dic6—24no—
578Dic6C22×Dic312yescomplemented
579C3×C8—22no—
580C3×C8—32no—
581C3×C8—61no—
582C3×C8C2×C4×D312yescomplemented
583C3×C8C22×Dic312yescomplemented
584C3⋊C8—21no—
585C3⋊C8—61no—
586C3⋊C8—61no—
587C3⋊C8—121no—
588C3⋊C8C22×Dic312yescomplemented
589C2×C32—42no—
590C2×C32C2×C4×D411yescharacteristic
591C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
592C2×C32C2×#13711yescharacteristic
593C3×D3—42no—
594C3×D3#44014yescomplemented
595C24—61no—
596C2×Q8—34no—
597C2×Q8—31no—
598C2×Q8—61no—
599C2×Q8—62no—
600C2×Q8C2×D3211yescharacteristic
601C2×D4—34no—
602C2×D4—31no—
603C2×D4—62no—
604C2×D4—61no—
605C2×D4C2×D3211yescharacteristic
606C22×C4—31no—
607C22×C4—61no—
608C22×C4—61no—
609C22×C4—91no—
610C22×C4—91no—
611C22×C4—181no—
612C22×C4—181no—
613C22×C4—181no—
614C22×C4—181no—
615C22×C4—181no—
616C22×C4—364no—
617SD16—34no—
618SD16—34no—
619SD16—34no—
620SD16D3×Dic314yescomplemented
621C2×C8—31no—
622C2×C8—34no—
623C2×C8—31no—
624C2×C8—91no—
625C2×C8—182no—
626C2×C8C2×D3211yescharacteristic
627C4⋊C4—31no—
628C4⋊C4—31no—
629C4⋊C4—61no—
630C4⋊C4—91no—
631C4⋊C4—91no—
632C4⋊C4—181no—
633C4⋊C4—181no—
634C4⋊C4—181no—
635C4⋊C4—181no—
636C4⋊C4—181no—
637C22⋊C4—61no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C22⋊C4—181no—
641C42—31no—
642C42—61no—
643C42—91no—
644C42—91no—
645C42—91no—
646C42—181no—
647C42—181no—
648C42—181no—
649C22×C3—22no—
650C22×C3—22no—
651C22×C3—21no—
652C22×C3—32no—
653C22×C3—32no—
654C22×C3—32no—
655C22×C3—42no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—62no—
661C22×C3—81no—
662C22×C3—81no—
663C22×C3—128no—
664C22×C3—121no—
665C22×C3—121no—
666C22×C3C2×D3×D411yescharacteristic
667C22×C3C2×D3×D411yescharacteristic
668C2×D3—22no—
669C2×D3—41no—
670C2×D3—41no—
671C2×D3—48no—
672C2×D3#91412yes—
673C2×D3#91512yes—
674C2×D3D4×Dic312yes—
675C3×C4—22no—
676C3×C4—22no—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—32no—
680C3×C4—42no—
681C3×C4—61no—
682C3×C4—61no—
683C3×C4—62no—
684C3×C4—121no—
685C3×C4—121no—
686C3×C4C22×C4×D311yescharacteristic
687C3×C4C2×#23711yescharacteristic
688C3×C4D3×#4111yescharacteristic
689C3×C4C23×Dic311yescharacteristic
690Dic3—21no—
691Dic3—21no—
692Dic3—22no—
693Dic3—41no—
694Dic3—41no—
695Dic3—61no—
696Dic3—61no—
697Dic3—61no—
698Dic3—61no—
699Dic3—121no—
700Dic3—121no—
701Dic3—121no—
702Dic3—121no—
703Dic3—121no—
704Dic3—121no—
705Dic3—241no—
706Dic3—241no—
707Dic3D4×Dic312yes—
708C32C2×#44011yescharacteristic, complemented, Sylow
709C23—21no—
710C23—31no—
711C23—64no—
712C23—61no—
713C23—122no—
714C23—122no—
715Q8—21no—
716Q8—32no—
717Q8—64no—
718Q8—61no—
719Q8C2×D3×Dic312yescomplemented
720D4—21no—
721D4—32no—
722D4—64no—
723D4—61no—
724D4C2×D3×Dic312yes—
725C2×C4—21no—
726C2×C4—31no—
727C2×C4—32no—
728C2×C4—32no—
729C2×C4—31no—
730C2×C4—31no—
731C2×C4—64no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—91no—
736C2×C4—91no—
737C2×C4—122no—
738C2×C4—182no—
739C2×C4—182no—
740C2×C4—181no—
741C2×C4—181no—
742C2×C4—362no—
743C2×C4—362no—
744C2×C4—362no—
745C2×C4—362no—
746C2×C4—362no—
747C2×C4C22×D3211yescharacteristic
748C8—32no—
749C8—61no—
750C8—181no—
751C8C2×D3×Dic312yescomplemented
