Finite Group Databasebeta

← #11662355

Subgroups — #11662355

Order 768.

2918 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5828C211yesmaximal, characteristic, complemented
2C2×#5822C211yesmaximal, characteristic, complemented
3C22×D3×M16C211yesmaximal, characteristic, complemented
4C2×#5524C211yesmaximal, characteristic, complemented
5C3×#2896C211yesmaximal, characteristic, complemented
6#83768C211yesmaximal, characteristic, complemented
7#82207C211yesmaximal, characteristic, complemented
8#78962C214yesmaximal, complemented
9#78930C214yesmaximal, complemented
10#78889C214yesmaximal, complemented
11#78888C214yesmaximal, complemented
12#78839C214yesmaximal, complemented
13#78838C214yesmaximal, complemented
14#60444—31nomaximal, Sylow
15C22×C3×#41C2211yescharacteristic
16C22×#235C2211yescharacteristic
17C23×C4×D3C2211yescharacteristic
18C22×C3×M16C2211yescharacteristic
19C2×C3×#117C2211yescharacteristic
20#5828—21no—
21#5828—21no—
22#5828—22no—
23#5828C2214yes—
24#5828C2212yescomplemented
25#5828C2212yescomplemented
26C2×#951C2212yescomplemented
27#5822—28no—
28C2×#950C2214yescomplemented
29C2×#949C2212yescomplemented
30C2×#946C2212yescomplemented
31C2×#942C2212yescomplemented
32C2×#938C2212yescomplemented
33C2×#937—21no—
34C2×#935—21no—
35C2×#932C2212yescomplemented
36C2×C4×#67—22no—
37C2×#926C2211yescharacteristic
38C22×#208C2211yescharacteristic
39C2×D3×M16—28no—
40C2×D3×M16C2214yescomplemented
41C2×D3×M16C2214yescomplemented
42C22×ΓL(1,𝔽25)C2212yescomplemented
43C22×D3×C8C2212yescomplemented
44#5524—21no—
45#5524—21no—
46#5524—22no—
47#5524C2214yes—
48#5524C2212yescomplemented
49#5524C2212yescomplemented
50C2×#897C2212yescomplemented
51C2×#895C2212yescomplemented
52C2×#886—21no—
53C2×#882—21no—
54C2×C4×D12—22no—
55C3×#419C2212yescomplemented
56C3×#418C2212yescomplemented
57C3×#417C2214yescomplemented
58C3×#416C2214yescomplemented
59#5133C2214yescomplemented
60#5131C2212yescomplemented
61#5120C2212yescomplemented
62#5113C2214yescomplemented
63#4998C2214yescomplemented
64#4995C2214yescomplemented
65#4964C2214yescomplemented
66#4816C2218yescomplemented
67#4813C2218yescomplemented
68#4812C2218yescomplemented
69#4807C2218yescomplemented
70#4782C2218yescomplemented
71#4780C2218yescomplemented
72#4778C2218yescomplemented
73#4775C2218yescomplemented
74C2×#575—31no—
75C23×M16—31no—
76C2×#525—31no—
77C2×#525—31no—
78#3056—34no—
79#3056—34no—
80#3055—34no—
81#3055—34no—
82#3054—34no—
83#3050—34no—
84#2911—31no—
85#2896—31no—
86#2896D311yescharacteristic, complemented
87C24×D3D411yescharacteristic
88C2×C3×#41—21no—
89C2×C3×#41—21no—
90C2×C3×#41—24no—
91C2×C3×#41—24no—
92C2×C3×#41C2312yes—
93C2×C3×#41C2312yes—
94C22×C3×Q8C2311yescharacteristic
95C22×C3×D4—21no—
96C22×C3×D4C2311yescharacteristic
97C23×C3×C4—21no—
98C23×C3×C4C2311yescharacteristic
