Finite Group Databasebeta

← D3×#3165 #11664830

Subgroups — D3×#3165 #11664830

Order 768.

2118 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#533C211yesmaximal, characteristic
2C2×D3×C4⋊Q8C211yesmaximal, characteristic
3C3×#3165C211yesmaximal, characteristic, complemented
4#83341C211yesmaximal, characteristic, complemented
5#83207C211yesmaximal, characteristic, complemented
6#81976C214yesmaximal, complemented
7D3×#501C214yesmaximal, complemented
8#81940C212yesmaximal, complemented
9D3×#500C212yesmaximal, complemented
10#81893C212yesmaximal, complemented
11D3×#498C212yesmaximal, complemented
12D3×#428C214yesmaximal
13#79203C214yesmaximal, complemented
14C4×D3×M16C211yesmaximal, characteristic
15#78506C211yesmaximal, characteristic, complemented
16C2×#3165—31nomaximal, Sylow
17C22×D3×Q8—21no—
18C3×#533C2211yescharacteristic
19C2×C3×C4⋊Q8C2211yescharacteristic
20C2×#944—21no—
21C2×D3×M16C2212yes—
22#5728C2211yescharacteristic
23#5728C2211yescharacteristic
24D3×C4⋊Q8—21no—
25D3×C4⋊Q8—21no—
26D3×C4⋊Q8—21no—
27D3×C4⋊Q8—21no—
28D3×C4⋊Q8C2211yescharacteristic
29D3×C4⋊Q8C2211yescharacteristic
30D3×C4⋊Q8C2212yes—
31D3×C4⋊Q8C2212yes—
32D3×C4⋊Q8C2212yes—
33D3×C4⋊Q8C2212yes—
34#5688C2212yes—
35D3×#125C2212yes—
36D3×C22⋊Q8—21no—
37D3×C22⋊Q8—21no—
38#5622—21no—
39#5622—21no—
40#5578—21no—
41#5578—21no—
42C4×D3×Q8—21no—
43C4×D3×Q8—21no—
44D3×#117C2212yes—
45#5517C2212yes—
46C2×D3×C4⋊C4—21no—
47C2×D3×C4⋊C4C2212yes—
48C2×#888—21no—
49C2×#888C2212yes—
50C2×C42×D3C2211yescharacteristic
51#5470C2211yescharacteristic
52C2×#869C2211yescharacteristic
53C3×#501C2214yescomplemented
54C3×#500C2212yescomplemented
55C3×#498C2212yescomplemented
56C3×#428C2214yes—
57C3×C4×M16C2211yescharacteristic
58#5121C2214yes—
59Dic3×M16C2212yes—
60#5081C2214yescomplemented
61#5080C2212yescomplemented
62#5080C2212yescomplemented
63#5078C2212yescomplemented
64#5078C2212yescomplemented
65#5064C2214yescomplemented
66#4995C2214yes—
67#4964C2214yes—
68C4×#208C2211yescharacteristic
69#4881C2218yes—
70D3×#107C2218yes—
71#4876C2218yescomplemented
72#4874C2218yescomplemented
73#4861C2218yes—
74D3×#106C2218yes—
75#4856C2218yescomplemented
76#4855C2218yescomplemented
77#4707C2212yes—
78D3×#97C2212yes—
79#4702C2214yescomplemented
80C4×ΓL(1,𝔽25)C2212yes—
81C4×D3×C8C2212yes—
82#4682C2212yescomplemented
83#4680C2212yescomplemented
84C2×#533—31no—
85C22×C4⋊Q8—31no—
86#3165—34no—
87#3165—32no—
88#3165—32no—
89#3165—34no—
90#3165—31no—
91#3165—31no—
92#3165—31no—
93#3165D311yescharacteristic, direct product factor
94C2×#501—34no—
95C2×#500—32no—
96C2×#498—32no—
97C2×#428—34no—
98C2×C4×M16—31no—
99C22×C3×Q8—21no—
100C2×D3×Q8—22no—