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—21no—
755C2×C3—34no—
756C2×C3—42no—
757C2×C3—42no—
758C2×C3—82no—
759C2×C3—122no—
760C2×C3C4×D3×D411yescharacteristic
761C2×C3C2×#91411yescharacteristic
762C2×C3C2×#91511yescharacteristic
763C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
764C2×C3D3×#13711yescharacteristic
765C2×C3C2×D4×Dic311yescharacteristic
766D3—42no—
767D3#516414yesdirect product factor
768C22—22no—
769C22—32no—
770C22—32no—
771C22—32no—
772C22—41no—
773C22—41no—
774C22—62no—
775C22—128no—
776C22—121no—
777C22—121no—
778C22D32×D411yescharacteristic
779C4—22no—
780C4—32no—
781C4—62no—
782C4—61no—
783C4—61no—
784C4—121no—
785C4—121no—
786C4—181no—
787C4—181no—
788C4—361no—
789C4—361no—
790C4D3×#23711yescharacteristic
791C4C22×D3×Dic311yescharacteristic
792C3—21no—
793C3D3×#44011yescharacteristic, complemented
794C3C2×#516411yescharacteristic, complemented
795C2—34no—
796C2—42no—
797C2—122no—
798C2D3×#91411yescharacteristic
799C2D3×#91511yescharacteristic
800C2D3×D4×Dic311yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radicalC2×C3×D3×D4C22
cosocleC2×C32×C4C24
hypercenterC2×SD16D32
hypocenterC32C2×#440
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
2. D3×Q8×Dic3C2semidirect
4. #10592863C2semidirect
5. C3×#5164C2semidirect
6. #10591572C2semidirect
7. #10591566C2semidirect
8. D3×#835C2semidirect
9. #10591446C2semidirect
10. #10591440C2semidirect
12. #10590779C2semidirect
13. #10590766C2semidirect
14. D3×#818C2semidirect
15. D3×#815C2semidirect
22. Q8×C3⋊Dic3C22semidirect
24. C3×Q8×Dic3C22semidirect
28. C3×D3×SD16C4semidirect
42. #63843C22semidirect
44. Dic3×Dic6C22semidirect
46. #63662C22semidirect
48. #63645C22semidirect
49. #63642C22semidirect
50. C3×#835C22semidirect
52. C3×#818C22semidirect
53. C3×#815C22semidirect
54. #63575C22semidirect
55. #63575C22semidirect
56. #63566C22semidirect
57. #63565C22semidirect
60. #63555C22semidirect
61. #63554C22semidirect
80. #5164D3direct (N × H)
100. C3×D3×Q8C2×C4semidirect
115. C32×SD16C2×C4semidirect
125. C3×#215C2×C4semidirect
126. C3×#214C2×C4semidirect
134. C3×#204C2×C4semidirect
135. C3×D3×C8C2×C4semidirect
172. Q8×Dic3C2×D3semidirect
190. D3×SD16Dic3semidirect
216. #835C2×D3semidirect
229. #818C2×D3semidirect
237. #815C2×D3semidirect
250. C32×Q8C22×C4semidirect
275. C3×Dic6C22×C4semidirect
282. C32×C8C22×C4semidirect
285. C3×C3⋊C8C22×C4semidirect
333. D3×Q8C2×Dic3semidirect
352. C3×SD16C4×D3semidirect
353. C3×SD16C2×Dic3semidirect
372. #215C2×Dic3semidirect
373. #214C2×Dic3semidirect
418. #204C2×Dic3semidirect
420. D3×C8C2×Dic3semidirect
509. C3×Q8C2×C4×D3semidirect
510. C3×Q8C22×Dic3semidirect
578. Dic6C22×Dic3semidirect
582. C3×C8C2×C4×D3semidirect
583. C3×C8C22×Dic3semidirect
588. C3⋊C8C22×Dic3semidirect
594. C3×D3#440semidirect
620. SD16D3×Dic3semidirect
708. C32C2×#440semidirect
719. Q8C2×D3×Dic3semidirect
751. C8C2×D3×Dic3semidirect
767. D3#5164direct (N × H)
793. C3D3×#440semidirect
794. C3C2×#5164semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×SD162
D3×Q8×Dic32
D3×D4×Dic32
#105928632
C3×#51642
#105915722
#105915662
D3×#8352
#105914462
#105914402
D3×#8322
#105907792
#105907662
D3×#8182
D3×#8152
C2×#51643
D3×#4403