Finite Group Databasebeta

← D3×#2486 #10964232

Subgroups — D3×#2486 #10964232

Order 768.

3678 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#123C212yesmaximal
2C2×C4×D3×D4C211yesmaximal, characteristic
3C22×D3×C4⋊C4C211yesmaximal, characteristic, complemented
4C3×#2486C211yesmaximal, characteristic, complemented
5#82856C212yesmaximal, complemented
6#82373C211yesmaximal, characteristic, complemented
7#82196C211yesmaximal, characteristic, complemented
8D3×#398C212yesmaximal, complemented
9#77764C212yesmaximal, complemented
10D3×#397C212yesmaximal, complemented
11#77485C212yesmaximal, complemented
12#76231C212yesmaximal, complemented
13D3×#389C212yesmaximal, complemented
14D3×#381C212yesmaximal, complemented
15#74075C212yesmaximal, complemented
16#74027C211yesmaximal, characteristic, complemented
17D3×#380C211yesmaximal, characteristic, complemented
18D3×#380C212yesmaximal, complemented
19#73911C212yesmaximal, complemented
20C2×#2486—31nomaximal, Sylow
21C22×D3×D4C2211yescharacteristic
22C23×C4×D3C2211yescharacteristic
23C23×C4×D3C2212yes—
24C23×C4×D3C2211yescharacteristic
25C2×C3×#123C2212yes—
26C2×C3×C4×D4C2211yescharacteristic
27C22×C3×C4⋊C4C2211yescharacteristic, complemented
28C2×#935C2212yes—
29C2×D4×Dic3C2211yescharacteristic
30C2×#929C2212yes—
31C2×C4×#67C2211yescharacteristic
32C2×C4×#67C2211yescharacteristic
33C22×C4⋊Dic3C2211yescharacteristic, complemented
34C22×Dic3⋊C4C2212yescomplemented
35D3×#123—216no—
36C4×D3×D4—28no—
37C2×#894C2214yes—
38C2×#893C2211yescharacteristic
39C2×D3×C4⋊C4—28no—
40C2×D3×C4⋊C4C2211yescharacteristic
41C2×D3×C4⋊C4C2212yes—
42C2×D3×C4⋊C4C2212yes—
43C2×D3×C4⋊C4C2212yes—
44C2×D3×C4⋊C4C2214yes—
45C2×D3×C4⋊C4C2212yescomplemented
46C2×D3×C4⋊C4C2212yescomplemented
47C2×#886C2212yes—
48C2×#883C2214yes—
49C2×#67⋊C4C2211yescharacteristic
50C2×#67⋊C4C2211yescharacteristic
51C2×D3×C22⋊C4C2211yescharacteristic
52C2×D3×C22⋊C4C2211yescharacteristic
53C2×D3×C22⋊C4C2214yes—
54C2×D3×C22⋊C4C2212yes—
55C2×C4×D12C2211yescharacteristic
56C2×C42×D3C2211yescharacteristic
57C3×#398C2212yescomplemented
58C3×#397C2212yescomplemented
59C3×#389C2212yescomplemented
60C3×#381C2212yescomplemented
61C3×#380C2211yescharacteristic, complemented
62C3×#380C2212yescomplemented
63#5212C2211yescharacteristic, complemented
64#5212C2212yescomplemented
65#5211C2212yescomplemented
66#4992C2212yescomplemented
67#4987C2212yescomplemented
68#4987C2212yescomplemented
69#4987C2212yescomplemented
70#4984C2212yescomplemented
71#4983C2212yescomplemented
72#4982C2214yescomplemented
73#4981C2212yescomplemented
74#4976C2214yescomplemented
75#4972C2212yescomplemented
76#4953C2212yescomplemented
77#4952C2214yescomplemented