99C22×#67—21no—
100C22×#67—22no—
101C23×Dic3D411yescharacteristic
102C2×#235—21no—
103C2×#235—21no—
104C2×#235—24no—
105C2×#235—24no—
106C2×#235C2312yes—
107C2×#235C2312yes—
108C22×D12—22no—
109C22×D12C2311yescharacteristic
110C22×C4×D3—24no—
111C22×C4×D3—24no—
112C22×C4×D3—21no—
113C22×C4×D3D412yes—
114C22×C4×D3D412yes—
115C22×C4×D3D411yescharacteristic
116C22×C4×D3D411yescharacteristic
117C22×C4×D3C2311yescharacteristic
118C22×C4×D3C2311yescharacteristic
119C22×C4×D3C2312yes—
120C22×C4×D3C2312yes—
121C22×Dic6C2311yescharacteristic
122C2×C3×M16—24no—
123C2×C3×M16C2312yes—
124C2×C3×M16C2312yes—
125C22×C3×C8C2312yes—
126C3×#117—21no—
127C3×#117—21no—
128C3×#117C2312yes—
129C3×#117C2312yes—
130C2×C3×C4⋊C4C2312yes—
131C2×C3×C22⋊C4—21no—
132C2×C3×C42—21no—
133C2×#217—21no—
134C2×#217—22no—
135#951—28no—
136#950—216no—
137#949—28no—
138#946—22no—
139#946—22no—
140#946C2314yes—
141#946C2314yes—
142C2×#216C2314yescomplemented
143#942—28no—
144C2×#215C2314yescomplemented
145#938—22no—
146#938—22no—
147#938C2314yes—
148#938C2314yes—
149#937—24no—
150#937—22no—
151#937—22no—
152#935—24no—
153#935—22no—
154#935—22no—
155C2×#214C2314yescomplemented
156#932—28no—
157C2×#213C2314yescomplemented
158C4×#67—24no—
159C4×#67—24no—
160C4×#67—24no—
161C4×#67—24no—
162C2×(C2×D3)⋊C4—22no—
163C2×(C2×D3)⋊C4—22no—
164C2×(C2×D3)⋊C4—22no—
165#926—21no—
166#926—21no—
167#926C2312yes—
168#926C2312yes—
169C2×C4⋊Dic3—22no—
170C2×C4⋊Dic3C2312yes—
171C2×Dic3⋊C4—22no—
172C2×C4×Dic3—21no—
173C2×#208D418yescomplemented
174C2×#208C2312yes—
175C2×#208C2312yes—
176C22×C3⋊C8C2312yes—
177D3×M16—216no—
178D3×M16—216no—
179C2×ΓL(1,𝔽25)—28no—
180C2×ΓL(1,𝔽25)C2318yes—
181C2×D3×C8—28no—
182C2×D3×C8C2318yes—
183#897—22no—
184#897—22no—
185#897C2314yes—
186#897C2314yes—
187#895—22no—
188#895—22no—
189#895C2314yes—
190#895C2314yes—
191#886—24no—
192#886—22no—
193#886—22no—
194#882—24no—
195#882—22no—
196#882—22no—
197C4×D12—24no—
198C4×D12—24no—
199C4×D12—24no—
200C4×D12—24no—
201C3×#103C2318yescomplemented
202C3×#102C2318yescomplemented
203#821C2318yescomplemented
204#816C2318yescomplemented
205#808C2318yescomplemented
206#807C2318yescomplemented
207C22×#41—31no—
208C22×#41C2×D311yescharacteristic
209C24×C4—31no—
210#575—68no—
211C2×#137—32no—
212C2×#137—32no—
213C2×AGL(1,ℤ/8)—32no—
214C2×AGL(1,ℤ/8)—32no—
215C2×#135—34no—
216C22×M16—31no—
217C22×M16—34no—
218C22×M16—34no—
219C22×M16—32no—
220C22×M16—68no—
221C22×M16C2×D311yescharacteristic
222C23×C8—32no—
223#525—34no—
224#525—32no—
225#525—32no—
226#525—34no—
227#525—32no—
228#525—32no—
229#525—62no—
230#525—61no—
231#525—61no—
232#525—62no—
233#525—61no—
234#525—61no—
235C2×#123—61no—
236C2×#123—61no—
237C2×C22⋊Q8—32no—
238C2×C22⋊Q8—32no—
239C2×#121—32no—
240C2×#121—32no—
241C2×#120—61no—
242C2×#120—61no—
243C2×C4×D4—62no—