101C2×D3×Q8—22no—
102C2×D3×Q8—22no—
103C2×D3×Q8—22no—
104C2×D3×Q8—21no—
105C2×D3×Q8—21no—
106C2×D3×Q8—48no—
107C22×C4×D3—22no—
108C22×C4×D3D411yescharacteristic
109C22×C4×D3D411yescharacteristic
110C22×C4×D3C2311yescharacteristic
111C22×Dic6—21no—
112C22×Dic6—22no—
113C2×C3×M16C2312yes—
114C3×C4⋊Q8—21no—
115C3×C4⋊Q8—21no—
116C3×C4⋊Q8C2312yes—
117C3×C4⋊Q8C2312yes—
118C3×C4⋊Q8C2311yescharacteristic
119C3×C4⋊Q8C2311yescharacteristic
120C3×#125C2312yes—
121C3×C22⋊Q8—21no—
122C3×C22⋊Q8—21no—
123C3×C4×Q8—21no—
124C3×C4×Q8—21no—
125C3×#117C2312yes—
126C2×C3×C4⋊C4—21no—
127C2×C3×C4⋊C4C2312yes—
128C2×C3×C42C2311yescharacteristic
129#946—21no—
130#946—21no—
131Q8×Dic3—21no—
132Q8×Dic3—21no—
133#944—22no—
134#944—22no—
135#944—22no—
136#944—22no—
137#944—21no—
138#944—21no—
139#926C2312yes—
140C2×C4⋊Dic3—21no—
141C2×C4⋊Dic3C2312yes—
142#924—21no—
143#924—21no—
144C2×Dic3⋊C4—22no—
145C2×Dic3⋊C4—22no—
146C2×C4×Dic3D411yescharacteristic
147C2×C4×Dic3D411yescharacteristic
148C2×C4×Dic3C2311yescharacteristic
149C2×#208C2312yes—
150D3×M16Q8116yescomplemented
151C2×ΓL(1,𝔽25)C2314yes—
152C2×D3×C8C2314yes—
153#897—21no—
154#897—21no—
155#896—22no—
156#896—22no—
157#892C2312yes—
158#892C2312yes—
159D3×C4⋊C4—22no—
160D3×C4⋊C4—22no—
161D3×C4⋊C4—22no—
162D3×C4⋊C4—22no—
163D3×C4⋊C4—22no—
164D3×C4⋊C4—22no—
165D3×C4⋊C4—22no—
166D3×C4⋊C4—22no—
167D3×C4⋊C4—21no—
168D3×C4⋊C4—21no—
169D3×C4⋊C4C2312yes—
170D3×C4⋊C4C2314yes—
171D3×C4⋊C4C2314yes—
172D3×C4⋊C4C2312yes—
173#890C2312yes—
174#890C2312yes—
175#889—22no—
176#889—22no—
177#888—22no—
178#888—22no—
179#888—22no—
180#888—22no—
181#888—22no—
182#888—22no—
183#888—21no—
184#888—21no—
185#888C2312yes—
186#888C2314yes—
187#888C2314yes—
188#888C2312yes—
189#887—22no—
190#887—22no—
191#887—21no—
192#887—21no—
193D3×C22⋊C4—22no—
194#878—22no—
195#878—22no—
196#877—22no—
197#872—22no—
198C42×D3—22no—
199C42×D3D411yescharacteristic
200C42×D3D411yescharacteristic
201C42×D3D411yescharacteristic
202C42×D3D411yescharacteristic
203C42×D3C2311yescharacteristic
204C42×D3C2311yescharacteristic
205C42×D3C2311yescharacteristic
206C42×D3C2311yescharacteristic
207#870C2312yes—
208#869—21no—
209#869—21no—
210#869C2311yescharacteristic
211#869C2312yes—
212#869C2311yescharacteristic
213#869C2312yes—
214C4×Dic6—21no—
215C4×Dic6—21no—
216C4×Dic6—22no—
217C4×Dic6—22no—
218C3×#107C2318yes—
219C3×#106C2318yes—
220C3×#97C2312yes—
221C3×C4×C8C2312yes—
222#818C2318yes—
223#817C2318yes—
224#815C2314yes—
225C8×Dic3C2314yes—
226#808C2318yes—
227#808C2318yes—
228#807C2318yes—
229#807C2318yes—
230#803C2312yes—
231C4×C3⋊C8C2312yes—
232C23×Q8—61no—
233C22×M16—32no—
234#533—31no—
235#533—31no—