78#4943C2212yescomplemented
79#4943C2212yescomplemented
80#4942C2212yescomplemented
81#4942C2214yescomplemented
82#4928C2212yescomplemented
83#4675C2214yescomplemented
84#4674C2212yescomplemented
85#4667C2214yescomplemented
86#4667C2212yescomplemented
87#4664C2214yescomplemented
88#4664C2214yescomplemented
89D3×#95C2212yes—
90D3×#95C2214yes—
91D3×#95C2214yes—
92#4661C2212yescomplemented
93#4657C2214yescomplemented
94#4647C2214yescomplemented
95C22×#123—32no—
96C22×C4×D4—31no—
97C23×C4⋊C4—31no—
98#2486—32no—
99#2486—32no—
100#2486—32no—
101#2486—32no—
102#2486—31no—
103#2486—32no—
104#2486—32no—
105#2486—31no—
106#2486—31no—
107#2486D311yescharacteristic, direct product factor
108C2×#398—32no—
109C2×#397—32no—
110C2×#389—32no—
111C2×#381—32no—
112C2×#380—32no—
113C2×#380—31no—
114C24×D3C2311yescharacteristic
115C24×D3C2311yescharacteristic
116C22×C3×D4C2311yescharacteristic
117C23×C3×C4C2312yes—
118C23×C3×C4C2311yescharacteristic
119C23×C3×C4C2311yescharacteristic
120C22×#67C2311yescharacteristic
121C22×#67C2311yescharacteristic
122C23×Dic3C2311yescharacteristic
123C23×Dic3C2312yes—
124C23×Dic3C2311yescharacteristic
125C2×D3×D4—24no—
126C2×D3×D4—24no—
127C2×D3×D4D418yes—
128C22×D12C2311yescharacteristic
129C22×C4×D3—28no—
130C22×C4×D3—28no—
131C22×C4×D3—28no—
132C22×C4×D3—28no—
133C22×C4×D3—24no—
134C22×C4×D3—28no—
135C22×C4×D3D418yes—
136C22×C4×D3C2311yescharacteristic
137C22×C4×D3C2311yescharacteristic
138C22×C4×D3C2314yes—
139C22×C4×D3C2314yes—
140C22×C4×D3C2314yes—
141C22×C4×D3C2311yescharacteristic
142C22×C4×D3C2311yescharacteristic
143C22×C4×D3C2311yescharacteristic
144C22×C4×D3C2311yescharacteristic
145C22×C4×D3C2311yescharacteristic
146C22×C4×D3C2311yescharacteristic
147C22×C4×D3C2311yescharacteristic
148C3×#123—28no—
149C3×C4×D4—24no—
150C2×C3×C4⋊C4—24no—
151C2×C3×C4⋊C4C2312yes—
152C2×C3×C4⋊C4C2314yes—
153C2×C3×C4⋊C4C2311yescharacteristic
154C2×C3×C4⋊C4C2312yes—
155C2×C3×C4⋊C4C2312yes—
156C2×C3×C22⋊C4C2312yes—
157C2×C3×C22⋊C4C2314yes—
158C2×C3×C22⋊C4C2311yescharacteristic
159C2×C3×C22⋊C4C2311yescharacteristic
160C2×C3×C42C2311yescharacteristic
161C2×#217C2312yes—
162C2×#217C2314yes—
163C2×#217C2311yescharacteristic
164C2×#217C2311yescharacteristic
165#935—28no—
166D4×Dic3—24no—
167#929—28no—
168C4×#67—24no—
169C4×#67—24no—
170C2×(C2×D3)⋊C4C2311yescharacteristic
171C2×(C2×D3)⋊C4C2311yescharacteristic
172C2×(C2×D3)⋊C4C2314yes—
173C2×(C2×D3)⋊C4C2314yes—
174C2×(C2×D3)⋊C4C2314yes—
175C2×(C2×D3)⋊C4C2311yescharacteristic
176C2×(C2×D3)⋊C4C2311yescharacteristic
177C2×C4⋊Dic3—24no—
178C2×C4⋊Dic3C2314yes—
179C2×C4⋊Dic3C2312yes—
180C2×C4⋊Dic3C2312yes—
181C2×C4⋊Dic3C2312yes—
182C2×C4⋊Dic3C2311yescharacteristic
183C2×Dic3⋊C4—28no—
184C2×Dic3⋊C4C2314yes—