244C2×C4×D4—62no—
245C2×#117—31no—
246C2×#117C2×D311yescharacteristic
247#470—38no—
248#469—38no—
249#468—38no—
250#468—38no—
251#467—38no—
252#466—38no—
253#465—38no—
254#465—38no—
255#428—34no—
256#428—34no—
257#427—34no—
258#419—32no—
259#419C2×D312yescomplemented
260#418—32no—
261#418C2×D312yescomplemented
262#417—34no—
263#417C2×D314yescomplemented
264#416—34no—
265#416C2×D314yescomplemented
266C24×C3—21no—
267C24×C3C2×D411yescharacteristic
268C23×D3—24no—
269C23×D3—21no—
270C23×D3—44no—
271C23×D3C2×D411yescharacteristic
272C23×D3C2×D412yes—
273C23×D3C2×D412yes—
274C23×D3C2×D411yescharacteristic
275C3×#41—24no—
276C3×#41—24no—
277C3×#41—24no—
278C3×#41—24no—
279C3×#41—44no—
280C3×#41—44no—
281C2×C3×Q8—21no—
282C2×C3×Q8—22no—
283C2×C3×Q8—22no—
284C2×C3×Q8C2412yes—
285C2×C3×D4—22no—
286C2×C3×D4—22no—
287C2×C3×D4—22no—
288C2×C3×D4—21no—
289C2×C3×D4—22no—
290C2×C3×D4—44no—
291C2×C3×D4C2412yes—
292C22×C3×C4—21no—
293C22×C3×C4—22no—
294C22×C3×C4—22no—
295C22×C3×C4—22no—
296C22×C3×C4—44no—
297C22×C3×C4C2×D411yescharacteristic
298C22×C3×C4C2×D411yescharacteristic
299C22×C3×C4C2×D411yescharacteristic
300C22×C3×C4C2×D414yes—
301C22×C3×C4#4114yes—
302C22×C3×C4C2411yescharacteristic
303C22×C3×C4C2411yescharacteristic
304C22×C3×C4C2411yescharacteristic
305C2×#67—22no—
306C2×#67—22no—
307C2×#67—24no—
308C2×#67—24no—
309C2×#67—48no—
310C2×#67—44no—
311C22×Dic3—24no—
312C22×Dic3—22no—
313C22×Dic3—21no—
314C22×Dic3C2×D412yes—
315C22×Dic3C2×D411yescharacteristic
316C22×Dic3C2×D411yescharacteristic
317C22×Dic3C2×D412yes—
318#235—24no—
319#235—24no—
320#235—24no—
321#235—24no—
322#235—44no—
323#235—44no—
324C2×D12—22no—
325C2×D12—22no—
326C2×D12—24no—
327C2×D12—24no—
328C2×D12—21no—
329C2×D12—48no—
330C2×D12C2412yes—
331C2×C4×D3—28no—
332C2×C4×D3—28no—
333C2×C4×D3—24no—
334C2×C4×D3—24no—
335C2×C4×D3—22no—
336C2×C4×D3—22no—
337C2×C4×D3—24no—
338C2×C4×D3—24no—
339C2×C4×D3—24no—
340C2×C4×D3—24no—
341C2×C4×D3—22no—
342C2×C4×D3—22no—
343C2×C4×D3—22no—
344C2×C4×D3—22no—
345C2×C4×D3—44no—
346C2×C4×D3C2×D412yes—
347C2×C4×D3C2×D412yes—
348C2×C4×D3C2×D412yes—
349C2×C4×D3C2×D412yes—
350C2×C4×D3C2×D412yes—
351C2×C4×D3C2×D412yes—
352C2×C4×D3C2412yes—
353C2×C4×D3C2412yes—
354C2×Dic6—22no—
355C2×Dic6—22no—
356C2×Dic6—21no—
357C2×Dic6C2412yes—
358C3×M16—24no—
359C3×M16—24no—
360C2×C3×C8—24no—
361C2×C3×C8C2414yes—
362C3×C4⋊C4—22no—
363C3×C4⋊C4C2414yes—
364C3×C22⋊C4—22no—
365C3×C22⋊C4—22no—
366C3×C42—22no—
367C3×C42—22no—
368#217—22no—
369#217—22no—
370#217—24no—
371#217—24no—
372#216—28no—
373#215—28no—
374#214—28no—
375#213—28no—
376(C2×D3)⋊C4—24no—
377(C2×D3)⋊C4—24no—
378(C2×D3)⋊C4—24no—
379(C2×D3)⋊C4—24no—
380(C2×D3)⋊C4—24no—
381(C2×D3)⋊C4—24no—
382C4⋊Dic3—22no—
383C4⋊Dic3—24no—
384C4⋊Dic3—24no—
385C4⋊Dic3C2414yes—
386Dic3⋊C4—24no—
387Dic3⋊C4—24no—
388C4×Dic3—22no—