236#533—32no—
237#533—32no—
238#533—31no—
239#533—61no—
240#533—61no—
241#533—61no—
242#533—61no—
243#533C2×D311yescharacteristic
244C2×C4⋊Q8—31no—
245C2×C4⋊Q8—32no—
246C2×C4⋊Q8—31no—
247C2×C4⋊Q8—32no—
248C2×C4⋊Q8—32no—
249C2×C4⋊Q8—32no—
250C2×C4⋊Q8—32no—
251C2×C4⋊Q8—31no—
252C2×C4⋊Q8—61no—
253C2×C4⋊Q8—61no—
254C2×C4⋊Q8—61no—
255C2×C4⋊Q8—61no—
256C2×C4⋊Q8—61no—
257C2×C4⋊Q8—61no—
258C2×C4⋊Q8C2×D311yescharacteristic
259C2×#125—32no—
260C2×C22⋊Q8—61no—
261C2×C22⋊Q8—61no—
262C2×C4×Q8—61no—
263C2×C4×Q8—61no—
264C2×#117—32no—
265C22×C4⋊C4—32no—
266C22×C4⋊C4—61no—
267C22×C42—31no—
268#501—34no—
269#501—34no—
270#501—38no—
271#501—38no—
272#501—34no—
273#501C2×D314yescomplemented
274#500—32no—
275#500—32no—
276#500—38no—
277#500—32no—
278#500C2×D312yescomplemented
279#498—32no—
280#498—32no—
281#498—38no—
282#498—32no—
283#498C2×D312yescomplemented
284#428—34no—
285#428—34no—
286#428—34no—
287#428—38no—
288#428—38no—
289#428C2×D314yes—
290C2×#107—38no—
291C2×#106—38no—
292C4×M16—32no—
293C4×M16—31no—
294C4×M16—32no—
295C4×M16—32no—
296C4×M16C2×D311yescharacteristic
297C2×#97—32no—
298C2×C4×C8—32no—
299C23×D3C2×D411yescharacteristic
300C2×C3×Q8—22no—
301C2×C3×Q8—22no—
302C2×C3×Q8—21no—
303C2×C3×Q8—21no—
304C2×C3×Q8—44no—
305C22×C3×C4—22no—
306C22×C3×C4C2×D411yescharacteristic
307C22×C3×C4C2×D411yescharacteristic
308C22×C3×C4C2411yescharacteristic
309C22×Dic3—22no—
310C22×Dic3C2×D411yescharacteristic
311C22×Dic3C2×D411yescharacteristic
312C22×Dic3C2×D411yescharacteristic
313D3×Q8—48no—
314D3×Q8—48no—
315D3×Q8—48no—
316D3×Q8—44no—
317D3×Q8—48no—
318D3×Q8—44no—
319C2×C4×D3—24no—
320C2×C4×D3—24no—
321C2×C4×D3—22no—
322C2×C4×D3—22no—
323C2×C4×D3—24no—
324C2×C4×D3—24no—
325C2×C4×D3—48no—
326C2×C4×D3C2×D411yescharacteristic
327C2×C4×D3C2×D411yescharacteristic
328C2×C4×D3C2×D411yescharacteristic
329C2×C4×D3C2×D411yescharacteristic
330C2×C4×D3C2×D411yescharacteristic
331C2×C4×D3C2×D411yescharacteristic
332C2×C4×D3C2×D411yescharacteristic
333C2×C4×D3C2×D411yescharacteristic
334C2×C4×D3C2×D411yescharacteristic
335C2×C4×D3C2×D411yescharacteristic
336C2×C4×D3C2×Q818yes—
337C2×C4×D3C2411yescharacteristic
338C2×C4×D3C2411yescharacteristic
339C2×Dic6—21no—
340C2×Dic6—21no—
341C2×Dic6—22no—
342C2×Dic6—22no—
343C2×Dic6—22no—
344C2×Dic6—22no—
345C2×Dic6—24no—
346C2×Dic6—24no—
347C2×Dic6—48no—
348C2×Dic6—44no—
349C3×M16C2×Q818yescomplemented
350C2×C3×C8C2414yes—
351C3×C4⋊C4—21no—
352C3×C4⋊C4—21no—
353C3×C4⋊C4—22no—
354C3×C4⋊C4—22no—
355C3×C4⋊C4—22no—
356C3×C4⋊C4—22no—
357C3×C4⋊C4—22no—
358C3×C4⋊C4C2412yes—
359C3×C4⋊C4C2414yes—
360C3×C4⋊C4C2412yes—
361C3×C22⋊C4—22no—
362C3×C42—22no—
363C3×C42C2×D411yescharacteristic