185C2×Dic3⋊C4C2314yes—
186C2×Dic3⋊C4C2314yes—
187C2×Dic3⋊C4C2311yescharacteristic
188C2×Dic3⋊C4C2314yes—
189C2×Dic3⋊C4C2311yescharacteristic
190C2×Dic3⋊C4C2314yes—
191C2×C4×Dic3C2311yescharacteristic
192C2×C4×Dic3C2311yescharacteristic
193C2×C4×Dic3C2311yescharacteristic
194#894—216no—
195#893—24no—
196D3×C4⋊C4—216no—
197D3×C4⋊C4—28no—
198D3×C4⋊C4—28no—
199D3×C4⋊C4—28no—
200D3×C4⋊C4—28no—
201D3×C4⋊C4—24no—
202D3×C4⋊C4—28no—
203#886—28no—
204#883—216no—
205#67⋊C4—24no—
206#67⋊C4—24no—
207D3×C22⋊C4—28no—
208D3×C22⋊C4—216no—
209D3×C22⋊C4—24no—
210D3×C22⋊C4—24no—
211C4×D12—24no—
212C42×D3—24no—
213C3×#95C2314yes—
214C3×#95C2314yes—
215C3×#95C2312yes—
216C3⋊#95C2314yes—
217C3⋊#95C2314yes—
218C3⋊#95C2314yes—
219C3⋊#95C2314yes—
220C3⋊#95C2314yes—
221C3⋊#95C2314yes—
222C3⋊#95C2314yes—
223C3⋊#95C2312yes—
224C23×D4—31no—
225C24×C4—31no—
226C24×C4—32no—
227C24×C4—31no—
228C2×#123—32no—
229C2×#123—32no—
230C2×#123—34no—
231C2×#123—34no—
232C2×#123—32no—
233C2×#123—616no—
234C2×#123C2×D312yes—
235C2×C4×D4—31no—
236C2×C4×D4—31no—
237C2×C4×D4—31no—
238C2×C4×D4—31no—
239C2×C4×D4—31no—
240C2×C4×D4—31no—
241C2×C4×D4—31no—
242C2×C4×D4—68no—
243C2×C4×D4C2×D311yescharacteristic
244C22×C4⋊C4—32no—
245C22×C4⋊C4—31no—
246C22×C4⋊C4—32no—
247C22×C4⋊C4—31no—
248C22×C4⋊C4—34no—
249C22×C4⋊C4—32no—
250C22×C4⋊C4—32no—
251C22×C4⋊C4—32no—
252C22×C4⋊C4—32no—
253C22×C4⋊C4—68no—
254C22×C4⋊C4C2×D311yescharacteristic, complemented
255C22×C22⋊C4—31no—
256C22×C22⋊C4—34no—
257C22×C22⋊C4—31no—
258C22×C22⋊C4—32no—
259C22×C42—31no—
260#398—32no—
261#398—34no—
262#398—32no—
263#398—34no—
264#398—32no—
265#398C2×D312yescomplemented
266#397—32no—
267#397—34no—
268#397—32no—
269#397—32no—
270#397—34no—
271#397C2×D312yescomplemented
272#389—32no—
273#389—34no—
274#389—32no—
275#389—32no—
276#389—34no—
277#389C2×D312yescomplemented
278#381—32no—
279#381—32no—
280#381—32no—
281#381—34no—
282#381—34no—
283#381C2×D312yescomplemented
284#380—32no—
285#380—31no—
286#380—32no—
287#380—32no—
288#380—32no—
289#380—34no—
290#380—32no—
291#380—34no—
292#380—32no—
293#380C2×D312yescomplemented
294#380C2×D311yescharacteristic, complemented
295C2×#95—32no—
296C2×#95—34no—
297C2×#95—34no—
298C24×C3C2411yescharacteristic
299C24×C3C2411yescharacteristic
300C23×D3—24no—
301C23×D3—24no—
302C23×D3—22no—
303C23×D3—24no—
304C23×D3—22no—
305C23×D3—24no—
306C23×D3C2×D414yes—
307C23×D3C2×D414yes—
308C23×D3C2×D414yes—
309C23×D3#4114yes—
310C23×D3C2411yescharacteristic
311C23×D3C2411yescharacteristic
312C23×D3C2411yescharacteristic
313C2×C3×D4—22no—
314C2×C3×D4—22no—
315C2×C3×D4C2×D414yes—
316C22×C3×C4—24no—
317C22×C3×C4—24no—
318C22×C3×C4—24no—
319C22×C3×C4—24no—
320C22×C3×C4—22no—