389C4×Dic3—22no—
390#208C2×D418yescomplemented
391#208C2×D418yescomplemented
392C2×C3⋊C8C2×D418yescomplemented
393C2×C3⋊C8C2414yes—
394ΓL(1,𝔽25)—216no—
395D3×C8—216no—
396C25—31no—
397C2×#41—21no—
398C2×#41—21no—
399C2×#41—24no—
400C2×#41—24no—
401C2×#41—32no—
402C2×#41—32no—
403C2×#41—61no—
404C2×#41—61no—
405C2×#41—64no—
406C2×#41—64no—
407C2×#41C22×D312yes—
408C2×#41C22×D312yes—
409C22×Q8—31no—
410C22×Q8C22×D311yescharacteristic
411C22×D4—21no—
412C22×D4—31no—
413C22×D4—62no—
414C22×D4—62no—
415C22×D4—61no—
416C22×D4C22×D311yescharacteristic
417C23×C4—21no—
418C23×C4—31no—
419C23×C4—32no—
420C23×C4—32no—
421C23×C4—31no—
422C23×C4—31no—
423C23×C4—32no—
424C23×C4—32no—
425C23×C4—31no—
426C23×C4—31no—
427C23×C4—64no—
428C23×C4—64no—
429C23×C4—61no—
430C23×C4C22×D311yescharacteristic
431#137—68no—
432#137—68no—
433AGL(1,ℤ/8)—68no—
434AGL(1,ℤ/8)—68no—
435#135—616no—
436C2×Q16—34no—
437C2×SD16—34no—
438C2×SD16—34no—
439C2×D8—34no—
440C2×M16—24no—
441C2×M16—38no—
442C2×M16—32no—
443C2×M16—32no—
444C2×M16—38no—
445C2×M16—68no—
446C2×M16—616no—
447C2×M16—616no—
448C2×M16C22×D312yes—
449C2×M16C22×D312yes—
450C22×C8—32no—
451C22×C8—38no—
452C22×C8—68no—
453C22×C8C22×D312yes—
454#123—64no—
455#123—62no—
456#123—62no—
457#123—64no—
458#123—62no—
459#123—62no—
460C22⋊Q8—34no—
461C22⋊Q8—34no—
462C22⋊Q8—34no—
463C22⋊Q8—34no—
464C22⋊Q8—62no—
465C22⋊Q8—62no—
466C22⋊Q8—62no—
467C22⋊Q8—62no—
468#121—34no—
469#121—34no—
470#121—34no—
471#121—34no—
472#121—62no—
473#121—62no—
474#121—62no—
475#121—62no—
476#120—62no—
477#120—64no—
478#120—62no—
479#120—62no—
480#120—64no—
481#120—62no—
482C4×D4—64no—
483C4×D4—64no—
484C4×D4—64no—
485C4×D4—64no—
486C4×D4—64no—
487C4×D4—64no—
488C4×D4—64no—
489C4×D4—64no—
490#117—21no—
491#117—21no—
492#117—32no—
493#117—32no—
494#117—61no—
495#117—61no—
496#117C22×D312yes—
497#117C22×D312yes—
498C2×C4⋊C4—32no—
499C2×C4⋊C4—62no—
500C2×C4⋊C4—62no—
501C2×C4⋊C4C22×D312yes—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—62no—
504C2×C22⋊C4—62no—
505C2×C22⋊C4—62no—
506C2×C22⋊C4—62no—
507C2×C22⋊C4—61no—
508C2×C42—21no—
509C2×C42—61no—
510#107—38no—
511#106—38no—
512#103—38no—
513#103C22×D318yescomplemented
514#102—38no—
515#102C22×D318yescomplemented
516C23×C3—22no—
517C23×C3—42no—
518C23×C3—44no—
519C23×C3—42no—
520C23×C3#12114yes—
521C23×C3C22×D411yescharacteristic
522C23×C3C22×D411yescharacteristic
523C23×C3C22×D411yescharacteristic
524C22×D3—22no—
525C22×D3—24no—
526C22×D3—24no—
527C22×D3—24no—
528C22×D3—22no—
529C22×D3—24no—
530C22×D3—24no—
531C22×D3—22no—
532C22×D3—42no—
533C22×D3—42no—
534C22×D3—42no—
535C22×D3—416no—
536C22×D3—44no—
537C22×D3—42no—
538C22×D3C22×D412yes—
539C22×D3C22×D412yes—
540C3×Q8—22no—
541C3×Q8—22no—
542C3×Q8—42no—
543C3×D4—22no—
544C3×D4—22no—
545C3×D4—44no—
546C3×D4—44no—
547C3×D4—42no—
548C2×C3×C4—22no—