364C3×C42C2×D411yescharacteristic
365C3×C42C2411yescharacteristic
366C3×C42C2411yescharacteristic
367#217—22no—
368(C2×D3)⋊C4—22no—
369(C2×D3)⋊C4—22no—
370C4⋊Dic3—21no—
371C4⋊Dic3—21no—
372C4⋊Dic3—22no—
373C4⋊Dic3—22no—
374C4⋊Dic3—22no—
375C4⋊Dic3—22no—
376C4⋊Dic3—22no—
377C4⋊Dic3C2412yes—
378C4⋊Dic3C2414yes—
379C4⋊Dic3C2412yes—
380Dic3⋊C4—22no—
381Dic3⋊C4—22no—
382Dic3⋊C4—22no—
383Dic3⋊C4—22no—
384Dic3⋊C4—22no—
385Dic3⋊C4—22no—
386Dic3⋊C4—22no—
387Dic3⋊C4—22no—
388Dic3⋊C4—24no—
389Dic3⋊C4—24no—
390Dic3⋊C4—24no—
391Dic3⋊C4—24no—
392C4×Dic3—22no—
393C4×Dic3—22no—
394C4×Dic3—22no—
395C4×Dic3C2×D411yescharacteristic
396C4×Dic3C2×D411yescharacteristic
397C4×Dic3C2×D411yescharacteristic
398C4×Dic3C2×D411yescharacteristic
399C4×Dic3C2×D411yescharacteristic
400C4×Dic3C2×D411yescharacteristic
401C4×Dic3C2×D411yescharacteristic
402C4×Dic3C2×D411yescharacteristic
403C4×Dic3C2×D411yescharacteristic
404C4×Dic3C2×D411yescharacteristic
405C4×Dic3C2411yescharacteristic
406C4×Dic3C2411yescharacteristic
407#208C2×Q818yescomplemented
408C2×C3⋊C8C2414yes—
409ΓL(1,𝔽25)C2×Q8116yescomplemented
410D3×C8C2×Q8116yescomplemented
411C22×Q8—21no—
412C22×Q8—62no—
413C22×Q8—61no—
414C22×Q8—61no—
415C22×Q8—62no—
416C22×Q8—62no—
417C22×Q8—62no—
418C22×Q8—62no—
419C22×Q8—61no—
420C22×Q8—128no—
421C23×C4—31no—
422C23×C4—31no—
423C23×C4—31no—
424C23×C4—62no—
425C2×M16—32no—
426C2×M16—316no—
427C2×M16—34no—
428C2×M16C22×D312yes—
429C22×C8—34no—
430C4⋊Q8—21no—
431C4⋊Q8—21no—
432C4⋊Q8—34no—
433C4⋊Q8—34no—
434C4⋊Q8—32no—
435C4⋊Q8—32no—
436C4⋊Q8—32no—
437C4⋊Q8—32no—
438C4⋊Q8—31no—
439C4⋊Q8—31no—
440C4⋊Q8—62no—
441C4⋊Q8—62no—
442C4⋊Q8—62no—
443C4⋊Q8—62no—
444C4⋊Q8—62no—
445C4⋊Q8—62no—
446C4⋊Q8—61no—
447C4⋊Q8—61no—
448C4⋊Q8—62no—
449C4⋊Q8—62no—
450C4⋊Q8—62no—
451C4⋊Q8—62no—
452C4⋊Q8—61no—
453C4⋊Q8—61no—
454C4⋊Q8—61no—
455C4⋊Q8—61no—
456C4⋊Q8C22×D312yes—
457C4⋊Q8C22×D312yes—
458C4⋊Q8C22×D311yescharacteristic
459C4⋊Q8C22×D311yescharacteristic
460#125—32no—
461#125—32no—
462#125—32no—
463#125—62no—
464#125—62no—
465#125C22×D312yes—
466C22⋊Q8—21no—
467C22⋊Q8—21no—
468C22⋊Q8—62no—
469C22⋊Q8—62no—
470C22⋊Q8—62no—
471C22⋊Q8—62no—
472C22⋊Q8—61no—
473C22⋊Q8—61no—
474C22⋊Q8—61no—
475C22⋊Q8—61no—
476C22⋊Q8—61no—
477C22⋊Q8—61no—
478C4×Q8—21no—
479C4×Q8—21no—
480C4×Q8—62no—
481C4×Q8—62no—
482C4×Q8—62no—
483C4×Q8—62no—
484C4×Q8—61no—
485C4×Q8—61no—
486C4×Q8—61no—
487C4×Q8—61no—
488C4×Q8—61no—
489C4×Q8—61no—
490#117—32no—
491#117—32no—
492#117—32no—
493#117—62no—
494#117—62no—
495#117C22×D312yes—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—32no—
498C2×C4⋊C4—34no—
499C2×C4⋊C4—34no—
500C2×C4⋊C4—32no—
501C2×C4⋊C4—32no—