321C22×C3×C4—24no—
322C22×C3×C4C2×D414yes—
323C22×C3×C4C2411yescharacteristic
324C22×C3×C4C2411yescharacteristic
325C22×C3×C4C2414yes—
326C22×C3×C4C2414yes—
327C22×C3×C4C2411yescharacteristic
328C22×C3×C4C2411yescharacteristic
329C22×C3×C4C2411yescharacteristic
330C2×#67—22no—
331C2×#67—22no—
332C2×#67—22no—
333C2×#67—22no—
334C2×#67C2×D414yes—
335C2×#67C2×D414yes—
336C22×Dic3—24no—
337C22×Dic3—24no—
338C22×Dic3—24no—
339C22×Dic3—24no—
340C22×Dic3—22no—
341C22×Dic3—24no—
342C22×Dic3C2×D414yes—
343C22×Dic3C2411yescharacteristic
344C22×Dic3C2411yescharacteristic
345C22×Dic3C2414yes—
346C22×Dic3C2414yes—
347C22×Dic3C2411yescharacteristic
348C22×Dic3C2411yescharacteristic
349C22×Dic3C2411yescharacteristic
350D3×D4—232no—
351C2×D12—22no—
352C2×D12—22no—
353C2×D12C2×D414yes—
354C2×C4×D3—22no—
355C2×C4×D3—24no—
356C2×C4×D3—22no—
357C2×C4×D3—24no—
358C2×C4×D3—24no—
359C2×C4×D3—232no—
360C2×C4×D3—22no—
361C2×C4×D3—28no—
362C2×C4×D3—28no—
363C2×C4×D3—22no—
364C2×C4×D3—28no—
365C2×C4×D3—28no—
366C2×C4×D3—28no—
367C2×C4×D3—28no—
368C2×C4×D3—28no—
369C2×C4×D3—28no—
370C2×C4×D3—24no—
371C2×C4×D3—24no—
372C2×C4×D3—28no—
373C2×C4×D3—22no—
374C2×C4×D3—24no—
375C2×C4×D3—22no—
376C2×C4×D3—24no—
377C2×C4×D3—432no—
378C2×C4×D3—416no—
379C2×C4×D3C2×D414yes—
380C2×C4×D3C2×D414yes—
381C2×C4×D3C2×D414yes—
382C2×C4×D3C2×D414yes—
383C2×C4×D3C2×D414yes—
384C2×C4×D3#4118yes—
385C3×C4⋊C4—24no—
386C3×C4⋊C4—24no—
387C3×C4⋊C4—22no—
388C3×C4⋊C4—28no—
389C3×C4⋊C4—24no—
390C3×C22⋊C4—22no—
391C3×C22⋊C4—28no—
392C3×C22⋊C4—24no—
393C3×C22⋊C4—22no—
394C3×C42—22no—
395#217—28no—
396#217—22no—
397#217—24no—
398#217—22no—
399(C2×D3)⋊C4—22no—
400(C2×D3)⋊C4—28no—
401(C2×D3)⋊C4—28no—
402(C2×D3)⋊C4—22no—
403(C2×D3)⋊C4—28no—
404(C2×D3)⋊C4—22no—
405(C2×D3)⋊C4—22no—
406C4⋊Dic3—24no—
407C4⋊Dic3—24no—
408C4⋊Dic3—24no—
409C4⋊Dic3—22no—
410C4⋊Dic3—28no—
411Dic3⋊C4—22no—
412Dic3⋊C4—28no—
413Dic3⋊C4—22no—
414Dic3⋊C4—28no—
415Dic3⋊C4—28no—
416Dic3⋊C4—28no—
417Dic3⋊C4—28no—
418C4×Dic3—22no—
419C4×Dic3—22no—
420C4×Dic3—22no—
421C25—31no—
422C25—31no—
423C22×D4—31no—
424C22×D4—31no—
425C22×D4—38no—
426C22×D4—31no—
427C22×D4—64no—
428C22×D4—64no—
429C22×D4C22×D311yescharacteristic
430C23×C4—31no—
431C23×C4—31no—
432C23×C4—38no—
433C23×C4—31no—
434C23×C4—31no—
435C23×C4—31no—
436C23×C4—31no—
437C23×C4—32no—
438C23×C4—31no—
439C23×C4—34no—
440C23×C4—31no—
441C23×C4—34no—
442C23×C4—31no—
443C23×C4—34no—
444C23×C4—31no—
445C23×C4—31no—
446C23×C4—68no—
447C23×C4—64no—
448C23×C4—68no—
449C23×C4—68no—
450C23×C4—68no—
451C23×C4—68no—
452C23×C4C22×D312yes—
453C23×C4C22×D311yescharacteristic
454C23×C4C22×D311yescharacteristic
455#123—28no—
456#123—616no—
457#123—68no—
458#123—616no—
459#123—68no—