549C2×C3×C4—24no—
550C2×C3×C4—44no—
551C2×C3×C4—42no—
552C2×C3×C4—44no—
553C2×C3×C4—44no—
554C2×C3×C4#12114yes—
555C2×C3×C4#12114yes—
556C2×C3×C4#12114yes—
557C2×C3×C4C22×D411yescharacteristic
558C2×C3×C4C22×D411yescharacteristic
559C2×C3×C4C22×D412yes—
560C2×C3×C4C22×D412yes—
561C2×C3×C4C22×D412yes—
562C2×C3×C4C22×D411yescharacteristic
563C2×C3×C4C2×#4112yes—
564C2×C3×C4C2×#4112yes—
565C2×C3×C4C2×#4112yes—
566C2×C3×C4C2511yescharacteristic
567#67—48no—
568#67—44no—
569#67—44no—
570#67—48no—
571C2×Dic3—24no—
572C2×Dic3—24no—
573C2×Dic3—22no—
574C2×Dic3—22no—
575C2×Dic3—24no—
576C2×Dic3—22no—
577C2×Dic3—44no—
578C2×Dic3—42no—
579C2×Dic3C22×D412yes—
580C2×Dic3C22×D412yes—
581D12—22no—
582D12—22no—
583D12—48no—
584D12—48no—
585D12—42no—
586C4×D3—24no—
587C4×D3—24no—
588C4×D3—24no—
589C4×D3—24no—
590C4×D3—24no—
591C4×D3—24no—
592C4×D3—22no—
593C4×D3—22no—
594C4×D3—22no—
595C4×D3—22no—
596C4×D3—44no—
597C4×D3—44no—
598Dic6—22no—
599Dic6—22no—
600Dic6—42no—
601C3×C8—24no—
602C3⋊C8C22×D418yes—
603C24—21no—
604C24—31no—
605C24—32no—
606C24—32no—
607C24—31no—
608C24—64no—
609C24—61no—
610C24—124no—
611C24D3×D411yescharacteristic
612#41—24no—
613#41—24no—
614#41—24no—
615#41—24no—
616#41—44no—
617#41—44no—
618#41—64no—
619#41—64no—
620#41—64no—
621#41—64no—
622#41—124no—
623#41—124no—
624C2×Q8—21no—
625C2×Q8—22no—
626C2×Q8—22no—
627C2×Q8—32no—
628C2×Q8—61no—
629C2×Q8—62no—
630C2×Q8—62no—
631C2×Q8C23×D312yes—
632C2×D4—22no—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—22no—
636C2×D4—21no—
637C2×D4—32no—
638C2×D4—44no—
639C2×D4—64no—
640C2×D4—64no—
641C2×D4—64no—
642C2×D4—64no—
643C2×D4—62no—
644C2×D4—62no—
645C2×D4—62no—
646C2×D4—62no—
647C2×D4—61no—
648C2×D4—128no—
649C2×D4—128no—
650C2×D4—124no—
651C2×D4C23×D312yes—
652C22×C4—22no—
653C22×C4—21no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—32no—
657C22×C4—32no—
658C22×C4—31no—
659C22×C4—31no—
660C22×C4—32no—
661C22×C4—32no—
662C22×C4—32no—
663C22×C4—32no—
664C22×C4—32no—
665C22×C4—32no—
666C22×C4—32no—
667C22×C4—32no—
668C22×C4—44no—
669C22×C4—64no—
670C22×C4—68no—
671C22×C4—68no—
672C22×C4—64no—
673C22×C4—64no—
674C22×C4—64no—
675C22×C4—64no—
676C22×C4—62no—
677C22×C4—62no—
678C22×C4—62no—
679C22×C4—64no—
680C22×C4—64no—
681C22×C4—62no—
682C22×C4—62no—
683C22×C4—61no—
684C22×C4—62no—
685C22×C4—62no—
686C22×C4—124no—
687C22×C4#23514yes—
688C22×C4D3×D411yescharacteristic
689C22×C4D3×D411yescharacteristic
690C22×C4D3×D411yescharacteristic
691C22×C4D3×D414yes—
692C22×C4C23×D311yescharacteristic
693C22×C4C23×D311yescharacteristic
694C22×C4C23×D311yescharacteristic
695Q16—68no—
696SD16—68no—
697SD16—68no—
698D8—68no—
699M16—24no—
700M16—24no—
701M16—38no—
702M16—38no—
703M16—616no—
704C2×C8—24no—
705C2×C8—38no—
706C2×C8—34no—
707C2×C8—616no—
708C2×C8C23×D314yes—
709C4⋊C4—22no—