502C2×C4⋊C4—62no—
503C2×C4⋊C4—62no—
504C2×C4⋊C4—62no—
505C2×C4⋊C4—62no—
506C2×C4⋊C4—62no—
507C2×C4⋊C4—62no—
508C2×C4⋊C4—62no—
509C2×C4⋊C4—62no—
510C2×C4⋊C4—61no—
511C2×C4⋊C4—61no—
512C2×C4⋊C4—62no—
513C2×C4⋊C4—62no—
514C2×C4⋊C4—61no—
515C2×C4⋊C4C22×D312yes—
516C2×C22⋊C4—62no—
517C2×C42—31no—
518C2×C42—31no—
519C2×C42—31no—
520C2×C42—31no—
521C2×C42—31no—
522C2×C42—31no—
523C2×C42—31no—
524C2×C42—31no—
525C2×C42—31no—
526C2×C42—31no—
527C2×C42—31no—
528C2×C42—62no—
529C2×C42C22×D311yescharacteristic
530#107—38no—
531#107—38no—
532#107—38no—
533#107C22×D318yes—
534#106—38no—
535#106—38no—
536#106—38no—
537#106C22×D318yes—
538#97—34no—
539#97—32no—
540#97C22×D312yes—
541C4×C8—34no—
542C4×C8—32no—
543C4×C8C22×D312yes—
544C23×C3C22×D411yescharacteristic
545C22×D3—22no—
546C22×D3—22no—
547C22×D3C4⋊Q814yes—
548C22×D3C22×D411yescharacteristic
549C22×D3C22×D411yescharacteristic
550C3×Q8—44no—
551C3×Q8—44no—
552C3×Q8—42no—
553C3×Q8—42no—
554C2×C3×C4—22no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
558C2×C3×C4—24no—
559C2×C3×C4—44no—
560C2×C3×C4C22×D411yescharacteristic
561C2×C3×C4C22×D411yescharacteristic
562C2×C3×C4C22×D411yescharacteristic
563C2×C3×C4C22×D411yescharacteristic
564C2×C3×C4C22×D411yescharacteristic
565C2×C3×C4C22×Q814yes—
566C2×C3×C4C2511yescharacteristic
567C2×Dic3—22no—
568C2×Dic3—22no—
569C2×Dic3—22no—
570C2×Dic3—22no—
571C2×Dic3—24no—
572C2×Dic3—44no—
573C2×Dic3C4⋊Q814yes—
574C2×Dic3C22×D411yescharacteristic
575C2×Dic3C22×D411yescharacteristic
576C2×Dic3C22×D411yescharacteristic
577C2×Dic3C22×D411yescharacteristic
578C2×Dic3C22×D411yescharacteristic
579C2×Dic3C22×D411yescharacteristic
580C4×D3—22no—
581C4×D3—22no—
582C4×D3—22no—
583C4×D3—22no—
584C4×D3—22no—
585C4×D3—22no—
586C4×D3—48no—
587C4×D3—48no—
588C4×D3—44no—
589C4×D3—44no—
590C4×D3C4⋊Q814yes—
591C4×D3C4⋊Q814yes—
592C4×D3AGL(1,ℤ/8)14yes—
593C4×D3#13714yes—
594C4×D3C22×Q814yes—
595C4×D3C22×Q814yes—
596Dic6—48no—
597Dic6—44no—
598Dic6—44no—
599Dic6—42no—
600Dic6—42no—
601Dic6—48no—
602Dic6—44no—
603Dic6—44no—
604C3×C8C22×Q818yescomplemented
605C3⋊C8C22×Q818yescomplemented
606C24—31no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—22no—
610C2×Q8—22no—
611C2×Q8—44no—
612C2×Q8—62no—
613C2×Q8—62no—
614C2×Q8—64no—
615C2×Q8—64no—
616C2×Q8—61no—
617C2×Q8—61no—
618C2×Q8—62no—
619C2×Q8—62no—
620C2×Q8—124no—
621C2×Q8—128no—
622C2×Q8—124no—
623C2×Q8—124no—
624C2×Q8—128no—
625C2×Q8—128no—
626C2×Q8—128no—
627C2×Q8—128no—
628C22×C4—22no—
629C22×C4—31no—
630C22×C4—31no—
631C22×C4—31no—
632C22×C4—31no—
633C22×C4—31no—
634C22×C4—38no—
635C22×C4—31no—
636C22×C4—31no—
637C22×C4—31no—
638C22×C4—31no—
639C22×C4—31no—