460#123—68no—
461C4×D4—24no—
462C4×D4—64no—
463C4×D4—64no—
464C4×D4—64no—
465C4×D4—64no—
466C4×D4—64no—
467C4×D4—64no—
468C4×D4—64no—
469C2×C4⋊C4—24no—
470C2×C4⋊C4—34no—
471C2×C4⋊C4—32no—
472C2×C4⋊C4—34no—
473C2×C4⋊C4—32no—
474C2×C4⋊C4—31no—
475C2×C4⋊C4—31no—
476C2×C4⋊C4—31no—
477C2×C4⋊C4—34no—
478C2×C4⋊C4—34no—
479C2×C4⋊C4—34no—
480C2×C4⋊C4—34no—
481C2×C4⋊C4—32no—
482C2×C4⋊C4—68no—
483C2×C4⋊C4—68no—
484C2×C4⋊C4—68no—
485C2×C4⋊C4—68no—
486C2×C4⋊C4—64no—
487C2×C4⋊C4—616no—
488C2×C4⋊C4—68no—
489C2×C4⋊C4—68no—
490C2×C4⋊C4—64no—
491C2×C4⋊C4C22×D312yes—
492C2×C4⋊C4C22×D312yes—
493C2×C4⋊C4C22×D311yescharacteristic
494C2×C4⋊C4C22×D314yes—
495C2×C4⋊C4C22×D312yes—
496C2×C22⋊C4—31no—
497C2×C22⋊C4—31no—
498C2×C22⋊C4—32no—
499C2×C22⋊C4—34no—
500C2×C22⋊C4—31no—
501C2×C22⋊C4—31no—
502C2×C22⋊C4—31no—
503C2×C22⋊C4—31no—
504C2×C22⋊C4—34no—
505C2×C22⋊C4—34no—
506C2×C22⋊C4—34no—
507C2×C22⋊C4—64no—
508C2×C22⋊C4—64no—
509C2×C22⋊C4—68no—
510C2×C22⋊C4—616no—
511C2×C22⋊C4C22×D311yescharacteristic
512C2×C22⋊C4C22×D311yescharacteristic
513C2×C22⋊C4C22×D312yes—
514C2×C22⋊C4C22×D314yes—
515C2×C42—31no—
516C2×C42—31no—
517C2×C42—31no—
518C2×C42—64no—
519C2×C42C22×D311yescharacteristic
520#95—34no—
521#95—34no—
522#95—34no—
523#95—34no—
524#95—32no—
525#95—34no—
526#95—34no—
527#95—34no—
528#95C22×D314yes—
529#95C22×D312yes—
530#95C22×D314yes—
531C23×C3—22no—
532C23×C3—22no—
533C23×C3—21no—
534C23×C3—22no—
535C23×C3—21no—
536C23×C3—22no—
537C23×C3C22×D412yes—
538C23×C3C22×D412yes—
539C23×C3C22×D412yes—
540C23×C3C2×#4112yes—
541C23×C3C2511yescharacteristic
542C22×D3—22no—
543C22×D3—22no—
544C22×D3—28no—
545C22×D3—28no—
546C22×D3—216no—
547C22×D3—216no—
548C22×D3—21no—
549C22×D3—22no—
550C22×D3—21no—
551C22×D3—22no—
552C22×D3—28no—
553C22×D3—216no—
554C22×D3—44no—
555C22×D3—44no—
556C22×D3—48no—
557C22×D3#121116yes—
558C22×D3C22×D412yes—
559C22×D3C22×D412yes—
560C22×D3C22×D412yes—
561C22×D3C22×D412yes—
562C22×D3C22×D412yes—
563C22×D3C2×#4112yes—
564C22×D3C2×#4112yes—
565C22×D3C2×#4114yes—
566C22×D32−1+414yes—
567C3×D4—28no—
568C2×C3×C4—21no—
569C2×C3×C4—22no—
570C2×C3×C4—21no—
571C2×C3×C4—28no—
572C2×C3×C4—21no—
573C2×C3×C4—24no—
574C2×C3×C4—24no—
575C2×C3×C4—21no—
576C2×C3×C4—24no—
577C2×C3×C4—24no—
578C2×C3×C4—24no—
579C2×C3×C4—22no—
580C2×C3×C4—22no—
581C2×C3×C4—24no—
582C2×C3×C4—48no—
583C2×C3×C4—44no—
584C2×C3×C4C22×D412yes—
585C2×C3×C4C22×D412yes—
586C2×C3×C4C22×D412yes—
587C2×C3×C4C2×#4114yes—
588#67—28no—
589#67—28no—
590C2×Dic3—21no—
591C2×Dic3—22no—
592C2×Dic3—21no—
593C2×Dic3—28no—
594C2×Dic3—21no—
595C2×Dic3—24no—
596C2×Dic3—24no—
597C2×Dic3—24no—
598C2×Dic3—21no—
599C2×Dic3—24no—
600C2×Dic3—24no—
601C2×Dic3—22no—
602C2×Dic3—22no—
603C2×Dic3—24no—