710C4⋊C4—34no—
711C4⋊C4—64no—
712C4⋊C4—64no—
713C4⋊C4—64no—
714C4⋊C4—64no—
715C4⋊C4—62no—
716C4⋊C4C23×D314yes—
717C22⋊C4—22no—
718C22⋊C4—22no—
719C22⋊C4—64no—
720C22⋊C4—64no—
721C22⋊C4—64no—
722C22⋊C4—64no—
723C22⋊C4—64no—
724C22⋊C4—64no—
725C22⋊C4—64no—
726C22⋊C4—64no—
727C22⋊C4—62no—
728C22⋊C4—62no—
729C42—22no—
730C42—22no—
731C42—62no—
732C42—62no—
733C22×C3—22no—
734C22×C3—22no—
735C22×C3—22no—
736C22×C3—44no—
737C22×C3—42no—
738C22×C3—44no—
739C22×C3—84no—
740C22×C3C2×#12112yes—
741C22×C3C2×#12112yes—
742C22×C3C2×#12112yes—
743C22×C3C23×D411yescharacteristic
744C2×D3—28no—
745C2×D3—22no—
746C2×D3—22no—
747C2×D3—22no—
748C2×D3—22no—
749C2×D3—22no—
750C2×D3—48no—
751C2×D3—48no—
752C2×D3—44no—
753C2×D3—42no—
754C2×D3—44no—
755C2×D3—84no—
756C2×D3#57514yescomplemented
757C3×C4—42no—
758C3×C4—44no—
759C3×C4C2×#12112yes—
760C3×C4C2×#12112yes—
761C3×C4C2×#12112yes—
762C3×C4C23×D411yescharacteristic
763C3×C4C22×#4111yescharacteristic
764Dic3—22no—
765Dic3—22no—
766Dic3—42no—
767Dic3—44no—
768C23—22no—
769C23—32no—
770C23—32no—
771C23—42no—
772C23—44no—
773C23—42no—
774C23—64no—
775C23—64no—
776C23—64no—
777C23—62no—
778C23—64no—
779C23—64no—
780C23—62no—
781C23—62no—
782C23—122no—
783C23—122no—
784C23—122no—
785C23—124no—
786C23—1216no—
787C23—122no—
788C23#88414yes—
789C23C2×D3×D411yescharacteristic
790C23C2×D3×D411yescharacteristic
791C23C2×D3×D411yescharacteristic
792Q8—22no—
793Q8—22no—
794Q8—42no—
795Q8—62no—
796Q8—62no—
797Q8—122no—
798D4—22no—
799D4—22no—
800D4—44no—
801D4—44no—
802D4—42no—
803D4—62no—
804D4—62no—
805D4—128no—
806D4—128no—
807D4—128no—
808D4—128no—
809D4—124no—
810D4—124no—
811D4—122no—
812C2×C4—24no—
813C2×C4—22no—
814C2×C4—32no—
815C2×C4—32no—
816C2×C4—44no—
817C2×C4—42no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—64no—
821C2×C4—64no—
822C2×C4—62no—
823C2×C4—62no—
824C2×C4—62no—
825C2×C4—62no—
826C2×C4—62no—
827C2×C4—62no—
828C2×C4—64no—
829C2×C4—64no—
830C2×C4—64no—
831C2×C4—64no—
832C2×C4—64no—
833C2×C4—64no—
834C2×C4—64no—
835C2×C4—62no—
836C2×C4—124no—
837C2×C4—122no—
838C2×C4—124no—
839C2×C4—124no—
840C2×C4#88414yes—
841C2×C4#88414yes—
842C2×C4#88414yes—
843C2×C4C2×#23512yes—
844C2×C4C2×#23512yes—
845C2×C4C2×#23512yes—
846C2×C4C2×D3×D412yes—
847C2×C4C2×D3×D412yes—
848C2×C4C2×D3×D412yes—
849C2×C4C2×D3×D411yescharacteristic
850C2×C4C2×D3×D411yescharacteristic
851C2×C4C2×D3×D411yescharacteristic
852C2×C4C24×D311yescharacteristic
853C8—24no—
854C8—38no—
855C2×C3—22no—
856C2×C3—22no—
857C2×C3—22no—
858C2×C3—82no—
859C2×C3C22×#12111yescharacteristic
860C2×C3C2×#57512yes—
861D3—24no—
862D3—42no—
863D3—82no—
864C22—22no—
865C22—22no—
866C22—22no—
867C22—34no—
868C22—44no—
869C22—44no—
870C22—42no—
871C22—68no—
872C22—62no—
873C22—62no—
874C22—62no—
875C22—62no—
876C22—62no—
877C22—84no—
878C22—128no—
879C22—128no—