640C22×C4—31no—
641C22×C4—31no—
642C22×C4—31no—
643C22×C4—31no—
644C22×C4—31no—
645C22×C4—64no—
646C22×C4—64no—
647C22×C4—62no—
648C22×C4—62no—
649C22×C4—64no—
650C22×C4—64no—
651C22×C4—62no—
652C22×C4—128no—
653C22×C4D3×D411yescharacteristic
654C22×C4D3×D411yescharacteristic
655C22×C4C23×D311yescharacteristic
656M16—38no—
657M16—316no—
658M16D3×Q818yescomplemented
659C2×C8—34no—
660C2×C8—316no—
661C2×C8C23×D314yes—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—22no—
666C4⋊C4—22no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—32no—
670C4⋊C4—34no—
671C4⋊C4—32no—
672C4⋊C4—64no—
673C4⋊C4—64no—
674C4⋊C4—62no—
675C4⋊C4—62no—
676C4⋊C4—64no—
677C4⋊C4—64no—
678C4⋊C4—62no—
679C4⋊C4—62no—
680C4⋊C4—62no—
681C4⋊C4—62no—
682C4⋊C4—62no—
683C4⋊C4—62no—
684C4⋊C4—62no—
685C4⋊C4—62no—
686C4⋊C4—62no—
687C4⋊C4—62no—
688C4⋊C4—62no—
689C4⋊C4—61no—
690C4⋊C4—61no—
691C4⋊C4C23×D312yes—
692C4⋊C4C23×D314yes—
693C4⋊C4C23×D312yes—
694C22⋊C4—22no—
695C22⋊C4—62no—
696C22⋊C4—62no—
697C22⋊C4—62no—
698C42—22no—
699C42—31no—
700C42—31no—
701C42—31no—
702C42—31no—
703C42—31no—
704C42—31no—
705C42—31no—
706C42—31no—
707C42—31no—
708C42—31no—
709C42—31no—
710C42—31no—
711C42—62no—
712C42—62no—
713C42—62no—
714C42D3×D411yescharacteristic
715C42D3×D411yescharacteristic
716C42C23×D311yescharacteristic
717C42C23×D311yescharacteristic
718C22×C3—21no—
719C22×C3—21no—
720C22×C3C2×C4⋊Q812yes—
721C22×C3C23×D411yescharacteristic
722C2×D3—21no—
723C2×D3—21no—
724C2×D3—28no—
725C2×D3C2×C4⋊Q812yes—
726C2×D3C2×C4⋊Q812yes—
727C2×D3C2×AGL(1,ℤ/8)12yes—
728C2×D3C2×#13712yes—
729C3×C4—21no—
730C3×C4—21no—
731C3×C4—44no—
732C3×C4—42no—
733C3×C4—42no—
734C3×C4C2×C4⋊Q812yes—
735C3×C4C2×AGL(1,ℤ/8)12yes—
736C3×C4C2×#13712yes—
737C3×C4C23×Q812yes—
738Dic3—21no—
739Dic3—21no—
740Dic3—44no—
741Dic3—42no—
742Dic3—42no—
743Dic3C2×C4⋊Q812yes—
744Dic3C2×C4⋊Q812yes—
745Dic3C2×AGL(1,ℤ/8)12yes—
746Dic3C2×#13712yes—
747C23—31no—
748C23—31no—
749C23—34no—
750C23—62no—
751C23—62no—
752C23C2×D3×D411yescharacteristic
753Q8—44no—
754Q8—44no—
755Q8—42no—
756Q8—42no—
757Q8—124no—
758Q8—128no—
759Q8—124no—
760Q8—124no—
761Q8—128no—
762Q8—124no—
763Q8—122no—
764Q8—122no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—24no—
770C2×C4—31no—
771C2×C4—31no—
772C2×C4—31no—
773C2×C4—31no—
774C2×C4—34no—
775C2×C4—34no—
776C2×C4—34no—
777C2×C4—34no—
778C2×C4—34no—
779C2×C4—34no—
780C2×C4—34no—
781C2×C4—31no—
782C2×C4—31no—
783C2×C4—44no—
784C2×C4—62no—
785C2×C4—62no—
786C2×C4—62no—
787C2×C4—62no—
788C2×C4—62no—
789C2×C4—62no—
790C2×C4—62no—
791C2×C4—62no—
792C2×C4—62no—
793C2×C4—62no—
794C2×C4—64no—
795C2×C4—128no—
796C2×C4—124no—
797C2×C4—124no—
798C2×C4—128no—