604C2×Dic3—48no—
605C2×Dic3—44no—
606C2×Dic3C22×D412yes—
607C2×Dic3C22×D412yes—
608C2×Dic3C22×D412yes—
609C2×Dic3C2×#4114yes—
610D12—28no—
611C4×D3—28no—
612C4×D3—28no—
613C4×D3—28no—
614C4×D3—28no—
615C4×D3—416no—
616C4×D3—416no—
617C4×D3—44no—
618C4×D3—44no—
619C4×D3—416no—
620C4×D3—44no—
621C4×D3—44no—
622C4×D3#123116yescomplemented
623C24—31no—
624C24—34no—
625C24—34no—
626C24—34no—
627C24—31no—
628C24—34no—
629C24—31no—
630C24—64no—
631C24—64no—
632C24—62no—
633C24—64no—
634C24—62no—
635C24—64no—
636C24C23×D311yescharacteristic
637C24C23×D311yescharacteristic
638C2×D4—22no—
639C2×D4—22no—
640C2×D4—34no—
641C2×D4—34no—
642C2×D4—34no—
643C2×D4—62no—
644C2×D4—62no—
645C2×D4—632no—
646C2×D4—62no—
647C2×D4—62no—
648C2×D4—62no—
649C2×D4—62no—
650C2×D4D3×D414yes—
651C22×C4—24no—
652C22×C4—24no—
653C22×C4—24no—
654C22×C4—24no—
655C22×C4—22no—
656C22×C4—24no—
657C22×C4—31no—
658C22×C4—34no—
659C22×C4—38no—
660C22×C4—34no—
661C22×C4—31no—
662C22×C4—31no—
663C22×C4—34no—
664C22×C4—34no—
665C22×C4—34no—
666C22×C4—34no—
667C22×C4—31no—
668C22×C4—31no—
669C22×C4—34no—
670C22×C4—34no—
671C22×C4—64no—
672C22×C4—632no—
673C22×C4—62no—
674C22×C4—64no—
675C22×C4—62no—
676C22×C4—64no—
677C22×C4—62no—
678C22×C4—62no—
679C22×C4—68no—
680C22×C4—62no—
681C22×C4—68no—
682C22×C4—68no—
683C22×C4—68no—
684C22×C4—68no—
685C22×C4—68no—
686C22×C4—64no—
687C22×C4—68no—
688C22×C4—68no—
689C22×C4—68no—
690C22×C4—64no—
691C22×C4—64no—
692C22×C4—62no—
693C22×C4—64no—
694C22×C4—64no—
695C22×C4—64no—
696C22×C4—64no—
697C22×C4—64no—
698C22×C4—62no—
699C22×C4—64no—
700C22×C4—1216no—
701C22×C4—1232no—
702C22×C4D3×D414yes—
703C22×C4C23×D311yescharacteristic
704C22×C4C23×D311yescharacteristic
705C22×C4C23×D314yes—
706C22×C4C23×D314yes—
707C22×C4C23×D311yescharacteristic
708C22×C4C23×D311yescharacteristic
709C22×C4C23×D311yescharacteristic
710C4⋊C4—24no—
711C4⋊C4—24no—
712C4⋊C4—22no—
713C4⋊C4—28no—
714C4⋊C4—24no—
715C4⋊C4—68no—
716C4⋊C4—68no—
717C4⋊C4—62no—
718C4⋊C4—62no—
719C4⋊C4—68no—
720C4⋊C4—68no—
721C4⋊C4—68no—
722C4⋊C4—64no—
723C4⋊C4—64no—
724C4⋊C4—62no—
725C4⋊C4—68no—
726C4⋊C4—64no—
727C22⋊C4—22no—
728C22⋊C4—24no—
729C22⋊C4—28no—
730C22⋊C4—22no—
731C22⋊C4—62no—
732C22⋊C4—62no—
733C22⋊C4—62no—
734C22⋊C4—68no—
735C22⋊C4—68no—
736C22⋊C4—68no—
737C22⋊C4—62no—
738C22⋊C4—62no—
739C22⋊C4—64no—
740C22⋊C4—68no—
741C22⋊C4—62no—
742C42—22no—
743C42—62no—
744C42—62no—
745C42—62no—
746C22×C3—22no—
747C22×C3—22no—
748C22×C3—24no—
749C22×C3—24no—
750C22×C3—22no—
751C22×C3—24no—
752C22×C3—41no—
753C22×C3—41no—
754C22×C3—42no—
755C22×C3C2×#12114yes—
756C22×C3C23×D411yescharacteristic
757C22×C3C23×D411yescharacteristic
758C22×C3C22×#4111yescharacteristic
759C22×C3C22×#4112yes—