880C22—124no—
881C22—124no—
882C22—122no—
883C22—244no—
884C22C2×#88412yes—
885C22C2×#88412yes—
886C22C2×#88412yes—
887C22C22×D3×D411yescharacteristic
888C4—44no—
889C4—42no—
890C4—62no—
891C4—62no—
892C4—124no—
893C4—122no—
894C4C2×#88412yes—
895C4C2×#88412yes—
896C4C2×#88412yes—
897C4C22×#23511yescharacteristic
898C4C22×D3×D411yescharacteristic
899C3#6044411yescharacteristic, complemented, Sylow
900C2—22no—
901C2—22no—
902C2—22no—
903C2—64no—
904C2—82no—
905C2—122no—
906C2—242no—
907C2C22×#88411yescharacteristic
908C2D3×#57512yes—
subgroupG/H
centerC2×C4C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#2896C2
socleC22×C3C23×D4
hypercenter#2896D3
hypocenterC3#60444
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #2896

Complements

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

NH ≅ G/Ntype
1. C2×#5828C2semidirect
2. C2×#5822C2semidirect
3. C22×D3×M16C2semidirect
4. C2×#5524C2semidirect
5. C3×#2896C2semidirect
6. #83768C2semidirect
7. #82207C2semidirect
8. #78962C2semidirect
9. #78930C2semidirect
10. #78889C2semidirect
11. #78888C2semidirect
12. #78839C2semidirect
13. #78838C2semidirect
24. #5828C22semidirect
25. #5828C22semidirect
26. C2×#951C22semidirect
28. C2×#950C22semidirect
29. C2×#949C22semidirect
30. C2×#946C22semidirect
31. C2×#942C22semidirect
32. C2×#938C22semidirect
35. C2×#932C22semidirect
40. C2×D3×M16C22semidirect
41. C2×D3×M16C22semidirect
42. C22×ΓL(1,𝔽25)C22semidirect
43. C22×D3×C8C22semidirect
48. #5524C22semidirect
49. #5524C22semidirect
50. C2×#897C22semidirect
51. C2×#895C22semidirect
55. C3×#419C22semidirect
56. C3×#418C22semidirect
57. C3×#417C22semidirect
58. C3×#416C22semidirect
59. #5133C22semidirect
60. #5131C22semidirect
61. #5120C22semidirect
62. #5113C22semidirect
63. #4998C22semidirect
64. #4995C22semidirect
65. #4964C22semidirect
66. #4816C22semidirect
67. #4813C22semidirect
68. #4812C22semidirect
69. #4807C22semidirect
70. #4782C22semidirect
71. #4780C22semidirect
72. #4778C22semidirect
73. #4775C22semidirect
86. #2896D3semidirect
142. C2×#216C23semidirect
144. C2×#215C23semidirect
155. C2×#214C23semidirect
157. C2×#213C23semidirect
173. C2×#208D4semidirect
201. C3×#103C23semidirect
202. C3×#102C23semidirect
203. #821C23semidirect
204. #816C23semidirect
205. #808C23semidirect
206. #807C23semidirect
259. #419C2×D3semidirect
261. #418C2×D3semidirect
263. #417C2×D3semidirect
265. #416C2×D3semidirect
390. #208C2×D4semidirect
391. #208C2×D4semidirect
392. C2×C3⋊C8C2×D4semidirect
513. #103C22×D3semidirect
515. #102C22×D3semidirect
756. C2×D3#575semidirect
899. C3#60444semidirect

Maximal subgroups

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

subgroupindex
C2×#58282
C2×#58222
C22×D3×M162
C2×#55242
C3×#28962
#837682
#822072
#789622
#789302
#788892
#788882
#788392
#788382
#604443