799C2×C4—124no—
800C2×C4C2×D3×D411yescharacteristic
801C2×C4C2×D3×D411yescharacteristic
802C2×C4C2×D3×D411yescharacteristic
803C2×C4C2×D3×D411yescharacteristic
804C2×C4C2×D3×D411yescharacteristic
805C2×C4C2×D3×Q814yes—
806C2×C4C24×D311yescharacteristic
807C8—38no—
808C8C2×D3×Q818yescomplemented
809C2×C3—22no—
810C2×C3C22×C4⋊Q811yescharacteristic
811C2×C3C22×AGL(1,ℤ/8)11yescharacteristic
812C2×C3C22×#13711yescharacteristic
813D3—22no—
814D3#316514yesdirect product factor
815C22—21no—
816C22—21no—
817C22—32no—
818C22—32no—
819C22—32no—
820C22—32no—
821C22—68no—
822C22—61no—
823C22—61no—
824C22D3×C4⋊Q812yes—
825C22C22×D3×D411yescharacteristic
826C4—21no—
827C4—21no—
828C4—32no—
829C4—32no—
830C4—32no—
831C4—32no—
832C4—44no—
833C4—42no—
834C4—42no—
835C4—61no—
836C4—61no—
837C4—124no—
838C4—122no—
839C4—122no—
840C4D3×C4⋊Q812yes—
841C4D3×AGL(1,ℤ/8)12yes—
842C4D3×#13712yes—
843C4C22×D3×Q812yes—
844C3C2×#316511yescharacteristic, complemented, Sylow
845C2—22no—
846C2—34no—
847C2—62no—
848C2C2×D3×C4⋊Q811yescharacteristic
849C2C2×D3×AGL(1,ℤ/8)11yescharacteristic
850C2C2×D3×#13711yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3165C2
socleC22×C3C23×D4
prime radicalC23×D3C2×D4
hypercenter#3165D3
hypocenterC3C2×#3165
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3165

Complements

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

NH ≅ G/Ntype
3. C3×#3165C2semidirect
4. #83341C2semidirect
5. #83207C2semidirect
6. #81976C2semidirect
7. D3×#501C2semidirect
8. #81940C2semidirect
9. D3×#500C2semidirect
10. #81893C2semidirect
11. D3×#498C2semidirect
13. #79203C2semidirect
15. #78506C2semidirect
53. C3×#501C22semidirect
54. C3×#500C22semidirect
55. C3×#498C22semidirect
60. #5081C22semidirect
61. #5080C22semidirect
62. #5080C22semidirect
63. #5078C22semidirect
64. #5078C22semidirect
65. #5064C22semidirect
71. #4876C22semidirect
72. #4874C22semidirect
75. #4856C22semidirect
76. #4855C22semidirect
79. #4702C22semidirect
82. #4682C22semidirect
83. #4680C22semidirect
93. #3165D3direct (N × H)
150. D3×M16Q8semidirect
273. #501C2×D3semidirect
278. #500C2×D3semidirect
283. #498C2×D3semidirect
349. C3×M16C2×Q8semidirect
407. #208C2×Q8semidirect
409. ΓL(1,𝔽25)C2×Q8semidirect
410. D3×C8C2×Q8semidirect
604. C3×C8C22×Q8semidirect
605. C3⋊C8C22×Q8semidirect
658. M16D3×Q8semidirect
808. C8C2×D3×Q8semidirect
814. D3#3165direct (N × H)
844. C3C2×#3165semidirect

Maximal subgroups

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

subgroupindex
D3×#5332
C2×D3×C4⋊Q82
C3×#31652
#833412
#832072
#819762
D3×#5012
#819402
D3×#5002
#818932
D3×#4982
D3×#4282
#792032
C4×D3×M162
#785062
C2×#31653