760C22×C3C2×2−1+412yes—
761C2×D3—22no—
762C2×D3—22no—
763C2×D3—24no—
764C2×D3—24no—
765C2×D3—232no—
766C2×D3—22no—
767C2×D3—24no—
768C2×D3—41no—
769C2×D3—41no—
770C2×D3—42no—
771C2×D3—416no—
772C2×D3C2×#12114yes—
773C2×D3C2×#12114yes—
774C2×D3C2×#12314yes—
775C2×D3#53614yes—
776C2×D3#54718yes—
777C2×D3#55218yes—
778C3×C4—22no—
779C3×C4—22no—
780C3×C4—44no—
781C3×C4—41no—
782C3×C4—41no—
783C3×C4—44no—
784C3×C4C2×#12314yescomplemented
785Dic3—22no—
786Dic3—22no—
787Dic3—44no—
788Dic3—41no—
789Dic3—41no—
790Dic3—44no—
791Dic3C2×#12314yescomplemented
792C23—22no—
793C23—22no—
794C23—21no—
795C23—22no—
796C23—21no—
797C23—22no—
798C23—32no—
799C23—32no—
800C23—34no—
801C23—32no—
802C23—34no—
803C23—32no—
804C23—32no—
805C23—32no—
806C23—316no—
807C23—32no—
808C23—68no—
809C23—616no—
810C23—68no—
811C23—616no—
812C23—68no—
813C23—616no—
814C23—62no—
815C23—62no—
816C23—61no—
817C23—62no—
818C23—61no—
819C23—62no—
820C23—124no—
821C23—128no—
822C23—124no—
823C23C2×D3×D412yes—
824C23C2×D3×D412yes—
825C23C2×D3×D412yes—
826C23D3×#4112yes—
827C23C24×D311yescharacteristic
828D4—28no—
829D4—68no—
830D4—68no—
831D4—68no—
832C2×C4—21no—
833C2×C4—22no—
834C2×C4—21no—
835C2×C4—28no—
836C2×C4—21no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—21no—
840C2×C4—24no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—24no—
846C2×C4—32no—
847C2×C4—34no—
848C2×C4—316no—
849C2×C4—32no—
850C2×C4—32no—
851C2×C4—48no—
852C2×C4—44no—
853C2×C4—68no—
854C2×C4—68no—
855C2×C4—68no—
856C2×C4—68no—
857C2×C4—61no—
858C2×C4—62no—
859C2×C4—61no—
860C2×C4—68no—
861C2×C4—61no—
862C2×C4—64no—
863C2×C4—64no—
864C2×C4—61no—
865C2×C4—64no—
866C2×C4—64no—
867C2×C4—64no—
868C2×C4—62no—
869C2×C4—62no—
870C2×C4—64no—
871C2×C4—124no—
872C2×C4—124no—
873C2×C4—1216no—
874C2×C4—1216no—
875C2×C4—124no—
876C2×C4—124no—
877C2×C4—1216no—
878C2×C4—128no—
879C2×C4—124no—
880C2×C4C2×D3×D412yes—
881C2×C4C2×D3×D412yes—
882C2×C4C2×D3×D412yes—
883C2×C4D3×#4114yes—
884C2×C3—24no—
885C2×C3—42no—
886C2×C3C22×#12111yescharacteristic
887C2×C3C22×#12311yescharacteristic
888C2×C3C2×#53611yescharacteristic
889C2×C3C2×#54712yes—
890C2×C3C2×#55212yes—
891D3—24no—
892D3—42no—
893D3#248618yesdirect product factor
894C22—24no—
895C22—22no—
896C22—24no—
897C22—22no—
898C22—24no—
899C22—22no—
900C22—38no—
901C22—34no—
902C22—38no—
903C22—34no—
904C22—34no—
905C22—34no—
906C22—42no—
907C22—41no—
908C22—41no—
909C22—632no—
910C22—64no—
911C22—62no—
912C22—64no—
913C22—62no—
914C22—64no—
915C22—62no—
916C22—1216no—
917C22—122no—
918C22—121no—
919C22—121no—
920C22D3×#12114yes—
921C22C22×D3×D411yescharacteristic
922C22C22×D3×D411yescharacteristic
923C22C2×D3×#4111yescharacteristic
924C22C2×D3×#4112yes—
925C22D3×2−1+412yes—
926C4—22no—
927C4—22no—
928C4—34no—
929C4—41no—
930C4—44no—
931C4—44no—
932C4—41no—
933C4—62no—
934C4—62no—
935C4—121no—
936C4—124no—
937C4—124no—
938C4—121no—
939C4D3×#12314yescomplemented
940C3C2×#248611yescharacteristic, complemented, Sylow
941C2—24no—
942C2—38no—
943C2—42no—
944C2—64no—
945C2—122no—
946C2C2×D3×#12111yescharacteristic
947C2C2×D3×#12311yescharacteristic
948C2D3×#53611yescharacteristic
949C2D3×#54712yes—
950C2D3×#55212yes—
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2486C2
prime radicalC22×D3×D4C22
hypercenter#2486D3
hypocenterC3C2×#2486
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2486

Complements

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

NH ≅ G/Ntype
3. C22×D3×C4⋊C4C2semidirect
4. C3×#2486C2semidirect
5. #82856C2semidirect
6. #82373C2semidirect
7. #82196C2semidirect
8. D3×#398C2semidirect
9. #77764C2semidirect
10. D3×#397C2semidirect
11. #77485C2semidirect
12. #76231C2semidirect
13. D3×#389C2semidirect
14. D3×#381C2semidirect
15. #74075C2semidirect
16. #74027C2semidirect
17. D3×#380C2semidirect
18. D3×#380C2semidirect
19. #73911C2semidirect
27. C22×C3×C4⋊C4C22semidirect
33. C22×C4⋊Dic3C22semidirect
34. C22×Dic3⋊C4C22semidirect
45. C2×D3×C4⋊C4C22semidirect
46. C2×D3×C4⋊C4C22semidirect
57. C3×#398C22semidirect
58. C3×#397C22semidirect
59. C3×#389C22semidirect
60. C3×#381C22semidirect
61. C3×#380C22semidirect
62. C3×#380C22semidirect
63. #5212C22semidirect
64. #5212C22semidirect
65. #5211C22semidirect
66. #4992C22semidirect
67. #4987C22semidirect
68. #4987C22semidirect
69. #4987C22semidirect
70. #4984C22semidirect
71. #4983C22semidirect
72. #4982C22semidirect
73. #4981C22semidirect
74. #4976C22semidirect
75. #4972C22semidirect
76. #4953C22semidirect
77. #4952C22semidirect
78. #4943C22semidirect
79. #4943C22semidirect
80. #4942C22semidirect
81. #4942C22semidirect
82. #4928C22semidirect
83. #4675C22semidirect
84. #4674C22semidirect
85. #4667C22semidirect
86. #4667C22semidirect
87. #4664C22semidirect
88. #4664C22semidirect
92. #4661C22semidirect
93. #4657C22semidirect
94. #4647C22semidirect
107. #2486D3direct (N × H)
254. C22×C4⋊C4C2×D3semidirect
265. #398C2×D3semidirect
271. #397C2×D3semidirect
277. #389C2×D3semidirect
283. #381C2×D3semidirect
293. #380C2×D3semidirect
294. #380C2×D3semidirect
622. C4×D3#123semidirect
784. C3×C4C2×#123semidirect
791. Dic3C2×#123semidirect
893. D3#2486direct (N × H)
939. C4D3×#123semidirect
940. C3C2×#2486semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#1232
C2×C4×D3×D42
C22×D3×C4⋊C42
C3×#24862
#828562
#823732
#821962
D3×#3982
#777642
D3×#3972
#774852
#762312
D3×#3892
D3×#3812
#740752
#740272
D3×#3802
#739112
C2×#24863